Subgroups — Dic₄₉₄₅ #34089909

Order 19780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₉₈₉	—	5	1	no	maximal, Hall
4	C₂×C₂₃×C₄₃	D₅	1	1	yes	characteristic
5	C₂₃×C₄₃	Dic₅	1	1	yes	characteristic, complemented, Hall
6	Dic₂₁₅	—	23	1	no	maximal, Hall
7	Dic₁₁₅	—	43	1	no	maximal, Hall
8	C₂×C₅×C₄₃	D₂₃	1	1	yes	characteristic
9	C₂×C₅×C₂₃	D₄₃	1	1	yes	characteristic
10	C₅×C₄₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	Dic₄₃	—	115	1	no	Hall
12	C₅×C₂₃	Dic₄₃	1	1	yes	characteristic, complemented, Hall
13	Dic₂₃	—	215	1	no	Hall
14	C₂×C₄₃	D₁₁₅	1	1	yes	characteristic
15	C₂×C₂₃	D₂₁₅	1	1	yes	characteristic
16	C₄₃	Dic₁₁₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₃	Dic₂₁₅	1	1	yes	characteristic, complemented, Sylow
18	Dic₅	—	989	1	no	Hall
19	C₂×C₅	D₉₈₉	1	1	yes	characteristic
20	C₅	Dic₉₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	4945	1	no	Sylow
22	C₂	D₄₉₄₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₄₉₄₅
commutator, hypocenter	C₅×C₂₃×C₄₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₂₃×C₄₃	C₂
LCS	G ▷ C₅×C₂₃×C₄₃
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.