Subgroups — C₅×C₅⋊(D₁₃⋊C₃) #14519607

Order 1950.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊(D₁₃⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×D₁₃⋊C₃	—	5	1	no	maximal
5	C₅²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₅×C₁₃⋊C₃	—	2	2	no	—
7	C₅×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented
8	C₅×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₅×D₅	—	13	1	no	maximal, Hall
10	D₆₅	C₃×C₅	1	1	yes	characteristic, complemented
11	C₅×D₁₃	—	5	1	no	—
12	D₁₃⋊C₃	—	5	1	no	Hall
13	C₃×C₅²	—	13	1	no	Hall
14	C₅×C₁₃	—	2	2	no	—
15	C₅×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
16	C₅×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
17	C₅×D₅	—	13	1	no	Hall
18	C₁₃⋊C₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅	—	65	1	no	—
20	C₃×D₅	—	13	1	no	—
21	D₁₃	—	5	1	no	Hall
22	C₅²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₅	—	13	1	no	—
24	C₃×C₅	—	13	1	no	—
25	C₃×C₅	—	26	2	no	—
26	C₁₃	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	65	1	no	—
28	D₅	—	13	1	no	—
29	C₂×C₃	—	65	1	no	Hall
30	C₅	—	2	2	no	—
31	C₅	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₅	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
33	C₃	—	13	1	no	Sylow
34	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₅⋊(D₁₃⋊C₃)
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₁₃
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.