Subgroups — #13116441

Order 1664.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×#88052	C₂	1	2	yes	maximal
3	#11718058	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₁₃×#117	C₄	1	1	yes	characteristic
7	C₁₃×#97	C₂²	1	2	yes	—
8	C₄×C₈×C₁₃	C₄	1	2	yes	—
9	#88052	C₄	1	4	yes	complemented
10	#88052	C₂²	1	4	yes	—
11	C₂×#6090	C₄	1	4	yes	complemented
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₁₃×M₁₆	—	2	2	no	—
14	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×C₄⋊C₄	—	2	1	no	—
20	C₁₃×C₂²⋊C₄	—	2	1	no	—
21	C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	#6090	C₂×C₄	1	8	yes	—
23	#2110	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	2	no	—
26	C₂×C₄×C₁₃	C₄²	1	2	yes	—
27	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₁₃	—	2	2	no	—
31	C₈×C₁₃	C₄²	1	1	yes	characteristic
32	C₈×C₁₃	C₄²	1	1	yes	characteristic
33	C₈×C₁₃	C₂²×C₄	1	2	yes	—
34	C₂×M₃₂	—	13	2	no	—
35	#405	D₁₃	1	1	yes	characteristic
36	#347	—	13	4	no	—
37	C₂²×C₁₃	—	4	1	no	—
38	C₂²×C₁₃	#97	1	2	yes	—
39	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₁₃	—	4	2	no	—
41	C₄×C₁₃	#97	1	2	yes	—
42	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
44	C₂×M₁₆	Dic₁₃	1	1	yes	characteristic
45	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
46	#117	Dic₁₃	1	1	yes	characteristic
47	M₃₂	—	13	4	no	—
48	M₃₂	—	13	4	no	—
49	C₂×C₁₆	—	13	4	no	—
50	#97	C₂×D₁₃	1	2	yes	—
51	C₄×C₈	Dic₁₃	1	2	yes	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	—	2	2	no	—
54	C₂×C₁₃	C₂×#97	1	1	yes	characteristic
55	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
56	M₁₆	—	2	2	no	—
57	C₂×C₈	C₄×D₁₃	1	2	yes	—
58	C₂×C₈	C₄×D₁₃	1	2	yes	—
59	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
60	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
62	C₄⋊C₄	—	2	1	no	—
63	C₂²⋊C₄	—	2	1	no	—
64	C₄²	C₂×Dic₁₃	1	2	yes	—
65	C₁₆	—	13	8	no	—
66	C₁₃	#2110	1	1	yes	characteristic, complemented, Sylow
67	C₂³	#6099	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	#6099	1	2	yes	—
70	C₂×C₄	#6099	1	1	yes	characteristic
71	C₂×C₄	C₄×Dic₁₃	1	2	yes	—
72	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₈	C₄×Dic₁₃	1	1	yes	characteristic
75	C₈	C₄×Dic₁₃	1	1	yes	characteristic
76	C₈	C₂×C₄×D₁₃	1	2	yes	—
77	C₂²	—	4	1	no	—
78	C₂²	#88043	1	2	yes	—
79	C₂²	C₂×#6099	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#88043	1	2	yes	—
82	C₄	C₂×#6099	1	1	yes	characteristic
83	C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#88043	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₁₃
commutator	C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#405	C₂
socle	C₂×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	#405	D₁₃
hypocenter	C₁₃	#2110
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #11718058	C₂	semidirect
9. #88052	C₄	semidirect
11. C₂×#6090	C₄	semidirect
66. C₁₃	#2110	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#405	2
C₂×#88052	2
#11718058	2
#2110	13