Subgroups — #1309×C₂₅₁ #44545896

Order 32128.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#423×C₂₅₁	C₂	1	3	yes	maximal
2	C₂×M₁₆×C₂₅₁	C₄	1	6	yes	—
3	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic
4	C₄⋊C₈×C₂₅₁	—	2	6	no	—
5	C₂²×C₄×C₂₅₁	C₂×C₄	1	3	yes	—
6	M₁₆×C₂₅₁	—	4	6	no	—
7	C₂×C₈×C₂₅₁	—	2	6	no	—
8	C₄²×C₂₅₁	D₄	1	3	yes	—
9	C₄²×C₂₅₁	Q₈	1	1	yes	characteristic
10	C₂³×C₂₅₁	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₂₅₁	—	2	3	no	—
12	C₂×C₄×C₂₅₁	—	2	3	no	—
13	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	3	yes	—
14	C₂×C₄×C₂₅₁	C₄⋊C₄	1	3	yes	—
15	C₈×C₂₅₁	—	4	6	no	—
16	C₂²×C₂₅₁	—	2	3	no	—
17	C₂²×C₂₅₁	#95	1	1	yes	characteristic
18	C₄×C₂₅₁	—	2	3	no	—
19	C₄×C₂₅₁	#100	1	3	yes	—
20	C₄×C₂₅₁	#101	1	3	yes	—
21	C₂×C₂₅₁	—	4	1	no	—
22	C₂×C₂₅₁	#343	1	3	yes	—
23	C₂₅₁	#1309	1	1	yes	characteristic, direct product factor, Sylow
24	#1309	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	#423	C₂×C₂₅₁	1	3	yes	—
26	C₂×M₁₆	C₄×C₂₅₁	1	6	yes	—
27	C₂×C₄²	C₂²×C₂₅₁	1	1	yes	characteristic
28	C₄⋊C₈	—	2	6	no	—
29	C₂²×C₄	C₂×C₄×C₂₅₁	1	3	yes	—
30	M₁₆	—	4	6	no	—
31	C₂×C₈	—	2	6	no	—
32	C₄²	D₄×C₂₅₁	1	3	yes	—
33	C₄²	Q₈×C₂₅₁	1	1	yes	characteristic
34	C₂³	C₄²×C₂₅₁	1	1	yes	characteristic
35	C₂×C₄	—	2	3	no	—
36	C₂×C₄	—	2	3	no	—
37	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	3	yes	—
38	C₂×C₄	C₄⋊C₄×C₂₅₁	1	3	yes	—
39	C₈	—	4	6	no	—
40	C₂²	—	2	3	no	—
41	C₂²	#95×C₂₅₁	1	1	yes	characteristic
42	C₄	—	2	3	no	—
43	C₄	#100×C₂₅₁	1	3	yes	—
44	C₄	#101×C₂₅₁	1	3	yes	—
45	C₂	—	4	1	no	—
46	C₂	#343×C₂₅₁	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₅₁	#95
commutator	C₂³	C₄²×C₂₅₁
Frattini, cosocle	C₂×C₄²	C₂²×C₂₅₁
prime radical	C₂³×C₂₅₁	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ C₂×C₄²×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
23. C₂₅₁	#1309	direct (N × H)
24. #1309	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
#423×C₂₅₁	2
#1309	251

Subgroups — #1309×C251 #44545896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1309×C₂₅₁ #44545896