Subgroups — C₂×C₄×A₄×C₁₃ #11929252

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

	subgroup	G/H
center, hypercenter	C₂×C₄×C₁₃	A₄
commutator, hypocenter	C₂²	C₂×C₃×C₄×C₁₃
Frattini	C₂	C₂²×A₄×C₁₃
Fitting	C₂³×C₄×C₁₃	C₃
socle	C₂⁴×C₁₃	C₂×C₃
prime radical	C₂²×A₄×C₁₃	C₂
cosocle	C₂³	C₂²×C₃×C₁₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₄×A₄×C₁₃	C₂	direct (N × H)
3. C₂³×C₄×C₁₃	C₃	semidirect
4. C₂×A₄×C₁₃	C₄	direct (N × H)
11. C₂²×C₄×C₁₃	C₂×C₃	semidirect
13. A₄×C₁₃	C₂×C₄	direct (N × H)
18. C₂³×C₁₃	C₃×C₄	semidirect
25. C₂×C₄×C₁₃	A₄	direct (N × H)
26. C₂×C₄×A₄	C₁₃	direct (N × H)
36. C₂²×C₁₃	C₂×C₃×C₄	semidirect
39. C₄×C₁₃	C₂×A₄	direct (N × H)
41. C₄×A₄	C₂×C₁₃	direct (N × H)
43. C₂³×C₄	C₃×C₁₃	semidirect
47. C₂×C₁₃	C₄×A₄	direct (N × H)
49. C₂×A₄	C₄×C₁₃	direct (N × H)
56. C₂²×C₄	C₂×C₃×C₁₃	semidirect
57. C₁₃	C₂×C₄×A₄	direct (N × H)
59. A₄	C₂×C₄×C₁₃	direct (N × H)
64. C₂³	C₃×C₄×C₁₃	semidirect
71. C₂×C₄	A₄×C₁₃	direct (N × H)
81. C₂²	C₂×C₃×C₄×C₁₃	semidirect
84. C₄	C₂×A₄×C₁₃	direct (N × H)
89. C₂	C₄×A₄×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
C₂²×A₄×C₁₃	2
C₄×A₄×C₁₃	2
C₂³×C₄×C₁₃	3
C₂×C₃×C₄×C₁₃	4
C₂×C₄×A₄	13

Subgroups — C2×C4×A4×C13 #11929252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×A₄×C₁₃ #11929252