Subgroups — C₂×#11719061 #13131282

Order 1664.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂×#261)⋊C₄	C₂	1	6	yes	maximal
3	#11719061	C₂	1	8	yes	maximal, direct product factor
4	C₂³×#261	C₂²	1	4	yes	—
5	C₂²×C₄×D₁₃	C₂²	1	3	yes	—
6	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×Dic₁₃	C₄	1	3	yes	complemented
8	C₄²×D₁₃	C₄	1	4	yes	complemented
9	C₄²×D₁₃	C₂²	1	4	yes	—
10	(C₂×#261)⋊C₄	C₂²	1	24	yes	—
11	C₂³×D₁₃	C₂³	1	1	yes	characteristic
12	C₂²×#261	—	2	24	no	—
13	C₂²×#261	C₂³	1	8	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
15	C₂²×Dic₁₃	C₂×C₄	1	3	yes	—
16	C₂×C₄×D₁₃	—	2	12	no	—
17	C₂×C₄×D₁₃	C₂×C₄	1	6	yes	—
18	C₂×C₄×D₁₃	C₂³	1	6	yes	—
19	C₄²×C₁₃	C₂×C₄	1	4	yes	complemented
20	C₄×Dic₁₃	C₂×C₄	1	12	yes	complemented
21	C₂×#383	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂²×D₁₃	#41	1	12	yes	—
25	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
26	C₂×#261	—	2	24	no	—
27	C₂×#261	—	4	16	no	—
28	C₂×C₄×C₁₃	—	2	6	no	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
30	C₂×Dic₁₃	—	2	6	no	—
31	C₂×Dic₁₃	C₂²×C₄	1	6	yes	—
32	C₄×D₁₃	—	2	12	no	—
33	C₄×D₁₃	—	2	12	no	—
34	C₂²×C₄²	—	13	1	no	—
35	#383	—	13	8	no	—
36	C₂×#95	—	13	6	no	—
37	C₂²×C₁₃	#117	1	6	yes	—
38	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
39	C₂×D₁₃	#117	1	6	yes	—
40	C₂×D₁₃	#126	1	16	yes	—
41	C₂×D₁₃	C₂×#41	1	6	yes	—
42	#261	—	4	8	no	—
43	C₄×C₁₃	—	2	6	no	—
44	Dic₁₃	—	2	6	no	—
45	C₂³×C₄	—	13	3	no	—
46	C₂³×C₄	—	13	4	no	—
47	C₂×C₄²	—	13	3	no	—
48	C₂×C₄²	—	13	4	no	—
49	C₂×C₄²	—	13	4	no	—
50	C₂×C₄²	#261	1	1	yes	characteristic, complemented
51	#95	—	13	24	no	—
52	C₂×C₁₃	#383	1	4	yes	complemented
53	C₂×C₁₃	C₂×#117	1	3	yes	—
54	D₁₃	#383	1	4	yes	complemented
55	D₁₃	C₂×#126	1	4	yes	—
56	C₂⁴	—	13	1	no	—
57	C₂²×C₄	—	13	3	no	—
58	C₂²×C₄	—	13	6	no	—
59	C₂²×C₄	—	13	6	no	—
60	C₂²×C₄	—	13	8	no	—
61	C₂²×C₄	—	26	12	no	—
62	C₂²×C₄	—	26	24	no	—
63	C₂²×C₄	C₂×#261	1	3	yes	—
64	C₄²	—	13	12	no	—
65	C₄²	C₂×#261	1	4	yes	complemented
66	C₁₃	C₂×#383	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	13	12	no	—
68	C₂³	—	13	1	no	—
69	C₂³	—	13	1	no	—
70	C₂³	C₂²×#261	1	1	yes	characteristic
71	C₂×C₄	—	2	6	no	—
72	C₂×C₄	—	13	6	no	—
73	C₂×C₄	—	26	12	no	—
74	C₂×C₄	—	26	12	no	—
75	C₂×C₄	—	26	6	no	—
76	C₂×C₄	—	26	24	no	—
77	C₂×C₄	—	52	16	no	—
78	C₂×C₄	C₂²×#261	1	6	yes	—
79	C₂²	—	13	16	no	—
80	C₂²	—	13	6	no	—
81	C₂²	—	13	6	no	—
82	C₂²	#88237	1	6	yes	—
83	C₂²	C₂³×#261	1	1	yes	characteristic
84	C₄	—	2	6	no	—
85	C₄	—	26	6	no	—
86	C₄	—	52	8	no	—
87	C₂	—	13	4	no	—
88	C₂	—	13	4	no	—
89	C₂	#11719061	1	4	yes	direct product factor
90	C₂	C₂×#88237	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×#261
commutator	C₂²×C₁₃	C₂³×C₄
Frattini	C₂²	C₂³×#261
Fitting	C₂×C₄²×C₁₃	C₄
socle	C₂³×C₁₃	C₂²×C₄
prime radical	C₂³×D₁₃	C₂³
cosocle	C₂²×D₁₃	C₂⁴
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	C₂×#383
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #11719061	C₂	direct (N × H)
6. C₂×C₄²×C₁₃	C₄	semidirect
7. C₂×C₄×Dic₁₃	C₄	semidirect
8. C₄²×D₁₃	C₄	semidirect
19. C₄²×C₁₃	C₂×C₄	semidirect
20. C₄×Dic₁₃	C₂×C₄	semidirect
50. C₂×C₄²	#261	semidirect
52. C₂×C₁₃	#383	semidirect
54. D₁₃	#383	semidirect
65. C₄²	C₂×#261	semidirect
66. C₁₃	C₂×#383	semidirect
89. C₂	#11719061	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₁₃	2
C₂×(C₂×#261)⋊C₄	2
#11719061	2
C₂×#383	13

Subgroups — C2×#11719061 #13131282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719061 #13131282