Subgroups — C₅×#71747 #14284126

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₅×#4926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4543	C₂	1	2	yes	maximal, complemented
5	C₅×#4540	C₂	1	2	yes	maximal, complemented
6	C₅×#1529	—	3	1	no	maximal, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₂²	1	1	yes	characteristic
9	C₃×C₅×#124	C₂²	1	1	yes	characteristic
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#121	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	—	2	1	no	—
19	C₅×#830	—	2	1	no	—
20	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₅×#803	C₂²	1	2	yes	—
22	C₅×#803	C₂²	1	2	yes	—
23	C₄×C₅×C₃⋊C₈	—	2	1	no	—
24	#71747	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#529	D₃	1	1	yes	characteristic
26	C₅×#432	—	3	1	no	—
27	C₄×C₅×M₁₆	—	3	1	no	—
28	C₅×#330	—	3	2	no	—
29	C₅×#329	—	3	2	no	—
30	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₄	—	2	1	no	—
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×#208	—	2	4	no	—
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₃×#529	C₂×C₅	1	1	yes	characteristic
57	#4926	C₂×C₅	1	1	yes	characteristic, complemented
58	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
59	#4543	C₂×C₅	1	2	yes	complemented
60	#4540	C₂×C₅	1	2	yes	complemented
61	C₂×C₅×M₁₆	—	6	1	no	—
62	C₅×#126	—	2	1	no	—
63	C₅×#125	C₂×D₃	1	1	yes	characteristic
64	C₅×#124	C₂×D₃	1	1	yes	characteristic
65	C₅×#123	—	2	1	no	—
66	C₅×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
67	C₅×#121	Dic₃	1	1	yes	characteristic
68	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
71	C₅×#117	—	2	1	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	6	1	no	—
74	C₅×C₂²⋊C₈	—	6	1	no	—
75	C₅×#97	—	3	2	no	—
76	C₅×#97	—	3	2	no	—
77	C₄×C₅×C₈	—	6	1	no	—
78	#1529	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	4	1	no	—
82	C₃×C₅×D₄	—	4	1	no	—
83	C₃×C₅×D₄	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	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	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
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×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₅×C₃⋊C₈	—	2	4	no	—
98	C₅×C₃⋊C₈	—	4	2	no	—
99	C₃×#126	—	2	1	no	—
100	C₃×#125	C₂²×C₅	1	1	yes	characteristic
101	C₃×#124	C₂²×C₅	1	1	yes	characteristic
102	C₃×#123	—	2	1	no	—
103	C₃×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
104	C₃×#121	C₄×C₅	1	1	yes	characteristic
105	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
106	C₃×C₄×D₄	—	2	1	no	—
107	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
108	C₃×#117	—	2	1	no	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₂×#208	—	2	1	no	—
111	#830	—	2	1	no	—
112	C₄⋊(C₃⋊C₈)	—	2	1	no	—
113	#803	C₂²×C₅	1	2	yes	—
114	#803	C₂²×C₅	1	2	yes	—
115	C₄×C₃⋊C₈	—	2	1	no	—
116	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	#67	1	1	yes	characteristic
122	C₂²×C₄×C₅	#67	1	1	yes	characteristic
123	C₅×M₁₆	—	6	4	no	—
124	C₂×C₅×C₈	—	6	2	no	—
125	C₂×C₅×C₈	—	6	2	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
131	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
132	C₅×C₂²⋊C₄	—	2	1	no	—
133	C₅×C₂²⋊C₄	—	2	1	no	—
134	C₅×C₂²⋊C₄	—	2	1	no	—
135	C₅×C₂²⋊C₄	—	2	1	no	—
136	C₅×C₂²⋊C₄	—	2	1	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
139	C₄²×C₅	#67	1	1	yes	characteristic
140	C₄²×C₅	#67	1	1	yes	characteristic
141	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
142	#529	C₅×D₃	1	1	yes	characteristic
143	#432	—	3	1	no	—
144	C₄×M₁₆	—	3	1	no	—
145	#330	—	3	2	no	—
146	#329	—	3	2	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	4	1	no	—
151	C₂²×C₃×C₅	—	4	1	no	—
152	C₂²×C₃×C₅	—	4	1	no	—
153	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₃×C₄×C₅	—	2	1	no	—
155	C₃×C₄×C₅	—	2	1	no	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×C₄×C₅	—	2	1	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	4	1	no	—
160	C₃×C₄×C₅	—	4	1	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	#104	1	2	yes	—
163	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
164	C₂×C₃×D₄	—	2	1	no	—
165	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
176	C₃×C₂²⋊C₄	—	2	1	no	—
177	C₃×C₂²⋊C₄	—	2	1	no	—
178	C₃×C₂²⋊C₄	—	2	1	no	—
179	C₃×C₂²⋊C₄	—	2	1	no	—
180	C₃×C₂²⋊C₄	—	2	1	no	—
181	C₃×C₄²	—	2	1	no	—
182	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
183	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
184	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
185	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
186	#208	—	2	4	no	—
187	C₂×C₃⋊C₈	—	2	2	no	—
188	C₂×C₃⋊C₈	—	2	2	no	—
189	C₂³×C₅	—	2	1	no	—
190	C₂³×C₅	#217	1	1	yes	characteristic
191	C₅×Q₈	—	4	1	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	4	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	#217	1	1	yes	characteristic
202	C₂×C₄×C₅	#217	1	1	yes	characteristic
203	C₂×C₄×C₅	#217	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
207	C₅×C₈	—	6	4	no	—
208	C₅×C₈	—	12	2	no	—
209	C₂×M₁₆	—	6	1	no	—
210	#126	—	2	1	no	—
211	#125	C₂×C₅×D₃	1	1	yes	characteristic
212	#124	C₂×C₅×D₃	1	1	yes	characteristic
213	#123	—	2	1	no	—
214	C₂²⋊Q₈	C₅×Dic₃	1	1	yes	characteristic
215	#121	C₅×Dic₃	1	1	yes	characteristic
216	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
219	#117	—	2	1	no	—
220	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
221	C₄⋊C₈	—	6	1	no	—
222	C₂²⋊C₈	—	6	1	no	—
223	#97	—	3	2	no	—
224	#97	—	3	2	no	—
225	C₄×C₈	—	6	1	no	—
226	C₂×C₃×C₅	—	4	1	no	—
227	C₂×C₃×C₅	—	8	1	no	—
228	C₂×C₃×C₅	#413	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
230	C₂×C₃×C₅	#421	1	1	yes	characteristic
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
233	C₃×Q₈	—	4	1	no	—
234	C₃×D₄	—	4	1	no	—
235	C₃×D₄	—	4	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	1	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
249	C₃⋊C₈	—	2	4	no	—
250	C₃⋊C₈	—	4	2	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	4	1	no	—
255	C₂²×C₅	—	4	1	no	—
256	C₂²×C₅	—	4	1	no	—
257	C₂²×C₅	C₂×#217	1	1	yes	characteristic
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	2	1	no	—
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	4	1	no	—
264	C₄×C₅	—	4	1	no	—
265	C₄×C₅	—	4	1	no	—
266	C₄×C₅	#837	1	2	yes	—
267	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
272	C₂²×C₄	C₅×#67	1	1	yes	characteristic
273	C₂²×C₄	C₅×#67	1	1	yes	characteristic
274	M₁₆	—	6	4	no	—
275	C₂×C₈	—	6	2	no	—
276	C₂×C₈	—	6	2	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
282	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
283	C₂²⋊C₄	—	2	1	no	—
284	C₂²⋊C₄	—	2	1	no	—
285	C₂²⋊C₄	—	2	1	no	—
286	C₂²⋊C₄	—	2	1	no	—
287	C₂²⋊C₄	—	2	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
290	C₄²	C₅×#67	1	1	yes	characteristic
291	C₄²	C₅×#67	1	1	yes	characteristic
292	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
293	C₃×C₅	#1529	1	1	yes	characteristic, complemented, Hall
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	1	no	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	4	1	no	—
298	C₂²×C₃	—	4	1	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	4	1	no	—
307	C₃×C₄	—	4	1	no	—
308	C₃×C₄	—	4	1	no	—
309	C₃×C₄	C₅×#104	1	2	yes	—
310	C₂×C₅	—	4	1	no	—
311	C₂×C₅	—	8	1	no	—
312	C₂×C₅	C₂×#837	1	1	yes	characteristic
313	C₂×C₅	#5236	1	1	yes	characteristic
314	C₂×C₅	#5237	1	1	yes	characteristic
315	C₂³	—	2	1	no	—
316	C₂³	C₅×#217	1	1	yes	characteristic
317	Q₈	—	4	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	4	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₅×#217	1	1	yes	characteristic
328	C₂×C₄	C₅×#217	1	1	yes	characteristic
329	C₂×C₄	C₅×#217	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
331	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
332	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
333	C₈	—	6	4	no	—
334	C₈	—	12	2	no	—
335	C₂×C₃	—	4	1	no	—
336	C₂×C₃	—	8	1	no	—
337	C₂×C₃	C₅×#413	1	1	yes	characteristic
338	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
339	C₂×C₃	C₅×#421	1	1	yes	characteristic
340	C₅	#71747	1	1	yes	characteristic, direct product factor, Sylow
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	C₂×C₅×#217	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	1	no	—
355	C₄	—	4	1	no	—
356	C₄	C₅×#837	1	2	yes	—
357	C₃	C₅×#1529	1	1	yes	characteristic, complemented, Sylow
358	C₂	—	4	1	no	—
359	C₂	—	8	1	no	—
360	C₂	C₂×C₅×#837	1	1	yes	characteristic
361	C₂	C₅×#5236	1	1	yes	characteristic
362	C₂	C₅×#5237	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×#217
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#1529
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
2. C₅×#4926	C₂	semidirect
3. C₄×C₅×#208	C₂	semidirect
4. C₅×#4543	C₂	semidirect
5. C₅×#4540	C₂	semidirect
24. #71747	C₅	direct (N × H)
57. #4926	C₂×C₅	semidirect
58. C₄×#208	C₂×C₅	semidirect
59. #4543	C₂×C₅	semidirect
60. #4540	C₂×C₅	semidirect
293. C₃×C₅	#1529	semidirect
340. C₅	#71747	direct (N × H)
357. C₃	C₅×#1529	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
C₅×#4926	2
C₄×C₅×#208	2
C₅×#4543	2
C₅×#4540	2
C₅×#1529	3
#71747	5

Subgroups — C5×#71747 #14284126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71747 #14284126