Subgroups — C₂⁴×C₄×Dic₁₃ #16769468

Order 3328.

24030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₁₃	C₂	1	2	yes	maximal
2	C₂³×C₄×Dic₁₃	C₂	1	60	yes	maximal, direct product factor
3	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
5	C₂⁴×C₄×C₁₃	C₄	1	32	yes	complemented
6	C₂⁴×C₄×C₁₃	C₂²	1	30	yes	—
7	C₂⁴×Dic₁₃	C₄	1	64	yes	direct product factor
8	C₂⁴×Dic₁₃	C₂²	1	60	yes	—
9	C₂²×C₄×Dic₁₃	C₂²	1	560	yes	direct product factor
10	C₂⁵×C₁₃	C₂×C₄	1	32	yes	—
11	C₂⁵×C₁₃	C₂×C₄	1	16	yes	—
12	C₂⁵×C₁₃	C₂³	1	15	yes	—
13	C₂³×C₄×C₁₃	C₂×C₄	1	480	yes	complemented
14	C₂³×C₄×C₁₃	C₂³	1	140	yes	—
15	C₂³×Dic₁₃	C₂×C₄	1	960	yes	direct product factor
16	C₂³×Dic₁₃	C₂³	1	280	yes	—
17	C₂×C₄×Dic₁₃	C₂³	1	960	yes	direct product factor
18	C₂⁴×C₄²	—	13	1	no	maximal, Sylow
19	C₂⁴×C₁₃	C₄²	1	256	yes	complemented
20	C₂⁴×C₁₃	C₂²×C₄	1	240	yes	—
21	C₂⁴×C₁₃	C₂²×C₄	1	120	yes	—
22	C₂⁴×C₁₃	C₂⁴	1	35	yes	—
23	C₂²×C₄×C₁₃	C₂²×C₄	1	1120	yes	complemented
24	C₂²×C₄×C₁₃	C₂⁴	1	120	yes	—
25	C₂²×Dic₁₃	C₂²×C₄	1	2240	yes	direct product factor
26	C₂²×Dic₁₃	C₂⁴	1	240	yes	—
27	C₄×Dic₁₃	C₂⁴	1	256	yes	direct product factor
28	C₂⁵×C₄	—	13	2	no	—
29	C₂⁵×C₄	D₁₃	1	1	yes	characteristic
30	C₂³×C₄²	—	13	60	no	—
31	C₂³×C₁₃	C₂×C₄²	1	960	yes	complemented
32	C₂³×C₁₃	C₂³×C₄	1	280	yes	—
33	C₂³×C₁₃	C₂³×C₄	1	140	yes	—
34	C₂³×C₁₃	C₂⁵	1	15	yes	—
35	C₂×C₄×C₁₃	C₂³×C₄	1	480	yes	complemented
36	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
37	C₂×Dic₁₃	C₂³×C₄	1	960	yes	direct product factor
38	C₂×Dic₁₃	C₂⁵	1	32	yes	—
39	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
40	C₂⁴×C₄	—	13	64	no	—
41	C₂⁴×C₄	—	13	60	no	—
42	C₂⁴×C₄	Dic₁₃	1	32	yes	direct product factor
43	C₂⁴×C₄	C₂×D₁₃	1	30	yes	—
44	C₂²×C₄²	—	13	560	no	—
45	C₂²×C₁₃	C₂²×C₄²	1	560	yes	complemented
46	C₂²×C₁₃	C₂⁴×C₄	1	60	yes	—
47	C₂²×C₁₃	C₂⁴×C₄	1	30	yes	—
48	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
49	C₄×C₁₃	C₂⁴×C₄	1	32	yes	complemented
50	Dic₁₃	C₂⁴×C₄	1	64	yes	direct product factor
51	C₂⁵	C₄×D₁₃	1	32	yes	—
52	C₂⁵	C₂×Dic₁₃	1	16	yes	—
53	C₂⁵	C₂²×D₁₃	1	15	yes	—
54	C₂³×C₄	—	13	960	no	—
55	C₂³×C₄	—	13	280	no	—
56	C₂³×C₄	C₂×Dic₁₃	1	480	yes	direct product factor
57	C₂³×C₄	C₂²×D₁₃	1	140	yes	—
58	C₂×C₄²	—	13	960	no	—
59	C₂×C₁₃	C₂³×C₄²	1	60	yes	complemented
60	C₂×C₁₃	C₂⁵×C₄	1	2	yes	—
61	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
62	C₂⁴	C₄×Dic₁₃	1	256	yes	direct product factor
63	C₂⁴	C₂×C₄×D₁₃	1	240	yes	—
64	C₂⁴	C₂²×Dic₁₃	1	120	yes	—
65	C₂⁴	C₂³×D₁₃	1	35	yes	—
66	C₂²×C₄	—	13	2240	no	—
67	C₂²×C₄	—	13	240	no	—
68	C₂²×C₄	C₂²×Dic₁₃	1	1120	yes	direct product factor
69	C₂²×C₄	C₂³×D₁₃	1	120	yes	—
70	C₄²	—	13	256	no	—
71	C₁₃	C₂⁴×C₄²	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂×C₄×Dic₁₃	1	960	yes	direct product factor
73	C₂³	C₂²×C₄×D₁₃	1	280	yes	—
74	C₂³	C₂³×Dic₁₃	1	140	yes	—
75	C₂³	C₂⁴×D₁₃	1	15	yes	—
76	C₂×C₄	—	13	960	no	—
77	C₂×C₄	—	13	32	no	—
78	C₂×C₄	C₂³×Dic₁₃	1	480	yes	direct product factor
79	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
80	C₂²	C₂²×C₄×Dic₁₃	1	560	yes	direct product factor
81	C₂²	C₂³×C₄×D₁₃	1	60	yes	—
82	C₂²	C₂⁴×Dic₁₃	1	30	yes	—
83	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
84	C₄	—	13	64	no	—
85	C₄	C₂⁴×Dic₁₃	1	32	yes	direct product factor
86	C₂	C₂³×C₄×Dic₁₃	1	60	yes	direct product factor
87	C₂	C₂⁴×C₄×D₁₃	1	2	yes	—
88	C₂	C₂⁵×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵×C₄	D₁₃
commutator, hypocenter	C₁₃	C₂⁴×C₄²
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂⁵×C₄×C₁₃	C₂
socle, prime radical	C₂⁶×C₁₃	C₂²
cosocle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×Dic₁₃	C₂	direct (N × H)
5. C₂⁴×C₄×C₁₃	C₄	semidirect
7. C₂⁴×Dic₁₃	C₄	direct (N × H)
9. C₂²×C₄×Dic₁₃	C₂²	direct (N × H)
13. C₂³×C₄×C₁₃	C₂×C₄	semidirect
15. C₂³×Dic₁₃	C₂×C₄	direct (N × H)
17. C₂×C₄×Dic₁₃	C₂³	direct (N × H)
19. C₂⁴×C₁₃	C₄²	semidirect
23. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
25. C₂²×Dic₁₃	C₂²×C₄	direct (N × H)
27. C₄×Dic₁₃	C₂⁴	direct (N × H)
31. C₂³×C₁₃	C₂×C₄²	semidirect
35. C₂×C₄×C₁₃	C₂³×C₄	semidirect
37. C₂×Dic₁₃	C₂³×C₄	direct (N × H)
42. C₂⁴×C₄	Dic₁₃	direct (N × H)
45. C₂²×C₁₃	C₂²×C₄²	semidirect
49. C₄×C₁₃	C₂⁴×C₄	semidirect
50. Dic₁₃	C₂⁴×C₄	direct (N × H)
56. C₂³×C₄	C₂×Dic₁₃	direct (N × H)
59. C₂×C₁₃	C₂³×C₄²	semidirect
62. C₂⁴	C₄×Dic₁₃	direct (N × H)
68. C₂²×C₄	C₂²×Dic₁₃	direct (N × H)
71. C₁₃	C₂⁴×C₄²	semidirect
72. C₂³	C₂×C₄×Dic₁₃	direct (N × H)
78. C₂×C₄	C₂³×Dic₁₃	direct (N × H)
80. C₂²	C₂²×C₄×Dic₁₃	direct (N × H)
85. C₄	C₂⁴×Dic₁₃	direct (N × H)
86. C₂	C₂³×C₄×Dic₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₁₃	2
C₂³×C₄×Dic₁₃	2
C₂⁵×C₄×C₁₃	2
C₂⁴×C₄²	13

Subgroups — C24×C4×Dic13 #16769468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×Dic₁₃ #16769468