Subgroups — #13112971

Order 1664.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	#11718094	C₂	1	1	yes	maximal, characteristic
3	#11718091	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₁₃×C₃₂	C₄	1	2	yes	complemented
8	#88034	C₄	1	2	yes	complemented
9	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₁₃	C₈	1	1	yes	characteristic
11	C₂×#1055	C₈	1	1	yes	characteristic
12	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
14	#6090	C₈	1	2	yes	—
15	#1398	—	13	1	no	maximal, Sylow
16	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₃	—	2	1	no	—
18	C₈×C₁₃	C₄²	1	1	yes	characteristic
19	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
20	#1055	—	2	1	no	—
21	M₆₄	—	13	1	no	—
22	M₆₄	D₁₃	1	1	yes	characteristic
23	#346	—	13	1	no	—
24	C₂²×C₁₃	M₃₂	1	1	yes	characteristic
25	C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
26	C₄×C₁₃	M₃₂	1	1	yes	characteristic
27	Dic₁₃	—	4	1	no	—
28	C₂×C₁₆	—	13	1	no	—
29	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
30	C₄×C₈	—	13	1	no	—
31	C₃₂	—	13	2	no	—
32	C₃₂	Dic₁₃	1	2	yes	complemented
33	C₂×C₁₃	—	2	1	no	—
34	C₂×C₁₃	#346	1	1	yes	characteristic
35	C₂×C₈	—	13	1	no	—
36	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
37	C₄²	—	13	1	no	—
38	C₁₆	—	13	2	no	—
39	C₁₆	C₄×D₁₃	1	1	yes	characteristic
40	C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
41	C₁₃	#1398	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₄	—	26	1	no	—
43	C₂×C₄	C₈×D₁₃	1	1	yes	characteristic
44	C₈	—	26	1	no	—
45	C₈	C₈×D₁₃	1	1	yes	characteristic
46	C₈	C₄×Dic₁₃	1	1	yes	characteristic
47	C₂²	#88038	1	1	yes	characteristic
48	C₄	—	52	1	no	—
49	C₄	#88038	1	1	yes	characteristic
50	C₄	C₈×Dic₁₃	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#11718094	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₁₃
commutator	C₄×C₁₃	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×M₆₄	C₂
socle	C₂×C₁₃	#346
prime radical	C₂²×C₁₃	M₃₂
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	M₆₄	D₁₃
hypocenter	C₁₃	#1398
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₁₃×C₃₂	C₄	semidirect
8. #88034	C₄	semidirect
32. C₃₂	Dic₁₃	semidirect
41. 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×M₆₄	2
#11718094	2
#11718091	2
#1398	13