Finite Group Databasebeta

← #14302572

Subgroups — #14302572

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756581C211yesmaximal, characteristic
2C4×#6817C211yesmaximal, characteristic, complemented
3C2×C3×C5×#104C211yesmaximal, characteristic, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11751240C211yesmaximal, characteristic, complemented
6#11746377C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10601184—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13#91840—21no—
14#91839—22no—
15#91838—21no—
16#91831C412yescomplemented
17#91821C412yescomplemented
18C4×#1220—22no—
19#91815C2211yescharacteristic
20#91815C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22C4×D60—21no—
23#91761—21no—
24C42×D15—21no—
25C4×Dic30—21no—
26C3×C5×#104—21no—
27C3×C5×#104—21no—
28#91118—22no—
29#91109—22no—
30#70391—51nomaximal, Hall
31#66156—31no—
32C4×#709—31no—
33C2×C5×#104D311yescharacteristic, complemented
34#65529—31no—
35#65428—31no—
36#64776—31no—
37#64743—31no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C2×C3×C5×Q8C2×C411yescharacteristic, complemented
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4C2×C411yescharacteristic, complemented
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5C2311yescharacteristic
48C2×#1220—21no—
49#6817—21no—
50#6817—21no—
51#6817C2×C412yes—
52#6817D412yes—
53C2×D60D411yescharacteristic
54C2×C4×D15—21no—
55C2×C4×D15—22no—
56C2×Dic30D411yescharacteristic
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C2×C3×C5×C8—21no—
60C3×C42×C5—21no—
61C3×C42×C5D411yescharacteristic
62C3×C42×C5D411yescharacteristic
63#6719—21no—
64#6719D412yes—
65#6718—22no—
66#6717—22no—
67#6716—22no—
68#6715—22no—
69#6714—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15—21no—
72#6712—22no—
73C4×Dic15—22no—
74C4×Dic15—21no—
75C4×Dic15—21no—
76#6710—21no—
77#6710C2×C412yescomplemented
78C2×C3⋊#168—21no—
79#5822—51no—
80C4×#235—51no—
81C2×C3×#104D511yescharacteristic, complemented
82#5240—51no—
83#5139—51no—
84#4556—51no—
85#4523—51no—
86C2×C5×#41C2×D311yescharacteristic
87C2×#709—31no—
88C2×C5×M16C2×D311yescharacteristic
89C2×C42×C5C2×D311yescharacteristic
90#4097—61no—
91#4096—62no—
92#4095—61no—
93#4088—32no—
94#4078—32no—
95C4×C22⋊D5—62no—
96#4072—31no—
97#4072—31no—
98C2×#681—31no—
99C4×D20—61no—
100#4018—61no—
101C42×D5—61no—
102C4×Dic10—61no—
103C5×#104—21no—
104C5×#104—21no—
105#3966—62no—
106#3957—62no—
107#1906—151noSylow
108C23×C3×C5—21no—
109C23×C3×C5C2×D411yescharacteristic
110C22×D15—21no—
111C3×C5×Q8—21no—
112C3×C5×Q8—21no—
113C3×C5×D4—21no—
114C3×C5×D4—21no—
115C3×C5×D4—41no—
116C3×C5×D4—41no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5C22×C411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5#4111yescharacteristic
128C2×C3×C4×C5#4111yescharacteristic
129#1220—22no—
130#1220—22no—
131C2×Dic15—21no—
132C2×Dic15—22no—
133C2×Dic15—41no—
134D60—21no—
135D60C22⋊C412yes—
136C4×D15—22no—
137C4×D15—22no—
138C4×D15—44no—
139Dic30—21no—
140Dic30C22⋊C412yes—
141C3×C5×C8—41no—
142C3⋊#168—22no—
143C2×C3×#41C2×D511yescharacteristic
144C2×#235—51no—
145C2×C3×M16C2×D511yescharacteristic
146C2×C3×C42C2×D511yescharacteristic
147#951—101no—
148#950—102no—
149#949—101no—
150#942—52no—
151#932—52no—
152C4×#67—102no—
153#926—51no—
154#926—51no—
155C2×#208—51no—
156C4×D12—101no—
157#872—101no—
158C42×D3—101no—
159C4×Dic6—101no—
160C3×#104—21no—
161C3×#104—21no—
162#834—102no—
163#825—102no—
164C5×#41—21no—
165C5×#41—21no—
166C5×#41—21no—
167C5×#41—21no—
168C2×C5×Q8C4×D311yescharacteristic, complemented
169C2×C5×D4—21no—
170C2×C5×D4C4×D311yescharacteristic, complemented
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5C22×D311yescharacteristic
174C2×C22⋊D5—61no—
175#709—32no—
176#709—32no—
177#709—61no—
178#709—61no—
179C2×D20—31no—
180C2×C4×D5—61no—
181C2×C4×D5—62no—
182C2×Dic10—31no—
183C5×M16—21no—
184C5×M16—21no—
185C2×C5×C8—21no—
186C42×C5—21no—
187C42×C5#6711yescharacteristic
188C42×C5#6711yescharacteristic
189C22⋊Dic5—32no—
190C22⋊Dic5—61no—
191#689—62no—
192#688—62no—
193#687—62no—
194#686—62no—
195#685—62no—
196C4⋊Dic5—61no—
197C4⋊Dic5—61no—
198#683—62no—
199C4×Dic5—62no—
200C4×Dic5—61no—
201C4×Dic5—61no—
202#681—32no—
203#681—61no—
204C2×#168—61no—
205#575—151no—
206C4×#41—151no—
207#421—151no—
208C2×#104D1511yescharacteristic, complemented
209#410—151no—
210#344—151no—
211#339—151no—
212C22×C3×C5—41no—
213C22×C3×C5—41no—
214C22×C3×C5—81no—
215C22×C3×C5C4×D411yescharacteristic
216C22×C3×C5#12011yescharacteristic
217C22×C3×C5#12111yescharacteristic
218C2×D15—22no—
219C2×D15—42no—
220C3×C4×C5—22no—
221C3×C4×C5—41no—
222C3×C4×C5—41no—
223C3×C4×C5C2×C22⋊C411yescharacteristic
224C3×C4×C5C4×D411yescharacteristic
225C3×C4×C5#12111yescharacteristic
226C3×C4×C5#12311yescharacteristic
227Dic15—22no—
228Dic15—42no—
229Dic15—81no—
230C3×#41—21no—
231C3×#41—21no—
232C3×#41—21no—
233C3×#41—21no—
234C2×C3×Q8C4×D511yescharacteristic, complemented
235C2×C3×D4—21no—
236C2×C3×D4C4×D511yescharacteristic, complemented
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4C22×D511yescharacteristic
240C2×#67—101no—
241#235—52no—
242#235—52no—
243#235—101no—
244#235—101no—
245C2×D12—51no—
246C2×C4×D3—101no—
247C2×C4×D3—102no—
248C2×Dic6—51no—
249C3×M16—21no—
250C3×M16—21no—
251C2×C3×C8—21no—
252C3×C42—21no—
253C3×C42C22⋊D511yescharacteristic
254C3×C42C22⋊D511yescharacteristic
255#217—52no—
256#217—101no—
257#216—102no—
258#215—102no—
259#214—102no—
260#213—102no—
261(C2×D3)⋊C4—102no—
262C4⋊Dic3—101no—
263C4⋊Dic3—101no—
264Dic3⋊C4—102no—
265C4×Dic3—102no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268#208—52no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5—21no—
272C23×C5D3×D411yescharacteristic
273C22×D5—61no—
274C5×Q8—21no—
275C5×Q8—21no—
276C5×D4—21no—
277C5×D4—21no—
278C5×D4—41no—
279C5×D4—41no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—42no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5C2×C4×D311yescharacteristic
287C2×C4×C5#23511yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5#23711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C22⋊D5—62no—
293C22⋊D5—62no—
294C2×Dic5—61no—
295C2×Dic5—62no—
296C2×Dic5—121no—
297D20—32no—
298D20—61no—
299C4×D5—62no—
300C4×D5—62no—
301C4×D5—124no—
302Dic10—32no—
303Dic10—61no—
304C5×C8—41no—
305#168—62no—
306C2×#41—151no—
307C2×#41C2×D1511yescharacteristic
308#137—152no—
309#137—301no—
310AGL(1,ℤ/8)—152no—
311AGL(1,ℤ/8)—301no—
312#135—302no—
313C2×M16—151no—
314C2×M16C2×D1511yescharacteristic
315C4×Q8—301no—
316C4×D4—301no—
317C4×D4—302no—
318#117—151no—
319#117—151no—
320#117—301no—
321C2×C42—301no—
322C2×C42C2×D1511yescharacteristic
323#104—21no—
324#104—21no—
325#104—302no—
326#99—302no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5—21no—
330C2×C3×C5—81no—
331C2×C3×C5#38611yescharacteristic
332D15—42no—
333C23×C3—21no—
334C23×C3D4×D511yescharacteristic
335C22×D3—101no—
336C3×Q8—21no—
337C3×Q8—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—41no—
341C3×D4—41no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—42no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4C2×C4×D511yescharacteristic
349C2×C3×C4#70911yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4#71111yescharacteristic
353C2×C3×C4C2×C22⋊D511yescharacteristic
354#67—102no—
355#67—102no—
356C2×Dic3—101no—
357C2×Dic3—102no—
358C2×Dic3—201no—
359D12—52no—
360D12—101no—
361C4×D3—102no—
362C4×D3—102no—
363C4×D3—204no—
364Dic6—52no—
365Dic6—101no—
366C3×C8—41no—
367C3⋊C8—102no—
368C22×C5—41no—
369C22×C5—41no—
370C22×C5—81no—
371C22×C5#67⋊C411yescharacteristic
372C22×C5#88411yescharacteristic
373C22×C5#93711yescharacteristic
374C2×D5—62no—
375C2×D5—122no—
376C4×C5—22no—
377C4×C5—41no—
378C4×C5—41no—
379C4×C5D3×C22⋊C411yescharacteristic
380C4×C5#88311yescharacteristic
381C4×C5C4×#6711yescharacteristic
382C4×C5#93811yescharacteristic
383Dic5—62no—
384Dic5—122no—
385Dic5—241no—
386#41—21no—
387#41—21no—
388#41—21no—
389#41—21no—
390#41—152no—
391#41—152no—
392#41—301no—
393#41—301no—
394C2×Q8—151no—
395C2×Q8C4×D1511yescharacteristic, complemented
396C2×D4—21no—
397C2×D4—151no—
398C2×D4—301no—
399C2×D4C4×D1511yescharacteristic, complemented
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—302no—
403C22×C4—301no—
404C22×C4C22×D1511yescharacteristic
405Q16—302no—
406SD16—302no—
407SD16—302no—
408D8—302no—
409M16—21no—
410M16—21no—
411M16—152no—
412M16—301no—
413C2×C8—21no—
414C2×C8—301no—
415C4⋊C4—302no—
416C4⋊C4—301no—
417C4⋊C4—301no—
418C22⋊C4—152no—
419C22⋊C4—302no—
420C22⋊C4—301no—
421C42—21no—
422C42—302no—
423C42—301no—
424C42—301no—
425C42#122011yescharacteristic
426C42#122011yescharacteristic
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—81no—
431C22×C3#402711yescharacteristic
432C22×C3#403011yescharacteristic
433C22×C3#408311yescharacteristic
434C2×D3—102no—
435C2×D3—202no—
436C3×C4—22no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4D5×C22⋊C411yescharacteristic
440C3×C4#402911yescharacteristic
441C3×C4C4×C22⋊D511yescharacteristic
442C3×C4#408411yescharacteristic
443Dic3—102no—
444Dic3—202no—
445Dic3—401no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—81no—
450C2×C5#495611yescharacteristic
451D5—122no—
452C23—21no—
453C23—301no—
454C23D4×D1511yescharacteristic
455Q8—21no—
456Q8—21no—
457Q8—152no—
458Q8—301no—
459D4—21no—
460D4—21no—
461D4—41no—
462D4—41no—
463D4—152no—
464D4—302no—
465D4—302no—
466D4—301no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—301no—
474C2×C4—302no—
475C2×C4—302no—
476C2×C4—302no—
477C2×C4—604no—
478C2×C4—601no—
479C2×C4C2×C4×D1511yescharacteristic
480C2×C4#681711yescharacteristic
481C2×C4D4×D1511yescharacteristic
482C2×C4D4×D1511yescharacteristic
483C2×C4#681911yescharacteristic
484C2×C4C2×#122011yescharacteristic
485C8—41no—
486C8—302no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—81no—
491C2×C3#6524511yescharacteristic
492D3—202no—
493C5#7039111yescharacteristic, complemented, Sylow
494C22—41no—
495C22—41no—
496C22—81no—
497C22—302no—
498C22—602no—
499C22#9177011yescharacteristic
500C22#9177311yescharacteristic
501C22#9182611yescharacteristic
502C4—22no—
503C4—41no—
504C4—41no—
505C4—302no—
506C4—602no—
507C4—1201no—
508C4C22⋊C4×D1511yescharacteristic
509C4#9177211yescharacteristic
510C4C4×#122011yescharacteristic
511C4#9182711yescharacteristic
512C3#1060118411yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—81no—
517C2—602no—
518C2#1175105711yescharacteristic
subgroupG/H
centerC4#91827
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC2×C3×C5#386
prime radical#11756581C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5#1906
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C4×#6817C2semidirect
3. C2×C3×C5×#104C2semidirect
4. #11751341C2semidirect
5. #11751240C2semidirect
6. #11746377C2semidirect
7. #11746344C2semidirect
16. #91831C4semidirect
17. #91821C4semidirect
33. C2×C5×#104D3semidirect
42. C2×C3×C5×Q8C2×C4semidirect
44. C2×C3×C5×D4C2×C4semidirect
77. #6710C2×C4semidirect
81. C2×C3×#104D5semidirect
168. C2×C5×Q8C4×D3semidirect
170. C2×C5×D4C4×D3semidirect
208. C2×#104D15semidirect
234. C2×C3×Q8C4×D5semidirect
236. C2×C3×D4C4×D5semidirect
395. C2×Q8C4×D15semidirect
399. C2×D4C4×D15semidirect
427. C3×C5#1906semidirect
493. C5#70391semidirect
512. C3#10601184semidirect

Maximal subgroups

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

subgroupindex
#117565812
C4×#68172
C2×C3×C5×#1042
#117513412
#117512402
#117463772
#117463442
#106011843
#703915