Subgroups — C₂⁶×C₂₅₆ #72194321

Order 16384.

213921 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₂₅₆	C₂	1	126	yes	maximal, direct product factor
3	C₂⁶×C₆₄	C₄	1	1	yes	characteristic
4	C₂⁵×C₁₂₈	C₄	1	63	yes	—
5	C₂⁵×C₁₂₈	C₂²	1	63	yes	—
6	C₂⁴×C₂₅₆	C₂²	1	2604	yes	direct product factor
7	C₂⁶×C₃₂	C₈	1	1	yes	characteristic
8	C₂⁵×C₆₄	C₈	1	63	yes	—
9	C₂⁵×C₆₄	C₂×C₄	1	63	yes	—
10	C₂⁴×C₁₂₈	C₂×C₄	1	1953	yes	—
11	C₂⁴×C₁₂₈	C₂³	1	651	yes	—
12	C₂³×C₂₅₆	C₂³	1	11160	yes	direct product factor
13	C₂⁶×C₁₆	C₁₆	1	1	yes	characteristic
14	C₂⁵×C₃₂	C₁₆	1	63	yes	—
15	C₂⁵×C₃₂	C₂×C₈	1	63	yes	—
16	C₂⁴×C₆₄	C₂×C₈	1	1953	yes	—
17	C₂⁴×C₆₄	C₂²×C₄	1	651	yes	—
18	C₂³×C₁₂₈	C₂²×C₄	1	9765	yes	—
19	C₂³×C₁₂₈	C₂⁴	1	1395	yes	—
20	C₂²×C₂₅₆	C₂⁴	1	10416	yes	direct product factor
21	C₂⁶×C₈	C₃₂	1	1	yes	characteristic
22	C₂⁵×C₁₆	C₃₂	1	63	yes	—
23	C₂⁵×C₁₆	C₂×C₁₆	1	63	yes	—
24	C₂⁴×C₃₂	C₂×C₁₆	1	1953	yes	—
25	C₂⁴×C₃₂	C₂²×C₈	1	651	yes	—
26	C₂³×C₆₄	C₂²×C₈	1	9765	yes	—
27	C₂³×C₆₄	C₂³×C₄	1	1395	yes	—
28	C₂²×C₁₂₈	C₂³×C₄	1	9765	yes	—
29	C₂²×C₁₂₈	C₂⁵	1	651	yes	—
30	C₂×C₂₅₆	C₂⁵	1	2016	yes	direct product factor
31	C₂⁶×C₄	C₆₄	1	1	yes	characteristic
32	C₂⁵×C₈	C₆₄	1	63	yes	—
33	C₂⁵×C₈	C₂×C₃₂	1	63	yes	—
34	C₂⁴×C₁₆	C₂×C₃₂	1	1953	yes	—
35	C₂⁴×C₁₆	C₂²×C₁₆	1	651	yes	—
36	C₂³×C₃₂	C₂²×C₁₆	1	9765	yes	—
37	C₂³×C₃₂	C₂³×C₈	1	1395	yes	—
38	C₂²×C₆₄	C₂³×C₈	1	9765	yes	—
39	C₂²×C₆₄	C₂⁴×C₄	1	651	yes	—
40	C₂×C₁₂₈	C₂⁴×C₄	1	1953	yes	—
41	C₂×C₁₂₈	C₂⁶	1	63	yes	—
42	C₂₅₆	C₂⁶	1	64	yes	direct product factor
43	C₂⁷	C₁₂₈	1	1	yes	characteristic
44	C₂⁵×C₄	C₁₂₈	1	63	yes	—
45	C₂⁵×C₄	C₂×C₆₄	1	63	yes	—
46	C₂⁴×C₈	C₂×C₆₄	1	1953	yes	—
47	C₂⁴×C₈	C₂²×C₃₂	1	651	yes	—
48	C₂³×C₁₆	C₂²×C₃₂	1	9765	yes	—
49	C₂³×C₁₆	C₂³×C₁₆	1	1395	yes	—
50	C₂²×C₃₂	C₂³×C₁₆	1	9765	yes	—
51	C₂²×C₃₂	C₂⁴×C₈	1	651	yes	—
52	C₂×C₆₄	C₂⁴×C₈	1	1953	yes	—
53	C₂×C₆₄	C₂⁵×C₄	1	63	yes	—
54	C₁₂₈	C₂⁵×C₄	1	63	yes	—
55	C₁₂₈	C₂⁷	1	1	yes	characteristic
56	C₂⁶	C₂₅₆	1	64	yes	direct product factor
57	C₂⁶	C₂×C₁₂₈	1	63	yes	—
58	C₂⁴×C₄	C₂×C₁₂₈	1	1953	yes	—
59	C₂⁴×C₄	C₂²×C₆₄	1	651	yes	—
60	C₂³×C₈	C₂²×C₆₄	1	9765	yes	—
61	C₂³×C₈	C₂³×C₃₂	1	1395	yes	—
62	C₂²×C₁₆	C₂³×C₃₂	1	9765	yes	—
63	C₂²×C₁₆	C₂⁴×C₁₆	1	651	yes	—
64	C₂×C₃₂	C₂⁴×C₁₆	1	1953	yes	—
65	C₂×C₃₂	C₂⁵×C₈	1	63	yes	—
66	C₆₄	C₂⁵×C₈	1	63	yes	—
67	C₆₄	C₂⁶×C₄	1	1	yes	characteristic
68	C₂⁵	C₂×C₂₅₆	1	2016	yes	direct product factor
69	C₂⁵	C₂²×C₁₂₈	1	651	yes	—
70	C₂³×C₄	C₂²×C₁₂₈	1	9765	yes	—
71	C₂³×C₄	C₂³×C₆₄	1	1395	yes	—
72	C₂²×C₈	C₂³×C₆₄	1	9765	yes	—
73	C₂²×C₈	C₂⁴×C₃₂	1	651	yes	—
74	C₂×C₁₆	C₂⁴×C₃₂	1	1953	yes	—
75	C₂×C₁₆	C₂⁵×C₁₆	1	63	yes	—
76	C₃₂	C₂⁵×C₁₆	1	63	yes	—
77	C₃₂	C₂⁶×C₈	1	1	yes	characteristic
78	C₂⁴	C₂²×C₂₅₆	1	10416	yes	direct product factor
79	C₂⁴	C₂³×C₁₂₈	1	1395	yes	—
80	C₂²×C₄	C₂³×C₁₂₈	1	9765	yes	—
81	C₂²×C₄	C₂⁴×C₆₄	1	651	yes	—
82	C₂×C₈	C₂⁴×C₆₄	1	1953	yes	—
83	C₂×C₈	C₂⁵×C₃₂	1	63	yes	—
84	C₁₆	C₂⁵×C₃₂	1	63	yes	—
85	C₁₆	C₂⁶×C₁₆	1	1	yes	characteristic
86	C₂³	C₂³×C₂₅₆	1	11160	yes	direct product factor
87	C₂³	C₂⁴×C₁₂₈	1	651	yes	—
88	C₂×C₄	C₂⁴×C₁₂₈	1	1953	yes	—
89	C₂×C₄	C₂⁵×C₆₄	1	63	yes	—
90	C₈	C₂⁵×C₆₄	1	63	yes	—
91	C₈	C₂⁶×C₃₂	1	1	yes	characteristic
92	C₂²	C₂⁴×C₂₅₆	1	2604	yes	direct product factor
93	C₂²	C₂⁵×C₁₂₈	1	63	yes	—
94	C₄	C₂⁵×C₁₂₈	1	63	yes	—
95	C₄	C₂⁶×C₆₄	1	1	yes	characteristic
96	C₂	C₂⁵×C₂₅₆	1	126	yes	direct product factor
97	C₂	C₂⁶×C₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₂₈	C₂⁷
socle, prime radical	C₂⁷	C₁₂₈
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₁₂₈ ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₂₅₆	C₂	direct (N × H)
6. C₂⁴×C₂₅₆	C₂²	direct (N × H)
12. C₂³×C₂₅₆	C₂³	direct (N × H)
20. C₂²×C₂₅₆	C₂⁴	direct (N × H)
30. C₂×C₂₅₆	C₂⁵	direct (N × H)
42. C₂₅₆	C₂⁶	direct (N × H)
56. C₂⁶	C₂₅₆	direct (N × H)
68. C₂⁵	C₂×C₂₅₆	direct (N × H)
78. C₂⁴	C₂²×C₂₅₆	direct (N × H)
86. C₂³	C₂³×C₂₅₆	direct (N × H)
92. C₂²	C₂⁴×C₂₅₆	direct (N × H)
96. C₂	C₂⁵×C₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×C₁₂₈	2
C₂⁵×C₂₅₆	2

Subgroups — C26×C256 #72194321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₂₅₆ #72194321