Subgroups — D₅×D₆₅ #13049941

Order 1300.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₆₅	—	5	1	no	maximal
6	D₅×D₁₃	—	5	1	no	maximal
7	C₂×C₅×C₁₃	—	5	1	no	—
8	D₆₅	—	5	1	no	—
9	D₆₅	—	5	1	no	—
10	D₆₅	—	10	2	no	—
11	D₆₅	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₁₃	—	5	1	no	—
13	D₅×C₁₃	D₅	1	1	yes	characteristic, complemented
14	D₅²	—	13	1	no	maximal, Hall
15	C₅×C₁₃	—	2	2	no	—
16	C₅×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented
17	C₅×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented
18	C₂×D₁₃	—	25	1	no	Hall
19	C₅⋊D₅	—	13	1	no	—
20	C₅×D₅	—	13	1	no	—
21	C₅×D₅	D₁₃	1	1	yes	characteristic, complemented
22	C₂×C₁₃	—	5	1	no	—
23	D₁₃	—	5	1	no	—
24	D₁₃	—	25	1	no	—
25	C₅²	C₂×D₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×D₅	—	65	1	no	—
27	C₂×D₅	—	65	1	no	—
28	C₁₃	D₅²	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	5	1	no	—
30	C₂×C₅	—	65	1	no	—
31	D₅	—	13	1	no	—
32	D₅	—	65	1	no	—
33	D₅	—	65	1	no	—
34	D₅	—	130	2	no	—
35	D₅	D₆₅	1	1	yes	characteristic, direct product factor
36	C₅	—	2	2	no	—
37	C₅	D₅×D₁₃	1	1	yes	characteristic, complemented
38	C₅	C₂×D₆₅	1	1	yes	characteristic, complemented
39	C₂²	—	325	1	no	Sylow
40	C₂	—	5	1	no	—
41	C₂	—	65	1	no	—
42	C₂	—	325	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₃	C₂²
LCS	G ▷ C₅²×C₁₃
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.