Subgroups — C₂×D₃×Q₈×C₁₃ #11929292

Order 1248.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×Q₈×C₁₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₃×C₁₃	C₂	1	3	yes	maximal
4	C₂×C₁₃×Dic₆	C₂	1	3	yes	maximal, complemented
5	C₂²×Q₈×C₁₃	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₃×Q₈×C₁₃	C₂²	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
9	C₂×Dic₃×C₁₃	C₂²	1	3	yes	—
10	C₄×D₃×C₁₃	C₂²	1	12	yes	—
11	C₁₃×Dic₆	C₂²	1	12	yes	complemented
12	C₂×Q₈×C₁₃	—	3	8	no	—
13	C₂×Q₈×C₁₃	—	3	3	no	—
14	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic, direct product factor
15	C₂²×C₄×C₁₃	—	3	3	no	—
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₁₃	Q₈	1	4	yes	direct product factor
18	C₂×D₃×C₁₃	C₂³	1	2	yes	—
19	C₃×C₄×C₁₃	C₂³	1	6	yes	—
20	Dic₃×C₁₃	C₂³	1	6	yes	—
21	C₂³×C₁₃	—	3	1	no	—
22	Q₈×C₁₃	—	3	12	no	—
23	Q₈×C₁₃	C₂×D₃	1	4	yes	direct product factor
24	C₂×C₄×C₁₃	—	3	3	no	—
25	C₂×C₄×C₁₃	—	3	12	no	—
26	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
27	C₂×D₃×Q₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	complemented
29	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
30	D₃×C₁₃	C₂×Q₈	1	4	yes	direct product factor
31	C₂²×C₁₃	—	3	4	no	—
32	C₂²×C₁₃	—	3	2	no	—
33	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
34	C₄×C₁₃	—	3	6	no	—
35	C₄×C₁₃	C₂²×D₃	1	6	yes	—
36	C₂×C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
37	D₃×Q₈	C₂×C₁₃	1	8	yes	direct product factor
38	C₂×C₄×D₃	C₂×C₁₃	1	3	yes	—
39	C₂×Dic₆	C₂×C₁₃	1	3	yes	complemented
40	C₃×C₁₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
41	C₂²×Q₈	—	3	1	no	Sylow
42	C₂×C₁₃	—	3	4	no	—
43	C₂×C₁₃	D₃×Q₈	1	2	yes	direct product factor
44	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
45	C₂²×D₃	C₂²×C₁₃	1	1	yes	characteristic
46	C₃×Q₈	C₂²×C₁₃	1	4	yes	complemented
47	C₂×C₃×C₄	C₂²×C₁₃	1	3	yes	—
48	C₂×Dic₃	C₂²×C₁₃	1	3	yes	—
49	C₄×D₃	C₂²×C₁₃	1	12	yes	—
50	Dic₆	C₂²×C₁₃	1	12	yes	complemented
51	C₂×Q₈	—	3	8	no	—
52	C₂×Q₈	—	3	3	no	—
53	C₂×Q₈	D₃×C₁₃	1	1	yes	characteristic, direct product factor
54	C₂²×C₄	—	3	3	no	—
55	C₁₃	C₂×D₃×Q₈	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
57	C₂×D₃	Q₈×C₁₃	1	4	yes	direct product factor
58	C₂×D₃	C₂³×C₁₃	1	2	yes	—
59	C₃×C₄	C₂³×C₁₃	1	6	yes	—
60	Dic₃	C₂³×C₁₃	1	6	yes	—
61	C₂³	—	3	1	no	—
62	Q₈	—	3	12	no	—
63	Q₈	C₂×D₃×C₁₃	1	4	yes	direct product factor
64	C₂×C₄	—	3	3	no	—
65	C₂×C₄	—	3	12	no	—
66	C₂×C₄	C₂×D₃×C₁₃	1	3	yes	—
67	C₂×C₃	C₂×Q₈×C₁₃	1	2	yes	complemented
68	C₂×C₃	C₂⁴×C₁₃	1	1	yes	characteristic
69	D₃	C₂×Q₈×C₁₃	1	4	yes	direct product factor
70	C₂²	—	3	4	no	—
71	C₂²	—	3	2	no	—
72	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
73	C₄	—	3	6	no	—
74	C₄	C₂²×D₃×C₁₃	1	6	yes	—
75	C₃	C₂²×Q₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	4	no	—
77	C₂	D₃×Q₈×C₁₃	1	2	yes	direct product factor
78	C₂	C₂³×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂⁴×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂²×D₃×C₁₃	C₂²
hypercenter	C₂×Q₈×C₁₃	D₃
hypocenter	C₃	C₂²×Q₈×C₁₃
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₃	C₂	semidirect
2. D₃×Q₈×C₁₃	C₂	direct (N × H)
4. C₂×C₁₃×Dic₆	C₂	semidirect
7. C₃×Q₈×C₁₃	C₂²	semidirect
11. C₁₃×Dic₆	C₂²	semidirect
14. C₂×Q₈×C₁₃	D₃	direct (N × H)
17. C₂×D₃×C₁₃	Q₈	direct (N × H)
23. Q₈×C₁₃	C₂×D₃	direct (N × H)
27. C₂×D₃×Q₈	C₁₃	direct (N × H)
28. C₂×C₃×C₁₃	C₂×Q₈	semidirect
30. D₃×C₁₃	C₂×Q₈	direct (N × H)
36. C₂×C₃×Q₈	C₂×C₁₃	semidirect
37. D₃×Q₈	C₂×C₁₃	direct (N × H)
39. C₂×Dic₆	C₂×C₁₃	semidirect
40. C₃×C₁₃	C₂²×Q₈	semidirect
43. C₂×C₁₃	D₃×Q₈	direct (N × H)
46. C₃×Q₈	C₂²×C₁₃	semidirect
50. Dic₆	C₂²×C₁₃	semidirect
53. C₂×Q₈	D₃×C₁₃	direct (N × H)
55. C₁₃	C₂×D₃×Q₈	direct (N × H)
57. C₂×D₃	Q₈×C₁₃	direct (N × H)
63. Q₈	C₂×D₃×C₁₃	direct (N × H)
67. C₂×C₃	C₂×Q₈×C₁₃	semidirect
69. D₃	C₂×Q₈×C₁₃	direct (N × H)
75. C₃	C₂²×Q₈×C₁₃	semidirect
77. C₂	D₃×Q₈×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
C₂×C₃×Q₈×C₁₃	2
D₃×Q₈×C₁₃	2
C₂×C₄×D₃×C₁₃	2
C₂×C₁₃×Dic₆	2
C₂²×Q₈×C₁₃	3
C₂×D₃×Q₈	13

Subgroups — C2×D3×Q8×C13 #11929292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×Q₈×C₁₃ #11929292