Subgroups — C₅×#71369 #14290375

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5726	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1647	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₅×#946	—	2	1	no	—
13	C₂×C₅×#215	—	2	1	no	—
14	C₅×#895	—	2	1	no	—
15	C₅×#894	—	2	2	no	—
16	C₅×D₃×C₄⋊C₄	—	2	1	no	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₃×C₅×#107	—	2	2	no	—
20	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₅×#835	—	2	1	no	—
22	C₅×#809	—	2	1	no	—
23	C₅×#807	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#71369	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#547	—	3	1	no	—
28	C₅×#500	D₃	1	1	yes	characteristic, complemented
29	C₅×#474	—	3	1	no	—
30	C₅×#461	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₅×#239	—	4	2	no	—
37	C₅×#239	—	4	2	no	—
38	C₂×C₅×D₁₂	—	2	2	no	—
39	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
40	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
49	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₅×#215	—	4	2	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
55	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
56	C₅×Dic₃⋊C₄	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	#5726	C₂×C₅	1	1	yes	characteristic
60	C₃×#500	C₂×C₅	1	1	yes	characteristic, complemented
61	#5087	C₂×C₅	1	1	yes	characteristic, complemented
62	#5083	C₂×C₅	1	1	yes	characteristic, complemented
63	#4547	C₂×C₅	1	1	yes	characteristic, complemented
64	#4459	C₂×C₅	1	1	yes	characteristic, complemented
65	#4459	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	—	6	1	no	—
67	C₂×C₅×SD₁₆	—	6	1	no	—
68	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
69	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
70	C₅×#123	—	6	2	no	—
71	C₅×C₂²⋊Q₈	—	6	1	no	—
72	C₅×#121	—	6	1	no	—
73	C₄×C₅×D₄	—	3	1	no	—
74	C₄×C₅×D₄	—	3	1	no	—
75	C₂×C₅×C₄⋊C₄	—	6	1	no	—
76	C₅×#107	—	2	2	no	—
77	C₅×#107	—	6	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×#103	—	6	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	#1647	—	3	1	no	Sylow
84	C₂²×C₅×D₃	—	2	1	no	—
85	C₂²×C₅×D₃	—	2	1	no	—
86	C₃×C₅×Q₈	—	4	1	no	—
87	C₃×C₅×Q₈	—	4	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₂×C₅×Dic₃	—	2	1	no	—
97	C₅×D₁₂	—	2	1	no	—
98	C₅×D₁₂	—	2	1	no	—
99	C₅×D₁₂	—	2	1	no	—
100	C₅×D₁₂	—	4	4	no	—
101	C₅×D₁₂	D₈	1	2	yes	—
102	C₄×C₅×D₃	—	4	4	no	—
103	C₄×C₅×D₃	—	4	1	no	—
104	C₄×C₅×D₃	—	4	1	no	—
105	C₄×C₅×D₃	—	4	1	no	—
106	C₄×C₅×D₃	—	4	1	no	—
107	C₃×C₅×C₈	—	2	2	no	—
108	C₅×C₃⋊C₈	—	4	1	no	—
109	C₅×C₃⋊C₈	—	4	1	no	—
110	C₂×#239	—	2	1	no	—
111	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
112	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
113	#946	—	2	1	no	—
114	C₂×#215	—	2	1	no	—
115	#895	—	2	1	no	—
116	#894	—	2	2	no	—
117	D₃×C₄⋊C₄	—	2	1	no	—
118	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
119	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
120	C₃×#107	—	2	2	no	—
121	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
122	#835	—	2	1	no	—
123	#809	—	2	1	no	—
124	#807	—	2	1	no	—
125	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
126	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
127	C₅×#41	—	12	2	no	—
128	C₅×#41	—	12	2	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×D₄	—	3	1	no	—
132	C₂×C₅×D₄	—	3	1	no	—
133	C₂×C₅×D₄	—	6	2	no	—
134	C₂²×C₄×C₅	—	6	2	no	—
135	C₂²×C₄×C₅	—	6	1	no	—
136	C₂²×C₄×C₅	—	6	1	no	—
137	C₅×SD₁₆	—	12	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	6	1	no	—
140	C₂×C₅×C₈	—	6	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	3	1	no	—
145	C₅×C₄⋊C₄	—	3	1	no	—
146	C₅×C₄⋊C₄	—	6	2	no	—
147	C₅×C₄⋊C₄	#67	1	2	yes	—
148	C₅×C₂²⋊C₄	—	6	2	no	—
149	C₅×C₂²⋊C₄	—	6	1	no	—
150	C₅×C₂²⋊C₄	—	6	1	no	—
151	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
152	#547	—	3	1	no	—
153	#500	C₅×D₃	1	1	yes	characteristic, complemented
154	#474	—	3	1	no	—
155	#461	—	3	1	no	—
156	#332	—	3	1	no	—
157	D₄⋊C₈	—	3	1	no	—
158	D₄⋊C₈	—	3	1	no	—
159	C₂²×C₃×C₅	#120	1	1	yes	characteristic
160	C₂×C₅×D₃	—	2	2	no	—
161	C₂×C₅×D₃	—	4	1	no	—
162	C₂×C₅×D₃	—	4	1	no	—
163	C₂×C₅×D₃	—	4	1	no	—
164	C₂×C₅×D₃	—	4	1	no	—
165	C₂×C₅×D₃	—	4	1	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	4	2	no	—
168	C₃×C₄×C₅	—	8	1	no	—
169	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
170	C₃×C₄×C₅	#135	1	1	yes	characteristic
171	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₃×C₄×C₅	#137	1	1	yes	characteristic
173	C₅×Dic₃	—	4	1	no	—
174	C₅×Dic₃	—	4	1	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	—	2	1	no	—
177	#239	—	4	2	no	—
178	#239	—	4	2	no	—
179	C₂×D₁₂	—	2	2	no	—
180	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
181	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
182	C₂×C₄×D₃	—	2	2	no	—
183	C₂×C₄×D₃	—	2	1	no	—
184	C₂×C₄×D₃	—	2	1	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
190	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
191	#215	—	4	2	no	—
192	(C₂×D₃)⋊C₄	—	2	2	no	—
193	(C₂×D₃)⋊C₄	—	2	1	no	—
194	(C₂×D₃)⋊C₄	—	2	1	no	—
195	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
196	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
197	Dic₃⋊C₄	—	2	2	no	—
198	C₂×C₃⋊C₈	—	2	1	no	—
199	C₂×C₃⋊C₈	—	2	1	no	—
200	C₂³×C₅	—	6	1	no	—
201	C₂³×C₅	—	6	1	no	—
202	C₅×Q₈	—	4	1	no	—
203	C₅×Q₈	—	4	1	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×Q₈	—	4	1	no	—
206	C₅×D₄	—	3	2	no	—
207	C₅×D₄	—	6	1	no	—
208	C₅×D₄	—	6	1	no	—
209	C₅×D₄	—	6	1	no	—
210	C₅×D₄	—	12	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	6	1	no	—
214	C₂×C₄×C₅	—	6	1	no	—
215	C₂×C₄×C₅	—	12	4	no	—
216	C₂×C₄×C₅	—	12	1	no	—
217	C₂×C₄×C₅	—	12	1	no	—
218	C₂×C₄×C₅	—	12	1	no	—
219	C₂×C₄×C₅	—	12	1	no	—
220	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	12	1	no	—
225	C₅×C₈	—	12	1	no	—
226	C₂×#41	—	6	1	no	—
227	C₂×SD₁₆	—	6	1	no	—
228	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
229	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
230	#123	—	6	2	no	—
231	C₂²⋊Q₈	—	6	1	no	—
232	#121	—	6	1	no	—
233	C₄×D₄	—	3	1	no	—
234	C₄×D₄	—	3	1	no	—
235	C₂×C₄⋊C₄	—	6	1	no	—
236	#107	—	2	2	no	—
237	#107	—	6	1	no	—
238	C₄⋊C₈	—	3	1	no	—
239	C₄⋊C₈	—	3	1	no	—
240	#103	—	6	1	no	—
241	#102	—	6	1	no	—
242	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
243	C₂×C₃×C₅	#447	1	1	yes	characteristic
244	C₂×C₃×C₅	#452	1	1	yes	characteristic
245	C₂×C₃×C₅	#456	1	1	yes	characteristic
246	C₅×D₃	—	4	2	no	—
247	C₅×D₃	—	8	1	no	—
248	C₂²×D₃	—	2	1	no	—
249	C₂²×D₃	—	2	1	no	—
250	C₃×Q₈	—	4	1	no	—
251	C₃×Q₈	—	4	1	no	—
252	C₃×Q₈	—	4	1	no	—
253	C₃×Q₈	—	4	1	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	4	1	no	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×Dic₃	—	2	1	no	—
260	C₂×Dic₃	—	2	1	no	—
261	D₁₂	—	2	1	no	—
262	D₁₂	—	2	1	no	—
263	D₁₂	—	2	1	no	—
264	D₁₂	—	4	4	no	—
265	D₁₂	C₅×D₈	1	2	yes	—
266	C₄×D₃	—	4	4	no	—
267	C₄×D₃	—	4	1	no	—
268	C₄×D₃	—	4	1	no	—
269	C₄×D₃	—	4	1	no	—
270	C₄×D₃	—	4	1	no	—
271	C₃×C₈	—	2	2	no	—
272	C₃⋊C₈	—	4	1	no	—
273	C₃⋊C₈	—	4	1	no	—
274	C₂²×C₅	—	6	2	no	—
275	C₂²×C₅	—	12	1	no	—
276	C₂²×C₅	—	12	1	no	—
277	C₂²×C₅	—	12	1	no	—
278	C₂²×C₅	—	12	1	no	—
279	C₂²×C₅	—	12	1	no	—
280	C₂²×C₅	#937	1	1	yes	characteristic
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	8	1	no	—
284	C₄×C₅	—	12	1	no	—
285	C₄×C₅	—	12	1	no	—
286	C₄×C₅	D₃×D₈	1	1	yes	characteristic
287	C₄×C₅	#911	1	1	yes	characteristic
288	C₄×C₅	#918	1	1	yes	characteristic
289	C₄×C₅	#919	1	1	yes	characteristic
290	#41	—	12	2	no	—
291	#41	—	12	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	3	1	no	—
295	C₂×D₄	—	3	1	no	—
296	C₂×D₄	—	6	2	no	—
297	C₂²×C₄	—	6	2	no	—
298	C₂²×C₄	—	6	1	no	—
299	C₂²×C₄	—	6	1	no	—
300	SD₁₆	—	12	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	6	1	no	—
303	C₂×C₈	—	6	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	3	1	no	—
308	C₄⋊C₄	—	3	1	no	—
309	C₄⋊C₄	—	6	2	no	—
310	C₄⋊C₄	C₅×#67	1	2	yes	—
311	C₂²⋊C₄	—	6	2	no	—
312	C₂²⋊C₄	—	6	1	no	—
313	C₂²⋊C₄	—	6	1	no	—
314	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
315	C₃×C₅	#1647	1	1	yes	characteristic, complemented, Hall
316	C₂²×C₃	C₅×#120	1	1	yes	characteristic
317	C₂×D₃	—	2	2	no	—
318	C₂×D₃	—	4	1	no	—
319	C₂×D₃	—	4	1	no	—
320	C₂×D₃	—	4	1	no	—
321	C₂×D₃	—	4	1	no	—
322	C₂×D₃	—	4	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	—	8	1	no	—
326	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
327	C₃×C₄	C₅×#135	1	1	yes	characteristic
328	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
329	C₃×C₄	C₅×#137	1	1	yes	characteristic
330	Dic₃	—	4	1	no	—
331	Dic₃	—	4	1	no	—
332	C₂×C₅	—	12	2	no	—
333	C₂×C₅	—	24	1	no	—
334	C₂×C₅	#5095	1	1	yes	characteristic
335	C₂×C₅	#5156	1	1	yes	characteristic
336	C₂×C₅	#5187	1	1	yes	characteristic
337	C₂³	—	6	1	no	—
338	C₂³	—	6	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	D₄	—	3	2	no	—
344	D₄	—	6	1	no	—
345	D₄	—	6	1	no	—
346	D₄	—	6	1	no	—
347	D₄	—	12	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	6	1	no	—
351	C₂×C₄	—	6	1	no	—
352	C₂×C₄	—	12	4	no	—
353	C₂×C₄	—	12	1	no	—
354	C₂×C₄	—	12	1	no	—
355	C₂×C₄	—	12	1	no	—
356	C₂×C₄	—	12	1	no	—
357	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
358	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	12	1	no	—
362	C₈	—	12	1	no	—
363	C₂×C₃	C₅×#447	1	1	yes	characteristic
364	C₂×C₃	C₅×#452	1	1	yes	characteristic
365	C₂×C₃	C₅×#456	1	1	yes	characteristic
366	D₃	—	4	2	no	—
367	D₃	—	8	1	no	—
368	C₅	#71369	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	6	2	no	—
370	C₂²	—	12	1	no	—
371	C₂²	—	12	1	no	—
372	C₂²	—	12	1	no	—
373	C₂²	—	12	1	no	—
374	C₂²	—	12	1	no	—
375	C₂²	C₅×#937	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	—	12	1	no	—
380	C₄	—	12	1	no	—
381	C₄	C₅×D₃×D₈	1	1	yes	characteristic
382	C₄	C₅×#911	1	1	yes	characteristic
383	C₄	C₅×#918	1	1	yes	characteristic
384	C₄	C₅×#919	1	1	yes	characteristic
385	C₃	C₅×#1647	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	12	2	no	—
387	C₂	—	24	1	no	—
388	C₂	C₅×#5095	1	1	yes	characteristic
389	C₂	C₅×#5156	1	1	yes	characteristic
390	C₂	C₅×#5187	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#500	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5726	C₂
hypercenter	C₅×#500	D₃
hypocenter	C₃	C₅×#1647
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#500

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#500	C₂	semidirect
3. C₅×#5087	C₂	semidirect
4. C₅×#5083	C₂	semidirect
5. C₅×#4547	C₂	semidirect
6. C₅×#4459	C₂	semidirect
7. C₅×#4459	C₂	semidirect
26. #71369	C₅	direct (N × H)
28. C₅×#500	D₃	semidirect
60. C₃×#500	C₂×C₅	semidirect
61. #5087	C₂×C₅	semidirect
62. #5083	C₂×C₅	semidirect
63. #4547	C₂×C₅	semidirect
64. #4459	C₂×C₅	semidirect
65. #4459	C₂×C₅	semidirect
153. #500	C₅×D₃	semidirect
315. C₃×C₅	#1647	semidirect
368. C₅	#71369	direct (N × H)
385. C₃	C₅×#1647	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5726	2
C₃×C₅×#500	2
C₅×#5087	2
C₅×#5083	2
C₅×#4547	2
C₅×#4459	2
C₅×#1647	3
#71369	5

Subgroups — C5×#71369 #14290375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71369 #14290375