Subgroups — C₅×#71870 #14313303

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic
2	C₅×#5240	C₂	1	1	yes	maximal, characteristic
3	C₅×#5237	C₂	1	1	yes	maximal, characteristic
4	C₅×#4539	C₂	1	4	yes	maximal, complemented
5	C₅×#2123	—	3	1	no	maximal, Hall
6	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
8	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
9	C₃×C₅×#124	—	2	1	no	—
10	C₃×C₅×#123	C₄	1	2	yes	complemented
11	C₃×C₅×#123	C₂²	1	2	yes	—
12	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
14	C₃×C₅×#117	C₄	1	1	yes	characteristic, complemented
15	C₅×#926	—	2	1	no	—
16	C₂×C₅×#208	—	2	1	no	—
17	C₅×#836	—	2	1	no	—
18	C₅×#834	—	2	1	no	—
19	C₅×#834	C₂²	1	2	yes	—
20	C₅×#833	C₂²	1	2	yes	—
21	#71870	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₅×#536	D₃	1	1	yes	characteristic
23	C₅×#413	—	3	1	no	—
24	C₅×#410	—	3	1	no	—
25	C₅×#352	—	3	4	no	—
26	C₃×C₅×#41	—	4	1	no	—
27	C₃×C₅×#41	—	4	1	no	—
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	—	2	1	no	—
30	C₂×C₃×C₅×Q₈	—	4	1	no	—
31	C₂×C₃×C₅×Q₈	—	4	1	no	—
32	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
35	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	—	2	2	no	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₅×#217	—	2	2	no	—
48	C₅×C₄⋊Dic₃	—	4	1	no	—
49	C₄×C₅×Dic₃	—	4	1	no	—
50	C₅×#208	—	2	2	no	—
51	C₅×#208	—	4	1	no	—
52	C₂×C₅×C₃⋊C₈	—	4	1	no	—
53	C₃×#536	C₂×C₅	1	1	yes	characteristic
54	#5240	C₂×C₅	1	1	yes	characteristic
55	#5237	C₂×C₅	1	1	yes	characteristic
56	#4539	C₂×C₅	1	4	yes	complemented
57	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
58	C₂²×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
59	C₂×C₅×M₁₆	—	6	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×#123	Dic₃	1	2	yes	complemented
63	C₅×#123	C₂×D₃	1	2	yes	—
64	C₅×C₂²⋊Q₈	—	2	1	no	—
65	C₅×C₂²⋊Q₈	—	2	1	no	—
66	C₅×#117	—	6	1	no	—
67	C₅×#117	Dic₃	1	1	yes	characteristic, complemented
68	C₅×#101	—	6	1	no	—
69	C₅×#100	—	3	2	no	—
70	C₅×#99	—	3	2	no	—
71	C₅×#99	—	6	1	no	—
72	#2123	—	3	1	no	Sylow
73	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
76	C₃×C₅×Q₈	—	4	1	no	—
77	C₃×C₅×Q₈	—	4	2	no	—
78	C₃×C₅×Q₈	—	4	1	no	—
79	C₃×C₅×Q₈	—	4	1	no	—
80	C₃×C₅×D₄	—	4	1	no	—
81	C₃×C₅×D₄	—	4	1	no	—
82	C₃×C₅×D₄	—	4	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₅×Dic₃	—	4	2	no	—
97	C₅×C₃⋊C₈	—	4	2	no	—
98	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
99	C₂²×C₃×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
100	C₃×C₄⋊Q₈	—	2	1	no	—
101	C₃×#124	—	2	1	no	—
102	C₃×#123	C₄×C₅	1	2	yes	complemented
103	C₃×#123	C₂²×C₅	1	2	yes	—
104	C₃×C₂²⋊Q₈	—	2	1	no	—
105	C₃×C₂²⋊Q₈	—	2	1	no	—
106	C₃×#117	C₄×C₅	1	1	yes	characteristic, complemented
107	#926	—	2	1	no	—
108	C₂×#208	—	2	1	no	—
109	#836	—	2	1	no	—
110	#834	—	2	1	no	—
111	#834	C₂²×C₅	1	2	yes	—
112	#833	C₂²×C₅	1	2	yes	—
113	C₅×#41	—	4	1	no	—
114	C₅×#41	—	4	1	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	4	1	no	—
118	C₂×C₅×Q₈	—	4	1	no	—
119	C₂×C₅×Q₈	#67	1	1	yes	characteristic
120	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
121	C₂×C₅×D₄	#67	1	1	yes	characteristic
122	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
125	C₂²×C₄×C₅	#67	1	1	yes	characteristic
126	C₂²×C₄×C₅	#67	1	1	yes	characteristic
127	C₅×M₁₆	—	6	2	no	—
128	C₅×M₁₆	—	12	1	no	—
129	C₂×C₅×C₈	—	12	1	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	12	1	no	—
134	C₅×C₂²⋊C₄	—	2	2	no	—
135	C₅×C₂²⋊C₄	—	2	2	no	—
136	C₅×C₂²⋊C₄	—	6	2	no	—
137	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	12	1	no	—
140	#536	C₅×D₃	1	1	yes	characteristic
141	#413	—	3	1	no	—
142	#410	—	3	1	no	—
143	#352	—	3	4	no	—
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	4	1	no	—
148	C₂²×C₃×C₅	—	4	1	no	—
149	C₂²×C₃×C₅	—	4	1	no	—
150	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×C₄×C₅	—	2	1	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	4	2	no	—
156	C₃×C₄×C₅	#99	1	1	yes	characteristic
157	C₃×C₄×C₅	#99	1	1	yes	characteristic
158	C₅×Dic₃	—	8	2	no	—
159	C₃×#41	—	4	1	no	—
160	C₃×#41	—	4	1	no	—
161	C₂×C₃×Q₈	—	2	1	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	4	1	no	—
164	C₂×C₃×Q₈	—	4	1	no	—
165	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
166	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
167	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
168	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
171	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₂²⋊C₄	—	2	2	no	—
177	C₃×C₂²⋊C₄	—	2	2	no	—
178	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
179	C₃×C₄²	—	2	1	no	—
180	#217	—	2	2	no	—
181	C₄⋊Dic₃	—	4	1	no	—
182	C₄×Dic₃	—	4	1	no	—
183	#208	—	2	2	no	—
184	#208	—	4	1	no	—
185	C₂×C₃⋊C₈	—	4	1	no	—
186	C₂³×C₅	#217	1	1	yes	characteristic
187	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
188	C₂³×C₅	C₂×#67	1	1	yes	characteristic
189	C₅×Q₈	—	4	1	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×Q₈	—	4	1	no	—
192	C₅×Q₈	—	4	1	no	—
193	C₅×D₄	—	4	1	no	—
194	C₅×D₄	—	4	1	no	—
195	C₅×D₄	—	4	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	12	2	no	—
206	C₂×C₄×C₅	#217	1	1	yes	characteristic
207	C₂×C₄×C₅	#217	1	1	yes	characteristic
208	C₂×C₄×C₅	#217	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
210	C₅×C₈	—	12	2	no	—
211	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
212	C₂²×Q₈	C₅×Dic₃	1	1	yes	characteristic, complemented
213	C₂×M₁₆	—	6	1	no	—
214	C₄⋊Q₈	—	2	1	no	—
215	#124	—	2	1	no	—
216	#123	C₅×Dic₃	1	2	yes	complemented
217	#123	C₂×C₅×D₃	1	2	yes	—
218	C₂²⋊Q₈	—	2	1	no	—
219	C₂²⋊Q₈	—	2	1	no	—
220	#117	—	6	1	no	—
221	#117	C₅×Dic₃	1	1	yes	characteristic, complemented
222	#101	—	6	1	no	—
223	#100	—	3	2	no	—
224	#99	—	3	2	no	—
225	#99	—	6	1	no	—
226	C₂×C₃×C₅	—	2	1	no	—
227	C₂×C₃×C₅	—	4	1	no	—
228	C₂×C₃×C₅	—	4	1	no	—
229	C₂×C₃×C₅	—	4	1	no	—
230	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
231	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
232	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
233	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
234	C₃×Q₈	—	4	1	no	—
235	C₃×Q₈	—	4	2	no	—
236	C₃×Q₈	—	4	1	no	—
237	C₃×Q₈	—	4	1	no	—
238	C₃×D₄	—	4	1	no	—
239	C₃×D₄	—	4	1	no	—
240	C₃×D₄	—	4	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	4	2	no	—
250	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×Dic₃	—	4	2	no	—
255	C₃⋊C₈	—	4	2	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	4	1	no	—
260	C₂²×C₅	—	4	1	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	C₂×#217	1	1	yes	characteristic
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	4	2	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	24	2	no	—
269	C₄×C₅	#834	1	1	yes	characteristic
270	C₄×C₅	#834	1	1	yes	characteristic
271	#41	—	4	1	no	—
272	#41	—	4	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	C₅×#67	1	1	yes	characteristic
278	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
279	C₂×D₄	C₅×#67	1	1	yes	characteristic
280	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
283	C₂²×C₄	C₅×#67	1	1	yes	characteristic
284	C₂²×C₄	C₅×#67	1	1	yes	characteristic
285	M₁₆	—	6	2	no	—
286	M₁₆	—	12	1	no	—
287	C₂×C₈	—	12	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	12	1	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	6	2	no	—
295	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
296	C₄²	—	2	1	no	—
297	C₄²	—	12	1	no	—
298	C₃×C₅	#2123	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	—	4	1	no	—
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	C₅×#99	1	1	yes	characteristic
312	C₃×C₄	C₅×#99	1	1	yes	characteristic
313	Dic₃	—	8	2	no	—
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	4	1	no	—
316	C₂×C₅	—	4	1	no	—
317	C₂×C₅	—	4	1	no	—
318	C₂×C₅	C₂×#834	1	1	yes	characteristic
319	C₂³	C₅×#217	1	1	yes	characteristic
320	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
321	C₂³	C₂×C₅×#67	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	4	1	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	12	2	no	—
339	C₂×C₄	C₅×#217	1	1	yes	characteristic
340	C₂×C₄	C₅×#217	1	1	yes	characteristic
341	C₂×C₄	C₅×#217	1	1	yes	characteristic
342	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
343	C₈	—	12	2	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	4	1	no	—
346	C₂×C₃	—	4	1	no	—
347	C₂×C₃	—	4	1	no	—
348	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
349	C₅	#71870	1	1	yes	characteristic, direct product factor, Sylow
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	C₂×C₅×#217	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	24	2	no	—
363	C₄	C₅×#834	1	1	yes	characteristic
364	C₄	C₅×#834	1	1	yes	characteristic
365	C₃	C₅×#2123	1	1	yes	characteristic, complemented, Sylow
366	C₂	—	2	1	no	—
367	C₂	—	4	1	no	—
368	C₂	—	4	1	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×C₅×#834	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#834
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂×D₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#536	C₂
socle	C₂×C₃×C₅	C₂×#99
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂×C₃×D₄	C₂³×C₅
hypercenter	C₅×#536	D₃
hypocenter	C₃	C₅×#2123
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#41 ◁ C₅×#536

Complements

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

N	H ≅ G/N	type
4. C₅×#4539	C₂	semidirect
7. C₂²×C₃×C₅×Q₈	C₄	semidirect
10. C₃×C₅×#123	C₄	semidirect
14. C₃×C₅×#117	C₄	semidirect
21. #71870	C₅	direct (N × H)
56. #4539	C₂×C₅	semidirect
58. C₂²×C₅×Q₈	Dic₃	semidirect
62. C₅×#123	Dic₃	semidirect
67. C₅×#117	Dic₃	semidirect
99. C₂²×C₃×Q₈	C₄×C₅	semidirect
102. C₃×#123	C₄×C₅	semidirect
106. C₃×#117	C₄×C₅	semidirect
212. C₂²×Q₈	C₅×Dic₃	semidirect
216. #123	C₅×Dic₃	semidirect
221. #117	C₅×Dic₃	semidirect
298. C₃×C₅	#2123	semidirect
349. C₅	#71870	direct (N × H)
365. C₃	C₅×#2123	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#536	2
C₅×#5240	2
C₅×#5237	2
C₅×#4539	2
C₅×#2123	3
#71870	5

Subgroups — C5×#71870 #14313303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71870 #14313303