Subgroups — C₂×C₅×#2483 #11957466

Order 1280.

4382 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
2	C₅×#2483	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#397	C₂	1	4	yes	maximal, complemented
4	C₂×C₅×#385	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#381	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#379	C₂	1	1	yes	maximal, characteristic
7	C₂⁶×C₅	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
10	C₂²×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
11	C₂²×C₅×C₂²⋊C₄	—	2	16	no	—
12	C₂²×C₅×C₂²⋊C₄	C₂²	1	16	yes	—
13	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₅×#397	C₂²	1	32	yes	complemented
18	C₅×#385	C₂²	1	32	yes	complemented
19	C₅×#381	C₂²	1	32	yes	complemented
20	C₅×#379	C₂²	1	8	yes	—
21	C₂×C₅×#95	C₂²	1	4	yes	complemented
22	C₂×C₅×#95	C₂²	1	8	yes	complemented
23	C₂×#2483	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂⁵×C₅	—	2	16	no	—
25	C₂⁵×C₅	—	4	4	no	—
26	C₂⁵×C₅	D₄	1	8	yes	—
27	C₂⁵×C₅	C₂³	1	1	yes	characteristic
28	C₂⁵×C₅	C₂³	1	4	yes	—
29	C₂⁵×C₅	C₂³	1	2	yes	—
30	C₂³×C₄×C₅	—	2	8	no	—
31	C₂³×C₄×C₅	—	2	8	no	—
32	C₂³×C₄×C₅	—	2	16	no	—
33	C₂³×C₄×C₅	—	4	8	no	—
34	C₂³×C₄×C₅	C₂³	1	8	yes	—
35	C₂³×C₄×C₅	C₂³	1	4	yes	—
36	C₂³×C₄×C₅	C₂³	1	4	yes	—
37	C₂³×C₄×C₅	C₂³	1	4	yes	—
38	C₂³×C₄×C₅	C₂³	1	8	yes	—
39	C₂×C₅×C₄⋊C₄	—	4	8	no	—
40	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	complemented
41	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
42	C₂×C₅×C₂²⋊C₄	—	2	64	no	—
43	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
44	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
45	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
46	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
47	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
48	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
49	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
50	C₅×#95	C₂³	1	16	yes	complemented
51	C₅×#95	C₂³	1	32	yes	complemented
52	C₂³×C₂²⋊C₄	C₂×C₅	1	2	yes	—
53	#2483	C₂×C₅	1	16	yes	direct product factor
54	C₂×#397	C₂×C₅	1	4	yes	complemented
55	C₂×#385	C₂×C₅	1	4	yes	complemented
56	C₂×#381	C₂×C₅	1	4	yes	complemented
57	C₂×#379	C₂×C₅	1	1	yes	characteristic
58	C₂⁴×C₅	—	2	8	no	—
59	C₂⁴×C₅	—	2	8	no	—
60	C₂⁴×C₅	—	2	64	no	—
61	C₂⁴×C₅	—	2	32	no	—
62	C₂⁴×C₅	—	2	8	no	—
63	C₂⁴×C₅	—	2	4	no	—
64	C₂⁴×C₅	—	4	16	no	—
65	C₂⁴×C₅	—	4	8	no	—
66	C₂⁴×C₅	—	4	64	no	—
67	C₂⁴×C₅	C₂×D₄	1	4	yes	—
68	C₂⁴×C₅	C₂×D₄	1	16	yes	—
69	C₂⁴×C₅	C₂×D₄	1	8	yes	—
70	C₂⁴×C₅	#41	1	16	yes	—
71	C₂⁴×C₅	C₂⁴	1	2	yes	—
72	C₂⁴×C₅	C₂⁴	1	4	yes	—
73	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
74	C₂²×C₄×C₅	—	2	16	no	—
75	C₂²×C₄×C₅	—	2	16	no	—
76	C₂²×C₄×C₅	—	2	8	no	—
77	C₂²×C₄×C₅	—	2	8	no	—
78	C₂²×C₄×C₅	—	2	16	no	—
79	C₂²×C₄×C₅	—	2	32	no	—
80	C₂²×C₄×C₅	—	2	16	no	—
81	C₂²×C₄×C₅	—	2	8	no	—
82	C₂²×C₄×C₅	—	2	16	no	—
83	C₂²×C₄×C₅	—	4	16	no	—
84	C₂²×C₄×C₅	—	4	32	no	—
85	C₂²×C₄×C₅	—	4	32	no	—
86	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
87	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
89	C₅×C₄⋊C₄	—	4	16	no	—
90	C₅×C₂²⋊C₄	—	2	32	no	—
91	C₅×C₂²⋊C₄	—	2	32	no	—
92	C₅×C₂²⋊C₄	—	2	32	no	—
93	C₅×C₂²⋊C₄	—	4	8	no	—
94	C₂⁶	C₂²×C₅	1	1	yes	characteristic
95	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
96	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
97	C₂²×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
98	C₂²×C₂²⋊C₄	—	2	16	no	—
99	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
100	C₂²×C₂²⋊C₄	C₂²×C₅	1	16	yes	—
101	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
102	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
103	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
104	#397	C₂²×C₅	1	32	yes	complemented
105	#385	C₂²×C₅	1	32	yes	complemented
106	#381	C₂²×C₅	1	32	yes	complemented
107	#379	C₂²×C₅	1	8	yes	—
108	C₂×#95	C₂²×C₅	1	4	yes	complemented
109	C₂×#95	C₂²×C₅	1	8	yes	complemented
110	C₂³×C₅	—	2	16	no	—
111	C₂³×C₅	—	2	16	no	—
112	C₂³×C₅	—	2	64	no	—
113	C₂³×C₅	—	2	8	no	—
114	C₂³×C₅	—	2	8	no	—
115	C₂³×C₅	—	2	64	no	—
116	C₂³×C₅	—	2	16	no	—
117	C₂³×C₅	—	2	8	no	—
118	C₂³×C₅	—	2	8	no	—
119	C₂³×C₅	—	2	4	no	—
120	C₂³×C₅	—	4	16	no	—
121	C₂³×C₅	—	4	64	no	—
122	C₂³×C₅	—	4	128	no	—
123	C₂³×C₅	—	4	16	no	—
124	C₂³×C₅	#123	1	32	yes	—
125	C₂³×C₅	C₂²×D₄	1	4	yes	—
126	C₂³×C₅	C₂²×D₄	1	8	yes	—
127	C₂³×C₅	C₂²×D₄	1	2	yes	—
128	C₂³×C₅	C₂×#41	1	16	yes	—
129	C₂³×C₅	C₂×#41	1	8	yes	—
130	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
131	C₂³×C₅	C₂⁵	1	1	yes	characteristic
132	C₂×C₄×C₅	—	2	8	no	—
133	C₂×C₄×C₅	—	2	8	no	—
134	C₂×C₄×C₅	—	2	16	no	—
135	C₂×C₄×C₅	—	2	16	no	—
136	C₂×C₄×C₅	—	2	8	no	—
137	C₂×C₄×C₅	—	2	16	no	—
138	C₂×C₄×C₅	—	4	32	no	—
139	C₂×C₄×C₅	—	4	32	no	—
140	C₂×C₄×C₅	—	4	16	no	—
141	C₂×C₄×C₅	—	4	16	no	—
142	C₂×C₄×C₅	—	4	16	no	—
143	C₂⁵	—	2	16	no	—
144	C₂⁵	—	4	4	no	—
145	C₂⁵	C₅×D₄	1	8	yes	—
146	C₂⁵	C₂³×C₅	1	1	yes	characteristic
147	C₂⁵	C₂³×C₅	1	4	yes	—
148	C₂⁵	C₂³×C₅	1	2	yes	—
149	C₂³×C₄	—	2	8	no	—
150	C₂³×C₄	—	2	8	no	—
151	C₂³×C₄	—	2	16	no	—
152	C₂³×C₄	—	4	8	no	—
153	C₂³×C₄	C₂³×C₅	1	4	yes	—
154	C₂³×C₄	C₂³×C₅	1	4	yes	—
155	C₂³×C₄	C₂³×C₅	1	4	yes	—
156	C₂³×C₄	C₂³×C₅	1	8	yes	—
157	C₂³×C₄	C₂³×C₅	1	8	yes	—
158	C₂×C₄⋊C₄	—	4	8	no	—
159	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	complemented
160	C₂×C₂²⋊C₄	—	2	16	no	—
161	C₂×C₂²⋊C₄	—	2	64	no	—
162	C₂×C₂²⋊C₄	—	2	16	no	—
163	C₂×C₂²⋊C₄	—	2	16	no	—
164	C₂×C₂²⋊C₄	—	4	4	no	—
165	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
166	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
167	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
168	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
169	#95	C₂³×C₅	1	16	yes	complemented
170	#95	C₂³×C₅	1	32	yes	complemented
171	C₂²×C₅	—	2	8	no	—
172	C₂²×C₅	—	2	8	no	—
173	C₂²×C₅	—	2	32	no	—
174	C₂²×C₅	—	2	64	no	—
175	C₂²×C₅	—	2	8	no	—
176	C₂²×C₅	—	2	4	no	—
177	C₂²×C₅	—	4	64	no	—
178	C₂²×C₅	—	4	8	no	—
179	C₂²×C₅	—	4	16	no	—
180	C₂²×C₅	C₂×#123	1	16	yes	—
181	C₂²×C₅	C₂×#123	1	8	yes	—
182	C₂²×C₅	#534	1	4	yes	—
183	C₂²×C₅	#551	1	16	yes	—
184	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₅	C₂²×#41	1	4	yes	—
186	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
187	C₄×C₅	—	4	8	no	—
188	C₄×C₅	—	4	8	no	—
189	C₄×C₅	—	4	8	no	—
190	C₂⁴	—	2	8	no	—
191	C₂⁴	—	2	8	no	—
192	C₂⁴	—	2	64	no	—
193	C₂⁴	—	2	32	no	—
194	C₂⁴	—	2	8	no	—
195	C₂⁴	—	2	4	no	—
196	C₂⁴	—	4	16	no	—
197	C₂⁴	—	4	8	no	—
198	C₂⁴	—	4	64	no	—
199	C₂⁴	C₂×C₅×D₄	1	4	yes	—
200	C₂⁴	C₂×C₅×D₄	1	16	yes	—
201	C₂⁴	C₂×C₅×D₄	1	8	yes	—
202	C₂⁴	C₅×#41	1	16	yes	—
203	C₂⁴	C₂⁴×C₅	1	2	yes	—
204	C₂⁴	C₂⁴×C₅	1	4	yes	—
205	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
206	C₂²×C₄	—	2	16	no	—
207	C₂²×C₄	—	2	16	no	—
208	C₂²×C₄	—	2	8	no	—
209	C₂²×C₄	—	2	8	no	—
210	C₂²×C₄	—	2	16	no	—
211	C₂²×C₄	—	2	32	no	—
212	C₂²×C₄	—	2	16	no	—
213	C₂²×C₄	—	2	8	no	—
214	C₂²×C₄	—	2	16	no	—
215	C₂²×C₄	—	4	16	no	—
216	C₂²×C₄	—	4	32	no	—
217	C₂²×C₄	—	4	32	no	—
218	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
219	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
220	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
221	C₄⋊C₄	—	4	16	no	—
222	C₂²⋊C₄	—	2	32	no	—
223	C₂²⋊C₄	—	2	32	no	—
224	C₂²⋊C₄	—	2	32	no	—
225	C₂²⋊C₄	—	4	8	no	—
226	C₂×C₅	—	2	16	no	—
227	C₂×C₅	—	4	4	no	—
228	C₂×C₅	#2483	1	8	yes	direct product factor
229	C₂×C₅	C₂²×#123	1	2	yes	—
230	C₂×C₅	C₂×#534	1	1	yes	characteristic
231	C₂×C₅	C₂×#551	1	4	yes	—
232	C₂³	—	2	16	no	—
233	C₂³	—	2	16	no	—
234	C₂³	—	2	64	no	—
235	C₂³	—	2	8	no	—
236	C₂³	—	2	8	no	—
237	C₂³	—	2	64	no	—
238	C₂³	—	2	16	no	—
239	C₂³	—	2	8	no	—
240	C₂³	—	2	8	no	—
241	C₂³	—	2	4	no	—
242	C₂³	—	4	16	no	—
243	C₂³	—	4	128	no	—
244	C₂³	—	4	64	no	—
245	C₂³	—	4	16	no	—
246	C₂³	C₅×#123	1	32	yes	—
247	C₂³	C₂²×C₅×D₄	1	4	yes	—
248	C₂³	C₂²×C₅×D₄	1	8	yes	—
249	C₂³	C₂²×C₅×D₄	1	2	yes	—
250	C₂³	C₂×C₅×#41	1	16	yes	—
251	C₂³	C₂×C₅×#41	1	8	yes	—
252	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
253	C₂³	C₂⁵×C₅	1	1	yes	characteristic
254	C₂×C₄	—	2	8	no	—
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	16	no	—
257	C₂×C₄	—	2	16	no	—
258	C₂×C₄	—	2	8	no	—
259	C₂×C₄	—	2	16	no	—
260	C₂×C₄	—	4	32	no	—
261	C₂×C₄	—	4	32	no	—
262	C₂×C₄	—	4	16	no	—
263	C₂×C₄	—	4	16	no	—
264	C₂×C₄	—	4	16	no	—
265	C₅	C₂×#2483	1	1	yes	characteristic, direct product factor, Sylow
266	C₂²	—	2	64	no	—
267	C₂²	—	2	8	no	—
268	C₂²	—	2	8	no	—
269	C₂²	—	2	32	no	—
270	C₂²	—	2	8	no	—
271	C₂²	—	2	4	no	—
272	C₂²	—	4	64	no	—
273	C₂²	—	4	16	no	—
274	C₂²	—	4	8	no	—
275	C₂²	C₂×C₅×#123	1	16	yes	—
276	C₂²	C₂×C₅×#123	1	8	yes	—
277	C₂²	C₅×#534	1	4	yes	—
278	C₂²	C₅×#551	1	16	yes	—
279	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
280	C₂²	C₂²×C₅×#41	1	4	yes	—
281	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
282	C₄	—	4	8	no	—
283	C₄	—	4	8	no	—
284	C₄	—	4	8	no	—
285	C₂	—	2	16	no	—
286	C₂	—	4	4	no	—
287	C₂	C₅×#2483	1	8	yes	direct product factor
288	C₂	C₂²×C₅×#123	1	2	yes	—
289	C₂	C₂×C₅×#534	1	1	yes	characteristic
290	C₂	C₂×C₅×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁶×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2483	C₂	direct (N × H)
3. C₂×C₅×#397	C₂	semidirect
4. C₂×C₅×#385	C₂	semidirect
5. C₂×C₅×#381	C₂	semidirect
10. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
17. C₅×#397	C₂²	semidirect
18. C₅×#385	C₂²	semidirect
19. C₅×#381	C₂²	semidirect
21. C₂×C₅×#95	C₂²	semidirect
22. C₂×C₅×#95	C₂²	semidirect
23. C₂×#2483	C₅	direct (N × H)
40. C₂×C₅×C₄⋊C₄	C₂³	semidirect
50. C₅×#95	C₂³	semidirect
51. C₅×#95	C₂³	semidirect
53. #2483	C₂×C₅	direct (N × H)
54. C₂×#397	C₂×C₅	semidirect
55. C₂×#385	C₂×C₅	semidirect
56. C₂×#381	C₂×C₅	semidirect
97. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
104. #397	C₂²×C₅	semidirect
105. #385	C₂²×C₅	semidirect
106. #381	C₂²×C₅	semidirect
108. C₂×#95	C₂²×C₅	semidirect
109. C₂×#95	C₂²×C₅	semidirect
159. C₂×C₄⋊C₄	C₂³×C₅	semidirect
169. #95	C₂³×C₅	semidirect
170. #95	C₂³×C₅	semidirect
228. C₂×C₅	#2483	direct (N × H)
265. C₅	C₂×#2483	direct (N × H)
287. C₂	C₅×#2483	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×C₅×C₂²⋊C₄	2
C₅×#2483	2
C₂×C₅×#397	2
C₂×C₅×#385	2
C₂×C₅×#381	2
C₂×C₅×#379	2
C₂×#2483	5

Subgroups — C2×C5×#2483 #11957466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2483 #11957466