Subgroups — #1658×C₂₅₁ #44546245

Order 32128.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#564×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#490×C₂₅₁	C₂	1	3	yes	maximal
3	#330×C₂₅₁	C₂	1	3	yes	maximal, complemented
4	#127×C₂₅₁	C₂²	1	1	yes	characteristic
5	#125×C₂₅₁	—	2	6	no	—
6	#125×C₂₅₁	C₂²	1	3	yes	—
7	#102×C₂₅₁	—	2	6	no	—
8	#97×C₂₅₁	C₂²	1	3	yes	—
9	C₂×D₄×C₂₅₁	—	2	3	no	—
10	C₂×C₈×C₂₅₁	—	2	3	no	—
11	C₄⋊C₄×C₂₅₁	—	2	6	no	—
12	C₄⋊C₄×C₂₅₁	—	2	6	no	—
13	C₄⋊C₄×C₂₅₁	D₄	1	6	yes	—
14	C₄²×C₂₅₁	—	2	2	no	—
15	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
16	C₂³×C₂₅₁	—	4	1	no	—
17	D₄×C₂₅₁	—	4	6	no	—
18	C₂×C₄×C₂₅₁	—	2	6	no	—
19	C₂×C₄×C₂₅₁	C₂×D₄	1	3	yes	—
20	C₈×C₂₅₁	—	4	3	no	—
21	C₂²×C₂₅₁	—	8	3	no	—
22	C₂²×C₂₅₁	#120	1	1	yes	characteristic
23	C₄×C₂₅₁	—	2	3	no	—
24	C₄×C₂₅₁	—	4	6	no	—
25	C₂×C₂₅₁	—	16	1	no	—
26	C₂×C₂₅₁	#454	1	3	yes	—
27	C₂₅₁	#1658	1	1	yes	characteristic, direct product factor, Sylow
28	#1658	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	#564	C₂×C₂₅₁	1	1	yes	characteristic, complemented
30	#490	C₂×C₂₅₁	1	3	yes	—
31	#330	C₂×C₂₅₁	1	3	yes	complemented
32	#127	C₂²×C₂₅₁	1	1	yes	characteristic
33	#125	—	2	6	no	—
34	#125	C₂²×C₂₅₁	1	3	yes	—
35	#102	—	2	6	no	—
36	#97	C₂²×C₂₅₁	1	3	yes	—
37	C₂×D₄	—	2	3	no	—
38	C₂×C₈	—	2	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	D₄×C₂₅₁	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
44	C₂³	—	4	1	no	—
45	D₄	—	4	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×D₄×C₂₅₁	1	3	yes	—
48	C₈	—	4	3	no	—
49	C₂²	—	8	3	no	—
50	C₂²	#120×C₂₅₁	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	16	1	no	—
54	C₂	#454×C₂₅₁	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₅₁	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₅₁
prime radical	#127×C₂₅₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ C₄²×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #564×C₂₅₁	C₂	semidirect
3. #330×C₂₅₁	C₂	semidirect
27. C₂₅₁	#1658	direct (N × H)
28. #1658	C₂₅₁	direct (N × H)
29. #564	C₂×C₂₅₁	semidirect
31. #330	C₂×C₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#564×C₂₅₁	2
#490×C₂₅₁	2
#330×C₂₅₁	2
#1658	251

Subgroups — #1658×C251 #44546245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1658×C₂₅₁ #44546245