Finite Group Databasebeta

← #14306029

Subgroups — #14306029

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 504 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
6#11751033C211yesmaximal, characteristic, complemented
7C2×#91089C211yesmaximal, characteristic, complemented
8#10601150—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×Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22C3×C5×#104—22no—
23#91121—22no—
24#91115—22no—
25#91109—22no—
26#91098—22no—
27#91089—22no—
28#70357—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104D311yescharacteristic, complemented
31C2×#3969—31no—
32C2×#3957—31no—
33#65407—31no—
34#65221—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—21no—
66C4×Dic15C2×C411yescharacteristic
67C4×Dic15C2×C411yescharacteristic
68C4×Dic15D412yes—
69C4×Dic15D412yescomplemented
70#6710—21no—
71#6710—21no—
72C2×C3⋊#168—21no—
73#5832—51no—
74C2×C3×#104D511yescharacteristic, complemented
75C2×#837—51no—
76C2×#825—51no—
77#5118—51no—
78#4932—51no—
79C2×#805—51no—
80C2×C5×#41C2×D311yescharacteristic
81C2×#709—31no—
82C2×C5×M16C2×D311yescharacteristic
83C2×C42×C5C2×D311yescharacteristic
84#4093—31no—
85#4090—31no—
86#4086—31no—
87#4085—62no—
88#4082—31no—
89C4×C22⋊D5—62no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—31no—
92C2×#681—31no—
93C5×#104—22no—
94#3969—62no—
95#3963—62no—
96#3957—62no—
97#3946—62no—
98#3937—62no—
99#1963—151noSylow
100C23×C3×C5—21no—
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C3×C5×Q8—21no—
104C3×C5×Q8—21no—
105C3×C5×D4—21no—
106C3×C5×D4—21no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—42no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120#1220—44no—
121#1220—41no—
122#1220—41no—
123C2×Dic15—21no—
124C2×Dic15—22no—
125C2×Dic15—42no—
126C2×Dic15—42no—
127C2×Dic15C22⋊C412yes—
128C2×Dic15C22⋊C412yes—
129D60—21no—
130D60—21no—
131C4×D15—41no—
132C4×D15—41no—
133Dic30—21no—
134Dic30—21no—
135C3×C5×C8—41no—
136C3⋊#168—41no—
137C2×C3×#41C2×D511yescharacteristic
138C2×#235—51no—
139C2×C3×M16C2×D511yescharacteristic
140C2×C3×C42C2×D511yescharacteristic
141#947—51no—
142#944—51no—
143#940—51no—
144#939—102no—
145#936—51no—
146C4×#67—102no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3—51no—
149C2×#208—51no—
150C3×#104—22no—
151#837—102no—
152C3⋊#95—102no—
153#825—102no—
154Dic3⋊C8—102no—
155#805—102no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C2×C5×Q8C4×D311yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C4×D311yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—62no—
167C2×C22⋊D5—61no—
168C22×Dic5—32no—
169C22×Dic5—61no—
170#709—61no—
171#709—61no—
172#709—61no—
173#709—61no—
174C2×D20—31no—
175C2×C4×D5—61no—
176C2×Dic10—31no—
177C5×M16—21no—
178C5×M16—21no—
179C2×C5×C8—21no—
180C42×C5—21no—
181C42×C5#6712yescomplemented
182C22⋊Dic5—62no—
183#685—62no—
184#683—62no—
185C4×Dic5—31no—
186C4×Dic5—31no—
187C4×Dic5—32no—
188C4×Dic5—32no—
189C4×Dic5—61no—
190#681—61no—
191#681—61no—
192C2×#168—61no—
193#532—151no—
194#423—151no—
195C2×#104—151no—
196C2×#104—151no—
197C2×#104—151no—
198C2×#104D1511yescharacteristic, complemented
199#376—151no—
200C22×C3×C5—22no—
201C22×C3×C5—41no—
202C22×C3×C5—42no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×D15—41no—
207C2×D15—42no—
208C3×C4×C5—42no—
209C3×C4×C5—41no—
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12411yescharacteristic
213C3×C4×C5#12711yescharacteristic
214Dic15—22no—
215Dic15—22no—
216Dic15—42no—
217Dic15—41no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C2×C3×Q8C4×D511yescharacteristic
223C2×C3×D4—21no—
224C2×C3×D4C4×D511yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4C22×D511yescharacteristic
228C2×#67—102no—
229C2×#67—101no—
230C22×Dic3—52no—
231C22×Dic3—101no—
232#235—101no—
233#235—101no—
234#235—101no—
235#235—101no—
236C2×D12—51no—
237C2×C4×D3—101no—
238C2×Dic6—51no—
239C3×M16—21no—
240C3×M16—21no—
241C2×C3×C8—21no—
242C3×C42—21no—
243C3×C42C22⋊D512yescomplemented
244#217—102no—
245(C2×D3)⋊C4—102no—
246Dic3⋊C4—102no—
247C4×Dic3—51no—
248C4×Dic3—51no—
249C4×Dic3—52no—
250C4×Dic3—52no—
251C4×Dic3—101no—
252#208—101no—
253#208—101no—
254C2×C3⋊C8—101no—
255C23×C5—21no—
256C23×C5D3×D411yescharacteristic
257C22×D5—61no—
258C5×Q8—21no—
259C5×Q8—21no—
260C5×D4—21no—
261C5×D4—21no—
262C5×D4—41no—
263C5×D4—41no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—42no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5C2×C4×D311yescharacteristic
270C2×C4×C5#23511yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5#23711yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C22⋊D5—124no—
276C22⋊D5—121no—
277C22⋊D5—121no—
278C2×Dic5—32no—
279C2×Dic5—32no—
280C2×Dic5—61no—
281C2×Dic5—62no—
282C2×Dic5—122no—
283C2×Dic5—122no—
284D20—61no—
285D20—61no—
286C4×D5—121no—
287C4×D5—121no—
288Dic10—61no—
289Dic10—61no—
290C5×C8—41no—
291#168—121no—
292C2×#41—151no—
293C2×#41C2×D1511yescharacteristic
294C2×M16—151no—
295C2×M16C2×D1511yescharacteristic
296C4⋊Q8—151no—
297#127—151no—
298#124—151no—
299#124—151no—
300#121—302no—
301C4×D4—302no—
302C2×C42—151no—
303C2×C42—151no—
304C2×C42C2×D1511yescharacteristic
305C4⋊C8—302no—
306#104—22no—
307#104—302no—
308#104—302no—
309#104—302no—
310#95—302no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5—81no—
314C2×C3×C5#39011yescharacteristic
315C2×C3×C5#42112yes—
316D15—81no—
317C23×C3—21no—
318C23×C3D4×D511yescharacteristic
319C22×D3—101no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×D4—21no—
323C3×D4—21no—
324C3×D4—41no—
325C3×D4—41no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4C2×C4×D511yescharacteristic
332C2×C3×C4#70911yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4#71111yescharacteristic
336C2×C3×C4C2×C22⋊D511yescharacteristic
337#67—204no—
338#67—201no—
339#67—201no—
340C2×Dic3—52no—
341C2×Dic3—52no—
342C2×Dic3—101no—
343C2×Dic3—102no—
344C2×Dic3—202no—
345C2×Dic3—202no—
346D12—101no—
347D12—101no—
348C4×D3—201no—
349C4×D3—201no—
350Dic6—101no—
351Dic6—101no—
352C3×C8—41no—
353C3⋊C8—201no—
354C22×C5—22no—
355C22×C5—41no—
356C22×C5—42no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88411yescharacteristic
359C22×C5#93911yescharacteristic
360C2×D5—121no—
361C2×D5—122no—
362C4×C5—42no—
363C4×C5—41no—
364C4×C5#67⋊C411yescharacteristic
365C4×C5#88511yescharacteristic
366C4×C5C4×#6711yescharacteristic
367C4×C5#94011yescharacteristic
368Dic5—62no—
369Dic5—62no—
370Dic5—122no—
371Dic5—121no—
372#41—21no—
373#41—21no—
374#41—21no—
375#41—21no—
376#41—301no—
377#41—301no—
378#41—301no—
379#41—301no—
380C2×Q8—151no—
381C2×Q8C4×D1511yescharacteristic
382C2×D4—21no—
383C2×D4—151no—
384C2×D4—302no—
385C2×D4—301no—
386C2×D4C4×D1511yescharacteristic
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—152no—
390C22×C4—301no—
391C22×C4—301no—
392C22×C4C22×D1511yescharacteristic
393M16—21no—
394M16—21no—
395M16—301no—
396M16—301no—
397C2×C8—21no—
398C2×C8—301no—
399C4⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C42—21no—
403C42—151no—
404C42—151no—
405C42—152no—
406C42—152no—
407C42—301no—
408C42#122012yescomplemented
409C3×C5#196311yescharacteristic, complemented, Hall
410C22×C3—22no—
411C22×C3—42no—
412C22×C3—41no—
413C22×C3D5×C22⋊C411yescharacteristic
414C22×C3#403011yescharacteristic
415C22×C3#408511yescharacteristic
416C2×D3—202no—
417C2×D3—201no—
418C3×C4—42no—
419C3×C4—41no—
420C3×C4#402711yescharacteristic
421C3×C4#403111yescharacteristic
422C3×C4C4×C22⋊D511yescharacteristic
423C3×C4#408611yescharacteristic
424Dic3—102no—
425Dic3—102no—
426Dic3—202no—
427Dic3—201no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—81no—
431C2×C5#482112yes—
432C2×C5#495711yescharacteristic
433D5—241no—
434C23—21no—
435C23—301no—
436C23D4×D1511yescharacteristic
437Q8—21no—
438Q8—21no—
439Q8—301no—
440Q8—301no—
441D4—21no—
442D4—21no—
443D4—41no—
444D4—41no—
445D4—301no—
446D4—301no—
447D4—604no—
448D4—601no—
449D4—601no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—152no—
456C2×C4—152no—
457C2×C4—301no—
458C2×C4—302no—
459C2×C4—602no—
460C2×C4—602no—
461C2×C4—601no—
462C2×C4—601no—
463C2×C4C2×C4×D1511yescharacteristic
464C2×C4#681711yescharacteristic
465C2×C4D4×D1511yescharacteristic
466C2×C4D4×D1511yescharacteristic
467C2×C4#681911yescharacteristic
468C2×C4C2×#122011yescharacteristic
469C8—41no—
470C8—601no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—81no—
474C2×C3#6511012yes—
475C2×C3#6524611yescharacteristic
476D3—401no—
477C5#7035711yescharacteristic, complemented, Sylow
478C22—22no—
479C22—42no—
480C22—41no—
481C22—602no—
482C22—601no—
483C22C22⋊C4×D1511yescharacteristic
484C22#9177311yescharacteristic
485C22#9182811yescharacteristic
486C4—42no—
487C4—41no—
488C4—302no—
489C4—302no—
490C4—602no—
491C4—601no—
492C4#9177011yescharacteristic
493C4#9177411yescharacteristic
494C4C4×#122011yescharacteristic
495C4#9182911yescharacteristic
496C3#1060115011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—81no—
500C2—1201no—
501C2#1175092212yes—
502C2#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#1963
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. #11751033C2semidirect
7. C2×#91089C2semidirect
13. #91836C4semidirect
14. #91833C4semidirect
15. #91829C4semidirect
17. #91825C4semidirect
30. C2×C5×#104D3semidirect
61. C3×C42×C5D4semidirect
69. C4×Dic15D4semidirect
74. C2×C3×#104D5semidirect
181. C42×C5#67semidirect
198. C2×#104D15semidirect
243. C3×C42C22⋊D5semidirect
408. C42#1220semidirect
409. C3×C5#1963semidirect
477. C5#70357semidirect
496. C3#10601150semidirect

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
#117510332
C2×#910892
#106011503
#703575