Subgroups — C₇⋊(D₃₁⋊C₂₅) #24925749

Order 10850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₂₁₇	C₅	1	1	yes	maximal, characteristic
3	D₃₁⋊C₂₅	—	7	1	no	maximal, Hall
4	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic
5	C₃₁⋊C₂₅	D₇	1	1	yes	characteristic, complemented, Hall
6	D₂₁₇	C₂₅	1	1	yes	characteristic, complemented, Hall
7	D₇×C₂₅	—	31	1	no	maximal, Hall
8	C₅×D₃₁	—	7	1	no	—
9	C₇×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₇×C₂₅	—	31	1	no	Hall
11	C₅×C₃₁	C₅×D₇	1	1	yes	characteristic
12	C₅×D₇	—	31	1	no	—
13	D₃₁	—	7	1	no	Hall
14	C₂×C₂₅	—	217	1	no	Hall
15	C₅×C₇	D₃₁⋊C₅	1	1	yes	characteristic
16	C₃₁	D₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₅	—	31	1	no	Sylow
18	D₇	—	31	1	no	Hall
19	C₂×C₅	—	217	1	no	—
20	C₇	D₃₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₇⋊(D₃₁⋊C₅)	1	1	yes	characteristic
22	C₂	—	217	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₇⋊(D₃₁⋊C₅)
commutator, hypocenter	C₇×C₃₁	C₂×C₂₅
Fitting, socle, cosocle	C₅×C₇×C₃₁	C₂×C₅
prime radical	C₅×D₂₁₇	C₅
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₅

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

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