Subgroups — C₂×C₁₃×#519 #13112484

Order 1664.

1488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#519	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄×Q₈×C₁₃	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₃×#117	C₂	1	6	yes	maximal
5	C₂²×Q₈×C₁₃	C₄	1	16	yes	complemented
6	C₂²×Q₈×C₁₃	C₂²	1	4	yes	—
7	C₂²×Q₈×C₁₃	C₂²	1	8	yes	—
8	C₂³×C₄×C₁₃	C₂²	1	3	yes	—
9	C₄×Q₈×C₁₃	C₂²	1	64	yes	complemented
10	C₁₃×#117	C₂²	1	48	yes	—
11	C₂×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
12	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄²×C₁₃	C₂²	1	12	yes	—
14	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×Q₈×C₁₃	C₂×C₄	1	32	yes	—
16	C₂×Q₈×C₁₃	C₂×C₄	1	64	yes	complemented
17	C₂×Q₈×C₁₃	C₂³	1	16	yes	—
18	C₂²×C₄×C₁₃	C₂×C₄	1	24	yes	—
19	C₂²×C₄×C₁₃	C₂³	1	8	yes	—
20	C₂²×C₄×C₁₃	C₂³	1	12	yes	—
21	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
22	C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
23	C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
24	C₄²×C₁₃	C₂³	1	48	yes	—
25	C₂×#519	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂³×C₁₃	—	2	4	no	—
27	C₂³×C₁₃	C₂²×C₄	1	4	yes	—
28	C₂³×C₁₃	C₂⁴	1	2	yes	—
29	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
30	Q₈×C₁₃	C₂²×C₄	1	64	yes	—
31	C₂×C₄×C₁₃	—	2	16	no	—
32	C₂×C₄×C₁₃	C₂²×C₄	1	24	yes	—
33	C₂×C₄×C₁₃	C₂²×C₄	1	48	yes	—
34	C₂×C₄×C₁₃	C₂⁴	1	16	yes	—
35	C₂×C₄×C₁₃	C₂⁴	1	12	yes	—
36	C₂³×Q₈	C₂×C₁₃	1	1	yes	characteristic
37	#519	C₂×C₁₃	1	16	yes	direct product factor
38	C₂×C₄×Q₈	C₂×C₁₃	1	8	yes	complemented
39	C₂×#117	C₂×C₁₃	1	6	yes	—
40	C₂²×C₁₃	—	2	8	no	—
41	C₂²×C₁₃	—	2	4	no	—
42	C₂²×C₁₃	C₂³×C₄	1	4	yes	—
43	C₂²×C₁₃	C₂³×C₄	1	2	yes	—
44	C₂²×C₁₃	2₋¹⁺⁴	1	4	yes	—
45	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
46	C₄×C₁₃	—	2	16	no	—
47	C₄×C₁₃	C₂³×C₄	1	24	yes	—
48	C₂²×Q₈	C₄×C₁₃	1	16	yes	complemented
49	C₂²×Q₈	C₂²×C₁₃	1	4	yes	—
50	C₂²×Q₈	C₂²×C₁₃	1	8	yes	—
51	C₂³×C₄	C₂²×C₁₃	1	3	yes	—
52	C₄×Q₈	C₂²×C₁₃	1	64	yes	complemented
53	#117	C₂²×C₁₃	1	48	yes	—
54	C₂×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
55	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
56	C₂×C₄²	C₂²×C₁₃	1	12	yes	—
57	C₂×C₁₃	—	2	4	no	—
58	C₂×C₁₃	#519	1	4	yes	direct product factor
59	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
60	C₂×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
61	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
62	C₂×Q₈	C₂×C₄×C₁₃	1	32	yes	—
63	C₂×Q₈	C₂×C₄×C₁₃	1	64	yes	complemented
64	C₂×Q₈	C₂³×C₁₃	1	16	yes	—
65	C₂²×C₄	C₂×C₄×C₁₃	1	24	yes	—
66	C₂²×C₄	C₂³×C₁₃	1	8	yes	—
67	C₂²×C₄	C₂³×C₁₃	1	6	yes	—
68	C₂²×C₄	C₂³×C₁₃	1	12	yes	—
69	C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
70	C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
71	C₄²	C₂³×C₁₃	1	48	yes	—
72	C₁₃	C₂×#519	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³	—	2	4	no	—
74	C₂³	C₂²×C₄×C₁₃	1	4	yes	—
75	C₂³	C₂⁴×C₁₃	1	2	yes	—
76	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
77	Q₈	C₂²×C₄×C₁₃	1	64	yes	—
78	C₂×C₄	—	2	16	no	—
79	C₂×C₄	C₂²×C₄×C₁₃	1	24	yes	—
80	C₂×C₄	C₂²×C₄×C₁₃	1	48	yes	—
81	C₂×C₄	C₂⁴×C₁₃	1	16	yes	—
82	C₂×C₄	C₂⁴×C₁₃	1	12	yes	—
83	C₂²	—	2	8	no	—
84	C₂²	—	2	4	no	—
85	C₂²	C₂³×C₄×C₁₃	1	4	yes	—
86	C₂²	C₂³×C₄×C₁₃	1	2	yes	—
87	C₂²	C₁₃×2₋¹⁺⁴	1	4	yes	—
88	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
89	C₄	—	2	16	no	—
90	C₄	C₂³×C₄×C₁₃	1	24	yes	—
91	C₂	—	2	4	no	—
92	C₂	C₁₃×#519	1	4	yes	direct product factor
93	C₂	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
94	C₂	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator	C₂	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂²	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#519	C₂	direct (N × H)
3. C₂×C₄×Q₈×C₁₃	C₂	semidirect
5. C₂²×Q₈×C₁₃	C₄	semidirect
9. C₄×Q₈×C₁₃	C₂²	semidirect
16. C₂×Q₈×C₁₃	C₂×C₄	semidirect
25. C₂×#519	C₁₃	direct (N × H)
37. #519	C₂×C₁₃	direct (N × H)
38. C₂×C₄×Q₈	C₂×C₁₃	semidirect
48. C₂²×Q₈	C₄×C₁₃	semidirect
52. C₄×Q₈	C₂²×C₁₃	semidirect
58. C₂×C₁₃	#519	direct (N × H)
63. C₂×Q₈	C₂×C₄×C₁₃	semidirect
72. C₁₃	C₂×#519	direct (N × H)
92. C₂	C₁₃×#519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×C₁₃	2
C₁₃×#519	2
C₂×C₄×Q₈×C₁₃	2
C₂×C₁₃×#117	2
C₂×#519	13

Subgroups — C2×C13×#519 #13112484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#519 #13112484