Subgroups — C₅×#6475 #11765070

Order 1120.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1159	C₂	1	2	yes	maximal, complemented
2	C₅×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1142	C₂	1	2	yes	maximal, complemented
4	C₅×Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×C₇×D₄	C₂²	1	2	yes	—
7	C₅×C₂²⋊D₇	—	2	2	no	—
8	C₂×C₅×Dic₇	—	2	2	no	—
9	C₄×C₅×D₇	C₂²	1	1	yes	characteristic
10	C₅×Dic₁₄	C₂²	1	2	yes	—
11	C₅×C₇×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₇⋊C₈	C₂²	1	1	yes	characteristic
13	#6475	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×#135	—	7	1	no	maximal, Hall
15	C₂²×C₅×C₇	—	2	2	no	—
16	C₂×C₅×D₇	D₄	1	1	yes	characteristic
17	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
18	C₅×Dic₇	—	2	2	no	—
19	C₅×Dic₇	D₄	1	1	yes	characteristic
20	#1159	C₂×C₅	1	2	yes	complemented
21	C₇×D₈	C₂×C₅	1	1	yes	characteristic, complemented
22	#1142	C₂×C₅	1	2	yes	complemented
23	Dic₂₈	C₂×C₅	1	1	yes	characteristic, complemented
24	C₈×D₇	C₂×C₅	1	1	yes	characteristic, complemented
25	C₅×#41	—	7	2	no	—
26	C₅×Q₁₆	—	7	1	no	—
27	C₅×SD₁₆	—	7	2	no	—
28	C₅×D₈	D₇	1	1	yes	characteristic, complemented
29	C₂×C₅×C₈	—	7	1	no	—
30	C₂×C₅×C₇	—	4	2	no	—
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	C₅×D₇	—	2	1	no	—
33	C₇×D₄	C₂²×C₅	1	2	yes	—
34	C₂²⋊D₇	—	2	2	no	—
35	C₂×Dic₇	—	2	2	no	—
36	C₄×D₇	C₂²×C₅	1	1	yes	characteristic
37	Dic₁₄	C₂²×C₅	1	2	yes	—
38	C₇×C₈	C₂²×C₅	1	1	yes	characteristic
39	C₇⋊C₈	C₂²×C₅	1	1	yes	characteristic
40	C₅×Q₈	—	7	2	no	—
41	C₅×D₄	—	14	2	no	—
42	C₅×D₄	C₂×D₇	1	2	yes	—
43	C₂×C₄×C₅	—	7	1	no	—
44	C₂×C₄×C₅	—	14	2	no	—
45	C₅×C₈	—	7	1	no	—
46	C₅×C₈	C₂×D₇	1	1	yes	characteristic
47	C₅×C₇	#135	1	1	yes	characteristic, complemented, Hall
48	#135	—	7	1	no	Sylow
49	C₂²×C₇	—	2	2	no	—
50	C₂×D₇	C₅×D₄	1	1	yes	characteristic
51	C₄×C₇	C₂³×C₅	1	1	yes	characteristic
52	Dic₇	—	2	2	no	—
53	Dic₇	C₅×D₄	1	1	yes	characteristic
54	C₂²×C₅	—	2	2	no	—
55	C₂²×C₅	—	7	1	no	—
56	C₄×C₅	—	7	1	no	—
57	C₄×C₅	—	14	2	no	—
58	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
59	#41	—	7	2	no	—
60	Q₁₆	—	7	1	no	—
61	SD₁₆	—	7	2	no	—
62	D₈	C₅×D₇	1	1	yes	characteristic, complemented
63	C₂×C₈	—	7	1	no	—
64	C₂×C₇	—	4	2	no	—
65	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
66	D₇	—	2	1	no	—
67	C₂×C₅	—	4	2	no	—
68	C₂×C₅	—	14	1	no	—
69	C₂×C₅	D₄×D₇	1	1	yes	characteristic
70	Q₈	—	7	2	no	—
71	D₄	—	14	2	no	—
72	D₄	C₂×C₅×D₇	1	2	yes	—
73	C₂×C₄	—	7	1	no	—
74	C₂×C₄	—	14	2	no	—
75	C₈	—	7	1	no	—
76	C₈	C₂×C₅×D₇	1	1	yes	characteristic
77	C₇	C₅×#135	1	1	yes	characteristic, complemented, Sylow
78	C₅	#6475	1	1	yes	characteristic, direct product factor, Sylow
79	C₂²	—	2	2	no	—
80	C₂²	—	7	1	no	—
81	C₄	—	7	1	no	—
82	C₄	—	14	2	no	—
83	C₄	C₂²×C₅×D₇	1	1	yes	characteristic
84	C₂	—	4	2	no	—
85	C₂	—	14	1	no	—
86	C₂	C₅×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₄×D₇
commutator, cosocle	C₄×C₇	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₇
Fitting	C₅×C₇×D₈	C₂
socle	C₂×C₅×C₇	C₂×D₄
hypercenter	C₅×D₈	D₇
hypocenter	C₇	C₅×#135
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₅×#1159	C₂	semidirect
2. C₅×C₇×D₈	C₂	semidirect
3. C₅×#1142	C₂	semidirect
4. C₅×Dic₂₈	C₂	semidirect
5. C₅×C₈×D₇	C₂	semidirect
13. #6475	C₅	direct (N × H)
20. #1159	C₂×C₅	semidirect
21. C₇×D₈	C₂×C₅	semidirect
22. #1142	C₂×C₅	semidirect
23. Dic₂₈	C₂×C₅	semidirect
24. C₈×D₇	C₂×C₅	semidirect
28. C₅×D₈	D₇	semidirect
47. C₅×C₇	#135	semidirect
62. D₈	C₅×D₇	semidirect
77. C₇	C₅×#135	semidirect
78. C₅	#6475	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1159	2
C₅×C₇×D₈	2
C₅×#1142	2
C₅×Dic₂₈	2
C₅×C₈×D₇	2
#6475	5
C₅×#135	7

Subgroups — C5×#6475 #11765070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6475 #11765070