Finite Group Databasebeta

← C22×C5×#339 #11943061

Subgroups — C22×C5×#339 #11943061

Order 1280.

2830 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×M16C211yesmaximal, characteristic
2C22×C5×#117C211yesmaximal, characteristic
3C23×C42×C5C211yesmaximal, characteristic
4C2×C5×#339C2112yesmaximal, direct product factor
5C24×C4×C5—21no—
6C24×C4×C5C2211yescharacteristic
7C22×C5×M16—24no—
8C22×C5×M16—23no—
9C22×C5×M16C418yescomplemented
10C22×C5×M16C2216yes—
11C23×C5×C8—21no—
12C2×C5×#117—23no—
13C2×C5×#117—23no—
14C2×C5×#117C416yescomplemented
15C2×C5×#117C2216yes—
16C22×C5×C4⋊C4C412yescomplemented
17C22×C5×C22⋊C4—21no—
18C22×C42×C5—23no—
19C22×C42×C5—24no—
20C22×C42×C5—21no—
21C22×C42×C5C418yescomplemented
22C22×C42×C5C2216yes—
23C5×#339C22116yesdirect product factor
24C22×#339C511yesmaximal, characteristic, direct product factor, Sylow
25C25×C5D411yescharacteristic
26C23×C4×C5—216no—
27C23×C4×C5—28no—
28C23×C4×C5—26no—
29C23×C4×C5—22no—
30C23×C4×C5C2×C414yes—
31C23×C4×C5C2×C414yes—
32C23×C4×C5C2×C411yescharacteristic
33C23×C4×C5C2×C413yes—
34C23×C4×C5D413yes—
35C23×C4×C5D414yes—
36C23×C4×C5D413yes—
37C23×C4×C5D411yescharacteristic
38C23×C4×C5Q814yes—
39C23×C4×C5C2313yes—
40C2×C5×M16—224no—
41C2×C5×M16—212no—
42C2×C5×M16—26no—
43C2×C5×M16C2×C4124yescomplemented
44C2×C5×M16C2314yes—
45C22×C5×C8—28no—
46C22×C5×C8—26no—
47C5×#117—212no—
48C5×#117—26no—
49C5×#117—26no—
50C5×#117C2×C4112yescomplemented
51C5×#117C2314yes—
52C2×C5×C4⋊C4—26no—
53C2×C5×C4⋊C4C2×C4112yescomplemented
54C2×C5×C22⋊C4—26no—
55C2×C5×C22⋊C4—26no—
56C2×C42×C5—224no—
57C2×C42×C5—26no—
58C2×C42×C5—26no—
59C2×C42×C5—212no—
60C2×C42×C5—26no—
61C2×C42×C5C2×C4124yescomplemented
62C2×C42×C5C2314yes—
63C23×M16C2×C511yescharacteristic
64C22×#117C2×C511yescharacteristic
65C23×C42C2×C511yescharacteristic
66C2×#339C2×C5112yesdirect product factor
67C24×C5—28no—
68C24×C5C22⋊C413yes—
69C24×C5C22⋊C414yes—
70C24×C5C22⋊C411yescharacteristic
71C24×C5C4⋊C414yes—
72C24×C5C2×D413yes—
73C22×C4×C5—264no—
74C22×C4×C5—248no—
75C22×C4×C5—224no—
76C22×C4×C5—24no—
77C22×C4×C5—212no—
78C22×C4×C5—48no—
79C22×C4×C5C42112yes—
80C22×C4×C5C4214yes—
81C22×C4×C5C22⋊C4112yes—
82C22×C4×C5C22⋊C413yes—
83C22×C4×C5C22⋊C413yes—
84C22×C4×C5C22⋊C416yes—
85C22×C4×C5C22⋊C414yes—
86C22×C4×C5C22⋊C4112yes—
87C22×C4×C5C4⋊C4112yes—
88C22×C4×C5C4⋊C4112yes—
89C22×C4×C5C4⋊C4112yes—
90C22×C4×C5C4⋊C414yes—
91C22×C4×C5C4⋊C414yes—
92C22×C4×C5C22×C416yes—
93C22×C4×C5C22×C416yes—
94C22×C4×C5C22×C413yes—
95C22×C4×C5C22×C413yes—
96C22×C4×C5C2×D413yes—
97C22×C4×C5C2×D413yes—
98C22×C4×C5C2×D416yes—
99C22×C4×C5C2×D413yes—
100C22×C4×C5C2×Q816yes—
101C22×C4×C5C2411yescharacteristic
102C5×M16—224no—
103C5×M16—24no—
104C5×M16C22×C418yescomplemented
105C2×C5×C8—224no—
106C2×C5×C8—24no—
107C5×C4⋊C4—212no—
108C5×C4⋊C4C22×C418yescomplemented
109C5×C22⋊C4—212no—
110C5×C22⋊C4—24no—
111C42×C5—224no—
112C42×C5—212no—
113C42×C5—24no—
114C42×C5—24no—
115C42×C5C22×C418yescomplemented
116C24×C4—21no—
117C24×C4C22×C511yescharacteristic
118C22×M16—24no—
119C22×M16—23no—
120C22×M16C4×C518yescomplemented
121C22×M16C22×C516yes—
122C23×C8—21no—
123C2×#117—23no—
124C2×#117—23no—
125C2×#117C4×C516yescomplemented
126C2×#117C22×C516yes—
127C22×C4⋊C4C4×C512yescomplemented
128C22×C22⋊C4—21no—
129C22×C42—23no—
130C22×C42—24no—
131C22×C42—21no—
132C22×C42C4×C518yescomplemented
133C22×C42C22×C516yes—
134#339C22×C5116yesdirect product factor
135C23×C5—216no—
136C23×C5—216no—
137C23×C5—212no—
138C23×C5—212no—
139C23×C5#95112yes—
140C23×C5#9514yes—
141C23×C5#10418yes—
142C23×C5C2×C22⋊C413yes—
143C23×C5C2×C22⋊C416yes—
144C23×C5C2×C22⋊C413yes—
145C23×C5C2×C4⋊C416yes—
146C23×C5C22×D411yescharacteristic
147C2×C4×C5—216no—
148C2×C4×C5—296no—
149C2×C4×C5—28no—
150C2×C4×C5—28no—
151C2×C4×C5—424no—
152C2×C4×C5#95124yes—
153C2×C4×C5#95112yes—
154C2×C4×C5#95112yes—
155C2×C4×C5C2×C4216yes—
156C2×C4×C5C2×C4216yes—
157C2×C4×C5C2×C22⋊C416yes—
158C2×C4×C5C2×C22⋊C416yes—
159C2×C4×C5C2×C22⋊C416yes—
160C2×C4×C5C2×C22⋊C413yes—
161C2×C4×C5C2×C22⋊C413yes—
162C2×C4×C5C2×C4⋊C416yes—
163C2×C4×C5C2×C4⋊C416yes—
164C2×C4×C5C2×C4⋊C416yes—
165C2×C4×C5C2×C4⋊C416yes—
166C2×C4×C5C2×C4⋊C416yes—
167C2×C4×C5C23×C411yescharacteristic
168C2×C4×C5C23×C411yescharacteristic
169C2×C4×C5C23×C411yescharacteristic
170C2×C4×C5C22×D411yescharacteristic
171C2×C4×C5C22×D411yescharacteristic
172C2×C4×C5C22×Q811yescharacteristic
173C5×C8—28no—
174C25C5×D411yescharacteristic
175C23×C4—216no—
176C23×C4—28no—
177C23×C4—26no—
178C23×C4—22no—
179C23×C4C2×C4×C514yes—
180C23×C4C2×C4×C511yescharacteristic
181C23×C4C2×C4×C513yes—
182C23×C4C2×C4×C514yes—
183C23×C4C5×D413yes—
184C23×C4C5×D413yes—
185C23×C4C5×D411yescharacteristic
186C23×C4C5×D414yes—
187C23×C4C5×Q814yes—
188C23×C4C23×C513yes—
189C2×M16—224no—
190C2×M16—212no—
191C2×M16—26no—
192C2×M16C2×C4×C5124yescomplemented
193C2×M16C23×C514yes—
194C22×C8—28no—
195C22×C8—26no—
196#117—212no—
197#117—26no—
198#117—26no—
199#117C2×C4×C5112yescomplemented
200#117C23×C514yes—
201C2×C4⋊C4—26no—
202C2×C4⋊C4C2×C4×C5112yescomplemented
203C2×C22⋊C4—26no—
204C2×C22⋊C4—26no—
205C2×C42—26no—
206C2×C42—224no—
207C2×C42—26no—
208C2×C42—26no—
209C2×C42—212no—
210C2×C42C2×C4×C5124yescomplemented
211C2×C42C23×C514yes—
212C22×C5—22no—
213C22×C5—26no—
214C22×C5—212no—
215C22×C5—224no—
216C22×C5—212no—
217C22×C5#339116yesdirect product factor
218C22×C5C2×#9516yes—
219C22×C5C2×#9516yes—
220C22×C5C2×#104112yes—
221C22×C5C22×C22⋊C411yescharacteristic
222C22×C5C22×C22⋊C411yescharacteristic
223C22×C5C22×C4⋊C411yescharacteristic
224C4×C5—216no—
225C4×C5—48no—
226C4×C5C2×#9516yes—
227C4×C5C2×#9516yes—
228C4×C5C22×C4211yescharacteristic
229C4×C5C22×C22⋊C411yescharacteristic
230C4×C5C22×C4⋊C411yescharacteristic
231C4×C5C22×C4⋊C411yescharacteristic
232C24—28no—
233C24C5×C22⋊C413yes—
234C24C5×C22⋊C414yes—
235C24C5×C22⋊C411yescharacteristic
236C24C5×C4⋊C414yes—
237C24C2×C5×D413yes—
238C22×C4—264no—
239C22×C4—248no—
240C22×C4—224no—
241C22×C4—24no—
242C22×C4—212no—
243C22×C4—48no—
244C22×C4C42×C5112yes—
245C22×C4C42×C514yes—
246C22×C4C5×C22⋊C414yes—
247C22×C4C5×C22⋊C4112yes—
248C22×C4C5×C22⋊C4112yes—
249C22×C4C5×C22⋊C413yes—
250C22×C4C5×C22⋊C413yes—
251C22×C4C5×C22⋊C416yes—
252C22×C4C5×C4⋊C4112yes—
253C22×C4C5×C4⋊C4112yes—
254C22×C4C5×C4⋊C414yes—
255C22×C4C5×C4⋊C414yes—
256C22×C4C5×C4⋊C4112yes—
257C22×C4C22×C4×C516yes—
258C22×C4C22×C4×C516yes—
259C22×C4C22×C4×C513yes—
260C22×C4C22×C4×C513yes—
261C22×C4C2×C5×D413yes—
262C22×C4C2×C5×D413yes—
263C22×C4C2×C5×D416yes—
264C22×C4C2×C5×D413yes—
265C22×C4C2×C5×Q816yes—
266C22×C4C24×C511yescharacteristic
267M16—224no—
268M16—24no—
269M16C22×C4×C518yescomplemented
270C2×C8—224no—
271C2×C8—24no—
272C4⋊C4—212no—
273C4⋊C4C22×C4×C518yescomplemented
274C22⋊C4—212no—
275C22⋊C4—24no—
276C42—224no—
277C42—212no—
278C42—24no—
279C42—24no—
280C42C22×C4×C518yescomplemented
281C2×C5—21no—
282C2×C5—21no—
283C2×C5—26no—
284C2×C5C2×#339112yesdirect product factor
285C2×C5C22×#9511yescharacteristic
286C2×C5C22×#10412yes—
287C23—216no—
288C23—216no—
289C23—212no—
290C23—212no—
291C23C5×#95112yes—
292C23C5×#9514yes—
293C23C5×#10418yes—
294C23C2×C5×C22⋊C413yes—
295C23C2×C5×C22⋊C416yes—
296C23C2×C5×C22⋊C413yes—
297C23C2×C5×C4⋊C416yes—
298C23C22×C5×D411yescharacteristic
299C2×C4—216no—
300C2×C4—296no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—424no—
304C2×C4C5×#95124yes—
305C2×C4C5×#95112yes—
306C2×C4C5×#95112yes—
307C2×C4C2×C42×C516yes—
308C2×C4C2×C42×C516yes—
309C2×C4C2×C5×C22⋊C416yes—
310C2×C4C2×C5×C22⋊C413yes—
311C2×C4C2×C5×C22⋊C413yes—
312C2×C4C2×C5×C22⋊C416yes—
313C2×C4C2×C5×C22⋊C416yes—
314C2×C4C2×C5×C4⋊C416yes—
315C2×C4C2×C5×C4⋊C416yes—
316C2×C4C2×C5×C4⋊C416yes—
317C2×C4C2×C5×C4⋊C416yes—
318C2×C4C2×C5×C4⋊C416yes—
319C2×C4C23×C4×C511yescharacteristic
320C2×C4C23×C4×C511yescharacteristic
321C2×C4C23×C4×C511yescharacteristic
322C2×C4C22×C5×D411yescharacteristic
323C2×C4C22×C5×D411yescharacteristic
324C2×C4C22×C5×Q811yescharacteristic
325C8—28no—
326C5C22×#33911yescharacteristic, direct product factor, Sylow
327C22—22no—
328C22—26no—
329C22—212no—
330C22—212no—
331C22—224no—
332C22C5×#339116yesdirect product factor
333C22C2×C5×#9516yes—
334C22C2×C5×#9516yes—
335C22C2×C5×#104112yes—
336C22C22×C5×C22⋊C411yescharacteristic
337C22C22×C5×C22⋊C411yescharacteristic
338C22C22×C5×C4⋊C411yescharacteristic
339C4—216no—
340C4—48no—
341C4C2×C5×#9516yes—
342C4C2×C5×#9516yes—
343C4C22×C42×C511yescharacteristic
344C4C22×C5×C22⋊C411yescharacteristic
345C4C22×C5×C4⋊C411yescharacteristic
346C4C22×C5×C4⋊C411yescharacteristic
347C2—21no—
348C2—26no—
349C2—21no—
350C2C2×C5×#339112yesdirect product factor
351C2C22×C5×#9511yescharacteristic
352C2C22×C5×#10412yes—
subgroupG/H
centerC23×C4×C5D4
commutatorC4C22×C42×C5
Frattini, cosocleC22×C4C24×C5
socleC24×C5C22⋊C4
prime radicalC25×C5D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4×C5 ◁ C24×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C5×#339C2direct (N × H)
9. C22×C5×M16C4semidirect
14. C2×C5×#117C4semidirect
16. C22×C5×C4⋊C4C4semidirect
21. C22×C42×C5C4semidirect
23. C5×#339C22direct (N × H)
24. C22×#339C5direct (N × H)
43. C2×C5×M16C2×C4semidirect
50. C5×#117C2×C4semidirect
53. C2×C5×C4⋊C4C2×C4semidirect
61. C2×C42×C5C2×C4semidirect
66. C2×#339C2×C5direct (N × H)
104. C5×M16C22×C4semidirect
108. C5×C4⋊C4C22×C4semidirect
115. C42×C5C22×C4semidirect
120. C22×M16C4×C5semidirect
125. C2×#117C4×C5semidirect
127. C22×C4⋊C4C4×C5semidirect
132. C22×C42C4×C5semidirect
134. #339C22×C5direct (N × H)
192. C2×M16C2×C4×C5semidirect
199. #117C2×C4×C5semidirect
202. C2×C4⋊C4C2×C4×C5semidirect
210. C2×C42C2×C4×C5semidirect
217. C22×C5#339direct (N × H)
269. M16C22×C4×C5semidirect
273. C4⋊C4C22×C4×C5semidirect
280. C42C22×C4×C5semidirect
284. C2×C5C2×#339direct (N × H)
326. C5C22×#339direct (N × H)
332. C22C5×#339direct (N × H)
350. C2C2×C5×#339direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×M162
C22×C5×#1172
C23×C42×C52
C2×C5×#3392
C22×#3395