Subgroups — C₅×C₇²×C₃⋊D₃ #17984410

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	C₅×D₃×C₇²	—	3	4	no	maximal
3	C₇²×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇²	D₃	1	4	yes	complemented
5	C₅×C₇×C₃⋊D₃	C₇	1	8	yes	maximal, direct product factor
6	C₂×C₅×C₇²	—	9	1	no	Hall
7	C₃²×C₇²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₇	C₂×C₇	1	8	yes	complemented
9	D₃×C₇²	—	3	4	no	—
10	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₃×C₇	—	3	32	no	—
12	C₃×C₇²	C₅×D₃	1	4	yes	complemented
13	C₇×C₃⋊D₃	C₅×C₇	1	8	yes	direct product factor
14	C₃×C₅×C₇	D₃×C₇	1	32	yes	complemented
15	C₂×C₇²	—	9	1	no	Hall
16	C₅×C₃⋊D₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₇	—	9	8	no	—
18	C₃²×C₇	C₂×C₅×C₇	1	8	yes	complemented
19	C₇²	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₃²×C₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
21	D₃×C₇	—	3	32	no	—
22	C₅×C₇	C₇×C₃⋊D₃	1	8	yes	direct product factor
23	C₅×D₃	—	3	4	no	—
24	C₃×C₇	C₅×D₃×C₇	1	32	yes	complemented
25	C₃⋊D₃	C₅×C₇²	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅	D₃×C₇²	1	4	yes	complemented
27	C₂×C₇	—	9	8	no	—
28	C₂×C₅	—	9	1	no	Hall
29	C₃²	C₂×C₅×C₇²	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₅×C₇×C₃⋊D₃	1	8	yes	direct product factor
31	D₃	—	3	4	no	—
32	C₅	C₇²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×D₃×C₇²	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₇²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇²	C₂	semidirect
3. C₇²×C₃⋊D₃	C₅	direct (N × H)
4. C₃×C₅×C₇²	D₃	semidirect
5. C₅×C₇×C₃⋊D₃	C₇	direct (N × H)
7. C₃²×C₇²	C₂×C₅	semidirect
8. C₃²×C₅×C₇	C₂×C₇	semidirect
10. C₅×C₇²	C₃⋊D₃	direct (N × H)
12. C₃×C₇²	C₅×D₃	semidirect
13. C₇×C₃⋊D₃	C₅×C₇	direct (N × H)
14. C₃×C₅×C₇	D₃×C₇	semidirect
16. C₅×C₃⋊D₃	C₇²	direct (N × H)
18. C₃²×C₇	C₂×C₅×C₇	semidirect
19. C₇²	C₅×C₃⋊D₃	direct (N × H)
20. C₃²×C₅	C₂×C₇²	semidirect
22. C₅×C₇	C₇×C₃⋊D₃	direct (N × H)
24. C₃×C₇	C₅×D₃×C₇	semidirect
25. C₃⋊D₃	C₅×C₇²	direct (N × H)
26. C₃×C₅	D₃×C₇²	semidirect
29. C₃²	C₂×C₅×C₇²	semidirect
30. C₇	C₅×C₇×C₃⋊D₃	direct (N × H)
32. C₅	C₇²×C₃⋊D₃	direct (N × H)
33. C₃	C₅×D₃×C₇²	semidirect

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
C₅×D₃×C₇²	3
C₇²×C₃⋊D₃	5
C₅×C₇×C₃⋊D₃	7

Subgroups — C5×C72×C3⋊D3 #17984410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇²×C₃⋊D₃ #17984410