Subgroups — #13112940

Order 1664.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#88059	C₂	1	2	yes	maximal
3	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
4	C₂×#6099	—	2	2	no	—
5	C₁₃×M₃₂	—	2	2	no	—
6	C₂×C₁₃×C₁₆	C₄	1	2	yes	—
7	#88059	—	2	2	no	—
8	#88059	C₄	1	4	yes	—
9	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₃	D₄	1	2	yes	—
13	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
14	#6099	—	2	4	no	—
15	#6099	—	4	2	no	—
16	C₂×#1055	—	4	2	no	—
17	C₁₃×C₁₆	—	2	2	no	—
18	#1385	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	SD₁₆	1	2	yes	—
24	C₈×C₁₃	C₄²	1	1	yes	characteristic
25	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
27	#1055	—	4	4	no	—
28	C₂×M₃₂	D₁₃	1	1	yes	characteristic
29	C₂×#108	—	13	2	no	—
30	C₂²×C₁₃	—	4	1	no	—
31	C₂²×C₁₃	#103	1	2	yes	—
32	C₂²×C₁₃	#107	1	1	yes	characteristic
33	C₄×C₁₃	#95	1	1	yes	characteristic
34	C₄×C₁₃	#102	1	2	yes	—
35	C₄×C₁₃	#106	1	1	yes	characteristic
36	C₂×M₁₆	—	26	2	no	—
37	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
38	M₃₂	—	2	2	no	—
39	C₂×C₁₆	Dic₁₃	1	2	yes	—
40	#108	—	13	4	no	—
41	#108	—	26	2	no	—
42	C₂×C₁₃	—	2	2	no	—
43	C₂×C₁₃	—	2	1	no	—
44	C₂×C₁₃	#340	1	1	yes	characteristic
45	C₂²×C₄	D₅₂	1	1	yes	characteristic
46	M₁₆	—	26	4	no	—
47	M₁₆	—	52	2	no	—
48	C₂×C₈	—	52	2	no	—
49	C₂×C₈	Dic₂₆	1	1	yes	characteristic
50	C₂×C₈	C₄×D₁₃	1	2	yes	—
51	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
53	C₁₆	—	2	2	no	—
54	C₁₃	#1385	1	1	yes	characteristic, complemented, Sylow
55	C₂³	Dic₅₂	1	1	yes	characteristic
56	C₂×C₄	#6095	1	2	yes	—
57	C₂×C₄	D₁₀₄	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
59	C₂×C₄	#6103	1	2	yes	—
60	C₈	—	52	4	no	—
61	C₈	C₄×Dic₁₃	1	1	yes	characteristic
62	C₈	#6101	1	2	yes	—
63	C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
64	C₂²	—	4	1	no	—
65	C₂²	#88056	1	2	yes	—
66	C₂²	#88058	1	1	yes	characteristic
67	C₄	#88057	1	1	yes	characteristic
68	C₄	#88061	1	2	yes	—
69	C₄	#88071	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	#11718143	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88057
commutator	C₈×C₁₃	C₄²
Frattini	C₂²×C₈	C₂×D₁₃
Fitting	C₂×C₁₃×M₃₂	C₂
socle	C₂×C₁₃	#340
prime radical	C₂³×C₁₃	Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂²
hypercenter	C₂×M₃₂	D₁₃
hypocenter	C₁₃	#1385
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
54. C₁₃	#1385	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×M₃₂	2
C₂×#88059	2
#1385	13