Subgroups — C₃×C₅×#3188 #14276222

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3188	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	—	2	1	no	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
20	C₃×C₅×#123	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#121	—	2	1	no	—
24	C₃×C₅×#121	—	2	1	no	—
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₃×C₅×#121	C₂²	1	2	yes	—
27	C₃×C₅×#121	C₂²	1	1	yes	characteristic
28	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#120	—	2	1	no	—
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₄×C₅×D₄	—	2	1	no	—
32	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
35	C₃×C₅×#107	C₂²	1	2	yes	complemented
36	C₃×C₅×#106	C₂²	1	2	yes	complemented
37	C₃×C₅×#103	C₂²	1	2	yes	complemented
38	C₃×C₅×#102	C₂²	1	2	yes	complemented
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₃×C₅×#102	C₂²	1	2	yes	complemented
41	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
44	C₃×#3188	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#484	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#482	C₂×C₃	1	2	yes	complemented
49	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#466	C₂×C₃	1	2	yes	complemented
51	C₅×#465	C₂×C₃	1	2	yes	complemented
52	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#449	C₂×C₃	1	2	yes	complemented
54	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
58	C₃×C₅×#41	—	4	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	1	no	—
66	C₂×C₃×C₅×D₄	—	4	2	no	—
67	C₂×C₃×C₅×D₄	—	4	4	no	—
68	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
69	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	—	2	1	no	—
71	C₂²×C₃×C₄×C₅	—	2	1	no	—
72	C₂²×C₃×C₄×C₅	—	4	2	no	—
73	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×SD₁₆	—	4	2	no	—
80	C₃×C₅×D₈	—	4	2	no	—
81	C₂×C₃×C₅×C₈	—	4	2	no	—
82	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
83	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
84	C₃×C₅×C₄⋊C₄	—	2	1	no	—
85	C₃×C₅×C₄⋊C₄	—	2	1	no	—
86	C₃×C₅×C₄⋊C₄	—	2	1	no	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
94	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₃×C₄²×C₅	—	2	1	no	—
98	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#482	C₂×C₅	1	2	yes	complemented
102	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#466	C₂×C₅	1	2	yes	complemented
104	C₃×#465	C₂×C₅	1	2	yes	complemented
105	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
106	C₃×#449	C₂×C₅	1	2	yes	complemented
107	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₂²×C₅×D₄	—	2	1	no	—
111	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
112	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
114	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
115	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
116	C₅×#123	—	2	1	no	—
117	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₅×#121	—	2	1	no	—
120	C₅×#121	—	2	1	no	—
121	C₅×#121	C₂²×C₃	1	1	yes	characteristic
122	C₅×#121	C₂²×C₃	1	2	yes	—
123	C₅×#121	C₂²×C₃	1	2	yes	—
124	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₅×#120	—	2	1	no	—
126	C₄×C₅×D₄	—	2	1	no	—
127	C₄×C₅×D₄	—	2	1	no	—
128	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
131	C₅×#107	C₂²×C₃	1	2	yes	complemented
132	C₅×#106	C₂²×C₃	1	2	yes	complemented
133	C₅×#103	C₂²×C₃	1	2	yes	complemented
134	C₅×#102	C₂²×C₃	1	2	yes	complemented
135	C₅×#102	C₂²×C₃	1	2	yes	complemented
136	C₅×#102	C₂²×C₃	1	2	yes	complemented
137	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
138	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
139	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
140	#3188	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	2	no	—
143	C₂³×C₃×C₅	—	2	1	no	—
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	4	1	no	—
146	C₂³×C₃×C₅	—	4	2	no	—
147	C₂³×C₃×C₅	—	4	2	no	—
148	C₂³×C₃×C₅	—	4	2	no	—
149	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×D₄	—	2	2	no	—
154	C₃×C₅×D₄	—	2	2	no	—
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	4	2	no	—
157	C₃×C₅×D₄	—	4	4	no	—
158	C₃×C₅×D₄	—	4	2	no	—
159	C₃×C₅×D₄	—	4	2	no	—
160	C₃×C₅×D₄	—	4	2	no	—
161	C₃×C₅×D₄	—	4	4	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	2	1	no	—
166	C₂×C₃×C₄×C₅	—	2	1	no	—
167	C₂×C₃×C₄×C₅	—	2	1	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	4	1	no	—
170	C₂×C₃×C₄×C₅	—	4	1	no	—
171	C₂×C₃×C₄×C₅	—	4	1	no	—
172	C₂×C₃×C₄×C₅	—	4	2	no	—
173	C₂×C₃×C₄×C₅	—	4	2	no	—
174	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₃×C₅×C₈	—	2	2	no	—
179	C₃×C₅×C₈	—	2	2	no	—
180	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₂²×C₃×D₄	—	2	1	no	—
182	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
183	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
185	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
186	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
187	C₃×#123	—	2	1	no	—
188	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₃×#121	—	2	1	no	—
191	C₃×#121	—	2	1	no	—
192	C₃×#121	C₂²×C₅	1	1	yes	characteristic
193	C₃×#121	C₂²×C₅	1	2	yes	—
194	C₃×#121	C₂²×C₅	1	2	yes	—
195	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₃×#120	—	2	1	no	—
197	C₃×C₄×D₄	—	2	1	no	—
198	C₃×C₄×D₄	—	2	1	no	—
199	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
200	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
202	C₃×#107	C₂²×C₅	1	2	yes	complemented
203	C₃×#106	C₂²×C₅	1	2	yes	complemented
204	C₃×#103	C₂²×C₅	1	2	yes	complemented
205	C₃×#102	C₂²×C₅	1	2	yes	complemented
206	C₃×#102	C₂²×C₅	1	2	yes	complemented
207	C₃×#102	C₂²×C₅	1	2	yes	complemented
208	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
209	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
210	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
211	C₂⁴×C₅	—	2	1	no	—
212	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
213	C₅×#41	—	4	2	no	—
214	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₅×D₄	—	2	1	no	—
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	1	no	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	2	no	—
220	C₂×C₅×D₄	—	2	1	no	—
221	C₂×C₅×D₄	—	4	2	no	—
222	C₂×C₅×D₄	—	4	4	no	—
223	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
224	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₄×C₅	—	2	1	no	—
226	C₂²×C₄×C₅	—	2	1	no	—
227	C₂²×C₄×C₅	—	4	2	no	—
228	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₅×SD₁₆	—	4	2	no	—
235	C₅×D₈	—	4	2	no	—
236	C₂×C₅×C₈	—	4	2	no	—
237	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
238	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
243	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
244	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	2	1	no	—
247	C₅×C₂²⋊C₄	—	2	1	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	2	2	no	—
250	C₅×C₂²⋊C₄	—	2	1	no	—
251	C₅×C₂²⋊C₄	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
254	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#482	C₂×C₃×C₅	1	2	yes	complemented
257	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	#466	C₂×C₃×C₅	1	2	yes	complemented
259	#465	C₂×C₃×C₅	1	2	yes	complemented
260	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	#449	C₂×C₃×C₅	1	2	yes	complemented
262	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
263	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
264	C₂²×C₃×C₅	—	2	1	no	—
265	C₂²×C₃×C₅	—	2	1	no	—
266	C₂²×C₃×C₅	—	2	1	no	—
267	C₂²×C₃×C₅	—	2	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	2	1	no	—
270	C₂²×C₃×C₅	—	2	1	no	—
271	C₂²×C₃×C₅	—	4	4	no	—
272	C₂²×C₃×C₅	—	4	1	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	1	no	—
275	C₂²×C₃×C₅	—	4	2	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	1	no	—
278	C₂²×C₃×C₅	—	8	4	no	—
279	C₂²×C₃×C₅	#135	1	2	yes	—
280	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
281	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₃×C₄×C₅	—	2	1	no	—
283	C₃×C₄×C₅	—	2	1	no	—
284	C₃×C₄×C₅	—	2	1	no	—
285	C₃×C₄×C₅	—	4	1	no	—
286	C₃×C₄×C₅	—	4	1	no	—
287	C₃×C₄×C₅	—	4	2	no	—
288	C₃×C₄×C₅	—	4	1	no	—
289	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
290	C₂⁴×C₃	—	2	1	no	—
291	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
292	C₃×#41	—	4	2	no	—
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	—	2	1	no	—
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	2	1	no	—
300	C₂×C₃×D₄	—	4	2	no	—
301	C₂×C₃×D₄	—	4	4	no	—
302	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
303	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
304	C₂²×C₃×C₄	—	2	1	no	—
305	C₂²×C₃×C₄	—	2	1	no	—
306	C₂²×C₃×C₄	—	4	2	no	—
307	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
313	C₃×SD₁₆	—	4	2	no	—
314	C₃×D₈	—	4	2	no	—
315	C₂×C₃×C₈	—	4	2	no	—
316	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
317	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
318	C₃×C₄⋊C₄	—	2	1	no	—
319	C₃×C₄⋊C₄	—	2	1	no	—
320	C₃×C₄⋊C₄	—	2	1	no	—
321	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
322	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
323	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
324	C₃×C₂²⋊C₄	—	2	1	no	—
325	C₃×C₂²⋊C₄	—	2	1	no	—
326	C₃×C₂²⋊C₄	—	2	1	no	—
327	C₃×C₂²⋊C₄	—	2	2	no	—
328	C₃×C₂²⋊C₄	—	2	2	no	—
329	C₃×C₂²⋊C₄	—	2	1	no	—
330	C₃×C₂²⋊C₄	—	2	1	no	—
331	C₃×C₄²	—	2	1	no	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	2	no	—
334	C₂³×C₅	—	2	1	no	—
335	C₂³×C₅	—	2	2	no	—
336	C₂³×C₅	—	4	1	no	—
337	C₂³×C₅	—	4	2	no	—
338	C₂³×C₅	—	4	2	no	—
339	C₂³×C₅	—	4	2	no	—
340	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
342	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
343	C₅×Q₈	—	2	2	no	—
344	C₅×D₄	—	2	2	no	—
345	C₅×D₄	—	2	2	no	—
346	C₅×D₄	—	2	2	no	—
347	C₅×D₄	—	4	2	no	—
348	C₅×D₄	—	4	4	no	—
349	C₅×D₄	—	4	2	no	—
350	C₅×D₄	—	4	2	no	—
351	C₅×D₄	—	4	2	no	—
352	C₅×D₄	—	4	4	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	2	no	—
364	C₂×C₄×C₅	—	4	2	no	—
365	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
369	C₅×C₈	—	2	2	no	—
370	C₅×C₈	—	2	2	no	—
371	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
374	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
375	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
376	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
377	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
378	#123	—	2	1	no	—
379	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
380	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	C₂²×C₃×C₅	1	2	yes	—
384	#121	C₂²×C₃×C₅	1	2	yes	—
385	#121	C₂²×C₃×C₅	1	1	yes	characteristic
386	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
387	#120	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
391	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	#107	C₂²×C₃×C₅	1	2	yes	complemented
394	#106	C₂²×C₃×C₅	1	2	yes	complemented
395	#103	C₂²×C₃×C₅	1	2	yes	complemented
396	#102	C₂²×C₃×C₅	1	2	yes	complemented
397	#102	C₂²×C₃×C₅	1	2	yes	complemented
398	#102	C₂²×C₃×C₅	1	2	yes	complemented
399	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
400	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
401	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
402	C₂×C₃×C₅	—	2	2	no	—
403	C₂×C₃×C₅	—	2	2	no	—
404	C₂×C₃×C₅	—	4	1	no	—
405	C₂×C₃×C₅	—	8	1	no	—
406	C₂×C₃×C₅	—	8	2	no	—
407	C₂×C₃×C₅	#534	1	1	yes	characteristic
408	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
409	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₂³×C₃	—	2	2	no	—
411	C₂³×C₃	—	2	2	no	—
412	C₂³×C₃	—	2	1	no	—
413	C₂³×C₃	—	2	2	no	—
414	C₂³×C₃	—	4	1	no	—
415	C₂³×C₃	—	4	2	no	—
416	C₂³×C₃	—	4	2	no	—
417	C₂³×C₃	—	4	2	no	—
418	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
420	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
421	C₃×Q₈	—	2	2	no	—
422	C₃×D₄	—	2	2	no	—
423	C₃×D₄	—	2	2	no	—
424	C₃×D₄	—	2	2	no	—
425	C₃×D₄	—	4	2	no	—
426	C₃×D₄	—	4	4	no	—
427	C₃×D₄	—	4	2	no	—
428	C₃×D₄	—	4	2	no	—
429	C₃×D₄	—	4	2	no	—
430	C₃×D₄	—	4	4	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	4	1	no	—
439	C₂×C₃×C₄	—	4	1	no	—
440	C₂×C₃×C₄	—	4	1	no	—
441	C₂×C₃×C₄	—	4	2	no	—
442	C₂×C₃×C₄	—	4	2	no	—
443	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
447	C₃×C₈	—	2	2	no	—
448	C₃×C₈	—	2	2	no	—
449	C₂²×C₅	—	2	1	no	—
450	C₂²×C₅	—	2	1	no	—
451	C₂²×C₅	—	2	1	no	—
452	C₂²×C₅	—	2	1	no	—
453	C₂²×C₅	—	2	1	no	—
454	C₂²×C₅	—	2	1	no	—
455	C₂²×C₅	—	2	1	no	—
456	C₂²×C₅	—	4	4	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	2	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	4	1	no	—
461	C₂²×C₅	—	4	1	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	8	4	no	—
464	C₂²×C₅	C₃×#135	1	2	yes	—
465	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
466	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
467	C₄×C₅	—	2	1	no	—
468	C₄×C₅	—	2	1	no	—
469	C₄×C₅	—	2	1	no	—
470	C₄×C₅	—	4	1	no	—
471	C₄×C₅	—	4	2	no	—
472	C₄×C₅	—	4	1	no	—
473	C₄×C₅	—	4	1	no	—
474	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
475	C₂⁴	—	2	1	no	—
476	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
477	#41	—	4	2	no	—
478	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
488	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
493	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
494	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
495	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
496	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
497	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
498	SD₁₆	—	4	2	no	—
499	D₈	—	4	2	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
502	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₃×C₅	#3188	1	1	yes	characteristic, direct product factor, Hall
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	1	no	—
525	C₂²×C₃	—	4	4	no	—
526	C₂²×C₃	—	4	1	no	—
527	C₂²×C₃	—	4	2	no	—
528	C₂²×C₃	—	4	1	no	—
529	C₂²×C₃	—	4	2	no	—
530	C₂²×C₃	—	4	2	no	—
531	C₂²×C₃	—	4	1	no	—
532	C₂²×C₃	—	8	4	no	—
533	C₂²×C₃	C₅×#135	1	2	yes	—
534	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
535	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
536	C₃×C₄	—	2	1	no	—
537	C₃×C₄	—	2	1	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	4	1	no	—
540	C₃×C₄	—	4	1	no	—
541	C₃×C₄	—	4	2	no	—
542	C₃×C₄	—	4	1	no	—
543	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
544	C₂×C₅	—	2	2	no	—
545	C₂×C₅	—	2	2	no	—
546	C₂×C₅	—	4	1	no	—
547	C₂×C₅	—	8	2	no	—
548	C₂×C₅	—	8	1	no	—
549	C₂×C₅	C₃×#534	1	1	yes	characteristic
550	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
551	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
561	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
562	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
563	Q₈	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	4	no	—
572	D₄	—	4	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
586	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
587	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
588	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
589	C₈	—	2	2	no	—
590	C₈	—	2	2	no	—
591	C₂×C₃	—	2	2	no	—
592	C₂×C₃	—	2	2	no	—
593	C₂×C₃	—	4	1	no	—
594	C₂×C₃	—	8	2	no	—
595	C₂×C₃	—	8	1	no	—
596	C₂×C₃	C₅×#534	1	1	yes	characteristic
597	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
598	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
599	C₅	C₃×#3188	1	1	yes	characteristic, direct product factor, Sylow
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	8	4	no	—
615	C₂²	C₃×C₅×#135	1	2	yes	—
616	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
617	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	1	no	—
625	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
626	C₃	C₅×#3188	1	1	yes	characteristic, direct product factor, Sylow
627	C₂	—	2	2	no	—
628	C₂	—	2	2	no	—
629	C₂	—	4	1	no	—
630	C₂	—	8	2	no	—
631	C₂	—	8	1	no	—
632	C₂	C₃×C₅×#534	1	1	yes	characteristic
633	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
634	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
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
1. C₃×C₅×#525	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₃×C₅×#484	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#466	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₅×#450	C₂	semidirect
9. C₃×C₅×#449	C₂	semidirect
10. C₃×C₅×#447	C₂	semidirect
11. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
12. C₅×#3188	C₃	direct (N × H)
13. C₂×C₃×C₅×#41	C₂²	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₂²×C₃×C₅×C₈	C₂²	semidirect
22. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₃×C₅×#121	C₂²	semidirect
32. C₃×C₅×#117	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#106	C₂²	semidirect
37. C₃×C₅×#103	C₂²	semidirect
38. C₃×C₅×#102	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₃×C₅×#102	C₂²	semidirect
43. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
44. C₃×#3188	C₅	direct (N × H)
45. C₅×#525	C₂×C₃	semidirect
46. C₂×C₅×#121	C₂×C₃	semidirect
47. C₅×#484	C₂×C₃	semidirect
48. C₅×#482	C₂×C₃	semidirect
49. C₅×#481	C₂×C₃	semidirect
50. C₅×#466	C₂×C₃	semidirect
51. C₅×#465	C₂×C₃	semidirect
52. C₅×#450	C₂×C₃	semidirect
53. C₅×#449	C₂×C₃	semidirect
54. C₅×#447	C₂×C₃	semidirect
55. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
98. C₃×#525	C₂×C₅	semidirect
99. C₂×C₃×#121	C₂×C₅	semidirect
100. C₃×#484	C₂×C₅	semidirect
101. C₃×#482	C₂×C₅	semidirect
102. C₃×#481	C₂×C₅	semidirect
103. C₃×#466	C₂×C₅	semidirect
104. C₃×#465	C₂×C₅	semidirect
105. C₃×#450	C₂×C₅	semidirect
106. C₃×#449	C₂×C₅	semidirect
107. C₃×#447	C₂×C₅	semidirect
108. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
109. C₂×C₅×#41	C₂²×C₃	semidirect
113. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
114. C₂×C₅×D₈	C₂²×C₃	semidirect
115. C₂²×C₅×C₈	C₂²×C₃	semidirect
118. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
124. C₅×#121	C₂²×C₃	semidirect
128. C₅×#117	C₂²×C₃	semidirect
131. C₅×#107	C₂²×C₃	semidirect
132. C₅×#106	C₂²×C₃	semidirect
133. C₅×#103	C₂²×C₃	semidirect
134. C₅×#102	C₂²×C₃	semidirect
135. C₅×#102	C₂²×C₃	semidirect
136. C₅×#102	C₂²×C₃	semidirect
139. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
140. #3188	C₃×C₅	direct (N × H)
180. C₂×C₃×#41	C₂²×C₅	semidirect
184. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
185. C₂×C₃×D₈	C₂²×C₅	semidirect
186. C₂²×C₃×C₈	C₂²×C₅	semidirect
189. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
195. C₃×#121	C₂²×C₅	semidirect
199. C₃×#117	C₂²×C₅	semidirect
202. C₃×#107	C₂²×C₅	semidirect
203. C₃×#106	C₂²×C₅	semidirect
204. C₃×#103	C₂²×C₅	semidirect
205. C₃×#102	C₂²×C₅	semidirect
206. C₃×#102	C₂²×C₅	semidirect
207. C₃×#102	C₂²×C₅	semidirect
210. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
253. #525	C₂×C₃×C₅	semidirect
254. C₂×#121	C₂×C₃×C₅	semidirect
255. #484	C₂×C₃×C₅	semidirect
256. #482	C₂×C₃×C₅	semidirect
257. #481	C₂×C₃×C₅	semidirect
258. #466	C₂×C₃×C₅	semidirect
259. #465	C₂×C₃×C₅	semidirect
260. #450	C₂×C₃×C₅	semidirect
261. #449	C₂×C₃×C₅	semidirect
262. #447	C₂×C₃×C₅	semidirect
263. C₂×C₂²⋊C₈	C₂×C₃×C₅	semidirect
371. C₂×#41	C₂²×C₃×C₅	semidirect
375. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
376. C₂×D₈	C₂²×C₃×C₅	semidirect
377. C₂²×C₈	C₂²×C₃×C₅	semidirect
380. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
386. #121	C₂²×C₃×C₅	semidirect
390. #117	C₂²×C₃×C₅	semidirect
393. #107	C₂²×C₃×C₅	semidirect
394. #106	C₂²×C₃×C₅	semidirect
395. #103	C₂²×C₃×C₅	semidirect
396. #102	C₂²×C₃×C₅	semidirect
397. #102	C₂²×C₃×C₅	semidirect
398. #102	C₂²×C₃×C₅	semidirect
401. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
517. C₃×C₅	#3188	direct (N × H)
599. C₅	C₃×#3188	direct (N × H)
626. C₃	C₅×#3188	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#525	2
C₂×C₃×C₅×#121	2
C₃×C₅×#484	2
C₃×C₅×#482	2
C₃×C₅×#481	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#3188	3
C₃×#3188	5

Subgroups — C3×C5×#3188 #14276222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3188 #14276222