Subgroups — C₅×#83275 #14415232

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	2	yes	maximal, complemented
3	C₅×#5234	C₂	1	2	yes	maximal, complemented
4	C₅×#5012	C₂	1	4	yes	maximal, complemented
5	C₅×D₄×C₃⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2931	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₃×C₅×#127	C₄	1	1	yes	characteristic
12	C₃×C₅×#124	C₄	1	2	yes	—
13	C₃×C₅×#121	C₄	1	4	yes	—
14	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#948	—	2	8	no	—
17	C₂×C₅×#208	C₂²	1	2	yes	—
18	C₂×C₅×#208	C₂²	1	4	yes	—
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	—
21	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₅×#830	C₂²	1	8	yes	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	—
24	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
25	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
26	#83275	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×#131	—	3	2	no	—
28	C₅×#532	D₃	1	1	yes	characteristic
29	C₅×#436	—	3	4	no	—
30	C₅×C₈×D₄	—	3	4	no	—
31	C₅×#423	—	3	1	no	—
32	C₅×#408	—	3	2	no	—
33	C₂×C₄×C₅×C₈	—	3	1	no	—
34	C₃×C₅×#41	—	2	4	no	—
35	C₃×C₅×#41	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
38	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
44	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
45	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	C₂³	1	2	yes	—
48	C₅×#208	—	2	4	no	—
49	C₅×#208	—	2	8	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	—	2	8	no	—
52	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
53	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
54	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
55	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
56	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
57	C₃×#532	C₂×C₅	1	1	yes	characteristic
58	C₂×#948	C₂×C₅	1	2	yes	complemented
59	#5234	C₂×C₅	1	2	yes	complemented
60	#5012	C₂×C₅	1	4	yes	complemented
61	D₄×C₃⋊C₈	C₂×C₅	1	4	yes	complemented
62	#4924	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₅×#41	C₂×D₃	1	2	yes	—
65	C₅×#131	—	6	8	no	—
66	C₂×C₅×M₁₆	—	3	2	no	—
67	C₂×C₅×M₁₆	—	3	4	no	—
68	C₂²×C₅×C₈	—	3	1	no	—
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂²×C₅×C₈	—	3	4	no	—
71	C₅×C₄⋊Q₈	Dic₃	1	1	yes	characteristic
72	C₅×#127	Dic₃	1	1	yes	characteristic
73	C₅×#124	Dic₃	1	2	yes	—
74	C₅×#121	Dic₃	1	4	yes	—
75	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	C₅×C₄⋊C₈	—	3	4	no	—
78	C₅×C₂²⋊C₈	—	3	8	no	—
79	C₄×C₅×C₈	—	3	2	no	—
80	C₄×C₅×C₈	—	3	2	no	—
81	#2931	—	3	1	no	Sylow
82	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
83	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₃×C₅×Q₈	—	2	4	no	—
85	C₃×C₅×D₄	—	2	8	no	—
86	C₃×C₅×D₄	—	2	4	no	—
87	C₃×C₅×D₄	—	2	8	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	#41	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
98	C₅×C₃⋊C₈	—	2	4	no	—
99	C₅×C₃⋊C₈	—	2	2	no	—
100	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
101	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
102	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
103	C₃×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
104	C₃×#127	C₄×C₅	1	1	yes	characteristic
105	C₃×#124	C₄×C₅	1	2	yes	—
106	C₃×#121	C₄×C₅	1	4	yes	—
107	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	#948	—	2	8	no	—
110	C₂×#208	C₂²×C₅	1	2	yes	—
111	C₂×#208	C₂²×C₅	1	4	yes	—
112	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	—
114	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
115	#830	C₂²×C₅	1	8	yes	—
116	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	—
117	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
118	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
119	C₅×#41	—	2	4	no	—
120	C₅×#41	—	2	4	no	—
121	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
122	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
123	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
124	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
125	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
126	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
127	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
128	C₅×M₁₆	—	6	8	no	—
129	C₅×M₁₆	—	6	4	no	—
130	C₂×C₅×C₈	—	3	4	no	—
131	C₂×C₅×C₈	—	3	1	no	—
132	C₂×C₅×C₈	—	3	1	no	—
133	C₂×C₅×C₈	—	3	4	no	—
134	C₂×C₅×C₈	—	3	2	no	—
135	C₂×C₅×C₈	—	6	8	no	—
136	C₂×C₅×C₈	—	6	2	no	—
137	C₅×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
138	C₅×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
139	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
140	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
141	C₄²×C₅	C₂²×D₃	1	2	yes	—
142	C₂×#131	—	3	2	no	—
143	#532	C₅×D₃	1	1	yes	characteristic
144	#436	—	3	4	no	—
145	C₈×D₄	—	3	4	no	—
146	#423	—	3	1	no	—
147	#408	—	3	2	no	—
148	C₂×C₄×C₈	—	3	1	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	2	8	no	—
152	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₃×C₄×C₅	—	2	4	no	—
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
157	C₃×C₄×C₅	#131	1	4	yes	complemented
158	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
160	C₃×#41	—	2	4	no	—
161	C₃×#41	—	2	4	no	—
162	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
163	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
164	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
165	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
170	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
171	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
172	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
173	C₃×C₄²	C₂³×C₅	1	2	yes	—
174	#208	—	2	4	no	—
175	#208	—	2	8	no	—
176	C₂×C₃⋊C₈	—	2	2	no	—
177	C₂×C₃⋊C₈	—	2	8	no	—
178	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
179	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
180	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
181	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
182	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
183	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
184	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
185	C₅×Q₈	—	2	4	no	—
186	C₅×D₄	—	2	8	no	—
187	C₅×D₄	—	2	4	no	—
188	C₅×D₄	—	2	8	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	#237	1	2	yes	—
194	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
195	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
196	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
198	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
199	C₅×C₈	—	3	2	no	—
200	C₅×C₈	—	3	2	no	—
201	C₅×C₈	—	6	4	no	—
202	C₅×C₈	—	6	2	no	—
203	C₂×#41	C₂×C₅×D₃	1	2	yes	—
204	#131	—	6	8	no	—
205	C₂×M₁₆	—	3	2	no	—
206	C₂×M₁₆	—	3	4	no	—
207	C₂²×C₈	—	3	1	no	—
208	C₂²×C₈	—	3	4	no	—
209	C₂²×C₈	—	3	1	no	—
210	C₄⋊Q₈	C₅×Dic₃	1	1	yes	characteristic
211	#127	C₅×Dic₃	1	1	yes	characteristic
212	#124	C₅×Dic₃	1	2	yes	—
213	#121	C₅×Dic₃	1	4	yes	—
214	C₄×D₄	C₂×C₅×D₃	1	4	yes	—
215	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
216	C₄⋊C₈	—	3	4	no	—
217	C₂²⋊C₈	—	3	8	no	—
218	C₄×C₈	—	3	2	no	—
219	C₄×C₈	—	3	2	no	—
220	C₂×C₃×C₅	—	2	2	no	—
221	C₂×C₃×C₅	—	4	4	no	—
222	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂×C₃×C₅	C₂×#131	1	2	yes	—
224	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
225	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
226	C₃×Q₈	—	2	4	no	—
227	C₃×D₄	—	2	8	no	—
228	C₃×D₄	—	2	4	no	—
229	C₃×D₄	—	2	8	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
234	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
235	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
237	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
238	C₂×C₃×C₄	C₅×#41	1	2	yes	—
239	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
240	C₃⋊C₈	—	2	4	no	—
241	C₃⋊C₈	—	2	2	no	—
242	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
243	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	—	2	8	no	—
247	C₂²×C₅	D₄×Dic₃	1	2	yes	—
248	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
249	C₄×C₅	—	2	4	no	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	D₄×Dic₃	1	2	yes	—
252	C₄×C₅	#948	1	4	yes	complemented
253	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
254	C₄×C₅	C₂×#237	1	1	yes	characteristic
255	#41	—	2	4	no	—
256	#41	—	2	4	no	—
257	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
258	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
259	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
260	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
261	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
262	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
263	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
264	M₁₆	—	6	8	no	—
265	M₁₆	—	6	4	no	—
266	C₂×C₈	—	3	4	no	—
267	C₂×C₈	—	3	1	no	—
268	C₂×C₈	—	3	1	no	—
269	C₂×C₈	—	3	2	no	—
270	C₂×C₈	—	3	4	no	—
271	C₂×C₈	—	6	8	no	—
272	C₂×C₈	—	6	2	no	—
273	C₄⋊C₄	C₂×C₅×Dic₃	1	4	yes	—
274	C₂²⋊C₄	C₂×C₅×Dic₃	1	8	yes	—
275	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
276	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
277	C₄²	C₂²×C₅×D₃	1	2	yes	—
278	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
279	C₂²×C₃	—	2	2	no	—
280	C₂²×C₃	—	2	4	no	—
281	C₂²×C₃	—	2	8	no	—
282	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
283	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
284	C₃×C₄	—	2	4	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
287	C₃×C₄	C₅×#131	1	4	yes	complemented
288	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
289	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
290	C₂×C₅	—	2	2	no	—
291	C₂×C₅	—	4	4	no	—
292	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
293	C₂×C₅	C₂×#948	1	2	yes	—
294	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
295	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
296	Q₈	—	2	4	no	—
297	D₄	—	2	8	no	—
298	D₄	—	2	4	no	—
299	D₄	—	2	8	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
304	C₂×C₄	C₅×#237	1	2	yes	—
305	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
306	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
307	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
308	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
309	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
310	C₈	—	3	2	no	—
311	C₈	—	3	2	no	—
312	C₈	—	6	4	no	—
313	C₈	—	6	2	no	—
314	C₂×C₃	—	2	2	no	—
315	C₂×C₃	—	4	4	no	—
316	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
317	C₂×C₃	C₂×C₅×#131	1	2	yes	—
318	C₅	#83275	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²	—	2	2	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	8	no	—
322	C₂²	C₅×D₄×Dic₃	1	2	yes	—
323	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
324	C₄	—	2	4	no	—
325	C₄	—	2	2	no	—
326	C₄	C₅×D₄×Dic₃	1	2	yes	—
327	C₄	C₅×#948	1	4	yes	complemented
328	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
329	C₄	C₂×C₅×#237	1	1	yes	characteristic
330	C₃	C₅×#2931	1	1	yes	characteristic, complemented, Sylow
331	C₂	—	2	2	no	—
332	C₂	—	4	4	no	—
333	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic
334	C₂	C₂×C₅×#948	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₅×#5234	C₂	semidirect
4. C₅×#5012	C₂	semidirect
5. C₅×D₄×C₃⋊C₈	C₂	semidirect
6. C₅×#4924	C₂	semidirect
7. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
26. #83275	C₅	direct (N × H)
52. C₂×C₅×C₃⋊C₈	D₄	semidirect
58. C₂×#948	C₂×C₅	semidirect
59. #5234	C₂×C₅	semidirect
60. #5012	C₂×C₅	semidirect
61. D₄×C₃⋊C₈	C₂×C₅	semidirect
62. #4924	C₂×C₅	semidirect
63. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
157. C₃×C₄×C₅	#131	semidirect
178. C₂×C₃⋊C₈	C₅×D₄	semidirect
252. C₄×C₅	#948	semidirect
278. C₃×C₅	#2931	semidirect
287. C₃×C₄	C₅×#131	semidirect
318. C₅	#83275	direct (N × H)
327. C₄	C₅×#948	semidirect
330. C₃	C₅×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₂×C₅×#948	2
C₅×#5234	2
C₅×#5012	2
C₅×D₄×C₃⋊C₈	2
C₅×#4924	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#2931	3
#83275	5

Subgroups — C5×#83275 #14415232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83275 #14415232