Subgroups — #15750813

Order 3328.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀₈	C₂	1	1	yes	maximal, characteristic
2	#13113040	C₂	1	1	yes	maximal, characteristic
3	C₁₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₄	—	2	1	no	—
5	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
6	#11718098	—	2	1	no	—
7	Dic₂₀₈	—	2	1	no	—
8	Dic₂₀₈	C₄	1	2	yes	—
9	C₁₃×C₆₄	—	2	1	no	—
10	C₂×Dic₅₂	—	4	1	no	—
11	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
12	#88059	—	4	1	no	—
13	Dic₁₀₄	—	2	2	no	—
14	Dic₁₀₄	—	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×Dic₂₆	—	8	1	no	—
19	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
20	#6099	—	8	1	no	—
21	Dic₅₂	—	4	2	no	—
22	Dic₅₂	—	8	1	no	—
23	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×Q₆₄	—	13	1	no	—
26	M₁₂₈	D₁₃	1	1	yes	characteristic
27	#1425	—	13	1	no	—
28	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
29	C₂×Dic₁₃	—	16	1	no	—
30	Dic₂₆	—	8	2	no	—
31	Dic₂₆	—	16	1	no	—
32	C₈×C₁₃	#102	1	1	yes	characteristic
33	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
34	#1055	—	16	1	no	—
35	C₂×Q₃₂	—	26	1	no	—
36	Q₆₄	—	13	2	no	—
37	Q₆₄	—	26	1	no	—
38	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
39	#368	—	26	1	no	—
40	C₆₄	—	2	1	no	—
41	C₂²×C₁₃	SD₆₄	1	1	yes	characteristic
42	C₄×C₁₃	#357	1	1	yes	characteristic
43	C₄×C₁₃	D₃₂	1	1	yes	characteristic
44	Dic₁₃	—	16	2	no	—
45	C₂×Q₁₆	—	52	1	no	—
46	Q₃₂	—	26	2	no	—
47	Q₃₂	—	52	1	no	—
48	C₂×C₁₆	D₅₂	1	1	yes	characteristic
49	#108	—	52	1	no	—
50	C₃₂	C₄×D₁₃	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	—	104	1	no	—
55	Q₁₆	—	52	2	no	—
56	Q₁₆	—	104	1	no	—
57	M₁₆	—	104	1	no	—
58	C₂×C₈	D₁₀₄	1	1	yes	characteristic
59	C₁₆	#6095	1	1	yes	characteristic
60	C₁₆	#6103	1	1	yes	characteristic
61	C₁₃	#7542	1	1	yes	characteristic, complemented, Sylow
62	Q₈	—	104	2	no	—
63	Q₈	—	208	1	no	—
64	C₂×C₄	—	208	1	no	—
65	C₂×C₄	D₂₀₈	1	1	yes	characteristic
66	C₈	—	208	1	no	—
67	C₈	#88040	1	1	yes	characteristic
68	C₈	#88061	1	1	yes	characteristic
69	C₂²	#11718041	1	1	yes	characteristic
70	C₄	—	208	2	no	—
71	C₄	D₄₁₆	1	1	yes	characteristic
72	C₄	#11718101	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#13113015	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13113015
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₁₃×M₁₂₈	C₂
socle	C₂×C₁₃	#1415
prime radical	C₂²×C₁₃	SD₆₄
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	M₁₂₈	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 ◁ M₁₂₈

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
C₂×Dic₂₀₈	2
#13113040	2
C₁₃×M₁₂₈	2
#7542	13