Subgroups — C₅×#71160 #14289418

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5577	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1631	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#215	—	2	2	no	—
13	C₅×#895	—	2	2	no	—
14	C₅×#895	—	2	1	no	—
15	C₅×#874	—	2	1	no	—
16	C₅×#874	C₂²	1	1	yes	characteristic
17	C₄×C₅×D₁₂	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₃×C₅×#107	—	2	1	no	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#103	—	2	1	no	—
22	C₅×#809	—	2	1	no	—
23	C₅×#808	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	#71160	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#550	—	3	1	no	—
28	C₅×#492	—	3	1	no	—
29	C₅×#477	D₃	1	1	yes	characteristic, complemented
30	C₅×#476	—	3	1	no	—
31	C₅×#331	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
36	C₅×#239	—	4	2	no	—
37	C₅×#239	—	4	2	no	—
38	C₂×C₅×D₁₂	—	2	2	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	2	no	—
42	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
43	C₂×C₅×D₁₂	D₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	—	2	2	no	—
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×#215	—	4	4	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
56	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	#5577	C₂×C₅	1	1	yes	characteristic
60	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
61	#5085	C₂×C₅	1	1	yes	characteristic, complemented
62	#5084	C₂×C₅	1	1	yes	characteristic, complemented
63	#4535	C₂×C₅	1	1	yes	characteristic, complemented
64	#4485	C₂×C₅	1	1	yes	characteristic, complemented
65	#4483	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	—	6	1	no	—
67	C₂×C₅×SD₁₆	—	6	2	no	—
68	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
69	C₅×#127	—	3	1	no	—
70	C₅×#127	—	6	1	no	—
71	C₅×#121	—	6	2	no	—
72	C₅×#121	—	6	1	no	—
73	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
74	C₄×C₅×D₄	—	3	1	no	—
75	C₄×C₅×D₄	—	6	1	no	—
76	C₅×#107	—	2	1	no	—
77	C₅×#106	—	6	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#103	—	2	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₄×C₅×C₈	—	3	1	no	—
83	#1631	—	3	1	no	Sylow
84	C₂²×C₅×D₃	—	2	1	no	—
85	C₂²×C₅×D₃	—	2	2	no	—
86	C₃×C₅×Q₈	—	2	1	no	—
87	C₃×C₅×Q₈	—	4	2	no	—
88	C₃×C₅×Q₈	SD₁₆	1	2	yes	complemented
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	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	C₅×D₁₂	—	2	1	no	—
97	C₅×D₁₂	—	2	1	no	—
98	C₅×D₁₂	—	4	4	no	—
99	C₅×D₁₂	—	4	2	no	—
100	C₅×D₁₂	—	4	1	no	—
101	C₅×D₁₂	—	4	1	no	—
102	C₅×D₁₂	—	4	1	no	—
103	C₅×D₁₂	—	4	1	no	—
104	C₅×D₁₂	—	8	2	no	—
105	C₄×C₅×D₃	—	4	4	no	—
106	C₄×C₅×D₃	—	4	1	no	—
107	C₄×C₅×D₃	—	4	1	no	—
108	C₃×C₅×C₈	—	4	1	no	—
109	C₅×C₃⋊C₈	—	2	2	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₂×#239	—	2	1	no	—
112	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
113	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
114	C₂×#215	—	2	2	no	—
115	#895	—	2	2	no	—
116	#895	—	2	1	no	—
117	#874	—	2	1	no	—
118	#874	C₂²×C₅	1	1	yes	characteristic
119	C₄×D₁₂	—	2	1	no	—
120	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
121	C₃×#107	—	2	1	no	—
122	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
123	C₃×#103	—	2	1	no	—
124	#809	—	2	1	no	—
125	#808	—	2	1	no	—
126	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
127	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
128	C₅×#41	—	12	2	no	—
129	C₅×#41	—	12	2	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	#67	1	1	yes	characteristic
132	C₂×C₅×D₄	—	3	1	no	—
133	C₂×C₅×D₄	—	3	2	no	—
134	C₂×C₅×D₄	—	6	2	no	—
135	C₂×C₅×D₄	—	6	2	no	—
136	C₂×C₅×D₄	—	6	1	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₅×SD₁₆	—	12	4	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	6	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	3	1	no	—
148	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
149	C₅×C₂²⋊C₄	—	6	2	no	—
150	C₅×C₂²⋊C₄	—	6	1	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	#550	—	3	1	no	—
154	#492	—	3	1	no	—
155	#477	C₅×D₃	1	1	yes	characteristic, complemented
156	#476	—	3	1	no	—
157	#331	—	3	1	no	—
158	Q₈⋊C₈	—	3	1	no	—
159	D₄⋊C₈	—	3	1	no	—
160	C₂²×C₃×C₅	#120	1	1	yes	characteristic
161	C₂×C₅×D₃	—	4	2	no	—
162	C₂×C₅×D₃	—	4	1	no	—
163	C₂×C₅×D₃	—	4	1	no	—
164	C₂×C₅×D₃	—	4	2	no	—
165	C₂×C₅×D₃	—	4	2	no	—
166	C₂×C₅×D₃	—	4	1	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	4	1	no	—
170	C₃×C₄×C₅	—	8	1	no	—
171	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
172	C₃×C₄×C₅	#135	1	1	yes	characteristic
173	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₃×C₄×C₅	#137	1	1	yes	characteristic
175	C₅×Dic₃	—	4	1	no	—
176	C₂×C₃×Q₈	—	2	1	no	—
177	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
178	#239	—	4	2	no	—
179	#239	—	4	2	no	—
180	C₂×D₁₂	—	2	2	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	—	2	1	no	—
183	C₂×D₁₂	—	2	2	no	—
184	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
185	C₂×D₁₂	C₅×D₄	1	2	yes	—
186	C₂×C₄×D₃	—	2	2	no	—
187	C₂×C₄×D₃	—	2	1	no	—
188	C₂×C₃×C₈	—	2	1	no	—
189	C₃×C₄⋊C₄	—	2	1	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
195	#215	—	4	4	no	—
196	(C₂×D₃)⋊C₄	—	2	2	no	—
197	(C₂×D₃)⋊C₄	—	2	1	no	—
198	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
199	C₂×C₃⋊C₈	—	2	1	no	—
200	C₂×C₃⋊C₈	—	2	1	no	—
201	C₂³×C₅	—	6	1	no	—
202	C₂³×C₅	—	6	2	no	—
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	—	4	2	no	—
205	C₅×Q₈	#215	1	2	yes	complemented
206	C₅×D₄	—	6	1	no	—
207	C₅×D₄	—	6	1	no	—
208	C₅×D₄	—	12	2	no	—
209	C₅×D₄	—	12	4	no	—
210	C₅×D₄	—	12	1	no	—
211	C₅×D₄	—	12	1	no	—
212	C₅×D₄	—	12	1	no	—
213	C₅×D₄	—	12	1	no	—
214	C₅×D₄	—	24	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	6	1	no	—
219	C₂×C₄×C₅	—	12	4	no	—
220	C₂×C₄×C₅	—	12	1	no	—
221	C₂×C₄×C₅	—	12	1	no	—
222	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
225	C₅×C₈	—	4	1	no	—
226	C₅×C₈	—	6	2	no	—
227	C₅×C₈	—	12	1	no	—
228	C₂×#41	—	6	1	no	—
229	C₂×SD₁₆	—	6	2	no	—
230	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
231	#127	—	3	1	no	—
232	#127	—	6	1	no	—
233	#121	—	6	2	no	—
234	#121	—	6	1	no	—
235	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
236	C₄×D₄	—	3	1	no	—
237	C₄×D₄	—	6	1	no	—
238	#107	—	2	1	no	—
239	#106	—	6	1	no	—
240	C₄⋊C₈	—	3	1	no	—
241	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
242	#103	—	2	1	no	—
243	#102	—	6	1	no	—
244	C₄×C₈	—	3	1	no	—
245	C₂×C₃×C₅	#450	1	1	yes	characteristic
246	C₂×C₃×C₅	#452	1	1	yes	characteristic
247	C₂×C₃×C₅	#453	1	1	yes	characteristic
248	C₅×D₃	—	8	1	no	—
249	C₅×D₃	—	8	2	no	—
250	C₂²×D₃	—	2	1	no	—
251	C₂²×D₃	—	2	2	no	—
252	C₃×Q₈	—	2	1	no	—
253	C₃×Q₈	—	4	2	no	—
254	C₃×Q₈	C₅×SD₁₆	1	2	yes	complemented
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂×Dic₃	—	2	1	no	—
262	D₁₂	—	2	1	no	—
263	D₁₂	—	2	1	no	—
264	D₁₂	—	4	2	no	—
265	D₁₂	—	4	4	no	—
266	D₁₂	—	4	1	no	—
267	D₁₂	—	4	1	no	—
268	D₁₂	—	4	1	no	—
269	D₁₂	—	4	1	no	—
270	D₁₂	—	8	2	no	—
271	C₄×D₃	—	4	4	no	—
272	C₄×D₃	—	4	1	no	—
273	C₄×D₃	—	4	1	no	—
274	C₃×C₈	—	4	1	no	—
275	C₃⋊C₈	—	2	2	no	—
276	C₃⋊C₈	—	4	1	no	—
277	C₂²×C₅	—	12	1	no	—
278	C₂²×C₅	—	12	2	no	—
279	C₂²×C₅	—	12	2	no	—
280	C₂²×C₅	—	12	1	no	—
281	C₂²×C₅	—	12	2	no	—
282	C₂²×C₅	—	12	1	no	—
283	C₂²×C₅	#937	1	1	yes	characteristic
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	4	1	no	—
287	C₄×C₅	—	8	1	no	—
288	C₄×C₅	—	12	1	no	—
289	C₄×C₅	#918	1	1	yes	characteristic
290	C₄×C₅	#919	1	1	yes	characteristic
291	C₄×C₅	C₂×#215	1	1	yes	characteristic
292	C₄×C₅	#949	1	1	yes	characteristic
293	#41	—	12	2	no	—
294	#41	—	12	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	C₅×#67	1	1	yes	characteristic
297	C₂×D₄	—	3	1	no	—
298	C₂×D₄	—	3	2	no	—
299	C₂×D₄	—	6	2	no	—
300	C₂×D₄	—	6	2	no	—
301	C₂×D₄	—	6	1	no	—
302	C₂×D₄	—	6	1	no	—
303	C₂²×C₄	—	6	2	no	—
304	C₂²×C₄	—	6	1	no	—
305	SD₁₆	—	12	4	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	6	1	no	—
308	C₂×C₈	—	6	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
314	C₂²⋊C₄	—	6	2	no	—
315	C₂²⋊C₄	—	6	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
318	C₃×C₅	#1631	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	C₅×#120	1	1	yes	characteristic
320	C₂×D₃	—	4	2	no	—
321	C₂×D₃	—	4	1	no	—
322	C₂×D₃	—	4	1	no	—
323	C₂×D₃	—	4	2	no	—
324	C₂×D₃	—	4	2	no	—
325	C₂×D₃	—	4	1	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	4	1	no	—
329	C₃×C₄	—	8	1	no	—
330	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
331	C₃×C₄	C₅×#135	1	1	yes	characteristic
332	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₃×C₄	C₅×#137	1	1	yes	characteristic
334	Dic₃	—	4	1	no	—
335	C₂×C₅	—	24	1	no	—
336	C₂×C₅	—	24	2	no	—
337	C₂×C₅	#5046	1	1	yes	characteristic
338	C₂×C₅	#5187	1	1	yes	characteristic
339	C₂×C₅	#5198	1	1	yes	characteristic
340	C₂³	—	6	1	no	—
341	C₂³	—	6	2	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	C₅×#215	1	2	yes	complemented
345	D₄	—	6	1	no	—
346	D₄	—	6	1	no	—
347	D₄	—	12	2	no	—
348	D₄	—	12	4	no	—
349	D₄	—	12	1	no	—
350	D₄	—	12	1	no	—
351	D₄	—	12	1	no	—
352	D₄	—	12	1	no	—
353	D₄	—	24	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	6	1	no	—
358	C₂×C₄	—	12	4	no	—
359	C₂×C₄	—	12	1	no	—
360	C₂×C₄	—	12	1	no	—
361	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
362	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
364	C₈	—	4	1	no	—
365	C₈	—	6	2	no	—
366	C₈	—	12	1	no	—
367	C₂×C₃	C₅×#450	1	1	yes	characteristic
368	C₂×C₃	C₅×#452	1	1	yes	characteristic
369	C₂×C₃	C₅×#453	1	1	yes	characteristic
370	D₃	—	8	1	no	—
371	D₃	—	8	2	no	—
372	C₅	#71160	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	12	1	no	—
374	C₂²	—	12	2	no	—
375	C₂²	—	12	2	no	—
376	C₂²	—	12	1	no	—
377	C₂²	—	12	2	no	—
378	C₂²	—	12	1	no	—
379	C₂²	C₅×#937	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	8	1	no	—
384	C₄	—	12	1	no	—
385	C₄	C₅×#918	1	1	yes	characteristic
386	C₄	C₅×#919	1	1	yes	characteristic
387	C₄	C₂×C₅×#215	1	1	yes	characteristic
388	C₄	C₅×#949	1	1	yes	characteristic
389	C₃	C₅×#1631	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	24	1	no	—
391	C₂	—	24	2	no	—
392	C₂	C₅×#5046	1	1	yes	characteristic
393	C₂	C₅×#5187	1	1	yes	characteristic
394	C₂	C₅×#5198	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×#477	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5577	C₂
hypercenter	C₅×#477	D₃
hypocenter	C₃	C₅×#1631
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#477

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#477	C₂	semidirect
3. C₅×#5085	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#4535	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4483	C₂	semidirect
26. #71160	C₅	direct (N × H)
29. C₅×#477	D₃	semidirect
60. C₃×#477	C₂×C₅	semidirect
61. #5085	C₂×C₅	semidirect
62. #5084	C₂×C₅	semidirect
63. #4535	C₂×C₅	semidirect
64. #4485	C₂×C₅	semidirect
65. #4483	C₂×C₅	semidirect
88. C₃×C₅×Q₈	SD₁₆	semidirect
155. #477	C₅×D₃	semidirect
205. C₅×Q₈	#215	semidirect
254. C₃×Q₈	C₅×SD₁₆	semidirect
318. C₃×C₅	#1631	semidirect
344. Q₈	C₅×#215	semidirect
372. C₅	#71160	direct (N × H)
389. C₃	C₅×#1631	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5577	2
C₃×C₅×#477	2
C₅×#5085	2
C₅×#5084	2
C₅×#4535	2
C₅×#4485	2
C₅×#4483	2
C₅×#1631	3
#71160	5

Subgroups — C5×#71160 #14289418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71160 #14289418