Subgroups — C₃⋊(C₅₃⋊((C₅⋊D₅)⋊C₃)) #37558721

Order 23850.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₂₆₅)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅₃⋊((C₅⋊D₅)⋊C₃)	—	3	1	no	maximal
4	C₅₃×C₅²⋊C₃	—	2	1	no	—
5	C₅₃×C₅²⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₅²×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊D₂₆₅	—	3	1	no	Hall
8	D₇₉₅	—	15	2	no	—
9	C₅²×C₅₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₅₉	—	25	1	no	maximal, Hall
11	C₃×C₅×C₅₃	—	3	2	no	—
12	D₂₆₅	—	45	2	no	—
13	C₃²×C₅₃	—	50	1	no	Hall
14	C₃⋊((C₅⋊D₅)⋊C₃)	—	53	1	no	maximal, Hall
15	D₁₅₉	—	25	1	no	—
16	C₃×D₅₃	—	75	1	no	—
17	C₅×C₅₃	—	3	2	no	—
18	C₃×C₅²⋊C₃	D₅₃	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅₃	—	50	1	no	—
20	C₃×C₅₃	—	50	1	no	—
21	C₃×C₅₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
22	C₃⋊(C₅⋊D₅)	—	53	1	no	—
23	(C₅⋊D₅)⋊C₃	—	159	1	no	—
24	D₅₃	—	75	1	no	Hall
25	C₃×C₅²	C₃×D₅₃	1	1	yes	characteristic, complemented
26	C₅²⋊C₃	—	2	1	no	—
27	C₅²⋊C₃	D₁₅₉	1	1	yes	characteristic, complemented
28	C₅₃	C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, complemented, Sylow
29	C₅⋊D₅	—	159	1	no	Hall
30	D₁₅	—	795	2	no	—
31	C₅²	C₃×D₁₅₉	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₃	—	1325	1	no	Hall
33	C₃×C₅	—	3	2	no	—
34	D₅	—	2385	2	no	—
35	C₃²	—	50	1	no	Sylow
36	C₂×C₃	—	3975	1	no	—
37	D₃	—	1325	1	no	—
38	C₅	—	3	2	no	—
39	C₃	—	50	1	no	—
40	C₃	—	50	1	no	—
41	C₃	C₅₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, complemented
42	C₂	—	3975	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₅₃	C₂×C₃
LCS	G ▷ C₃×C₅²×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₃×C₅²⋊C₃	C₂	semidirect
2. C₃⋊(C₅⋊D₂₆₅)	C₃	semidirect
5. C₅₃×C₅²⋊C₃	D₃	semidirect
6. C₃×C₅²×C₅₃	C₂×C₃	semidirect
9. C₅²×C₅₃	C₃×D₃	semidirect
18. C₃×C₅²⋊C₃	D₅₃	semidirect
21. C₃×C₅₃	(C₅⋊D₅)⋊C₃	semidirect
25. C₃×C₅²	C₃×D₅₃	semidirect
27. C₅²⋊C₃	D₁₅₉	semidirect
28. C₅₃	C₃⋊((C₅⋊D₅)⋊C₃)	semidirect
31. C₅²	C₃×D₁₅₉	semidirect
41. C₃	C₅₃⋊((C₅⋊D₅)⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅₃×C₅²⋊C₃	2
C₃⋊(C₅⋊D₂₆₅)	3
C₅₃⋊((C₅⋊D₅)⋊C₃)	3
C₃×D₁₅₉	25
C₃⋊((C₅⋊D₅)⋊C₃)	53

Subgroups — C3⋊(C53⋊((C5⋊D5)⋊C3)) #37558721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅₃⋊((C₅⋊D₅)⋊C₃)) #37558721