Subgroups — C₅×#68485 #14285021

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 384 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×#4835	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#333	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4546	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×#1551	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	C₄	1	2	yes	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₅×#947	C₄	1	2	yes	—
12	C₂×C₅×D₃×C₈	—	2	1	no	—
13	C₅×#895	—	2	1	no	—
14	C₅×#895	—	2	1	no	—
15	C₅×#893	—	2	1	no	—
16	C₅×#893	—	2	1	no	—
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×#815	—	2	1	no	—
23	C₅×Dic₃⋊C₈	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#68485	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#532	—	3	1	no	—
28	C₅×#432	—	3	1	no	—
29	C₂×C₅×C₄⋊C₈	—	3	1	no	—
30	C₅×#333	—	3	1	no	—
31	C₅×#333	D₃	1	1	yes	characteristic, complemented
32	C₅×#331	—	3	1	no	—
33	C₅×#331	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
35	C₅×#239	—	4	4	no	—
36	C₂×C₅×D₁₂	—	2	2	no	—
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
53	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₂×C₅×C₃⋊C₈	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₅×D₃×C₈	—	4	2	no	—
57	#5725	C₂×C₅	1	1	yes	characteristic
58	#4835	C₂×C₅	1	1	yes	characteristic, complemented
59	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
60	C₃×#333	C₂×C₅	1	1	yes	characteristic, complemented
61	#4546	C₂×C₅	1	1	yes	characteristic, complemented
62	#4485	C₂×C₅	1	1	yes	characteristic, complemented
63	#4485	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₅×#41	—	3	2	no	—
65	C₂²×C₅×C₈	—	6	1	no	—
66	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
67	C₅×#127	—	3	1	no	—
68	C₅×#124	—	3	2	no	—
69	C₅×#121	—	6	1	no	—
70	C₅×#121	—	6	1	no	—
71	C₄×C₅×D₄	—	6	1	no	—
72	C₄×C₅×D₄	—	6	1	no	—
73	C₂×C₄²×C₅	—	3	1	no	—
74	C₅×C₄⋊C₈	—	3	1	no	—
75	C₅×C₄⋊C₈	—	3	1	no	—
76	C₅×C₄⋊C₈	—	6	1	no	—
77	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×C₂²⋊C₈	—	6	1	no	—
80	C₅×#97	—	6	1	no	—
81	#1551	—	3	1	no	Sylow
82	C₂²×C₅×D₃	—	2	2	no	—
83	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₃×C₅×Q₈	—	4	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₅×D₁₂	—	4	2	no	—
93	C₅×D₁₂	—	4	4	no	—
94	C₅×D₁₂	—	4	1	no	—
95	C₅×D₁₂	—	4	1	no	—
96	C₅×D₁₂	—	4	1	no	—
97	C₅×D₁₂	—	4	1	no	—
98	C₄×C₅×D₃	—	2	2	no	—
99	C₄×C₅×D₃	—	2	1	no	—
100	C₄×C₅×D₃	—	2	1	no	—
101	C₄×C₅×D₃	—	2	1	no	—
102	C₄×C₅×D₃	—	2	1	no	—
103	C₄×C₅×D₃	—	4	4	no	—
104	C₃×C₅×C₈	—	4	1	no	—
105	C₃×C₅×C₈	—	4	1	no	—
106	C₅×C₃⋊C₈	—	4	1	no	—
107	C₅×C₃⋊C₈	—	4	1	no	—
108	C₂×#239	C₄×C₅	1	2	yes	—
109	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
110	#947	C₄×C₅	1	2	yes	—
111	C₂×D₃×C₈	—	2	1	no	—
112	#895	—	2	1	no	—
113	#895	—	2	1	no	—
114	#893	—	2	1	no	—
115	#893	—	2	1	no	—
116	#874	C₂²×C₅	1	1	yes	characteristic
117	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
119	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
120	(C₂×D₃)⋊C₈	—	2	1	no	—
121	#815	—	2	1	no	—
122	Dic₃⋊C₈	—	2	1	no	—
123	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
124	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
125	C₅×#41	—	12	4	no	—
126	C₂×C₅×Q₈	C₄×D₃	1	2	yes	—
127	C₂×C₅×D₄	—	3	2	no	—
128	C₂×C₅×D₄	—	6	2	no	—
129	C₂×C₅×D₄	—	6	1	no	—
130	C₂×C₅×D₄	—	6	1	no	—
131	C₂²×C₄×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	—	3	1	no	—
134	C₂²×C₄×C₅	—	6	2	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	6	1	no	—
138	C₂×C₅×C₈	—	6	1	no	—
139	C₂×C₅×C₈	—	12	2	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₂²⋊C₄	—	6	2	no	—
143	C₅×C₂²⋊C₄	—	6	2	no	—
144	C₄²×C₅	—	3	1	no	—
145	C₄²×C₅	—	3	1	no	—
146	C₄²×C₅	—	3	1	no	—
147	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
148	#532	—	3	1	no	—
149	#432	—	3	1	no	—
150	C₂×C₄⋊C₈	—	3	1	no	—
151	#333	—	3	1	no	—
152	#333	C₅×D₃	1	1	yes	characteristic, complemented
153	#331	—	3	1	no	—
154	#331	—	3	1	no	—
155	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₅×D₃	—	2	1	no	—
157	C₂×C₅×D₃	—	2	1	no	—
158	C₂×C₅×D₃	—	4	2	no	—
159	C₂×C₅×D₃	—	4	2	no	—
160	C₂×C₅×D₃	—	4	2	no	—
161	C₂×C₅×D₃	#100	1	2	yes	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	4	2	no	—
164	C₃×C₄×C₅	#135	1	1	yes	characteristic
165	C₃×C₄×C₅	#135	1	1	yes	characteristic
166	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₃×C₄×C₅	#137	1	1	yes	characteristic
168	C₅×Dic₃	—	2	1	no	—
169	C₅×Dic₃	—	2	1	no	—
170	C₅×Dic₃	—	2	1	no	—
171	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
172	#239	—	4	4	no	—
173	C₂×D₁₂	—	2	2	no	—
174	C₂×D₁₂	—	2	1	no	—
175	C₂×D₁₂	—	2	1	no	—
176	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
177	C₂×C₄×D₃	—	2	2	no	—
178	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
179	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
180	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
181	C₂×C₃×C₈	—	2	1	no	—
182	C₂×C₃×C₈	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
186	(C₂×D₃)⋊C₄	—	2	2	no	—
187	(C₂×D₃)⋊C₄	—	2	2	no	—
188	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
189	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
190	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
191	C₂×C₃⋊C₈	—	2	1	no	—
192	C₂×C₃⋊C₈	—	2	1	no	—
193	D₃×C₈	—	4	2	no	—
194	C₂³×C₅	—	3	1	no	—
195	C₂³×C₅	—	6	2	no	—
196	C₅×Q₈	—	4	2	no	—
197	C₅×D₄	—	12	2	no	—
198	C₅×D₄	—	12	4	no	—
199	C₅×D₄	—	12	1	no	—
200	C₅×D₄	—	12	1	no	—
201	C₅×D₄	—	12	1	no	—
202	C₅×D₄	—	12	1	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	3	1	no	—
205	C₂×C₄×C₅	—	3	1	no	—
206	C₂×C₄×C₅	—	3	1	no	—
207	C₂×C₄×C₅	—	6	2	no	—
208	C₂×C₄×C₅	—	6	1	no	—
209	C₂×C₄×C₅	—	6	1	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	6	1	no	—
212	C₂×C₄×C₅	—	12	4	no	—
213	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
214	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
216	C₅×C₈	—	4	1	no	—
217	C₅×C₈	—	4	1	no	—
218	C₅×C₈	—	12	1	no	—
219	C₅×C₈	—	12	1	no	—
220	C₂×#41	—	3	2	no	—
221	C₂²×C₈	—	6	1	no	—
222	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
223	#127	—	3	1	no	—
224	#124	—	3	2	no	—
225	#121	—	6	1	no	—
226	#121	—	6	1	no	—
227	C₄×D₄	—	6	1	no	—
228	C₄×D₄	—	6	1	no	—
229	C₂×C₄²	—	3	1	no	—
230	C₄⋊C₈	—	3	1	no	—
231	C₄⋊C₈	—	3	1	no	—
232	C₄⋊C₈	—	6	1	no	—
233	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
234	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂²⋊C₈	—	6	1	no	—
236	#97	—	6	1	no	—
237	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
238	C₂×C₃×C₅	#416	1	1	yes	characteristic
239	C₂×C₃×C₅	#417	1	1	yes	characteristic
240	C₅×D₃	—	2	2	no	—
241	C₅×D₃	—	8	2	no	—
242	C₂²×D₃	—	2	2	no	—
243	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
244	C₃×Q₈	—	4	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
249	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	D₁₂	—	4	2	no	—
253	D₁₂	—	4	4	no	—
254	D₁₂	—	4	1	no	—
255	D₁₂	—	4	1	no	—
256	D₁₂	—	4	1	no	—
257	D₁₂	—	4	1	no	—
258	C₄×D₃	—	2	2	no	—
259	C₄×D₃	—	2	1	no	—
260	C₄×D₃	—	2	1	no	—
261	C₄×D₃	—	2	1	no	—
262	C₄×D₃	—	2	1	no	—
263	C₄×D₃	—	4	4	no	—
264	C₃×C₈	—	4	1	no	—
265	C₃×C₈	—	4	1	no	—
266	C₃⋊C₈	—	4	1	no	—
267	C₃⋊C₈	—	4	1	no	—
268	C₂²×C₅	—	3	2	no	—
269	C₂²×C₅	—	6	1	no	—
270	C₂²×C₅	—	6	1	no	—
271	C₂²×C₅	—	12	2	no	—
272	C₂²×C₅	—	12	2	no	—
273	C₂²×C₅	—	12	2	no	—
274	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	—	6	1	no	—
278	C₄×C₅	—	6	1	no	—
279	C₄×C₅	—	6	1	no	—
280	C₄×C₅	#914	1	1	yes	characteristic
281	C₄×C₅	#916	1	1	yes	characteristic
282	C₄×C₅	#918	1	1	yes	characteristic
283	C₄×C₅	#919	1	1	yes	characteristic
284	#41	—	12	4	no	—
285	C₂×Q₈	C₄×C₅×D₃	1	2	yes	—
286	C₂×D₄	—	3	2	no	—
287	C₂×D₄	—	6	2	no	—
288	C₂×D₄	—	6	1	no	—
289	C₂×D₄	—	6	1	no	—
290	C₂²×C₄	—	3	1	no	—
291	C₂²×C₄	—	3	1	no	—
292	C₂²×C₄	—	3	1	no	—
293	C₂²×C₄	—	6	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	6	1	no	—
297	C₂×C₈	—	6	1	no	—
298	C₂×C₈	—	12	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	6	2	no	—
302	C₂²⋊C₄	—	6	2	no	—
303	C₄²	—	3	1	no	—
304	C₄²	—	3	1	no	—
305	C₄²	—	3	1	no	—
306	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
307	C₃×C₅	#1551	1	1	yes	characteristic, complemented, Hall
308	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×D₃	—	2	1	no	—
310	C₂×D₃	—	2	1	no	—
311	C₂×D₃	—	4	2	no	—
312	C₂×D₃	—	4	2	no	—
313	C₂×D₃	—	4	2	no	—
314	C₂×D₃	C₅×#100	1	2	yes	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	C₅×#135	1	1	yes	characteristic
318	C₃×C₄	C₅×#135	1	1	yes	characteristic
319	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₃×C₄	C₅×#137	1	1	yes	characteristic
321	Dic₃	—	2	1	no	—
322	Dic₃	—	2	1	no	—
323	Dic₃	—	2	1	no	—
324	C₂×C₅	—	6	2	no	—
325	C₂×C₅	—	24	2	no	—
326	C₂×C₅	D₃×#100	1	1	yes	characteristic
327	C₂×C₅	#4803	1	1	yes	characteristic
328	C₂×C₅	#4804	1	1	yes	characteristic
329	C₂³	—	3	1	no	—
330	C₂³	—	6	2	no	—
331	Q₈	—	4	2	no	—
332	D₄	—	12	2	no	—
333	D₄	—	12	4	no	—
334	D₄	—	12	1	no	—
335	D₄	—	12	1	no	—
336	D₄	—	12	1	no	—
337	D₄	—	12	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	3	1	no	—
340	C₂×C₄	—	3	1	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	—	6	1	no	—
344	C₂×C₄	—	6	1	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	6	1	no	—
347	C₂×C₄	—	12	4	no	—
348	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
349	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
350	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
351	C₈	—	4	1	no	—
352	C₈	—	4	1	no	—
353	C₈	—	12	1	no	—
354	C₈	—	12	1	no	—
355	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
356	C₂×C₃	C₅×#416	1	1	yes	characteristic
357	C₂×C₃	C₅×#417	1	1	yes	characteristic
358	D₃	—	2	2	no	—
359	D₃	—	8	2	no	—
360	C₅	#68485	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	3	2	no	—
362	C₂²	—	6	1	no	—
363	C₂²	—	6	1	no	—
364	C₂²	—	12	2	no	—
365	C₂²	—	12	2	no	—
366	C₂²	—	12	2	no	—
367	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	6	1	no	—
371	C₄	—	6	1	no	—
372	C₄	—	6	1	no	—
373	C₄	C₅×#914	1	1	yes	characteristic
374	C₄	C₅×#916	1	1	yes	characteristic
375	C₄	C₅×#918	1	1	yes	characteristic
376	C₄	C₅×#919	1	1	yes	characteristic
377	C₃	C₅×#1551	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	6	2	no	—
379	C₂	—	24	2	no	—
380	C₂	C₅×D₃×#100	1	1	yes	characteristic
381	C₂	C₅×#4803	1	1	yes	characteristic
382	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×#333	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5725	C₂
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#333	D₃
hypocenter	C₃	C₅×#1551
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#333

Complements

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

N	H ≅ G/N	type
2. C₅×#4835	C₂	semidirect
3. C₅×D₃×C₄⋊C₈	C₂	semidirect
4. C₃×C₅×#333	C₂	semidirect
5. C₅×#4546	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4485	C₂	semidirect
26. #68485	C₅	direct (N × H)
31. C₅×#333	D₃	semidirect
58. #4835	C₂×C₅	semidirect
59. D₃×C₄⋊C₈	C₂×C₅	semidirect
60. C₃×#333	C₂×C₅	semidirect
61. #4546	C₂×C₅	semidirect
62. #4485	C₂×C₅	semidirect
63. #4485	C₂×C₅	semidirect
152. #333	C₅×D₃	semidirect
307. C₃×C₅	#1551	semidirect
360. C₅	#68485	direct (N × H)
377. C₃	C₅×#1551	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×#4835	2
C₅×D₃×C₄⋊C₈	2
C₃×C₅×#333	2
C₅×#4546	2
C₅×#4485	2
C₅×#1551	3
#68485	5

Subgroups — C5×#68485 #14285021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68485 #14285021