Subgroups — Dic₇×C₂₇₁⋊C₅ #49182003

Order 37940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₂₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₇₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇×C₂₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄×C₂₇₁⋊C₅	—	7	1	no	maximal, Hall
5	C₂×C₇×C₂₇₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₂₇₁⋊C₅	D₇	1	1	yes	characteristic
7	C₇×C₂₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂₇₁⋊C₅	Dic₇	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₂₇₁	—	7	1	no	Hall
10	C₂×C₂₇₁	C₅×D₇	1	1	yes	characteristic
11	C₂₇₁	C₅×Dic₇	1	1	yes	characteristic, complemented, Sylow
12	C₅×Dic₇	—	271	1	no	maximal, Hall
13	C₂×C₅×C₇	—	271	1	no	—
14	C₅×C₇	—	271	1	no	Hall
15	Dic₇	C₂₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₄×C₅	—	1897	1	no	Hall
17	C₂×C₇	C₂×C₂₇₁⋊C₅	1	1	yes	characteristic
18	C₂×C₅	—	271	1	no	—
19	C₇	C₄×C₂₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
20	C₅	—	271	1	no	Sylow
21	C₄	—	7	1	no	Sylow
22	C₂	D₇×C₂₇₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×C₂₇₁⋊C₅
commutator, hypocenter	C₇×C₂₇₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₇×C₂₇₁	C₂×C₅
prime radical	C₂×C₇×C₂₇₁⋊C₅	C₂
LCS	G ▷ C₇×C₂₇₁
UCS	C₁ ◁ C₂

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.