Subgroups — C₃²×C₇²×D₂₅ #36347769

Order 22050.

360 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×C₇²×D₂₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇²×D₅	—	5	1	no	maximal
4	C₃×C₇²×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₃²×C₇×D₂₅	C₇	1	8	yes	maximal, direct product factor
6	C₇²×D₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇²	D₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	C₂×C₇	1	8	yes	complemented
9	C₃×C₇²×D₅	—	5	4	no	—
10	C₇²×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×D₂₅	C₃×C₇	1	32	yes	direct product factor
12	C₂×C₃²×C₇²	—	25	1	no	Hall
13	C₃×C₅×C₇²	C₃×D₅	1	4	yes	—
14	C₃²×C₇×D₅	—	5	8	no	—
15	C₃×C₇×C₂₅	C₂×C₃×C₇	1	32	yes	complemented
16	C₇²×D₅	—	5	1	no	—
17	C₃²×D₂₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₇²	D₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₇×D₂₅	C₃²×C₇	1	8	yes	direct product factor
20	C₃²×C₅×C₇	C₇×D₅	1	8	yes	—
21	C₂×C₃×C₇²	—	25	4	no	—
22	C₅×C₇²	C₃²×D₅	1	1	yes	characteristic
23	C₃²×C₂₅	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇×D₅	—	5	32	no	—
25	C₇×C₂₅	C₂×C₃²×C₇	1	8	yes	complemented
26	C₃×D₂₅	C₃×C₇²	1	4	yes	direct product factor
27	C₃×C₇²	C₃×D₂₅	1	4	yes	direct product factor
28	C₂×C₃²×C₇	—	25	8	no	—
29	C₃×C₅×C₇	C₃×C₇×D₅	1	32	yes	—
30	C₂×C₇²	—	25	1	no	Hall
31	C₃²×D₅	—	5	1	no	—
32	C₃×C₂₅	C₂×C₃×C₇²	1	4	yes	complemented
33	C₇×D₅	—	5	8	no	—
34	C₃²×C₇	C₇×D₂₅	1	8	yes	direct product factor
35	D₂₅	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Hall
36	C₇²	C₃²×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²×C₅	C₇²×D₅	1	1	yes	characteristic
38	C₂×C₃×C₇	—	25	32	no	—
39	C₅×C₇	C₃²×C₇×D₅	1	8	yes	—
40	C₃×D₅	—	5	4	no	—
41	C₂₅	C₂×C₃²×C₇²	1	1	yes	characteristic, complemented, Sylow
42	C₃×C₇	C₃×C₇×D₂₅	1	32	yes	direct product factor
43	C₂×C₃²	—	25	1	no	Hall
44	C₃×C₅	C₃×C₇²×D₅	1	4	yes	—
45	C₂×C₇	—	25	8	no	—
46	D₅	—	5	1	no	—
47	C₃²	C₇²×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₃²×C₇×D₂₅	1	8	yes	direct product factor
49	C₂×C₃	—	25	4	no	—
50	C₅	C₃²×C₇²×D₅	1	1	yes	characteristic
51	C₃	C₃×C₇²×D₂₅	1	4	yes	direct product factor
52	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇²	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃²×C₇²
Frattini	C₅	C₃²×C₇²×D₅
Fitting	C₃²×C₇²×C₂₅	C₂
socle	C₃²×C₅×C₇²	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃²×C₇²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
2. C₃×C₇²×D₂₅	C₃	direct (N × H)
4. C₃×C₇²×C₂₅	C₂×C₃	semidirect
5. C₃²×C₇×D₂₅	C₇	direct (N × H)
6. C₇²×D₂₅	C₃²	direct (N × H)
8. C₃²×C₇×C₂₅	C₂×C₇	semidirect
10. C₇²×C₂₅	C₂×C₃²	semidirect
11. C₃×C₇×D₂₅	C₃×C₇	direct (N × H)
15. C₃×C₇×C₂₅	C₂×C₃×C₇	semidirect
17. C₃²×D₂₅	C₇²	direct (N × H)
18. C₃²×C₇²	D₂₅	direct (N × H)
19. C₇×D₂₅	C₃²×C₇	direct (N × H)
23. C₃²×C₂₅	C₂×C₇²	semidirect
25. C₇×C₂₅	C₂×C₃²×C₇	semidirect
26. C₃×D₂₅	C₃×C₇²	direct (N × H)
27. C₃×C₇²	C₃×D₂₅	direct (N × H)
32. C₃×C₂₅	C₂×C₃×C₇²	semidirect
34. C₃²×C₇	C₇×D₂₅	direct (N × H)
35. D₂₅	C₃²×C₇²	direct (N × H)
36. C₇²	C₃²×D₂₅	direct (N × H)
41. C₂₅	C₂×C₃²×C₇²	semidirect
42. C₃×C₇	C₃×C₇×D₂₅	direct (N × H)
47. C₃²	C₇²×D₂₅	direct (N × H)
48. C₇	C₃²×C₇×D₂₅	direct (N × H)
51. C₃	C₃×C₇²×D₂₅	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×C₇²×D₂₅	3
C₃²×C₇²×D₅	5
C₃²×C₇×D₂₅	7

Subgroups — C32×C72×D25 #36347769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇²×D₂₅ #36347769