Subgroups — #13123113

Order 1664.

3422 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#88207	C₂	1	7	yes	maximal, complemented
3	#11718908	C₂	1	7	yes	maximal, complemented
4	C₂⁵×C₁₃	—	2	28	no	—
5	C₂⁵×C₁₃	C₂²	1	7	yes	—
6	C₂²×C₂²⋊D₁₃	C₂²	1	7	yes	complemented
7	#88207	—	2	28	no	—
8	C₂×C₂²⋊Dic₁₃	C₂²	1	21	yes	complemented
9	C₂⁴×C₁₃	—	2	224	no	—
10	C₂⁴×C₁₃	—	2	84	no	—
11	C₂⁴×C₁₃	D₄	1	28	yes	complemented
12	C₂⁴×C₁₃	C₂³	1	7	yes	—
13	C₂³×D₁₃	C₂³	1	1	yes	characteristic, complemented
14	C₂×C₂²⋊D₁₃	—	2	42	no	—
15	C₂²×Dic₁₃	C₂³	1	7	yes	complemented
16	C₂²⋊Dic₁₃	—	2	42	no	—
17	#2846	—	13	1	no	maximal, Sylow
18	C₂³×C₁₃	—	2	256	no	—
19	C₂³×C₁₃	—	2	224	no	—
20	C₂³×C₁₃	—	2	168	no	—
21	C₂³×C₁₃	—	2	28	no	—
22	C₂³×C₁₃	C₂×D₄	1	42	yes	—
23	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
24	C₂²×D₁₃	—	2	7	no	—
25	C₂²⋊D₁₃	—	4	28	no	—
26	C₂×Dic₁₃	—	2	21	no	—
27	C₂⁶	D₁₃	1	1	yes	characteristic, complemented
28	C₂×#120	—	13	7	no	—
29	#379	—	13	7	no	—
30	C₂²×C₁₃	—	2	224	no	—
31	C₂²×C₁₃	—	2	84	no	—
32	C₂²×C₁₃	#120	1	28	yes	complemented
33	C₂²×C₁₃	C₂²×D₄	1	7	yes	—
34	C₂×D₁₃	—	4	7	no	—
35	Dic₁₃	—	4	7	no	—
36	C₂⁵	—	2	28	no	—
37	C₂⁵	C₂×D₁₃	1	7	yes	—
38	C₂²×D₄	—	13	7	no	—
39	#120	—	26	28	no	—
40	C₂×C₂²⋊C₄	—	13	21	no	—
41	C₂×C₁₃	—	2	28	no	—
42	C₂×C₁₃	C₂×#120	1	7	yes	—
43	D₁₃	—	8	1	no	—
44	C₂⁴	—	2	224	no	—
45	C₂⁴	—	2	84	no	—
46	C₂⁴	—	13	1	no	—
47	C₂⁴	C₂²⋊D₁₃	1	28	yes	complemented
48	C₂⁴	C₂²×D₁₃	1	7	yes	—
49	C₂×D₄	—	26	42	no	—
50	C₂²×C₄	—	13	7	no	—
51	C₂²⋊C₄	—	26	42	no	—
52	C₁₃	#2846	1	1	yes	characteristic, complemented, Sylow
53	C₂³	—	2	256	no	—
54	C₂³	—	2	224	no	—
55	C₂³	—	2	168	no	—
56	C₂³	—	2	28	no	—
57	C₂³	—	26	7	no	—
58	C₂³	C₂×C₂²⋊D₁₃	1	42	yes	—
59	C₂³	C₂³×D₁₃	1	1	yes	characteristic
60	D₄	—	52	28	no	—
61	C₂×C₄	—	26	21	no	—
62	C₂²	—	2	224	no	—
63	C₂²	—	2	84	no	—
64	C₂²	—	52	7	no	—
65	C₂²	#88207	1	28	yes	complemented
66	C₂²	C₂²×C₂²⋊D₁₃	1	7	yes	—
67	C₄	—	52	7	no	—
68	C₂	—	2	28	no	—
69	C₂	—	104	1	no	—
70	C₂	C₂×#88207	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₂⁶×C₁₃	C₂
hypercenter	C₂⁶	D₁₃
hypocenter	C₁₃	#2846
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁶×C₁₃	C₂	semidirect
2. C₂×#88207	C₂	semidirect
3. #11718908	C₂	semidirect
6. C₂²×C₂²⋊D₁₃	C₂²	semidirect
8. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
11. C₂⁴×C₁₃	D₄	semidirect
13. C₂³×D₁₃	C₂³	semidirect
15. C₂²×Dic₁₃	C₂³	semidirect
27. C₂⁶	D₁₃	semidirect
32. C₂²×C₁₃	#120	semidirect
47. C₂⁴	C₂²⋊D₁₃	semidirect
52. C₁₃	#2846	semidirect
65. C₂²	#88207	semidirect

Maximal subgroups

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

subgroup	index
C₂⁶×C₁₃	2
C₂×#88207	2
#11718908	2
#2846	13