Subgroups — C₅×#20268664 #45682198

Order 32980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₆₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#20268664	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	D₁₆₄₉	C₂×C₅	1	1	yes	characteristic
5	C₅×#87604	—	17	1	no	maximal, Hall
6	C₁₇×C₉₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₉₇	—	17	1	no	—
8	C₅×C₉₇	#595	1	1	yes	characteristic, complemented, Hall
9	#87604	—	17	1	no	Hall
10	C₅×#595	—	97	1	no	maximal, Hall
11	D₉₇	—	17	1	no	—
12	C₅×D₁₇	—	97	1	no	—
13	C₉₇	C₅×#595	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₇	#87604	1	1	yes	characteristic, complemented, Hall
15	#595	—	97	1	no	Hall
16	D₁₇	—	97	1	no	—
17	C₄×C₅	—	1649	1	no	Hall
18	C₁₇	C₅×#87604	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	1649	1	no	—
20	C₅	#20268664	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1649	1	no	Sylow
22	C₂	—	1649	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.