Finite Group Databasebeta

← #14305986

Subgroups — #14305986

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756591C211yesmaximal, characteristic
2C2×C3×C5×#104C211yesmaximal, characteristic, complemented
3C2×#91121C211yesmaximal, characteristic, complemented
4C2×#91109C211yesmaximal, characteristic, complemented
5#11751219C211yesmaximal, characteristic, complemented
6C42×Dic15C211yesmaximal, characteristic, complemented
7C2×#91089C211yesmaximal, characteristic, complemented
8#10601149—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13#91836C411yescharacteristic, complemented
14#91833C411yescharacteristic, complemented
15#91829C411yescharacteristic, complemented
16#91828—22no—
17#91825C411yescharacteristic, complemented
18C4×#1220—22no—
19C2×C4×Dic15—22no—
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C3×C5×#104—22no—
24#91121—22no—
25#91109—22no—
26#91098—22no—
27#91089—22no—
28#70356—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104D311yescharacteristic, complemented
31C2×#3969—31no—
32C2×#3957—31no—
33#65407—31no—
34C42×Dic5—31no—
35C2×#3937—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220—21no—
47C2×#1220—22no—
48C22×Dic15—21no—
49C22×Dic15D412yes—
50#6817—21no—
51#6817—21no—
52#6817—21no—
53#6817—21no—
54C2×D60C2×C411yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2×C411yescharacteristic
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C2×C3×C5×C8—21no—
60C3×C42×C5—21no—
61C3×C42×C5D412yescomplemented
62#6719—22no—
63#6714—22no—
64#6712—22no—
65C4×Dic15—28no—
66C4×Dic15—21no—
67C4×Dic15C2×C411yescharacteristic
68C4×Dic15C2×C411yescharacteristic
69C4×Dic15D412yes—
70C4×Dic15D412yescomplemented
71#6710—21no—
72#6710—21no—
73C2×C3⋊#168—21no—
74#5832—51no—
75C2×C3×#104D511yescharacteristic, complemented
76C2×#837—51no—
77C2×#825—51no—
78#5118—51no—
79C42×Dic3—51no—
80C2×#805—51no—
81C2×C5×#41C2×D311yescharacteristic
82C2×#709—31no—
83C2×C5×M16C2×D311yescharacteristic
84C2×C42×C5C2×D311yescharacteristic
85#4093—31no—
86#4090—31no—
87#4086—31no—
88#4085—62no—
89#4082—31no—
90C4×C22⋊D5—62no—
91C2×C4×Dic5—31no—
92C2×C4×Dic5—31no—
93C2×C4×Dic5—62no—
94C2×#681—31no—
95C5×#104—22no—
96#3969—62no—
97#3957—62no—
98#3946—62no—
99#3937—62no—
100#1962—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5C2×D411yescharacteristic
103C22×D15—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8—21no—
106C3×C5×D4—21no—
107C3×C5×D4—21no—
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C2×C3×C4×C5—24no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121#1220—41no—
122#1220—41no—
123#1220—44no—
124C2×Dic15—24no—
125C2×Dic15—22no—
126C2×Dic15—24no—
127C2×Dic15—21no—
128C2×Dic15C22⋊C412yes—
129C2×Dic15C22⋊C412yes—
130D60—21no—
131D60—21no—
132C4×D15—41no—
133C4×D15—41no—
134Dic30—21no—
135Dic30—21no—
136C3×C5×C8—41no—
137C3⋊#168—41no—
138C2×C3×#41C2×D511yescharacteristic
139C2×#235—51no—
140C2×C3×M16C2×D511yescharacteristic
141C2×C3×C42C2×D511yescharacteristic
142#947—51no—
143#944—51no—
144#940—51no—
145#939—102no—
146#936—51no—
147C4×#67—102no—
148C2×C4×Dic3—51no—
149C2×C4×Dic3—51no—
150C2×C4×Dic3—102no—
151C2×#208—51no—
152C3×#104—22no—
153#837—102no—
154#825—102no—
155Dic3⋊C8—102no—
156#805—102no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C5×#41—21no—
161C2×C5×Q8C4×D311yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4C4×D311yescharacteristic
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—62no—
168C2×C22⋊D5—61no—
169C22×Dic5—32no—
170C22×Dic5—61no—
171#709—61no—
172#709—61no—
173#709—61no—
174#709—61no—
175C2×D20—31no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C42×C5—21no—
182C42×C5#6712yescomplemented
183C22⋊Dic5—62no—
184#685—62no—
185#683—62no—
186C4×Dic5—31no—
187C4×Dic5—31no—
188C4×Dic5—32no—
189C4×Dic5—32no—
190C4×Dic5—68no—
191C4×Dic5—61no—
192#681—61no—
193#681—61no—
194C2×#168—61no—
195#532—151no—
196#423—151no—
197C2×#104—151no—
198C2×#104—151no—
199C2×#104—151no—
200C2×#104D1511yescharacteristic, complemented
201C43—151no—
202C22×C3×C5—22no—
203C22×C3×C5—41no—
204C22×C3×C5—42no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×D15—41no—
209C2×D15—42no—
210C3×C4×C5—24no—
211C3×C4×C5—41no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12411yescharacteristic
215C3×C4×C5#12711yescharacteristic
216Dic15—24no—
217Dic15—22no—
218Dic15—41no—
219Dic15#10414yescomplemented
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C2×C3×Q8C4×D511yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4C4×D511yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—102no—
231C2×#67—101no—
232C22×Dic3—52no—
233C22×Dic3—101no—
234#235—101no—
235#235—101no—
236#235—101no—
237#235—101no—
238C2×D12—51no—
239C2×C4×D3—101no—
240C2×Dic6—51no—
241C3×M16—21no—
242C3×M16—21no—
243C2×C3×C8—21no—
244C3×C42—21no—
245C3×C42C22⋊D512yescomplemented
246#217—102no—
247(C2×D3)⋊C4—102no—
248Dic3⋊C4—102no—
249C4×Dic3—51no—
250C4×Dic3—51no—
251C4×Dic3—52no—
252C4×Dic3—52no—
253C4×Dic3—108no—
254C4×Dic3—101no—
255#208—101no—
256#208—101no—
257C2×C3⋊C8—101no—
258C23×C5—21no—
259C23×C5D3×D411yescharacteristic
260C22×D5—61no—
261C5×Q8—21no—
262C5×Q8—21no—
263C5×D4—21no—
264C5×D4—21no—
265C5×D4—41no—
266C5×D4—41no—
267C2×C4×C5—24no—
268C2×C4×C5—22no—
269C2×C4×C5—21no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5#23711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—124no—
279C22⋊D5—121no—
280C22⋊D5—121no—
281C2×Dic5—32no—
282C2×Dic5—32no—
283C2×Dic5—64no—
284C2×Dic5—64no—
285C2×Dic5—62no—
286C2×Dic5—61no—
287D20—61no—
288D20—61no—
289C4×D5—121no—
290C4×D5—121no—
291Dic10—61no—
292Dic10—61no—
293C5×C8—41no—
294#168—121no—
295C2×#41—151no—
296C2×#41C2×D1511yescharacteristic
297C2×M16—151no—
298C2×M16C2×D1511yescharacteristic
299C4⋊Q8—151no—
300#127—151no—
301#124—151no—
302#124—151no—
303#121—302no—
304C4×D4—302no—
305C2×C42—151no—
306C2×C42—151no—
307C2×C42—302no—
308C2×C42C2×D1511yescharacteristic
309C4⋊C8—302no—
310#104—22no—
311#104—302no—
312#104—302no—
313#104—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#39011yescharacteristic
318C2×C3×C5C2×#10412yes—
319D15—81no—
320C23×C3—21no—
321C23×C3D4×D511yescharacteristic
322C22×D3—101no—
323C3×Q8—21no—
324C3×Q8—21no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—41no—
328C3×D4—41no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4C2×C4×D511yescharacteristic
335C2×C3×C4#70911yescharacteristic
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4#71111yescharacteristic
339C2×C3×C4C2×C22⋊D511yescharacteristic
340#67—204no—
341#67—201no—
342#67—201no—
343C2×Dic3—52no—
344C2×Dic3—52no—
345C2×Dic3—104no—
346C2×Dic3—104no—
347C2×Dic3—102no—
348C2×Dic3—101no—
349D12—101no—
350D12—101no—
351C4×D3—201no—
352C4×D3—201no—
353Dic6—101no—
354Dic6—101no—
355C3×C8—41no—
356C3⋊C8—201no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—42no—
360C22×C5D3×C22⋊C411yescharacteristic
361C22×C5#88411yescharacteristic
362C22×C5#93911yescharacteristic
363C2×D5—121no—
364C2×D5—122no—
365C4×C5—24no—
366C4×C5—41no—
367C4×C5#67⋊C411yescharacteristic
368C4×C5#88511yescharacteristic
369C4×C5C4×#6711yescharacteristic
370C4×C5#94011yescharacteristic
371Dic5—34no—
372Dic5—64no—
373Dic5—62no—
374Dic5—121no—
375#41—21no—
376#41—21no—
377#41—21no—
378#41—21no—
379#41—301no—
380#41—301no—
381#41—301no—
382#41—301no—
383C2×Q8—151no—
384C2×Q8C4×D1511yescharacteristic
385C2×D4—21no—
386C2×D4—151no—
387C2×D4—302no—
388C2×D4—301no—
389C2×D4C4×D1511yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—152no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4C22×D1511yescharacteristic
396M16—21no—
397M16—21no—
398M16—301no—
399M16—301no—
400C2×C8—21no—
401C2×C8—301no—
402C4⋊C4—302no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C42—21no—
406C42—151no—
407C42—151no—
408C42—152no—
409C42—152no—
410C42—308no—
411C42—301no—
412C42#122012yescomplemented
413C3×C5#196211yescharacteristic, complemented, Hall
414C22×C3—22no—
415C22×C3—42no—
416C22×C3—41no—
417C22×C3D5×C22⋊C411yescharacteristic
418C22×C3#403011yescharacteristic
419C22×C3#408511yescharacteristic
420C2×D3—202no—
421C2×D3—201no—
422C3×C4—24no—
423C3×C4—41no—
424C3×C4#402711yescharacteristic
425C3×C4#403111yescharacteristic
426C3×C4C4×C22⋊D511yescharacteristic
427C3×C4#408611yescharacteristic
428Dic3—54no—
429Dic3—104no—
430Dic3—102no—
431Dic3—201no—
432C2×C5—21no—
433C2×C5—21no—
434C2×C5—81no—
435C2×C5D3×#10412yes—
436C2×C5#495711yescharacteristic
437D5—241no—
438C23—21no—
439C23—301no—
440C23D4×D1511yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—301no—
444Q8—301no—
445D4—21no—
446D4—21no—
447D4—41no—
448D4—41no—
449D4—301no—
450D4—301no—
451D4—604no—
452D4—601no—
453D4—601no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—152no—
460C2×C4—152no—
461C2×C4—304no—
462C2×C4—304no—
463C2×C4—302no—
464C2×C4—301no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4C2×C4×D1511yescharacteristic
468C2×C4#681711yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4D4×D1511yescharacteristic
471C2×C4#681911yescharacteristic
472C2×C4C2×#122011yescharacteristic
473C8—41no—
474C8—601no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—81no—
478C2×C3D5×#10412yes—
479C2×C3#6524611yescharacteristic
480D3—401no—
481C5#7035611yescharacteristic, complemented, Sylow
482C22—22no—
483C22—42no—
484C22—41no—
485C22—602no—
486C22—601no—
487C22C22⋊C4×D1511yescharacteristic
488C22#9177311yescharacteristic
489C22#9182811yescharacteristic
490C4—24no—
491C4—41no—
492C4—154no—
493C4—304no—
494C4—302no—
495C4—601no—
496C4#9177011yescharacteristic
497C4#9177411yescharacteristic
498C4C4×#122011yescharacteristic
499C4#9182911yescharacteristic
500C3#1060114911yescharacteristic, complemented, Sylow
501C2—21no—
502C2—21no—
503C2—81no—
504C2—1201no—
505C2D15×#10412yes—
506C2#1175105811yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756591C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5#1962
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#104C2semidirect
3. C2×#91121C2semidirect
4. C2×#91109C2semidirect
5. #11751219C2semidirect
6. C42×Dic15C2semidirect
7. C2×#91089C2semidirect
13. #91836C4semidirect
14. #91833C4semidirect
15. #91829C4semidirect
17. #91825C4semidirect
30. C2×C5×#104D3semidirect
61. C3×C42×C5D4semidirect
70. C4×Dic15D4semidirect
75. C2×C3×#104D5semidirect
182. C42×C5#67semidirect
200. C2×#104D15semidirect
219. Dic15#104semidirect
245. C3×C42C22⋊D5semidirect
412. C42#1220semidirect
413. C3×C5#1962semidirect
481. C5#70356semidirect
500. C3#10601149semidirect

Maximal subgroups

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

subgroupindex
#117565912
C2×C3×C5×#1042
C2×#911212
C2×#911092
#117512192
C42×Dic152
C2×#910892
#106011493
#703565