Finite Group Databasebeta

← #14412751

Subgroups — #14412751

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
2C2×C5×#901C211yesmaximal, characteristic, complemented
3#11754513C211yesmaximal, characteristic, complemented
4C2×#91100C211yesmaximal, characteristic, complemented
5C3×#65402C211yesmaximal, characteristic, complemented
6#11748415C211yesmaximal, characteristic, complemented
7#11748369C211yesmaximal, characteristic, complemented
8#11748138C212yesmaximal, complemented
9#11748137C212yesmaximal, complemented
10#11748123C212yesmaximal, complemented
11D3×#3948C212yesmaximal, complemented
12#10615537—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—
23C22×C3×C5×C8C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C5×#208C2211yescharacteristic
26C5×#901—24no—
27C2×C5×ΓL(1,𝔽25)C2212yes—
28C2×C5×D3×C8C2212yes—
29C3×#4072C2211yescharacteristic
30#67⋊Dic5—22no—
31D3×C4⋊Dic5C2212yes—
32Dic5×D12—21no—
33#91338C2212yes—
34Dic5×Dic6—21no—
35#91100C2212yes—
36#91100C2212yes—
37C3×#3953C2211yescharacteristic
38C3×#3953C2211yescharacteristic
39C3×#3948C2211yescharacteristic
40C3×#3948C2211yescharacteristic
41#90974C2212yes—
42#90974C2212yes—
43#90971C2212yes—
44#90965C2212yes—
45#78832—51nomaximal, Hall
46C2×#4150—31no—
47C2×C5×#131—31no—
48#66161—31no—
49#65422—32no—
50#65422—31no—
51#65409—31no—
52#65409—32no—
53#65402—32no—
54#65402D311yescharacteristic, complemented
55C2×#3948—32no—
56C2×#3948—31no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15—21no—
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×D3C2312yes—
69C2×C5×Dic6D411yescharacteristic
70C2×C3×C22⋊D5—21no—
71C3×#709—22no—
72C3×#709C2×C414yescomplemented
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×Dic10C2311yescharacteristic
76C2×#1204—22no—
77C2×#1201—22no—
78C2×D3×Dic5—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—
88C2×C3×C5×C8—22no—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C4⋊Dic15—21no—
92C4⋊Dic15C2312yes—
93C5×#208—22no—
94C2×C5×C3⋊C8C2312yes—
95C5×ΓL(1,𝔽25)—24no—
96C5×D3×C8—24no—
97C3×C22⋊Dic5—21no—
98C3×C4⋊Dic5C2311yescharacteristic
99C3×C4⋊Dic5C2311yescharacteristic
100C3×C4×Dic5—21no—
101Dic3⋊Dic5—22no—
102(C2×D3)⋊Dic5—22no—
103Dic3×Dic5—22no—
104C2×#1010—51no—
105C2×#901D511yescharacteristic, complemented
106#5523—51no—
107C3×#416—51no—
108#5232—51no—
109C2×#816—51no—
110#5004—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—
125C5×#131—64no—
126C2×C5×M16—31no—
127C2×C5×M16—32no—
128C22×C5×C8—32no—
129C22×C5×C8C2×D311yescharacteristic
130Q8×Dic5—61no—
131D4×Dic5—61no—
132D4×Dic5—62no—
133#4072—32no—
134#4072C2×D311yescharacteristic
135C2×C4⋊Dic5—31no—
136C2×C4⋊Dic5—32no—
137#3953—32no—
138#3953C2×D311yescharacteristic
139#3953C2×D311yescharacteristic
140#3948—32no—
141#3948—32no—
142#3948—32no—
143#3948—32no—
144#3948—32no—
145#3948C2×D311yescharacteristic
146#3948C2×D311yescharacteristic
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×C5×D3C2×D412yes—
150C22×C3×D5—21no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2411yescharacteristic
155C2×Dic15—24no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—81no—
159Dic30—24no—
160Dic30—22no—
161Dic30C22×C414yes—
162C5×#67C22⋊C418yes—
163C2×C5×Dic3C2×D412yes—
164C5×D12C22⋊C414yes—
165C4×C5×D3C22×C414yes—
166C4×C5×D3C2×D414yes—
167C5×Dic6C22⋊C414yes—
168C3×C22⋊D5—24no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C3×D20—21no—
173C3×D20C22×C412yes—
174C3×C4×D5—24no—
175C3×Dic10—21no—
176C3×Dic10C22×C412yes—
177#1204—28no—
178#1201—28no—
179D3×Dic5—28no—
180D3×Dic5—82no—
181D5×Dic3—28no—
182C3×C5×C8—21no—
183C3×C5×C8—21no—
184C5×C3⋊C8—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—
195C22×C3×C8C2×D511yescharacteristic
196C3×#117—51no—
197C2×C4⋊Dic3—51no—
198C2×#208C2×D511yescharacteristic
199#901—24no—
200C2×ΓL(1,𝔽25)C2×D512yes—
201C2×D3×C8C2×D512yes—
202#892—52no—
203D3×C4⋊C4—52no—
204#67⋊C4—102no—
205C4×D12—101no—
206C4×Dic6—101no—
207C3×#103—51no—
208C3×#103—51no—
209C3×#102—51no—
210C3×#102—51no—
211#835—52no—
212#832—52no—
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—32no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—62no—
226C22×Dic5—62no—
227C22×Dic5—62no—
228C22×Dic5—61no—
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×M16—64no—
249C5×M16—62no—
250C2×C5×C8—22no—
251C2×C5×C8—32no—
252C2×C5×C8—64no—
253C2×C5×C8C22×D311yescharacteristic
254C2×C5×C8C22×D311yescharacteristic
255C22⋊Dic5—21no—
256C22⋊Dic5—62no—
257C4⋊Dic5—32no—
258C4⋊Dic5—62no—
259C4⋊Dic5—61no—
260C4⋊Dic5C22×D311yescharacteristic
261C4⋊Dic5C22×D311yescharacteristic
262C4×Dic5—21no—
263C4×Dic5—62no—
264C2×2−1+4—151no—
265C2×#131—31no—
266#520—151no—
267#419—152no—
268#419—151no—
269#417—152no—
270#417—151no—
271#416—51no—
272#416—152no—
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×C5C2×C22⋊C412yes—
286C3×C4×C5C23×C411yescharacteristic
287C3×C4×C5C22×D411yescharacteristic
288Dic15—24no—
289Dic15—42no—
290C3×Dic5—22no—
291C3×Dic5—41no—
292C3×Dic5—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—101no—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—102no—
302C2×#67D2012yes—
303C22×Dic3—101no—
304C22×Dic3—102no—
305C22×Dic3—101no—
306D3×Q8—58no—
307D3×Q8—104no—
308#237—58no—
309#237—1016no—
310#237—104no—
311#235—108no—
312#235C4×D514yes—
313#235C22⋊D514yes—
314C2×D12D2011yescharacteristic
315C2×C4×D3—102no—
316C2×C4×D3—102no—
317C2×C4×D3C22×D512yes—
318C2×Dic6—54no—
319C2×Dic6—52no—
320C2×Dic6—101no—
321C2×Dic6—102no—
322C2×Dic6—102no—
323C2×Dic6—108no—
324C2×Dic6D2011yescharacteristic
325C2×C3×C8—22no—
326C2×C3×C8C22×D511yescharacteristic
327C2×C3×C8C22×D511yescharacteristic
328C3×C4⋊C4—51no—
329C3×C4⋊C4—51no—
330C3×C22⋊C4—101no—
331C3×C42—101no—
332(C2×D3)⋊C4—102no—
333C4⋊Dic3—52no—
334C4⋊Dic3—101no—
335Dic3⋊C4—102no—
336C4×Dic3—102no—
337#208—22no—
338C2×C3⋊C8C22×D512yes—
339ΓL(1,𝔽25)—24no—
340D3×C8—24no—
341C23×C5—32no—
342C23×C5D3×D411yescharacteristic
343C22×D5—21no—
344C5×Q8—34no—
345C5×D4—38no—
346C5×D4—34no—
347C2×C4×C5—32no—
348C2×C4×C5—34no—
349C2×C4×C5—34no—
350C2×C4×C5C2×C4×D312yes—
351C2×C4×C5D3×D411yescharacteristic
352C2×C4×C5D3×D412yes—
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—24no—
355C22⋊D5—68no—
356C2×Dic5—21no—
357C2×Dic5—21no—
358C2×Dic5—21no—
359C2×Dic5—68no—
360C2×Dic5—64no—
361C2×Dic5—62no—
362C2×Dic5—62no—
363C2×Dic5—242no—
364C2×Dic5—241no—
365D20—21no—
366D20C2×C4×D312yes—
367C4×D5—24no—
368C4×D5—68no—
369Dic10—21no—
370Dic10—34no—
371Dic10—68no—
372Dic10—64no—
373Dic10—62no—
374Dic10C2×C4×D312yes—
375C5×C8—21no—
376C5×C8—21no—
377C5×C8—62no—
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—64no—
389C2×M16—31no—
390C2×M16—32no—
391C22×C8—32no—
392C22×C8D3×D511yescharacteristic
393C4×Q8—301no—
394C4×D4—301no—
395C4×D4—302no—
396#117—51no—
397#117—152no—
398C2×C4⋊C4—152no—
399C2×C4⋊C4—151no—
400#103—51no—
401#103—51no—
402#103—152no—
403#103—152no—
404#103—152no—
405#103—152no—
406#103—152no—
407#102—51no—
408#102—51no—
409#102—152no—
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×D2011yescharacteristic
418C22×D3C2×D2012yes—
419C3×Q8—52no—
420C3×Q8—101no—
421C3×D4—52no—
422C3×D4—104no—
423C3×D4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—104no—
426C2×C3×C4—101no—
427C2×C3×C4—101no—
428C2×C3×C4C2×C4×D512yes—
429C2×C3×C4C2×D2011yescharacteristic
430C2×C3×C4C2×C22⋊D512yes—
431C2×C3×C4C23×D511yescharacteristic
432#67—108no—
433#67#68518yes—
434C2×Dic3—102no—
435C2×Dic3—104no—
436C2×Dic3—108no—
437C2×Dic3—102no—
438C2×Dic3—401no—
439C2×Dic3C2×D2012yes—
440D12#68514yes—
441C4×D3—108no—
442C4×D3—402no—
443C4×D3C2×C4×D514yes—
444C4×D3C2×C22⋊D514yes—
445Dic6—54no—
446Dic6—102no—
447Dic6—104no—
448Dic6—108no—
449Dic6#68514yes—
450C3×C8—21no—
451C3×C8—21no—
452C3⋊C8—22no—
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×C5D3×C22⋊C412yes—
465C4×C5C22×C4×D311yescharacteristic
466C4×C5C2×D3×D411yescharacteristic
467Dic5—22no—
468Dic5—41no—
469Dic5—41no—
470Dic5—64no—
471Dic5—122no—
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—301no—
489C2×Q8—302no—
490C2×D4—32no—
491C2×D4—31no—
492C2×D4—51no—
493C2×D4—101no—
494C2×D4—302no—
495C22×C4—32no—
496C22×C4—101no—
497C22×C4—302no—
498C22×C4—302no—
499C22×C4—302no—
500C22×C4—301no—
501C22×C4—301no—
502C22×C4C2×D3×D511yescharacteristic
503M16—64no—
504M16—62no—
505C2×C8—22no—
506C2×C8—32no—
507C2×C8—64no—
508C2×C8C2×D3×D511yescharacteristic
509C2×C8C2×D3×D511yescharacteristic
510C4⋊C4—51no—
511C4⋊C4—51no—
512C4⋊C4—152no—
513C4⋊C4—302no—
514C4⋊C4—301no—
515C22⋊C4—101no—
516C22⋊C4—302no—
517C42—101no—
518C42—302no—
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×D2011yescharacteristic
527C2×D3—22no—
528C2×D3—22no—
529C2×D3C2×#68514yes—
530C3×C4—102no—
531C3×C4—201no—
532C3×C4—201no—
533C3×C4C2×#68512yes—
534C3×C4C22×C4×D511yescharacteristic
535C3×C4C22×C22⋊D511yescharacteristic
536Dic3—104no—
537Dic3—202no—
538Dic3C2×#68514yes—
539C2×C5—22no—
540C2×C5—64no—
541C2×C5C2×D3×C22⋊C411yescharacteristic
542C2×C5#577011yescharacteristic
543C2×C5#577111yescharacteristic
544D5—42no—
545C23—32no—
546C23—101no—
547C23D3×D2011yescharacteristic
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—32no—
562C2×C4—34no—
563C2×C4—34no—
564C2×C4—101no—
565C2×C4—104no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—308no—
569C2×C4—308no—
570C2×C4—304no—
571C2×C4—302no—
572C2×C4—302no—
573C2×C4—1202no—
574C2×C4—1201no—
575C2×C4C4×D3×D512yes—
576C2×C4D3×D2011yescharacteristic
577C2×C4D3×C22⋊D512yes—
578C2×C4C22×D3×D511yescharacteristic
579C8—21no—
580C8—21no—
581C8—62no—
582C2×C3—22no—
583C2×C3—202no—
584C2×C3#6608511yescharacteristic
585C2×C3#6608711yescharacteristic
586C2×C3C22×#68511yescharacteristic
587D3—24no—
588C5#7883211yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—34no—
592C22—62no—
593C22—62no—
594C22—102no—
595C22—201no—
596C22—201no—
597C22D3×#68512yes—
598C22C2×D3×D2011yescharacteristic
599C4—34no—
600C4—102no—
601C4—201no—
602C4—201no—
603C4—304no—
604C4—602no—
605C4D3×#68512yes—
606C4C2×C4×D3×D511yescharacteristic
607C4C2×D3×C22⋊D511yescharacteristic
608C3#1061553711yescharacteristic, complemented, Sylow
609C2—22no—
610C2—64no—
611C2—202no—
612C2#1175397211yescharacteristic
613C2#1175400311yescharacteristic
614C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92001C2
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×C5×#901C2semidirect
3. #11754513C2semidirect
4. C2×#91100C2semidirect
5. C3×#65402C2semidirect
6. #11748415C2semidirect
7. #11748369C2semidirect
8. #11748138C2semidirect
9. #11748137C2semidirect
10. #11748123C2semidirect
11. D3×#3948C2semidirect
20. #92001C4semidirect
54. #65402D3semidirect
62. C2×Dic30C2×C4semidirect
72. C3×#709C2×C4semidirect
84. D3×Dic10C2×C4semidirect
86. #6765C2×C4semidirect
105. C2×#901D5semidirect
236. #709C4×D3semidirect
519. C3×C5#2898semidirect
588. C5#78832semidirect
608. C3#10615537semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C2×C5×#9012
#117545132
C2×#911002
C3×#654022
#117484152
#117483692
#117481382
#117481372
#117481232
D3×#39482
#106155373
#788325