Subgroups — C₂₃×D₅₃₁ #37567663

Order 24426.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₁₇₇	—	3	1	no	maximal
3	C₃×C₂₃×C₅₉	D₃	1	1	yes	characteristic
4	C₂₃×D₅₉	—	9	1	no	Hall
5	C₂₃×C₅₉	D₉	1	1	yes	characteristic, complemented, Hall
6	D₅₃₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₅₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	D₉×C₂₃	—	59	1	no	maximal, Hall
9	D₁₇₇	—	3	1	no	—
10	C₉×C₂₃	D₅₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅₉	D₃×C₂₃	1	1	yes	characteristic
12	D₃×C₂₃	—	177	1	no	—
13	D₅₉	—	9	1	no	Hall
14	C₃×C₂₃	D₁₇₇	1	1	yes	characteristic
15	C₅₉	D₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	—	531	1	no	Hall
17	C₂₃	D₅₃₁	1	1	yes	characteristic, direct product factor, Sylow
18	D₉	—	59	1	no	Hall
19	C₉	C₂₃×D₅₉	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	177	1	no	—
21	C₃	C₂₃×D₁₇₇	1	1	yes	characteristic
22	C₂	—	531	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	D₅₃₁
commutator, cosocle, hypocenter	C₉×C₅₉	C₂×C₂₃
Frattini	C₃	C₂₃×D₁₇₇
Fitting	C₉×C₂₃×C₅₉	C₂
socle	C₃×C₂₃×C₅₉	D₃
LCS	G ▷ C₉×C₅₉
UCS	C₁ ◁ C₂₃

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.