Subgroups — C₂₃×#60042 #19207668

Order 5888.

1648 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2734	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2731	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2721	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2612	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2604	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2574	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2545	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#2529	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2521	C₂	1	2	yes	maximal
11	C₂₃×#2519	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2479	C₂	1	2	yes	maximal
13	C₂₃×#2441	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2373	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2372	C₂	1	1	yes	maximal, characteristic
16	C₂₃×#2371	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2298	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#126	C₂²	1	2	yes	—
23	C₂×C₂₃×#126	C₂²	1	2	yes	—
24	C₂×C₂₃×#125	C₂²	1	2	yes	—
25	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#117	C₂²	1	2	yes	—
31	C₂₃×#400	C₂²	1	2	yes	—
32	C₂₃×#399	C₂²	1	2	yes	—
33	C₂₃×#399	C₂²	1	2	yes	—
34	C₂₃×#399	C₂²	1	2	yes	—
35	C₂₃×#398	C₂²	1	2	yes	—
36	C₂₃×#398	C₂²	1	2	yes	—
37	C₂₃×#398	C₂²	1	2	yes	—
38	C₂₃×#398	C₂²	1	2	yes	—
39	C₂₃×#397	C₂²	1	2	yes	—
40	C₂₃×#396	C₂²	1	2	yes	—
41	C₂₃×#396	C₂²	1	2	yes	—
42	C₂₃×#396	C₂²	1	2	yes	—
43	C₂₃×#395	C₂²	1	2	yes	—
44	C₂₃×#395	C₂²	1	2	yes	—
45	C₂₃×#394	C₂²	1	2	yes	—
46	C₂₃×#393	C₂²	1	2	yes	—
47	C₂₃×#391	C₂²	1	1	yes	characteristic
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#391	C₂²	1	2	yes	—
50	C₂₃×#391	C₂²	1	1	yes	characteristic
51	C₂₃×#391	C₂²	1	1	yes	characteristic
52	C₂₃×#391	C₂²	1	1	yes	characteristic
53	C₂₃×#390	C₂²	1	1	yes	characteristic
54	C₂₃×#389	C₂²	1	2	yes	—
55	C₂₃×#389	C₂²	1	2	yes	—
56	C₂₃×#389	C₂²	1	2	yes	—
57	C₂₃×#389	C₂²	1	2	yes	—
58	C₂₃×#389	C₂²	1	2	yes	—
59	C₂₃×#389	C₂²	1	2	yes	—
60	C₂₃×#388	C₂²	1	2	yes	—
61	C₂₃×#388	C₂²	1	2	yes	—
62	C₂₃×#388	C₂²	1	2	yes	—
63	C₂₃×#388	C₂²	1	2	yes	—
64	C₂₃×#388	C₂²	1	2	yes	—
65	C₂₃×#388	C₂²	1	2	yes	—
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#387	C₂²	1	2	yes	—
85	C₂₃×#386	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#384	C₂²	1	1	yes	characteristic
88	C₂₃×#384	C₂²	1	1	yes	characteristic
89	C₂₃×#382	C₂²	1	2	yes	—
90	C₂₃×#382	C₂²	1	1	yes	characteristic
91	C₂₃×#380	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₂₃×#376	C₂²	1	2	yes	—
104	C₂₃×#376	C₂²	1	2	yes	—
105	C₂₃×#376	C₂²	1	2	yes	—
106	C₄³×C₂₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂₃×C₄⋊Q₈	—	2	4	no	—
113	C₂₃×C₄⋊Q₈	—	2	4	no	—
114	C₂₃×#126	—	2	8	no	—
115	C₂₃×#126	—	4	4	no	—
116	C₂₃×#125	—	2	8	no	—
117	C₂₃×#125	—	4	2	no	—
118	C₂₃×#124	—	2	4	no	—
119	C₂₃×#124	—	4	2	no	—
120	C₄×Q₈×C₂₃	—	4	2	no	—
121	C₄×Q₈×C₂₃	—	4	2	no	—
122	C₂₃×#117	—	2	8	no	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	2	yes	—
185	C₂₃×#95	C₂³	1	2	yes	—
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	2	yes	—
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₂₃	—	2	2	no	—
207	C₂×Q₈×C₂₃	—	2	2	no	—
208	C₂×Q₈×C₂₃	—	4	1	no	—
209	C₂×Q₈×C₂₃	—	4	1	no	—
210	C₂×Q₈×C₂₃	—	4	1	no	—
211	C₂×Q₈×C₂₃	—	4	1	no	—
212	C₂×Q₈×C₂₃	—	4	1	no	—
213	C₂×Q₈×C₂₃	—	4	1	no	—
214	C₂×Q₈×C₂₃	#41	1	4	yes	—
215	C₂×D₄×C₂₃	—	2	2	no	—
216	C₂×D₄×C₂₃	—	4	1	no	—
217	C₂×D₄×C₂₃	—	4	1	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	—	2	4	no	—
220	C₂²×C₄×C₂₃	—	4	2	no	—
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	4	2	no	—
254	C₄⋊C₄×C₂₃	—	4	1	no	—
255	C₄⋊C₄×C₂₃	—	4	1	no	—
256	C₄⋊C₄×C₂₃	—	4	1	no	—
257	C₄⋊C₄×C₂₃	—	4	1	no	—
258	C₄⋊C₄×C₂₃	—	4	2	no	—
259	C₄⋊C₄×C₂₃	—	4	1	no	—
260	C₄⋊C₄×C₂₃	—	4	1	no	—
261	C₄⋊C₄×C₂₃	—	4	2	no	—
262	C₄⋊C₄×C₂₃	—	4	2	no	—
263	C₄⋊C₄×C₂₃	—	4	2	no	—
264	C₄⋊C₄×C₂₃	#41	1	8	yes	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	4	2	no	—
275	C₂²⋊C₄×C₂₃	—	4	2	no	—
276	C₂²⋊C₄×C₂₃	—	4	2	no	—
277	C₂²⋊C₄×C₂₃	—	4	2	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	—	2	4	no	—
280	C₄²×C₂₃	—	2	2	no	—
281	C₄²×C₂₃	—	2	4	no	—
282	C₄²×C₂₃	—	2	4	no	—
283	C₄²×C₂₃	—	2	2	no	—
284	C₄²×C₂₃	—	2	2	no	—
285	C₄²×C₂₃	—	2	2	no	—
286	C₄²×C₂₃	—	2	2	no	—
287	C₄²×C₂₃	—	2	2	no	—
288	C₄²×C₂₃	—	2	4	no	—
289	C₄²×C₂₃	—	2	4	no	—
290	C₄²×C₂₃	—	2	4	no	—
291	C₄²×C₂₃	—	4	1	no	—
292	C₄²×C₂₃	—	4	2	no	—
293	C₄²×C₂₃	—	4	1	no	—
294	C₄²×C₂₃	—	4	1	no	—
295	#60042	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₂₃	—	2	2	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	—	2	2	no	—
303	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
304	Q₈×C₂₃	—	4	4	no	—
305	Q₈×C₂₃	—	4	4	no	—
306	Q₈×C₂₃	—	8	2	no	—
307	D₄×C₂₃	—	8	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	1	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	4	8	no	—
351	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
352	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
354	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
355	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
357	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
358	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
359	#2734	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#2731	C₂×C₂₃	1	1	yes	characteristic
361	#2721	C₂×C₂₃	1	2	yes	complemented
362	#2612	C₂×C₂₃	1	2	yes	complemented
363	#2604	C₂×C₂₃	1	2	yes	complemented
364	#2574	C₂×C₂₃	1	2	yes	complemented
365	#2565	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#2545	C₂×C₂₃	1	1	yes	characteristic
367	#2529	C₂×C₂₃	1	2	yes	complemented
368	#2521	C₂×C₂₃	1	2	yes	—
369	#2519	C₂×C₂₃	1	2	yes	complemented
370	#2479	C₂×C₂₃	1	2	yes	—
371	#2441	C₂×C₂₃	1	2	yes	complemented
372	#2373	C₂×C₂₃	1	2	yes	complemented
373	#2372	C₂×C₂₃	1	1	yes	characteristic
374	#2371	C₂×C₂₃	1	2	yes	complemented
375	#2369	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₄×C₄⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#2298	C₂×C₂₃	1	2	yes	complemented
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	2	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	2	no	—
384	C₂²×C₂₃	—	4	2	no	—
385	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
386	C₂²×C₂₃	C₂²×#41	1	2	yes	—
387	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
389	C₂²×C₂₃	#585	1	1	yes	characteristic
390	C₄×C₂₃	—	2	4	no	—
391	C₄×C₂₃	—	2	4	no	—
392	C₄×C₂₃	—	2	4	no	—
393	C₄×C₂₃	—	2	4	no	—
394	C₄×C₂₃	—	2	2	no	—
395	C₄×C₂₃	—	2	2	no	—
396	C₄×C₂₃	—	2	2	no	—
397	C₄×C₂₃	—	2	2	no	—
398	C₄×C₂₃	—	4	2	no	—
399	C₄×C₂₃	—	4	1	no	—
400	C₄×C₂₃	—	4	2	no	—
401	C₄×C₂₃	—	4	2	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	4	2	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	4	2	no	—
407	C₄×C₂₃	—	4	2	no	—
408	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#126	C₂²×C₂₃	1	2	yes	—
411	C₂×#126	C₂²×C₂₃	1	2	yes	—
412	C₂×#125	C₂²×C₂₃	1	2	yes	—
413	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#117	C₂²×C₂₃	1	2	yes	—
419	#400	C₂²×C₂₃	1	2	yes	—
420	#399	C₂²×C₂₃	1	2	yes	—
421	#399	C₂²×C₂₃	1	2	yes	—
422	#399	C₂²×C₂₃	1	2	yes	—
423	#398	C₂²×C₂₃	1	2	yes	—
424	#398	C₂²×C₂₃	1	2	yes	—
425	#398	C₂²×C₂₃	1	2	yes	—
426	#398	C₂²×C₂₃	1	2	yes	—
427	#397	C₂²×C₂₃	1	2	yes	—
428	#396	C₂²×C₂₃	1	2	yes	—
429	#396	C₂²×C₂₃	1	2	yes	—
430	#396	C₂²×C₂₃	1	2	yes	—
431	#395	C₂²×C₂₃	1	2	yes	—
432	#395	C₂²×C₂₃	1	2	yes	—
433	#394	C₂²×C₂₃	1	2	yes	—
434	#393	C₂²×C₂₃	1	2	yes	—
435	#391	C₂²×C₂₃	1	1	yes	characteristic
436	#391	C₂²×C₂₃	1	1	yes	characteristic
437	#391	C₂²×C₂₃	1	1	yes	characteristic
438	#391	C₂²×C₂₃	1	1	yes	characteristic
439	#391	C₂²×C₂₃	1	1	yes	characteristic
440	#391	C₂²×C₂₃	1	2	yes	—
441	#390	C₂²×C₂₃	1	1	yes	characteristic
442	#389	C₂²×C₂₃	1	2	yes	—
443	#389	C₂²×C₂₃	1	2	yes	—
444	#389	C₂²×C₂₃	1	2	yes	—
445	#389	C₂²×C₂₃	1	2	yes	—
446	#389	C₂²×C₂₃	1	2	yes	—
447	#389	C₂²×C₂₃	1	2	yes	—
448	#388	C₂²×C₂₃	1	2	yes	—
449	#388	C₂²×C₂₃	1	2	yes	—
450	#388	C₂²×C₂₃	1	2	yes	—
451	#388	C₂²×C₂₃	1	2	yes	—
452	#388	C₂²×C₂₃	1	2	yes	—
453	#388	C₂²×C₂₃	1	2	yes	—
454	#388	C₂²×C₂₃	1	2	yes	—
455	#388	C₂²×C₂₃	1	2	yes	—
456	#388	C₂²×C₂₃	1	2	yes	—
457	#388	C₂²×C₂₃	1	2	yes	—
458	#388	C₂²×C₂₃	1	2	yes	—
459	#388	C₂²×C₂₃	1	2	yes	—
460	#387	C₂²×C₂₃	1	2	yes	—
461	#387	C₂²×C₂₃	1	2	yes	—
462	#387	C₂²×C₂₃	1	2	yes	—
463	#387	C₂²×C₂₃	1	2	yes	—
464	#387	C₂²×C₂₃	1	2	yes	—
465	#387	C₂²×C₂₃	1	2	yes	—
466	#387	C₂²×C₂₃	1	2	yes	—
467	#387	C₂²×C₂₃	1	2	yes	—
468	#387	C₂²×C₂₃	1	2	yes	—
469	#387	C₂²×C₂₃	1	2	yes	—
470	#387	C₂²×C₂₃	1	2	yes	—
471	#387	C₂²×C₂₃	1	2	yes	—
472	#387	C₂²×C₂₃	1	2	yes	—
473	#386	C₂²×C₂₃	1	2	yes	—
474	#385	C₂²×C₂₃	1	2	yes	—
475	#384	C₂²×C₂₃	1	1	yes	characteristic
476	#384	C₂²×C₂₃	1	1	yes	characteristic
477	#382	C₂²×C₂₃	1	1	yes	characteristic
478	#382	C₂²×C₂₃	1	2	yes	—
479	#380	C₂²×C₂₃	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
483	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
491	#376	C₂²×C₂₃	1	2	yes	—
492	#376	C₂²×C₂₃	1	2	yes	—
493	#376	C₂²×C₂₃	1	2	yes	—
494	C₄³	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₂₃	—	8	2	no	—
496	C₂×C₂₃	#3482	1	2	yes	—
497	C₂×C₂₃	#3483	1	1	yes	characteristic
498	C₂×C₂₃	#3495	1	2	yes	—
499	C₂×C₂₃	#3505	1	1	yes	characteristic
500	C₂×C₂₃	#3544	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
506	C₄⋊Q₈	—	2	4	no	—
507	C₄⋊Q₈	—	2	4	no	—
508	#126	—	2	8	no	—
509	#126	—	4	4	no	—
510	#125	—	2	8	no	—
511	#125	—	4	2	no	—
512	#124	—	2	4	no	—
513	#124	—	4	2	no	—
514	C₄×Q₈	—	4	2	no	—
515	C₄×Q₈	—	4	2	no	—
516	#117	—	2	8	no	—
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
556	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
573	#95	C₂³×C₂₃	1	2	yes	—
574	#95	C₂³×C₂₃	1	2	yes	—
575	#95	C₂³×C₂₃	1	2	yes	—
576	#95	C₂³×C₂₃	1	2	yes	—
577	#95	C₂³×C₂₃	1	2	yes	—
578	#95	C₂³×C₂₃	1	2	yes	—
579	#95	C₂³×C₂₃	1	2	yes	—
580	#95	C₂³×C₂₃	1	2	yes	—
581	#95	C₂³×C₂₃	1	2	yes	—
582	#95	C₂³×C₂₃	1	2	yes	—
583	#95	C₂³×C₂₃	1	2	yes	—
584	#95	C₂³×C₂₃	1	2	yes	—
585	#95	C₂³×C₂₃	1	2	yes	—
586	#95	C₂³×C₂₃	1	2	yes	—
587	#95	C₂³×C₂₃	1	2	yes	—
588	#95	C₂³×C₂₃	1	2	yes	—
589	#95	C₂³×C₂₃	1	2	yes	—
590	#95	C₂³×C₂₃	1	2	yes	—
591	#95	C₂³×C₂₃	1	2	yes	—
592	#95	C₂³×C₂₃	1	2	yes	—
593	#95	C₂³×C₂₃	1	2	yes	—
594	#95	C₂³×C₂₃	1	2	yes	—
595	#95	C₂³×C₂₃	1	2	yes	—
596	#95	C₂³×C₂₃	1	2	yes	—
597	#95	C₂³×C₂₃	1	2	yes	—
598	#95	C₂³×C₂₃	1	2	yes	—
599	C₂₃	#60042	1	1	yes	characteristic, direct product factor, Sylow
600	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	4	1	no	—
604	C₂×Q₈	—	4	1	no	—
605	C₂×Q₈	—	4	1	no	—
606	C₂×Q₈	—	4	1	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	#41×C₂₃	1	4	yes	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	—	4	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	4	1	no	—
649	C₄⋊C₄	—	4	1	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	—	4	1	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	#41×C₂₃	1	8	yes	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	4	1	no	—
687	C₄²	—	4	2	no	—
688	C₄²	—	4	1	no	—
689	C₄²	—	4	1	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
698	Q₈	—	4	4	no	—
699	Q₈	—	4	4	no	—
700	Q₈	—	8	2	no	—
701	D₄	—	8	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
746	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
747	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
748	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
749	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
750	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
751	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
752	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
761	C₂²	C₂²×#41×C₂₃	1	2	yes	—
762	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
764	C₂²	C₂₃×#585	1	1	yes	characteristic
765	C₄	—	2	4	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂₃×#3482	1	2	yes	—
785	C₂	C₂₃×#3483	1	1	yes	characteristic
786	C₂	C₂₃×#3495	1	2	yes	—
787	C₂	C₂₃×#3505	1	1	yes	characteristic
788	C₂	C₂₃×#3544	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2734	C₂	semidirect
3. C₂₃×#2721	C₂	semidirect
4. C₂₃×#2612	C₂	semidirect
5. C₂₃×#2604	C₂	semidirect
6. C₂₃×#2574	C₂	semidirect
7. C₂₃×#2565	C₂	semidirect
9. C₂₃×#2529	C₂	semidirect
11. C₂₃×#2519	C₂	semidirect
13. C₂₃×#2441	C₂	semidirect
14. C₂₃×#2373	C₂	semidirect
16. C₂₃×#2371	C₂	semidirect
17. C₂₃×#2369	C₂	semidirect
18. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
19. C₂₃×#2298	C₂	semidirect
295. #60042	C₂₃	direct (N × H)
359. #2734	C₂×C₂₃	semidirect
361. #2721	C₂×C₂₃	semidirect
362. #2612	C₂×C₂₃	semidirect
363. #2604	C₂×C₂₃	semidirect
364. #2574	C₂×C₂₃	semidirect
365. #2565	C₂×C₂₃	semidirect
367. #2529	C₂×C₂₃	semidirect
369. #2519	C₂×C₂₃	semidirect
371. #2441	C₂×C₂₃	semidirect
372. #2373	C₂×C₂₃	semidirect
374. #2371	C₂×C₂₃	semidirect
375. #2369	C₂×C₂₃	semidirect
376. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
377. #2298	C₂×C₂₃	semidirect
599. C₂₃	#60042	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×#2734	2
C₂₃×#2731	2
C₂₃×#2721	2
C₂₃×#2612	2
C₂₃×#2604	2
C₂₃×#2574	2
C₂₃×#2565	2
C₂₃×#2545	2
C₂₃×#2529	2
C₂₃×#2521	2
C₂₃×#2519	2
C₂₃×#2479	2
C₂₃×#2441	2
C₂₃×#2373	2
C₂₃×#2372	2
C₂₃×#2371	2
C₂₃×#2369	2
C₄×C₂₃×C₄⋊Q₈	2
C₂₃×#2298	2
#60042	23

Subgroups — C23×#60042 #19207668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60042 #19207668