Subgroups — C₃⋊(C₃⋊(C₇⋊D₁₇₅)) #36347783

Order 22050.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₇⋊D₁₇₅)	—	3	4	no	maximal
3	C₃⋊(C₃⋊(C₅⋊(C₇⋊D₇)))	—	5	1	no	maximal
4	C₃×C₇²×C₂₅	D₃	1	4	yes	complemented
5	C₃⋊D₅₂₅	—	7	8	no	maximal
6	C₇⋊D₁₇₅	—	9	1	no	Hall
7	C₃²×C₅×C₇²	D₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	D₇	1	8	yes	complemented
9	C₃⋊(C₅⋊(C₇⋊D₇))	—	15	4	no	—
10	C₇²×C₂₅	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	D₅₂₅	—	21	32	no	—
12	C₃⋊(C₃⋊(C₇⋊D₇))	—	25	1	no	Hall
13	C₃×C₅×C₇²	D₁₅	1	4	yes	—
14	C₃⋊D₁₀₅	—	35	8	no	—
15	C₃×C₇×C₂₅	D₂₁	1	32	yes	complemented
16	C₅⋊(C₇⋊D₇)	—	45	1	no	—
17	C₃⋊D₇₅	—	49	1	no	Hall
18	C₃²×C₇²	D₂₅	1	1	yes	characteristic, complemented, Hall
19	D₁₇₅	—	63	8	no	—
20	C₃²×C₅×C₇	D₃₅	1	8	yes	—
21	C₃⋊(C₇⋊D₇)	—	75	4	no	—
22	C₅×C₇²	C₃⋊D₁₅	1	1	yes	characteristic
23	C₃²×C₂₅	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
24	D₁₀₅	—	105	32	no	—
25	C₇×C₂₅	C₃⋊D₂₁	1	8	yes	complemented
26	D₇₅	—	147	4	no	—
27	C₃×C₇²	D₇₅	1	4	yes	complemented
28	C₃⋊D₂₁	—	175	8	no	—
29	C₃×C₅×C₇	D₁₀₅	1	32	yes	—
30	C₇⋊D₇	—	225	1	no	Hall
31	C₃⋊D₁₅	—	245	1	no	—
32	C₃×C₂₅	C₃⋊(C₇⋊D₇)	1	4	yes	complemented
33	D₃₅	—	315	8	no	—
34	C₃²×C₇	D₁₇₅	1	8	yes	complemented
35	D₂₅	—	441	1	no	Hall
36	C₇²	C₃⋊D₇₅	1	1	yes	characteristic, complemented, Sylow
37	C₃²×C₅	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic
38	D₂₁	—	525	32	no	—
39	C₅×C₇	C₃⋊D₁₀₅	1	8	yes	—
40	D₁₅	—	735	4	no	—
41	C₂₅	C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, complemented, Sylow
42	C₃×C₇	D₅₂₅	1	32	yes	complemented
43	C₃⋊D₃	—	1225	1	no	Hall
44	C₃×C₅	C₃⋊(C₅⋊(C₇⋊D₇))	1	4	yes	—
45	D₇	—	1575	8	no	—
46	D₅	—	2205	1	no	—
47	C₃²	C₇⋊D₁₇₅	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₃⋊D₅₂₅	1	8	yes	complemented
49	D₃	—	3675	4	no	—
50	C₅	C₃⋊(C₃⋊(C₅⋊(C₇⋊D₇)))	1	1	yes	characteristic
51	C₃	C₃⋊(C₇⋊D₁₇₅)	1	4	yes	complemented
52	C₂	—	11025	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₇²×C₂₅	C₂
Frattini	C₅	C₃⋊(C₃⋊(C₅⋊(C₇⋊D₇)))
socle	C₃²×C₅×C₇²	D₅
LCS	G ▷ C₃²×C₇²×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
4. C₃×C₇²×C₂₅	D₃	semidirect
8. C₃²×C₇×C₂₅	D₇	semidirect
10. C₇²×C₂₅	C₃⋊D₃	semidirect
15. C₃×C₇×C₂₅	D₂₁	semidirect
18. C₃²×C₇²	D₂₅	semidirect
23. C₃²×C₂₅	C₇⋊D₇	semidirect
25. C₇×C₂₅	C₃⋊D₂₁	semidirect
27. C₃×C₇²	D₇₅	semidirect
32. C₃×C₂₅	C₃⋊(C₇⋊D₇)	semidirect
34. C₃²×C₇	D₁₇₅	semidirect
36. C₇²	C₃⋊D₇₅	semidirect
41. C₂₅	C₃⋊(C₃⋊(C₇⋊D₇))	semidirect
42. C₃×C₇	D₅₂₅	semidirect
47. C₃²	C₇⋊D₁₇₅	semidirect
48. C₇	C₃⋊D₅₂₅	semidirect
51. C₃	C₃⋊(C₇⋊D₁₇₅)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×C₂₅	2
C₃⋊(C₇⋊D₁₇₅)	3
C₃⋊(C₃⋊(C₅⋊(C₇⋊D₇)))	5
C₃⋊D₅₂₅	7

Subgroups — C3⋊(C3⋊(C7⋊D175)) #36347783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊(C₇⋊D₁₇₅)) #36347783