Subgroups — C₂₃×#60951 #19208577

Order 5888.

2082 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3254	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3253	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3235	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3217	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3214	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3194	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3171	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3106	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3101	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3100	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₂₃	—	2	1	no	—
16	C₂₃×#533	C₂²	1	1	yes	characteristic
17	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
18	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#532	—	2	1	no	—
20	C₂₃×#532	—	2	1	no	—
21	C₂₃×#532	—	2	1	no	—
22	C₂₃×#532	—	2	1	no	—
23	C₂₃×#532	C₂²	1	2	yes	—
24	C₂₃×#532	C₂²	1	2	yes	—
25	C₂₃×#532	C₂²	1	2	yes	—
26	C₂₃×#532	C₂²	1	2	yes	—
27	C₂₃×#532	C₂²	1	1	yes	characteristic
28	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
32	C₂₃×#529	—	2	1	no	—
33	C₂₃×#529	—	2	1	no	—
34	C₂₃×#529	—	2	1	no	—
35	C₂₃×#529	—	2	1	no	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	complemented
38	C₂×C₂₃×#124	—	2	1	no	—
39	C₂₃×#525	—	2	1	no	—
40	C₂₃×#525	—	2	1	no	—
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₂×C₂₃×#121	—	2	1	no	—
43	C₂×C₂₃×#121	C₂²	1	2	yes	—
44	C₄×#41×C₂₃	—	2	1	no	—
45	C₄×#41×C₂₃	—	2	1	no	—
46	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₂₃	—	2	1	no	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
49	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#501	C₂²	1	4	yes	complemented
51	C₂₃×#496	C₂²	1	4	yes	complemented
52	C₂₃×#490	C₂²	1	4	yes	complemented
53	C₂₃×#489	C₂²	1	4	yes	complemented
54	C₂₃×#483	C₂²	1	4	yes	—
55	C₂₃×#482	C₂²	1	8	yes	complemented
56	C₂₃×#480	C₂²	1	4	yes	—
57	C₂₃×#477	C₂²	1	4	yes	complemented
58	C₂₃×#476	C₂²	1	4	yes	complemented
59	C₂₃×#476	C₂²	1	4	yes	complemented
60	C₂₃×#474	C₂²	1	4	yes	complemented
61	C₂₃×#469	C₂²	1	8	yes	complemented
62	C₂₃×#468	C₂²	1	8	yes	complemented
63	C₂₃×#461	C₂²	1	4	yes	complemented
64	C₂₃×#460	C₂²	1	4	yes	complemented
65	C₂₃×#459	C₂²	1	4	yes	complemented
66	C₂₃×#459	C₂²	1	4	yes	complemented
67	C₂₃×#450	C₂²	1	4	yes	—
68	C₂₃×#449	C₂²	1	8	yes	complemented
69	C₂₃×#447	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
71	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
72	C₂₃×#432	C₂²	1	2	yes	—
73	C₂₃×#432	C₂²	1	2	yes	complemented
74	C₂₃×#431	C₂²	1	2	yes	—
75	C₂₃×#431	C₂²	1	2	yes	complemented
76	C₂₃×#423	C₂²	1	2	yes	complemented
77	C₂₃×#407	C₂²	1	2	yes	—
78	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
79	C₂×#41×C₂₃	—	2	2	no	—
80	C₂×#41×C₂₃	—	2	2	no	—
81	C₂×#41×C₂₃	—	2	2	no	—
82	C₂×#41×C₂₃	—	2	2	no	—
83	C₂×#41×C₂₃	—	2	1	no	—
84	C₂×#41×C₂₃	—	2	1	no	—
85	C₂×#41×C₂₃	—	4	8	no	—
86	C₂×#41×C₂₃	C₂³	1	2	yes	—
87	C₂²×Q₈×C₂₃	—	2	1	no	—
88	C₂²×D₄×C₂₃	—	2	2	no	—
89	C₂²×D₄×C₂₃	—	2	1	no	—
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₂₃	—	2	2	no	—
93	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
97	C₂×D₈×C₂₃	C₂³	1	8	yes	—
98	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂₃×C₄⋊Q₈	—	2	1	no	—
100	C₂₃×C₄⋊Q₈	—	2	1	no	—
101	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₂₃×#127	—	2	1	no	—
107	C₂₃×#127	—	2	1	no	—
108	C₂₃×#127	C₂³	1	1	yes	characteristic
109	C₂₃×#127	C₂³	1	2	yes	—
110	C₂₃×#127	C₂³	1	2	yes	—
111	C₂₃×#126	—	2	2	no	—
112	C₂₃×#126	—	2	2	no	—
113	C₂₃×#125	—	2	1	no	—
114	C₂₃×#125	—	2	1	no	—
115	C₂₃×#125	C₂³	1	2	yes	—
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#124	—	2	2	no	—
118	C₂₃×#124	—	2	2	no	—
119	C₂₃×#124	—	2	2	no	—
120	C₂₃×#124	—	2	1	no	—
121	C₂₃×#124	—	2	1	no	—
122	C₂₃×#124	C₂³	1	2	yes	—
123	C₂₃×#123	—	2	2	no	—
124	C₂₃×#123	—	2	2	no	—
125	C₂₃×#123	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	1	no	—
127	C₂₃×C₂²⋊Q₈	—	2	1	no	—
128	C₂₃×C₂²⋊Q₈	—	2	1	no	—
129	C₂₃×C₂²⋊Q₈	—	2	1	no	—
130	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
131	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₂₃×#121	—	2	2	no	—
133	C₂₃×#121	—	2	2	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	2	no	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	—	2	1	no	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	1	no	—
142	C₂₃×#121	C₂³	1	2	yes	—
143	C₂₃×#121	C₂³	1	4	yes	—
144	C₂₃×#121	C₂³	1	4	yes	—
145	C₂₃×#121	C₂³	1	2	yes	—
146	C₂₃×#120	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	—	2	1	no	—
149	C₄×Q₈×C₂₃	—	2	1	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	2	no	—
155	C₄×D₄×C₂₃	—	2	2	no	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₄×D₄×C₂₃	C₂³	1	4	yes	—
171	C₄×D₄×C₂₃	C₂³	1	2	yes	—
172	C₄×D₄×C₂₃	C₂³	1	4	yes	—
173	C₂₃×#117	—	2	1	no	—
174	C₂₃×#117	—	2	1	no	—
175	C₂₃×#117	—	2	2	no	—
176	C₂₃×#117	—	2	2	no	—
177	C₂₃×#117	—	2	2	no	—
178	C₂₃×#117	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
182	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
183	C₂×C₄²×C₂₃	—	2	2	no	—
184	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
196	C₂₃×#107	C₂³	1	8	yes	—
197	C₂₃×#106	C₂³	1	8	yes	—
198	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
200	C₂₃×#103	C₂³	1	8	yes	—
201	C₂₃×#102	C₂³	1	8	yes	—
202	C₂₃×#102	C₂³	1	8	yes	—
203	C₂₃×#102	C₂³	1	8	yes	—
204	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
205	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₂₃×#97	C₂³	1	4	yes	—
207	C₄×C₈×C₂₃	C₂³	1	4	yes	—
208	C₂⁴×C₂₃	—	2	2	no	—
209	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
210	#41×C₂₃	—	4	4	no	—
211	#41×C₂₃	—	4	4	no	—
212	#41×C₂₃	—	4	8	no	—
213	#41×C₂₃	—	4	8	no	—
214	#41×C₂₃	—	4	8	no	—
215	#41×C₂₃	—	4	8	no	—
216	#41×C₂₃	—	4	4	no	—
217	C₂×Q₈×C₂₃	—	2	1	no	—
218	C₂×Q₈×C₂₃	—	2	1	no	—
219	C₂×Q₈×C₂₃	—	2	2	no	—
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	—	4	4	no	—
222	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₂₃	—	2	2	no	—
224	C₂×D₄×C₂₃	—	2	2	no	—
225	C₂×D₄×C₂₃	—	2	2	no	—
226	C₂×D₄×C₂₃	—	2	4	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	2	no	—
233	C₂×D₄×C₂₃	—	2	2	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	4	4	no	—
236	C₂×D₄×C₂₃	—	4	4	no	—
237	C₂×D₄×C₂₃	—	4	4	no	—
238	C₂×D₄×C₂₃	—	4	8	no	—
239	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₂₃	—	2	4	no	—
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	4	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	4	no	—
248	C₂²×C₄×C₂₃	—	4	2	no	—
249	C₂²×C₄×C₂₃	—	4	2	no	—
250	C₂²×C₄×C₂₃	—	4	8	no	—
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	SD₁₆×C₂₃	—	4	8	no	—
270	D₈×C₂₃	—	4	8	no	—
271	M₁₆×C₂₃	—	4	4	no	—
272	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	—	2	4	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	no	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	—	2	2	no	—
297	C₂²⋊C₄×C₂₃	—	2	2	no	—
298	C₂²⋊C₄×C₂₃	—	2	2	no	—
299	C₂²⋊C₄×C₂₃	—	2	2	no	—
300	C₂²⋊C₄×C₂₃	—	2	2	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₄²×C₂₃	—	2	2	no	—
303	C₄²×C₂₃	—	2	2	no	—
304	C₄²×C₂₃	—	2	2	no	—
305	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
321	#60951	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₂₃	—	2	2	no	—
323	C₂³×C₂₃	—	2	2	no	—
324	C₂³×C₂₃	—	2	4	no	—
325	C₂³×C₂₃	—	4	1	no	—
326	C₂³×C₂₃	—	4	1	no	—
327	C₂³×C₂₃	—	4	4	no	—
328	C₂³×C₂₃	—	4	4	no	—
329	C₂³×C₂₃	—	4	4	no	—
330	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₂₃	—	2	4	no	—
334	Q₈×C₂₃	—	4	4	no	—
335	Q₈×C₂₃	—	4	4	no	—
336	Q₈×C₂₃	—	4	2	no	—
337	Q₈×C₂₃	—	4	2	no	—
338	D₄×C₂₃	—	2	4	no	—
339	D₄×C₂₃	—	2	4	no	—
340	D₄×C₂₃	—	2	4	no	—
341	D₄×C₂₃	—	4	4	no	—
342	D₄×C₂₃	—	4	4	no	—
343	D₄×C₂₃	—	4	4	no	—
344	D₄×C₂₃	—	4	4	no	—
345	D₄×C₂₃	—	4	2	no	—
346	D₄×C₂₃	—	4	8	no	—
347	D₄×C₂₃	—	4	8	no	—
348	D₄×C₂₃	—	4	4	no	—
349	D₄×C₂₃	—	4	4	no	—
350	D₄×C₂₃	—	4	4	no	—
351	D₄×C₂₃	—	4	2	no	—
352	D₄×C₂₃	—	4	4	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	4	no	—
368	C₂×C₄×C₂₃	—	4	1	no	—
369	C₂×C₄×C₂₃	—	4	1	no	—
370	C₂×C₄×C₂₃	—	4	1	no	—
371	C₂×C₄×C₂₃	—	4	1	no	—
372	C₂×C₄×C₂₃	—	4	1	no	—
373	C₂×C₄×C₂₃	—	4	1	no	—
374	C₂×C₄×C₂₃	—	4	4	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	8	no	—
377	C₂×C₄×C₂₃	—	4	8	no	—
378	C₂×C₄×C₂₃	—	4	4	no	—
379	C₂×C₄×C₂₃	—	4	4	no	—
380	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₂₃	—	2	8	no	—
394	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
395	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#3254	C₂×C₂₃	1	2	yes	complemented
397	#3253	C₂×C₂₃	1	2	yes	complemented
398	#3238	C₂×C₂₃	1	2	yes	complemented
399	#3235	C₂×C₂₃	1	2	yes	complemented
400	#3217	C₂×C₂₃	1	2	yes	complemented
401	#3214	C₂×C₂₃	1	2	yes	complemented
402	#3194	C₂×C₂₃	1	4	yes	complemented
403	#3171	C₂×C₂₃	1	4	yes	complemented
404	#3106	C₂×C₂₃	1	4	yes	complemented
405	#3101	C₂×C₂₃	1	2	yes	complemented
406	#3100	C₂×C₂₃	1	2	yes	complemented
407	#2920	C₂×C₂₃	1	1	yes	characteristic, complemented
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	2	1	no	—
410	C₂²×C₂₃	—	2	1	no	—
411	C₂²×C₂₃	—	2	1	no	—
412	C₂²×C₂₃	—	2	1	no	—
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	2	1	no	—
416	C₂²×C₂₃	—	4	4	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	4	no	—
419	C₂²×C₂₃	—	4	4	no	—
420	C₂²×C₂₃	—	4	2	no	—
421	C₂²×C₂₃	—	4	2	no	—
422	C₂²×C₂₃	—	4	4	no	—
423	C₂²×C₂₃	—	8	8	no	—
424	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
425	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₂₃	—	2	1	no	—
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	1	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	1	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	4	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
439	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
440	C₄×C₂₃	#575	1	2	yes	—
441	C₄×C₂₃	#585	1	2	yes	—
442	C₂²×#41	—	2	1	no	—
443	#533	C₂²×C₂₃	1	1	yes	characteristic
444	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	#532	—	2	1	no	—
447	#532	—	2	1	no	—
448	#532	—	2	1	no	—
449	#532	—	2	1	no	—
450	#532	C₂²×C₂₃	1	1	yes	characteristic
451	#532	C₂²×C₂₃	1	2	yes	—
452	#532	C₂²×C₂₃	1	2	yes	—
453	#532	C₂²×C₂₃	1	2	yes	—
454	#532	C₂²×C₂₃	1	2	yes	—
455	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
457	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
459	#529	—	2	1	no	—
460	#529	—	2	1	no	—
461	#529	—	2	1	no	—
462	#529	—	2	1	no	—
463	#529	C₂²×C₂₃	1	2	yes	—
464	#529	C₂²×C₂₃	1	2	yes	complemented
465	C₂×#124	—	2	1	no	—
466	#525	—	2	1	no	—
467	#525	—	2	1	no	—
468	#525	C₂²×C₂₃	1	2	yes	—
469	C₂×#121	—	2	1	no	—
470	C₂×#121	C₂²×C₂₃	1	2	yes	—
471	C₄×#41	—	2	1	no	—
472	C₄×#41	—	2	1	no	—
473	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
474	C₂×C₄×D₄	—	2	1	no	—
475	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
476	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
477	#501	C₂²×C₂₃	1	4	yes	complemented
478	#496	C₂²×C₂₃	1	4	yes	complemented
479	#490	C₂²×C₂₃	1	4	yes	complemented
480	#489	C₂²×C₂₃	1	4	yes	complemented
481	#483	C₂²×C₂₃	1	4	yes	—
482	#482	C₂²×C₂₃	1	8	yes	complemented
483	#480	C₂²×C₂₃	1	4	yes	—
484	#477	C₂²×C₂₃	1	4	yes	complemented
485	#476	C₂²×C₂₃	1	4	yes	complemented
486	#476	C₂²×C₂₃	1	4	yes	complemented
487	#474	C₂²×C₂₃	1	4	yes	complemented
488	#469	C₂²×C₂₃	1	8	yes	complemented
489	#468	C₂²×C₂₃	1	8	yes	complemented
490	#461	C₂²×C₂₃	1	4	yes	complemented
491	#460	C₂²×C₂₃	1	4	yes	complemented
492	#459	C₂²×C₂₃	1	4	yes	complemented
493	#459	C₂²×C₂₃	1	4	yes	complemented
494	#450	C₂²×C₂₃	1	4	yes	—
495	#449	C₂²×C₂₃	1	8	yes	complemented
496	#447	C₂²×C₂₃	1	4	yes	—
497	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
498	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
499	#432	C₂²×C₂₃	1	2	yes	—
500	#432	C₂²×C₂₃	1	2	yes	complemented
501	#431	C₂²×C₂₃	1	2	yes	—
502	#431	C₂²×C₂₃	1	2	yes	complemented
503	#423	C₂²×C₂₃	1	2	yes	complemented
504	#407	C₂²×C₂₃	1	2	yes	—
505	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
506	C₂×C₂₃	—	2	2	no	—
507	C₂×C₂₃	—	4	1	no	—
508	C₂×C₂₃	—	4	1	no	—
509	C₂×C₂₃	—	8	2	no	—
510	C₂×C₂₃	—	8	4	no	—
511	C₂×C₂₃	#3449	1	1	yes	characteristic
512	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
513	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
514	C₂×#41	—	2	1	no	—
515	C₂×#41	—	2	1	no	—
516	C₂×#41	—	2	2	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	4	8	no	—
521	C₂×#41	C₂³×C₂₃	1	2	yes	—
522	C₂²×Q₈	—	2	1	no	—
523	C₂²×D₄	—	2	2	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
527	C₂³×C₄	—	2	2	no	—
528	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
529	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
532	C₂×D₈	C₂³×C₂₃	1	8	yes	—
533	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
538	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
541	#127	—	2	1	no	—
542	#127	—	2	1	no	—
543	#127	C₂³×C₂₃	1	2	yes	—
544	#127	C₂³×C₂₃	1	2	yes	—
545	#127	C₂³×C₂₃	1	1	yes	characteristic
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#125	—	2	1	no	—
549	#125	—	2	1	no	—
550	#125	C₂³×C₂₃	1	2	yes	—
551	#124	—	2	2	no	—
552	#124	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	—	2	1	no	—
556	#124	—	2	1	no	—
557	#124	C₂³×C₂₃	1	2	yes	—
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	#123	—	2	2	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
566	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	1	no	—
577	#121	C₂³×C₂₃	1	4	yes	—
578	#121	C₂³×C₂₃	1	4	yes	—
579	#121	C₂³×C₂₃	1	2	yes	—
580	#121	C₂³×C₂₃	1	2	yes	—
581	#120	—	2	2	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
587	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	C₂³×C₂₃	1	4	yes	—
605	C₄×D₄	C₂³×C₂₃	1	4	yes	—
606	C₄×D₄	C₂³×C₂₃	1	2	yes	—
607	C₄×D₄	C₂³×C₂₃	1	2	yes	—
608	#117	—	2	1	no	—
609	#117	—	2	1	no	—
610	#117	—	2	2	no	—
611	#117	—	2	2	no	—
612	#117	—	2	2	no	—
613	#117	C₂³×C₂₃	1	2	yes	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₂²⋊C₄	—	2	2	no	—
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₄²	—	2	2	no	—
619	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
620	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
621	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
622	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
624	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
631	#107	C₂³×C₂₃	1	8	yes	—
632	#106	C₂³×C₂₃	1	8	yes	—
633	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
634	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
635	#103	C₂³×C₂₃	1	8	yes	—
636	#102	C₂³×C₂₃	1	8	yes	—
637	#102	C₂³×C₂₃	1	8	yes	—
638	#102	C₂³×C₂₃	1	8	yes	—
639	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
641	#97	C₂³×C₂₃	1	4	yes	—
642	C₄×C₈	C₂³×C₂₃	1	4	yes	—
643	C₂₃	#60951	1	1	yes	characteristic, direct product factor, Sylow
644	C₂⁴	—	2	2	no	—
645	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
646	#41	—	4	4	no	—
647	#41	—	4	8	no	—
648	#41	—	4	8	no	—
649	#41	—	4	8	no	—
650	#41	—	4	8	no	—
651	#41	—	4	4	no	—
652	#41	—	4	4	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	4	4	no	—
658	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	8	no	—
675	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
676	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	8	no	—
687	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
705	SD₁₆	—	4	8	no	—
706	D₈	—	4	8	no	—
707	M₁₆	—	4	4	no	—
708	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
751	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
752	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
753	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
755	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
766	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
767	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	Q₈	—	2	4	no	—
769	Q₈	—	4	4	no	—
770	Q₈	—	4	4	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	4	2	no	—
773	D₄	—	2	4	no	—
774	D₄	—	2	4	no	—
775	D₄	—	2	4	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	2	no	—
787	D₄	—	4	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
828	C₈	—	2	8	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	8	8	no	—
845	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
846	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	4	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
860	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
861	C₄	C₂₃×#575	1	2	yes	—
862	C₄	C₂₃×#585	1	2	yes	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	4	1	no	—
866	C₂	—	8	4	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂₃×#3449	1	1	yes	characteristic
869	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
870	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3444	C₂	semidirect
2. C₂×C₂₃×#532	C₂	semidirect
3. C₂₃×#3254	C₂	semidirect
4. C₂₃×#3253	C₂	semidirect
5. C₂₃×#3238	C₂	semidirect
6. C₂₃×#3235	C₂	semidirect
7. C₂₃×#3217	C₂	semidirect
8. C₂₃×#3214	C₂	semidirect
9. C₂₃×#3194	C₂	semidirect
10. C₂₃×#3171	C₂	semidirect
11. C₂₃×#3106	C₂	semidirect
12. C₂₃×#3101	C₂	semidirect
13. C₂₃×#3100	C₂	semidirect
14. C₂₃×#2920	C₂	semidirect
17. C₂₃×#533	C₂²	semidirect
18. C₂₃×#533	C₂²	semidirect
28. C₂₃×#532	C₂²	semidirect
29. C₂₃×#532	C₂²	semidirect
37. C₂₃×#529	C₂²	semidirect
46. C₄×#41×C₂₃	C₂²	semidirect
50. C₂₃×#501	C₂²	semidirect
51. C₂₃×#496	C₂²	semidirect
52. C₂₃×#490	C₂²	semidirect
53. C₂₃×#489	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
57. C₂₃×#477	C₂²	semidirect
58. C₂₃×#476	C₂²	semidirect
59. C₂₃×#476	C₂²	semidirect
60. C₂₃×#474	C₂²	semidirect
61. C₂₃×#469	C₂²	semidirect
62. C₂₃×#468	C₂²	semidirect
63. C₂₃×#461	C₂²	semidirect
64. C₂₃×#460	C₂²	semidirect
65. C₂₃×#459	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
68. C₂₃×#449	C₂²	semidirect
70. C₄×SD₁₆×C₂₃	C₂²	semidirect
71. C₄×D₈×C₂₃	C₂²	semidirect
73. C₂₃×#432	C₂²	semidirect
75. C₂₃×#431	C₂²	semidirect
76. C₂₃×#423	C₂²	semidirect
78. C₄×M₁₆×C₂₃	C₂²	semidirect
321. #60951	C₂₃	direct (N × H)
394. #3444	C₂×C₂₃	semidirect
395. C₂×#532	C₂×C₂₃	semidirect
396. #3254	C₂×C₂₃	semidirect
397. #3253	C₂×C₂₃	semidirect
398. #3238	C₂×C₂₃	semidirect
399. #3235	C₂×C₂₃	semidirect
400. #3217	C₂×C₂₃	semidirect
401. #3214	C₂×C₂₃	semidirect
402. #3194	C₂×C₂₃	semidirect
403. #3171	C₂×C₂₃	semidirect
404. #3106	C₂×C₂₃	semidirect
405. #3101	C₂×C₂₃	semidirect
406. #3100	C₂×C₂₃	semidirect
407. #2920	C₂×C₂₃	semidirect
444. #533	C₂²×C₂₃	semidirect
445. #533	C₂²×C₂₃	semidirect
455. #532	C₂²×C₂₃	semidirect
456. #532	C₂²×C₂₃	semidirect
464. #529	C₂²×C₂₃	semidirect
473. C₄×#41	C₂²×C₂₃	semidirect
477. #501	C₂²×C₂₃	semidirect
478. #496	C₂²×C₂₃	semidirect
479. #490	C₂²×C₂₃	semidirect
480. #489	C₂²×C₂₃	semidirect
482. #482	C₂²×C₂₃	semidirect
484. #477	C₂²×C₂₃	semidirect
485. #476	C₂²×C₂₃	semidirect
486. #476	C₂²×C₂₃	semidirect
487. #474	C₂²×C₂₃	semidirect
488. #469	C₂²×C₂₃	semidirect
489. #468	C₂²×C₂₃	semidirect
490. #461	C₂²×C₂₃	semidirect
491. #460	C₂²×C₂₃	semidirect
492. #459	C₂²×C₂₃	semidirect
493. #459	C₂²×C₂₃	semidirect
495. #449	C₂²×C₂₃	semidirect
497. C₄×SD₁₆	C₂²×C₂₃	semidirect
498. C₄×D₈	C₂²×C₂₃	semidirect
500. #432	C₂²×C₂₃	semidirect
502. #431	C₂²×C₂₃	semidirect
503. #423	C₂²×C₂₃	semidirect
505. C₄×M₁₆	C₂²×C₂₃	semidirect
643. C₂₃	#60951	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×#3444	2
C₂×C₂₃×#532	2
C₂₃×#3254	2
C₂₃×#3253	2
C₂₃×#3238	2
C₂₃×#3235	2
C₂₃×#3217	2
C₂₃×#3214	2
C₂₃×#3194	2
C₂₃×#3171	2
C₂₃×#3106	2
C₂₃×#3101	2
C₂₃×#3100	2
C₂₃×#2920	2
#60951	23

Subgroups — C23×#60951 #19208577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60951 #19208577