Subgroups — #15750803

Order 3328.

88 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, complemented
2	#13113040	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2262	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#508	—	2	1	no	—
5	C₁₃×Q₆₄	C₄	1	1	yes	characteristic
6	C₁₃×SD₆₄	—	2	1	no	—
7	C₁₃×D₃₂	C₄	1	1	yes	characteristic
8	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
9	#11718098	—	2	1	no	—
10	#11718035	—	2	1	no	—
11	C₁₃×#135	—	4	1	no	—
12	C₁₃×Q₃₂	—	2	1	no	—
13	C₁₃×SD₃₂	—	4	1	no	—
14	C₁₃×D₁₆	—	2	1	no	—
15	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
16	#88059	—	4	1	no	—
17	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₃×C₃₂	D₄	1	1	yes	characteristic
19	#7539	—	13	1	no	maximal, Sylow
20	C₁₃×#41	—	8	1	no	—
21	C₁₃×Q₁₆	—	4	1	no	—
22	C₁₃×SD₁₆	—	8	1	no	—
23	C₁₃×D₈	—	4	1	no	—
24	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
25	#6099	—	8	1	no	—
26	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
28	#2262	D₁₃	1	1	yes	characteristic
29	C₂×C₆₄	—	13	1	no	—
30	#1425	—	13	1	no	—
31	Q₈×C₁₃	—	8	1	no	—
32	D₄×C₁₃	—	8	1	no	—
33	D₄×C₁₃	—	16	1	no	—
34	C₂×C₄×C₁₃	—	16	1	no	—
35	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
36	C₈×C₁₃	#102	1	1	yes	characteristic
37	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
38	#1055	—	16	1	no	—
39	#508	—	2	1	no	—
40	Q₆₄	Dic₁₃	1	1	yes	characteristic
41	SD₆₄	—	2	1	no	—
42	D₃₂	Dic₁₃	1	1	yes	characteristic
43	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
44	#368	—	26	1	no	—
45	C₆₄	—	26	1	no	—
46	C₂²×C₁₃	—	16	1	no	—
47	C₂²×C₁₃	SD₆₄	1	1	yes	characteristic
48	C₄×C₁₃	—	16	1	no	—
49	C₄×C₁₃	#357	1	1	yes	characteristic
50	C₄×C₁₃	D₃₂	1	1	yes	characteristic
51	#135	—	4	1	no	—
52	Q₃₂	—	2	1	no	—
53	SD₃₂	—	4	1	no	—
54	D₁₆	—	2	1	no	—
55	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
56	#108	—	52	1	no	—
57	C₃₂	C₂×Dic₁₃	1	1	yes	characteristic
58	C₃₂	C₂²⋊D₁₃	1	1	yes	characteristic
59	C₂×C₁₃	—	2	1	no	—
60	C₂×C₁₃	—	32	1	no	—
61	C₂×C₁₃	#1415	1	1	yes	characteristic
62	#41	—	8	1	no	—
63	Q₁₆	—	4	1	no	—
64	SD₁₆	—	8	1	no	—
65	D₈	—	4	1	no	—
66	M₁₆	—	104	1	no	—
67	C₂×C₈	#6104	1	1	yes	characteristic
68	C₁₆	#6105	1	1	yes	characteristic
69	C₁₆	C₂²⋊Dic₁₃	1	1	yes	characteristic
70	C₁₃	#7539	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	8	1	no	—
72	D₄	—	8	1	no	—
73	D₄	—	16	1	no	—
74	C₂×C₄	—	16	1	no	—
75	C₂×C₄	#88066	1	1	yes	characteristic
76	C₈	—	208	1	no	—
77	C₈	#88067	1	1	yes	characteristic
78	C₈	#88072	1	1	yes	characteristic
79	C₂²	—	16	1	no	—
80	C₂²	#11718112	1	1	yes	characteristic
81	C₄	—	16	1	no	—
82	C₄	#11718111	1	1	yes	characteristic
83	C₄	#11718154	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	32	1	no	—
86	C₂	#13113014	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718111
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting, prime radical	C₁₃×#2262	C₂
socle	C₂×C₁₃	#1415
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	#2262	D₁₃
hypocenter	C₁₃	#7539
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #2262

Complements

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

N	H ≅ G/N	type
1. C₂×#11718035	C₂	semidirect
2. #13113040	C₂	semidirect
70. C₁₃	#7539	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×#2262	2
#7539	13