Subgroups — #13129843

Order 1664.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718730	C₂	1	1	yes	maximal, characteristic
2	#11718232	C₂	1	2	yes	maximal
3	C₁₃×#125	C₄	1	1	yes	characteristic
4	#88123	C₄	1	1	yes	characteristic
5	#88106	—	2	2	no	—
6	#88050	—	2	2	no	—
7	#88043	C₂²	1	1	yes	characteristic
8	C₂×Dic₂₆	—	2	1	no	—
9	C₁₃×C₄⋊C₄	—	2	1	no	—
10	C₁₃×C₄⋊C₄	—	4	1	no	—
11	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₄⋊Dic₁₃	—	4	1	no	—
13	C₂×#1055	D₄	1	2	yes	—
14	#6092	—	2	4	no	—
15	#1356	—	13	1	no	maximal, Sylow
16	C₂×C₄×C₁₃	—	2	1	no	—
17	C₂×C₄×C₁₃	—	4	1	no	—
18	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₁₃	—	4	1	no	—
20	Dic₂₆	—	4	2	no	—
21	#1055	—	2	2	no	—
22	#491	—	13	1	no	—
23	#347	—	13	2	no	—
24	C₂²×C₁₃	#100	1	1	yes	characteristic
25	C₄×C₁₃	—	4	1	no	—
26	C₄×C₁₃	—	8	1	no	—
27	C₄×C₁₃	#104	1	2	yes	—
28	Dic₁₃	—	8	1	no	—
29	C₄⋊Q₈	—	13	1	no	—
30	#125	#261	1	1	yes	characteristic
31	M₃₂	—	26	2	no	—
32	#103	—	26	2	no	—
33	#97	—	13	1	no	—
34	C₂×C₁₃	—	2	1	no	—
35	C₂×C₁₃	#329	1	1	yes	characteristic
36	C₂×Q₈	—	26	1	no	—
37	C₂×C₈	—	13	2	no	—
38	C₄⋊C₄	—	2	1	no	—
39	C₄⋊C₄	—	4	1	no	—
40	C₄⋊C₄	—	52	1	no	—
41	C₄²	C₂×#261	1	1	yes	characteristic
42	C₁₆	—	26	4	no	—
43	C₁₃	#1356	1	1	yes	characteristic, complemented, Sylow
44	Q₈	—	52	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	52	1	no	—
48	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
49	C₈	—	26	2	no	—
50	C₂²	#88121	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	104	1	no	—
54	C₄	#88118	1	2	yes	—
55	C₂	—	2	1	no	—
56	C₂	#11718299	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718299
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting	C₁₃×#125	C₄
socle	C₂×C₁₃	#329
prime radical	C₂²×C₁₃	#100
cosocle	#88043	C₂²
hypercenter	#125	#261
hypocenter	C₁₃	#1356
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
43. C₁₃	#1356	semidirect

Maximal subgroups

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

subgroup	index
#11718730	2
#11718232	2
#1356	13