Subgroups — C₁₁⋊C₅×D₃₂₃ #48001055

Order 35530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₃₂₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₃₂₃	—	11	1	no	maximal, Hall
5	D₁₉×C₁₁⋊C₅	—	17	1	no	maximal, Hall
6	D₁₇×C₁₁⋊C₅	—	19	1	no	maximal, Hall
7	C₅×C₁₇×C₁₉	—	11	1	no	Hall
8	C₁₉×C₁₁⋊C₅	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₁₁⋊C₅	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₃₂₃	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×D₁₉	—	17	1	no	Hall
12	C₁₁×D₁₇	—	19	1	no	Hall
13	C₁₇×C₁₉	C₂×C₁₁⋊C₅	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	C₂×C₁₁⋊C₅	—	323	1	no	Hall
19	C₅×C₁₉	—	11	1	no	Hall
20	C₅×C₁₇	—	11	1	no	Hall
21	C₁₁⋊C₅	D₃₂₃	1	1	yes	characteristic, direct product factor, Hall
22	D₁₉	—	17	1	no	Hall
23	D₁₇	—	19	1	no	Hall
24	C₂×C₁₁	—	323	1	no	Hall
25	C₁₉	D₁₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	D₁₉×C₁₁⋊C₅	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	—	11	1	no	Sylow
30	C₂	—	323	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₁₉×C₁₁⋊C₅	C₂	semidirect
2. C₁₁×D₃₂₃	C₅	semidirect
3. C₁₁×C₁₇×C₁₉	C₂×C₅	semidirect
8. C₁₉×C₁₁⋊C₅	D₁₇	semidirect
9. C₁₇×C₁₁⋊C₅	D₁₉	semidirect
10. D₃₂₃	C₁₁⋊C₅	direct (N × H)
13. C₁₇×C₁₉	C₂×C₁₁⋊C₅	semidirect
14. C₁₁×C₁₉	C₅×D₁₇	semidirect
16. C₁₁×C₁₇	C₅×D₁₉	semidirect
21. C₁₁⋊C₅	D₃₂₃	direct (N × H)
25. C₁₉	D₁₇×C₁₁⋊C₅	semidirect
26. C₁₇	D₁₉×C₁₁⋊C₅	semidirect
27. C₁₁	C₅×D₃₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₁₉×C₁₁⋊C₅	2
C₁₁×D₃₂₃	5
C₅×D₃₂₃	11
D₁₉×C₁₁⋊C₅	17
D₁₇×C₁₁⋊C₅	19

Subgroups — C11⋊C5×D323 #48001055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊C₅×D₃₂₃ #48001055