Subgroups — C₁₇×#14546129 #49150402

Order 37060.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×#89137	—	5	1	no	maximal, Hall
4	C₁₇×D₁₀₉	D₅	1	1	yes	characteristic
5	#14546129	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₁₀₉	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₁₀₉	C₂×C₁₇	1	1	yes	characteristic
8	C₅×C₁₀₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
9	#89137	—	5	1	no	Hall
10	C₁₇×Dic₅	—	109	1	no	maximal, Hall
11	D₁₀₉	D₅×C₁₇	1	1	yes	characteristic
12	C₂×C₅×C₁₇	—	109	1	no	—
13	C₁₀₉	C₁₇×Dic₅	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₇	#89137	1	1	yes	characteristic, complemented, Hall
15	C₄×C₁₇	—	545	1	no	Hall
16	C₂×C₁₇	—	109	1	no	—
17	Dic₅	—	109	1	no	Hall
18	C₁₇	#14546129	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	109	1	no	—
20	C₅	C₁₇×#89137	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	545	1	no	Sylow
22	C₂	—	109	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.