Subgroups — D₈₃₈₅ #30680796

Order 16770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₇₉₅	—	3	1	no	maximal, Hall
3	D₁₆₇₇	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₄₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₆₄₅	—	13	1	no	maximal, Hall
7	D₅₅₉	—	15	1	no	Hall
8	C₃×C₅×C₄₃	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₄₃	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₂₁₅	—	39	1	no	Hall
11	D₁₉₅	—	43	1	no	maximal, Hall
12	D₁₂₉	—	65	1	no	Hall
13	C₅×C₄₃	D₃₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₃	D₄₃	1	1	yes	characteristic, complemented, Hall
15	D₆₅	—	129	1	no	Hall
16	C₃×C₄₃	D₆₅	1	1	yes	characteristic, complemented, Hall
17	D₄₃	—	195	1	no	Hall
18	D₃₉	—	215	1	no	Hall
19	C₅×C₁₃	D₁₂₉	1	1	yes	characteristic, complemented, Hall
20	C₄₃	D₁₉₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₃	D₂₁₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	559	1	no	Hall
23	D₁₃	—	645	1	no	Hall
24	C₃×C₅	D₅₅₉	1	1	yes	characteristic, complemented, Hall
25	C₁₃	D₆₄₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	1677	1	no	Hall
27	D₃	—	2795	1	no	Hall
28	C₅	D₁₆₇₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₂₇₉₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	8385	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₃×C₄₃	C₂
LCS	G ▷ C₃×C₅×C₁₃×C₄₃
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.