Subgroups — #13116722

Order 1664.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#508	C₂	1	1	yes	maximal, characteristic
2	#11718857	C₂	1	2	yes	maximal, complemented
3	#11718159	C₂	1	2	yes	maximal, complemented
4	#11718098	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#135	C₂²	1	2	yes	—
7	#88202	—	2	2	no	—
8	C₁₃×Q₃₂	C₄	1	1	yes	characteristic, complemented
9	C₁₃×SD₃₂	C₄	1	2	yes	complemented
10	C₁₃×D₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	#88077	—	2	2	no	—
13	#88059	C₂²	1	2	yes	—
14	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₂×#6090	C₂²	1	1	yes	characteristic
16	C₁₃×#41	—	2	2	no	—
17	C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
18	C₁₃×SD₁₆	—	2	2	no	—
19	C₁₃×D₈	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₄×Dic₁₃	D₄	1	1	yes	characteristic
22	#6099	—	2	2	no	—
23	#6099	—	4	2	no	—
24	C₂×#1055	—	4	2	no	—
25	C₂×#1055	D₄	1	1	yes	characteristic
26	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
27	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
28	#6090	—	2	1	no	—
29	#2179	—	13	1	no	maximal, Sylow
30	Q₈×C₁₃	—	2	2	no	—
31	D₄×C₁₃	—	2	2	no	—
32	D₄×C₁₃	—	4	2	no	—
33	C₂×C₄×C₁₃	—	4	2	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₁₃	—	2	1	no	—
36	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₁₃	#41	1	1	yes	characteristic
38	#1055	—	4	2	no	—
39	#1055	D₈	1	2	yes	—
40	#508	D₁₃	1	1	yes	characteristic
41	#443	—	13	2	no	—
42	#368	—	13	1	no	—
43	#359	—	13	2	no	—
44	#346	—	13	1	no	—
45	C₂²×C₁₃	—	4	2	no	—
46	C₂²×C₁₃	#135	1	1	yes	characteristic
47	C₄×C₁₃	—	4	2	no	—
48	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
49	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
50	Dic₁₃	—	4	1	no	—
51	#135	C₂×D₁₃	1	2	yes	—
52	#131	—	26	2	no	—
53	Q₃₂	Dic₁₃	1	1	yes	characteristic, complemented
54	SD₃₂	Dic₁₃	1	2	yes	complemented
55	D₁₆	Dic₁₃	1	1	yes	characteristic, complemented
56	C₂×C₁₆	—	13	1	no	—
57	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
58	#108	—	13	2	no	—
59	#104	—	26	2	no	—
60	C₄×C₈	—	13	1	no	—
61	C₂×C₁₃	—	2	1	no	—
62	C₂×C₁₃	—	8	2	no	—
63	C₂×C₁₃	C₄×D₈	1	1	yes	characteristic
64	#41	—	2	2	no	—
65	Q₁₆	C₂×Dic₁₃	1	2	yes	—
66	SD₁₆	—	2	2	no	—
67	D₈	C₂×Dic₁₃	1	2	yes	—
68	M₁₆	—	26	2	no	—
69	M₁₆	—	52	2	no	—
70	C₂×C₈	—	13	1	no	—
71	C₂×C₈	—	52	2	no	—
72	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
73	C₄²	—	13	1	no	—
74	C₁₆	—	26	1	no	—
75	C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
76	C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
77	C₁₃	#2179	1	1	yes	characteristic, complemented, Sylow
78	Q₈	—	2	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	4	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	26	1	no	—
83	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
84	C₈	—	13	2	no	—
85	C₈	—	52	2	no	—
86	C₈	#6129	1	1	yes	characteristic
87	C₈	C₂²×Dic₁₃	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	#88166	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	52	1	no	—
92	C₄	D₈×D₁₃	1	1	yes	characteristic
93	C₄	D₄×Dic₁₃	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	8	2	no	—
96	C₂	D₈×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₁₃
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting, prime radical	C₁₃×#508	C₂
socle	C₂×C₁₃	C₄×D₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	#508	D₁₃
hypocenter	C₁₃	#2179
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

Complements

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

N	H ≅ G/N	type
2. #11718857	C₂	semidirect
3. #11718159	C₂	semidirect
4. #11718098	C₂	semidirect
5. #11718094	C₂	semidirect
8. C₁₃×Q₃₂	C₄	semidirect
9. C₁₃×SD₃₂	C₄	semidirect
10. C₁₃×D₁₆	C₄	semidirect
53. Q₃₂	Dic₁₃	semidirect
54. SD₃₂	Dic₁₃	semidirect
55. D₁₆	Dic₁₃	semidirect
77. C₁₃	#2179	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#508	2
#11718857	2
#11718159	2
#11718098	2
#11718094	2
#2179	13