Subgroups — C₂₅×C₃⋊(C₃⋊(C₇⋊D₇)) #36347780

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	C₂₅×C₃⋊(C₇⋊D₇)	—	3	4	no	maximal
3	C₅×C₃⋊(C₃⋊(C₇⋊D₇))	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇²×C₂₅	D₃	1	4	yes	complemented
5	C₂₅×C₃⋊D₂₁	—	7	8	no	maximal
6	C₂₅×C₇⋊D₇	—	9	1	no	Hall
7	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	D₇	1	8	yes	complemented
9	C₅×C₃⋊(C₇⋊D₇)	—	3	4	no	—
10	C₇²×C₂₅	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₂₅×D₂₁	—	21	32	no	—
12	C₃⋊(C₃⋊(C₇⋊D₇))	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇²	C₅×D₃	1	4	yes	—
14	C₅×C₃⋊D₂₁	—	7	8	no	—
15	C₃×C₇×C₂₅	D₂₁	1	32	yes	complemented
16	C₅×C₇⋊D₇	—	9	1	no	—
17	C₃⋊D₃×C₂₅	—	49	1	no	Hall
18	C₃²×C₇²	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
19	D₇×C₂₅	—	63	8	no	—
20	C₃²×C₅×C₇	C₅×D₇	1	8	yes	—
21	C₃⋊(C₇⋊D₇)	—	3	4	no	—
22	C₅×C₇²	C₅×C₃⋊D₃	1	1	yes	characteristic
23	C₃²×C₂₅	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
24	C₅×D₂₁	—	21	32	no	—
25	C₇×C₂₅	C₃⋊D₂₁	1	8	yes	complemented
26	D₃×C₂₅	—	147	4	no	—
27	C₃×C₇²	D₃×C₂₅	1	4	yes	complemented
28	C₃⋊D₂₁	—	7	8	no	—
29	C₃×C₅×C₇	C₅×D₂₁	1	32	yes	—
30	C₇⋊D₇	—	9	1	no	Hall
31	C₅×C₃⋊D₃	—	49	1	no	—
32	C₃×C₂₅	C₃⋊(C₇⋊D₇)	1	4	yes	complemented
33	C₅×D₇	—	63	8	no	—
34	C₃²×C₇	D₇×C₂₅	1	8	yes	complemented
35	C₂×C₂₅	—	441	1	no	Hall
36	C₇²	C₃⋊D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
37	C₃²×C₅	C₅×C₇⋊D₇	1	1	yes	characteristic
38	D₂₁	—	21	32	no	—
39	C₅×C₇	C₅×C₃⋊D₂₁	1	8	yes	—
40	C₅×D₃	—	147	4	no	—
41	C₂₅	C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₇	C₂₅×D₂₁	1	32	yes	complemented
43	C₃⋊D₃	—	49	1	no	Hall
44	C₃×C₅	C₅×C₃⋊(C₇⋊D₇)	1	4	yes	—
45	D₇	—	63	8	no	—
46	C₂×C₅	—	441	1	no	—
47	C₃²	C₂₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₂₅×C₃⋊D₂₁	1	8	yes	complemented
49	D₃	—	147	4	no	—
50	C₅	C₅×C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic
51	C₃	C₂₅×C₃⋊(C₇⋊D₇)	1	4	yes	complemented
52	C₂	—	441	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅	C₃⋊(C₃⋊(C₇⋊D₇))
commutator, hypocenter	C₃²×C₇²	C₂×C₂₅
Frattini	C₅	C₅×C₃⋊(C₃⋊(C₇⋊D₇))
Fitting	C₃²×C₇²×C₂₅	C₂
socle, cosocle	C₃²×C₅×C₇²	C₂×C₅
prime radical	C₅×C₃⋊(C₃⋊(C₇⋊D₇))	C₅
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
4. C₃×C₇²×C₂₅	D₃	semidirect
8. C₃²×C₇×C₂₅	D₇	semidirect
10. C₇²×C₂₅	C₃⋊D₃	semidirect
12. C₃⋊(C₃⋊(C₇⋊D₇))	C₂₅	direct (N × H)
15. C₃×C₇×C₂₅	D₂₁	semidirect
18. C₃²×C₇²	C₂×C₂₅	semidirect
23. C₃²×C₂₅	C₇⋊D₇	semidirect
25. C₇×C₂₅	C₃⋊D₂₁	semidirect
27. C₃×C₇²	D₃×C₂₅	semidirect
32. C₃×C₂₅	C₃⋊(C₇⋊D₇)	semidirect
34. C₃²×C₇	D₇×C₂₅	semidirect
36. C₇²	C₃⋊D₃×C₂₅	semidirect
41. C₂₅	C₃⋊(C₃⋊(C₇⋊D₇))	direct (N × H)
42. C₃×C₇	C₂₅×D₂₁	semidirect
47. C₃²	C₂₅×C₇⋊D₇	semidirect
48. C₇	C₂₅×C₃⋊D₂₁	semidirect
51. C₃	C₂₅×C₃⋊(C₇⋊D₇)	semidirect

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
C₂₅×C₃⋊(C₇⋊D₇)	3
C₅×C₃⋊(C₃⋊(C₇⋊D₇))	5
C₂₅×C₃⋊D₂₁	7

Subgroups — C25×C3⋊(C3⋊(C7⋊D7)) #36347780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₃⋊(C₃⋊(C₇⋊D₇)) #36347780