Subgroups — C₂×C₃×D₇×C₁₁⋊C₂₅ #37528254

Order 23100.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇×C₁₁⋊C₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇×C₁₁⋊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×C₁₁×D₇	C₅	1	1	yes	maximal, characteristic
6	C₂×C₇×C₁₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
7	D₇×C₁₁⋊C₂₅	C₂×C₃	1	2	yes	direct product factor
8	C₂²×C₃×C₁₁⋊C₂₅	—	7	1	no	maximal, Hall
9	C₃×C₅×C₁₁×D₇	C₂×C₅	1	2	yes	—
10	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic
11	C₂×C₃×D₇×C₂₅	—	11	1	no	maximal, Hall
12	C₇×C₁₁⋊C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₁⋊C₂₅	—	7	2	no	—
14	C₂×C₃×C₁₁⋊C₂₅	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₅×C₁₁×D₇	C₃×C₅	1	1	yes	characteristic
16	C₃×C₅×C₇×C₁₁	C₂²×C₅	1	1	yes	characteristic
17	C₂²×C₁₁⋊C₂₅	—	7	1	no	Hall
18	C₂×C₃×C₇×C₂₅	—	11	1	no	—
19	C₃×D₇×C₂₅	—	11	2	no	—
20	C₂×C₃×C₁₁×D₇	C₂₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁⋊C₂₅	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×C₇×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
23	C₅×C₁₁×D₇	C₂×C₃×C₅	1	2	yes	—
24	C₂×D₇×C₂₅	—	11	1	no	Hall
25	C₂²×C₃×C₅×C₁₁	—	7	1	no	—
26	C₂×C₁₁⋊C₂₅	—	7	2	no	—
27	C₂×C₁₁⋊C₂₅	C₃×D₇	1	1	yes	characteristic, direct product factor
28	C₃×C₇×C₂₅	—	11	1	no	Hall
29	C₂×C₃×C₇×C₁₁	C₂×C₂₅	1	1	yes	characteristic, complemented
30	C₃×C₁₁×D₇	C₂×C₂₅	1	2	yes	complemented
31	C₂×C₃×C₅×D₇	C₁₁⋊C₅	1	1	yes	characteristic
32	C₅×C₇×C₁₁	C₂²×C₃×C₅	1	1	yes	characteristic
33	C₂×C₇×C₂₅	—	11	1	no	—
34	D₇×C₂₅	—	11	2	no	—
35	C₂×C₃×C₅×C₁₁	—	7	2	no	—
36	C₂×C₃×C₅×C₁₁	C₅×D₇	1	1	yes	characteristic
37	C₂×C₁₁×D₇	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₃×C₂₅	—	77	1	no	Hall
39	C₁₁⋊C₂₅	C₂×C₃×D₇	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₇×C₁₁	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₅×C₁₁	—	7	1	no	—
42	C₂×C₃×C₅×C₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic
43	C₃×C₅×D₇	C₂×C₁₁⋊C₅	1	2	yes	—
44	C₇×C₂₅	—	11	1	no	Hall
45	C₃×C₅×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic
46	C₂×C₇×C₁₁	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
47	C₁₁×D₇	C₂×C₃×C₂₅	1	2	yes	complemented
48	C₂×C₃×C₂₅	—	11	1	no	—
49	C₂×C₃×C₂₅	—	77	2	no	—
50	C₂×C₅×D₇	C₃×C₁₁⋊C₅	1	1	yes	characteristic
51	C₂²×C₃×C₁₁	—	7	1	no	Hall
52	C₂×C₅×C₁₁	—	7	2	no	—
53	C₂×C₅×C₁₁	C₃×C₅×D₇	1	1	yes	characteristic
54	C₃×C₅×C₇	C₂²×C₁₁⋊C₅	1	1	yes	characteristic
55	C₂²×C₂₅	—	77	1	no	Hall
56	C₂×C₃×D₇	C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
57	C₇×C₁₁	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
58	C₃×C₂₅	—	11	1	no	Hall
59	C₂×C₅×C₇	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic
60	C₅×D₇	C₂×C₃×C₁₁⋊C₅	1	2	yes	—
61	C₂×C₃×C₁₁	—	7	2	no	—
62	C₂×C₃×C₁₁	D₇×C₂₅	1	1	yes	characteristic, complemented
63	C₂²×C₃×C₅	—	7	1	no	—
64	C₅×C₁₁	C₂×C₃×C₅×D₇	1	1	yes	characteristic
65	C₂×C₂₅	—	11	1	no	—
66	C₂×C₂₅	—	77	2	no	—
67	C₂²×C₁₁	—	7	1	no	Hall
68	C₂×C₃×C₇	C₂×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented
69	C₃×D₇	C₂×C₁₁⋊C₂₅	1	2	yes	direct product factor
70	C₅×C₇	C₂²×C₃×C₁₁⋊C₅	1	1	yes	characteristic
71	C₃×C₁₁	C₂×D₇×C₂₅	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	—	7	2	no	—
73	C₂×C₃×C₅	D₇×C₁₁⋊C₅	1	1	yes	characteristic
74	C₂×D₇	C₃×C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
75	C₂₅	—	11	1	no	Sylow
76	C₂×C₁₁	—	7	2	no	—
77	C₂×C₁₁	C₃×D₇×C₂₅	1	1	yes	characteristic, complemented
78	C₃×C₇	C₂²×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Hall
79	C₂²×C₅	—	7	1	no	—
80	C₃×C₅	C₂×D₇×C₁₁⋊C₅	1	1	yes	characteristic
81	C₂×C₇	C₂×C₃×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented
82	D₇	C₂×C₃×C₁₁⋊C₂₅	1	2	yes	direct product factor
83	C₂²×C₃	—	7	1	no	Hall
84	C₁₁	C₂×C₃×D₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	7	2	no	—
86	C₂×C₅	C₃×D₇×C₁₁⋊C₅	1	1	yes	characteristic
87	C₇	C₂²×C₃×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	7	2	no	—
89	C₂×C₃	D₇×C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor
90	C₅	C₂×C₃×D₇×C₁₁⋊C₅	1	1	yes	characteristic
91	C₂²	—	7	1	no	Sylow
92	C₃	C₂×D₇×C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	—	7	2	no	—
94	C₂	C₃×D₇×C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₇×C₁₁⋊C₅
commutator, hypocenter	C₇×C₁₁	C₂²×C₃×C₂₅
Frattini	C₅	C₂×C₃×D₇×C₁₁⋊C₅
Fitting, socle	C₂×C₃×C₅×C₇×C₁₁	C₂×C₅
prime radical	C₂×C₃×C₅×C₁₁×D₇	C₅
cosocle	C₅×C₇×C₁₁	C₂²×C₃×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×D₇×C₁₁⋊C₂₅	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁⋊C₂₅	C₂	semidirect
3. C₂×D₇×C₁₁⋊C₂₅	C₃	direct (N × H)
4. C₃×C₇×C₁₁⋊C₂₅	C₂²	semidirect
6. C₂×C₇×C₁₁⋊C₂₅	C₂×C₃	semidirect
7. D₇×C₁₁⋊C₂₅	C₂×C₃	direct (N × H)
12. C₇×C₁₁⋊C₂₅	C₂²×C₃	semidirect
14. C₂×C₃×C₁₁⋊C₂₅	D₇	direct (N × H)
20. C₂×C₃×C₁₁×D₇	C₂₅	semidirect
21. C₃×C₁₁⋊C₂₅	C₂×D₇	direct (N × H)
27. C₂×C₁₁⋊C₂₅	C₃×D₇	direct (N × H)
29. C₂×C₃×C₇×C₁₁	C₂×C₂₅	semidirect
30. C₃×C₁₁×D₇	C₂×C₂₅	semidirect
37. C₂×C₁₁×D₇	C₃×C₂₅	semidirect
39. C₁₁⋊C₂₅	C₂×C₃×D₇	direct (N × H)
40. C₃×C₇×C₁₁	C₂²×C₂₅	semidirect
46. C₂×C₇×C₁₁	C₂×C₃×C₂₅	semidirect
47. C₁₁×D₇	C₂×C₃×C₂₅	semidirect
56. C₂×C₃×D₇	C₁₁⋊C₂₅	direct (N × H)
57. C₇×C₁₁	C₂²×C₃×C₂₅	semidirect
62. C₂×C₃×C₁₁	D₇×C₂₅	semidirect
68. C₂×C₃×C₇	C₂×C₁₁⋊C₂₅	semidirect
69. C₃×D₇	C₂×C₁₁⋊C₂₅	direct (N × H)
71. C₃×C₁₁	C₂×D₇×C₂₅	semidirect
74. C₂×D₇	C₃×C₁₁⋊C₂₅	direct (N × H)
77. C₂×C₁₁	C₃×D₇×C₂₅	semidirect
78. C₃×C₇	C₂²×C₁₁⋊C₂₅	semidirect
81. C₂×C₇	C₂×C₃×C₁₁⋊C₂₅	semidirect
82. D₇	C₂×C₃×C₁₁⋊C₂₅	direct (N × H)
84. C₁₁	C₂×C₃×D₇×C₂₅	semidirect
87. C₇	C₂²×C₃×C₁₁⋊C₂₅	semidirect
89. C₂×C₃	D₇×C₁₁⋊C₂₅	direct (N × H)
92. C₃	C₂×D₇×C₁₁⋊C₂₅	direct (N × H)
94. C₂	C₃×D₇×C₁₁⋊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×D₇×C₁₁⋊C₂₅	2
C₂×C₃×C₇×C₁₁⋊C₂₅	2
C₂×D₇×C₁₁⋊C₂₅	3
C₂×C₃×C₅×C₁₁×D₇	5
C₂²×C₃×C₁₁⋊C₂₅	7
C₂×C₃×D₇×C₂₅	11

Subgroups — C2×C3×D7×C11⋊C25 #37528254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₇×C₁₁⋊C₂₅ #37528254