Subgroups — C₃²×C₇×D₇×C₂₅ #36347767

Order 22050.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₇×C₂₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₇×D₇	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇²×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₃²×D₇×C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₇×C₂₅	—	7	1	no	maximal
7	C₇×D₇×C₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
9	C₃²×C₇×C₂₅	—	2	3	no	—
10	C₃²×C₇×C₂₅	D₇	1	1	yes	characteristic, direct product factor
11	C₃²×C₇×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×D₇	C₃×C₅	1	4	yes	—
13	C₇²×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₇×C₂₅	—	7	4	no	—
15	C₃×D₇×C₂₅	C₃×C₇	1	4	yes	direct product factor
16	C₃²×C₇×D₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅×C₇²	C₂×C₃×C₅	1	4	yes	—
18	C₂×C₃²×C₅×C₇	—	7	1	no	—
19	C₃²×C₅×D₇	C₅×C₇	1	1	yes	characteristic
20	C₃×C₇×C₂₅	—	2	12	no	—
21	C₃×C₇×C₂₅	C₃×D₇	1	4	yes	direct product factor
22	C₃×C₇×C₂₅	C₂×C₃×C₇	1	4	yes	complemented
23	C₅×C₇×D₇	C₃²×C₅	1	1	yes	characteristic
24	C₂×C₃²×C₂₅	—	7	1	no	Hall
25	C₃²×C₇²	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×C₂₅	—	7	1	no	—
27	D₇×C₂₅	C₃²×C₇	1	1	yes	characteristic, direct product factor
28	C₃²×C₅×C₇	—	2	3	no	—
29	C₃²×C₅×C₇	C₅×D₇	1	1	yes	characteristic
30	C₃²×C₅×C₇	C₂×C₅×C₇	1	1	yes	characteristic
31	C₃×C₇×D₇	C₃×C₂₅	1	4	yes	direct product factor
32	C₅×C₇²	C₂×C₃²×C₅	1	1	yes	characteristic
33	C₃²×C₂₅	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅×C₇	—	7	4	no	—
35	C₃×C₅×D₇	C₃×C₅×C₇	1	4	yes	—
36	C₇×C₂₅	—	2	3	no	—
37	C₇×C₂₅	C₃²×D₇	1	1	yes	characteristic, direct product factor
38	C₇×C₂₅	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
39	C₂×C₃×C₂₅	—	7	4	no	—
40	C₃×C₇²	C₂×C₃×C₂₅	1	4	yes	complemented
41	C₂×C₃²×C₇	—	7	1	no	—
42	C₃²×D₇	C₇×C₂₅	1	1	yes	characteristic, direct product factor
43	C₃×C₅×C₇	—	2	12	no	—
44	C₃×C₅×C₇	C₃×C₅×D₇	1	4	yes	—
45	C₃×C₅×C₇	C₂×C₃×C₅×C₇	1	4	yes	—
46	C₇×D₇	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
47	C₂×C₃²×C₅	—	7	1	no	—
48	C₃×C₂₅	C₃×C₇×D₇	1	4	yes	direct product factor
49	C₂×C₅×C₇	—	7	1	no	—
50	C₅×D₇	C₃²×C₅×C₇	1	1	yes	characteristic
51	C₃²×C₇	—	2	3	no	—
52	C₃²×C₇	D₇×C₂₅	1	1	yes	characteristic, direct product factor
53	C₃²×C₇	C₂×C₇×C₂₅	1	1	yes	characteristic, complemented
54	C₂×C₂₅	—	7	1	no	Hall
55	C₇²	C₂×C₃²×C₂₅	1	1	yes	characteristic, complemented, Sylow
56	C₃²×C₅	C₅×C₇×D₇	1	1	yes	characteristic
57	C₂×C₃×C₇	—	7	4	no	—
58	C₃×D₇	C₃×C₇×C₂₅	1	4	yes	direct product factor
59	C₅×C₇	—	2	3	no	—
60	C₅×C₇	C₃²×C₅×D₇	1	1	yes	characteristic
61	C₅×C₇	C₂×C₃²×C₅×C₇	1	1	yes	characteristic
62	C₂×C₃×C₅	—	7	4	no	—
63	C₂₅	C₃²×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×C₇	—	2	12	no	—
65	C₃×C₇	C₃×D₇×C₂₅	1	4	yes	direct product factor
66	C₃×C₇	C₂×C₃×C₇×C₂₅	1	4	yes	complemented
67	C₂×C₃²	—	7	1	no	Hall
68	C₃×C₅	C₃×C₅×C₇×D₇	1	4	yes	—
69	C₂×C₇	—	7	1	no	—
70	D₇	C₃²×C₇×C₂₅	1	1	yes	characteristic, direct product factor
71	C₂×C₅	—	7	1	no	—
72	C₃²	C₇×D₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₇	—	2	3	no	—
74	C₇	C₂×C₃²×C₇×C₂₅	1	1	yes	characteristic, complemented
75	C₇	C₃²×D₇×C₂₅	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	7	4	no	—
77	C₅	C₃²×C₅×C₇×D₇	1	1	yes	characteristic
78	C₃	C₃×C₇×D₇×C₂₅	1	4	yes	direct product factor
79	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇×C₂₅	D₇
commutator, hypocenter	C₇	C₂×C₃²×C₇×C₂₅
Frattini	C₅	C₃²×C₅×C₇×D₇
Fitting	C₃²×C₇²×C₂₅	C₂
socle	C₃²×C₅×C₇²	C₂×C₅
prime radical	C₃²×C₅×C₇×D₇	C₅
cosocle	C₅×C₇	C₂×C₃²×C₅×C₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
2. C₃×C₇×D₇×C₂₅	C₃	direct (N × H)
4. C₃×C₇²×C₂₅	C₂×C₃	semidirect
5. C₃²×D₇×C₂₅	C₇	direct (N × H)
7. C₇×D₇×C₂₅	C₃²	direct (N × H)
10. C₃²×C₇×C₂₅	D₇	direct (N × H)
11. C₃²×C₇×C₂₅	C₂×C₇	semidirect
13. C₇²×C₂₅	C₂×C₃²	semidirect
15. C₃×D₇×C₂₅	C₃×C₇	direct (N × H)
16. C₃²×C₇×D₇	C₂₅	direct (N × H)
21. C₃×C₇×C₂₅	C₃×D₇	direct (N × H)
22. C₃×C₇×C₂₅	C₂×C₃×C₇	semidirect
25. C₃²×C₇²	C₂×C₂₅	semidirect
27. D₇×C₂₅	C₃²×C₇	direct (N × H)
31. C₃×C₇×D₇	C₃×C₂₅	direct (N × H)
33. C₃²×C₂₅	C₇×D₇	direct (N × H)
37. C₇×C₂₅	C₃²×D₇	direct (N × H)
38. C₇×C₂₅	C₂×C₃²×C₇	semidirect
40. C₃×C₇²	C₂×C₃×C₂₅	semidirect
42. C₃²×D₇	C₇×C₂₅	direct (N × H)
46. C₇×D₇	C₃²×C₂₅	direct (N × H)
48. C₃×C₂₅	C₃×C₇×D₇	direct (N × H)
52. C₃²×C₇	D₇×C₂₅	direct (N × H)
53. C₃²×C₇	C₂×C₇×C₂₅	semidirect
55. C₇²	C₂×C₃²×C₂₅	semidirect
58. C₃×D₇	C₃×C₇×C₂₅	direct (N × H)
63. C₂₅	C₃²×C₇×D₇	direct (N × H)
65. C₃×C₇	C₃×D₇×C₂₅	direct (N × H)
66. C₃×C₇	C₂×C₃×C₇×C₂₅	semidirect
70. D₇	C₃²×C₇×C₂₅	direct (N × H)
72. C₃²	C₇×D₇×C₂₅	direct (N × H)
74. C₇	C₂×C₃²×C₇×C₂₅	semidirect
75. C₇	C₃²×D₇×C₂₅	direct (N × H)
78. C₃	C₃×C₇×D₇×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
C₃²×C₇²×C₂₅	2
C₃×C₇×D₇×C₂₅	3
C₃²×C₅×C₇×D₇	5
C₃²×D₇×C₂₅	7
C₂×C₃²×C₇×C₂₅	7

Subgroups — C32×C7×D7×C25 #36347767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₇×C₂₅ #36347767