Subgroups — #15750604

Order 3328.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13112912	C₂	1	2	yes	maximal
2	C₁₃×#1397	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
5	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	#11718055	—	2	2	no	—
7	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
9	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
10	#88052	—	4	2	no	—
11	C₁₃×C₃₂	—	2	1	no	—
12	C₁₃×C₃₂	C₈	1	2	yes	—
13	#7464	—	13	1	no	maximal, Sylow
14	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
16	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
17	C₁₃×C₁₆	—	2	1	no	—
18	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
20	#6090	—	8	2	no	—
21	#1397	D₁₃	1	1	yes	characteristic
22	#1373	—	13	2	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
25	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₃	#108	1	1	yes	characteristic
27	C₈×C₁₃	SD₃₂	1	2	yes	—
28	C₂×C₃₂	Dic₁₃	1	1	yes	characteristic
29	C₂×C₃₂	Dic₁₃	1	1	yes	characteristic
30	#364	—	26	2	no	—
31	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
32	C₂²×C₁₃	#368	1	1	yes	characteristic
33	C₄×C₁₃	—	4	1	no	—
34	C₄×C₁₃	#335	1	1	yes	characteristic
35	C₄×C₁₃	#367	1	1	yes	characteristic
36	M₃₂	—	52	2	no	—
37	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
39	C₄×C₈	D₅₂	1	1	yes	characteristic
40	C₃₂	—	2	1	no	—
41	C₃₂	#1055	1	2	yes	—
42	C₂×C₁₃	—	2	1	no	—
43	C₂×C₁₃	#1372	1	1	yes	characteristic
44	C₂×C₈	D₁₀₄	1	1	yes	characteristic
45	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
46	C₄²	Dic₅₂	1	1	yes	characteristic
47	C₁₆	—	2	1	no	—
48	C₁₆	—	104	2	no	—
49	C₁₆	C₂×#1055	1	1	yes	characteristic
50	C₁₆	#6099	1	1	yes	characteristic
51	C₁₃	#7464	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	#88058	1	1	yes	characteristic
54	C₈	#88040	1	2	yes	—
55	C₈	C₄⋊#1055	1	1	yes	characteristic
56	C₈	#88059	1	1	yes	characteristic
57	C₂²	#11718098	1	1	yes	characteristic
58	C₄	—	4	1	no	—
59	C₄	#11718050	1	1	yes	characteristic
60	C₄	#11718097	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#13112910	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718097
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#1397	C₂
socle	C₂×C₁₃	#1372
prime radical	C₂²×C₁₃	#368
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#1397	D₁₃
hypocenter	C₁₃	#7464
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

Complements

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

N	H ≅ G/N	type
51. C₁₃	#7464	semidirect

Maximal subgroups

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

subgroup	index
#13112912	2
C₁₃×#1397	2
#7464	13