Finite Group Databasebeta

← #14412752

Subgroups — #14412752

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92004C211yesmaximal, characteristic
2C2×#91790C211yesmaximal, characteristic, complemented
3#11754496C211yesmaximal, characteristic, complemented
4C5×#5113C211yesmaximal, characteristic, complemented
5C2×C3×#3948C211yesmaximal, characteristic, complemented
6#11748399C211yesmaximal, characteristic, complemented
7#11748384C211yesmaximal, characteristic, complemented
8#11748146C212yesmaximal, complemented
9#11748145C212yesmaximal, complemented
10#11747644C212yesmaximal, complemented
11#11747609C212yesmaximal, complemented
12#10610563—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C2×#6782—22no—
17C2×D15⋊Q8C2212yes—
18C2×#6769—21no—
19#92004—24no—
20#92004C418yescomplemented
21C2×#6768C2212yes—
22C2×D3×Dic10—21no—
23C22×C3×C5×C8C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25#91790—24no—
26C2×#6705C2212yes—
27C2×C8×D15C2212yes—
28C5×#926C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30#91552—22no—
31#91437C2212yes—
32#91428—21no—
33#91347C2212yes—
34#91340—21no—
35C5×#821C2211yescharacteristic
36C5×#821C2211yescharacteristic
37C5×#816C2211yescharacteristic
38C5×#816C2211yescharacteristic
39C3×#3948C2212yes—
40C3×#3948C2212yes—
41#90972C2212yes—
42#90970C2212yes—
43#90970C2212yes—
44#90966C2212yes—
45#78790—51nomaximal, Hall
46C2×#4150—31no—
47C2×#4047—31no—
48#65857—31no—
49C5×#416—31no—
50#65521—31no—
51C2×#3948D311yescharacteristic, complemented
52#65293—31no—
53#65091—32no—
54D5×#103—32no—
55#65061—32no—
56#65060—32no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220D412yes—
59#6817C2×C414yes—
60#6817D414yes—
61C2×D60D411yescharacteristic
62C2×C4×D15C2312yes—
63C2×Dic30D411yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235C2×C414yescomplemented
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5—21no—
71C22×C3×Dic5—21no—
72C2×C3×Dic10—21no—
73C2×C3×Dic10—22no—
74C2×C3×Dic10C2×C414yescomplemented
75C2×C3×Dic10C2312yes—
76C2×#1204—22no—
77C2×#1203—22no—
78C2×#1200—22no—
79C2×#1200—22no—
80#6782—216no—
81C2×D3×Dic5—22no—
82D15⋊Q8—24no—
83D15⋊Q8C2×C418yescomplemented
84#6769—28no—
85#6768—24no—
86#6768C2×C418yescomplemented
87D3×Dic10—28no—
88C2×C3×C5×C8—22no—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91#6710—22no—
92C2×C3⋊#168C2312yes—
93#6705—24no—
94C8×D15—24no—
95C5×#217—21no—
96C5×C4⋊Dic3C2311yescharacteristic
97C5×C4⋊Dic3C2311yescharacteristic
98C4×C5×Dic3—21no—
99C3×C4⋊Dic5—21no—
100C3×C4⋊Dic5C2312yes—
101#6669—22no—
102#6667—22no—
103Dic3×Dic5—22no—
104C2×#1007—51no—
105C2×#901—51no—
106#5504—51no—
107C2×C3×#103—51no—
108#5225—51no—
109#5113D511yescharacteristic, complemented
110#4966—51no—
111#4804—52no—
112#4803—52no—
113#4802—52no—
114D3×#103—52no—
115C2×C5×#41—31no—
116#4150—38no—
117#4150—64no—
118C2×Q8×D5—32no—
119C2×#711—32no—
120C2×#711—62no—
121C2×#709—31no—
122C2×#709—61no—
123C22×Dic10—61no—
124C22×Dic10C2×D311yescharacteristic
125C22×C5×C8C2×D311yescharacteristic
126C5×#117—31no—
127C2×C4⋊Dic5C2×D311yescharacteristic
128C2×#681—31no—
129#4047—64no—
130C2×#676—32no—
131C2×C8×D5—32no—
132#4038—32no—
133D5×C4⋊C4—32no—
134#4027—62no—
135C4×D20—61no—
136C4×Dic10—61no—
137C5×#103—31no—
138C5×#103—31no—
139C5×#102—31no—
140C5×#102—31no—
141#3967—32no—
142#3964—32no—
143#3948C2×D312yes—
144#3948C2×D312yes—
145#3942—32no—
146#3942—32no—
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15C2×D412yes—
150C22×C5×D3—21no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2411yescharacteristic
155#1220C22⋊C418yes—
156C2×Dic15C2×D412yes—
157D60C22⋊C414yes—
158C4×D15C22×C414yes—
159C4×D15C2×D414yes—
160Dic30C22⋊C414yes—
161C5×#67—24no—
162C2×C5×Dic3—21no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C5×D12—21no—
166C5×D12C22×C412yes—
167C4×C5×D3—24no—
168C5×Dic6—21no—
169C5×Dic6C22×C412yes—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—81no—
174C3×Dic10—24no—
175C3×Dic10—22no—
176C3×Dic10C22×C414yes—
177#1204—28no—
178#1203—28no—
179#1200—28no—
180#1200—82no—
181D3×Dic5—28no—
182C3×C5×C8—21no—
183C3×C5×C8—21no—
184C3⋊#168—22no—
185C22×C3×Q8—51no—
186#1007—58no—
187#1007—104no—
188C2×#239—52no—
189C2×#239—101no—
190C2×D3×Q8—52no—
191C2×D3×Q8—101no—
192C2×#235—51no—
193C2×#235—102no—
194C2×#235C2×D511yescharacteristic
195C22×C3×C8C2×D511yescharacteristic
196C2×C3×C4⋊C4—51no—
197C4×#67—102no—
198#926C2×D511yescharacteristic
199C2×#208—51no—
200#901—104no—
201C2×ΓL(1,𝔽25)—52no—
202C2×D3×C8—52no—
203#893—101no—
204#892—52no—
205D3×C4⋊C4—52no—
206#887—101no—
207C3×#103—52no—
208C3×#103—52no—
209#835—52no—
210#835—52no—
211#821C2×D511yescharacteristic
212#821C2×D511yescharacteristic
213#816C2×D511yescharacteristic
214#816C2×D511yescharacteristic
215#810—52no—
216#809—52no—
217C5×#41—34no—
218C5×#41—62no—
219C2×C5×Q8—31no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—32no—
225C2×C22⋊D5—62no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—62no—
229Q8×D5—38no—
230Q8×D5—64no—
231#711—38no—
232#711—64no—
233#711—616no—
234#709—34no—
235#709—34no—
236#709—68no—
237C2×D20—31no—
238C2×C4×D5—32no—
239C2×C4×D5—62no—
240C2×C4×D5—62no—
241C2×Dic10—21no—
242C2×Dic10—22no—
243C2×Dic10—31no—
244C2×Dic10—68no—
245C2×Dic10—62no—
246C2×Dic10C4×D314yescomplemented
247C2×Dic10C22×D312yes—
248C2×C5×C8—22no—
249C2×C5×C8C22×D311yescharacteristic
250C2×C5×C8C22×D311yescharacteristic
251C5×C4⋊C4—31no—
252C5×C4⋊C4—31no—
253C5×C22⋊C4—61no—
254C42×C5—61no—
255#685—62no—
256C4⋊Dic5—21no—
257C4⋊Dic5C22×D312yes—
258#683—62no—
259C4×Dic5—62no—
260#681—62no—
261C2×#168—32no—
262#676—64no—
263C8×D5—64no—
264C2×2−1+4—151no—
265C2×#131—151no—
266#520—151no—
267#419—152no—
268#419—151no—
269#417—152no—
270#417—151no—
271#416—31no—
272#416—152no—
273C2×#103—51no—
274C2×#103—152no—
275C22×C3×C5—21no—
276C22×C3×C5—21no—
277C22×C3×C5C2×C22⋊C412yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×D15—22no—
280C2×D15—22no—
281C2×D15C2×C22⋊C414yes—
282C2×C5×D3—22no—
283C2×C5×D3—41no—
284C2×C5×D3—41no—
285C3×C4×C5C2×C22⋊C412yes—
286C3×C4×C5C23×C411yescharacteristic
287C3×C4×C5C22×D411yescharacteristic
288Dic15C2×C22⋊C414yes—
289C3×Dic5—24no—
290C3×Dic5—42no—
291C5×Dic3—22no—
292C5×Dic3—41no—
293C5×Dic3—41no—
294C2×C3×Q8—54no—
295C2×C3×Q8—52no—
296C2×C3×Q8—101no—
297C2×C3×Q8—102no—
298C22×C3×C4—101no—
299C22×C3×C4—101no—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—21no—
302C2×#67—52no—
303#239—58no—
304#239—108no—
305#239—104no—
306D3×Q8—58no—
307D3×Q8—104no—
308D3×Q8—108no—
309#235—22no—
310#235—54no—
311#235—54no—
312#235—1016no—
313#235C4×D514yescomplemented
314C2×D12—51no—
315C2×D12—102no—
316C2×D12C22×D511yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—52no—
319C2×C4×D3—102no—
320C2×C4×D3—102no—
321C2×C4×D3—102no—
322C2×Dic6—51no—
323C2×Dic6—102no—
324C2×Dic6C22×D511yescharacteristic
325C2×C3×C8—22no—
326C2×C3×C8C22×D511yescharacteristic
327C2×C3×C8C22×D511yescharacteristic
328C3×C4⋊C4—52no—
329C3×C4⋊C4—101no—
330#217—21no—
331(C2×D3)⋊C4—102no—
332C4⋊Dic3C22×D511yescharacteristic
333C4⋊Dic3C22×D511yescharacteristic
334Dic3⋊C4—102no—
335C4×Dic3—21no—
336C4×Dic3—102no—
337#208—102no—
338C2×C3⋊C8—52no—
339ΓL(1,𝔽25)—104no—
340D3×C8—104no—
341C23×C5—61no—
342C23×C5D3×D411yescharacteristic
343C22×D5—32no—
344C5×Q8—32no—
345C5×Q8—61no—
346C5×D4—32no—
347C5×D4—64no—
348C5×D4—61no—
349C2×C4×C5—61no—
350C2×C4×C5—64no—
351C2×C4×C5—61no—
352C2×C4×C5—61no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5D3×D412yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—38no—
358C22⋊D5—68no—
359C2×Dic5—24no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—32no—
363C2×Dic5—68no—
364C2×Dic5—81no—
365D20—34no—
366C4×D5—34no—
367C4×D5—34no—
368C4×D5—68no—
369C4×D5—242no—
370Dic10—24no—
371Dic10—22no—
372Dic10—34no—
373Dic10—68no—
374Dic10C2×C4×D314yes—
375C5×C8—21no—
376C5×C8—21no—
377#168—62no—
3782−1+4—158no—
3792−1+4—304no—
380C2×#41—31no—
381C2×#41—151no—
382C2×#41—152no—
383C2×#41—301no—
384C2×#41—302no—
385C22×Q8—51no—
386C22×Q8—152no—
387C22×Q8—301no—
388#131—304no—
389C2×M16—151no—
390C2×M16—152no—
391C22×C8—152no—
392C22×C8D3×D511yescharacteristic
393C4×Q8—301no—
394C4×D4—301no—
395C4×D4—302no—
396#117—31no—
397#117—152no—
398C2×C4⋊C4—51no—
399C2×C4⋊C4—152no—
400#103—31no—
401#103—31no—
402#103—52no—
403#103—52no—
404#103—152no—
405#103—152no—
406#103—152no—
407#102—31no—
408#102—31no—
409#102—152no—
410C2×C3×C5—22no—
411C2×C3×C5C22×C22⋊C411yescharacteristic
412C2×C3×C5#57711yescharacteristic
413C2×C3×C5#57811yescharacteristic
414D15—24no—
415C5×D3—42no—
416C23×C3D4×D511yescharacteristic
417C22×D3—21no—
418C22×D3—52no—
419C3×Q8—54no—
420C3×Q8—102no—
421C3×Q8—104no—
422C2×C3×C4—102no—
423C2×C3×C4—104no—
424C2×C3×C4—102no—
425C2×C3×C4—401no—
426C2×C3×C4C2×C4×D512yes—
427C2×C3×C4D4×D511yescharacteristic
428C2×C3×C4D4×D512yes—
429C2×C3×C4C23×D511yescharacteristic
430#67—24no—
431#67—58no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—52no—
436D12—21no—
437D12—54no—
438D12—108no—
439D12C2×C4×D512yes—
440C4×D3—24no—
441C4×D3—54no—
442C4×D3—54no—
443C4×D3—108no—
444C4×D3—108no—
445C4×D3—402no—
446Dic6—21no—
447Dic6—54no—
448Dic6—108no—
449Dic6C2×C4×D512yes—
450C3×C8—21no—
451C3×C8—21no—
452C3⋊C8—102no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5—62no—
456C22×C5—121no—
457C22×C5—121no—
458C22×C5D3×C22⋊C412yes—
459C22×C5C2×D3×D411yescharacteristic
460C2×D5—34no—
461C2×D5—62no—
462C2×D5—62no—
463C4×C5—62no—
464C4×C5—121no—
465C4×C5—121no—
466C4×C5D3×C22⋊C412yes—
467C4×C5C22×C4×D311yescharacteristic
468C4×C5C2×D3×D411yescharacteristic
469Dic5—24no—
470Dic5—34no—
471Dic5—42no—
472#41—34no—
473#41—62no—
474#41—154no—
475#41—154no—
476#41—158no—
477#41—308no—
478#41—3016no—
479#41—304no—
480C2×Q8—31no—
481C2×Q8—54no—
482C2×Q8—52no—
483C2×Q8—101no—
484C2×Q8—102no—
485C2×Q8—151no—
486C2×Q8—158no—
487C2×Q8—302no—
488C2×Q8—308no—
489C2×Q8—304no—
490C2×D4—31no—
491C2×D4—61no—
492C2×D4—152no—
493C2×D4—151no—
494C2×D4—302no—
495C22×C4—61no—
496C22×C4—101no—
497C22×C4—101no—
498C22×C4—152no—
499C22×C4—302no—
500C22×C4—302no—
501C22×C4—302no—
502C22×C4C2×D3×D511yescharacteristic
503M16—304no—
504M16—302no—
505C2×C8—22no—
506C2×C8—152no—
507C2×C8—304no—
508C2×C8C2×D3×D511yescharacteristic
509C2×C8C2×D3×D511yescharacteristic
510C4⋊C4—31no—
511C4⋊C4—31no—
512C4⋊C4—52no—
513C4⋊C4—101no—
514C4⋊C4—302no—
515C22⋊C4—61no—
516C22⋊C4—302no—
517C42—61no—
518C42—302no—
519C3×C5#289811yescharacteristic, complemented, Hall
520C22×C3—21no—
521C22×C3—21no—
522C22×C3D5×C22⋊C412yes—
523C22×C3C2×D4×D511yescharacteristic
524C2×D3—22no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—54no—
528C2×D3—102no—
529C2×D3—102no—
530C3×C4—104no—
531C3×C4—202no—
532C3×C4D5×C22⋊C412yes—
533C3×C4C22×C4×D511yescharacteristic
534C3×C4C2×D4×D511yescharacteristic
535Dic3—22no—
536Dic3—41no—
537Dic3—41no—
538Dic3—54no—
539C2×C5—22no—
540C2×C5—122no—
541C2×C5C2×D3×C22⋊C411yescharacteristic
542C2×C5#576211yescharacteristic
543C2×C5#576611yescharacteristic
544D5—64no—
545C23—61no—
546C23—152no—
547C23#677711yescharacteristic
548Q8—32no—
549Q8—54no—
550Q8—61no—
551Q8—104no—
552Q8—102no—
553Q8—154no—
554Q8—308no—
555D4—32no—
556D4—64no—
557D4—61no—
558D4—158no—
559D4—154no—
560D4—308no—
561C2×C4—61no—
562C2×C4—64no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—104no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—152no—
569C2×C4—154no—
570C2×C4—154no—
571C2×C4—308no—
572C2×C4—308no—
573C2×C4—401no—
574C2×C4—1202no—
575C2×C4C4×D3×D512yes—
576C2×C4#677711yescharacteristic
577C2×C4#679012yes—
578C2×C4C22×D3×D511yescharacteristic
579C8—21no—
580C8—21no—
581C8—302no—
582C2×C3—22no—
583C2×C3C2×D5×C22⋊C411yescharacteristic
584C2×C3#6610411yescharacteristic
585C2×C3#6610511yescharacteristic
586D3—42no—
587D3—104no—
588C5#7879011yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—62no—
592C22—121no—
593C22—121no—
594C22—154no—
595C22—302no—
596C22—302no—
597C22#9147312yes—
598C22C2×#677711yescharacteristic
599C4—62no—
600C4—104no—
601C4—121no—
602C4—121no—
603C4—154no—
604C4—202no—
605C4#9147312yes—
606C4C2×C4×D3×D511yescharacteristic
607C4C2×#679011yescharacteristic
608C3#1061056311yescharacteristic, complemented, Sylow
609C2—22no—
610C2—122no—
611C2—304no—
612C2#1175398011yescharacteristic
613C2#1175401111yescharacteristic
614C2C2×#9147311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92004C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#91790C2semidirect
3. #11754496C2semidirect
4. C5×#5113C2semidirect
5. C2×C3×#3948C2semidirect
6. #11748399C2semidirect
7. #11748384C2semidirect
8. #11748146C2semidirect
9. #11748145C2semidirect
10. #11747644C2semidirect
11. #11747609C2semidirect
20. #92004C4semidirect
51. C2×#3948D3semidirect
66. C5×#235C2×C4semidirect
74. C2×C3×Dic10C2×C4semidirect
83. D15⋊Q8C2×C4semidirect
86. #6768C2×C4semidirect
109. #5113D5semidirect
246. C2×Dic10C4×D3semidirect
313. #235C4×D5semidirect
519. C3×C5#2898semidirect
588. C5#78790semidirect
608. C3#10610563semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
C2×#917902
#117544962
C5×#51132
C2×C3×#39482
#117483992
#117483842
#117481462
#117481452
#117476442
#117476092
#106105633
#787905