Subgroups — C₂×D₁₃⋊C₃₂ #13131255

Order 1664.

120 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	C₂×#88036	C₂	1	2	yes	maximal, complemented
3	D₁₃⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
5	C₂×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂×#6090	C₂²	1	1	yes	characteristic
7	C₁₆×D₁₃	C₄	1	2	yes	—
8	C₁₆×D₁₃	C₂²	1	2	yes	—
9	#88036	C₂²	1	4	yes	complemented
10	C₂×C₄×D₁₃	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×#1055	C₈	1	1	yes	characteristic
13	C₈×D₁₃	C₈	1	2	yes	—
14	C₈×D₁₃	C₂×C₄	1	2	yes	—
15	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
16	#6090	C₂×C₄	1	1	yes	characteristic
17	#6090	C₂³	1	1	yes	characteristic
18	C₂²×C₃₂	—	13	1	no	maximal, Sylow
19	C₂²×D₁₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₁₃	C₁₆	1	1	yes	characteristic
22	C₄×D₁₃	C₁₆	1	2	yes	—
23	C₄×D₁₃	C₂×C₈	1	2	yes	—
24	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	#1055	C₂×C₈	1	2	yes	—
27	C₂²×C₁₆	—	13	1	no	—
28	C₂×C₃₂	—	13	4	no	—
29	C₂×C₃₂	—	13	2	no	—
30	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₁₃	C₃₂	1	4	yes	complemented
32	C₂×D₁₃	C₂×C₁₆	1	2	yes	—
33	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
34	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
35	Dic₁₃	C₂×C₁₆	1	2	yes	—
36	C₂²×C₈	—	13	1	no	—
37	C₂×C₁₆	—	13	1	no	—
38	C₂×C₁₆	—	13	2	no	—
39	C₂×C₁₆	—	13	2	no	—
40	C₂×C₁₆	#261	1	1	yes	characteristic
41	C₃₂	—	13	4	no	—
42	C₂×C₁₃	C₂×C₃₂	1	2	yes	complemented
43	C₂×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
44	D₁₃	C₂×C₃₂	1	4	yes	complemented
45	C₂²×C₄	—	13	1	no	—
46	C₂×C₈	—	13	1	no	—
47	C₂×C₈	—	13	2	no	—
48	C₂×C₈	—	13	2	no	—
49	C₂×C₈	C₂×#261	1	1	yes	characteristic
50	C₁₆	—	13	1	no	—
51	C₁₆	—	13	1	no	—
52	C₁₆	C₂×#261	1	2	yes	—
53	C₁₃	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
54	C₂³	—	13	1	no	—
55	C₂×C₄	—	13	1	no	—
56	C₂×C₄	—	13	2	no	—
57	C₂×C₄	—	13	2	no	—
58	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
59	C₈	—	13	2	no	—
60	C₈	D₁₃⋊C₈	1	1	yes	characteristic
61	C₈	C₂²×#261	1	1	yes	characteristic
62	C₂²	—	13	4	no	—
63	C₂²	—	13	2	no	—
64	C₂²	D₁₃⋊C₁₆	1	1	yes	characteristic
65	C₄	—	13	2	no	—
66	C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
67	C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
68	C₂	—	13	4	no	—
69	C₂	D₁₃⋊C₃₂	1	2	yes	direct product factor
70	C₂	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	#261
commutator, hypocenter	C₁₃	C₂²×C₃₂
Frattini	C₈	C₂²×#261
Fitting	C₂×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×C₁₆
prime radical	C₂²×D₁₃	C₁₆
cosocle	#6090	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#88036	C₂	semidirect
3. D₁₃⋊C₃₂	C₂	direct (N × H)
9. #88036	C₂²	semidirect
31. C₂×D₁₃	C₃₂	semidirect
42. C₂×C₁₃	C₂×C₃₂	semidirect
44. D₁₃	C₂×C₃₂	semidirect
53. C₁₃	C₂²×C₃₂	semidirect
69. C₂	D₁₃⋊C₃₂	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×C₁₆×D₁₃	2
C₂×#88036	2
D₁₃⋊C₃₂	2
C₂²×C₃₂	13

Subgroups — C2×D13⋊C32 #13131255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊C₃₂ #13131255