Subgroups — Dic₃₁×C₂₉⋊C₇ #38737745

Order 25172.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₉×Dic₃₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₂₉×C₃₁	C₂×C₇	1	1	yes	characteristic
5	C₂₉×C₃₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×Dic₃₁	—	29	1	no	maximal, Hall
7	C₄×C₂₉⋊C₇	—	31	1	no	maximal, Hall
8	C₂×C₇×C₃₁	—	29	1	no	—
9	C₂×C₂₉⋊C₇	D₃₁	1	1	yes	characteristic
10	C₇×C₃₁	—	29	1	no	Hall
11	C₂₉⋊C₇	Dic₃₁	1	1	yes	characteristic, direct product factor, Hall
12	Dic₃₁	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₂₉	—	31	1	no	Hall
14	C₂×C₃₁	C₂×C₂₉⋊C₇	1	1	yes	characteristic
15	C₂×C₂₉	C₇×D₃₁	1	1	yes	characteristic
16	C₃₁	C₄×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₇×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₇	—	899	1	no	Hall
19	C₂×C₇	—	29	1	no	—
20	C₇	—	29	1	no	Sylow
21	C₄	—	31	1	no	Sylow
22	C₂	D₃₁×C₂₉⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₁×C₂₉⋊C₇
commutator, hypocenter	C₂₉×C₃₁	C₄×C₇
Fitting, socle, cosocle	C₂×C₂₉×C₃₁	C₂×C₇
prime radical	C₂×C₃₁×C₂₉⋊C₇	C₂
LCS	G ▷ C₂₉×C₃₁
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.