Subgroups — Dic₁₇×C₄₁⋊C₅ #28358276

Order 13940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₁×Dic₁₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₇×C₄₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₄₁⋊C₅	—	17	1	no	maximal, Hall
6	C₁₇×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₄₁⋊C₅	D₁₇	1	1	yes	characteristic
8	C₅×Dic₁₇	—	41	1	no	maximal, Hall
9	C₄₁⋊C₅	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₇	—	41	1	no	—
11	C₄×C₄₁	—	17	1	no	Hall
12	C₅×C₁₇	—	41	1	no	Hall
13	C₂×C₄₁	C₅×D₁₇	1	1	yes	characteristic
14	Dic₁₇	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₄₁	C₅×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₇	C₂×C₄₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	697	1	no	Hall
18	C₁₇	C₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	41	1	no	—
20	C₅	—	41	1	no	Sylow
21	C₄	—	17	1	no	Sylow
22	C₂	D₁₇×C₄₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₇×C₄₁⋊C₅
commutator, hypocenter	C₁₇×C₄₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₇×C₄₁	C₂×C₅
prime radical	C₂×C₁₇×C₄₁⋊C₅	C₂
LCS	G ▷ C₁₇×C₄₁
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.