Subgroups — C₂²×C₄×D₁₃⋊C₃ #11929131

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₁₃⋊C₃	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₄×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂³×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	C₂²×D₁₃⋊C₃	C₄	1	8	yes	direct product factor
8	C₂²×D₁₃⋊C₃	C₂²	1	6	yes	—
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	6	yes	complemented
10	C₂×Dic₁₃⋊C₃	C₂²	1	6	yes	complemented
11	C₄×D₁₃⋊C₃	C₂²	1	16	yes	direct product factor
12	C₂³×D₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂²×Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₄×D₁₃	C₂×C₃	1	12	yes	complemented
16	C₂²×C₁₃⋊C₃	C₂×C₄	1	4	yes	complemented
17	C₂²×C₁₃⋊C₃	C₂³	1	3	yes	—
18	C₂×D₁₃⋊C₃	C₂×C₄	1	24	yes	direct product factor
19	C₂×D₁₃⋊C₃	C₂³	1	4	yes	—
20	C₄×C₁₃⋊C₃	C₂³	1	4	yes	complemented
21	Dic₁₃⋊C₃	C₂³	1	4	yes	complemented
22	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
23	C₂²×D₁₃	C₃×C₄	1	8	yes	complemented
24	C₂²×D₁₃	C₂²×C₃	1	6	yes	—
25	C₂×C₄×C₁₃	C₂²×C₃	1	6	yes	complemented
26	C₂×Dic₁₃	C₂²×C₃	1	6	yes	complemented
27	C₄×D₁₃	C₂²×C₃	1	16	yes	complemented
28	C₂³×C₃×C₄	—	13	1	no	maximal, Hall
29	C₂×C₁₃⋊C₃	C₂²×C₄	1	6	yes	complemented
30	C₂×C₁₃⋊C₃	C₂⁴	1	1	yes	characteristic
31	D₁₃⋊C₃	C₂²×C₄	1	8	yes	direct product factor
32	C₂²×C₁₃	C₂×C₃×C₄	1	4	yes	complemented
33	C₂²×C₁₃	C₂³×C₃	1	3	yes	—
34	C₂×D₁₃	C₂×C₃×C₄	1	24	yes	complemented
35	C₂×D₁₃	C₂³×C₃	1	4	yes	—
36	C₄×C₁₃	C₂³×C₃	1	4	yes	complemented
37	Dic₁₃	C₂³×C₃	1	4	yes	complemented
38	C₂⁴×C₃	—	13	1	no	—
39	C₂²×C₃×C₄	—	13	12	no	—
40	C₂²×C₃×C₄	—	13	1	no	—
41	C₂²×C₃×C₄	—	13	1	no	—
42	C₁₃⋊C₃	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
43	C₂³×C₄	—	13	1	no	Sylow
44	C₂×C₁₃	C₂²×C₃×C₄	1	6	yes	complemented
45	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
46	D₁₃	C₂²×C₃×C₄	1	8	yes	complemented
47	C₂³×C₃	—	13	8	no	—
48	C₂³×C₃	—	13	6	no	—
49	C₂³×C₃	—	13	1	no	—
50	C₂×C₃×C₄	—	13	16	no	—
51	C₂×C₃×C₄	—	13	6	no	—
52	C₂×C₃×C₄	—	13	6	no	—
53	C₂⁴	—	13	1	no	—
54	C₂²×C₄	—	13	1	no	—
55	C₂²×C₄	—	13	12	no	—
56	C₂²×C₄	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
57	C₁₃	C₂³×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	—	13	4	no	—
59	C₂²×C₃	—	13	24	no	—
60	C₂²×C₃	—	13	4	no	—
61	C₂²×C₃	—	13	3	no	—
62	C₃×C₄	—	13	4	no	—
63	C₃×C₄	—	13	4	no	—
64	C₂³	—	13	8	no	—
65	C₂³	—	13	6	no	—
66	C₂³	C₂×D₁₃⋊C₃	1	1	yes	characteristic
67	C₂×C₄	—	13	6	no	—
68	C₂×C₄	—	13	16	no	—
69	C₂×C₄	C₂×D₁₃⋊C₃	1	6	yes	direct product factor
70	C₂×C₃	—	13	8	no	—
71	C₂×C₃	—	13	6	no	—
72	C₂×C₃	—	13	1	no	—
73	C₂²	—	13	24	no	—
74	C₂²	—	13	4	no	—
75	C₂²	C₄×D₁₃⋊C₃	1	4	yes	direct product factor
76	C₂²	C₂²×D₁₃⋊C₃	1	3	yes	—
77	C₄	—	13	4	no	—
78	C₄	C₂²×D₁₃⋊C₃	1	4	yes	direct product factor
79	C₃	—	13	1	no	Sylow
80	C₂	—	13	8	no	—
81	C₂	C₂×C₄×D₁₃⋊C₃	1	6	yes	direct product factor
82	C₂	C₂³×D₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂³×C₃×C₄
Frattini	C₂	C₂³×D₁₃⋊C₃
Fitting	C₂²×C₄×C₁₃	C₂×C₃
socle	C₂³×C₁₃	C₂²×C₃
prime radical	C₂³×D₁₃⋊C₃	C₂
cosocle	C₂×C₁₃	C₂⁴×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₃⋊C₃	C₂	semidirect
3. C₂²×Dic₁₃⋊C₃	C₂	semidirect
4. C₂×C₄×D₁₃⋊C₃	C₂	direct (N × H)
5. C₂²×C₄×D₁₃	C₃	semidirect
7. C₂²×D₁₃⋊C₃	C₄	direct (N × H)
9. C₂×C₄×C₁₃⋊C₃	C₂²	semidirect
10. C₂×Dic₁₃⋊C₃	C₂²	semidirect
11. C₄×D₁₃⋊C₃	C₂²	direct (N × H)
13. C₂²×C₄×C₁₃	C₂×C₃	semidirect
14. C₂²×Dic₁₃	C₂×C₃	semidirect
15. C₂×C₄×D₁₃	C₂×C₃	semidirect
16. C₂²×C₁₃⋊C₃	C₂×C₄	semidirect
18. C₂×D₁₃⋊C₃	C₂×C₄	direct (N × H)
20. C₄×C₁₃⋊C₃	C₂³	semidirect
21. Dic₁₃⋊C₃	C₂³	semidirect
23. C₂²×D₁₃	C₃×C₄	semidirect
25. C₂×C₄×C₁₃	C₂²×C₃	semidirect
26. C₂×Dic₁₃	C₂²×C₃	semidirect
27. C₄×D₁₃	C₂²×C₃	semidirect
29. C₂×C₁₃⋊C₃	C₂²×C₄	semidirect
31. D₁₃⋊C₃	C₂²×C₄	direct (N × H)
32. C₂²×C₁₃	C₂×C₃×C₄	semidirect
34. C₂×D₁₃	C₂×C₃×C₄	semidirect
36. C₄×C₁₃	C₂³×C₃	semidirect
37. Dic₁₃	C₂³×C₃	semidirect
42. C₁₃⋊C₃	C₂³×C₄	semidirect
44. C₂×C₁₃	C₂²×C₃×C₄	semidirect
46. D₁₃	C₂²×C₃×C₄	semidirect
56. C₂²×C₄	D₁₃⋊C₃	direct (N × H)
57. C₁₃	C₂³×C₃×C₄	semidirect
69. C₂×C₄	C₂×D₁₃⋊C₃	direct (N × H)
75. C₂²	C₄×D₁₃⋊C₃	direct (N × H)
78. C₄	C₂²×D₁₃⋊C₃	direct (N × H)
81. C₂	C₂×C₄×D₁₃⋊C₃	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×D₁₃⋊C₃	2
C₂²×C₄×C₁₃⋊C₃	2
C₂²×Dic₁₃⋊C₃	2
C₂×C₄×D₁₃⋊C₃	2
C₂²×C₄×D₁₃	3
C₂³×C₃×C₄	13

Subgroups — C22×C4×D13⋊C3 #11929131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₁₃⋊C₃ #11929131