Subgroups — C₂×C₃×D₅×C₁₃² #23778612

Order 10140.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₃²	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₁₃²	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅×C₁₃²	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₃²	—	5	2	no	—
9	C₂×C₃×C₁₃²	D₅	1	1	yes	characteristic, direct product factor
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₅×C₁₃	C₁₃	1	14	yes	maximal, direct product factor
12	C₂²×C₁₃²	—	5	1	no	Hall
13	C₃×C₁₃²	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₁₃	C₂×C₁₃	1	14	yes	complemented
15	C₃×D₅×C₁₃	C₂×C₁₃	1	28	yes	direct product factor
16	C₂×C₁₃²	—	5	2	no	—
17	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, direct product factor
18	C₂×D₅×C₁₃	C₃×C₁₃	1	14	yes	direct product factor
19	C₃×C₅×C₁₃	C₂²×C₁₃	1	14	yes	complemented
20	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₃×C₁₃	—	5	14	no	—
22	C₂×C₅×C₁₃	C₂×C₃×C₁₃	1	14	yes	complemented
23	D₅×C₁₃	C₂×C₃×C₁₃	1	28	yes	direct product factor
24	C₂×C₃×C₁₃	—	5	28	no	—
25	C₂×C₃×C₁₃	D₅×C₁₃	1	14	yes	direct product factor
26	C₅×C₁₃	C₂²×C₃×C₁₃	1	14	yes	complemented
27	C₂×C₃×D₅	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₁₃	—	5	14	no	—
29	C₃×C₁₃	C₂×D₅×C₁₃	1	14	yes	direct product factor
30	C₂×C₃×C₅	C₂×C₁₃²	1	1	yes	characteristic, complemented
31	C₃×D₅	C₂×C₁₃²	1	2	yes	direct product factor
32	C₂×C₁₃	—	5	28	no	—
33	C₂×C₁₃	C₃×D₅×C₁₃	1	14	yes	direct product factor
34	C₂×D₅	C₃×C₁₃²	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₅	C₂²×C₁₃²	1	1	yes	characteristic, complemented, Hall
36	C₁₃	C₂×C₃×D₅×C₁₃	1	14	yes	direct product factor
37	C₂²×C₃	—	5	1	no	Hall
38	C₂×C₅	C₂×C₃×C₁₃²	1	1	yes	characteristic, complemented
39	D₅	C₂×C₃×C₁₃²	1	2	yes	direct product factor
40	C₂×C₃	—	5	2	no	—
41	C₂×C₃	D₅×C₁₃²	1	1	yes	characteristic, direct product factor
42	C₅	C₂²×C₃×C₁₃²	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	5	1	no	Sylow
44	C₃	C₂×D₅×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	5	2	no	—
46	C₂	C₃×D₅×C₁₃²	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃²	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₁₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₃²

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×C₁₃²	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃²	C₂	semidirect
3. C₂×D₅×C₁₃²	C₃	direct (N × H)
4. C₃×C₅×C₁₃²	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. D₅×C₁₃²	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₃²	D₅	direct (N × H)
10. C₅×C₁₃²	C₂²×C₃	semidirect
11. C₂×C₃×D₅×C₁₃	C₁₃	direct (N × H)
13. C₃×C₁₃²	C₂×D₅	direct (N × H)
14. C₂×C₃×C₅×C₁₃	C₂×C₁₃	semidirect
15. C₃×D₅×C₁₃	C₂×C₁₃	direct (N × H)
17. C₂×C₁₃²	C₃×D₅	direct (N × H)
18. C₂×D₅×C₁₃	C₃×C₁₃	direct (N × H)
19. C₃×C₅×C₁₃	C₂²×C₁₃	semidirect
20. C₁₃²	C₂×C₃×D₅	direct (N × H)
22. C₂×C₅×C₁₃	C₂×C₃×C₁₃	semidirect
23. D₅×C₁₃	C₂×C₃×C₁₃	direct (N × H)
25. C₂×C₃×C₁₃	D₅×C₁₃	direct (N × H)
26. C₅×C₁₃	C₂²×C₃×C₁₃	semidirect
27. C₂×C₃×D₅	C₁₃²	direct (N × H)
29. C₃×C₁₃	C₂×D₅×C₁₃	direct (N × H)
30. C₂×C₃×C₅	C₂×C₁₃²	semidirect
31. C₃×D₅	C₂×C₁₃²	direct (N × H)
33. C₂×C₁₃	C₃×D₅×C₁₃	direct (N × H)
34. C₂×D₅	C₃×C₁₃²	direct (N × H)
35. C₃×C₅	C₂²×C₁₃²	semidirect
36. C₁₃	C₂×C₃×D₅×C₁₃	direct (N × H)
38. C₂×C₅	C₂×C₃×C₁₃²	semidirect
39. D₅	C₂×C₃×C₁₃²	direct (N × H)
41. C₂×C₃	D₅×C₁₃²	direct (N × H)
42. C₅	C₂²×C₃×C₁₃²	semidirect
44. C₃	C₂×D₅×C₁₃²	direct (N × H)
46. C₂	C₃×D₅×C₁₃²	direct (N × H)

Subgroups — C2×C3×D5×C132 #23778612

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₅×C₁₃² #23778612