Subgroups — #13113035

Order 1664.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#366	C₂	1	1	yes	maximal, characteristic
2	#11718096	C₂	1	1	yes	maximal, characteristic
3	C₂×#88034	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₁₃×#107	—	2	1	no	—
6	#88058	—	2	1	no	—
7	#88034	C₄	1	2	yes	complemented
8	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
9	C₁₃×C₄⋊C₄	—	4	1	no	—
10	C₄⋊Dic₁₃	—	4	1	no	—
11	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₁₃×C₁₆	Q₈	1	1	yes	characteristic
13	#1423	—	13	1	no	maximal, Sylow
14	C₂×C₄×C₁₃	—	8	1	no	—
15	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
16	C₂×Dic₁₃	—	8	1	no	—
17	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₂	—	13	1	no	—
20	#366	—	13	1	no	—
21	#366	D₁₃	1	1	yes	characteristic
22	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
23	C₄×C₁₃	—	16	1	no	—
24	C₄×C₁₃	#107	1	1	yes	characteristic
25	C₄×C₁₃	Q₃₂	1	1	yes	characteristic
26	Dic₁₃	—	16	1	no	—
27	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
28	#107	—	2	1	no	—
29	#107	—	26	1	no	—
30	C₃₂	—	13	2	no	—
31	C₂×C₁₃	#366	1	1	yes	characteristic
32	C₂×C₁₃	D₃₂	1	1	yes	characteristic
33	C₂×C₁₃	Q₆₄	1	1	yes	characteristic
34	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₄⋊C₄	—	52	1	no	—
37	C₁₆	Dic₂₆	1	1	yes	characteristic
38	C₁₆	C₄×D₁₃	1	1	yes	characteristic
39	C₁₃	#1423	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	104	1	no	—
42	C₂×C₄	#6104	1	1	yes	characteristic
43	C₈	#6101	1	1	yes	characteristic
44	C₈	#6107	1	1	yes	characteristic
45	C₂²	#88066	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	208	1	no	—
48	C₄	#88047	1	1	yes	characteristic
49	C₄	#88069	1	1	yes	characteristic
50	C₂	#11718081	1	1	yes	characteristic
51	C₂	#11718111	1	1	yes	characteristic
52	C₂	#11718114	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88066
commutator	C₁₃×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×#366	C₂
socle, prime radical	C₂²×C₁₃	D₁₆
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	#366	D₁₃
hypocenter	C₁₃	#1423
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
7. #88034	C₄	semidirect
39. C₁₃	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#366	2
#11718096	2
C₂×#88034	2
#1423	13