Subgroups — C₂×C₅×#5189 #14428032

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#946	C₂	1	2	yes	maximal
3	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#835	C₂	1	2	yes	maximal, complemented
5	C₅×#5189	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#470	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
11	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#946	—	2	4	no	—
14	C₅×#946	C₂²	1	8	yes	—
15	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
21	C₅×#835	C₂²	1	8	yes	complemented
22	C₅×#817	C₂²	1	4	yes	complemented
23	C₂×#5189	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
25	C₂²×C₅×M₁₆	—	3	1	no	—
26	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
27	C₅×#470	—	3	8	no	—
28	C₂×C₅×#106	—	3	1	no	—
29	C₂×C₅×#103	—	3	2	no	—
30	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
31	C₂×C₃×C₅×Q₈	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	—	2	4	no	—
33	C₂×C₃×C₅×Q₈	—	2	4	no	—
34	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	—	2	2	no	—
38	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	—	2	2	no	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
43	C₃×C₅×Q₁₆	—	2	8	no	—
44	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
45	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
46	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
47	C₅×C₄⋊Dic₃	—	2	2	no	—
48	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
49	C₅×Dic₃⋊C₄	—	2	8	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
52	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
53	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂×#946	C₂×C₅	1	2	yes	—
55	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic
56	C₂×#835	C₂×C₅	1	2	yes	complemented
57	#5189	C₂×C₅	1	8	yes	direct product factor
58	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
60	C₂³×C₄×C₅	—	3	1	no	—
61	C₂×C₅×Q₁₆	—	2	4	no	—
62	C₂×C₅×Q₁₆	C₂×D₃	1	4	yes	complemented
63	C₂×C₅×M₁₆	—	3	4	no	—
64	C₂×C₅×M₁₆	—	6	4	no	—
65	C₂²×C₅×C₈	—	3	1	no	—
66	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
67	C₅×C₂²⋊Q₈	—	3	8	no	—
68	C₅×C₂²⋊Q₈	—	6	4	no	—
69	C₂×C₅×C₄⋊C₄	—	3	2	no	—
70	C₂×C₅×C₄⋊C₄	—	6	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
72	C₅×#106	—	3	4	no	—
73	C₅×#103	—	3	8	no	—
74	C₂×#470	—	3	1	no	Sylow
75	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₅×D₃	—	2	2	no	—
77	C₂²×C₅×D₃	—	2	4	no	—
78	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
79	C₃×C₅×Q₈	—	2	4	no	—
80	C₃×C₅×Q₈	—	2	4	no	—
81	C₃×C₅×Q₈	—	4	4	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	4	4	no	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	#41	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
88	C₂×C₅×Dic₃	—	2	2	no	—
89	C₂×C₅×Dic₃	—	2	4	no	—
90	C₂×C₅×Dic₃	—	4	4	no	—
91	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
92	C₄×C₅×D₃	—	2	4	no	—
93	C₄×C₅×D₃	—	2	2	no	—
94	C₄×C₅×D₃	—	2	2	no	—
95	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
96	C₅×C₃⋊C₈	—	2	2	no	—
97	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
98	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×Q₁₆	—	2	4	no	—
100	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
101	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
102	#946	—	2	4	no	—
103	#946	C₂²×C₅	1	8	yes	—
104	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
105	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
106	C₂×Dic₃⋊C₄	—	2	2	no	—
107	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
109	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
110	#835	C₂²×C₅	1	8	yes	complemented
111	#817	C₂²×C₅	1	4	yes	complemented
112	C₂⁴×C₅	—	3	1	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	4	no	—
116	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	3	2	no	—
120	C₂²×C₄×C₅	—	3	2	no	—
121	C₂²×C₄×C₅	—	6	2	no	—
122	C₂²×C₄×C₅	—	6	2	no	—
123	C₂²×C₄×C₅	—	6	2	no	—
124	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₅×Q₁₆	—	2	8	no	—
126	C₅×M₁₆	—	6	8	no	—
127	C₂×C₅×C₈	—	3	2	no	—
128	C₂×C₅×C₈	—	6	2	no	—
129	C₂×C₅×C₈	#67	1	4	yes	—
130	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
131	C₅×C₄⋊C₄	—	3	4	no	—
132	C₅×C₄⋊C₄	—	6	8	no	—
133	C₅×C₄⋊C₄	—	6	2	no	—
134	C₅×C₂²⋊C₄	—	6	8	no	—
135	C₂²×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
136	C₂²×M₁₆	—	3	1	no	—
137	C₂×C₂²⋊Q₈	—	3	2	no	—
138	#470	—	3	8	no	—
139	C₂×#106	—	3	1	no	—
140	C₂×#103	—	3	2	no	—
141	C₂²×C₃×C₅	#121	1	2	yes	—
142	C₂²×C₃×C₅	#137	1	4	yes	—
143	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₅×D₃	—	2	2	no	—
145	C₂×C₅×D₃	—	2	4	no	—
146	C₂×C₅×D₃	—	4	4	no	—
147	C₃×C₄×C₅	—	4	4	no	—
148	C₃×C₄×C₅	#121	1	2	yes	—
149	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
150	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
151	C₅×Dic₃	—	2	2	no	—
152	C₅×Dic₃	—	4	4	no	—
153	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
154	C₂×C₃×Q₈	—	2	2	no	—
155	C₂×C₃×Q₈	—	2	4	no	—
156	C₂×C₃×Q₈	—	2	4	no	—
157	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
158	C₂²×C₃×C₄	—	2	2	no	—
159	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
160	C₂²×Dic₃	—	2	2	no	—
161	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
162	C₂×C₄×D₃	—	2	2	no	—
163	C₂×C₄×D₃	—	2	2	no	—
164	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
165	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
166	C₃×Q₁₆	—	2	8	no	—
167	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
168	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
169	(C₂×D₃)⋊C₄	—	2	8	no	—
170	C₄⋊Dic₃	—	2	2	no	—
171	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
172	Dic₃⋊C₄	—	2	8	no	—
173	C₂×C₃⋊C₈	—	2	2	no	—
174	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
175	ΓL(1,𝔽₂₅)	—	2	8	no	—
176	C₂³×C₅	—	3	2	no	—
177	C₂³×C₅	—	6	4	no	—
178	C₂³×C₅	—	6	2	no	—
179	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
180	C₅×Q₈	—	2	4	no	—
181	C₅×Q₈	—	2	4	no	—
182	C₅×Q₈	—	4	4	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	3	2	no	—
185	C₂×C₄×C₅	—	4	4	no	—
186	C₂×C₄×C₅	—	6	2	no	—
187	C₂×C₄×C₅	—	6	4	no	—
188	C₂×C₄×C₅	—	6	2	no	—
189	C₂×C₄×C₅	—	6	2	no	—
190	C₂×C₄×C₅	—	6	4	no	—
191	C₂×C₄×C₅	—	12	4	no	—
192	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	#237	1	2	yes	—
194	C₂×C₄×C₅	C₂×#67	1	2	yes	—
195	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
196	C₅×C₈	—	6	2	no	—
197	C₅×C₈	C₂×#67	1	4	yes	—
198	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
199	C₂³×C₄	—	3	1	no	—
200	C₂×Q₁₆	—	2	4	no	—
201	C₂×Q₁₆	C₂×C₅×D₃	1	4	yes	complemented
202	C₂×M₁₆	—	3	4	no	—
203	C₂×M₁₆	—	6	4	no	—
204	C₂²×C₈	—	3	1	no	—
205	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
206	C₂²⋊Q₈	—	3	8	no	—
207	C₂²⋊Q₈	—	6	4	no	—
208	C₂×C₄⋊C₄	—	3	2	no	—
209	C₂×C₄⋊C₄	—	6	2	no	—
210	C₂×C₂²⋊C₄	—	6	2	no	—
211	#106	—	3	4	no	—
212	#103	—	3	8	no	—
213	C₂×C₃×C₅	#470	1	4	yes	complemented
214	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂×#137	1	2	yes	—
216	C₅×D₃	—	4	2	no	—
217	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
218	C₂²×D₃	—	2	2	no	—
219	C₂²×D₃	—	2	4	no	—
220	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
221	C₃×Q₈	—	2	4	no	—
222	C₃×Q₈	—	2	4	no	—
223	C₃×Q₈	—	4	4	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	4	4	no	—
226	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
228	C₂×C₃×C₄	C₅×#41	1	2	yes	—
229	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
230	C₂×Dic₃	—	2	2	no	—
231	C₂×Dic₃	—	2	4	no	—
232	C₂×Dic₃	—	4	4	no	—
233	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
234	C₄×D₃	—	2	4	no	—
235	C₄×D₃	—	2	2	no	—
236	C₄×D₃	—	2	2	no	—
237	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
238	C₃⋊C₈	—	2	2	no	—
239	C₂²×C₅	—	6	4	no	—
240	C₂²×C₅	—	6	2	no	—
241	C₂²×C₅	—	12	4	no	—
242	C₂²×C₅	#918	1	4	yes	—
243	C₂²×C₅	#938	1	2	yes	—
244	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
245	C₄×C₅	—	4	4	no	—
246	C₄×C₅	—	6	2	no	—
247	C₄×C₅	—	12	4	no	—
248	C₄×C₅	#938	1	2	yes	—
249	C₄×C₅	C₂×#237	1	1	yes	characteristic
250	C₄×C₅	C₂²×#67	1	1	yes	characteristic
251	C₂⁴	—	3	1	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	3	1	no	—
258	C₂²×C₄	—	3	2	no	—
259	C₂²×C₄	—	3	2	no	—
260	C₂²×C₄	—	6	2	no	—
261	C₂²×C₄	—	6	2	no	—
262	C₂²×C₄	—	6	2	no	—
263	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
264	Q₁₆	—	2	8	no	—
265	M₁₆	—	6	8	no	—
266	C₂×C₈	—	3	2	no	—
267	C₂×C₈	—	6	2	no	—
268	C₂×C₈	C₅×#67	1	4	yes	—
269	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
270	C₄⋊C₄	—	3	4	no	—
271	C₄⋊C₄	—	6	8	no	—
272	C₄⋊C₄	—	6	2	no	—
273	C₂²⋊C₄	—	6	8	no	—
274	C₃×C₅	C₂×#470	1	1	yes	characteristic, complemented, Hall
275	C₂²×C₃	C₅×#121	1	2	yes	—
276	C₂²×C₃	C₅×#137	1	4	yes	—
277	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
278	C₂×D₃	—	2	2	no	—
279	C₂×D₃	—	2	4	no	—
280	C₂×D₃	—	4	4	no	—
281	C₃×C₄	—	4	4	no	—
282	C₃×C₄	C₅×#121	1	2	yes	—
283	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
284	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
285	Dic₃	—	2	2	no	—
286	Dic₃	—	4	4	no	—
287	C₂×C₅	—	12	2	no	—
288	C₂×C₅	#5189	1	4	yes	direct product factor
289	C₂×C₅	C₂×#918	1	2	yes	—
290	C₂×C₅	C₂×#938	1	1	yes	characteristic
291	C₂³	—	3	2	no	—
292	C₂³	—	6	4	no	—
293	C₂³	—	6	2	no	—
294	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
295	Q₈	—	2	4	no	—
296	Q₈	—	2	4	no	—
297	Q₈	—	4	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	3	2	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	6	2	no	—
302	C₂×C₄	—	6	4	no	—
303	C₂×C₄	—	6	2	no	—
304	C₂×C₄	—	6	2	no	—
305	C₂×C₄	—	6	4	no	—
306	C₂×C₄	—	12	4	no	—
307	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
308	C₂×C₄	C₅×#237	1	2	yes	—
309	C₂×C₄	C₂×C₅×#67	1	2	yes	—
310	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
311	C₈	—	6	2	no	—
312	C₈	C₂×C₅×#67	1	4	yes	—
313	C₂×C₃	C₅×#470	1	4	yes	complemented
314	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
315	C₂×C₃	C₂×C₅×#137	1	2	yes	—
316	D₃	—	4	2	no	—
317	C₅	C₂×#5189	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²	—	6	4	no	—
319	C₂²	—	6	2	no	—
320	C₂²	—	12	4	no	—
321	C₂²	C₅×#918	1	4	yes	—
322	C₂²	C₅×#938	1	2	yes	—
323	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
324	C₄	—	4	4	no	—
325	C₄	—	6	2	no	—
326	C₄	—	12	4	no	—
327	C₄	C₅×#938	1	2	yes	—
328	C₄	C₂×C₅×#237	1	1	yes	characteristic
329	C₄	C₂²×C₅×#67	1	1	yes	characteristic
330	C₃	C₂×C₅×#470	1	1	yes	characteristic, complemented, Sylow
331	C₂	—	12	2	no	—
332	C₂	C₅×#5189	1	4	yes	direct product factor
333	C₂	C₂×C₅×#918	1	2	yes	—
334	C₂	C₂×C₅×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
hypercenter	C₂²×C₅×Q₁₆	D₃
hypocenter	C₃	C₂×C₅×#470
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₂×C₅×#835	C₂	semidirect
5. C₅×#5189	C₂	direct (N × H)
6. C₂×C₅×#817	C₂	semidirect
11. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
21. C₅×#835	C₂²	semidirect
22. C₅×#817	C₂²	semidirect
23. C₂×#5189	C₅	direct (N × H)
24. C₂²×C₅×Q₁₆	D₃	semidirect
53. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
56. C₂×#835	C₂×C₅	semidirect
57. #5189	C₂×C₅	direct (N × H)
58. C₂×#817	C₂×C₅	semidirect
62. C₂×C₅×Q₁₆	C₂×D₃	semidirect
100. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
110. #835	C₂²×C₅	semidirect
111. #817	C₂²×C₅	semidirect
135. C₂²×Q₁₆	C₅×D₃	semidirect
201. C₂×Q₁₆	C₂×C₅×D₃	semidirect
213. C₂×C₃×C₅	#470	semidirect
274. C₃×C₅	C₂×#470	semidirect
288. C₂×C₅	#5189	direct (N × H)
313. C₂×C₃	C₅×#470	semidirect
317. C₅	C₂×#5189	direct (N × H)
330. C₃	C₂×C₅×#470	semidirect
332. C₂	C₅×#5189	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×Q₁₆	2
C₂×C₅×#946	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂×C₅×#835	2
C₅×#5189	2
C₂×C₅×#817	2
C₂×C₅×#470	3
C₂×#5189	5

Subgroups — C2×C5×#5189 #14428032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5189 #14428032