Subgroups — C₂₃×#61340 #19208966

Order 5888.

1792 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3372	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3367	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3360	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3359	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3042	C₂	1	2	yes	maximal
14	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
20	C₂₃×#557	C₂²	1	2	yes	complemented
21	C₂₃×#557	C₂²	1	2	yes	complemented
22	C₂₃×#556	C₂²	1	2	yes	complemented
23	C₂₃×#556	C₂²	1	2	yes	complemented
24	C₂₃×#554	—	2	1	no	—
25	C₂₃×#554	—	2	2	no	—
26	C₂₃×#554	C₂²	1	2	yes	—
27	C₂₃×#554	C₂²	1	4	yes	—
28	C₂₃×#552	—	2	2	no	—
29	C₂₃×#552	—	2	2	no	—
30	D₄×Q₈×C₂₃	—	2	1	no	—
31	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#544	C₂²	1	2	yes	—
33	C₂₃×#543	—	2	2	no	—
34	C₂₃×#541	—	2	2	no	—
35	C₂₃×#536	C₂²	1	2	yes	—
36	C₂₃×#533	—	2	1	no	—
37	C₂₃×#533	—	2	1	no	—
38	C₂₃×#533	C₂²	1	1	yes	characteristic
39	C₂₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
42	C₂₃×#519	C₂²	1	2	yes	—
43	C₂₃×#518	C₂²	1	2	yes	—
44	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#491	C₂²	1	4	yes	complemented
47	C₂₃×#491	C₂²	1	4	yes	complemented
48	C₂₃×#489	C₂²	1	4	yes	complemented
49	C₂₃×#488	C₂²	1	4	yes	complemented
50	C₂₃×#487	C₂²	1	2	yes	complemented
51	C₂₃×#487	C₂²	1	4	yes	complemented
52	C₂₃×#487	C₂²	1	2	yes	complemented
53	C₂₃×#479	C₂²	1	2	yes	complemented
54	C₂₃×#479	C₂²	1	4	yes	complemented
55	C₂₃×#479	C₂²	1	4	yes	complemented
56	C₂₃×#478	C₂²	1	2	yes	complemented
57	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#477	C₂²	1	4	yes	complemented
59	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#475	C₂²	1	4	yes	complemented
62	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#463	C₂²	1	4	yes	—
64	C₂₃×#463	C₂²	1	4	yes	—
65	C₂₃×#461	C₂²	1	2	yes	—
66	C₂₃×#461	C₂²	1	2	yes	—
67	C₂₃×#461	C₂²	1	4	yes	—
68	C₂₃×#461	C₂²	1	4	yes	—
69	C₂₃×#461	C₂²	1	4	yes	—
70	C₂₃×#446	C₂²	1	2	yes	complemented
71	C₂₃×#446	C₂²	1	4	yes	complemented
72	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
73	C₂₃×#442	C₂²	1	2	yes	—
74	C₂₃×#440	C₂²	1	2	yes	—
75	C₂₃×#440	C₂²	1	4	yes	—
76	C₂₃×#440	C₂²	1	4	yes	—
77	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
79	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
80	C₄×D₈×C₂₃	C₂²	1	2	yes	—
81	C₂₃×#428	C₂²	1	1	yes	characteristic
82	C₂₃×#427	C₂²	1	2	yes	—
83	C₂₃×#424	C₂²	1	2	yes	—
84	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₂₃×#419	C₂²	1	2	yes	—
86	C₂₃×#419	C₂²	1	2	yes	—
87	C₂₃×#418	C₂²	1	1	yes	characteristic
88	C₂₃×#417	C₂²	1	1	yes	characteristic
89	C₂₃×#416	C₂²	1	2	yes	—
90	C₂×C₂₃×#103	C₂²	1	2	yes	—
91	C₂₃×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₂₃	—	2	2	no	—
95	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	—	2	1	no	—
98	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
99	C₂×SD₁₆×C₂₃	—	2	8	no	—
100	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂×D₈×C₂₃	C₂³	1	2	yes	—
104	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₂₃×#126	—	2	4	no	—
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	4	no	—
123	C₂₃×#125	—	2	4	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	D₄	1	2	yes	—
126	C₂₃×#125	C₂³	1	2	yes	—
127	C₂₃×#125	C₂³	1	4	yes	—
128	C₂₃×#124	C₂³	1	4	yes	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	4	no	—
134	C₂₃×C₂²⋊Q₈	—	2	1	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	4	no	—
137	C₂₃×C₂²⋊Q₈	—	2	2	no	—
138	C₂₃×C₂²⋊Q₈	—	2	4	no	—
139	C₂₃×C₂²⋊Q₈	—	2	4	no	—
140	C₂₃×C₂²⋊Q₈	—	2	4	no	—
141	C₂₃×C₂²⋊Q₈	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	—	2	2	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
153	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
158	C₄×D₄×C₂₃	—	2	1	no	—
159	C₄×D₄×C₂₃	—	2	1	no	—
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	C₂³	1	2	yes	—
165	C₄×D₄×C₂₃	C₂³	1	4	yes	—
166	C₄×D₄×C₂₃	C₂³	1	4	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂₃×#117	—	2	2	no	—
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	—	2	4	no	—
173	C₂₃×#117	—	2	1	no	—
174	C₂₃×#117	C₂³	1	2	yes	—
175	C₂₃×#117	C₂³	1	1	yes	characteristic
176	C₂₃×#117	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
178	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
184	C₂×C₄²×C₂₃	—	2	1	no	—
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂₃×#107	C₂³	1	2	yes	—
187	C₂₃×#107	C₂³	1	2	yes	—
188	C₂₃×#107	C₂³	1	2	yes	—
189	C₂₃×#106	C₂³	1	2	yes	—
190	C₂₃×#106	C₂³	1	2	yes	—
191	C₂₃×#106	C₂³	1	2	yes	—
192	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₂₃×#103	C₂³	1	4	yes	—
198	C₂₃×#103	C₂³	1	4	yes	—
199	C₂₃×#103	C₂³	1	2	yes	—
200	C₂₃×#103	C₂³	1	2	yes	—
201	C₂₃×#103	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	4	yes	—
203	C₂₃×#103	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	2	yes	—
207	C₂₃×#102	C₂³	1	2	yes	—
208	C₂₃×#102	C₂³	1	2	yes	—
209	C₂₃×#102	C₂³	1	2	yes	—
210	C₂₃×#102	C₂³	1	2	yes	—
211	C₂₃×#97	C₂³	1	2	yes	—
212	C₂₃×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₂₃	C₂³	1	2	yes	—
214	C₄×C₈×C₂₃	C₂³	1	4	yes	—
215	C₂⁴×C₂₃	—	2	1	no	—
216	#41×C₂₃	—	2	2	no	—
217	#41×C₂₃	—	2	2	no	—
218	C₂×Q₈×C₂₃	—	2	2	no	—
219	C₂×Q₈×C₂₃	—	2	1	no	—
220	C₂×Q₈×C₂₃	—	2	1	no	—
221	C₂×Q₈×C₂₃	—	2	4	no	—
222	C₂×Q₈×C₂₃	—	2	4	no	—
223	C₂×Q₈×C₂₃	—	2	4	no	—
224	C₂×Q₈×C₂₃	—	8	4	no	—
225	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
228	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	1	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	#41	1	4	yes	—
233	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₂₃	—	2	2	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	1	no	—
238	C₂²×C₄×C₂₃	—	2	1	no	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	2	no	—
241	C₂²×C₄×C₂₃	—	2	4	no	—
242	C₂²×C₄×C₂₃	—	2	4	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	8	2	no	—
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	SD₁₆×C₂₃	—	2	8	no	—
249	SD₁₆×C₂₃	—	2	8	no	—
250	SD₁₆×C₂₃	—	2	4	no	—
251	D₈×C₂₃	—	2	4	no	—
252	M₁₆×C₂₃	—	2	2	no	—
253	M₁₆×C₂₃	—	2	2	no	—
254	C₂×C₈×C₂₃	—	2	4	no	—
255	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₂₃	—	2	2	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	2	no	—
262	C₄⋊C₄×C₂₃	—	2	2	no	—
263	C₄⋊C₄×C₂₃	—	2	4	no	—
264	C₄⋊C₄×C₂₃	—	2	4	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	4	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²⋊C₄×C₂₃	—	2	2	no	—
289	C₂²⋊C₄×C₂₃	—	2	1	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂²⋊C₄×C₂₃	—	2	4	no	—
297	C₂²⋊C₄×C₂₃	—	2	4	no	—
298	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
299	C₄²×C₂₃	—	2	1	no	—
300	C₄²×C₂₃	—	2	1	no	—
301	C₄²×C₂₃	—	2	1	no	—
302	C₄²×C₂₃	—	2	4	no	—
303	C₄²×C₂₃	—	2	4	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	C₂⁴	1	1	yes	characteristic
308	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₄²×C₂₃	C₂⁴	1	4	yes	—
310	#61340	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂³×C₂₃	—	2	2	no	—
312	C₂³×C₂₃	—	2	4	no	—
313	C₂³×C₂₃	—	2	1	no	—
314	C₂³×C₂₃	—	8	1	no	—
315	C₂³×C₂₃	—	8	1	no	—
316	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₂₃	—	2	4	no	—
318	Q₈×C₂₃	—	2	4	no	—
319	Q₈×C₂₃	—	2	1	no	—
320	Q₈×C₂₃	—	2	4	no	—
321	Q₈×C₂₃	—	2	1	no	—
322	Q₈×C₂₃	—	4	2	no	—
323	Q₈×C₂₃	—	4	4	no	—
324	Q₈×C₂₃	—	4	2	no	—
325	Q₈×C₂₃	—	8	1	no	—
326	Q₈×C₂₃	—	8	4	no	—
327	D₄×C₂₃	—	2	4	no	—
328	D₄×C₂₃	—	2	1	no	—
329	D₄×C₂₃	—	2	2	no	—
330	D₄×C₂₃	—	2	1	no	—
331	D₄×C₂₃	—	4	2	no	—
332	D₄×C₂₃	C₂×#41	1	4	yes	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	4	no	—
337	C₂×C₄×C₂₃	—	2	1	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	2	no	—
343	C₂×C₄×C₂₃	—	4	4	no	—
344	C₂×C₄×C₂₃	—	4	2	no	—
345	C₂×C₄×C₂₃	—	4	2	no	—
346	C₂×C₄×C₂₃	—	4	4	no	—
347	C₂×C₄×C₂₃	—	8	4	no	—
348	C₂×C₄×C₂₃	—	8	2	no	—
349	C₂×C₄×C₂₃	—	8	4	no	—
350	C₂×C₄×C₂₃	—	8	1	no	—
351	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
353	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
359	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
360	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
361	C₈×C₂₃	—	2	2	no	—
362	C₈×C₂₃	—	2	2	no	—
363	C₈×C₂₃	—	2	2	no	—
364	C₈×C₂₃	—	2	2	no	—
365	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#3501	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#3376	C₂×C₂₃	1	4	yes	complemented
368	#3372	C₂×C₂₃	1	2	yes	complemented
369	#3372	C₂×C₂₃	1	4	yes	complemented
370	#3367	C₂×C₂₃	1	2	yes	complemented
371	#3360	C₂×C₂₃	1	2	yes	complemented
372	#3359	C₂×C₂₃	1	2	yes	complemented
373	#3139	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#3137	C₂×C₂₃	1	2	yes	complemented
375	#3082	C₂×C₂₃	1	2	yes	complemented
376	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#3042	C₂×C₂₃	1	2	yes	—
378	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2949	C₂×C₂₃	1	2	yes	complemented
381	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic
382	C₂²×C₂₃	—	2	1	no	—
383	C₂²×C₂₃	—	2	1	no	—
384	C₂²×C₂₃	—	2	4	no	—
385	C₂²×C₂₃	—	4	2	no	—
386	C₂²×C₂₃	—	4	2	no	—
387	C₂²×C₂₃	—	4	1	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	4	1	no	—
390	C₂²×C₂₃	—	8	4	no	—
391	C₂²×C₂₃	#548	1	2	yes	—
392	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₂₃	—	2	1	no	—
394	C₄×C₂₃	—	2	1	no	—
395	C₄×C₂₃	—	2	4	no	—
396	C₄×C₂₃	—	2	1	no	—
397	C₄×C₂₃	—	2	4	no	—
398	C₄×C₂₃	—	4	1	no	—
399	C₄×C₂₃	—	4	2	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	—	4	4	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	2	no	—
404	C₄×C₂₃	—	4	2	no	—
405	C₄×C₂₃	#548	1	2	yes	—
406	C₄×C₂₃	#577	1	2	yes	—
407	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
408	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
410	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
411	#557	C₂²×C₂₃	1	2	yes	complemented
412	#557	C₂²×C₂₃	1	2	yes	complemented
413	#556	C₂²×C₂₃	1	2	yes	complemented
414	#556	C₂²×C₂₃	1	2	yes	complemented
415	#554	—	2	1	no	—
416	#554	—	2	2	no	—
417	#554	C₂²×C₂₃	1	2	yes	—
418	#554	C₂²×C₂₃	1	4	yes	—
419	#552	—	2	2	no	—
420	#552	—	2	2	no	—
421	D₄×Q₈	—	2	1	no	—
422	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
423	#544	C₂²×C₂₃	1	2	yes	—
424	#543	—	2	2	no	—
425	#541	—	2	2	no	—
426	#536	C₂²×C₂₃	1	2	yes	—
427	#533	—	2	1	no	—
428	#533	—	2	1	no	—
429	#533	C₂²×C₂₃	1	1	yes	characteristic
430	#533	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	—	2	2	no	—
433	#519	C₂²×C₂₃	1	2	yes	—
434	#518	C₂²×C₂₃	1	2	yes	—
435	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
437	#491	C₂²×C₂₃	1	4	yes	complemented
438	#491	C₂²×C₂₃	1	4	yes	complemented
439	#489	C₂²×C₂₃	1	4	yes	complemented
440	#488	C₂²×C₂₃	1	4	yes	complemented
441	#487	C₂²×C₂₃	1	2	yes	complemented
442	#487	C₂²×C₂₃	1	4	yes	complemented
443	#487	C₂²×C₂₃	1	2	yes	complemented
444	#479	C₂²×C₂₃	1	2	yes	complemented
445	#479	C₂²×C₂₃	1	4	yes	complemented
446	#479	C₂²×C₂₃	1	4	yes	complemented
447	#478	C₂²×C₂₃	1	2	yes	complemented
448	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#477	C₂²×C₂₃	1	4	yes	complemented
450	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	#475	C₂²×C₂₃	1	4	yes	complemented
453	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#463	C₂²×C₂₃	1	4	yes	—
455	#463	C₂²×C₂₃	1	4	yes	—
456	#461	C₂²×C₂₃	1	2	yes	—
457	#461	C₂²×C₂₃	1	4	yes	—
458	#461	C₂²×C₂₃	1	2	yes	—
459	#461	C₂²×C₂₃	1	4	yes	—
460	#461	C₂²×C₂₃	1	4	yes	—
461	#446	C₂²×C₂₃	1	2	yes	complemented
462	#446	C₂²×C₂₃	1	4	yes	complemented
463	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
464	#442	C₂²×C₂₃	1	2	yes	—
465	#440	C₂²×C₂₃	1	4	yes	—
466	#440	C₂²×C₂₃	1	2	yes	—
467	#440	C₂²×C₂₃	1	4	yes	—
468	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
469	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
470	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
471	C₄×D₈	C₂²×C₂₃	1	2	yes	—
472	#428	C₂²×C₂₃	1	1	yes	characteristic
473	#427	C₂²×C₂₃	1	2	yes	—
474	#424	C₂²×C₂₃	1	2	yes	—
475	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
476	#419	C₂²×C₂₃	1	2	yes	—
477	#419	C₂²×C₂₃	1	2	yes	—
478	#418	C₂²×C₂₃	1	1	yes	characteristic
479	#417	C₂²×C₂₃	1	1	yes	characteristic
480	#416	C₂²×C₂₃	1	2	yes	—
481	C₂×#103	C₂²×C₂₃	1	2	yes	—
482	#405	C₂²×C₂₃	1	2	yes	—
483	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×C₂₃	—	2	2	no	—
485	C₂×C₂₃	—	4	4	no	—
486	C₂×C₂₃	—	8	1	no	—
487	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
488	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
489	C₂×C₂₃	#3586	1	1	yes	characteristic
490	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
491	C₂²×Q₈	—	2	2	no	—
492	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
493	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
494	C₂³×C₄	—	2	1	no	—
495	AGL(1,ℤ/8)	—	2	4	no	—
496	C₂×SD₁₆	—	2	8	no	—
497	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
498	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
499	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
500	C₂×D₈	C₂³×C₂₃	1	2	yes	—
501	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
508	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
510	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
511	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
515	#126	—	2	4	no	—
516	#126	—	2	4	no	—
517	#125	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	4	no	—
520	#125	—	2	4	no	—
521	#125	—	2	2	no	—
522	#125	D₄×C₂₃	1	2	yes	—
523	#125	C₂³×C₂₃	1	2	yes	—
524	#125	C₂³×C₂₃	1	4	yes	—
525	#124	C₂³×C₂₃	1	4	yes	—
526	#123	—	2	4	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
542	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
550	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
552	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
553	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
554	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	C₂³×C₂₃	1	2	yes	—
562	C₄×D₄	C₂³×C₂₃	1	2	yes	—
563	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
564	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
565	C₄×D₄	C₂³×C₂₃	1	4	yes	—
566	C₄×D₄	C₂³×C₂₃	1	4	yes	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	—	2	4	no	—
570	#117	—	2	1	no	—
571	#117	C₂³×C₂₃	1	1	yes	characteristic
572	#117	C₂³×C₂₃	1	2	yes	—
573	#117	C₂³×C₂₃	1	2	yes	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	4	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	4	no	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
583	#107	C₂³×C₂₃	1	2	yes	—
584	#107	C₂³×C₂₃	1	2	yes	—
585	#107	C₂³×C₂₃	1	2	yes	—
586	#106	C₂³×C₂₃	1	2	yes	—
587	#106	C₂³×C₂₃	1	2	yes	—
588	#106	C₂³×C₂₃	1	2	yes	—
589	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
590	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
592	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
593	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
594	#103	C₂³×C₂₃	1	4	yes	—
595	#103	C₂³×C₂₃	1	4	yes	—
596	#103	C₂³×C₂₃	1	2	yes	—
597	#103	C₂³×C₂₃	1	2	yes	—
598	#103	C₂³×C₂₃	1	2	yes	—
599	#103	C₂³×C₂₃	1	4	yes	—
600	#103	C₂³×C₂₃	1	4	yes	—
601	#103	C₂³×C₂₃	1	4	yes	—
602	#103	C₂³×C₂₃	1	4	yes	—
603	#102	C₂³×C₂₃	1	2	yes	—
604	#102	C₂³×C₂₃	1	2	yes	—
605	#102	C₂³×C₂₃	1	2	yes	—
606	#102	C₂³×C₂₃	1	2	yes	—
607	#102	C₂³×C₂₃	1	2	yes	—
608	#97	C₂³×C₂₃	1	2	yes	—
609	#97	C₂³×C₂₃	1	4	yes	—
610	C₄×C₈	C₂³×C₂₃	1	2	yes	—
611	C₄×C₈	C₂³×C₂₃	1	4	yes	—
612	C₂₃	#61340	1	1	yes	characteristic, direct product factor, Sylow
613	C₂⁴	—	2	1	no	—
614	#41	—	2	2	no	—
615	#41	—	2	2	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	4	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	8	4	no	—
623	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
624	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
626	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	#41×C₂₃	1	4	yes	—
631	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
632	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	8	2	no	—
643	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	2	8	no	—
648	SD₁₆	—	2	4	no	—
649	D₈	—	2	4	no	—
650	M₁₆	—	2	2	no	—
651	M₁₆	—	2	2	no	—
652	C₂×C₈	—	2	4	no	—
653	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
654	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
656	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
677	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
704	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
705	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
706	C₄²	C₂⁴×C₂₃	1	4	yes	—
707	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	1	no	—
713	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
714	Q₈	—	2	4	no	—
715	Q₈	—	2	4	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	4	no	—
718	Q₈	—	2	1	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	4	4	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	8	4	no	—
723	Q₈	—	8	1	no	—
724	D₄	—	2	4	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	1	no	—
728	D₄	—	4	2	no	—
729	D₄	C₂×#41×C₂₃	1	4	yes	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	2	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	4	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
751	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
755	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
756	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
757	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	8	4	no	—
771	C₂²	C₂₃×#548	1	2	yes	—
772	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	4	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	4	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	2	no	—
785	C₄	C₂₃×#548	1	2	yes	—
786	C₄	C₂₃×#577	1	2	yes	—
787	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
788	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
789	C₂	—	2	2	no	—
790	C₂	—	4	4	no	—
791	C₂	—	8	1	no	—
792	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
793	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
794	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3509	C₂	semidirect
2. C₂₃×#3501	C₂	semidirect
3. C₂₃×#3376	C₂	semidirect
4. C₂₃×#3372	C₂	semidirect
5. C₂₃×#3372	C₂	semidirect
6. C₂₃×#3367	C₂	semidirect
7. C₂₃×#3360	C₂	semidirect
8. C₂₃×#3359	C₂	semidirect
9. C₂₃×#3139	C₂	semidirect
10. C₂₃×#3137	C₂	semidirect
11. C₂₃×#3082	C₂	semidirect
12. C₂₃×#3076	C₂	semidirect
14. C₂×C₂₃×#461	C₂	semidirect
15. C₂₃×#2962	C₂	semidirect
16. C₂₃×#2949	C₂	semidirect
20. C₂₃×#557	C₂²	semidirect
21. C₂₃×#557	C₂²	semidirect
22. C₂₃×#556	C₂²	semidirect
23. C₂₃×#556	C₂²	semidirect
46. C₂₃×#491	C₂²	semidirect
47. C₂₃×#491	C₂²	semidirect
48. C₂₃×#489	C₂²	semidirect
49. C₂₃×#488	C₂²	semidirect
50. C₂₃×#487	C₂²	semidirect
51. C₂₃×#487	C₂²	semidirect
52. C₂₃×#487	C₂²	semidirect
53. C₂₃×#479	C₂²	semidirect
54. C₂₃×#479	C₂²	semidirect
55. C₂₃×#479	C₂²	semidirect
56. C₂₃×#478	C₂²	semidirect
57. C₂₃×#477	C₂²	semidirect
58. C₂₃×#477	C₂²	semidirect
59. C₂₃×#476	C₂²	semidirect
60. C₂₃×#475	C₂²	semidirect
61. C₂₃×#475	C₂²	semidirect
62. C₂₃×#474	C₂²	semidirect
70. C₂₃×#446	C₂²	semidirect
71. C₂₃×#446	C₂²	semidirect
72. C₈×Q₈×C₂₃	C₂²	semidirect
310. #61340	C₂₃	direct (N × H)
365. #3509	C₂×C₂₃	semidirect
366. #3501	C₂×C₂₃	semidirect
367. #3376	C₂×C₂₃	semidirect
368. #3372	C₂×C₂₃	semidirect
369. #3372	C₂×C₂₃	semidirect
370. #3367	C₂×C₂₃	semidirect
371. #3360	C₂×C₂₃	semidirect
372. #3359	C₂×C₂₃	semidirect
373. #3139	C₂×C₂₃	semidirect
374. #3137	C₂×C₂₃	semidirect
375. #3082	C₂×C₂₃	semidirect
376. #3076	C₂×C₂₃	semidirect
378. C₂×#461	C₂×C₂₃	semidirect
379. #2962	C₂×C₂₃	semidirect
380. #2949	C₂×C₂₃	semidirect
411. #557	C₂²×C₂₃	semidirect
412. #557	C₂²×C₂₃	semidirect
413. #556	C₂²×C₂₃	semidirect
414. #556	C₂²×C₂₃	semidirect
437. #491	C₂²×C₂₃	semidirect
438. #491	C₂²×C₂₃	semidirect
439. #489	C₂²×C₂₃	semidirect
440. #488	C₂²×C₂₃	semidirect
441. #487	C₂²×C₂₃	semidirect
442. #487	C₂²×C₂₃	semidirect
443. #487	C₂²×C₂₃	semidirect
444. #479	C₂²×C₂₃	semidirect
445. #479	C₂²×C₂₃	semidirect
446. #479	C₂²×C₂₃	semidirect
447. #478	C₂²×C₂₃	semidirect
448. #477	C₂²×C₂₃	semidirect
449. #477	C₂²×C₂₃	semidirect
450. #476	C₂²×C₂₃	semidirect
451. #475	C₂²×C₂₃	semidirect
452. #475	C₂²×C₂₃	semidirect
453. #474	C₂²×C₂₃	semidirect
461. #446	C₂²×C₂₃	semidirect
462. #446	C₂²×C₂₃	semidirect
463. C₈×Q₈	C₂²×C₂₃	semidirect
612. C₂₃	#61340	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×#3509	2
C₂₃×#3501	2
C₂₃×#3376	2
C₂₃×#3372	2
C₂₃×#3367	2
C₂₃×#3360	2
C₂₃×#3359	2
C₂₃×#3139	2
C₂₃×#3137	2
C₂₃×#3082	2
C₂₃×#3076	2
C₂₃×#3042	2
C₂×C₂₃×#461	2
C₂₃×#2962	2
C₂₃×#2949	2
C₄×C₂₃×AGL(1,ℤ/8)	2
#61340	23

Subgroups — C23×#61340 #19208966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61340 #19208966