Subgroups — C₂×C₂₅₇⋊#401 #45667616

Order 32896.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅₇⋊#401	C₂	1	8	yes	maximal, direct product factor
2	C₂×#22551499	C₂	1	3	yes	maximal
3	C₂×#22551499	C₂	1	3	yes	maximal
4	C₂×#95×C₂₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₂₅₇	C₂²	1	3	yes	—
6	C₂³×Dic₂₅₇	C₂²	1	1	yes	characteristic
7	#22551499	C₂²	1	12	yes	—
8	#22551499	C₂²	1	12	yes	—
9	C₂³×C₄×C₂₅₇	C₂²	1	3	yes	—
10	#95×C₂₅₇	C₂²	1	4	yes	—
11	C₂²×Dic₂₅₇	—	2	6	no	—
12	C₂²×Dic₂₅₇	—	2	6	no	—
13	C₂²×Dic₂₅₇	—	2	6	no	—
14	C₂²×Dic₂₅₇	—	2	6	no	—
15	C₂²×Dic₂₅₇	C₂³	1	6	yes	—
16	C₂²×Dic₂₅₇	C₂³	1	2	yes	—
17	C₂⁴×C₂₅₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₂₅₇	—	2	12	no	—
19	C₂²×C₄×C₂₅₇	—	2	6	no	—
20	C₂²×C₄×C₂₅₇	C₂³	1	6	yes	—
21	C₂×Dic₂₅₇	—	2	6	no	—
22	C₂×Dic₂₅₇	—	2	6	no	—
23	C₂×Dic₂₅₇	—	2	6	no	—
24	C₂×Dic₂₅₇	—	2	6	no	—
25	C₂×Dic₂₅₇	—	4	4	no	—
26	C₂×Dic₂₅₇	—	4	12	no	—
27	C₂³×C₂₅₇	#41	1	6	yes	—
28	C₂³×C₂₅₇	#41	1	6	yes	—
29	C₂³×C₂₅₇	#41	1	2	yes	—
30	C₂³×C₂₅₇	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₂₅₇	—	2	12	no	—
32	C₂×C₄×C₂₅₇	—	2	6	no	—
33	C₂×C₄×C₂₅₇	—	4	12	no	—
34	C₂²×C₂₅₇	#126	1	12	yes	—
35	C₂²×C₂₅₇	#126	1	4	yes	—
36	C₂²×C₂₅₇	#126	1	12	yes	—
37	C₂²×C₂₅₇	C₂×#41	1	3	yes	—
38	C₂²×C₂₅₇	C₂×#41	1	3	yes	—
39	C₂²×C₂₅₇	C₂×#41	1	1	yes	characteristic
40	C₄×C₂₅₇	—	4	6	no	—
41	Dic₂₅₇	—	4	2	no	—
42	Dic₂₅₇	—	4	6	no	—
43	C₂×C₂₅₇	#401	1	8	yes	complemented
44	C₂×C₂₅₇	C₂×#126	1	3	yes	—
45	C₂×C₂₅₇	C₂×#126	1	1	yes	characteristic
46	C₂×C₂₅₇	C₂×#126	1	3	yes	—
47	C₂₅₇	C₂×#401	1	1	yes	characteristic, complemented, Sylow
48	C₂×#401	—	257	1	no	maximal, Sylow
49	#401	—	257	8	no	—
50	C₂×#95	—	257	3	no	—
51	C₂×#95	—	257	3	no	—
52	C₂×#95	D₂₅₇	1	1	yes	characteristic
53	C₂³×C₄	—	257	3	no	—
54	C₂³×C₄	—	257	1	no	—
55	C₂³×C₄	C₂×D₂₅₇	1	3	yes	—
56	#95	—	257	12	no	—
57	#95	—	257	12	no	—
58	#95	C₂×D₂₅₇	1	4	yes	—
59	C₂⁴	C₂²×D₂₅₇	1	1	yes	characteristic
60	C₂²×C₄	—	257	6	no	—
61	C₂²×C₄	—	257	2	no	—
62	C₂²×C₄	—	2	12	no	—
63	C₂²×C₄	—	2	6	no	—
64	C₂²×C₄	—	514	6	no	—
65	C₂²×C₄	—	514	6	no	—
66	C₂²×C₄	—	514	6	no	—
67	C₂²×C₄	—	514	6	no	—
68	C₂²×C₄	C₂²×D₂₅₇	1	6	yes	—
69	C₂³	#16861617	1	6	yes	—
70	C₂³	#16861618	1	6	yes	—
71	C₂³	#16861619	1	2	yes	—
72	C₂³	C₂³×D₂₅₇	1	1	yes	characteristic
73	C₂×C₄	—	2	12	no	—
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	514	6	no	—
76	C₂×C₄	—	514	6	no	—
77	C₂×C₄	—	514	6	no	—
78	C₂×C₄	—	514	6	no	—
79	C₂×C₄	—	4	12	no	—
80	C₂×C₄	—	1028	4	no	—
81	C₂×C₄	—	1028	12	no	—
82	C₂²	#22551585	1	12	yes	—
83	C₂²	#22551586	1	4	yes	—
84	C₂²	#22551587	1	12	yes	—
85	C₂²	C₂×#16861617	1	3	yes	—
86	C₂²	C₂×#16861618	1	3	yes	—
87	C₂²	C₂×#16861619	1	1	yes	characteristic
88	C₄	—	4	6	no	—
89	C₄	—	1028	2	no	—
90	C₄	—	1028	6	no	—
91	C₂	C₂₅₇⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#22551585	1	3	yes	—
93	C₂	C₂×#22551586	1	1	yes	characteristic
94	C₂	C₂×#22551587	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₂₅₇
commutator, cosocle	C₂³×C₂₅₇	C₂⁴
Frattini	C₂³	C₂³×D₂₅₇
Fitting	C₂×#95×C₂₅₇	C₂
socle, prime radical	C₂⁴×C₂₅₇	C₂³
hypercenter	C₂×#95	D₂₅₇
hypocenter	C₂₅₇	C₂×#401
LCS	G ▷ C₂³×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₂₅₇⋊#401	C₂	direct (N × H)
43. C₂×C₂₅₇	#401	semidirect
47. C₂₅₇	C₂×#401	semidirect
91. C₂	C₂₅₇⋊#401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅₇⋊#401	2
C₂×#22551499	2
C₂×#95×C₂₅₇	2
C₂×#401	257

Subgroups — C2×C257⋊#401 #45667616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅₇⋊#401 #45667616