Subgroups — (C₂×AGL(1,𝔽₁₃))⋊C₄ #11928186

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,𝔽₁₃)	C₂	1	2	yes	maximal
2	C₂×C₄×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
3	(C₂×#261)⋊C₄	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂²×D₁₃⋊C₃	C₂²	1	1	yes	characteristic
5	C₂×AGL(1,𝔽₁₃)	—	2	2	no	—
6	C₂×AGL(1,𝔽₁₃)	—	2	2	no	—
7	C₂×AGL(1,𝔽₁₃)	C₄	1	4	yes	complemented
8	C₂×C₄×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented
9	C₂×Dic₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented
10	C₄×D₁₃⋊C₃	—	2	2	no	—
11	C₂²×#261	C₂×C₃	1	2	yes	—
12	C₂×C₄×D₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
14	C₂×D₁₃⋊C₃	C₂×C₄	1	2	yes	—
15	C₂×D₁₃⋊C₃	D₄	1	1	yes	characteristic
16	C₂×D₁₃⋊C₃	D₄	1	2	yes	—
17	C₂×D₁₃⋊C₃	Q₈	1	1	yes	characteristic
18	AGL(1,𝔽₁₃)	—	2	4	no	—
19	C₄×C₁₃⋊C₃	—	2	1	no	—
20	Dic₁₃⋊C₃	—	2	1	no	—
21	C₂²×D₁₃	C₂²×C₃	1	1	yes	characteristic
22	C₂×#261	—	2	2	no	—
23	C₂×#261	—	2	2	no	—
24	C₂×#261	C₃×C₄	1	4	yes	complemented
25	C₂×C₄×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
26	C₂×Dic₁₃	C₃×C₄	1	1	yes	characteristic, complemented
27	C₄×D₁₃	—	2	2	no	—
28	C₃×#95	—	13	1	no	maximal, Hall
29	C₂×C₁₃⋊C₃	C₄²	1	1	yes	characteristic
30	C₂×C₁₃⋊C₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₁₃⋊C₃	C₄⋊C₄	1	1	yes	characteristic
32	D₁₃⋊C₃	C₂²⋊C₄	1	2	yes	—
33	D₁₃⋊C₃	C₄⋊C₄	1	2	yes	—
34	C₂²×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
35	C₂×D₁₃	C₂×C₃×C₄	1	2	yes	—
36	C₂×D₁₃	C₃×D₄	1	1	yes	characteristic
37	C₂×D₁₃	C₃×D₄	1	2	yes	—
38	C₂×D₁₃	C₃×Q₈	1	1	yes	characteristic
39	#261	—	2	4	no	—
40	C₄×C₁₃	—	2	1	no	—
41	Dic₁₃	—	2	1	no	—
42	C₂²×C₃×C₄	—	13	1	no	—
43	C₂²×C₃×C₄	—	13	2	no	—
44	C₁₃⋊C₃	#95	1	1	yes	characteristic, complemented, Hall
45	#95	—	13	1	no	Sylow
46	C₂×C₁₃	C₃×C₄²	1	1	yes	characteristic
47	C₂×C₁₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₁₃	C₃×C₄⋊C₄	1	1	yes	characteristic
49	D₁₃	C₃×C₂²⋊C₄	1	2	yes	—
50	D₁₃	C₃×C₄⋊C₄	1	2	yes	—
51	C₂³×C₃	—	13	1	no	—
52	C₂×C₃×C₄	—	13	1	no	—
53	C₂×C₃×C₄	—	13	4	no	—
54	C₂×C₃×C₄	—	13	1	no	—
55	C₂×C₃×C₄	—	26	2	no	—
56	C₂×C₃×C₄	—	26	2	no	—
57	C₂×C₃×C₄	—	26	2	no	—
58	C₂²×C₄	—	13	2	no	—
59	C₂²×C₄	—	13	1	no	—
60	C₁₃	C₃×#95	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	—	13	2	no	—
62	C₂²×C₃	—	13	1	no	—
63	C₂²×C₃	—	13	2	no	—
64	C₂²×C₃	—	13	1	no	—
65	C₂²×C₃	—	13	1	no	—
66	C₃×C₄	—	26	1	no	—
67	C₃×C₄	—	26	1	no	—
68	C₃×C₄	—	26	4	no	—
69	C₂³	—	13	1	no	—
70	C₂×C₄	—	13	4	no	—
71	C₂×C₄	—	13	1	no	—
72	C₂×C₄	—	26	2	no	—
73	C₂×C₄	—	26	2	no	—
74	C₂×C₄	—	26	2	no	—
75	C₂×C₄	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
76	C₂×C₃	—	13	2	no	—
77	C₂×C₃	—	13	2	no	—
78	C₂×C₃	—	13	1	no	—
79	C₂×C₃	—	13	1	no	—
80	C₂×C₃	—	13	1	no	—
81	C₂²	—	13	2	no	—
82	C₂²	—	13	1	no	—
83	C₂²	—	13	1	no	—
84	C₂²	—	13	2	no	—
85	C₂²	C₂×AGL(1,𝔽₁₃)	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	26	4	no	—
88	C₄	—	26	1	no	—
89	C₃	—	13	1	no	Sylow
90	C₂	—	13	2	no	—
91	C₂	—	13	2	no	—
92	C₂	C₄×AGL(1,𝔽₁₃)	1	1	yes	characteristic
93	C₂	C₄⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic
94	C₂	(C₂²⋊#261)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×AGL(1,𝔽₁₃)
commutator	C₂×C₁₃	C₃×C₄²
Fitting	C₂×C₄×C₁₃	C₃×C₄
socle	C₂²×C₁₃	C₂×C₃×C₄
prime radical	C₂²×D₁₃⋊C₃	C₂²
cosocle	C₂²×D₁₃	C₂²×C₃
hypercenter	C₂×C₄	AGL(1,𝔽₁₃)
hypocenter	C₁₃	C₃×#95
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. (C₂×#261)⋊C₄	C₃	semidirect
7. C₂×AGL(1,𝔽₁₃)	C₄	semidirect
8. C₂×C₄×C₁₃⋊C₃	C₄	semidirect
9. C₂×Dic₁₃⋊C₃	C₄	semidirect
24. C₂×#261	C₃×C₄	semidirect
25. C₂×C₄×C₁₃	C₃×C₄	semidirect
26. C₂×Dic₁₃	C₃×C₄	semidirect
44. C₁₃⋊C₃	#95	semidirect
60. C₁₃	C₃×#95	semidirect
75. C₂×C₄	AGL(1,𝔽₁₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,𝔽₁₃)	2
C₂×C₄×D₁₃⋊C₃	2
(C₂×#261)⋊C₄	3
C₃×#95	13

Subgroups — (C2×AGL(1,𝔽13))⋊C4 #11928186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×AGL(1,𝔽₁₃))⋊C₄ #11928186