Subgroups — #13117112

Order 1664.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#499	C₂	1	1	yes	maximal, characteristic
2	#11718344	C₂	1	1	yes	maximal, characteristic
3	#11718082	C₂	1	2	yes	maximal
4	#11718081	C₂	1	2	yes	maximal
5	C₄×#6090	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#125	—	2	1	no	—
7	#88124	—	2	1	no	—
8	C₁₃×#107	C₂²	1	2	yes	—
9	C₁₃×#106	—	2	1	no	—
10	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	#88058	C₂²	1	2	yes	—
12	#88057	—	2	1	no	—
13	C₂×#6090	C₂²	1	1	yes	characteristic
14	C₂×#6090	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₄⋊C₄	—	4	2	no	—
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₃	—	2	2	no	—
21	#6101	—	4	2	no	—
22	#6090	Q₈	1	2	yes	—
23	#6090	Q₈	1	2	yes	—
24	#2253	—	13	1	no	maximal, Sylow
25	C₂×C₄×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	D₈	1	2	yes	—
27	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₁₃	—	4	2	no	—
29	C₈×C₁₃	Q₁₆	1	2	yes	—
30	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
31	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
32	#499	—	13	1	no	—
33	#499	D₁₃	1	1	yes	characteristic
34	#367	—	13	2	no	—
35	#366	—	13	2	no	—
36	C₄×C₁₆	—	13	1	no	—
37	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
38	C₄×C₁₃	—	2	2	no	—
39	C₄×C₁₃	—	8	2	no	—
40	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
41	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₁₃	—	8	2	no	—
43	#125	—	2	1	no	—
44	#125	—	26	1	no	—
45	C₂×C₁₆	—	13	1	no	—
46	C₂×C₁₆	—	13	1	no	—
47	#107	—	13	2	no	—
48	#107	C₂×D₁₃	1	2	yes	—
49	#106	—	2	1	no	—
50	#106	—	26	1	no	—
51	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
52	C₂×C₁₃	#500	1	1	yes	characteristic
53	C₂×C₁₃	#508	1	2	yes	—
54	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
55	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
56	C₄⋊C₄	—	2	2	no	—
57	C₄⋊C₄	—	4	2	no	—
58	C₄⋊C₄	—	26	2	no	—
59	C₄⋊C₄	—	52	2	no	—
60	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
61	C₁₆	—	13	2	no	—
62	C₁₆	—	13	2	no	—
63	C₁₃	#2253	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	52	2	no	—
66	C₂×C₄	#6104	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
68	C₈	#6107	1	2	yes	—
69	C₈	Q₈×D₁₃	1	1	yes	characteristic
70	C₈	Q₈×D₁₃	1	1	yes	characteristic
71	C₂²	C₂×#6104	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	104	2	no	—
75	C₄	C₂×#6107	1	1	yes	characteristic
76	C₄	#88198	1	1	yes	characteristic
77	C₂	#11718739	1	1	yes	characteristic
78	C₂	#11718855	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#499	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#499	D₁₃
hypocenter	C₁₃	#2253
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
63. C₁₃	#2253	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#499	2
#11718344	2
#11718082	2
#11718081	2
C₄×#6090	2
#2253	13