Subgroups — #13131729

Order 1664.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	Q₈×#1057	C₂	1	8	yes	maximal, complemented
3	#11719119	C₂	1	6	yes	maximal
4	C₂²×Q₈×C₁₃	C₄	1	1	yes	characteristic
5	Q₈×Dic₁₃	C₄	1	4	yes	—
6	Q₈×Dic₁₃	C₂²	1	4	yes	—
7	C₂×C₄⋊Dic₁₃	C₄	1	3	yes	—
8	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
9	C₂²⋊#1057	C₂²	1	4	yes	—
10	C₄⋊#1057	C₂²	1	12	yes	—
11	C₄×#1057	C₂²	1	12	yes	—
12	C₂×Q₈×C₁₃	C₈	1	8	yes	complemented
13	C₂×Q₈×C₁₃	C₂×C₄	1	4	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
15	C₂²×Dic₁₃	C₂×C₄	1	3	yes	—
16	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
17	C₂×#1057	C₂³	1	8	yes	—
18	C₄⋊Dic₁₃	C₂×C₄	1	12	yes	—
19	C₄×Dic₁₃	C₂×C₄	1	6	yes	—
20	C₄×Dic₁₃	C₂³	1	6	yes	—
21	#2982	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	Q₈×C₁₃	C₂×C₈	1	16	yes	—
24	C₂×C₄×C₁₃	C₂×C₈	1	12	yes	—
25	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
26	C₂×Dic₁₃	—	2	2	no	—
27	C₂×Dic₁₃	—	4	3	no	—
28	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₁₃	C₂²×C₄	1	6	yes	—
30	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
31	#1057	—	2	8	no	—
32	C₂×C₄×Q₈	—	13	1	no	—
33	C₈×Q₈	—	13	8	no	—
34	#431	—	13	6	no	—
35	C₂²×C₁₃	—	2	1	no	—
36	C₂²×C₁₃	—	2	1	no	—
37	C₂²×C₁₃	C₂²×C₈	1	2	yes	—
38	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
39	C₄×C₁₃	C₂²×C₈	1	12	yes	—
40	Dic₁₃	—	2	1	no	—
41	Dic₁₃	—	2	6	no	—
42	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
43	C₂²×Q₈	#261	1	1	yes	characteristic
44	C₄×Q₈	—	13	4	no	—
45	C₄×Q₈	—	13	4	no	—
46	C₂×C₄⋊C₄	—	13	3	no	—
47	C₂×C₄²	—	13	3	no	—
48	C₄⋊C₈	—	13	12	no	—
49	C₂²⋊C₈	—	13	4	no	—
50	C₄×C₈	—	13	12	no	—
51	C₂×C₁₃	—	2	2	no	—
52	C₂×C₁₃	#519	1	1	yes	characteristic
53	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
54	C₂×C₁₃	#568	1	1	yes	characteristic
55	C₂×Q₈	#1057	1	8	yes	complemented
56	C₂×Q₈	C₂×#261	1	4	yes	—
57	C₂²×C₄	—	13	1	no	—
58	C₂²×C₄	—	13	3	no	—
59	C₂²×C₄	C₂×#261	1	3	yes	—
60	C₂×C₈	—	13	8	no	—
61	C₄⋊C₄	—	13	12	no	—
62	C₄²	—	13	6	no	—
63	C₄²	—	13	6	no	—
64	C₁₃	#2982	1	1	yes	characteristic, complemented, Sylow
65	C₂³	C₂²×#261	1	1	yes	characteristic
66	Q₈	C₂×#1057	1	16	yes	—
67	C₂×C₄	—	13	1	no	—
68	C₂×C₄	—	13	1	no	—
69	C₂×C₄	—	13	6	no	—
70	C₂×C₄	—	26	2	no	—
71	C₂×C₄	—	52	3	no	—
72	C₂×C₄	C₂×#1057	1	12	yes	—
73	C₂×C₄	C₂²×#261	1	6	yes	—
74	C₈	—	26	8	no	—
75	C₂²	—	2	1	no	—
76	C₂²	—	2	1	no	—
77	C₂²	C₂²×#1057	1	2	yes	—
78	C₂²	C₂³×#261	1	1	yes	characteristic
79	C₄	—	13	2	no	—
80	C₄	—	26	6	no	—
81	C₄	—	26	1	no	—
82	C₄	C₂²×#1057	1	12	yes	—
83	C₂	—	2	2	no	—
84	C₂	#11719625	1	1	yes	characteristic
85	C₂	#11719627	1	1	yes	characteristic
86	C₂	C₂³×#1057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#261
commutator	C₂×C₁₃	C₂³×C₈
Fitting	C₂²×Q₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₂³×C₁₃	C₂²×C₄
cosocle	C₂×Dic₁₃	C₂⁴
hypercenter	C₂²×Q₈	#261
hypocenter	C₁₃	#2982
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#1057	C₂	semidirect
12. C₂×Q₈×C₁₃	C₈	semidirect
55. C₂×Q₈	#1057	semidirect
64. C₁₃	#2982	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×Dic₁₃	2
Q₈×#1057	2
#11719119	2
#2982	13