Subgroups — #13129863

Order 1664.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718261	C₂	1	2	yes	maximal
2	#11718094	C₂	1	1	yes	maximal, characteristic
3	#88106	—	2	2	no	—
4	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₁₃	Q₈	1	1	yes	characteristic
9	C₂×#1055	D₄	1	1	yes	characteristic
10	#6092	—	4	2	no	—
11	C₁₃×C₁₆	C₈	1	2	yes	—
12	#6090	—	2	1	no	—
13	#1369	—	13	1	no	maximal, Sylow
14	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×Dic₁₃	—	2	1	no	—
16	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₃	M₁₆	1	1	yes	characteristic
18	#1055	SD₁₆	1	2	yes	—
19	#364	—	13	2	no	—
20	#346	—	13	1	no	—
21	C₂²×C₁₃	#108	1	1	yes	characteristic
22	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₃	#106	1	1	yes	characteristic
24	Dic₁₃	—	4	1	no	—
25	M₃₂	—	26	2	no	—
26	C₂×C₁₆	—	13	1	no	—
27	C₂×C₁₆	#261	1	1	yes	characteristic
28	C₄×C₈	—	13	1	no	—
29	C₂×C₁₃	—	2	1	no	—
30	C₂×C₁₃	#334	1	1	yes	characteristic
31	C₂×C₈	—	13	1	no	—
32	C₂×C₈	C₂×#261	1	1	yes	characteristic
33	C₄²	—	13	1	no	—
34	C₁₆	—	26	1	no	—
35	C₁₆	—	52	2	no	—
36	C₁₆	#1057	1	2	yes	—
37	C₁₃	#1369	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₄	—	26	1	no	—
39	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
40	C₈	—	13	2	no	—
41	C₈	#6118	1	1	yes	characteristic
42	C₈	C₂×#1057	1	1	yes	characteristic
43	C₂²	#88103	1	1	yes	characteristic
44	C₄	—	52	1	no	—
45	C₄	#88101	1	1	yes	characteristic
46	C₄	C₄⋊#1057	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#11718253	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88101
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	#334
prime radical	C₂²×C₁₃	#108
cosocle	C₈×Dic₁₃	C₂²
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	#1369
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
37. C₁₃	#1369	semidirect

Maximal subgroups

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

subgroup	index
#11718261	2
#11718094	2
#1369	13