Subgroups — C₅²×C₇×D₃₁ #24925769

Order 10850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₃₁	C₅	1	6	yes	maximal, direct product factor
3	C₅²×D₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₃₁	C₂×C₅	1	6	yes	complemented
5	C₅²×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₃₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅²×C₇	—	31	1	no	maximal, Hall
8	C₅×D₃₁	C₅×C₇	1	6	yes	direct product factor
9	C₇×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	C₅²×C₇	D₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₃₁	C₂×C₅×C₇	1	6	yes	complemented
12	C₂×C₅×C₇	—	31	6	no	—
13	D₃₁	C₅²×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅²	—	31	1	no	Hall
15	C₅×C₇	C₅×D₃₁	1	6	yes	direct product factor
16	C₃₁	C₂×C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
17	C₅²	C₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇	—	31	1	no	Hall
19	C₂×C₅	—	31	6	no	—
20	C₇	C₅²×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₅×C₇×D₃₁	1	6	yes	direct product factor
22	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅²×C₇

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.