Subgroups — #13112903

Order 1664.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#364	C₂	1	1	yes	maximal, characteristic
2	#11718055	C₂	1	1	yes	maximal, characteristic
3	#11718053	C₂	1	1	yes	maximal, characteristic
4	C₁₃×M₃₂	—	2	1	no	—
5	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	#88052	—	2	1	no	—
7	C₂×#6090	C₄	1	1	yes	characteristic
8	C₂×#6090	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
11	C₄²×C₁₃	Q₈	1	1	yes	characteristic
12	C₁₃×C₁₆	—	4	1	no	—
13	#6090	—	2	1	no	—
14	#6090	—	4	1	no	—
15	#6090	C₈	1	2	yes	—
16	#1369	—	13	1	no	maximal, Sylow
17	C₂×C₄×C₁₃	—	2	1	no	—
18	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₃	M₁₆	1	1	yes	characteristic
21	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
22	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
23	#364	—	13	1	no	—
24	#364	D₁₃	1	1	yes	characteristic
25	#346	—	13	1	no	—
26	C₂²×C₁₃	#108	1	1	yes	characteristic
27	C₄×C₁₃	—	4	1	no	—
28	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
29	C₄×C₁₃	#106	1	1	yes	characteristic
30	M₃₂	—	2	1	no	—
31	M₃₂	—	26	1	no	—
32	C₂×C₁₆	—	13	1	no	—
33	C₂×C₁₆	—	13	1	no	—
34	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
35	C₂×C₁₃	—	2	1	no	—
36	C₂×C₁₃	#334	1	1	yes	characteristic
37	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
38	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
39	C₄²	Dic₂₆	1	1	yes	characteristic
40	C₁₆	—	4	1	no	—
41	C₁₆	—	13	2	no	—
42	C₁₆	—	26	1	no	—
43	C₁₆	—	52	1	no	—
44	C₁₃	#1369	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	#6101	1	1	yes	characteristic
47	C₈	C₈×D₁₃	1	1	yes	characteristic
48	C₈	#6094	1	1	yes	characteristic
49	C₈	#6105	1	1	yes	characteristic
50	C₈	#6106	1	1	yes	characteristic
51	C₂²	#88062	1	1	yes	characteristic
52	C₄	—	4	1	no	—
53	C₄	#88048	1	1	yes	characteristic
54	C₄	#88054	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#11718072	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88048
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₁₃×#364	C₂
socle	C₂×C₁₃	#334
prime radical	C₂²×C₁₃	#108
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	#364	D₁₃
hypocenter	C₁₃	#1369
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
44. C₁₃	#1369	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#364	2
#11718055	2
#11718053	2
#1369	13