Subgroups — #13129784

Order 1664.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718660	C₂	1	1	yes	maximal, characteristic
2	#11718284	C₂	1	2	yes	maximal
3	C₁₃×#117	C₄	1	1	yes	characteristic
4	C₂×#6099	C₂²	1	1	yes	characteristic
5	C₂²×#1055	C₄	1	1	yes	characteristic
6	#88106	—	2	2	no	—
7	C₄⋊#1055	—	2	2	no	—
8	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₁₃×C₄⋊C₄	—	2	1	no	—
10	C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
11	C₄²×C₁₃	—	2	1	no	—
12	#6099	—	4	1	no	—
13	C₂×#1055	—	2	1	no	—
14	C₂×#1055	—	4	1	no	—
15	C₂×#1055	D₄	1	2	yes	—
16	#6092	—	4	2	no	—
17	#1328	—	13	1	no	maximal, Sylow
18	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₁₃	—	2	1	no	—
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	2	2	no	—
22	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
24	#1055	—	2	2	no	—
25	#1055	—	4	1	no	—
26	#424	—	13	1	no	—
27	#349	—	13	2	no	—
28	C₂²×C₁₃	—	2	1	no	—
29	C₂²×C₁₃	—	4	1	no	—
30	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₁₃	—	2	1	no	—
32	C₄×C₁₃	—	4	2	no	—
33	C₄×C₁₃	#99	1	1	yes	characteristic
34	C₄×C₁₃	#101	1	1	yes	characteristic
35	C₂×M₁₆	—	13	1	no	—
36	C₂²×C₈	—	13	1	no	—
37	#117	#261	1	1	yes	characteristic
38	M₃₂	—	26	2	no	—
39	C₄⋊C₈	—	26	2	no	—
40	C₂×C₁₃	—	2	1	no	—
41	C₂×C₁₃	—	4	1	no	—
42	C₂×C₁₃	#324	1	1	yes	characteristic
43	C₂²×C₄	C₂×#261	1	1	yes	characteristic
44	M₁₆	—	52	1	no	—
45	C₂×C₈	—	13	2	no	—
46	C₂×C₈	—	26	1	no	—
47	C₂×C₈	—	52	1	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₂²⋊C₄	#1057	1	2	yes	—
50	C₄²	—	2	1	no	—
51	C₁₆	—	52	2	no	—
52	C₁₃	#1328	1	1	yes	characteristic, complemented, Sylow
53	C₂³	C₂×#1057	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	#6122	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
59	C₈	—	26	2	no	—
60	C₈	—	52	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₂²⋊#1057	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	#88107	1	1	yes	characteristic
67	C₄	#88113	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	#11718285	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88107
commutator, prime radical	C₂³×C₁₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#261
Fitting	C₁₃×#117	C₄
socle	C₂×C₁₃	#324
cosocle	C₂×#6099	C₂²
hypercenter	#117	#261
hypocenter	C₁₃	#1328
LCS	G ▷ C₂³×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
52. C₁₃	#1328	semidirect

Maximal subgroups

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

subgroup	index
#11718660	2
#11718284	2
#1328	13