Subgroups — C₃×C₄²×D₁₃ #11928761

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₃	C₂	1	3	yes	maximal
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×Dic₁₃	C₂	1	3	yes	maximal, complemented
4	C₄²×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂×C₃×Dic₁₃	C₂²	1	3	yes	—
8	C₃×C₄×D₁₃	C₄	1	12	yes	direct product factor
9	C₂×C₄×D₁₃	C₂×C₃	1	3	yes	—
10	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₄×Dic₁₃	C₂×C₃	1	3	yes	complemented
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×C₃×D₁₃	C₂×C₄	1	6	yes	—
14	C₃×C₄×C₁₃	C₂×C₄	1	6	yes	complemented
15	C₃×Dic₁₃	C₂×C₄	1	6	yes	complemented
16	C₂²×D₁₃	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₄×C₁₃	C₂²×C₃	1	3	yes	—
18	C₂×Dic₁₃	C₂²×C₃	1	3	yes	—
19	C₄×D₁₃	C₃×C₄	1	12	yes	direct product factor
20	C₂×C₃×C₄²	—	13	1	no	maximal, Hall
21	C₂×C₃×C₁₃	C₂²×C₄	1	3	yes	—
22	C₃×D₁₃	C₄²	1	4	yes	direct product factor
23	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
24	C₂×D₁₃	C₂×C₃×C₄	1	6	yes	—
25	C₄×C₁₃	C₂×C₃×C₄	1	6	yes	complemented
26	Dic₁₃	C₂×C₃×C₄	1	6	yes	complemented
27	C₂²×C₃×C₄	—	13	3	no	—
28	C₃×C₄²	—	13	3	no	—
29	C₃×C₄²	D₁₃	1	1	yes	characteristic, direct product factor
30	C₃×C₁₃	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₄²	—	13	1	no	Sylow
32	C₂×C₁₃	C₂²×C₃×C₄	1	3	yes	—
33	D₁₃	C₃×C₄²	1	4	yes	direct product factor
34	C₂³×C₃	—	13	1	no	—
35	C₂×C₃×C₄	—	13	3	no	—
36	C₂×C₃×C₄	—	13	12	no	—
37	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
38	C₂²×C₄	—	13	3	no	—
39	C₄²	—	13	3	no	—
40	C₄²	C₃×D₁₃	1	1	yes	characteristic, direct product factor
41	C₁₃	C₂×C₃×C₄²	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₃	—	13	6	no	—
43	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
44	C₃×C₄	—	13	6	no	—
45	C₃×C₄	C₄×D₁₃	1	6	yes	direct product factor
46	C₂³	—	13	1	no	—
47	C₂×C₄	—	13	3	no	—
48	C₂×C₄	—	13	12	no	—
49	C₂×C₄	C₂×C₃×D₁₃	1	3	yes	—
50	C₂×C₃	—	13	4	no	—
51	C₂×C₃	C₂×C₄×D₁₃	1	3	yes	—
52	C₂²	—	13	6	no	—
53	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
54	C₄	—	13	6	no	—
55	C₄	C₃×C₄×D₁₃	1	6	yes	direct product factor
56	C₃	C₄²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	13	4	no	—
58	C₂	C₂×C₃×C₄×D₁₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₄²	D₁₃
commutator, hypocenter	C₁₃	C₂×C₃×C₄²
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×C₃×D₁₃	C₂²
cosocle	C₂²×C₁₃	C₂³×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₁₃	C₂	semidirect
3. C₃×C₄×Dic₁₃	C₂	semidirect
4. C₄²×D₁₃	C₃	direct (N × H)
8. C₃×C₄×D₁₃	C₄	direct (N × H)
10. C₄²×C₁₃	C₂×C₃	semidirect
11. C₄×Dic₁₃	C₂×C₃	semidirect
14. C₃×C₄×C₁₃	C₂×C₄	semidirect
15. C₃×Dic₁₃	C₂×C₄	semidirect
19. C₄×D₁₃	C₃×C₄	direct (N × H)
22. C₃×D₁₃	C₄²	direct (N × H)
25. C₄×C₁₃	C₂×C₃×C₄	semidirect
26. Dic₁₃	C₂×C₃×C₄	semidirect
29. C₃×C₄²	D₁₃	direct (N × H)
30. C₃×C₁₃	C₂×C₄²	semidirect
33. D₁₃	C₃×C₄²	direct (N × H)
40. C₄²	C₃×D₁₃	direct (N × H)
41. C₁₃	C₂×C₃×C₄²	semidirect
45. C₃×C₄	C₄×D₁₃	direct (N × H)
55. C₄	C₃×C₄×D₁₃	direct (N × H)
56. C₃	C₄²×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
C₂×C₃×C₄×D₁₃	2
C₃×C₄²×C₁₃	2
C₃×C₄×Dic₁₃	2
C₄²×D₁₃	3
C₂×C₃×C₄²	13

Subgroups — C3×C42×D13 #11928761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄²×D₁₃ #11928761