Subgroups — C₂×C₃×C₇×D₁₁×C₂₅ #37528313

Order 23100.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₂₅	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₃×C₇×C₂₅
Frattini	C₅	C₂×C₃×C₅×C₇×D₁₁
Fitting	C₂×C₃×C₇×C₁₁×C₂₅	C₂
socle	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅
prime radical	C₂×C₃×C₅×C₇×D₁₁	C₅
cosocle	C₅×C₁₁	C₂²×C₃×C₅×C₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₁₁×C₂₅	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁×C₂₅	C₂	semidirect
3. C₂×C₇×D₁₁×C₂₅	C₃	direct (N × H)
4. C₃×C₇×C₁₁×C₂₅	C₂²	semidirect
6. C₇×D₁₁×C₂₅	C₂×C₃	direct (N × H)
7. C₂×C₇×C₁₁×C₂₅	C₂×C₃	semidirect
8. C₂×C₃×D₁₁×C₂₅	C₇	direct (N × H)
12. C₇×C₁₁×C₂₅	C₂²×C₃	semidirect
13. C₂×C₃×C₁₁×C₂₅	C₂×C₇	semidirect
14. C₃×D₁₁×C₂₅	C₂×C₇	direct (N × H)
17. C₂×D₁₁×C₂₅	C₃×C₇	direct (N × H)
19. C₂×C₃×C₇×C₂₅	D₁₁	direct (N × H)
20. C₂×C₃×C₇×D₁₁	C₂₅	direct (N × H)
21. C₃×C₁₁×C₂₅	C₂²×C₇	semidirect
26. C₂×C₁₁×C₂₅	C₂×C₃×C₇	semidirect
27. D₁₁×C₂₅	C₂×C₃×C₇	direct (N × H)
28. C₃×C₇×C₂₅	C₂×D₁₁	direct (N × H)
29. C₂×C₃×C₇×C₁₁	C₂×C₂₅	semidirect
30. C₃×C₇×D₁₁	C₂×C₂₅	direct (N × H)
34. C₂×C₇×C₂₅	C₃×D₁₁	direct (N × H)
37. C₂×C₇×D₁₁	C₃×C₂₅	direct (N × H)
39. C₁₁×C₂₅	C₂²×C₃×C₇	semidirect
40. C₃×C₇×C₁₁	C₂²×C₂₅	semidirect
44. C₇×C₂₅	C₂×C₃×D₁₁	direct (N × H)
46. C₂×C₇×C₁₁	C₂×C₃×C₂₅	semidirect
47. C₇×D₁₁	C₂×C₃×C₂₅	direct (N × H)
49. C₂×C₃×C₂₅	C₇×D₁₁	direct (N × H)
51. C₂×C₃×D₁₁	C₇×C₂₅	direct (N × H)
57. C₇×C₁₁	C₂²×C₃×C₂₅	semidirect
58. C₃×C₂₅	C₂×C₇×D₁₁	direct (N × H)
61. C₂×C₃×C₁₁	C₂×C₇×C₂₅	semidirect
62. C₃×D₁₁	C₂×C₇×C₂₅	direct (N × H)
66. C₂×C₂₅	C₃×C₇×D₁₁	direct (N × H)
67. C₂×D₁₁	C₃×C₇×C₂₅	direct (N × H)
69. C₂×C₃×C₇	D₁₁×C₂₅	direct (N × H)
71. C₃×C₁₁	C₂²×C₇×C₂₅	semidirect
75. C₂₅	C₂×C₃×C₇×D₁₁	direct (N × H)
76. C₂×C₁₁	C₂×C₃×C₇×C₂₅	semidirect
77. D₁₁	C₂×C₃×C₇×C₂₅	direct (N × H)
78. C₃×C₇	C₂×D₁₁×C₂₅	direct (N × H)
82. C₂×C₇	C₃×D₁₁×C₂₅	direct (N × H)
84. C₁₁	C₂²×C₃×C₇×C₂₅	semidirect
87. C₇	C₂×C₃×D₁₁×C₂₅	direct (N × H)
89. C₂×C₃	C₇×D₁₁×C₂₅	direct (N × H)
92. C₃	C₂×C₇×D₁₁×C₂₅	direct (N × H)
94. C₂	C₃×C₇×D₁₁×C₂₅	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×D₁₁×C₂₅	2
C₂×C₃×C₇×C₁₁×C₂₅	2
C₂×C₇×D₁₁×C₂₅	3
C₂×C₃×C₅×C₇×D₁₁	5
C₂×C₃×D₁₁×C₂₅	7
C₂²×C₃×C₇×C₂₅	11

Subgroups — C2×C3×C7×D11×C25 #37528313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×D₁₁×C₂₅ #37528313