Subgroups — D₁₅₈₈₅ #44540927

Order 31770.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₉₅	—	3	1	no	maximal
3	D₃₁₇₇	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₅₃	D₃	1	1	yes	characteristic
5	D₁₇₆₅	—	9	1	no	Hall
6	C₉×C₃₅₃	D₅	1	1	yes	characteristic, complemented, Hall
7	D₁₀₅₉	—	15	1	no	—
8	C₅×C₃₅₃	D₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₅₃	D₁₅	1	1	yes	characteristic
10	D₃₅₃	—	45	1	no	Hall
11	C₃₅₃	D₄₅	1	1	yes	characteristic, complemented, Sylow
12	D₄₅	—	353	1	no	maximal, Hall
13	C₅×C₉	D₃₅₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	1059	1	no	—
15	D₉	—	1765	1	no	Hall
16	C₃×C₅	D₁₀₅₉	1	1	yes	characteristic
17	D₅	—	3177	1	no	Hall
18	C₉	D₁₇₆₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	5295	1	no	—
20	C₅	D₃₁₇₇	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₅₂₉₅	1	1	yes	characteristic
22	C₂	—	15885	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₃₅₃	C₂
Frattini	C₃	D₅₂₉₅
socle	C₃×C₅×C₃₅₃	D₃
LCS	G ▷ C₅×C₉×C₃₅₃
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.