Finite Group Databasebeta

← #14439174

Subgroups — #14439174

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×#91821C211yesmaximal, characteristic, complemented
2C2×C5×#932C211yesmaximal, characteristic, complemented
3C2×C3×#4086C211yesmaximal, characteristic, complemented
4#11754572C211yesmaximal, characteristic, complemented
5C2×#91312C211yesmaximal, characteristic, complemented
6C2×#91298C211yesmaximal, characteristic, complemented
7#11749106C212yesmaximal, complemented
8#11749093C212yesmaximal, complemented
9#11749069C212yesmaximal, complemented
10#11749066C212yesmaximal, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10615668—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×C22⋊D5—22no—
17C22×C3×D20C2211yescharacteristic
18C2×#6716C2212yescomplemented
19#91821—24no—
20C2×#6715C2212yescomplemented
21C2×#6710C2211yescharacteristic
22C2×C5×#214C2212yescomplemented
23C5×#932—24no—
24C2×C5×#213C2212yescomplemented
25C2×C5×#208C2211yescharacteristic
26C3×#4086—22no—
27C3×#4086C2212yes—
28C3×#4086C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30#91566—22no—
31#91451C2211yescharacteristic, complemented
32C4×#1203—22no—
33#91376C2211yescharacteristic, complemented
34#91375C2211yescharacteristic, complemented
35#91373C2211yescharacteristic, complemented
36#91312—24no—
37C2×#6657C2212yescomplemented
38C2×#6655C2212yescomplemented
39C2×#6653C2212yescomplemented
40#91298—24no—
41C2×#6652C2212yescomplemented
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83163—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66166—31no—
47C2×#4095—31no—
48C2×#4086D311yescharacteristic, complemented
49C2×#4078—31no—
50C2×#4054—31no—
51#65465—32no—
52#65464—32no—
53#65443—32no—
54#65440—32no—
55M16×Dic5—31no—
56C24×C3×C5—21no—
57C23×C3×D5—21no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×#67—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6C2311yescharacteristic
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5—24no—
77C2×C3×C22⋊D5—48no—
78C22×C3×Dic5D412yes—
79C2×C3×D20—22no—
80C2×C3×D20—22no—
81C2×C3×D20—21no—
82C2×C3×D20C2312yes—
83C2×#1203—22no—
84#6716—24no—
85#6715—24no—
86#6710D414yescomplemented
87C2×C3⋊#168C2312yes—
88C5×#214—24no—
89C5×#213—24no—
90C5×#208D414yescomplemented
91C2×C5×C3⋊C8C2312yes—
92C3×C4×Dic5D412yes—
93C3×C4×Dic5C2311yescharacteristic
94C3×C4×Dic5C2311yescharacteristic
95#6668—22no—
96#6667—22no—
97(C2×D3)⋊Dic5—22no—
98#6657—24no—
99#6655—24no—
100#6653—24no—
101#6652—24no—
102C2×C3×#127—51no—
103C2×#932—51no—
104C2×#932—51no—
105C2×#932—51no—
106C2×#932D511yescharacteristic, complemented
107#5477—51no—
108#5076—52no—
109#5074—52no—
110#5074—52no—
111#5073—52no—
112C4×#208—51no—
113C2×C5×#41—31no—
114C22×C5×D4C2×D311yescharacteristic
115C22×C22⋊D5—22no—
116C2×#709—31no—
117C22×D20C2×D311yescharacteristic
118C5×AGL(1,ℤ/8)—64no—
119C2×C5×SD16—32no—
120C2×C5×D8—32no—
121C2×C5×M16—31no—
122#4095—64no—
123#4093—31no—
124#4090—31no—
125C2×#688—32no—
126#4086—22no—
127#4086—31no—
128#4086C2×D312yes—
129#4086C2×D312yes—
130#4085—62no—
131#4082—31no—
132C2×#687—32no—
133#4078—64no—
134C2×#686—32no—
135C2×#686—32no—
136C4×C22⋊D5—62no—
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—22no—
146C23×C3×C5—44no—
147C23×C3×C5—42no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×C5×D3—21no—
151C22×C3×D5—22no—
152C22×C3×D5—44no—
153C22×C3×D5—42no—
154C3×C5×D4—22no—
155C3×C5×D4—22no—
156C3×C5×D4—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—42no—
162C2×Dic15—21no—
163D60—21no—
164D60—21no—
165C4×D15—42no—
166Dic30—21no—
167Dic30—21no—
168C5×#67—42no—
169C2×C5×Dic3—21no—
170C5×D12—21no—
171C5×D12—21no—
172C4×C5×D3—42no—
173C5×Dic6—21no—
174C5×Dic6—21no—
175C3×C22⋊D5—48no—
176C3×C22⋊D5—48no—
177C2×C3×Dic5—24no—
178C2×C3×Dic5C2×D412yes—
179C2×C3×Dic5C2×D412yes—
180C3×D20—22no—
181C3×D20—22no—
182C3×D20—42no—
183#1203—44no—
184C3⋊#168C2×D414yescomplemented
185C5×C3⋊C8C2×D414yescomplemented
186C22×C3×D4—51no—
187C22×C3×D4—102no—
188C22×C3×D4C2×D511yescharacteristic
189C2×#235—51no—
190C2×#235C2×D511yescharacteristic
191C3×#127—52no—
192C3×#127—52no—
193C3×#127—102no—
194C2×C3×C42—51no—
195C2×#214—52no—
196C2×#214—52no—
197C2×#214—52no—
198C2×#214C2×D512yescomplemented
199#932—24no—
200#932—104no—
201#932—104no—
202#932—104no—
203C2×#213—52no—
204C2×#213—52no—
205C2×#213—52no—
206C2×#213C2×D512yescomplemented
207#930—102no—
208C2×#208—51no—
209C2×#208C2×D511yescharacteristic
210#875—51no—
211#875—51no—
212#874—51no—
213C4×D12—102no—
214#869—51no—
215#803—52no—
216C4×C3⋊C8—52no—
217C24×C5—21no—
218C23×D5—21no—
219C5×#41—62no—
220C5×#41—62no—
221C2×C5×Q8—31no—
222C2×C5×D4—22no—
223C2×C5×D4—22no—
224C2×C5×D4—21no—
225C2×C5×D4—31no—
226C2×C5×D4—61no—
227C2×C5×D4C22×D312yes—
228C22×C4×C5—61no—
229C22×C4×C5C22×D311yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—48no—
233C2×C22⋊D5—61no—
234C2×C22⋊D5—62no—
235C22×Dic5#6712yes—
236#709—62no—
237#709—62no—
238C2×D20—22no—
239C2×D20—22no—
240C2×D20—21no—
241C2×D20—31no—
242C2×D20C22×D312yes—
243C2×C4×D5—61no—
244C2×Dic10—31no—
245C5×SD16—64no—
246C5×D8—64no—
247C5×M16—34no—
248C2×C5×C8—32no—
249C22⋊Dic5—62no—
250#688—64no—
251#687—64no—
252#686—64no—
253#686—64no—
254#685—62no—
255#683—62no—
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—151no—
268C2×#127—51no—
269#496—152no—
270#496—152no—
271#493—152no—
272#492—152no—
273C4×M16—151no—
274C22×C3×C5—22no—
275C22×C3×C5—42no—
276C22×C3×C5—44no—
277C22×C3×C5—84no—
278C22×C3×C5#12712yes—
279C22×C3×C5C22×D411yescharacteristic
280C2×D15—41no—
281C2×D15—42no—
282C2×C5×D3—41no—
283C2×C5×D3—42no—
284C2×C3×D5—42no—
285C2×C3×D5—44no—
286C2×C3×D5—84no—
287C3×C4×C5#12712yes—
288C3×C4×C5C22×D411yescharacteristic
289C3×C4×C5C22×D411yescharacteristic
290Dic15—41no—
291C3×Dic5—22no—
292C3×Dic5AGL(1,ℤ/8)14yescomplemented
293C5×Dic3—41no—
294C24×C3—21no—
295C24×C3—101no—
296C2×C3×D4—22no—
297C2×C3×D4—21no—
298C2×C3×D4—22no—
299C2×C3×D4—52no—
300C2×C3×D4—104no—
301C2×C3×D4—104no—
302C2×C3×D4—102no—
303C2×C3×D4—101no—
304C2×C3×D4—102no—
305C2×C3×D4—208no—
306C2×C3×D4C22×D512yes—
307C22×C3×C4—52no—
308C22×C3×C4C22×D511yescharacteristic
309C2×#67—21no—
310C2×#67—101no—
311#235—22no—
312#235—22no—
313#235—102no—
314#235—102no—
315C2×D12—51no—
316C2×D12—102no—
317C2×D12C22×D511yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—101no—
320C2×Dic6—51no—
321C2×Dic6C22×D511yescharacteristic
322C3×C42—52no—
323C3×C42—51no—
324C3×C42—51no—
325#214—24no—
326#214—104no—
327#214—104no—
328#214—104no—
329#213—24no—
330#213—104no—
331#213—104no—
332#213—104no—
333(C2×D3)⋊C4—102no—
334(C2×D3)⋊C4—102no—
335C4⋊Dic3—102no—
336#208—54no—
337#208C22⋊D514yescomplemented
338C2×C3⋊C8—52no—
339C2×C3⋊C8C22×D512yes—
340C23×C5—22no—
341C23×C5—44no—
342C23×C5—42no—
343C23×C5—61no—
344C23×C5C2×#6711yescharacteristic
345C22×D5—22no—
346C22×D5—44no—
347C22×D5—42no—
348C22×D5—61no—
349C5×Q8—61no—
350C5×Q8—61no—
351C5×D4—22no—
352C5×D4—22no—
353C5×D4—42no—
354C5×D4—61no—
355C5×D4—61no—
356C5×D4—122no—
357C2×C4×C5—61no—
358C2×C4×C5—122no—
359C2×C4×C5D3×D412yes—
360C2×C4×C5D3×D412yes—
361C2×C4×C5C2×#6711yescharacteristic
362C2×C4×C5C23×D311yescharacteristic
363C22⋊D5—48no—
364C22⋊D5—48no—
365C22⋊D5—122no—
366C22⋊D5—124no—
367C2×Dic5—24no—
368C2×Dic5—61no—
369C2×Dic5C2×#6712yes—
370C2×Dic5C2×#6712yes—
371D20—22no—
372D20—22no—
373D20—42no—
374D20—61no—
375D20—61no—
376C4×D5—122no—
377Dic10—61no—
378Dic10—61no—
379C5×C8—34no—
380#168—34no—
381C2×#41—31no—
382C2×#41—151no—
383C22×D4—51no—
384C22×D4—102no—
385C22×D4D3×D511yescharacteristic
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—151no—
401#127—52no—
402#127—52no—
403#127—102no—
404#127—151no—
405#124—151no—
406#124—151no—
407#121—302no—
408C4×D4—302no—
409C2×C42—51no—
410#97—152no—
411C4×C8—152no—
412C2×C3×C5—22no—
413C2×C3×C5—82no—
414C2×C3×C5C2×#12711yescharacteristic
415C2×C3×C5C2×AGL(1,ℤ/8)12yes—
416D15—81no—
417C3×D5—82no—
418C5×D3—81no—
419C23×C3—22no—
420C23×C3—44no—
421C23×C3—42no—
422C23×C3—102no—
423C23×C3—204no—
424C23×C3—202no—
425C23×C3D4×D511yescharacteristic
426C22×D3—21no—
427C22×D3—101no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—42no—
431C3×D4—102no—
432C3×D4—102no—
433C3×D4—208no—
434C3×D4—208no—
435C3×D4—202no—
436C2×C3×C4—52no—
437C2×C3×C4—52no—
438C2×C3×C4—104no—
439C2×C3×C4D4×D511yescharacteristic
440C2×C3×C4D4×D512yes—
441C2×C3×C4C2×C22⋊D512yes—
442C2×C3×C4C23×D511yescharacteristic
443#67—42no—
444#67—202no—
445C2×Dic3—21no—
446C2×Dic3—101no—
447D12—21no—
448D12—21no—
449D12—101no—
450D12—101no—
451D12—204no—
452C4×D3—42no—
453C4×D3—202no—
454Dic6—21no—
455Dic6—21no—
456Dic6—101no—
457Dic6—101no—
458C3⋊C8—54no—
459C3⋊C8C2×C22⋊D514yescomplemented
460C22×C5—22no—
461C22×C5—44no—
462C22×C5—42no—
463C22×C5—84no—
464C22×C5—122no—
465C22×C5—121no—
466C22×C5#94012yes—
467C22×C5C22×#6711yescharacteristic
468C2×D5—44no—
469C2×D5—42no—
470C2×D5—84no—
471C2×D5—122no—
472C2×D5—121no—
473C4×C5—121no—
474C4×C5#94012yes—
475C4×C5C2×D3×D411yescharacteristic
476C4×C5C2×D3×D411yescharacteristic
477Dic5—22no—
478Dic5—121no—
479Dic5#93214yescomplemented
480C24—21no—
481C24—101no—
482#41—62no—
483#41—62no—
484#41—302no—
485#41—302no—
486C2×Q8—31no—
487C2×Q8—151no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—31no—
492C2×D4—52no—
493C2×D4—61no—
494C2×D4—104no—
495C2×D4—104no—
496C2×D4—101no—
497C2×D4—102no—
498C2×D4—102no—
499C2×D4—151no—
500C2×D4—208no—
501C2×D4—302no—
502C2×D4—301no—
503C2×D4C2×D3×D512yes—
504C22×C4—52no—
505C22×C4—61no—
506C22×C4—301no—
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—302no—
521C22⋊C4—302no—
522C22⋊C4—302no—
523C42—52no—
524C42—51no—
525C42—51no—
526C3×C5#315111yescharacteristic, complemented, Hall
527C22×C3—22no—
528C22×C3—44no—
529C22×C3—42no—
530C22×C3—84no—
531C22×C3—204no—
532C22×C3—202no—
533C22×C3—404no—
534C22×C3#408612yes—
535C22×C3C2×D4×D511yescharacteristic
536C2×D3—42no—
537C2×D3—41no—
538C2×D3—202no—
539C2×D3—201no—
540C3×C4—54no—
541C3×C4—102no—
542C3×C4#408612yes—
543C3×C4C2×D4×D511yescharacteristic
544C3×C4C22×C22⋊D511yescharacteristic
545Dic3—41no—
546Dic3—201no—
547C2×C5—22no—
548C2×C5—82no—
549C2×C5—241no—
550C2×C5C2×#93212yes—
551C2×C5C2×#94011yescharacteristic
552D5—82no—
553D5—241no—
554C23—22no—
555C23—44no—
556C23—42no—
557C23—61no—
558C23—102no—
559C23—204no—
560C23—202no—
561C23—301no—
562C23D5×#6711yescharacteristic
563Q8—61no—
564Q8—61no—
565Q8—301no—
566Q8—301no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—61no—
571D4—61no—
572D4—102no—
573D4—102no—
574D4—122no—
575D4—208no—
576D4—208no—
577D4—202no—
578D4—301no—
579D4—301no—
580D4—604no—
581D4—602no—
582C2×C4—52no—
583C2×C4—52no—
584C2×C4—61no—
585C2×C4—104no—
586C2×C4—122no—
587C2×C4—301no—
588C2×C4—602no—
589C2×C4D5×#6711yescharacteristic
590C2×C4D3×C22⋊D512yes—
591C2×C4#679012yes—
592C2×C4C22×D3×D511yescharacteristic
593C8—34no—
594C8—154no—
595C2×C3—22no—
596C2×C3—82no—
597C2×C3—402no—
598C2×C3D5×AGL(1,ℤ/8)12yes—
599C2×C3C2×#408611yescharacteristic
600D3—81no—
601D3—401no—
602C5#8316311yescharacteristic, complemented, Sylow
603C22—22no—
604C22—42no—
605C22—44no—
606C22—84no—
607C22—121no—
608C22—122no—
609C22—202no—
610C22—204no—
611C22—404no—
612C22—601no—
613C22—602no—
614C22#9156712yes—
615C22C2×D5×#6711yescharacteristic
616C4—54no—
617C4—102no—
618C4—121no—
619C4—601no—
620C4#9156712yes—
621C4C2×D3×C22⋊D511yescharacteristic
622C4C2×#679011yescharacteristic
623C3#1061566811yescharacteristic, complemented, Sylow
624C2—22no—
625C2—82no—
626C2—241no—
627C2—402no—
628C2—1201no—
629C2D5×#93212yes—
630C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3151
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91821C2semidirect
2. C2×C5×#932C2semidirect
3. C2×C3×#4086C2semidirect
4. #11754572C2semidirect
5. C2×#91312C2semidirect
6. C2×#91298C2semidirect
7. #11749106C2semidirect
8. #11749093C2semidirect
9. #11749069C2semidirect
10. #11749066C2semidirect
11. Dic5×#208C2semidirect
18. C2×#6716C22semidirect
20. C2×#6715C22semidirect
22. C2×C5×#214C22semidirect
24. C2×C5×#213C22semidirect
31. #91451C22semidirect
33. #91376C22semidirect
34. #91375C22semidirect
35. #91373C22semidirect
37. C2×#6657C22semidirect
38. C2×#6655C22semidirect
39. C2×#6653C22semidirect
41. C2×#6652C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
48. C2×#4086D3semidirect
86. #6710D4semidirect
90. C5×#208D4semidirect
106. C2×#932D5semidirect
184. C3⋊#168C2×D4semidirect
185. C5×C3⋊C8C2×D4semidirect
198. C2×#214C2×D5semidirect
206. C2×#213C2×D5semidirect
292. C3×Dic5AGL(1,ℤ/8)semidirect
337. #208C22⋊D5semidirect
459. C3⋊C8C2×C22⋊D5semidirect
479. Dic5#932semidirect
526. C3×C5#3151semidirect
602. C5#83163semidirect
623. C3#10615668semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C2×C5×#9322
C2×C3×#40862
#117545722
C2×#913122
C2×#912982
#117491062
#117490932
#117490692
#117490662
Dic5×#2082
#106156683
#831635