Subgroups — C₂×C₂₃×#1438 #19161461

Order 5888.

8190 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊C₄×C₂₃	C₂	1	4	yes	maximal, complemented
3	C₂²×C₂₃×#95	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1438	C₂	1	8	yes	maximal, direct product factor
5	C₂⁶×C₂₃	C₂²	1	2	yes	—
6	C₂³×D₄×C₂₃	—	2	16	no	—
7	C₂³×D₄×C₂₃	—	2	8	no	—
8	C₂³×D₄×C₂₃	C₄	1	8	yes	complemented
9	C₂³×D₄×C₂₃	C₂²	1	4	yes	—
10	C₂⁴×C₄×C₂₃	C₂²	1	4	yes	—
11	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₂₃	—	2	16	no	—
13	C₂²×C₂²⋊C₄×C₂₃	—	2	32	no	—
14	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	16	yes	complemented
15	C₂×C₂₃×#95	—	2	8	no	—
16	C₂×C₂₃×#95	C₂²	1	8	yes	complemented
17	C₂⁵×C₂₃	—	2	8	no	—
18	C₂⁵×C₂₃	—	2	8	no	—
19	C₂⁵×C₂₃	—	2	16	no	—
20	C₂⁵×C₂₃	—	2	16	no	—
21	C₂⁵×C₂₃	C₂×C₄	1	8	yes	—
22	C₂⁵×C₂₃	D₄	1	16	yes	—
23	C₂⁵×C₂₃	C₂³	1	4	yes	—
24	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
25	C₂²×D₄×C₂₃	—	2	128	no	—
26	C₂²×D₄×C₂₃	—	2	64	no	—
27	C₂²×D₄×C₂₃	—	2	32	no	—
28	C₂²×D₄×C₂₃	—	2	32	no	—
29	C₂²×D₄×C₂₃	—	2	16	no	—
30	C₂²×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
31	C₂³×C₄×C₂₃	—	2	8	no	—
32	C₂³×C₄×C₂₃	—	2	8	no	—
33	C₂³×C₄×C₂₃	—	2	16	no	—
34	C₂³×C₄×C₂₃	—	2	16	no	—
35	C₂³×C₄×C₂₃	—	2	8	no	—
36	C₂³×C₄×C₂₃	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₂₃	D₄	1	8	yes	—
38	C₂³×C₄×C₂₃	D₄	1	16	yes	complemented
39	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
40	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
41	C₂×C₂²⋊C₄×C₂₃	—	2	128	no	—
42	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
43	C₂×C₂²⋊C₄×C₂₃	—	2	64	no	—
44	C₂₃×#95	—	2	16	no	—
45	C₂⁴×C₂₃	—	2	16	no	—
46	C₂⁴×C₂₃	—	2	16	no	—
47	C₂⁴×C₂₃	—	2	64	no	—
48	C₂⁴×C₂₃	—	2	32	no	—
49	C₂⁴×C₂₃	—	2	64	no	—
50	C₂⁴×C₂₃	—	2	64	no	—
51	C₂⁴×C₂₃	—	2	32	no	—
52	C₂⁴×C₂₃	—	2	16	no	—
53	C₂⁴×C₂₃	—	2	8	no	—
54	C₂⁴×C₂₃	—	2	8	no	—
55	C₂⁴×C₂₃	—	2	16	no	—
56	C₂⁴×C₂₃	—	4	16	no	—
57	C₂⁴×C₂₃	—	4	32	no	—
58	C₂⁴×C₂₃	—	4	32	no	—
59	C₂⁴×C₂₃	—	4	16	no	—
60	C₂⁴×C₂₃	—	4	16	no	—
61	C₂⁴×C₂₃	—	4	16	no	—
62	C₂⁴×C₂₃	C₂²⋊C₄	1	32	yes	complemented
63	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
64	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
65	C₂⁴×C₂₃	C₂×D₄	1	16	yes	—
66	C₂⁴×C₂₃	C₂×D₄	1	8	yes	—
67	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
68	C₂⁴×C₂₃	C₂×D₄	1	8	yes	—
69	C₂⁴×C₂₃	#41	1	8	yes	—
70	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
71	C₂×D₄×C₂₃	—	2	128	no	—
72	C₂×D₄×C₂₃	—	2	256	no	—
73	C₂×D₄×C₂₃	—	2	64	no	—
74	C₂×D₄×C₂₃	—	2	32	no	—
75	C₂²×C₄×C₂₃	—	2	16	no	—
76	C₂²×C₄×C₂₃	—	2	32	no	—
77	C₂²×C₄×C₂₃	—	2	8	no	—
78	C₂²×C₄×C₂₃	—	2	64	no	—
79	C₂²×C₄×C₂₃	—	2	32	no	—
80	C₂²×C₄×C₂₃	—	2	16	no	—
81	C₂²×C₄×C₂₃	—	2	16	no	—
82	C₂²×C₄×C₂₃	—	2	8	no	—
83	C₂²×C₄×C₂₃	—	2	8	no	—
84	C₂²×C₄×C₂₃	—	4	16	no	—
85	C₂²×C₄×C₂₃	—	4	32	no	—
86	C₂²×C₄×C₂₃	—	4	16	no	—
87	C₂²×C₄×C₂₃	C₂²⋊C₄	1	16	yes	complemented
88	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	complemented
91	C₂²⋊C₄×C₂₃	—	2	128	no	—
92	C₂×#1438	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂³×C₂₃	—	2	8	no	—
94	C₂³×C₂₃	—	2	8	no	—
95	C₂³×C₂₃	—	2	32	no	—
96	C₂³×C₂₃	—	2	16	no	—
97	C₂³×C₂₃	—	2	32	no	—
98	C₂³×C₂₃	—	2	32	no	—
99	C₂³×C₂₃	—	2	16	no	—
100	C₂³×C₂₃	—	2	64	no	—
101	C₂³×C₂₃	—	2	128	no	—
102	C₂³×C₂₃	—	4	8	no	—
103	C₂³×C₂₃	—	4	16	no	—
104	C₂³×C₂₃	—	4	16	no	—
105	C₂³×C₂₃	—	4	8	no	—
106	C₂³×C₂₃	—	4	8	no	—
107	C₂³×C₂₃	—	4	8	no	—
108	C₂³×C₂₃	—	4	64	no	—
109	C₂³×C₂₃	—	4	64	no	—
110	C₂³×C₂₃	—	4	128	no	—
111	C₂³×C₂₃	—	4	128	no	—
112	C₂³×C₂₃	C₂×C₂²⋊C₄	1	8	yes	—
113	C₂³×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
114	C₂³×C₂₃	C₂×C₂²⋊C₄	1	16	yes	complemented
115	C₂³×C₂₃	C₄×D₄	1	16	yes	—
116	C₂³×C₂₃	#120	1	16	yes	—
117	C₂³×C₂₃	#120	1	16	yes	—
118	C₂³×C₂₃	#121	1	32	yes	—
119	C₂³×C₂₃	#121	1	16	yes	—
120	C₂³×C₂₃	#123	1	16	yes	—
121	C₂³×C₂₃	#124	1	8	yes	—
122	C₂³×C₂₃	#127	1	8	yes	—
123	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
124	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
125	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
126	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
127	C₂³×C₂₃	C₂×#41	1	4	yes	—
128	D₄×C₂₃	—	2	128	no	—
129	C₂×C₄×C₂₃	—	2	8	no	—
130	C₂×C₄×C₂₃	—	2	16	no	—
131	C₂×C₄×C₂₃	—	2	32	no	—
132	C₂×C₄×C₂₃	—	2	32	no	—
133	C₂×C₄×C₂₃	—	2	16	no	—
134	C₂×C₄×C₂₃	—	4	8	no	—
135	C₂×C₄×C₂₃	—	4	16	no	—
136	C₂×C₄×C₂₃	—	4	8	no	—
137	C₂×C₄×C₂₃	—	4	64	no	—
138	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	8	yes	complemented
139	C₂⁴×D₄	C₂×C₂₃	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂×C₂₃	1	4	yes	complemented
141	C₂²×#95	C₂×C₂₃	1	2	yes	complemented
142	#1438	C₂×C₂₃	1	8	yes	direct product factor
143	C₂²×C₂₃	—	2	16	no	—
144	C₂²×C₂₃	—	2	32	no	—
145	C₂²×C₂₃	—	4	32	no	—
146	C₂²×C₂₃	—	4	32	no	—
147	C₂²×C₂₃	—	4	128	no	—
148	C₂²×C₂₃	—	4	16	no	—
149	C₂²×C₂₃	—	4	16	no	—
150	C₂²×C₂₃	#379	1	8	yes	—
151	C₂²×C₂₃	#386	1	32	yes	—
152	C₂²×C₂₃	#390	1	16	yes	—
153	C₂²×C₂₃	#392	1	32	yes	—
154	C₂²×C₂₃	#394	1	32	yes	—
155	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
156	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₂₃	C₂×C₄×D₄	1	4	yes	—
158	C₂²×C₂₃	C₂×#120	1	4	yes	—
159	C₂²×C₂₃	C₂×#120	1	4	yes	—
160	C₂²×C₂₃	C₂×#121	1	8	yes	—
161	C₂²×C₂₃	C₂×#121	1	4	yes	—
162	C₂²×C₂₃	C₂×#123	1	4	yes	—
163	C₂²×C₂₃	C₂×#124	1	2	yes	—
164	C₂²×C₂₃	C₂×#127	1	2	yes	—
165	C₄×C₂₃	—	2	8	no	—
166	C₄×C₂₃	—	4	16	no	—
167	C₂⁶	C₂²×C₂₃	1	2	yes	—
168	C₂³×D₄	—	2	16	no	—
169	C₂³×D₄	—	2	8	no	—
170	C₂³×D₄	C₄×C₂₃	1	8	yes	complemented
171	C₂³×D₄	C₂²×C₂₃	1	4	yes	—
172	C₂⁴×C₄	C₂²×C₂₃	1	4	yes	—
173	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
174	C₂²×C₂²⋊C₄	—	2	16	no	—
175	C₂²×C₂²⋊C₄	—	2	32	no	—
176	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	16	yes	complemented
177	C₂×#95	—	2	8	no	—
178	C₂×#95	C₂²×C₂₃	1	8	yes	complemented
179	C₂×C₂₃	—	4	16	no	—
180	C₂×C₂₃	#1438	1	16	yes	direct product factor
181	C₂×C₂₃	C₂×#379	1	1	yes	characteristic
182	C₂×C₂₃	C₂×#386	1	4	yes	—
183	C₂×C₂₃	C₂×#390	1	2	yes	—
184	C₂×C₂₃	C₂×#392	1	4	yes	—
185	C₂×C₂₃	C₂×#394	1	4	yes	—
186	C₂⁵	—	2	16	no	—
187	C₂⁵	—	2	8	no	—
188	C₂⁵	—	2	8	no	—
189	C₂⁵	—	2	16	no	—
190	C₂⁵	C₂×C₄×C₂₃	1	8	yes	—
191	C₂⁵	D₄×C₂₃	1	16	yes	—
192	C₂⁵	C₂³×C₂₃	1	4	yes	—
193	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
194	C₂²×D₄	—	2	128	no	—
195	C₂²×D₄	—	2	64	no	—
196	C₂²×D₄	—	2	32	no	—
197	C₂²×D₄	—	2	32	no	—
198	C₂²×D₄	—	2	16	no	—
199	C₂²×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
200	C₂³×C₄	—	2	8	no	—
201	C₂³×C₄	—	2	16	no	—
202	C₂³×C₄	—	2	16	no	—
203	C₂³×C₄	—	2	8	no	—
204	C₂³×C₄	—	2	8	no	—
205	C₂³×C₄	C₂×C₄×C₂₃	1	4	yes	—
206	C₂³×C₄	D₄×C₂₃	1	8	yes	—
207	C₂³×C₄	D₄×C₂₃	1	16	yes	complemented
208	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
209	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
210	C₂×C₂²⋊C₄	—	2	128	no	—
211	C₂×C₂²⋊C₄	—	2	32	no	—
212	C₂×C₂²⋊C₄	—	2	64	no	—
213	#95	—	2	16	no	—
214	C₂₃	C₂×#1438	1	1	yes	characteristic, direct product factor, Sylow
215	C₂⁴	—	2	16	no	—
216	C₂⁴	—	2	16	no	—
217	C₂⁴	—	2	64	no	—
218	C₂⁴	—	2	32	no	—
219	C₂⁴	—	2	64	no	—
220	C₂⁴	—	2	64	no	—
221	C₂⁴	—	2	32	no	—
222	C₂⁴	—	2	16	no	—
223	C₂⁴	—	2	8	no	—
224	C₂⁴	—	2	8	no	—
225	C₂⁴	—	2	16	no	—
226	C₂⁴	—	4	16	no	—
227	C₂⁴	—	4	32	no	—
228	C₂⁴	—	4	32	no	—
229	C₂⁴	—	4	16	no	—
230	C₂⁴	—	4	16	no	—
231	C₂⁴	—	4	16	no	—
232	C₂⁴	C₂²⋊C₄×C₂₃	1	32	yes	complemented
233	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
234	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
235	C₂⁴	C₂×D₄×C₂₃	1	16	yes	—
236	C₂⁴	C₂×D₄×C₂₃	1	8	yes	—
237	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
238	C₂⁴	C₂×D₄×C₂₃	1	8	yes	—
239	C₂⁴	#41×C₂₃	1	8	yes	—
240	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
241	C₂×D₄	—	2	256	no	—
242	C₂×D₄	—	2	128	no	—
243	C₂×D₄	—	2	64	no	—
244	C₂×D₄	—	2	32	no	—
245	C₂²×C₄	—	2	16	no	—
246	C₂²×C₄	—	2	32	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	64	no	—
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	16	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	4	16	no	—
255	C₂²×C₄	—	4	32	no	—
256	C₂²×C₄	—	4	16	no	—
257	C₂²×C₄	C₂²⋊C₄×C₂₃	1	16	yes	complemented
258	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
260	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	complemented
261	C₂²⋊C₄	—	2	128	no	—
262	C₂³	—	2	64	no	—
263	C₂³	—	2	128	no	—
264	C₂³	—	2	8	no	—
265	C₂³	—	2	8	no	—
266	C₂³	—	2	32	no	—
267	C₂³	—	2	16	no	—
268	C₂³	—	2	32	no	—
269	C₂³	—	2	32	no	—
270	C₂³	—	2	16	no	—
271	C₂³	—	4	64	no	—
272	C₂³	—	4	64	no	—
273	C₂³	—	4	128	no	—
274	C₂³	—	4	128	no	—
275	C₂³	—	4	8	no	—
276	C₂³	—	4	16	no	—
277	C₂³	—	4	16	no	—
278	C₂³	—	4	8	no	—
279	C₂³	—	4	8	no	—
280	C₂³	—	4	8	no	—
281	C₂³	C₂×C₂²⋊C₄×C₂₃	1	8	yes	—
282	C₂³	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
283	C₂³	C₂×C₂²⋊C₄×C₂₃	1	16	yes	complemented
284	C₂³	C₄×D₄×C₂₃	1	16	yes	—
285	C₂³	C₂₃×#120	1	16	yes	—
286	C₂³	C₂₃×#120	1	16	yes	—
287	C₂³	C₂₃×#121	1	32	yes	—
288	C₂³	C₂₃×#121	1	16	yes	—
289	C₂³	C₂₃×#123	1	16	yes	—
290	C₂³	C₂₃×#124	1	8	yes	—
291	C₂³	C₂₃×#127	1	8	yes	—
292	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
293	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
294	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
295	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
296	C₂³	C₂×#41×C₂₃	1	4	yes	—
297	D₄	—	2	128	no	—
298	C₂×C₄	—	2	32	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	4	64	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	16	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	8	yes	complemented
308	C₂²	—	2	16	no	—
309	C₂²	—	2	32	no	—
310	C₂²	—	4	128	no	—
311	C₂²	—	4	16	no	—
312	C₂²	—	4	16	no	—
313	C₂²	—	4	32	no	—
314	C₂²	—	4	32	no	—
315	C₂²	C₂₃×#379	1	8	yes	—
316	C₂²	C₂₃×#386	1	32	yes	—
317	C₂²	C₂₃×#390	1	16	yes	—
318	C₂²	C₂₃×#392	1	32	yes	—
319	C₂²	C₂₃×#394	1	32	yes	—
320	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
321	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
322	C₂²	C₂×C₄×D₄×C₂₃	1	4	yes	—
323	C₂²	C₂×C₂₃×#120	1	4	yes	—
324	C₂²	C₂×C₂₃×#120	1	4	yes	—
325	C₂²	C₂×C₂₃×#121	1	8	yes	—
326	C₂²	C₂×C₂₃×#121	1	4	yes	—
327	C₂²	C₂×C₂₃×#123	1	4	yes	—
328	C₂²	C₂×C₂₃×#124	1	2	yes	—
329	C₂²	C₂×C₂₃×#127	1	2	yes	—
330	C₄	—	2	8	no	—
331	C₄	—	4	16	no	—
332	C₂	—	4	16	no	—
333	C₂	C₂₃×#1438	1	16	yes	direct product factor
334	C₂	C₂×C₂₃×#379	1	1	yes	characteristic
335	C₂	C₂×C₂₃×#386	1	4	yes	—
336	C₂	C₂×C₂₃×#390	1	2	yes	—
337	C₂	C₂×C₂₃×#392	1	4	yes	—
338	C₂	C₂×C₂₃×#394	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁵×C₂₃	C₂³
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂⁴×C₂₃
prime radical	C₂⁴×D₄×C₂₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₂²⋊C₄×C₂₃	C₂	semidirect
3. C₂²×C₂₃×#95	C₂	semidirect
4. C₂₃×#1438	C₂	direct (N × H)
8. C₂³×D₄×C₂₃	C₄	semidirect
14. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
16. C₂×C₂₃×#95	C₂²	semidirect
30. C₂²×D₄×C₂₃	C₂×C₄	semidirect
38. C₂³×C₄×C₂₃	D₄	semidirect
62. C₂⁴×C₂₃	C₂²⋊C₄	semidirect
87. C₂²×C₄×C₂₃	C₂²⋊C₄	semidirect
90. C₂²×C₄×C₂₃	C₂×D₄	semidirect
92. C₂×#1438	C₂₃	direct (N × H)
114. C₂³×C₂₃	C₂×C₂²⋊C₄	semidirect
138. C₂×C₄×C₂₃	C₂×C₂²⋊C₄	semidirect
140. C₂³×C₂²⋊C₄	C₂×C₂₃	semidirect
141. C₂²×#95	C₂×C₂₃	semidirect
142. #1438	C₂×C₂₃	direct (N × H)
170. C₂³×D₄	C₄×C₂₃	semidirect
176. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
178. C₂×#95	C₂²×C₂₃	semidirect
180. C₂×C₂₃	#1438	direct (N × H)
199. C₂²×D₄	C₂×C₄×C₂₃	semidirect
207. C₂³×C₄	D₄×C₂₃	semidirect
214. C₂₃	C₂×#1438	direct (N × H)
232. C₂⁴	C₂²⋊C₄×C₂₃	semidirect
257. C₂²×C₄	C₂²⋊C₄×C₂₃	semidirect
260. C₂²×C₄	C₂×D₄×C₂₃	semidirect
283. C₂³	C₂×C₂²⋊C₄×C₂₃	semidirect
307. C₂×C₄	C₂×C₂²⋊C₄×C₂₃	semidirect
333. C₂	C₂₃×#1438	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₂₃	2
C₂³×C₂²⋊C₄×C₂₃	2
C₂²×C₂₃×#95	2
C₂₃×#1438	2
C₂×#1438	23

Subgroups — C2×C23×#1438 #19161461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1438 #19161461