Finite Group Databasebeta

← #14412575

Subgroups — #14412575

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#713C211yesmaximal, characteristic
2D5×#926C211yesmaximal, characteristic, complemented
3C2×D5×#208C211yesmaximal, characteristic, complemented
4#11751326C211yesmaximal, characteristic, complemented
5C5×#5225C211yesmaximal, characteristic, complemented
6#11749207C214yesmaximal, complemented
7#11749198C214yesmaximal, complemented
8#11748367C211yesmaximal, characteristic, complemented
9#11748366C211yesmaximal, characteristic, complemented
10#10610687—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C2×C3×#713—24no—
13C2×C3×#713—21no—
14C2×C3×#713—21no—
15C2×C3×#713C418yescomplemented
16C2×C3×#713C2212yes—
17C2×C3×#713C2212yes—
18C22×C3×D20—21no—
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5—21no—
21C22×C3×C4×D5C2211yescharacteristic
22#91815C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24C5×#926C2211yescharacteristic
25C2×C5×#208C2211yescharacteristic
26D5×#217—21no—
27#91528—21no—
28D5×C4⋊Dic3C2212yescomplemented
29C4×D5×Dic3—21no—
30#91358C2212yescomplemented
31#91357—21no—
32C2×#6649C2212yescomplemented
33D5×#208—24no—
34C2×D5×C3⋊C8C2212yescomplemented
35#91119C2214yescomplemented
36C5×#835C2214yescomplemented
37#90965C2214yescomplemented
38#90964C2214yescomplemented
39#84072—51nomaximal, Hall
40C22×#713D311yescharacteristic
41C2×D5×M16—31no—
42D5×#117—31no—
43C5×#419—31no—
44#65514—31no—
45#65420—31no—
46#65290—31no—
47#65093—34no—
48#65092—34no—
49C23×C3×D5—21no—
50C23×C3×D5D411yescharacteristic
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—21no—
53C2×C3×C5×Q8C2×C414yescomplemented
54C2×C3×C5×Q8C2312yes—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×Dic5D411yescharacteristic
58C3×#713—28no—
59C3×#713—28no—
60C3×#713—24no—
61C3×#713—24no—
62C3×#713C2×C418yes—
63C3×#713C2×C418yescomplemented
64C2×C3×D20—28no—
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20—21no—
68C2×C3×D20—22no—
69C2×C3×D20C2×C414yescomplemented
70C2×C3×D20C2312yes—
71C2×C3×C4×D5—28no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5C2×C414yes—
75C2×C3×C4×D5D411yescharacteristic
76C2×C3×C4×D5D411yescharacteristic
77C2×C3×C4×D5D414yes—
78C2×C3×C4×D5C2311yescharacteristic
79C2×C3×C4×D5C2311yescharacteristic
80C2×D5×Dic3—22no—
81#6719—21no—
82C4⋊Dic15C2312yes—
83C4×Dic15—21no—
84#6710—22no—
85C2×C3⋊#168C2312yes—
86C5×#217—21no—
87C5×C4⋊Dic3C2312yes—
88C4×C5×Dic3—21no—
89C5×#208—22no—
90C2×C5×C3⋊C8C2312yes—
91#6668—22no—
92#6665—22no—
93Dic3×Dic5—22no—
94#6649—24no—
95D5×C3⋊C8—24no—
96C22×C3×#41—51no—
97C2×#926—51no—
98C22×#208—51no—
99#5233—54no—
100#5232—54no—
101#5225—51no—
102#5225D511yescharacteristic, complemented
103#5215—51no—
104#5215—51no—
105C22×C5×Q8C2×D311yescharacteristic
106C2×#713—24no—
107C2×#713—21no—
108C2×#713—21no—
109C2×#713Dic318yescomplemented
110C2×#713C2×D312yes—
111C2×#713C2×D312yes—
112C22×D20—21no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—21no—
115C22×C4×D5C2×D311yescharacteristic
116C2×C5×M16—31no—
117C5×#117—31no—
118#4072—31no—
119C2×#681—31no—
120D5×M16—64no—
121C2×#676—32no—
122C2×C8×D5—32no—
123#4038—32no—
124D5×C4⋊C4—32no—
125D5×C22⋊C4—61no—
126#4023—61no—
127#4018—61no—
128C42×D5—61no—
129C5×#103—34no—
130#3967—34no—
131#3953—34no—
132#3941—34no—
133#2896—151noSylow
134C23×C3×C5C2×D411yescharacteristic
135C22×C3×D5—24no—
136C22×C3×D5—22no—
137C22×C3×D5—42no—
138C22×C3×D5—44no—
139C22×C3×D5C22⋊C414yes—
140C22×C3×D5C2×D411yescharacteristic
141C22×C3×D5C2×D411yescharacteristic
142C3×C5×Q8—24no—
143C3×C5×Q8—22no—
144C3×C5×Q8C22×C414yes—
145C2×C3×C4×C5—24no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—22no—
152C2×C5×Dic3—22no—
153C2×C3×Dic5C22⋊C414yes—
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C3×D20—28no—
157C3×D20—28no—
158C3×D20—24no—
159C3×D20—22no—
160C3×D20C22×C414yes—
161C3×C4×D5—28no—
162C3×C4×D5—28no—
163C3×C4×D5C22⋊C414yes—
164C3×C4×D5C22⋊C414yes—
165C3×C4×D5C22×C412yes—
166C3×C4×D5C22×C412yes—
167C3×C4×D5C2×D412yes—
168C3×C4×D5C2×D412yes—
169D5×Dic3—44no—
170C3⋊#168—22no—
171C5×C3⋊C8—22no—
172C2×C3×#41—58no—
173C2×C3×#41—52no—
174C2×C3×#41—52no—
175C2×C3×#41—104no—
176C2×C3×#41—101no—
177C2×C3×#41—101no—
178C22×C3×Q8C2×D511yescharacteristic
179C22×C3×D4—51no—
180C22×C3×D4—101no—
181C23×C3×C4—51no—
182C23×C3×C4—101no—
183C2×#217—101no—
184#926—51no—
185#926—52no—
186#926—101no—
187#926—101no—
188#926C2×D511yescharacteristic
189C2×C4⋊Dic3—52no—
190C2×C4×Dic3—101no—
191C2×#208—51no—
192C2×#208—52no—
193C2×#208—104no—
194C2×#208C2×D511yescharacteristic
195C22×C3⋊C8—52no—
196#835—54no—
197#835C2×D514yescomplemented
198#832—54no—
199#832—54no—
200C23×D5—21no—
201C23×D5#6711yescharacteristic
202C2×C5×Q8—22no—
203C2×C5×Q8—21no—
204C2×C5×Q8C2×Dic314yescomplemented
205C2×C5×Q8C22×D312yes—
206C22×C4×C5—21no—
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5#6711yescharacteristic
209#713—28no—
210#713—28no—
211#713—24no—
212#713—24no—
213#713C2×Dic318yes—
214#713C2×Dic318yescomplemented
215C2×D20—28no—
216C2×D20—22no—
217C2×D20—22no—
218C2×D20—21no—
219C2×D20—22no—
220C2×D20C2×Dic314yescomplemented
221C2×D20C22×D312yes—
222C2×C4×D5—28no—
223C2×C4×D5—22no—
224C2×C4×D5—22no—
225C2×C4×D5—62no—
226C2×C4×D5C2×Dic314yes—
227C2×C4×D5#6711yescharacteristic
228C2×C4×D5#6711yescharacteristic
229C2×C4×D5#6714yes—
230C2×C4×D5C22×D311yescharacteristic
231C2×C4×D5C22×D311yescharacteristic
232C5×M16—62no—
233C2×C5×C8—32no—
234C5×C4⋊C4—32no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237C22⋊Dic5—61no—
238#685—62no—
239C4⋊Dic5—32no—
240#683—62no—
241C4×Dic5—61no—
242C4×Dic5—62no—
243#681—62no—
244C2×#168—32no—
245#676—64no—
246C8×D5—64no—
247C22×#41—51no—
248C22×M16—151no—
249C2×#117—151no—
250#419—31no—
251#419—151no—
252#418—151no—
253#418—151no—
254#417—154no—
255#416—154no—
256C22×C3×C5—22no—
257C22×C3×C5C2×C22⋊C412yes—
258C22×C3×C5C22×D411yescharacteristic
259C2×C3×D5—22no—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C2×C3×D5—44no—
263C2×C3×D5—48no—
264C2×C3×D5—44no—
265C2×C3×D5C2×C22⋊C412yes—
266C2×C3×D5C2×C22⋊C412yes—
267C3×C4×C5—24no—
268C3×C4×C5C2×C22⋊C412yes—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—42no—
272C3×Dic5C2×C22⋊C412yes—
273C3×Dic5C2×C22⋊C412yes—
274C5×Dic3—42no—
275C24×C3—51no—
276C24×C3—101no—
277C3×#41—58no—
278C3×#41—58no—
279C3×#41—104no—
280C3×#41—104no—
281C3×#41—108no—
282C3×#41—108no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8C4×D514yescomplemented
286C2×C3×Q8C22×D512yes—
287C2×C3×D4—54no—
288C2×C3×D4—52no—
289C2×C3×D4—102no—
290C2×C3×D4—102no—
291C2×C3×D4—108no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C22×C3×C4—21no—
295C22×C3×C4—51no—
296C22×C3×C4—54no—
297C22×C3×C4—54no—
298C22×C3×C4—51no—
299C22×C3×C4—51no—
300C22×C3×C4—51no—
301C22×C3×C4—51no—
302C22×C3×C4—102no—
303C22×C3×C4—102no—
304C22×C3×C4—108no—
305C22×C3×C4C22×D511yescharacteristic
306C22×Dic3—102no—
307#217—21no—
308#217—102no—
309#217—101no—
310C4⋊Dic3—52no—
311C4⋊Dic3—102no—
312C4⋊Dic3C22×D512yes—
313C4×Dic3—21no—
314C4×Dic3—102no—
315C4×Dic3—101no—
316#208—22no—
317#208—104no—
318#208—102no—
319C2×C3⋊C8—52no—
320C2×C3⋊C8—104no—
321C2×C3⋊C8C22×D512yes—
322C23×C5C2×#6711yescharacteristic
323C22×D5—24no—
324C22×D5—22no—
325C22×D5—42no—
326C22×D5—44no—
327C22×D5#21714yes—
328C22×D5C2×#6711yescharacteristic
329C22×D5C2×#6711yescharacteristic
330C5×Q8—24no—
331C5×Q8—22no—
332C5×Q8C22×Dic314yes—
333C2×C4×C5—24no—
334C2×C4×C5—22no—
335C2×C4×C5—62no—
336C2×C4×C5C22×Dic312yes—
337C2×C4×C5C2×#6711yescharacteristic
338C2×C4×C5C2×#6712yes—
339C2×C4×C5C23×D311yescharacteristic
340C2×Dic5—62no—
341C2×Dic5#21714yes—
342C2×Dic5C2×#6711yescharacteristic
343C2×Dic5C2×#6711yescharacteristic
344D20—28no—
345D20—28no—
346D20—24no—
347D20—22no—
348D20C22×Dic314yes—
349C4×D5—28no—
350C4×D5—28no—
351C4×D5—124no—
352C4×D5#21714yes—
353C4×D5#21714yes—
354C4×D5C22×Dic312yes—
355C4×D5C22×Dic312yes—
356C4×D5C2×#6712yes—
357C4×D5C2×#6712yes—
358C5×C8—62no—
359#168—62no—
360C2×#41—58no—
361C2×#41—52no—
362C2×#41—52no—
363C2×#41—101no—
364C2×#41—101no—
365C2×#41—104no—
366C22×Q8D3×D511yescharacteristic
367C22×D4—51no—
368C22×D4—101no—
369C23×C4—51no—
370C23×C4—101no—
371C2×M16—31no—
372C2×M16—152no—
373C2×M16—151no—
374C2×M16—304no—
375C22×C8—152no—
376#117—31no—
377#117—152no—
378#117—151no—
379#117—301no—
380#117—301no—
381C2×C4⋊C4—152no—
382C2×C22⋊C4—301no—
383C2×C42—301no—
384#103—34no—
385#103—154no—
386#102—154no—
387#102—154no—
388C2×C3×C5—22no—
389C2×C3×C5C22×C22⋊C411yescharacteristic
390C2×C3×C5#57512yes—
391C3×D5—22no—
392C3×D5—22no—
393C3×D5—44no—
394C23×C3—51no—
395C23×C3—51no—
396C23×C3—54no—
397C23×C3—102no—
398C23×C3—104no—
399C23×C3—202no—
400C23×C3—204no—
401C23×C3D4×D511yescharacteristic
402C3×Q8—22no—
403C3×Q8—24no—
404C3×Q8C2×C4×D514yes—
405C3×D4—54no—
406C3×D4—108no—
407C3×D4—108no—
408C3×D4—102no—
409C3×D4—104no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—51no—
413C2×C3×C4—51no—
414C2×C3×C4—54no—
415C2×C3×C4—52no—
416C2×C3×C4—52no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—54no—
420C2×C3×C4—54no—
421C2×C3×C4—108no—
422C2×C3×C4—108no—
423C2×C3×C4C2×C4×D512yes—
424C2×C3×C4D4×D512yes—
425C2×C3×C4D4×D511yescharacteristic
426C2×C3×C4C23×D511yescharacteristic
427C2×Dic3—22no—
428C2×Dic3—102no—
429C2×Dic3—204no—
430C3⋊C8—22no—
431C3⋊C8—102no—
432C22×C5—22no—
433C22×C5C2×#21712yes—
434C22×C5C22×#6711yescharacteristic
435C2×D5—22no—
436C2×D5—22no—
437C2×D5—24no—
438C2×D5—44no—
439C2×D5—48no—
440C2×D5—44no—
441C2×D5C2×#21712yes—
442C2×D5C2×#21712yes—
443C4×C5—24no—
444C4×C5—122no—
445C4×C5C2×#21712yes—
446C4×C5C23×Dic311yescharacteristic
447C4×C5C22×#6711yescharacteristic
448Dic5—122no—
449Dic5C2×#21712yes—
450Dic5C2×#21712yes—
451C24—51no—
452C24—101no—
453#41—58no—
454#41—58no—
455#41—104no—
456#41—104no—
457#41—108no—
458#41—108no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8D5×Dic314yescomplemented
462C2×Q8C2×D3×D512yes—
463C2×D4—54no—
464C2×D4—52no—
465C2×D4—102no—
466C2×D4—102no—
467C2×D4—108no—
468C2×D4—102no—
469C2×D4—101no—
470C22×C4—21no—
471C22×C4—51no—
472C22×C4—54no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—54no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—108no—
481C22×C4—302no—
482C22×C4C2×D3×D511yescharacteristic
483M16—62no—
484M16—304no—
485M16—302no—
486C2×C8—32no—
487C2×C8—152no—
488C2×C8—304no—
489C4⋊C4—32no—
490C4⋊C4—152no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—302no—
494C22⋊C4—301no—
495C42—61no—
496C42—302no—
497C42—301no—
498C3×C5#289611yescharacteristic, complemented, Hall
499C22×C3—22no—
500C22×C3—52no—
501C22×C3—52no—
502C22×C3—102no—
503C22×C3—102no—
504C22×C3—104no—
505C22×C3—204no—
506C22×C3—208no—
507C22×C3—204no—
508C22×C3D5×C22⋊C412yes—
509C22×C3C2×D4×D511yescharacteristic
510C3×C4—24no—
511C3×C4—52no—
512C3×C4—52no—
513C3×C4D5×C22⋊C412yes—
514C3×C4C22×C4×D511yescharacteristic
515C3×C4C2×D4×D511yescharacteristic
516Dic3—42no—
517Dic3—202no—
518C2×C5—22no—
519C2×C5#582212yes—
520C2×C5C22×#21711yescharacteristic
521D5—22no—
522D5—22no—
523D5—44no—
524C23—51no—
525C23—51no—
526C23—54no—
527C23—102no—
528C23—104no—
529C23—202no—
530C23—204no—
531C23D5×#6711yescharacteristic
532Q8—22no—
533Q8—24no—
534Q8C2×D5×Dic314yes—
535D4—54no—
536D4—108no—
537D4—108no—
538D4—102no—
539D4—104no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—51no—
543C2×C4—51no—
544C2×C4—54no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—52no—
549C2×C4—54no—
550C2×C4—54no—
551C2×C4—62no—
552C2×C4—108no—
553C2×C4—108no—
554C2×C4—302no—
555C2×C4—604no—
556C2×C4C2×D5×Dic312yes—
557C2×C4D5×#6712yes—
558C2×C4D5×#6711yescharacteristic
559C2×C4C22×D3×D511yescharacteristic
560C8—62no—
561C8—302no—
562C2×C3—22no—
563C2×C3—102no—
564C2×C3—102no—
565C2×C3—204no—
566C2×C3C2×D5×C22⋊C411yescharacteristic
567C2×C3#6611112yes—
568C5#8407211yescharacteristic, complemented, Sylow
569C22—22no—
570C22—52no—
571C22—52no—
572C22—102no—
573C22—102no—
574C22—104no—
575C22—204no—
576C22—208no—
577C22—204no—
578C22D5×#21712yes—
579C22C2×D5×#6711yescharacteristic
580C4—24no—
581C4—52no—
582C4—52no—
583C4—122no—
584C4—602no—
585C4D5×#21712yes—
586C4C22×D5×Dic311yescharacteristic
587C4C2×D5×#6711yescharacteristic
588C3#1061068711yescharacteristic, complemented, Sylow
589C2—22no—
590C2—102no—
591C2—102no—
592C2—204no—
593C2#1175508412yes—
594C2C2×D5×#21711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×#713C2
cosocleC2×C3×C4×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2896
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. D5×#926C2semidirect
3. C2×D5×#208C2semidirect
4. #11751326C2semidirect
5. C5×#5225C2semidirect
6. #11749207C2semidirect
7. #11749198C2semidirect
8. #11748367C2semidirect
9. #11748366C2semidirect
15. C2×C3×#713C4semidirect
28. D5×C4⋊Dic3C22semidirect
30. #91358C22semidirect
32. C2×#6649C22semidirect
34. C2×D5×C3⋊C8C22semidirect
35. #91119C22semidirect
36. C5×#835C22semidirect
37. #90965C22semidirect
38. #90964C22semidirect
53. C2×C3×C5×Q8C2×C4semidirect
63. C3×#713C2×C4semidirect
69. C2×C3×D20C2×C4semidirect
102. #5225D5semidirect
109. C2×#713Dic3semidirect
197. #835C2×D5semidirect
204. C2×C5×Q8C2×Dic3semidirect
214. #713C2×Dic3semidirect
220. C2×D20C2×Dic3semidirect
285. C2×C3×Q8C4×D5semidirect
461. C2×Q8D5×Dic3semidirect
498. C3×C5#2896semidirect
568. C5#84072semidirect
588. C3#10610687semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7132
D5×#9262
C2×D5×#2082
#117513262
C5×#52252
#117492072
#117491982
#117483672
#117483662
#106106873
#840725