Finite Group Databasebeta

← #14305912

Subgroups — #14305912

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#947C211yesmaximal, characteristic
2C2×#91119C211yesmaximal, characteristic, complemented
3C2×C3×#3967C211yesmaximal, characteristic, complemented
4#11748861C211yesmaximal, characteristic, complemented
5C2×#90967C211yesmaximal, characteristic
6C2×#90966C211yesmaximal, characteristic
7C2×#90953C211yesmaximal, characteristic, complemented
8#10602519—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C5×#947—22no—
14C5×#947C414yescomplemented
15C2×C5×(C2×D3)⋊C4—22no—
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C2×Dic3⋊Dic5—22no—
20#91119—22no—
21C3×#3967—22no—
22#90967—22no—
23#90966—22no—
24#90953—22no—
25#70227—51nomaximal, Hall
26C2×C5×#124—31no—
27C2×#3967—31no—
28C2×#3967D311yescharacteristic, complemented
29C2×#3964—31no—
30C2×#3964—31no—
31#65224—31no—
32C2×#3935—31no—
33C23×C5×D3—21no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yes—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C22×C5×Dic3D412yes—
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12C2×C412yes—
50C22×C3×Dic5—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D412yes—
56C5×(C2×D3)⋊C4—28no—
57C4×C5×Dic3C2×C412yes—
58C4×C5×Dic3D412yes—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168D412yes—
64Dic3⋊Dic5—44no—
65C2×#947D511yescharacteristic
66C2×C3×#103—51no—
67C2×#835—51no—
68C2×#821—51no—
69C2×#815—51no—
70#4975—51no—
71C2×#809—51no—
72C22×C5×Q8C2×D311yescharacteristic
73C22×C5×D4—31no—
74C5×#124—34no—
75C5×#124—62no—
76C2×C5×C22⋊C4—62no—
77C2×C42×C5—31no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5—62no—
80C2×C4⋊Dic5C2×D311yescharacteristic
81C22×#168—31no—
82C22×#168C2×D311yescharacteristic
83#3967—22no—
84#3967—62no—
85#3964—62no—
86#3964—62no—
87#3935—62no—
88#1959—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C5×D3—22no—
91C22×C5×D3—41no—
92C22×C5×D3—41no—
93C22×C5×D3—42no—
94C22×C5×D3—42no—
95C3×C5×Q8—22no—
96C3×C5×Q8—22no—
97C3×C5×Q8—41no—
98C3×C5×Q8—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×Dic15—41no—
109C2×Dic15—42no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3C22⋊C414yes—
113C5×D12—22no—
114C5×D12—22no—
115C5×D12—41no—
116C5×D12—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—42no—
119C3⋊#168—22no—
120C3×#168—22no—
121C22×C3×Q8C2×D511yescharacteristic
122C22×D12C2×D511yescharacteristic
123C22×C3×C8—51no—
124C2×C3×C4⋊C4—51no—
125#947—22no—
126#947Dic514yescomplemented
127C2×(C2×D3)⋊C4—22no—
128C2×C4⋊Dic3—51no—
129C2×Dic3⋊C4—102no—
130C2×C4×Dic3C2×D511yescharacteristic
131C22×C3⋊C8—51no—
132C3×#103—102no—
133#835—102no—
134#821—102no—
135#815—102no—
136#809—102no—
137C24×C5—61no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8—21no—
142C2×C5×Q8—21no—
143C2×C5×Q8C4×D312yes—
144C2×C5×D4—32no—
145C2×C5×D4—61no—
146C2×C5×D4—61no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C22×C4×C5—21no—
151C22×C4×C5—32no—
152C22×C4×C5C22×D311yescharacteristic
153C22×Dic5—21no—
154C22×Dic5—61no—
155C5×C22⋊C4—68no—
156C42×C5—32no—
157C42×C5—32no—
158C4⋊Dic5—21no—
159C4⋊Dic5—21no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5—124no—
163C2×#168—21no—
164C2×#168—21no—
165C2×#168—32no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#168#6712yes—
169C2×#124—31no—
170C2×#103—51no—
171C2×#103—151no—
172C2×#102—151no—
173C2×#102—151no—
174C2×#97—151no—
175#384—151no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12411yescharacteristic
178C22×C3×C5#12711yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)12yes—
180C22×C3×C5#13712yes—
181C2×C5×D3—42no—
182C2×C5×D3—44no—
183C2×C5×D3—82no—
184C2×C5×D3—81no—
185C2×C5×D3—81no—
186C3×C4×C5—42no—
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5#12111yescharacteristic
190C3×C4×C5#12111yescharacteristic
191Dic15—81no—
192C3×Dic5—81no—
193C5×Dic3—24no—
194C23×D3—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8C2×Dic512yes—
201C22×C3×C4—21no—
202C22×C3×C4—101no—
203C22×C3×C4C22×D511yescharacteristic
204C22×Dic3—101no—
205C22×Dic3C22⋊D512yes—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C2×Dic512yes—
212C2×C3×C8—52no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217(C2×D3)⋊C4—28no—
218C4⋊Dic3—101no—
219C4⋊Dic3—101no—
220Dic3⋊C4—204no—
221C4×Dic3C2×Dic512yes—
222C4×Dic3C22⋊D512yes—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C23×C5—62no—
227C23×C5—121no—
228C23×C5—122no—
229C23×C5—122no—
230C23×C5—121no—
231C23×C5D3×D411yescharacteristic
232C5×Q8—22no—
233C5×Q8—22no—
234C5×Q8—41no—
235C5×Q8—41no—
236C5×D4—62no—
237C5×D4—62no—
238C5×D4—121no—
239C5×D4—121no—
240C2×C4×C5—22no—
241C2×C4×C5—34no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—62no—
245C2×C4×C5—62no—
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C2×Dic5—42no—
253C2×Dic5—41no—
254C2×Dic5—122no—
255C2×Dic5—121no—
256#168—22no—
257#168—62no—
258C22×Q8D3×D511yescharacteristic
259C22×D4—31no—
260C22×C8—51no—
261C22×C8—151no—
262#124—34no—
263#124—62no—
264C2×C4⋊C4—51no—
265C2×C4⋊C4—151no—
266C2×C4⋊C4—302no—
267C2×C22⋊C4—62no—
268C2×C42—31no—
269#103—102no—
270#103—302no—
271#102—302no—
272#102—302no—
273#97—302no—
274C2×C3×C5#39011yescharacteristic
275C2×C3×C5#41712yes—
276C2×C3×C5#48912yes—
277C2×C3×C5#49611yescharacteristic
278C2×C3×C5#49711yescharacteristic
279C5×D3—82no—
280C23×C3C2×C22⋊D511yescharacteristic
281C22×D3—22no—
282C22×D3—42no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—42no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—41no—
289C3×Q8—41no—
290C2×C3×C4—22no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—201no—
294C2×C3×C4—202no—
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×C3×C4C22×Dic511yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—201no—
304C2×Dic3—202no—
305C2×Dic3C22⋊Dic514yes—
306D12—22no—
307D12—22no—
308D12—41no—
309D12—41no—
310C3×C8—102no—
311C3⋊C8—102no—
312C22×C5—122no—
313C22×C5—124no—
314C22×C5—241no—
315C22×C5—241no—
316C22×C5—242no—
317C22×C5D3×C22⋊C411yescharacteristic
318C22×C5#88511yescharacteristic
319C22×C5#91412yes—
320C22×C5#91812yes—
321C22×C5#94011yescharacteristic
322C4×C5—42no—
323C4×C5—64no—
324C4×C5#67⋊C411yescharacteristic
325C4×C5#88411yescharacteristic
326C4×C5C4×#6711yescharacteristic
327C4×C5#93911yescharacteristic
328Dic5—81no—
329Dic5—241no—
330C24—61no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8D3×Dic512yes—
337C2×D4—32no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C2×D4—61no—
342C2×D4—61no—
343C22×C4—21no—
344C22×C4—32no—
345C22×C4—101no—
346C22×C4—301no—
347C22×C4C2×D3×D511yescharacteristic
348C2×C8—52no—
349C2×C8—101no—
350C2×C8—101no—
351C2×C8—152no—
352C2×C8—301no—
353C2×C8—301no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—68no—
360C42—32no—
361C42—32no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3#408211yescharacteristic
364C22×C3#408611yescharacteristic
365C22×C3#409512yes—
366C22×C3#409712yes—
367C22×C3C2×C22⋊Dic511yescharacteristic
368C2×D3—42no—
369C2×D3—44no—
370C2×D3—82no—
371C2×D3—81no—
372C2×D3—81no—
373C3×C4—42no—
374C3×C4—401no—
375C3×C4D4×Dic511yescharacteristic
376C3×C4D4×Dic511yescharacteristic
377C3×C4#408411yescharacteristic
378C3×C4#408411yescharacteristic
379Dic3—24no—
380Dic3—401no—
381C2×C5—242no—
382C2×C5#479412yes—
383C2×C5#480312yes—
384C2×C5#495711yescharacteristic
385C2×C5#517611yescharacteristic
386C2×C5#519011yescharacteristic
387C23—62no—
388C23—122no—
389C23—122no—
390C23—121no—
391C23—121no—
392C23D3×C22⋊D511yescharacteristic
393Q8—22no—
394Q8—22no—
395Q8—41no—
396Q8—41no—
397D4—62no—
398D4—62no—
399D4—121no—
400D4—121no—
401C2×C4—22no—
402C2×C4—34no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—202no—
408C2×C4—201no—
409C2×C4—602no—
410C2×C4—601no—
411C2×C4#678011yescharacteristic
412C2×C4C2×D3×Dic511yescharacteristic
413C2×C4#678211yescharacteristic
414C2×C4D5×#6711yescharacteristic
415C2×C4D3×C22⋊D511yescharacteristic
416C2×C4#679011yescharacteristic
417C8—102no—
418C8—302no—
419C2×C3#6534412yes—
420C2×C3#6534711yescharacteristic
421C2×C3#6534911yescharacteristic
422C2×C3#6551011yescharacteristic
423C2×C3#6552112yes—
424D3—82no—
425C5#7022711yescharacteristic, complemented, Sylow
426C22—124no—
427C22—122no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#9150412yes—
432C22#9151012yes—
433C22#9152511yescharacteristic
434C22D3×C22⋊Dic511yescharacteristic
435C22#9156711yescharacteristic
436C4—42no—
437C4—64no—
438C4—401no—
439C4—1201no—
440C4#9154911yescharacteristic
441C4Dic5×#6711yescharacteristic
442C4#9155711yescharacteristic
443C4#67⋊Dic511yescharacteristic
444C3#1060251911yescharacteristic, complemented, Sylow
445C2—242no—
446C2#1174919112yes—
447C2#1174920112yes—
448C2#1174934211yescharacteristic
449C2#1174935411yescharacteristic
450C2#1174948211yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91119C2semidirect
3. C2×C3×#3967C2semidirect
4. #11748861C2semidirect
7. C2×#90953C2semidirect
14. C5×#947C4semidirect
28. C2×#3967D3semidirect
126. #947Dic5semidirect
362. C3×C5#1959semidirect
425. C5#70227semidirect
444. C3#10602519semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9472
C2×#911192
C2×C3×#39672
#117488612
C2×#909672
C2×#909662
C2×#909532
#106025193
#702275