Subgroups — C₂×C₁₃×C₂₅×D₁₃ #30683409

Order 16900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₅×D₁₃	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×C₅×C₁₃×D₁₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₅×C₁₃²	C₂×C₅	1	1	yes	characteristic
6	C₅×C₁₃×D₁₃	C₂×C₅	1	2	yes	—
7	C₂²×C₁₃×C₂₅	—	13	1	no	maximal
8	C₂×C₂₅×D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
9	C₅×C₁₃²	C₂²×C₅	1	1	yes	characteristic
10	C₂×C₁₃×D₁₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₃×C₂₅	—	2	6	no	—
12	C₂×C₁₃×C₂₅	—	13	2	no	—
13	C₂×C₁₃×C₂₅	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂×C₁₃×C₂₅	C₂×C₁₃	1	1	yes	characteristic, complemented
15	C₂₅×D₁₃	C₂×C₁₃	1	2	yes	direct product factor
16	C₂×C₁₃²	C₂×C₂₅	1	1	yes	characteristic, complemented
17	C₁₃×D₁₃	C₂×C₂₅	1	2	yes	direct product factor
18	C₁₃×C₂₅	—	2	6	no	—
19	C₁₃×C₂₅	C₂×D₁₃	1	1	yes	characteristic, direct product factor
20	C₁₃×C₂₅	C₂²×C₁₃	1	1	yes	characteristic, complemented
21	C₂²×C₅×C₁₃	—	13	1	no	—
22	C₂×C₅×D₁₃	C₅×C₁₃	1	1	yes	characteristic
23	C₁₃²	C₂²×C₂₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₅×C₁₃	—	2	6	no	—
25	C₂×C₅×C₁₃	—	13	2	no	—
26	C₂×C₅×C₁₃	C₅×D₁₃	1	1	yes	characteristic
27	C₂×C₅×C₁₃	C₂×C₅×C₁₃	1	1	yes	characteristic
28	C₅×D₁₃	C₂×C₅×C₁₃	1	2	yes	—
29	C₂²×C₂₅	—	13	1	no	Hall
30	C₅×C₁₃	—	2	6	no	—
31	C₅×C₁₃	C₂×C₅×D₁₃	1	1	yes	characteristic
32	C₅×C₁₃	C₂²×C₅×C₁₃	1	1	yes	characteristic
33	C₂²×C₁₃	—	13	1	no	—
34	C₂×D₁₃	C₁₃×C₂₅	1	1	yes	characteristic, direct product factor
35	C₂×C₂₅	—	13	2	no	—
36	C₂×C₂₅	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
37	C₂×C₁₃	—	2	6	no	—
38	C₂×C₁₃	—	13	2	no	—
39	C₂×C₁₃	C₂₅×D₁₃	1	1	yes	characteristic, direct product factor
40	C₂×C₁₃	C₂×C₁₃×C₂₅	1	1	yes	characteristic, complemented
41	D₁₃	C₂×C₁₃×C₂₅	1	2	yes	direct product factor
42	C₂₅	C₂×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	—	13	1	no	—
44	C₁₃	—	2	6	no	—
45	C₁₃	C₂×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor
46	C₁₃	C₂²×C₁₃×C₂₅	1	1	yes	characteristic, complemented
47	C₂×C₅	—	13	2	no	—
48	C₂×C₅	C₅×C₁₃×D₁₃	1	1	yes	characteristic
49	C₅	C₂×C₅×C₁₃×D₁₃	1	1	yes	characteristic
50	C₂²	—	13	1	no	Sylow
51	C₂	—	13	2	no	—
52	C₂	C₁₃×C₂₅×D₁₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₂₅×D₁₃	C₂	direct (N × H)
2. C₂×C₁₃²×C₂₅	C₂	semidirect
3. C₁₃²×C₂₅	C₂²	semidirect
8. C₂×C₂₅×D₁₃	C₁₃	direct (N × H)
10. C₂×C₁₃×D₁₃	C₂₅	direct (N × H)
13. C₂×C₁₃×C₂₅	D₁₃	direct (N × H)
14. C₂×C₁₃×C₂₅	C₂×C₁₃	semidirect
15. C₂₅×D₁₃	C₂×C₁₃	direct (N × H)
16. C₂×C₁₃²	C₂×C₂₅	semidirect
17. C₁₃×D₁₃	C₂×C₂₅	direct (N × H)
19. C₁₃×C₂₅	C₂×D₁₃	direct (N × H)
20. C₁₃×C₂₅	C₂²×C₁₃	semidirect
23. C₁₃²	C₂²×C₂₅	semidirect
34. C₂×D₁₃	C₁₃×C₂₅	direct (N × H)
36. C₂×C₂₅	C₁₃×D₁₃	direct (N × H)
39. C₂×C₁₃	C₂₅×D₁₃	direct (N × H)
40. C₂×C₁₃	C₂×C₁₃×C₂₅	semidirect
41. D₁₃	C₂×C₁₃×C₂₅	direct (N × H)
42. C₂₅	C₂×C₁₃×D₁₃	direct (N × H)
45. C₁₃	C₂×C₂₅×D₁₃	direct (N × H)
46. C₁₃	C₂²×C₁₃×C₂₅	semidirect
52. C₂	C₁₃×C₂₅×D₁₃	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×C₂₅×D₁₃	2
C₂×C₁₃²×C₂₅	2
C₂×C₅×C₁₃×D₁₃	5
C₂²×C₁₃×C₂₅	13
C₂×C₂₅×D₁₃	13

Subgroups — C2×C13×C25×D13 #30683409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₂₅×D₁₃ #30683409