Subgroups — C₁₃×#2264 #13111322

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#508	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×Q₆₄	C₂	1	2	yes	maximal, complemented
4	C₁₃×SD₆₄	C₂	1	2	yes	maximal, complemented
5	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#135	—	2	1	no	—
7	C₂×C₁₃×Q₁₆	—	2	1	no	—
8	C₁₃×Q₃₂	—	2	1	no	—
9	C₁₃×Q₃₂	C₂²	1	2	yes	—
10	C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
11	C₁₃×SD₃₂	—	2	1	no	—
12	C₁₃×D₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
14	C₁₃×C₃₂	C₂²	1	2	yes	—
15	C₁₃×#41	—	4	1	no	—
16	C₂×Q₈×C₁₃	—	4	1	no	—
17	C₁₃×Q₁₆	—	2	1	no	—
18	C₁₃×Q₁₆	—	2	2	no	—
19	C₁₃×Q₁₆	—	4	1	no	—
20	C₁₃×SD₁₆	—	4	1	no	—
21	C₁₃×D₈	—	2	1	no	—
22	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₁₃×C₁₆	D₄	1	1	yes	characteristic
24	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
25	#2264	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	Q₈×C₁₃	—	4	1	no	—
27	Q₈×C₁₃	—	4	2	no	—
28	Q₈×C₁₃	—	8	1	no	—
29	D₄×C₁₃	—	4	1	no	—
30	D₄×C₁₃	—	8	1	no	—
31	C₂×C₄×C₁₃	—	8	1	no	—
32	C₂×C₄×C₁₃	—	8	1	no	—
33	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
34	C₈×C₁₃	D₈	1	1	yes	characteristic
35	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
36	#508	C₂×C₁₃	1	1	yes	characteristic
37	C₂×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
38	Q₆₄	C₂×C₁₃	1	2	yes	complemented
39	SD₆₄	C₂×C₁₃	1	2	yes	complemented
40	M₆₄	C₂×C₁₃	1	1	yes	characteristic, complemented
41	C₂²×C₁₃	—	8	1	no	—
42	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
43	C₄×C₁₃	—	8	1	no	—
44	C₄×C₁₃	—	8	2	no	—
45	C₄×C₁₃	D₁₆	1	1	yes	characteristic
46	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
47	#135	—	2	1	no	—
48	C₂×Q₁₆	—	2	1	no	—
49	Q₃₂	—	2	1	no	—
50	Q₃₂	C₂²×C₁₃	1	2	yes	—
51	Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
52	SD₃₂	—	2	1	no	—
53	D₁₆	C₂²×C₁₃	1	1	yes	characteristic
54	C₂×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
55	C₃₂	C₂²×C₁₃	1	2	yes	—
56	C₂×C₁₃	—	2	1	no	—
57	C₂×C₁₃	—	16	1	no	—
58	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
59	#41	—	4	1	no	—
60	C₂×Q₈	—	4	1	no	—
61	Q₁₆	—	2	1	no	—
62	Q₁₆	—	2	2	no	—
63	Q₁₆	—	4	1	no	—
64	SD₁₆	—	4	1	no	—
65	D₈	—	2	1	no	—
66	C₂×C₈	D₄×C₁₃	1	1	yes	characteristic
67	C₁₆	D₄×C₁₃	1	1	yes	characteristic
68	C₁₆	C₂³×C₁₃	1	1	yes	characteristic
69	C₁₃	#2264	1	1	yes	characteristic, direct product factor, Sylow
70	Q₈	—	4	1	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	8	1	no	—
73	D₄	—	4	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	8	1	no	—
77	C₂×C₄	C₁₃×D₈	1	1	yes	characteristic
78	C₈	C₁₃×D₈	1	1	yes	characteristic
79	C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
80	C₂²	—	8	1	no	—
81	C₂²	C₁₃×D₁₆	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	8	2	no	—
84	C₄	C₁₃×D₁₆	1	1	yes	characteristic
85	C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×C₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₁₃
prime radical	C₁₃×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₂×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×Q₃₂	C₂	semidirect
3. C₁₃×Q₆₄	C₂	semidirect
4. C₁₃×SD₆₄	C₂	semidirect
5. C₁₃×M₆₄	C₂	semidirect
25. #2264	C₁₃	direct (N × H)
37. C₂×Q₃₂	C₂×C₁₃	semidirect
38. Q₆₄	C₂×C₁₃	semidirect
39. SD₆₄	C₂×C₁₃	semidirect
40. M₆₄	C₂×C₁₃	semidirect
69. C₁₃	#2264	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#508	2
C₂×C₁₃×Q₃₂	2
C₁₃×Q₆₄	2
C₁₃×SD₆₄	2
C₁₃×M₆₄	2
#2264	13

Subgroups — C13×#2264 #13111322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2264 #13111322