Subgroups — C₂×C₇×C₂₅×D₄₇ #45681663

Order 32900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×D₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₅×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₅×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₇×D₄₇	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅×D₄₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₄₇	C₂×C₅	1	2	yes	—
7	C₂×C₅×C₇×C₄₇	C₂×C₅	1	1	yes	characteristic
8	C₂₅×D₄₇	C₂×C₇	1	2	yes	direct product factor
9	C₂×C₂₅×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented
10	C₅×C₇×C₄₇	C₂²×C₅	1	1	yes	characteristic
11	C₂×C₇×D₄₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂₅×C₄₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×D₄₇	C₅×C₇	1	1	yes	characteristic
14	C₂²×C₇×C₂₅	—	47	1	no	maximal, Hall
15	C₂×C₇×C₄₇	C₂×C₂₅	1	1	yes	characteristic, complemented
16	C₇×D₄₇	C₂×C₂₅	1	2	yes	direct product factor
17	C₂×C₅×C₄₇	C₂×C₅×C₇	1	1	yes	characteristic
18	C₅×D₄₇	C₂×C₅×C₇	1	2	yes	—
19	C₂×C₇×C₂₅	—	47	2	no	—
20	C₂×C₇×C₂₅	D₄₇	1	1	yes	characteristic, direct product factor
21	C₇×C₄₇	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₅×C₄₇	C₂²×C₅×C₇	1	1	yes	characteristic
23	C₂×D₄₇	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₂₅	C₂×D₄₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₅×C₇	—	47	1	no	—
26	C₂²×C₂₅	—	47	1	no	Hall
27	C₂×C₄₇	C₂×C₇×C₂₅	1	1	yes	characteristic, complemented
28	D₄₇	C₂×C₇×C₂₅	1	2	yes	direct product factor
29	C₂×C₅×C₇	—	47	2	no	—
30	C₂×C₅×C₇	C₅×D₄₇	1	1	yes	characteristic
31	C₂×C₂₅	—	47	2	no	—
32	C₂×C₂₅	C₇×D₄₇	1	1	yes	characteristic, direct product factor
33	C₄₇	C₂²×C₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	C₂×C₅×D₄₇	1	1	yes	characteristic
35	C₂²×C₇	—	47	1	no	Hall
36	C₂₅	C₂×C₇×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₅	—	47	1	no	—
38	C₂×C₇	—	47	2	no	—
39	C₂×C₇	C₂₅×D₄₇	1	1	yes	characteristic, direct product factor
40	C₂×C₅	—	47	2	no	—
41	C₂×C₅	C₅×C₇×D₄₇	1	1	yes	characteristic
42	C₇	C₂×C₂₅×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₅	C₂×C₅×C₇×D₄₇	1	1	yes	characteristic
44	C₂²	—	47	1	no	Sylow
45	C₂	—	47	2	no	—
46	C₂	C₇×C₂₅×D₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₅	D₄₇
commutator, hypocenter	C₄₇	C₂²×C₇×C₂₅
Frattini	C₅	C₂×C₅×C₇×D₄₇
Fitting	C₂×C₇×C₂₅×C₄₇	C₂
socle	C₂×C₅×C₇×C₄₇	C₂×C₅
prime radical	C₂×C₅×C₇×D₄₇	C₅
cosocle	C₅×C₄₇	C₂²×C₅×C₇
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₅×D₄₇	C₂	direct (N × H)
2. C₂×C₇×C₂₅×C₄₇	C₂	semidirect
3. C₇×C₂₅×C₄₇	C₂²	semidirect
5. C₂×C₂₅×D₄₇	C₇	direct (N × H)
8. C₂₅×D₄₇	C₂×C₇	direct (N × H)
9. C₂×C₂₅×C₄₇	C₂×C₇	semidirect
11. C₂×C₇×D₄₇	C₂₅	direct (N × H)
12. C₂₅×C₄₇	C₂²×C₇	semidirect
15. C₂×C₇×C₄₇	C₂×C₂₅	semidirect
16. C₇×D₄₇	C₂×C₂₅	direct (N × H)
20. C₂×C₇×C₂₅	D₄₇	direct (N × H)
21. C₇×C₄₇	C₂²×C₂₅	semidirect
23. C₂×D₄₇	C₇×C₂₅	direct (N × H)
24. C₇×C₂₅	C₂×D₄₇	direct (N × H)
27. C₂×C₄₇	C₂×C₇×C₂₅	semidirect
28. D₄₇	C₂×C₇×C₂₅	direct (N × H)
32. C₂×C₂₅	C₇×D₄₇	direct (N × H)
33. C₄₇	C₂²×C₇×C₂₅	semidirect
36. C₂₅	C₂×C₇×D₄₇	direct (N × H)
39. C₂×C₇	C₂₅×D₄₇	direct (N × H)
42. C₇	C₂×C₂₅×D₄₇	direct (N × H)
46. C₂	C₇×C₂₅×D₄₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×C₂₅×D₄₇	2
C₂×C₇×C₂₅×C₄₇	2
C₂×C₅×C₇×D₄₇	5
C₂×C₂₅×D₄₇	7
C₂²×C₇×C₂₅	47

Subgroups — C2×C7×C25×D47 #45681663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₅×D₄₇ #45681663