Subgroups — C₇×C₉×D₂₇₅ #46831366

Order 34650.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₇₅	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×D₅₅	—	5	1	no	maximal
4	C₃×C₇×C₁₁×C₂₅	C₂×C₃	1	1	yes	characteristic
5	C₉×D₂₇₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₂₇₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₇×C₉×C₁₁	D₅	1	1	yes	characteristic
8	C₇×C₉×D₂₅	—	11	1	no	maximal, Hall
9	C₉×C₁₁×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₅₅	—	5	1	no	—
11	C₇×C₁₁×C₂₅	C₂×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×D₂₇₅	C₃×C₇	1	1	yes	characteristic
13	C₇×C₉×C₂₅	D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₇×C₉×D₁₁	—	25	1	no	Hall
15	C₃×C₅×C₇×C₁₁	C₃×D₅	1	1	yes	characteristic
16	C₃×C₇×D₂₅	—	11	1	no	—
17	C₉×D₅₅	—	5	1	no	—
18	C₃×C₁₁×C₂₅	C₂×C₃×C₇	1	1	yes	characteristic
19	C₇×D₅₅	—	5	1	no	—
20	C₇×C₉×C₁₁	D₂₅	1	1	yes	characteristic, complemented, Hall
21	C₇×C₉×D₅	—	55	1	no	—
22	D₂₇₅	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₇×C₂₅	C₃×D₁₁	1	1	yes	characteristic
24	C₅×C₉×C₁₁	C₇×D₅	1	1	yes	characteristic
25	C₃×C₇×D₁₁	—	25	1	no	—
26	C₉×D₂₅	—	11	1	no	Hall
27	C₅×C₇×C₁₁	C₉×D₅	1	1	yes	characteristic
28	C₇×D₂₅	—	11	1	no	Hall
29	C₃×D₅₅	—	5	1	no	—
30	C₅×C₇×C₉	D₅₅	1	1	yes	characteristic
31	C₁₁×C₂₅	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₃×D₂₅	1	1	yes	characteristic
33	C₉×C₂₅	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₇×D₅	—	55	1	no	—
35	C₉×D₁₁	—	25	1	no	Hall
36	C₇×C₂₅	C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₁	C₃×C₇×D₅	1	1	yes	characteristic
38	C₇×D₁₁	—	25	1	no	Hall
39	C₃×D₂₅	—	11	1	no	—
40	C₂×C₇×C₉	—	275	1	no	Hall
41	D₅₅	—	5	1	no	—
42	C₃×C₅×C₇	C₃×D₅₅	1	1	yes	characteristic
43	C₉×C₁₁	C₇×D₂₅	1	1	yes	characteristic, complemented, Hall
44	C₉×D₅	—	55	1	no	—
45	C₇×C₁₁	C₉×D₂₅	1	1	yes	characteristic, complemented, Hall
46	C₃×C₂₅	C₃×C₇×D₁₁	1	1	yes	characteristic
47	C₇×D₅	—	55	1	no	—
48	C₃×D₁₁	—	25	1	no	—
49	C₇×C₉	D₂₇₅	1	1	yes	characteristic, direct product factor, Hall
50	C₅×C₁₁	C₇×C₉×D₅	1	1	yes	characteristic
51	D₂₅	—	11	1	no	Hall
52	C₅×C₉	C₇×D₅₅	1	1	yes	characteristic
53	C₂×C₃×C₇	—	275	1	no	—
54	C₅×C₇	C₉×D₅₅	1	1	yes	characteristic
55	C₃×C₁₁	C₃×C₇×D₂₅	1	1	yes	characteristic
56	C₃×D₅	—	55	1	no	—
57	C₂₅	C₇×C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
58	D₁₁	—	25	1	no	Hall
59	C₃×C₇	C₃×D₂₇₅	1	1	yes	characteristic
60	C₂×C₉	—	275	1	no	Hall
61	C₃×C₅	C₃×C₇×D₅₅	1	1	yes	characteristic
62	C₂×C₇	—	275	1	no	Hall
63	C₁₁	C₇×C₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
64	D₅	—	55	1	no	—
65	C₉	C₇×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₇	C₉×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₃	—	275	1	no	—
68	C₅	C₇×C₉×D₅₅	1	1	yes	characteristic
69	C₃	C₃×C₇×D₂₇₅	1	1	yes	characteristic
70	C₂	—	275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₉	D₂₇₅
commutator, hypocenter	C₁₁×C₂₅	C₂×C₇×C₉
Frattini	C₃×C₅	C₃×C₇×D₅₅
Fitting	C₇×C₉×C₁₁×C₂₅	C₂
socle	C₃×C₅×C₇×C₁₁	C₃×D₅
prime radical	C₃×C₇×D₂₇₅	C₃
cosocle	C₃×C₁₁×C₂₅	C₂×C₃×C₇
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₇×C₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₁×C₂₅	C₂	semidirect
5. C₉×D₂₇₅	C₇	direct (N × H)
6. C₇×D₂₇₅	C₉	direct (N × H)
9. C₉×C₁₁×C₂₅	C₂×C₇	semidirect
11. C₇×C₁₁×C₂₅	C₂×C₉	semidirect
13. C₇×C₉×C₂₅	D₁₁	semidirect
20. C₇×C₉×C₁₁	D₂₅	semidirect
22. D₂₇₅	C₇×C₉	direct (N × H)
31. C₁₁×C₂₅	C₂×C₇×C₉	semidirect
33. C₉×C₂₅	C₇×D₁₁	semidirect
36. C₇×C₂₅	C₉×D₁₁	semidirect
43. C₉×C₁₁	C₇×D₂₅	semidirect
45. C₇×C₁₁	C₉×D₂₅	semidirect
49. C₇×C₉	D₂₇₅	direct (N × H)
57. C₂₅	C₇×C₉×D₁₁	semidirect
63. C₁₁	C₇×C₉×D₂₅	semidirect
65. C₉	C₇×D₂₇₅	direct (N × H)
66. C₇	C₉×D₂₇₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₁₁×C₂₅	2
C₃×C₇×D₂₇₅	3
C₇×C₉×D₅₅	5
C₉×D₂₇₅	7
C₇×C₉×D₂₅	11

Subgroups — C7×C9×D275 #46831366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×D₂₇₅ #46831366