Subgroups — C₃×D₁₅×C₅₃ #18012016

Order 4770.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅×C₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₅×C₅₃	—	3	1	no	maximal
4	C₃×D₃×C₅₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₅₃	—	2	1	no	—
6	C₃×C₅×C₅₃	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₅₃	—	3	1	no	Hall
9	C₃²×C₅₃	D₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅₃	—	15	1	no	—
11	D₃×C₅₃	—	5	1	no	—
12	C₅×C₅₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅₃	—	2	1	no	—
14	C₃×C₅₃	C₃×D₅	1	1	yes	characteristic, complemented
15	C₃×C₅₃	D₁₅	1	1	yes	characteristic, direct product factor
16	C₂×C₅₃	—	15	1	no	Hall
17	C₃×D₁₅	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₅₃	C₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²×C₅	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
20	D₁₅	C₃×C₅₃	1	1	yes	characteristic, direct product factor
21	C₃×D₅	—	3	1	no	—
22	C₃×D₃	—	5	1	no	Hall
23	C₃×C₅	—	2	1	no	—
24	C₃×C₅	D₃×C₅₃	1	1	yes	characteristic, complemented
25	C₃×C₅	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented
26	D₅	—	3	1	no	Hall
27	C₃²	D₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	15	1	no	—
29	D₃	—	5	1	no	—
30	C₅	C₃×D₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
31	C₃	—	2	1	no	—
32	C₃	C₃×D₅×C₅₃	1	1	yes	characteristic, complemented
33	C₃	D₁₅×C₅₃	1	1	yes	characteristic, direct product factor
34	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₅₃	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₅₃	C₂	semidirect
2. D₁₅×C₅₃	C₃	direct (N × H)
6. C₃×C₅×C₅₃	D₃	semidirect
7. C₃×C₅×C₅₃	C₂×C₃	semidirect
9. C₃²×C₅₃	D₅	semidirect
12. C₅×C₅₃	C₃×D₃	semidirect
14. C₃×C₅₃	C₃×D₅	semidirect
15. C₃×C₅₃	D₁₅	direct (N × H)
17. C₃×D₁₅	C₅₃	direct (N × H)
18. C₅₃	C₃×D₁₅	direct (N × H)
19. C₃²×C₅	C₂×C₅₃	semidirect
20. D₁₅	C₃×C₅₃	direct (N × H)
24. C₃×C₅	D₃×C₅₃	semidirect
25. C₃×C₅	C₂×C₃×C₅₃	semidirect
27. C₃²	D₅×C₅₃	semidirect
30. C₅	C₃×D₃×C₅₃	semidirect
32. C₃	C₃×D₅×C₅₃	semidirect
33. C₃	D₁₅×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₅₃	2
D₁₅×C₅₃	3
C₃×D₅×C₅₃	3
C₃×D₃×C₅₃	5
C₃×D₁₅	53

Subgroups — C3×D15×C53 #18012016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₅×C₅₃ #18012016