Subgroups — C₂×C₅²×C₇₁⋊C₇ #38733113

Order 24850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇₁⋊C₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇₁⋊C₇	C₅	1	6	yes	maximal, direct product factor
3	C₂×C₅²×C₇₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₇₁⋊C₇	C₂×C₅	1	6	yes	direct product factor
5	C₅²×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇₁⋊C₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₇₁	C₅×C₇	1	6	yes	complemented
8	C₇₁⋊C₇	C₂×C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₇₁	C₂×C₅×C₇	1	6	yes	complemented
10	C₂×C₅²×C₇	—	71	1	no	maximal, Hall
11	C₅²×C₇	—	71	1	no	Hall
12	C₂×C₇₁	C₅²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇₁	C₂×C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅×C₇	—	71	6	no	—
15	C₂×C₅²	C₇₁⋊C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇	—	71	6	no	—
17	C₅²	C₂×C₇₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇	—	71	1	no	Hall
19	C₂×C₅	C₅×C₇₁⋊C₇	1	6	yes	direct product factor
20	C₇	—	71	1	no	Sylow
21	C₅	C₂×C₅×C₇₁⋊C₇	1	6	yes	direct product factor
22	C₂	C₅²×C₇₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅²	C₇₁⋊C₇
commutator, cosocle, hypocenter	C₇₁	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇₁	C₇
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₅²

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.