Subgroups — #13114990

Order 1664.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#1055	C₂	1	6	yes	maximal
3	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
4	C₂²×#1055	C₂²	1	4	yes	—
5	C₁₃×#95	C₄	1	4	yes	—
6	C₄⋊#1055	—	2	12	no	—
7	C₂²×C₄×C₁₃	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
9	C₄²×C₁₃	D₄	1	6	yes	—
10	C₄²×C₁₃	Q₈	1	6	yes	—
11	C₂×#1055	—	2	12	no	—
12	#1843	—	13	1	no	maximal, Sylow
13	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₃	—	2	12	no	—
15	C₂×C₄×C₁₃	C₄⋊C₄	1	12	yes	—
16	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
17	C₂×C₄×C₁₃	C₂×Q₈	1	3	yes	—
18	#1055	—	4	4	no	—
19	C₂×C₄⋊C₈	—	13	6	no	—
20	#376	D₁₃	1	1	yes	characteristic
21	C₂²×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
22	C₂²×C₁₃	#131	1	4	yes	—
23	C₄×C₁₃	—	2	12	no	—
24	C₄×C₁₃	#127	1	1	yes	characteristic
25	C₄×C₁₃	C₄⋊Q₈	1	3	yes	—
26	C₂²×C₈	—	13	4	no	—
27	C₂×C₄²	C₂×D₁₃	1	3	yes	—
28	C₄⋊C₈	—	26	12	no	—
29	#95	Dic₁₃	1	4	yes	—
30	C₂×C₁₃	#384	1	1	yes	characteristic
31	C₂×C₁₃	#424	1	6	yes	—
32	C₂²×C₄	C₂×Dic₁₃	1	6	yes	—
33	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
34	C₂×C₈	—	26	12	no	—
35	C₄²	Dic₂₆	1	6	yes	—
36	C₄²	D₅₂	1	6	yes	—
37	C₁₃	#1843	1	1	yes	characteristic, complemented, Sylow
38	C₂³	C₂²×Dic₁₃	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₁₃	1	12	yes	—
41	C₂×C₄	C₂×Dic₂₆	1	3	yes	—
42	C₂×C₄	C₂×D₅₂	1	3	yes	—
43	C₈	—	52	4	no	—
44	C₂²	C₂×C₄⋊Dic₁₃	1	3	yes	—
45	C₂²	#88202	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#88123	1	3	yes	—
48	C₄	#88128	1	1	yes	characteristic
49	C₂	#11718596	1	1	yes	characteristic
50	C₂	#11718660	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#376	C₂
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#376	D₁₃
hypocenter	C₁₃	#1843
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
37. C₁₃	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#376	2
C₂×C₄⋊#1055	2
#1843	13