Subgroups — #13130763

Order 1664.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	#11718290	C₂	1	6	yes	maximal
3	C₂²×#1057	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₁₃	C₄	1	3	yes	—
6	C₂×C₄×Dic₁₃	C₂²	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	C₄²×C₁₃	C₈	1	4	yes	complemented
12	C₄×Dic₁₃	—	2	6	no	—
13	C₄×Dic₁₃	—	2	6	no	—
14	#1839	—	13	1	no	maximal, Sylow
15	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₃	—	2	3	no	—
17	C₂×C₄×C₁₃	—	2	3	no	—
18	C₂×C₄×C₁₃	C₂×C₈	1	6	yes	—
19	C₂×Dic₁₃	—	2	3	no	—
20	C₂×Dic₁₃	—	2	3	no	—
21	C₂×Dic₁₃	M₁₆	1	6	yes	—
22	C₂×Dic₁₃	#41	1	6	yes	—
23	#1057	—	4	4	no	—
24	C₄³	—	13	1	no	—
25	#336	—	13	6	no	—
26	C₂²×C₁₃	#117	1	3	yes	—
27	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
28	C₂²×C₁₃	C₂×M₁₆	1	3	yes	—
29	C₄×C₁₃	—	2	6	no	—
30	Dic₁₃	—	2	6	no	—
31	Dic₁₃	#126	1	4	yes	—
32	C₂²×C₈	—	13	4	no	—
33	C₂×C₄²	—	13	3	no	—
34	C₂×C₄²	—	13	3	no	—
35	C₂×C₄²	#261	1	1	yes	characteristic
36	C₂×C₁₃	#383	1	1	yes	characteristic
37	C₂×C₁₃	#431	1	3	yes	—
38	C₂×C₁₃	#432	1	3	yes	—
39	C₂²×C₄	—	13	1	no	—
40	C₂²×C₄	—	13	3	no	—
41	C₂²×C₄	C₂×#261	1	3	yes	—
42	C₂×C₈	—	26	12	no	—
43	C₄²	—	26	6	no	—
44	C₄²	—	26	6	no	—
45	C₄²	#1057	1	4	yes	complemented
46	C₁₃	#1839	1	1	yes	characteristic, complemented, Sylow
47	C₂³	C₂²×#261	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	13	6	no	—
51	C₂×C₄	—	13	6	no	—
52	C₂×C₄	—	26	3	no	—
53	C₂×C₄	—	26	3	no	—
54	C₂×C₄	C₂×#1057	1	6	yes	—
55	C₈	—	52	4	no	—
56	C₂²	D₁₃⋊M₁₆	1	3	yes	—
57	C₂²	#88237	1	3	yes	—
58	C₂²	C₂²×#1057	1	1	yes	characteristic
59	C₄	—	2	6	no	—
60	C₄	—	13	4	no	—
61	C₄	—	26	6	no	—
62	C₂	#11719055	1	3	yes	—
63	C₂	#11719061	1	1	yes	characteristic
64	C₂	#11719119	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#261
commutator	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₄²×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#1839
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
11. C₄²×C₁₃	C₈	semidirect
45. C₄²	#1057	semidirect
46. C₁₃	#1839	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₁₃	2
#11718290	2
#1839	13