Subgroups — C₂×#11718801 #13127935

Order 1664.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	#11718801	C₂	1	8	yes	maximal, direct product factor
3	C₂×#88052	C₂	1	3	yes	maximal, complemented
4	C₂²×#6090	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
6	C₁₃×#131	C₄	1	4	yes	—
7	C₁₃×#131	C₂²	1	4	yes	—
8	C₂×C₁₃×M₁₆	C₄	1	3	yes	—
9	C₂²×C₈×C₁₃	C₂²	1	3	yes	—
10	#88052	C₂²	1	12	yes	complemented
11	C₂×#6090	C₂²	1	1	yes	characteristic
12	C₂×#6090	C₂²	1	3	yes	—
13	C₂×#6090	C₂²	1	12	yes	complemented
14	C₁₃×#41	C₈	1	4	yes	—
15	C₁₃×#41	C₂×C₄	1	4	yes	—
16	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
17	C₂×D₄×C₁₃	C₈	1	3	yes	—
18	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
19	C₁₃×M₁₆	C₂×C₄	1	12	yes	—
20	C₂×C₈×C₁₃	C₂×C₄	1	3	yes	—
21	C₂×C₈×C₁₃	C₂×C₄	1	6	yes	—
22	C₂×C₈×C₁₃	C₂³	1	6	yes	—
23	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	#6090	C₂³	1	2	yes	—
25	#6090	C₂³	1	6	yes	—
26	C₂×#504	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂×C₈	1	3	yes	—
28	Q₈×C₁₃	C₂×C₈	1	4	yes	—
29	D₄×C₁₃	C₂×C₈	1	12	yes	—
30	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
31	C₂×C₄×C₁₃	C₂×C₈	1	6	yes	—
32	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
34	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₃	C₂²×C₄	1	6	yes	—
36	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
37	C₂×#131	D₁₃	1	1	yes	characteristic
38	#504	—	13	8	no	—
39	C₂×M₃₂	—	13	3	no	—
40	C₂²×C₁₆	—	13	3	no	—
41	C₂²×C₁₃	—	2	6	no	—
42	C₂²×C₁₃	C₂²×C₈	1	6	yes	—
43	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₁₃	C₂²×C₈	1	6	yes	—
46	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
47	C₂×#41	Dic₁₃	1	1	yes	characteristic
48	#131	Dic₁₃	1	4	yes	—
49	#131	C₂×D₁₃	1	4	yes	—
50	C₂×M₁₆	Dic₁₃	1	3	yes	—
51	C₂²×C₈	C₂×D₁₃	1	3	yes	—
52	M₃₂	—	13	12	no	—
53	C₂×C₁₆	—	13	12	no	—
54	C₂×C₁₆	—	13	1	no	—
55	C₂×C₁₆	—	13	3	no	—
56	C₂×C₁₃	—	2	6	no	—
57	C₂×C₁₃	#504	1	2	yes	complemented
58	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
59	#41	#1055	1	4	yes	—
60	#41	C₂×Dic₁₃	1	4	yes	—
61	C₂×Q₈	#1055	1	1	yes	characteristic
62	C₂×D₄	#1055	1	3	yes	—
63	C₂²×C₄	C₂×Dic₁₃	1	3	yes	—
64	M₁₆	C₂×Dic₁₃	1	12	yes	—
65	C₂×C₈	C₂×Dic₁₃	1	3	yes	—
66	C₂×C₈	C₂×Dic₁₃	1	6	yes	—
67	C₂×C₈	C₂²×D₁₃	1	6	yes	—
68	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
69	C₁₆	—	13	2	no	—
70	C₁₆	—	13	6	no	—
71	C₁₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₂×#1055	1	3	yes	—
73	Q₈	C₂×#1055	1	4	yes	—
74	D₄	C₂×#1055	1	12	yes	—
75	C₂×C₄	C₂×#1055	1	3	yes	—
76	C₂×C₄	C₂×#1055	1	6	yes	—
77	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
78	C₂×C₄	C₂²×Dic₁₃	1	6	yes	—
79	C₈	C₂²×Dic₁₃	1	1	yes	characteristic
80	C₈	C₂²×Dic₁₃	1	6	yes	—
81	C₈	C₂³×D₁₃	1	1	yes	characteristic
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#1055	1	6	yes	—
84	C₂²	C₂²×#1055	1	1	yes	characteristic
85	C₄	C₂²×#1055	1	1	yes	characteristic
86	C₄	C₂²×#1055	1	6	yes	—
87	C₄	C₂³×Dic₁₃	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#11718801	1	2	yes	direct product factor
90	C₂	C₂³×#1055	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂³×C₈
Frattini	C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#131	C₂
socle	C₂²×C₁₃	C₂²×C₈
prime radical	C₂×C₁₃×#41	C₄
cosocle	C₈×C₁₃	C₂⁴
hypercenter	C₂×#131	D₁₃
hypocenter	C₁₃	C₂×#504
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
2. #11718801	C₂	direct (N × H)
3. C₂×#88052	C₂	semidirect
4. C₂²×#6090	C₂	semidirect
10. #88052	C₂²	semidirect
13. C₂×#6090	C₂²	semidirect
57. C₂×C₁₃	#504	semidirect
71. C₁₃	C₂×#504	semidirect
89. C₂	#11718801	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×C₁₃×#131	2
#11718801	2
C₂×#88052	2
C₂²×#6090	2
C₂×#504	13

Subgroups — C2×#11718801 #13127935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718801 #13127935