Subgroups — C₂₃×#34999 #19182625

Order 5888.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2853	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2852	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2652	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2649	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2523	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2505	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2493	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2493	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2488	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2481	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2473	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2466	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2460	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2450	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2419	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2412	C₂	1	1	yes	maximal, characteristic
24	C₂₃×#2412	C₂	1	1	yes	maximal, characteristic
25	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂₃×#120	C₂	1	1	yes	maximal, characteristic
30	C₂×C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#401	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#400	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#399	C₂²	1	1	yes	characteristic
61	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#397	C₂²	1	1	yes	characteristic
65	C₂₃×#397	C₂²	1	1	yes	characteristic
66	C₂₃×#397	C₂²	1	1	yes	characteristic
67	C₂₃×#397	C₂²	1	1	yes	characteristic
68	C₂₃×#397	C₂²	1	1	yes	characteristic
69	C₂₃×#397	C₂²	1	1	yes	characteristic
70	C₂₃×#397	C₂²	1	1	yes	characteristic
71	C₂₃×#397	C₂²	1	1	yes	characteristic
72	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#396	C₂²	1	1	yes	characteristic
75	C₂₃×#396	C₂²	1	1	yes	characteristic
76	C₂₃×#396	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#394	C₂²	1	1	yes	characteristic
78	C₂₃×#394	C₂²	1	1	yes	characteristic
79	C₂₃×#394	C₂²	1	1	yes	characteristic
80	C₂₃×#394	C₂²	1	1	yes	characteristic
81	C₂₃×#393	C₂²	1	1	yes	characteristic
82	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
98	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
118	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
121	C₂₃×#386	C₂²	1	1	yes	characteristic
122	C₂₃×#386	C₂²	1	1	yes	characteristic
123	C₂₃×#386	C₂²	1	1	yes	characteristic
124	C₂₃×#386	C₂²	1	1	yes	characteristic
125	C₂₃×#386	C₂²	1	1	yes	characteristic
126	C₂₃×#386	C₂²	1	1	yes	characteristic
127	C₂₃×#386	C₂²	1	1	yes	characteristic
128	C₂₃×#386	C₂²	1	1	yes	characteristic
129	C₂₃×#386	C₂²	1	1	yes	characteristic
130	C₂₃×#385	C₂²	1	1	yes	characteristic
131	C₂₃×#385	C₂²	1	1	yes	characteristic
132	C₂₃×#385	C₂²	1	1	yes	characteristic
133	C₂₃×#385	C₂²	1	1	yes	characteristic
134	C₂₃×#385	C₂²	1	1	yes	characteristic
135	C₂₃×#385	C₂²	1	1	yes	characteristic
136	C₂₃×#385	C₂²	1	1	yes	characteristic
137	C₂₃×#385	C₂²	1	1	yes	characteristic
138	C₂₃×#385	C₂²	1	1	yes	characteristic
139	C₂₃×#385	C₂²	1	1	yes	characteristic
140	C₂₃×#385	C₂²	1	1	yes	characteristic
141	C₂₃×#385	C₂²	1	1	yes	characteristic
142	C₂₃×#385	C₂²	1	1	yes	characteristic
143	C₂₃×#385	C₂²	1	1	yes	characteristic
144	C₂₃×#385	C₂²	1	1	yes	characteristic
145	C₂₃×#385	C₂²	1	1	yes	characteristic
146	C₂₃×#385	C₂²	1	1	yes	characteristic
147	C₂₃×#385	C₂²	1	1	yes	characteristic
148	C₂₃×#385	C₂²	1	1	yes	characteristic
149	C₂₃×#385	C₂²	1	1	yes	characteristic
150	C₂₃×#385	C₂²	1	1	yes	characteristic
151	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
152	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
153	C₂₃×#383	C₂²	1	1	yes	characteristic, complemented
154	C₂₃×#383	C₂²	1	1	yes	characteristic, complemented
155	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
156	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
157	C₂₃×#381	C₂²	1	1	yes	characteristic
158	C₂₃×#381	C₂²	1	1	yes	characteristic
159	C₂₃×#381	C₂²	1	1	yes	characteristic
160	C₂₃×#381	C₂²	1	1	yes	characteristic
161	C₂₃×#381	C₂²	1	1	yes	characteristic
162	C₂₃×#381	C₂²	1	1	yes	characteristic
163	C₂₃×#381	C₂²	1	1	yes	characteristic, complemented
164	C₂₃×#380	C₂²	1	1	yes	characteristic
165	C₂₃×#380	C₂²	1	1	yes	characteristic
166	C₂₃×#380	C₂²	1	1	yes	characteristic
167	C₂₃×#380	C₂²	1	1	yes	characteristic
168	C₂₃×#380	C₂²	1	1	yes	characteristic
169	C₂₃×#380	C₂²	1	1	yes	characteristic
170	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
171	C₂₃×#379	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
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
182	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
183	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
184	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
185	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
186	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
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	C₂³×C₄×C₂₃	—	2	4	no	—
193	C₂³×C₄×C₂₃	—	4	2	no	—
194	C₂³×C₄×C₂₃	—	4	2	no	—
195	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×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×#125	—	4	2	no	—
212	C₂₃×#123	—	2	4	no	—
213	C₂₃×#123	—	4	2	no	—
214	C₂₃×C₂²⋊Q₈	—	2	4	no	—
215	C₂₃×C₂²⋊Q₈	—	4	2	no	—
216	C₂₃×#120	—	2	4	no	—
217	C₄×D₄×C₂₃	—	2	4	no	—
218	C₄×D₄×C₂₃	—	4	2	no	—
219	C₄×D₄×C₂₃	—	4	2	no	—
220	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
221	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
222	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	—	2	4	no	—
255	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
256	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
258	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₄²×C₂₃	—	4	2	no	—
295	C₂×C₄²×C₂₃	—	4	2	no	—
296	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
307	C₂₃×#95	C₂³	1	1	yes	characteristic
308	C₂₃×#95	C₂³	1	1	yes	characteristic
309	C₂₃×#95	C₂³	1	1	yes	characteristic
310	C₂₃×#95	C₂³	1	1	yes	characteristic
311	C₂₃×#95	C₂³	1	1	yes	characteristic
312	C₂₃×#95	C₂³	1	1	yes	characteristic
313	C₂₃×#95	C₂³	1	1	yes	characteristic
314	C₂₃×#95	C₂³	1	1	yes	characteristic
315	C₂₃×#95	C₂³	1	1	yes	characteristic
316	C₂₃×#95	C₂³	1	1	yes	characteristic
317	C₂₃×#95	C₂³	1	1	yes	characteristic
318	C₂₃×#95	C₂³	1	1	yes	characteristic
319	C₂₃×#95	C₂³	1	1	yes	characteristic
320	C₂₃×#95	C₂³	1	1	yes	characteristic
321	C₂₃×#95	C₂³	1	1	yes	characteristic
322	C₂₃×#95	C₂³	1	1	yes	characteristic
323	C₂₃×#95	C₂³	1	1	yes	characteristic
324	C₂₃×#95	C₂³	1	1	yes	characteristic
325	C₂₃×#95	C₂³	1	1	yes	characteristic
326	C₂₃×#95	C₂³	1	1	yes	characteristic
327	C₂₃×#95	C₂³	1	1	yes	characteristic
328	C₂₃×#95	C₂³	1	1	yes	characteristic
329	C₂₃×#95	C₂³	1	1	yes	characteristic
330	C₂₃×#95	C₂³	1	1	yes	characteristic
331	C₂₃×#95	C₂³	1	1	yes	characteristic
332	C₂₃×#95	C₂³	1	1	yes	characteristic
333	C₂₃×#95	C₂³	1	1	yes	characteristic
334	C₂₃×#95	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	C₂⁴×C₂₃	—	2	2	no	—
364	C₂⁴×C₂₃	—	2	2	no	—
365	C₂⁴×C₂₃	—	2	2	no	—
366	C₂⁴×C₂₃	—	2	2	no	—
367	C₂⁴×C₂₃	—	4	1	no	—
368	C₂⁴×C₂₃	—	4	1	no	—
369	C₂⁴×C₂₃	#41	1	4	yes	—
370	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×Q₈×C₂₃	—	2	2	no	—
375	C₂×Q₈×C₂₃	—	4	1	no	—
376	C₂×Q₈×C₂₃	—	4	1	no	—
377	C₂×D₄×C₂₃	—	2	2	no	—
378	C₂×D₄×C₂₃	—	2	2	no	—
379	C₂×D₄×C₂₃	—	2	2	no	—
380	C₂×D₄×C₂₃	—	2	2	no	—
381	C₂×D₄×C₂₃	—	2	2	no	—
382	C₂×D₄×C₂₃	—	2	2	no	—
383	C₂×D₄×C₂₃	—	2	2	no	—
384	C₂×D₄×C₂₃	—	4	1	no	—
385	C₂×D₄×C₂₃	—	4	1	no	—
386	C₂²×C₄×C₂₃	—	2	2	no	—
387	C₂²×C₄×C₂₃	—	2	2	no	—
388	C₂²×C₄×C₂₃	—	2	2	no	—
389	C₂²×C₄×C₂₃	—	2	2	no	—
390	C₂²×C₄×C₂₃	—	2	2	no	—
391	C₂²×C₄×C₂₃	—	2	2	no	—
392	C₂²×C₄×C₂₃	—	2	2	no	—
393	C₂²×C₄×C₂₃	—	2	2	no	—
394	C₂²×C₄×C₂₃	—	2	2	no	—
395	C₂²×C₄×C₂₃	—	2	2	no	—
396	C₂²×C₄×C₂₃	—	2	2	no	—
397	C₂²×C₄×C₂₃	—	2	2	no	—
398	C₂²×C₄×C₂₃	—	2	2	no	—
399	C₂²×C₄×C₂₃	—	2	2	no	—
400	C₂²×C₄×C₂₃	—	2	2	no	—
401	C₂²×C₄×C₂₃	—	2	2	no	—
402	C₂²×C₄×C₂₃	—	2	2	no	—
403	C₂²×C₄×C₂₃	—	2	2	no	—
404	C₂²×C₄×C₂₃	—	2	2	no	—
405	C₂²×C₄×C₂₃	—	2	2	no	—
406	C₂²×C₄×C₂₃	—	2	2	no	—
407	C₂²×C₄×C₂₃	—	2	2	no	—
408	C₂²×C₄×C₂₃	—	2	2	no	—
409	C₂²×C₄×C₂₃	—	2	2	no	—
410	C₂²×C₄×C₂₃	—	2	2	no	—
411	C₂²×C₄×C₂₃	—	4	1	no	—
412	C₂²×C₄×C₂₃	—	4	1	no	—
413	C₂²×C₄×C₂₃	—	4	1	no	—
414	C₂²×C₄×C₂₃	—	4	1	no	—
415	C₂²×C₄×C₂₃	—	4	1	no	—
416	C₂²×C₄×C₂₃	—	4	1	no	—
417	C₂²×C₄×C₂₃	—	4	1	no	—
418	C₂²×C₄×C₂₃	—	4	1	no	—
419	C₂²×C₄×C₂₃	—	4	1	no	—
420	C₂²×C₄×C₂₃	—	4	1	no	—
421	C₂²×C₄×C₂₃	—	4	1	no	—
422	C₂²×C₄×C₂₃	—	4	1	no	—
423	C₂²×C₄×C₂₃	—	4	1	no	—
424	C₂²×C₄×C₂₃	—	4	1	no	—
425	C₂²×C₄×C₂₃	—	4	1	no	—
426	C₂²×C₄×C₂₃	—	4	1	no	—
427	C₂²×C₄×C₂₃	—	4	1	no	—
428	C₂²×C₄×C₂₃	—	4	1	no	—
429	C₂²×C₄×C₂₃	—	4	1	no	—
430	C₂²×C₄×C₂₃	—	4	16	no	—
431	C₂²×C₄×C₂₃	#41	1	4	yes	—
432	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	—	2	2	no	—
460	C₄⋊C₄×C₂₃	—	2	2	no	—
461	C₄⋊C₄×C₂₃	—	2	2	no	—
462	C₄⋊C₄×C₂₃	—	2	2	no	—
463	C₄⋊C₄×C₂₃	—	2	2	no	—
464	C₄⋊C₄×C₂₃	—	2	2	no	—
465	C₄⋊C₄×C₂₃	—	2	2	no	—
466	C₄⋊C₄×C₂₃	—	2	2	no	—
467	C₄⋊C₄×C₂₃	—	2	2	no	—
468	C₄⋊C₄×C₂₃	—	2	2	no	—
469	C₄⋊C₄×C₂₃	—	2	2	no	—
470	C₄⋊C₄×C₂₃	—	2	2	no	—
471	C₄⋊C₄×C₂₃	—	2	2	no	—
472	C₄⋊C₄×C₂₃	—	4	1	no	—
473	C₄⋊C₄×C₂₃	—	4	1	no	—
474	C₄⋊C₄×C₂₃	—	4	1	no	—
475	C₄⋊C₄×C₂₃	—	4	1	no	—
476	C₄⋊C₄×C₂₃	—	4	1	no	—
477	C₄⋊C₄×C₂₃	—	4	1	no	—
478	C₄⋊C₄×C₂₃	—	4	1	no	—
479	C₄⋊C₄×C₂₃	—	4	1	no	—
480	C₄⋊C₄×C₂₃	—	4	1	no	—
481	C₄⋊C₄×C₂₃	—	4	1	no	—
482	C₄⋊C₄×C₂₃	—	4	1	no	—
483	C₄⋊C₄×C₂₃	—	4	1	no	—
484	C₄⋊C₄×C₂₃	—	4	1	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	C₂²⋊C₄×C₂₃	—	2	2	no	—
492	C₂²⋊C₄×C₂₃	—	2	2	no	—
493	C₂²⋊C₄×C₂₃	—	2	2	no	—
494	C₂²⋊C₄×C₂₃	—	2	2	no	—
495	C₂²⋊C₄×C₂₃	—	2	2	no	—
496	C₂²⋊C₄×C₂₃	—	2	2	no	—
497	C₂²⋊C₄×C₂₃	—	2	2	no	—
498	C₂²⋊C₄×C₂₃	—	2	2	no	—
499	C₂²⋊C₄×C₂₃	—	2	2	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	—	4	1	no	—
516	C₂²⋊C₄×C₂₃	—	4	1	no	—
517	C₂²⋊C₄×C₂₃	—	4	1	no	—
518	C₂²⋊C₄×C₂₃	—	4	1	no	—
519	C₂²⋊C₄×C₂₃	—	4	1	no	—
520	C₂²⋊C₄×C₂₃	—	4	1	no	—
521	C₂²⋊C₄×C₂₃	—	4	1	no	—
522	C₂²⋊C₄×C₂₃	—	4	1	no	—
523	C₂²⋊C₄×C₂₃	—	4	1	no	—
524	C₂²⋊C₄×C₂₃	—	4	1	no	—
525	C₂²⋊C₄×C₂₃	—	4	1	no	—
526	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
527	C₄²×C₂₃	—	2	2	no	—
528	C₄²×C₂₃	—	2	2	no	—
529	C₄²×C₂₃	—	2	2	no	—
530	C₄²×C₂₃	—	4	1	no	—
531	C₄²×C₂₃	—	4	1	no	—
532	C₄²×C₂₃	—	4	1	no	—
533	C₄²×C₂₃	—	4	1	no	—
534	C₄²×C₂₃	—	4	1	no	—
535	C₄²×C₂₃	—	4	1	no	—
536	C₄²×C₂₃	—	4	1	no	—
537	C₄²×C₂₃	—	4	1	no	—
538	#34999	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
539	C₂³×C₂₃	—	2	1	no	—
540	C₂³×C₂₃	—	2	1	no	—
541	C₂³×C₂₃	—	2	1	no	—
542	C₂³×C₂₃	—	2	1	no	—
543	C₂³×C₂₃	—	2	1	no	—
544	C₂³×C₂₃	—	2	1	no	—
545	C₂³×C₂₃	—	2	1	no	—
546	C₂³×C₂₃	—	2	1	no	—
547	C₂³×C₂₃	—	2	8	no	—
548	C₂³×C₂₃	—	2	8	no	—
549	C₂³×C₂₃	—	2	1	no	—
550	C₂³×C₂₃	—	2	1	no	—
551	C₂³×C₂₃	—	2	1	no	—
552	C₂³×C₂₃	—	2	1	no	—
553	C₂³×C₂₃	—	2	1	no	—
554	C₂³×C₂₃	—	2	1	no	—
555	C₂³×C₂₃	—	2	1	no	—
556	C₂³×C₂₃	—	2	1	no	—
557	C₂³×C₂₃	—	2	1	no	—
558	C₂³×C₂₃	—	2	1	no	—
559	C₂³×C₂₃	—	2	1	no	—
560	C₂³×C₂₃	—	2	1	no	—
561	C₂³×C₂₃	—	2	1	no	—
562	C₂³×C₂₃	—	4	4	no	—
563	C₂³×C₂₃	—	4	4	no	—
564	C₂³×C₂₃	—	4	4	no	—
565	C₂³×C₂₃	—	4	4	no	—
566	C₂³×C₂₃	—	4	4	no	—
567	C₂³×C₂₃	C₂×#41	1	2	yes	—
568	C₂³×C₂₃	C₂×#41	1	2	yes	—
569	C₂³×C₂₃	C₂×#41	1	2	yes	—
570	C₂³×C₂₃	C₂×#41	1	2	yes	—
571	C₂³×C₂₃	C₂×#41	1	2	yes	—
572	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
573	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
574	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
575	Q₈×C₂₃	—	8	2	no	—
576	D₄×C₂₃	—	4	4	no	—
577	D₄×C₂₃	—	4	4	no	—
578	D₄×C₂₃	—	4	4	no	—
579	C₂×C₄×C₂₃	—	2	8	no	—
580	C₂×C₄×C₂₃	—	2	1	no	—
581	C₂×C₄×C₂₃	—	2	1	no	—
582	C₂×C₄×C₂₃	—	2	1	no	—
583	C₂×C₄×C₂₃	—	2	1	no	—
584	C₂×C₄×C₂₃	—	2	1	no	—
585	C₂×C₄×C₂₃	—	2	1	no	—
586	C₂×C₄×C₂₃	—	2	1	no	—
587	C₂×C₄×C₂₃	—	2	1	no	—
588	C₂×C₄×C₂₃	—	2	1	no	—
589	C₂×C₄×C₂₃	—	2	1	no	—
590	C₂×C₄×C₂₃	—	2	1	no	—
591	C₂×C₄×C₂₃	—	2	1	no	—
592	C₂×C₄×C₂₃	—	2	1	no	—
593	C₂×C₄×C₂₃	—	2	1	no	—
594	C₂×C₄×C₂₃	—	2	1	no	—
595	C₂×C₄×C₂₃	—	2	1	no	—
596	C₂×C₄×C₂₃	—	2	1	no	—
597	C₂×C₄×C₂₃	—	2	1	no	—
598	C₂×C₄×C₂₃	—	2	1	no	—
599	C₂×C₄×C₂₃	—	2	1	no	—
600	C₂×C₄×C₂₃	—	2	1	no	—
601	C₂×C₄×C₂₃	—	2	1	no	—
602	C₂×C₄×C₂₃	—	2	1	no	—
603	C₂×C₄×C₂₃	—	2	1	no	—
604	C₂×C₄×C₂₃	—	2	1	no	—
605	C₂×C₄×C₂₃	—	2	1	no	—
606	C₂×C₄×C₂₃	—	2	1	no	—
607	C₂×C₄×C₂₃	—	2	1	no	—
608	C₂×C₄×C₂₃	—	2	1	no	—
609	C₂×C₄×C₂₃	—	2	1	no	—
610	C₂×C₄×C₂₃	—	2	1	no	—
611	C₂×C₄×C₂₃	—	2	1	no	—
612	C₂×C₄×C₂₃	—	2	1	no	—
613	C₂×C₄×C₂₃	—	2	1	no	—
614	C₂×C₄×C₂₃	—	2	1	no	—
615	C₂×C₄×C₂₃	—	2	1	no	—
616	C₂×C₄×C₂₃	—	2	1	no	—
617	C₂×C₄×C₂₃	—	2	1	no	—
618	C₂×C₄×C₂₃	—	2	1	no	—
619	C₂×C₄×C₂₃	—	2	1	no	—
620	C₂×C₄×C₂₃	—	2	1	no	—
621	C₂×C₄×C₂₃	—	2	1	no	—
622	C₂×C₄×C₂₃	—	2	1	no	—
623	C₂×C₄×C₂₃	—	2	1	no	—
624	C₂×C₄×C₂₃	—	2	1	no	—
625	C₂×C₄×C₂₃	—	2	1	no	—
626	C₂×C₄×C₂₃	—	2	1	no	—
627	C₂×C₄×C₂₃	—	2	1	no	—
628	C₂×C₄×C₂₃	—	2	1	no	—
629	C₂×C₄×C₂₃	—	2	1	no	—
630	C₂×C₄×C₂₃	—	2	1	no	—
631	C₂×C₄×C₂₃	—	2	1	no	—
632	C₂×C₄×C₂₃	—	2	1	no	—
633	C₂×C₄×C₂₃	—	2	1	no	—
634	C₂×C₄×C₂₃	—	2	1	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	—	4	4	no	—
657	C₂×C₄×C₂₃	—	4	4	no	—
658	C₂×C₄×C₂₃	—	4	4	no	—
659	C₂×C₄×C₂₃	—	4	4	no	—
660	C₂×C₄×C₂₃	—	4	4	no	—
661	C₂×C₄×C₂₃	—	4	4	no	—
662	C₂×C₄×C₂₃	—	4	4	no	—
663	C₂×C₄×C₂₃	—	4	4	no	—
664	C₂×C₄×C₂₃	—	4	4	no	—
665	C₂×C₄×C₂₃	—	4	4	no	—
666	C₂×C₄×C₂₃	—	4	4	no	—
667	C₂×C₄×C₂₃	—	8	2	no	—
668	C₂×C₄×C₂₃	—	8	2	no	—
669	C₂×C₄×C₂₃	—	8	2	no	—
670	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
671	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
672	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
673	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
674	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
675	#2855	C₂×C₂₃	1	1	yes	characteristic, complemented
676	#2853	C₂×C₂₃	1	1	yes	characteristic, complemented
677	#2852	C₂×C₂₃	1	1	yes	characteristic, complemented
678	#2851	C₂×C₂₃	1	1	yes	characteristic, complemented
679	#2653	C₂×C₂₃	1	1	yes	characteristic, complemented
680	#2652	C₂×C₂₃	1	1	yes	characteristic, complemented
681	#2652	C₂×C₂₃	1	1	yes	characteristic, complemented
682	#2649	C₂×C₂₃	1	1	yes	characteristic, complemented
683	#2523	C₂×C₂₃	1	1	yes	characteristic, complemented
684	#2517	C₂×C₂₃	1	1	yes	characteristic, complemented
685	#2505	C₂×C₂₃	1	1	yes	characteristic, complemented
686	#2493	C₂×C₂₃	1	1	yes	characteristic, complemented
687	#2493	C₂×C₂₃	1	1	yes	characteristic, complemented
688	#2488	C₂×C₂₃	1	1	yes	characteristic, complemented
689	#2483	C₂×C₂₃	1	1	yes	characteristic, complemented
690	#2481	C₂×C₂₃	1	1	yes	characteristic, complemented
691	#2473	C₂×C₂₃	1	1	yes	characteristic, complemented
692	#2466	C₂×C₂₃	1	1	yes	characteristic, complemented
693	#2460	C₂×C₂₃	1	1	yes	characteristic, complemented
694	#2450	C₂×C₂₃	1	1	yes	characteristic, complemented
695	#2437	C₂×C₂₃	1	1	yes	characteristic, complemented
696	#2419	C₂×C₂₃	1	1	yes	characteristic, complemented
697	#2412	C₂×C₂₃	1	1	yes	characteristic
698	#2412	C₂×C₂₃	1	1	yes	characteristic
699	#2329	C₂×C₂₃	1	1	yes	characteristic, complemented
700	#2322	C₂×C₂₃	1	1	yes	characteristic, complemented
701	#2318	C₂×C₂₃	1	1	yes	characteristic, complemented
702	#2313	C₂×C₂₃	1	1	yes	characteristic, complemented
703	C₄×#120	C₂×C₂₃	1	1	yes	characteristic
704	C₂×#385	C₂×C₂₃	1	1	yes	characteristic, complemented
705	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
706	C₂²×C₂₃	—	2	2	no	—
707	C₂²×C₂₃	—	2	2	no	—
708	C₂²×C₂₃	—	2	2	no	—
709	C₂²×C₂₃	—	2	2	no	—
710	C₂²×C₂₃	—	2	2	no	—
711	C₂²×C₂₃	—	2	2	no	—
712	C₂²×C₂₃	—	2	2	no	—
713	C₂²×C₂₃	—	2	2	no	—
714	C₂²×C₂₃	—	2	2	no	—
715	C₂²×C₂₃	—	2	2	no	—
716	C₂²×C₂₃	—	2	2	no	—
717	C₂²×C₂₃	—	2	2	no	—
718	C₂²×C₂₃	—	2	2	no	—
719	C₂²×C₂₃	—	2	2	no	—
720	C₂²×C₂₃	—	2	2	no	—
721	C₂²×C₂₃	—	4	16	no	—
722	C₂²×C₂₃	—	4	1	no	—
723	C₂²×C₂₃	—	4	1	no	—
724	C₂²×C₂₃	—	4	1	no	—
725	C₂²×C₂₃	—	4	1	no	—
726	C₂²×C₂₃	—	4	1	no	—
727	C₂²×C₂₃	—	4	1	no	—
728	C₂²×C₂₃	—	4	1	no	—
729	C₂²×C₂₃	—	4	1	no	—
730	C₂²×C₂₃	—	4	1	no	—
731	C₂²×C₂₃	—	4	1	no	—
732	C₂²×C₂₃	—	4	1	no	—
733	C₂²×C₂₃	#529	1	4	yes	—
734	C₂²×C₂₃	#539	1	4	yes	—
735	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
736	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
737	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
738	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
739	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
741	C₂²×C₂₃	#585	1	1	yes	characteristic
742	C₄×C₂₃	—	2	2	no	—
743	C₄×C₂₃	—	2	2	no	—
744	C₄×C₂₃	—	2	2	no	—
745	C₄×C₂₃	—	2	2	no	—
746	C₄×C₂₃	—	2	2	no	—
747	C₄×C₂₃	—	4	1	no	—
748	C₄×C₂₃	—	4	1	no	—
749	C₄×C₂₃	—	4	1	no	—
750	C₄×C₂₃	—	4	1	no	—
751	C₄×C₂₃	—	4	1	no	—
752	C₄×C₂₃	—	4	1	no	—
753	C₄×C₂₃	—	4	1	no	—
754	C₄×C₂₃	—	4	1	no	—
755	C₄×C₂₃	—	4	1	no	—
756	C₄×C₂₃	—	4	1	no	—
757	C₄×C₂₃	—	4	1	no	—
758	C₄×C₂₃	—	4	1	no	—
759	C₄×C₂₃	—	4	1	no	—
760	C₄×C₂₃	—	4	1	no	—
761	C₄×C₂₃	—	4	1	no	—
762	C₄×C₂₃	—	4	1	no	—
763	C₄×C₂₃	—	4	1	no	—
764	C₄×C₂₃	—	4	1	no	—
765	C₄×C₂₃	—	4	1	no	—
766	C₄×C₂₃	—	4	1	no	—
767	C₄×C₂₃	—	4	1	no	—
768	C₄×C₂₃	—	4	1	no	—
769	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
770	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic, complemented
771	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
772	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
773	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
774	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
775	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
776	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
777	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
778	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
779	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
780	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
781	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
782	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
783	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
784	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
785	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
786	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
787	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
788	#401	C₂²×C₂₃	1	1	yes	characteristic, complemented
789	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
790	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
791	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
792	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
793	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
794	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
795	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
796	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
797	#399	C₂²×C₂₃	1	1	yes	characteristic
798	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
799	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
800	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
801	#397	C₂²×C₂₃	1	1	yes	characteristic
802	#397	C₂²×C₂₃	1	1	yes	characteristic
803	#397	C₂²×C₂₃	1	1	yes	characteristic
804	#397	C₂²×C₂₃	1	1	yes	characteristic
805	#397	C₂²×C₂₃	1	1	yes	characteristic
806	#397	C₂²×C₂₃	1	1	yes	characteristic
807	#397	C₂²×C₂₃	1	1	yes	characteristic
808	#397	C₂²×C₂₃	1	1	yes	characteristic
809	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
810	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
811	#396	C₂²×C₂₃	1	1	yes	characteristic
812	#396	C₂²×C₂₃	1	1	yes	characteristic
813	#396	C₂²×C₂₃	1	1	yes	characteristic, complemented
814	#394	C₂²×C₂₃	1	1	yes	characteristic
815	#394	C₂²×C₂₃	1	1	yes	characteristic
816	#394	C₂²×C₂₃	1	1	yes	characteristic
817	#394	C₂²×C₂₃	1	1	yes	characteristic
818	#393	C₂²×C₂₃	1	1	yes	characteristic
819	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
820	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
821	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
822	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
823	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
824	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
825	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
826	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
827	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
828	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
829	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
830	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
831	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
832	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
833	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
834	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
835	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
836	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
837	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
838	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
839	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
840	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
841	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
842	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
843	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
844	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
845	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
846	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
847	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
848	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
849	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
850	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
851	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
852	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
853	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
854	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
855	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
856	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
857	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
858	#386	C₂²×C₂₃	1	1	yes	characteristic
859	#386	C₂²×C₂₃	1	1	yes	characteristic
860	#386	C₂²×C₂₃	1	1	yes	characteristic
861	#386	C₂²×C₂₃	1	1	yes	characteristic
862	#386	C₂²×C₂₃	1	1	yes	characteristic
863	#386	C₂²×C₂₃	1	1	yes	characteristic
864	#386	C₂²×C₂₃	1	1	yes	characteristic
865	#386	C₂²×C₂₃	1	1	yes	characteristic
866	#386	C₂²×C₂₃	1	1	yes	characteristic
867	#385	C₂²×C₂₃	1	1	yes	characteristic
868	#385	C₂²×C₂₃	1	1	yes	characteristic
869	#385	C₂²×C₂₃	1	1	yes	characteristic
870	#385	C₂²×C₂₃	1	1	yes	characteristic
871	#385	C₂²×C₂₃	1	1	yes	characteristic
872	#385	C₂²×C₂₃	1	1	yes	characteristic
873	#385	C₂²×C₂₃	1	1	yes	characteristic
874	#385	C₂²×C₂₃	1	1	yes	characteristic
875	#385	C₂²×C₂₃	1	1	yes	characteristic
876	#385	C₂²×C₂₃	1	1	yes	characteristic
877	#385	C₂²×C₂₃	1	1	yes	characteristic
878	#385	C₂²×C₂₃	1	1	yes	characteristic
879	#385	C₂²×C₂₃	1	1	yes	characteristic
880	#385	C₂²×C₂₃	1	1	yes	characteristic
881	#385	C₂²×C₂₃	1	1	yes	characteristic
882	#385	C₂²×C₂₃	1	1	yes	characteristic
883	#385	C₂²×C₂₃	1	1	yes	characteristic
884	#385	C₂²×C₂₃	1	1	yes	characteristic
885	#385	C₂²×C₂₃	1	1	yes	characteristic
886	#385	C₂²×C₂₃	1	1	yes	characteristic
887	#385	C₂²×C₂₃	1	1	yes	characteristic
888	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
889	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
890	#383	C₂²×C₂₃	1	1	yes	characteristic, complemented
891	#383	C₂²×C₂₃	1	1	yes	characteristic, complemented
892	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
893	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
894	#381	C₂²×C₂₃	1	1	yes	characteristic
895	#381	C₂²×C₂₃	1	1	yes	characteristic
896	#381	C₂²×C₂₃	1	1	yes	characteristic
897	#381	C₂²×C₂₃	1	1	yes	characteristic
898	#381	C₂²×C₂₃	1	1	yes	characteristic
899	#381	C₂²×C₂₃	1	1	yes	characteristic
900	#381	C₂²×C₂₃	1	1	yes	characteristic, complemented
901	#380	C₂²×C₂₃	1	1	yes	characteristic
902	#380	C₂²×C₂₃	1	1	yes	characteristic
903	#380	C₂²×C₂₃	1	1	yes	characteristic
904	#380	C₂²×C₂₃	1	1	yes	characteristic
905	#380	C₂²×C₂₃	1	1	yes	characteristic
906	#380	C₂²×C₂₃	1	1	yes	characteristic
907	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
908	#379	C₂²×C₂₃	1	1	yes	characteristic
909	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
910	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
911	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
912	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
913	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
914	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
915	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
916	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
917	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
918	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
919	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
920	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
921	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
922	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
923	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
924	C₂×C₂₃	—	2	4	no	—
925	C₂×C₂₃	—	2	4	no	—
926	C₂×C₂₃	—	4	2	no	—
927	C₂×C₂₃	—	8	1	no	—
928	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
929	C₂×C₂₃	C₂×#539	1	1	yes	characteristic
930	C₂×C₂₃	#3459	1	1	yes	characteristic
931	C₂×C₂₃	#3490	1	1	yes	characteristic
932	C₂×C₂₃	#3495	1	1	yes	characteristic
933	C₂×C₂₃	#3513	1	1	yes	characteristic
934	C₂×C₂₃	#3520	1	1	yes	characteristic
935	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
936	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
937	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
938	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
939	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
940	C₂³×C₄	—	2	4	no	—
941	C₂³×C₄	—	4	2	no	—
942	C₂³×C₄	—	4	2	no	—
943	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
944	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
945	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
946	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
947	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
948	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
949	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
950	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
951	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
952	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
953	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
954	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
955	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
956	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
957	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
958	#126	—	4	2	no	—
959	#125	—	4	2	no	—
960	#123	—	2	4	no	—
961	#123	—	4	2	no	—
962	C₂²⋊Q₈	—	2	4	no	—
963	C₂²⋊Q₈	—	4	2	no	—
964	#120	—	2	4	no	—
965	C₄×D₄	—	2	4	no	—
966	C₄×D₄	—	4	2	no	—
967	C₄×D₄	—	4	2	no	—
968	C₂×C₄⋊C₄	—	2	4	no	—
969	C₂×C₄⋊C₄	—	4	2	no	—
970	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
982	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
983	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	—	2	4	no	—
1003	C₂×C₂²⋊C₄	—	2	4	no	—
1004	C₂×C₂²⋊C₄	—	2	4	no	—
1005	C₂×C₂²⋊C₄	—	4	2	no	—
1006	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1016	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1018	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1042	C₂×C₄²	—	4	2	no	—
1043	C₂×C₄²	—	4	2	no	—
1044	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1045	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1046	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1047	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1048	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1049	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1050	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1051	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1052	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1053	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1054	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1055	#95	C₂³×C₂₃	1	1	yes	characteristic
1056	#95	C₂³×C₂₃	1	1	yes	characteristic
1057	#95	C₂³×C₂₃	1	1	yes	characteristic
1058	#95	C₂³×C₂₃	1	1	yes	characteristic
1059	#95	C₂³×C₂₃	1	1	yes	characteristic
1060	#95	C₂³×C₂₃	1	1	yes	characteristic
1061	#95	C₂³×C₂₃	1	1	yes	characteristic
1062	#95	C₂³×C₂₃	1	1	yes	characteristic
1063	#95	C₂³×C₂₃	1	1	yes	characteristic
1064	#95	C₂³×C₂₃	1	1	yes	characteristic
1065	#95	C₂³×C₂₃	1	1	yes	characteristic
1066	#95	C₂³×C₂₃	1	1	yes	characteristic
1067	#95	C₂³×C₂₃	1	1	yes	characteristic
1068	#95	C₂³×C₂₃	1	1	yes	characteristic
1069	#95	C₂³×C₂₃	1	1	yes	characteristic
1070	#95	C₂³×C₂₃	1	1	yes	characteristic
1071	#95	C₂³×C₂₃	1	1	yes	characteristic
1072	#95	C₂³×C₂₃	1	1	yes	characteristic
1073	#95	C₂³×C₂₃	1	1	yes	characteristic
1074	#95	C₂³×C₂₃	1	1	yes	characteristic
1075	#95	C₂³×C₂₃	1	1	yes	characteristic
1076	#95	C₂³×C₂₃	1	1	yes	characteristic
1077	#95	C₂³×C₂₃	1	1	yes	characteristic
1078	#95	C₂³×C₂₃	1	1	yes	characteristic
1079	#95	C₂³×C₂₃	1	1	yes	characteristic
1080	#95	C₂³×C₂₃	1	1	yes	characteristic
1081	#95	C₂³×C₂₃	1	1	yes	characteristic
1082	#95	C₂³×C₂₃	1	1	yes	characteristic
1083	#95	C₂³×C₂₃	1	1	yes	characteristic
1084	#95	C₂³×C₂₃	1	1	yes	characteristic
1085	#95	C₂³×C₂₃	1	1	yes	characteristic
1086	#95	C₂³×C₂₃	1	1	yes	characteristic
1087	#95	C₂³×C₂₃	1	1	yes	characteristic
1088	#95	C₂³×C₂₃	1	1	yes	characteristic
1089	#95	C₂³×C₂₃	1	1	yes	characteristic
1090	#95	C₂³×C₂₃	1	1	yes	characteristic
1091	#95	C₂³×C₂₃	1	1	yes	characteristic
1092	#95	C₂³×C₂₃	1	1	yes	characteristic
1093	#95	C₂³×C₂₃	1	1	yes	characteristic
1094	#95	C₂³×C₂₃	1	1	yes	characteristic
1095	#95	C₂³×C₂₃	1	1	yes	characteristic
1096	#95	C₂³×C₂₃	1	1	yes	characteristic
1097	#95	C₂³×C₂₃	1	1	yes	characteristic
1098	#95	C₂³×C₂₃	1	1	yes	characteristic
1099	#95	C₂³×C₂₃	1	1	yes	characteristic
1100	#95	C₂³×C₂₃	1	1	yes	characteristic
1101	#95	C₂³×C₂₃	1	1	yes	characteristic
1102	#95	C₂³×C₂₃	1	1	yes	characteristic
1103	#95	C₂³×C₂₃	1	1	yes	characteristic
1104	#95	C₂³×C₂₃	1	1	yes	characteristic
1105	#95	C₂³×C₂₃	1	1	yes	characteristic
1106	#95	C₂³×C₂₃	1	1	yes	characteristic
1107	#95	C₂³×C₂₃	1	1	yes	characteristic
1108	#95	C₂³×C₂₃	1	1	yes	characteristic
1109	#95	C₂³×C₂₃	1	1	yes	characteristic
1110	#95	C₂³×C₂₃	1	1	yes	characteristic
1111	C₂₃	#34999	1	1	yes	characteristic, direct product factor, Sylow
1112	C₂⁴	—	2	2	no	—
1113	C₂⁴	—	2	2	no	—
1114	C₂⁴	—	2	2	no	—
1115	C₂⁴	—	2	2	no	—
1116	C₂⁴	—	4	1	no	—
1117	C₂⁴	—	4	1	no	—
1118	C₂⁴	#41×C₂₃	1	4	yes	—
1119	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1120	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1121	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1122	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1123	C₂×Q₈	—	2	2	no	—
1124	C₂×Q₈	—	4	1	no	—
1125	C₂×Q₈	—	4	1	no	—
1126	C₂×D₄	—	2	2	no	—
1127	C₂×D₄	—	2	2	no	—
1128	C₂×D₄	—	2	2	no	—
1129	C₂×D₄	—	2	2	no	—
1130	C₂×D₄	—	2	2	no	—
1131	C₂×D₄	—	2	2	no	—
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	4	1	no	—
1134	C₂×D₄	—	4	1	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	2	no	—
1137	C₂²×C₄	—	2	2	no	—
1138	C₂²×C₄	—	2	2	no	—
1139	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	2	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	2	2	no	—
1144	C₂²×C₄	—	2	2	no	—
1145	C₂²×C₄	—	2	2	no	—
1146	C₂²×C₄	—	2	2	no	—
1147	C₂²×C₄	—	2	2	no	—
1148	C₂²×C₄	—	2	2	no	—
1149	C₂²×C₄	—	2	2	no	—
1150	C₂²×C₄	—	2	2	no	—
1151	C₂²×C₄	—	2	2	no	—
1152	C₂²×C₄	—	2	2	no	—
1153	C₂²×C₄	—	2	2	no	—
1154	C₂²×C₄	—	2	2	no	—
1155	C₂²×C₄	—	2	2	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	2	no	—
1160	C₂²×C₄	—	4	1	no	—
1161	C₂²×C₄	—	4	1	no	—
1162	C₂²×C₄	—	4	1	no	—
1163	C₂²×C₄	—	4	1	no	—
1164	C₂²×C₄	—	4	1	no	—
1165	C₂²×C₄	—	4	1	no	—
1166	C₂²×C₄	—	4	1	no	—
1167	C₂²×C₄	—	4	1	no	—
1168	C₂²×C₄	—	4	1	no	—
1169	C₂²×C₄	—	4	1	no	—
1170	C₂²×C₄	—	4	1	no	—
1171	C₂²×C₄	—	4	1	no	—
1172	C₂²×C₄	—	4	1	no	—
1173	C₂²×C₄	—	4	1	no	—
1174	C₂²×C₄	—	4	1	no	—
1175	C₂²×C₄	—	4	1	no	—
1176	C₂²×C₄	—	4	1	no	—
1177	C₂²×C₄	—	4	1	no	—
1178	C₂²×C₄	—	4	1	no	—
1179	C₂²×C₄	—	4	16	no	—
1180	C₂²×C₄	#41×C₂₃	1	4	yes	—
1181	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1182	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1184	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1185	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1186	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1187	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1188	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1189	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1191	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1192	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1193	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1195	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1196	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1200	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1202	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1203	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1204	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1205	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1206	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1207	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1208	C₄⋊C₄	—	2	2	no	—
1209	C₄⋊C₄	—	2	2	no	—
1210	C₄⋊C₄	—	2	2	no	—
1211	C₄⋊C₄	—	2	2	no	—
1212	C₄⋊C₄	—	2	2	no	—
1213	C₄⋊C₄	—	2	2	no	—
1214	C₄⋊C₄	—	2	2	no	—
1215	C₄⋊C₄	—	2	2	no	—
1216	C₄⋊C₄	—	2	2	no	—
1217	C₄⋊C₄	—	2	2	no	—
1218	C₄⋊C₄	—	2	2	no	—
1219	C₄⋊C₄	—	2	2	no	—
1220	C₄⋊C₄	—	2	2	no	—
1221	C₄⋊C₄	—	4	1	no	—
1222	C₄⋊C₄	—	4	1	no	—
1223	C₄⋊C₄	—	4	1	no	—
1224	C₄⋊C₄	—	4	1	no	—
1225	C₄⋊C₄	—	4	1	no	—
1226	C₄⋊C₄	—	4	1	no	—
1227	C₄⋊C₄	—	4	1	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	1	no	—
1233	C₄⋊C₄	—	4	1	no	—
1234	C₄⋊C₄	—	4	1	no	—
1235	C₄⋊C₄	—	4	1	no	—
1236	C₄⋊C₄	—	4	1	no	—
1237	C₄⋊C₄	—	4	1	no	—
1238	C₄⋊C₄	—	4	1	no	—
1239	C₄⋊C₄	—	4	1	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	—	2	2	no	—
1246	C₂²⋊C₄	—	2	2	no	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	2	2	no	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	2	2	no	—
1251	C₂²⋊C₄	—	2	2	no	—
1252	C₂²⋊C₄	—	2	2	no	—
1253	C₂²⋊C₄	—	2	2	no	—
1254	C₂²⋊C₄	—	2	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	no	—
1259	C₂²⋊C₄	—	2	2	no	—
1260	C₂²⋊C₄	—	2	2	no	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	4	1	no	—
1266	C₂²⋊C₄	—	4	1	no	—
1267	C₂²⋊C₄	—	4	1	no	—
1268	C₂²⋊C₄	—	4	1	no	—
1269	C₂²⋊C₄	—	4	1	no	—
1270	C₂²⋊C₄	—	4	1	no	—
1271	C₂²⋊C₄	—	4	1	no	—
1272	C₂²⋊C₄	—	4	1	no	—
1273	C₂²⋊C₄	—	4	1	no	—
1274	C₂²⋊C₄	—	4	1	no	—
1275	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
1276	C₄²	—	2	2	no	—
1277	C₄²	—	2	2	no	—
1278	C₄²	—	2	2	no	—
1279	C₄²	—	4	1	no	—
1280	C₄²	—	4	1	no	—
1281	C₄²	—	4	1	no	—
1282	C₄²	—	4	1	no	—
1283	C₄²	—	4	1	no	—
1284	C₄²	—	4	1	no	—
1285	C₄²	—	4	1	no	—
1286	C₄²	—	4	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	8	no	—
1302	C₂³	—	2	8	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	2	1	no	—
1305	C₂³	—	2	1	no	—
1306	C₂³	—	2	1	no	—
1307	C₂³	—	2	1	no	—
1308	C₂³	—	2	1	no	—
1309	C₂³	—	2	1	no	—
1310	C₂³	—	4	4	no	—
1311	C₂³	—	4	4	no	—
1312	C₂³	—	4	4	no	—
1313	C₂³	—	4	4	no	—
1314	C₂³	—	4	4	no	—
1315	C₂³	C₂×#41×C₂₃	1	2	yes	—
1316	C₂³	C₂×#41×C₂₃	1	2	yes	—
1317	C₂³	C₂×#41×C₂₃	1	2	yes	—
1318	C₂³	C₂×#41×C₂₃	1	2	yes	—
1319	C₂³	C₂×#41×C₂₃	1	2	yes	—
1320	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
1321	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
1322	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1323	Q₈	—	8	2	no	—
1324	D₄	—	4	4	no	—
1325	D₄	—	4	4	no	—
1326	D₄	—	4	4	no	—
1327	C₂×C₄	—	2	8	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	4	4	no	—
1405	C₂×C₄	—	4	4	no	—
1406	C₂×C₄	—	4	4	no	—
1407	C₂×C₄	—	4	4	no	—
1408	C₂×C₄	—	4	4	no	—
1409	C₂×C₄	—	4	4	no	—
1410	C₂×C₄	—	4	4	no	—
1411	C₂×C₄	—	4	4	no	—
1412	C₂×C₄	—	4	4	no	—
1413	C₂×C₄	—	4	4	no	—
1414	C₂×C₄	—	4	4	no	—
1415	C₂×C₄	—	8	2	no	—
1416	C₂×C₄	—	8	2	no	—
1417	C₂×C₄	—	8	2	no	—
1418	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1419	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1420	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1421	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1422	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	2	2	no	—
1425	C₂²	—	2	2	no	—
1426	C₂²	—	2	2	no	—
1427	C₂²	—	2	2	no	—
1428	C₂²	—	2	2	no	—
1429	C₂²	—	2	2	no	—
1430	C₂²	—	2	2	no	—
1431	C₂²	—	2	2	no	—
1432	C₂²	—	2	2	no	—
1433	C₂²	—	2	2	no	—
1434	C₂²	—	2	2	no	—
1435	C₂²	—	2	2	no	—
1436	C₂²	—	2	2	no	—
1437	C₂²	—	2	2	no	—
1438	C₂²	—	4	16	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	4	1	no	—
1441	C₂²	—	4	1	no	—
1442	C₂²	—	4	1	no	—
1443	C₂²	—	4	1	no	—
1444	C₂²	—	4	1	no	—
1445	C₂²	—	4	1	no	—
1446	C₂²	—	4	1	no	—
1447	C₂²	—	4	1	no	—
1448	C₂²	—	4	1	no	—
1449	C₂²	—	4	1	no	—
1450	C₂²	C₂₃×#529	1	4	yes	—
1451	C₂²	C₂₃×#539	1	4	yes	—
1452	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1453	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1454	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1455	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1456	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1457	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1458	C₂²	C₂₃×#585	1	1	yes	characteristic
1459	C₄	—	2	2	no	—
1460	C₄	—	2	2	no	—
1461	C₄	—	2	2	no	—
1462	C₄	—	2	2	no	—
1463	C₄	—	2	2	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	4	1	no	—
1468	C₄	—	4	1	no	—
1469	C₄	—	4	1	no	—
1470	C₄	—	4	1	no	—
1471	C₄	—	4	1	no	—
1472	C₄	—	4	1	no	—
1473	C₄	—	4	1	no	—
1474	C₄	—	4	1	no	—
1475	C₄	—	4	1	no	—
1476	C₄	—	4	1	no	—
1477	C₄	—	4	1	no	—
1478	C₄	—	4	1	no	—
1479	C₄	—	4	1	no	—
1480	C₄	—	4	1	no	—
1481	C₄	—	4	1	no	—
1482	C₄	—	4	1	no	—
1483	C₄	—	4	1	no	—
1484	C₄	—	4	1	no	—
1485	C₄	—	4	1	no	—
1486	C₂	—	2	4	no	—
1487	C₂	—	2	4	no	—
1488	C₂	—	4	2	no	—
1489	C₂	—	8	1	no	—
1490	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
1491	C₂	C₂×C₂₃×#539	1	1	yes	characteristic
1492	C₂	C₂₃×#3459	1	1	yes	characteristic
1493	C₂	C₂₃×#3490	1	1	yes	characteristic
1494	C₂	C₂₃×#3495	1	1	yes	characteristic
1495	C₂	C₂₃×#3513	1	1	yes	characteristic
1496	C₂	C₂₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#120	C₂²
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×#2855	C₂	semidirect
2. C₂₃×#2853	C₂	semidirect
3. C₂₃×#2852	C₂	semidirect
4. C₂₃×#2851	C₂	semidirect
5. C₂₃×#2653	C₂	semidirect
6. C₂₃×#2652	C₂	semidirect
7. C₂₃×#2652	C₂	semidirect
8. C₂₃×#2649	C₂	semidirect
9. C₂₃×#2523	C₂	semidirect
10. C₂₃×#2517	C₂	semidirect
11. C₂₃×#2505	C₂	semidirect
12. C₂₃×#2493	C₂	semidirect
13. C₂₃×#2493	C₂	semidirect
14. C₂₃×#2488	C₂	semidirect
15. C₂₃×#2483	C₂	semidirect
16. C₂₃×#2481	C₂	semidirect
17. C₂₃×#2473	C₂	semidirect
18. C₂₃×#2466	C₂	semidirect
19. C₂₃×#2460	C₂	semidirect
20. C₂₃×#2450	C₂	semidirect
21. C₂₃×#2437	C₂	semidirect
22. C₂₃×#2419	C₂	semidirect
25. C₂₃×#2329	C₂	semidirect
26. C₂₃×#2322	C₂	semidirect
27. C₂₃×#2318	C₂	semidirect
28. C₂₃×#2313	C₂	semidirect
30. C₂×C₂₃×#385	C₂	semidirect
31. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
33. C₂×C₂₃×#126	C₂²	semidirect
34. C₂×C₂₃×#125	C₂²	semidirect
51. C₂₃×#401	C₂²	semidirect
52. C₂₃×#400	C₂²	semidirect
53. C₂₃×#400	C₂²	semidirect
54. C₂₃×#400	C₂²	semidirect
55. C₂₃×#400	C₂²	semidirect
56. C₂₃×#400	C₂²	semidirect
57. C₂₃×#400	C₂²	semidirect
58. C₂₃×#400	C₂²	semidirect
59. C₂₃×#400	C₂²	semidirect
61. C₂₃×#398	C₂²	semidirect
62. C₂₃×#398	C₂²	semidirect
63. C₂₃×#398	C₂²	semidirect
72. C₂₃×#397	C₂²	semidirect
73. C₂₃×#397	C₂²	semidirect
76. C₂₃×#396	C₂²	semidirect
82. C₂₃×#393	C₂²	semidirect
83. C₂₃×#391	C₂²	semidirect
84. C₂₃×#391	C₂²	semidirect
85. C₂₃×#391	C₂²	semidirect
86. C₂₃×#389	C₂²	semidirect
87. C₂₃×#389	C₂²	semidirect
88. C₂₃×#389	C₂²	semidirect
89. C₂₃×#389	C₂²	semidirect
90. C₂₃×#389	C₂²	semidirect
91. C₂₃×#388	C₂²	semidirect
92. C₂₃×#388	C₂²	semidirect
93. C₂₃×#388	C₂²	semidirect
94. C₂₃×#388	C₂²	semidirect
95. C₂₃×#388	C₂²	semidirect
96. C₂₃×#388	C₂²	semidirect
97. C₂₃×#388	C₂²	semidirect
98. C₂₃×#387	C₂²	semidirect
99. C₂₃×#387	C₂²	semidirect
100. C₂₃×#387	C₂²	semidirect
101. C₂₃×#387	C₂²	semidirect
102. C₂₃×#387	C₂²	semidirect
103. C₂₃×#387	C₂²	semidirect
104. C₂₃×#387	C₂²	semidirect
105. C₂₃×#387	C₂²	semidirect
106. C₂₃×#387	C₂²	semidirect
107. C₂₃×#387	C₂²	semidirect
108. C₂₃×#387	C₂²	semidirect
109. C₂₃×#387	C₂²	semidirect
110. C₂₃×#387	C₂²	semidirect
111. C₂₃×#387	C₂²	semidirect
112. C₂₃×#387	C₂²	semidirect
113. C₂₃×#387	C₂²	semidirect
114. C₂₃×#387	C₂²	semidirect
115. C₂₃×#387	C₂²	semidirect
116. C₂₃×#387	C₂²	semidirect
117. C₂₃×#387	C₂²	semidirect
118. C₂₃×#387	C₂²	semidirect
119. C₂₃×#387	C₂²	semidirect
120. C₂₃×#387	C₂²	semidirect
151. C₂₃×#385	C₂²	semidirect
152. C₂₃×#385	C₂²	semidirect
153. C₂₃×#383	C₂²	semidirect
154. C₂₃×#383	C₂²	semidirect
155. C₂₃×#382	C₂²	semidirect
156. C₂₃×#382	C₂²	semidirect
163. C₂₃×#381	C₂²	semidirect
170. C₂₃×#380	C₂²	semidirect
538. #34999	C₂₃	direct (N × H)
675. #2855	C₂×C₂₃	semidirect
676. #2853	C₂×C₂₃	semidirect
677. #2852	C₂×C₂₃	semidirect
678. #2851	C₂×C₂₃	semidirect
679. #2653	C₂×C₂₃	semidirect
680. #2652	C₂×C₂₃	semidirect
681. #2652	C₂×C₂₃	semidirect
682. #2649	C₂×C₂₃	semidirect
683. #2523	C₂×C₂₃	semidirect
684. #2517	C₂×C₂₃	semidirect
685. #2505	C₂×C₂₃	semidirect
686. #2493	C₂×C₂₃	semidirect
687. #2493	C₂×C₂₃	semidirect
688. #2488	C₂×C₂₃	semidirect
689. #2483	C₂×C₂₃	semidirect
690. #2481	C₂×C₂₃	semidirect
691. #2473	C₂×C₂₃	semidirect
692. #2466	C₂×C₂₃	semidirect
693. #2460	C₂×C₂₃	semidirect
694. #2450	C₂×C₂₃	semidirect
695. #2437	C₂×C₂₃	semidirect
696. #2419	C₂×C₂₃	semidirect
699. #2329	C₂×C₂₃	semidirect
700. #2322	C₂×C₂₃	semidirect
701. #2318	C₂×C₂₃	semidirect
702. #2313	C₂×C₂₃	semidirect
704. C₂×#385	C₂×C₂₃	semidirect
705. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
770. C₂×#126	C₂²×C₂₃	semidirect
771. C₂×#125	C₂²×C₂₃	semidirect
788. #401	C₂²×C₂₃	semidirect
789. #400	C₂²×C₂₃	semidirect
790. #400	C₂²×C₂₃	semidirect
791. #400	C₂²×C₂₃	semidirect
792. #400	C₂²×C₂₃	semidirect
793. #400	C₂²×C₂₃	semidirect
794. #400	C₂²×C₂₃	semidirect
795. #400	C₂²×C₂₃	semidirect
796. #400	C₂²×C₂₃	semidirect
798. #398	C₂²×C₂₃	semidirect
799. #398	C₂²×C₂₃	semidirect
800. #398	C₂²×C₂₃	semidirect
809. #397	C₂²×C₂₃	semidirect
810. #397	C₂²×C₂₃	semidirect
813. #396	C₂²×C₂₃	semidirect
819. #393	C₂²×C₂₃	semidirect
820. #391	C₂²×C₂₃	semidirect
821. #391	C₂²×C₂₃	semidirect
822. #391	C₂²×C₂₃	semidirect
823. #389	C₂²×C₂₃	semidirect
824. #389	C₂²×C₂₃	semidirect
825. #389	C₂²×C₂₃	semidirect
826. #389	C₂²×C₂₃	semidirect
827. #389	C₂²×C₂₃	semidirect
828. #388	C₂²×C₂₃	semidirect
829. #388	C₂²×C₂₃	semidirect
830. #388	C₂²×C₂₃	semidirect
831. #388	C₂²×C₂₃	semidirect
832. #388	C₂²×C₂₃	semidirect
833. #388	C₂²×C₂₃	semidirect
834. #388	C₂²×C₂₃	semidirect
835. #387	C₂²×C₂₃	semidirect
836. #387	C₂²×C₂₃	semidirect
837. #387	C₂²×C₂₃	semidirect
838. #387	C₂²×C₂₃	semidirect
839. #387	C₂²×C₂₃	semidirect
840. #387	C₂²×C₂₃	semidirect
841. #387	C₂²×C₂₃	semidirect
842. #387	C₂²×C₂₃	semidirect
843. #387	C₂²×C₂₃	semidirect
844. #387	C₂²×C₂₃	semidirect
845. #387	C₂²×C₂₃	semidirect
846. #387	C₂²×C₂₃	semidirect
847. #387	C₂²×C₂₃	semidirect
848. #387	C₂²×C₂₃	semidirect
849. #387	C₂²×C₂₃	semidirect
850. #387	C₂²×C₂₃	semidirect
851. #387	C₂²×C₂₃	semidirect
852. #387	C₂²×C₂₃	semidirect
853. #387	C₂²×C₂₃	semidirect
854. #387	C₂²×C₂₃	semidirect
855. #387	C₂²×C₂₃	semidirect
856. #387	C₂²×C₂₃	semidirect
857. #387	C₂²×C₂₃	semidirect
888. #385	C₂²×C₂₃	semidirect
889. #385	C₂²×C₂₃	semidirect
890. #383	C₂²×C₂₃	semidirect
891. #383	C₂²×C₂₃	semidirect
892. #382	C₂²×C₂₃	semidirect
893. #382	C₂²×C₂₃	semidirect
900. #381	C₂²×C₂₃	semidirect
907. #380	C₂²×C₂₃	semidirect
1111. C₂₃	#34999	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×#2855	2
C₂₃×#2853	2
C₂₃×#2852	2
C₂₃×#2851	2
C₂₃×#2653	2
C₂₃×#2652	2
C₂₃×#2649	2
C₂₃×#2523	2
C₂₃×#2517	2
C₂₃×#2505	2
C₂₃×#2493	2
C₂₃×#2488	2
C₂₃×#2483	2
C₂₃×#2481	2
C₂₃×#2473	2
C₂₃×#2466	2
C₂₃×#2460	2
C₂₃×#2450	2
C₂₃×#2437	2
C₂₃×#2419	2
C₂₃×#2412	2
C₂₃×#2329	2
C₂₃×#2322	2
C₂₃×#2318	2
C₂₃×#2313	2
C₄×C₂₃×#120	2
C₂×C₂₃×#385	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
#34999	23

Subgroups — C23×#34999 #19182625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34999 #19182625