Subgroups — D₄×A₄×C₁₃ #11929253

Order 1248.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×A₄×C₁₃	C₂	1	2	yes	maximal, complemented
2	C₄×A₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×A₄×C₁₃	—	2	2	no	—
5	C₂×A₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₃×D₄×C₁₃	—	4	1	no	maximal
7	C₂⁴×C₁₃	C₂×C₃	1	2	yes	complemented
8	C₂×D₄×C₁₃	—	3	1	no	—
9	C₂×D₄×C₁₃	—	3	1	no	—
10	C₂×D₄×C₁₃	—	3	2	no	—
11	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²×C₃×C₁₃	—	4	2	no	—
13	A₄×C₁₃	D₄	1	1	yes	characteristic, direct product factor
14	C₃×C₄×C₁₃	—	4	1	no	—
15	C₂³×C₁₃	—	2	2	no	—
16	C₂³×C₁₃	—	3	2	no	—
17	C₂³×C₁₃	—	3	2	no	—
18	C₂³×C₁₃	—	6	2	no	—
19	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
20	D₄×C₁₃	—	3	2	no	—
21	D₄×C₁₃	—	3	2	no	—
22	D₄×C₁₃	—	3	1	no	—
23	D₄×C₁₃	A₄	1	1	yes	characteristic, direct product factor
24	C₂×C₄×C₁₃	—	3	1	no	—
25	C₂×C₄×C₁₃	—	3	1	no	—
26	D₄×A₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₃×C₁₃	—	4	1	no	—
28	C₂×C₃×C₁₃	—	8	2	no	—
29	C₂²×C₁₃	—	3	1	no	—
30	C₂²×C₁₃	—	3	1	no	—
31	C₂²×C₁₃	—	3	2	no	—
32	C₂²×C₁₃	—	6	2	no	—
33	C₂²×C₁₃	—	6	2	no	—
34	C₂²×C₁₃	—	6	2	no	—
35	C₂²×C₁₃	—	6	2	no	—
36	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic, complemented
37	C₂²×C₁₃	C₂×A₄	1	2	yes	complemented
38	C₄×C₁₃	—	3	1	no	—
39	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic, complemented
40	C₂²×A₄	C₂×C₁₃	1	2	yes	complemented
41	C₄×A₄	C₂×C₁₃	1	1	yes	characteristic, complemented
42	C₃×C₁₃	—	4	1	no	Hall
43	C₂²×D₄	C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₁₃	—	2	2	no	—
45	C₂×C₁₃	—	3	1	no	—
46	C₂×C₁₃	—	3	1	no	—
47	C₂×C₁₃	—	6	2	no	—
48	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
49	C₂×A₄	—	2	2	no	—
50	C₂×A₄	C₂²×C₁₃	1	1	yes	characteristic
51	C₃×D₄	—	4	1	no	—
52	C₂⁴	C₂×C₃×C₁₃	1	2	yes	complemented
53	C₂×D₄	—	3	1	no	—
54	C₂×D₄	—	3	1	no	—
55	C₂×D₄	—	3	2	no	—
56	C₂²×C₄	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
57	C₁₃	D₄×A₄	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₃	—	4	2	no	—
59	A₄	D₄×C₁₃	1	1	yes	characteristic, direct product factor
60	C₃×C₄	—	4	1	no	—
61	C₂³	—	2	2	no	—
62	C₂³	—	3	2	no	—
63	C₂³	—	3	2	no	—
64	C₂³	—	6	2	no	—
65	C₂³	C₂²×C₃×C₁₃	1	1	yes	characteristic
66	D₄	—	3	2	no	—
67	D₄	—	3	2	no	—
68	D₄	—	3	1	no	—
69	D₄	A₄×C₁₃	1	1	yes	characteristic, direct product factor
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₃	—	4	1	no	—
73	C₂×C₃	—	8	2	no	—
74	C₂²	—	3	1	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	3	2	no	—
77	C₂²	—	6	2	no	—
78	C₂²	—	6	2	no	—
79	C₂²	—	6	2	no	—
80	C₂²	—	6	2	no	—
81	C₂²	C₃×D₄×C₁₃	1	1	yes	characteristic, complemented
82	C₂²	C₂×A₄×C₁₃	1	2	yes	complemented
83	C₄	—	3	1	no	—
84	C₄	C₂×A₄×C₁₃	1	1	yes	characteristic, complemented
85	C₃	—	4	1	no	Sylow
86	C₂	—	2	2	no	—
87	C₂	—	3	1	no	—
88	C₂	—	3	1	no	—
89	C₂	—	6	2	no	—
90	C₂	C₂²×A₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	C₂²×A₄
commutator, cosocle	C₂³	C₂²×C₃×C₁₃
Frattini	C₂	C₂²×A₄×C₁₃
Fitting	C₂²×D₄×C₁₃	C₃
socle	C₂³×C₁₃	C₂²×C₃
hypercenter	D₄×C₁₃	A₄
hypocenter	C₂²	C₃×D₄×C₁₃
LCS	G ▷ C₂³ ▷ C₂²
UCS	C₁ ◁ C₂×C₁₃ ◁ D₄×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×A₄×C₁₃	C₂	semidirect
2. C₄×A₄×C₁₃	C₂	semidirect
3. C₂²×D₄×C₁₃	C₃	semidirect
7. C₂⁴×C₁₃	C₂×C₃	semidirect
11. C₂²×C₄×C₁₃	C₂×C₃	semidirect
13. A₄×C₁₃	D₄	direct (N × H)
23. D₄×C₁₃	A₄	direct (N × H)
26. D₄×A₄	C₁₃	direct (N × H)
36. C₂²×C₁₃	C₃×D₄	semidirect
37. C₂²×C₁₃	C₂×A₄	semidirect
39. C₄×C₁₃	C₂×A₄	semidirect
40. C₂²×A₄	C₂×C₁₃	semidirect
41. C₄×A₄	C₂×C₁₃	semidirect
43. C₂²×D₄	C₃×C₁₃	semidirect
52. C₂⁴	C₂×C₃×C₁₃	semidirect
56. C₂²×C₄	C₂×C₃×C₁₃	semidirect
57. C₁₃	D₄×A₄	direct (N × H)
59. A₄	D₄×C₁₃	direct (N × H)
69. D₄	A₄×C₁₃	direct (N × H)
81. C₂²	C₃×D₄×C₁₃	semidirect
82. C₂²	C₂×A₄×C₁₃	semidirect
84. C₄	C₂×A₄×C₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×A₄×C₁₃	2
C₄×A₄×C₁₃	2
C₂²×D₄×C₁₃	3
C₃×D₄×C₁₃	4
D₄×A₄	13

Subgroups — D4×A4×C13 #11929253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×A₄×C₁₃ #11929253