Subgroups — C₃×D₃×C₇²×C₂₅ #36347772

Order 22050.

270 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	D₃×C₇²×C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₇²×C₂₅	—	3	1	no	maximal
4	C₃×C₅×D₃×C₇²	C₅	1	1	yes	maximal, characteristic
5	C₃×C₇²×C₂₅	—	2	1	no	—
6	C₃×C₇²×C₂₅	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₇²×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₃×C₇×C₂₅	C₇	1	8	yes	maximal, direct product factor
9	C₂×C₇²×C₂₅	—	3	1	no	Hall
10	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
11	C₃²×C₇×C₂₅	C₂×C₇	1	8	yes	complemented
12	C₂×C₃×C₅×C₇²	—	3	1	no	—
13	C₅×D₃×C₇²	C₃×C₅	1	1	yes	characteristic
14	C₇²×C₂₅	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₇×C₂₅	—	3	8	no	—
16	D₃×C₇×C₂₅	C₃×C₇	1	8	yes	direct product factor
17	C₃×D₃×C₇²	C₂₅	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×C₇²	—	2	1	no	—
19	C₃×C₅×C₇²	C₅×D₃	1	1	yes	characteristic
20	C₃×C₅×C₇²	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₅×D₃×C₇	C₅×C₇	1	8	yes	—
22	C₃×C₇×C₂₅	—	2	8	no	—
23	C₃×C₇×C₂₅	D₃×C₇	1	8	yes	direct product factor
24	C₃×C₇×C₂₅	C₂×C₃×C₇	1	8	yes	complemented
25	C₂×C₅×C₇²	—	3	1	no	—
26	C₃×D₃×C₂₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
27	C₃²×C₇²	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₇×C₂₅	—	3	8	no	—
29	C₃²×C₅×C₇	C₂×C₅×C₇	1	8	yes	—
30	C₂×C₃×C₇²	—	3	1	no	—
31	D₃×C₇²	C₃×C₂₅	1	1	yes	characteristic, direct product factor
32	C₅×C₇²	C₃×C₅×D₃	1	1	yes	characteristic
33	C₃²×C₂₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅×C₇	—	3	8	no	—
35	C₅×D₃×C₇	C₃×C₅×C₇	1	8	yes	—
36	C₇×C₂₅	C₃×D₃×C₇	1	8	yes	direct product factor
37	C₂×C₃×C₂₅	—	3	1	no	—
38	D₃×C₂₅	C₃×C₇²	1	1	yes	characteristic, direct product factor
39	C₃×C₇²	—	2	1	no	—
40	C₃×C₇²	D₃×C₂₅	1	1	yes	characteristic, direct product factor
41	C₃×C₇²	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
42	C₃×D₃×C₇	C₇×C₂₅	1	8	yes	direct product factor
43	C₃×C₅×C₇	—	2	8	no	—
44	C₃×C₅×C₇	C₅×D₃×C₇	1	8	yes	—
45	C₃×C₅×C₇	C₂×C₃×C₅×C₇	1	8	yes	—
46	C₂×C₇²	—	3	1	no	Hall
47	C₃×C₅×D₃	C₅×C₇²	1	1	yes	characteristic
48	C₃×C₂₅	—	2	1	no	—
49	C₃×C₂₅	D₃×C₇²	1	1	yes	characteristic, direct product factor
50	C₃×C₂₅	C₂×C₃×C₇²	1	1	yes	characteristic, complemented
51	C₂×C₅×C₇	—	3	8	no	—
52	C₃²×C₇	C₂×C₇×C₂₅	1	8	yes	complemented
53	C₂×C₂₅	—	3	1	no	Hall
54	C₇²	C₃×D₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
55	C₃²×C₅	C₂×C₅×C₇²	1	1	yes	characteristic
56	C₂×C₃×C₇	—	3	8	no	—
57	D₃×C₇	C₃×C₇×C₂₅	1	8	yes	direct product factor
58	C₅×C₇	C₃×C₅×D₃×C₇	1	8	yes	—
59	C₂×C₃×C₅	—	3	1	no	—
60	C₅×D₃	C₃×C₅×C₇²	1	1	yes	characteristic
61	C₂₅	C₃×D₃×C₇²	1	1	yes	characteristic, direct product factor, Sylow
62	C₃×C₇	—	2	8	no	—
63	C₃×C₇	D₃×C₇×C₂₅	1	8	yes	direct product factor
64	C₃×C₇	C₂×C₃×C₇×C₂₅	1	8	yes	complemented
65	C₃×D₃	C₇²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
66	C₃×C₅	—	2	1	no	—
67	C₃×C₅	C₅×D₃×C₇²	1	1	yes	characteristic
68	C₃×C₅	C₂×C₃×C₅×C₇²	1	1	yes	characteristic
69	C₂×C₇	—	3	8	no	—
70	C₂×C₅	—	3	1	no	—
71	C₃²	C₂×C₇²×C₂₅	1	1	yes	characteristic, complemented, Sylow
72	C₇	C₃×D₃×C₇×C₂₅	1	8	yes	direct product factor
73	C₂×C₃	—	3	1	no	—
74	D₃	C₃×C₇²×C₂₅	1	1	yes	characteristic, direct product factor
75	C₅	C₃×C₅×D₃×C₇²	1	1	yes	characteristic
76	C₃	—	2	1	no	—
77	C₃	C₂×C₃×C₇²×C₂₅	1	1	yes	characteristic, complemented
78	C₃	D₃×C₇²×C₂₅	1	1	yes	characteristic, direct product factor
79	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇²×C₂₅	D₃
commutator, hypocenter	C₃	C₂×C₃×C₇²×C₂₅
Frattini	C₅	C₃×C₅×D₃×C₇²
Fitting	C₃²×C₇²×C₂₅	C₂
socle	C₃²×C₅×C₇²	C₂×C₅
prime radical	C₃×C₅×D₃×C₇²	C₅
cosocle	C₃×C₅	C₂×C₃×C₅×C₇²
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₇²×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
2. D₃×C₇²×C₂₅	C₃	direct (N × H)
6. C₃×C₇²×C₂₅	D₃	direct (N × H)
7. C₃×C₇²×C₂₅	C₂×C₃	semidirect
8. C₃×D₃×C₇×C₂₅	C₇	direct (N × H)
11. C₃²×C₇×C₂₅	C₂×C₇	semidirect
14. C₇²×C₂₅	C₃×D₃	direct (N × H)
16. D₃×C₇×C₂₅	C₃×C₇	direct (N × H)
17. C₃×D₃×C₇²	C₂₅	direct (N × H)
23. C₃×C₇×C₂₅	D₃×C₇	direct (N × H)
24. C₃×C₇×C₂₅	C₂×C₃×C₇	semidirect
26. C₃×D₃×C₂₅	C₇²	direct (N × H)
27. C₃²×C₇²	C₂×C₂₅	semidirect
31. D₃×C₇²	C₃×C₂₅	direct (N × H)
33. C₃²×C₂₅	C₂×C₇²	semidirect
36. C₇×C₂₅	C₃×D₃×C₇	direct (N × H)
38. D₃×C₂₅	C₃×C₇²	direct (N × H)
40. C₃×C₇²	D₃×C₂₅	direct (N × H)
41. C₃×C₇²	C₂×C₃×C₂₅	semidirect
42. C₃×D₃×C₇	C₇×C₂₅	direct (N × H)
49. C₃×C₂₅	D₃×C₇²	direct (N × H)
50. C₃×C₂₅	C₂×C₃×C₇²	semidirect
52. C₃²×C₇	C₂×C₇×C₂₅	semidirect
54. C₇²	C₃×D₃×C₂₅	direct (N × H)
57. D₃×C₇	C₃×C₇×C₂₅	direct (N × H)
61. C₂₅	C₃×D₃×C₇²	direct (N × H)
63. C₃×C₇	D₃×C₇×C₂₅	direct (N × H)
64. C₃×C₇	C₂×C₃×C₇×C₂₅	semidirect
65. C₃×D₃	C₇²×C₂₅	direct (N × H)
71. C₃²	C₂×C₇²×C₂₅	semidirect
72. C₇	C₃×D₃×C₇×C₂₅	direct (N × H)
74. D₃	C₃×C₇²×C₂₅	direct (N × H)
77. C₃	C₂×C₃×C₇²×C₂₅	semidirect
78. C₃	D₃×C₇²×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
D₃×C₇²×C₂₅	3
C₂×C₃×C₇²×C₂₅	3
C₃×C₅×D₃×C₇²	5
C₃×D₃×C₇×C₂₅	7

Subgroups — C3×D3×C72×C25 #36347772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₇²×C₂₅ #36347772