Subgroups — C₁₇×Dic₁₀₁⋊C₅ #46805113

Order 34340.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₀₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₀₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×Dic₁₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₇×C₁₀₁	C₂×C₅	1	1	yes	characteristic
5	Dic₁₀₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₁₀₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₀₁⋊C₅	C₂×C₁₇	1	1	yes	characteristic
8	C₁₀₁⋊C₅	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₄×C₅×C₁₇	—	101	1	no	maximal, Hall
11	C₂×C₁₀₁	C₂×C₅×C₁₇	1	1	yes	characteristic
12	C₂×C₅×C₁₇	—	101	1	no	—
13	C₁₀₁	C₄×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₇	—	101	1	no	Hall
15	C₄×C₁₇	—	101	1	no	Hall
16	C₂×C₁₇	D₁₀₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	101	1	no	Hall
18	C₁₇	Dic₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	101	1	no	—
20	C₅	—	101	1	no	Sylow
21	C₄	—	101	1	no	Sylow
22	C₂	C₁₇×D₁₀₁⋊C₅	1	1	yes	characteristic

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.