Subgroups — D₁₃⋊M₆₄ #13131257

Order 1664.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#11718249	C₂	1	2	yes	maximal, complemented
3	#11718214	C₂	1	2	yes	maximal, complemented
4	D₁₃⋊C₃₂	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
6	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
7	C₂×#6090	C₂²	1	1	yes	characteristic
8	C₁₆×D₁₃	C₄	1	1	yes	characteristic
9	C₁₆×D₁₃	C₄	1	1	yes	characteristic
10	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₁₆×D₁₃	C₂²	1	1	yes	characteristic
12	#88036	C₂²	1	4	yes	complemented
13	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×#1055	C₈	1	1	yes	characteristic
16	C₈×D₁₃	C₈	1	1	yes	characteristic
17	C₈×D₁₃	C₈	1	1	yes	characteristic
18	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	#6090	C₂×C₄	1	1	yes	characteristic
23	#6090	C₂³	1	1	yes	characteristic
24	C₂×M₆₄	—	13	1	no	maximal, Sylow
25	C₂²×D₁₃	C₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
27	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
28	C₄×D₁₃	C₁₆	1	1	yes	characteristic
29	C₄×D₁₃	C₁₆	1	1	yes	characteristic
30	C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
31	C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	#1055	C₂×C₈	1	1	yes	characteristic
35	#1055	C₂×C₈	1	1	yes	characteristic
36	C₂²×C₁₆	—	13	1	no	—
37	M₆₄	—	13	2	no	—
38	M₆₄	—	13	2	no	—
39	C₂×C₃₂	—	13	2	no	—
40	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
41	C₂×D₁₃	—	2	2	no	—
42	C₂×D₁₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂×D₁₃	C₂×C₁₆	1	1	yes	characteristic
44	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
45	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
46	Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
47	Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
48	C₂²×C₈	—	13	1	no	—
49	C₂×C₁₆	—	13	1	no	—
50	C₂×C₁₆	—	13	1	no	—
51	C₂×C₁₆	—	13	1	no	—
52	C₂×C₁₆	—	13	1	no	—
53	C₂×C₁₆	—	13	1	no	—
54	C₂×C₁₆	#261	1	1	yes	characteristic
55	C₃₂	—	13	4	no	—
56	C₂×C₁₃	—	2	1	no	—
57	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
58	D₁₃	—	2	1	no	—
59	D₁₃	M₆₄	1	2	yes	complemented
60	C₂²×C₄	—	13	1	no	—
61	C₂×C₈	—	13	1	no	—
62	C₂×C₈	—	13	1	no	—
63	C₂×C₈	—	13	1	no	—
64	C₂×C₈	—	13	1	no	—
65	C₂×C₈	—	13	1	no	—
66	C₂×C₈	C₂×#261	1	1	yes	characteristic
67	C₁₆	—	13	1	no	—
68	C₁₆	—	13	1	no	—
69	C₁₆	C₂×#261	1	1	yes	characteristic
70	C₁₆	C₂×#261	1	1	yes	characteristic
71	C₁₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	13	1	no	—
73	C₂×C₄	—	13	1	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	—	13	1	no	—
76	C₂×C₄	—	13	1	no	—
77	C₂×C₄	—	13	1	no	—
78	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
79	C₈	—	13	1	no	—
80	C₈	—	13	1	no	—
81	C₈	D₁₃⋊C₈	1	1	yes	characteristic
82	C₈	C₂²×#261	1	1	yes	characteristic
83	C₂²	—	13	1	no	—
84	C₂²	—	13	1	no	—
85	C₂²	—	26	2	no	—
86	C₂²	D₁₃⋊C₁₆	1	1	yes	characteristic
87	C₄	—	13	1	no	—
88	C₄	—	13	1	no	—
89	C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
90	C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	13	2	no	—
93	C₂	—	26	1	no	—
94	C₂	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×#261
commutator, socle	C₂×C₁₃	C₂²×C₁₆
Frattini	C₈	C₂²×#261
Fitting	C₂×C₁₃×C₁₆	C₄
prime radical	C₂²×D₁₃	C₁₆
cosocle	#6090	C₂³
hypercenter	C₂×C₁₆	#261
hypocenter	C₁₃	C₂×M₆₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #11718249	C₂	semidirect
3. #11718214	C₂	semidirect
4. D₁₃⋊C₃₂	C₂	semidirect
12. #88036	C₂²	semidirect
59. D₁₃	M₆₄	semidirect
71. C₁₃	C₂×M₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₃	2
#11718249	2
#11718214	2
D₁₃⋊C₃₂	2
C₂×M₆₄	13

Subgroups — D13⋊M64 #13131257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊M₆₄ #13131257