Subgroups — C₅×#71746 #14283919

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 368 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	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#803	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×#1524	—	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	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
20	C₅×#803	—	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	#71746	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#529	D₃	1	1	yes	characteristic
26	C₄×C₅×M₁₆	—	3	1	no	—
27	C₂×C₅×#97	—	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	4	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₃×#529	C₂×C₅	1	1	yes	characteristic
58	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
60	#4543	C₂×C₅	1	2	yes	complemented
61	#4540	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×M₁₆	—	6	1	no	—
63	C₂²×C₅×C₈	—	6	1	no	—
64	C₅×#126	—	2	1	no	—
65	C₅×#125	C₂×D₃	1	1	yes	characteristic
66	C₅×#124	C₂×D₃	1	1	yes	characteristic
67	C₅×#123	—	2	1	no	—
68	C₅×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
69	C₅×#121	Dic₃	1	1	yes	characteristic
70	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
73	C₅×#117	—	2	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×#97	—	3	2	no	—
76	C₅×#97	—	3	2	no	—
77	C₅×#97	—	6	1	no	—
78	C₄×C₅×C₈	—	6	1	no	—
79	#1524	—	3	1	no	Sylow
80	C₂³×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	4	1	no	—
83	C₃×C₅×D₄	—	4	1	no	—
84	C₃×C₅×D₄	—	4	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	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	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₅×C₃⋊C₈	—	2	4	no	—
99	C₅×C₃⋊C₈	—	2	4	no	—
100	C₃×#126	—	2	1	no	—
101	C₃×#125	C₂²×C₅	1	1	yes	characteristic
102	C₃×#124	C₂²×C₅	1	1	yes	characteristic
103	C₃×#123	—	2	1	no	—
104	C₃×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
105	C₃×#121	C₄×C₅	1	1	yes	characteristic
106	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
107	C₃×C₄×D₄	—	2	1	no	—
108	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
109	C₃×#117	—	2	1	no	—
110	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₂×#208	—	2	1	no	—
112	C₂²×C₃⋊C₈	—	2	1	no	—
113	#803	—	2	1	no	—
114	#803	C₂²×C₅	1	2	yes	—
115	#803	C₂²×C₅	1	2	yes	—
116	C₄×C₃⋊C₈	—	2	1	no	—
117	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	#67	1	1	yes	characteristic
123	C₂²×C₄×C₅	#67	1	1	yes	characteristic
124	C₅×M₁₆	—	6	4	no	—
125	C₂×C₅×C₈	—	6	4	no	—
126	C₂×C₅×C₈	—	6	2	no	—
127	C₂×C₅×C₈	—	6	2	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
133	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
134	C₅×C₂²⋊C₄	—	2	1	no	—
135	C₅×C₂²⋊C₄	—	2	1	no	—
136	C₅×C₂²⋊C₄	—	2	1	no	—
137	C₅×C₂²⋊C₄	—	2	1	no	—
138	C₅×C₂²⋊C₄	—	2	1	no	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
141	C₄²×C₅	#67	1	1	yes	characteristic
142	C₄²×C₅	#67	1	1	yes	characteristic
143	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
144	#529	C₅×D₃	1	1	yes	characteristic
145	C₄×M₁₆	—	3	1	no	—
146	C₂×#97	—	3	1	no	—
147	#330	—	3	2	no	—
148	#329	—	3	2	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	4	1	no	—
152	C₂²×C₃×C₅	—	4	1	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	#104	1	2	yes	—
155	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	—	4	1	no	—
163	C₃×C₄×C₅	—	4	1	no	—
164	C₃×C₄×C₅	#104	1	2	yes	—
165	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
177	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
178	C₃×C₂²⋊C₄	—	2	1	no	—
179	C₃×C₂²⋊C₄	—	2	1	no	—
180	C₃×C₂²⋊C₄	—	2	1	no	—
181	C₃×C₂²⋊C₄	—	2	1	no	—
182	C₃×C₂²⋊C₄	—	2	1	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
185	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
186	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
187	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
188	#208	—	2	4	no	—
189	C₂×C₃⋊C₈	—	2	4	no	—
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	—	2	2	no	—
192	C₂³×C₅	—	2	1	no	—
193	C₂³×C₅	#217	1	1	yes	characteristic
194	C₅×Q₈	—	4	1	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	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	—	4	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	#217	1	1	yes	characteristic
205	C₂×C₄×C₅	#217	1	1	yes	characteristic
206	C₂×C₄×C₅	#217	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
210	C₅×C₈	—	6	4	no	—
211	C₅×C₈	—	6	4	no	—
212	C₂×M₁₆	—	6	1	no	—
213	C₂²×C₈	—	6	1	no	—
214	#126	—	2	1	no	—
215	#125	C₂×C₅×D₃	1	1	yes	characteristic
216	#124	C₂×C₅×D₃	1	1	yes	characteristic
217	#123	—	2	1	no	—
218	C₂²⋊Q₈	C₅×Dic₃	1	1	yes	characteristic
219	#121	C₅×Dic₃	1	1	yes	characteristic
220	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
223	#117	—	2	1	no	—
224	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
225	#97	—	3	2	no	—
226	#97	—	3	2	no	—
227	#97	—	6	1	no	—
228	C₄×C₈	—	6	1	no	—
229	C₂×C₃×C₅	—	2	2	no	—
230	C₂×C₃×C₅	—	8	1	no	—
231	C₂×C₃×C₅	#413	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
236	C₃×Q₈	—	4	1	no	—
237	C₃×D₄	—	4	1	no	—
238	C₃×D₄	—	4	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	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	—	4	1	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₃⋊C₈	—	2	4	no	—
253	C₃⋊C₈	—	2	4	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	4	1	no	—
257	C₂²×C₅	—	4	1	no	—
258	C₂²×C₅	—	4	1	no	—
259	C₂²×C₅	#837	1	2	yes	—
260	C₂²×C₅	C₂×#217	1	1	yes	characteristic
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	4	1	no	—
267	C₄×C₅	—	4	1	no	—
268	C₄×C₅	—	4	1	no	—
269	C₄×C₅	#837	1	2	yes	—
270	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
275	C₂²×C₄	C₅×#67	1	1	yes	characteristic
276	C₂²×C₄	C₅×#67	1	1	yes	characteristic
277	M₁₆	—	6	4	no	—
278	C₂×C₈	—	6	4	no	—
279	C₂×C₈	—	6	2	no	—
280	C₂×C₈	—	6	2	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
286	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
287	C₂²⋊C₄	—	2	1	no	—
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
294	C₄²	C₅×#67	1	1	yes	characteristic
295	C₄²	C₅×#67	1	1	yes	characteristic
296	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
297	C₃×C₅	#1524	1	1	yes	characteristic, complemented, Hall
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	C₅×#104	1	2	yes	—
304	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	4	1	no	—
311	C₃×C₄	—	4	1	no	—
312	C₃×C₄	—	4	1	no	—
313	C₃×C₄	C₅×#104	1	2	yes	—
314	C₂×C₅	—	2	2	no	—
315	C₂×C₅	—	8	1	no	—
316	C₂×C₅	C₂×#837	1	1	yes	characteristic
317	C₂×C₅	C₂×#837	1	1	yes	characteristic
318	C₂×C₅	#5237	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	C₅×#217	1	1	yes	characteristic
321	Q₈	—	4	1	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₅×#217	1	1	yes	characteristic
332	C₂×C₄	C₅×#217	1	1	yes	characteristic
333	C₂×C₄	C₅×#217	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
335	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
336	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
337	C₈	—	6	4	no	—
338	C₈	—	6	4	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	8	1	no	—
341	C₂×C₃	C₅×#413	1	1	yes	characteristic
342	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
343	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
344	C₅	#71746	1	1	yes	characteristic, direct product factor, Sylow
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	C₅×#837	1	2	yes	—
351	C₂²	C₂×C₅×#217	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	C₅×#837	1	2	yes	—
361	C₃	C₅×#1524	1	1	yes	characteristic, complemented, Sylow
362	C₂	—	2	2	no	—
363	C₂	—	8	1	no	—
364	C₂	C₂×C₅×#837	1	1	yes	characteristic
365	C₂	C₂×C₅×#837	1	1	yes	characteristic
366	C₂	C₅×#5237	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#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×#1524
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×#208	C₂	semidirect
3. C₂×C₅×#803	C₂	semidirect
4. C₅×#4543	C₂	semidirect
5. C₅×#4540	C₂	semidirect
24. #71746	C₅	direct (N × H)
58. C₄×#208	C₂×C₅	semidirect
59. C₂×#803	C₂×C₅	semidirect
60. #4543	C₂×C₅	semidirect
61. #4540	C₂×C₅	semidirect
297. C₃×C₅	#1524	semidirect
344. C₅	#71746	direct (N × H)
361. C₃	C₅×#1524	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
C₄×C₅×#208	2
C₂×C₅×#803	2
C₅×#4543	2
C₅×#4540	2
C₅×#1524	3
#71746	5

Subgroups — C5×#71746 #14283919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71746 #14283919