Subgroups — D₁₃×D₃₂₅ #30683403

Order 16900.

96 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	C₁₃×D₃₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂₅×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃²×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₆₅	—	5	1	no	maximal
6	C₅⋊(C₁₃⋊D₁₃)	—	5	1	no	—
7	C₁₃×D₆₅	—	5	1	no	—
8	C₅×C₁₃×D₁₃	D₅	1	1	yes	characteristic
9	C₂×D₃₂₅	—	13	1	no	maximal
10	D₁₃×D₂₅	—	13	1	no	maximal
11	C₅×C₁₃²	C₂×D₅	1	1	yes	characteristic
12	D₁₃²	—	25	1	no	Hall
13	C₂×C₁₃×C₂₅	—	13	1	no	—
14	D₃₂₅	—	13	1	no	—
15	D₃₂₅	—	13	1	no	—
16	D₃₂₅	—	26	6	no	—
17	D₃₂₅	D₁₃	1	1	yes	characteristic, direct product factor
18	C₂₅×D₁₃	D₁₃	1	1	yes	characteristic, complemented
19	C₁₃×D₂₅	—	13	1	no	—
20	C₁₃⋊D₁₃	—	25	1	no	—
21	C₁₃×D₁₃	—	25	1	no	—
22	C₁₃×D₁₃	D₂₅	1	1	yes	characteristic, complemented
23	C₁₃×C₂₅	—	2	6	no	—
24	C₁₃×C₂₅	C₂×D₁₃	1	1	yes	characteristic, complemented
25	C₁₃×C₂₅	C₂×D₁₃	1	1	yes	characteristic, complemented
26	C₂×D₆₅	—	65	1	no	—
27	D₅×D₁₃	—	65	1	no	—
28	C₁₃²	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₁₃	—	13	1	no	—
30	D₆₅	—	5	1	no	—
31	D₆₅	—	65	1	no	—
32	D₆₅	—	65	1	no	—
33	D₆₅	—	130	6	no	—
34	C₅×D₁₃	D₆₅	1	1	yes	characteristic
35	D₅×C₁₃	—	65	1	no	—
36	C₂×D₂₅	—	169	1	no	Hall
37	C₅×C₁₃	—	2	6	no	—
38	C₅×C₁₃	D₅×D₁₃	1	1	yes	characteristic
39	C₅×C₁₃	C₂×D₆₅	1	1	yes	characteristic
40	C₂×D₁₃	—	325	1	no	—
41	C₂×D₁₃	—	325	1	no	—
42	C₂×C₂₅	—	13	1	no	—
43	D₂₅	—	13	1	no	—
44	D₂₅	—	169	1	no	—
45	C₂×C₁₃	—	13	1	no	—
46	C₂×C₁₃	—	325	1	no	—
47	D₁₃	—	25	1	no	—
48	D₁₃	—	325	1	no	—
49	D₁₃	—	325	1	no	—
50	D₁₃	—	650	6	no	—
51	D₁₃	D₃₂₅	1	1	yes	characteristic, direct product factor
52	C₂₅	D₁₃²	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₅	—	845	1	no	—
54	C₁₃	—	2	6	no	—
55	C₁₃	D₁₃×D₂₅	1	1	yes	characteristic, complemented
56	C₁₃	C₂×D₃₂₅	1	1	yes	characteristic, complemented
57	C₂×C₅	—	13	1	no	—
58	D₅	—	65	1	no	—
59	D₅	—	845	1	no	—
60	C₅	D₁₃×D₆₅	1	1	yes	characteristic
61	C₂²	—	4225	1	no	Sylow
62	C₂	—	13	1	no	—
63	C₂	—	325	1	no	—
64	C₂	—	4225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₃²×C₂₅	C₂²
Frattini	C₅	D₁₃×D₆₅
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. C₁₃×D₃₂₅	C₂	semidirect
3. C₁₃×C₂₅×D₁₃	C₂	semidirect
4. C₁₃²×C₂₅	C₂²	semidirect
17. D₃₂₅	D₁₃	direct (N × H)
18. C₂₅×D₁₃	D₁₃	semidirect
22. C₁₃×D₁₃	D₂₅	semidirect
24. C₁₃×C₂₅	C₂×D₁₃	semidirect
25. C₁₃×C₂₅	C₂×D₁₃	semidirect
28. C₁₃²	C₂×D₂₅	semidirect
51. D₁₃	D₃₂₅	direct (N × H)
52. C₂₅	D₁₃²	semidirect
55. C₁₃	D₁₃×D₂₅	semidirect
56. C₁₃	C₂×D₃₂₅	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
C₁₃×D₃₂₅	2
C₁₃×C₂₅×D₁₃	2
D₁₃×D₆₅	5
C₂×D₃₂₅	13
D₁₃×D₂₅	13

Subgroups — D13×D325 #30683403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₃₂₅ #30683403