Subgroups — C₃×C₅×#3189 #14276223

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
2	C₃×C₅×#484	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#467	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#451	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₅×#3189	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
12	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
13	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
14	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
18	C₃×C₅×#107	C₂²	1	4	yes	complemented
19	C₃×C₅×#103	C₂²	1	8	yes	complemented
20	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
21	C₃×#3189	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
23	C₅×#484	C₂×C₃	1	4	yes	complemented
24	C₅×#467	C₂×C₃	1	4	yes	complemented
25	C₅×#451	C₂×C₃	1	4	yes	complemented
26	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂×C₃×C₅×Q₈	—	2	2	no	—
29	C₂×C₃×C₅×Q₈	—	4	4	no	—
30	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	4	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₃×C₅×Q₁₆	—	4	4	no	—
39	C₂×C₃×C₅×C₈	—	4	2	no	—
40	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
45	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
47	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
48	C₃×#484	C₂×C₅	1	4	yes	complemented
49	C₃×#467	C₂×C₅	1	4	yes	complemented
50	C₃×#451	C₂×C₅	1	4	yes	complemented
51	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
52	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
53	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
55	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
56	C₅×C₂²⋊Q₈	—	2	2	no	—
57	C₅×C₂²⋊Q₈	—	2	2	no	—
58	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
59	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₅×#107	C₂²×C₃	1	4	yes	complemented
64	C₅×#103	C₂²×C₃	1	8	yes	complemented
65	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
66	#3189	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂³×C₃×C₅	—	4	1	no	—
68	C₂³×C₃×C₅	—	4	1	no	—
69	C₂³×C₃×C₅	Q₁₆	1	4	yes	complemented
70	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
71	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
72	C₃×C₅×Q₈	—	2	8	no	—
73	C₃×C₅×Q₈	—	4	4	no	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	4	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	2	4	no	—
78	C₂×C₃×C₄×C₅	—	4	2	no	—
79	C₂×C₃×C₄×C₅	—	4	1	no	—
80	C₂×C₃×C₄×C₅	—	4	4	no	—
81	C₂×C₃×C₄×C₅	—	4	4	no	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
85	C₃×C₅×C₈	—	2	4	no	—
86	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
87	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
88	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
89	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
90	C₃×C₂²⋊Q₈	—	2	2	no	—
91	C₃×C₂²⋊Q₈	—	2	2	no	—
92	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
93	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
94	C₂×C₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
96	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
97	C₃×#107	C₂²×C₅	1	4	yes	complemented
98	C₃×#103	C₂²×C₅	1	8	yes	complemented
99	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
100	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	—	4	4	no	—
103	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	4	2	no	—
107	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
108	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
110	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
111	C₅×Q₁₆	—	4	4	no	—
112	C₂×C₅×C₈	—	4	2	no	—
113	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₄⋊C₄	—	2	2	no	—
117	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
118	C₅×C₂²⋊C₄	—	2	4	no	—
119	C₅×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	—
121	#484	C₂×C₃×C₅	1	4	yes	complemented
122	#467	C₂×C₃×C₅	1	4	yes	complemented
123	#451	C₂×C₃×C₅	1	4	yes	complemented
124	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	2	1	no	—
127	C₂²×C₃×C₅	—	2	2	no	—
128	C₂²×C₃×C₅	—	2	1	no	—
129	C₂²×C₃×C₅	—	4	4	no	—
130	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
131	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	—
132	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
133	C₃×C₄×C₅	—	2	1	no	—
134	C₃×C₄×C₅	—	2	2	no	—
135	C₃×C₄×C₅	—	4	4	no	—
136	C₃×C₄×C₅	—	4	4	no	—
137	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
138	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
139	C₂×C₃×Q₈	—	2	2	no	—
140	C₂×C₃×Q₈	—	4	4	no	—
141	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	4	2	no	—
145	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
146	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
148	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
149	C₃×Q₁₆	—	4	4	no	—
150	C₂×C₃×C₈	—	4	2	no	—
151	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
152	C₃×C₄⋊C₄	—	2	4	no	—
153	C₃×C₄⋊C₄	—	2	4	no	—
154	C₃×C₄⋊C₄	—	2	2	no	—
155	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
156	C₃×C₂²⋊C₄	—	2	4	no	—
157	C₃×C₂²⋊C₄	—	2	4	no	—
158	C₂³×C₅	—	4	1	no	—
159	C₂³×C₅	—	4	1	no	—
160	C₂³×C₅	C₃×Q₁₆	1	4	yes	complemented
161	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
162	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
163	C₅×Q₈	—	2	8	no	—
164	C₅×Q₈	—	4	4	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	4	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	4	2	no	—
170	C₂×C₄×C₅	—	4	1	no	—
171	C₂×C₄×C₅	—	4	4	no	—
172	C₂×C₄×C₅	—	4	4	no	—
173	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
175	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
176	C₅×C₈	—	2	4	no	—
177	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
178	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
179	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	complemented
180	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
181	C₂²⋊Q₈	—	2	2	no	—
182	C₂²⋊Q₈	—	2	2	no	—
183	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
184	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
185	C₂×C₄⋊C₄	—	2	2	no	—
186	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
187	C₂×C₂²⋊C₄	—	2	2	no	—
188	#107	C₂²×C₃×C₅	1	4	yes	complemented
189	#103	C₂²×C₃×C₅	1	8	yes	complemented
190	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	—
191	C₂×C₃×C₅	—	2	4	no	—
192	C₂×C₃×C₅	—	2	2	no	—
193	C₂×C₃×C₅	#534	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
195	C₂×C₃×C₅	#575	1	1	yes	characteristic
196	C₂³×C₃	—	4	1	no	—
197	C₂³×C₃	—	4	1	no	—
198	C₂³×C₃	C₅×Q₁₆	1	4	yes	complemented
199	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
200	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
201	C₃×Q₈	—	2	8	no	—
202	C₃×Q₈	—	4	4	no	—
203	C₂×C₃×C₄	—	2	2	no	—
204	C₂×C₃×C₄	—	2	4	no	—
205	C₂×C₃×C₄	—	2	4	no	—
206	C₂×C₃×C₄	—	2	4	no	—
207	C₂×C₃×C₄	—	4	2	no	—
208	C₂×C₃×C₄	—	4	1	no	—
209	C₂×C₃×C₄	—	4	4	no	—
210	C₂×C₃×C₄	—	4	4	no	—
211	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
213	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
214	C₃×C₈	—	2	4	no	—
215	C₂²×C₅	—	2	2	no	—
216	C₂²×C₅	—	2	1	no	—
217	C₂²×C₅	—	2	2	no	—
218	C₂²×C₅	—	2	1	no	—
219	C₂²×C₅	—	4	4	no	—
220	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
221	C₂²×C₅	C₂×C₃×Q₁₆	1	4	yes	—
222	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
223	C₄×C₅	—	2	1	no	—
224	C₄×C₅	—	2	2	no	—
225	C₄×C₅	—	4	4	no	—
226	C₄×C₅	—	4	4	no	—
227	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
228	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
229	C₂×Q₈	—	2	2	no	—
230	C₂×Q₈	—	4	4	no	—
231	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	4	2	no	—
235	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
236	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
237	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
238	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
239	Q₁₆	—	4	4	no	—
240	C₂×C₈	—	4	2	no	—
241	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
242	C₄⋊C₄	—	2	4	no	—
243	C₄⋊C₄	—	2	4	no	—
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
246	C₂²⋊C₄	—	2	4	no	—
247	C₂²⋊C₄	—	2	4	no	—
248	C₃×C₅	#3189	1	1	yes	characteristic, direct product factor, Hall
249	C₂²×C₃	—	2	2	no	—
250	C₂²×C₃	—	2	1	no	—
251	C₂²×C₃	—	2	2	no	—
252	C₂²×C₃	—	2	1	no	—
253	C₂²×C₃	—	4	4	no	—
254	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
255	C₂²×C₃	C₂×C₅×Q₁₆	1	4	yes	—
256	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
257	C₃×C₄	—	2	1	no	—
258	C₃×C₄	—	2	2	no	—
259	C₃×C₄	—	4	4	no	—
260	C₃×C₄	—	4	4	no	—
261	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
262	C₂×C₅	—	2	4	no	—
263	C₂×C₅	—	2	2	no	—
264	C₂×C₅	C₃×#534	1	1	yes	characteristic
265	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
266	C₂×C₅	C₃×#575	1	1	yes	characteristic
267	C₂³	—	4	1	no	—
268	C₂³	—	4	1	no	—
269	C₂³	C₃×C₅×Q₁₆	1	4	yes	complemented
270	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
271	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
272	Q₈	—	2	8	no	—
273	Q₈	—	4	4	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
283	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
284	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
285	C₈	—	2	4	no	—
286	C₂×C₃	—	2	4	no	—
287	C₂×C₃	—	2	2	no	—
288	C₂×C₃	C₅×#534	1	1	yes	characteristic
289	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
290	C₂×C₃	C₅×#575	1	1	yes	characteristic
291	C₅	C₃×#3189	1	1	yes	characteristic, direct product factor, Sylow
292	C₂²	—	2	2	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	2	no	—
295	C₂²	—	2	1	no	—
296	C₂²	—	4	4	no	—
297	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
298	C₂²	C₂×C₃×C₅×Q₁₆	1	4	yes	—
299	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
300	C₄	—	2	2	no	—
301	C₄	—	2	1	no	—
302	C₄	—	4	4	no	—
303	C₄	—	4	4	no	—
304	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
305	C₃	C₅×#3189	1	1	yes	characteristic, direct product factor, Sylow
306	C₂	—	2	4	no	—
307	C₂	—	2	2	no	—
308	C₂	C₃×C₅×#534	1	1	yes	characteristic
309	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
310	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#484	C₂	semidirect
3. C₃×C₅×#467	C₂	semidirect
4. C₃×C₅×#451	C₂	semidirect
6. C₅×#3189	C₃	direct (N × H)
9. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₃×C₅×#107	C₂²	semidirect
19. C₃×C₅×#103	C₂²	semidirect
21. C₃×#3189	C₅	direct (N × H)
23. C₅×#484	C₂×C₃	semidirect
24. C₅×#467	C₂×C₃	semidirect
25. C₅×#451	C₂×C₃	semidirect
48. C₃×#484	C₂×C₅	semidirect
49. C₃×#467	C₂×C₅	semidirect
50. C₃×#451	C₂×C₅	semidirect
54. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
63. C₅×#107	C₂²×C₃	semidirect
64. C₅×#103	C₂²×C₃	semidirect
66. #3189	C₃×C₅	direct (N × H)
69. C₂³×C₃×C₅	Q₁₆	semidirect
88. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
97. C₃×#107	C₂²×C₅	semidirect
98. C₃×#103	C₂²×C₅	semidirect
121. #484	C₂×C₃×C₅	semidirect
122. #467	C₂×C₃×C₅	semidirect
123. #451	C₂×C₃×C₅	semidirect
160. C₂³×C₅	C₃×Q₁₆	semidirect
179. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
188. #107	C₂²×C₃×C₅	semidirect
189. #103	C₂²×C₃×C₅	semidirect
198. C₂³×C₃	C₅×Q₁₆	semidirect
248. C₃×C₅	#3189	direct (N × H)
269. C₂³	C₃×C₅×Q₁₆	semidirect
291. C₅	C₃×#3189	direct (N × H)
305. C₃	C₅×#3189	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×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#484	2
C₃×C₅×#467	2
C₃×C₅×#451	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#3189	3
C₃×#3189	5

Subgroups — C3×C5×#3189 #14276223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3189 #14276223