Finite Group Databasebeta

← #14412739

Subgroups — #14412739

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×#92001C211yesmaximal, characteristic
2C5×#5504C211yesmaximal, characteristic, complemented
3C2×#91288C211yesmaximal, characteristic, complemented
4C2×#91094C211yesmaximal, characteristic, complemented
5C3×#65255C211yesmaximal, characteristic, complemented
6#11748417C211yesmaximal, characteristic, complemented
7#11748364C211yesmaximal, characteristic, complemented
8#11747503C212yesmaximal, complemented
9#11747502C212yesmaximal, complemented
10#11747489C212yesmaximal, complemented
11D3×#3942C212yesmaximal, complemented
12#10614301—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C2×#6780—22no—
17C2×#6772—21no—
18C2×D3×Dic10C2212yes—
19#92001—24no—
20#92001C418yescomplemented
21C2×#6765C2212yes—
22C2×D5×Dic6—21no—
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25C4×C5×#67—22no—
26C5×#926C2211yescharacteristic
27C5×#893—21no—
28C5×#892C2212yes—
29C5×D3×C4⋊C4C2212yes—
30C5×#887—21no—
31C2×C3×#681C2211yescharacteristic
32C2×#6650C2212yes—
33#91288—24no—
34C2×D3×#168C2212yes—
35#91094C2212yes—
36#91094C2212yes—
37C3×#3942C2212yes—
38C3×#3941C2212yes—
39#90975C2212yes—
40#90975C2212yes—
41#90970C2211yescharacteristic
42#90970C2211yescharacteristic
43#90964C2211yescharacteristic
44#90964C2211yescharacteristic
45#78883—51nomaximal, Hall
46C2×#4150—31no—
47C5×#520—31no—
48C2×#4094—31no—
49#65293—31no—
50#65293—32no—
51#65291—32no—
52#65291—31no—
53C2×#3942—32no—
54C2×#3942—31no—
55#65255—32no—
56#65255D311yescharacteristic, complemented
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C2×Dic30—21no—
61C2×Dic30—22no—
62C2×Dic30C2×C414yescomplemented
63C2×Dic30C2312yes—
64C2×C5×#67D412yes—
65C5×#235C2×C414yes—
66C5×#235D414yes—
67C2×C5×D12D411yescharacteristic
68C2×C4×C5×D3—22no—
69C2×C4×C5×D3C2312yes—
70C2×C5×Dic6D411yescharacteristic
71C2×C3×C22⋊D5—21no—
72C3×#709—22no—
73C3×#709C2×C414yescomplemented
74C2×C3×D20C2311yescharacteristic
75C2×C3×C4×D5—21no—
76C2×C3×Dic10C2311yescharacteristic
77C2×#1204—22no—
78C2×#1201—22no—
79C2×D3×Dic5—22no—
80#6780—216no—
81C2×D5×Dic3—22no—
82#6772—28no—
83D3×Dic10—24no—
84D3×Dic10C2×C418yescomplemented
85#6765—24no—
86#6765C2×C418yescomplemented
87D5×Dic6—28no—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2312yes—
90C2×C3⋊#168—22no—
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93C5×#217—21no—
94C5×(C2×D3)⋊C4—22no—
95C5×C4⋊Dic3C2311yescharacteristic
96C5×C4⋊Dic3C2311yescharacteristic
97C5×Dic3⋊C4—22no—
98C4×C5×Dic3—21no—
99C4×C5×Dic3—22no—
100C3×#681—22no—
101C2×C3×#168C2312yes—
102#6650—24no—
103D3×#168—24no—
104C2×#1010—51no—
105C2×#907—51no—
106#5504D511yescharacteristic, complemented
107C3×#417—51no—
108#5233—51no—
109#5120—51no—
110C2×#810—51no—
111#4802—52no—
112D3×#103—52no—
113#4772—52no—
114#4771—52no—
115C2×C5×#41—31no—
116#4150—38no—
117#4150—64no—
118C2×Q8×D5—61no—
119C2×#711—61no—
120C2×#711—62no—
121C2×#709—32no—
122C2×#709C2×D311yescharacteristic
123C22×Dic10—31no—
124C22×Dic10—32no—
125C4×C5×Q8—61no—
126C4×C5×D4—61no—
127C4×C5×D4—62no—
128C5×#117—31no—
129C5×#117—32no—
130C2×C5×C4⋊C4—32no—
131C2×C5×C4⋊C4C2×D311yescharacteristic
132#4094—64no—
133C2×#681—32no—
134C2×#681C2×D311yescharacteristic
135C22×#168—31no—
136C22×#168—32no—
137#3942—31no—
138#3942—31no—
139#3942—32no—
140#3942—32no—
141#3942—32no—
142#3942—32no—
143#3942C2×D312yes—
144#3941—31no—
145#3941—31no—
146#3941C2×D312yes—
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×C5×D3C2×D412yes—
150C22×C3×D5—21no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—81no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—24no—
158C2×Dic15—22no—
159Dic30—24no—
160Dic30—22no—
161Dic30C22×C414yes—
162C5×#67C22⋊C418yes—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3C2×D412yes—
166C5×D12C22⋊C414yes—
167C4×C5×D3—82no—
168C4×C5×D3C22×C414yes—
169C4×C5×D3C2×D414yes—
170C5×Dic6C22⋊C414yes—
171C3×C22⋊D5—24no—
172C2×C3×Dic5—21no—
173C3×D20—21no—
174C3×D20C22×C412yes—
175C3×C4×D5—24no—
176C3×Dic10—21no—
177C3×Dic10C22×C412yes—
178#1204—28no—
179#1201—28no—
180D3×Dic5—28no—
181D5×Dic3—28no—
182C3⋊#168—21no—
183C3⋊#168—21no—
184C3×#168—22no—
185C2×C3×#41—51no—
186#1010—58no—
187#1010—104no—
188C2×D3×Q8—52no—
189C2×#237—52no—
190C2×#237—102no—
191C2×#235—101no—
192C2×#235C2×D511yescharacteristic
193C22×Dic6—51no—
194C22×Dic6—101no—
195C2×C3×M16—51no—
196C2×C3×C4⋊C4C2×D511yescharacteristic
197C4×#67—22no—
198#926C2×D511yescharacteristic
199C22×C3⋊C8—51no—
200#907—104no—
201C2×ΓL(1,𝔽25)—52no—
202C2×D3×C8—52no—
203#893—21no—
204#892C2×D512yes—
205D3×C4⋊C4C2×D512yes—
206#887—21no—
207C3×#103—52no—
208C3×#102—52no—
209#835—51no—
210#835—51no—
211#832—51no—
212#832—51no—
213#816—52no—
214#816—52no—
215#810—52no—
216#810—52no—
217C5×#41—34no—
218C5×#41—34no—
219C2×C5×Q8—31no—
220C2×C5×D4—32no—
221C2×C5×D4—31no—
222C22×C4×C5—21no—
223C22×C4×C5—32no—
224C22×C4×C5—62no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—21no—
227C2×C22⋊D5—62no—
228C22×Dic5—62no—
229C22×Dic5—61no—
230Q8×D5—68no—
231#711—68no—
232#711—616no—
233#709—22no—
234#709—38no—
235#709—64no—
236#709C4×D314yescomplemented
237C2×D20C22×D311yescharacteristic
238C2×C4×D5—21no—
239C2×C4×D5—62no—
240C2×Dic10—34no—
241C2×Dic10—32no—
242C2×Dic10—38no—
243C2×Dic10—64no—
244C2×Dic10—62no—
245C2×Dic10—61no—
246C2×Dic10—62no—
247C2×Dic10C22×D311yescharacteristic
248C5×C4⋊C4—21no—
249C5×C4⋊C4—31no—
250C5×C4⋊C4—31no—
251C5×C4⋊C4—62no—
252C5×C4⋊C4C22×D312yes—
253C5×C22⋊C4—62no—
254C5×C22⋊C4—61no—
255C42×C5—62no—
256C42×C5—61no—
257#681—22no—
258#681—64no—
259C2×#168—31no—
260C2×#168—31no—
261C2×#168—64no—
262C2×#168—62no—
263C2×#168C22×D312yes—
264C2×2−1+4—151no—
265C2×#131—151no—
266#520—31no—
267#419—152no—
268#419—151no—
269#417—51no—
270#417—152no—
271#416—152no—
272#416—151no—
273C2×#103—152no—
274C2×#103—151no—
275C22×C3×C5—21no—
276C22×C3×C5—21no—
277C22×C3×C5C2×C22⋊C412yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×C5×D3—22no—
280C2×C5×D3—22no—
281C2×C5×D3C2×C22⋊C414yes—
282C2×C3×D5—22no—
283C2×C3×D5—41no—
284C2×C3×D5—41no—
285C3×C4×C5—42no—
286C3×C4×C5C2×C22⋊C412yes—
287C3×C4×C5C23×C411yescharacteristic
288C3×C4×C5C22×D411yescharacteristic
289Dic15—24no—
290C3×Dic5—22no—
291C5×Dic3—41no—
292C5×Dic3—41no—
293C5×Dic3C2×C22⋊C414yes—
294C3×#41—54no—
295C3×#41—102no—
296C2×C3×Q8—51no—
297C2×C3×D4—51no—
298C2×C3×D4—101no—
299C22×C3×C4—21no—
300C22×C3×C4—101no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—102no—
303C2×#67C22⋊D512yes—
304C22×Dic3—101no—
305C22×Dic3—102no—
306D3×Q8—58no—
307D3×Q8—104no—
308#237—58no—
309#237—1016no—
310#237—104no—
311#235—108no—
312#235C4×D514yes—
313#235D2014yes—
314C2×D12C22⋊D511yescharacteristic
315C2×C4×D3—22no—
316C2×C4×D3—102no—
317C2×C4×D3C22×D512yes—
318C2×Dic6—54no—
319C2×Dic6—52no—
320C2×Dic6—102no—
321C2×Dic6—101no—
322C2×Dic6—102no—
323C2×Dic6—108no—
324C2×Dic6C22⋊D511yescharacteristic
325C3×M16—102no—
326C2×C3×C8—52no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4C22×D512yes—
329#217—21no—
330(C2×D3)⋊C4—22no—
331C4⋊Dic3C22×D511yescharacteristic
332C4⋊Dic3C22×D511yescharacteristic
333Dic3⋊C4—22no—
334C4×Dic3—21no—
335C4×Dic3—22no—
336C2×C3⋊C8—51no—
337C2×C3⋊C8—51no—
338C2×C3⋊C8—102no—
339ΓL(1,𝔽25)—104no—
340D3×C8—104no—
341C23×C5—32no—
342C23×C5D3×D411yescharacteristic
343C22×D5—21no—
344C5×Q8—34no—
345C5×D4—38no—
346C5×D4—34no—
347C2×C4×C5—22no—
348C2×C4×C5—32no—
349C2×C4×C5—34no—
350C2×C4×C5—34no—
351C2×C4×C5—61no—
352C2×C4×C5—61no—
353C2×C4×C5—81no—
354C2×C4×C5—242no—
355C2×C4×C5C2×C4×D312yes—
356C2×C4×C5D3×D412yes—
357C2×C4×C5D3×D411yescharacteristic
358C2×C4×C5C23×D311yescharacteristic
359C22⋊D5—24no—
360C22⋊D5—68no—
361C2×Dic5—21no—
362C2×Dic5—68no—
363C2×Dic5—64no—
364C2×Dic5—62no—
365D20—21no—
366D20C2×C4×D312yes—
367C4×D5—24no—
368C4×D5—68no—
369Dic10—21no—
370Dic10—34no—
371Dic10—68no—
372Dic10—64no—
373Dic10—62no—
374Dic10C2×C4×D312yes—
375#168—22no—
376#168—61no—
377#168—61no—
3782−1+4—158no—
3792−1+4—304no—
380C2×#41—31no—
381C2×#41—51no—
382C2×#41—152no—
383C2×#41—301no—
384C2×#41—302no—
385C22×Q8—152no—
386C22×Q8—151no—
387C22×Q8—301no—
388#131—304no—
389C2×M16—51no—
390C2×M16—152no—
391C22×C8—152no—
392C22×C8—151no—
393C4×Q8—61no—
394C4×D4—61no—
395C4×D4—62no—
396#117—31no—
397#117—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4D3×D511yescharacteristic
400#103—52no—
401#103—152no—
402#103—152no—
403#103—151no—
404#103—151no—
405#103—152no—
406#103—152no—
407#102—52no—
408#102—151no—
409#102—151no—
410C2×C3×C5—22no—
411C2×C3×C5C22×C22⋊C411yescharacteristic
412C2×C3×C5#57711yescharacteristic
413C2×C3×C5#57811yescharacteristic
414C3×D5—42no—
415C5×D3—24no—
416C23×C3—101no—
417C23×C3C2×C22⋊D511yescharacteristic
418C22×D3C2×C22⋊D512yes—
419C3×Q8—52no—
420C3×Q8—101no—
421C3×D4—52no—
422C3×D4—104no—
423C3×D4—101no—
424C2×C3×C4—22no—
425C2×C3×C4—81no—
426C2×C3×C4—101no—
427C2×C3×C4—104no—
428C2×C3×C4C2×C4×D512yes—
429C2×C3×C4C2×D2012yes—
430C2×C3×C4C2×C22⋊D511yescharacteristic
431C2×C3×C4C23×D511yescharacteristic
432#67—108no—
433#67#68518yes—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—102no—
437C2×Dic3—104no—
438C2×Dic3—108no—
439C2×Dic3C2×C22⋊D512yes—
440D12#68514yes—
441C4×D3—82no—
442C4×D3—108no—
443C4×D3C2×C4×D514yes—
444C4×D3C2×D2014yes—
445Dic6—54no—
446Dic6—102no—
447Dic6—104no—
448Dic6—108no—
449Dic6#68514yes—
450C3×C8—102no—
451C3⋊C8—101no—
452C3⋊C8—101no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5—34no—
456C22×C5—62no—
457C22×C5—62no—
458C22×C5D3×C22⋊C412yes—
459C22×C5C2×D3×D411yescharacteristic
460C2×D5—22no—
461C2×D5—41no—
462C2×D5—41no—
463C4×C5—34no—
464C4×C5—42no—
465C4×C5—121no—
466C4×C5—121no—
467C4×C5D3×C22⋊C412yes—
468C4×C5C22×C4×D311yescharacteristic
469C4×C5C2×D3×D411yescharacteristic
470Dic5—22no—
471Dic5—64no—
472#41—34no—
473#41—34no—
474#41—54no—
475#41—102no—
476#41—158no—
477#41—304no—
478#41—308no—
479#41—3016no—
480C2×Q8—31no—
481C2×Q8—51no—
482C2×Q8—158no—
483C2×Q8—154no—
484C2×Q8—152no—
485C2×Q8—302no—
486C2×Q8—304no—
487C2×Q8—308no—
488C2×Q8—302no—
489C2×Q8—301no—
490C2×D4—32no—
491C2×D4—31no—
492C2×D4—51no—
493C2×D4—101no—
494C2×D4—302no—
495C22×C4—21no—
496C22×C4—32no—
497C22×C4—62no—
498C22×C4—101no—
499C22×C4—302no—
500C22×C4—302no—
501C22×C4—301no—
502C22×C4C2×D3×D511yescharacteristic
503M16—102no—
504M16—304no—
505C2×C8—52no—
506C2×C8—151no—
507C2×C8—151no—
508C2×C8—304no—
509C2×C8—302no—
510C4⋊C4—21no—
511C4⋊C4—31no—
512C4⋊C4—31no—
513C4⋊C4—62no—
514C4⋊C4C2×D3×D512yes—
515C22⋊C4—62no—
516C22⋊C4—61no—
517C42—62no—
518C42—61no—
519C3×C5#289811yescharacteristic, complemented, Hall
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—102no—
523C22×C3—201no—
524C22×C3—201no—
525C22×C3C2×#68512yes—
526C22×C3C22×C22⋊D511yescharacteristic
527C2×D3—22no—
528C2×D3—22no—
529C2×D3C2×#68514yes—
530C3×C4—42no—
531C3×C4—102no—
532C3×C4C2×#68512yes—
533C3×C4C22×C4×D511yescharacteristic
534C3×C4C22×D2011yescharacteristic
535Dic3—41no—
536Dic3—41no—
537Dic3—104no—
538Dic3C2×#68514yes—
539C2×C5—22no—
540C2×C5—64no—
541C2×C5C2×D3×C22⋊C411yescharacteristic
542C2×C5#577511yescharacteristic
543C2×C5#577911yescharacteristic
544D5—42no—
545C23—32no—
546C23—101no—
547C23D3×C22⋊D511yescharacteristic
548Q8—34no—
549Q8—52no—
550Q8—101no—
551Q8—154no—
552Q8—308no—
553Q8—304no—
554Q8—302no—
555D4—38no—
556D4—34no—
557D4—52no—
558D4—104no—
559D4—101no—
560D4—308no—
561C2×C4—22no—
562C2×C4—32no—
563C2×C4—34no—
564C2×C4—34no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—81no—
568C2×C4—101no—
569C2×C4—104no—
570C2×C4—242no—
571C2×C4—308no—
572C2×C4—308no—
573C2×C4—304no—
574C2×C4—302no—
575C2×C4C4×D3×D512yes—
576C2×C4D3×D2012yes—
577C2×C4D3×C22⋊D511yescharacteristic
578C2×C4C22×D3×D511yescharacteristic
579C8—102no—
580C8—301no—
581C8—301no—
582C2×C3—22no—
583C2×C3—202no—
584C2×C3C22×#68511yescharacteristic
585C2×C3#6617011yescharacteristic
586C2×C3#6617211yescharacteristic
587D3—24no—
588C5#7888311yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—34no—
592C22—62no—
593C22—62no—
594C22—102no—
595C22—201no—
596C22—201no—
597C22D3×#68512yes—
598C22C2×D3×C22⋊D511yescharacteristic
599C4—34no—
600C4—42no—
601C4—102no—
602C4—121no—
603C4—121no—
604C4—304no—
605C4D3×#68512yes—
606C4C2×C4×D3×D511yescharacteristic
607C4C2×D3×D2011yescharacteristic
608C3#1061430111yescharacteristic, complemented, Sylow
609C2—22no—
610C2—64no—
611C2—202no—
612C2C2×D3×#68511yescharacteristic
613C2#1175472011yescharacteristic
614C2#1175511411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#92001C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2898
LCSG ▷ 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
2. C5×#5504C2semidirect
3. C2×#91288C2semidirect
4. C2×#91094C2semidirect
5. C3×#65255C2semidirect
6. #11748417C2semidirect
7. #11748364C2semidirect
8. #11747503C2semidirect
9. #11747502C2semidirect
10. #11747489C2semidirect
11. D3×#3942C2semidirect
20. #92001C4semidirect
56. #65255D3semidirect
62. C2×Dic30C2×C4semidirect
73. C3×#709C2×C4semidirect
84. D3×Dic10C2×C4semidirect
86. #6765C2×C4semidirect
106. #5504D5semidirect
236. #709C4×D3semidirect
519. C3×C5#2898semidirect
588. C5#78883semidirect
608. C3#10614301semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C5×#55042
C2×#912882
C2×#910942
C3×#652552
#117484172
#117483642
#117475032
#117475022
#117474892
D3×#39422
#106143013
#788835