Subgroups — C₁₃×#907 #11928883

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×M₁₆	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	2	yes	maximal, complemented
5	D₃×C₈×C₁₃	C₂	1	2	yes	maximal, complemented
6	C₁₃×#131	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#67	C₄	1	2	yes	—
9	C₁₃×D₁₂	C₄	1	1	yes	characteristic
10	C₄×D₃×C₁₃	C₂²	1	2	yes	—
11	C₁₃×Dic₆	C₄	1	1	yes	characteristic
12	C₃×C₈×C₁₃	C₂²	1	2	yes	—
13	C₁₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₁₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₃×#41	—	3	1	no	—
16	C₁₃×M₁₆	—	3	2	no	—
17	C₁₃×M₁₆	D₃	1	1	yes	characteristic, complemented
18	C₂×C₈×C₁₃	—	3	1	no	—
19	C₂×C₈×C₁₃	—	3	2	no	—
20	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×D₃×C₁₃	C₂×C₄	1	2	yes	—
22	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	Dic₃×C₁₃	C₂×C₄	1	2	yes	—
25	Q₈×C₁₃	—	3	1	no	—
26	D₄×C₁₃	—	3	2	no	—
27	D₄×C₁₃	—	3	1	no	—
28	C₂×C₄×C₁₃	—	3	2	no	—
29	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
30	C₈×C₁₃	—	3	1	no	—
31	C₈×C₁₃	—	3	1	no	—
32	C₈×C₁₃	C₂×D₃	1	2	yes	—
33	#907	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₃×C₁₃	—	2	1	no	—
35	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	D₃×C₁₃	—	2	2	no	—
37	C₂²×C₁₃	—	3	2	no	—
38	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
39	C₄×C₁₃	—	3	2	no	—
40	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
41	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
42	#235	C₂×C₁₃	1	1	yes	characteristic
43	C₃×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
44	C₂×C₃⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
45	ΓL(1,𝔽₂₅)	C₂×C₁₃	1	2	yes	complemented
46	D₃×C₈	C₂×C₁₃	1	2	yes	complemented
47	C₃×C₁₃	#131	1	1	yes	characteristic, complemented, Hall
48	#131	—	3	1	no	Sylow
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	—	6	2	no	—
51	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
52	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
53	#67	C₄×C₁₃	1	2	yes	—
54	D₁₂	C₄×C₁₃	1	1	yes	characteristic
55	C₄×D₃	C₂²×C₁₃	1	2	yes	—
56	Dic₆	C₄×C₁₃	1	1	yes	characteristic
57	C₃×C₈	C₂²×C₁₃	1	2	yes	—
58	C₃⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
59	C₃⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
60	#41	—	3	1	no	—
61	M₁₆	—	3	2	no	—
62	M₁₆	D₃×C₁₃	1	1	yes	characteristic, complemented
63	C₂×C₈	—	3	1	no	—
64	C₂×C₈	—	3	2	no	—
65	C₁₃	#907	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²×C₃	C₂×C₄×C₁₃	1	1	yes	characteristic
67	C₂×D₃	C₂×C₄×C₁₃	1	2	yes	—
68	C₃×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
69	C₃×C₄	C₂³×C₁₃	1	1	yes	characteristic
70	Dic₃	C₂×C₄×C₁₃	1	2	yes	—
71	Q₈	—	3	1	no	—
72	D₄	—	3	2	no	—
73	D₄	—	3	1	no	—
74	C₂×C₄	—	3	2	no	—
75	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
76	C₈	—	3	1	no	—
77	C₈	—	3	1	no	—
78	C₈	C₂×D₃×C₁₃	1	2	yes	—
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
81	D₃	—	2	2	no	—
82	C₂²	—	3	2	no	—
83	C₂²	C₄×D₃×C₁₃	1	1	yes	characteristic
84	C₄	—	3	2	no	—
85	C₄	C₄×D₃×C₁₃	1	1	yes	characteristic
86	C₄	C₂²×D₃×C₁₃	1	1	yes	characteristic
87	C₃	C₁₃×#131	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	2	1	no	—
89	C₂	—	6	2	no	—
90	C₂	C₂×C₄×D₃×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₂²×C₄
prime radical	C₁₃×#235	C₂
cosocle	C₃×C₄	C₂³×C₁₃
hypercenter	C₁₃×M₁₆	D₃
hypocenter	C₃	C₁₃×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₁₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×M₁₆	C₂	semidirect
3. C₂×C₁₃×C₃⋊C₈	C₂	semidirect
4. C₁₃×ΓL(1,𝔽₂₅)	C₂	semidirect
5. D₃×C₈×C₁₃	C₂	semidirect
17. C₁₃×M₁₆	D₃	semidirect
33. #907	C₁₃	direct (N × H)
43. C₃×M₁₆	C₂×C₁₃	semidirect
44. C₂×C₃⋊C₈	C₂×C₁₃	semidirect
45. ΓL(1,𝔽₂₅)	C₂×C₁₃	semidirect
46. D₃×C₈	C₂×C₁₃	semidirect
47. C₃×C₁₃	#131	semidirect
62. M₁₆	D₃×C₁₃	semidirect
65. C₁₃	#907	direct (N × H)
87. C₃	C₁₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#235	2
C₃×C₁₃×M₁₆	2
C₂×C₁₃×C₃⋊C₈	2
C₁₃×ΓL(1,𝔽₂₅)	2
D₃×C₈×C₁₃	2
C₁₃×#131	3
#907	13

Subgroups — C13×#907 #11928883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#907 #11928883