Subgroups — C₂×C₃×C₇×C₃₁⋊C₂₅ #45654366

Order 32550.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₃₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₃₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₇×C₃₁	C₅	1	1	yes	maximal, characteristic
4	C₇×C₃₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₃₁⋊C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₃×C₃₁⋊C₂₅	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₅×C₇×C₃₁	C₃×C₅	1	1	yes	characteristic
9	C₂×C₃₁⋊C₂₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₃×C₇×C₂₅	—	31	1	no	maximal, Hall
13	C₂×C₃×C₅×C₃₁	C₅×C₇	1	1	yes	characteristic
14	C₃₁⋊C₂₅	C₂×C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₂₅	—	31	1	no	Hall
17	C₃×C₅×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic
18	C₂×C₇×C₃₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₅	—	31	1	no	Hall
20	C₂×C₅×C₃₁	C₃×C₅×C₇	1	1	yes	characteristic
21	C₇×C₃₁	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅×C₇	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
23	C₂×C₃×C₃₁	C₇×C₂₅	1	1	yes	characteristic, complemented, Hall
24	C₇×C₂₅	—	31	1	no	Hall
25	C₅×C₃₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
26	C₂×C₃×C₂₅	—	31	1	no	Hall
27	C₃×C₅×C₇	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
28	C₃×C₃₁	C₂×C₇×C₂₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₂₅	—	31	1	no	Hall
30	C₂×C₅×C₇	C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
31	C₂×C₃₁	C₃×C₇×C₂₅	1	1	yes	characteristic, complemented, Hall
32	C₂×C₂₅	—	31	1	no	Hall
33	C₂×C₃×C₇	C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₇	C₂×C₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
35	C₃₁	C₂×C₃×C₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
37	C₂₅	—	31	1	no	Sylow
38	C₃×C₇	C₂×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₅	C₂×C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
40	C₂×C₇	C₃×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅	C₃×C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
42	C₇	C₂×C₃×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₇×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
44	C₅	C₂×C₃×C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
45	C₃	C₂×C₇×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₇×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₇	ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃₁	C₂×C₃×C₇×C₂₅
Frattini	C₅	C₂×C₃×C₇×ΓL(1,𝔽₃₂)
Fitting, socle, prime radical	C₂×C₃×C₅×C₇×C₃₁	C₅
cosocle	C₅×C₃₁	C₂×C₃×C₅×C₇
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₃₁⋊C₂₅	C₂	direct (N × H)
2. C₂×C₇×C₃₁⋊C₂₅	C₃	direct (N × H)
4. C₇×C₃₁⋊C₂₅	C₂×C₃	direct (N × H)
5. C₂×C₃×C₃₁⋊C₂₅	C₇	direct (N × H)
7. C₃×C₃₁⋊C₂₅	C₂×C₇	direct (N × H)
9. C₂×C₃₁⋊C₂₅	C₃×C₇	direct (N × H)
10. C₂×C₃×C₇×C₃₁	C₂₅	semidirect
14. C₃₁⋊C₂₅	C₂×C₃×C₇	direct (N × H)
15. C₃×C₇×C₃₁	C₂×C₂₅	semidirect
18. C₂×C₇×C₃₁	C₃×C₂₅	semidirect
21. C₇×C₃₁	C₂×C₃×C₂₅	semidirect
23. C₂×C₃×C₃₁	C₇×C₂₅	semidirect
28. C₃×C₃₁	C₂×C₇×C₂₅	semidirect
31. C₂×C₃₁	C₃×C₇×C₂₅	semidirect
33. C₂×C₃×C₇	C₃₁⋊C₂₅	direct (N × H)
35. C₃₁	C₂×C₃×C₇×C₂₅	semidirect
38. C₃×C₇	C₂×C₃₁⋊C₂₅	direct (N × H)
40. C₂×C₇	C₃×C₃₁⋊C₂₅	direct (N × H)
42. C₇	C₂×C₃×C₃₁⋊C₂₅	direct (N × H)
43. C₂×C₃	C₇×C₃₁⋊C₂₅	direct (N × H)
45. C₃	C₂×C₇×C₃₁⋊C₂₅	direct (N × H)
46. C₂	C₃×C₇×C₃₁⋊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
C₃×C₇×C₃₁⋊C₂₅	2
C₂×C₇×C₃₁⋊C₂₅	3
C₂×C₃×C₅×C₇×C₃₁	5
C₂×C₃×C₃₁⋊C₂₅	7
C₂×C₃×C₇×C₂₅	31

Subgroups — C2×C3×C7×C31⋊C25 #45654366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₃₁⋊C₂₅ #45654366