Subgroups — #13112972

Order 1664.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#346	C₂	1	1	yes	maximal, characteristic
2	#11718091	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	#88034	C₄	1	4	yes	complemented
7	C₂×C₈×C₁₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₃	C₈	1	1	yes	characteristic
10	C₁₃×C₁₆	C₈	1	2	yes	—
11	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
12	#1398	—	13	1	no	maximal, Sylow
13	C₂×C₄×C₁₃	—	2	1	no	—
14	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₃	—	2	1	no	—
16	C₈×C₁₃	C₄²	1	1	yes	characteristic
17	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
18	M₆₄	—	13	2	no	—
19	#346	D₁₃	1	1	yes	characteristic
20	C₂²×C₁₃	M₃₂	1	1	yes	characteristic
21	C₄×C₁₃	—	4	1	no	—
22	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
23	C₄×C₁₃	M₃₂	1	1	yes	characteristic
24	C₂×C₁₆	Dic₁₃	1	1	yes	characteristic
25	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
26	C₄×C₈	Dic₁₃	1	1	yes	characteristic
27	C₃₂	—	13	4	no	—
28	C₂×C₁₃	—	2	1	no	—
29	C₂×C₁₃	#346	1	1	yes	characteristic
30	C₂×C₈	#1055	1	1	yes	characteristic
31	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
32	C₄²	#1055	1	1	yes	characteristic
33	C₁₆	#1055	1	2	yes	—
34	C₁₆	C₄×D₁₃	1	2	yes	—
35	C₁₃	#1398	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×#1055	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂×#1055	1	1	yes	characteristic
40	C₈	C₄×Dic₁₃	1	1	yes	characteristic
41	C₂²	#88052	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	C₄×#1055	1	1	yes	characteristic
44	C₄	#88052	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#11718053	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₁₃
commutator	C₄×C₁₃	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×#346	C₂
socle	C₂×C₁₃	#346
prime radical	C₂²×C₁₃	M₃₂
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	#346	D₁₃
hypocenter	C₁₃	#1398
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
6. #88034	C₄	semidirect
35. C₁₃	#1398	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#346	2
#11718091	2
#1398	13