Subgroups — C₂²×C₄×D₅⋊C₈ #13044376

Order 1280.

4638 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅⋊C₈	C₂	1	2	yes	maximal
2	C₂²×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×#170	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×D₅⋊C₈	C₂	1	24	yes	maximal, direct product factor
5	C₂³×C₄×D₅	C₄	1	2	yes	—
6	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂³×#170	C₂²	1	4	yes	—
8	C₂²×D₅⋊C₈	C₄	1	32	yes	direct product factor
9	C₂²×D₅⋊C₈	C₂²	1	24	yes	—
10	C₂²×C₄²×C₅	C₄	1	1	yes	characteristic
11	C₂²×C₄×Dic₅	C₄	1	1	yes	characteristic
12	C₂²×C₄×Dic₅	C₂²	1	2	yes	—
13	C₂×C₄²×D₅	C₄	1	12	yes	—
14	C₂×C₄²×D₅	C₂²	1	12	yes	—
15	C₂×C₄×#170	C₂²	1	48	yes	complemented
16	C₄×D₅⋊C₈	C₂²	1	64	yes	direct product factor
17	C₂³×C₄×C₈	—	5	1	no	maximal, Sylow
18	C₂⁴×D₅	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
21	C₂³×Dic₅	C₂×C₄	1	2	yes	—
22	C₂³×Dic₅	C₂³	1	1	yes	characteristic
23	C₂²×C₄×D₅	C₈	1	32	yes	complemented
24	C₂²×C₄×D₅	C₂×C₄	1	6	yes	—
25	C₂²×C₄×D₅	C₂×C₄	1	16	yes	—
26	C₂²×C₄×D₅	C₂×C₄	1	24	yes	—
27	C₂²×C₄×D₅	C₂³	1	6	yes	—
28	C₂²×#170	C₂×C₄	1	32	yes	complemented
29	C₂²×#170	C₂³	1	24	yes	—
30	C₂×D₅⋊C₈	C₂×C₄	1	192	yes	direct product factor
31	C₂×D₅⋊C₈	C₂³	1	32	yes	—
32	C₂×C₄²×C₅	C₂×C₄	1	12	yes	—
33	C₂×C₄×Dic₅	C₂×C₄	1	12	yes	—
34	C₂×C₄×Dic₅	C₂×C₄	1	12	yes	—
35	C₂×C₄×Dic₅	C₂³	1	12	yes	—
36	C₄²×D₅	C₂×C₄	1	48	yes	—
37	C₄²×D₅	C₂³	1	16	yes	—
38	C₄×#170	C₂³	1	64	yes	complemented
39	C₂⁴×C₈	—	5	2	no	—
40	C₂³×C₄²	—	5	1	no	—
41	C₂²×C₄×C₈	—	5	4	no	—
42	C₂²×C₄×C₈	—	5	24	no	—
43	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
44	C₂³×D₅	C₄²	1	8	yes	—
45	C₂³×D₅	C₂×C₈	1	16	yes	—
46	C₂³×D₅	C₂²×C₄	1	6	yes	—
47	C₂²×C₄×C₅	C₄²	1	8	yes	—
48	C₂²×C₄×C₅	C₂×C₈	1	16	yes	complemented
49	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
50	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	—
51	C₂²×Dic₅	C₂×C₈	1	16	yes	complemented
52	C₂²×Dic₅	C₂²×C₄	1	3	yes	—
53	C₂²×Dic₅	C₂²×C₄	1	8	yes	—
54	C₂²×Dic₅	C₂²×C₄	1	12	yes	—
55	C₂²×Dic₅	C₂⁴	1	3	yes	—
56	C₂×C₄×D₅	C₄²	1	48	yes	—
57	C₂×C₄×D₅	C₂×C₈	1	192	yes	complemented
58	C₂×C₄×D₅	C₂²×C₄	1	12	yes	—
59	C₂×C₄×D₅	C₂²×C₄	1	48	yes	—
60	C₂×C₄×D₅	C₂²×C₄	1	32	yes	—
61	C₂×C₄×D₅	C₂⁴	1	4	yes	—
62	C₂×#170	C₂²×C₄	1	96	yes	complemented
63	C₂×#170	C₂⁴	1	16	yes	—
64	D₅⋊C₈	C₂²×C₄	1	128	yes	direct product factor
65	C₄²×C₅	C₂²×C₄	1	16	yes	—
66	C₄×Dic₅	C₂²×C₄	1	24	yes	—
67	C₄×Dic₅	C₂²×C₄	1	16	yes	—
68	C₄×Dic₅	C₂⁴	1	8	yes	—
69	C₂⁴×C₄	—	5	2	no	—
70	C₂⁴×C₄	—	5	1	no	—
71	C₂³×C₈	—	5	24	no	—
72	C₂³×C₈	—	5	4	no	—
73	C₂³×C₈	—	5	32	no	—
74	C₂²×C₄²	—	5	2	no	—
75	C₂²×C₄²	—	5	1	no	—
76	C₂²×C₄²	—	5	12	no	—
77	C₂²×C₄²	—	5	12	no	—
78	C₂²×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
79	C₂×C₄×C₈	—	5	64	no	—
80	C₂×C₄×C₈	—	5	48	no	—
81	C₂³×C₅	C₂×C₄²	1	4	yes	—
82	C₂³×C₅	C₂²×C₈	1	8	yes	—
83	C₂³×C₅	C₂³×C₄	1	3	yes	—
84	C₂²×D₅	C₄×C₈	1	64	yes	complemented
85	C₂²×D₅	C₂×C₄²	1	24	yes	—
86	C₂²×D₅	C₂²×C₈	1	48	yes	—
87	C₂²×D₅	C₂³×C₄	1	4	yes	—
88	C₂×C₄×C₅	C₂×C₄²	1	24	yes	—
89	C₂×C₄×C₅	C₂²×C₈	1	48	yes	complemented
90	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
91	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
92	C₂×Dic₅	C₂×C₄²	1	12	yes	—
93	C₂×Dic₅	C₂²×C₈	1	48	yes	complemented
94	C₂×Dic₅	C₂³×C₄	1	8	yes	—
95	C₂×Dic₅	C₂³×C₄	1	12	yes	—
96	C₂×Dic₅	C₂³×C₄	1	3	yes	—
97	C₂×Dic₅	C₂⁵	1	1	yes	characteristic
98	C₄×D₅	C₂×C₄²	1	48	yes	—
99	C₄×D₅	C₂²×C₈	1	128	yes	complemented
100	C₄×D₅	C₂³×C₄	1	16	yes	—
101	#170	C₂³×C₄	1	32	yes	complemented
102	C₂⁵	—	5	1	no	—
103	C₂³×C₄	—	5	1	no	—
104	C₂³×C₄	—	5	2	no	—
105	C₂³×C₄	—	5	32	no	—
106	C₂³×C₄	—	5	16	no	—
107	C₂³×C₄	—	5	24	no	—
108	C₂³×C₄	—	5	6	no	—
109	C₂³×C₄	—	5	6	no	—
110	C₂³×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
111	C₂³×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
112	C₂²×C₈	—	5	192	no	—
113	C₂²×C₈	—	5	32	no	—
114	C₂²×C₈	—	5	32	no	—
115	C₂²×C₈	—	5	24	no	—
116	C₂×C₄²	—	5	12	no	—
117	C₂×C₄²	—	5	12	no	—
118	C₂×C₄²	—	5	12	no	—
119	C₂×C₄²	—	5	16	no	—
120	C₂×C₄²	—	5	48	no	—
121	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	12	yes	—
122	C₄×C₈	—	5	64	no	—
123	C₂²×C₅	C₂×C₄×C₈	1	16	yes	complemented
124	C₂²×C₅	C₂²×C₄²	1	6	yes	—
125	C₂²×C₅	C₂³×C₈	1	12	yes	—
126	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
127	C₂×D₅	C₂×C₄×C₈	1	96	yes	complemented
128	C₂×D₅	C₂²×C₄²	1	8	yes	—
129	C₂×D₅	C₂³×C₈	1	16	yes	—
130	C₄×C₅	C₂²×C₄²	1	8	yes	—
131	C₄×C₅	C₂³×C₈	1	16	yes	complemented
132	Dic₅	C₂²×C₄²	1	6	yes	—
133	Dic₅	C₂³×C₈	1	16	yes	complemented
134	Dic₅	C₂⁴×C₄	1	2	yes	—
135	C₂⁴	—	5	16	no	—
136	C₂⁴	—	5	8	no	—
137	C₂⁴	—	5	6	no	—
138	C₂⁴	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
139	C₂²×C₄	—	5	16	no	—
140	C₂²×C₄	—	5	8	no	—
141	C₂²×C₄	—	5	3	no	—
142	C₂²×C₄	—	5	12	no	—
143	C₂²×C₄	—	5	3	no	—
144	C₂²×C₄	—	5	192	no	—
145	C₂²×C₄	—	5	48	no	—
146	C₂²×C₄	—	5	48	no	—
147	C₂²×C₄	—	5	4	no	—
148	C₂²×C₄	—	5	32	no	—
149	C₂²×C₄	—	5	12	no	—
150	C₂²×C₄	D₅⋊C₈	1	16	yes	direct product factor
151	C₂²×C₄	C₄×AGL(1,𝔽₅)	1	8	yes	—
152	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	12	yes	—
153	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	6	yes	—
154	C₂×C₈	—	5	16	no	—
155	C₂×C₈	—	5	128	no	—
156	C₂×C₈	—	5	96	no	—
157	C₄²	—	5	8	no	—
158	C₄²	—	5	24	no	—
159	C₄²	—	5	16	no	—
160	C₄²	C₂²×AGL(1,𝔽₅)	1	16	yes	—
161	C₂×C₅	C₂²×C₄×C₈	1	12	yes	complemented
162	C₂×C₅	C₂³×C₄²	1	1	yes	characteristic
163	C₂×C₅	C₂⁴×C₈	1	2	yes	—
164	D₅	C₂²×C₄×C₈	1	16	yes	complemented
165	C₂³	—	5	64	no	—
166	C₂³	—	5	48	no	—
167	C₂³	—	5	24	no	—
168	C₂³	—	5	4	no	—
169	C₂³	C₂×D₅⋊C₈	1	8	yes	—
170	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	4	yes	—
171	C₂³	C₂³×AGL(1,𝔽₅)	1	3	yes	—
172	C₂×C₄	—	5	48	no	—
173	C₂×C₄	—	5	12	no	—
174	C₂×C₄	—	5	12	no	—
175	C₂×C₄	—	5	1	no	—
176	C₂×C₄	—	5	8	no	—
177	C₂×C₄	—	5	3	no	—
178	C₂×C₄	—	5	128	no	—
179	C₂×C₄	—	5	16	no	—
180	C₂×C₄	—	5	48	no	—
181	C₂×C₄	C₂×D₅⋊C₈	1	48	yes	direct product factor
182	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	24	yes	—
183	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	8	yes	—
184	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	4	yes	—
185	C₈	—	5	32	no	—
186	C₅	C₂³×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
187	C₂²	—	5	16	no	—
188	C₂²	—	5	8	no	—
189	C₂²	—	5	96	no	—
190	C₂²	C₄×D₅⋊C₈	1	16	yes	direct product factor
191	C₂²	C₂²×D₅⋊C₈	1	12	yes	—
192	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	6	yes	—
193	C₂²	C₂⁴×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₄	—	5	16	no	—
195	C₄	—	5	2	no	—
196	C₄	—	5	6	no	—
197	C₄	C₂²×D₅⋊C₈	1	16	yes	direct product factor
198	C₄	C₂²×C₄×AGL(1,𝔽₅)	1	8	yes	—
199	C₂	—	5	16	no	—
200	C₂	C₂×C₄×D₅⋊C₈	1	12	yes	direct product factor
201	C₂	C₂³×D₅⋊C₈	1	2	yes	—
202	C₂	C₂³×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄²	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₂³×C₄×C₈
Frattini	C₂²	C₂⁴×AGL(1,𝔽₅)
Fitting	C₂²×C₄²×C₅	C₄
socle	C₂⁴×C₅	C₂²×C₄
prime radical	C₂⁴×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂⁵
LCS	G ▷ C₅
UCS	C₁ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×#170	C₂	semidirect
4. C₂×C₄×D₅⋊C₈	C₂	direct (N × H)
8. C₂²×D₅⋊C₈	C₄	direct (N × H)
15. C₂×C₄×#170	C₂²	semidirect
16. C₄×D₅⋊C₈	C₂²	direct (N × H)
23. C₂²×C₄×D₅	C₈	semidirect
28. C₂²×#170	C₂×C₄	semidirect
30. C₂×D₅⋊C₈	C₂×C₄	direct (N × H)
38. C₄×#170	C₂³	semidirect
48. C₂²×C₄×C₅	C₂×C₈	semidirect
51. C₂²×Dic₅	C₂×C₈	semidirect
57. C₂×C₄×D₅	C₂×C₈	semidirect
62. C₂×#170	C₂²×C₄	semidirect
64. D₅⋊C₈	C₂²×C₄	direct (N × H)
84. C₂²×D₅	C₄×C₈	semidirect
89. C₂×C₄×C₅	C₂²×C₈	semidirect
93. C₂×Dic₅	C₂²×C₈	semidirect
99. C₄×D₅	C₂²×C₈	semidirect
101. #170	C₂³×C₄	semidirect
123. C₂²×C₅	C₂×C₄×C₈	semidirect
127. C₂×D₅	C₂×C₄×C₈	semidirect
131. C₄×C₅	C₂³×C₈	semidirect
133. Dic₅	C₂³×C₈	semidirect
150. C₂²×C₄	D₅⋊C₈	direct (N × H)
161. C₂×C₅	C₂²×C₄×C₈	semidirect
164. D₅	C₂²×C₄×C₈	semidirect
181. C₂×C₄	C₂×D₅⋊C₈	direct (N × H)
186. C₅	C₂³×C₄×C₈	semidirect
190. C₂²	C₄×D₅⋊C₈	direct (N × H)
197. C₄	C₂²×D₅⋊C₈	direct (N × H)
200. C₂	C₂×C₄×D₅⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₅⋊C₈	2
C₂²×C₄²×D₅	2
C₂²×C₄×#170	2
C₂×C₄×D₅⋊C₈	2
C₂³×C₄×C₈	5

Subgroups — C22×C4×D5⋊C8 #13044376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₅⋊C₈ #13044376