Subgroups — C₅×C₇×#95 #11764591

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	3	yes	maximal
2	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
3	C₂×C₄×C₅×C₇	—	2	6	no	—
4	C₂×C₄×C₅×C₇	C₄	1	6	yes	complemented
5	C₇×#95	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×#95	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₇	C₂×C₄	1	3	yes	—
8	C₂²×C₅×C₇	D₄	1	3	yes	—
9	C₂²×C₅×C₇	Q₈	1	1	yes	characteristic
10	C₄×C₅×C₇	—	2	6	no	—
11	C₂²×C₄×C₇	C₂×C₅	1	3	yes	—
12	C₂²×C₄×C₅	C₂×C₇	1	3	yes	—
13	C₂×C₅×C₇	C₄²	1	1	yes	characteristic
14	C₂×C₅×C₇	C₂²⋊C₄	1	3	yes	—
15	C₂×C₅×C₇	C₄⋊C₄	1	3	yes	—
16	C₂³×C₇	C₂²×C₅	1	1	yes	characteristic
17	C₂×C₄×C₇	—	2	6	no	—
18	C₂×C₄×C₇	C₄×C₅	1	6	yes	complemented
19	C₂³×C₅	C₂²×C₇	1	1	yes	characteristic
20	C₂×C₄×C₅	—	2	6	no	—
21	C₂×C₄×C₅	C₄×C₇	1	6	yes	complemented
22	C₅×C₇	#95	1	1	yes	characteristic, direct product factor, Hall
23	#95	C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₇	C₂×C₄×C₅	1	3	yes	—
25	C₂²×C₇	C₅×D₄	1	3	yes	—
26	C₂²×C₇	C₅×Q₈	1	1	yes	characteristic
27	C₄×C₇	—	2	6	no	—
28	C₂²×C₅	C₂×C₄×C₇	1	3	yes	—
29	C₂²×C₅	C₇×D₄	1	3	yes	—
30	C₂²×C₅	C₇×Q₈	1	1	yes	characteristic
31	C₄×C₅	—	2	6	no	—
32	C₂²×C₄	C₂×C₅×C₇	1	3	yes	—
33	C₂×C₇	C₄²×C₅	1	1	yes	characteristic
34	C₂×C₇	C₅×C₂²⋊C₄	1	3	yes	—
35	C₂×C₇	C₅×C₄⋊C₄	1	3	yes	—
36	C₂×C₅	C₄²×C₇	1	1	yes	characteristic
37	C₂×C₅	C₇×C₂²⋊C₄	1	3	yes	—
38	C₂×C₅	C₇×C₄⋊C₄	1	3	yes	—
39	C₂³	C₂²×C₅×C₇	1	1	yes	characteristic
40	C₂×C₄	—	2	6	no	—
41	C₂×C₄	C₄×C₅×C₇	1	6	yes	complemented
42	C₇	C₅×#95	1	1	yes	characteristic, direct product factor, Sylow
43	C₅	C₇×#95	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₂×C₄×C₅×C₇	1	3	yes	—
45	C₂²	C₅×C₇×D₄	1	3	yes	—
46	C₂²	C₅×C₇×Q₈	1	1	yes	characteristic
47	C₄	—	2	6	no	—
48	C₂	C₄²×C₅×C₇	1	1	yes	characteristic
49	C₂	C₅×C₇×C₂²⋊C₄	1	3	yes	—
50	C₂	C₅×C₇×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅×C₇	C₂²
commutator	C₂	C₄²×C₅×C₇
Frattini, cosocle	C₂³	C₂²×C₅×C₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄×C₅×C₇	C₄	semidirect
5. C₇×#95	C₅	direct (N × H)
6. C₅×#95	C₇	direct (N × H)
18. C₂×C₄×C₇	C₄×C₅	semidirect
21. C₂×C₄×C₅	C₄×C₇	semidirect
22. C₅×C₇	#95	direct (N × H)
23. #95	C₅×C₇	direct (N × H)
41. C₂×C₄	C₄×C₅×C₇	semidirect
42. C₇	C₅×#95	direct (N × H)
43. C₅	C₇×#95	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
C₇×#95	5
C₅×#95	7

Subgroups — C5×C7×#95 #11764591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×#95 #11764591