Subgroups — #13117153

Order 1664.

104 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	C₂×Dic₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718114	C₂	1	2	yes	maximal, complemented
4	#11718112	C₂	1	2	yes	maximal, complemented
5	#11718091	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#135	—	2	1	no	—
7	C₂×Dic₅₂	—	2	1	no	—
8	C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
9	C₁₃×SD₃₂	—	2	1	no	—
10	C₁₃×D₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	Dic₁₀₄	—	2	1	no	—
13	Dic₁₀₄	C₂²	1	2	yes	—
14	#88034	C₂²	1	2	yes	—
15	C₁₃×#41	—	4	1	no	—
16	C₂×Dic₂₆	—	4	1	no	—
17	C₁₃×Q₁₆	—	2	1	no	—
18	C₁₃×SD₁₆	—	4	1	no	—
19	C₁₃×D₈	—	2	1	no	—
20	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
21	Dic₅₂	—	2	2	no	—
22	Dic₅₂	—	4	1	no	—
23	C₁₃×C₁₆	D₄	1	1	yes	characteristic
24	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
25	#2264	—	13	1	no	maximal, Sylow
26	Q₈×C₁₃	—	4	1	no	—
27	D₄×C₁₃	—	4	1	no	—
28	D₄×C₁₃	—	8	1	no	—
29	C₂×C₄×C₁₃	—	8	1	no	—
30	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
31	C₂×Dic₁₃	—	8	1	no	—
32	Dic₂₆	—	4	2	no	—
33	Dic₂₆	—	8	1	no	—
34	C₈×C₁₃	D₈	1	1	yes	characteristic
35	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
36	#508	D₁₃	1	1	yes	characteristic
37	C₂×Q₃₂	—	13	1	no	—
38	Q₆₄	—	13	2	no	—
39	SD₆₄	—	13	2	no	—
40	M₆₄	—	13	1	no	—
41	C₂²×C₁₃	—	8	1	no	—
42	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
43	C₄×C₁₃	—	8	1	no	—
44	C₄×C₁₃	D₁₆	1	1	yes	characteristic
45	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
46	Dic₁₃	—	8	2	no	—
47	#135	—	2	1	no	—
48	C₂×Q₁₆	—	26	1	no	—
49	Q₃₂	—	13	2	no	—
50	Q₃₂	—	26	1	no	—
51	Q₃₂	C₂×D₁₃	1	1	yes	characteristic
52	SD₃₂	—	2	1	no	—
53	D₁₆	C₂×D₁₃	1	1	yes	characteristic
54	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
55	C₃₂	—	13	2	no	—
56	C₂×C₁₃	—	2	1	no	—
57	C₂×C₁₃	—	16	1	no	—
58	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
59	#41	—	4	1	no	—
60	C₂×Q₈	—	52	1	no	—
61	Q₁₆	—	2	1	no	—
62	Q₁₆	—	26	2	no	—
63	Q₁₆	—	52	1	no	—
64	SD₁₆	—	4	1	no	—
65	D₈	—	2	1	no	—
66	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
67	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
68	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
69	C₁₃	#2264	1	1	yes	characteristic, complemented, Sylow
70	Q₈	—	4	1	no	—
71	Q₈	—	52	2	no	—
72	Q₈	—	104	1	no	—
73	D₄	—	4	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	104	1	no	—
77	C₂×C₄	#6104	1	1	yes	characteristic
78	C₈	#6104	1	1	yes	characteristic
79	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
80	C₂²	—	8	1	no	—
81	C₂²	#88066	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	104	2	no	—
84	C₄	#88066	1	1	yes	characteristic
85	C₄	C₂×#6104	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×#88066	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#88066
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting, prime radical	C₁₃×#508	C₂
socle	C₂×C₁₃	C₂×D₁₆
hypercenter	#508	D₁₃
hypocenter	C₁₃	#2264
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₀₄	C₂	semidirect
3. #11718114	C₂	semidirect
4. #11718112	C₂	semidirect
5. #11718091	C₂	semidirect
69. C₁₃	#2264	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
C₂×Dic₁₀₄	2
#11718114	2
#11718112	2
#11718091	2
#2264	13