Subgroups — D₅×C₁₃⋊C₃×C₆₁ #37558201

Order 23790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₃⋊C₃×C₆₁	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊C₃×C₆₁	D₅	1	1	yes	characteristic, direct product factor, Hall
6	C₃×D₅×C₆₁	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₆₁	—	5	1	no	Hall
8	C₃×C₅×C₆₁	—	13	1	no	Hall
9	C₁₃×C₆₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×C₆₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	D₅×C₁₃⋊C₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₆₁	—	65	1	no	Hall
13	C₅×C₆₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₃⋊C₃	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	—	13	1	no	Hall
16	D₅×C₁₃	C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₆₁	—	5	1	no	Hall
18	C₂×C₁₃⋊C₃	—	5	1	no	Hall
19	C₅×C₁₃	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
20	C₆₁	D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₁₃⋊C₃	D₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃×D₅	—	13	1	no	Hall
23	C₂×C₁₃	—	5	1	no	Hall
24	C₃×C₅	—	13	1	no	Hall
25	C₁₃	C₃×D₅×C₆₁	1	1	yes	characteristic, complemented, Sylow
26	D₅	C₁₃⋊C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	65	1	no	Hall
28	C₅	C₂×C₁₃⋊C₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	13	1	no	Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₁	D₅×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₆₁	C₂×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₆₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃⋊C₃×C₆₁	C₂	semidirect
2. D₅×C₁₃×C₆₁	C₃	semidirect
4. C₅×C₁₃×C₆₁	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₆₁	D₅	direct (N × H)
9. C₁₃×C₆₁	C₃×D₅	semidirect
10. D₅×C₆₁	C₁₃⋊C₃	direct (N × H)
11. D₅×C₁₃⋊C₃	C₆₁	direct (N × H)
13. C₅×C₆₁	C₂×C₁₃⋊C₃	semidirect
14. C₅×C₁₃⋊C₃	C₂×C₆₁	semidirect
16. D₅×C₁₃	C₃×C₆₁	semidirect
19. C₅×C₁₃	C₂×C₃×C₆₁	semidirect
20. C₆₁	D₅×C₁₃⋊C₃	direct (N × H)
21. C₁₃⋊C₃	D₅×C₆₁	direct (N × H)
25. C₁₃	C₃×D₅×C₆₁	semidirect
26. D₅	C₁₃⋊C₃×C₆₁	direct (N × H)
28. C₅	C₂×C₁₃⋊C₃×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃⋊C₃×C₆₁	2
D₅×C₁₃×C₆₁	3
C₂×C₁₃⋊C₃×C₆₁	5
C₃×D₅×C₆₁	13
D₅×C₁₃⋊C₃	61

Subgroups — D5×C13⋊C3×C61 #37558201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₃⋊C₃×C₆₁ #37558201