Subgroups — C₅×#6489 #11765084

Order 1120.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂²⋊Dic₇	C₂	1	2	yes	maximal
3	C₅×C₄⋊Dic₇	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×Dic₇	C₂	1	2	yes	maximal, complemented
5	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅×C₇	C₄	1	4	yes	complemented
7	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₇	C₂²	1	4	yes	—
10	#6489	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×#117	—	7	1	no	maximal, Hall
12	C₂²×C₅×C₇	—	2	2	no	—
13	C₂²×C₅×C₇	C₂×C₄	1	2	yes	—
14	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
15	C₄×C₅×C₇	C₂×C₄	1	2	yes	—
16	C₄×C₅×C₇	C₂×C₄	1	2	yes	—
17	C₅×Dic₇	—	2	4	no	—
18	C₂²×C₄×C₇	C₂×C₅	1	1	yes	characteristic
19	C₂²⋊Dic₇	C₂×C₅	1	2	yes	—
20	C₄⋊Dic₇	C₂×C₅	1	2	yes	complemented
21	C₄×Dic₇	C₂×C₅	1	2	yes	complemented
22	C₂²×C₄×C₅	D₇	1	1	yes	characteristic
23	C₅×C₄⋊C₄	—	7	2	no	—
24	C₅×C₂²⋊C₄	—	7	2	no	—
25	C₄²×C₅	—	7	2	no	—
26	C₂×C₅×C₇	—	2	2	no	—
27	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₅×C₇	#41	1	2	yes	—
29	C₂³×C₇	C₂²×C₅	1	1	yes	characteristic
30	C₂×C₄×C₇	C₄×C₅	1	4	yes	complemented
31	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
32	C₂×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
33	C₂×Dic₇	C₂²×C₅	1	4	yes	—
34	C₂³×C₅	C₂×D₇	1	1	yes	characteristic
35	C₂×C₄×C₅	—	7	4	no	—
36	C₂×C₄×C₅	Dic₇	1	4	yes	complemented
37	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
38	C₂×C₄×C₅	C₂×D₇	1	1	yes	characteristic
39	C₅×C₇	#117	1	1	yes	characteristic, complemented, Hall
40	#117	—	7	1	no	Sylow
41	C₂²×C₇	—	2	2	no	—
42	C₂²×C₇	C₂×C₄×C₅	1	2	yes	—
43	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
44	C₄×C₇	C₂×C₄×C₅	1	2	yes	—
45	C₄×C₇	C₂×C₄×C₅	1	2	yes	—
46	Dic₇	—	2	4	no	—
47	C₂²×C₅	—	2	2	no	—
48	C₂²×C₅	C₂×Dic₇	1	2	yes	—
49	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
50	C₄×C₅	—	14	4	no	—
51	C₄×C₅	C₂×Dic₇	1	2	yes	—
52	C₄×C₅	C₂×Dic₇	1	2	yes	—
53	C₂²×C₄	C₅×D₇	1	1	yes	characteristic
54	C₄⋊C₄	—	7	2	no	—
55	C₂²⋊C₄	—	7	2	no	—
56	C₄²	—	7	2	no	—
57	C₂×C₇	—	2	2	no	—
58	C₂×C₇	C₂²×C₄×C₅	1	1	yes	characteristic
59	C₂×C₇	C₅×#41	1	2	yes	—
60	C₂×C₅	—	2	2	no	—
61	C₂×C₅	#1157	1	2	yes	—
62	C₂×C₅	C₂²×Dic₇	1	1	yes	characteristic
63	C₂³	C₂×C₅×D₇	1	1	yes	characteristic
64	C₂×C₄	—	7	4	no	—
65	C₂×C₄	C₅×Dic₇	1	4	yes	complemented
66	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
67	C₂×C₄	C₂×C₅×D₇	1	1	yes	characteristic
68	C₇	C₅×#117	1	1	yes	characteristic, complemented, Sylow
69	C₅	#6489	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²	—	2	2	no	—
71	C₂²	C₂×C₅×Dic₇	1	2	yes	—
72	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
73	C₄	—	14	4	no	—
74	C₄	C₂×C₅×Dic₇	1	2	yes	—
75	C₄	C₂×C₅×Dic₇	1	2	yes	—
76	C₂	—	2	2	no	—
77	C₂	C₅×#1157	1	2	yes	—
78	C₂	C₂²×C₅×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₇
commutator	C₂×C₇	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting	C₂²×C₄×C₅×C₇	C₂
socle	C₂²×C₅×C₇	C₂³
prime radical	C₂³×C₅×C₇	C₂²
cosocle	C₂²×C₇	C₂³×C₅
hypercenter	C₂²×C₄×C₅	D₇
hypocenter	C₇	C₅×#117
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×C₄⋊Dic₇	C₂	semidirect
4. C₄×C₅×Dic₇	C₂	semidirect
6. C₂×C₄×C₅×C₇	C₄	semidirect
10. #6489	C₅	direct (N × H)
20. C₄⋊Dic₇	C₂×C₅	semidirect
21. C₄×Dic₇	C₂×C₅	semidirect
30. C₂×C₄×C₇	C₄×C₅	semidirect
36. C₂×C₄×C₅	Dic₇	semidirect
39. C₅×C₇	#117	semidirect
65. C₂×C₄	C₅×Dic₇	semidirect
68. C₇	C₅×#117	semidirect
69. C₅	#6489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×C₇	2
C₅×C₂²⋊Dic₇	2
C₅×C₄⋊Dic₇	2
C₄×C₅×Dic₇	2
#6489	5
C₅×#117	7

Subgroups — C5×#6489 #11765084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#6489 #11765084