Subgroups — Dic₅₇₈₅ #37528947

Order 23140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₅₇	—	5	1	no	maximal, Hall
4	C₂×C₁₃×C₈₉	D₅	1	1	yes	characteristic
5	Dic₄₄₅	—	13	1	no	maximal, Hall
6	C₁₃×C₈₉	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₈₉	D₁₃	1	1	yes	characteristic
8	C₅×C₈₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
9	Dic₈₉	—	65	1	no	Hall
10	Dic₆₅	—	89	1	no	maximal, Hall
11	C₂×C₈₉	D₆₅	1	1	yes	characteristic
12	C₂×C₅×C₁₃	D₈₉	1	1	yes	characteristic
13	C₈₉	Dic₆₅	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₃	Dic₈₉	1	1	yes	characteristic, complemented, Hall
15	Dic₁₃	—	445	1	no	Hall
16	C₂×C₁₃	D₄₄₅	1	1	yes	characteristic
17	Dic₅	—	1157	1	no	Hall
18	C₁₃	Dic₄₄₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	D₁₁₅₇	1	1	yes	characteristic
20	C₅	Dic₁₁₅₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5785	1	no	Sylow
22	C₂	D₅₇₈₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₇₈₅
commutator, hypocenter	C₅×C₁₃×C₈₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₃×C₈₉	C₂
LCS	G ▷ C₅×C₁₃×C₈₉
UCS	C₁ ◁ C₂

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.