Subgroups — C₂₃×#36858 #19184484

Order 5888.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2781	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2780	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2757	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2738	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2729	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2715	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2706	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2700	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2696	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2685	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2684	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2674	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2670	C₂	1	1	yes	maximal, characteristic
19	C₂₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2636	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2575	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2574	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2560	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#2553	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#2461	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#2457	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂₃×#2337	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#120	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	C₂₃×#400	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×#399	C₂²	1	1	yes	characteristic
56	C₂₃×#399	C₂²	1	1	yes	characteristic
57	C₂₃×#399	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#397	C₂²	1	1	yes	characteristic
63	C₂₃×#397	C₂²	1	1	yes	characteristic
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, complemented
68	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#397	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#396	C₂²	1	1	yes	characteristic
73	C₂₃×#396	C₂²	1	1	yes	characteristic
74	C₂₃×#396	C₂²	1	1	yes	characteristic
75	C₂₃×#396	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#396	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#396	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#396	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#395	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#395	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#395	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#394	C₂²	1	1	yes	characteristic
83	C₂₃×#394	C₂²	1	1	yes	characteristic
84	C₂₃×#394	C₂²	1	1	yes	characteristic
85	C₂₃×#394	C₂²	1	1	yes	characteristic
86	C₂₃×#394	C₂²	1	1	yes	characteristic
87	C₂₃×#394	C₂²	1	1	yes	characteristic
88	C₂₃×#394	C₂²	1	1	yes	characteristic
89	C₂₃×#394	C₂²	1	1	yes	characteristic
90	C₂₃×#394	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#393	C₂²	1	1	yes	characteristic
92	C₂₃×#393	C₂²	1	1	yes	characteristic
93	C₂₃×#393	C₂²	1	1	yes	characteristic
94	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#392	C₂²	1	1	yes	characteristic
97	C₂₃×#392	C₂²	1	1	yes	characteristic
98	C₂₃×#392	C₂²	1	1	yes	characteristic
99	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#390	C₂²	1	1	yes	characteristic
104	C₂₃×#390	C₂²	1	1	yes	characteristic
105	C₂₃×#390	C₂²	1	1	yes	characteristic
106	C₂₃×#390	C₂²	1	1	yes	characteristic
107	C₂₃×#390	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×#387	C₂²	1	1	yes	characteristic, complemented
131	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
136	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
137	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
138	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
139	C₂₃×#386	C₂²	1	1	yes	characteristic
140	C₂₃×#386	C₂²	1	1	yes	characteristic
141	C₂₃×#386	C₂²	1	1	yes	characteristic
142	C₂₃×#386	C₂²	1	1	yes	characteristic
143	C₂₃×#386	C₂²	1	1	yes	characteristic
144	C₂₃×#386	C₂²	1	1	yes	characteristic
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, complemented
150	C₂₃×#385	C₂²	1	1	yes	characteristic
151	C₂₃×#385	C₂²	1	1	yes	characteristic
152	C₂₃×#385	C₂²	1	1	yes	characteristic
153	C₂₃×#385	C₂²	1	1	yes	characteristic
154	C₂₃×#385	C₂²	1	1	yes	characteristic
155	C₂₃×#385	C₂²	1	1	yes	characteristic
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, complemented
164	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
165	C₂₃×#383	C₂²	1	1	yes	characteristic, complemented
166	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
167	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
168	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
169	C₂₃×#381	C₂²	1	1	yes	characteristic
170	C₂₃×#381	C₂²	1	1	yes	characteristic
171	C₂₃×#381	C₂²	1	1	yes	characteristic, complemented
172	C₂₃×#380	C₂²	1	1	yes	characteristic
173	C₂₃×#380	C₂²	1	1	yes	characteristic
174	C₂₃×#380	C₂²	1	1	yes	characteristic
175	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
176	C₂₃×#379	C₂²	1	1	yes	characteristic
177	C₂₃×#379	C₂²	1	1	yes	characteristic
178	C₂₃×#379	C₂²	1	1	yes	characteristic
179	C₂₃×#379	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×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×Q₈×C₂₃	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×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	C₂³×C₄×C₂₃	—	4	2	no	—
199	C₂³×C₄×C₂₃	—	4	2	no	—
200	C₂³×C₄×C₂₃	—	4	2	no	—
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⋊Q₈	—	4	2	no	—
210	C₂₃×#126	—	2	4	no	—
211	C₂₃×#126	—	4	2	no	—
212	C₂₃×#124	—	2	4	no	—
213	C₂₃×#124	—	4	2	no	—
214	C₂₃×#124	—	4	2	no	—
215	C₂₃×#123	—	4	2	no	—
216	C₂₃×#123	—	4	2	no	—
217	C₂₃×#123	—	4	2	no	—
218	C₂₃×C₂²⋊Q₈	—	4	2	no	—
219	C₂₃×C₂²⋊Q₈	—	4	2	no	—
220	C₂₃×C₂²⋊Q₈	—	4	2	no	—
221	C₂₃×C₂²⋊Q₈	—	4	2	no	—
222	C₂₃×#120	—	2	4	no	—
223	C₂₃×#120	—	4	2	no	—
224	C₄×D₄×C₂₃	—	4	2	no	—
225	C₄×D₄×C₂₃	—	4	2	no	—
226	C₄×D₄×C₂₃	—	4	2	no	—
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×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×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×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×C₄²×C₂₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₂₃	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	—	4	1	no	—
367	C₂⁴×C₂₃	—	4	1	no	—
368	C₂⁴×C₂₃	—	4	1	no	—
369	C₂⁴×C₂₃	—	4	1	no	—
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	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₂×Q₈×C₂₃	—	2	2	no	—
376	C₂×Q₈×C₂₃	—	2	2	no	—
377	C₂×Q₈×C₂₃	—	4	1	no	—
378	C₂×Q₈×C₂₃	—	4	1	no	—
379	C₂×Q₈×C₂₃	—	4	1	no	—
380	C₂×Q₈×C₂₃	—	4	1	no	—
381	C₂×Q₈×C₂₃	—	4	1	no	—
382	C₂×Q₈×C₂₃	—	4	1	no	—
383	C₂×Q₈×C₂₃	—	4	1	no	—
384	C₂×D₄×C₂₃	—	2	2	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	—	4	1	no	—
393	C₂×D₄×C₂₃	—	4	1	no	—
394	C₂×D₄×C₂₃	—	4	1	no	—
395	C₂×D₄×C₂₃	—	4	1	no	—
396	C₂×D₄×C₂₃	—	4	1	no	—
397	C₂×D₄×C₂₃	—	4	1	no	—
398	C₂×D₄×C₂₃	—	4	1	no	—
399	C₂×D₄×C₂₃	—	4	1	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	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	—	2	2	no	—
412	C₂²×C₄×C₂₃	—	2	2	no	—
413	C₂²×C₄×C₂₃	—	2	2	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	16	no	—
430	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	—	2	2	no	—
457	C₄⋊C₄×C₂₃	—	2	2	no	—
458	C₄⋊C₄×C₂₃	—	2	2	no	—
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	—	4	1	no	—
466	C₄⋊C₄×C₂₃	—	4	1	no	—
467	C₄⋊C₄×C₂₃	—	4	1	no	—
468	C₄⋊C₄×C₂₃	—	4	1	no	—
469	C₄⋊C₄×C₂₃	—	4	1	no	—
470	C₄⋊C₄×C₂₃	—	4	1	no	—
471	C₄⋊C₄×C₂₃	—	4	1	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	C₂²⋊C₄×C₂₃	—	2	2	no	—
489	C₂²⋊C₄×C₂₃	—	2	2	no	—
490	C₂²⋊C₄×C₂₃	—	2	2	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	—	4	1	no	—
505	C₂²⋊C₄×C₂₃	—	4	1	no	—
506	C₂²⋊C₄×C₂₃	—	4	1	no	—
507	C₂²⋊C₄×C₂₃	—	4	1	no	—
508	C₂²⋊C₄×C₂₃	—	4	1	no	—
509	C₂²⋊C₄×C₂₃	—	4	1	no	—
510	C₂²⋊C₄×C₂₃	—	4	1	no	—
511	C₂²⋊C₄×C₂₃	—	4	1	no	—
512	C₂²⋊C₄×C₂₃	—	4	1	no	—
513	C₂²⋊C₄×C₂₃	—	4	1	no	—
514	C₂²⋊C₄×C₂₃	—	4	1	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	—	4	1	no	—
527	C₂²⋊C₄×C₂₃	—	4	1	no	—
528	C₂²⋊C₄×C₂₃	—	4	1	no	—
529	C₂²⋊C₄×C₂₃	—	4	1	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	#41	1	4	yes	—
538	C₄²×C₂₃	—	2	2	no	—
539	C₄²×C₂₃	—	2	2	no	—
540	C₄²×C₂₃	—	2	2	no	—
541	C₄²×C₂₃	—	4	1	no	—
542	C₄²×C₂₃	—	4	1	no	—
543	C₄²×C₂₃	—	4	1	no	—
544	C₄²×C₂₃	—	4	1	no	—
545	C₄²×C₂₃	—	4	1	no	—
546	C₄²×C₂₃	—	4	1	no	—
547	C₄²×C₂₃	—	4	1	no	—
548	#36858	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
563	C₂³×C₂₃	—	2	1	no	—
564	C₂³×C₂₃	—	2	1	no	—
565	C₂³×C₂₃	—	2	1	no	—
566	C₂³×C₂₃	—	2	1	no	—
567	C₂³×C₂₃	—	2	1	no	—
568	C₂³×C₂₃	—	2	1	no	—
569	C₂³×C₂₃	—	2	1	no	—
570	C₂³×C₂₃	—	2	1	no	—
571	C₂³×C₂₃	—	2	1	no	—
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	—	4	4	no	—
582	C₂³×C₂₃	—	4	4	no	—
583	C₂³×C₂₃	—	4	4	no	—
584	C₂³×C₂₃	—	4	4	no	—
585	C₂³×C₂₃	—	4	4	no	—
586	C₂³×C₂₃	—	4	4	no	—
587	C₂³×C₂₃	—	4	4	no	—
588	C₂³×C₂₃	C₂×#41	1	2	yes	—
589	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
590	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
591	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
592	Q₈×C₂₃	—	8	2	no	—
593	Q₈×C₂₃	—	8	2	no	—
594	Q₈×C₂₃	—	8	2	no	—
595	D₄×C₂₃	—	4	4	no	—
596	D₄×C₂₃	—	4	4	no	—
597	D₄×C₂₃	—	4	4	no	—
598	D₄×C₂₃	—	8	2	no	—
599	D₄×C₂₃	—	8	2	no	—
600	D₄×C₂₃	—	8	2	no	—
601	D₄×C₂₃	—	8	2	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	—	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	—	4	4	no	—
677	C₂×C₄×C₂₃	—	4	4	no	—
678	C₂×C₄×C₂₃	—	4	4	no	—
679	C₂×C₄×C₂₃	—	4	4	no	—
680	C₂×C₄×C₂₃	—	4	4	no	—
681	C₂×C₄×C₂₃	—	4	4	no	—
682	C₂×C₄×C₂₃	—	8	2	no	—
683	C₂×C₄×C₂₃	—	8	2	no	—
684	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
685	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
686	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
687	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
688	#2849	C₂×C₂₃	1	1	yes	characteristic, complemented
689	#2848	C₂×C₂₃	1	1	yes	characteristic, complemented
690	#2797	C₂×C₂₃	1	1	yes	characteristic, complemented
691	#2781	C₂×C₂₃	1	1	yes	characteristic, complemented
692	#2780	C₂×C₂₃	1	1	yes	characteristic, complemented
693	#2763	C₂×C₂₃	1	1	yes	characteristic, complemented
694	#2757	C₂×C₂₃	1	1	yes	characteristic, complemented
695	#2738	C₂×C₂₃	1	1	yes	characteristic, complemented
696	#2735	C₂×C₂₃	1	1	yes	characteristic, complemented
697	#2729	C₂×C₂₃	1	1	yes	characteristic, complemented
698	#2715	C₂×C₂₃	1	1	yes	characteristic, complemented
699	#2706	C₂×C₂₃	1	1	yes	characteristic, complemented
700	#2700	C₂×C₂₃	1	1	yes	characteristic, complemented
701	#2696	C₂×C₂₃	1	1	yes	characteristic, complemented
702	#2685	C₂×C₂₃	1	1	yes	characteristic, complemented
703	#2684	C₂×C₂₃	1	1	yes	characteristic, complemented
704	#2674	C₂×C₂₃	1	1	yes	characteristic, complemented
705	#2670	C₂×C₂₃	1	1	yes	characteristic
706	#2638	C₂×C₂₃	1	1	yes	characteristic, complemented
707	#2636	C₂×C₂₃	1	1	yes	characteristic, complemented
708	#2575	C₂×C₂₃	1	1	yes	characteristic, complemented
709	#2574	C₂×C₂₃	1	1	yes	characteristic, complemented
710	#2560	C₂×C₂₃	1	1	yes	characteristic, complemented
711	#2553	C₂×C₂₃	1	1	yes	characteristic, complemented
712	#2461	C₂×C₂₃	1	1	yes	characteristic, complemented
713	#2457	C₂×C₂₃	1	1	yes	characteristic, complemented
714	#2452	C₂×C₂₃	1	1	yes	characteristic, complemented
715	#2447	C₂×C₂₃	1	1	yes	characteristic, complemented
716	#2337	C₂×C₂₃	1	1	yes	characteristic, complemented
717	#2334	C₂×C₂₃	1	1	yes	characteristic, complemented
718	C₄×#120	C₂×C₂₃	1	1	yes	characteristic, complemented
719	C₂²×C₂₃	—	2	2	no	—
720	C₂²×C₂₃	—	2	2	no	—
721	C₂²×C₂₃	—	2	2	no	—
722	C₂²×C₂₃	—	2	2	no	—
723	C₂²×C₂₃	—	2	2	no	—
724	C₂²×C₂₃	—	2	2	no	—
725	C₂²×C₂₃	—	2	2	no	—
726	C₂²×C₂₃	—	2	2	no	—
727	C₂²×C₂₃	—	2	2	no	—
728	C₂²×C₂₃	—	4	16	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	—	4	1	no	—
734	C₂²×C₂₃	—	4	1	no	—
735	C₂²×C₂₃	—	4	1	no	—
736	C₂²×C₂₃	—	4	1	no	—
737	C₂²×C₂₃	—	4	1	no	—
738	C₂²×C₂₃	—	4	1	no	—
739	C₂²×C₂₃	—	4	1	no	—
740	C₂²×C₂₃	—	4	1	no	—
741	C₂²×C₂₃	—	4	1	no	—
742	C₂²×C₂₃	—	4	1	no	—
743	C₂²×C₂₃	—	4	1	no	—
744	C₂²×C₂₃	—	4	1	no	—
745	C₂²×C₂₃	—	4	1	no	—
746	C₂²×C₂₃	—	4	1	no	—
747	C₂²×C₂₃	—	4	1	no	—
748	C₂²×C₂₃	—	4	1	no	—
749	C₂²×C₂₃	—	4	1	no	—
750	C₂²×C₂₃	—	4	1	no	—
751	C₂²×C₂₃	—	4	1	no	—
752	C₂²×C₂₃	—	4	1	no	—
753	C₂²×C₂₃	—	4	1	no	—
754	C₂²×C₂₃	—	4	1	no	—
755	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
756	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
757	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
759	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
760	C₂²×C₂₃	#585	1	1	yes	characteristic
761	C₂²×C₂₃	#585	1	1	yes	characteristic
762	C₄×C₂₃	—	2	2	no	—
763	C₄×C₂₃	—	2	2	no	—
764	C₄×C₂₃	—	2	2	no	—
765	C₄×C₂₃	—	2	2	no	—
766	C₄×C₂₃	—	4	1	no	—
767	C₄×C₂₃	—	4	1	no	—
768	C₄×C₂₃	—	4	1	no	—
769	C₄×C₂₃	—	4	1	no	—
770	C₄×C₂₃	—	4	1	no	—
771	C₄×C₂₃	—	4	1	no	—
772	C₄×C₂₃	—	4	1	no	—
773	C₄×C₂₃	—	4	1	no	—
774	C₄×C₂₃	—	4	1	no	—
775	C₄×C₂₃	—	4	1	no	—
776	C₄×C₂₃	—	4	1	no	—
777	C₄×C₂₃	—	4	1	no	—
778	C₄×C₂₃	—	4	1	no	—
779	C₄×C₂₃	—	4	1	no	—
780	C₄×C₂₃	—	4	1	no	—
781	C₄×C₂₃	—	4	1	no	—
782	C₄×C₂₃	—	4	1	no	—
783	C₄×C₂₃	—	4	1	no	—
784	C₄×C₂₃	—	4	1	no	—
785	C₄×C₂₃	—	4	1	no	—
786	C₄×C₂₃	—	4	1	no	—
787	C₄×C₂₃	—	4	1	no	—
788	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
789	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
790	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
791	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic, complemented
792	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
793	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
794	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
795	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
796	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
797	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic, complemented
798	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
799	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
800	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
801	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
802	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
803	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
804	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
805	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
806	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
807	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
808	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
809	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
810	#400	C₂²×C₂₃	1	1	yes	characteristic, complemented
811	#399	C₂²×C₂₃	1	1	yes	characteristic
812	#399	C₂²×C₂₃	1	1	yes	characteristic
813	#399	C₂²×C₂₃	1	1	yes	characteristic, complemented
814	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
815	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
816	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
817	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
818	#397	C₂²×C₂₃	1	1	yes	characteristic
819	#397	C₂²×C₂₃	1	1	yes	characteristic
820	#397	C₂²×C₂₃	1	1	yes	characteristic
821	#397	C₂²×C₂₃	1	1	yes	characteristic
822	#397	C₂²×C₂₃	1	1	yes	characteristic
823	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
824	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
825	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
826	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
827	#397	C₂²×C₂₃	1	1	yes	characteristic, complemented
828	#396	C₂²×C₂₃	1	1	yes	characteristic
829	#396	C₂²×C₂₃	1	1	yes	characteristic
830	#396	C₂²×C₂₃	1	1	yes	characteristic
831	#396	C₂²×C₂₃	1	1	yes	characteristic, complemented
832	#396	C₂²×C₂₃	1	1	yes	characteristic, complemented
833	#396	C₂²×C₂₃	1	1	yes	characteristic, complemented
834	#396	C₂²×C₂₃	1	1	yes	characteristic, complemented
835	#395	C₂²×C₂₃	1	1	yes	characteristic, complemented
836	#395	C₂²×C₂₃	1	1	yes	characteristic, complemented
837	#395	C₂²×C₂₃	1	1	yes	characteristic, complemented
838	#394	C₂²×C₂₃	1	1	yes	characteristic
839	#394	C₂²×C₂₃	1	1	yes	characteristic
840	#394	C₂²×C₂₃	1	1	yes	characteristic
841	#394	C₂²×C₂₃	1	1	yes	characteristic
842	#394	C₂²×C₂₃	1	1	yes	characteristic
843	#394	C₂²×C₂₃	1	1	yes	characteristic
844	#394	C₂²×C₂₃	1	1	yes	characteristic
845	#394	C₂²×C₂₃	1	1	yes	characteristic
846	#394	C₂²×C₂₃	1	1	yes	characteristic, complemented
847	#393	C₂²×C₂₃	1	1	yes	characteristic
848	#393	C₂²×C₂₃	1	1	yes	characteristic
849	#393	C₂²×C₂₃	1	1	yes	characteristic
850	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
851	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
852	#392	C₂²×C₂₃	1	1	yes	characteristic
853	#392	C₂²×C₂₃	1	1	yes	characteristic
854	#392	C₂²×C₂₃	1	1	yes	characteristic
855	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
856	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
857	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
858	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
859	#390	C₂²×C₂₃	1	1	yes	characteristic
860	#390	C₂²×C₂₃	1	1	yes	characteristic
861	#390	C₂²×C₂₃	1	1	yes	characteristic
862	#390	C₂²×C₂₃	1	1	yes	characteristic
863	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
864	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
865	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
866	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
867	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
868	#388	C₂²×C₂₃	1	1	yes	characteristic
869	#388	C₂²×C₂₃	1	1	yes	characteristic
870	#388	C₂²×C₂₃	1	1	yes	characteristic
871	#388	C₂²×C₂₃	1	1	yes	characteristic
872	#388	C₂²×C₂₃	1	1	yes	characteristic
873	#388	C₂²×C₂₃	1	1	yes	characteristic
874	#388	C₂²×C₂₃	1	1	yes	characteristic
875	#388	C₂²×C₂₃	1	1	yes	characteristic
876	#388	C₂²×C₂₃	1	1	yes	characteristic
877	#388	C₂²×C₂₃	1	1	yes	characteristic
878	#388	C₂²×C₂₃	1	1	yes	characteristic
879	#388	C₂²×C₂₃	1	1	yes	characteristic
880	#388	C₂²×C₂₃	1	1	yes	characteristic
881	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
882	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
883	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
884	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
885	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
886	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
887	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
888	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
889	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
890	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
891	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
892	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
893	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
894	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
895	#386	C₂²×C₂₃	1	1	yes	characteristic
896	#386	C₂²×C₂₃	1	1	yes	characteristic
897	#386	C₂²×C₂₃	1	1	yes	characteristic
898	#386	C₂²×C₂₃	1	1	yes	characteristic
899	#386	C₂²×C₂₃	1	1	yes	characteristic
900	#386	C₂²×C₂₃	1	1	yes	characteristic
901	#386	C₂²×C₂₃	1	1	yes	characteristic
902	#386	C₂²×C₂₃	1	1	yes	characteristic
903	#386	C₂²×C₂₃	1	1	yes	characteristic
904	#386	C₂²×C₂₃	1	1	yes	characteristic
905	#386	C₂²×C₂₃	1	1	yes	characteristic, complemented
906	#385	C₂²×C₂₃	1	1	yes	characteristic
907	#385	C₂²×C₂₃	1	1	yes	characteristic
908	#385	C₂²×C₂₃	1	1	yes	characteristic
909	#385	C₂²×C₂₃	1	1	yes	characteristic
910	#385	C₂²×C₂₃	1	1	yes	characteristic
911	#385	C₂²×C₂₃	1	1	yes	characteristic
912	#385	C₂²×C₂₃	1	1	yes	characteristic
913	#385	C₂²×C₂₃	1	1	yes	characteristic
914	#385	C₂²×C₂₃	1	1	yes	characteristic
915	#385	C₂²×C₂₃	1	1	yes	characteristic
916	#385	C₂²×C₂₃	1	1	yes	characteristic
917	#385	C₂²×C₂₃	1	1	yes	characteristic
918	#385	C₂²×C₂₃	1	1	yes	characteristic
919	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
920	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
921	#383	C₂²×C₂₃	1	1	yes	characteristic, complemented
922	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
923	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
924	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
925	#381	C₂²×C₂₃	1	1	yes	characteristic
926	#381	C₂²×C₂₃	1	1	yes	characteristic
927	#381	C₂²×C₂₃	1	1	yes	characteristic, complemented
928	#380	C₂²×C₂₃	1	1	yes	characteristic
929	#380	C₂²×C₂₃	1	1	yes	characteristic
930	#380	C₂²×C₂₃	1	1	yes	characteristic
931	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
932	#379	C₂²×C₂₃	1	1	yes	characteristic
933	#379	C₂²×C₂₃	1	1	yes	characteristic
934	#379	C₂²×C₂₃	1	1	yes	characteristic
935	#379	C₂²×C₂₃	1	1	yes	characteristic
936	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
937	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
938	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
939	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
940	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
941	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
942	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
943	C₂×C₂₃	—	4	2	no	—
944	C₂×C₂₃	—	4	2	no	—
945	C₂×C₂₃	—	4	2	no	—
946	C₂×C₂₃	—	8	1	no	—
947	C₂×C₂₃	—	8	1	no	—
948	C₂×C₂₃	#3460	1	1	yes	characteristic
949	C₂×C₂₃	#3513	1	1	yes	characteristic
950	C₂×C₂₃	#3520	1	1	yes	characteristic
951	C₂×C₂₃	#3532	1	1	yes	characteristic
952	C₂×C₂₃	#3535	1	1	yes	characteristic
953	C₂×C₂₃	#3540	1	1	yes	characteristic
954	C₂×C₂₃	#3541	1	1	yes	characteristic
955	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
956	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
957	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
958	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
959	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
960	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
961	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
962	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
963	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
964	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
965	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
966	C₂³×C₄	—	4	2	no	—
967	C₂³×C₄	—	4	2	no	—
968	C₂³×C₄	—	4	2	no	—
969	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
970	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
971	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
972	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
973	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
974	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
975	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
976	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
977	C₄⋊Q₈	—	4	2	no	—
978	#126	—	2	4	no	—
979	#126	—	4	2	no	—
980	#124	—	2	4	no	—
981	#124	—	4	2	no	—
982	#124	—	4	2	no	—
983	#123	—	4	2	no	—
984	#123	—	4	2	no	—
985	#123	—	4	2	no	—
986	C₂²⋊Q₈	—	4	2	no	—
987	C₂²⋊Q₈	—	4	2	no	—
988	C₂²⋊Q₈	—	4	2	no	—
989	C₂²⋊Q₈	—	4	2	no	—
990	#120	—	2	4	no	—
991	#120	—	4	2	no	—
992	C₄×D₄	—	4	2	no	—
993	C₄×D₄	—	4	2	no	—
994	C₄×D₄	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1005	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1018	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1023	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1026	C₂×C₄⋊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×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1060	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1065	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1066	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1078	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1079	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1080	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1081	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1082	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1083	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1084	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1085	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1086	C₂×C₄²	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	#95	C₂³×C₂₃	1	1	yes	characteristic
1112	#95	C₂³×C₂₃	1	1	yes	characteristic
1113	#95	C₂³×C₂₃	1	1	yes	characteristic
1114	#95	C₂³×C₂₃	1	1	yes	characteristic
1115	#95	C₂³×C₂₃	1	1	yes	characteristic
1116	#95	C₂³×C₂₃	1	1	yes	characteristic
1117	#95	C₂³×C₂₃	1	1	yes	characteristic
1118	#95	C₂³×C₂₃	1	1	yes	characteristic
1119	#95	C₂³×C₂₃	1	1	yes	characteristic
1120	#95	C₂³×C₂₃	1	1	yes	characteristic
1121	#95	C₂³×C₂₃	1	1	yes	characteristic
1122	#95	C₂³×C₂₃	1	1	yes	characteristic
1123	#95	C₂³×C₂₃	1	1	yes	characteristic
1124	#95	C₂³×C₂₃	1	1	yes	characteristic
1125	#95	C₂³×C₂₃	1	1	yes	characteristic
1126	#95	C₂³×C₂₃	1	1	yes	characteristic
1127	#95	C₂³×C₂₃	1	1	yes	characteristic
1128	#95	C₂³×C₂₃	1	1	yes	characteristic
1129	#95	C₂³×C₂₃	1	1	yes	characteristic
1130	#95	C₂³×C₂₃	1	1	yes	characteristic
1131	C₂₃	#36858	1	1	yes	characteristic, direct product factor, Sylow
1132	C₂⁴	—	2	2	no	—
1133	C₂⁴	—	2	2	no	—
1134	C₂⁴	—	2	2	no	—
1135	C₂⁴	—	4	1	no	—
1136	C₂⁴	—	4	1	no	—
1137	C₂⁴	—	4	1	no	—
1138	C₂⁴	—	4	1	no	—
1139	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1140	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1141	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1142	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1143	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
1144	C₂×Q₈	—	2	2	no	—
1145	C₂×Q₈	—	2	2	no	—
1146	C₂×Q₈	—	4	1	no	—
1147	C₂×Q₈	—	4	1	no	—
1148	C₂×Q₈	—	4	1	no	—
1149	C₂×Q₈	—	4	1	no	—
1150	C₂×Q₈	—	4	1	no	—
1151	C₂×Q₈	—	4	1	no	—
1152	C₂×Q₈	—	4	1	no	—
1153	C₂×D₄	—	2	2	no	—
1154	C₂×D₄	—	2	2	no	—
1155	C₂×D₄	—	2	2	no	—
1156	C₂×D₄	—	2	2	no	—
1157	C₂×D₄	—	2	2	no	—
1158	C₂×D₄	—	2	2	no	—
1159	C₂×D₄	—	2	2	no	—
1160	C₂×D₄	—	2	2	no	—
1161	C₂×D₄	—	4	1	no	—
1162	C₂×D₄	—	4	1	no	—
1163	C₂×D₄	—	4	1	no	—
1164	C₂×D₄	—	4	1	no	—
1165	C₂×D₄	—	4	1	no	—
1166	C₂×D₄	—	4	1	no	—
1167	C₂×D₄	—	4	1	no	—
1168	C₂×D₄	—	4	1	no	—
1169	C₂×D₄	—	4	1	no	—
1170	C₂×D₄	—	4	1	no	—
1171	C₂×D₄	—	4	1	no	—
1172	C₂×D₄	—	4	1	no	—
1173	C₂×D₄	—	4	1	no	—
1174	C₂²×C₄	—	2	2	no	—
1175	C₂²×C₄	—	2	2	no	—
1176	C₂²×C₄	—	2	2	no	—
1177	C₂²×C₄	—	2	2	no	—
1178	C₂²×C₄	—	2	2	no	—
1179	C₂²×C₄	—	2	2	no	—
1180	C₂²×C₄	—	2	2	no	—
1181	C₂²×C₄	—	2	2	no	—
1182	C₂²×C₄	—	2	2	no	—
1183	C₂²×C₄	—	4	1	no	—
1184	C₂²×C₄	—	4	1	no	—
1185	C₂²×C₄	—	4	1	no	—
1186	C₂²×C₄	—	4	1	no	—
1187	C₂²×C₄	—	4	1	no	—
1188	C₂²×C₄	—	4	1	no	—
1189	C₂²×C₄	—	4	1	no	—
1190	C₂²×C₄	—	4	1	no	—
1191	C₂²×C₄	—	4	1	no	—
1192	C₂²×C₄	—	4	1	no	—
1193	C₂²×C₄	—	4	1	no	—
1194	C₂²×C₄	—	4	1	no	—
1195	C₂²×C₄	—	4	1	no	—
1196	C₂²×C₄	—	4	1	no	—
1197	C₂²×C₄	—	4	1	no	—
1198	C₂²×C₄	—	4	16	no	—
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	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1209	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1210	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1211	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1223	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1224	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	2	2	no	—
1227	C₄⋊C₄	—	2	2	no	—
1228	C₄⋊C₄	—	2	2	no	—
1229	C₄⋊C₄	—	2	2	no	—
1230	C₄⋊C₄	—	2	2	no	—
1231	C₄⋊C₄	—	2	2	no	—
1232	C₄⋊C₄	—	2	2	no	—
1233	C₄⋊C₄	—	2	2	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	C₄⋊C₄	—	4	1	no	—
1241	C₄⋊C₄	—	4	1	no	—
1242	C₄⋊C₄	—	4	1	no	—
1243	C₄⋊C₄	—	4	1	no	—
1244	C₄⋊C₄	—	4	1	no	—
1245	C₄⋊C₄	—	4	1	no	—
1246	C₄⋊C₄	—	4	1	no	—
1247	C₄⋊C₄	—	4	1	no	—
1248	C₄⋊C₄	—	4	1	no	—
1249	C₄⋊C₄	—	4	1	no	—
1250	C₄⋊C₄	—	4	1	no	—
1251	C₄⋊C₄	—	4	1	no	—
1252	C₄⋊C₄	—	4	1	no	—
1253	C₄⋊C₄	—	4	1	no	—
1254	C₄⋊C₄	—	4	1	no	—
1255	C₄⋊C₄	—	4	1	no	—
1256	C₄⋊C₄	—	4	1	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	—	2	2	no	—
1265	C₂²⋊C₄	—	2	2	no	—
1266	C₂²⋊C₄	—	2	2	no	—
1267	C₂²⋊C₄	—	2	2	no	—
1268	C₂²⋊C₄	—	2	2	no	—
1269	C₂²⋊C₄	—	2	2	no	—
1270	C₂²⋊C₄	—	2	2	no	—
1271	C₂²⋊C₄	—	2	2	no	—
1272	C₂²⋊C₄	—	2	2	no	—
1273	C₂²⋊C₄	—	4	1	no	—
1274	C₂²⋊C₄	—	4	1	no	—
1275	C₂²⋊C₄	—	4	1	no	—
1276	C₂²⋊C₄	—	4	1	no	—
1277	C₂²⋊C₄	—	4	1	no	—
1278	C₂²⋊C₄	—	4	1	no	—
1279	C₂²⋊C₄	—	4	1	no	—
1280	C₂²⋊C₄	—	4	1	no	—
1281	C₂²⋊C₄	—	4	1	no	—
1282	C₂²⋊C₄	—	4	1	no	—
1283	C₂²⋊C₄	—	4	1	no	—
1284	C₂²⋊C₄	—	4	1	no	—
1285	C₂²⋊C₄	—	4	1	no	—
1286	C₂²⋊C₄	—	4	1	no	—
1287	C₂²⋊C₄	—	4	1	no	—
1288	C₂²⋊C₄	—	4	1	no	—
1289	C₂²⋊C₄	—	4	1	no	—
1290	C₂²⋊C₄	—	4	1	no	—
1291	C₂²⋊C₄	—	4	1	no	—
1292	C₂²⋊C₄	—	4	1	no	—
1293	C₂²⋊C₄	—	4	1	no	—
1294	C₂²⋊C₄	—	4	1	no	—
1295	C₂²⋊C₄	—	4	1	no	—
1296	C₂²⋊C₄	—	4	1	no	—
1297	C₂²⋊C₄	—	4	1	no	—
1298	C₂²⋊C₄	—	4	1	no	—
1299	C₂²⋊C₄	—	4	1	no	—
1300	C₂²⋊C₄	—	4	1	no	—
1301	C₂²⋊C₄	—	4	1	no	—
1302	C₂²⋊C₄	—	4	1	no	—
1303	C₂²⋊C₄	—	4	1	no	—
1304	C₂²⋊C₄	—	4	1	no	—
1305	C₂²⋊C₄	—	4	1	no	—
1306	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
1307	C₄²	—	2	2	no	—
1308	C₄²	—	2	2	no	—
1309	C₄²	—	2	2	no	—
1310	C₄²	—	4	1	no	—
1311	C₄²	—	4	1	no	—
1312	C₄²	—	4	1	no	—
1313	C₄²	—	4	1	no	—
1314	C₄²	—	4	1	no	—
1315	C₄²	—	4	1	no	—
1316	C₄²	—	4	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	1	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	—	2	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	1	no	—
1336	C₂³	—	2	1	no	—
1337	C₂³	—	2	1	no	—
1338	C₂³	—	2	1	no	—
1339	C₂³	—	2	1	no	—
1340	C₂³	—	2	1	no	—
1341	C₂³	—	2	1	no	—
1342	C₂³	—	2	1	no	—
1343	C₂³	—	2	1	no	—
1344	C₂³	—	2	1	no	—
1345	C₂³	—	2	1	no	—
1346	C₂³	—	2	1	no	—
1347	C₂³	—	2	1	no	—
1348	C₂³	—	2	1	no	—
1349	C₂³	—	4	4	no	—
1350	C₂³	—	4	4	no	—
1351	C₂³	—	4	4	no	—
1352	C₂³	—	4	4	no	—
1353	C₂³	—	4	4	no	—
1354	C₂³	—	4	4	no	—
1355	C₂³	—	4	4	no	—
1356	C₂³	C₂×#41×C₂₃	1	2	yes	—
1357	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
1358	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
1359	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1360	Q₈	—	8	2	no	—
1361	Q₈	—	8	2	no	—
1362	Q₈	—	8	2	no	—
1363	D₄	—	4	4	no	—
1364	D₄	—	4	4	no	—
1365	D₄	—	4	4	no	—
1366	D₄	—	8	2	no	—
1367	D₄	—	8	2	no	—
1368	D₄	—	8	2	no	—
1369	D₄	—	8	2	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	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	4	4	no	—
1445	C₂×C₄	—	4	4	no	—
1446	C₂×C₄	—	4	4	no	—
1447	C₂×C₄	—	4	4	no	—
1448	C₂×C₄	—	4	4	no	—
1449	C₂×C₄	—	4	4	no	—
1450	C₂×C₄	—	8	2	no	—
1451	C₂×C₄	—	8	2	no	—
1452	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1453	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1454	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1455	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1456	C₂²	—	2	2	no	—
1457	C₂²	—	2	2	no	—
1458	C₂²	—	2	2	no	—
1459	C₂²	—	2	2	no	—
1460	C₂²	—	2	2	no	—
1461	C₂²	—	2	2	no	—
1462	C₂²	—	2	2	no	—
1463	C₂²	—	2	2	no	—
1464	C₂²	—	2	2	no	—
1465	C₂²	—	4	16	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	4	1	no	—
1470	C₂²	—	4	1	no	—
1471	C₂²	—	4	1	no	—
1472	C₂²	—	4	1	no	—
1473	C₂²	—	4	1	no	—
1474	C₂²	—	4	1	no	—
1475	C₂²	—	4	1	no	—
1476	C₂²	—	4	1	no	—
1477	C₂²	—	4	1	no	—
1478	C₂²	—	4	1	no	—
1479	C₂²	—	4	1	no	—
1480	C₂²	—	4	1	no	—
1481	C₂²	—	4	1	no	—
1482	C₂²	—	4	1	no	—
1483	C₂²	—	4	1	no	—
1484	C₂²	—	4	1	no	—
1485	C₂²	—	4	1	no	—
1486	C₂²	—	4	1	no	—
1487	C₂²	—	4	1	no	—
1488	C₂²	—	4	1	no	—
1489	C₂²	—	4	1	no	—
1490	C₂²	—	4	1	no	—
1491	C₂²	—	4	1	no	—
1492	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1493	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1494	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1495	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1496	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1497	C₂²	C₂₃×#585	1	1	yes	characteristic
1498	C₂²	C₂₃×#585	1	1	yes	characteristic
1499	C₄	—	2	2	no	—
1500	C₄	—	2	2	no	—
1501	C₄	—	2	2	no	—
1502	C₄	—	2	2	no	—
1503	C₄	—	4	1	no	—
1504	C₄	—	4	1	no	—
1505	C₄	—	4	1	no	—
1506	C₄	—	4	1	no	—
1507	C₄	—	4	1	no	—
1508	C₄	—	4	1	no	—
1509	C₄	—	4	1	no	—
1510	C₄	—	4	1	no	—
1511	C₄	—	4	1	no	—
1512	C₄	—	4	1	no	—
1513	C₄	—	4	1	no	—
1514	C₄	—	4	1	no	—
1515	C₄	—	4	1	no	—
1516	C₄	—	4	1	no	—
1517	C₄	—	4	1	no	—
1518	C₄	—	4	1	no	—
1519	C₄	—	4	1	no	—
1520	C₄	—	4	1	no	—
1521	C₄	—	4	1	no	—
1522	C₄	—	4	1	no	—
1523	C₄	—	4	1	no	—
1524	C₄	—	4	1	no	—
1525	C₂	—	4	2	no	—
1526	C₂	—	4	2	no	—
1527	C₂	—	4	2	no	—
1528	C₂	—	8	1	no	—
1529	C₂	—	8	1	no	—
1530	C₂	C₂₃×#3460	1	1	yes	characteristic
1531	C₂	C₂₃×#3513	1	1	yes	characteristic
1532	C₂	C₂₃×#3520	1	1	yes	characteristic
1533	C₂	C₂₃×#3532	1	1	yes	characteristic
1534	C₂	C₂₃×#3535	1	1	yes	characteristic
1535	C₂	C₂₃×#3540	1	1	yes	characteristic
1536	C₂	C₂₃×#3541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2670	C₂
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×#2849	C₂	semidirect
2. C₂₃×#2848	C₂	semidirect
3. C₂₃×#2797	C₂	semidirect
4. C₂₃×#2781	C₂	semidirect
5. C₂₃×#2780	C₂	semidirect
6. C₂₃×#2763	C₂	semidirect
7. C₂₃×#2757	C₂	semidirect
8. C₂₃×#2738	C₂	semidirect
9. C₂₃×#2735	C₂	semidirect
10. C₂₃×#2729	C₂	semidirect
11. C₂₃×#2715	C₂	semidirect
12. C₂₃×#2706	C₂	semidirect
13. C₂₃×#2700	C₂	semidirect
14. C₂₃×#2696	C₂	semidirect
15. C₂₃×#2685	C₂	semidirect
16. C₂₃×#2684	C₂	semidirect
17. C₂₃×#2674	C₂	semidirect
19. C₂₃×#2638	C₂	semidirect
20. C₂₃×#2636	C₂	semidirect
21. C₂₃×#2575	C₂	semidirect
22. C₂₃×#2574	C₂	semidirect
23. C₂₃×#2560	C₂	semidirect
24. C₂₃×#2553	C₂	semidirect
25. C₂₃×#2461	C₂	semidirect
26. C₂₃×#2457	C₂	semidirect
27. C₂₃×#2452	C₂	semidirect
28. C₂₃×#2447	C₂	semidirect
29. C₂₃×#2337	C₂	semidirect
30. C₂₃×#2334	C₂	semidirect
31. C₄×C₂₃×#120	C₂	semidirect
33. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₂₃×#126	C₂²	semidirect
41. C₂×C₂₃×#123	C₂²	semidirect
45. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
51. C₂₃×#400	C₂²	semidirect
52. C₂₃×#400	C₂²	semidirect
53. C₂₃×#400	C₂²	semidirect
54. C₂₃×#400	C₂²	semidirect
57. C₂₃×#399	C₂²	semidirect
58. C₂₃×#398	C₂²	semidirect
59. C₂₃×#398	C₂²	semidirect
60. C₂₃×#398	C₂²	semidirect
61. C₂₃×#398	C₂²	semidirect
67. C₂₃×#397	C₂²	semidirect
68. C₂₃×#397	C₂²	semidirect
69. C₂₃×#397	C₂²	semidirect
70. C₂₃×#397	C₂²	semidirect
71. C₂₃×#397	C₂²	semidirect
75. C₂₃×#396	C₂²	semidirect
76. C₂₃×#396	C₂²	semidirect
77. C₂₃×#396	C₂²	semidirect
78. C₂₃×#396	C₂²	semidirect
79. C₂₃×#395	C₂²	semidirect
80. C₂₃×#395	C₂²	semidirect
81. C₂₃×#395	C₂²	semidirect
90. C₂₃×#394	C₂²	semidirect
94. C₂₃×#393	C₂²	semidirect
95. C₂₃×#393	C₂²	semidirect
99. C₂₃×#391	C₂²	semidirect
100. C₂₃×#391	C₂²	semidirect
101. C₂₃×#391	C₂²	semidirect
102. C₂₃×#391	C₂²	semidirect
107. C₂₃×#390	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×#387	C₂²	semidirect
131. C₂₃×#387	C₂²	semidirect
132. C₂₃×#387	C₂²	semidirect
133. C₂₃×#387	C₂²	semidirect
134. C₂₃×#387	C₂²	semidirect
135. C₂₃×#387	C₂²	semidirect
136. C₂₃×#387	C₂²	semidirect
137. C₂₃×#387	C₂²	semidirect
138. C₂₃×#387	C₂²	semidirect
149. C₂₃×#386	C₂²	semidirect
163. C₂₃×#385	C₂²	semidirect
164. C₂₃×#385	C₂²	semidirect
165. C₂₃×#383	C₂²	semidirect
166. C₂₃×#382	C₂²	semidirect
167. C₂₃×#382	C₂²	semidirect
168. C₂₃×#382	C₂²	semidirect
171. C₂₃×#381	C₂²	semidirect
175. C₂₃×#380	C₂²	semidirect
180. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
181. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
182. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
548. #36858	C₂₃	direct (N × H)
688. #2849	C₂×C₂₃	semidirect
689. #2848	C₂×C₂₃	semidirect
690. #2797	C₂×C₂₃	semidirect
691. #2781	C₂×C₂₃	semidirect
692. #2780	C₂×C₂₃	semidirect
693. #2763	C₂×C₂₃	semidirect
694. #2757	C₂×C₂₃	semidirect
695. #2738	C₂×C₂₃	semidirect
696. #2735	C₂×C₂₃	semidirect
697. #2729	C₂×C₂₃	semidirect
698. #2715	C₂×C₂₃	semidirect
699. #2706	C₂×C₂₃	semidirect
700. #2700	C₂×C₂₃	semidirect
701. #2696	C₂×C₂₃	semidirect
702. #2685	C₂×C₂₃	semidirect
703. #2684	C₂×C₂₃	semidirect
704. #2674	C₂×C₂₃	semidirect
706. #2638	C₂×C₂₃	semidirect
707. #2636	C₂×C₂₃	semidirect
708. #2575	C₂×C₂₃	semidirect
709. #2574	C₂×C₂₃	semidirect
710. #2560	C₂×C₂₃	semidirect
711. #2553	C₂×C₂₃	semidirect
712. #2461	C₂×C₂₃	semidirect
713. #2457	C₂×C₂₃	semidirect
714. #2452	C₂×C₂₃	semidirect
715. #2447	C₂×C₂₃	semidirect
716. #2337	C₂×C₂₃	semidirect
717. #2334	C₂×C₂₃	semidirect
718. C₄×#120	C₂×C₂₃	semidirect
789. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
791. C₂×#126	C₂²×C₂₃	semidirect
797. C₂×#123	C₂²×C₂₃	semidirect
801. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
807. #400	C₂²×C₂₃	semidirect
808. #400	C₂²×C₂₃	semidirect
809. #400	C₂²×C₂₃	semidirect
810. #400	C₂²×C₂₃	semidirect
813. #399	C₂²×C₂₃	semidirect
814. #398	C₂²×C₂₃	semidirect
815. #398	C₂²×C₂₃	semidirect
816. #398	C₂²×C₂₃	semidirect
817. #398	C₂²×C₂₃	semidirect
823. #397	C₂²×C₂₃	semidirect
824. #397	C₂²×C₂₃	semidirect
825. #397	C₂²×C₂₃	semidirect
826. #397	C₂²×C₂₃	semidirect
827. #397	C₂²×C₂₃	semidirect
831. #396	C₂²×C₂₃	semidirect
832. #396	C₂²×C₂₃	semidirect
833. #396	C₂²×C₂₃	semidirect
834. #396	C₂²×C₂₃	semidirect
835. #395	C₂²×C₂₃	semidirect
836. #395	C₂²×C₂₃	semidirect
837. #395	C₂²×C₂₃	semidirect
846. #394	C₂²×C₂₃	semidirect
850. #393	C₂²×C₂₃	semidirect
851. #393	C₂²×C₂₃	semidirect
855. #391	C₂²×C₂₃	semidirect
856. #391	C₂²×C₂₃	semidirect
857. #391	C₂²×C₂₃	semidirect
858. #391	C₂²×C₂₃	semidirect
863. #390	C₂²×C₂₃	semidirect
864. #389	C₂²×C₂₃	semidirect
865. #389	C₂²×C₂₃	semidirect
866. #389	C₂²×C₂₃	semidirect
867. #389	C₂²×C₂₃	semidirect
881. #388	C₂²×C₂₃	semidirect
882. #388	C₂²×C₂₃	semidirect
883. #388	C₂²×C₂₃	semidirect
884. #388	C₂²×C₂₃	semidirect
885. #388	C₂²×C₂₃	semidirect
886. #387	C₂²×C₂₃	semidirect
887. #387	C₂²×C₂₃	semidirect
888. #387	C₂²×C₂₃	semidirect
889. #387	C₂²×C₂₃	semidirect
890. #387	C₂²×C₂₃	semidirect
891. #387	C₂²×C₂₃	semidirect
892. #387	C₂²×C₂₃	semidirect
893. #387	C₂²×C₂₃	semidirect
894. #387	C₂²×C₂₃	semidirect
905. #386	C₂²×C₂₃	semidirect
919. #385	C₂²×C₂₃	semidirect
920. #385	C₂²×C₂₃	semidirect
921. #383	C₂²×C₂₃	semidirect
922. #382	C₂²×C₂₃	semidirect
923. #382	C₂²×C₂₃	semidirect
924. #382	C₂²×C₂₃	semidirect
927. #381	C₂²×C₂₃	semidirect
931. #380	C₂²×C₂₃	semidirect
936. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
937. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
938. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
942. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
1131. C₂₃	#36858	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×#2849	2
C₂₃×#2848	2
C₂₃×#2797	2
C₂₃×#2781	2
C₂₃×#2780	2
C₂₃×#2763	2
C₂₃×#2757	2
C₂₃×#2738	2
C₂₃×#2735	2
C₂₃×#2729	2
C₂₃×#2715	2
C₂₃×#2706	2
C₂₃×#2700	2
C₂₃×#2696	2
C₂₃×#2685	2
C₂₃×#2684	2
C₂₃×#2674	2
C₂₃×#2670	2
C₂₃×#2638	2
C₂₃×#2636	2
C₂₃×#2575	2
C₂₃×#2574	2
C₂₃×#2560	2
C₂₃×#2553	2
C₂₃×#2461	2
C₂₃×#2457	2
C₂₃×#2452	2
C₂₃×#2447	2
C₂₃×#2337	2
C₂₃×#2334	2
C₄×C₂₃×#120	2
#36858	23

Subgroups — C23×#36858 #19184484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36858 #19184484