Subgroups — #15750812

Order 3328.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113047	C₂	1	1	yes	maximal, characteristic
2	#13113040	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₃₂	—	2	1	no	—
5	C₁₃×Q₆₄	—	2	1	no	—
6	C₁₃×Q₆₄	C₄	1	2	yes	—
7	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
8	#11718098	—	2	1	no	—
9	#11718035	—	2	1	no	—
10	C₂×C₁₃×Q₁₆	—	4	1	no	—
11	C₁₃×Q₃₂	—	2	2	no	—
12	C₁₃×Q₃₂	—	4	1	no	—
13	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
14	#88059	—	4	1	no	—
15	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₃×C₃₂	D₄	1	1	yes	characteristic
17	#7542	—	13	1	no	maximal, Sylow
18	C₂×Q₈×C₁₃	—	8	1	no	—
19	C₁₃×Q₁₆	—	4	2	no	—
20	C₁₃×Q₁₆	—	8	1	no	—
21	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
22	#6099	—	8	1	no	—
23	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×Q₆₄	D₁₃	1	1	yes	characteristic
26	M₁₂₈	—	13	1	no	—
27	#1425	—	13	1	no	—
28	Q₈×C₁₃	—	8	2	no	—
29	Q₈×C₁₃	—	16	1	no	—
30	C₂×C₄×C₁₃	—	16	1	no	—
31	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
32	C₈×C₁₃	#102	1	1	yes	characteristic
33	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
34	#1055	—	16	1	no	—
35	C₂×Q₃₂	—	2	1	no	—
36	Q₆₄	—	2	1	no	—
37	Q₆₄	Dic₁₃	1	2	yes	—
38	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
39	#368	—	26	1	no	—
40	C₆₄	—	26	1	no	—
41	C₂²×C₁₃	SD₆₄	1	1	yes	characteristic
42	C₄×C₁₃	—	16	2	no	—
43	C₄×C₁₃	#357	1	1	yes	characteristic
44	C₄×C₁₃	D₃₂	1	1	yes	characteristic
45	C₂×Q₁₆	—	4	1	no	—
46	Q₃₂	—	2	2	no	—
47	Q₃₂	—	4	1	no	—
48	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
49	#108	—	52	1	no	—
50	C₃₂	C₂×Dic₁₃	1	1	yes	characteristic
51	C₃₂	C₂²⋊D₁₃	1	1	yes	characteristic
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	#1415	1	1	yes	characteristic
54	C₂×Q₈	—	8	1	no	—
55	Q₁₆	—	4	2	no	—
56	Q₁₆	—	8	1	no	—
57	M₁₆	—	104	1	no	—
58	C₂×C₈	#6104	1	1	yes	characteristic
59	C₁₆	#6105	1	1	yes	characteristic
60	C₁₆	C₂²⋊Dic₁₃	1	1	yes	characteristic
61	C₁₃	#7542	1	1	yes	characteristic, complemented, Sylow
62	Q₈	—	8	2	no	—
63	Q₈	—	16	1	no	—
64	C₂×C₄	—	16	1	no	—
65	C₂×C₄	#88066	1	1	yes	characteristic
66	C₈	—	208	1	no	—
67	C₈	#88067	1	1	yes	characteristic
68	C₈	#88072	1	1	yes	characteristic
69	C₂²	#11718112	1	1	yes	characteristic
70	C₄	—	16	2	no	—
71	C₄	#11718111	1	1	yes	characteristic
72	C₄	#11718154	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#13113014	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13113014
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₂×C₁₃×Q₆₄	C₂
socle	C₂×C₁₃	#1415
prime radical	C₂²×C₁₃	SD₆₄
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	C₂×Q₆₄	D₁₃
hypocenter	C₁₃	#7542
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
61. C₁₃	#7542	semidirect

Maximal subgroups

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

subgroup	index
#13113047	2
#13113040	2
C₂×C₁₃×Q₆₄	2
#7542	13