Subgroups — #13112747

Order 1664.

130 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	#11718587	C₂	1	2	yes	maximal
3	C₂×C₁₃×M₁₆	C₄	1	2	yes	—
4	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
5	C₁₃×C₄⋊C₈	—	2	2	no	—
6	C₂²⋊#1055	C₄	1	4	yes	—
7	C₄⋊#1055	—	2	2	no	—
8	#88043	—	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	C₂×#1055	—	2	4	no	—
17	#1307	—	13	1	no	maximal, Sylow
18	C₂³×C₁₃	C₄²	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	2	1	no	—
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	4	2	no	—
22	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
26	C₈×C₁₃	—	4	2	no	—
27	#1055	—	4	4	no	—
28	#432	—	13	2	no	—
29	#423	D₁₃	1	1	yes	characteristic
30	C₂²×C₁₃	—	2	1	no	—
31	C₂²×C₁₃	—	2	2	no	—
32	C₂²×C₁₃	#95	1	1	yes	characteristic
33	C₄×C₁₃	—	2	1	no	—
34	C₄×C₁₃	—	2	2	no	—
35	C₄×C₁₃	—	2	2	no	—
36	C₄×C₁₃	#100	1	1	yes	characteristic
37	C₄×C₁₃	#101	1	1	yes	characteristic
38	C₂×M₁₆	Dic₁₃	1	2	yes	—
39	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
40	C₄⋊C₈	—	2	2	no	—
41	C₄⋊C₈	—	26	2	no	—
42	C₂²⋊C₈	—	13	4	no	—
43	#97	—	26	2	no	—
44	C₂×C₁₃	—	4	1	no	—
45	C₂×C₁₃	#343	1	1	yes	characteristic
46	C₂×C₁₃	#344	1	2	yes	—
47	C₂²×C₄	C₄×D₁₃	1	2	yes	—
48	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
49	M₁₆	—	4	2	no	—
50	C₂×C₈	—	2	2	no	—
51	C₂×C₈	—	26	4	no	—
52	C₄²	Dic₂₆	1	1	yes	characteristic
53	C₄²	D₅₂	1	1	yes	characteristic
54	C₄²	C₂²⋊D₁₃	1	2	yes	—
55	C₁₃	#1307	1	1	yes	characteristic, complemented, Sylow
56	C₂³	C₄×Dic₁₃	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	#6101	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
62	C₂×C₄	#6103	1	2	yes	—
63	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
64	C₈	—	4	2	no	—
65	C₈	—	52	4	no	—
66	C₂²	—	2	2	no	—
67	C₂²	—	2	1	no	—
68	C₂²	#88071	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	#88073	1	1	yes	characteristic
73	C₄	#88076	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	#11718122	1	1	yes	characteristic
76	C₂	#11718151	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	#1307
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
55. C₁₃	#1307	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
#11718587	2
#1307	13