Subgroups — Dic₇₈₄₅ #44535930

Order 31380.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₅₂₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₁₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₅₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₅₆₉	—	5	1	no	maximal, Hall
5	C₂×C₅×C₅₂₃	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅₂₃	D₅	1	1	yes	characteristic
7	C₅×C₅₂₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₅₂₃	—	15	1	no	Hall
9	C₃×C₅₂₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅₂₃	D₁₅	1	1	yes	characteristic
11	C₅₂₃	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₅	—	523	1	no	maximal, Hall
13	C₂×C₃×C₅	D₅₂₃	1	1	yes	characteristic
14	Dic₅	—	1569	1	no	Hall
15	C₃×C₅	Dic₅₂₃	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	2615	1	no	Hall
17	C₂×C₅	D₁₅₆₉	1	1	yes	characteristic
18	C₂×C₃	D₂₆₁₅	1	1	yes	characteristic
19	C₅	Dic₁₅₆₉	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	7845	1	no	Sylow
21	C₃	Dic₂₆₁₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₇₈₄₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₈₄₅
commutator, hypocenter	C₃×C₅×C₅₂₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₅₂₃	C₂
LCS	G ▷ C₃×C₅×C₅₂₃
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.