Finite Group Databasebeta

← #14412768

Subgroups — #14412768

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×C5×#907C211yesmaximal, characteristic, complemented
3#11754513C211yesmaximal, characteristic, complemented
4#11751234C211yesmaximal, characteristic, complemented
5C3×#65409C211yesmaximal, characteristic, complemented
6#11748411C211yesmaximal, characteristic, complemented
7C2×#90971C211yesmaximal, characteristic, complemented
8#11748123C212yesmaximal, complemented
9#11747643C212yesmaximal, complemented
10#11747608C212yesmaximal, complemented
11D3×#3948C212yesmaximal, complemented
12#10615537—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C2×#6782—22no—
17C2×D15⋊Q8—21no—
18C2×#6769C2212yes—
19#92004—24no—
20#92004C418yescomplemented
21C2×#6768—21no—
22C2×D3×Dic10C2212yes—
23C2×C3×C5×M16C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C22×C5×C3⋊C8C2211yescharacteristic
26C5×#907—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#91105C2212yes—
36#91100C2212yes—
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90974C2211yescharacteristic
40#90974C2211yescharacteristic
41#90971C2212yes—
42#90971C2212yes—
43#90968C2211yescharacteristic
44#90968C2211yescharacteristic
45#78957—51nomaximal, Hall
46C2×#4150—31no—
47C2×C5×#131—31no—
48#66161—31no—
49#65422—32no—
50#65422—31no—
51#65409—32no—
52#65409D311yescharacteristic, complemented
53#65402—31no—
54#65402—32no—
55C2×#3948—32no—
56C2×#3948—31no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59C22×Dic15—21no—
60#6817—22no—
61#6817C2×C414yescomplemented
62C2×D60C2311yescharacteristic
63C2×C4×D15—21no—
64C2×Dic30C2311yescharacteristic
65C2×C5×#67D412yes—
66C5×#235C2×C414yes—
67C5×#235D414yes—
68C2×C5×D12D411yescharacteristic
69C2×C4×C5×D3C2312yes—
70C2×C5×Dic6D411yescharacteristic
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—
79#6782—216no—
80C2×D3×Dic5—22no—
81C2×D3×Dic5—22no—
82D15⋊Q8—28no—
83#6769—24no—
84#6769C2×C418yescomplemented
85#6768—28no—
86D3×Dic10—24no—
87D3×Dic10C2×C418yescomplemented
88C3×C5×M16—22no—
89C2×C3×C5×C8C2312yes—
90C4⋊Dic15—21no—
91C4⋊Dic15C2312yes—
92C2×C5×C3⋊C8—22no—
93C2×C5×C3⋊C8C2311yescharacteristic
94C2×C5×C3⋊C8C2311yescharacteristic
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×#1007—51no—
105C2×#907D511yescharacteristic, complemented
106#5523—51no—
107C3×#419—51no—
108C2×#835—51no—
109#5133—51no—
110#5002—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—61no—
119C2×#711—61no—
120C2×#711—62no—
121C2×#709—31no—
122C2×#709—32no—
123C22×Dic10—32no—
124C22×Dic10C2×D311yescharacteristic
125C5×#131—64no—
126C2×C5×M16—32no—
127C2×C5×M16C2×D311yescharacteristic
128C22×C5×C8—31no—
129C22×C5×C8—32no—
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#3953—31no—
139#3953—31no—
140#3948—32no—
141#3948—32no—
142#3948—32no—
143#3948—31no—
144#3948—31no—
145#3948C2×D312yes—
146#3948C2×D312yes—
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×C5×D3C2×D412yes—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2411yescharacteristic
155#1220—24no—
156C2×Dic15—21no—
157C2×Dic15—22no—
158C2×Dic15—81no—
159D60—21no—
160D60C22×C412yes—
161C4×D15—24no—
162Dic30—21no—
163Dic30C22×C412yes—
164C5×#67C22⋊C418yes—
165C2×C5×Dic3C2×D412yes—
166C5×D12C22⋊C414yes—
167C4×C5×D3C22×C414yes—
168C4×C5×D3C2×D414yes—
169C5×Dic6C22⋊C414yes—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—21no—
173C2×C3×Dic5—21no—
174C3×Dic10—24no—
175C3×Dic10—22no—
176C3×Dic10C22×C414yes—
177#1204—28no—
178#1203—28no—
179#1200—28no—
180D3×Dic5—28no—
181D3×Dic5—82no—
182C3×C5×C8—22no—
183C5×C3⋊C8—21no—
184C5×C3⋊C8—21no—
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
195C2×C3×M16C2×D511yescharacteristic
196C3×#117—51no—
197C2×C4⋊Dic3—51no—
198C22×C3⋊C8C2×D511yescharacteristic
199#907—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—52no—
208C3×#103—52no—
209#835—52no—
210#835—52no—
211#821—52no—
212#816—52no—
213#810—51no—
214#810—51no—
215#809—51no—
216#809—51no—
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—62no—
225C2×C22⋊D5—61no—
226C22×Dic5—21no—
227C22×Dic5—62no—
228C22×Dic5—62no—
229C22×Dic5—61no—
230Q8×D5—68no—
231#711—68no—
232#711—616no—
233#709—34no—
234#709—38no—
235#709—64no—
236#709—62no—
237C2×D20—31no—
238C2×C4×D5—62no—
239C2×C4×D5—61no—
240C2×Dic10—21no—
241C2×Dic10—22no—
242C2×Dic10—31no—
243C2×Dic10—38no—
244C2×Dic10—64no—
245C2×Dic10—62no—
246C2×Dic10C4×D314yescomplemented
247C2×Dic10C22×D312yes—
248C5×M16—22no—
249C5×M16—64no—
250C2×C5×C8—31no—
251C2×C5×C8—31no—
252C2×C5×C8—64no—
253C2×C5×C8—62no—
254C2×C5×C8C22×D312yes—
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—51no—
268#419—152no—
269#417—152no—
270#417—151no—
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×D15—22no—
280C2×D15—41no—
281C2×D15—41no—
282C2×C5×D3—22no—
283C2×C5×D3—22no—
284C2×C5×D3C2×C22⋊C414yes—
285C3×C4×C5C2×C22⋊C412yes—
286C3×C4×C5C23×C411yescharacteristic
287C3×C4×C5C22×D411yescharacteristic
288Dic15—22no—
289Dic15—42no—
290C3×Dic5—24no—
291C3×Dic5—41no—
292C3×Dic5—41no—
293C5×Dic3C2×C22⋊C414yes—
294C2×C3×Q8—54no—
295C2×C3×Q8—52no—
296C2×C3×Q8—101no—
297C2×C3×Q8—102no—
298C22×C3×C4—101no—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—101no—
301C2×#67D2012yes—
302C22×Dic3—101no—
303#239—58no—
304#239—108no—
305#239—104no—
306D3×Q8—58no—
307D3×Q8—104no—
308D3×Q8—108no—
309#235—54no—
310#235—102no—
311#235—1016no—
312#235C4×D514yes—
313#235C22⋊D514yes—
314C2×D12—51no—
315C2×D12—102no—
316C2×D12D2011yescharacteristic
317C2×C4×D3—102no—
318C2×C4×D3—101no—
319C2×C4×D3—102no—
320C2×C4×D3—102no—
321C2×C4×D3C22×D512yes—
322C2×Dic6—51no—
323C2×Dic6—102no—
324C2×Dic6D2011yescharacteristic
325C3×M16—22no—
326C2×C3×C8C22×D512yes—
327C3×C4⋊C4—51no—
328C3×C4⋊C4—51no—
329C3×C22⋊C4—101no—
330C3×C42—101no—
331(C2×D3)⋊C4—102no—
332C4⋊Dic3—52no—
333C4⋊Dic3—101no—
334Dic3⋊C4—102no—
335C4×Dic3—102no—
336C2×C3⋊C8—22no—
337C2×C3⋊C8C22×D511yescharacteristic
338C2×C3⋊C8C22×D511yescharacteristic
339ΓL(1,𝔽25)—24no—
340D3×C8—24no—
341C23×C5—32no—
342C23×C5D3×D411yescharacteristic
343C22×D5—61no—
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—68no—
355C22⋊D5—64no—
356C2×Dic5—24no—
357C2×Dic5—22no—
358C2×Dic5—21no—
359C2×Dic5—21no—
360C2×Dic5—68no—
361C2×Dic5—61no—
362C2×Dic5—62no—
363C2×Dic5—242no—
364C2×Dic5—241no—
365D20—32no—
366D20—61no—
367C4×D5—68no—
368C4×D5—64no—
369Dic10—24no—
370Dic10—22no—
371Dic10—32no—
372Dic10—68no—
373Dic10—61no—
374Dic10C2×C4×D314yes—
375C5×C8—22no—
376C5×C8—61no—
377C5×C8—61no—
3782−1+4—158no—
3792−1+4—304no—
380C2×#41—31no—
381C2×#41—152no—
382C2×#41—151no—
383C2×#41—302no—
384C2×#41—301no—
385C22×Q8—51no—
386C22×Q8—152no—
387C22×Q8—301no—
388#131—64no—
389C2×M16—32no—
390C2×M16D3×D511yescharacteristic
391C22×C8—31no—
392C22×C8—32no—
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—52no—
401#103—52no—
402#103—151no—
403#103—151no—
404#103—152no—
405#103—152no—
406#103—152no—
407#102—151no—
408#102—151no—
409#102—152no—
410C2×C3×C5—22no—
411C2×C3×C5C22×C22⋊C411yescharacteristic
412C2×C3×C5#57711yescharacteristic
413C2×C3×C5#57811yescharacteristic
414D15—42no—
415C5×D3—24no—
416C23×C3C2×D2011yescharacteristic
417C22×D3—101no—
418C22×D3C2×D2012yes—
419C3×Q8—54no—
420C3×Q8—102no—
421C3×Q8—104no—
422C2×C3×C4—102no—
423C2×C3×C4—104no—
424C2×C3×C4—101no—
425C2×C3×C4—101no—
426C2×C3×C4C2×C4×D512yes—
427C2×C3×C4C2×D2011yescharacteristic
428C2×C3×C4C2×C22⋊D512yes—
429C2×C3×C4C23×D511yescharacteristic
430#67—104no—
431#67#68518yes—
432C2×Dic3—101no—
433C2×Dic3—102no—
434C2×Dic3—401no—
435C2×Dic3C2×D2012yes—
436D12—52no—
437D12—108no—
438D12—101no—
439D12#68514yes—
440C4×D3—108no—
441C4×D3—104no—
442C4×D3—108no—
443C4×D3—402no—
444C4×D3C2×C4×D514yes—
445C4×D3C2×C22⋊D514yes—
446Dic6—52no—
447Dic6—101no—
448Dic6—108no—
449Dic6#68514yes—
450C3×C8—22no—
451C3⋊C8—21no—
452C3⋊C8—21no—
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—62no—
461C2×D5—121no—
462C2×D5—121no—
463C4×C5—34no—
464C4×C5D3×C22⋊C412yes—
465C4×C5C22×C4×D311yescharacteristic
466C4×C5C2×D3×D411yescharacteristic
467Dic5—24no—
468Dic5—41no—
469Dic5—41no—
470Dic5—62no—
471Dic5—122no—
472#41—34no—
473#41—34no—
474#41—158no—
475#41—154no—
476#41—304no—
477#41—3016no—
478#41—308no—
479#41—302no—
480C2×Q8—31no—
481C2×Q8—54no—
482C2×Q8—52no—
483C2×Q8—101no—
484C2×Q8—102no—
485C2×Q8—158no—
486C2×Q8—151no—
487C2×Q8—302no—
488C2×Q8—304no—
489C2×Q8—308no—
490C2×D4—32no—
491C2×D4—31no—
492C2×D4—151no—
493C2×D4—302no—
494C2×D4—301no—
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—22no—
504M16—64no—
505C2×C8—31no—
506C2×C8—31no—
507C2×C8—64no—
508C2×C8—62no—
509C2×C8C2×D3×D512yes—
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×C3C2×#68512yes—
523C22×C3C22×D2011yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—102no—
527C2×D3—201no—
528C2×D3—201no—
529C2×D3C2×#68514yes—
530C3×C4—104no—
531C3×C4—201no—
532C3×C4—201no—
533C3×C4C2×#68512yes—
534C3×C4C22×C4×D511yescharacteristic
535C3×C4C22×C22⋊D511yescharacteristic
536Dic3—102no—
537Dic3—202no—
538Dic3C2×#68514yes—
539C2×C5—22no—
540C2×C5—64no—
541C2×C5C2×D3×C22⋊C411yescharacteristic
542C2×C5#577811yescharacteristic
543C2×C5#577911yescharacteristic
544D5—122no—
545C23—32no—
546C23—301no—
547C23D3×D2011yescharacteristic
548Q8—34no—
549Q8—54no—
550Q8—104no—
551Q8—102no—
552Q8—152no—
553Q8—308no—
554Q8—301no—
555D4—38no—
556D4—34no—
557D4—152no—
558D4—308no—
559D4—304no—
560D4—301no—
561C2×C4—32no—
562C2×C4—34no—
563C2×C4—34no—
564C2×C4—104no—
565C2×C4—102no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—308no—
569C2×C4—308no—
570C2×C4—301no—
571C2×C4—304no—
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—22no—
580C8—61no—
581C8—61no—
582C2×C3—22no—
583C2×C3#6608511yescharacteristic
584C2×C3#6608711yescharacteristic
585C2×C3C22×#68511yescharacteristic
586D3—24no—
587D3—202no—
588C5#7895711yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—34no—
592C22—62no—
593C22—62no—
594C22—302no—
595C22—601no—
596C22—601no—
597C22D3×#68512yes—
598C22C2×D3×D2011yescharacteristic
599C4—34no—
600C4—104no—
601C4—201no—
602C4—201no—
603C4—302no—
604C4—602no—
605C4D3×#68512yes—
606C4C2×C4×D3×D511yescharacteristic
607C4C2×D3×C22⋊D511yescharacteristic
608C3#1061553711yescharacteristic, complemented, Sylow
609C2—22no—
610C2—64no—
611C2—602no—
612C2#1175403211yescharacteristic
613C2#1175404211yescharacteristic
614C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#92004C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C5×#907C2semidirect
3. #11754513C2semidirect
4. #11751234C2semidirect
5. C3×#65409C2semidirect
6. #11748411C2semidirect
7. C2×#90971C2semidirect
8. #11748123C2semidirect
9. #11747643C2semidirect
10. #11747608C2semidirect
11. D3×#3948C2semidirect
20. #92004C4semidirect
52. #65409D3semidirect
61. #6817C2×C4semidirect
74. C2×C3×Dic10C2×C4semidirect
84. #6769C2×C4semidirect
87. D3×Dic10C2×C4semidirect
105. C2×#907D5semidirect
246. C2×Dic10C4×D3semidirect
519. C3×C5#2898semidirect
588. C5#78957semidirect
608. C3#10615537semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
C2×C5×#9072
#117545132
#117512342
C3×#654092
#117484112
C2×#909712
#117481232
#117476432
#117476082
D3×#39482
#106155373
#789575