Subgroups — C₂×C₄×Dic₃×C₁₃ #11928898

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×Dic₃×C₁₃	C₂	1	2	yes	maximal
3	C₄×Dic₃×C₁₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄²×C₁₃	—	3	1	no	maximal, 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×Dic₃×C₁₃	C₄	1	8	yes	direct product factor
9	C₂×Dic₃×C₁₃	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₃	—	3	2	no	—
11	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic
12	C₄²×C₁₃	—	3	4	no	—
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	Dic₃×C₁₃	C₂×C₄	1	8	yes	direct product factor
18	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	3	8	no	—
20	C₂×C₄×C₁₃	—	3	4	no	—
21	C₂×C₄×C₁₃	Dic₃	1	4	yes	direct product factor
22	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
23	C₂×C₄×Dic₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, 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	C₄×D₃	1	4	yes	—
28	C₂²×C₁₃	C₂×Dic₃	1	2	yes	—
29	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
30	C₄×C₁₃	—	3	8	no	—
31	C₄×C₁₃	C₂×Dic₃	1	4	yes	direct product factor
32	C₂²×C₃×C₄	C₂×C₁₃	1	1	yes	characteristic
33	C₂²×Dic₃	C₂×C₁₃	1	2	yes	—
34	C₄×Dic₃	C₂×C₁₃	1	4	yes	direct product factor
35	C₃×C₁₃	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
36	C₂×C₄²	—	3	1	no	Sylow
37	C₂×C₁₃	C₄×Dic₃	1	4	yes	direct product factor
38	C₂×C₁₃	C₂×C₄×D₃	1	2	yes	—
39	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
40	C₂³×C₃	C₂²×C₁₃	1	1	yes	characteristic
41	C₂×C₃×C₄	C₄×C₁₃	1	4	yes	complemented
42	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
43	C₂×Dic₃	C₄×C₁₃	1	8	yes	direct product factor
44	C₂×Dic₃	C₂²×C₁₃	1	4	yes	—
45	C₂²×C₄	—	3	2	no	—
46	C₂²×C₄	D₃×C₁₃	1	1	yes	characteristic
47	C₄²	—	3	4	no	—
48	C₁₃	C₂×C₄×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₃	C₂×C₄×C₁₃	1	4	yes	—
50	C₂²×C₃	C₂×C₄×C₁₃	1	2	yes	—
51	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
52	C₃×C₄	C₂×C₄×C₁₃	1	4	yes	complemented
53	Dic₃	C₂×C₄×C₁₃	1	8	yes	direct product factor
54	C₂³	C₂×D₃×C₁₃	1	1	yes	characteristic
55	C₂×C₄	—	3	8	no	—
56	C₂×C₄	—	3	4	no	—
57	C₂×C₄	Dic₃×C₁₃	1	4	yes	direct product factor
58	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
59	C₂×C₃	C₄²×C₁₃	1	4	yes	complemented
60	C₂×C₃	C₂²×C₄×C₁₃	1	2	yes	—
61	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
62	C₂²	C₄×D₃×C₁₃	1	4	yes	—
63	C₂²	C₂×Dic₃×C₁₃	1	2	yes	—
64	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
65	C₄	—	3	8	no	—
66	C₄	C₂×Dic₃×C₁₃	1	4	yes	direct product factor
67	C₃	C₂×C₄²×C₁₃	1	1	yes	characteristic, complemented, Sylow
68	C₂	C₄×Dic₃×C₁₃	1	4	yes	direct product factor
69	C₂	C₂×C₄×D₃×C₁₃	1	2	yes	—
70	C₂	C₂²×Dic₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄×C₁₃	D₃
commutator, hypocenter	C₃	C₂×C₄²×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle, prime radical	C₂³×C₃×C₁₃	C₂²
cosocle	C₂²×C₃	C₂³×C₁₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₄×Dic₃×C₁₃	C₂	direct (N × H)
6. C₂×C₃×C₄×C₁₃	C₄	semidirect
8. C₂×Dic₃×C₁₃	C₄	direct (N × H)
16. C₃×C₄×C₁₃	C₂×C₄	semidirect
17. Dic₃×C₁₃	C₂×C₄	direct (N × H)
21. C₂×C₄×C₁₃	Dic₃	direct (N × H)
23. C₂×C₄×Dic₃	C₁₃	direct (N × H)
24. C₂×C₃×C₁₃	C₄²	semidirect
31. C₄×C₁₃	C₂×Dic₃	direct (N × H)
34. C₄×Dic₃	C₂×C₁₃	direct (N × H)
35. C₃×C₁₃	C₂×C₄²	semidirect
37. C₂×C₁₃	C₄×Dic₃	direct (N × H)
41. C₂×C₃×C₄	C₄×C₁₃	semidirect
43. C₂×Dic₃	C₄×C₁₃	direct (N × H)
48. C₁₃	C₂×C₄×Dic₃	direct (N × H)
52. C₃×C₄	C₂×C₄×C₁₃	semidirect
53. Dic₃	C₂×C₄×C₁₃	direct (N × H)
57. C₂×C₄	Dic₃×C₁₃	direct (N × H)
59. C₂×C₃	C₄²×C₁₃	semidirect
66. C₄	C₂×Dic₃×C₁₃	direct (N × H)
67. C₃	C₂×C₄²×C₁₃	semidirect
68. C₂	C₄×Dic₃×C₁₃	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×Dic₃×C₁₃	2
C₄×Dic₃×C₁₃	2
C₂×C₄²×C₁₃	3
C₂×C₄×Dic₃	13

Subgroups — C2×C4×Dic3×C13 #11928898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₃×C₁₃ #11928898