Subgroups — C₅×#21042 #11943762

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2911	C₂	1	1	yes	maximal, characteristic
2	C₅×#2905	C₂	1	1	yes	maximal, characteristic
3	C₅×#2873	C₂	1	1	yes	maximal, characteristic
4	C₅×#1922	C₂	1	8	yes	maximal, complemented
5	C₅×#1738	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic
8	C₅×#1728	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#428	C₄	1	4	yes	complemented
17	C₅×#428	C₄	1	4	yes	complemented
18	C₅×#427	C₂²	1	4	yes	—
19	C₅×#424	—	2	2	no	—
20	C₅×#424	C₂²	1	4	yes	—
21	C₅×#423	—	2	2	no	—
22	C₅×#405	—	2	2	no	—
23	C₅×#405	C₂²	1	4	yes	—
24	C₄×C₅×M₁₆	—	2	2	no	—
25	C₅×#341	C₂²	1	4	yes	—
26	C₅×#339	C₂²	1	4	yes	—
27	C₅×#339	C₂²	1	4	yes	—
28	C₅×#336	C₂²	1	4	yes	—
29	#21042	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂³×C₄×C₅	—	2	1	no	—
31	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₂×C₅×M₁₆	—	2	1	no	—
33	C₂×C₅×M₁₆	—	2	2	no	—
34	C₂×C₅×M₁₆	—	2	2	no	—
35	C₂×C₅×M₁₆	—	2	2	no	—
36	C₂×C₅×M₁₆	—	2	2	no	—
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	—	2	1	no	—
39	C₂×C₅×M₁₆	—	2	2	no	—
40	C₂×C₅×M₁₆	—	2	2	no	—
41	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
43	C₂×C₅×M₁₆	D₄	1	2	yes	—
44	C₂×C₅×M₁₆	D₄	1	2	yes	—
45	C₂×C₅×M₁₆	Q₈	1	4	yes	—
46	C₂×C₅×M₁₆	C₂³	1	2	yes	—
47	C₂×C₅×M₁₆	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	—	2	1	no	—
49	C₂²×C₅×C₈	—	2	1	no	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₅×#117	—	2	1	no	—
53	C₅×#117	—	2	1	no	—
54	C₅×#117	—	2	1	no	—
55	C₅×#117	—	2	1	no	—
56	C₅×#117	C₂×C₄	1	2	yes	—
57	C₅×#117	C₂×C₄	1	2	yes	—
58	C₅×#117	C₂³	1	2	yes	—
59	C₅×#117	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	—	2	2	no	—
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₅×#107	C₂×C₄	1	8	yes	complemented
71	C₅×#106	C₂×C₄	1	8	yes	complemented
72	C₅×C₄⋊C₈	—	2	8	no	—
73	C₅×#97	—	2	4	no	—
74	C₄×C₅×C₈	—	2	4	no	—
75	#2911	C₂×C₅	1	1	yes	characteristic
76	#2905	C₂×C₅	1	1	yes	characteristic
77	#2873	C₂×C₅	1	1	yes	characteristic
78	#1922	C₂×C₅	1	8	yes	complemented
79	#1738	C₂×C₅	1	1	yes	characteristic
80	C₂×#339	C₂×C₅	1	1	yes	characteristic
81	C₂×#339	C₂×C₅	1	1	yes	characteristic
82	#1728	C₂×C₅	1	1	yes	characteristic
83	C₂⁴×C₅	#41	1	1	yes	characteristic
84	C₂²×C₄×C₅	—	2	2	no	—
85	C₂²×C₄×C₅	—	2	2	no	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	4	4	no	—
88	C₂²×C₄×C₅	—	4	2	no	—
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₅	#41	1	2	yes	—
95	C₂²×C₄×C₅	#41	1	2	yes	—
96	C₂²×C₄×C₅	#41	1	1	yes	characteristic
97	C₂²×C₄×C₅	#41	1	2	yes	—
98	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₅×M₁₆	—	2	4	no	—
100	C₅×M₁₆	—	2	4	no	—
101	C₅×M₁₆	—	2	4	no	—
102	C₅×M₁₆	—	2	4	no	—
103	C₅×M₁₆	—	2	4	no	—
104	C₅×M₁₆	—	2	2	no	—
105	C₅×M₁₆	—	2	2	no	—
106	C₅×M₁₆	—	2	2	no	—
107	C₅×M₁₆	—	4	2	no	—
108	C₅×M₁₆	C₂×Q₈	1	4	yes	—
109	C₂×C₅×C₈	—	2	4	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	4	2	no	—
117	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
118	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
122	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
123	C₅×C₂²⋊C₄	—	2	2	no	—
124	C₅×C₂²⋊C₄	—	2	2	no	—
125	C₅×C₂²⋊C₄	—	2	2	no	—
126	C₅×C₂²⋊C₄	—	2	2	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	4	2	no	—
134	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
135	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
136	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
137	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
138	C₂×#117	C₂²×C₅	1	1	yes	characteristic
139	C₂×#117	C₂²×C₅	1	1	yes	characteristic
140	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
141	#428	C₄×C₅	1	4	yes	complemented
142	#428	C₄×C₅	1	4	yes	complemented
143	#427	C₂²×C₅	1	4	yes	—
144	#424	—	2	2	no	—
145	#424	C₂²×C₅	1	4	yes	—
146	#423	—	2	2	no	—
147	#405	—	2	2	no	—
148	#405	C₂²×C₅	1	4	yes	—
149	C₄×M₁₆	—	2	2	no	—
150	#341	C₂²×C₅	1	4	yes	—
151	#339	C₂²×C₅	1	4	yes	—
152	#339	C₂²×C₅	1	4	yes	—
153	#336	C₂²×C₅	1	4	yes	—
154	C₂³×C₅	—	4	2	no	—
155	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
156	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
157	C₂³×C₅	#125	1	2	yes	—
158	C₂³×C₅	#126	1	2	yes	—
159	C₂³×C₅	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₅	—	2	4	no	—
161	C₂×C₄×C₅	—	2	4	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	4	2	no	—
164	C₂×C₄×C₅	—	4	8	no	—
165	C₂×C₄×C₅	—	4	2	no	—
166	C₂×C₄×C₅	—	8	2	no	—
167	C₂×C₄×C₅	—	8	2	no	—
168	C₂×C₄×C₅	#117	1	2	yes	—
169	C₂×C₄×C₅	#117	1	2	yes	—
170	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
173	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
174	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₅	#123	1	2	yes	—
177	C₂×C₄×C₅	#123	1	2	yes	—
178	C₂×C₄×C₅	#125	1	2	yes	—
179	C₂×C₄×C₅	#126	1	2	yes	—
180	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
186	C₅×C₈	—	2	4	no	—
187	C₅×C₈	—	2	4	no	—
188	C₅×C₈	—	2	4	no	—
189	C₅×C₈	—	4	2	no	—
190	C₂³×C₄	—	2	1	no	—
191	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂×M₁₆	—	2	1	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	2	2	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	2	1	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
202	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
203	C₂×M₁₆	C₅×D₄	1	2	yes	—
204	C₂×M₁₆	C₅×D₄	1	2	yes	—
205	C₂×M₁₆	C₅×Q₈	1	4	yes	—
206	C₂×M₁₆	C₂³×C₅	1	2	yes	—
207	C₂×M₁₆	C₂³×C₅	1	2	yes	—
208	C₂²×C₈	—	2	1	no	—
209	C₂²×C₈	—	2	1	no	—
210	C₂²×C₈	C₂³×C₅	1	2	yes	—
211	C₂²×C₈	C₂³×C₅	1	2	yes	—
212	#117	—	2	1	no	—
213	#117	—	2	1	no	—
214	#117	—	2	1	no	—
215	#117	—	2	1	no	—
216	#117	C₂×C₄×C₅	1	2	yes	—
217	#117	C₂×C₄×C₅	1	2	yes	—
218	#117	C₂³×C₅	1	2	yes	—
219	#117	C₂³×C₅	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	2	1	no	—
229	C₂×C₄²	C₂³×C₅	1	2	yes	—
230	#107	C₂×C₄×C₅	1	8	yes	complemented
231	#106	C₂×C₄×C₅	1	8	yes	complemented
232	C₄⋊C₈	—	2	8	no	—
233	#97	—	2	4	no	—
234	C₄×C₈	—	2	4	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	4	2	no	—
239	C₂²×C₅	—	4	2	no	—
240	C₂²×C₅	#387	1	2	yes	—
241	C₂²×C₅	#387	1	2	yes	—
242	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₅	C₂×#125	1	1	yes	characteristic
244	C₂²×C₅	C₂×#126	1	1	yes	characteristic
245	C₄×C₅	—	4	4	no	—
246	C₄×C₅	—	4	4	no	—
247	C₄×C₅	—	4	4	no	—
248	C₄×C₅	#387	1	2	yes	—
249	C₄×C₅	#387	1	2	yes	—
250	C₄×C₅	C₂×#117	1	1	yes	characteristic
251	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
252	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
253	C₄×C₅	C₂×#123	1	1	yes	characteristic
254	C₂⁴	C₅×#41	1	1	yes	characteristic
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
265	C₂²×C₄	C₅×#41	1	2	yes	—
266	C₂²×C₄	C₅×#41	1	2	yes	—
267	C₂²×C₄	C₅×#41	1	1	yes	characteristic
268	C₂²×C₄	C₅×#41	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
270	M₁₆	—	2	4	no	—
271	M₁₆	—	2	4	no	—
272	M₁₆	—	2	4	no	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	4	no	—
275	M₁₆	—	2	2	no	—
276	M₁₆	—	2	2	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	C₂×C₅×Q₈	1	4	yes	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
289	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
293	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	4	2	no	—
305	C₂×C₅	—	2	1	no	—
306	C₂×C₅	—	2	1	no	—
307	C₂×C₅	—	2	2	no	—
308	C₂×C₅	—	2	2	no	—
309	C₂×C₅	C₂×#387	1	1	yes	characteristic
310	C₂×C₅	#2956	1	2	yes	—
311	C₂³	—	4	2	no	—
312	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
313	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
314	C₂³	C₅×#125	1	2	yes	—
315	C₂³	C₅×#126	1	2	yes	—
316	C₂³	C₂×C₅×#41	1	1	yes	characteristic
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	2	no	—
325	C₂×C₄	C₅×#117	1	2	yes	—
326	C₂×C₄	C₅×#117	1	2	yes	—
327	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
328	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
329	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
330	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
331	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
332	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
333	C₂×C₄	C₅×#123	1	2	yes	—
334	C₂×C₄	C₅×#123	1	2	yes	—
335	C₂×C₄	C₅×#125	1	2	yes	—
336	C₂×C₄	C₅×#126	1	2	yes	—
337	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
340	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
341	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
342	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
343	C₈	—	2	4	no	—
344	C₈	—	2	4	no	—
345	C₈	—	2	4	no	—
346	C₈	—	4	2	no	—
347	C₅	#21042	1	1	yes	characteristic, direct product factor, Sylow
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	C₅×#387	1	2	yes	—
354	C₂²	C₅×#387	1	2	yes	—
355	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
356	C₂²	C₂×C₅×#125	1	1	yes	characteristic
357	C₂²	C₂×C₅×#126	1	1	yes	characteristic
358	C₄	—	4	4	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	4	no	—
361	C₄	C₅×#387	1	2	yes	—
362	C₄	C₅×#387	1	2	yes	—
363	C₄	C₂×C₅×#117	1	1	yes	characteristic
364	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
365	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
366	C₄	C₂×C₅×#123	1	1	yes	characteristic
367	C₂	—	2	1	no	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	—	2	1	no	—
371	C₂	C₂×C₅×#387	1	1	yes	characteristic
372	C₂	C₅×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1922	C₂	semidirect
16. C₅×#428	C₄	semidirect
17. C₅×#428	C₄	semidirect
29. #21042	C₅	direct (N × H)
70. C₅×#107	C₂×C₄	semidirect
71. C₅×#106	C₂×C₄	semidirect
78. #1922	C₂×C₅	semidirect
141. #428	C₄×C₅	semidirect
142. #428	C₄×C₅	semidirect
230. #107	C₂×C₄×C₅	semidirect
231. #106	C₂×C₄×C₅	semidirect
347. C₅	#21042	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2911	2
C₅×#2905	2
C₅×#2873	2
C₅×#1922	2
C₅×#1738	2
C₂×C₅×#339	2
C₅×#1728	2
#21042	5

Subgroups — C5×#21042 #11943762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21042 #11943762