Subgroups — #13113009

Order 1664.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#491	C₂	1	1	yes	maximal, characteristic
2	#11718140	C₂	1	2	yes	maximal
3	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
4	C₁₃×#125	C₄	1	1	yes	characteristic
5	C₁₃×#103	—	2	2	no	—
6	C₁₃×#97	C₄	1	1	yes	characteristic
7	#88076	—	2	2	no	—
8	C₂×Q₈×C₁₃	D₄	1	2	yes	—
9	C₂×C₈×C₁₃	—	2	1	no	—
10	C₁₃×C₄⋊C₄	—	2	1	no	—
11	C₁₃×C₄⋊C₄	—	4	1	no	—
12	C₁₃×C₄⋊C₄	—	4	1	no	—
13	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
14	#6099	—	4	2	no	—
15	#1413	—	13	1	no	maximal, Sylow
16	Q₈×C₁₃	—	4	2	no	—
17	C₂×C₄×C₁₃	—	2	2	no	—
18	C₂×C₄×C₁₃	—	2	1	no	—
19	C₂×C₄×C₁₃	—	4	1	no	—
20	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₃	—	4	1	no	—
22	#1055	—	8	2	no	—
23	#491	D₁₃	1	1	yes	characteristic
24	#356	—	13	2	no	—
25	C₂²×C₁₃	#99	1	1	yes	characteristic
26	C₄×C₁₃	—	2	1	no	—
27	C₄×C₁₃	—	4	1	no	—
28	C₄×C₁₃	—	4	2	no	—
29	C₄×C₁₃	—	8	1	no	—
30	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
31	#125	Dic₁₃	1	1	yes	characteristic
32	#103	—	2	2	no	—
33	#101	—	26	2	no	—
34	#97	Dic₁₃	1	1	yes	characteristic
35	C₂×C₁₃	—	2	1	no	—
36	C₂×C₁₃	#354	1	1	yes	characteristic
37	C₂×Q₈	C₂²⋊D₁₃	1	2	yes	—
38	M₁₆	—	52	2	no	—
39	C₂×C₈	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	—	4	1	no	—
42	C₄⋊C₄	—	4	1	no	—
43	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
44	C₁₃	#1413	1	1	yes	characteristic, complemented, Sylow
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	4	1	no	—
49	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	104	2	no	—
52	C₂²	#88074	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	4	2	no	—
56	C₄	—	8	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#11718133	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718133
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₁₃
Fitting	C₁₃×#491	C₂
socle	C₂×C₁₃	#354
prime radical	C₂²×C₁₃	#99
cosocle	C₁₃×C₄⋊Q₈	C₂²
hypercenter	#491	D₁₃
hypocenter	C₁₃	#1413
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #491

Complements

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

N	H ≅ G/N	type
44. C₁₃	#1413	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#491	2
#11718140	2
#1413	13