Subgroups — #1328×C₂₅₁ #44545915

Order 32128.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#424×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	#349×C₂₅₁	C₂	1	2	yes	maximal
3	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
4	C₂²×C₈×C₂₅₁	C₄	1	1	yes	characteristic
5	#117×C₂₅₁	C₄	1	1	yes	characteristic
6	M₃₂×C₂₅₁	—	2	2	no	—
7	C₄⋊C₈×C₂₅₁	—	2	2	no	—
8	C₂²×C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
9	M₁₆×C₂₅₁	—	4	1	no	—
10	C₂×C₈×C₂₅₁	—	2	1	no	—
11	C₂×C₈×C₂₅₁	—	4	1	no	—
12	C₂×C₈×C₂₅₁	D₄	1	2	yes	—
13	C₄⋊C₄×C₂₅₁	—	2	1	no	—
14	C₂²⋊C₄×C₂₅₁	C₈	1	2	yes	—
15	C₄²×C₂₅₁	—	2	1	no	—
16	C₁₆×C₂₅₁	—	4	2	no	—
17	C₂³×C₂₅₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₂₅₁	—	2	1	no	—
19	C₂×C₄×C₂₅₁	—	2	1	no	—
20	C₂×C₄×C₂₅₁	—	2	2	no	—
21	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₅₁	M₁₆	1	1	yes	characteristic
23	C₈×C₂₅₁	—	2	2	no	—
24	C₈×C₂₅₁	—	4	1	no	—
25	C₂²×C₂₅₁	—	2	1	no	—
26	C₂²×C₂₅₁	—	4	1	no	—
27	C₂²×C₂₅₁	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₂₅₁	—	2	1	no	—
29	C₄×C₂₅₁	—	4	2	no	—
30	C₄×C₂₅₁	#99	1	1	yes	characteristic
31	C₄×C₂₅₁	#101	1	1	yes	characteristic
32	C₂×C₂₅₁	—	2	1	no	—
33	C₂×C₂₅₁	—	4	1	no	—
34	C₂×C₂₅₁	#324	1	1	yes	characteristic
35	C₂₅₁	#1328	1	1	yes	characteristic, direct product factor, Sylow
36	#1328	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	#424	C₂×C₂₅₁	1	1	yes	characteristic
38	#349	C₂×C₂₅₁	1	2	yes	—
39	C₂×M₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
40	C₂²×C₈	C₄×C₂₅₁	1	1	yes	characteristic
41	#117	C₄×C₂₅₁	1	1	yes	characteristic
42	M₃₂	—	2	2	no	—
43	C₄⋊C₈	—	2	2	no	—
44	C₂²×C₄	C₂×C₄×C₂₅₁	1	1	yes	characteristic
45	M₁₆	—	4	1	no	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	4	1	no	—
48	C₂×C₈	D₄×C₂₅₁	1	2	yes	—
49	C₄⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	C₈×C₂₅₁	1	2	yes	—
51	C₄²	—	2	1	no	—
52	C₁₆	—	4	2	no	—
53	C₂³	C₂×C₈×C₂₅₁	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
58	C₂×C₄	M₁₆×C₂₅₁	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	—	4	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₂²⋊C₈×C₂₅₁	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	#99×C₂₅₁	1	1	yes	characteristic
67	C₄	#101×C₂₅₁	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	#324×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₅₁	#99
commutator	C₂³	C₂×C₈×C₂₅₁
Frattini, cosocle	C₂×M₁₆	C₂²×C₂₅₁
socle	C₂×C₂₅₁	#324
prime radical	C₂³×C₂₅₁	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₅₁ ◁ C₂×C₄×C₂₅₁ ◁ C₂×M₁₆×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
35. C₂₅₁	#1328	direct (N × H)
36. #1328	C₂₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#424×C₂₅₁	2
#349×C₂₅₁	2
#1328	251

Subgroups — #1328×C251 #44545915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1328×C₂₅₁ #44545915