Subgroups — D₇₆₀₅ #29503549

Order 15210.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₅₃₅	—	3	1	no	maximal
3	D₁₅₂₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₆₉	D₃	1	1	yes	characteristic
5	D₈₄₅	—	9	1	no	Hall
6	C₉×C₁₆₉	D₅	1	1	yes	characteristic, complemented, Hall
7	D₅₈₅	—	13	1	no	maximal
8	D₅₀₇	—	15	1	no	—
9	C₅×C₁₆₉	D₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₁₃	D₁₃	1	1	yes	characteristic
11	C₃×C₁₆₉	D₁₅	1	1	yes	characteristic
12	D₁₉₅	—	39	1	no	—
13	D₁₆₉	—	45	1	no	Hall
14	D₁₁₇	—	65	1	no	—
15	C₃×C₅×C₁₃	D₃₉	1	1	yes	characteristic
16	C₁₆₉	D₄₅	1	1	yes	characteristic, complemented, Sylow
17	D₆₅	—	117	1	no	—
18	C₉×C₁₃	D₆₅	1	1	yes	characteristic
19	D₄₅	—	169	1	no	Hall
20	D₃₉	—	195	1	no	—
21	C₅×C₁₃	D₁₁₇	1	1	yes	characteristic
22	C₅×C₉	D₁₆₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₃	D₁₉₅	1	1	yes	characteristic
24	D₁₅	—	507	1	no	—
25	D₁₃	—	585	1	no	—
26	D₉	—	845	1	no	Hall
27	C₃×C₅	D₅₀₇	1	1	yes	characteristic
28	C₁₃	D₅₈₅	1	1	yes	characteristic
29	D₅	—	1521	1	no	Hall
30	C₉	D₈₄₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	2535	1	no	—
32	C₅	D₁₅₂₁	1	1	yes	characteristic, complemented, Sylow
33	C₃	D₂₅₃₅	1	1	yes	characteristic
34	C₂	—	7605	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₆₉	C₂
Frattini	C₃×C₁₃	D₁₉₅
socle	C₃×C₅×C₁₃	D₃₉
LCS	G ▷ C₅×C₉×C₁₆₉
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.