Subgroups — C₂₃×#61342 #19208968

Order 5888.

1724 conjugacy classes of subgroups.

The subgroup lattice has 772 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
2	C₂₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3374	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3364	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3363	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3137	C₂	1	2	yes	maximal
11	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#3044	C₂	1	2	yes	maximal
14	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2950	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic
18	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
20	Q₈²×C₂₃	—	2	1	no	—
21	Q₈²×C₂₃	C₂²	1	2	yes	—
22	C₂₃×#557	—	2	1	no	—
23	C₂₃×#557	—	2	2	no	—
24	C₂₃×#557	C₂²	1	2	yes	—
25	C₂₃×#557	C₂²	1	2	yes	—
26	C₂₃×#557	C₂²	1	2	yes	—
27	C₂₃×#557	C₂²	1	4	yes	—
28	C₂₃×#556	C₂²	1	2	yes	—
29	C₂₃×#556	C₂²	1	2	yes	—
30	C₂₃×#552	—	2	2	no	—
31	C₂₃×#552	—	2	2	no	—
32	C₂₃×#544	—	2	2	no	—
33	C₂₃×#544	C₂²	1	2	yes	—
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	—	2	2	no	—
39	C₂₃×#533	C₂²	1	1	yes	characteristic
40	C₂₃×#533	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂₃×#519	C₂²	1	2	yes	—
43	C₂₃×#519	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×#491	C₂²	1	4	yes	—
47	C₂₃×#491	C₂²	1	4	yes	—
48	C₂₃×#489	C₂²	1	4	yes	—
49	C₂₃×#488	C₂²	1	4	yes	—
50	C₂₃×#487	C₂²	1	2	yes	—
51	C₂₃×#487	C₂²	1	4	yes	—
52	C₂₃×#487	C₂²	1	2	yes	—
53	C₂₃×#479	C₂²	1	2	yes	—
54	C₂₃×#479	C₂²	1	4	yes	—
55	C₂₃×#479	C₂²	1	4	yes	—
56	C₂₃×#478	C₂²	1	2	yes	—
57	C₂₃×#477	C₂²	1	1	yes	characteristic
58	C₂₃×#477	C₂²	1	4	yes	—
59	C₂₃×#476	C₂²	1	1	yes	characteristic
60	C₂₃×#475	C₂²	1	1	yes	characteristic
61	C₂₃×#475	C₂²	1	4	yes	—
62	C₂₃×#474	C₂²	1	1	yes	characteristic
63	C₂₃×#464	C₂²	1	4	yes	—
64	C₂₃×#464	C₂²	1	4	yes	—
65	C₂₃×#462	C₂²	1	2	yes	—
66	C₂₃×#462	C₂²	1	2	yes	—
67	C₂₃×#462	C₂²	1	4	yes	—
68	C₂₃×#462	C₂²	1	4	yes	—
69	C₂₃×#462	C₂²	1	4	yes	—
70	C₂₃×#446	C₂²	1	2	yes	—
71	C₂₃×#446	C₂²	1	4	yes	—
72	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
73	C₂₃×#441	C₂²	1	2	yes	—
74	C₂₃×#441	C₂²	1	4	yes	—
75	C₂₃×#441	C₂²	1	4	yes	—
76	C₂₃×#440	C₂²	1	2	yes	—
77	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
80	C₄×SD₁₆×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	1	yes	characteristic
86	C₂₃×#419	C₂²	1	2	yes	—
87	C₂₃×#419	C₂²	1	2	yes	—
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	C₂³	1	2	yes	—
95	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂₃×#137	—	2	4	no	—
97	C₂×Q₁₆×C₂₃	—	2	8	no	—
98	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
100	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
105	C₂₃×C₄⋊Q₈	—	2	2	no	—
106	C₂₃×C₄⋊Q₈	—	2	4	no	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	—	2	4	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×#126	—	2	4	no	—
121	C₂₃×#126	—	2	4	no	—
122	C₂₃×#125	—	2	2	no	—
123	C₂₃×#125	—	2	2	no	—
124	C₂₃×#125	—	2	4	no	—
125	C₂₃×#125	—	2	4	no	—
126	C₂₃×#125	—	2	2	no	—
127	C₂₃×#125	—	2	4	no	—
128	C₂₃×#125	—	2	4	no	—
129	C₂₃×#125	—	2	4	no	—
130	C₂₃×#125	D₄	1	2	yes	—
131	C₂₃×#125	C₂³	1	2	yes	—
132	C₂₃×#125	C₂³	1	4	yes	—
133	C₂₃×#124	C₂³	1	4	yes	—
134	C₂₃×#123	—	2	4	no	—
135	C₂₃×C₂²⋊Q₈	—	2	2	no	—
136	C₂₃×C₂²⋊Q₈	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	1	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	—	2	2	no	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	4	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	2	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	4	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	—	2	2	no	—
173	C₂₃×#117	—	2	4	no	—
174	C₂₃×#117	—	2	4	no	—
175	C₂₃×#117	—	2	1	no	—
176	C₂₃×#117	C₂³	1	2	yes	—
177	C₂₃×#117	C₂³	1	1	yes	characteristic
178	C₂₃×#117	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	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	2	yes	—
203	C₂₃×#103	C₂³	1	2	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#103	C₂³	1	4	yes	—
206	C₂₃×#103	C₂³	1	4	yes	—
207	C₂₃×#103	C₂³	1	4	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	#41×C₂₃	—	2	2	no	—
216	#41×C₂₃	—	2	2	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	1	no	—
221	C₂×Q₈×C₂₃	—	2	4	no	—
222	C₂×Q₈×C₂₃	—	2	2	no	—
223	C₂×Q₈×C₂₃	—	2	4	no	—
224	C₂×Q₈×C₂₃	—	2	4	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	—
228	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
229	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₂₃	—	2	1	no	—
232	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	2	no	—
235	C₂²×C₄×C₂₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₂₃	—	2	8	no	—
243	Q₁₆×C₂₃	—	2	8	no	—
244	Q₁₆×C₂₃	—	2	4	no	—
245	SD₁₆×C₂₃	—	2	4	no	—
246	M₁₆×C₂₃	—	2	2	no	—
247	M₁₆×C₂₃	—	2	2	no	—
248	C₂×C₈×C₂₃	—	2	4	no	—
249	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₂₃	—	2	2	no	—
254	C₄⋊C₄×C₂₃	—	2	2	no	—
255	C₄⋊C₄×C₂₃	—	2	2	no	—
256	C₄⋊C₄×C₂₃	—	2	2	no	—
257	C₄⋊C₄×C₂₃	—	2	2	no	—
258	C₄⋊C₄×C₂₃	—	2	2	no	—
259	C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	4	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	1	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	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	4	no	—
275	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²⋊C₄×C₂₃	—	2	1	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	1	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	C₂×D₄	1	4	yes	—
293	C₄²×C₂₃	—	2	1	no	—
294	C₄²×C₂₃	—	2	1	no	—
295	C₄²×C₂₃	—	2	1	no	—
296	C₄²×C₂₃	—	2	2	no	—
297	C₄²×C₂₃	—	2	2	no	—
298	C₄²×C₂₃	—	2	4	no	—
299	C₄²×C₂₃	—	2	4	no	—
300	C₄²×C₂₃	—	2	4	no	—
301	C₄²×C₂₃	—	2	4	no	—
302	C₄²×C₂₃	—	2	2	no	—
303	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₄²×C₂₃	C₂⁴	1	4	yes	—
308	#61342	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₂₃	—	2	1	no	—
310	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₂₃	—	2	4	no	—
312	Q₈×C₂₃	—	2	4	no	—
313	Q₈×C₂₃	—	2	2	no	—
314	Q₈×C₂₃	—	2	4	no	—
315	Q₈×C₂₃	—	2	1	no	—
316	Q₈×C₂₃	—	2	4	no	—
317	Q₈×C₂₃	—	2	1	no	—
318	Q₈×C₂₃	—	4	2	no	—
319	Q₈×C₂₃	—	4	4	no	—
320	Q₈×C₂₃	—	4	2	no	—
321	Q₈×C₂₃	—	8	1	no	—
322	Q₈×C₂₃	—	8	4	no	—
323	Q₈×C₂₃	C₂×#41	1	4	yes	—
324	D₄×C₂₃	—	2	1	no	—
325	D₄×C₂₃	—	2	1	no	—
326	D₄×C₂₃	—	4	2	no	—
327	C₂×C₄×C₂₃	—	2	4	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	4	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	2	no	—
339	C₂×C₄×C₂₃	—	4	4	no	—
340	C₂×C₄×C₂₃	—	4	2	no	—
341	C₂×C₄×C₂₃	—	4	2	no	—
342	C₂×C₄×C₂₃	—	8	1	no	—
343	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
351	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
352	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
353	C₈×C₂₃	—	2	2	no	—
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	2	2	no	—
357	#3509	C₂×C₂₃	1	1	yes	characteristic
358	#3502	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#3377	C₂×C₂₃	1	4	yes	complemented
360	#3374	C₂×C₂₃	1	2	yes	complemented
361	#3374	C₂×C₂₃	1	4	yes	complemented
362	#3369	C₂×C₂₃	1	2	yes	complemented
363	#3364	C₂×C₂₃	1	2	yes	complemented
364	#3363	C₂×C₂₃	1	2	yes	complemented
365	#3139	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#3137	C₂×C₂₃	1	2	yes	—
367	#3082	C₂×C₂₃	1	2	yes	complemented
368	#3076	C₂×C₂₃	1	1	yes	characteristic
369	#3044	C₂×C₂₃	1	2	yes	—
370	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#2950	C₂×C₂₃	1	2	yes	complemented
373	C₄×#137	C₂×C₂₃	1	1	yes	characteristic
374	C₂²×C₂₃	—	2	1	no	—
375	C₂²×C₂₃	—	2	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	#548	1	2	yes	—
380	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₂₃	—	2	1	no	—
382	C₄×C₂₃	—	2	1	no	—
383	C₄×C₂₃	—	2	4	no	—
384	C₄×C₂₃	—	2	4	no	—
385	C₄×C₂₃	—	2	1	no	—
386	C₄×C₂₃	—	2	4	no	—
387	C₄×C₂₃	—	4	1	no	—
388	C₄×C₂₃	—	4	2	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	1	no	—
391	C₄×C₂₃	—	4	4	no	—
392	C₄×C₂₃	—	4	1	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	#548	1	2	yes	—
395	C₄×C₂₃	#578	1	2	yes	—
396	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
397	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
399	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
400	Q₈²	—	2	1	no	—
401	Q₈²	C₂²×C₂₃	1	2	yes	—
402	#557	—	2	1	no	—
403	#557	—	2	2	no	—
404	#557	C₂²×C₂₃	1	2	yes	—
405	#557	C₂²×C₂₃	1	2	yes	—
406	#557	C₂²×C₂₃	1	2	yes	—
407	#557	C₂²×C₂₃	1	4	yes	—
408	#556	C₂²×C₂₃	1	2	yes	—
409	#556	C₂²×C₂₃	1	2	yes	—
410	#552	—	2	2	no	—
411	#552	—	2	2	no	—
412	#544	—	2	2	no	—
413	#544	C₂²×C₂₃	1	2	yes	—
414	#541	—	2	2	no	—
415	#536	C₂²×C₂₃	1	2	yes	—
416	#533	—	2	1	no	—
417	#533	—	2	1	no	—
418	#533	—	2	2	no	—
419	#533	C₂²×C₂₃	1	1	yes	characteristic
420	#533	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
422	#519	C₂²×C₂₃	1	2	yes	—
423	#519	C₂²×C₂₃	1	2	yes	—
424	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
426	#491	C₂²×C₂₃	1	4	yes	—
427	#491	C₂²×C₂₃	1	4	yes	—
428	#489	C₂²×C₂₃	1	4	yes	—
429	#488	C₂²×C₂₃	1	4	yes	—
430	#487	C₂²×C₂₃	1	2	yes	—
431	#487	C₂²×C₂₃	1	4	yes	—
432	#487	C₂²×C₂₃	1	2	yes	—
433	#479	C₂²×C₂₃	1	2	yes	—
434	#479	C₂²×C₂₃	1	4	yes	—
435	#479	C₂²×C₂₃	1	4	yes	—
436	#478	C₂²×C₂₃	1	2	yes	—
437	#477	C₂²×C₂₃	1	1	yes	characteristic
438	#477	C₂²×C₂₃	1	4	yes	—
439	#476	C₂²×C₂₃	1	1	yes	characteristic
440	#475	C₂²×C₂₃	1	1	yes	characteristic
441	#475	C₂²×C₂₃	1	4	yes	—
442	#474	C₂²×C₂₃	1	1	yes	characteristic
443	#464	C₂²×C₂₃	1	4	yes	—
444	#464	C₂²×C₂₃	1	4	yes	—
445	#462	C₂²×C₂₃	1	2	yes	—
446	#462	C₂²×C₂₃	1	4	yes	—
447	#462	C₂²×C₂₃	1	2	yes	—
448	#462	C₂²×C₂₃	1	4	yes	—
449	#462	C₂²×C₂₃	1	4	yes	—
450	#446	C₂²×C₂₃	1	2	yes	—
451	#446	C₂²×C₂₃	1	4	yes	—
452	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
453	#441	C₂²×C₂₃	1	4	yes	—
454	#441	C₂²×C₂₃	1	2	yes	—
455	#441	C₂²×C₂₃	1	4	yes	—
456	#440	C₂²×C₂₃	1	2	yes	—
457	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
458	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
459	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
460	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
461	#428	C₂²×C₂₃	1	1	yes	characteristic
462	#427	C₂²×C₂₃	1	2	yes	—
463	#424	C₂²×C₂₃	1	2	yes	—
464	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
465	#419	C₂²×C₂₃	1	2	yes	—
466	#419	C₂²×C₂₃	1	2	yes	—
467	#419	C₂²×C₂₃	1	1	yes	characteristic
468	#417	C₂²×C₂₃	1	1	yes	characteristic
469	#416	C₂²×C₂₃	1	2	yes	—
470	C₂×#103	C₂²×C₂₃	1	2	yes	—
471	#405	C₂²×C₂₃	1	2	yes	—
472	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₂₃	—	2	2	no	—
474	C₂×C₂₃	—	8	1	no	—
475	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
476	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
477	C₂×C₂₃	#3586	1	1	yes	characteristic
478	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
480	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
481	#137	—	2	4	no	—
482	C₂×Q₁₆	—	2	8	no	—
483	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
484	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
485	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
486	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
487	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
490	C₄⋊Q₈	—	2	2	no	—
491	C₄⋊Q₈	—	2	4	no	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	—	2	4	no	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	1	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
498	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
500	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
501	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
502	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
505	#126	—	2	4	no	—
506	#126	—	2	4	no	—
507	#125	—	2	2	no	—
508	#125	—	2	2	no	—
509	#125	—	2	4	no	—
510	#125	—	2	4	no	—
511	#125	—	2	4	no	—
512	#125	—	2	4	no	—
513	#125	—	2	4	no	—
514	#125	—	2	2	no	—
515	#125	D₄×C₂₃	1	2	yes	—
516	#125	C₂³×C₂₃	1	2	yes	—
517	#125	C₂³×C₂₃	1	4	yes	—
518	#124	C₂³×C₂₃	1	4	yes	—
519	#123	—	2	4	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
528	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	4	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
543	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
544	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
547	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
548	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
549	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
550	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
551	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
555	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
556	#117	—	2	2	no	—
557	#117	—	2	2	no	—
558	#117	—	2	4	no	—
559	#117	—	2	4	no	—
560	#117	—	2	1	no	—
561	#117	C₂³×C₂₃	1	1	yes	characteristic
562	#117	C₂³×C₂₃	1	2	yes	—
563	#117	C₂³×C₂₃	1	2	yes	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
571	#107	C₂³×C₂₃	1	2	yes	—
572	#107	C₂³×C₂₃	1	2	yes	—
573	#107	C₂³×C₂₃	1	2	yes	—
574	#106	C₂³×C₂₃	1	2	yes	—
575	#106	C₂³×C₂₃	1	2	yes	—
576	#106	C₂³×C₂₃	1	2	yes	—
577	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
578	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
579	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
580	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
581	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
582	#103	C₂³×C₂₃	1	4	yes	—
583	#103	C₂³×C₂₃	1	4	yes	—
584	#103	C₂³×C₂₃	1	2	yes	—
585	#103	C₂³×C₂₃	1	2	yes	—
586	#103	C₂³×C₂₃	1	2	yes	—
587	#103	C₂³×C₂₃	1	2	yes	—
588	#103	C₂³×C₂₃	1	2	yes	—
589	#103	C₂³×C₂₃	1	4	yes	—
590	#103	C₂³×C₂₃	1	4	yes	—
591	#103	C₂³×C₂₃	1	4	yes	—
592	#103	C₂³×C₂₃	1	4	yes	—
593	#102	C₂³×C₂₃	1	2	yes	—
594	#102	C₂³×C₂₃	1	2	yes	—
595	#102	C₂³×C₂₃	1	2	yes	—
596	#97	C₂³×C₂₃	1	2	yes	—
597	#97	C₂³×C₂₃	1	4	yes	—
598	C₄×C₈	C₂³×C₂₃	1	2	yes	—
599	C₄×C₈	C₂³×C₂₃	1	4	yes	—
600	C₂₃	#61342	1	1	yes	characteristic, direct product factor, Sylow
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
613	C₂×Q₈	#41×C₂₃	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
615	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
616	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
628	Q₁₆	—	2	8	no	—
629	Q₁₆	—	2	8	no	—
630	Q₁₆	—	2	4	no	—
631	SD₁₆	—	2	4	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	2	no	—
634	C₂×C₈	—	2	4	no	—
635	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
636	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
637	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
664	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
665	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
666	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
667	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₄²	C₂⁴×C₂₃	1	4	yes	—
693	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
694	C₂³	—	2	1	no	—
695	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
696	Q₈	—	2	4	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	4	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	4	no	—
702	Q₈	—	2	1	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	4	4	no	—
705	Q₈	—	4	2	no	—
706	Q₈	—	8	1	no	—
707	Q₈	—	8	4	no	—
708	Q₈	C₂×#41×C₂₃	1	4	yes	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	4	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	8	1	no	—
728	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
730	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
736	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
737	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	2	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	C₂₃×#548	1	2	yes	—
748	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
749	C₄	—	2	4	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	4	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	C₂₃×#548	1	2	yes	—
763	C₄	C₂₃×#578	1	2	yes	—
764	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
765	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
766	C₂	—	2	2	no	—
767	C₂	—	8	1	no	—
768	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
769	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
770	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×#41×C₂₃	C₂³
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×#3377	C₂	semidirect
4. C₂₃×#3374	C₂	semidirect
5. C₂₃×#3374	C₂	semidirect
6. C₂₃×#3369	C₂	semidirect
7. C₂₃×#3364	C₂	semidirect
8. C₂₃×#3363	C₂	semidirect
9. C₂₃×#3139	C₂	semidirect
11. C₂₃×#3082	C₂	semidirect
14. C₂×C₂₃×#462	C₂	semidirect
15. C₂₃×#2962	C₂	semidirect
16. C₂₃×#2950	C₂	semidirect
308. #61342	C₂₃	direct (N × H)
358. #3502	C₂×C₂₃	semidirect
359. #3377	C₂×C₂₃	semidirect
360. #3374	C₂×C₂₃	semidirect
361. #3374	C₂×C₂₃	semidirect
362. #3369	C₂×C₂₃	semidirect
363. #3364	C₂×C₂₃	semidirect
364. #3363	C₂×C₂₃	semidirect
365. #3139	C₂×C₂₃	semidirect
367. #3082	C₂×C₂₃	semidirect
370. C₂×#462	C₂×C₂₃	semidirect
371. #2962	C₂×C₂₃	semidirect
372. #2950	C₂×C₂₃	semidirect
600. C₂₃	#61342	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×#3502	2
C₂₃×#3377	2
C₂₃×#3374	2
C₂₃×#3369	2
C₂₃×#3364	2
C₂₃×#3363	2
C₂₃×#3139	2
C₂₃×#3137	2
C₂₃×#3082	2
C₂₃×#3076	2
C₂₃×#3044	2
C₂×C₂₃×#462	2
C₂₃×#2962	2
C₂₃×#2950	2
C₄×C₂₃×#137	2
#61342	23

Subgroups — C23×#61342 #19208968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61342 #19208968