Subgroups — C₂₃×#61278 #19208904

Order 5888.

1860 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3354	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3347	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3346	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3340	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3334	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3098	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2913	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#131	C₂²	1	2	yes	—
20	C₂₃×#559	—	2	2	no	—
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#556	C₂²	1	2	yes	complemented
23	C₂₃×#555	C₂²	1	2	yes	—
24	C₂₃×#555	C₂²	1	2	yes	complemented
25	C₂₃×#554	C₂²	1	2	yes	complemented
26	C₂₃×#553	—	2	2	no	—
27	C₂₃×#553	C₂²	1	4	yes	—
28	C₂₃×#550	—	2	1	no	—
29	C₂₃×#548	—	2	2	no	—
30	C₂₃×#547	C₂²	1	2	yes	—
31	C₂₃×#547	C₂²	1	2	yes	complemented
32	C₂₃×#542	—	2	2	no	—
33	C₂₃×#538	—	2	2	no	—
34	C₂₃×#537	C₂²	1	2	yes	—
35	C₂₃×#535	C₂²	1	2	yes	—
36	C₂₃×#533	—	2	1	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#532	—	2	1	no	—
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂₃×#525	—	2	2	no	—
42	C₂₃×#520	C₂²	1	2	yes	—
43	C₂₃×#520	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×#501	C₂²	1	4	yes	complemented
47	C₂₃×#500	C₂²	1	2	yes	complemented
48	C₂₃×#498	C₂²	1	2	yes	complemented
49	C₂₃×#485	C₂²	1	4	yes	complemented
50	C₂₃×#484	C₂²	1	4	yes	complemented
51	C₂₃×#482	C₂²	1	4	yes	—
52	C₂₃×#482	C₂²	1	4	yes	—
53	C₂₃×#482	C₂²	1	4	yes	complemented
54	C₂₃×#481	C₂²	1	4	yes	—
55	C₂₃×#480	C₂²	1	4	yes	—
56	C₂₃×#480	C₂²	1	4	yes	complemented
57	C₂₃×#479	C₂²	1	2	yes	complemented
58	C₂₃×#478	C₂²	1	2	yes	complemented
59	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#474	C₂²	1	2	yes	—
63	C₂₃×#474	C₂²	1	4	yes	—
64	C₂₃×#474	C₂²	1	2	yes	—
65	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#469	C₂²	1	4	yes	—
67	C₂₃×#468	C₂²	1	4	yes	—
68	C₂₃×#466	C₂²	1	4	yes	—
69	C₂₃×#465	C₂²	1	4	yes	—
70	C₂₃×#442	C₂²	1	2	yes	—
71	C₂₃×#440	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
73	C₄×D₈×C₂₃	C₂²	1	2	yes	—
74	C₂₃×#436	C₂²	1	2	yes	complemented
75	C₂₃×#435	C₂²	1	4	yes	complemented
76	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
77	C₂₃×#428	C₂²	1	2	yes	—
78	C₂₃×#428	C₂²	1	2	yes	—
79	C₂₃×#428	C₂²	1	1	yes	characteristic
80	C₂₃×#428	C₂²	1	4	yes	complemented
81	C₂₃×#428	C₂²	1	4	yes	complemented
82	C₂₃×#427	C₂²	1	2	yes	—
83	C₂₃×#427	C₂²	1	4	yes	complemented
84	C₂×C₂₃×#107	C₂²	1	2	yes	—
85	C₂×C₂₃×#107	C₂²	1	4	yes	complemented
86	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#102	C₂²	1	2	yes	—
91	C₂₃×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₂₃	—	2	2	no	—
94	C₂×#41×C₂₃	—	2	2	no	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	—	2	1	no	—
100	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
101	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×D₈×C₂₃	C₂³	1	2	yes	—
103	C₂₃×#131	—	2	8	no	—
104	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×#127	—	2	2	no	—
117	C₂₃×#127	D₄	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	C₂³	1	2	yes	—
122	C₂₃×#124	—	2	2	no	—
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#124	—	2	4	no	—
125	C₂₃×#124	—	2	4	no	—
126	C₂₃×#124	D₄	1	2	yes	—
127	C₂₃×#123	—	2	4	no	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	1	no	—
132	C₂₃×C₂²⋊Q₈	—	2	1	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	4	no	—
136	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₂₃×#121	—	2	4	no	—
138	C₂₃×#121	—	2	4	no	—
139	C₂₃×#121	—	2	2	no	—
140	C₂₃×#121	—	2	2	no	—
141	C₂₃×#121	—	2	2	no	—
142	C₂₃×#121	D₄	1	2	yes	—
143	C₂₃×#121	D₄	1	2	yes	—
144	C₂₃×#121	C₂³	1	4	yes	—
145	C₂₃×#121	C₂³	1	4	yes	—
146	C₂₃×#121	C₂³	1	4	yes	—
147	C₂₃×#120	—	2	4	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	2	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	—	2	1	no	—
153	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₄×D₄×C₂₃	—	2	4	no	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	2	no	—
158	C₄×D₄×C₂₃	—	2	4	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	1	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	4	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₄×D₄×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	—	2	2	no	—
173	C₂₃×#117	—	2	1	no	—
174	C₂₃×#117	C₂³	1	4	yes	—
175	C₂₃×#117	C₂³	1	4	yes	—
176	C₂₃×#117	C₂³	1	2	yes	—
177	C₂₃×#117	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
184	C₂×C₄²×C₂₃	—	2	1	no	—
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂₃×#107	C₂³	1	4	yes	—
187	C₂₃×#107	C₂³	1	4	yes	—
188	C₂₃×#107	C₂³	1	2	yes	—
189	C₂₃×#107	C₂³	1	2	yes	—
190	C₂₃×#107	C₂³	1	4	yes	—
191	C₂₃×#107	C₂³	1	2	yes	—
192	C₂₃×#107	C₂³	1	4	yes	—
193	C₂₃×#106	C₂³	1	2	yes	—
194	C₂₃×#106	C₂³	1	2	yes	—
195	C₂₃×#106	C₂³	1	2	yes	—
196	C₂₃×#106	C₂³	1	4	yes	—
197	C₂₃×#106	C₂³	1	4	yes	—
198	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
200	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₂₃×#103	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	2	yes	—
203	C₂₃×#103	C₂³	1	2	yes	—
204	C₂₃×#102	C₂³	1	4	yes	—
205	C₂₃×#102	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×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₂₃×#97	C₂³	1	2	yes	—
214	C₄×C₈×C₂₃	C₂³	1	2	yes	—
215	C₂⁴×C₂₃	—	2	1	no	—
216	#41×C₂₃	—	2	4	no	—
217	#41×C₂₃	—	2	4	no	—
218	#41×C₂₃	—	2	2	no	—
219	#41×C₂₃	—	2	2	no	—
220	#41×C₂₃	—	8	4	no	—
221	#41×C₂₃	—	8	4	no	—
222	C₂×Q₈×C₂₃	—	2	1	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	2	1	no	—
225	C₂×Q₈×C₂₃	—	2	2	no	—
226	C₂×Q₈×C₂₃	—	8	2	no	—
227	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	4	no	—
231	C₂×D₄×C₂₃	—	2	4	no	—
232	C₂×D₄×C₂₃	—	2	4	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	2	2	no	—
236	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₂₃	—	2	1	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	4	no	—
245	C₂²×C₄×C₂₃	—	2	4	no	—
246	C₂²×C₄×C₂₃	—	2	1	no	—
247	C₂²×C₄×C₂₃	—	2	1	no	—
248	C₂²×C₄×C₂₃	—	2	1	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	8	2	no	—
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	SD₁₆×C₂₃	—	2	4	no	—
257	D₈×C₂₃	—	2	4	no	—
258	M₁₆×C₂₃	—	2	2	no	—
259	M₁₆×C₂₃	—	2	8	no	—
260	M₁₆×C₂₃	#41	1	4	yes	complemented
261	C₂×C₈×C₂₃	—	2	4	no	—
262	C₂×C₈×C₂₃	—	2	8	no	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
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	1	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂²⋊C₄×C₂₃	—	2	4	no	—
298	C₂²⋊C₄×C₂₃	—	2	4	no	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
302	C₄²×C₂₃	—	2	1	no	—
303	C₄²×C₂₃	—	2	1	no	—
304	C₄²×C₂₃	—	2	1	no	—
305	C₄²×C₂₃	—	2	4	no	—
306	C₄²×C₂₃	—	2	4	no	—
307	C₄²×C₂₃	—	2	2	no	—
308	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
312	#61278	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂³×C₂₃	—	2	1	no	—
314	C₂³×C₂₃	—	2	2	no	—
315	C₂³×C₂₃	—	4	2	no	—
316	C₂³×C₂₃	—	8	1	no	—
317	C₂³×C₂₃	—	8	1	no	—
318	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
319	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₂₃	—	2	4	no	—
321	Q₈×C₂₃	—	2	1	no	—
322	Q₈×C₂₃	—	2	1	no	—
323	Q₈×C₂₃	—	4	4	no	—
324	Q₈×C₂₃	—	4	2	no	—
325	Q₈×C₂₃	—	8	1	no	—
326	Q₈×C₂₃	—	8	2	no	—
327	D₄×C₂₃	—	2	8	no	—
328	D₄×C₂₃	—	2	4	no	—
329	D₄×C₂₃	—	2	4	no	—
330	D₄×C₂₃	—	2	1	no	—
331	D₄×C₂₃	—	2	2	no	—
332	D₄×C₂₃	—	2	2	no	—
333	D₄×C₂₃	—	2	1	no	—
334	D₄×C₂₃	—	4	2	no	—
335	D₄×C₂₃	—	4	2	no	—
336	D₄×C₂₃	—	4	2	no	—
337	D₄×C₂₃	—	8	4	no	—
338	D₄×C₂₃	—	8	4	no	—
339	D₄×C₂₃	—	8	4	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	4	no	—
342	C₂×C₄×C₂₃	—	2	4	no	—
343	C₂×C₄×C₂₃	—	2	1	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	4	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	2	no	—
352	C₂×C₄×C₂₃	—	4	2	no	—
353	C₂×C₄×C₂₃	—	4	4	no	—
354	C₂×C₄×C₂₃	—	4	2	no	—
355	C₂×C₄×C₂₃	—	8	2	no	—
356	C₂×C₄×C₂₃	—	8	1	no	—
357	C₂×C₄×C₂₃	—	8	2	no	—
358	C₂×C₄×C₂₃	—	8	4	no	—
359	C₂×C₄×C₂₃	—	8	4	no	—
360	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
367	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
368	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
369	C₈×C₂₃	—	2	2	no	—
370	C₈×C₂₃	—	2	2	no	—
371	C₈×C₂₃	—	2	2	no	—
372	C₈×C₂₃	C₂×#41	1	4	yes	—
373	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#3354	C₂×C₂₃	1	2	yes	complemented
376	#3353	C₂×C₂₃	1	2	yes	complemented
377	#3347	C₂×C₂₃	1	4	yes	complemented
378	#3346	C₂×C₂₃	1	4	yes	complemented
379	#3340	C₂×C₂₃	1	2	yes	complemented
380	#3334	C₂×C₂₃	1	2	yes	complemented
381	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#3098	C₂×C₂₃	1	2	yes	complemented
383	#3096	C₂×C₂₃	1	2	yes	complemented
384	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
385	C₂×#474	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#3062	C₂×C₂₃	1	2	yes	complemented
387	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#2913	C₂×C₂₃	1	2	yes	complemented
390	C₂²×C₂₃	—	2	1	no	—
391	C₂²×C₂₃	—	2	1	no	—
392	C₂²×C₂₃	—	2	4	no	—
393	C₂²×C₂₃	—	2	4	no	—
394	C₂²×C₂₃	—	2	4	no	—
395	C₂²×C₂₃	—	4	1	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	4	1	no	—
398	C₂²×C₂₃	—	4	2	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	4	1	no	—
401	C₂²×C₂₃	—	8	4	no	—
402	C₂²×C₂₃	#547	1	2	yes	—
403	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₂₃	—	2	1	no	—
405	C₄×C₂₃	—	2	1	no	—
406	C₄×C₂₃	—	2	4	no	—
407	C₄×C₂₃	—	2	1	no	—
408	C₄×C₂₃	—	4	1	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	4	1	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	1	no	—
413	C₄×C₂₃	—	4	2	no	—
414	C₄×C₂₃	—	4	4	no	—
415	C₄×C₂₃	#547	1	2	yes	—
416	C₄×C₂₃	#576	1	2	yes	—
417	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
418	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#131	C₂²×C₂₃	1	2	yes	—
421	#559	—	2	2	no	—
422	#556	—	2	1	no	—
423	#556	C₂²×C₂₃	1	2	yes	complemented
424	#555	C₂²×C₂₃	1	2	yes	—
425	#555	C₂²×C₂₃	1	2	yes	complemented
426	#554	C₂²×C₂₃	1	2	yes	complemented
427	#553	—	2	2	no	—
428	#553	C₂²×C₂₃	1	4	yes	—
429	#550	—	2	1	no	—
430	#548	—	2	2	no	—
431	#547	C₂²×C₂₃	1	2	yes	—
432	#547	C₂²×C₂₃	1	2	yes	complemented
433	#542	—	2	2	no	—
434	#538	—	2	2	no	—
435	#537	C₂²×C₂₃	1	2	yes	—
436	#535	C₂²×C₂₃	1	2	yes	—
437	#533	—	2	1	no	—
438	#533	C₂²×C₂₃	1	1	yes	characteristic
439	#532	—	2	1	no	—
440	#532	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
442	#525	—	2	2	no	—
443	#520	C₂²×C₂₃	1	2	yes	—
444	#520	C₂²×C₂₃	1	2	yes	—
445	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
447	#501	C₂²×C₂₃	1	4	yes	complemented
448	#500	C₂²×C₂₃	1	2	yes	complemented
449	#498	C₂²×C₂₃	1	2	yes	complemented
450	#485	C₂²×C₂₃	1	4	yes	complemented
451	#484	C₂²×C₂₃	1	4	yes	complemented
452	#482	C₂²×C₂₃	1	4	yes	—
453	#482	C₂²×C₂₃	1	4	yes	—
454	#482	C₂²×C₂₃	1	4	yes	complemented
455	#481	C₂²×C₂₃	1	4	yes	—
456	#480	C₂²×C₂₃	1	4	yes	—
457	#480	C₂²×C₂₃	1	4	yes	complemented
458	#479	C₂²×C₂₃	1	2	yes	complemented
459	#478	C₂²×C₂₃	1	2	yes	complemented
460	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	#474	C₂²×C₂₃	1	2	yes	—
464	#474	C₂²×C₂₃	1	4	yes	—
465	#474	C₂²×C₂₃	1	2	yes	—
466	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	#469	C₂²×C₂₃	1	4	yes	—
468	#468	C₂²×C₂₃	1	4	yes	—
469	#466	C₂²×C₂₃	1	4	yes	—
470	#465	C₂²×C₂₃	1	4	yes	—
471	#442	C₂²×C₂₃	1	2	yes	—
472	#440	C₂²×C₂₃	1	2	yes	—
473	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
474	C₄×D₈	C₂²×C₂₃	1	2	yes	—
475	#436	C₂²×C₂₃	1	2	yes	complemented
476	#435	C₂²×C₂₃	1	4	yes	complemented
477	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
478	#428	C₂²×C₂₃	1	2	yes	—
479	#428	C₂²×C₂₃	1	2	yes	—
480	#428	C₂²×C₂₃	1	1	yes	characteristic
481	#428	C₂²×C₂₃	1	4	yes	complemented
482	#428	C₂²×C₂₃	1	4	yes	complemented
483	#427	C₂²×C₂₃	1	2	yes	—
484	#427	C₂²×C₂₃	1	4	yes	complemented
485	C₂×#107	C₂²×C₂₃	1	2	yes	—
486	C₂×#107	C₂²×C₂₃	1	4	yes	complemented
487	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
488	#418	C₂²×C₂₃	1	1	yes	characteristic
489	#417	C₂²×C₂₃	1	1	yes	characteristic
490	#416	C₂²×C₂₃	1	2	yes	—
491	C₂×#102	C₂²×C₂₃	1	2	yes	—
492	#408	C₂²×C₂₃	1	2	yes	—
493	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×C₂₃	—	2	2	no	—
495	C₂×C₂₃	—	4	4	no	—
496	C₂×C₂₃	—	8	1	no	—
497	C₂×C₂₃	—	8	2	no	—
498	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
499	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
500	C₂×C₂₃	#3586	1	1	yes	characteristic
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×#41	C₂³×C₂₃	1	2	yes	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	AGL(1,ℤ/8)	—	2	4	no	—
509	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
510	C₂×D₈	C₂³×C₂₃	1	2	yes	—
511	#131	—	2	8	no	—
512	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
513	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
514	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
516	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
521	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
523	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
524	#127	—	2	2	no	—
525	#127	D₄×C₂₃	1	1	yes	characteristic
526	#126	—	2	4	no	—
527	#126	—	2	4	no	—
528	#125	—	2	2	no	—
529	#125	C₂³×C₂₃	1	2	yes	—
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#124	—	2	4	no	—
533	#124	—	2	4	no	—
534	#124	D₄×C₂₃	1	2	yes	—
535	#123	—	2	4	no	—
536	#123	—	2	4	no	—
537	#123	—	2	4	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	D₄×C₂₃	1	2	yes	—
551	#121	D₄×C₂₃	1	2	yes	—
552	#121	C₂³×C₂₃	1	4	yes	—
553	#121	C₂³×C₂₃	1	4	yes	—
554	#121	C₂³×C₂₃	1	4	yes	—
555	#120	—	2	4	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	4	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	C₂³×C₂₃	1	2	yes	—
574	C₄×D₄	C₂³×C₂₃	1	2	yes	—
575	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
576	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
577	C₄×D₄	C₂³×C₂₃	1	2	yes	—
578	C₄×D₄	C₂³×C₂₃	1	2	yes	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	—	2	1	no	—
582	#117	C₂³×C₂₃	1	1	yes	characteristic
583	#117	C₂³×C₂₃	1	2	yes	—
584	#117	C₂³×C₂₃	1	4	yes	—
585	#117	C₂³×C₂₃	1	4	yes	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
590	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
594	#107	C₂³×C₂₃	1	4	yes	—
595	#107	C₂³×C₂₃	1	4	yes	—
596	#107	C₂³×C₂₃	1	2	yes	—
597	#107	C₂³×C₂₃	1	2	yes	—
598	#107	C₂³×C₂₃	1	4	yes	—
599	#107	C₂³×C₂₃	1	2	yes	—
600	#107	C₂³×C₂₃	1	4	yes	—
601	#106	C₂³×C₂₃	1	2	yes	—
602	#106	C₂³×C₂₃	1	2	yes	—
603	#106	C₂³×C₂₃	1	2	yes	—
604	#106	C₂³×C₂₃	1	4	yes	—
605	#106	C₂³×C₂₃	1	4	yes	—
606	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
608	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
609	#103	C₂³×C₂₃	1	2	yes	—
610	#103	C₂³×C₂₃	1	2	yes	—
611	#103	C₂³×C₂₃	1	2	yes	—
612	#102	C₂³×C₂₃	1	4	yes	—
613	#102	C₂³×C₂₃	1	4	yes	—
614	#102	C₂³×C₂₃	1	2	yes	—
615	#102	C₂³×C₂₃	1	2	yes	—
616	#102	C₂³×C₂₃	1	2	yes	—
617	#102	C₂³×C₂₃	1	2	yes	—
618	#102	C₂³×C₂₃	1	2	yes	—
619	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
620	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
621	#97	C₂³×C₂₃	1	2	yes	—
622	C₄×C₈	C₂³×C₂₃	1	2	yes	—
623	C₂₃	#61278	1	1	yes	characteristic, direct product factor, Sylow
624	C₂⁴	—	2	1	no	—
625	#41	—	2	4	no	—
626	#41	—	2	4	no	—
627	#41	—	2	2	no	—
628	#41	—	2	2	no	—
629	#41	—	8	4	no	—
630	#41	—	8	4	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	8	2	no	—
636	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
637	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
646	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
647	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
648	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
649	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
650	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	8	2	no	—
661	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
664	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
665	SD₁₆	—	2	4	no	—
666	D₈	—	2	4	no	—
667	M₁₆	—	2	2	no	—
668	M₁₆	—	2	8	no	—
669	M₁₆	#41×C₂₃	1	4	yes	complemented
670	C₂×C₈	—	2	4	no	—
671	C₂×C₈	—	2	8	no	—
672	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
673	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
674	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
675	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
690	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
694	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
710	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	2	no	—
717	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
720	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	8	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
727	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
728	Q₈	—	2	4	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	4	4	no	—
732	Q₈	—	4	2	no	—
733	Q₈	—	8	2	no	—
734	Q₈	—	8	1	no	—
735	D₄	—	2	8	no	—
736	D₄	—	2	4	no	—
737	D₄	—	2	4	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	1	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	2	no	—
745	D₄	—	8	4	no	—
746	D₄	—	8	4	no	—
747	D₄	—	8	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	—	8	1	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
769	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
774	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
775	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
776	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	C₂×#41×C₂₃	1	4	yes	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	4	no	—
793	C₂²	C₂₃×#547	1	2	yes	—
794	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
795	C₄	—	2	4	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	4	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	2	no	—
806	C₄	C₂₃×#547	1	2	yes	—
807	C₄	C₂₃×#576	1	2	yes	—
808	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
809	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
810	C₂	—	2	2	no	—
811	C₂	—	4	4	no	—
812	C₂	—	8	2	no	—
813	C₂	—	8	1	no	—
814	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
815	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
816	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₂₃×#3506	C₂	semidirect
3. C₂₃×#3354	C₂	semidirect
4. C₂₃×#3353	C₂	semidirect
5. C₂₃×#3347	C₂	semidirect
6. C₂₃×#3346	C₂	semidirect
7. C₂₃×#3340	C₂	semidirect
8. C₂₃×#3334	C₂	semidirect
9. C₂₃×#3165	C₂	semidirect
10. C₂₃×#3098	C₂	semidirect
11. C₂₃×#3096	C₂	semidirect
12. C₂₃×#3076	C₂	semidirect
13. C₂×C₂₃×#474	C₂	semidirect
14. C₂₃×#3062	C₂	semidirect
15. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
16. C₂₃×#2935	C₂	semidirect
17. C₂₃×#2913	C₂	semidirect
22. C₂₃×#556	C₂²	semidirect
24. C₂₃×#555	C₂²	semidirect
25. C₂₃×#554	C₂²	semidirect
31. C₂₃×#547	C₂²	semidirect
46. C₂₃×#501	C₂²	semidirect
47. C₂₃×#500	C₂²	semidirect
48. C₂₃×#498	C₂²	semidirect
49. C₂₃×#485	C₂²	semidirect
50. C₂₃×#484	C₂²	semidirect
53. C₂₃×#482	C₂²	semidirect
56. C₂₃×#480	C₂²	semidirect
57. C₂₃×#479	C₂²	semidirect
58. C₂₃×#478	C₂²	semidirect
59. C₂₃×#477	C₂²	semidirect
60. C₂₃×#476	C₂²	semidirect
61. C₂₃×#475	C₂²	semidirect
65. C₂₃×#474	C₂²	semidirect
74. C₂₃×#436	C₂²	semidirect
75. C₂₃×#435	C₂²	semidirect
76. C₈×D₄×C₂₃	C₂²	semidirect
80. C₂₃×#428	C₂²	semidirect
81. C₂₃×#428	C₂²	semidirect
83. C₂₃×#427	C₂²	semidirect
85. C₂×C₂₃×#107	C₂²	semidirect
260. M₁₆×C₂₃	#41	semidirect
312. #61278	C₂₃	direct (N × H)
373. #3511	C₂×C₂₃	semidirect
374. #3506	C₂×C₂₃	semidirect
375. #3354	C₂×C₂₃	semidirect
376. #3353	C₂×C₂₃	semidirect
377. #3347	C₂×C₂₃	semidirect
378. #3346	C₂×C₂₃	semidirect
379. #3340	C₂×C₂₃	semidirect
380. #3334	C₂×C₂₃	semidirect
381. #3165	C₂×C₂₃	semidirect
382. #3098	C₂×C₂₃	semidirect
383. #3096	C₂×C₂₃	semidirect
384. #3076	C₂×C₂₃	semidirect
385. C₂×#474	C₂×C₂₃	semidirect
386. #3062	C₂×C₂₃	semidirect
387. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
388. #2935	C₂×C₂₃	semidirect
389. #2913	C₂×C₂₃	semidirect
423. #556	C₂²×C₂₃	semidirect
425. #555	C₂²×C₂₃	semidirect
426. #554	C₂²×C₂₃	semidirect
432. #547	C₂²×C₂₃	semidirect
447. #501	C₂²×C₂₃	semidirect
448. #500	C₂²×C₂₃	semidirect
449. #498	C₂²×C₂₃	semidirect
450. #485	C₂²×C₂₃	semidirect
451. #484	C₂²×C₂₃	semidirect
454. #482	C₂²×C₂₃	semidirect
457. #480	C₂²×C₂₃	semidirect
458. #479	C₂²×C₂₃	semidirect
459. #478	C₂²×C₂₃	semidirect
460. #477	C₂²×C₂₃	semidirect
461. #476	C₂²×C₂₃	semidirect
462. #475	C₂²×C₂₃	semidirect
466. #474	C₂²×C₂₃	semidirect
475. #436	C₂²×C₂₃	semidirect
476. #435	C₂²×C₂₃	semidirect
477. C₈×D₄	C₂²×C₂₃	semidirect
481. #428	C₂²×C₂₃	semidirect
482. #428	C₂²×C₂₃	semidirect
484. #427	C₂²×C₂₃	semidirect
486. C₂×#107	C₂²×C₂₃	semidirect
623. C₂₃	#61278	direct (N × H)
669. M₁₆	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3511	2
C₂₃×#3506	2
C₂₃×#3354	2
C₂₃×#3353	2
C₂₃×#3347	2
C₂₃×#3346	2
C₂₃×#3340	2
C₂₃×#3334	2
C₂₃×#3165	2
C₂₃×#3098	2
C₂₃×#3096	2
C₂₃×#3076	2
C₂×C₂₃×#474	2
C₂₃×#3062	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#2935	2
C₂₃×#2913	2
#61278	23

Subgroups — C23×#61278 #19208904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61278 #19208904