Subgroups — C₃×C₁₇×#6157 #24925201

Order 10812.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#6157	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₅₃	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₅₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#6157	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×D₅₃	C₂×C₁₇	1	1	yes	characteristic
8	#6157	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄×C₁₇	—	53	1	no	maximal, Hall
10	C₃×C₅₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
11	D₅₃	C₂×C₃×C₁₇	1	1	yes	characteristic
12	C₂×C₃×C₁₇	—	53	1	no	—
13	C₄×C₁₇	—	53	1	no	Hall
14	C₅₃	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₇	#6157	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₇	—	53	1	no	—
17	C₁₇	C₃×#6157	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	53	1	no	Hall
19	C₂×C₃	—	53	1	no	—
20	C₄	—	53	1	no	Sylow
21	C₃	C₁₇×#6157	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	53	1	no	—

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.