Finite Group Databasebeta

← #14438613

Subgroups — #14438613

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
1#11756591C211yesmaximal, characteristic
2C2×#91470C211yesmaximal, characteristic, complemented
3C5×#5232C211yesmaximal, characteristic, complemented
4C3×#65521C211yesmaximal, characteristic, complemented
5#11749363C212yesmaximal, complemented
6#11749189C212yesmaximal, complemented
7#11749117C212yesmaximal, complemented
8#11748943C212yesmaximal, complemented
9#11748413C211yesmaximal, characteristic, complemented
10#11748394C211yesmaximal, characteristic, complemented
11#11748328C211yesmaximal, characteristic, complemented
12#10610609—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×#1204—21no—
16#91836C2211yescharacteristic
17#91833C2211yescharacteristic
18#91829C2211yescharacteristic
19#91828—21no—
20#91828—21no—
21#91825C2211yescharacteristic
22C4×#1220—21no—
23C4×#1220—21no—
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×#208C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29C2×#6669—21no—
30#91470—21no—
31#91470—21no—
32#91470C2212yes—
33#91470C2212yes—
34C5×#835C2212yes—
35C5×#832C2212yes—
36C3×#3967C2212yes—
37C3×#3964C2212yes—
38#90975C2212yes—
39#90974C2212yes—
40#90969C2212yes—
41#90968C2212yes—
42#90954C2212yes—
43#90951C2212yes—
44#78878—51nomaximal, Hall
45#66166—31no—
46C2×#4034—31no—
47C5×#417—31no—
48#65521D311yescharacteristic, complemented
49#65422—31no—
50M16×Dic5—31no—
51#65255—31no—
52#65084—32no—
53#65081—32no—
54#65054—32no—
55#65049—32no—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C2×#1220—21no—
65C2×#1220—21no—
66C22×Dic15D411yescharacteristic
67C22×Dic15D411yescharacteristic
68#6817—22no—
69#6817—22no—
70C2×D60C2311yescharacteristic
71C2×C4×D15—21no—
72C2×Dic30C2311yescharacteristic
73C22×C5×Dic3—21no—
74C22×C3×Dic5—21no—
75C2×#1204—22no—
76C2×#1204—22no—
77C2×#1204—44no—
78#6719—21no—
79#6719—21no—
80#6714—21no—
81#6714—21no—
82#6712—21no—
83#6712—21no—
84C4×Dic15D411yescharacteristic
85C4×Dic15D411yescharacteristic
86C4×Dic15C2311yescharacteristic
87C4×Dic15C2311yescharacteristic
88C5×C4⋊Dic3—21no—
89C5×C4⋊Dic3C2312yes—
90C5×#208—22no—
91C2×C5×C3⋊C8C2312yes—
92C3×C4⋊Dic5—21no—
93C3×C4⋊Dic5C2312yes—
94C3×#681—22no—
95C2×C3×#168C2312yes—
96#6669—22no—
97#6669—22no—
98#5832—51no—
99C2×#888—51no—
100C3×#417—51no—
101#5232D511yescharacteristic, complemented
102#5133—51no—
103Dic3×M16—51no—
104#4966—51no—
105#4794—52no—
106#4792—52no—
107#4765—52no—
108#4760—52no—
109C2×C5×#41C2×D311yescharacteristic
110C2×#709—31no—
111C22×Dic10—61no—
112C2×C5×M16—31no—
113C2×C5×C4⋊C4—31no—
114#4093—31no—
115#4090—31no—
116#4086—31no—
117#4085—61no—
118#4085—61no—
119#4082—31no—
120C4×C22⋊D5—61no—
121C4×C22⋊D5—61no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C2×#683—61no—
124C2×C4×Dic5—31no—
125C2×#681C2×D311yescharacteristic
126#4034—32no—
127#4034—32no—
128#4034—61no—
129#4034—61no—
130C5×#103—32no—
131C5×#102—32no—
132#3967C2×D312yes—
133#3964C2×D312yes—
134#3953—32no—
135#3948—32no—
136#3947—32no—
137C8×Dic5—32no—
138#3942—32no—
139#3941—32no—
140#3141—151noSylow
141C23×C3×C5—21no—
142C23×C3×C5C2×D411yescharacteristic
143C22×D15—21no—
144C3×C5×Q8—21no—
145C3×C5×Q8—21no—
146C3×C5×D4—21no—
147C3×C5×D4—21no—
148C3×C5×D4—42no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—42no—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5#4112yes—
154C2×C3×C4×C5C2411yescharacteristic
155#1220—42no—
156#1220—42no—
157#1220—42no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—21no—
161C2×Dic15C2×D411yescharacteristic
162C2×Dic15C2×D411yescharacteristic
163C2×Dic15C2×D411yescharacteristic
164C2×Dic15C2×D411yescharacteristic
165D60—21no—
166D60—21no—
167C4×D15—42no—
168Dic30—21no—
169Dic30—21no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—42no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—42no—
174#1204—44no—
175#1204—44no—
176C3×#168—22no—
177C5×C3⋊C8—22no—
178C2×C3×#41C2×D511yescharacteristic
179C2×#235—51no—
180C22×Dic6—101no—
181C2×C3×M16—51no—
182C2×C3×C4⋊C4—51no—
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—101no—
193C2×C4×Dic3—51no—
194C2×#208C2×D511yescharacteristic
195#888—52no—
196#888—52no—
197#888—101no—
198#888—101no—
199C3×#103—52no—
200C3×#102—52no—
201#835C2×D512yes—
202#832C2×D512yes—
203#821—52no—
204#816—52no—
205#815—52no—
206C8×Dic3—52no—
207#810—52no—
208#809—52no—
209C5×#41—22no—
210C5×#41—22no—
211C2×C5×Q8C22×D311yescharacteristic
212C2×C5×D4—21no—
213C2×C5×D4C22×D311yescharacteristic
214C22×C4×C5—21no—
215C22×C4×C5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—61no—
218C2×C22⋊D5—61no—
219C2×C22⋊D5—61no—
220C22×Dic5—21no—
221C22×Dic5—31no—
222C22×Dic5—31no—
223#709—62no—
224#709—62no—
225C2×D20—31no—
226C2×C4×D5—61no—
227C2×Dic10—31no—
228C2×Dic10—62no—
229C2×Dic10—62no—
230C2×Dic10—124no—
231C5×M16—62no—
232C2×C5×C8—32no—
233C5×C4⋊C4—32no—
234C5×C4⋊C4—61no—
235C22⋊Dic5—61no—
236C22⋊Dic5—61no—
237#685—61no—
238#685—61no—
239C4⋊Dic5—21no—
240C4⋊Dic5C22×D312yes—
241#683—62no—
242#683—62no—
243#683—61no—
244#683—61no—
245C4×Dic5—31no—
246C4×Dic5—31no—
247C4×Dic5—31no—
248C4×Dic5—31no—
249#681—22no—
250C2×#168C22×D312yes—
251#532—151no—
252C2×C4⋊Q8—151no—
253#489—152no—
254#489—152no—
255#487—152no—
256#486—152no—
257#417—31no—
258#417—51no—
259#417—151no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5—41no—
265C22×C3×C5—41no—
266C22×C3×C5—41no—
267C22×C3×C5#12412yes—
268C22×C3×C5C22×D411yescharacteristic
269C2×D15—41no—
270C2×D15—41no—
271C2×D15—41no—
272C3×C4×C5—41no—
273C3×C4×C5#12412yes—
274C3×C4×C5C2×#4111yescharacteristic
275C3×C4×C5C2×#4111yescharacteristic
276Dic15—21no—
277Dic15—21no—
278Dic15—41no—
279Dic15AGL(1,ℤ/8)12yes—
280Dic15#13712yes—
281C3×Dic5—42no—
282C5×Dic3—42no—
283C3×#41—22no—
284C3×#41—22no—
285C2×C3×Q8C22×D511yescharacteristic
286C2×C3×D4—21no—
287C2×C3×D4C22×D511yescharacteristic
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×Dic3—51no—
296C22×Dic3—51no—
297#235—102no—
298#235—102no—
299C2×D12—51no—
300C2×C4×D3—101no—
301C2×Dic6—51no—
302C2×Dic6—102no—
303C2×Dic6—102no—
304C2×Dic6—204no—
305C3×M16—102no—
306C2×C3×C8—52no—
307C3×C4⋊C4—52no—
308C3×C4⋊C4—101no—
309#217—101no—
310#217—101no—
311(C2×D3)⋊C4—101no—
312(C2×D3)⋊C4—101no—
313C4⋊Dic3—21no—
314C4⋊Dic3C22×D512yes—
315Dic3⋊C4—102no—
316Dic3⋊C4—102no—
317Dic3⋊C4—101no—
318Dic3⋊C4—101no—
319C4×Dic3—51no—
320C4×Dic3—51no—
321C4×Dic3—51no—
322C4×Dic3—51no—
323#208—22no—
324C2×C3⋊C8C22×D512yes—
325C23×C5—21no—
326C23×C5D3×D411yescharacteristic
327C22×D5—61no—
328C5×Q8—21no—
329C5×Q8—21no—
330C5×D4—21no—
331C5×D4—21no—
332C5×D4—42no—
333C2×C4×C5—21no—
334C2×C4×C5—42no—
335C2×C4×C5—62no—
336C2×C4×C5—122no—
337C2×C4×C5#23512yes—
338C2×C4×C5D3×D411yescharacteristic
339C2×C4×C5#23712yes—
340C2×C4×C5C23×D311yescharacteristic
341C22⋊D5—122no—
342C22⋊D5—122no—
343C22⋊D5—122no—
344C2×Dic5—22no—
345C2×Dic5—31no—
346C2×Dic5—31no—
347C2×Dic5—31no—
348C2×Dic5—31no—
349C2×Dic5—42no—
350C2×Dic5—62no—
351C2×Dic5—62no—
352C2×Dic5—61no—
353D20—61no—
354D20—61no—
355C4×D5—122no—
356Dic10—61no—
357Dic10—61no—
358Dic10—124no—
359Dic10—124no—
360C5×C8—62no—
361#168—22no—
362C2×#41—151no—
363C2×#41D3×D511yescharacteristic
364C22×Q8—301no—
365C2×M16—31no—
366C2×M16—51no—
367C4⋊Q8—152no—
368C4⋊Q8—152no—
369C4⋊Q8—151no—
370C4⋊Q8—301no—
371C4⋊Q8—301no—
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—51no—
381C2×C4⋊C4—301no—
382C2×C42—151no—
383#103—32no—
384#103—52no—
385#103—152no—
386#103—152no—
387#102—32no—
388#102—52no—
389#102—152no—
390#102—152no—
391#97—152no—
392C4×C8—152no—
393C2×C3×C5—22no—
394C2×C3×C5—81no—
395C2×C3×C5C2×#12411yescharacteristic
396C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C3×C5C2×#13711yescharacteristic
398D15—81no—
399C23×C3—21no—
400C23×C3D4×D511yescharacteristic
401C22×D3—101no—
402C3×Q8—21no—
403C3×Q8—21no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—42no—
407C2×C3×C4—21no—
408C2×C3×C4—42no—
409C2×C3×C4—102no—
410C2×C3×C4—202no—
411C2×C3×C4#70912yes—
412C2×C3×C4D4×D511yescharacteristic
413C2×C3×C4#71112yes—
414C2×C3×C4C23×D511yescharacteristic
415#67—202no—
416#67—202no—
417#67—202no—
418C2×Dic3—22no—
419C2×Dic3—42no—
420C2×Dic3—51no—
421C2×Dic3—51no—
422C2×Dic3—51no—
423C2×Dic3—51no—
424C2×Dic3—102no—
425C2×Dic3—102no—
426C2×Dic3—101no—
427D12—101no—
428D12—101no—
429C4×D3—202no—
430Dic6—101no—
431Dic6—101no—
432Dic6—204no—
433Dic6—204no—
434C3×C8—102no—
435C3⋊C8—22no—
436C22×C5—21no—
437C22×C5—21no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5#88512yes—
442C22×C5C2×D3×D411yescharacteristic
443C2×D5—121no—
444C2×D5—121no—
445C2×D5—121no—
446C4×C5—41no—
447C4×C5—122no—
448C4×C5#88512yes—
449C4×C5C2×#23511yescharacteristic
450C4×C5C2×#23711yescharacteristic
451Dic5—32no—
452Dic5—32no—
453Dic5—42no—
454Dic5—61no—
455Dic5—61no—
456Dic5—121no—
457#41—22no—
458#41—22no—
459#41—302no—
460#41—302no—
461C2×Q8—151no—
462C2×Q8—302no—
463C2×Q8—302no—
464C2×Q8—604no—
465C2×Q8C2×D3×D511yescharacteristic
466C2×D4—21no—
467C2×D4—151no—
468C2×D4—301no—
469C2×D4—301no—
470C2×D4—301no—
471C2×D4C2×D3×D511yescharacteristic
472C22×C4—21no—
473C22×C4—61no—
474C22×C4—101no—
475C22×C4—151no—
476C22×C4—151no—
477C22×C4—301no—
478C22×C4C2×D3×D511yescharacteristic
479M16—62no—
480M16—102no—
481C2×C8—32no—
482C2×C8—52no—
483C4⋊C4—32no—
484C4⋊C4—52no—
485C4⋊C4—61no—
486C4⋊C4—101no—
487C4⋊C4—301no—
488C4⋊C4—301no—
489C4⋊C4—302no—
490C4⋊C4—302no—
491C22⋊C4—301no—
492C22⋊C4—301no—
493C22⋊C4—301no—
494C22⋊C4—301no—
495C42—151no—
496C42—151no—
497C42—151no—
498C42—151no—
499C3×C5#314111yescharacteristic, complemented, Hall
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3#403112yes—
506C22×C3C2×D4×D511yescharacteristic
507C2×D3—201no—
508C2×D3—201no—
509C2×D3—201no—
510C3×C4—41no—
511C3×C4—202no—
512C3×C4#403112yes—
513C3×C4C2×#70911yescharacteristic
514C3×C4C2×#71111yescharacteristic
515Dic3—42no—
516Dic3—52no—
517Dic3—52no—
518Dic3—101no—
519Dic3—101no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5C2×#88511yescharacteristic
524C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
525C2×C5D3×#13711yescharacteristic
526D5—241no—
527C23—21no—
528C23—301no—
529C23#679011yescharacteristic
530Q8—21no—
531Q8—21no—
532Q8—301no—
533Q8—301no—
534Q8—604no—
535Q8—604no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—301no—
540D4—301no—
541D4—602no—
542D4—602no—
543D4—602no—
544C2×C4—21no—
545C2×C4—42no—
546C2×C4—62no—
547C2×C4—102no—
548C2×C4—122no—
549C2×C4—151no—
550C2×C4—151no—
551C2×C4—151no—
552C2×C4—151no—
553C2×C4—202no—
554C2×C4—302no—
555C2×C4—302no—
556C2×C4—301no—
557C2×C4—602no—
558C2×C4#677912yes—
559C2×C4#678212yes—
560C2×C4#679011yescharacteristic
561C2×C4C22×D3×D511yescharacteristic
562C8—62no—
563C8—102no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3C2×#403111yescharacteristic
567C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
568C2×C3D5×#13711yescharacteristic
569D3—401no—
570C5#7887811yescharacteristic, complemented, Sylow
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—601no—
577C22—601no—
578C22—601no—
579C22#9152612yes—
580C22C2×#679011yescharacteristic
581C4—41no—
582C4—122no—
583C4—152no—
584C4—152no—
585C4—202no—
586C4—301no—
587C4—301no—
588C4—601no—
589C4#9152612yes—
590C4C2×#677911yescharacteristic
591C4C2×#678211yescharacteristic
592C3#1061060911yescharacteristic, complemented, Sylow
593C2—22no—
594C2—81no—
595C2—1201no—
596C2#1175532711yescharacteristic
597C2#1175534211yescharacteristic
598C2C2×#9152611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radical#11756591C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91470C2semidirect
3. C5×#5232C2semidirect
4. C3×#65521C2semidirect
5. #11749363C2semidirect
6. #11749189C2semidirect
7. #11749117C2semidirect
8. #11748943C2semidirect
9. #11748413C2semidirect
10. #11748394C2semidirect
11. #11748328C2semidirect
48. #65521D3semidirect
101. #5232D5semidirect
499. C3×C5#3141semidirect
570. C5#78878semidirect
592. C3#10610609semidirect

Maximal subgroups

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

subgroupindex
#117565912
C2×#914702
C5×#52322
C3×#655212
#117493632
#117491892
#117491172
#117489432
#117484132
#117483942
#117483282
#106106093
#788785