Subgroups — C₂×C₁₇×C₁₉×C₁₁⋊C₅ #48001037

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, direct product factor, Hall
2	C₂×C₁₁×C₁₇×C₁₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₇×C₁₉	—	11	1	no	maximal, Hall
5	C₂×C₁₉×C₁₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₇×C₁₁⋊C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₇×C₁₉	—	11	1	no	Hall
8	C₁₉×C₁₁⋊C₅	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₁₁⋊C₅	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₇×C₁₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁×C₁₉	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₇	C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
13	C₁₇×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×C₁₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₉	—	11	1	no	Hall
16	C₁₁×C₁₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₇	—	11	1	no	Hall
18	C₂×C₁₁⋊C₅	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₉	—	11	1	no	Hall
20	C₅×C₁₇	—	11	1	no	Hall
21	C₁₁⋊C₅	C₂×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₉	C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₇	C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₁₁	C₅×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₁₉	C₂×C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₁₇	C₂×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₂×C₅×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	—	11	1	no	Hall
29	C₅	—	11	1	no	Sylow
30	C₂	C₁₇×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₁₉×C₁₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₁×C₁₇×C₁₉	C₅	semidirect
3. C₁₁×C₁₇×C₁₉	C₂×C₅	semidirect
5. C₂×C₁₉×C₁₁⋊C₅	C₁₇	direct (N × H)
6. C₂×C₁₇×C₁₁⋊C₅	C₁₉	direct (N × H)
8. C₁₉×C₁₁⋊C₅	C₂×C₁₇	direct (N × H)
9. C₁₇×C₁₁⋊C₅	C₂×C₁₉	direct (N × H)
10. C₂×C₁₇×C₁₉	C₁₁⋊C₅	direct (N × H)
11. C₂×C₁₁×C₁₉	C₅×C₁₇	semidirect
12. C₂×C₁₁×C₁₇	C₅×C₁₉	semidirect
13. C₁₇×C₁₉	C₂×C₁₁⋊C₅	direct (N × H)
14. C₁₁×C₁₉	C₂×C₅×C₁₇	semidirect
16. C₁₁×C₁₇	C₂×C₅×C₁₉	semidirect
18. C₂×C₁₁⋊C₅	C₁₇×C₁₉	direct (N × H)
21. C₁₁⋊C₅	C₂×C₁₇×C₁₉	direct (N × H)
22. C₂×C₁₉	C₁₇×C₁₁⋊C₅	direct (N × H)
23. C₂×C₁₇	C₁₉×C₁₁⋊C₅	direct (N × H)
24. C₂×C₁₁	C₅×C₁₇×C₁₉	semidirect
25. C₁₉	C₂×C₁₇×C₁₁⋊C₅	direct (N × H)
26. C₁₇	C₂×C₁₉×C₁₁⋊C₅	direct (N × H)
27. C₁₁	C₂×C₅×C₁₇×C₁₉	semidirect
30. C₂	C₁₇×C₁₉×C₁₁⋊C₅	direct (N × H)

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
C₂×C₁₁×C₁₇×C₁₉	5
C₂×C₅×C₁₇×C₁₉	11
C₂×C₁₉×C₁₁⋊C₅	17
C₂×C₁₇×C₁₁⋊C₅	19

Subgroups — C2×C17×C19×C11⋊C5 #48001037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₁₉×C₁₁⋊C₅ #48001037