Subgroups — C₁₇×C₅⋊(D₄₃⋊C₃) #36346709

Order 21930.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₂₁₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×D₄₃⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₄₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₄₃	—	5	1	no	Hall
7	C₅⋊(D₄₃⋊C₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₄₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₄₃⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₅×C₁₇	—	43	1	no	maximal, Hall
11	D₂₁₅	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
12	D₄₃⋊C₃	—	5	1	no	Hall
13	C₃×C₅×C₁₇	—	43	1	no	Hall
14	C₅×C₄₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	D₅×C₁₇	—	43	1	no	Hall
16	C₄₃⋊C₃	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₇	—	215	1	no	Hall
18	D₄₃	—	5	1	no	Hall
19	C₅×C₁₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₇	—	43	1	no	Hall
21	C₄₃	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₇	—	215	1	no	Hall
23	C₃×D₅	—	43	1	no	Hall
24	C₁₇	C₅⋊(D₄₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	—	43	1	no	Hall
26	D₅	—	43	1	no	Hall
27	C₂×C₃	—	215	1	no	Hall
28	C₅	C₁₇×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	43	1	no	Sylow
30	C₂	—	215	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	C₅⋊(D₄₃⋊C₃)
commutator, cosocle, hypocenter	C₅×C₄₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₄₃	C₂×C₃
LCS	G ▷ C₅×C₄₃
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₄₃⋊C₃	C₂	semidirect
2. C₁₇×D₂₁₅	C₃	semidirect
4. C₅×C₁₇×C₄₃	C₂×C₃	semidirect
5. C₁₇×C₄₃⋊C₃	D₅	semidirect
7. C₅⋊(D₄₃⋊C₃)	C₁₇	direct (N × H)
8. C₁₇×C₄₃	C₃×D₅	semidirect
9. C₅×C₄₃⋊C₃	C₂×C₁₇	semidirect
11. D₂₁₅	C₃×C₁₇	semidirect
14. C₅×C₄₃	C₂×C₃×C₁₇	semidirect
16. C₄₃⋊C₃	D₅×C₁₇	semidirect
19. C₅×C₁₇	D₄₃⋊C₃	semidirect
21. C₄₃	C₃×D₅×C₁₇	semidirect
24. C₁₇	C₅⋊(D₄₃⋊C₃)	direct (N × H)
28. C₅	C₁₇×D₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₇×C₄₃⋊C₃	2
C₁₇×D₂₁₅	3
C₁₇×D₄₃⋊C₃	5
C₅⋊(D₄₃⋊C₃)	17
C₃×D₅×C₁₇	43

Subgroups — C17×C5⋊(D43⋊C3) #36346709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₅⋊(D₄₃⋊C₃) #36346709