Subgroups — D₅×C₁₁×C₁₇×C₁₉ #48001045

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	C₂×C₁₁×C₁₇×C₁₉	—	5	1	no	maximal, Hall
3	C₁₁×C₁₇×C₁₉	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₇×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₅×C₁₁×C₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	D₅×C₁₁×C₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₇×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇×C₁₉	—	5	1	no	Hall
11	C₂×C₁₁×C₁₉	—	5	1	no	Hall
12	C₂×C₁₁×C₁₇	—	5	1	no	Hall
13	C₁₇×C₁₉	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×C₁₉	D₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	D₅×C₁₉	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×C₁₇	D₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
17	D₅×C₁₇	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	D₅×C₁₁	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₉	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₇	C₂×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₁	C₂×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₉	—	5	1	no	Hall
23	C₂×C₁₇	—	5	1	no	Hall
24	C₂×C₁₁	—	5	1	no	Hall
25	C₁₉	D₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₁₇	D₅×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	D₅×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
28	D₅	C₁₁×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₅	C₂×C₁₁×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₁×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₁×C₁₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₇×C₁₉	C₂	semidirect
3. C₁₁×C₁₇×C₁₉	D₅	direct (N × H)
4. D₅×C₁₇×C₁₉	C₁₁	direct (N × H)
5. D₅×C₁₁×C₁₉	C₁₇	direct (N × H)
6. D₅×C₁₁×C₁₇	C₁₉	direct (N × H)
7. C₅×C₁₇×C₁₉	C₂×C₁₁	semidirect
8. C₅×C₁₁×C₁₉	C₂×C₁₇	semidirect
9. C₅×C₁₁×C₁₇	C₂×C₁₉	semidirect
13. C₁₇×C₁₉	D₅×C₁₁	direct (N × H)
14. C₁₁×C₁₉	D₅×C₁₇	direct (N × H)
15. D₅×C₁₉	C₁₁×C₁₇	direct (N × H)
16. C₁₁×C₁₇	D₅×C₁₉	direct (N × H)
17. D₅×C₁₇	C₁₁×C₁₉	direct (N × H)
18. D₅×C₁₁	C₁₇×C₁₉	direct (N × H)
19. C₅×C₁₉	C₂×C₁₁×C₁₇	semidirect
20. C₅×C₁₇	C₂×C₁₁×C₁₉	semidirect
21. C₅×C₁₁	C₂×C₁₇×C₁₉	semidirect
25. C₁₉	D₅×C₁₁×C₁₇	direct (N × H)
26. C₁₇	D₅×C₁₁×C₁₉	direct (N × H)
27. C₁₁	D₅×C₁₇×C₁₉	direct (N × H)
28. D₅	C₁₁×C₁₇×C₁₉	direct (N × H)
29. C₅	C₂×C₁₁×C₁₇×C₁₉	semidirect

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
C₂×C₁₁×C₁₇×C₁₉	5
D₅×C₁₇×C₁₉	11
D₅×C₁₁×C₁₉	17
D₅×C₁₁×C₁₇	19

Subgroups — D5×C11×C17×C19 #48001045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×C₁₇×C₁₉ #48001045