Finite Group Databasebeta

← #14438627

Subgroups — #14438627

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756236C211yesmaximal, characteristic
2C2×C5×#869C211yesmaximal, characteristic, complemented
3C3×C4×#681C211yesmaximal, characteristic, complemented
4#11748394C214yesmaximal, complemented
5#11746930C212yesmaximal, complemented
6#11746914C214yesmaximal, complemented
7#11746912C212yesmaximal, complemented
8#10614930—31nomaximal, Hall
9C2×#6817C2212yes—
10C22×C5×Dic6—21no—
11C2×C3×C42×C5C2211yescharacteristic
12#91819—21no—
13#91819—21no—
14#91764C2212yes—
15#91763C2211yescharacteristic
16C4×D60—21no—
17C4×D60—21no—
18#91758C2211yescharacteristic
19C2×C5×C4⋊Dic3—21no—
20C2×C5×C4⋊Dic3C2212yes—
21C5×#869—21no—
22C5×#869—21no—
23C5×#869C2212yes—
24C5×#869C2212yes—
25C2×C3×#681C2212yes—
26C3×#3935C2212yes—
27C3×C4×#168C2212yes—
28#90975C2218yes—
29#90969C2218yes—
30#78528—51nomaximal, Hall
31C2×C5×C4⋊Q8—31no—
32#65811—31no—
33#65382—32no—
34#65378—34no—
35#65377—32no—
36#65255—34no—
37C4×#681D311yescharacteristic, complemented
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C2×#1220—22no—
42#6817—28no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60C2312yes—
46C2×C4×D15—22no—
47C2×Dic30C2312yes—
48C22×C5×Dic3—22no—
49C2×C5×Dic6—22no—
50C2×C5×Dic6—22no—
51C2×C5×Dic6—44no—
52C3×C42×C5D411yescharacteristic
53C3×C42×C5D411yescharacteristic
54C3×C42×C5C2311yescharacteristic
55C3×C42×C5C2311yescharacteristic
56#6714—22no—
57#6714—22no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C5×C4⋊Dic3—22no—
61C5×C4⋊Dic3—22no—
62C5×C4⋊Dic3—22no—
63C5×C4⋊Dic3C2314yes—
64C3×#681—24no—
65C2×C3×#168C2314yes—
66#5477—51no—
67C2×#869D511yescharacteristic, complemented
68C3×C4×M16—51no—
69#5133—54no—
70#4714—54no—
71#4694—52no—
72#4681—52no—
73C22×C5×Q8—61no—
74C2×#709—32no—
75C5×C4⋊Q8—32no—
76C5×C4⋊Q8—32no—
77C5×C4⋊Q8—61no—
78C5×C4⋊Q8—61no—
79C2×C5×C4⋊C4—32no—
80C2×C5×C4⋊C4—61no—
81C2×C42×C5C2×D311yescharacteristic
82#4076—61no—
83#4076—61no—
84C2×#681C2×D312yes—
85#4021—32no—
86#4020—31no—
87C4×D20—61no—
88C4×D20—61no—
89#4015—31no—
90#3942—38no—
91#3941—38no—
92#3935C2×D312yes—
93C4×#168C2×D312yes—
94#3141—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4114yes—
105C2×C3×C4×C5C2411yescharacteristic
106#1220—44no—
107C2×Dic15—22no—
108D60—24no—
109D60—42no—
110D60—42no—
111C4×D15—44no—
112Dic30—24no—
113C2×C5×Dic3—24no—
114C2×C5×Dic3—44no—
115C5×Dic6—44no—
116C5×Dic6—44no—
117C3×#168—24no—
118C2×#235—52no—
119C22×Dic6—21no—
120C2×C3×M16—52no—
121C2×C3×C42C2×D511yescharacteristic
122#930—101no—
123#930—101no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2×D512yes—
126#875—52no—
127#874—51no—
128C4×D12—101no—
129C4×D12—101no—
130#869—21no—
131#869—21no—
132#869—51no—
133#869C2×D512yes—
134#869C2×D512yes—
135C3×#97—52no—
136C3×C4×C8—52no—
137#821—58no—
138#816—58no—
139C2×C5×Q8—62no—
140C2×C5×Q8—62no—
141C2×C5×Q8—124no—
142C22×C4×C5—62no—
143C22×C4×C5D1211yescharacteristic
144C22×C4×C5D1211yescharacteristic
145C22×C4×C5C22×D311yescharacteristic
146C2×C22⋊D5—62no—
147#709—68no—
148C2×D20—32no—
149C2×D20—61no—
150C2×D20—61no—
151C2×C4×D5—62no—
152C2×Dic10—32no—
153C5×C4⋊C4—34no—
154C5×C4⋊C4—62no—
155C5×C4⋊C4—62no—
156C5×C4⋊C4—62no—
157C42×C5D1211yescharacteristic
158C42×C5D1211yescharacteristic
159C42×C5C22×D311yescharacteristic
160C42×C5C22×D311yescharacteristic
161#685—62no—
162#685—62no—
163C4⋊Dic5—61no—
164C4⋊Dic5—61no—
165#681—24no—
166C2×#168C22×D314yes—
167#532—151no—
168C2×C4⋊Q8—31no—
169#489—154no—
170#487—152no—
171#486—152no—
172#417—154no—
173C4×M16—51no—
174C22×C3×C5—21no—
175C22×C3×C5—21no—
176C22×C3×C5#12412yes—
177C22×C3×C5C22×D411yescharacteristic
178C2×D15—42no—
179C2×D15—42no—
180C2×D15—42no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5#12412yes—
184C3×C4×C5AGL(1,ℤ/8)12yes—
185C3×C4×C5#13712yes—
186C3×C4×C5C2×#4112yes—
187Dic15—42no—
188C5×Dic3—44no—
189C22×C3×C4C22⋊D511yescharacteristic
190C22×C3×C4C22⋊D511yescharacteristic
191C22×C3×C4C22×D511yescharacteristic
192C2×#67—102no—
193C22×Dic3—22no—
194#235—108no—
195C2×D12—52no—
196C2×D12—101no—
197C2×D12—101no—
198C2×C4×D3—102no—
199C2×Dic6—22no—
200C2×Dic6—22no—
201C2×Dic6—44no—
202C2×Dic6—52no—
203C3×M16—104no—
204C2×C3×C8—54no—
205C3×C42C22⋊D511yescharacteristic
206C3×C42C22⋊D511yescharacteristic
207C3×C42C22×D511yescharacteristic
208C3×C42C22×D511yescharacteristic
209(C2×D3)⋊C4—102no—
210(C2×D3)⋊C4—102no—
211C4⋊Dic3—22no—
212C4⋊Dic3—22no—
213C4⋊Dic3—22no—
214C4⋊Dic3—101no—
215C4⋊Dic3—101no—
216C4⋊Dic3C22×D514yes—
217C23×C5C2×D1211yescharacteristic
218C22×D5—62no—
219C5×Q8—124no—
220C5×Q8—124no—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—64no—
224C2×C4×C5—124no—
225C2×C4×C5C2×D1211yescharacteristic
226C2×C4×C5C2×D1211yescharacteristic
227C2×C4×C5C2×D1211yescharacteristic
228C2×C4×C5C2×D1211yescharacteristic
229C2×C4×C5C2×D1211yescharacteristic
230C2×C4×C5#23514yes—
231C2×C4×C5C23×D311yescharacteristic
232C22⋊D5—124no—
233C2×Dic5—62no—
234D20—64no—
235D20—122no—
236D20—122no—
237C4×D5—124no—
238Dic10—64no—
239#168—24no—
240C2×#41—152no—
241C22×Q8—61no—
242C2×M16—52no—
243C4⋊Q8—32no—
244C4⋊Q8—32no—
245C4⋊Q8—61no—
246C4⋊Q8—61no—
247C4⋊Q8—151no—
248#127—151no—
249#124—152no—
250#121—301no—
251#121—301no—
252C4×D4—301no—
253C4×D4—301no—
254C2×C4⋊C4—32no—
255C2×C4⋊C4—61no—
256C2×C42D3×D511yescharacteristic
257#103—158no—
258#102—158no—
259#97—52no—
260C4×C8—52no—
261C2×C3×C5—22no—
262C2×C3×C5C2×#12411yescharacteristic
263C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
264C2×C3×C5C2×#13711yescharacteristic
265D15—82no—
266C23×C3C2×C22⋊D511yescharacteristic
267C22×D3—102no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4#71314yes—
271C2×C3×C4C2×C22⋊D511yescharacteristic
272C2×C3×C4C2×C22⋊D511yescharacteristic
273C2×C3×C4C2×C22⋊D511yescharacteristic
274C2×C3×C4C2×C22⋊D511yescharacteristic
275C2×C3×C4C2×C22⋊D511yescharacteristic
276C2×C3×C4C23×D511yescharacteristic
277#67—204no—
278C2×Dic3—24no—
279C2×Dic3—44no—
280C2×Dic3—102no—
281D12—104no—
282D12—202no—
283D12—202no—
284C4×D3—204no—
285Dic6—44no—
286Dic6—44no—
287Dic6—104no—
288C3×C8—104no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5#87512yes—
292C22×C5C22×D1211yescharacteristic
293C2×D5—122no—
294C2×D5—122no—
295C2×D5—122no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—124no—
299C4×C5#87512yes—
300C4×C5#90812yes—
301C4×C5#90912yes—
302C4×C5C2×#23512yes—
303Dic5—122no—
304#41—308no—
305C2×Q8—62no—
306C2×Q8—62no—
307C2×Q8—124no—
308C2×Q8—152no—
309C2×D4—152no—
310C2×D4—302no—
311C2×D4—301no—
312C2×D4—301no—
313C22×C4—62no—
314C22×C4—302no—
315C22×C4#120311yescharacteristic
316C22×C4#120311yescharacteristic
317C22×C4C2×D3×D511yescharacteristic
318M16—104no—
319C2×C8—54no—
320C4⋊C4—34no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C4⋊C4—62no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C22⋊C4—302no—
327C22⋊C4—302no—
328C42#120311yescharacteristic
329C42#120311yescharacteristic
330C42C2×D3×D511yescharacteristic
331C42C2×D3×D511yescharacteristic
332C3×C5#314111yescharacteristic, complemented, Hall
333C22×C3—21no—
334C22×C3—21no—
335C22×C3#409312yes—
336C22×C3C22×C22⋊D511yescharacteristic
337C2×D3—202no—
338C2×D3—202no—
339C2×D3—202no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4#407812yes—
343C3×C4#408812yes—
344C3×C4#409312yes—
345C3×C4C2×#71312yes—
346Dic3—44no—
347Dic3—202no—
348C2×C5—22no—
349C2×C5C2×#87511yescharacteristic
350C2×C5C2×#90811yescharacteristic
351C2×C5C2×#90911yescharacteristic
352D5—242no—
353C23—302no—
354C23C2×#120311yescharacteristic
355Q8—124no—
356Q8—124no—
357Q8—304no—
358D4—304no—
359D4—604no—
360D4—602no—
361D4—602no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—64no—
365C2×C4—124no—
366C2×C4—302no—
367C2×C4—604no—
368C2×C4#677314yes—
369C2×C4C2×#120311yescharacteristic
370C2×C4C2×#120311yescharacteristic
371C2×C4C2×#120311yescharacteristic
372C2×C4C2×#120311yescharacteristic
373C2×C4C2×#120311yescharacteristic
374C2×C4C22×D3×D511yescharacteristic
375C8—104no—
376C2×C3—22no—
377C2×C3C2×#407811yescharacteristic
378C2×C3C2×#408811yescharacteristic
379C2×C3C2×#409311yescharacteristic
380D3—402no—
381C5#7852811yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—602no—
385C22—602no—
386C22—602no—
387C22#9137512yes—
388C22C22×#120311yescharacteristic
389C4—21no—
390C4—21no—
391C4—124no—
392C4—602no—
393C4#9130412yes—
394C4#9132112yes—
395C4#9137512yes—
396C4C2×#677312yes—
397C3#1061493011yescharacteristic, complemented, Sylow
398C2—22no—
399C2—1202no—
400C2C2×#9130411yescharacteristic
401C2C2×#9132111yescharacteristic
402C2C2×#9137511yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
prime radical#11756236C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C5×#869C2semidirect
3. C3×C4×#681C2semidirect
4. #11748394C2semidirect
5. #11746930C2semidirect
6. #11746914C2semidirect
7. #11746912C2semidirect
37. C4×#681D3semidirect
67. C2×#869D5semidirect
332. C3×C5#3141semidirect
381. C5#78528semidirect
397. C3#10614930semidirect

Maximal subgroups

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

subgroupindex
#117562362
C2×C5×#8692
C3×C4×#6812
#117483942
#117469302
#117469142
#117469122
#106149303
#785285