Subgroups — Dic₂₆₃₉ #24902205

Order 10556.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₃₇₇	—	7	1	no	maximal, Hall
4	Dic₂₀₃	—	13	1	no	maximal, Hall
5	C₂×C₁₃×C₂₉	D₇	1	1	yes	characteristic
6	C₂×C₇×C₂₉	D₁₃	1	1	yes	characteristic
7	C₁₃×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
8	Dic₉₁	—	29	1	no	maximal, Hall
9	C₇×C₂₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₁₃	D₂₉	1	1	yes	characteristic
11	Dic₂₉	—	91	1	no	Hall
12	C₇×C₁₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₉	D₉₁	1	1	yes	characteristic
14	Dic₁₃	—	203	1	no	Hall
15	C₂₉	Dic₉₁	1	1	yes	characteristic, complemented, Sylow
16	Dic₇	—	377	1	no	Hall
17	C₂×C₁₃	D₂₀₃	1	1	yes	characteristic
18	C₂×C₇	D₃₇₇	1	1	yes	characteristic
19	C₁₃	Dic₂₀₃	1	1	yes	characteristic, complemented, Sylow
20	C₇	Dic₃₇₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	2639	1	no	Sylow
22	C₂	D₂₆₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₆₃₉
commutator, hypocenter	C₇×C₁₃×C₂₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₃×C₂₉	C₂
LCS	G ▷ C₇×C₁₃×C₂₉
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.