Subgroups — (C₁₃⋊D₁₃)⋊D₂₅ #30683404

Order 16900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₃₂₅	C₂	1	2	yes	maximal, complemented
2	C₂₅×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₆₅⋊D₁₃	—	5	1	no	maximal
5	C₁₃×D₆₅	—	5	2	no	—
6	C₅×C₁₃⋊D₁₃	D₅	1	1	yes	characteristic
7	D₁₃×D₂₅	—	13	2	no	maximal
8	C₅×C₁₃²	C₂×D₅	1	1	yes	characteristic
9	D₁₃²	—	25	1	no	Hall
10	D₃₂₅	D₁₃	1	2	yes	complemented
11	C₂₅×D₁₃	—	13	2	no	—
12	C₂₅×D₁₃	—	26	6	no	—
13	C₁₃×D₂₅	—	13	2	no	—
14	C₁₃⋊D₁₃	D₂₅	1	1	yes	characteristic, complemented
15	C₁₃×D₁₃	—	25	2	no	—
16	C₁₃×C₂₅	—	2	6	no	—
17	C₁₃×C₂₅	C₂×D₁₃	1	2	yes	complemented
18	D₅×D₁₃	—	65	2	no	—
19	C₁₃²	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
20	D₆₅	—	5	2	no	—
21	C₅×D₁₃	—	13	2	no	—
22	C₅×D₁₃	—	26	6	no	—
23	D₅×C₁₃	—	65	2	no	—
24	C₂×D₂₅	—	169	1	no	Hall
25	C₅×C₁₃	—	2	6	no	—
26	C₅×C₁₃	D₅×D₁₃	1	2	yes	—
27	C₂×D₁₃	—	325	2	no	—
28	C₂×C₂₅	—	169	1	no	—
29	D₂₅	—	13	2	no	—
30	C₂×C₁₃	—	325	2	no	—
31	D₁₃	—	13	2	no	—
32	D₁₃	—	25	2	no	—
33	D₁₃	—	26	6	no	—
34	C₂₅	D₁₃²	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	845	1	no	—
36	C₁₃	—	2	6	no	—
37	C₁₃	D₁₃×D₂₅	1	2	yes	complemented
38	C₂×C₅	—	169	1	no	—
39	D₅	—	65	2	no	—
40	C₅	D₆₅⋊D₁₃	1	1	yes	characteristic
41	C₂²	—	4225	1	no	Sylow
42	C₂	—	325	2	no	—
43	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₃²×C₂₅	C₂²
Frattini	C₅	D₆₅⋊D₁₃
socle	C₅×C₁₃²	C₂×D₅
LCS	G ▷ C₁₃²×C₂₅
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.