Subgroups — C₈₉×#63121 #37528964

Order 23140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#261×C₈₉	—	5	1	no	maximal, Hall
4	D₁₃×C₈₉	—	5	1	no	—
5	AGL(1,𝔽₅)×C₈₉	—	13	1	no	maximal, Hall
6	C₁₃×C₈₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₈₉	—	13	1	no	—
8	C₅×C₈₉	#261	1	1	yes	characteristic, complemented, Hall
9	C₄×C₈₉	—	65	1	no	Hall
10	#63121	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₈₉	—	65	1	no	—
12	D₆₅	C₂×C₈₉	1	1	yes	characteristic
13	C₈₉	#63121	1	1	yes	characteristic, direct product factor, Sylow
14	C₅×C₁₃	C₄×C₈₉	1	1	yes	characteristic, complemented, Hall
15	#261	—	5	1	no	Hall
16	D₁₃	—	5	1	no	—
17	AGL(1,𝔽₅)	—	13	1	no	Hall
18	C₁₃	AGL(1,𝔽₅)×C₈₉	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	13	1	no	—
20	C₅	#261×C₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	65	1	no	Sylow
22	C₂	—	65	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.