Subgroups — #13130765

Order 1664.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718309	C₂	1	1	yes	maximal, characteristic
2	#11718290	C₂	1	6	yes	maximal
3	C₂²×#1057	C₂²	1	4	yes	—
4	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
5	C₁₃×#95	C₄	1	1	yes	characteristic
6	#88071	C₄	1	3	yes	—
7	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
8	C₂²×Dic₁₃	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
10	C₂×#1057	—	2	12	no	—
11	C₄×Dic₁₃	—	2	6	no	—
12	#1840	—	13	1	no	maximal, Sylow
13	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₃	—	2	3	no	—
15	C₂×C₄×C₁₃	—	2	6	no	—
16	C₂×Dic₁₃	—	2	3	no	—
17	C₂×Dic₁₃	—	2	3	no	—
18	C₂×Dic₁₃	—	2	3	no	—
19	C₂×Dic₁₃	#41	1	6	yes	—
20	#1057	—	4	4	no	—
21	#376	—	13	1	no	—
22	#336	—	13	6	no	—
23	C₂²×C₁₃	#117	1	3	yes	—
24	C₂²×C₁₃	#131	1	3	yes	—
25	C₂²×C₁₃	#131	1	1	yes	characteristic
26	C₄×C₁₃	—	4	3	no	—
27	Dic₁₃	—	4	3	no	—
28	Dic₁₃	#126	1	4	yes	—
29	C₂²×C₈	—	13	4	no	—
30	C₂×C₄²	—	13	3	no	—
31	#95	—	13	3	no	—
32	#95	#261	1	1	yes	characteristic
33	C₂×C₁₃	#383	1	1	yes	characteristic
34	C₂×C₁₃	#433	1	3	yes	—
35	C₂×C₁₃	#433	1	3	yes	—
36	C₂²×C₄	—	13	1	no	—
37	C₂²×C₄	—	13	3	no	—
38	C₂²×C₄	C₂×#261	1	3	yes	—
39	C₂×C₈	—	26	12	no	—
40	C₄²	—	26	6	no	—
41	C₁₃	#1840	1	1	yes	characteristic, complemented, Sylow
42	C₂³	C₂²×#261	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	13	6	no	—
46	C₂×C₄	—	26	3	no	—
47	C₂×C₄	—	26	3	no	—
48	C₂×C₄	—	26	3	no	—
49	C₈	—	52	4	no	—
50	C₂²	#88237	1	3	yes	—
51	C₂²	#88238	1	3	yes	—
52	C₂²	#88240	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	13	4	no	—
55	C₄	—	52	3	no	—
56	C₂	#11719061	1	1	yes	characteristic
57	C₂	#11719068	1	3	yes	—
58	C₂	#11719077	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#261
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#95	C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	#95	#261
hypocenter	C₁₃	#1840
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
41. C₁₃	#1840	semidirect

Maximal subgroups

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

subgroup	index
#11718309	2
#11718290	2
#1840	13