Subgroups — C₂₃×#11761507 #37567178

Order 24380.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×Dic₅₃	—	5	1	no	maximal, Hall
4	C₂×C₂₃×C₅₃	—	5	1	no	—
5	C₂₃×C₅₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
6	#11761507	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅×C₅₃	C₂×C₂₃	1	1	yes	characteristic
8	AGL(1,𝔽₅)×C₂₃	—	53	1	no	maximal, Hall
9	C₅×C₅₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
10	D₅×C₂₃	D₅₃	1	1	yes	characteristic
11	Dic₅₃	—	5	1	no	Hall
12	C₅×C₂₃	Dic₅₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₃	—	5	1	no	—
14	C₄×C₂₃	—	265	1	no	Hall
15	C₅₃	AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	—	5	1	no	—
17	C₂₃	#11761507	1	1	yes	characteristic, direct product factor, Sylow
18	AGL(1,𝔽₅)	—	53	1	no	Hall
19	D₅	C₂₃×D₅₃	1	1	yes	characteristic
20	C₅	C₂₃×Dic₅₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	265	1	no	Sylow
22	C₂	—	5	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.