Subgroups — C₁₇×Dic₅×C₇₉ #41001695

Order 26860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₇×C₇₉	—	5	1	no	maximal, Hall
4	C₂×C₁₇×C₇₉	D₅	1	1	yes	characteristic
5	Dic₅×C₇₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₇₉	Dic₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₇₉	C₂×C₁₇	1	1	yes	characteristic
8	C₅×C₇₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×Dic₅	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₇₉	—	5	1	no	Hall
11	C₂×C₅×C₁₇	C₂×C₇₉	1	1	yes	characteristic
12	C₂×C₇₉	D₅×C₁₇	1	1	yes	characteristic
13	C₅×C₁₇	C₄×C₇₉	1	1	yes	characteristic, complemented, Hall
14	C₇₉	C₁₇×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₄×C₁₇	—	5	1	no	Hall
16	C₂×C₁₇	D₅×C₇₉	1	1	yes	characteristic
17	Dic₅	C₁₇×C₇₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	Dic₅×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₇×C₇₉	1	1	yes	characteristic
20	C₅	C₄×C₁₇×C₇₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	D₅×C₁₇×C₇₉	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.