Subgroups — C₅×D₂₀₆₅ #35207648

Order 20650.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₀₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₄₁₃	—	5	1	no	maximal
4	C₅×D₂₉₅	—	7	1	no	maximal, Hall
5	C₅×C₇×C₅₉	—	2	2	no	—
6	C₅×C₇×C₅₉	D₅	1	1	yes	characteristic, complemented
7	C₅×C₇×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×C₅₉	D₇	1	1	yes	characteristic, complemented, Hall
9	D₄₁₃	—	5	1	no	Hall
10	D₂₉₅	—	7	1	no	—
11	C₅×D₅₉	—	35	1	no	—
12	C₇×C₅₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
13	C₅×D₃₅	—	59	1	no	maximal, Hall
14	C₅×C₅₉	—	2	2	no	—
15	C₅×C₅₉	C₅×D₇	1	1	yes	characteristic, complemented
16	C₅×C₅₉	D₃₅	1	1	yes	characteristic, complemented
17	C₅²×C₇	D₅₉	1	1	yes	characteristic, complemented, Hall
18	D₅₉	—	35	1	no	Hall
19	D₃₅	—	59	1	no	—
20	C₅×D₇	—	295	1	no	—
21	C₅₉	C₅×D₃₅	1	1	yes	characteristic, complemented, Sylow
22	C₅×D₅	—	413	1	no	Hall
23	C₅×C₇	—	2	2	no	—
24	C₅×C₇	C₅×D₅₉	1	1	yes	characteristic, complemented
25	C₅×C₇	D₂₉₅	1	1	yes	characteristic, complemented
26	C₅²	D₄₁₃	1	1	yes	characteristic, complemented, Sylow
27	D₇	—	295	1	no	Hall
28	C₂×C₅	—	2065	1	no	—
29	D₅	—	413	1	no	—
30	C₇	C₅×D₂₉₅	1	1	yes	characteristic, complemented, Sylow
31	C₅	—	2	2	no	—
32	C₅	C₅×D₄₁₃	1	1	yes	characteristic, complemented
33	C₅	D₂₀₆₅	1	1	yes	characteristic, direct product factor
34	C₂	—	2065	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₀₆₅
commutator, cosocle, hypocenter	C₅×C₇×C₅₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₅₉	C₂
LCS	G ▷ C₅×C₇×C₅₉
UCS	C₁ ◁ C₅

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.