Finite Group Databasebeta

← #14439186

Subgroups — #14439186

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91838C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3C3×#66166C211yesmaximal, characteristic, complemented
4C2×#91451C211yesmaximal, characteristic, complemented
5C2×#91301C211yesmaximal, characteristic, complemented
6C2×#91299C211yesmaximal, characteristic, complemented
7#11749340C212yesmaximal, complemented
8#11749339C212yesmaximal, complemented
9#11749094C212yesmaximal, complemented
10#11749093C212yesmaximal, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10615668—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C22×#1203—22no—
18#91838—24no—
19C2×#6717C2212yescomplemented
20C2×#6715C2212yescomplemented
21C2×#6710C2211yescharacteristic
22C5×#949—24no—
23C2×C5×#215C2212yescomplemented
24C2×C5×#213C2212yescomplemented
25C2×C5×#208C2211yescharacteristic
26C3×#4093C2211yescharacteristic, complemented
27C3×#4090C2211yescharacteristic, complemented
28C3×#4086C2211yescharacteristic, complemented
29C3×#4085—22no—
30C3×#4082C2211yescharacteristic, complemented
31C3×C4×C22⋊D5—22no—
32C2×C3×C4×Dic5C2211yescharacteristic
33#91451—22no—
34#91451C2212yes—
35#91451C2212yes—
36C2×#6658C2212yescomplemented
37C2×#6656C2212yescomplemented
38#91301—24no—
39C2×#6653C2212yescomplemented
40#91299—24no—
41C2×#6652C2212yescomplemented
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83287—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66166D311yescharacteristic, complemented
47C2×#4095—31no—
48C2×#4086—31no—
49C2×#4078—31no—
50C2×#4054—31no—
51#65465—32no—
52#65464—32no—
53#65443—32no—
54#65440—32no—
55M16×Dic5—31no—
56C23×D15—21no—
57C23×C5×D3—21no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×D60—22no—
66C2×D60—22no—
67C2×D60—21no—
68C2×D60C2312yes—
69C2×C5×D12—22no—
70C2×C5×D12—22no—
71C2×C5×D12—21no—
72C2×C5×D12C2312yes—
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—22no—
75C22×C3×Dic5D412yes—
76C3×#709—22no—
77C3×#709—22no—
78C2×C3×D20C2311yescharacteristic
79C2×C3×C4×D5—21no—
80C2×C3×Dic10C2311yescharacteristic
81C2×#1203—24no—
82C2×#1203—24no—
83C2×#1203—48no—
84#6717—24no—
85#6715—24no—
86#6710D414yescomplemented
87C2×C3⋊#168C2312yes—
88C5×#215—24no—
89C5×#213—24no—
90C5×#208D414yescomplemented
91C2×C5×C3⋊C8C2312yes—
92C3×C22⋊Dic5—22no—
93C3×#685—22no—
94C3×#683—22no—
95C3×C4×Dic5D412yes—
96C3×C4×Dic5C2311yescharacteristic
97C3×C4×Dic5C2311yescharacteristic
98#6658—24no—
99#6656—24no—
100#6653—24no—
101#6652—24no—
102C3×#532—51no—
103C2×#949—51no—
104C2×#949—51no—
105C2×#949—51no—
106C2×#949D511yescharacteristic, complemented
107C2×#874—51no—
108#5085—52no—
109#5073—52no—
110#5058—52no—
111#5058—52no—
112C4×#208—51no—
113C2×C5×#41C2×D311yescharacteristic
114C22×C5×D4—31no—
115C22×C22⋊D5—62no—
116C2×#709C2×D311yescharacteristic
117C22×D20—31no—
118C5×AGL(1,ℤ/8)—64no—
119C2×C5×SD16—32no—
120C2×C5×D8—32no—
121C2×C5×M16—31no—
122#4095—64no—
123#4093C2×D311yescharacteristic, complemented
124#4090C2×D311yescharacteristic, complemented
125C2×#688—32no—
126#4086—32no—
127#4086—32no—
128#4086—62no—
129#4086C2×D311yescharacteristic, complemented
130#4085—22no—
131#4082C2×D311yescharacteristic, complemented
132C2×#687—32no—
133#4078—64no—
134C2×#686—32no—
135C2×#686—32no—
136C4×C22⋊D5—22no—
137C2×C4×Dic5C2×D311yescharacteristic
138C2×#681—31no—
139#4054—64no—
140C2×D40—32no—
141C2×#677—32no—
142#3947—32no—
143C8×Dic5—32no—
144#3151—151noSylow
145C23×C3×C5—21no—
146C23×C3×C5C2×D411yescharacteristic
147C22×D15—22no—
148C22×D15—44no—
149C22×D15—42no—
150C22×C5×D3—22no—
151C22×C5×D3—44no—
152C22×C5×D3—42no—
153C22×C3×D5—21no—
154C3×C5×Q8—21no—
155C3×C5×Q8—21no—
156C3×C5×D4—21no—
157C3×C5×D4—21no—
158C3×C5×D4—42no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—42no—
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2411yescharacteristic
165D60—22no—
166D60—22no—
167D60—42no—
168C5×D12—22no—
169C5×D12—22no—
170C5×D12—42no—
171C3×C22⋊D5—42no—
172C3×C22⋊D5—44no—
173C2×C3×Dic5—24no—
174C2×C3×Dic5—21no—
175C2×C3×Dic5C2×D412yes—
176C2×C3×Dic5C2×D412yes—
177C3×D20—21no—
178C3×D20—21no—
179C3×C4×D5—42no—
180C3×Dic10—21no—
181C3×Dic10—21no—
182#1203—48no—
183#1203—48no—
184C3⋊#168C2×D414yescomplemented
185C5×C3⋊C8C2×D414yescomplemented
186C2×C3×#41—51no—
187C2×C3×#41C2×D511yescharacteristic
188C22×D12—51no—
189C22×D12—102no—
190C22×D12C2×D511yescharacteristic
191C3×C4⋊Q8—51no—
192C3×#127—51no—
193C3×#124—51no—
194C3×#124—51no—
195C3×#121—102no—
196C3×C4×D4—102no—
197C2×C3×C42—51no—
198#949—24no—
199#949—104no—
200#949—104no—
201#949—104no—
202C2×#215—52no—
203C2×#215—52no—
204C2×#215—52no—
205C2×#215C2×D512yescomplemented
206C2×#213—52no—
207C2×#213—52no—
208C2×#213—52no—
209C2×#213C2×D512yescomplemented
210C2×#208—51no—
211C2×#208C2×D511yescharacteristic
212#874—52no—
213#874—52no—
214#874—102no—
215#803—52no—
216C4×C3⋊C8—52no—
217C24×C5—61no—
218C23×D5—61no—
219C5×#41—22no—
220C5×#41—22no—
221C2×C5×Q8C22×D311yescharacteristic
222C2×C5×D4—21no—
223C2×C5×D4—32no—
224C2×C5×D4—62no—
225C2×C5×D4—62no—
226C2×C5×D4—61no—
227C2×C5×D4C22×D311yescharacteristic
228C22×C4×C5—21no—
229C22×C4×C5C22×D311yescharacteristic
230C2×C22⋊D5—21no—
231C2×C22⋊D5—22no—
232C2×C22⋊D5—64no—
233C2×C22⋊D5—64no—
234C2×C22⋊D5—128no—
235C22×Dic5#6712yes—
236#709—22no—
237#709—22no—
238C2×D20—32no—
239C2×D20—62no—
240C2×D20—62no—
241C2×D20—61no—
242C2×D20C22×D311yescharacteristic
243C2×C4×D5—21no—
244C2×Dic10C22×D311yescharacteristic
245C5×SD16—64no—
246C5×D8—64no—
247C5×M16—34no—
248C2×C5×C8—32no—
249C22⋊Dic5—22no—
250#688—64no—
251#687—64no—
252#686—64no—
253#686—64no—
254#685—22no—
255#683—22no—
256C4×Dic5#6712yes—
257C4×Dic5C22×D311yescharacteristic
258C4×Dic5C22×D311yescharacteristic
259#681—34no—
260C2×#168—32no—
261D40—64no—
262#677—64no—
263C2×AGL(1,ℤ/8)—31no—
264C2×AGL(1,ℤ/8)—151no—
265C2×AGL(1,ℤ/8)—151no—
266C2×AGL(1,ℤ/8)—151no—
267#532—51no—
268C2×#127—151no—
269#496—152no—
270#496—152no—
271#493—152no—
272#492—152no—
273C4×M16—151no—
274C22×C3×C5—22no—
275C22×C3×C5—41no—
276C22×C3×C5—42no—
277C22×C3×C5#12712yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×D15—42no—
280C2×D15—44no—
281C2×D15—84no—
282C2×C5×D3—42no—
283C2×C5×D3—44no—
284C2×C5×D3—84no—
285C2×C3×D5—41no—
286C2×C3×D5—42no—
287C3×C4×C5—41no—
288C3×C4×C5#12712yes—
289C3×C4×C5C22×D411yescharacteristic
290C3×C4×C5C22×D411yescharacteristic
291C3×Dic5—22no—
292C3×Dic5—41no—
293C3×Dic5AGL(1,ℤ/8)14yescomplemented
294C23×D3—21no—
295C23×D3—101no—
296C3×#41—22no—
297C3×#41—22no—
298C3×#41—102no—
299C3×#41—102no—
300C2×C3×Q8—51no—
301C2×C3×Q8C22×D511yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—51no—
304C2×C3×D4—102no—
305C2×C3×D4—101no—
306C2×C3×D4C22×D511yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—52no—
309C22×C3×C4—101no—
310C22×C3×C4C22×D511yescharacteristic
311C2×D12—22no—
312C2×D12—22no—
313C2×D12—21no—
314C2×D12—52no—
315C2×D12—102no—
316C2×D12—102no—
317C2×D12—104no—
318C2×D12—104no—
319C2×D12—101no—
320C2×D12—208no—
321C2×D12C22×D512yes—
322C3×C4⋊C4—102no—
323C3×C22⋊C4—102no—
324C3×C22⋊C4—102no—
325C3×C42—52no—
326C3×C42—51no—
327C3×C42—51no—
328#215—24no—
329#215—104no—
330#215—104no—
331#215—104no—
332#213—24no—
333#213—104no—
334#213—104no—
335#213—104no—
336#208—54no—
337#208C22⋊D514yescomplemented
338C2×C3⋊C8—52no—
339C2×C3⋊C8C22×D512yes—
340C23×C5—21no—
341C23×C5—62no—
342C23×C5—124no—
343C23×C5—122no—
344C23×C5C2×#6711yescharacteristic
345C22×D5—21no—
346C22×D5—62no—
347C22×D5—124no—
348C22×D5—122no—
349C5×Q8—21no—
350C5×Q8—21no—
351C5×D4—21no—
352C5×D4—21no—
353C5×D4—42no—
354C5×D4—62no—
355C5×D4—62no—
356C5×D4—122no—
357C2×C4×C5—21no—
358C2×C4×C5—42no—
359C2×C4×C5D3×D412yes—
360C2×C4×C5D3×D412yes—
361C2×C4×C5C2×#6711yescharacteristic
362C2×C4×C5C23×D311yescharacteristic
363C22⋊D5—42no—
364C22⋊D5—44no—
365C22⋊D5—128no—
366C22⋊D5—128no—
367C2×Dic5—24no—
368C2×Dic5—21no—
369C2×Dic5C2×#6712yes—
370C2×Dic5C2×#6712yes—
371D20—21no—
372D20—21no—
373D20—62no—
374D20—62no—
375D20—122no—
376C4×D5—42no—
377Dic10—21no—
378Dic10—21no—
379C5×C8—34no—
380#168—34no—
381C2×#41—51no—
382C2×#41D3×D511yescharacteristic
383C22×D4—31no—
384C22×D4—151no—
385C22×D4—302no—
386AGL(1,ℤ/8)—64no—
387AGL(1,ℤ/8)—304no—
388AGL(1,ℤ/8)—304no—
389AGL(1,ℤ/8)—304no—
390C2×SD16—32no—
391C2×SD16—152no—
392C2×SD16—152no—
393C2×SD16—152no—
394C2×D8—32no—
395C2×D8—152no—
396C2×D8—152no—
397C2×D8—152no—
398C2×M16—31no—
399C2×M16—151no—
400C4⋊Q8—51no—
401#127—51no—
402#127—152no—
403#127—152no—
404#127—302no—
405#124—51no—
406#124—51no—
407#121—102no—
408C4×D4—102no—
409C2×C42—51no—
410#97—152no—
411C4×C8—152no—
412C2×C3×C5—22no—
413C2×C3×C5—81no—
414C2×C3×C5C2×#12711yescharacteristic
415C2×C3×C5C2×AGL(1,ℤ/8)12yes—
416D15—82no—
417C3×D5—81no—
418C5×D3—82no—
419C23×C3—21no—
420C23×C3—101no—
421C23×C3D4×D511yescharacteristic
422C22×D3—22no—
423C22×D3—44no—
424C22×D3—42no—
425C22×D3—102no—
426C22×D3—204no—
427C22×D3—202no—
428C3×Q8—21no—
429C3×Q8—21no—
430C3×Q8—101no—
431C3×Q8—101no—
432C3×D4—21no—
433C3×D4—21no—
434C3×D4—42no—
435C3×D4—101no—
436C3×D4—101no—
437C3×D4—204no—
438C3×D4—202no—
439C2×C3×C4—21no—
440C2×C3×C4—42no—
441C2×C3×C4—52no—
442C2×C3×C4—52no—
443C2×C3×C4—104no—
444C2×C3×C4—101no—
445C2×C3×C4—202no—
446C2×C3×C4D4×D511yescharacteristic
447C2×C3×C4D4×D512yes—
448C2×C3×C4C2×C22⋊D512yes—
449C2×C3×C4C23×D511yescharacteristic
450D12—22no—
451D12—22no—
452D12—42no—
453D12—102no—
454D12—102no—
455D12—208no—
456D12—208no—
457D12—202no—
458C3⋊C8—54no—
459C3⋊C8C2×C22⋊D514yescomplemented
460C22×C5—22no—
461C22×C5—41no—
462C22×C5—42no—
463C22×C5—122no—
464C22×C5—124no—
465C22×C5—244no—
466C22×C5#94012yes—
467C22×C5C22×#6711yescharacteristic
468C2×D5—41no—
469C2×D5—42no—
470C2×D5—122no—
471C2×D5—124no—
472C2×D5—244no—
473C4×C5—41no—
474C4×C5#94012yes—
475C4×C5C2×D3×D411yescharacteristic
476C4×C5C2×D3×D411yescharacteristic
477Dic5—22no—
478Dic5—41no—
479Dic5#94914yescomplemented
480C24—61no—
481C24—301no—
482#41—22no—
483#41—22no—
484#41—102no—
485#41—102no—
486C2×Q8—51no—
487C2×Q8C2×D3×D511yescharacteristic
488C2×D4—21no—
489C2×D4—32no—
490C2×D4—51no—
491C2×D4—61no—
492C2×D4—62no—
493C2×D4—62no—
494C2×D4—102no—
495C2×D4—101no—
496C2×D4—152no—
497C2×D4—304no—
498C2×D4—304no—
499C2×D4—301no—
500C2×D4—302no—
501C2×D4—302no—
502C2×D4—608no—
503C2×D4C2×D3×D511yescharacteristic
504C22×C4—21no—
505C22×C4—52no—
506C22×C4—101no—
507C22×C4C2×D3×D511yescharacteristic
508SD16—64no—
509SD16—304no—
510SD16—304no—
511SD16—304no—
512D8—64no—
513D8—304no—
514D8—304no—
515D8—304no—
516M16—34no—
517M16—154no—
518C2×C8—32no—
519C2×C8—152no—
520C4⋊C4—102no—
521C22⋊C4—102no—
522C22⋊C4—102no—
523C42—52no—
524C42—51no—
525C42—51no—
526C3×C5#315111yescharacteristic, complemented, Hall
527C22×C3—22no—
528C22×C3—42no—
529C22×C3—41no—
530C22×C3—202no—
531C22×C3—201no—
532C22×C3#408612yes—
533C22×C3C2×D4×D511yescharacteristic
534C2×D3—44no—
535C2×D3—42no—
536C2×D3—84no—
537C2×D3—204no—
538C2×D3—202no—
539C2×D3—404no—
540C3×C4—41no—
541C3×C4—54no—
542C3×C4—102no—
543C3×C4—201no—
544C3×C4#408612yes—
545C3×C4C2×D4×D511yescharacteristic
546C3×C4C22×C22⋊D511yescharacteristic
547C2×C5—22no—
548C2×C5—81no—
549C2×C5—242no—
550C2×C5C2×#94011yescharacteristic
551C2×C5C2×#94912yes—
552D5—81no—
553D5—242no—
554C23—21no—
555C23—62no—
556C23—101no—
557C23—124no—
558C23—122no—
559C23—302no—
560C23—604no—
561C23—602no—
562C23D5×#6711yescharacteristic
563Q8—21no—
564Q8—21no—
565Q8—101no—
566Q8—101no—
567D4—21no—
568D4—21no—
569D4—42no—
570D4—62no—
571D4—62no—
572D4—101no—
573D4—101no—
574D4—122no—
575D4—204no—
576D4—202no—
577D4—302no—
578D4—302no—
579D4—608no—
580D4—608no—
581D4—602no—
582C2×C4—21no—
583C2×C4—42no—
584C2×C4—52no—
585C2×C4—52no—
586C2×C4—104no—
587C2×C4—101no—
588C2×C4—202no—
589C2×C4D5×#6711yescharacteristic
590C2×C4D3×C22⋊D512yes—
591C2×C4#679012yes—
592C2×C4C22×D3×D511yescharacteristic
593C8—34no—
594C8—154no—
595C2×C3—22no—
596C2×C3—81no—
597C2×C3—401no—
598C2×C3D5×AGL(1,ℤ/8)12yes—
599C2×C3C2×#408611yescharacteristic
600D3—82no—
601D3—402no—
602C5#8328711yescharacteristic, complemented, Sylow
603C22—22no—
604C22—42no—
605C22—41no—
606C22—124no—
607C22—122no—
608C22—202no—
609C22—201no—
610C22—244no—
611C22—604no—
612C22—602no—
613C22—1204no—
614C22#9156712yes—
615C22C2×D5×#6711yescharacteristic
616C4—41no—
617C4—54no—
618C4—102no—
619C4—201no—
620C4#9156712yes—
621C4C2×D3×C22⋊D511yescharacteristic
622C4C2×#679011yescharacteristic
623C3#1061566811yescharacteristic, complemented, Sylow
624C2—22no—
625C2—81no—
626C2—242no—
627C2—401no—
628C2—1202no—
629C2D5×#94912yes—
630C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3151
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91838C2semidirect
2. C2×C5×#949C2semidirect
3. C3×#66166C2semidirect
4. C2×#91451C2semidirect
5. C2×#91301C2semidirect
6. C2×#91299C2semidirect
7. #11749340C2semidirect
8. #11749339C2semidirect
9. #11749094C2semidirect
10. #11749093C2semidirect
11. Dic5×#208C2semidirect
19. C2×#6717C22semidirect
20. C2×#6715C22semidirect
23. C2×C5×#215C22semidirect
24. C2×C5×#213C22semidirect
26. C3×#4093C22semidirect
27. C3×#4090C22semidirect
28. C3×#4086C22semidirect
30. C3×#4082C22semidirect
36. C2×#6658C22semidirect
37. C2×#6656C22semidirect
39. C2×#6653C22semidirect
41. C2×#6652C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
46. #66166D3semidirect
86. #6710D4semidirect
90. C5×#208D4semidirect
106. C2×#949D5semidirect
123. #4093C2×D3semidirect
124. #4090C2×D3semidirect
129. #4086C2×D3semidirect
131. #4082C2×D3semidirect
184. C3⋊#168C2×D4semidirect
185. C5×C3⋊C8C2×D4semidirect
205. C2×#215C2×D5semidirect
209. C2×#213C2×D5semidirect
293. C3×Dic5AGL(1,ℤ/8)semidirect
337. #208C22⋊D5semidirect
459. C3⋊C8C2×C22⋊D5semidirect
479. Dic5#949semidirect
526. C3×C5#3151semidirect
602. C5#83287semidirect
623. C3#10615668semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C2×C5×#9492
C3×#661662
C2×#914512
C2×#913012
C2×#912992
#117493402
#117493392
#117490942
#117490932
Dic5×#2082
#106156683
#832875