Subgroups — D₁₅₈₅₅ #44540256

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₈₅	—	3	1	no	maximal, Hall
3	D₃₁₇₁	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₅₁	D₃	1	1	yes	characteristic, complemented, Hall
5	D₂₂₆₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₅₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	D₇	1	1	yes	characteristic, complemented, Hall
8	D₁₀₅₇	—	15	1	no	Hall
9	D₇₅₅	—	21	1	no	Hall
10	C₇×C₁₅₁	D₁₅	1	1	yes	characteristic, complemented, Hall
11	D₄₅₃	—	35	1	no	Hall
12	C₅×C₁₅₁	D₂₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	D₃₅	1	1	yes	characteristic, complemented, Hall
14	D₁₅₁	—	105	1	no	Hall
15	D₁₀₅	—	151	1	no	maximal, Hall
16	C₁₅₁	D₁₀₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₅₁	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	453	1	no	Hall
19	D₂₁	—	755	1	no	Hall
20	C₅×C₇	D₄₅₃	1	1	yes	characteristic, complemented, Hall
21	D₁₅	—	1057	1	no	Hall
22	C₃×C₇	D₇₅₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₁₀₅₇	1	1	yes	characteristic, complemented, Hall
24	D₇	—	2265	1	no	Hall
25	D₅	—	3171	1	no	Hall
26	C₇	D₂₂₆₅	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	5285	1	no	Hall
28	C₅	D₃₁₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅₂₈₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15855	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₃×C₅×C₇×C₁₅₁
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.