Finite Group Databasebeta

← #14424157

Subgroups — #14424157

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6817C211yesmaximal, characteristic
2C2×C5×#924C211yesmaximal, characteristic, complemented
3C2×#91321C212yesmaximal, complemented
4C3×#65496C211yesmaximal, characteristic, complemented
5#11748566C214yesmaximal, complemented
6#11748565C212yesmaximal, complemented
7#11748554C212yesmaximal, complemented
8#11748394C212yesmaximal, complemented
9#10614466—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×#1220—21no—
12C2×#6817—21no—
13C2×#6817—21no—
14C2×#6817—28no—
15C2×#6817C2212yes—
16C2×#6817C2212yes—
17C22×D60C2211yescharacteristic
18C22×C4×D15—21no—
19C22×Dic30C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic, complemented
21C2×C5×#217—21no—
22C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
23C5×#924—21no—
24C5×#924—21no—
25C5×#924C2212yes—
26C5×#924C2212yescomplemented
27C2×C5×Dic3⋊C4—21no—
28C2×C3×#681C2212yescomplemented
29#91321—28no—
30C2×#6663C2214yescomplemented
31C2×#6660C2214yescomplemented
32C3×C22⋊#168C2212yes—
33C3×C22⋊#168C2212yescomplemented
34#90975C2214yescomplemented
35#90969C2214yescomplemented
36#78640—51nomaximal, Hall
37C22×#709—31no—
38C2×C5×C22⋊Q8—31no—
39C2×#4088—32no—
40#65496D311yescharacteristic, complemented
41#65339—32no—
42#65336—34no—
43#65335—32no—
44#65255—32no—
45C24×C3×C5D411yescharacteristic
46C23×D15—21no—
47C22×C3×C4×C5—24no—
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5D411yescharacteristic
50C22×C3×C4×C5D411yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C2×#1220—28no—
55C2×#1220—22no—
56C2×#1220—22no—
57C22×Dic15—21no—
58#6817—28no—
59#6817—28no—
60#6817—24no—
61#6817—24no—
62#6817—24no—
63#6817D418yes—
64C2×D60—21no—
65C2×D60—24no—
66C2×D60C2312yes—
67C2×C4×D15—28no—
68C2×C4×D15—22no—
69C2×C4×D15—22no—
70C2×Dic30—21no—
71C2×Dic30—24no—
72C2×Dic30C2312yes—
73C22×C5×Dic3—21no—
74C22×C5×Dic3—21no—
75C2×C5×Dic6—24no—
76C2×C5×Dic6—21no—
77C2×C5×Dic6C2312yes—
78C5×#217—22no—
79C5×#217—22no—
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3C2312yes—
82C5×Dic3⋊C4—22no—
83C5×Dic3⋊C4—22no—
84C3×#681—24no—
85C2×C3×#168C2314yes—
86#6663—28no—
87#6660—28no—
88C22×#235—51no—
89C2×#924D511yescharacteristic, complemented
90C2×#909—52no—
91C3×#407—51no—
92#5133—52no—
93#4739—52no—
94#4733—54no—
95#4731—52no—
96C22×C5×Q8—31no—
97C23×C4×C5C2×D311yescharacteristic
98C22×C22⋊D5—61no—
99C2×#709—32no—
100C2×#709—32no—
101C2×#709—68no—
102C2×#709—61no—
103C2×#709—61no—
104C22×D20—31no—
105C22×C4×D5—61no—
106C22×Dic10—31no—
107C5×C22⋊Q8—32no—
108C5×C22⋊Q8—32no—
109C5×C22⋊Q8—61no—
110C5×C22⋊Q8—61no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—61no—
113C2×C5×C22⋊C4—61no—
114C2×#689—34no—
115#4088—68no—
116C2×#688—34no—
117C2×#681C2×D312yescomplemented
118C22⋊#168C2×D312yes—
119C22⋊#168C2×D312yescomplemented
120#3942—34no—
121#3941—34no—
122#3007—151noSylow
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—41no—
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C22×D15—24no—
130C22×D15—22no—
131C22×D15—42no—
132C22×D15—42no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D414yes—
142C2×C3×C4×C5C2411yescharacteristic
143#1220—28no—
144#1220—28no—
145C2×Dic15—24no—
146C2×Dic15—22no—
147D60—24no—
148D60—22no—
149D60C2×D414yes—
150C4×D15—28no—
151C4×D15—28no—
152Dic30—24no—
153Dic30—22no—
154Dic30C2×D414yes—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—42no—
158C2×C5×Dic3—42no—
159C5×Dic6—24no—
160C5×Dic6—42no—
161C3×#168—24no—
162C23×C3×C4C2×D511yescharacteristic
163C22×#67—101no—
164C2×#235—52no—
165C2×#235—52no—
166C2×#235—108no—
167C2×#235—101no—
168C2×#235—101no—
169C22×D12—51no—
170C22×C4×D3—101no—
171C22×Dic6—51no—
172C22×Dic6C2×D511yescharacteristic, complemented
173C2×C3×M16—52no—
174C2×#217—21no—
175C2×C4⋊Dic3C2×D511yescharacteristic, complemented
176#924—21no—
177#924—21no—
178#924C2×D512yes—
179#924C2×D512yescomplemented
180C2×Dic3⋊C4—21no—
181#909—108no—
182C2×Dic12—54no—
183C2×#204—54no—
184C3×C22⋊C8—52no—
185C3×C22⋊C8—52no—
186#821—54no—
187#816—54no—
188C24×C5D1211yescharacteristic
189C23×D5—61no—
190C2×C5×Q8—32no—
191C2×C5×Q8—61no—
192C2×C5×Q8—64no—
193C22×C4×C5—24no—
194C22×C4×C5—61no—
195C22×C4×C5—61no—
196C22×C4×C5D1211yescharacteristic
197C22×C4×C5D1211yescharacteristic
198C22×C4×C5D1211yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×C4×C5C22×D311yescharacteristic
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—68no—
203C2×C22⋊D5—62no—
204C2×C22⋊D5—62no—
205C22×Dic5—61no—
206#709—38no—
207#709—64no—
208#709—64no—
209#709—68no—
210#709—68no—
211#709—64no—
212C2×D20—32no—
213C2×D20—64no—
214C2×D20—61no—
215C2×C4×D5—68no—
216C2×C4×D5—62no—
217C2×C4×D5—62no—
218C2×Dic10—32no—
219C2×Dic10—64no—
220C2×Dic10—61no—
221C5×C4⋊C4—32no—
222C5×C4⋊C4—61no—
223C5×C4⋊C4—62no—
224C5×C4⋊C4—62no—
225C5×C22⋊C4—62no—
226C5×C22⋊C4—62no—
227#689—68no—
228#688—68no—
229#681—24no—
230C2×#168C22×D314yes—
231C22×#41—151no—
232C2×#137—152no—
233C2×C22⋊Q8—31no—
234#452—154no—
235#451—152no—
236#450—152no—
237#417—152no—
238#407—51no—
239C22×C3×C5—21no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5—44no—
247C22×C3×C5#12012yes—
248C22×C3×C5#13712yescomplemented
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—24no—
251C2×D15—48no—
252C2×D15—42no—
253C2×D15—42no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5#12012yes—
257C3×C4×C5C22×D412yes—
258Dic15—24no—
259C5×Dic3—42no—
260C5×Dic3—42no—
261C24×C3C22⋊D511yescharacteristic
262C23×D3—101no—
263C22×C3×C4—24no—
264C22×C3×C4C22⋊D511yescharacteristic
265C22×C3×C4C22⋊D511yescharacteristic
266C22×C3×C4C22⋊D511yescharacteristic
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—108no—
271C2×#67—102no—
272C2×#67—102no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—101no—
276#235—58no—
277#235—104no—
278#235—104no—
279#235—108no—
280#235—108no—
281#235—104no—
282C2×D12—52no—
283C2×D12—104no—
284C2×D12—101no—
285C2×C4×D3—108no—
286C2×C4×D3—102no—
287C2×C4×D3—102no—
288C2×Dic6—24no—
289C2×Dic6—21no—
290C2×Dic6—52no—
291C2×Dic6—104no—
292C2×Dic6—101no—
293C2×Dic6C22×D512yes—
294C3×M16—104no—
295C2×C3×C8—54no—
296#217—22no—
297#217—22no—
298C4⋊Dic3—21no—
299C4⋊Dic3C22×D512yes—
300Dic3⋊C4—22no—
301Dic3⋊C4—22no—
302Dic12—108no—
303#204—108no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—41no—
307C23×C5C2×D1211yescharacteristic
308C23×C5C2×D1211yescharacteristic
309C23×C5C2×D1211yescharacteristic
310C22×D5—64no—
311C22×D5—62no—
312C22×D5—122no—
313C22×D5—122no—
314C5×Q8—64no—
315C5×Q8—122no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—62no—
322C2×C4×C5—62no—
323C2×C4×C5—122no—
324C2×C4×C5—122no—
325C2×C4×C5C2×D1211yescharacteristic
326C2×C4×C5C2×D1211yescharacteristic
327C2×C4×C5C2×D1211yescharacteristic
328C2×C4×C5D3×D414yes—
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—68no—
331C22⋊D5—68no—
332C2×Dic5—64no—
333C2×Dic5—62no—
334D20—34no—
335D20—64no—
336D20—62no—
337C4×D5—68no—
338C4×D5—68no—
339Dic10—34no—
340Dic10—64no—
341Dic10—62no—
342#168—24no—
343C2×#41—152no—
344C2×#41—152no—
345C2×#41—308no—
346C2×#41—301no—
347C2×#41—301no—
348C22×Q8—31no—
349C22×Q8—151no—
350C22×D4—151no—
351C22×D4—301no—
352C23×C4—301no—
353C23×C4D3×D511yescharacteristic
354#137—308no—
355C2×Q16—154no—
356C2×SD16—154no—
357C2×M16—52no—
358C22⋊Q8—32no—
359C22⋊Q8—32no—
360C22⋊Q8—61no—
361C22⋊Q8—61no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C22⋊C4—61no—
365#103—154no—
366#102—154no—
367C22⋊C8—52no—
368C22⋊C8—52no—
369C2×C3×C5—22no—
370C2×C3×C5—22no—
371C2×C3×C5—41no—
372C2×C3×C5C2×#12011yescharacteristic
373C2×C3×C5C2×#13711yescharacteristic
374C2×C3×C5#57511yescharacteristic
375D15—44no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3C2×C22⋊D511yescharacteristic
380C23×C3C2×C22⋊D511yescharacteristic
381C23×C3C2×C22⋊D511yescharacteristic
382C22×D3—104no—
383C22×D3—102no—
384C22×D3—202no—
385C22×D3—202no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4D4×D514yes—
392C2×C3×C4C2×C22⋊D511yescharacteristic
393C2×C3×C4C2×C22⋊D511yescharacteristic
394C2×C3×C4C2×C22⋊D511yescharacteristic
395C2×C3×C4C23×D511yescharacteristic
396#67—108no—
397#67—108no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—42no—
401C2×Dic3—42no—
402C2×Dic3—104no—
403C2×Dic3—102no—
404D12—54no—
405D12—104no—
406D12—102no—
407C4×D3—108no—
408C4×D3—108no—
409Dic6—24no—
410Dic6—42no—
411Dic6—54no—
412Dic6—104no—
413Dic6—102no—
414C3×C8—104no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—44no—
423C22×C5#88212yes—
424C22×C5#90912yescomplemented
425C22×C5C22×D1211yescharacteristic
426C2×D5—64no—
427C2×D5—128no—
428C2×D5—122no—
429C2×D5—122no—
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—122no—
433C4×C5—122no—
434C4×C5#88212yes—
435C4×C5C2×D3×D412yes—
436Dic5—64no—
437C24—301no—
438C24#120311yescharacteristic
439#41—158no—
440#41—304no—
441#41—304no—
442#41—308no—
443#41—308no—
444#41—304no—
445C2×Q8—32no—
446C2×Q8—61no—
447C2×Q8—64no—
448C2×Q8—152no—
449C2×Q8—304no—
450C2×Q8—301no—
451C2×D4—152no—
452C2×D4—304no—
453C2×D4—308no—
454C2×D4—302no—
455C2×D4—302no—
456C2×D4—301no—
457C22×C4—24no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—308no—
461C22×C4—301no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4#120311yescharacteristic
465C22×C4#120311yescharacteristic
466C22×C4#120311yescharacteristic
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470Q16—308no—
471SD16—308no—
472M16—104no—
473C2×C8—54no—
474C4⋊C4—32no—
475C4⋊C4—61no—
476C4⋊C4—62no—
477C4⋊C4—62no—
478C22⋊C4—62no—
479C22⋊C4—62no—
480C3×C5#300711yescharacteristic, complemented, Hall
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—44no—
489C22×C3#408312yes—
490C22×C3#408812yescomplemented
491C22×C3C22×C22⋊D511yescharacteristic
492C2×D3—104no—
493C2×D3—208no—
494C2×D3—202no—
495C2×D3—202no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4#408312yes—
499C3×C4C2×D4×D512yes—
500Dic3—42no—
501Dic3—42no—
502Dic3—104no—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5C2×#88211yescharacteristic
507C2×C5C2×#90911yescharacteristic
508C2×C5#574811yescharacteristic
509D5—124no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—304no—
514C23—302no—
515C23—602no—
516C23—602no—
517C23C2×#120311yescharacteristic
518C23C2×#120311yescharacteristic
519C23C2×#120311yescharacteristic
520Q8—64no—
521Q8—122no—
522Q8—154no—
523Q8—304no—
524Q8—302no—
525D4—154no—
526D4—304no—
527D4—308no—
528D4—308no—
529D4—302no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—122no—
539C2×C4—308no—
540C2×C4—304no—
541C2×C4—302no—
542C2×C4—308no—
543C2×C4C2×#120311yescharacteristic
544C2×C4C2×#120311yescharacteristic
545C2×C4C2×#120311yescharacteristic
546C2×C4#679014yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—104no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3C2×#408311yescharacteristic
553C2×C3C2×#408811yescharacteristic
554C2×C3#6615611yescharacteristic
555D3—204no—
556C5#7864011yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—44no—
565C22—304no—
566C22—608no—
567C22—602no—
568C22—602no—
569C22#9132112yescomplemented
570C22#9157312yes—
571C22C22×#120311yescharacteristic
572C4—21no—
573C4—21no—
574C4—122no—
575C4—122no—
576C4—304no—
577C4#9157312yes—
578C4C2×#679012yes—
579C3#1061446611yescharacteristic, complemented, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—604no—
584C2#1175414511yescharacteristic
585C2C2×#9132111yescharacteristic
586C2C2×#9157311yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C22×D4
prime radicalC22×#6817C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#924C2semidirect
3. C2×#91321C2semidirect
4. C3×#65496C2semidirect
5. #11748566C2semidirect
6. #11748565C2semidirect
7. #11748554C2semidirect
8. #11748394C2semidirect
20. C22×C5×Dic6C22semidirect
22. C2×C5×C4⋊Dic3C22semidirect
26. C5×#924C22semidirect
28. C2×C3×#681C22semidirect
30. C2×#6663C22semidirect
31. C2×#6660C22semidirect
33. C3×C22⋊#168C22semidirect
34. #90975C22semidirect
35. #90969C22semidirect
40. #65496D3semidirect
89. C2×#924D5semidirect
117. C2×#681C2×D3semidirect
119. C22⋊#168C2×D3semidirect
172. C22×Dic6C2×D5semidirect
175. C2×C4⋊Dic3C2×D5semidirect
179. #924C2×D5semidirect
248. C22×C3×C5#137semidirect
424. C22×C5#909semidirect
480. C3×C5#3007semidirect
490. C22×C3#4088semidirect
556. C5#78640semidirect
569. C22#91321semidirect
579. C3#10614466semidirect

Maximal subgroups

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

subgroupindex
C22×#68172
C2×C5×#9242
C2×#913212
C3×#654962
#117485662
#117485652
#117485542
#117483942
#106144663
#786405