Subgroups — C₃×C₁₃×C₁₇×C₁₁⋊C₅ #49140708

Order 36465.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₁×C₁₃×C₁₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×C₅×C₁₃×C₁₇	—	11	1	no	maximal, Hall
4	C₃×C₁₇×C₁₁⋊C₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁×C₁₃×C₁₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₁₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×C₁₇	—	11	1	no	Hall
8	C₁₇×C₁₁⋊C₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₁₃×C₁₁⋊C₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃×C₁₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₁₁×C₁₇	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₃	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₁₇	—	11	1	no	Hall
14	C₁₃×C₁₇	C₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₁₃	—	11	1	no	Hall
16	C₁₁×C₁₇	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₁₁⋊C₅	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₁×C₁₃	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₇	—	11	1	no	Hall
20	C₅×C₁₃	—	11	1	no	Hall
21	C₁₁⋊C₅	C₃×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₇	C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₃	C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₁	C₅×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₁₇	C₃×C₁₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₅	—	11	1	no	Hall
27	C₁₃	C₃×C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₁₁	C₃×C₅×C₁₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₅	—	11	1	no	Sylow
30	C₃	C₁₃×C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₇	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₃×C₅×C₁₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₁₇	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₁₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₇×C₁₁⋊C₅	C₃	direct (N × H)
2. C₃×C₁₁×C₁₃×C₁₇	C₅	semidirect
4. C₃×C₁₇×C₁₁⋊C₅	C₁₃	direct (N × H)
5. C₁₁×C₁₃×C₁₇	C₃×C₅	semidirect
6. C₃×C₁₃×C₁₁⋊C₅	C₁₇	direct (N × H)
8. C₁₇×C₁₁⋊C₅	C₃×C₁₃	direct (N × H)
9. C₁₃×C₁₁⋊C₅	C₃×C₁₇	direct (N × H)
10. C₃×C₁₃×C₁₇	C₁₁⋊C₅	direct (N × H)
11. C₃×C₁₁×C₁₇	C₅×C₁₃	semidirect
12. C₃×C₁₁×C₁₃	C₅×C₁₇	semidirect
14. C₁₃×C₁₇	C₃×C₁₁⋊C₅	direct (N × H)
16. C₁₁×C₁₇	C₃×C₅×C₁₃	semidirect
17. C₃×C₁₁⋊C₅	C₁₃×C₁₇	direct (N × H)
18. C₁₁×C₁₃	C₃×C₅×C₁₇	semidirect
21. C₁₁⋊C₅	C₃×C₁₃×C₁₇	direct (N × H)
22. C₃×C₁₇	C₁₃×C₁₁⋊C₅	direct (N × H)
23. C₃×C₁₃	C₁₇×C₁₁⋊C₅	direct (N × H)
24. C₃×C₁₁	C₅×C₁₃×C₁₇	semidirect
25. C₁₇	C₃×C₁₃×C₁₁⋊C₅	direct (N × H)
27. C₁₃	C₃×C₁₇×C₁₁⋊C₅	direct (N × H)
28. C₁₁	C₃×C₅×C₁₃×C₁₇	semidirect
30. C₃	C₁₃×C₁₇×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
C₁₃×C₁₇×C₁₁⋊C₅	3
C₃×C₁₁×C₁₃×C₁₇	5
C₃×C₅×C₁₃×C₁₇	11
C₃×C₁₇×C₁₁⋊C₅	13
C₃×C₁₃×C₁₁⋊C₅	17

Subgroups — C3×C13×C17×C11⋊C5 #49140708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₁₇×C₁₁⋊C₅ #49140708