Subgroups — D₅₀₀₅ #23756331

Order 10010.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₀₁	—	5	1	no	maximal, Hall
3	D₇₁₅	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented, Hall
5	D₄₅₅	—	11	1	no	maximal, Hall
6	D₃₈₅	—	13	1	no	maximal, Hall
7	C₅×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₅×C₇×C₁₁	D₁₃	1	1	yes	characteristic, complemented, Hall
10	D₁₄₃	—	35	1	no	Hall
11	D₉₁	—	55	1	no	Hall
12	D₇₇	—	65	1	no	Hall
13	C₁₁×C₁₃	D₃₅	1	1	yes	characteristic, complemented, Hall
14	D₆₅	—	77	1	no	Hall
15	D₅₅	—	91	1	no	Hall
16	C₇×C₁₃	D₅₅	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₁	D₆₅	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	143	1	no	Hall
19	C₅×C₁₃	D₇₇	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₁	D₉₁	1	1	yes	characteristic, complemented, Hall
21	C₅×C₇	D₁₄₃	1	1	yes	characteristic, complemented, Hall
22	D₁₃	—	385	1	no	Hall
23	D₁₁	—	455	1	no	Hall
24	D₇	—	715	1	no	Hall
25	C₁₃	D₃₈₅	1	1	yes	characteristic, complemented, Sylow
26	C₁₁	D₄₅₅	1	1	yes	characteristic, complemented, Sylow
27	D₅	—	1001	1	no	Hall
28	C₇	D₇₁₅	1	1	yes	characteristic, complemented, Sylow
29	C₅	D₁₀₀₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	5005	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₅×C₇×C₁₁×C₁₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.