Subgroups — D₁₆₁₈₅ #44569166

Order 32370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₃₉₅	—	3	1	no	maximal, Hall
3	D₃₂₃₇	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₈₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₈₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₂₄₅	—	13	1	no	maximal, Hall
7	D₁₀₇₉	—	15	1	no	Hall
8	C₃×C₅×C₈₃	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₈₃	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₄₁₅	—	39	1	no	Hall
11	D₂₄₉	—	65	1	no	Hall
12	C₅×C₈₃	D₃₉	1	1	yes	characteristic, complemented, Hall
13	D₁₉₅	—	83	1	no	maximal, Hall
14	C₃×C₈₃	D₆₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₃	D₈₃	1	1	yes	characteristic, complemented, Hall
16	D₈₃	—	195	1	no	Hall
17	D₆₅	—	249	1	no	Hall
18	C₈₃	D₁₉₅	1	1	yes	characteristic, complemented, Sylow
19	D₃₉	—	415	1	no	Hall
20	C₅×C₁₃	D₂₄₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₃	D₄₁₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	1079	1	no	Hall
23	D₁₃	—	1245	1	no	Hall
24	C₃×C₅	D₁₀₇₉	1	1	yes	characteristic, complemented, Hall
25	C₁₃	D₁₂₄₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	3237	1	no	Hall
27	D₃	—	5395	1	no	Hall
28	C₅	D₃₂₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅₃₉₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	16185	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₃×C₈₃	C₂
LCS	G ▷ C₃×C₅×C₁₃×C₈₃
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.