Subgroups — C₁₉×D₆₄₅ #37587771

Order 24510.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₂₁₅	—	3	1	no	maximal, Hall
3	C₁₉×D₁₂₉	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₄₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₄₃	—	15	1	no	Hall
7	D₆₄₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₄₃	D₁₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×D₁₅	—	43	1	no	maximal, Hall
11	D₂₁₅	—	3	1	no	Hall
12	C₃×C₅×C₁₉	D₄₃	1	1	yes	characteristic, complemented, Hall
13	D₁₂₉	—	5	1	no	Hall
14	C₅×C₄₃	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
15	D₅×C₁₉	—	129	1	no	Hall
16	C₃×C₄₃	D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
17	D₃×C₁₉	—	215	1	no	Hall
18	C₅×C₁₉	D₁₂₉	1	1	yes	characteristic, complemented, Hall
19	D₄₃	—	15	1	no	Hall
20	C₃×C₁₉	D₂₁₅	1	1	yes	characteristic, complemented, Hall
21	C₄₃	C₁₉×D₁₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₉	—	645	1	no	Hall
23	D₁₅	—	43	1	no	Hall
24	C₁₉	D₆₄₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₁₉×D₄₃	1	1	yes	characteristic, complemented, Hall
26	D₅	—	129	1	no	Hall
27	D₃	—	215	1	no	Hall
28	C₅	C₁₉×D₁₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₉×D₂₁₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	645	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₆₄₅
commutator, cosocle, hypocenter	C₃×C₅×C₄₃	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉×C₄₃	C₂
LCS	G ▷ C₃×C₅×C₄₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₄₃	C₂	semidirect
4. C₅×C₁₉×C₄₃	D₃	semidirect
5. C₃×C₁₉×C₄₃	D₅	semidirect
7. D₆₄₅	C₁₉	direct (N × H)
8. C₁₉×C₄₃	D₁₅	semidirect
9. C₃×C₅×C₄₃	C₂×C₁₉	semidirect
12. C₃×C₅×C₁₉	D₄₃	semidirect
14. C₅×C₄₃	D₃×C₁₉	semidirect
16. C₃×C₄₃	D₅×C₁₉	semidirect
18. C₅×C₁₉	D₁₂₉	semidirect
20. C₃×C₁₉	D₂₁₅	semidirect
21. C₄₃	C₁₉×D₁₅	semidirect
24. C₁₉	D₆₄₅	direct (N × H)
25. C₃×C₅	C₁₉×D₄₃	semidirect
28. C₅	C₁₉×D₁₂₉	semidirect
29. C₃	C₁₉×D₂₁₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉×C₄₃	2
C₁₉×D₂₁₅	3
C₁₉×D₁₂₉	5
D₆₄₅	19
C₁₉×D₁₅	43

Subgroups — C19×D645 #37587771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₆₄₅ #37587771