Subgroups — #13113010

Order 1664.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718717	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#354	C₂	1	1	yes	maximal, characteristic
3	#11718134	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#124	C₂²	1	1	yes	characteristic
5	#88124	C₄	1	1	yes	characteristic, complemented
6	C₁₃×#99	—	2	1	no	—
7	#88076	—	2	1	no	—
8	#88075	—	2	1	no	—
9	#88072	—	2	1	no	—
10	C₄×#1055	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
13	C₁₃×C₂²⋊C₄	—	4	1	no	—
14	C₁₃×C₂²⋊C₄	—	4	1	no	—
15	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₁₃	—	2	1	no	—
17	#6101	—	4	1	no	—
18	#6099	—	4	1	no	—
19	C₂×#1055	—	2	1	no	—
20	#1414	—	13	1	no	maximal, Sylow
21	C₂³×C₁₃	—	2	1	no	—
22	Q₈×C₁₃	—	4	1	no	—
23	D₄×C₁₃	—	4	1	no	—
24	C₂×C₄×C₁₃	—	2	1	no	—
25	C₂×C₄×C₁₃	—	2	1	no	—
26	C₂×C₄×C₁₃	—	8	1	no	—
27	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₃	—	4	1	no	—
29	#1055	—	4	1	no	—
30	#1055	—	8	1	no	—
31	#488	—	13	1	no	—
32	#355	—	13	1	no	—
33	#354	D₁₃	1	1	yes	characteristic
34	C₂²×C₁₃	—	4	1	no	—
35	C₂²×C₁₃	—	8	1	no	—
36	C₂²×C₁₃	#99	1	1	yes	characteristic
37	C₄×C₁₃	—	2	1	no	—
38	C₄×C₁₃	—	4	1	no	—
39	C₄×C₁₃	—	4	1	no	—
40	C₄×C₁₃	—	16	1	no	—
41	Dic₁₃	—	8	1	no	—
42	#125	—	13	1	no	—
43	#124	C₂×D₁₃	1	1	yes	characteristic
44	#103	—	26	1	no	—
45	#102	—	26	1	no	—
46	#101	—	26	1	no	—
47	#99	—	2	1	no	—
48	C₄×C₈	—	13	1	no	—
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	—	8	1	no	—
51	C₂×C₁₃	#354	1	1	yes	characteristic
52	C₂×Q₈	D₅₂	1	1	yes	characteristic
53	C₂×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
54	M₁₆	—	52	1	no	—
55	C₂×C₈	—	26	1	no	—
56	C₄⋊C₄	—	26	1	no	—
57	C₄⋊C₄	—	52	1	no	—
58	C₂²⋊C₄	—	4	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₄²	C₄×D₁₃	1	1	yes	characteristic
61	C₁₃	#1414	1	1	yes	characteristic, complemented, Sylow
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	8	1	no	—
68	C₂×C₄	—	52	1	no	—
69	C₂×C₄	#6103	1	1	yes	characteristic
70	C₈	—	52	1	no	—
71	C₈	—	104	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#88046	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	16	1	no	—
79	C₄	—	104	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#11718065	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718065
commutator	C₄²×C₁₃	C₂×C₄
Frattini	#124	C₂×D₁₃
Fitting	C₁₃×#354	C₂
socle	C₂×C₁₃	#354
prime radical	C₂×D₄×C₁₃	D₄
cosocle	C₁₃×#124	C₂²
hypercenter	#354	D₁₃
hypocenter	C₁₃	#1414
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
5. #88124	C₄	semidirect
10. C₄×#1055	C₄	semidirect
61. C₁₃	#1414	semidirect

Maximal subgroups

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

subgroup	index
#11718717	2
C₁₃×#354	2
#11718134	2
#1414	13