Subgroups — C₂×C₁₃×D₃₂₅ #30683406

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, direct product factor
2	C₂×C₁₃²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×D₆₅	—	5	1	no	maximal
5	C₂×C₅×C₁₃²	D₅	1	1	yes	characteristic
6	C₁₃×D₆₅	—	5	2	no	—
7	C₂×D₃₂₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₁₃×D₂₅	—	13	1	no	maximal
9	C₅×C₁₃²	C₂×D₅	1	1	yes	characteristic
10	C₂×C₁₃×D₁₃	—	25	1	no	Hall
11	C₂×C₁₃×C₂₅	—	2	6	no	—
12	C₂×C₁₃×C₂₅	D₁₃	1	1	yes	characteristic, complemented
13	C₂×C₁₃×C₂₅	C₂×C₁₃	1	1	yes	characteristic, complemented
14	D₃₂₅	C₂×C₁₃	1	2	yes	direct product factor
15	C₁₃×D₂₅	—	13	2	no	—
16	C₂×C₁₃²	D₂₅	1	1	yes	characteristic, complemented
17	C₁₃×D₁₃	—	25	2	no	—
18	C₁₃×C₂₅	—	2	6	no	—
19	C₁₃×C₂₅	C₂×D₁₃	1	1	yes	characteristic, complemented
20	C₁₃×C₂₅	C₂²×C₁₃	1	1	yes	characteristic, complemented
21	C₂×D₆₅	—	5	1	no	—
22	C₂×D₅×C₁₃	—	65	1	no	—
23	C₁₃²	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₅×C₁₃	—	2	6	no	—
25	C₂×C₅×C₁₃	D₅×C₁₃	1	1	yes	characteristic
26	C₂×C₅×C₁₃	D₆₅	1	1	yes	characteristic
27	D₆₅	—	5	2	no	—
28	D₅×C₁₃	—	65	2	no	—
29	C₂×D₂₅	—	13	1	no	Hall
30	C₅×C₁₃	—	2	6	no	—
31	C₅×C₁₃	C₂×D₅×C₁₃	1	1	yes	characteristic
32	C₅×C₁₃	C₂×D₆₅	1	1	yes	characteristic
33	C₂²×C₁₃	—	325	1	no	—
34	C₂×D₁₃	—	25	1	no	—
35	C₂×C₂₅	C₁₃×D₁₃	1	1	yes	characteristic, complemented
36	D₂₅	—	13	2	no	—
37	C₂×C₁₃	—	2	6	no	—
38	C₂×C₁₃	—	325	2	no	—
39	C₂×C₁₃	C₁₃×D₂₅	1	1	yes	characteristic, complemented
40	C₂×C₁₃	D₃₂₅	1	1	yes	characteristic, direct product factor
41	D₁₃	—	25	2	no	—
42	C₂₅	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	65	1	no	—
44	C₁₃	—	2	6	no	—
45	C₁₃	C₂×C₁₃×D₂₅	1	1	yes	characteristic, complemented
46	C₁₃	C₂×D₃₂₅	1	1	yes	characteristic, direct product factor
47	C₂×C₅	C₁₃×D₆₅	1	1	yes	characteristic
48	D₅	—	65	2	no	—
49	C₅	C₂×C₁₃×D₆₅	1	1	yes	characteristic
50	C₂²	—	325	1	no	Sylow
51	C₂	—	325	2	no	—
52	C₂	C₁₃×D₃₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₃₂₅
commutator, cosocle, hypocenter	C₁₃×C₂₅	C₂²×C₁₃
Frattini	C₅	C₂×C₁₃×D₆₅
Fitting	C₂×C₁₃²×C₂₅	C₂
socle	C₂×C₅×C₁₃²	D₅
LCS	G ▷ C₁₃×C₂₅
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₃₂₅	C₂	direct (N × H)
2. C₂×C₁₃²×C₂₅	C₂	semidirect
3. C₁₃²×C₂₅	C₂²	semidirect
7. C₂×D₃₂₅	C₁₃	direct (N × H)
12. C₂×C₁₃×C₂₅	D₁₃	semidirect
13. C₂×C₁₃×C₂₅	C₂×C₁₃	semidirect
14. D₃₂₅	C₂×C₁₃	direct (N × H)
16. C₂×C₁₃²	D₂₅	semidirect
19. C₁₃×C₂₅	C₂×D₁₃	semidirect
20. C₁₃×C₂₅	C₂²×C₁₃	semidirect
23. C₁₃²	C₂×D₂₅	semidirect
35. C₂×C₂₅	C₁₃×D₁₃	semidirect
39. C₂×C₁₃	C₁₃×D₂₅	semidirect
40. C₂×C₁₃	D₃₂₅	direct (N × H)
42. C₂₅	C₂×C₁₃×D₁₃	semidirect
45. C₁₃	C₂×C₁₃×D₂₅	semidirect
46. C₁₃	C₂×D₃₂₅	direct (N × H)
52. C₂	C₁₃×D₃₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₃₂₅	2
C₂×C₁₃²×C₂₅	2
C₂×C₁₃×D₆₅	5
C₂×D₃₂₅	13
C₂×C₁₃×D₂₅	13

Subgroups — C2×C13×D325 #30683406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₃₂₅ #30683406