Subgroups — #13129871

Order 1664.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718261	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#88106	—	2	2	no	—
4	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂×#6090	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₁₃	Q₈	1	1	yes	characteristic
9	C₂×#1055	D₄	1	1	yes	characteristic
10	#6092	—	4	2	no	—
11	C₁₃×C₁₆	C₈	1	2	yes	—
12	#6090	—	2	1	no	—
13	#1373	—	13	1	no	maximal, Sylow
14	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×Dic₁₃	—	2	1	no	—
16	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₃	M₁₆	1	1	yes	characteristic
18	#1055	D₈	1	1	yes	characteristic
19	#1055	Q₁₆	1	1	yes	characteristic
20	#364	—	13	2	no	—
21	C₄×C₁₆	—	13	1	no	—
22	C₂²×C₁₃	#108	1	1	yes	characteristic
23	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₁₃	#107	1	1	yes	characteristic
25	Dic₁₃	—	2	2	no	—
26	M₃₂	—	26	2	no	—
27	C₂×C₁₆	—	13	1	no	—
28	C₂×C₁₆	#261	1	1	yes	characteristic
29	C₄×C₈	—	13	1	no	—
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	#335	1	1	yes	characteristic
32	C₂×C₈	—	13	1	no	—
33	C₂×C₈	C₂×#261	1	1	yes	characteristic
34	C₄²	—	13	1	no	—
35	C₁₆	—	26	1	no	—
36	C₁₆	—	52	2	no	—
37	C₁₆	#1057	1	2	yes	—
38	C₁₃	#1373	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄	—	26	1	no	—
40	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
41	C₈	—	13	1	no	—
42	C₈	—	13	1	no	—
43	C₈	#6118	1	1	yes	characteristic
44	C₈	C₂×#1057	1	1	yes	characteristic
45	C₂²	#88104	1	1	yes	characteristic
46	C₄	—	26	2	no	—
47	C₄	#88102	1	1	yes	characteristic
48	C₄	C₄⋊#1057	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#11718254	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88102
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	#335
prime radical	C₂²×C₁₃	#108
cosocle	C₈×Dic₁₃	C₂²
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	#1373
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
38. C₁₃	#1373	semidirect

Maximal subgroups

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

subgroup	index
#11718261	2
C₁₆×Dic₁₃	2
#1373	13