Subgroups — #13112910

Order 1664.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#11718050	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₄⋊#1055	—	2	2	no	—
7	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
9	C₄²×C₁₃	D₄	1	1	yes	characteristic
10	C₂×#1055	—	4	2	no	—
11	C₁₃×C₁₆	—	2	1	no	—
12	C₁₃×C₁₆	C₈	1	2	yes	complemented
13	#1372	—	13	1	no	maximal, Sylow
14	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
16	C₂×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
17	C₈×C₁₃	—	2	1	no	—
18	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₃	M₁₆	1	1	yes	characteristic
20	#1055	—	8	2	no	—
21	C₄×C₁₆	D₁₃	1	1	yes	characteristic
22	#335	—	13	2	no	—
23	C₂²×C₁₃	#107	1	1	yes	characteristic
24	C₄×C₁₃	—	2	1	no	—
25	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₁₃	#108	1	1	yes	characteristic
27	C₄×C₁₃	SD₃₂	1	2	yes	—
28	C₂×C₁₆	Dic₁₃	1	1	yes	characteristic
29	C₂×C₁₆	Dic₁₃	1	1	yes	characteristic
30	C₄⋊C₈	—	26	2	no	—
31	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
32	C₂×C₁₃	#335	1	1	yes	characteristic
33	C₂×C₁₃	#367	1	1	yes	characteristic
34	C₂×C₁₃	#368	1	1	yes	characteristic
35	C₂×C₈	—	52	2	no	—
36	C₂×C₈	Dic₂₆	1	1	yes	characteristic
37	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
38	C₄²	D₅₂	1	1	yes	characteristic
39	C₁₆	—	2	1	no	—
40	C₁₆	#1055	1	2	yes	complemented
41	C₁₃	#1372	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₄	D₁₀₄	1	1	yes	characteristic
43	C₂×C₄	Dic₅₂	1	1	yes	characteristic
44	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	104	2	no	—
47	C₈	C₂×#1055	1	1	yes	characteristic
48	C₈	#6099	1	1	yes	characteristic
49	C₂²	#88058	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	#88040	1	2	yes	—
52	C₄	C₄⋊#1055	1	1	yes	characteristic
53	C₄	#88059	1	1	yes	characteristic
54	C₂	#11718050	1	1	yes	characteristic
55	C₂	#11718097	1	1	yes	characteristic
56	C₂	#11718098	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	#107
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	C₄×C₁₆	D₁₃
hypocenter	C₁₃	#1372
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₃×C₁₆	C₈	semidirect
40. C₁₆	#1055	semidirect
41. C₁₃	#1372	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×C₁₆	2
#11718050	2
#1372	13