Subgroups — #15750816

Order 3328.

70 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	C₃₂×Dic₁₃	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	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂×#88034	C₄	1	1	yes	characteristic
7	C₁₃×C₆₄	—	2	1	no	—
8	#11718035	—	2	1	no	—
9	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₁₃	C₈	1	1	yes	characteristic
11	C₂×#6090	C₈	1	1	yes	characteristic
12	C₁₃×C₃₂	D₄	1	1	yes	characteristic
13	C₁₃×C₃₂	Q₈	1	1	yes	characteristic
14	#88034	—	2	1	no	—
15	#7544	—	13	1	no	maximal, Sylow
16	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
18	C₂×#1055	C₁₆	1	1	yes	characteristic
19	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
20	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
21	#6090	—	2	1	no	—
22	M₁₂₈	—	13	1	no	—
23	M₁₂₈	D₁₃	1	1	yes	characteristic
24	C₄×C₃₂	—	13	1	no	—
25	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
26	C₂×Dic₁₃	—	2	1	no	—
27	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₁₃	M₃₂	1	1	yes	characteristic
29	#1055	C₃₂	1	2	yes	—
30	C₂×C₃₂	—	13	1	no	—
31	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
32	C₄×C₁₆	—	13	1	no	—
33	C₆₄	—	2	1	no	—
34	C₆₄	—	26	1	no	—
35	C₂²×C₁₃	M₆₄	1	1	yes	characteristic
36	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
37	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
38	Dic₁₃	—	2	2	no	—
39	C₂×C₁₆	—	13	1	no	—
40	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
41	C₄×C₈	—	13	1	no	—
42	C₃₂	—	26	1	no	—
43	C₃₂	Dic₂₆	1	1	yes	characteristic
44	C₃₂	C₂²⋊D₁₃	1	1	yes	characteristic
45	C₂×C₁₃	—	2	1	no	—
46	C₂×C₁₃	C₄⋊C₃₂	1	1	yes	characteristic
47	C₂×C₈	—	13	1	no	—
48	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
49	C₄²	—	13	1	no	—
50	C₁₆	—	26	1	no	—
51	C₁₆	#6094	1	1	yes	characteristic
52	C₁₆	#6101	1	1	yes	characteristic
53	C₁₃	#7544	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₄	—	26	1	no	—
55	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
56	C₈	—	13	2	no	—
57	C₈	#88038	1	1	yes	characteristic
58	C₈	#88054	1	1	yes	characteristic
59	C₂²	#11718039	1	1	yes	characteristic
60	C₄	—	26	2	no	—
61	C₄	D₁₃×C₃₂	1	1	yes	characteristic
62	C₄	#11718093	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#13113031	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₃
Fitting	C₁₃×M₁₂₈	C₂
socle	C₂×C₁₃	C₄⋊C₃₂
prime radical	C₂²×C₁₃	M₆₄
cosocle	C₂×C₁₃×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₃
hypocenter	C₁₃	#7544
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
53. C₁₃	#7544	semidirect

Maximal subgroups

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

subgroup	index
#13113047	2
C₃₂×Dic₁₃	2
C₁₃×M₁₂₈	2
#7544	13