Subgroups — C₃²×C₇⋊D₁₇₅ #36347771

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	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅⋊(C₇⋊D₇)	—	5	1	no	maximal
4	C₃×C₇²×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₃²×D₁₇₅	—	7	8	no	maximal
6	C₇⋊D₁₇₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇²	D₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	D₇	1	8	yes	complemented
9	C₃×C₅⋊(C₇⋊D₇)	—	5	4	no	—
10	C₇²×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₇₅	—	7	32	no	—
12	C₃²×C₇⋊D₇	—	25	1	no	Hall
13	C₃×C₅×C₇²	C₃×D₅	1	4	yes	—
14	C₃²×D₃₅	—	35	8	no	—
15	C₃×C₇×C₂₅	C₃×D₇	1	32	yes	complemented
16	C₅⋊(C₇⋊D₇)	—	5	1	no	—
17	C₃²×D₂₅	—	49	1	no	Hall
18	C₃²×C₇²	D₂₅	1	1	yes	characteristic, complemented, Hall
19	D₁₇₅	—	7	8	no	—
20	C₃²×C₅×C₇	D₃₅	1	8	yes	—
21	C₃×C₇⋊D₇	—	25	4	no	—
22	C₅×C₇²	C₃²×D₅	1	1	yes	characteristic
23	C₃²×C₂₅	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
24	C₃×D₃₅	—	35	32	no	—
25	C₇×C₂₅	C₃²×D₇	1	8	yes	complemented
26	C₃×D₂₅	—	49	4	no	—
27	C₃×C₇²	C₃×D₂₅	1	4	yes	complemented
28	C₃²×D₇	—	175	8	no	—
29	C₃×C₅×C₇	C₃×D₃₅	1	32	yes	—
30	C₇⋊D₇	—	25	1	no	Hall
31	C₃²×D₅	—	245	1	no	—
32	C₃×C₂₅	C₃×C₇⋊D₇	1	4	yes	complemented
33	D₃₅	—	35	8	no	—
34	C₃²×C₇	D₁₇₅	1	8	yes	complemented
35	D₂₅	—	49	1	no	Hall
36	C₇²	C₃²×D₂₅	1	1	yes	characteristic, complemented, Sylow
37	C₃²×C₅	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic
38	C₃×D₇	—	175	32	no	—
39	C₅×C₇	C₃²×D₃₅	1	8	yes	—
40	C₃×D₅	—	245	4	no	—
41	C₂₅	C₃²×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
42	C₃×C₇	C₃×D₁₇₅	1	32	yes	complemented
43	C₂×C₃²	—	1225	1	no	Hall
44	C₃×C₅	C₃×C₅⋊(C₇⋊D₇)	1	4	yes	—
45	D₇	—	175	8	no	—
46	D₅	—	245	1	no	—
47	C₃²	C₇⋊D₁₇₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₃²×D₁₇₅	1	8	yes	complemented
49	C₂×C₃	—	1225	4	no	—
50	C₅	C₃²×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic
51	C₃	C₃×C₇⋊D₁₇₅	1	4	yes	direct product factor
52	C₂	—	1225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₇⋊D₁₇₅
commutator, cosocle, hypocenter	C₇²×C₂₅	C₂×C₃²
Frattini	C₅	C₃²×C₅⋊(C₇⋊D₇)
Fitting	C₃²×C₇²×C₂₅	C₂
socle	C₃²×C₅×C₇²	D₅
LCS	G ▷ C₇²×C₂₅
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
2. C₃×C₇⋊D₁₇₅	C₃	direct (N × H)
4. C₃×C₇²×C₂₅	C₂×C₃	semidirect
6. C₇⋊D₁₇₅	C₃²	direct (N × H)
8. C₃²×C₇×C₂₅	D₇	semidirect
10. C₇²×C₂₅	C₂×C₃²	semidirect
15. C₃×C₇×C₂₅	C₃×D₇	semidirect
18. C₃²×C₇²	D₂₅	semidirect
23. C₃²×C₂₅	C₇⋊D₇	semidirect
25. C₇×C₂₅	C₃²×D₇	semidirect
27. C₃×C₇²	C₃×D₂₅	semidirect
32. C₃×C₂₅	C₃×C₇⋊D₇	semidirect
34. C₃²×C₇	D₁₇₅	semidirect
36. C₇²	C₃²×D₂₅	semidirect
41. C₂₅	C₃²×C₇⋊D₇	semidirect
42. C₃×C₇	C₃×D₁₇₅	semidirect
47. C₃²	C₇⋊D₁₇₅	direct (N × H)
48. C₇	C₃²×D₁₇₅	semidirect
51. C₃	C₃×C₇⋊D₁₇₅	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×C₇²×C₂₅	2
C₃×C₇⋊D₁₇₅	3
C₃²×C₅⋊(C₇⋊D₇)	5
C₃²×D₁₇₅	7

Subgroups — C32×C7⋊D175 #36347771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇⋊D₁₇₅ #36347771