Subgroups — D₁₆₄₈₅ #45682136

Order 32970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₄₉₅	—	3	1	no	maximal, Hall
3	D₃₂₉₇	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₅₇	D₃	1	1	yes	characteristic, complemented, Hall
5	D₂₃₅₅	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₅₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₇	D₇	1	1	yes	characteristic, complemented, Hall
8	D₁₀₉₉	—	15	1	no	Hall
9	D₇₈₅	—	21	1	no	Hall
10	C₇×C₁₅₇	D₁₅	1	1	yes	characteristic, complemented, Hall
11	D₄₇₁	—	35	1	no	Hall
12	C₅×C₁₅₇	D₂₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₇	D₃₅	1	1	yes	characteristic, complemented, Hall
14	D₁₅₇	—	105	1	no	Hall
15	D₁₀₅	—	157	1	no	maximal, Hall
16	C₁₅₇	D₁₀₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₅₇	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	471	1	no	Hall
19	D₂₁	—	785	1	no	Hall
20	C₅×C₇	D₄₇₁	1	1	yes	characteristic, complemented, Hall
21	D₁₅	—	1099	1	no	Hall
22	C₃×C₇	D₇₈₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₁₀₉₉	1	1	yes	characteristic, complemented, Hall
24	D₇	—	2355	1	no	Hall
25	D₅	—	3297	1	no	Hall
26	C₇	D₂₃₅₅	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	5495	1	no	Hall
28	C₅	D₃₂₉₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅₄₉₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	16485	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₁₅₇	C₂
LCS	G ▷ C₃×C₅×C₇×C₁₅₇
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.