Subgroups — #13113003

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#492	C₂	1	1	yes	maximal, characteristic
2	#11718140	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×SD₁₆	—	2	2	no	—
4	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
5	C₁₃×#127	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	#88076	—	2	2	no	—
8	C₂×Q₈×C₁₃	D₄	1	2	yes	—
9	C₂×D₄×C₁₃	—	2	1	no	—
10	C₂×D₄×C₁₃	—	4	1	no	—
11	C₁₃×SD₁₆	—	4	4	no	—
12	C₂×C₈×C₁₃	—	2	1	no	—
13	C₁₃×C₄⋊C₄	—	4	1	no	—
14	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
15	#6099	—	4	2	no	—
16	#1410	—	13	1	no	maximal, Sylow
17	C₂³×C₁₃	—	4	1	no	—
18	Q₈×C₁₃	—	4	2	no	—
19	D₄×C₁₃	—	4	2	no	—
20	D₄×C₁₃	—	8	2	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	2	2	no	—
23	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₁₃	—	2	2	no	—
25	#1055	—	8	2	no	—
26	#492	D₁₃	1	1	yes	characteristic
27	#356	—	13	2	no	—
28	C₂²×C₁₃	—	8	2	no	—
29	C₂²×C₁₃	—	8	1	no	—
30	C₂²×C₁₃	#99	1	1	yes	characteristic
31	C₄×C₁₃	—	2	2	no	—
32	C₄×C₁₃	—	2	1	no	—
33	C₄×C₁₃	—	4	2	no	—
34	C₂×SD₁₆	—	2	2	no	—
35	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
36	#127	Dic₁₃	1	1	yes	characteristic
37	#101	—	26	2	no	—
38	C₄×C₈	Dic₁₃	1	1	yes	characteristic
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	—	16	1	no	—
41	C₂×C₁₃	#353	1	1	yes	characteristic
42	C₂×Q₈	C₂²⋊D₁₃	1	2	yes	—
43	C₂×D₄	—	2	1	no	—
44	C₂×D₄	—	4	1	no	—
45	SD₁₆	—	4	4	no	—
46	M₁₆	—	52	2	no	—
47	C₂×C₈	—	2	1	no	—
48	C₄⋊C₄	—	4	1	no	—
49	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
50	C₁₃	#1410	1	1	yes	characteristic, complemented, Sylow
51	C₂³	—	4	1	no	—
52	Q₈	—	4	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	8	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	104	2	no	—
60	C₂²	—	8	2	no	—
61	C₂²	—	8	1	no	—
62	C₂²	#88074	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₂	—	2	1	no	—
67	C₂	—	16	1	no	—
68	C₂	#11718137	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718137
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₁₃
Fitting	C₁₃×#492	C₂
socle	C₂×C₁₃	#353
prime radical	C₁₃×#127	C₄
cosocle	C₁₃×C₄⋊Q₈	C₂²
hypercenter	#492	D₁₃
hypocenter	C₁₃	#1410
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #492

Complements

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

N	H ≅ G/N	type
2. #11718140	C₂	semidirect
50. C₁₃	#1410	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#492	2
#11718140	2
#1410	13