Subgroups — C₂₃×#10275 #19157901

Order 5888.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×#487	—	2	2	no	—
12	C₂₃×#487	—	2	2	no	—
13	C₂₃×#476	—	2	2	no	—
14	C₂₃×#476	—	2	2	no	—
15	C₂₃×#474	—	2	2	no	—
16	C₂₃×#474	—	2	2	no	—
17	C₂×C₂₃×#107	—	2	1	no	—
18	C₂×C₂₃×#106	—	2	1	no	—
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#103	—	2	2	no	—
23	C₂×C₂₃×#102	—	2	1	no	—
24	C₂×C₂₃×#102	—	2	1	no	—
25	C₂×C₂₃×C₂²⋊C₈	—	2	2	no	—
26	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#333	—	2	2	no	—
28	C₂₃×#332	—	2	2	no	—
29	C₂²×Q₈×C₂₃	—	2	1	no	—
30	C₂²×Q₈×C₂₃	—	2	1	no	—
31	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₃	—	2	1	no	—
33	C₂²×C₈×C₂₃	—	2	1	no	—
34	C₂²×C₈×C₂₃	—	2	1	no	—
35	C₂²×C₈×C₂₃	—	2	1	no	—
36	C₂²×C₈×C₂₃	D₄	1	2	yes	—
37	C₂₃×C₄⋊Q₈	—	2	1	no	—
38	C₂₃×C₄⋊Q₈	—	2	1	no	—
39	C₂₃×C₄⋊Q₈	—	2	1	no	—
40	C₂₃×C₄⋊Q₈	—	2	1	no	—
41	C₂₃×C₄⋊Q₈	—	2	1	no	—
42	C₂₃×C₄⋊Q₈	—	2	1	no	—
43	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
44	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
45	C₄×D₄×C₂₃	—	2	1	no	—
46	C₄×D₄×C₂₃	—	2	1	no	—
47	C₄×D₄×C₂₃	—	2	1	no	—
48	C₄×D₄×C₂₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
55	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
56	C₂₃×#107	—	2	4	no	—
57	C₂₃×#106	—	2	4	no	—
58	C₂₃×C₄⋊C₈	—	2	1	no	—
59	C₂₃×C₄⋊C₈	—	2	1	no	—
60	C₂₃×C₄⋊C₈	—	2	1	no	—
61	C₂₃×C₄⋊C₈	—	2	1	no	—
62	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
63	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
64	C₂₃×#103	—	2	8	no	—
65	C₂₃×#102	—	2	4	no	—
66	C₂₃×#102	—	2	4	no	—
67	C₂₃×C₂²⋊C₈	—	4	4	no	—
68	C₄×C₈×C₂₃	—	2	1	no	—
69	C₄×C₈×C₂₃	—	2	1	no	—
70	C₂⁴×C₂₃	—	2	1	no	—
71	C₂×Q₈×C₂₃	—	2	2	no	—
72	C₂×Q₈×C₂₃	—	2	2	no	—
73	C₂×Q₈×C₂₃	—	4	1	no	—
74	C₂×Q₈×C₂₃	—	4	1	no	—
75	C₂×Q₈×C₂₃	—	4	2	no	—
76	C₂×Q₈×C₂₃	—	4	2	no	—
77	C₂×Q₈×C₂₃	—	8	2	no	—
78	C₂×D₄×C₂₃	—	2	1	no	—
79	C₂×D₄×C₂₃	—	2	1	no	—
80	C₂×D₄×C₂₃	—	2	1	no	—
81	C₂×D₄×C₂₃	—	2	1	no	—
82	C₂×D₄×C₂₃	—	2	1	no	—
83	C₂×D₄×C₂₃	Q₁₆	1	2	yes	—
84	C₂²×C₄×C₂₃	—	2	1	no	—
85	C₂²×C₄×C₂₃	—	4	1	no	—
86	C₂²×C₄×C₂₃	—	4	1	no	—
87	C₂²×C₄×C₂₃	—	4	1	no	—
88	C₂²×C₄×C₂₃	—	4	1	no	—
89	C₂²×C₄×C₂₃	—	4	2	no	—
90	C₂²×C₄×C₂₃	—	4	2	no	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
94	C₂×C₈×C₂₃	—	2	2	no	—
95	C₂×C₈×C₂₃	—	2	2	no	—
96	C₂×C₈×C₂₃	—	2	2	no	—
97	C₂×C₈×C₂₃	—	2	2	no	—
98	C₂×C₈×C₂₃	—	2	2	no	—
99	C₂×C₈×C₂₃	—	4	1	no	—
100	C₂×C₈×C₂₃	—	4	1	no	—
101	C₂×C₈×C₂₃	—	4	1	no	—
102	C₂×C₈×C₂₃	—	4	1	no	—
103	C₂×C₈×C₂₃	—	4	1	no	—
104	C₂×C₈×C₂₃	—	4	2	no	—
105	C₄⋊C₄×C₂₃	—	2	2	no	—
106	C₄⋊C₄×C₂₃	—	2	2	no	—
107	C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₄⋊C₄×C₂₃	—	2	1	no	—
109	C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₄⋊C₄×C₂₃	—	2	2	no	—
111	C₄⋊C₄×C₂₃	—	4	1	no	—
112	C₄⋊C₄×C₂₃	—	4	1	no	—
113	C₄⋊C₄×C₂₃	—	4	1	no	—
114	C₄⋊C₄×C₂₃	—	4	1	no	—
115	C₂²⋊C₄×C₂₃	—	4	1	no	—
116	C₂²⋊C₄×C₂₃	—	4	1	no	—
117	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
121	#10275	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₂₃	—	2	2	no	—
123	C₂³×C₂₃	—	4	1	no	—
124	C₂³×C₂₃	—	4	2	no	—
125	C₂³×C₂₃	—	4	1	no	—
126	C₂³×C₂₃	—	4	2	no	—
127	C₂³×C₂₃	#121	1	1	yes	characteristic
128	Q₈×C₂₃	—	4	4	no	—
129	Q₈×C₂₃	—	8	2	no	—
130	Q₈×C₂₃	—	8	2	no	—
131	Q₈×C₂₃	—	8	1	no	—
132	Q₈×C₂₃	—	8	1	no	—
133	D₄×C₂₃	—	2	2	no	—
134	D₄×C₂₃	—	2	2	no	—
135	D₄×C₂₃	—	4	1	no	—
136	D₄×C₂₃	—	4	1	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	2	no	—
140	C₂×C₄×C₂₃	—	4	2	no	—
141	C₂×C₄×C₂₃	—	4	2	no	—
142	C₂×C₄×C₂₃	—	8	2	no	—
143	C₂×C₄×C₂₃	—	8	2	no	—
144	C₂×C₄×C₂₃	—	8	2	no	—
145	C₂×C₄×C₂₃	—	8	1	no	—
146	C₂×C₄×C₂₃	—	8	1	no	—
147	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
148	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
150	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
154	C₂×C₄×C₂₃	#135	1	2	yes	—
155	C₂×C₄×C₂₃	#135	1	1	yes	characteristic
156	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
158	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
159	C₈×C₂₃	—	4	2	no	—
160	C₈×C₂₃	—	4	2	no	—
161	C₈×C₂₃	—	4	2	no	—
162	C₈×C₂₃	—	8	1	no	—
163	C₂×#487	C₂×C₂₃	1	1	yes	characteristic, complemented
164	C₂×#476	C₂×C₂₃	1	1	yes	characteristic
165	C₂×#474	C₂×C₂₃	1	1	yes	characteristic
166	#1954	C₂×C₂₃	1	1	yes	characteristic
167	C₂×#333	C₂×C₂₃	1	1	yes	characteristic, complemented
168	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
169	#1277	C₂×C₂₃	1	1	yes	characteristic, complemented
170	C₂²×C₂₃	—	4	4	no	—
171	C₂²×C₂₃	—	4	2	no	—
172	C₂²×C₂₃	—	8	2	no	—
173	C₂²×C₂₃	—	8	1	no	—
174	C₂²×C₂₃	—	8	1	no	—
175	C₂²×C₂₃	#392	1	1	yes	characteristic
176	C₂²×C₂₃	#463	1	2	yes	—
177	C₂²×C₂₃	#467	1	1	yes	characteristic
178	C₂²×C₂₃	#470	1	1	yes	characteristic
179	C₂²×C₂₃	#471	1	2	yes	—
180	C₄×C₂₃	—	2	1	no	—
181	C₄×C₂₃	—	2	1	no	—
182	C₄×C₂₃	—	8	1	no	—
183	C₄×C₂₃	—	8	2	no	—
184	C₄×C₂₃	—	8	2	no	—
185	C₄×C₂₃	#449	1	2	yes	—
186	C₄×C₂₃	#451	1	1	yes	characteristic
187	C₄×C₂₃	#451	1	1	yes	characteristic
188	C₄×C₂₃	#452	1	1	yes	characteristic
189	C₄×C₂₃	#452	1	1	yes	characteristic
190	C₄×C₂₃	#495	1	1	yes	characteristic
191	C₄×C₂₃	#496	1	1	yes	characteristic
192	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
195	#487	—	2	2	no	—
196	#487	—	2	2	no	—
197	#476	—	2	2	no	—
198	#476	—	2	2	no	—
199	#474	—	2	2	no	—
200	#474	—	2	2	no	—
201	C₂×#107	—	2	1	no	—
202	C₂×#106	—	2	1	no	—
203	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×#103	—	2	2	no	—
207	C₂×#102	—	2	1	no	—
208	C₂×#102	—	2	1	no	—
209	C₂×C₂²⋊C₈	—	2	2	no	—
210	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
211	#333	—	2	2	no	—
212	#332	—	2	2	no	—
213	C₂×C₂₃	—	8	2	no	—
214	C₂×C₂₃	#1683	1	2	yes	—
215	C₂×C₂₃	#1703	1	2	yes	—
216	C₂×C₂₃	#2001	1	1	yes	characteristic
217	C₂×C₂₃	#2012	1	1	yes	characteristic
218	C₂×C₂₃	#2019	1	1	yes	characteristic
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
222	C₂³×C₄	—	2	1	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	D₄×C₂₃	1	2	yes	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
234	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
246	#107	—	2	4	no	—
247	#106	—	2	4	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
253	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
254	#103	—	2	8	no	—
255	#102	—	2	4	no	—
256	#102	—	2	4	no	—
257	C₂²⋊C₈	—	4	4	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₂₃	#10275	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	—	2	1	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	8	2	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	Q₁₆×C₂₃	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂₃×#121	1	1	yes	characteristic
318	Q₈	—	4	4	no	—
319	Q₈	—	8	2	no	—
320	Q₈	—	8	2	no	—
321	Q₈	—	8	1	no	—
322	Q₈	—	8	1	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	1	no	—
326	D₄	—	4	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
338	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
339	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
340	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
341	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
342	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
343	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
344	C₂×C₄	C₂₃×#135	1	2	yes	—
345	C₂×C₄	C₂₃×#135	1	1	yes	characteristic
346	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
347	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
348	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₈	—	4	2	no	—
352	C₈	—	8	1	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	1	no	—
358	C₂²	C₂₃×#392	1	1	yes	characteristic
359	C₂²	C₂₃×#463	1	2	yes	—
360	C₂²	C₂₃×#467	1	1	yes	characteristic
361	C₂²	C₂₃×#470	1	1	yes	characteristic
362	C₂²	C₂₃×#471	1	2	yes	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	2	no	—
368	C₄	C₂₃×#449	1	2	yes	—
369	C₄	C₂₃×#451	1	1	yes	characteristic
370	C₄	C₂₃×#451	1	1	yes	characteristic
371	C₄	C₂₃×#452	1	1	yes	characteristic
372	C₄	C₂₃×#452	1	1	yes	characteristic
373	C₄	C₂₃×#495	1	1	yes	characteristic
374	C₄	C₂₃×#496	1	1	yes	characteristic
375	C₂	—	8	2	no	—
376	C₂	C₂₃×#1683	1	2	yes	—
377	C₂	C₂₃×#1703	1	2	yes	—
378	C₂	C₂₃×#2001	1	1	yes	characteristic
379	C₂	C₂₃×#2012	1	1	yes	characteristic
380	C₂	C₂₃×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#487	C₂	semidirect
5. C₂×C₂₃×#333	C₂	semidirect
6. C₂×C₂₃×#332	C₂	semidirect
7. C₂₃×#1277	C₂	semidirect
121. #10275	C₂₃	direct (N × H)
163. C₂×#487	C₂×C₂₃	semidirect
167. C₂×#333	C₂×C₂₃	semidirect
168. C₂×#332	C₂×C₂₃	semidirect
169. #1277	C₂×C₂₃	semidirect
260. C₂₃	#10275	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#487	2
C₂×C₂₃×#476	2
C₂×C₂₃×#474	2
C₂₃×#1954	2
C₂×C₂₃×#333	2
C₂×C₂₃×#332	2
C₂₃×#1277	2
#10275	23

Subgroups — C23×#10275 #19157901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10275 #19157901