Subgroups — C₄²×D₃×C₁₃ #11928847

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×C₁₃	C₂	1	3	yes	maximal
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₃×C₁₃	C₂	1	3	yes	maximal, complemented
4	C₂×C₄²×C₁₃	—	3	1	no	maximal, Hall
5	C₂²×D₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂×Dic₃×C₁₃	C₂²	1	3	yes	—
8	C₄×D₃×C₁₃	C₄	1	12	yes	direct product factor
9	C₂²×C₄×C₁₃	—	3	3	no	—
10	C₄²×C₁₃	—	3	3	no	—
11	C₄²×C₁₃	D₃	1	1	yes	characteristic, direct product factor
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×D₃×C₁₃	C₂×C₄	1	6	yes	—
14	C₃×C₄×C₁₃	C₂×C₄	1	6	yes	complemented
15	Dic₃×C₁₃	C₂×C₄	1	6	yes	complemented
16	C₂³×C₁₃	—	3	1	no	—
17	C₂×C₄×C₁₃	—	3	3	no	—
18	C₂×C₄×C₁₃	—	3	12	no	—
19	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
20	C₄²×D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₁₃	C₂²×C₄	1	3	yes	—
22	D₃×C₁₃	C₄²	1	4	yes	direct product factor
23	C₂²×C₁₃	—	3	6	no	—
24	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
25	C₄×C₁₃	—	3	6	no	—
26	C₄×C₁₃	C₄×D₃	1	6	yes	direct product factor
27	C₂×C₄×D₃	C₂×C₁₃	1	3	yes	—
28	C₃×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₄×Dic₃	C₂×C₁₃	1	3	yes	complemented
30	C₃×C₁₃	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₄²	—	3	1	no	Sylow
32	C₂×C₁₃	—	3	4	no	—
33	C₂×C₁₃	C₂×C₄×D₃	1	3	yes	—
34	C₂²×D₃	C₂²×C₁₃	1	1	yes	characteristic
35	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
36	C₂×Dic₃	C₂²×C₁₃	1	3	yes	—
37	C₄×D₃	C₄×C₁₃	1	12	yes	direct product factor
38	C₂²×C₄	—	3	3	no	—
39	C₄²	—	3	3	no	—
40	C₄²	D₃×C₁₃	1	1	yes	characteristic, direct product factor
41	C₁₃	C₄²×D₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
43	C₂×D₃	C₂×C₄×C₁₃	1	6	yes	—
44	C₃×C₄	C₂×C₄×C₁₃	1	6	yes	complemented
45	Dic₃	C₂×C₄×C₁₃	1	6	yes	complemented
46	C₂³	—	3	1	no	—
47	C₂×C₄	—	3	3	no	—
48	C₂×C₄	—	3	12	no	—
49	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
50	C₂×C₃	C₂²×C₄×C₁₃	1	3	yes	—
51	D₃	C₄²×C₁₃	1	4	yes	direct product factor
52	C₂²	—	3	6	no	—
53	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
54	C₄	—	3	6	no	—
55	C₄	C₄×D₃×C₁₃	1	6	yes	direct product factor
56	C₃	C₂×C₄²×C₁₃	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	3	4	no	—
58	C₂	C₂×C₄×D₃×C₁₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²×C₁₃	D₃
commutator, hypocenter	C₃	C₂×C₄²×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×D₃×C₁₃	C₂²
cosocle	C₂²×C₃	C₂³×C₁₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₄²×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₁₃	C₂	semidirect
3. C₄×Dic₃×C₁₃	C₂	semidirect
8. C₄×D₃×C₁₃	C₄	direct (N × H)
11. C₄²×C₁₃	D₃	direct (N × H)
14. C₃×C₄×C₁₃	C₂×C₄	semidirect
15. Dic₃×C₁₃	C₂×C₄	semidirect
20. C₄²×D₃	C₁₃	direct (N × H)
22. D₃×C₁₃	C₄²	direct (N × H)
26. C₄×C₁₃	C₄×D₃	direct (N × H)
28. C₃×C₄²	C₂×C₁₃	semidirect
29. C₄×Dic₃	C₂×C₁₃	semidirect
30. C₃×C₁₃	C₂×C₄²	semidirect
37. C₄×D₃	C₄×C₁₃	direct (N × H)
40. C₄²	D₃×C₁₃	direct (N × H)
41. C₁₃	C₄²×D₃	direct (N × H)
44. C₃×C₄	C₂×C₄×C₁₃	semidirect
45. Dic₃	C₂×C₄×C₁₃	semidirect
51. D₃	C₄²×C₁₃	direct (N × H)
55. C₄	C₄×D₃×C₁₃	direct (N × H)
56. C₃	C₂×C₄²×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×C₁₃	2
C₃×C₄²×C₁₃	2
C₄×Dic₃×C₁₃	2
C₂×C₄²×C₁₃	3
C₄²×D₃	13

Subgroups — C42×D3×C13 #11928847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×D₃×C₁₃ #11928847