Subgroups — C₃²×C₇²×D₅ #17984401

Order 4410.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₅	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₇²	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇²	C₂×C₃	1	4	yes	complemented
5	C₃²×C₇×D₅	C₇	1	8	yes	maximal, direct product factor
6	C₇²×D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇²	D₅	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₅×C₇	C₂×C₇	1	8	yes	complemented
9	C₂×C₃×C₇²	—	5	4	no	—
10	C₅×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×D₅	C₃×C₇	1	32	yes	direct product factor
12	C₃×C₇²	C₃×D₅	1	4	yes	direct product factor
13	C₂×C₃²×C₇	—	5	8	no	—
14	C₃×C₅×C₇	C₂×C₃×C₇	1	32	yes	complemented
15	C₂×C₇²	—	5	1	no	Hall
16	C₃²×D₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₇×D₅	C₃²×C₇	1	8	yes	direct product factor
18	C₃²×C₇	C₇×D₅	1	8	yes	direct product factor
19	C₇²	C₃²×D₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₃²×C₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇	—	5	32	no	—
22	C₅×C₇	C₂×C₃²×C₇	1	8	yes	complemented
23	C₃×D₅	C₃×C₇²	1	4	yes	direct product factor
24	C₃×C₇	C₃×C₇×D₅	1	32	yes	direct product factor
25	C₂×C₃²	—	5	1	no	Hall
26	C₃×C₅	C₂×C₃×C₇²	1	4	yes	complemented
27	C₂×C₇	—	5	8	no	—
28	D₅	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Hall
29	C₃²	C₇²×D₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×C₇×D₅	1	8	yes	direct product factor
31	C₂×C₃	—	5	4	no	—
32	C₅	C₂×C₃²×C₇²	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃×C₇²×D₅	1	4	yes	direct product factor
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇²	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃²×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₇²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇²	C₂	semidirect
2. C₃×C₇²×D₅	C₃	direct (N × H)
4. C₃×C₅×C₇²	C₂×C₃	semidirect
5. C₃²×C₇×D₅	C₇	direct (N × H)
6. C₇²×D₅	C₃²	direct (N × H)
7. C₃²×C₇²	D₅	direct (N × H)
8. C₃²×C₅×C₇	C₂×C₇	semidirect
10. C₅×C₇²	C₂×C₃²	semidirect
11. C₃×C₇×D₅	C₃×C₇	direct (N × H)
12. C₃×C₇²	C₃×D₅	direct (N × H)
14. C₃×C₅×C₇	C₂×C₃×C₇	semidirect
16. C₃²×D₅	C₇²	direct (N × H)
17. C₇×D₅	C₃²×C₇	direct (N × H)
18. C₃²×C₇	C₇×D₅	direct (N × H)
19. C₇²	C₃²×D₅	direct (N × H)
20. C₃²×C₅	C₂×C₇²	semidirect
22. C₅×C₇	C₂×C₃²×C₇	semidirect
23. C₃×D₅	C₃×C₇²	direct (N × H)
24. C₃×C₇	C₃×C₇×D₅	direct (N × H)
26. C₃×C₅	C₂×C₃×C₇²	semidirect
28. D₅	C₃²×C₇²	direct (N × H)
29. C₃²	C₇²×D₅	direct (N × H)
30. C₇	C₃²×C₇×D₅	direct (N × H)
32. C₅	C₂×C₃²×C₇²	semidirect
33. C₃	C₃×C₇²×D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇²	2
C₃×C₇²×D₅	3
C₂×C₃²×C₇²	5
C₃²×C₇×D₅	7

Subgroups — C32×C72×D5 #17984401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇²×D₅ #17984401