Subgroups — C₂×C₃×C₄×Dic₁₃ #11928812

Order 1248.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₄	D₁₃
commutator, hypocenter	C₁₃	C₂×C₃×C₄²
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle, prime radical	C₂³×C₃×C₁₃	C₂²
cosocle	C₂²×C₁₃	C₂³×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×Dic₁₃	C₂	direct (N × H)
4. C₂×C₄×Dic₁₃	C₃	direct (N × H)
6. C₂×C₃×C₄×C₁₃	C₄	semidirect
8. C₂×C₃×Dic₁₃	C₄	direct (N × H)
12. C₄×Dic₁₃	C₂×C₃	direct (N × H)
16. C₃×C₄×C₁₃	C₂×C₄	semidirect
17. C₃×Dic₁₃	C₂×C₄	direct (N × H)
19. C₂×C₄×C₁₃	C₃×C₄	semidirect
21. C₂×Dic₁₃	C₃×C₄	direct (N × H)
24. C₂×C₃×C₁₃	C₄²	semidirect
30. C₄×C₁₃	C₂×C₃×C₄	semidirect
31. Dic₁₃	C₂×C₃×C₄	direct (N × H)
35. C₃×C₁₃	C₂×C₄²	semidirect
37. C₂×C₁₃	C₃×C₄²	semidirect
43. C₂×C₃×C₄	Dic₁₃	direct (N × H)
48. C₁₃	C₂×C₃×C₄²	semidirect
53. C₃×C₄	C₂×Dic₁₃	direct (N × H)
57. C₂×C₄	C₃×Dic₁₃	direct (N × H)
59. C₂×C₃	C₄×Dic₁₃	direct (N × H)
66. C₄	C₂×C₃×Dic₁₃	direct (N × H)
67. C₃	C₂×C₄×Dic₁₃	direct (N × H)
68. C₂	C₃×C₄×Dic₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
C₂²×C₃×Dic₁₃	2
C₃×C₄×Dic₁₃	2
C₂×C₄×Dic₁₃	3
C₂×C₃×C₄²	13

Subgroups — C2×C3×C4×Dic13 #11928812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×Dic₁₃ #11928812