Subgroups — C₂²×C₄×D₃×C₁₃ #11929286

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₄×C₁₃	D₃
commutator, hypocenter	C₃	C₂³×C₄×C₁₃
Frattini	C₂	C₂³×D₃×C₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle	C₂³×C₃×C₁₃	C₂²
prime radical	C₂³×D₃×C₁₃	C₂
cosocle	C₂×C₃	C₂⁴×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
2. C₂²×C₃×C₄×C₁₃	C₂	semidirect
3. C₂²×Dic₃×C₁₃	C₂	semidirect
4. C₂×C₄×D₃×C₁₃	C₂	direct (N × H)
7. C₂²×D₃×C₁₃	C₄	direct (N × H)
9. C₂×C₃×C₄×C₁₃	C₂²	semidirect
10. C₂×Dic₃×C₁₃	C₂²	semidirect
11. C₄×D₃×C₁₃	C₂²	direct (N × H)
15. C₂²×C₄×C₁₃	D₃	direct (N × H)
16. C₂²×C₃×C₁₃	C₂×C₄	semidirect
18. C₂×D₃×C₁₃	C₂×C₄	direct (N × H)
20. C₃×C₄×C₁₃	C₂³	semidirect
21. Dic₃×C₁₃	C₂³	semidirect
27. C₂×C₄×C₁₃	C₂×D₃	direct (N × H)
28. C₂²×C₄×D₃	C₁₃	direct (N × H)
29. C₂×C₃×C₁₃	C₂²×C₄	semidirect
31. D₃×C₁₃	C₂²×C₄	direct (N × H)
34. C₂²×C₁₃	C₄×D₃	direct (N × H)
37. C₄×C₁₃	C₂²×D₃	direct (N × H)
39. C₂²×C₃×C₄	C₂×C₁₃	semidirect
40. C₂²×Dic₃	C₂×C₁₃	semidirect
41. C₂×C₄×D₃	C₂×C₁₃	direct (N × H)
42. C₃×C₁₃	C₂³×C₄	semidirect
45. C₂×C₁₃	C₂×C₄×D₃	direct (N × H)
48. C₂²×D₃	C₄×C₁₃	direct (N × H)
50. C₂×C₃×C₄	C₂²×C₁₃	semidirect
51. C₂×Dic₃	C₂²×C₁₃	semidirect
52. C₄×D₃	C₂²×C₁₃	direct (N × H)
56. C₂²×C₄	D₃×C₁₃	direct (N × H)
57. C₁₃	C₂²×C₄×D₃	direct (N × H)
58. C₂²×C₃	C₂×C₄×C₁₃	semidirect
60. C₂×D₃	C₂×C₄×C₁₃	direct (N × H)
62. C₃×C₄	C₂³×C₁₃	semidirect
63. Dic₃	C₂³×C₁₃	semidirect
69. C₂×C₄	C₂×D₃×C₁₃	direct (N × H)
70. C₂×C₃	C₂²×C₄×C₁₃	semidirect
72. D₃	C₂²×C₄×C₁₃	direct (N × H)
75. C₂²	C₄×D₃×C₁₃	direct (N × H)
78. C₄	C₂²×D₃×C₁₃	direct (N × H)
79. C₃	C₂³×C₄×C₁₃	semidirect
81. C₂	C₂×C₄×D₃×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
C₂³×D₃×C₁₃	2
C₂²×C₃×C₄×C₁₃	2
C₂²×Dic₃×C₁₃	2
C₂×C₄×D₃×C₁₃	2
C₂³×C₄×C₁₃	3
C₂²×C₄×D₃	13

Subgroups — C22×C4×D3×C13 #11929286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₃×C₁₃ #11929286