Subgroups — C₃²×C₇×D₂₇₅ #46831435

Order 34650.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₂₇₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×D₅₅	—	5	1	no	maximal
4	C₃×C₇×C₁₁×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₃²×D₂₇₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₂₇₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇×C₁₁	D₅	1	1	yes	characteristic
8	C₃²×C₇×D₂₅	—	11	1	no	maximal, Hall
9	C₃²×C₁₁×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₅₅	—	5	4	no	—
11	C₇×C₁₁×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₂₇₅	C₃×C₇	1	4	yes	direct product factor
13	C₃²×C₇×C₂₅	D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₇×D₁₁	—	25	1	no	Hall
15	C₃×C₅×C₇×C₁₁	C₃×D₅	1	4	yes	—
16	C₃×C₇×D₂₅	—	11	4	no	—
17	C₃²×D₅₅	—	5	1	no	—
18	C₃×C₁₁×C₂₅	C₂×C₃×C₇	1	4	yes	complemented
19	C₇×D₅₅	—	5	1	no	—
20	C₃²×C₇×C₁₁	D₂₅	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₇×D₅	—	55	1	no	—
22	D₂₇₅	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₇×C₂₅	C₃×D₁₁	1	4	yes	complemented
24	C₃²×C₅×C₁₁	C₇×D₅	1	1	yes	characteristic
25	C₃×C₇×D₁₁	—	25	4	no	—
26	C₃²×D₂₅	—	11	1	no	Hall
27	C₅×C₇×C₁₁	C₃²×D₅	1	1	yes	characteristic
28	C₇×D₂₅	—	11	1	no	Hall
29	C₃×D₅₅	—	5	4	no	—
30	C₃²×C₅×C₇	D₅₅	1	1	yes	characteristic
31	C₁₁×C₂₅	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₃×D₂₅	1	4	yes	complemented
33	C₃²×C₂₅	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₇×D₅	—	55	4	no	—
35	C₃²×D₁₁	—	25	1	no	Hall
36	C₇×C₂₅	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₁	C₃×C₇×D₅	1	4	yes	—
38	C₇×D₁₁	—	25	1	no	Hall
39	C₃×D₂₅	—	11	4	no	—
40	C₂×C₃²×C₇	—	275	1	no	Hall
41	D₅₅	—	5	1	no	—
42	C₃×C₅×C₇	C₃×D₅₅	1	4	yes	—
43	C₃²×C₁₁	C₇×D₂₅	1	1	yes	characteristic, complemented, Hall
44	C₃²×D₅	—	55	1	no	—
45	C₇×C₁₁	C₃²×D₂₅	1	1	yes	characteristic, complemented, Hall
46	C₃×C₂₅	C₃×C₇×D₁₁	1	4	yes	complemented
47	C₇×D₅	—	55	1	no	—
48	C₃×D₁₁	—	25	4	no	—
49	C₃²×C₇	D₂₇₅	1	1	yes	characteristic, direct product factor, Hall
50	C₅×C₁₁	C₃²×C₇×D₅	1	1	yes	characteristic
51	D₂₅	—	11	1	no	Hall
52	C₃²×C₅	C₇×D₅₅	1	1	yes	characteristic
53	C₂×C₃×C₇	—	275	4	no	—
54	C₅×C₇	C₃²×D₅₅	1	1	yes	characteristic
55	C₃×C₁₁	C₃×C₇×D₂₅	1	4	yes	complemented
56	C₃×D₅	—	55	4	no	—
57	C₂₅	C₃²×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
58	D₁₁	—	25	1	no	Hall
59	C₃×C₇	C₃×D₂₇₅	1	4	yes	direct product factor
60	C₂×C₃²	—	275	1	no	Hall
61	C₃×C₅	C₃×C₇×D₅₅	1	4	yes	—
62	C₂×C₇	—	275	1	no	Hall
63	C₁₁	C₃²×C₇×D₂₅	1	1	yes	characteristic, complemented, Sylow
64	D₅	—	55	1	no	—
65	C₃²	C₇×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₇	C₃²×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₃	—	275	4	no	—
68	C₅	C₃²×C₇×D₅₅	1	1	yes	characteristic
69	C₃	C₃×C₇×D₂₇₅	1	4	yes	direct product factor
70	C₂	—	275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₂₇₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂×C₃²×C₇
Frattini	C₅	C₃²×C₇×D₅₅
Fitting	C₃²×C₇×C₁₁×C₂₅	C₂
socle	C₃²×C₅×C₇×C₁₁	D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₂₅	C₂	semidirect
2. C₃×C₇×D₂₇₅	C₃	direct (N × H)
4. C₃×C₇×C₁₁×C₂₅	C₂×C₃	semidirect
5. C₃²×D₂₇₅	C₇	direct (N × H)
6. C₇×D₂₇₅	C₃²	direct (N × H)
9. C₃²×C₁₁×C₂₅	C₂×C₇	semidirect
11. C₇×C₁₁×C₂₅	C₂×C₃²	semidirect
12. C₃×D₂₇₅	C₃×C₇	direct (N × H)
13. C₃²×C₇×C₂₅	D₁₁	semidirect
18. C₃×C₁₁×C₂₅	C₂×C₃×C₇	semidirect
20. C₃²×C₇×C₁₁	D₂₅	semidirect
22. D₂₇₅	C₃²×C₇	direct (N × H)
23. C₃×C₇×C₂₅	C₃×D₁₁	semidirect
31. C₁₁×C₂₅	C₂×C₃²×C₇	semidirect
32. C₃×C₇×C₁₁	C₃×D₂₅	semidirect
33. C₃²×C₂₅	C₇×D₁₁	semidirect
36. C₇×C₂₅	C₃²×D₁₁	semidirect
43. C₃²×C₁₁	C₇×D₂₅	semidirect
45. C₇×C₁₁	C₃²×D₂₅	semidirect
46. C₃×C₂₅	C₃×C₇×D₁₁	semidirect
49. C₃²×C₇	D₂₇₅	direct (N × H)
55. C₃×C₁₁	C₃×C₇×D₂₅	semidirect
57. C₂₅	C₃²×C₇×D₁₁	semidirect
59. C₃×C₇	C₃×D₂₇₅	direct (N × H)
63. C₁₁	C₃²×C₇×D₂₅	semidirect
65. C₃²	C₇×D₂₇₅	direct (N × H)
66. C₇	C₃²×D₂₇₅	direct (N × H)
69. C₃	C₃×C₇×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
C₃²×C₇×C₁₁×C₂₅	2
C₃×C₇×D₂₇₅	3
C₃²×C₇×D₅₅	5
C₃²×D₂₇₅	7
C₃²×C₇×D₂₅	11

Subgroups — C32×C7×D275 #46831435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₂₇₅ #46831435