Subgroups — C₂₃×#60010 #19207636

Order 5888.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2768	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2753	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2710	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2670	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2602	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2589	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2587	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2559	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2516	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2479	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2476	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2471	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2470	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2464	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2464	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2459	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2458	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2424	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2411	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#2342	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
58	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#399	C₂²	1	1	yes	characteristic
62	C₂₃×#399	C₂²	1	1	yes	characteristic
63	C₂₃×#399	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#396	C₂²	1	1	yes	characteristic
71	C₂₃×#396	C₂²	1	1	yes	characteristic
72	C₂₃×#396	C₂²	1	1	yes	characteristic
73	C₂₃×#394	C₂²	1	1	yes	characteristic
74	C₂₃×#394	C₂²	1	1	yes	characteristic
75	C₂₃×#394	C₂²	1	1	yes	characteristic
76	C₂₃×#394	C₂²	1	1	yes	characteristic
77	C₂₃×#394	C₂²	1	1	yes	characteristic
78	C₂₃×#394	C₂²	1	1	yes	characteristic
79	C₂₃×#394	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#394	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#394	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#394	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#393	C₂²	1	1	yes	characteristic
84	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#392	C₂²	1	1	yes	characteristic
86	C₂₃×#392	C₂²	1	1	yes	characteristic
87	C₂₃×#392	C₂²	1	1	yes	characteristic
88	C₂₃×#392	C₂²	1	1	yes	characteristic
89	C₂₃×#392	C₂²	1	1	yes	characteristic
90	C₂₃×#392	C₂²	1	1	yes	characteristic
91	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#390	C₂²	1	1	yes	characteristic
94	C₂₃×#390	C₂²	1	1	yes	characteristic
95	C₂₃×#390	C₂²	1	1	yes	characteristic
96	C₂₃×#390	C₂²	1	1	yes	characteristic
97	C₂₃×#390	C₂²	1	1	yes	characteristic
98	C₂₃×#390	C₂²	1	1	yes	characteristic
99	C₂₃×#390	C₂²	1	1	yes	characteristic
100	C₂₃×#390	C₂²	1	1	yes	characteristic
101	C₂₃×#390	C₂²	1	1	yes	characteristic
102	C₂₃×#390	C₂²	1	1	yes	characteristic
103	C₂₃×#390	C₂²	1	1	yes	characteristic
104	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#388	C₂²	1	1	yes	characteristic
113	C₂₃×#388	C₂²	1	1	yes	characteristic
114	C₂₃×#388	C₂²	1	1	yes	characteristic
115	C₂₃×#388	C₂²	1	1	yes	characteristic
116	C₂₃×#388	C₂²	1	1	yes	characteristic
117	C₂₃×#388	C₂²	1	1	yes	characteristic
118	C₂₃×#388	C₂²	1	1	yes	characteristic
119	C₂₃×#388	C₂²	1	1	yes	characteristic
120	C₂₃×#388	C₂²	1	1	yes	characteristic
121	C₂₃×#388	C₂²	1	1	yes	characteristic
122	C₂₃×#388	C₂²	1	1	yes	characteristic
123	C₂₃×#388	C₂²	1	1	yes	characteristic
124	C₂₃×#388	C₂²	1	1	yes	characteristic
125	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
126	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
131	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
136	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
137	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
138	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
139	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
140	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
141	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
142	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
143	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
144	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
145	C₂₃×#386	C₂²	1	1	yes	characteristic
146	C₂₃×#386	C₂²	1	1	yes	characteristic
147	C₂₃×#386	C₂²	1	1	yes	characteristic
148	C₂₃×#386	C₂²	1	1	yes	characteristic
149	C₂₃×#386	C₂²	1	1	yes	characteristic
150	C₂₃×#386	C₂²	1	1	yes	characteristic
151	C₂₃×#386	C₂²	1	1	yes	characteristic
152	C₂₃×#386	C₂²	1	1	yes	characteristic
153	C₂₃×#386	C₂²	1	1	yes	characteristic
154	C₂₃×#386	C₂²	1	1	yes	characteristic, complemented
155	C₂₃×#386	C₂²	1	1	yes	characteristic, complemented
156	C₂₃×#385	C₂²	1	1	yes	characteristic
157	C₂₃×#385	C₂²	1	1	yes	characteristic
158	C₂₃×#385	C₂²	1	1	yes	characteristic
159	C₂₃×#385	C₂²	1	1	yes	characteristic
160	C₂₃×#385	C₂²	1	1	yes	characteristic
161	C₂₃×#385	C₂²	1	1	yes	characteristic
162	C₂₃×#385	C₂²	1	1	yes	characteristic
163	C₂₃×#385	C₂²	1	1	yes	characteristic
164	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
165	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
166	C₂₃×#381	C₂²	1	1	yes	characteristic
167	C₂₃×#380	C₂²	1	1	yes	characteristic
168	C₂₃×#379	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
173	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
186	C₄³×C₂₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
200	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂₃×#126	—	4	2	no	—
211	C₂₃×#124	—	2	4	no	—
212	C₂₃×#124	—	2	4	no	—
213	C₂₃×#123	—	2	4	no	—
214	C₂₃×#123	—	4	2	no	—
215	C₂₃×#123	—	4	2	no	—
216	C₂₃×#123	—	4	2	no	—
217	C₂₃×#121	—	2	4	no	—
218	C₂₃×#121	—	4	2	no	—
219	C₂₃×#121	—	4	2	no	—
220	C₂₃×#121	—	4	2	no	—
221	C₂₃×#120	—	2	4	no	—
222	C₂₃×#120	—	2	4	no	—
223	C₂₃×#120	—	4	2	no	—
224	C₄×Q₈×C₂₃	—	4	2	no	—
225	C₄×D₄×C₂₃	—	2	4	no	—
226	C₄×D₄×C₂₃	—	2	4	no	—
227	C₄×D₄×C₂₃	—	4	2	no	—
228	C₄×D₄×C₂₃	—	4	2	no	—
229	C₄×D₄×C₂₃	—	4	2	no	—
230	C₂₃×#117	—	4	2	no	—
231	C₂₃×#117	—	4	2	no	—
232	C₂₃×#117	—	4	2	no	—
233	C₂₃×#117	—	4	2	no	—
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
263	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
264	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
320	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
322	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
323	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
324	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
325	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
326	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
327	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
328	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
329	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
330	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
332	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
335	C₂₃×#95	C₂³	1	1	yes	characteristic
336	C₂₃×#95	C₂³	1	1	yes	characteristic
337	C₂₃×#95	C₂³	1	1	yes	characteristic
338	C₂₃×#95	C₂³	1	1	yes	characteristic
339	C₂₃×#95	C₂³	1	1	yes	characteristic
340	C₂₃×#95	C₂³	1	1	yes	characteristic
341	C₂₃×#95	C₂³	1	1	yes	characteristic
342	C₂₃×#95	C₂³	1	1	yes	characteristic
343	C₂₃×#95	C₂³	1	1	yes	characteristic
344	C₂₃×#95	C₂³	1	1	yes	characteristic
345	C₂₃×#95	C₂³	1	1	yes	characteristic
346	C₂₃×#95	C₂³	1	1	yes	characteristic
347	C₂₃×#95	C₂³	1	1	yes	characteristic
348	C₂₃×#95	C₂³	1	1	yes	characteristic
349	C₂₃×#95	C₂³	1	1	yes	characteristic
350	C₂₃×#95	C₂³	1	1	yes	characteristic
351	C₂₃×#95	C₂³	1	1	yes	characteristic
352	C₂₃×#95	C₂³	1	1	yes	characteristic
353	C₂₃×#95	C₂³	1	1	yes	characteristic
354	C₂₃×#95	C₂³	1	1	yes	characteristic
355	C₂₃×#95	C₂³	1	1	yes	characteristic
356	C₂₃×#95	C₂³	1	1	yes	characteristic
357	C₂₃×#95	C₂³	1	1	yes	characteristic
358	C₂₃×#95	C₂³	1	1	yes	characteristic
359	C₂₃×#95	C₂³	1	1	yes	characteristic
360	C₂₃×#95	C₂³	1	1	yes	characteristic
361	C₂₃×#95	C₂³	1	1	yes	characteristic
362	C₂₃×#95	C₂³	1	1	yes	characteristic
363	C₂₃×#95	C₂³	1	1	yes	characteristic
364	C₂₃×#95	C₂³	1	1	yes	characteristic
365	C₂₃×#95	C₂³	1	1	yes	characteristic
366	C₂₃×#95	C₂³	1	1	yes	characteristic
367	C₂₃×#95	C₂³	1	1	yes	characteristic
368	C₂₃×#95	C₂³	1	1	yes	characteristic
369	C₂⁴×C₂₃	—	2	2	no	—
370	C₂⁴×C₂₃	—	2	2	no	—
371	C₂⁴×C₂₃	—	2	2	no	—
372	C₂⁴×C₂₃	—	4	1	no	—
373	C₂⁴×C₂₃	—	4	1	no	—
374	C₂⁴×C₂₃	—	4	1	no	—
375	C₂⁴×C₂₃	—	4	1	no	—
376	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₂×Q₈×C₂₃	—	2	2	no	—
383	C₂×Q₈×C₂₃	—	2	2	no	—
384	C₂×Q₈×C₂₃	—	4	1	no	—
385	C₂×D₄×C₂₃	—	2	2	no	—
386	C₂×D₄×C₂₃	—	2	2	no	—
387	C₂×D₄×C₂₃	—	2	2	no	—
388	C₂×D₄×C₂₃	—	2	2	no	—
389	C₂×D₄×C₂₃	—	2	2	no	—
390	C₂×D₄×C₂₃	—	2	2	no	—
391	C₂×D₄×C₂₃	—	2	2	no	—
392	C₂×D₄×C₂₃	—	2	2	no	—
393	C₂×D₄×C₂₃	—	2	2	no	—
394	C₂×D₄×C₂₃	—	2	2	no	—
395	C₂×D₄×C₂₃	—	2	2	no	—
396	C₂×D₄×C₂₃	—	2	2	no	—
397	C₂×D₄×C₂₃	—	2	2	no	—
398	C₂×D₄×C₂₃	—	2	2	no	—
399	C₂×D₄×C₂₃	—	2	2	no	—
400	C₂×D₄×C₂₃	—	4	1	no	—
401	C₂×D₄×C₂₃	—	4	1	no	—
402	C₂×D₄×C₂₃	—	4	1	no	—
403	C₂×D₄×C₂₃	—	4	1	no	—
404	C₂×D₄×C₂₃	—	4	1	no	—
405	C₂×D₄×C₂₃	—	4	1	no	—
406	C₂×D₄×C₂₃	—	4	1	no	—
407	C₂×D₄×C₂₃	—	4	1	no	—
408	C₂×D₄×C₂₃	—	4	1	no	—
409	C₂×D₄×C₂₃	—	4	1	no	—
410	C₂×D₄×C₂₃	—	4	1	no	—
411	C₂×D₄×C₂₃	—	4	1	no	—
412	C₂×D₄×C₂₃	—	4	1	no	—
413	C₂×D₄×C₂₃	—	4	1	no	—
414	C₂×D₄×C₂₃	—	4	1	no	—
415	C₂×D₄×C₂₃	—	4	1	no	—
416	C₂×D₄×C₂₃	—	4	1	no	—
417	C₂×D₄×C₂₃	—	4	1	no	—
418	C₂×D₄×C₂₃	—	4	1	no	—
419	C₂×D₄×C₂₃	—	4	1	no	—
420	C₂×D₄×C₂₃	—	4	1	no	—
421	C₂²×C₄×C₂₃	—	2	2	no	—
422	C₂²×C₄×C₂₃	—	2	2	no	—
423	C₂²×C₄×C₂₃	—	2	2	no	—
424	C₂²×C₄×C₂₃	—	2	2	no	—
425	C₂²×C₄×C₂₃	—	2	2	no	—
426	C₂²×C₄×C₂₃	—	2	2	no	—
427	C₂²×C₄×C₂₃	—	2	2	no	—
428	C₂²×C₄×C₂₃	—	2	2	no	—
429	C₂²×C₄×C₂₃	—	2	2	no	—
430	C₂²×C₄×C₂₃	—	2	2	no	—
431	C₂²×C₄×C₂₃	—	2	2	no	—
432	C₂²×C₄×C₂₃	—	2	2	no	—
433	C₂²×C₄×C₂₃	—	4	1	no	—
434	C₂²×C₄×C₂₃	—	4	1	no	—
435	C₂²×C₄×C₂₃	—	4	1	no	—
436	C₂²×C₄×C₂₃	—	4	1	no	—
437	C₂²×C₄×C₂₃	—	4	1	no	—
438	C₂²×C₄×C₂₃	—	4	1	no	—
439	C₂²×C₄×C₂₃	—	4	1	no	—
440	C₂²×C₄×C₂₃	—	4	1	no	—
441	C₂²×C₄×C₂₃	—	4	1	no	—
442	C₂²×C₄×C₂₃	—	4	1	no	—
443	C₂²×C₄×C₂₃	—	4	1	no	—
444	C₂²×C₄×C₂₃	—	4	1	no	—
445	C₂²×C₄×C₂₃	—	4	1	no	—
446	C₂²×C₄×C₂₃	—	4	1	no	—
447	C₂²×C₄×C₂₃	—	4	1	no	—
448	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
471	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
473	C₄⋊C₄×C₂₃	—	2	2	no	—
474	C₄⋊C₄×C₂₃	—	2	2	no	—
475	C₄⋊C₄×C₂₃	—	2	2	no	—
476	C₄⋊C₄×C₂₃	—	2	2	no	—
477	C₄⋊C₄×C₂₃	—	2	2	no	—
478	C₄⋊C₄×C₂₃	—	2	2	no	—
479	C₄⋊C₄×C₂₃	—	2	2	no	—
480	C₄⋊C₄×C₂₃	—	2	2	no	—
481	C₄⋊C₄×C₂₃	—	2	2	no	—
482	C₄⋊C₄×C₂₃	—	2	2	no	—
483	C₄⋊C₄×C₂₃	—	2	2	no	—
484	C₄⋊C₄×C₂₃	—	2	2	no	—
485	C₄⋊C₄×C₂₃	—	4	1	no	—
486	C₄⋊C₄×C₂₃	—	4	1	no	—
487	C₄⋊C₄×C₂₃	—	4	1	no	—
488	C₄⋊C₄×C₂₃	—	4	1	no	—
489	C₄⋊C₄×C₂₃	—	4	1	no	—
490	C₄⋊C₄×C₂₃	—	4	1	no	—
491	C₄⋊C₄×C₂₃	—	4	1	no	—
492	C₄⋊C₄×C₂₃	—	4	1	no	—
493	C₄⋊C₄×C₂₃	—	4	1	no	—
494	C₄⋊C₄×C₂₃	—	4	1	no	—
495	C₄⋊C₄×C₂₃	—	4	1	no	—
496	C₄⋊C₄×C₂₃	—	4	1	no	—
497	C₄⋊C₄×C₂₃	—	4	1	no	—
498	C₄⋊C₄×C₂₃	—	4	1	no	—
499	C₄⋊C₄×C₂₃	—	4	1	no	—
500	C₂²⋊C₄×C₂₃	—	2	2	no	—
501	C₂²⋊C₄×C₂₃	—	2	2	no	—
502	C₂²⋊C₄×C₂₃	—	2	2	no	—
503	C₂²⋊C₄×C₂₃	—	2	2	no	—
504	C₂²⋊C₄×C₂₃	—	2	2	no	—
505	C₂²⋊C₄×C₂₃	—	2	2	no	—
506	C₂²⋊C₄×C₂₃	—	2	2	no	—
507	C₂²⋊C₄×C₂₃	—	2	2	no	—
508	C₂²⋊C₄×C₂₃	—	2	2	no	—
509	C₂²⋊C₄×C₂₃	—	2	2	no	—
510	C₂²⋊C₄×C₂₃	—	2	2	no	—
511	C₂²⋊C₄×C₂₃	—	2	2	no	—
512	C₂²⋊C₄×C₂₃	—	2	2	no	—
513	C₂²⋊C₄×C₂₃	—	2	2	no	—
514	C₂²⋊C₄×C₂₃	—	2	2	no	—
515	C₂²⋊C₄×C₂₃	—	2	2	no	—
516	C₂²⋊C₄×C₂₃	—	2	2	no	—
517	C₂²⋊C₄×C₂₃	—	2	2	no	—
518	C₂²⋊C₄×C₂₃	—	2	2	no	—
519	C₂²⋊C₄×C₂₃	—	2	2	no	—
520	C₂²⋊C₄×C₂₃	—	2	2	no	—
521	C₂²⋊C₄×C₂₃	—	2	2	no	—
522	C₂²⋊C₄×C₂₃	—	2	2	no	—
523	C₂²⋊C₄×C₂₃	—	2	2	no	—
524	C₂²⋊C₄×C₂₃	—	2	2	no	—
525	C₂²⋊C₄×C₂₃	—	2	2	no	—
526	C₂²⋊C₄×C₂₃	—	2	2	no	—
527	C₂²⋊C₄×C₂₃	—	2	2	no	—
528	C₂²⋊C₄×C₂₃	—	2	2	no	—
529	C₂²⋊C₄×C₂₃	—	2	2	no	—
530	C₂²⋊C₄×C₂₃	—	4	1	no	—
531	C₂²⋊C₄×C₂₃	—	4	1	no	—
532	C₂²⋊C₄×C₂₃	—	4	1	no	—
533	C₂²⋊C₄×C₂₃	—	4	1	no	—
534	C₂²⋊C₄×C₂₃	—	4	1	no	—
535	C₂²⋊C₄×C₂₃	—	4	1	no	—
536	C₂²⋊C₄×C₂₃	—	4	1	no	—
537	C₂²⋊C₄×C₂₃	—	4	1	no	—
538	C₂²⋊C₄×C₂₃	—	4	1	no	—
539	C₂²⋊C₄×C₂₃	—	4	1	no	—
540	C₂²⋊C₄×C₂₃	—	4	1	no	—
541	C₂²⋊C₄×C₂₃	—	4	1	no	—
542	C₂²⋊C₄×C₂₃	—	4	1	no	—
543	C₂²⋊C₄×C₂₃	—	4	1	no	—
544	C₂²⋊C₄×C₂₃	—	4	1	no	—
545	C₂²⋊C₄×C₂₃	—	4	1	no	—
546	C₂²⋊C₄×C₂₃	—	4	1	no	—
547	C₂²⋊C₄×C₂₃	—	4	1	no	—
548	C₂²⋊C₄×C₂₃	—	4	1	no	—
549	C₂²⋊C₄×C₂₃	—	4	1	no	—
550	C₂²⋊C₄×C₂₃	—	4	1	no	—
551	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
552	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
553	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
554	C₄²×C₂₃	—	2	2	no	—
555	C₄²×C₂₃	—	2	2	no	—
556	C₄²×C₂₃	—	2	2	no	—
557	C₄²×C₂₃	—	2	2	no	—
558	C₄²×C₂₃	—	2	2	no	—
559	C₄²×C₂₃	—	2	2	no	—
560	C₄²×C₂₃	—	2	2	no	—
561	C₄²×C₂₃	—	4	1	no	—
562	C₄²×C₂₃	—	4	1	no	—
563	C₄²×C₂₃	—	4	1	no	—
564	C₄²×C₂₃	—	4	1	no	—
565	C₄²×C₂₃	—	4	1	no	—
566	C₄²×C₂₃	—	4	1	no	—
567	C₄²×C₂₃	—	4	1	no	—
568	C₄²×C₂₃	—	4	1	no	—
569	C₄²×C₂₃	—	4	1	no	—
570	C₄²×C₂₃	—	4	1	no	—
571	#60010	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂³×C₂₃	—	2	1	no	—
573	C₂³×C₂₃	—	2	1	no	—
574	C₂³×C₂₃	—	2	1	no	—
575	C₂³×C₂₃	—	2	1	no	—
576	C₂³×C₂₃	—	2	1	no	—
577	C₂³×C₂₃	—	2	1	no	—
578	C₂³×C₂₃	—	2	1	no	—
579	C₂³×C₂₃	—	2	1	no	—
580	C₂³×C₂₃	—	2	1	no	—
581	C₂³×C₂₃	—	2	1	no	—
582	C₂³×C₂₃	—	2	1	no	—
583	C₂³×C₂₃	—	2	1	no	—
584	C₂³×C₂₃	—	2	1	no	—
585	C₂³×C₂₃	—	2	1	no	—
586	C₂³×C₂₃	—	2	1	no	—
587	C₂³×C₂₃	—	2	1	no	—
588	C₂³×C₂₃	—	2	1	no	—
589	C₂³×C₂₃	—	2	1	no	—
590	C₂³×C₂₃	—	2	1	no	—
591	C₂³×C₂₃	—	2	1	no	—
592	C₂³×C₂₃	—	2	1	no	—
593	C₂³×C₂₃	—	2	1	no	—
594	C₂³×C₂₃	—	2	1	no	—
595	C₂³×C₂₃	—	2	1	no	—
596	C₂³×C₂₃	—	2	1	no	—
597	C₂³×C₂₃	—	2	1	no	—
598	C₂³×C₂₃	—	2	1	no	—
599	C₂³×C₂₃	—	2	1	no	—
600	C₂³×C₂₃	—	2	1	no	—
601	C₂³×C₂₃	—	2	1	no	—
602	C₂³×C₂₃	—	2	1	no	—
603	C₂³×C₂₃	—	2	1	no	—
604	C₂³×C₂₃	—	2	1	no	—
605	C₂³×C₂₃	—	2	1	no	—
606	C₂³×C₂₃	—	2	1	no	—
607	C₂³×C₂₃	—	2	1	no	—
608	C₂³×C₂₃	—	2	1	no	—
609	C₂³×C₂₃	—	2	1	no	—
610	C₂³×C₂₃	—	2	1	no	—
611	C₂³×C₂₃	—	4	4	no	—
612	C₂³×C₂₃	—	4	4	no	—
613	C₂³×C₂₃	—	4	4	no	—
614	C₂³×C₂₃	—	8	2	no	—
615	C₂³×C₂₃	—	8	2	no	—
616	C₂³×C₂₃	—	8	2	no	—
617	C₂³×C₂₃	—	8	2	no	—
618	C₂³×C₂₃	C₂×#41	1	2	yes	—
619	C₂³×C₂₃	C₂×#41	1	2	yes	—
620	C₂³×C₂₃	C₂×#41	1	2	yes	—
621	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
622	Q₈×C₂₃	—	4	4	no	—
623	D₄×C₂₃	—	4	4	no	—
624	D₄×C₂₃	—	4	4	no	—
625	D₄×C₂₃	—	4	4	no	—
626	D₄×C₂₃	—	4	4	no	—
627	D₄×C₂₃	—	4	4	no	—
628	D₄×C₂₃	—	8	2	no	—
629	D₄×C₂₃	—	8	2	no	—
630	D₄×C₂₃	—	8	2	no	—
631	D₄×C₂₃	—	8	2	no	—
632	D₄×C₂₃	—	8	2	no	—
633	D₄×C₂₃	—	8	2	no	—
634	D₄×C₂₃	—	8	2	no	—
635	C₂×C₄×C₂₃	—	2	1	no	—
636	C₂×C₄×C₂₃	—	2	1	no	—
637	C₂×C₄×C₂₃	—	2	1	no	—
638	C₂×C₄×C₂₃	—	2	1	no	—
639	C₂×C₄×C₂₃	—	2	1	no	—
640	C₂×C₄×C₂₃	—	2	1	no	—
641	C₂×C₄×C₂₃	—	2	1	no	—
642	C₂×C₄×C₂₃	—	2	1	no	—
643	C₂×C₄×C₂₃	—	2	1	no	—
644	C₂×C₄×C₂₃	—	2	1	no	—
645	C₂×C₄×C₂₃	—	2	1	no	—
646	C₂×C₄×C₂₃	—	2	1	no	—
647	C₂×C₄×C₂₃	—	2	1	no	—
648	C₂×C₄×C₂₃	—	2	1	no	—
649	C₂×C₄×C₂₃	—	2	1	no	—
650	C₂×C₄×C₂₃	—	2	1	no	—
651	C₂×C₄×C₂₃	—	2	1	no	—
652	C₂×C₄×C₂₃	—	2	1	no	—
653	C₂×C₄×C₂₃	—	2	1	no	—
654	C₂×C₄×C₂₃	—	2	1	no	—
655	C₂×C₄×C₂₃	—	2	1	no	—
656	C₂×C₄×C₂₃	—	2	1	no	—
657	C₂×C₄×C₂₃	—	2	1	no	—
658	C₂×C₄×C₂₃	—	2	1	no	—
659	C₂×C₄×C₂₃	—	2	1	no	—
660	C₂×C₄×C₂₃	—	2	1	no	—
661	C₂×C₄×C₂₃	—	2	1	no	—
662	C₂×C₄×C₂₃	—	2	1	no	—
663	C₂×C₄×C₂₃	—	2	1	no	—
664	C₂×C₄×C₂₃	—	2	1	no	—
665	C₂×C₄×C₂₃	—	2	1	no	—
666	C₂×C₄×C₂₃	—	2	1	no	—
667	C₂×C₄×C₂₃	—	2	1	no	—
668	C₂×C₄×C₂₃	—	2	1	no	—
669	C₂×C₄×C₂₃	—	2	1	no	—
670	C₂×C₄×C₂₃	—	2	1	no	—
671	C₂×C₄×C₂₃	—	2	1	no	—
672	C₂×C₄×C₂₃	—	2	1	no	—
673	C₂×C₄×C₂₃	—	2	1	no	—
674	C₂×C₄×C₂₃	—	2	1	no	—
675	C₂×C₄×C₂₃	—	2	1	no	—
676	C₂×C₄×C₂₃	—	2	1	no	—
677	C₂×C₄×C₂₃	—	2	1	no	—
678	C₂×C₄×C₂₃	—	2	1	no	—
679	C₂×C₄×C₂₃	—	2	1	no	—
680	C₂×C₄×C₂₃	—	2	1	no	—
681	C₂×C₄×C₂₃	—	2	1	no	—
682	C₂×C₄×C₂₃	—	2	1	no	—
683	C₂×C₄×C₂₃	—	2	1	no	—
684	C₂×C₄×C₂₃	—	2	1	no	—
685	C₂×C₄×C₂₃	—	2	1	no	—
686	C₂×C₄×C₂₃	—	2	1	no	—
687	C₂×C₄×C₂₃	—	2	1	no	—
688	C₂×C₄×C₂₃	—	2	1	no	—
689	C₂×C₄×C₂₃	—	2	1	no	—
690	C₂×C₄×C₂₃	—	2	1	no	—
691	C₂×C₄×C₂₃	—	2	1	no	—
692	C₂×C₄×C₂₃	—	2	1	no	—
693	C₂×C₄×C₂₃	—	2	1	no	—
694	C₂×C₄×C₂₃	—	2	1	no	—
695	C₂×C₄×C₂₃	—	2	1	no	—
696	C₂×C₄×C₂₃	—	2	1	no	—
697	C₂×C₄×C₂₃	—	2	1	no	—
698	C₂×C₄×C₂₃	—	2	1	no	—
699	C₂×C₄×C₂₃	—	2	1	no	—
700	C₂×C₄×C₂₃	—	2	1	no	—
701	C₂×C₄×C₂₃	—	4	4	no	—
702	C₂×C₄×C₂₃	—	4	4	no	—
703	C₂×C₄×C₂₃	—	4	4	no	—
704	C₂×C₄×C₂₃	—	4	4	no	—
705	C₂×C₄×C₂₃	—	8	2	no	—
706	C₂×C₄×C₂₃	—	8	2	no	—
707	C₂×C₄×C₂₃	—	8	2	no	—
708	C₂×C₄×C₂₃	—	8	2	no	—
709	C₂×C₄×C₂₃	—	8	2	no	—
710	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
711	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
712	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
713	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
714	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
715	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
716	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
717	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
718	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
719	#2768	C₂×C₂₃	1	1	yes	characteristic, complemented
720	#2753	C₂×C₂₃	1	1	yes	characteristic, complemented
721	#2710	C₂×C₂₃	1	1	yes	characteristic, complemented
722	#2670	C₂×C₂₃	1	1	yes	characteristic, complemented
723	#2602	C₂×C₂₃	1	1	yes	characteristic, complemented
724	#2589	C₂×C₂₃	1	1	yes	characteristic, complemented
725	#2587	C₂×C₂₃	1	1	yes	characteristic, complemented
726	#2559	C₂×C₂₃	1	1	yes	characteristic, complemented
727	#2554	C₂×C₂₃	1	1	yes	characteristic, complemented
728	#2539	C₂×C₂₃	1	1	yes	characteristic, complemented
729	#2516	C₂×C₂₃	1	1	yes	characteristic, complemented
730	#2479	C₂×C₂₃	1	1	yes	characteristic, complemented
731	#2476	C₂×C₂₃	1	1	yes	characteristic, complemented
732	#2471	C₂×C₂₃	1	1	yes	characteristic, complemented
733	#2470	C₂×C₂₃	1	1	yes	characteristic, complemented
734	#2464	C₂×C₂₃	1	1	yes	characteristic, complemented
735	#2464	C₂×C₂₃	1	1	yes	characteristic, complemented
736	#2459	C₂×C₂₃	1	1	yes	characteristic, complemented
737	#2458	C₂×C₂₃	1	1	yes	characteristic, complemented
738	#2424	C₂×C₂₃	1	1	yes	characteristic, complemented
739	#2414	C₂×C₂₃	1	1	yes	characteristic, complemented
740	#2411	C₂×C₂₃	1	1	yes	characteristic, complemented
741	#2374	C₂×C₂₃	1	1	yes	characteristic, complemented
742	#2367	C₂×C₂₃	1	1	yes	characteristic, complemented
743	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
744	#2358	C₂×C₂₃	1	1	yes	characteristic, complemented
745	#2358	C₂×C₂₃	1	1	yes	characteristic, complemented
746	#2342	C₂×C₂₃	1	1	yes	characteristic, complemented
747	C₄×#124	C₂×C₂₃	1	1	yes	characteristic, complemented
748	#2293	C₂×C₂₃	1	1	yes	characteristic, complemented
749	#2293	C₂×C₂₃	1	1	yes	characteristic, complemented
750	C₂²×C₂₃	—	2	2	no	—
751	C₂²×C₂₃	—	2	2	no	—
752	C₂²×C₂₃	—	2	2	no	—
753	C₂²×C₂₃	—	2	2	no	—
754	C₂²×C₂₃	—	2	2	no	—
755	C₂²×C₂₃	—	2	2	no	—
756	C₂²×C₂₃	—	2	2	no	—
757	C₂²×C₂₃	—	2	2	no	—
758	C₂²×C₂₃	—	2	2	no	—
759	C₂²×C₂₃	—	4	1	no	—
760	C₂²×C₂₃	—	4	1	no	—
761	C₂²×C₂₃	—	4	1	no	—
762	C₂²×C₂₃	—	4	1	no	—
763	C₂²×C₂₃	—	4	1	no	—
764	C₂²×C₂₃	—	4	1	no	—
765	C₂²×C₂₃	—	4	1	no	—
766	C₂²×C₂₃	—	4	1	no	—
767	C₂²×C₂₃	—	4	1	no	—
768	C₂²×C₂₃	—	4	1	no	—
769	C₂²×C₂₃	—	4	1	no	—
770	C₂²×C₂₃	—	4	1	no	—
771	C₂²×C₂₃	—	4	1	no	—
772	C₂²×C₂₃	—	4	1	no	—
773	C₂²×C₂₃	—	4	1	no	—
774	C₂²×C₂₃	—	4	1	no	—
775	C₂²×C₂₃	—	4	1	no	—
776	C₂²×C₂₃	—	4	1	no	—
777	C₂²×C₂₃	—	4	1	no	—
778	C₂²×C₂₃	—	4	1	no	—
779	C₂²×C₂₃	—	4	1	no	—
780	C₂²×C₂₃	—	4	1	no	—
781	C₂²×C₂₃	—	4	1	no	—
782	C₂²×C₂₃	—	4	1	no	—
783	C₂²×C₂₃	—	4	1	no	—
784	C₂²×C₂₃	—	4	1	no	—
785	C₂²×C₂₃	—	4	1	no	—
786	C₂²×C₂₃	—	4	1	no	—
787	C₂²×C₂₃	—	4	1	no	—
788	C₂²×C₂₃	—	4	1	no	—
789	C₂²×C₂₃	—	4	1	no	—
790	C₂²×C₂₃	—	4	1	no	—
791	C₂²×C₂₃	—	4	1	no	—
792	C₂²×C₂₃	—	8	8	no	—
793	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
794	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
795	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
796	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂²×C₂₃	#585	1	1	yes	characteristic
800	C₄×C₂₃	—	2	2	no	—
801	C₄×C₂₃	—	2	2	no	—
802	C₄×C₂₃	—	2	2	no	—
803	C₄×C₂₃	—	2	2	no	—
804	C₄×C₂₃	—	2	2	no	—
805	C₄×C₂₃	—	2	2	no	—
806	C₄×C₂₃	—	2	2	no	—
807	C₄×C₂₃	—	2	2	no	—
808	C₄×C₂₃	—	2	2	no	—
809	C₄×C₂₃	—	4	1	no	—
810	C₄×C₂₃	—	4	1	no	—
811	C₄×C₂₃	—	4	1	no	—
812	C₄×C₂₃	—	4	1	no	—
813	C₄×C₂₃	—	4	1	no	—
814	C₄×C₂₃	—	4	1	no	—
815	C₄×C₂₃	—	4	1	no	—
816	C₄×C₂₃	—	4	1	no	—
817	C₄×C₂₃	—	4	1	no	—
818	C₄×C₂₃	—	4	1	no	—
819	C₄×C₂₃	—	4	1	no	—
820	C₄×C₂₃	—	4	1	no	—
821	C₄×C₂₃	—	4	1	no	—
822	C₄×C₂₃	—	4	1	no	—
823	C₄×C₂₃	—	4	1	no	—
824	C₄×C₂₃	—	4	1	no	—
825	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic, complemented
826	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
827	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
828	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
829	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
830	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
831	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic, complemented
832	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
833	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
834	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
835	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
836	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
837	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
838	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
839	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
840	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
841	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
842	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
843	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
844	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
845	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
846	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
847	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
848	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
849	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
850	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
851	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
852	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
853	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
854	#399	C₂²×C₂₃	1	1	yes	characteristic
855	#399	C₂²×C₂₃	1	1	yes	characteristic
856	#399	C₂²×C₂₃	1	1	yes	characteristic, complemented
857	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
858	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
859	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
860	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
861	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
862	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
863	#396	C₂²×C₂₃	1	1	yes	characteristic
864	#396	C₂²×C₂₃	1	1	yes	characteristic
865	#396	C₂²×C₂₃	1	1	yes	characteristic
866	#394	C₂²×C₂₃	1	1	yes	characteristic
867	#394	C₂²×C₂₃	1	1	yes	characteristic
868	#394	C₂²×C₂₃	1	1	yes	characteristic
869	#394	C₂²×C₂₃	1	1	yes	characteristic
870	#394	C₂²×C₂₃	1	1	yes	characteristic
871	#394	C₂²×C₂₃	1	1	yes	characteristic
872	#394	C₂²×C₂₃	1	1	yes	characteristic, complemented
873	#394	C₂²×C₂₃	1	1	yes	characteristic, complemented
874	#394	C₂²×C₂₃	1	1	yes	characteristic, complemented
875	#394	C₂²×C₂₃	1	1	yes	characteristic, complemented
876	#393	C₂²×C₂₃	1	1	yes	characteristic
877	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
878	#392	C₂²×C₂₃	1	1	yes	characteristic
879	#392	C₂²×C₂₃	1	1	yes	characteristic
880	#392	C₂²×C₂₃	1	1	yes	characteristic
881	#392	C₂²×C₂₃	1	1	yes	characteristic
882	#392	C₂²×C₂₃	1	1	yes	characteristic
883	#392	C₂²×C₂₃	1	1	yes	characteristic
884	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
885	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
886	#390	C₂²×C₂₃	1	1	yes	characteristic
887	#390	C₂²×C₂₃	1	1	yes	characteristic
888	#390	C₂²×C₂₃	1	1	yes	characteristic
889	#390	C₂²×C₂₃	1	1	yes	characteristic
890	#390	C₂²×C₂₃	1	1	yes	characteristic
891	#390	C₂²×C₂₃	1	1	yes	characteristic
892	#390	C₂²×C₂₃	1	1	yes	characteristic
893	#390	C₂²×C₂₃	1	1	yes	characteristic
894	#390	C₂²×C₂₃	1	1	yes	characteristic
895	#390	C₂²×C₂₃	1	1	yes	characteristic
896	#390	C₂²×C₂₃	1	1	yes	characteristic
897	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
898	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
899	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
900	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
901	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
902	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
903	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
904	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
905	#388	C₂²×C₂₃	1	1	yes	characteristic
906	#388	C₂²×C₂₃	1	1	yes	characteristic
907	#388	C₂²×C₂₃	1	1	yes	characteristic
908	#388	C₂²×C₂₃	1	1	yes	characteristic
909	#388	C₂²×C₂₃	1	1	yes	characteristic
910	#388	C₂²×C₂₃	1	1	yes	characteristic
911	#388	C₂²×C₂₃	1	1	yes	characteristic
912	#388	C₂²×C₂₃	1	1	yes	characteristic
913	#388	C₂²×C₂₃	1	1	yes	characteristic
914	#388	C₂²×C₂₃	1	1	yes	characteristic
915	#388	C₂²×C₂₃	1	1	yes	characteristic
916	#388	C₂²×C₂₃	1	1	yes	characteristic
917	#388	C₂²×C₂₃	1	1	yes	characteristic
918	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
919	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
920	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
921	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
922	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
923	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
924	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
925	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
926	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
927	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
928	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
929	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
930	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
931	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
932	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
933	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
934	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
935	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
936	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
937	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
938	#386	C₂²×C₂₃	1	1	yes	characteristic
939	#386	C₂²×C₂₃	1	1	yes	characteristic
940	#386	C₂²×C₂₃	1	1	yes	characteristic
941	#386	C₂²×C₂₃	1	1	yes	characteristic
942	#386	C₂²×C₂₃	1	1	yes	characteristic
943	#386	C₂²×C₂₃	1	1	yes	characteristic
944	#386	C₂²×C₂₃	1	1	yes	characteristic
945	#386	C₂²×C₂₃	1	1	yes	characteristic
946	#386	C₂²×C₂₃	1	1	yes	characteristic
947	#386	C₂²×C₂₃	1	1	yes	characteristic, complemented
948	#386	C₂²×C₂₃	1	1	yes	characteristic, complemented
949	#385	C₂²×C₂₃	1	1	yes	characteristic
950	#385	C₂²×C₂₃	1	1	yes	characteristic
951	#385	C₂²×C₂₃	1	1	yes	characteristic
952	#385	C₂²×C₂₃	1	1	yes	characteristic
953	#385	C₂²×C₂₃	1	1	yes	characteristic
954	#385	C₂²×C₂₃	1	1	yes	characteristic
955	#385	C₂²×C₂₃	1	1	yes	characteristic
956	#385	C₂²×C₂₃	1	1	yes	characteristic
957	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
958	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
959	#381	C₂²×C₂₃	1	1	yes	characteristic
960	#380	C₂²×C₂₃	1	1	yes	characteristic
961	#379	C₂²×C₂₃	1	1	yes	characteristic
962	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
963	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
964	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
965	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
966	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
967	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
968	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
969	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
970	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
971	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
972	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
973	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
974	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
975	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
976	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
977	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
978	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
979	C₄³	C₂²×C₂₃	1	1	yes	characteristic, complemented
980	C₂×C₂₃	—	4	2	no	—
981	C₂×C₂₃	—	4	2	no	—
982	C₂×C₂₃	—	4	2	no	—
983	C₂×C₂₃	—	8	1	no	—
984	C₂×C₂₃	—	8	1	no	—
985	C₂×C₂₃	—	8	1	no	—
986	C₂×C₂₃	#3475	1	1	yes	characteristic
987	C₂×C₂₃	#3481	1	1	yes	characteristic
988	C₂×C₂₃	#3481	1	1	yes	characteristic
989	C₂×C₂₃	#3494	1	1	yes	characteristic
990	C₂×C₂₃	#3508	1	1	yes	characteristic
991	C₂×C₂₃	#3519	1	1	yes	characteristic
992	C₂×C₂₃	#3558	1	1	yes	characteristic
993	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
994	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
995	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
996	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
997	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
998	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
999	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1000	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1001	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1002	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1003	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1004	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1005	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1006	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1007	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1008	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1009	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1010	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1011	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1012	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1013	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1014	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1015	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
1016	#126	—	4	2	no	—
1017	#124	—	2	4	no	—
1018	#124	—	2	4	no	—
1019	#123	—	2	4	no	—
1020	#123	—	4	2	no	—
1021	#123	—	4	2	no	—
1022	#123	—	4	2	no	—
1023	#121	—	2	4	no	—
1024	#121	—	4	2	no	—
1025	#121	—	4	2	no	—
1026	#121	—	4	2	no	—
1027	#120	—	2	4	no	—
1028	#120	—	2	4	no	—
1029	#120	—	4	2	no	—
1030	C₄×Q₈	—	4	2	no	—
1031	C₄×D₄	—	2	4	no	—
1032	C₄×D₄	—	2	4	no	—
1033	C₄×D₄	—	4	2	no	—
1034	C₄×D₄	—	4	2	no	—
1035	C₄×D₄	—	4	2	no	—
1036	#117	—	4	2	no	—
1037	#117	—	4	2	no	—
1038	#117	—	4	2	no	—
1039	#117	—	4	2	no	—
1040	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1041	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1042	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1043	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1044	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1045	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1046	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1047	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1048	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1058	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1059	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1060	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1061	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1062	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1063	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1064	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1065	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1066	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	—	2	4	no	—
1068	C₂×C₂²⋊C₄	—	4	2	no	—
1069	C₂×C₂²⋊C₄	—	4	2	no	—
1070	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1076	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1077	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1078	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1079	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1080	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1081	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1082	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1083	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1084	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1085	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1086	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1087	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1088	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1089	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1095	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1104	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1105	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1106	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1107	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1108	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1109	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1110	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1111	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1112	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1113	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1114	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1115	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1116	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1119	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1122	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1123	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1124	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1125	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1126	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1127	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1128	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1129	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1130	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1131	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1132	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1133	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1134	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1135	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1136	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1137	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1138	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1139	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1140	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1141	#95	C₂³×C₂₃	1	1	yes	characteristic
1142	#95	C₂³×C₂₃	1	1	yes	characteristic
1143	#95	C₂³×C₂₃	1	1	yes	characteristic
1144	#95	C₂³×C₂₃	1	1	yes	characteristic
1145	#95	C₂³×C₂₃	1	1	yes	characteristic
1146	#95	C₂³×C₂₃	1	1	yes	characteristic
1147	#95	C₂³×C₂₃	1	1	yes	characteristic
1148	#95	C₂³×C₂₃	1	1	yes	characteristic
1149	#95	C₂³×C₂₃	1	1	yes	characteristic
1150	#95	C₂³×C₂₃	1	1	yes	characteristic
1151	#95	C₂³×C₂₃	1	1	yes	characteristic
1152	#95	C₂³×C₂₃	1	1	yes	characteristic
1153	#95	C₂³×C₂₃	1	1	yes	characteristic
1154	#95	C₂³×C₂₃	1	1	yes	characteristic
1155	#95	C₂³×C₂₃	1	1	yes	characteristic
1156	#95	C₂³×C₂₃	1	1	yes	characteristic
1157	#95	C₂³×C₂₃	1	1	yes	characteristic
1158	#95	C₂³×C₂₃	1	1	yes	characteristic
1159	#95	C₂³×C₂₃	1	1	yes	characteristic
1160	#95	C₂³×C₂₃	1	1	yes	characteristic
1161	#95	C₂³×C₂₃	1	1	yes	characteristic
1162	#95	C₂³×C₂₃	1	1	yes	characteristic
1163	#95	C₂³×C₂₃	1	1	yes	characteristic
1164	#95	C₂³×C₂₃	1	1	yes	characteristic
1165	#95	C₂³×C₂₃	1	1	yes	characteristic
1166	#95	C₂³×C₂₃	1	1	yes	characteristic
1167	#95	C₂³×C₂₃	1	1	yes	characteristic
1168	#95	C₂³×C₂₃	1	1	yes	characteristic
1169	#95	C₂³×C₂₃	1	1	yes	characteristic
1170	#95	C₂³×C₂₃	1	1	yes	characteristic
1171	#95	C₂³×C₂₃	1	1	yes	characteristic
1172	#95	C₂³×C₂₃	1	1	yes	characteristic
1173	#95	C₂³×C₂₃	1	1	yes	characteristic
1174	#95	C₂³×C₂₃	1	1	yes	characteristic
1175	C₂₃	#60010	1	1	yes	characteristic, direct product factor, Sylow
1176	C₂⁴	—	2	2	no	—
1177	C₂⁴	—	2	2	no	—
1178	C₂⁴	—	2	2	no	—
1179	C₂⁴	—	4	1	no	—
1180	C₂⁴	—	4	1	no	—
1181	C₂⁴	—	4	1	no	—
1182	C₂⁴	—	4	1	no	—
1183	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1184	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1185	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1186	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1187	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1188	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1189	C₂×Q₈	—	2	2	no	—
1190	C₂×Q₈	—	2	2	no	—
1191	C₂×Q₈	—	4	1	no	—
1192	C₂×D₄	—	2	2	no	—
1193	C₂×D₄	—	2	2	no	—
1194	C₂×D₄	—	2	2	no	—
1195	C₂×D₄	—	2	2	no	—
1196	C₂×D₄	—	2	2	no	—
1197	C₂×D₄	—	2	2	no	—
1198	C₂×D₄	—	2	2	no	—
1199	C₂×D₄	—	2	2	no	—
1200	C₂×D₄	—	2	2	no	—
1201	C₂×D₄	—	2	2	no	—
1202	C₂×D₄	—	2	2	no	—
1203	C₂×D₄	—	2	2	no	—
1204	C₂×D₄	—	2	2	no	—
1205	C₂×D₄	—	2	2	no	—
1206	C₂×D₄	—	2	2	no	—
1207	C₂×D₄	—	4	1	no	—
1208	C₂×D₄	—	4	1	no	—
1209	C₂×D₄	—	4	1	no	—
1210	C₂×D₄	—	4	1	no	—
1211	C₂×D₄	—	4	1	no	—
1212	C₂×D₄	—	4	1	no	—
1213	C₂×D₄	—	4	1	no	—
1214	C₂×D₄	—	4	1	no	—
1215	C₂×D₄	—	4	1	no	—
1216	C₂×D₄	—	4	1	no	—
1217	C₂×D₄	—	4	1	no	—
1218	C₂×D₄	—	4	1	no	—
1219	C₂×D₄	—	4	1	no	—
1220	C₂×D₄	—	4	1	no	—
1221	C₂×D₄	—	4	1	no	—
1222	C₂×D₄	—	4	1	no	—
1223	C₂×D₄	—	4	1	no	—
1224	C₂×D₄	—	4	1	no	—
1225	C₂×D₄	—	4	1	no	—
1226	C₂×D₄	—	4	1	no	—
1227	C₂×D₄	—	4	1	no	—
1228	C₂²×C₄	—	2	2	no	—
1229	C₂²×C₄	—	2	2	no	—
1230	C₂²×C₄	—	2	2	no	—
1231	C₂²×C₄	—	2	2	no	—
1232	C₂²×C₄	—	2	2	no	—
1233	C₂²×C₄	—	2	2	no	—
1234	C₂²×C₄	—	2	2	no	—
1235	C₂²×C₄	—	2	2	no	—
1236	C₂²×C₄	—	2	2	no	—
1237	C₂²×C₄	—	2	2	no	—
1238	C₂²×C₄	—	2	2	no	—
1239	C₂²×C₄	—	2	2	no	—
1240	C₂²×C₄	—	4	1	no	—
1241	C₂²×C₄	—	4	1	no	—
1242	C₂²×C₄	—	4	1	no	—
1243	C₂²×C₄	—	4	1	no	—
1244	C₂²×C₄	—	4	1	no	—
1245	C₂²×C₄	—	4	1	no	—
1246	C₂²×C₄	—	4	1	no	—
1247	C₂²×C₄	—	4	1	no	—
1248	C₂²×C₄	—	4	1	no	—
1249	C₂²×C₄	—	4	1	no	—
1250	C₂²×C₄	—	4	1	no	—
1251	C₂²×C₄	—	4	1	no	—
1252	C₂²×C₄	—	4	1	no	—
1253	C₂²×C₄	—	4	1	no	—
1254	C₂²×C₄	—	4	1	no	—
1255	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1256	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1257	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1258	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1259	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1260	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1261	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1262	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1263	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1264	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1265	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1266	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1267	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1268	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1269	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1270	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1271	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1272	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1273	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1274	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1275	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1276	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1277	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1278	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1279	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1280	C₄⋊C₄	—	2	2	no	—
1281	C₄⋊C₄	—	2	2	no	—
1282	C₄⋊C₄	—	2	2	no	—
1283	C₄⋊C₄	—	2	2	no	—
1284	C₄⋊C₄	—	2	2	no	—
1285	C₄⋊C₄	—	2	2	no	—
1286	C₄⋊C₄	—	2	2	no	—
1287	C₄⋊C₄	—	2	2	no	—
1288	C₄⋊C₄	—	2	2	no	—
1289	C₄⋊C₄	—	2	2	no	—
1290	C₄⋊C₄	—	2	2	no	—
1291	C₄⋊C₄	—	2	2	no	—
1292	C₄⋊C₄	—	4	1	no	—
1293	C₄⋊C₄	—	4	1	no	—
1294	C₄⋊C₄	—	4	1	no	—
1295	C₄⋊C₄	—	4	1	no	—
1296	C₄⋊C₄	—	4	1	no	—
1297	C₄⋊C₄	—	4	1	no	—
1298	C₄⋊C₄	—	4	1	no	—
1299	C₄⋊C₄	—	4	1	no	—
1300	C₄⋊C₄	—	4	1	no	—
1301	C₄⋊C₄	—	4	1	no	—
1302	C₄⋊C₄	—	4	1	no	—
1303	C₄⋊C₄	—	4	1	no	—
1304	C₄⋊C₄	—	4	1	no	—
1305	C₄⋊C₄	—	4	1	no	—
1306	C₄⋊C₄	—	4	1	no	—
1307	C₂²⋊C₄	—	2	2	no	—
1308	C₂²⋊C₄	—	2	2	no	—
1309	C₂²⋊C₄	—	2	2	no	—
1310	C₂²⋊C₄	—	2	2	no	—
1311	C₂²⋊C₄	—	2	2	no	—
1312	C₂²⋊C₄	—	2	2	no	—
1313	C₂²⋊C₄	—	2	2	no	—
1314	C₂²⋊C₄	—	2	2	no	—
1315	C₂²⋊C₄	—	2	2	no	—
1316	C₂²⋊C₄	—	2	2	no	—
1317	C₂²⋊C₄	—	2	2	no	—
1318	C₂²⋊C₄	—	2	2	no	—
1319	C₂²⋊C₄	—	2	2	no	—
1320	C₂²⋊C₄	—	2	2	no	—
1321	C₂²⋊C₄	—	2	2	no	—
1322	C₂²⋊C₄	—	2	2	no	—
1323	C₂²⋊C₄	—	2	2	no	—
1324	C₂²⋊C₄	—	2	2	no	—
1325	C₂²⋊C₄	—	2	2	no	—
1326	C₂²⋊C₄	—	2	2	no	—
1327	C₂²⋊C₄	—	2	2	no	—
1328	C₂²⋊C₄	—	2	2	no	—
1329	C₂²⋊C₄	—	2	2	no	—
1330	C₂²⋊C₄	—	2	2	no	—
1331	C₂²⋊C₄	—	2	2	no	—
1332	C₂²⋊C₄	—	2	2	no	—
1333	C₂²⋊C₄	—	2	2	no	—
1334	C₂²⋊C₄	—	2	2	no	—
1335	C₂²⋊C₄	—	2	2	no	—
1336	C₂²⋊C₄	—	2	2	no	—
1337	C₂²⋊C₄	—	4	1	no	—
1338	C₂²⋊C₄	—	4	1	no	—
1339	C₂²⋊C₄	—	4	1	no	—
1340	C₂²⋊C₄	—	4	1	no	—
1341	C₂²⋊C₄	—	4	1	no	—
1342	C₂²⋊C₄	—	4	1	no	—
1343	C₂²⋊C₄	—	4	1	no	—
1344	C₂²⋊C₄	—	4	1	no	—
1345	C₂²⋊C₄	—	4	1	no	—
1346	C₂²⋊C₄	—	4	1	no	—
1347	C₂²⋊C₄	—	4	1	no	—
1348	C₂²⋊C₄	—	4	1	no	—
1349	C₂²⋊C₄	—	4	1	no	—
1350	C₂²⋊C₄	—	4	1	no	—
1351	C₂²⋊C₄	—	4	1	no	—
1352	C₂²⋊C₄	—	4	1	no	—
1353	C₂²⋊C₄	—	4	1	no	—
1354	C₂²⋊C₄	—	4	1	no	—
1355	C₂²⋊C₄	—	4	1	no	—
1356	C₂²⋊C₄	—	4	1	no	—
1357	C₂²⋊C₄	—	4	1	no	—
1358	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
1359	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
1360	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
1361	C₄²	—	2	2	no	—
1362	C₄²	—	2	2	no	—
1363	C₄²	—	2	2	no	—
1364	C₄²	—	2	2	no	—
1365	C₄²	—	2	2	no	—
1366	C₄²	—	2	2	no	—
1367	C₄²	—	2	2	no	—
1368	C₄²	—	4	1	no	—
1369	C₄²	—	4	1	no	—
1370	C₄²	—	4	1	no	—
1371	C₄²	—	4	1	no	—
1372	C₄²	—	4	1	no	—
1373	C₄²	—	4	1	no	—
1374	C₄²	—	4	1	no	—
1375	C₄²	—	4	1	no	—
1376	C₄²	—	4	1	no	—
1377	C₄²	—	4	1	no	—
1378	C₂³	—	2	1	no	—
1379	C₂³	—	2	1	no	—
1380	C₂³	—	2	1	no	—
1381	C₂³	—	2	1	no	—
1382	C₂³	—	2	1	no	—
1383	C₂³	—	2	1	no	—
1384	C₂³	—	2	1	no	—
1385	C₂³	—	2	1	no	—
1386	C₂³	—	2	1	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	1	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	2	1	no	—
1393	C₂³	—	2	1	no	—
1394	C₂³	—	2	1	no	—
1395	C₂³	—	2	1	no	—
1396	C₂³	—	2	1	no	—
1397	C₂³	—	2	1	no	—
1398	C₂³	—	2	1	no	—
1399	C₂³	—	2	1	no	—
1400	C₂³	—	2	1	no	—
1401	C₂³	—	2	1	no	—
1402	C₂³	—	2	1	no	—
1403	C₂³	—	2	1	no	—
1404	C₂³	—	2	1	no	—
1405	C₂³	—	2	1	no	—
1406	C₂³	—	2	1	no	—
1407	C₂³	—	2	1	no	—
1408	C₂³	—	2	1	no	—
1409	C₂³	—	2	1	no	—
1410	C₂³	—	2	1	no	—
1411	C₂³	—	2	1	no	—
1412	C₂³	—	2	1	no	—
1413	C₂³	—	2	1	no	—
1414	C₂³	—	2	1	no	—
1415	C₂³	—	2	1	no	—
1416	C₂³	—	2	1	no	—
1417	C₂³	—	4	4	no	—
1418	C₂³	—	4	4	no	—
1419	C₂³	—	4	4	no	—
1420	C₂³	—	8	2	no	—
1421	C₂³	—	8	2	no	—
1422	C₂³	—	8	2	no	—
1423	C₂³	—	8	2	no	—
1424	C₂³	C₂×#41×C₂₃	1	2	yes	—
1425	C₂³	C₂×#41×C₂₃	1	2	yes	—
1426	C₂³	C₂×#41×C₂₃	1	2	yes	—
1427	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1428	Q₈	—	4	4	no	—
1429	D₄	—	4	4	no	—
1430	D₄	—	4	4	no	—
1431	D₄	—	4	4	no	—
1432	D₄	—	4	4	no	—
1433	D₄	—	4	4	no	—
1434	D₄	—	8	2	no	—
1435	D₄	—	8	2	no	—
1436	D₄	—	8	2	no	—
1437	D₄	—	8	2	no	—
1438	D₄	—	8	2	no	—
1439	D₄	—	8	2	no	—
1440	D₄	—	8	2	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	1	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	1	no	—
1462	C₂×C₄	—	2	1	no	—
1463	C₂×C₄	—	2	1	no	—
1464	C₂×C₄	—	2	1	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	2	1	no	—
1496	C₂×C₄	—	2	1	no	—
1497	C₂×C₄	—	2	1	no	—
1498	C₂×C₄	—	2	1	no	—
1499	C₂×C₄	—	2	1	no	—
1500	C₂×C₄	—	2	1	no	—
1501	C₂×C₄	—	2	1	no	—
1502	C₂×C₄	—	2	1	no	—
1503	C₂×C₄	—	2	1	no	—
1504	C₂×C₄	—	2	1	no	—
1505	C₂×C₄	—	2	1	no	—
1506	C₂×C₄	—	2	1	no	—
1507	C₂×C₄	—	4	4	no	—
1508	C₂×C₄	—	4	4	no	—
1509	C₂×C₄	—	4	4	no	—
1510	C₂×C₄	—	4	4	no	—
1511	C₂×C₄	—	8	2	no	—
1512	C₂×C₄	—	8	2	no	—
1513	C₂×C₄	—	8	2	no	—
1514	C₂×C₄	—	8	2	no	—
1515	C₂×C₄	—	8	2	no	—
1516	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1517	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1518	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1519	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1520	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1521	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1522	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1523	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1524	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1525	C₂²	—	2	2	no	—
1526	C₂²	—	2	2	no	—
1527	C₂²	—	2	2	no	—
1528	C₂²	—	2	2	no	—
1529	C₂²	—	2	2	no	—
1530	C₂²	—	2	2	no	—
1531	C₂²	—	2	2	no	—
1532	C₂²	—	2	2	no	—
1533	C₂²	—	2	2	no	—
1534	C₂²	—	4	1	no	—
1535	C₂²	—	4	1	no	—
1536	C₂²	—	4	1	no	—
1537	C₂²	—	4	1	no	—
1538	C₂²	—	4	1	no	—
1539	C₂²	—	4	1	no	—
1540	C₂²	—	4	1	no	—
1541	C₂²	—	4	1	no	—
1542	C₂²	—	4	1	no	—
1543	C₂²	—	4	1	no	—
1544	C₂²	—	4	1	no	—
1545	C₂²	—	4	1	no	—
1546	C₂²	—	4	1	no	—
1547	C₂²	—	4	1	no	—
1548	C₂²	—	4	1	no	—
1549	C₂²	—	4	1	no	—
1550	C₂²	—	4	1	no	—
1551	C₂²	—	4	1	no	—
1552	C₂²	—	4	1	no	—
1553	C₂²	—	4	1	no	—
1554	C₂²	—	4	1	no	—
1555	C₂²	—	4	1	no	—
1556	C₂²	—	4	1	no	—
1557	C₂²	—	4	1	no	—
1558	C₂²	—	4	1	no	—
1559	C₂²	—	4	1	no	—
1560	C₂²	—	4	1	no	—
1561	C₂²	—	4	1	no	—
1562	C₂²	—	4	1	no	—
1563	C₂²	—	4	1	no	—
1564	C₂²	—	4	1	no	—
1565	C₂²	—	4	1	no	—
1566	C₂²	—	4	1	no	—
1567	C₂²	—	8	8	no	—
1568	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1569	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1570	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1571	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1572	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1573	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1574	C₂²	C₂₃×#585	1	1	yes	characteristic
1575	C₄	—	2	2	no	—
1576	C₄	—	2	2	no	—
1577	C₄	—	2	2	no	—
1578	C₄	—	2	2	no	—
1579	C₄	—	2	2	no	—
1580	C₄	—	2	2	no	—
1581	C₄	—	2	2	no	—
1582	C₄	—	2	2	no	—
1583	C₄	—	2	2	no	—
1584	C₄	—	4	1	no	—
1585	C₄	—	4	1	no	—
1586	C₄	—	4	1	no	—
1587	C₄	—	4	1	no	—
1588	C₄	—	4	1	no	—
1589	C₄	—	4	1	no	—
1590	C₄	—	4	1	no	—
1591	C₄	—	4	1	no	—
1592	C₄	—	4	1	no	—
1593	C₄	—	4	1	no	—
1594	C₄	—	4	1	no	—
1595	C₄	—	4	1	no	—
1596	C₄	—	4	1	no	—
1597	C₄	—	4	1	no	—
1598	C₄	—	4	1	no	—
1599	C₄	—	4	1	no	—
1600	C₂	—	4	2	no	—
1601	C₂	—	4	2	no	—
1602	C₂	—	4	2	no	—
1603	C₂	—	8	1	no	—
1604	C₂	—	8	1	no	—
1605	C₂	—	8	1	no	—
1606	C₂	C₂₃×#3475	1	1	yes	characteristic
1607	C₂	C₂₃×#3481	1	1	yes	characteristic
1608	C₂	C₂₃×#3481	1	1	yes	characteristic
1609	C₂	C₂₃×#3494	1	1	yes	characteristic
1610	C₂	C₂₃×#3508	1	1	yes	characteristic
1611	C₂	C₂₃×#3519	1	1	yes	characteristic
1612	C₂	C₂₃×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#2768	C₂	semidirect
2. C₂₃×#2753	C₂	semidirect
3. C₂₃×#2710	C₂	semidirect
4. C₂₃×#2670	C₂	semidirect
5. C₂₃×#2602	C₂	semidirect
6. C₂₃×#2589	C₂	semidirect
7. C₂₃×#2587	C₂	semidirect
8. C₂₃×#2559	C₂	semidirect
9. C₂₃×#2554	C₂	semidirect
10. C₂₃×#2539	C₂	semidirect
11. C₂₃×#2516	C₂	semidirect
12. C₂₃×#2479	C₂	semidirect
13. C₂₃×#2476	C₂	semidirect
14. C₂₃×#2471	C₂	semidirect
15. C₂₃×#2470	C₂	semidirect
16. C₂₃×#2464	C₂	semidirect
17. C₂₃×#2464	C₂	semidirect
18. C₂₃×#2459	C₂	semidirect
19. C₂₃×#2458	C₂	semidirect
20. C₂₃×#2424	C₂	semidirect
21. C₂₃×#2414	C₂	semidirect
22. C₂₃×#2411	C₂	semidirect
23. C₂₃×#2374	C₂	semidirect
24. C₂₃×#2367	C₂	semidirect
25. C₂₃×#2363	C₂	semidirect
26. C₂₃×#2358	C₂	semidirect
27. C₂₃×#2358	C₂	semidirect
28. C₂₃×#2342	C₂	semidirect
29. C₄×C₂₃×#124	C₂	semidirect
30. C₂₃×#2293	C₂	semidirect
31. C₂₃×#2293	C₂	semidirect
32. C₂×C₂₃×#126	C₂²	semidirect
38. C₂×C₂₃×#123	C₂²	semidirect
42. C₂×C₂₃×#121	C₂²	semidirect
46. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
54. C₂×C₂₃×#117	C₂²	semidirect
55. C₂×C₂₃×#117	C₂²	semidirect
59. C₂₃×#400	C₂²	semidirect
60. C₂₃×#400	C₂²	semidirect
63. C₂₃×#399	C₂²	semidirect
64. C₂₃×#398	C₂²	semidirect
65. C₂₃×#398	C₂²	semidirect
66. C₂₃×#398	C₂²	semidirect
67. C₂₃×#398	C₂²	semidirect
68. C₂₃×#397	C₂²	semidirect
69. C₂₃×#397	C₂²	semidirect
79. C₂₃×#394	C₂²	semidirect
80. C₂₃×#394	C₂²	semidirect
81. C₂₃×#394	C₂²	semidirect
82. C₂₃×#394	C₂²	semidirect
84. C₂₃×#393	C₂²	semidirect
91. C₂₃×#391	C₂²	semidirect
92. C₂₃×#391	C₂²	semidirect
104. C₂₃×#390	C₂²	semidirect
105. C₂₃×#390	C₂²	semidirect
106. C₂₃×#389	C₂²	semidirect
107. C₂₃×#389	C₂²	semidirect
108. C₂₃×#389	C₂²	semidirect
109. C₂₃×#389	C₂²	semidirect
110. C₂₃×#389	C₂²	semidirect
111. C₂₃×#389	C₂²	semidirect
125. C₂₃×#388	C₂²	semidirect
126. C₂₃×#388	C₂²	semidirect
127. C₂₃×#388	C₂²	semidirect
128. C₂₃×#388	C₂²	semidirect
129. C₂₃×#388	C₂²	semidirect
130. C₂₃×#388	C₂²	semidirect
131. C₂₃×#388	C₂²	semidirect
132. C₂₃×#388	C₂²	semidirect
133. C₂₃×#388	C₂²	semidirect
134. C₂₃×#388	C₂²	semidirect
135. C₂₃×#388	C₂²	semidirect
136. C₂₃×#388	C₂²	semidirect
137. C₂₃×#388	C₂²	semidirect
138. C₂₃×#388	C₂²	semidirect
139. C₂₃×#387	C₂²	semidirect
140. C₂₃×#387	C₂²	semidirect
141. C₂₃×#387	C₂²	semidirect
142. C₂₃×#387	C₂²	semidirect
143. C₂₃×#387	C₂²	semidirect
144. C₂₃×#387	C₂²	semidirect
154. C₂₃×#386	C₂²	semidirect
155. C₂₃×#386	C₂²	semidirect
164. C₂₃×#385	C₂²	semidirect
165. C₂₃×#382	C₂²	semidirect
169. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
170. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
171. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
172. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
181. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
182. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
183. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
184. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
185. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
186. C₄³×C₂₃	C₂²	semidirect
571. #60010	C₂₃	direct (N × H)
719. #2768	C₂×C₂₃	semidirect
720. #2753	C₂×C₂₃	semidirect
721. #2710	C₂×C₂₃	semidirect
722. #2670	C₂×C₂₃	semidirect
723. #2602	C₂×C₂₃	semidirect
724. #2589	C₂×C₂₃	semidirect
725. #2587	C₂×C₂₃	semidirect
726. #2559	C₂×C₂₃	semidirect
727. #2554	C₂×C₂₃	semidirect
728. #2539	C₂×C₂₃	semidirect
729. #2516	C₂×C₂₃	semidirect
730. #2479	C₂×C₂₃	semidirect
731. #2476	C₂×C₂₃	semidirect
732. #2471	C₂×C₂₃	semidirect
733. #2470	C₂×C₂₃	semidirect
734. #2464	C₂×C₂₃	semidirect
735. #2464	C₂×C₂₃	semidirect
736. #2459	C₂×C₂₃	semidirect
737. #2458	C₂×C₂₃	semidirect
738. #2424	C₂×C₂₃	semidirect
739. #2414	C₂×C₂₃	semidirect
740. #2411	C₂×C₂₃	semidirect
741. #2374	C₂×C₂₃	semidirect
742. #2367	C₂×C₂₃	semidirect
743. #2363	C₂×C₂₃	semidirect
744. #2358	C₂×C₂₃	semidirect
745. #2358	C₂×C₂₃	semidirect
746. #2342	C₂×C₂₃	semidirect
747. C₄×#124	C₂×C₂₃	semidirect
748. #2293	C₂×C₂₃	semidirect
749. #2293	C₂×C₂₃	semidirect
825. C₂×#126	C₂²×C₂₃	semidirect
831. C₂×#123	C₂²×C₂₃	semidirect
835. C₂×#121	C₂²×C₂₃	semidirect
839. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
847. C₂×#117	C₂²×C₂₃	semidirect
848. C₂×#117	C₂²×C₂₃	semidirect
852. #400	C₂²×C₂₃	semidirect
853. #400	C₂²×C₂₃	semidirect
856. #399	C₂²×C₂₃	semidirect
857. #398	C₂²×C₂₃	semidirect
858. #398	C₂²×C₂₃	semidirect
859. #398	C₂²×C₂₃	semidirect
860. #398	C₂²×C₂₃	semidirect
861. #397	C₂²×C₂₃	semidirect
862. #397	C₂²×C₂₃	semidirect
872. #394	C₂²×C₂₃	semidirect
873. #394	C₂²×C₂₃	semidirect
874. #394	C₂²×C₂₃	semidirect
875. #394	C₂²×C₂₃	semidirect
877. #393	C₂²×C₂₃	semidirect
884. #391	C₂²×C₂₃	semidirect
885. #391	C₂²×C₂₃	semidirect
897. #390	C₂²×C₂₃	semidirect
898. #390	C₂²×C₂₃	semidirect
899. #389	C₂²×C₂₃	semidirect
900. #389	C₂²×C₂₃	semidirect
901. #389	C₂²×C₂₃	semidirect
902. #389	C₂²×C₂₃	semidirect
903. #389	C₂²×C₂₃	semidirect
904. #389	C₂²×C₂₃	semidirect
918. #388	C₂²×C₂₃	semidirect
919. #388	C₂²×C₂₃	semidirect
920. #388	C₂²×C₂₃	semidirect
921. #388	C₂²×C₂₃	semidirect
922. #388	C₂²×C₂₃	semidirect
923. #388	C₂²×C₂₃	semidirect
924. #388	C₂²×C₂₃	semidirect
925. #388	C₂²×C₂₃	semidirect
926. #388	C₂²×C₂₃	semidirect
927. #388	C₂²×C₂₃	semidirect
928. #388	C₂²×C₂₃	semidirect
929. #388	C₂²×C₂₃	semidirect
930. #388	C₂²×C₂₃	semidirect
931. #388	C₂²×C₂₃	semidirect
932. #387	C₂²×C₂₃	semidirect
933. #387	C₂²×C₂₃	semidirect
934. #387	C₂²×C₂₃	semidirect
935. #387	C₂²×C₂₃	semidirect
936. #387	C₂²×C₂₃	semidirect
937. #387	C₂²×C₂₃	semidirect
947. #386	C₂²×C₂₃	semidirect
948. #386	C₂²×C₂₃	semidirect
957. #385	C₂²×C₂₃	semidirect
958. #382	C₂²×C₂₃	semidirect
962. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
963. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
964. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
965. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
974. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
975. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
976. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
977. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
978. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
979. C₄³	C₂²×C₂₃	semidirect
1175. C₂₃	#60010	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#2768	2
C₂₃×#2753	2
C₂₃×#2710	2
C₂₃×#2670	2
C₂₃×#2602	2
C₂₃×#2589	2
C₂₃×#2587	2
C₂₃×#2559	2
C₂₃×#2554	2
C₂₃×#2539	2
C₂₃×#2516	2
C₂₃×#2479	2
C₂₃×#2476	2
C₂₃×#2471	2
C₂₃×#2470	2
C₂₃×#2464	2
C₂₃×#2459	2
C₂₃×#2458	2
C₂₃×#2424	2
C₂₃×#2414	2
C₂₃×#2411	2
C₂₃×#2374	2
C₂₃×#2367	2
C₂₃×#2363	2
C₂₃×#2358	2
C₂₃×#2342	2
C₄×C₂₃×#124	2
C₂₃×#2293	2
#60010	23

Subgroups — C23×#60010 #19207636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60010 #19207636