Subgroups — #15750822

Order 3328.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718035	C₂	1	1	yes	maximal, characteristic
2	#13113040	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1425	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₃×#368	—	2	1	no	—
6	#11718098	—	2	1	no	—
7	#11718035	C₄	1	2	yes	—
8	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
9	C₁₃×#108	—	4	1	no	—
10	#88059	—	4	1	no	—
11	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₃×C₃₂	Q₈	1	1	yes	characteristic
13	#7547	—	13	1	no	maximal, Sylow
14	C₁₃×M₁₆	—	8	1	no	—
15	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
16	#6099	—	8	1	no	—
17	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
19	C₂×C₆₄	—	13	1	no	—
20	#1425	—	13	1	no	—
21	#1425	D₁₃	1	1	yes	characteristic
22	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
23	C₈×C₁₃	—	16	1	no	—
24	C₈×C₁₃	#107	1	1	yes	characteristic
25	C₈×C₁₃	Q₃₂	1	1	yes	characteristic
26	#1055	—	16	1	no	—
27	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
28	#368	—	2	1	no	—
29	#368	—	26	1	no	—
30	C₆₄	—	13	2	no	—
31	C₂²×C₁₃	Q₆₄	1	1	yes	characteristic
32	C₄×C₁₃	#366	1	1	yes	characteristic
33	C₄×C₁₃	D₃₂	1	1	yes	characteristic
34	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
35	#108	—	4	1	no	—
36	#108	—	52	1	no	—
37	C₃₂	Dic₂₆	1	1	yes	characteristic
38	C₃₂	C₄×D₁₃	1	1	yes	characteristic
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	#1423	1	1	yes	characteristic
41	M₁₆	—	8	1	no	—
42	M₁₆	—	104	1	no	—
43	C₂×C₈	#6104	1	1	yes	characteristic
44	C₁₆	#6101	1	1	yes	characteristic
45	C₁₆	#6107	1	1	yes	characteristic
46	C₁₃	#7547	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄	#88066	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	208	1	no	—
50	C₈	#88047	1	1	yes	characteristic
51	C₈	#88069	1	1	yes	characteristic
52	C₂²	#11718114	1	1	yes	characteristic
53	C₄	#11718081	1	1	yes	characteristic
54	C₄	#11718111	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#13113035	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718111
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₁₃×#1425	C₂
socle	C₂×C₁₃	#1423
prime radical	C₂²×C₁₃	Q₆₄
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	#1425	D₁₃
hypocenter	C₁₃	#7547
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
46. C₁₃	#7547	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718035	2
#13113040	2
C₁₃×#1425	2
#7547	13