Subgroups — C₅×#64306 #13089319

Order 1440.

710 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#235	C₂	1	2	yes	maximal, complemented
3	C₅×#3811	C₂	1	2	yes	maximal, complemented
4	C₅×#3805	C₂	1	2	yes	maximal, complemented
5	C₅×#3802	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×D₃²	C₂	1	2	yes	maximal, complemented
7	C₅×#3798	C₂	1	2	yes	maximal, complemented
8	C₅×#3797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3796	C₂	1	2	yes	maximal, complemented
10	C₅×D₃×#41	—	3	2	no	maximal
11	C₂²×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂×C₅×D₃²	C₂²	1	2	yes	—
13	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
15	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
16	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
17	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
18	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#67	C₂²	1	4	yes	complemented
20	C₃×C₅×D₁₂	C₂²	1	2	yes	complemented
21	C₃×C₄×C₅×D₃	C₂²	1	4	yes	complemented
22	C₃×C₅×Dic₆	C₂²	1	2	yes	complemented
23	C₅×#627	C₂²	1	2	yes	complemented
24	C₅×#626	C₂²	1	4	yes	complemented
25	C₅×#625	C₂²	1	2	yes	complemented
26	C₅×#624	C₂²	1	2	yes	—
27	C₅×D₃×Dic₃	C₂²	1	4	yes	complemented
28	#64306	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₃×C₅×#41	—	3	2	no	—
30	C₅×#239	—	3	2	no	—
31	C₅×D₃×Q₈	—	3	2	no	—
32	C₅×#237	—	3	4	no	—
33	C₅×#237	—	3	2	no	—
34	C₅×D₃×D₄	—	3	4	no	—
35	C₅×D₃×D₄	—	3	2	no	—
36	C₅×#235	—	3	4	no	—
37	C₅×#235	D₃	1	2	yes	complemented
38	C₂×C₄×C₅×D₃	—	3	2	no	—
39	C₂×C₄×C₅×D₃	—	3	4	no	—
40	C₂×C₄×C₅×D₃	—	6	1	no	—
41	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×C₃⋊D₃	—	2	2	no	—
43	C₂×C₅×C₃⋊D₃	C₂³	1	1	yes	characteristic
44	C₂×C₅×C₃⋊D₃	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×D₃	C₂³	1	4	yes	—
46	C₅×D₃²	—	2	4	no	—
47	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₅×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
50	C₅×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
51	C₃×C₅×Dic₃	C₂³	1	4	yes	—
52	C₂×C₅×#41	—	9	1	no	Hall
53	C₂×C₄×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×#235	C₂×C₅	1	2	yes	complemented
55	#3811	C₂×C₅	1	2	yes	complemented
56	#3805	C₂×C₅	1	2	yes	complemented
57	#3802	C₂×C₅	1	1	yes	characteristic, complemented
58	C₄×D₃²	C₂×C₅	1	2	yes	complemented
59	#3798	C₂×C₅	1	2	yes	complemented
60	#3797	C₂×C₅	1	1	yes	characteristic, complemented
61	#3796	C₂×C₅	1	2	yes	complemented
62	C₂²×C₅×D₃	—	3	2	no	—
63	C₂²×C₅×D₃	—	3	4	no	—
64	C₂²×C₅×D₃	—	6	1	no	—
65	C₃×C₅×Q₈	—	3	2	no	—
66	C₃×C₅×D₄	—	3	4	no	—
67	C₃×C₅×D₄	—	3	2	no	—
68	C₂×C₃×C₄×C₅	—	2	1	no	—
69	C₂×C₃×C₄×C₅	—	3	4	no	—
70	C₂×C₃×C₄×C₅	C₂×D₃	1	2	yes	complemented
71	C₅×#67	—	3	4	no	—
72	C₅×#67	—	3	4	no	—
73	C₅×#67	C₂×D₃	1	4	yes	complemented
74	C₂×C₅×Dic₃	—	3	2	no	—
75	C₂×C₅×Dic₃	—	3	4	no	—
76	C₂×C₅×Dic₃	—	6	1	no	—
77	C₅×D₁₂	—	3	4	no	—
78	C₅×D₁₂	C₂×D₃	1	2	yes	complemented
79	C₄×C₅×D₃	—	3	4	no	—
80	C₄×C₅×D₃	—	3	2	no	—
81	C₄×C₅×D₃	—	3	2	no	—
82	C₄×C₅×D₃	—	3	2	no	—
83	C₄×C₅×D₃	—	3	2	no	—
84	C₄×C₅×D₃	—	3	4	no	—
85	C₄×C₅×D₃	—	6	1	no	—
86	C₄×C₅×D₃	—	6	1	no	—
87	C₄×C₅×D₃	—	6	1	no	—
88	C₄×C₅×D₃	—	6	1	no	—
89	C₄×C₅×D₃	C₂×D₃	1	4	yes	complemented
90	C₅×Dic₆	—	3	4	no	—
91	C₅×Dic₆	C₂×D₃	1	2	yes	complemented
92	D₃×#41	—	3	2	no	—
93	C₂×C₃²×C₅	—	2	1	no	—
94	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
95	C₅×C₃⋊D₃	—	2	1	no	—
96	C₅×C₃⋊D₃	#41	1	2	yes	complemented
97	C₃×C₅×D₃	—	2	4	no	—
98	C₅×#41	—	3	2	no	—
99	C₅×#41	—	9	2	no	—
100	C₅×#41	—	9	2	no	—
101	C₅×#41	—	9	2	no	—
102	C₂×C₅×Q₈	—	9	1	no	—
103	C₂×C₅×D₄	—	9	2	no	—
104	C₂×C₅×D₄	—	9	1	no	—
105	C₂²×C₄×C₅	—	9	2	no	—
106	C₂²×C₄×C₅	—	9	1	no	—
107	C₂²×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
108	C₂×D₃²	C₂²×C₅	1	2	yes	—
109	C₂×C₃²×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
110	C₂×C₃⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
111	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
112	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
113	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic, complemented
114	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic, complemented
115	C₃×#67	C₂²×C₅	1	4	yes	complemented
116	C₃×D₁₂	C₂²×C₅	1	2	yes	complemented
117	C₃×C₄×D₃	C₂²×C₅	1	4	yes	complemented
118	C₃×Dic₆	C₂²×C₅	1	2	yes	complemented
119	#627	C₂²×C₅	1	2	yes	complemented
120	#626	C₂²×C₅	1	4	yes	complemented
121	#625	C₂²×C₅	1	2	yes	complemented
122	#624	C₂²×C₅	1	2	yes	—
123	D₃×Dic₃	C₂²×C₅	1	4	yes	complemented
124	C₂²×C₃×C₅	—	2	1	no	—
125	C₂²×C₃×C₅	—	3	4	no	—
126	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
127	C₂×C₅×D₃	—	3	2	no	—
128	C₂×C₅×D₃	—	3	2	no	—
129	C₂×C₅×D₃	—	6	1	no	—
130	C₂×C₅×D₃	—	6	1	no	—
131	C₂×C₅×D₃	—	6	8	no	—
132	C₂×C₅×D₃	—	6	4	no	—
133	C₂×C₅×D₃	—	6	4	no	—
134	C₂×C₅×D₃	C₂²×D₃	1	4	yes	—
135	C₃×C₄×C₅	—	2	1	no	—
136	C₃×C₄×C₅	—	2	1	no	—
137	C₃×C₄×C₅	—	3	4	no	—
138	C₃×C₄×C₅	C₂²×D₃	1	2	yes	—
139	C₃×C₄×C₅	C₂²×D₃	1	2	yes	—
140	C₅×Dic₃	—	3	2	no	—
141	C₅×Dic₃	—	3	2	no	—
142	C₅×Dic₃	—	6	1	no	—
143	C₅×Dic₃	—	6	1	no	—
144	C₅×Dic₃	C₂²×D₃	1	4	yes	—
145	C₃×#41	—	3	2	no	—
146	#239	—	3	2	no	—
147	D₃×Q₈	—	3	2	no	—
148	#237	—	3	4	no	—
149	#237	—	3	2	no	—
150	D₃×D₄	—	3	4	no	—
151	D₃×D₄	—	3	2	no	—
152	#235	—	3	4	no	—
153	#235	C₅×D₃	1	2	yes	complemented
154	C₂×C₄×D₃	—	3	2	no	—
155	C₂×C₄×D₃	—	3	4	no	—
156	C₂×C₄×D₃	—	6	1	no	—
157	C₃²×C₅	C₂×#41	1	1	yes	characteristic, complemented, Hall
158	C₂³×C₅	—	9	2	no	—
159	C₂³×C₅	—	9	1	no	—
160	C₅×Q₈	—	3	2	no	—
161	C₅×Q₈	—	9	2	no	—
162	C₅×D₄	—	3	4	no	—
163	C₅×D₄	—	3	2	no	—
164	C₅×D₄	—	9	4	no	—
165	C₅×D₄	—	9	2	no	—
166	C₂×C₄×C₅	—	3	4	no	—
167	C₂×C₄×C₅	—	9	2	no	—
168	C₂×C₄×C₅	—	9	4	no	—
169	C₂×C₄×C₅	—	9	1	no	—
170	C₂×C₄×C₅	—	9	1	no	—
171	C₂×C₄×C₅	—	9	1	no	—
172	C₂×C₄×C₅	—	9	1	no	—
173	C₂×C₄×C₅	—	9	1	no	—
174	C₂×C₄×C₅	D₃²	1	1	yes	characteristic, complemented
175	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
176	C₂×C₃⋊D₃	—	2	2	no	—
177	C₂×C₃⋊D₃	C₂³×C₅	1	1	yes	characteristic
178	C₂×C₃⋊D₃	C₂³×C₅	1	1	yes	characteristic
179	C₂×C₃×D₃	C₂³×C₅	1	4	yes	—
180	D₃²	—	2	4	no	—
181	C₃²×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₃²×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₃⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
184	C₃⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
185	C₃×Dic₃	C₂³×C₅	1	4	yes	—
186	C₂×#41	—	9	1	no	Sylow
187	C₂×C₃×C₅	—	2	2	no	—
188	C₂×C₃×C₅	—	2	2	no	—
189	C₂×C₃×C₅	—	2	1	no	—
190	C₂×C₃×C₅	—	6	4	no	—
191	C₂×C₃×C₅	C₂³×D₃	1	2	yes	—
192	C₅×D₃	—	2	4	no	—
193	C₅×D₃	—	3	4	no	—
194	C₅×D₃	—	6	2	no	—
195	C₅×D₃	—	6	2	no	—
196	C₅×D₃	—	6	2	no	—
197	C₂²×D₃	—	3	2	no	—
198	C₂²×D₃	—	3	4	no	—
199	C₂²×D₃	—	6	1	no	—
200	C₃×Q₈	—	3	2	no	—
201	C₃×D₄	—	3	4	no	—
202	C₃×D₄	—	3	2	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	3	4	no	—
205	C₂×C₃×C₄	C₂×C₅×D₃	1	2	yes	complemented
206	#67	—	3	4	no	—
207	#67	—	3	4	no	—
208	#67	C₂×C₅×D₃	1	4	yes	complemented
209	C₂×Dic₃	—	3	2	no	—
210	C₂×Dic₃	—	3	4	no	—
211	C₂×Dic₃	—	6	1	no	—
212	D₁₂	—	3	4	no	—
213	D₁₂	C₂×C₅×D₃	1	2	yes	complemented
214	C₄×D₃	—	3	4	no	—
215	C₄×D₃	—	3	2	no	—
216	C₄×D₃	—	3	2	no	—
217	C₄×D₃	—	3	2	no	—
218	C₄×D₃	—	3	2	no	—
219	C₄×D₃	—	3	4	no	—
220	C₄×D₃	—	6	1	no	—
221	C₄×D₃	—	6	1	no	—
222	C₄×D₃	—	6	1	no	—
223	C₄×D₃	—	6	1	no	—
224	C₄×D₃	C₂×C₅×D₃	1	4	yes	complemented
225	Dic₆	—	3	4	no	—
226	Dic₆	C₂×C₅×D₃	1	2	yes	complemented
227	C₂²×C₅	—	3	4	no	—
228	C₂²×C₅	—	9	1	no	—
229	C₂²×C₅	—	9	1	no	—
230	C₂²×C₅	—	18	2	no	—
231	C₂²×C₅	—	18	4	no	—
232	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
233	C₄×C₅	—	3	4	no	—
234	C₄×C₅	—	9	1	no	—
235	C₄×C₅	—	9	1	no	—
236	C₄×C₅	C₂×D₃²	1	1	yes	characteristic
237	C₄×C₅	C₂×D₃²	1	1	yes	characteristic
238	C₂×C₃²	—	2	1	no	—
239	C₂×C₃²	C₂⁴×C₅	1	1	yes	characteristic
240	C₃⋊D₃	—	2	1	no	—
241	C₃⋊D₃	C₅×#41	1	2	yes	complemented
242	C₃×D₃	—	2	4	no	—
243	#41	—	3	2	no	—
244	#41	—	9	2	no	—
245	#41	—	9	2	no	—
246	#41	—	9	2	no	—
247	C₂×Q₈	—	9	1	no	—
248	C₂×D₄	—	9	2	no	—
249	C₂×D₄	—	9	1	no	—
250	C₂²×C₄	—	9	2	no	—
251	C₂²×C₄	—	9	1	no	—
252	C₃×C₅	—	2	1	no	—
253	C₃×C₅	D₃×#41	1	2	yes	complemented
254	C₂²×C₃	—	2	1	no	—
255	C₂²×C₃	—	3	4	no	—
256	C₂²×C₃	C₂²×C₅×D₃	1	2	yes	—
257	C₂×D₃	—	3	2	no	—
258	C₂×D₃	—	3	2	no	—
259	C₂×D₃	—	6	1	no	—
260	C₂×D₃	—	6	1	no	—
261	C₂×D₃	—	6	8	no	—
262	C₂×D₃	—	6	4	no	—
263	C₂×D₃	—	6	4	no	—
264	C₂×D₃	C₂²×C₅×D₃	1	4	yes	—
265	C₃×C₄	—	2	1	no	—
266	C₃×C₄	—	2	1	no	—
267	C₃×C₄	—	3	4	no	—
268	C₃×C₄	C₂²×C₅×D₃	1	2	yes	—
269	C₃×C₄	C₂²×C₅×D₃	1	2	yes	—
270	Dic₃	—	3	2	no	—
271	Dic₃	—	3	2	no	—
272	Dic₃	—	6	1	no	—
273	Dic₃	—	6	1	no	—
274	Dic₃	C₂²×C₅×D₃	1	4	yes	—
275	C₂×C₅	—	2	1	no	—
276	C₂×C₅	—	6	4	no	—
277	C₂×C₅	—	9	2	no	—
278	C₂×C₅	—	18	1	no	—
279	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
280	C₃²	C₂×C₅×#41	1	1	yes	characteristic, complemented, Sylow
281	C₂³	—	9	2	no	—
282	C₂³	—	9	1	no	—
283	Q₈	—	3	2	no	—
284	Q₈	—	9	2	no	—
285	D₄	—	3	4	no	—
286	D₄	—	3	2	no	—
287	D₄	—	9	4	no	—
288	D₄	—	9	2	no	—
289	C₂×C₄	—	3	4	no	—
290	C₂×C₄	—	9	2	no	—
291	C₂×C₄	—	9	4	no	—
292	C₂×C₄	—	9	1	no	—
293	C₂×C₄	—	9	1	no	—
294	C₂×C₄	—	9	1	no	—
295	C₂×C₄	—	9	1	no	—
296	C₂×C₄	—	9	1	no	—
297	C₂×C₄	C₅×D₃²	1	1	yes	characteristic, complemented
298	C₂×C₃	—	2	2	no	—
299	C₂×C₃	—	2	2	no	—
300	C₂×C₃	—	2	1	no	—
301	C₂×C₃	—	6	4	no	—
302	C₂×C₃	C₂³×C₅×D₃	1	2	yes	—
303	D₃	—	2	4	no	—
304	D₃	—	3	4	no	—
305	D₃	—	6	2	no	—
306	D₃	—	6	2	no	—
307	D₃	—	6	2	no	—
308	C₅	#64306	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²	—	3	4	no	—
310	C₂²	—	9	1	no	—
311	C₂²	—	9	1	no	—
312	C₂²	—	18	2	no	—
313	C₂²	—	18	4	no	—
314	C₂²	C₂×C₅×D₃²	1	1	yes	characteristic
315	C₄	—	3	4	no	—
316	C₄	—	9	1	no	—
317	C₄	—	9	1	no	—
318	C₄	C₂×C₅×D₃²	1	1	yes	characteristic
319	C₄	C₂×C₅×D₃²	1	1	yes	characteristic
320	C₃	—	2	1	no	—
321	C₃	C₅×D₃×#41	1	2	yes	complemented
322	C₂	—	2	1	no	—
323	C₂	—	6	4	no	—
324	C₂	—	9	2	no	—
325	C₂	—	18	1	no	—
326	C₂	C₂²×C₅×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃²
Fitting	C₂×C₃²×C₄×C₅	C₂²
socle	C₂×C₃²×C₅	C₂⁴
hypercenter	C₂×C₄×C₅	D₃²
hypocenter	C₃²	C₂×C₅×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×C₃⋊D₃	C₂	semidirect
2. C₃×C₅×#235	C₂	semidirect
3. C₅×#3811	C₂	semidirect
4. C₅×#3805	C₂	semidirect
5. C₅×#3802	C₂	semidirect
6. C₄×C₅×D₃²	C₂	semidirect
7. C₅×#3798	C₂	semidirect
8. C₅×#3797	C₂	semidirect
9. C₅×#3796	C₂	semidirect
13. C₂×C₃²×C₄×C₅	C₂²	semidirect
14. C₂×C₅×C₃⋊Dic₃	C₂²	semidirect
17. C₄×C₅×C₃⋊D₃	C₂²	semidirect
18. C₄×C₅×C₃⋊D₃	C₂²	semidirect
19. C₃×C₅×#67	C₂²	semidirect
20. C₃×C₅×D₁₂	C₂²	semidirect
21. C₃×C₄×C₅×D₃	C₂²	semidirect
22. C₃×C₅×Dic₆	C₂²	semidirect
23. C₅×#627	C₂²	semidirect
24. C₅×#626	C₂²	semidirect
25. C₅×#625	C₂²	semidirect
27. C₅×D₃×Dic₃	C₂²	semidirect
28. #64306	C₅	direct (N × H)
37. C₅×#235	D₃	semidirect
53. C₂×C₄×C₃⋊D₃	C₂×C₅	semidirect
54. C₃×#235	C₂×C₅	semidirect
55. #3811	C₂×C₅	semidirect
56. #3805	C₂×C₅	semidirect
57. #3802	C₂×C₅	semidirect
58. C₄×D₃²	C₂×C₅	semidirect
59. #3798	C₂×C₅	semidirect
60. #3797	C₂×C₅	semidirect
61. #3796	C₂×C₅	semidirect
70. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
73. C₅×#67	C₂×D₃	semidirect
78. C₅×D₁₂	C₂×D₃	semidirect
89. C₄×C₅×D₃	C₂×D₃	semidirect
91. C₅×Dic₆	C₂×D₃	semidirect
96. C₅×C₃⋊D₃	#41	semidirect
109. C₂×C₃²×C₄	C₂²×C₅	semidirect
110. C₂×C₃⋊Dic₃	C₂²×C₅	semidirect
113. C₄×C₃⋊D₃	C₂²×C₅	semidirect
114. C₄×C₃⋊D₃	C₂²×C₅	semidirect
115. C₃×#67	C₂²×C₅	semidirect
116. C₃×D₁₂	C₂²×C₅	semidirect
117. C₃×C₄×D₃	C₂²×C₅	semidirect
118. C₃×Dic₆	C₂²×C₅	semidirect
119. #627	C₂²×C₅	semidirect
120. #626	C₂²×C₅	semidirect
121. #625	C₂²×C₅	semidirect
123. D₃×Dic₃	C₂²×C₅	semidirect
153. #235	C₅×D₃	semidirect
157. C₃²×C₅	C₂×#41	semidirect
174. C₂×C₄×C₅	D₃²	semidirect
205. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
208. #67	C₂×C₅×D₃	semidirect
213. D₁₂	C₂×C₅×D₃	semidirect
224. C₄×D₃	C₂×C₅×D₃	semidirect
226. Dic₆	C₂×C₅×D₃	semidirect
241. C₃⋊D₃	C₅×#41	semidirect
253. C₃×C₅	D₃×#41	semidirect
280. C₃²	C₂×C₅×#41	semidirect
297. C₂×C₄	C₅×D₃²	semidirect
308. C₅	#64306	direct (N × H)
321. C₃	C₅×D₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₃⋊D₃	2
C₃×C₅×#235	2
C₅×#3811	2
C₅×#3805	2
C₅×#3802	2
C₄×C₅×D₃²	2
C₅×#3798	2
C₅×#3797	2
C₅×#3796	2
C₅×D₃×#41	3
#64306	5

Subgroups — C5×#64306 #13089319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64306 #13089319