Subgroups — D₂₅×C₁₃⋊D₁₃ #30683402

Order 16900.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₃²×C₂₅	C₂²
Frattini	C₅	D₅×C₁₃⋊D₁₃
socle	C₅×C₁₃²	C₂×D₅
LCS	G ▷ C₁₃²×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊D₃₂₅	C₂	semidirect
2. C₁₃²×D₂₅	C₂	semidirect
3. C₂₅×C₁₃⋊D₁₃	C₂	semidirect
4. C₁₃²×C₂₅	C₂²	semidirect
14. C₁₃×D₂₅	D₁₃	semidirect
17. C₁₃⋊D₁₃	D₂₅	direct (N × H)
18. C₁₃×C₂₅	C₂×D₁₃	semidirect
20. C₁₃²	C₂×D₂₅	semidirect
29. D₂₅	C₁₃⋊D₁₃	direct (N × H)
33. C₂₅	C₂×C₁₃⋊D₁₃	semidirect
35. C₁₃	D₁₃×D₂₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃⋊D₃₂₅	2
C₁₃²×D₂₅	2
C₂₅×C₁₃⋊D₁₃	2
D₅×C₁₃⋊D₁₃	5
D₁₃×D₂₅	13

Subgroups — D25×C13⋊D13 #30683402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₅×C₁₃⋊D₁₃ #30683402