Subgroups — C₃²×C₇×C₅⋊D₅ #15691304

Order 3150.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×C₅⋊D₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×D₅	—	5	6	no	maximal
4	C₃×C₅²×C₇	C₂×C₃	1	4	yes	complemented
5	C₃²×C₅⋊D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₅⋊D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇	D₅	1	6	yes	complemented
8	C₃²×C₅²	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×D₅	—	5	24	no	—
10	C₅²×C₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅⋊D₅	C₃×C₇	1	4	yes	direct product factor
12	C₂×C₃²×C₇	—	25	1	no	Hall
13	C₃×C₅×C₇	C₃×D₅	1	24	yes	complemented
14	C₃²×D₅	—	5	6	no	—
15	C₃×C₅²	C₂×C₃×C₇	1	4	yes	complemented
16	C₇×D₅	—	5	6	no	—
17	C₃²×C₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
18	C₅⋊D₅	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃²×C₅	C₇×D₅	1	6	yes	complemented
20	C₂×C₃×C₇	—	25	4	no	—
21	C₅×C₇	C₃²×D₅	1	6	yes	complemented
22	C₃×D₅	—	5	24	no	—
23	C₅²	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₃×C₅⋊D₅	1	4	yes	direct product factor
25	C₂×C₃²	—	25	1	no	Hall
26	C₃×C₅	C₃×C₇×D₅	1	24	yes	complemented
27	C₂×C₇	—	25	1	no	Hall
28	D₅	—	5	6	no	—
29	C₃²	C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	25	4	no	—
32	C₅	C₃²×C₇×D₅	1	6	yes	complemented
33	C₃	C₃×C₇×C₅⋊D₅	1	4	yes	direct product factor
34	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇	C₂	semidirect
2. C₃×C₇×C₅⋊D₅	C₃	direct (N × H)
4. C₃×C₅²×C₇	C₂×C₃	semidirect
5. C₃²×C₅⋊D₅	C₇	direct (N × H)
6. C₇×C₅⋊D₅	C₃²	direct (N × H)
7. C₃²×C₅×C₇	D₅	semidirect
8. C₃²×C₅²	C₂×C₇	semidirect
10. C₅²×C₇	C₂×C₃²	semidirect
11. C₃×C₅⋊D₅	C₃×C₇	direct (N × H)
13. C₃×C₅×C₇	C₃×D₅	semidirect
15. C₃×C₅²	C₂×C₃×C₇	semidirect
17. C₃²×C₇	C₅⋊D₅	direct (N × H)
18. C₅⋊D₅	C₃²×C₇	direct (N × H)
19. C₃²×C₅	C₇×D₅	semidirect
21. C₅×C₇	C₃²×D₅	semidirect
23. C₅²	C₂×C₃²×C₇	semidirect
24. C₃×C₇	C₃×C₅⋊D₅	direct (N × H)
26. C₃×C₅	C₃×C₇×D₅	semidirect
29. C₃²	C₇×C₅⋊D₅	direct (N × H)
30. C₇	C₃²×C₅⋊D₅	direct (N × H)
32. C₅	C₃²×C₇×D₅	semidirect
33. C₃	C₃×C₇×C₅⋊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×C₅²×C₇	2
C₃×C₇×C₅⋊D₅	3
C₃²×C₇×D₅	5
C₃²×C₅⋊D₅	7

Subgroups — C32×C7×C5⋊D5 #15691304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₅⋊D₅ #15691304