Subgroups — #15750825

Order 3328.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113040	C₂	1	1	yes	maximal, characteristic
2	#13113038	C₂	1	1	yes	maximal, characteristic
3	C₁₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
5	#11718098	—	2	1	no	—
6	#11718096	—	2	1	no	—
7	C₁₃×C₆₄	C₄	1	2	yes	complemented
8	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
9	#88059	—	4	1	no	—
10	#88058	—	4	1	no	—
11	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₃×C₃₂	Q₈	1	1	yes	characteristic
13	#7548	—	13	1	no	maximal, Sylow
14	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
15	C₄⋊Dic₁₃	—	8	1	no	—
16	#6099	—	8	1	no	—
17	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
19	M₁₂₈	D₁₃	1	1	yes	characteristic
20	#1425	—	13	1	no	—
21	#1424	—	13	1	no	—
22	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
23	C₂×Dic₁₃	—	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	—	26	1	no	—
29	#366	—	26	1	no	—
30	C₆₄	Dic₁₃	1	2	yes	complemented
31	C₂²×C₁₃	SD₆₄	1	1	yes	characteristic
32	C₄×C₁₃	#366	1	1	yes	characteristic
33	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
34	Dic₁₃	—	32	1	no	—
35	C₂×C₁₆	D₅₂	1	1	yes	characteristic
36	#108	—	52	1	no	—
37	#107	—	52	1	no	—
38	C₃₂	Dic₂₆	1	1	yes	characteristic
39	C₃₂	C₂×Dic₁₃	1	1	yes	characteristic
40	C₂×C₁₃	—	2	1	no	—
41	C₂×C₁₃	#1424	1	1	yes	characteristic
42	M₁₆	—	104	1	no	—
43	C₂×C₈	D₁₀₄	1	1	yes	characteristic
44	C₄⋊C₄	—	104	1	no	—
45	C₁₆	Dic₅₂	1	1	yes	characteristic
46	C₁₆	C₄⋊Dic₁₃	1	1	yes	characteristic
47	C₁₃	#7548	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	—	208	1	no	—
49	C₂×C₄	D₂₀₈	1	1	yes	characteristic
50	C₈	—	208	1	no	—
51	C₈	Dic₁₀₄	1	1	yes	characteristic
52	C₈	#88058	1	1	yes	characteristic
53	C₂²	#11718041	1	1	yes	characteristic
54	C₄	—	416	1	no	—
55	C₄	#11718041	1	1	yes	characteristic
56	C₄	#11718096	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#13113038	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13113038
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₁₃×M₁₂₈	C₂
socle	C₂×C₁₃	#1424
prime radical	C₂²×C₁₃	SD₆₄
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₃
hypocenter	C₁₃	#7548
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
7. C₁₃×C₆₄	C₄	semidirect
30. C₆₄	Dic₁₃	semidirect
47. C₁₃	#7548	semidirect

Maximal subgroups

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

subgroup	index
#13113040	2
#13113038	2
C₁₃×M₁₂₈	2
#7548	13