Subgroups — C₅×#6503 #11765091

Order 1120.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×C₂²⋊D₇	C₂	1	4	yes	maximal, complemented
3	C₂×C₅×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×C₇	C₂²	1	2	yes	—
6	C₂²×C₅×D₇	C₂²	1	2	yes	—
7	C₅×C₇×D₄	—	2	2	no	—
8	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
9	C₅×C₂²⋊D₇	—	2	8	no	—
10	C₂×C₅×Dic₇	C₂²	1	2	yes	—
11	C₅×D₂₈	—	2	2	no	—
12	#6503	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×#127	—	7	1	no	maximal, Hall
14	C₂²×C₅×C₇	—	2	4	no	—
15	C₂²×C₅×C₇	—	2	2	no	—
16	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
17	C₂×C₅×D₇	—	2	2	no	—
18	C₂×C₅×D₇	—	2	4	no	—
19	C₄×C₅×C₇	D₄	1	2	yes	complemented
20	C₅×Dic₇	D₄	1	4	yes	complemented
21	C₂×C₇×D₄	C₂×C₅	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊D₇	C₂×C₅	1	4	yes	complemented
23	C₂×D₂₈	C₂×C₅	1	1	yes	characteristic, complemented
24	C₄×Dic₇	C₂×C₅	1	1	yes	characteristic, complemented
25	C₂×C₅×D₄	—	7	4	no	—
26	C₂×C₅×D₄	—	7	1	no	—
27	C₂×C₅×D₄	D₇	1	1	yes	characteristic, complemented
28	C₄²×C₅	—	7	1	no	—
29	C₂×C₅×C₇	—	4	2	no	—
30	C₂×C₅×C₇	C₂×D₄	1	2	yes	—
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	C₅×D₇	—	4	2	no	—
33	C₂³×C₇	C₂²×C₅	1	2	yes	—
34	C₂²×D₇	C₂²×C₅	1	2	yes	—
35	C₇×D₄	—	2	2	no	—
36	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
37	C₂²⋊D₇	—	2	8	no	—
38	C₂×Dic₇	C₂²×C₅	1	2	yes	—
39	D₂₈	—	2	2	no	—
40	C₂³×C₅	—	7	2	no	—
41	C₂³×C₅	C₂×D₇	1	2	yes	—
42	C₅×D₄	—	2	2	no	—
43	C₅×D₄	—	14	8	no	—
44	C₅×D₄	—	14	2	no	—
45	C₂×C₄×C₅	—	7	2	no	—
46	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
47	C₅×C₇	#127	1	1	yes	characteristic, complemented, Hall
48	#127	—	7	1	no	Sylow
49	C₂²×C₇	—	2	4	no	—
50	C₂²×C₇	—	2	2	no	—
51	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
52	C₂×D₇	—	2	2	no	—
53	C₂×D₇	—	2	4	no	—
54	C₄×C₇	C₅×D₄	1	2	yes	complemented
55	Dic₇	C₅×D₄	1	4	yes	complemented
56	C₂²×C₅	—	2	4	no	—
57	C₂²×C₅	—	2	2	no	—
58	C₂²×C₅	—	14	4	no	—
59	C₂²×C₅	—	14	2	no	—
60	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
61	C₄×C₅	—	7	4	no	—
62	C₄×C₅	C₂²⋊D₇	1	2	yes	complemented
63	C₂×D₄	—	7	4	no	—
64	C₂×D₄	—	7	1	no	—
65	C₂×D₄	C₅×D₇	1	1	yes	characteristic, complemented
66	C₄²	—	7	1	no	—
67	C₂×C₇	—	4	2	no	—
68	C₂×C₇	C₂×C₅×D₄	1	2	yes	—
69	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
70	D₇	—	4	2	no	—
71	C₂×C₅	—	4	2	no	—
72	C₂×C₅	—	28	2	no	—
73	C₂×C₅	D₄×D₇	1	2	yes	—
74	C₂×C₅	C₂×C₂²⋊D₇	1	1	yes	characteristic
75	C₂³	—	7	2	no	—
76	C₂³	C₂×C₅×D₇	1	2	yes	—
77	D₄	—	2	2	no	—
78	D₄	—	14	8	no	—
79	D₄	—	14	2	no	—
80	C₂×C₄	—	7	2	no	—
81	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
82	C₇	C₅×#127	1	1	yes	characteristic, complemented, Sylow
83	C₅	#6503	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²	—	2	4	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	14	4	no	—
87	C₂²	—	14	2	no	—
88	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
89	C₄	—	7	4	no	—
90	C₄	C₅×C₂²⋊D₇	1	2	yes	complemented
91	C₂	—	4	2	no	—
92	C₂	—	28	2	no	—
93	C₂	C₅×D₄×D₇	1	2	yes	—
94	C₂	C₂×C₅×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting	C₂×C₅×C₇×D₄	C₂
socle	C₂²×C₅×C₇	C₂³
hypercenter	C₂×C₅×D₄	D₇
hypocenter	C₇	C₅×#127
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇×D₄	C₂	semidirect
2. C₂×C₅×C₂²⋊D₇	C₂	semidirect
3. C₂×C₅×D₂₈	C₂	semidirect
4. C₄×C₅×Dic₇	C₂	semidirect
12. #6503	C₅	direct (N × H)
19. C₄×C₅×C₇	D₄	semidirect
20. C₅×Dic₇	D₄	semidirect
21. C₂×C₇×D₄	C₂×C₅	semidirect
22. C₂×C₂²⋊D₇	C₂×C₅	semidirect
23. C₂×D₂₈	C₂×C₅	semidirect
24. C₄×Dic₇	C₂×C₅	semidirect
27. C₂×C₅×D₄	D₇	semidirect
47. C₅×C₇	#127	semidirect
54. C₄×C₇	C₅×D₄	semidirect
55. Dic₇	C₅×D₄	semidirect
62. C₄×C₅	C₂²⋊D₇	semidirect
65. C₂×D₄	C₅×D₇	semidirect
82. C₇	C₅×#127	semidirect
83. C₅	#6503	direct (N × H)
90. C₄	C₅×C₂²⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×D₄	2
C₂×C₅×C₂²⋊D₇	2
C₂×C₅×D₂₈	2
C₄×C₅×Dic₇	2
#6503	5
C₅×#127	7

Subgroups — C5×#6503 #11765091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6503 #11765091