Subgroups — C₅×C₈×C₁₇² #72190013

Order 11560.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₇²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₄×C₅×C₁₇²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₁₇²	C₄	1	1	yes	characteristic
4	C₅×C₁₇²	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₁₇²	C₂×C₅	1	1	yes	characteristic
6	C₅×C₈×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
7	C₂×C₁₇²	C₄×C₅	1	1	yes	characteristic
8	C₄×C₅×C₁₇	C₂×C₁₇	1	18	yes	—
9	C₁₇²	C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₅×C₁₇	C₄×C₁₇	1	18	yes	—
11	C₈×C₁₇	C₅×C₁₇	1	18	yes	direct product factor
12	C₅×C₁₇	C₈×C₁₇	1	18	yes	direct product factor
13	C₄×C₁₇	C₂×C₅×C₁₇	1	18	yes	—
14	C₅×C₈	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₇	C₄×C₅×C₁₇	1	18	yes	—
16	C₄×C₅	C₂×C₁₇²	1	1	yes	characteristic
17	C₁₇	C₅×C₈×C₁₇	1	18	yes	direct product factor
18	C₂×C₅	C₄×C₁₇²	1	1	yes	characteristic
19	C₈	C₅×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₈×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₂×C₅×C₁₇²	1	1	yes	characteristic
22	C₂	C₄×C₅×C₁₇²	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.