Subgroups — C₅×#68417 #14284577

Order 1920.

512 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×#5725	C₂	1	1	yes	maximal, characteristic
2	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1540	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₅×#947	—	2	1	no	—
12	C₂×C₅×D₃×C₈	—	2	1	no	—
13	C₅×#895	—	2	1	no	—
14	C₅×#895	C₄	1	2	yes	—
15	C₅×#893	—	2	1	no	—
16	C₅×#893	C₄	1	2	yes	—
17	C₅×#874	C₂²	1	1	yes	characteristic
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
22	C₅×Dic₃⋊C₈	—	2	1	no	—
23	C₅×C₈×Dic₃	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#68417	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#532	—	3	1	no	—
28	C₅×#431	—	3	1	no	—
29	C₂×C₅×C₄⋊C₈	—	3	1	no	—
30	C₅×#332	—	3	1	no	—
31	C₅×#332	D₃	1	1	yes	characteristic, complemented
32	C₅×#331	—	3	1	no	—
33	C₅×#331	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₅×#239	—	4	2	no	—
36	C₅×#239	—	4	2	no	—
37	C₂×C₅×D₁₂	—	2	2	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₅×D₃×C₈	—	4	2	no	—
58	#5725	C₂×C₅	1	1	yes	characteristic
59	#4833	C₂×C₅	1	1	yes	characteristic, complemented
60	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#332	C₂×C₅	1	1	yes	characteristic, complemented
62	#4547	C₂×C₅	1	1	yes	characteristic, complemented
63	#4485	C₂×C₅	1	1	yes	characteristic, complemented
64	#4485	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×C₅×#41	—	6	1	no	—
66	C₂²×C₅×C₈	—	6	1	no	—
67	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
68	C₅×#127	—	3	1	no	—
69	C₅×#124	—	6	1	no	—
70	C₅×#121	—	3	2	no	—
71	C₅×#121	—	6	1	no	—
72	C₄×C₅×D₄	—	3	2	no	—
73	C₄×C₅×D₄	—	6	1	no	—
74	C₂×C₄²×C₅	—	3	1	no	—
75	C₅×C₄⋊C₈	—	3	1	no	—
76	C₅×C₄⋊C₈	—	3	1	no	—
77	C₅×C₄⋊C₈	—	6	1	no	—
78	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×C₂²⋊C₈	—	6	1	no	—
81	C₄×C₅×C₈	—	6	1	no	—
82	#1540	—	3	1	no	Sylow
83	C₂²×C₅×D₃	—	2	2	no	—
84	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₃×C₅×Q₈	—	4	1	no	—
86	C₃×C₅×Q₈	—	4	1	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₅×D₁₂	—	4	2	no	—
95	C₅×D₁₂	—	4	4	no	—
96	C₅×D₁₂	—	4	1	no	—
97	C₅×D₁₂	—	4	1	no	—
98	C₅×D₁₂	—	4	1	no	—
99	C₅×D₁₂	—	4	1	no	—
100	C₄×C₅×D₃	—	2	1	no	—
101	C₄×C₅×D₃	—	2	1	no	—
102	C₄×C₅×D₃	—	4	1	no	—
103	C₄×C₅×D₃	—	4	4	no	—
104	C₄×C₅×D₃	D₈	1	2	yes	—
105	C₄×C₅×D₃	SD₁₆	1	2	yes	—
106	C₃×C₅×C₈	—	4	1	no	—
107	C₃×C₅×C₈	—	4	1	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	#947	—	2	1	no	—
113	C₂×D₃×C₈	—	2	1	no	—
114	#895	—	2	1	no	—
115	#895	C₄×C₅	1	2	yes	—
116	#893	—	2	1	no	—
117	#893	C₄×C₅	1	2	yes	—
118	#874	C₂²×C₅	1	1	yes	characteristic
119	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
120	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
122	(C₂×D₃)⋊C₈	—	2	1	no	—
123	Dic₃⋊C₈	—	2	1	no	—
124	C₈×Dic₃	—	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×D₄	—	3	2	no	—
131	C₂×C₅×D₄	—	6	2	no	—
132	C₂×C₅×D₄	—	6	1	no	—
133	C₂×C₅×D₄	—	6	1	no	—
134	C₂²×C₄×C₅	—	3	1	no	—
135	C₂²×C₄×C₅	—	3	1	no	—
136	C₂²×C₄×C₅	—	3	1	no	—
137	C₂²×C₄×C₅	—	6	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	6	1	no	—
141	C₂×C₅×C₈	—	6	1	no	—
142	C₂×C₅×C₈	—	12	2	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
145	C₅×C₂²⋊C₄	—	6	2	no	—
146	C₅×C₂²⋊C₄	—	6	2	no	—
147	C₄²×C₅	—	3	1	no	—
148	C₄²×C₅	—	3	1	no	—
149	C₄²×C₅	—	3	1	no	—
150	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
151	#532	—	3	1	no	—
152	#431	—	3	1	no	—
153	C₂×C₄⋊C₈	—	3	1	no	—
154	#332	—	3	1	no	—
155	#332	C₅×D₃	1	1	yes	characteristic, complemented
156	#331	—	3	1	no	—
157	#331	—	3	1	no	—
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₅×D₃	—	2	1	no	—
160	C₂×C₅×D₃	—	2	1	no	—
161	C₂×C₅×D₃	—	4	2	no	—
162	C₂×C₅×D₃	—	4	2	no	—
163	C₂×C₅×D₃	—	4	2	no	—
164	C₂×C₅×D₃	#102	1	2	yes	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	2	no	—
167	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
169	C₃×C₄×C₅	#135	1	1	yes	characteristic
170	C₃×C₄×C₅	#135	1	1	yes	characteristic
171	C₅×Dic₃	—	2	1	no	—
172	C₅×Dic₃	—	2	1	no	—
173	C₅×Dic₃	#102	1	2	yes	—
174	C₂×C₃×Q₈	—	2	1	no	—
175	#239	—	4	2	no	—
176	#239	—	4	2	no	—
177	C₂×D₁₂	—	2	2	no	—
178	C₂×D₁₂	—	2	1	no	—
179	C₂×D₁₂	—	2	1	no	—
180	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
181	C₂×C₄×D₃	—	2	2	no	—
182	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
183	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
184	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
189	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
190	(C₂×D₃)⋊C₄	—	2	2	no	—
191	(C₂×D₃)⋊C₄	—	2	2	no	—
192	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
193	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
194	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
195	C₂×C₃⋊C₈	—	2	1	no	—
196	C₂×C₃⋊C₈	—	2	1	no	—
197	D₃×C₈	—	4	2	no	—
198	C₂³×C₅	—	3	1	no	—
199	C₂³×C₅	—	6	2	no	—
200	C₅×Q₈	—	4	1	no	—
201	C₅×Q₈	—	4	1	no	—
202	C₅×D₄	—	12	2	no	—
203	C₅×D₄	—	12	4	no	—
204	C₅×D₄	—	12	1	no	—
205	C₅×D₄	—	12	1	no	—
206	C₅×D₄	—	12	1	no	—
207	C₅×D₄	—	12	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	3	1	no	—
210	C₂×C₄×C₅	—	3	2	no	—
211	C₂×C₄×C₅	—	3	2	no	—
212	C₂×C₄×C₅	—	3	1	no	—
213	C₂×C₄×C₅	—	3	1	no	—
214	C₂×C₄×C₅	—	6	1	no	—
215	C₂×C₄×C₅	—	6	1	no	—
216	C₂×C₄×C₅	—	12	1	no	—
217	C₂×C₄×C₅	—	12	4	no	—
218	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
221	C₅×C₈	—	4	1	no	—
222	C₅×C₈	—	4	1	no	—
223	C₅×C₈	—	12	1	no	—
224	C₅×C₈	—	12	1	no	—
225	C₂×#41	—	6	1	no	—
226	C₂²×C₈	—	6	1	no	—
227	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
228	#127	—	3	1	no	—
229	#124	—	6	1	no	—
230	#121	—	3	2	no	—
231	#121	—	6	1	no	—
232	C₄×D₄	—	3	2	no	—
233	C₄×D₄	—	6	1	no	—
234	C₂×C₄²	—	3	1	no	—
235	C₄⋊C₈	—	3	1	no	—
236	C₄⋊C₈	—	3	1	no	—
237	C₄⋊C₈	—	6	1	no	—
238	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
239	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
240	C₂²⋊C₈	—	6	1	no	—
241	C₄×C₈	—	6	1	no	—
242	C₂×C₃×C₅	#413	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
244	C₂×C₃×C₅	#416	1	1	yes	characteristic
245	C₅×D₃	—	2	2	no	—
246	C₅×D₃	—	8	2	no	—
247	C₂²×D₃	—	2	2	no	—
248	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₃×Q₈	—	4	1	no	—
250	C₃×Q₈	—	4	1	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
258	D₁₂	—	4	2	no	—
259	D₁₂	—	4	4	no	—
260	D₁₂	—	4	1	no	—
261	D₁₂	—	4	1	no	—
262	D₁₂	—	4	1	no	—
263	D₁₂	—	4	1	no	—
264	C₄×D₃	—	2	1	no	—
265	C₄×D₃	—	2	1	no	—
266	C₄×D₃	—	4	1	no	—
267	C₄×D₃	—	4	4	no	—
268	C₄×D₃	C₅×D₈	1	2	yes	—
269	C₄×D₃	C₅×SD₁₆	1	2	yes	—
270	C₃×C₈	—	4	1	no	—
271	C₃×C₈	—	4	1	no	—
272	C₃⋊C₈	—	4	1	no	—
273	C₃⋊C₈	—	4	1	no	—
274	C₂²×C₅	—	3	2	no	—
275	C₂²×C₅	—	6	1	no	—
276	C₂²×C₅	—	6	1	no	—
277	C₂²×C₅	—	12	2	no	—
278	C₂²×C₅	—	12	2	no	—
279	C₂²×C₅	—	12	2	no	—
280	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	3	2	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	6	1	no	—
285	C₄×C₅	—	6	1	no	—
286	C₄×C₅	D₃×D₈	1	1	yes	characteristic
287	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
288	C₄×C₅	#916	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×D₄	—	3	2	no	—
294	C₂×D₄	—	6	2	no	—
295	C₂×D₄	—	6	1	no	—
296	C₂×D₄	—	6	1	no	—
297	C₂²×C₄	—	3	1	no	—
298	C₂²×C₄	—	3	1	no	—
299	C₂²×C₄	—	3	1	no	—
300	C₂²×C₄	—	6	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	6	1	no	—
304	C₂×C₈	—	6	1	no	—
305	C₂×C₈	—	12	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
308	C₂²⋊C₄	—	6	2	no	—
309	C₂²⋊C₄	—	6	2	no	—
310	C₄²	—	3	1	no	—
311	C₄²	—	3	1	no	—
312	C₄²	—	3	1	no	—
313	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
314	C₃×C₅	#1540	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×D₃	—	2	1	no	—
317	C₂×D₃	—	2	1	no	—
318	C₂×D₃	—	4	2	no	—
319	C₂×D₃	—	4	2	no	—
320	C₂×D₃	—	4	2	no	—
321	C₂×D₃	C₅×#102	1	2	yes	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	4	2	no	—
324	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
325	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
326	C₃×C₄	C₅×#135	1	1	yes	characteristic
327	C₃×C₄	C₅×#135	1	1	yes	characteristic
328	Dic₃	—	2	1	no	—
329	Dic₃	—	2	1	no	—
330	Dic₃	C₅×#102	1	2	yes	—
331	C₂×C₅	—	6	2	no	—
332	C₂×C₅	—	24	2	no	—
333	C₂×C₅	#4751	1	1	yes	characteristic
334	C₂×C₅	D₃×#102	1	1	yes	characteristic
335	C₂×C₅	#4804	1	1	yes	characteristic
336	C₂³	—	3	1	no	—
337	C₂³	—	6	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	D₄	—	12	2	no	—
341	D₄	—	12	4	no	—
342	D₄	—	12	1	no	—
343	D₄	—	12	1	no	—
344	D₄	—	12	1	no	—
345	D₄	—	12	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	3	1	no	—
348	C₂×C₄	—	3	2	no	—
349	C₂×C₄	—	3	2	no	—
350	C₂×C₄	—	3	1	no	—
351	C₂×C₄	—	3	1	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	—	6	1	no	—
354	C₂×C₄	—	12	1	no	—
355	C₂×C₄	—	12	4	no	—
356	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
357	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
358	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
359	C₈	—	4	1	no	—
360	C₈	—	4	1	no	—
361	C₈	—	12	1	no	—
362	C₈	—	12	1	no	—
363	C₂×C₃	C₅×#413	1	1	yes	characteristic
364	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
365	C₂×C₃	C₅×#416	1	1	yes	characteristic
366	D₃	—	2	2	no	—
367	D₃	—	8	2	no	—
368	C₅	#68417	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	3	2	no	—
370	C₂²	—	6	1	no	—
371	C₂²	—	6	1	no	—
372	C₂²	—	12	2	no	—
373	C₂²	—	12	2	no	—
374	C₂²	—	12	2	no	—
375	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	3	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	6	1	no	—
380	C₄	—	6	1	no	—
381	C₄	C₅×D₃×D₈	1	1	yes	characteristic
382	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
383	C₄	C₅×#916	1	1	yes	characteristic
384	C₄	C₅×#919	1	1	yes	characteristic
385	C₃	C₅×#1540	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	6	2	no	—
387	C₂	—	24	2	no	—
388	C₂	C₅×#4751	1	1	yes	characteristic
389	C₂	C₅×D₃×#102	1	1	yes	characteristic
390	C₂	C₅×#4804	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#332	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5725	C₂
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#332	D₃
hypocenter	C₃	C₅×#1540
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#332

Complements

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

N	H ≅ G/N	type
2. C₅×#4833	C₂	semidirect
3. C₅×D₃×C₄⋊C₈	C₂	semidirect
4. C₃×C₅×#332	C₂	semidirect
5. C₅×#4547	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4485	C₂	semidirect
26. #68417	C₅	direct (N × H)
31. C₅×#332	D₃	semidirect
59. #4833	C₂×C₅	semidirect
60. D₃×C₄⋊C₈	C₂×C₅	semidirect
61. C₃×#332	C₂×C₅	semidirect
62. #4547	C₂×C₅	semidirect
63. #4485	C₂×C₅	semidirect
64. #4485	C₂×C₅	semidirect
155. #332	C₅×D₃	semidirect
314. C₃×C₅	#1540	semidirect
368. C₅	#68417	direct (N × H)
385. C₃	C₅×#1540	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5725	2
C₅×#4833	2
C₅×D₃×C₄⋊C₈	2
C₃×C₅×#332	2
C₅×#4547	2
C₅×#4485	2
C₅×#1540	3
#68417	5

Subgroups — C5×#68417 #14284577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68417 #14284577