Subgroups — C₅×D₃₅₅₃ #48001044

Order 35530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₅₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₃₂₃	—	11	1	no	maximal, Hall
5	C₅×D₂₀₉	—	17	1	no	maximal, Hall
6	C₅×D₁₈₇	—	19	1	no	maximal, Hall
7	C₅×C₁₇×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×C₁₉	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×C₁₇	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₃₂₃	—	11	1	no	Hall
11	D₂₀₉	—	17	1	no	Hall
12	D₁₈₇	—	19	1	no	Hall
13	C₁₇×C₁₉	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₉	—	187	1	no	Hall
16	C₁₁×C₁₇	C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₅×D₁₇	—	209	1	no	Hall
18	C₅×D₁₁	—	323	1	no	Hall
19	C₅×C₁₉	D₁₈₇	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₇	D₂₀₉	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₁	D₃₂₃	1	1	yes	characteristic, complemented, Hall
22	D₁₉	—	187	1	no	Hall
23	D₁₇	—	209	1	no	Hall
24	D₁₁	—	323	1	no	Hall
25	C₁₉	C₅×D₁₈₇	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	C₅×D₂₀₉	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₅×D₃₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	—	3553	1	no	Hall
29	C₅	D₃₅₅₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3553	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₅₅₃
commutator, cosocle, hypocenter	C₁₁×C₁₇×C₁₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₇×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₇×C₁₉	C₂	semidirect
2. D₃₅₅₃	C₅	direct (N × H)
3. C₁₁×C₁₇×C₁₉	C₂×C₅	semidirect
7. C₅×C₁₇×C₁₉	D₁₁	semidirect
8. C₅×C₁₁×C₁₉	D₁₇	semidirect
9. C₅×C₁₁×C₁₇	D₁₉	semidirect
13. C₁₇×C₁₉	C₅×D₁₁	semidirect
14. C₁₁×C₁₉	C₅×D₁₇	semidirect
16. C₁₁×C₁₇	C₅×D₁₉	semidirect
19. C₅×C₁₉	D₁₈₇	semidirect
20. C₅×C₁₇	D₂₀₉	semidirect
21. C₅×C₁₁	D₃₂₃	semidirect
25. C₁₉	C₅×D₁₈₇	semidirect
26. C₁₇	C₅×D₂₀₉	semidirect
27. C₁₁	C₅×D₃₂₃	semidirect
29. C₅	D₃₅₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×C₁₇×C₁₉	2
D₃₅₅₃	5
C₅×D₃₂₃	11
C₅×D₂₀₉	17
C₅×D₁₈₇	19

Subgroups — C5×D3553 #48001044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₅₅₃ #48001044