Finite Group Databasebeta

← #14438621

Subgroups — #14438621

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#888C211yesmaximal, characteristic, complemented
2#11754581C211yesmaximal, characteristic
3#11751067C211yesmaximal, characteristic, complemented
4C3×#65255C211yesmaximal, characteristic, complemented
5#11748394C211yesmaximal, characteristic, complemented
6#11748368C211yesmaximal, characteristic, complemented
7Dic3×#681C211yesmaximal, characteristic, complemented
8#11747422C212yesmaximal, complemented
9#11747403C212yesmaximal, complemented
10#11747380C212yesmaximal, complemented
11#11747376C212yesmaximal, complemented
12#10614930—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×Dic6—21no—
15C2×C3×#709C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C5×Dic3⋊C4—21no—
20C2×C4×C5×Dic3C2211yescharacteristic
21C5×#888—21no—
22C5×#888—21no—
23C5×#888C2212yes—
24C5×#888C2212yes—
25C2×C3×#681C2211yescharacteristic
26#91569—21no—
27#91569—21no—
28#91458C2211yescharacteristic
29C4×#1202—21no—
30C4×#1202—21no—
31#91389C2211yescharacteristic
32#91374C2211yescharacteristic
33#91364C2211yescharacteristic
34#91094C2212yes—
35#91093C2212yes—
36C3×#3942C2212yes—
37C3×#3941C2212yes—
38#90975C2212yes—
39#90970C2212yes—
40#90969C2212yes—
41#90964C2212yes—
42#90953C2212yes—
43Dic3×#168C2212yes—
44#78878—51nomaximal, Hall
45C2×C5×C4⋊Q8—31no—
46#65811—31no—
47#65382—32no—
48#65378—32no—
49#65378—32no—
50#65377—32no—
51#65255—31no—
52#65255—31no—
53#65255—31no—
54#65255D311yescharacteristic, complemented
55C4×#681—31no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C5×Dic3—21no—
65C22×C5×Dic3D411yescharacteristic
66C22×C5×Dic3D411yescharacteristic
67C2×C5×Dic6—22no—
68C2×C5×Dic6—22no—
69C2×C5×Dic6—44no—
70C2×C3×C22⋊D5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×Dic10C2311yescharacteristic
76C2×#1202—21no—
77C2×#1202—21no—
78C3×C5×C4⋊C4—21no—
79C3×C5×C4⋊C4C2312yes—
80#6710—22no—
81C2×C3⋊#168C2312yes—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3C2312yes—
84C5×Dic3⋊C4—22no—
85C5×Dic3⋊C4—22no—
86C4×C5×Dic3D411yescharacteristic
87C4×C5×Dic3D411yescharacteristic
88C4×C5×Dic3C2311yescharacteristic
89C4×C5×Dic3C2311yescharacteristic
90C3×#681—22no—
91C2×C3×#168C2312yes—
92Dic3⋊Dic5—21no—
93Dic3⋊Dic5—21no—
94#6667—21no—
95#6667—21no—
96#6665—21no—
97#6665—21no—
98#5832—51no—
99C2×#888D511yescharacteristic, complemented
100C3×#417—51no—
101#5232—51no—
102#5133—51no—
103Dic3×M16—51no—
104#4966—51no—
105#4794—52no—
106#4792—52no—
107#4765—52no—
108#4760—52no—
109C22×C5×Q8—61no—
110C2×#709—31no—
111C2×#709C2×D311yescharacteristic
112C5×C4⋊Q8—32no—
113C5×C4⋊Q8—32no—
114C5×C4⋊Q8—61no—
115C5×C4⋊Q8—61no—
116C2×C5×C4⋊C4—31no—
117C2×C5×C4⋊C4—61no—
118C2×C5×C4⋊C4C2×D311yescharacteristic
119C2×C42×C5—31no—
120#4076—61no—
121#4076—61no—
122C2×#681—31no—
123C2×#681C2×D311yescharacteristic
124#4021—31no—
125#4021—31no—
126#4020—31no—
127C4×D20—61no—
128C4×D20—61no—
129#4015—31no—
130#3942—32no—
131#3942—32no—
132#3942—32no—
133#3942C2×D312yes—
134#3941—32no—
135#3941—32no—
136#3941—32no—
137#3941C2×D312yes—
138#3935—32no—
139C4×#168—32no—
140#3141—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×D15—21no—
143C22×C3×D5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—42no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5#4112yes—
148C2×C3×C4×C5#4112yes—
149C2×C3×C4×C5C2411yescharacteristic
150#1220—42no—
151C2×Dic15—21no—
152D60—21no—
153D60—21no—
154C4×D15—42no—
155Dic30—21no—
156Dic30—21no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—42no—
161C2×C5×Dic3C2×D411yescharacteristic
162C2×C5×Dic3C2×D411yescharacteristic
163C2×C5×Dic3C2×D411yescharacteristic
164C2×C5×Dic3C2×D411yescharacteristic
165C5×Dic6—44no—
166C5×Dic6—44no—
167C3×C22⋊D5—42no—
168C2×C3×Dic5—21no—
169C3×D20—21no—
170C3×D20—21no—
171C3×C4×D5—42no—
172C3×Dic10—21no—
173C3×Dic10—21no—
174#1202—42no—
175#1202—42no—
176C3⋊#168—22no—
177C3×#168—22no—
178C2×C3×#41—51no—
179C2×#235—51no—
180C22×Dic6—21no—
181C2×C3×M16—51no—
182C2×C3×C4⋊C4C2×D511yescharacteristic
183#947—51no—
184#944—51no—
185#940—51no—
186#939—101no—
187#939—101no—
188#936—51no—
189C4×#67—101no—
190C4×#67—101no—
191C2×C4⋊Dic3C2×D511yescharacteristic
192C2×Dic3⋊C4—21no—
193C2×C4×Dic3C2×D511yescharacteristic
194C2×#208—51no—
195#888—21no—
196#888—21no—
197#888C2×D512yes—
198#888C2×D512yes—
199C3×#103—52no—
200C3×#102—52no—
201#835—52no—
202#832—52no—
203#821—52no—
204#816—52no—
205#815—52no—
206C8×Dic3—52no—
207#810—52no—
208#809—52no—
209C2×C5×Q8—62no—
210C2×C5×Q8—62no—
211C2×C5×Q8—124no—
212C22×C4×C5—21no—
213C22×C4×C5—31no—
214C22×C4×C5—31no—
215C22×C4×C5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—21no—
218C2×C22⋊D5—61no—
219#709—22no—
220#709—22no—
221#709—62no—
222#709—62no—
223C2×D20—31no—
224C2×D20—61no—
225C2×D20—61no—
226C2×D20C22×D311yescharacteristic
227C2×C4×D5—21no—
228C2×C4×D5—61no—
229C2×Dic10—31no—
230C2×Dic10C22×D311yescharacteristic
231C5×C4⋊C4—21no—
232C5×C4⋊C4—32no—
233C5×C4⋊C4—62no—
234C5×C4⋊C4—62no—
235C5×C4⋊C4—61no—
236C5×C4⋊C4C22×D312yes—
237C42×C5—31no—
238C42×C5—31no—
239C42×C5—31no—
240C42×C5—31no—
241#685—61no—
242#685—61no—
243#685—61no—
244#685—61no—
245C4⋊Dic5—61no—
246C4⋊Dic5—61no—
247#681—22no—
248#681—62no—
249C2×#168—32no—
250C2×#168C22×D312yes—
251#532—151no—
252C2×C4⋊Q8—31no—
253#489—152no—
254#489—152no—
255#487—152no—
256#486—152no—
257#417—51no—
258#417—151no—
259#417—151no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5#12412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×D15—41no—
267C2×D15—41no—
268C2×D15—41no—
269C2×C3×D5—41no—
270C2×C3×D5—41no—
271C2×C3×D5—41no—
272C3×C4×C5—42no—
273C3×C4×C5#12412yes—
274C3×C4×C5C2×#4111yescharacteristic
275C3×C4×C5C2×#4111yescharacteristic
276Dic15—41no—
277C3×Dic5—41no—
278C5×Dic3—21no—
279C5×Dic3—21no—
280C5×Dic3—42no—
281C5×Dic3AGL(1,ℤ/8)12yes—
282C5×Dic3#13712yes—
283C3×#41—102no—
284C3×#41—102no—
285C2×C3×Q8—51no—
286C2×C3×D4—51no—
287C2×C3×D4—101no—
288C22×C3×C4—21no—
289C22×C3×C4—101no—
290C22×C3×C4C22×D511yescharacteristic
291C2×#67—101no—
292C2×#67—101no—
293C2×#67—101no—
294C22×Dic3—21no—
295C22×Dic3C22⋊D511yescharacteristic
296C22×Dic3C22⋊D511yescharacteristic
297#235—102no—
298#235—102no—
299C2×D12—51no—
300C2×C4×D3—101no—
301C2×Dic6—22no—
302C2×Dic6—22no—
303C2×Dic6—44no—
304C2×Dic6—51no—
305C3×M16—102no—
306C2×C3×C8—52no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C22×D512yes—
309#217—101no—
310#217—101no—
311(C2×D3)⋊C4—101no—
312(C2×D3)⋊C4—101no—
313C4⋊Dic3—21no—
314C4⋊Dic3C22×D512yes—
315Dic3⋊C4—22no—
316Dic3⋊C4—22no—
317Dic3⋊C4—101no—
318Dic3⋊C4—101no—
319C4×Dic3C22⋊D511yescharacteristic
320C4×Dic3C22⋊D511yescharacteristic
321C4×Dic3C22×D511yescharacteristic
322C4×Dic3C22×D511yescharacteristic
323#208—102no—
324C2×C3⋊C8—52no—
325C23×C5D3×D411yescharacteristic
326C22×D5—21no—
327C22×D5—61no—
328C5×Q8—124no—
329C5×Q8—124no—
330C2×C4×C5—22no—
331C2×C4×C5—31no—
332C2×C4×C5—31no—
333C2×C4×C5—31no—
334C2×C4×C5—31no—
335C2×C4×C5—42no—
336C2×C4×C5—62no—
337C2×C4×C5—62no—
338C2×C4×C5—62no—
339C2×C4×C5—122no—
340C2×C4×C5#23512yes—
341C2×C4×C5D3×D411yescharacteristic
342C2×C4×C5#23712yes—
343C2×C4×C5C23×D311yescharacteristic
344C22⋊D5—42no—
345C22⋊D5—122no—
346C2×Dic5—21no—
347C2×Dic5—61no—
348D20—21no—
349D20—21no—
350D20—61no—
351D20—61no—
352D20—122no—
353D20—122no—
354C4×D5—42no—
355C4×D5—122no—
356Dic10—21no—
357Dic10—21no—
358Dic10—61no—
359Dic10—61no—
360#168—22no—
361#168—62no—
362C2×#41—51no—
363C2×#41—151no—
364C22×Q8—61no—
365C2×M16—51no—
366C2×M16—151no—
367C4⋊Q8—32no—
368C4⋊Q8—32no—
369C4⋊Q8—61no—
370C4⋊Q8—61no—
371C4⋊Q8—151no—
372#127—151no—
373#124—151no—
374#124—151no—
375#121—301no—
376#121—301no—
377C4×D4—301no—
378C4×D4—301no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C42—31no—
383#103—52no—
384#103—152no—
385#103—152no—
386#103—152no—
387#102—52no—
388#102—152no—
389#102—152no—
390#102—152no—
391#97—152no—
392C4×C8—152no—
393C2×C3×C5—22no—
394C2×C3×C5C2×#12411yescharacteristic
395C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C3×C5C2×#13711yescharacteristic
397D15—81no—
398C3×D5—81no—
399C23×C3—101no—
400C23×C3C2×C22⋊D511yescharacteristic
401C22×D3—101no—
402C3×Q8—101no—
403C3×Q8—101no—
404C3×D4—101no—
405C3×D4—101no—
406C3×D4—202no—
407C2×C3×C4—22no—
408C2×C3×C4—42no—
409C2×C3×C4—101no—
410C2×C3×C4—202no—
411C2×C3×C4#71312yes—
412C2×C3×C4#71312yes—
413C2×C3×C4C2×C22⋊D511yescharacteristic
414C2×C3×C4C23×D511yescharacteristic
415#67—202no—
416#67—202no—
417#67—202no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—42no—
422C2×Dic3—101no—
423C2×Dic3C2×C22⋊D511yescharacteristic
424C2×Dic3C2×C22⋊D511yescharacteristic
425C2×Dic3C2×C22⋊D511yescharacteristic
426C2×Dic3C2×C22⋊D511yescharacteristic
427D12—101no—
428D12—101no—
429C4×D3—202no—
430Dic6—44no—
431Dic6—44no—
432Dic6—101no—
433Dic6—101no—
434C3×C8—102no—
435C3⋊C8—102no—
436C22×C5—21no—
437C22×C5—21no—
438C22×C5#88512yes—
439C22×C5C2×D3×D411yescharacteristic
440C2×D5—41no—
441C2×D5—41no—
442C2×D5—41no—
443C2×D5—121no—
444C2×D5—121no—
445C2×D5—121no—
446C4×C5—32no—
447C4×C5—32no—
448C4×C5—42no—
449C4×C5—61no—
450C4×C5—61no—
451C4×C5—122no—
452C4×C5#88512yes—
453C4×C5C2×#23511yescharacteristic
454C4×C5C2×#23711yescharacteristic
455Dic5—41no—
456Dic5—121no—
457#41—102no—
458#41—102no—
459#41—302no—
460#41—302no—
461C2×Q8—51no—
462C2×Q8—62no—
463C2×Q8—62no—
464C2×Q8—124no—
465C2×Q8—151no—
466C2×D4—51no—
467C2×D4—101no—
468C2×D4—151no—
469C2×D4—301no—
470C2×D4—301no—
471C2×D4—301no—
472C22×C4—21no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—61no—
476C22×C4—101no—
477C22×C4—301no—
478C22×C4C2×D3×D511yescharacteristic
479M16—102no—
480M16—302no—
481C2×C8—52no—
482C2×C8—152no—
483C4⋊C4—21no—
484C4⋊C4—32no—
485C4⋊C4—62no—
486C4⋊C4—62no—
487C4⋊C4—61no—
488C4⋊C4—301no—
489C4⋊C4—301no—
490C4⋊C4C2×D3×D512yes—
491C22⋊C4—301no—
492C22⋊C4—301no—
493C22⋊C4—301no—
494C22⋊C4—301no—
495C42—31no—
496C42—31no—
497C42—31no—
498C42—31no—
499C3×C5#314111yescharacteristic, complemented, Hall
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—201no—
503C22×C3—201no—
504C22×C3—201no—
505C22×C3#409312yes—
506C22×C3C22×C22⋊D511yescharacteristic
507C2×D3—201no—
508C2×D3—201no—
509C2×D3—201no—
510C3×C4—42no—
511C3×C4—201no—
512C3×C4#409312yes—
513C3×C4C2×#71311yescharacteristic
514C3×C4C2×#71311yescharacteristic
515Dic3—21no—
516Dic3—21no—
517Dic3—42no—
518Dic3—201no—
519Dic3#407812yes—
520Dic3#408812yes—
521C2×C5—22no—
522C2×C5C2×#88511yescharacteristic
523C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
524C2×C5D3×#13711yescharacteristic
525D5—81no—
526D5—241no—
527C23—101no—
528C23—301no—
529C23D3×C22⋊D511yescharacteristic
530Q8—101no—
531Q8—101no—
532Q8—124no—
533Q8—124no—
534Q8—301no—
535Q8—301no—
536D4—101no—
537D4—101no—
538D4—202no—
539D4—301no—
540D4—301no—
541D4—602no—
542D4—602no—
543D4—602no—
544C2×C4—22no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—31no—
549C2×C4—42no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—101no—
554C2×C4—122no—
555C2×C4—202no—
556C2×C4—301no—
557C2×C4—602no—
558C2×C4#676612yes—
559C2×C4#677312yes—
560C2×C4D3×C22⋊D511yescharacteristic
561C2×C4C22×D3×D511yescharacteristic
562C8—102no—
563C8—302no—
564C2×C3—22no—
565C2×C3—401no—
566C2×C3C2×#407811yescharacteristic
567C2×C3C2×#408811yescharacteristic
568C2×C3C2×#409311yescharacteristic
569D3—401no—
570C5#7887811yescharacteristic, complemented, Sylow
571C22—21no—
572C22—21no—
573C22—201no—
574C22—201no—
575C22—201no—
576C22—601no—
577C22—601no—
578C22—601no—
579C22#9145512yes—
580C22C2×D3×C22⋊D511yescharacteristic
581C4—32no—
582C4—32no—
583C4—42no—
584C4—61no—
585C4—61no—
586C4—122no—
587C4—201no—
588C4—601no—
589C4#9145512yes—
590C4C2×#676611yescharacteristic
591C4C2×#677311yescharacteristic
592C3#1061493011yescharacteristic, complemented, Sylow
593C2—22no—
594C2—401no—
595C2—1201no—
596C2C2×#9145511yescharacteristic
597C2D3×#407811yescharacteristic
598C2D3×#408811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#11754581C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#888C2semidirect
3. #11751067C2semidirect
4. C3×#65255C2semidirect
5. #11748394C2semidirect
6. #11748368C2semidirect
7. Dic3×#681C2semidirect
8. #11747422C2semidirect
9. #11747403C2semidirect
10. #11747380C2semidirect
11. #11747376C2semidirect
54. #65255D3semidirect
99. C2×#888D5semidirect
499. C3×C5#3141semidirect
570. C5#78878semidirect
592. C3#10614930semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8882
#117545812
#117510672
C3×#652552
#117483942
#117483682
Dic3×#6812
#117474222
#117474032
#117473802
#117473762
#106149303
#788785