Subgroups — C₃×C₄×C₁₃×C₆₁⋊C₃ #43269751

Order 28548.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₆₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄×C₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₆₁⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₁₃×C₆₁⋊C₃	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic
7	C₄×C₁₃×C₆₁	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₃×C₆₁⋊C₃	C₃×C₄	1	3	yes	direct product factor
10	C₃×C₄×C₆₁⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₃×C₆₁	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃×C₆₁⋊C₃	C₂×C₁₃	1	1	yes	characteristic
13	C₁₃×C₆₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×C₄×C₆₁	C₃×C₁₃	1	1	yes	characteristic, complemented
15	C₄×C₆₁⋊C₃	C₃×C₁₃	1	3	yes	direct product factor
16	C₃×C₆₁⋊C₃	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃²×C₄×C₁₃	—	61	1	no	maximal, Hall
18	C₂×C₃×C₆₁	C₂×C₃×C₁₃	1	1	yes	characteristic
19	C₂×C₆₁⋊C₃	C₂×C₃×C₁₃	1	3	yes	—
20	C₄×C₆₁	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃²×C₁₃	—	61	1	no	—
22	C₃×C₆₁	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented
23	C₆₁⋊C₃	C₃×C₄×C₁₃	1	3	yes	direct product factor
24	C₃×C₄×C₁₃	—	61	3	no	—
25	C₃×C₄×C₁₃	C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
26	C₂×C₆₁	C₂×C₃²×C₁₃	1	1	yes	characteristic
27	C₃²×C₁₃	—	61	1	no	Hall
28	C₂×C₃×C₁₃	—	61	3	no	—
29	C₂×C₃×C₁₃	C₂×C₆₁⋊C₃	1	1	yes	characteristic
30	C₆₁	C₃²×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₃	C₃×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₃	—	61	3	no	—
33	C₃×C₁₃	C₄×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
34	C₃²×C₄	—	61	1	no	Hall
35	C₂×C₁₃	C₂×C₃×C₆₁⋊C₃	1	1	yes	characteristic
36	C₂×C₃²	—	61	1	no	—
37	C₁₃	C₃×C₄×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₄	—	61	3	no	—
39	C₃×C₄	C₁₃×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	61	1	no	Sylow
41	C₂×C₃	—	61	3	no	—
42	C₂×C₃	C₂×C₁₃×C₆₁⋊C₃	1	1	yes	characteristic
43	C₄	C₃×C₁₃×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	61	3	no	—
45	C₃	C₄×C₁₃×C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×C₁₃×C₆₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₃	C₆₁⋊C₃
commutator, hypocenter	C₆₁	C₃²×C₄×C₁₃
Frattini	C₂	C₂×C₃×C₁₃×C₆₁⋊C₃
Fitting	C₃×C₄×C₁₃×C₆₁	C₃
socle	C₂×C₃×C₁₃×C₆₁	C₂×C₃
prime radical	C₂×C₃×C₁₃×C₆₁⋊C₃	C₂
cosocle	C₂×C₆₁	C₂×C₃²×C₁₃
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₃×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₆₁⋊C₃	C₃	direct (N × H)
3. C₃×C₄×C₁₃×C₆₁	C₃	semidirect
4. C₃×C₁₃×C₆₁⋊C₃	C₄	direct (N × H)
7. C₄×C₁₃×C₆₁	C₃²	semidirect
8. C₃×C₁₃×C₆₁	C₃×C₄	semidirect
9. C₁₃×C₆₁⋊C₃	C₃×C₄	direct (N × H)
10. C₃×C₄×C₆₁⋊C₃	C₁₃	direct (N × H)
13. C₁₃×C₆₁	C₃²×C₄	semidirect
14. C₃×C₄×C₆₁	C₃×C₁₃	semidirect
15. C₄×C₆₁⋊C₃	C₃×C₁₃	direct (N × H)
16. C₃×C₆₁⋊C₃	C₄×C₁₃	direct (N × H)
20. C₄×C₆₁	C₃²×C₁₃	semidirect
22. C₃×C₆₁	C₃×C₄×C₁₃	semidirect
23. C₆₁⋊C₃	C₃×C₄×C₁₃	direct (N × H)
25. C₃×C₄×C₁₃	C₆₁⋊C₃	direct (N × H)
30. C₆₁	C₃²×C₄×C₁₃	semidirect
31. C₄×C₁₃	C₃×C₆₁⋊C₃	direct (N × H)
33. C₃×C₁₃	C₄×C₆₁⋊C₃	direct (N × H)
37. C₁₃	C₃×C₄×C₆₁⋊C₃	direct (N × H)
39. C₃×C₄	C₁₃×C₆₁⋊C₃	direct (N × H)
43. C₄	C₃×C₁₃×C₆₁⋊C₃	direct (N × H)
45. C₃	C₄×C₁₃×C₆₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃×C₆₁⋊C₃	2
C₄×C₁₃×C₆₁⋊C₃	3
C₃×C₄×C₁₃×C₆₁	3
C₃×C₄×C₆₁⋊C₃	13
C₃²×C₄×C₁₃	61

Subgroups — C3×C4×C13×C61⋊C3 #43269751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₁₃×C₆₁⋊C₃ #43269751