Subgroups — C₃₁×D₁₇₅ #24925745

Order 10850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₃₅	—	5	1	no	maximal
3	C₃₁×D₂₅	—	7	1	no	maximal, Hall
4	C₅×C₇×C₃₁	D₅	1	1	yes	characteristic
5	C₂₅×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	D₇×C₃₁	—	25	1	no	Hall
7	D₁₇₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₅×C₃₁	—	35	1	no	—
9	C₇×C₃₁	D₂₅	1	1	yes	characteristic, complemented, Hall
10	C₇×C₂₅	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	D₃₅	1	1	yes	characteristic
12	D₃₅	—	5	1	no	—
13	C₂×C₃₁	—	175	1	no	Hall
14	D₂₅	—	7	1	no	Hall
15	C₅×C₇	D₅×C₃₁	1	1	yes	characteristic
16	C₃₁	D₁₇₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₅	D₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
18	D₇	—	25	1	no	Hall
19	D₅	—	35	1	no	—
20	C₇	C₃₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₃₁×D₃₅	1	1	yes	characteristic
22	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₁₇₅
commutator, cosocle, hypocenter	C₇×C₂₅	C₂×C₃₁
Frattini	C₅	C₃₁×D₃₅
Fitting	C₇×C₂₅×C₃₁	C₂
socle	C₅×C₇×C₃₁	D₅
LCS	G ▷ C₇×C₂₅
UCS	C₁ ◁ C₃₁

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.