Subgroups — C₅×C₇²×D₄ #14520013

Order 1960.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₇²	C₂	1	2	yes	maximal, complemented
2	C₄×C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇²	—	2	2	no	—
4	C₂×C₅×C₇²	C₂²	1	1	yes	characteristic
5	C₇²×D₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₄	C₇	1	8	yes	maximal, direct product factor
7	C₅×C₇²	D₄	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₇²	C₂×C₅	1	2	yes	complemented
9	C₄×C₇²	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂²×C₅×C₇	C₂×C₇	1	16	yes	complemented
11	C₄×C₅×C₇	C₂×C₇	1	8	yes	complemented
12	C₂×C₇²	—	2	2	no	—
13	C₂×C₇²	C₂²×C₅	1	1	yes	characteristic
14	C₂×C₅×C₇	—	2	16	no	—
15	C₂×C₅×C₇	C₂²×C₇	1	8	yes	—
16	C₇×D₄	C₅×C₇	1	8	yes	direct product factor
17	C₇²	C₅×D₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₅×D₄	C₇²	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₇	C₇×D₄	1	8	yes	direct product factor
20	C₂²×C₇	C₂×C₅×C₇	1	16	yes	complemented
21	C₄×C₇	C₂×C₅×C₇	1	8	yes	complemented
22	C₂²×C₅	C₂×C₇²	1	2	yes	complemented
23	C₄×C₅	C₂×C₇²	1	1	yes	characteristic, complemented
24	C₂×C₇	—	2	16	no	—
25	C₂×C₇	C₂²×C₅×C₇	1	8	yes	—
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	C₂²×C₇²	1	1	yes	characteristic
28	D₄	C₅×C₇²	1	1	yes	characteristic, direct product factor, Sylow
29	C₇	C₅×C₇×D₄	1	8	yes	direct product factor
30	C₅	C₇²×D₄	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²	C₂×C₅×C₇²	1	2	yes	complemented
32	C₄	C₂×C₅×C₇²	1	1	yes	characteristic, complemented
33	C₂	—	2	2	no	—
34	C₂	C₂²×C₅×C₇²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅×C₇²	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₅×C₇²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₇² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₇²	C₂	semidirect
2. C₄×C₅×C₇²	C₂	semidirect
5. C₇²×D₄	C₅	direct (N × H)
6. C₅×C₇×D₄	C₇	direct (N × H)
7. C₅×C₇²	D₄	direct (N × H)
8. C₂²×C₇²	C₂×C₅	semidirect
9. C₄×C₇²	C₂×C₅	semidirect
10. C₂²×C₅×C₇	C₂×C₇	semidirect
11. C₄×C₅×C₇	C₂×C₇	semidirect
16. C₇×D₄	C₅×C₇	direct (N × H)
17. C₇²	C₅×D₄	direct (N × H)
18. C₅×D₄	C₇²	direct (N × H)
19. C₅×C₇	C₇×D₄	direct (N × H)
20. C₂²×C₇	C₂×C₅×C₇	semidirect
21. C₄×C₇	C₂×C₅×C₇	semidirect
22. C₂²×C₅	C₂×C₇²	semidirect
23. C₄×C₅	C₂×C₇²	semidirect
28. D₄	C₅×C₇²	direct (N × H)
29. C₇	C₅×C₇×D₄	direct (N × H)
30. C₅	C₇²×D₄	direct (N × H)
31. C₂²	C₂×C₅×C₇²	semidirect
32. C₄	C₂×C₅×C₇²	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₇²	2
C₄×C₅×C₇²	2
C₇²×D₄	5
C₅×C₇×D₄	7

Subgroups — C5×C72×D4 #14520013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇²×D₄ #14520013