Finite Group Databasebeta

← #14412025

Subgroups — #14412025

Order 1920.

1432 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92000C211yesmaximal, characteristic
2C5×#5516C211yesmaximal, characteristic, complemented
3#11754211C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5C3×#65295C211yesmaximal, characteristic, complemented
6#11748626C211yesmaximal, characteristic, complemented
7#11748624C211yesmaximal, characteristic, complemented
8#11747130C218yesmaximal, complemented
9#10614287—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×#6779C2214yes—
14C2×#6773C412yescomplemented
15C2×D15⋊Q8C412yescomplemented
16#92000—22no—
17#92000—22no—
18#92000—22no—
19#92000—22no—
20C2×#6766C412yescomplemented
21C2×D5×Dic6C412yescomplemented
22C3×C5×#117C2211yescharacteristic
23#91815C2211yescharacteristic
24C5×#926C2211yescharacteristic
25C5×#887—22no—
26C5×#877C2214yes—
27C4×C5×Dic6—22no—
28C3×#4072C2211yescharacteristic
29#91529C2214yes—
30#91344—22no—
31Dic5×Dic6—22no—
32#91090C2214yes—
33C3×#3938C2214yes—
34#90997C2214yes—
35#90995C2214yes—
36#78689—51nomaximal, Hall
37C2×#4147—31no—
38C5×#519—31no—
39#66146—31no—
40#65295—31no—
41#65295—38no—
42#65295—31no—
43#65295—31no—
44#65295D311yescharacteristic, complemented
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220C2312yes—
47#6817—21no—
48#6817—21no—
49#6817—21no—
50#6817—21no—
51C2×D60C2×C411yescharacteristic
52C2×C4×D15C2×C412yes—
53C2×Dic30C2×C411yescharacteristic
54C22×C5×Dic3C2312yes—
55C2×C5×Dic6C2×C412yes—
56C2×C5×Dic6C2×C412yes—
57C2×C5×Dic6D412yes—
58C2×C5×Dic6D412yes—
59C2×C5×Dic6D412yes—
60C2×C5×Dic6D412yes—
61C2×C3×C22⋊D5C2312yes—
62C3×#709—21no—
63C3×#709—21no—
64C3×#709—21no—
65C3×#709—21no—
66C2×C3×D20C2×C411yescharacteristic
67C2×C3×C4×D5C2×C412yes—
68C2×C3×Dic10C2×C411yescharacteristic
69C2×#1204C2×C414yes—
70C2×#1202C2×C414yes—
71C2×#1200C2×C414yes—
72#6779—28no—
73#6779—28no—
74C2×D5×Dic3C2×C414yes—
75#6773—24no—
76#6773—24no—
77D15⋊Q8—24no—
78D15⋊Q8—24no—
79#6766—24no—
80#6766—24no—
81D5×Dic6—24no—
82D5×Dic6—24no—
83C3×C5×C4⋊C4—21no—
84C3×C5×C22⋊C4C2312yes—
85C3×C42×C5—21no—
86#6719C2312yes—
87C4⋊Dic15—21no—
88C4×Dic15—21no—
89C5×#217C2312yes—
90C5×C4⋊Dic3—21no—
91C5×Dic3⋊C4—24no—
92C4×C5×Dic3—21no—
93C4×C5×Dic3—24no—
94C3×C22⋊Dic5C2312yes—
95C3×C4⋊Dic5—21no—
96C3×C4×Dic5—21no—
97Dic3⋊Dic5—24no—
98Dic3×Dic5—24no—
99C2×#1010—51no—
100#5516—51no—
101#5516D511yescharacteristic, complemented
102C3×#410—51no—
103#5240—51no—
104#5006—51no—
105#5006—51no—
106#4740—58no—
107C22×C5×Q8—31no—
108#4147—62no—
109#4147—62no—
110#4147—62no—
111#4147—62no—
112C2×#713—32no—
113C2×#713—32no—
114C2×Q8×D5—32no—
115C2×Q8×D5—32no—
116C2×#709—31no—
117C2×#709—34no—
118C2×#709C2×D311yescharacteristic
119C4×C5×Q8—62no—
120C4×C5×Q8—62no—
121C5×#117—31no—
122C5×#117—34no—
123C5×#117C2×D311yescharacteristic
124Q8×Dic5—62no—
125Q8×Dic5—62no—
126#4072—31no—
127#4072—34no—
128#4072C2×D311yescharacteristic
129#3938—34no—
130#3938—34no—
131#3938—34no—
132#3938C2×D314yes—
133#2884—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×D15C22×C412yes—
136C22×C3×D5C22×C412yes—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C411yescharacteristic
139C2×C3×C4×C5C22×C411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144#1220—22no—
145#1220—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C412yes—
148D60—21no—
149D60—21no—
150C4×D15—22no—
151C4×D15—22no—
152Dic30—21no—
153Dic30—21no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3C22×C414yes—
156C2×C5×Dic3C2×D414yes—
157C2×C5×Dic3C2×D414yes—
158C5×Dic6C22⋊C414yes—
159C5×Dic6C22⋊C414yes—
160C5×Dic6C22⋊C414yes—
161C5×Dic6C22⋊C414yes—
162C3×C22⋊D5—22no—
163C3×C22⋊D5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5C22×C412yes—
166C3×D20—21no—
167C3×D20—21no—
168C3×C4×D5—22no—
169C3×C4×D5—22no—
170C3×Dic10—21no—
171C3×Dic10—21no—
172#1204—28no—
173#1202—28no—
174#1200—28no—
175D5×Dic3—28no—
176C2×C3×#41—51no—
177#1010—102no—
178#1010—102no—
179#1010—102no—
180#1010—102no—
181C2×D3×Q8—52no—
182C2×#237—54no—
183C2×#237—52no—
184C2×#235—51no—
185C2×#235—52no—
186C22×Dic6—52no—
187C22×Dic6C2×D511yescharacteristic
188C3×#117—51no—
189C3×#117C2×D511yescharacteristic
190#926—51no—
191#926C2×D511yescharacteristic
192#887—22no—
193#887—102no—
194#877—54no—
195#877C2×D514yes—
196C4×Dic6—22no—
197C4×Dic6—102no—
198C3×#99—54no—
199#834—54no—
200#806—54no—
201#806—54no—
202C2×C5×Q8—32no—
203C2×C5×Q8—32no—
204C2×C5×Q8—32no—
205C2×C5×Q8—32no—
206C2×C5×Q8—32no—
207C2×C5×Q8—32no—
208C22×C4×C5—32no—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—32no—
211C2×C22⋊D5C22×D312yes—
212#713—64no—
213#713—64no—
214#713—64no—
215#713—64no—
216Q8×D5—64no—
217Q8×D5—64no—
218Q8×D5—64no—
219Q8×D5—64no—
220#709—21no—
221#709—21no—
222#709—21no—
223#709—21no—
224#709—68no—
225#709—68no—
226#709—61no—
227#709—61no—
228#709—61no—
229#709—61no—
230C2×D20—34no—
231C2×D20—31no—
232C2×D20C4×D311yescharacteristic
233C2×C4×D5—34no—
234C2×C4×D5—32no—
235C2×C4×D5—34no—
236C2×C4×D5C4×D312yes—
237C2×Dic10—31no—
238C2×Dic10—34no—
239C2×Dic10C4×D311yescharacteristic
240C5×C4⋊C4—21no—
241C5×C4⋊C4—64no—
242C5×C4⋊C4—61no—
243C5×C22⋊C4—32no—
244C5×C22⋊C4C22×D312yes—
245C42×C5—21no—
246C42×C5—64no—
247C42×C5—61no—
248C22⋊Dic5—32no—
249C22⋊Dic5C22×D312yes—
250C4⋊Dic5—21no—
251C4⋊Dic5—64no—
252C4⋊Dic5—61no—
253C4×Dic5—21no—
254C4×Dic5—64no—
255C4×Dic5—61no—
256C2×2−1+4—151no—
257#519—31no—
258#519—151no—
259#410—51no—
260#410—158no—
261#410—151no—
262#410—151no—
263#410—151no—
264C22×C3×C5—41no—
265C22×C3×C5C23×C411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—22no—
269C2×D15—42no—
270C2×C3×D5—22no—
271C2×C3×D5—42no—
272C3×C4×C5—42no—
273C3×C4×C5C2×C22⋊C411yescharacteristic
274C3×C4×C5C2×C22⋊C411yescharacteristic
275C3×C4×C5C2×C22⋊C411yescharacteristic
276C3×C4×C5C2×C22⋊C411yescharacteristic
277Dic15—22no—
278Dic15—42no—
279C3×Dic5—22no—
280C3×Dic5—42no—
281C5×Dic3—42no—
282C5×Dic3C2×C22⋊C418yes—
283C3×#41—101no—
284C3×#41—101no—
285C3×#41—101no—
286C3×#41—101no—
287C2×C3×Q8—51no—
288C2×C3×D4—52no—
289C2×C3×D4—51no—
290C22×C3×C4—52no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—52no—
293C2×#67—54no—
294C22×Dic3—54no—
295C22×Dic3C22×D512yes—
296D3×Q8—104no—
297D3×Q8—104no—
298#237—108no—
299#237—108no—
300#237—104no—
301#237—104no—
302#235—101no—
303#235—101no—
304#235—101no—
305#235—101no—
306#235—104no—
307#235—104no—
308C2×D12—51no—
309C2×C4×D3—52no—
310C2×C4×D3—54no—
311C2×Dic6—51no—
312C2×Dic6—54no—
313C2×Dic6—104no—
314C2×Dic6—104no—
315C2×Dic6C4×D512yes—
316C2×Dic6C4×D512yes—
317C2×Dic6D2012yes—
318C2×Dic6D2012yes—
319C2×Dic6C22⋊D512yes—
320C2×Dic6C22⋊D512yes—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—101no—
323C3×C22⋊C4—52no—
324C3×C22⋊C4C22×D512yes—
325C3×C42—21no—
326C3×C42—101no—
327#217—52no—
328#217C22×D512yes—
329C4⋊Dic3—21no—
330C4⋊Dic3—101no—
331Dic3⋊C4—24no—
332Dic3⋊C4—104no—
333C4×Dic3—21no—
334C4×Dic3—24no—
335C4×Dic3—101no—
336C4×Dic3—104no—
337C23×C5C23×D311yescharacteristic
338C22×D5—32no—
339C22×D5C2×C4×D312yes—
340C5×Q8—34no—
341C5×Q8—34no—
342C5×Q8—34no—
343C5×Q8—34no—
344C2×C4×C5—22no—
345C2×C4×C5—34no—
346C2×C4×C5—34no—
347C2×C4×C5—34no—
348C2×C4×C5—62no—
349C2×C4×C5C2×C4×D311yescharacteristic
350C2×C4×C5C2×C4×D311yescharacteristic
351C2×C4×C5D3×D411yescharacteristic
352C2×C4×C5D3×D411yescharacteristic
353C2×C4×C5D3×D411yescharacteristic
354C2×C4×C5D3×D411yescharacteristic
355C22⋊D5—22no—
356C22⋊D5—22no—
357C22⋊D5—62no—
358C22⋊D5—62no—
359C2×Dic5—22no—
360C2×Dic5—32no—
361C2×Dic5—62no—
362C2×Dic5C2×C4×D312yes—
363D20—21no—
364D20—21no—
365D20—68no—
366D20—61no—
367D20—61no—
368C4×D5—22no—
369C4×D5—22no—
370C4×D5—68no—
371C4×D5—68no—
372C4×D5—62no—
373C4×D5—62no—
374Dic10—21no—
375Dic10—21no—
376Dic10—68no—
377Dic10—61no—
378Dic10—61no—
3792−1+4—302no—
3802−1+4—302no—
3812−1+4—302no—
3822−1+4—302no—
383C2×#41—51no—
384C2×#41—154no—
385C2×#41—152no—
386C2×#41—152no—
387C2×#41—151no—
388C22×Q8—31no—
389C22×Q8—152no—
390C22×Q8—152no—
391C4×Q8—62no—
392C4×Q8—62no—
393C4×Q8—302no—
394C4×Q8—302no—
395#117—31no—
396#117—34no—
397#117—51no—
398#117—154no—
399#117—151no—
400#117D3×D511yescharacteristic
401#99—54no—
402#99—154no—
403#99—154no—
404#99—154no—
405C2×C3×C5—21no—
406C2×C3×C5—21no—
407C2×C3×C5—21no—
408C2×C3×C5C22×C22⋊C411yescharacteristic
409D15—42no—
410C3×D5—42no—
411C23×C3—52no—
412C23×C3C23×D511yescharacteristic
413C22×D3—52no—
414C3×Q8—101no—
415C3×Q8—101no—
416C3×D4—102no—
417C3×D4—102no—
418C3×D4—101no—
419C3×D4—101no—
420C2×C3×C4—22no—
421C2×C3×C4—52no—
422C2×C3×C4—102no—
423C2×C3×C4—102no—
424C2×C3×C4—102no—
425C2×C3×C4C2×C4×D511yescharacteristic
426C2×C3×C4C2×C4×D511yescharacteristic
427C2×C3×C4C2×D2011yescharacteristic
428C2×C3×C4C2×D2011yescharacteristic
429C2×C3×C4C2×C22⋊D511yescharacteristic
430C2×C3×C4C2×C22⋊D511yescharacteristic
431#67—102no—
432#67—102no—
433#67—108no—
434C2×Dic3—22no—
435C2×Dic3—52no—
436C2×Dic3—108no—
437C2×Dic3—102no—
438C2×Dic3C2×C4×D514yes—
439C2×Dic3C2×D2014yes—
440C2×Dic3C2×C22⋊D514yes—
441D12—101no—
442D12—101no—
443C4×D3—102no—
444C4×D3—102no—
445C4×D3—108no—
446Dic6—101no—
447Dic6—101no—
448Dic6—108no—
449Dic6#68514yes—
450Dic6#68514yes—
451Dic6#68514yes—
452Dic6#68514yes—
453C22×C5—41no—
454C22×C5C22×C4×D311yescharacteristic
455C22×C5C2×D3×D411yescharacteristic
456C22×C5C2×D3×D411yescharacteristic
457C2×D5—22no—
458C2×D5—42no—
459C2×D5—62no—
460C2×D5—122no—
461C4×C5—38no—
462C4×C5—42no—
463C4×C5—122no—
464C4×C5D3×C22⋊C411yescharacteristic
465C4×C5D3×C22⋊C411yescharacteristic
466C4×C5D3×C22⋊C411yescharacteristic
467C4×C5D3×C22⋊C411yescharacteristic
468Dic5—22no—
469Dic5—42no—
470Dic5—62no—
471Dic5—122no—
472#41—101no—
473#41—101no—
474#41—101no—
475#41—101no—
476#41—308no—
477#41—308no—
478#41—304no—
479#41—304no—
480#41—304no—
481#41—304no—
482#41—301no—
483#41—301no—
484#41—301no—
485#41—301no—
486C2×Q8—32no—
487C2×Q8—32no—
488C2×Q8—32no—
489C2×Q8—32no—
490C2×Q8—32no—
491C2×Q8—32no—
492C2×Q8—51no—
493C2×Q8—154no—
494C2×Q8—151no—
495C2×Q8—304no—
496C2×Q8—304no—
497C2×Q8—304no—
498C2×Q8—304no—
499C2×D4—52no—
500C2×D4—51no—
501C2×D4—154no—
502C2×D4—152no—
503C2×D4—151no—
504C22×C4—32no—
505C22×C4—52no—
506C22×C4—154no—
507C22×C4—154no—
508C22×C4—152no—
509C22×C4C2×D3×D511yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—64no—
512C4⋊C4—61no—
513C4⋊C4—101no—
514C4⋊C4—304no—
515C4⋊C4—301no—
516C22⋊C4—32no—
517C22⋊C4—52no—
518C22⋊C4—152no—
519C22⋊C4C2×D3×D512yes—
520C42—21no—
521C42—64no—
522C42—61no—
523C42—101no—
524C42—304no—
525C42—301no—
526C3×C5#288411yescharacteristic, complemented, Hall
527C22×C3—41no—
528C22×C3—102no—
529C22×C3—202no—
530C22×C3C22×C4×D511yescharacteristic
531C22×C3C22×D2011yescharacteristic
532C22×C3C22×C22⋊D511yescharacteristic
533C2×D3—102no—
534C2×D3—202no—
535C3×C4—42no—
536C3×C4—102no—
537C3×C4—202no—
538C3×C4C2×#68511yescharacteristic
539C3×C4C2×#68511yescharacteristic
540C3×C4C2×#68511yescharacteristic
541C3×C4C2×#68511yescharacteristic
542Dic3—42no—
543Dic3—102no—
544Dic3—202no—
545Dic3C2×#68518yes—
546C2×C5—21no—
547C2×C5—21no—
548C2×C5—21no—
549C2×C5C2×D3×C22⋊C411yescharacteristic
550D5—42no—
551D5—122no—
552C23—52no—
553C23—152no—
554C23C22×D3×D511yescharacteristic
555Q8—34no—
556Q8—34no—
557Q8—34no—
558Q8—34no—
559Q8—101no—
560Q8—101no—
561Q8—308no—
562Q8—301no—
563Q8—301no—
564D4—102no—
565D4—102no—
566D4—101no—
567D4—101no—
568D4—308no—
569D4—302no—
570D4—302no—
571D4—301no—
572D4—301no—
573C2×C4—22no—
574C2×C4—34no—
575C2×C4—34no—
576C2×C4—34no—
577C2×C4—52no—
578C2×C4—62no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—152no—
583C2×C4—308no—
584C2×C4—308no—
585C2×C4—302no—
586C2×C4—302no—
587C2×C4—302no—
588C2×C4C4×D3×D511yescharacteristic
589C2×C4C4×D3×D511yescharacteristic
590C2×C4D3×D2011yescharacteristic
591C2×C4D3×D2011yescharacteristic
592C2×C4D3×C22⋊D511yescharacteristic
593C2×C4D3×C22⋊D511yescharacteristic
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—202no—
598C2×C3C22×#68511yescharacteristic
599D3—202no—
600C5#7868911yescharacteristic, complemented, Sylow
601C22—41no—
602C22—102no—
603C22—202no—
604C22—302no—
605C22—602no—
606C22C2×C4×D3×D511yescharacteristic
607C22C2×D3×D2011yescharacteristic
608C22C2×D3×C22⋊D511yescharacteristic
609C4—38no—
610C4—42no—
611C4—102no—
612C4—122no—
613C4—202no—
614C4—302no—
615C4—602no—
616C4D3×#68511yescharacteristic
617C4D3×#68511yescharacteristic
618C4D3×#68511yescharacteristic
619C4D3×#68511yescharacteristic
620C3#1061428711yescharacteristic, complemented, Sylow
621C2—21no—
622C2—21no—
623C2—21no—
624C2—202no—
625C2—602no—
626C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC2C2×D3×#685
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92000C2
cosocleC23×C3×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2884
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C5×#5516C2semidirect
3. #11754211C2semidirect
4. #11751107C2semidirect
5. C3×#65295C2semidirect
6. #11748626C2semidirect
7. #11748624C2semidirect
8. #11747130C2semidirect
14. C2×#6773C4semidirect
15. C2×D15⋊Q8C4semidirect
20. C2×#6766C4semidirect
21. C2×D5×Dic6C4semidirect
44. #65295D3semidirect
101. #5516D5semidirect
526. C3×C5#2884semidirect
600. C5#78689semidirect
620. C3#10614287semidirect

Maximal subgroups

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

subgroupindex
C2×#920002
C5×#55162
#117542112
#117511072
C3×#652952
#117486262
#117486242
#117471302
#106142873
#786895