Subgroups — D₁₈₈₅₅ #49179556

Order 37710.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₄₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₂₈₅	—	3	1	no	maximal
3	D₃₇₇₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₄₁₉	D₃	1	1	yes	characteristic
5	D₂₀₉₅	—	9	1	no	Hall
6	C₉×C₄₁₉	D₅	1	1	yes	characteristic, complemented, Hall
7	D₁₂₅₇	—	15	1	no	—
8	C₅×C₄₁₉	D₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₄₁₉	D₁₅	1	1	yes	characteristic
10	D₄₁₉	—	45	1	no	Hall
11	C₄₁₉	D₄₅	1	1	yes	characteristic, complemented, Sylow
12	D₄₅	—	419	1	no	maximal, Hall
13	C₅×C₉	D₄₁₉	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	1257	1	no	—
15	D₉	—	2095	1	no	Hall
16	C₃×C₅	D₁₂₅₇	1	1	yes	characteristic
17	D₅	—	3771	1	no	Hall
18	C₉	D₂₀₉₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	6285	1	no	—
20	C₅	D₃₇₇₁	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₆₂₈₅	1	1	yes	characteristic
22	C₂	—	18855	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₄₁₉	C₂
Frattini	C₃	D₆₂₈₅
socle	C₃×C₅×C₄₁₉	D₃
LCS	G ▷ C₅×C₉×C₄₁₉
UCS	C₁

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.