Finite Group Databasebeta

← #14306015

Subgroups — #14306015

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×C5×#837C211yesmaximal, characteristic, complemented
3C2×C3×#3969C211yesmaximal, characteristic, complemented
4C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
5#11748437C211yesmaximal, characteristic, complemented
6C2×#90981C211yesmaximal, characteristic, complemented
7C2×#90980C211yesmaximal, characteristic, complemented
8#10601149—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11#91836C411yescharacteristic, complemented
12#91833C411yescharacteristic, complemented
13#91829C411yescharacteristic, complemented
14#91828—22no—
15#91825C411yescharacteristic, complemented
16C4×#1220—22no—
17C2×C4×Dic15C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22C2×Dic3×Dic5—22no—
23C5×#837—22no—
24C3×#3969—22no—
25#90983—22no—
26#90981—22no—
27#90980—22no—
28#70356—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104—31no—
31C2×#3969D311yescharacteristic, complemented
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×C5C2311yescharacteristic
45C2×#1220—21no—
46C2×#1220—22no—
47C22×Dic15D412yes—
48#6817—21no—
49#6817—21no—
50#6817—21no—
51#6817—21no—
52C2×D60C2×C411yescharacteristic
53C2×C4×D15—21no—
54C2×Dic30C2×C411yescharacteristic
55C22×C5×Dic3—21no—
56C22×C3×Dic5—21no—
57#6719—22no—
58#6714—22no—
59#6712—22no—
60C4×Dic15C2×C411yescharacteristic
61C4×Dic15C2×C411yescharacteristic
62C4×Dic15D412yes—
63C4×C5×Dic3—21no—
64C4×C5×Dic3D412yescomplemented
65C5×#208—21no—
66C5×#208—21no—
67C2×C5×C3⋊C8—21no—
68C3×C4×Dic5—21no—
69C3×C4×Dic5D412yescomplemented
70C3×#681—21no—
71C3×#681—21no—
72C2×C3×#168—21no—
73Dic3×Dic5—28no—
74#5832—51no—
75C2×C3×#104—51no—
76C2×#837D511yescharacteristic, complemented
77C2×#825—51no—
78#5118—51no—
79C42×Dic3—51no—
80C2×#805—51no—
81C2×C5×#41C2×D311yescharacteristic
82C2×#709—31no—
83C2×C5×M16—31no—
84C2×C42×C5—31no—
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—62no—
93C2×C4×Dic5C2×D311yescharacteristic
94C2×#681C2×D311yescharacteristic
95C5×#104—62no—
96#3969—22no—
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—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119#1220—41no—
120#1220—41no—
121#1220—44no—
122C2×Dic15—24no—
123C2×Dic15—21no—
124C2×Dic15C22⋊C412yes—
125C2×Dic15C22⋊C412yes—
126D60—21no—
127D60—21no—
128C4×D15—41no—
129C4×D15—41no—
130Dic30—21no—
131Dic30—21no—
132C2×C5×Dic3—24no—
133C2×C5×Dic3—22no—
134C2×C3×Dic5—24no—
135C2×C3×Dic5—22no—
136C3×#168—41no—
137C5×C3⋊C8—41no—
138C2×C3×#41C2×D511yescharacteristic
139C2×#235—51no—
140C2×C3×M16—51no—
141C2×C3×C42—51no—
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—102no—
150C2×C4×Dic3C2×D511yescharacteristic
151C2×#208C2×D511yescharacteristic
152C3×#104—102no—
153#837—22no—
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—61no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—62no—
168C2×C22⋊D5—61no—
169C22×Dic5—21no—
170C22×Dic5—32no—
171#709—61no—
172#709—61no—
173#709—61no—
174#709—61no—
175C2×D20—31no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C42×C5—32no—
182C42×C5—61no—
183C22⋊Dic5—62no—
184#685—62no—
185#683—62no—
186C4×Dic5—21no—
187C4×Dic5—31no—
188C4×Dic5—31no—
189C4×Dic5—32no—
190C4×Dic5—68no—
191C4×Dic5#6712yescomplemented
192#681—21no—
193#681—21no—
194C2×#168—21no—
195#532—151no—
196#423—151no—
197C2×#104—31no—
198C2×#104—51no—
199C2×#104—151no—
200C2×#104—151no—
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—41no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12411yescharacteristic
214C3×C4×C5#12711yescharacteristic
215Dic15—22no—
216Dic15—41no—
217Dic15#10414yescomplemented
218C3×Dic5—24no—
219C5×Dic3—24no—
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—101no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—102no—
231C2×#67—101no—
232C22×Dic3—21no—
233C22×Dic3—52no—
234#235—101no—
235#235—101no—
236#235—101no—
237#235—101no—
238C2×D12—51no—
239C2×C4×D3—101no—
240C2×Dic6—51no—
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—101no—
244C3×C42—52no—
245C3×C42—101no—
246#217—102no—
247(C2×D3)⋊C4—102no—
248Dic3⋊C4—102no—
249C4×Dic3—21no—
250C4×Dic3—51no—
251C4×Dic3—51no—
252C4×Dic3—52no—
253C4×Dic3—108no—
254C4×Dic3C22⋊D512yescomplemented
255#208—21no—
256#208—21no—
257C2×C3⋊C8—21no—
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—21no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—64no—
271C2×C4×C5—62no—
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—24no—
282C2×Dic5—22no—
283C2×Dic5—32no—
284C2×Dic5—32no—
285C2×Dic5—64no—
286C2×Dic5—61no—
287D20—61no—
288D20—61no—
289C4×D5—121no—
290C4×D5—121no—
291Dic10—61no—
292Dic10—61no—
293C5×C8—121no—
294#168—41no—
295C2×#41—151no—
296C2×#41D3×D511yescharacteristic
297C2×M16—31no—
298C2×M16—51no—
299C4⋊Q8—151no—
300#127—151no—
301#124—151no—
302#124—151no—
303#121—302no—
304C4×D4—302no—
305C2×C42—31no—
306C2×C42—51no—
307C2×C42—151no—
308C2×C42—302no—
309C4⋊C8—302no—
310#104—62no—
311#104—102no—
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—21no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—104no—
333C2×C3×C4—102no—
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—24no—
344C2×Dic3—22no—
345C2×Dic3—52no—
346C2×Dic3—52no—
347C2×Dic3—104no—
348C2×Dic3—101no—
349D12—101no—
350D12—101no—
351C4×D3—201no—
352C4×D3—201no—
353Dic6—101no—
354Dic6—101no—
355C3×C8—201no—
356C3⋊C8—41no—
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—41no—
366C4×C5—64no—
367C4×C5#67⋊C411yescharacteristic
368C4×C5#88511yescharacteristic
369C4×C5C4×#6711yescharacteristic
370C4×C5#94011yescharacteristic
371Dic5—24no—
372Dic5—34no—
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×Q8#120011yescharacteristic
385C2×D4—21no—
386C2×D4—151no—
387C2×D4—302no—
388C2×D4—301no—
389C2×D4#120011yescharacteristic
390C22×C4—21no—
391C22×C4—61no—
392C22×C4—101no—
393C22×C4—152no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—61no—
397M16—61no—
398M16—101no—
399M16—101no—
400C2×C8—61no—
401C2×C8—101no—
402C4⋊C4—302no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C42—32no—
406C42—52no—
407C42—61no—
408C42—101no—
409C42—151no—
410C42—151no—
411C42—152no—
412C42—308no—
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—41no—
423C3×C4—104no—
424C3×C4#402711yescharacteristic
425C3×C4#403111yescharacteristic
426C3×C4C4×C22⋊D511yescharacteristic
427C3×C4#408611yescharacteristic
428Dic3—24no—
429Dic3—54no—
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—
440C23#679011yescharacteristic
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—21no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—104no—
460C2×C4—102no—
461C2×C4—152no—
462C2×C4—152no—
463C2×C4—304no—
464C2×C4—301no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4#677911yescharacteristic
468C2×C4#678211yescharacteristic
469C2×C4C2×#120011yescharacteristic
470C2×C4D5×#6711yescharacteristic
471C2×C4D3×C22⋊D511yescharacteristic
472C2×C4#679011yescharacteristic
473C8—121no—
474C8—201no—
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—
487C22#9155011yescharacteristic
488C22#9155811yescharacteristic
489C22#9156111yescharacteristic
490C4—41no—
491C4—64no—
492C4—104no—
493C4—154no—
494C4—302no—
495C4—601no—
496C4#9152611yescharacteristic
497C4#9155211yescharacteristic
498C4#9155611yescharacteristic
499C4#9156711yescharacteristic
500C3#1060114911yescharacteristic, complemented, Sylow
501C2—21no—
502C2—21no—
503C2—81no—
504C2—1201no—
505C2#1174943012yes—
506C2#1174948311yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756591C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1962
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C5×#837C2semidirect
3. C2×C3×#3969C2semidirect
4. C4×Dic3×Dic5C2semidirect
5. #11748437C2semidirect
6. C2×#90981C2semidirect
7. C2×#90980C2semidirect
11. #91836C4semidirect
12. #91833C4semidirect
13. #91829C4semidirect
15. #91825C4semidirect
31. C2×#3969D3semidirect
64. C4×C5×Dic3D4semidirect
69. C3×C4×Dic5D4semidirect
76. C2×#837D5semidirect
191. C4×Dic5#67semidirect
217. Dic15#104semidirect
254. C4×Dic3C22⋊D5semidirect
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×C5×#8372
C2×C3×#39692
C4×Dic3×Dic52
#117484372
C2×#909812
C2×#909802
#106011493
#703565