Subgroups — C₅×#19096725 #37587776

Order 24510.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14578576	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#19096725	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#14578576	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₄₃⋊C₃	—	19	1	no	maximal, Hall
8	C₁₉×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₄₃⋊C₃	—	19	1	no	Hall
10	C₂×C₅×C₁₉⋊C₃	—	43	1	no	maximal, Hall
11	C₅×D₄₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₉⋊C₃	—	43	1	no	Hall
13	D₄₃⋊C₃	—	19	1	no	Hall
14	C₅×C₄₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₉	—	43	1	no	Hall
16	C₄₃⋊C₃	—	19	1	no	Hall
17	C₂×C₁₉⋊C₃	—	43	1	no	Hall
18	C₅×C₁₉	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
19	D₄₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₁₉⋊C₃	—	43	1	no	Hall
21	C₄₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₉	—	43	1	no	Hall
23	C₂×C₃×C₅	—	817	1	no	Hall
24	C₁₉	C₅×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	—	817	1	no	Hall
26	C₂×C₅	—	43	1	no	Hall
27	C₂×C₃	—	817	1	no	Hall
28	C₅	#19096725	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	817	1	no	Sylow
30	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#19096725
commutator, cosocle, hypocenter	C₁₉×C₄₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₄₃	C₂×C₃
LCS	G ▷ C₁₉×C₄₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14578576	C₂	semidirect
2. C₅×C₁₉×D₄₃	C₃	semidirect
3. #19096725	C₅	direct (N × H)
4. C₅×C₁₉×C₄₃	C₂×C₃	semidirect
5. #14578576	C₂×C₅	semidirect
6. C₁₉×D₄₃	C₃×C₅	semidirect
8. C₁₉×C₄₃	C₂×C₃×C₅	semidirect
11. C₅×D₄₃	C₁₉⋊C₃	semidirect
14. C₅×C₄₃	C₂×C₁₉⋊C₃	semidirect
18. C₅×C₁₉	D₄₃⋊C₃	semidirect
19. D₄₃	C₅×C₁₉⋊C₃	semidirect
21. C₄₃	C₂×C₅×C₁₉⋊C₃	semidirect
24. C₁₉	C₅×D₄₃⋊C₃	semidirect
28. C₅	#19096725	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#14578576	2
C₅×C₁₉×D₄₃	3
#19096725	5
C₅×D₄₃⋊C₃	19
C₂×C₅×C₁₉⋊C₃	43

Subgroups — C5×#19096725 #37587776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19096725 #37587776