Subgroups — C₂×C₃×C₇×D₂₇₅ #37528317

Order 23100.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₂₇₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₂₇₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₁×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×D₅₅	—	5	1	no	maximal
6	C₇×D₂₇₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₇×C₁₁×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×D₂₇₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇×D₅₅	—	5	2	no	—
10	C₂×C₃×C₅×C₇×C₁₁	D₅	1	1	yes	characteristic
11	C₂×C₃×C₇×D₂₅	—	11	1	no	maximal, Hall
12	C₇×C₁₁×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₁×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×D₂₇₅	C₂×C₇	1	2	yes	direct product factor
15	C₂×C₇×D₅₅	—	5	1	no	—
16	C₃×C₅×C₇×C₁₁	C₂×D₅	1	1	yes	characteristic
17	C₂×D₂₇₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇×C₂₅	D₁₁	1	1	yes	characteristic, complemented
19	C₃×C₇×D₂₅	—	11	2	no	—
20	C₂×C₃×C₇×D₁₁	—	25	1	no	Hall
21	C₃×C₁₁×C₂₅	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₇×C₁₁	C₃×D₅	1	1	yes	characteristic
23	C₇×D₅₅	—	5	2	no	—
24	C₂×C₇×D₂₅	—	11	1	no	Hall
25	C₂×C₃×D₅₅	—	5	1	no	—
26	C₂×C₁₁×C₂₅	C₂×C₃×C₇	1	1	yes	characteristic, complemented
27	D₂₇₅	C₂×C₃×C₇	1	2	yes	direct product factor
28	C₃×C₇×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇×C₁₁	D₂₅	1	1	yes	characteristic, complemented
30	C₃×C₇×D₁₁	—	25	2	no	—
31	C₂×C₃×C₇×D₅	—	55	1	no	—
32	C₅×C₇×C₁₁	C₂×C₃×D₅	1	1	yes	characteristic
33	C₂×C₇×C₂₅	C₃×D₁₁	1	1	yes	characteristic, complemented
34	C₇×D₂₅	—	11	2	no	—
35	C₂×C₃×C₅×C₁₁	C₇×D₅	1	1	yes	characteristic
36	C₃×D₅₅	—	5	2	no	—
37	C₂×C₇×D₁₁	—	25	1	no	Hall
38	C₂×C₃×D₂₅	—	11	1	no	Hall
39	C₁₁×C₂₅	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
40	C₃×C₇×C₁₁	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
41	C₂×D₅₅	—	5	1	no	—
42	C₂×C₃×C₅×C₇	D₅₅	1	1	yes	characteristic
43	C₃×C₇×D₅	—	55	2	no	—
44	C₇×C₂₅	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
45	C₃×C₅×C₁₁	C₂×C₇×D₅	1	1	yes	characteristic
46	C₂×C₇×C₁₁	C₃×D₂₅	1	1	yes	characteristic, complemented
47	C₇×D₁₁	—	25	2	no	—
48	C₂×C₃×C₂₅	C₇×D₁₁	1	1	yes	characteristic, complemented
49	C₃×D₂₅	—	11	2	no	—
50	C₂×C₇×D₅	—	55	1	no	—
51	C₂×C₃×D₁₁	—	25	1	no	Hall
52	C₂×C₅×C₁₁	C₃×C₇×D₅	1	1	yes	characteristic
53	D₅₅	—	5	2	no	—
54	C₃×C₅×C₇	C₂×D₅₅	1	1	yes	characteristic
55	C₂×D₂₅	—	11	1	no	Hall
56	C₂²×C₃×C₇	—	275	1	no	Hall
57	C₇×C₁₁	C₂×C₃×D₂₅	1	1	yes	characteristic, complemented, Hall
58	C₃×C₂₅	C₂×C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
59	C₂×C₅×C₇	C₃×D₅₅	1	1	yes	characteristic
60	C₇×D₅	—	55	2	no	—
61	C₂×C₃×C₁₁	C₇×D₂₅	1	1	yes	characteristic, complemented
62	C₃×D₁₁	—	25	2	no	—
63	C₂×C₃×D₅	—	55	1	no	—
64	C₅×C₁₁	C₂×C₃×C₇×D₅	1	1	yes	characteristic
65	C₂×C₂₅	C₃×C₇×D₁₁	1	1	yes	characteristic, complemented
66	D₂₅	—	11	2	no	—
67	C₂×D₁₁	—	25	1	no	Hall
68	C₂×C₃×C₇	—	275	2	no	—
69	C₂×C₃×C₇	D₂₇₅	1	1	yes	characteristic, direct product factor
70	C₅×C₇	C₂×C₃×D₅₅	1	1	yes	characteristic
71	C₃×C₁₁	C₂×C₇×D₂₅	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	C₇×D₅₅	1	1	yes	characteristic
73	C₃×D₅	—	55	2	no	—
74	C₂²×C₇	—	275	1	no	Hall
75	C₂₅	C₂×C₃×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₁₁	C₃×C₇×D₂₅	1	1	yes	characteristic, complemented
77	D₁₁	—	25	2	no	—
78	C₃×C₇	C₂×D₂₇₅	1	1	yes	characteristic, direct product factor, Hall
79	C₂×D₅	—	55	1	no	—
80	C₃×C₅	C₂×C₇×D₅₅	1	1	yes	characteristic
81	C₂×C₇	—	275	2	no	—
82	C₂×C₇	C₃×D₂₇₅	1	1	yes	characteristic, direct product factor
83	C₂²×C₃	—	275	1	no	Hall
84	C₁₁	C₂×C₃×C₇×D₂₅	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₃×C₇×D₅₅	1	1	yes	characteristic
86	D₅	—	55	2	no	—
87	C₇	C₂×C₃×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	275	2	no	—
89	C₂×C₃	C₇×D₂₇₅	1	1	yes	characteristic, direct product factor
90	C₅	C₂×C₃×C₇×D₅₅	1	1	yes	characteristic
91	C₂²	—	275	1	no	Sylow
92	C₃	C₂×C₇×D₂₇₅	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	—	275	2	no	—
94	C₂	C₃×C₇×D₂₇₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₂₇₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂²×C₃×C₇
Frattini	C₅	C₂×C₃×C₇×D₅₅
Fitting	C₂×C₃×C₇×C₁₁×C₂₅	C₂
socle	C₂×C₃×C₅×C₇×C₁₁	D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₂₇₅	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁×C₂₅	C₂	semidirect
3. C₂×C₇×D₂₇₅	C₃	direct (N × H)
4. C₃×C₇×C₁₁×C₂₅	C₂²	semidirect
6. C₇×D₂₇₅	C₂×C₃	direct (N × H)
7. C₂×C₇×C₁₁×C₂₅	C₂×C₃	semidirect
8. C₂×C₃×D₂₇₅	C₇	direct (N × H)
12. C₇×C₁₁×C₂₅	C₂²×C₃	semidirect
13. C₂×C₃×C₁₁×C₂₅	C₂×C₇	semidirect
14. C₃×D₂₇₅	C₂×C₇	direct (N × H)
17. C₂×D₂₇₅	C₃×C₇	direct (N × H)
18. C₂×C₃×C₇×C₂₅	D₁₁	semidirect
21. C₃×C₁₁×C₂₅	C₂²×C₇	semidirect
26. C₂×C₁₁×C₂₅	C₂×C₃×C₇	semidirect
27. D₂₇₅	C₂×C₃×C₇	direct (N × H)
28. C₃×C₇×C₂₅	C₂×D₁₁	semidirect
29. C₂×C₃×C₇×C₁₁	D₂₅	semidirect
33. C₂×C₇×C₂₅	C₃×D₁₁	semidirect
39. C₁₁×C₂₅	C₂²×C₃×C₇	semidirect
40. C₃×C₇×C₁₁	C₂×D₂₅	semidirect
44. C₇×C₂₅	C₂×C₃×D₁₁	semidirect
46. C₂×C₇×C₁₁	C₃×D₂₅	semidirect
48. C₂×C₃×C₂₅	C₇×D₁₁	semidirect
57. C₇×C₁₁	C₂×C₃×D₂₅	semidirect
58. C₃×C₂₅	C₂×C₇×D₁₁	semidirect
61. C₂×C₃×C₁₁	C₇×D₂₅	semidirect
65. C₂×C₂₅	C₃×C₇×D₁₁	semidirect
69. C₂×C₃×C₇	D₂₇₅	direct (N × H)
71. C₃×C₁₁	C₂×C₇×D₂₅	semidirect
75. C₂₅	C₂×C₃×C₇×D₁₁	semidirect
76. C₂×C₁₁	C₃×C₇×D₂₅	semidirect
78. C₃×C₇	C₂×D₂₇₅	direct (N × H)
82. C₂×C₇	C₃×D₂₇₅	direct (N × H)
84. C₁₁	C₂×C₃×C₇×D₂₅	semidirect
87. C₇	C₂×C₃×D₂₇₅	direct (N × H)
89. C₂×C₃	C₇×D₂₇₅	direct (N × H)
92. C₃	C₂×C₇×D₂₇₅	direct (N × H)
94. C₂	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
C₃×C₇×D₂₇₅	2
C₂×C₃×C₇×C₁₁×C₂₅	2
C₂×C₇×D₂₇₅	3
C₂×C₃×C₇×D₅₅	5
C₂×C₃×D₂₇₅	7
C₂×C₃×C₇×D₂₅	11

Subgroups — C2×C3×C7×D275 #37528317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×D₂₇₅ #37528317