Subgroups — #13117130

Order 1664.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#504	C₂	1	1	yes	maximal, characteristic
2	#11718091	C₂	1	3	yes	maximal, complemented
3	C₂×#88034	C₂	1	3	yes	maximal, complemented
4	C₁₃×#131	C₄	1	1	yes	characteristic
5	C₁₃×M₃₂	C₄	1	3	yes	—
6	C₂×C₁₃×C₁₆	C₂²	1	3	yes	—
7	#88034	C₂²	1	1	yes	characteristic
8	#88034	C₂²	1	3	yes	—
9	C₁₃×#41	C₈	1	1	yes	characteristic
10	C₁₃×M₁₆	C₈	1	3	yes	—
11	C₂×C₈×C₁₃	C₂×C₄	1	3	yes	—
12	C₁₃×C₁₆	C₂×C₄	1	3	yes	—
13	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
14	#2258	—	13	1	no	maximal, Sylow
15	Q₈×C₁₃	C₁₆	1	1	yes	characteristic
16	D₄×C₁₃	C₁₆	1	3	yes	—
17	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
18	C₈×C₁₃	C₂×C₈	1	3	yes	—
19	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
20	#504	D₁₃	1	1	yes	characteristic
21	M₆₄	—	13	3	no	—
22	C₂×C₃₂	—	13	3	no	—
23	C₂²×C₁₃	C₂×C₁₆	1	3	yes	—
24	C₄×C₁₃	C₂×C₁₆	1	3	yes	—
25	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
26	#131	Dic₁₃	1	1	yes	characteristic
27	M₃₂	Dic₁₃	1	3	yes	—
28	C₂×C₁₆	C₂×D₁₃	1	3	yes	—
29	C₃₂	—	13	1	no	—
30	C₃₂	—	13	3	no	—
31	C₂×C₁₃	—	2	3	no	—
32	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
33	#41	#1055	1	1	yes	characteristic
34	M₁₆	#1055	1	3	yes	—
35	C₂×C₈	C₂×Dic₁₃	1	3	yes	—
36	C₁₆	C₂×Dic₁₃	1	3	yes	—
37	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
38	C₁₃	#2258	1	1	yes	characteristic, complemented, Sylow
39	Q₈	#6090	1	1	yes	characteristic
40	D₄	#6090	1	3	yes	—
41	C₂×C₄	C₂×#1055	1	3	yes	—
42	C₈	C₂×#1055	1	3	yes	—
43	C₈	C₂²×Dic₁₃	1	1	yes	characteristic
44	C₂²	C₂×#6090	1	3	yes	—
45	C₄	C₂×#6090	1	3	yes	—
46	C₄	C₂²×#1055	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#6090	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₁₃
commutator, socle	C₂×C₁₃	C₂²×C₁₆
Fitting	C₁₃×#504	C₂
prime radical	C₁₃×#41	C₈
cosocle	C₁₃×C₁₆	C₂³
hypercenter	#504	D₁₃
hypocenter	C₁₃	#2258
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
2. #11718091	C₂	semidirect
3. C₂×#88034	C₂	semidirect
38. C₁₃	#2258	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#504	2
#11718091	2
C₂×#88034	2
#2258	13