Subgroups — C₂×C₁₃×ΓL(1,𝔽₂₅) #11928876

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×ΓL(1,𝔽₂₅)	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₁₃×M₁₆	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₃×C₁₃	C₄	1	1	yes	characteristic
9	C₄×D₃×C₁₃	C₄	1	2	yes	—
10	C₄×D₃×C₁₃	C₂²	1	2	yes	—
11	C₃×C₈×C₁₃	C₂²	1	2	yes	complemented
12	C₁₃×C₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₄×C₁₃	—	3	1	no	—
14	C₁₃×M₁₆	—	3	4	no	—
15	C₂×C₈×C₁₃	—	3	1	no	—
16	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×D₃×C₁₃	—	2	2	no	—
19	C₂×D₃×C₁₃	C₂×C₄	1	2	yes	—
20	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	Dic₃×C₁₃	C₂×C₄	1	2	yes	—
23	C₂³×C₁₃	—	3	1	no	—
24	C₂×C₄×C₁₃	—	3	1	no	—
25	C₂×C₄×C₁₃	—	3	2	no	—
26	C₂×C₄×C₁₃	—	3	2	no	—
27	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
28	C₈×C₁₃	—	3	2	no	—
29	C₈×C₁₃	C₂×D₃	1	2	yes	complemented
30	C₂×ΓL(1,𝔽₂₅)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₃×C₁₃	M₁₆	1	2	yes	complemented
32	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	D₃×C₁₃	—	2	2	no	—
34	C₂²×C₁₃	—	3	2	no	—
35	C₂²×C₁₃	—	6	2	no	—
36	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
37	C₄×C₁₃	—	3	2	no	—
38	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
39	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
40	C₂×C₄×D₃	C₂×C₁₃	1	1	yes	characteristic
41	C₂×C₃×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
42	C₂×C₃⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
43	ΓL(1,𝔽₂₅)	C₂×C₁₃	1	4	yes	direct product factor
44	C₃×C₁₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
45	C₂×M₁₆	—	3	1	no	Sylow
46	C₂×C₁₃	—	6	2	no	—
47	C₂×C₁₃	ΓL(1,𝔽₂₅)	1	2	yes	direct product factor
48	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
49	C₂²×D₃	C₄×C₁₃	1	1	yes	characteristic
50	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
51	C₂×Dic₃	C₄×C₁₃	1	1	yes	characteristic
52	C₄×D₃	C₄×C₁₃	1	2	yes	—
53	C₄×D₃	C₂²×C₁₃	1	2	yes	—
54	C₃×C₈	C₂²×C₁₃	1	2	yes	complemented
55	C₃⋊C₈	C₂²×C₁₃	1	2	yes	complemented
56	C₂²×C₄	—	3	1	no	—
57	M₁₆	—	3	4	no	—
58	C₂×C₈	—	3	1	no	—
59	C₂×C₈	D₃×C₁₃	1	1	yes	characteristic, complemented
60	C₁₃	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₃	C₂×C₄×C₁₃	1	1	yes	characteristic
62	C₂×D₃	—	2	2	no	—
63	C₂×D₃	C₂×C₄×C₁₃	1	2	yes	—
64	C₃×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
65	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
66	Dic₃	C₂×C₄×C₁₃	1	2	yes	—
67	C₂³	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	3	2	no	—
70	C₂×C₄	—	3	2	no	—
71	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
72	C₈	—	3	2	no	—
73	C₈	C₂×D₃×C₁₃	1	2	yes	complemented
74	C₂×C₃	C₁₃×M₁₆	1	2	yes	complemented
75	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
76	D₃	—	2	2	no	—
77	C₂²	—	3	2	no	—
78	C₂²	—	6	2	no	—
79	C₂²	C₄×D₃×C₁₃	1	1	yes	characteristic
80	C₄	—	3	2	no	—
81	C₄	C₄×D₃×C₁₃	1	1	yes	characteristic
82	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
83	C₃	C₂×C₁₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	6	2	no	—
85	C₂	C₁₃×ΓL(1,𝔽₂₅)	1	2	yes	direct product factor
86	C₂	C₂×C₄×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical	C₂²×D₃×C₁₃	C₄
cosocle	C₃×C₄	C₂³×C₁₃
hypercenter	C₂×C₈×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₈×C₁₃	C₂	semidirect
3. C₂×C₁₃×C₃⋊C₈	C₂	semidirect
4. C₁₃×ΓL(1,𝔽₂₅)	C₂	direct (N × H)
11. C₃×C₈×C₁₃	C₂²	semidirect
12. C₁₃×C₃⋊C₈	C₂²	semidirect
16. C₂×C₈×C₁₃	D₃	semidirect
29. C₈×C₁₃	C₂×D₃	semidirect
30. C₂×ΓL(1,𝔽₂₅)	C₁₃	direct (N × H)
31. C₂×C₃×C₁₃	M₁₆	semidirect
41. C₂×C₃×C₈	C₂×C₁₃	semidirect
42. C₂×C₃⋊C₈	C₂×C₁₃	semidirect
43. ΓL(1,𝔽₂₅)	C₂×C₁₃	direct (N × H)
44. C₃×C₁₃	C₂×M₁₆	semidirect
47. C₂×C₁₃	ΓL(1,𝔽₂₅)	direct (N × H)
54. C₃×C₈	C₂²×C₁₃	semidirect
55. C₃⋊C₈	C₂²×C₁₃	semidirect
59. C₂×C₈	D₃×C₁₃	semidirect
60. C₁₃	C₂×ΓL(1,𝔽₂₅)	direct (N × H)
73. C₈	C₂×D₃×C₁₃	semidirect
74. C₂×C₃	C₁₃×M₁₆	semidirect
83. C₃	C₂×C₁₃×M₁₆	semidirect
85. C₂	C₁₃×ΓL(1,𝔽₂₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×C₁₃	2
C₂×C₃×C₈×C₁₃	2
C₂×C₁₃×C₃⋊C₈	2
C₁₃×ΓL(1,𝔽₂₅)	2
C₂×C₁₃×M₁₆	3
C₂×ΓL(1,𝔽₂₅)	13

Subgroups — C2×C13×ΓL(1,𝔽25) #11928876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×ΓL(1,𝔽₂₅) #11928876