Subgroups — C₅⋊(D₇₁⋊C₄₉) #46852333

Order 34790.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇₁⋊C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₁⋊C₄₉	—	5	1	no	maximal, Hall
3	C₇×D₃₅₅	C₇	1	1	yes	maximal, characteristic
4	C₇₁⋊C₄₉	D₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₇₁	C₂×C₇	1	1	yes	characteristic
6	C₇×D₇₁	—	5	1	no	—
7	D₃₅₅	C₄₉	1	1	yes	characteristic, complemented, Hall
8	C₇×C₇₁	C₇×D₅	1	1	yes	characteristic
9	D₅×C₄₉	—	71	1	no	maximal, Hall
10	C₅×C₇₁	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₄₉	—	71	1	no	Hall
12	D₇₁	—	5	1	no	Hall
13	C₂×C₄₉	—	355	1	no	Hall
14	C₇₁	D₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
15	C₇×D₅	—	71	1	no	—
16	C₄₉	—	71	1	no	Sylow
17	C₅×C₇	D₇₁⋊C₇	1	1	yes	characteristic
18	C₂×C₇	—	355	1	no	—
19	D₅	—	71	1	no	Hall
20	C₇	C₅⋊(D₇₁⋊C₇)	1	1	yes	characteristic
21	C₅	D₇₁⋊C₄₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	355	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₇	C₅⋊(D₇₁⋊C₇)
commutator, hypocenter	C₅×C₇₁	C₂×C₄₉
Fitting, socle, cosocle	C₅×C₇×C₇₁	C₂×C₇
prime radical	C₇×D₃₅₅	C₇
LCS	G ▷ C₅×C₇₁
UCS	C₁ ◁ 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.