Subgroups — C₂₃×#61341 #19208967

Order 5888.

1844 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3371	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3368	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3368	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3362	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3081	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3043	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#460	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×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
20	C₂₃×#559	C₂²	1	2	yes	—
21	C₂₃×#559	C₂²	1	2	yes	—
22	Q₈²×C₂₃	—	2	1	no	—
23	Q₈²×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#557	—	2	1	no	—
25	C₂₃×#557	—	2	2	no	—
26	C₂₃×#557	C₂²	1	2	yes	complemented
27	C₂₃×#557	C₂²	1	4	yes	complemented
28	C₂₃×#550	C₂²	1	2	yes	—
29	C₂₃×#550	C₂²	1	2	yes	—
30	C₂₃×#546	—	2	2	no	—
31	C₂₃×#546	—	2	2	no	—
32	C₂₃×#544	—	2	2	no	—
33	C₂₃×#544	C₂²	1	2	yes	—
34	C₂₃×#540	—	2	2	no	—
35	C₂₃×#535	C₂²	1	2	yes	—
36	C₂₃×#533	—	2	2	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#533	C₂²	1	1	yes	characteristic
39	C₂₃×#532	—	2	1	no	—
40	C₂₃×#532	—	2	1	no	—
41	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
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×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#490	C₂²	1	4	yes	—
47	C₂₃×#490	C₂²	1	4	yes	complemented
48	C₂₃×#489	C₂²	1	4	yes	complemented
49	C₂₃×#488	C₂²	1	4	yes	complemented
50	C₂₃×#486	C₂²	1	2	yes	—
51	C₂₃×#486	C₂²	1	2	yes	—
52	C₂₃×#486	C₂²	1	4	yes	complemented
53	C₂₃×#479	C₂²	1	2	yes	complemented
54	C₂₃×#478	C₂²	1	2	yes	complemented
55	C₂₃×#478	C₂²	1	4	yes	complemented
56	C₂₃×#478	C₂²	1	4	yes	complemented
57	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#476	C₂²	1	4	yes	complemented
60	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#474	C₂²	1	4	yes	complemented
63	C₂₃×#464	C₂²	1	4	yes	complemented
64	C₂₃×#464	C₂²	1	4	yes	complemented
65	C₂₃×#460	C₂²	1	2	yes	—
66	C₂₃×#460	C₂²	1	4	yes	—
67	C₂₃×#460	C₂²	1	2	yes	—
68	C₂₃×#460	C₂²	1	4	yes	complemented
69	C₂₃×#460	C₂²	1	4	yes	complemented
70	C₂₃×#446	C₂²	1	4	yes	complemented
71	C₂₃×#446	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
73	C₂₃×#441	C₂²	1	2	yes	complemented
74	C₂₃×#440	C₂²	1	2	yes	complemented
75	C₂₃×#440	C₂²	1	4	yes	complemented
76	C₂₃×#440	C₂²	1	4	yes	complemented
77	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
78	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
79	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
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	1	yes	characteristic
86	C₂₃×#418	C₂²	1	2	yes	—
87	C₂₃×#418	C₂²	1	2	yes	—
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×#405	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	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₂₃	—	2	1	no	—
98	C₂²×D₄×C₂₃	—	2	1	no	—
99	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
100	C₂₃×#137	—	2	4	no	—
101	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₂₃	—	2	8	no	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	—	2	4	no	—
111	C₂₃×C₄⋊Q₈	—	2	2	no	—
112	C₂₃×C₄⋊Q₈	—	2	4	no	—
113	C₂₃×C₄⋊Q₈	—	2	2	no	—
114	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₂₃×#127	—	2	1	no	—
120	C₂₃×#127	—	2	1	no	—
121	C₂₃×#127	C₂³	1	4	yes	—
122	C₂₃×#127	C₂³	1	2	yes	—
123	C₂₃×#127	C₂³	1	2	yes	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	—	2	4	no	—
126	C₂₃×#125	—	2	4	no	—
127	C₂₃×#125	—	2	4	no	—
128	C₂₃×#125	D₄	1	2	yes	—
129	C₂₃×#125	C₂³	1	4	yes	—
130	C₂₃×#125	C₂³	1	2	yes	—
131	C₂₃×#124	—	2	2	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	C₂³	1	4	yes	—
134	C₂₃×#123	—	2	4	no	—
135	C₂₃×#123	—	2	4	no	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	4	no	—
139	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₂₃×#121	—	2	2	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	4	no	—
144	C₂₃×#121	—	2	4	no	—
145	C₂₃×#121	—	2	2	no	—
146	C₂₃×#121	—	2	2	no	—
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	4	no	—
151	C₄×Q₈×C₂₃	—	2	2	no	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	1	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₂₃	C₂³	1	4	yes	—
174	C₄×D₄×C₂₃	C₂³	1	4	yes	—
175	C₂₃×#117	—	2	4	no	—
176	C₂₃×#117	—	2	1	no	—
177	C₂₃×#117	C₂³	1	2	yes	—
178	C₂₃×#117	C₂³	1	1	yes	characteristic
179	C₂₃×#117	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
183	C₂×C₄²×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	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	2	yes	—
198	C₂₃×#103	C₂³	1	2	yes	—
199	C₂₃×#103	C₂³	1	2	yes	—
200	C₂₃×#103	C₂³	1	2	yes	—
201	C₂₃×#103	C₂³	1	2	yes	—
202	C₂₃×#102	C₂³	1	4	yes	—
203	C₂₃×#102	C₂³	1	4	yes	—
204	C₂₃×#102	C₂³	1	2	yes	—
205	C₂₃×#102	C₂³	1	2	yes	—
206	C₂₃×#102	C₂³	1	2	yes	—
207	C₂₃×#102	C₂³	1	4	yes	—
208	C₂₃×#102	C₂³	1	4	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×#102	C₂³	1	4	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	2	no	—
216	#41×C₂₃	—	2	2	no	—
217	#41×C₂₃	—	2	2	no	—
218	#41×C₂₃	—	8	4	no	—
219	#41×C₂₃	—	8	4	no	—
220	C₂×Q₈×C₂₃	—	2	1	no	—
221	C₂×Q₈×C₂₃	—	2	1	no	—
222	C₂×Q₈×C₂₃	—	2	1	no	—
223	C₂×Q₈×C₂₃	—	2	4	no	—
224	C₂×Q₈×C₂₃	—	2	2	no	—
225	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₂₃	#41	1	4	yes	complemented
228	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
230	C₂×D₄×C₂₃	—	2	1	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	4	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	2	no	—
237	C₂×D₄×C₂₃	—	2	2	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	4	no	—
240	C₂×D₄×C₂₃	—	8	2	no	—
241	C₂×D₄×C₂₃	—	8	2	no	—
242	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
243	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	—	2	1	no	—
245	C₂²×C₄×C₂₃	—	2	1	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	4	no	—
250	C₂²×C₄×C₂₃	—	2	4	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	C₂⁴	1	1	yes	characteristic
254	Q₁₆×C₂₃	—	2	4	no	—
255	SD₁₆×C₂₃	—	2	8	no	—
256	SD₁₆×C₂₃	—	2	8	no	—
257	SD₁₆×C₂₃	—	2	4	no	—
258	M₁₆×C₂₃	—	2	2	no	—
259	M₁₆×C₂₃	—	2	2	no	—
260	C₂×C₈×C₂₃	—	2	4	no	—
261	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	1	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	—	2	2	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
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	2	yes	—
283	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
284	C₄⋊C₄×C₂₃	C₂×D₄	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	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂²⋊C₄×C₂₃	—	2	1	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	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	2	no	—
303	C₄²×C₂₃	—	2	2	no	—
304	C₄²×C₂₃	—	2	4	no	—
305	C₄²×C₂₃	—	2	4	no	—
306	C₄²×C₂₃	—	2	2	no	—
307	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₂₃	C₂⁴	1	4	yes	—
312	#61341	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂³×C₂₃	—	2	4	no	—
314	C₂³×C₂₃	—	2	1	no	—
315	C₂³×C₂₃	—	4	4	no	—
316	C₂³×C₂₃	—	8	2	no	—
317	C₂³×C₂₃	—	8	2	no	—
318	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₂₃	—	2	4	no	—
320	Q₈×C₂₃	—	2	4	no	—
321	Q₈×C₂₃	—	2	2	no	—
322	Q₈×C₂₃	—	2	1	no	—
323	Q₈×C₂₃	—	2	1	no	—
324	Q₈×C₂₃	—	4	2	no	—
325	Q₈×C₂₃	—	4	2	no	—
326	Q₈×C₂₃	—	8	1	no	—
327	Q₈×C₂₃	—	8	4	no	—
328	Q₈×C₂₃	C₂×#41	1	4	yes	—
329	D₄×C₂₃	—	2	4	no	—
330	D₄×C₂₃	—	2	1	no	—
331	D₄×C₂₃	—	2	4	no	—
332	D₄×C₂₃	—	2	1	no	—
333	D₄×C₂₃	—	4	4	no	—
334	D₄×C₂₃	—	4	2	no	—
335	D₄×C₂₃	—	4	4	no	—
336	D₄×C₂₃	—	4	4	no	—
337	D₄×C₂₃	—	8	2	no	—
338	D₄×C₂₃	—	8	2	no	—
339	D₄×C₂₃	—	8	4	no	—
340	D₄×C₂₃	—	8	4	no	—
341	C₂×C₄×C₂₃	—	2	4	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	1	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	2	2	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	2	no	—
354	C₂×C₄×C₂₃	—	8	4	no	—
355	C₂×C₄×C₂₃	—	8	4	no	—
356	C₂×C₄×C₂₃	—	8	1	no	—
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
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	C₂×#41	1	2	yes	—
365	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
366	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
367	C₈×C₂₃	—	2	2	no	—
368	C₈×C₂₃	—	2	2	no	—
369	C₈×C₂₃	—	2	2	no	—
370	C₈×C₂₃	—	2	2	no	—
371	#3508	C₂×C₂₃	1	1	yes	characteristic
372	#3502	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#3375	C₂×C₂₃	1	2	yes	complemented
374	#3371	C₂×C₂₃	1	4	yes	complemented
375	#3368	C₂×C₂₃	1	2	yes	complemented
376	#3368	C₂×C₂₃	1	4	yes	complemented
377	#3365	C₂×C₂₃	1	2	yes	complemented
378	#3362	C₂×C₂₃	1	2	yes	complemented
379	#3138	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#3136	C₂×C₂₃	1	2	yes	complemented
381	#3081	C₂×C₂₃	1	2	yes	complemented
382	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
383	#3043	C₂×C₂₃	1	2	yes	complemented
384	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#2949	C₂×C₂₃	1	2	yes	complemented
387	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
388	C₂²×C₂₃	—	2	1	no	—
389	C₂²×C₂₃	—	2	1	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	4	4	no	—
392	C₂²×C₂₃	—	4	1	no	—
393	C₂²×C₂₃	—	4	4	no	—
394	C₂²×C₂₃	—	4	1	no	—
395	C₂²×C₂₃	—	4	4	no	—
396	C₂²×C₂₃	—	16	4	no	—
397	C₂²×C₂₃	#548	1	2	yes	—
398	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
399	C₄×C₂₃	—	2	1	no	—
400	C₄×C₂₃	—	2	1	no	—
401	C₄×C₂₃	—	2	4	no	—
402	C₄×C₂₃	—	2	4	no	—
403	C₄×C₂₃	—	2	1	no	—
404	C₄×C₂₃	—	2	4	no	—
405	C₄×C₂₃	—	4	1	no	—
406	C₄×C₂₃	—	4	2	no	—
407	C₄×C₂₃	—	4	2	no	—
408	C₄×C₂₃	—	4	1	no	—
409	C₄×C₂₃	—	4	1	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	#548	1	2	yes	—
412	C₄×C₂₃	#577	1	2	yes	—
413	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
414	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
415	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
416	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
417	#559	C₂²×C₂₃	1	2	yes	—
418	#559	C₂²×C₂₃	1	2	yes	—
419	Q₈²	—	2	1	no	—
420	Q₈²	C₂²×C₂₃	1	2	yes	complemented
421	#557	—	2	1	no	—
422	#557	—	2	2	no	—
423	#557	C₂²×C₂₃	1	2	yes	complemented
424	#557	C₂²×C₂₃	1	4	yes	complemented
425	#550	C₂²×C₂₃	1	2	yes	—
426	#550	C₂²×C₂₃	1	2	yes	—
427	#546	—	2	2	no	—
428	#546	—	2	2	no	—
429	#544	—	2	2	no	—
430	#544	C₂²×C₂₃	1	2	yes	—
431	#540	—	2	2	no	—
432	#535	C₂²×C₂₃	1	2	yes	—
433	#533	—	2	2	no	—
434	#533	C₂²×C₂₃	1	1	yes	characteristic
435	#533	C₂²×C₂₃	1	1	yes	characteristic
436	#532	—	2	1	no	—
437	#532	—	2	1	no	—
438	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
439	#519	C₂²×C₂₃	1	2	yes	—
440	#518	C₂²×C₂₃	1	2	yes	—
441	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
443	#490	C₂²×C₂₃	1	4	yes	—
444	#490	C₂²×C₂₃	1	4	yes	complemented
445	#489	C₂²×C₂₃	1	4	yes	complemented
446	#488	C₂²×C₂₃	1	4	yes	complemented
447	#486	C₂²×C₂₃	1	2	yes	—
448	#486	C₂²×C₂₃	1	2	yes	—
449	#486	C₂²×C₂₃	1	4	yes	complemented
450	#479	C₂²×C₂₃	1	2	yes	complemented
451	#478	C₂²×C₂₃	1	2	yes	complemented
452	#478	C₂²×C₂₃	1	4	yes	complemented
453	#478	C₂²×C₂₃	1	4	yes	complemented
454	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#476	C₂²×C₂₃	1	4	yes	complemented
457	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#474	C₂²×C₂₃	1	4	yes	complemented
460	#464	C₂²×C₂₃	1	4	yes	complemented
461	#464	C₂²×C₂₃	1	4	yes	complemented
462	#460	C₂²×C₂₃	1	2	yes	—
463	#460	C₂²×C₂₃	1	4	yes	—
464	#460	C₂²×C₂₃	1	2	yes	—
465	#460	C₂²×C₂₃	1	4	yes	complemented
466	#460	C₂²×C₂₃	1	4	yes	complemented
467	#446	C₂²×C₂₃	1	4	yes	complemented
468	#446	C₂²×C₂₃	1	2	yes	complemented
469	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
470	#441	C₂²×C₂₃	1	2	yes	complemented
471	#440	C₂²×C₂₃	1	2	yes	complemented
472	#440	C₂²×C₂₃	1	4	yes	complemented
473	#440	C₂²×C₂₃	1	4	yes	complemented
474	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
475	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
476	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
477	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
478	#428	C₂²×C₂₃	1	1	yes	characteristic
479	#427	C₂²×C₂₃	1	2	yes	—
480	#424	C₂²×C₂₃	1	2	yes	—
481	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
482	#419	C₂²×C₂₃	1	1	yes	characteristic
483	#418	C₂²×C₂₃	1	2	yes	—
484	#418	C₂²×C₂₃	1	2	yes	—
485	#417	C₂²×C₂₃	1	1	yes	characteristic
486	#416	C₂²×C₂₃	1	2	yes	—
487	C₂×#102	C₂²×C₂₃	1	2	yes	—
488	#405	C₂²×C₂₃	1	2	yes	—
489	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×C₂₃	—	2	2	no	—
491	C₂×C₂₃	—	8	1	no	—
492	C₂×C₂₃	—	8	4	no	—
493	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
494	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
495	C₂×C₂₃	#3585	1	1	yes	characteristic
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
503	#137	—	2	4	no	—
504	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
505	C₂×SD₁₆	—	2	8	no	—
506	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
509	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
510	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	—	2	4	no	—
514	C₄⋊Q₈	—	2	2	no	—
515	C₄⋊Q₈	—	2	4	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
518	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
520	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
522	#127	—	2	1	no	—
523	#127	—	2	1	no	—
524	#127	C₂³×C₂₃	1	2	yes	—
525	#127	C₂³×C₂₃	1	2	yes	—
526	#127	C₂³×C₂₃	1	4	yes	—
527	#125	—	2	4	no	—
528	#125	—	2	4	no	—
529	#125	—	2	4	no	—
530	#125	—	2	2	no	—
531	#125	D₄×C₂₃	1	2	yes	—
532	#125	C₂³×C₂₃	1	2	yes	—
533	#125	C₂³×C₂₃	1	4	yes	—
534	#124	—	2	2	no	—
535	#124	—	2	2	no	—
536	#124	C₂³×C₂₃	1	4	yes	—
537	#123	—	2	4	no	—
538	#123	—	2	4	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
543	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
544	#121	—	2	2	no	—
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	#120	—	2	4	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
561	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
562	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
563	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
564	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
565	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
566	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
567	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
575	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
576	C₄×D₄	C₂³×C₂₃	1	4	yes	—
577	C₄×D₄	C₂³×C₂₃	1	4	yes	—
578	#117	—	2	4	no	—
579	#117	—	2	1	no	—
580	#117	C₂³×C₂₃	1	1	yes	characteristic
581	#117	C₂³×C₂₃	1	2	yes	—
582	#117	C₂³×C₂₃	1	2	yes	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	—	2	4	no	—
586	C₂×C₄²	—	2	1	no	—
587	C₂×C₄²	—	2	1	no	—
588	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
589	#107	C₂³×C₂₃	1	2	yes	—
590	#107	C₂³×C₂₃	1	2	yes	—
591	#107	C₂³×C₂₃	1	2	yes	—
592	#106	C₂³×C₂₃	1	2	yes	—
593	#106	C₂³×C₂₃	1	2	yes	—
594	#106	C₂³×C₂₃	1	2	yes	—
595	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
596	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
598	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
599	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
600	#103	C₂³×C₂₃	1	2	yes	—
601	#103	C₂³×C₂₃	1	2	yes	—
602	#103	C₂³×C₂₃	1	2	yes	—
603	#103	C₂³×C₂₃	1	2	yes	—
604	#103	C₂³×C₂₃	1	2	yes	—
605	#102	C₂³×C₂₃	1	4	yes	—
606	#102	C₂³×C₂₃	1	4	yes	—
607	#102	C₂³×C₂₃	1	2	yes	—
608	#102	C₂³×C₂₃	1	2	yes	—
609	#102	C₂³×C₂₃	1	2	yes	—
610	#102	C₂³×C₂₃	1	4	yes	—
611	#102	C₂³×C₂₃	1	4	yes	—
612	#102	C₂³×C₂₃	1	4	yes	—
613	#102	C₂³×C₂₃	1	4	yes	—
614	#97	C₂³×C₂₃	1	2	yes	—
615	#97	C₂³×C₂₃	1	4	yes	—
616	C₄×C₈	C₂³×C₂₃	1	2	yes	—
617	C₄×C₈	C₂³×C₂₃	1	4	yes	—
618	C₂₃	#61341	1	1	yes	characteristic, direct product factor, Sylow
619	C₂⁴	—	2	2	no	—
620	#41	—	2	2	no	—
621	#41	—	2	2	no	—
622	#41	—	8	4	no	—
623	#41	—	8	4	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	4	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
630	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
631	C₂×Q₈	#41×C₂₃	1	4	yes	complemented
632	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
633	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	8	2	no	—
645	C₂×D₄	—	8	2	no	—
646	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
647	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
658	Q₁₆	—	2	4	no	—
659	SD₁₆	—	2	8	no	—
660	SD₁₆	—	2	8	no	—
661	SD₁₆	—	2	4	no	—
662	M₁₆	—	2	2	no	—
663	M₁₆	—	2	2	no	—
664	C₂×C₈	—	2	4	no	—
665	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
667	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
668	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
687	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
688	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
689	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	2	2	no	—
711	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
713	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
714	C₄²	C₂⁴×C₂₃	1	4	yes	—
715	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
716	C₂³	—	2	4	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	4	4	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	2	no	—
721	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
722	Q₈	—	2	4	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	Q₈	—	8	4	no	—
731	Q₈	C₂×#41×C₂₃	1	4	yes	—
732	D₄	—	2	4	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	2	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	2	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
764	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
767	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
768	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
769	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	16	4	no	—
783	C₂²	C₂₃×#548	1	2	yes	—
784	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
785	C₄	—	2	4	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	4	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	C₂₃×#548	1	2	yes	—
798	C₄	C₂₃×#577	1	2	yes	—
799	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
800	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	8	4	no	—
803	C₂	—	8	1	no	—
804	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
805	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
806	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3508	C₂
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
2. C₂₃×#3502	C₂	semidirect
3. C₂₃×#3375	C₂	semidirect
4. C₂₃×#3371	C₂	semidirect
5. C₂₃×#3368	C₂	semidirect
6. C₂₃×#3368	C₂	semidirect
7. C₂₃×#3365	C₂	semidirect
8. C₂₃×#3362	C₂	semidirect
9. C₂₃×#3138	C₂	semidirect
10. C₂₃×#3136	C₂	semidirect
11. C₂₃×#3081	C₂	semidirect
12. C₂₃×#3076	C₂	semidirect
13. C₂₃×#3043	C₂	semidirect
14. C₂×C₂₃×#460	C₂	semidirect
15. C₂₃×#2962	C₂	semidirect
16. C₂₃×#2949	C₂	semidirect
17. C₄×C₂₃×#137	C₂	semidirect
23. Q₈²×C₂₃	C₂²	semidirect
26. C₂₃×#557	C₂²	semidirect
27. C₂₃×#557	C₂²	semidirect
47. C₂₃×#490	C₂²	semidirect
48. C₂₃×#489	C₂²	semidirect
49. C₂₃×#488	C₂²	semidirect
52. C₂₃×#486	C₂²	semidirect
53. C₂₃×#479	C₂²	semidirect
54. C₂₃×#478	C₂²	semidirect
55. C₂₃×#478	C₂²	semidirect
56. C₂₃×#478	C₂²	semidirect
57. C₂₃×#477	C₂²	semidirect
58. C₂₃×#476	C₂²	semidirect
59. C₂₃×#476	C₂²	semidirect
60. C₂₃×#475	C₂²	semidirect
61. C₂₃×#474	C₂²	semidirect
62. C₂₃×#474	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#464	C₂²	semidirect
68. C₂₃×#460	C₂²	semidirect
69. C₂₃×#460	C₂²	semidirect
70. C₂₃×#446	C₂²	semidirect
71. C₂₃×#446	C₂²	semidirect
72. C₈×Q₈×C₂₃	C₂²	semidirect
73. C₂₃×#441	C₂²	semidirect
74. C₂₃×#440	C₂²	semidirect
75. C₂₃×#440	C₂²	semidirect
76. C₂₃×#440	C₂²	semidirect
77. C₄×Q₁₆×C₂₃	C₂²	semidirect
78. C₄×SD₁₆×C₂₃	C₂²	semidirect
79. C₄×SD₁₆×C₂₃	C₂²	semidirect
80. C₄×SD₁₆×C₂₃	C₂²	semidirect
227. C₂×Q₈×C₂₃	#41	semidirect
312. #61341	C₂₃	direct (N × H)
372. #3502	C₂×C₂₃	semidirect
373. #3375	C₂×C₂₃	semidirect
374. #3371	C₂×C₂₃	semidirect
375. #3368	C₂×C₂₃	semidirect
376. #3368	C₂×C₂₃	semidirect
377. #3365	C₂×C₂₃	semidirect
378. #3362	C₂×C₂₃	semidirect
379. #3138	C₂×C₂₃	semidirect
380. #3136	C₂×C₂₃	semidirect
381. #3081	C₂×C₂₃	semidirect
382. #3076	C₂×C₂₃	semidirect
383. #3043	C₂×C₂₃	semidirect
384. C₂×#460	C₂×C₂₃	semidirect
385. #2962	C₂×C₂₃	semidirect
386. #2949	C₂×C₂₃	semidirect
387. C₄×#137	C₂×C₂₃	semidirect
420. Q₈²	C₂²×C₂₃	semidirect
423. #557	C₂²×C₂₃	semidirect
424. #557	C₂²×C₂₃	semidirect
444. #490	C₂²×C₂₃	semidirect
445. #489	C₂²×C₂₃	semidirect
446. #488	C₂²×C₂₃	semidirect
449. #486	C₂²×C₂₃	semidirect
450. #479	C₂²×C₂₃	semidirect
451. #478	C₂²×C₂₃	semidirect
452. #478	C₂²×C₂₃	semidirect
453. #478	C₂²×C₂₃	semidirect
454. #477	C₂²×C₂₃	semidirect
455. #476	C₂²×C₂₃	semidirect
456. #476	C₂²×C₂₃	semidirect
457. #475	C₂²×C₂₃	semidirect
458. #474	C₂²×C₂₃	semidirect
459. #474	C₂²×C₂₃	semidirect
460. #464	C₂²×C₂₃	semidirect
461. #464	C₂²×C₂₃	semidirect
465. #460	C₂²×C₂₃	semidirect
466. #460	C₂²×C₂₃	semidirect
467. #446	C₂²×C₂₃	semidirect
468. #446	C₂²×C₂₃	semidirect
469. C₈×Q₈	C₂²×C₂₃	semidirect
470. #441	C₂²×C₂₃	semidirect
471. #440	C₂²×C₂₃	semidirect
472. #440	C₂²×C₂₃	semidirect
473. #440	C₂²×C₂₃	semidirect
474. C₄×Q₁₆	C₂²×C₂₃	semidirect
475. C₄×SD₁₆	C₂²×C₂₃	semidirect
476. C₄×SD₁₆	C₂²×C₂₃	semidirect
477. C₄×SD₁₆	C₂²×C₂₃	semidirect
618. C₂₃	#61341	direct (N × H)
631. C₂×Q₈	#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×#3508	2
C₂₃×#3502	2
C₂₃×#3375	2
C₂₃×#3371	2
C₂₃×#3368	2
C₂₃×#3365	2
C₂₃×#3362	2
C₂₃×#3138	2
C₂₃×#3136	2
C₂₃×#3081	2
C₂₃×#3076	2
C₂₃×#3043	2
C₂×C₂₃×#460	2
C₂₃×#2962	2
C₂₃×#2949	2
C₄×C₂₃×#137	2
#61341	23

Subgroups — C23×#61341 #19208967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61341 #19208967