Subgroups — C₂×C₃₂×D₁₃₁ #30668249

Order 16768.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₂×D₁₃₁	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₁₃₁	C₄	1	1	yes	characteristic
6	C₂×C₁₃₁⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₆×D₁₃₁	C₄	1	2	yes	—
8	C₁₆×D₁₃₁	C₂²	1	2	yes	—
9	C₁₃₁⋊C₃₂	C₂²	1	2	yes	complemented
10	C₂×C₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₃₂×C₁₃₁	C₂²	1	2	yes	complemented
12	C₂×C₄×D₁₃₁	C₈	1	1	yes	characteristic
13	C₂×C₁₃₁⋊C₈	C₈	1	1	yes	characteristic
14	C₈×D₁₃₁	C₈	1	2	yes	—
15	C₈×D₁₃₁	C₂×C₄	1	2	yes	—
16	C₁₃₁⋊C₁₆	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
20	C₂²×D₁₃₁	C₁₆	1	1	yes	characteristic
21	C₂×Dic₁₃₁	C₁₆	1	1	yes	characteristic
22	C₄×D₁₃₁	C₁₆	1	2	yes	—
23	C₄×D₁₃₁	C₂×C₈	1	2	yes	—
24	C₁₃₁⋊C₈	C₂×C₈	1	2	yes	—
25	C₂×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
26	C₈×C₁₃₁	C₂×C₈	1	1	yes	characteristic
27	C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₁₃₁	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₁₃₁	C₃₂	1	4	yes	direct product factor
30	C₂×D₁₃₁	C₂×C₁₆	1	2	yes	—
31	C₄×C₁₃₁	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
33	Dic₁₃₁	C₂×C₁₆	1	2	yes	—
34	C₂×C₁₃₁	C₂×C₃₂	1	2	yes	complemented
35	C₂×C₁₃₁	C₂²×C₁₆	1	1	yes	characteristic
36	D₁₃₁	C₂×C₃₂	1	4	yes	direct product factor
37	C₁₃₁	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃₂	—	131	1	no	maximal, Sylow
39	C₂²×C₁₆	—	131	1	no	—
40	C₂×C₃₂	—	131	1	no	—
41	C₂×C₃₂	—	131	4	no	—
42	C₂×C₃₂	D₁₃₁	1	1	yes	characteristic, direct product factor
43	C₂²×C₈	—	131	1	no	—
44	C₂×C₁₆	—	131	1	no	—
45	C₂×C₁₆	—	131	2	no	—
46	C₂×C₁₆	—	131	2	no	—
47	C₂×C₁₆	C₂×D₁₃₁	1	1	yes	characteristic
48	C₃₂	—	131	2	no	—
49	C₃₂	C₂×D₁₃₁	1	2	yes	direct product factor
50	C₂²×C₄	—	131	1	no	—
51	C₂×C₈	—	131	1	no	—
52	C₂×C₈	—	131	2	no	—
53	C₂×C₈	—	131	2	no	—
54	C₂×C₈	C₄×D₁₃₁	1	1	yes	characteristic
55	C₁₆	—	131	2	no	—
56	C₁₆	C₄×D₁₃₁	1	1	yes	characteristic
57	C₁₆	C₂²×D₁₃₁	1	1	yes	characteristic
58	C₂³	—	131	1	no	—
59	C₂×C₄	—	131	1	no	—
60	C₂×C₄	—	131	2	no	—
61	C₂×C₄	—	131	2	no	—
62	C₂×C₄	C₈×D₁₃₁	1	1	yes	characteristic
63	C₈	—	131	2	no	—
64	C₈	C₈×D₁₃₁	1	1	yes	characteristic
65	C₈	C₂×C₄×D₁₃₁	1	1	yes	characteristic
66	C₂²	—	131	4	no	—
67	C₂²	—	131	2	no	—
68	C₂²	C₁₆×D₁₃₁	1	1	yes	characteristic
69	C₄	—	131	2	no	—
70	C₄	C₁₆×D₁₃₁	1	1	yes	characteristic
71	C₄	C₂×C₈×D₁₃₁	1	1	yes	characteristic
72	C₂	—	131	4	no	—
73	C₂	C₃₂×D₁₃₁	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₁₃₁
commutator, hypocenter	C₁₃₁	C₂²×C₃₂
Frattini	C₁₆	C₂²×D₁₃₁
Fitting	C₂×C₃₂×C₁₃₁	C₂
socle	C₂²×C₁₃₁	C₂×C₁₆
prime radical	C₂²×D₁₃₁	C₁₆
cosocle	C₁₆×C₁₃₁	C₂³
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃₁⋊C₃₂	C₂	semidirect
3. C₃₂×D₁₃₁	C₂	direct (N × H)
4. C₂×C₃₂×C₁₃₁	C₂	semidirect
9. C₁₃₁⋊C₃₂	C₂²	semidirect
11. C₃₂×C₁₃₁	C₂²	semidirect
29. C₂×D₁₃₁	C₃₂	direct (N × H)
34. C₂×C₁₃₁	C₂×C₃₂	semidirect
36. D₁₃₁	C₂×C₃₂	direct (N × H)
37. C₁₃₁	C₂²×C₃₂	semidirect
42. C₂×C₃₂	D₁₃₁	direct (N × H)
49. C₃₂	C₂×D₁₃₁	direct (N × H)
73. C₂	C₃₂×D₁₃₁	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×D₁₃₁	2
C₂×C₁₃₁⋊C₃₂	2
C₃₂×D₁₃₁	2
C₂×C₃₂×C₁₃₁	2
C₂²×C₃₂	131

Subgroups — C2×C32×D131 #30668249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₂×D₁₃₁ #30668249