Subgroups — C₂×C₁₃×Dic₁₂ #11928881

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Dic₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×Dic₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×Q₁₆	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₃×C₁₃	—	2	2	no	—
7	C₁₃×Dic₆	—	2	2	no	—
8	C₁₃×Dic₆	C₂²	1	4	yes	—
9	C₃×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×Q₈×C₁₃	—	3	2	no	—
11	C₁₃×Q₁₆	—	3	4	no	—
12	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic
13	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
14	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
15	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	Dic₃×C₁₃	—	2	4	no	—
17	Q₈×C₁₃	—	3	4	no	—
18	Q₈×C₁₃	—	6	2	no	—
19	C₂×C₄×C₁₃	—	6	2	no	—
20	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
21	C₈×C₁₃	C₂×D₃	1	2	yes	—
22	C₂×Dic₁₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₃×C₁₃	Q₁₆	1	2	yes	complemented
24	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₁₃	D₁₂	1	1	yes	characteristic
26	C₄×C₁₃	—	6	4	no	—
27	C₄×C₁₃	D₁₂	1	1	yes	characteristic
28	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
29	C₂×Dic₆	C₂×C₁₃	1	2	yes	—
30	C₂×C₃×C₈	C₂×C₁₃	1	1	yes	characteristic
31	Dic₁₂	C₂×C₁₃	1	4	yes	direct product factor
32	C₃×C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
33	C₂×Q₁₆	—	3	1	no	Sylow
34	C₂×C₁₃	Dic₁₂	1	2	yes	direct product factor
35	C₂×C₁₃	C₂×D₁₂	1	1	yes	characteristic
36	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
37	C₂×Dic₃	—	2	2	no	—
38	Dic₆	—	2	2	no	—
39	Dic₆	C₂²×C₁₃	1	4	yes	—
40	C₃×C₈	C₂²×C₁₃	1	2	yes	—
41	C₂×Q₈	—	3	2	no	—
42	Q₁₆	—	3	4	no	—
43	C₂×C₈	D₃×C₁₃	1	1	yes	characteristic
44	C₁₃	C₂×Dic₁₂	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²×C₃	D₄×C₁₃	1	1	yes	characteristic
46	C₃×C₄	D₄×C₁₃	1	1	yes	characteristic
47	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
48	Dic₃	—	2	4	no	—
49	Q₈	—	3	4	no	—
50	Q₈	—	6	2	no	—
51	C₂×C₄	—	6	2	no	—
52	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
53	C₈	C₂×D₃×C₁₃	1	2	yes	—
54	C₂×C₃	C₁₃×Q₁₆	1	2	yes	complemented
55	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
56	C₂²	C₁₃×D₁₂	1	1	yes	characteristic
57	C₄	—	6	4	no	—
58	C₄	C₁₃×D₁₂	1	1	yes	characteristic
59	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
60	C₃	C₂×C₁₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂	C₁₃×Dic₁₂	1	2	yes	direct product factor
62	C₂	C₂×C₁₃×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	D₄
hypercenter	C₂×C₈×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₁₃×Dic₁₂	C₂	direct (N × H)
22. C₂×Dic₁₂	C₁₃	direct (N × H)
23. C₂×C₃×C₁₃	Q₁₆	semidirect
31. Dic₁₂	C₂×C₁₃	direct (N × H)
32. C₃×C₁₃	C₂×Q₁₆	semidirect
34. C₂×C₁₃	Dic₁₂	direct (N × H)
44. C₁₃	C₂×Dic₁₂	direct (N × H)
54. C₂×C₃	C₁₃×Q₁₆	semidirect
60. C₃	C₂×C₁₃×Q₁₆	semidirect
61. C₂	C₁₃×Dic₁₂	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×C₁₃×Dic₆	2
C₂×C₃×C₈×C₁₃	2
C₁₃×Dic₁₂	2
C₂×C₁₃×Q₁₆	3
C₂×Dic₁₂	13

Subgroups — C2×C13×Dic12 #11928881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×Dic₁₂ #11928881