Finite Group Databasebeta

← #14302396

Subgroups — #14302396

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91838C211yesmaximal, characteristic
2#11756280C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11751232C211yesmaximal, characteristic, complemented
6#11746380C211yesmaximal, characteristic, complemented
7#11746352C211yesmaximal, characteristic, complemented
8#10601200—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91838—22no—
14#91838—22no—
15C2×#6717C412yescomplemented
16C2×#6715C412yescomplemented
17#91815C2211yescharacteristic
18#91815C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20#91782—22no—
21C22⋊C4×D15—22no—
22C4×D60—22no—
23C3×C5×#104—22no—
24#91118—22no—
25#91105—22no—
26#70407—51nomaximal, Hall
27C2×#4095—31no—
28#65855—31no—
29C5×#421D311yescharacteristic, complemented
30#65529—31no—
31#65420—31no—
32#64779—31no—
33#64751—31no—
34C23×D15—21no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C2×C3×C5×Q8C2×C411yescharacteristic, complemented
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C411yescharacteristic, complemented
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C2×D60—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60C2×C412yes—
48C2×D60D412yes—
49C2×D60D412yes—
50C2×C4×D15—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C42×C5D412yes—
57#6719—21no—
58#6719D412yes—
59#6717—24no—
60#6715—24no—
61#6714—24no—
62C4⋊Dic15—21no—
63C4⋊Dic15—21no—
64C4×Dic15—21no—
65C4×Dic15—21no—
66#6710—21no—
67#6710—21no—
68C2×C3⋊#168C2×C412yescomplemented
69C2×#949—51no—
70#5521—51no—
71C3×#421D511yescharacteristic, complemented
72#5240—51no—
73#5131—51no—
74#4559—51no—
75#4531—51no—
76C2×C5×#41C2×D311yescharacteristic
77C22×D20—31no—
78C2×C5×M16C2×D311yescharacteristic
79C5×#117C2×D311yescharacteristic
80#4095—62no—
81#4095—62no—
82C2×#688—32no—
83C2×#686—32no—
84#4072—31no—
85#4072—31no—
86C2×#681—31no—
87#4039—62no—
88D5×C22⋊C4—62no—
89C4×D20—62no—
90C5×#104—22no—
91#3966—62no—
92#3953—62no—
93#1904—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C22×D15—22no—
98C22×D15—22no—
99C22×D15—82no—
100C3×C5×Q8—21no—
101C3×C5×Q8—21no—
102C3×C5×D4—21no—
103C3×C5×D4—21no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×Dic15—22no—
117C2×Dic15—41no—
118D60—22no—
119D60—22no—
120D60—22no—
121D60C22⋊C414yes—
122C4×D15—84no—
123C3×C5×C8—41no—
124C3⋊#168—22no—
125C2×C3×#41C2×D511yescharacteristic
126C22×D12—51no—
127C2×C3×M16C2×D511yescharacteristic
128C3×#117C2×D511yescharacteristic
129#949—102no—
130#949—102no—
131C2×#215—52no—
132C2×#213—52no—
133#926—51no—
134#926—51no—
135C2×#208—51no—
136#893—102no—
137D3×C22⋊C4—102no—
138C4×D12—102no—
139C3×#104—22no—
140#834—102no—
141#821—102no—
142C23×D5—61no—
143C5×#41—21no—
144C5×#41—21no—
145C5×#41—21no—
146C5×#41—21no—
147C2×C5×Q8C4×D311yescharacteristic, complemented
148C2×C5×D4—21no—
149C2×C5×D4C4×D311yescharacteristic, complemented
150C22×C4×C5—21no—
151C22×C4×C5C22×D311yescharacteristic
152C2×D20—32no—
153C2×D20—32no—
154C2×D20—32no—
155C2×D20—61no—
156C2×D20—61no—
157C2×D20—61no—
158C2×C4×D5—64no—
159C5×M16—21no—
160C5×M16—21no—
161C2×C5×C8—21no—
162C5×C4⋊C4—21no—
163C5×C22⋊C4—21no—
164C42×C5#6712yes—
165C22⋊Dic5—32no—
166C22⋊Dic5—61no—
167#688—64no—
168#686—64no—
169#685—64no—
170C4⋊Dic5—61no—
171C4⋊Dic5—61no—
172C4×Dic5—61no—
173C4×Dic5—61no—
174#681—61no—
175#681—61no—
176C2×#168—32no—
177C2×AGL(1,ℤ/8)—151no—
178#518—151no—
179#421D1511yescharacteristic, complemented
180#418—151no—
181#410—151no—
182#344—151no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—81no—
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5#12011yescharacteristic
189C22×C3×C5#12111yescharacteristic
190C2×D15—24no—
191C2×D15—44no—
192C2×D15—82no—
193C2×D15—82no—
194C3×C4×C5—42no—
195C3×C4×C5—41no—
196C3×C4×C5C2×C22⋊C411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12311yescharacteristic
200Dic15—42no—
201Dic15—81no—
202C23×D3—101no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C2×C3×Q8C4×D511yescharacteristic, complemented
208C2×C3×D4—21no—
209C2×C3×D4C4×D511yescharacteristic, complemented
210C22×C3×C4—21no—
211C22×C3×C4C22×D511yescharacteristic
212C2×D12—52no—
213C2×D12—52no—
214C2×D12—52no—
215C2×D12—101no—
216C2×D12—101no—
217C2×D12—101no—
218C2×C4×D3—104no—
219C3×M16—21no—
220C3×M16—21no—
221C2×C3×C8—21no—
222C3×C4⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C42C22⋊D512yes—
225#217—52no—
226#217—101no—
227#215—104no—
228#213—104no—
229(C2×D3)⋊C4—104no—
230C4⋊Dic3—101no—
231C4⋊Dic3—101no—
232C4×Dic3—101no—
233C4×Dic3—101no—
234#208—101no—
235#208—101no—
236C2×C3⋊C8—52no—
237C23×C5—21no—
238C23×C5D3×D411yescharacteristic
239C22×D5—62no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—242no—
243C5×Q8—21no—
244C5×Q8—21no—
245C5×D4—21no—
246C5×D4—21no—
247C5×D4—41no—
248C5×D4—41no—
249C2×C4×C5—21no—
250C2×C4×C5—22no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5C2×C4×D311yescharacteristic
254C2×C4×C5#23511yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5#23711yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C2×Dic5—62no—
260C2×Dic5—121no—
261D20—34no—
262D20—62no—
263D20—62no—
264D20—62no—
265C4×D5—244no—
266C5×C8—41no—
267#168—62no—
268C2×#41C2×D1511yescharacteristic
269C22×D4—151no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—151no—
275C2×M16C2×D1511yescharacteristic
276C4×D4—302no—
277C4×D4—302no—
278#117—151no—
279#117—151no—
280#117C2×D1511yescharacteristic
281C2×C22⋊C4—302no—
282#104—22no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5—81no—
289C2×C3×C5#38611yescharacteristic
290D15—44no—
291C23×C3—21no—
292C23×C3D4×D511yescharacteristic
293C22×D3—102no—
294C22×D3—102no—
295C22×D3—102no—
296C22×D3—402no—
297C3×Q8—21no—
298C3×Q8—21no—
299C3×D4—21no—
300C3×D4—21no—
301C3×D4—41no—
302C3×D4—41no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4C2×C4×D511yescharacteristic
308C2×C3×C4#70911yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4C2×C22⋊D511yescharacteristic
313C2×Dic3—102no—
314C2×Dic3—201no—
315D12—54no—
316D12—102no—
317D12—102no—
318D12—102no—
319C4×D3—404no—
320C3×C8—41no—
321C3⋊C8—102no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—81no—
325C22×C5#67⋊C411yescharacteristic
326C22×C5#88411yescharacteristic
327C22×C5#93711yescharacteristic
328C2×D5—64no—
329C2×D5—124no—
330C2×D5—242no—
331C2×D5—242no—
332C4×C5—42no—
333C4×C5—41no—
334C4×C5D3×C22⋊C411yescharacteristic
335C4×C5#88311yescharacteristic
336C4×C5C4×#6711yescharacteristic
337C4×C5#93811yescharacteristic
338Dic5—122no—
339Dic5—241no—
340C24—301no—
341#41—21no—
342#41—21no—
343#41—21no—
344#41—21no—
345C2×Q8C4×D1511yescharacteristic, complemented
346C2×D4—21no—
347C2×D4—152no—
348C2×D4—152no—
349C2×D4—152no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4C4×D1511yescharacteristic, complemented
354C22×C4—21no—
355C22×C4—304no—
356C22×C4C22×D1511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—21no—
360M16—21no—
361M16—301no—
362M16—301no—
363C2×C8—21no—
364C2×C8—152no—
365C4⋊C4—21no—
366C4⋊C4—301no—
367C4⋊C4—301no—
368C22⋊C4—21no—
369C22⋊C4—152no—
370C22⋊C4—304no—
371C22⋊C4—301no—
372C42—301no—
373C42—301no—
374C42#122012yes—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—81no—
379C22×C3#402711yescharacteristic
380C22×C3#403011yescharacteristic
381C22×C3#408311yescharacteristic
382C2×D3—104no—
383C2×D3—204no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—42no—
387C3×C4—41no—
388C3×C4D5×C22⋊C411yescharacteristic
389C3×C4#402911yescharacteristic
390C3×C4C4×C22⋊D511yescharacteristic
391C3×C4#408411yescharacteristic
392Dic3—202no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—81no—
398C2×C5#495611yescharacteristic
399D5—124no—
400C23—21no—
401C23—302no—
402C23—302no—
403C23—302no—
404C23—1202no—
405C23D4×D1511yescharacteristic
406Q8—21no—
407Q8—21no—
408D4—21no—
409D4—21no—
410D4—41no—
411D4—41no—
412D4—154no—
413D4—302no—
414D4—302no—
415D4—302no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—302no—
421C2×C4—601no—
422C2×C4—1204no—
423C2×C4C2×C4×D1511yescharacteristic
424C2×C4#681711yescharacteristic
425C2×C4D4×D1511yescharacteristic
426C2×C4D4×D1511yescharacteristic
427C2×C4#681911yescharacteristic
428C2×C4C2×#122011yescharacteristic
429C8—41no—
430C8—302no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—81no—
435C2×C3#6524511yescharacteristic
436D3—204no—
437C5#7040711yescharacteristic, complemented, Sylow
438C22—41no—
439C22—41no—
440C22—81no—
441C22—304no—
442C22—604no—
443C22—1202no—
444C22—1202no—
445C22#9177011yescharacteristic
446C22#9177311yescharacteristic
447C22#9182611yescharacteristic
448C4—42no—
449C4—41no—
450C4—602no—
451C4—1201no—
452C4C22⋊C4×D1511yescharacteristic
453C4#9177211yescharacteristic
454C4C4×#122011yescharacteristic
455C4#9182711yescharacteristic
456C3#1060120011yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—81no—
461C2—604no—
462C2#1175105711yescharacteristic
subgroupG/H
centerC2#11751057
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radicalC2×#91838C2
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #11756280C2semidirect
3. C3×C5×#421C2semidirect
4. #11751341C2semidirect
5. #11751232C2semidirect
6. #11746380C2semidirect
7. #11746352C2semidirect
15. C2×#6717C4semidirect
16. C2×#6715C4semidirect
29. C5×#421D3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
41. C2×C3×C5×D4C2×C4semidirect
68. C2×C3⋊#168C2×C4semidirect
71. C3×#421D5semidirect
147. C2×C5×Q8C4×D3semidirect
149. C2×C5×D4C4×D3semidirect
179. #421D15semidirect
207. C2×C3×Q8C4×D5semidirect
209. C2×C3×D4C4×D5semidirect
345. C2×Q8C4×D15semidirect
353. C2×D4C4×D15semidirect
375. C3×C5#1904semidirect
437. C5#70407semidirect
456. C3#10601200semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
#117562802
C3×C5×#4212
#117513412
#117512322
#117463802
#117463522
#106012003
#704075