Subgroups — Dic₆₂₃₅ #38735539

Order 24940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₉×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₄₇	—	5	1	no	maximal, Hall
4	C₂×C₂₉×C₄₃	D₅	1	1	yes	characteristic
5	C₂₉×C₄₃	Dic₅	1	1	yes	characteristic, complemented, Hall
6	Dic₂₁₅	—	29	1	no	maximal, Hall
7	Dic₁₄₅	—	43	1	no	maximal, Hall
8	C₂×C₅×C₄₃	D₂₉	1	1	yes	characteristic
9	C₂×C₅×C₂₉	D₄₃	1	1	yes	characteristic
10	C₅×C₄₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
11	Dic₄₃	—	145	1	no	Hall
12	C₅×C₂₉	Dic₄₃	1	1	yes	characteristic, complemented, Hall
13	Dic₂₉	—	215	1	no	Hall
14	C₂×C₄₃	D₁₄₅	1	1	yes	characteristic
15	C₂×C₂₉	D₂₁₅	1	1	yes	characteristic
16	C₄₃	Dic₁₄₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	Dic₂₁₅	1	1	yes	characteristic, complemented, Sylow
18	Dic₅	—	1247	1	no	Hall
19	C₂×C₅	D₁₂₄₇	1	1	yes	characteristic
20	C₅	Dic₁₂₄₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6235	1	no	Sylow
22	C₂	D₆₂₃₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₂₃₅
commutator, hypocenter	C₅×C₂₉×C₄₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₂₉×C₄₃	C₂
LCS	G ▷ C₅×C₂₉×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.