Subgroups — Dic₃×C₁₇×C₅₃ #24925196

Order 10812.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×C₅₃	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₅₃	D₃	1	1	yes	characteristic
5	C₁₇×C₅₃	Dic₃	1	1	yes	characteristic, direct product factor, Hall
6	Dic₃×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅₃	C₂×C₁₇	1	1	yes	characteristic
8	C₄×C₅₃	—	3	1	no	Hall
9	Dic₃×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅₃	D₃×C₁₇	1	1	yes	characteristic
12	C₂×C₃×C₁₇	C₂×C₅₃	1	1	yes	characteristic
13	C₄×C₁₇	—	3	1	no	Hall
14	C₅₃	Dic₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	D₃×C₅₃	1	1	yes	characteristic
17	C₁₇	Dic₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₇×C₅₃	1	1	yes	characteristic
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₁₇×C₅₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₁₇×C₅₃	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.