Subgroups — #13112749

Order 1664.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	#11718585	C₂	1	2	yes	maximal
3	C₂×C₁₃×M₁₆	C₄	1	2	yes	—
4	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×#6099	C₄	1	4	yes	—
6	C₁₃×C₄⋊C₈	—	2	2	no	—
7	C₄⋊#1055	—	2	2	no	—
8	C₄⋊#1055	—	2	2	no	—
9	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₁₃×M₁₆	—	4	2	no	—
12	C₂×C₈×C₁₃	—	2	2	no	—
13	C₄²×C₁₃	D₄	1	1	yes	characteristic
14	C₄²×C₁₃	D₄	1	2	yes	—
15	C₄²×C₁₃	Q₈	1	1	yes	characteristic
16	#6099	—	4	4	no	—
17	C₂×#1055	—	2	4	no	—
18	#1309	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	C₄²	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	2	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	2	2	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₈×C₁₃	—	4	2	no	—
29	#1055	—	4	4	no	—
30	#423	—	13	2	no	—
31	#423	D₁₃	1	1	yes	characteristic
32	C₂²×C₁₃	—	2	2	no	—
33	C₂²×C₁₃	—	2	1	no	—
34	C₂²×C₁₃	#95	1	1	yes	characteristic
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	—	2	1	no	—
37	C₄×C₁₃	#100	1	1	yes	characteristic
38	C₄×C₁₃	#100	1	2	yes	—
39	C₄×C₁₃	#101	1	2	yes	—
40	C₄×C₁₃	#101	1	1	yes	characteristic
41	C₂×M₁₆	—	13	4	no	—
42	C₂×M₁₆	Dic₁₃	1	2	yes	—
43	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
44	C₄⋊C₈	—	2	2	no	—
45	C₄⋊C₈	—	26	2	no	—
46	C₄⋊C₈	—	26	2	no	—
47	C₂×C₁₃	—	4	1	no	—
48	C₂×C₁₃	#343	1	2	yes	—
49	C₂×C₁₃	#343	1	1	yes	characteristic
50	C₂²×C₄	C₄×D₁₃	1	2	yes	—
51	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
52	M₁₆	—	4	2	no	—
53	M₁₆	—	52	4	no	—
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	—	26	4	no	—
56	C₄²	Dic₂₆	1	1	yes	characteristic
57	C₄²	D₅₂	1	1	yes	characteristic
58	C₄²	C₂²⋊D₁₃	1	2	yes	—
59	C₁₃	#1309	1	1	yes	characteristic, complemented, Sylow
60	C₂³	C₄×Dic₁₃	1	1	yes	characteristic
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	#6101	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
67	C₂×C₄	#6103	1	2	yes	—
68	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
69	C₈	—	4	2	no	—
70	C₈	—	52	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	2	1	no	—
73	C₂²	#88071	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	#88063	1	2	yes	—
77	C₄	#88064	1	2	yes	—
78	C₄	#88073	1	1	yes	characteristic
79	C₄	#88076	1	1	yes	characteristic
80	C₂	—	4	1	no	—
81	C₂	#11718122	1	1	yes	characteristic
82	C₂	#11718146	1	2	yes	—

	subgroup	G/H
center	C₂²	#88071
commutator, prime radical	C₂³×C₁₃	C₄²
Frattini	C₂×C₄²	C₂×D₁₃
Fitting	C₁₃×#423	C₂
socle	C₂²×C₁₃	#95
cosocle	C₂×C₄²×C₁₃	C₂²
hypercenter	#423	D₁₃
hypocenter	C₁₃	#1309
LCS	G ▷ C₂³×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
59. C₁₃	#1309	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#423	2
#11718585	2
#1309	13