Finite Group Databasebeta

← #14424397

Subgroups — #14424397

Order 1920.

1504 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
1C2×#92018C211yesmaximal, characteristic
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754278C211yesmaximal, characteristic, complemented
4C22×#6656C211yesmaximal, characteristic, complemented
5#11751230C211yesmaximal, characteristic, complemented
6C5×#5131C211yesmaximal, characteristic, complemented
7#11748364C211yesmaximal, characteristic, complemented
8#11748151C214yesmaximal, complemented
9#11748111C214yesmaximal, complemented
10#10610660—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13C2×C3×#709C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic, complemented
15C2×D3×C22⋊D5—22no—
16#92018—24no—
17#92018—24no—
18C2×#6777C2212yes—
19C2×D5×D12—21no—
20C2×#6772—21no—
21C2×#6768C2212yes—
22C2×C3×C5×M16C2211yescharacteristic, complemented
23C22×C3⋊#168C2211yescharacteristic, complemented
24C5×#926C2211yescharacteristic, complemented
25C3×#4055—24no—
26C2×C3×Dic20C2212yescomplemented
27C2×C3×#677C2212yescomplemented
28#91546—22no—
29#91390C2214yescomplemented
30#91389—21no—
31#91374—21no—
32C2×#6656—24no—
33C2×#6656C2214yescomplemented
34#91104C2214yescomplemented
35C5×#821C2214yescomplemented
36#90970C2212yescomplemented
37#90964C2212yescomplemented
38#83982—51nomaximal, Hall
39C2×#4144—31no—
40C22×#687—31no—
41C2×#4055D311yescharacteristic, complemented
42#65860—31no—
43C5×#418—31no—
44#65418—31no—
45#65291—31no—
46#65072—34no—
47#65065—34no—
48C23×C5×D3—21no—
49C22×D3×D5—22no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220D412yes—
52#6817—22no—
53#6817—22no—
54C2×D60D411yescharacteristic
55C2×C4×D15C2312yes—
56C2×Dic30D411yescharacteristic
57C2×C5×D12—21no—
58C2×C5×D12—22no—
59C2×C5×D12D414yes—
60C2×C5×D12C2312yes—
61C2×C3×C22⋊D5—21no—
62C22×C3×Dic5—21no—
63C3×#709—22no—
64C3×#709D414yes—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10—22no—
68C2×C3×Dic10—22no—
69C2×C3×Dic10—21no—
70C2×C3×Dic10C2312yes—
71C2×C3×Dic10C2311yescharacteristic
72D3×C22⋊D5—216no—
73C2×#1203—22no—
74C2×#1201—22no—
75C2×D3×Dic5—22no—
76#6777—24no—
77#6777—24no—
78D5×D12—28no—
79#6772—28no—
80#6768—24no—
81#6768—24no—
82C3×C5×M16—22no—
83C2×C3×C5×C8C2312yes—
84C2×C3⋊#168—22no—
85C2×C3⋊#168C2312yes—
86C5×#217—21no—
87C5×C4⋊Dic3C2312yes—
88C4×C5×Dic3—21no—
89C3×Dic20—24no—
90C3×#677—24no—
91Dic3⋊Dic5—24no—
92#6667—24no—
93#6656—28no—
94C2×#1009—51no—
95C2×C3×#137—51no—
96#5816—51no—
97C22×#215—51no—
98#5233—51no—
99#5187—54no—
100#5169—54no—
101#5131D511yescharacteristic, complemented
102#5129—51no—
103C22×C5×D4—31no—
104C22×C22⋊D5—62no—
105#4144—64no—
106#4144—64no—
107C2×#711—32no—
108C2×#711—61no—
109C2×D4×D5—32no—
110C2×D4×D5—61no—
111C2×#709—31no—
112C2×#709C2×D311yescharacteristic
113C22×Dic10C2×D311yescharacteristic, complemented
114C2×C5×M16C2×D311yescharacteristic, complemented
115C5×#117—31no—
116C2×#687—34no—
117C2×#687—64no—
118C22×#168—31no—
119#4055—24no—
120C2×Dic20C2×D312yescomplemented
121C2×#677C2×D312yescomplemented
122#4043—34no—
123#4032—62no—
124#4021—61no—
125#4015—61no—
126C5×#102—34no—
127#3952—34no—
128#3942—32no—
129#3941—32no—
130#3009—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15C2×D412yes—
133C22×C5×D3—22no—
134C22×C5×D3—24no—
135C22×C5×D3—82no—
136C22×C3×D5—21no—
137C2×D3×D5—28no—
138C2×D3×D5—84no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2411yescharacteristic
143#1220—24no—
144C2×Dic15C2×D412yes—
145D60—22no—
146C4×D15—22no—
147C4×D15—22no—
148Dic30—22no—
149C2×C5×Dic3—22no—
150C5×D12—24no—
151C5×D12—22no—
152C5×D12C2×D414yes—
153C3×C22⋊D5—24no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—42no—
157C3×D20—21no—
158C3×D20C2×D412yes—
159C3×C4×D5—24no—
160C3×Dic10—21no—
161C3×Dic10—22no—
162C3×Dic10—22no—
163C3×Dic10—42no—
164C3×Dic10C2×D412yes—
165#1203—28no—
166#1201—28no—
167D3×Dic5—28no—
168C3×C5×C8—22no—
169C3⋊#168—22no—
170C2×C3×#41—51no—
171C22×C3×Q8—51no—
172#1009—104no—
173#1009—104no—
174C2×#239—52no—
175C2×D3×D4—52no—
176C2×D3×D4—102no—
177C2×#235—51no—
178C2×#235—101no—
179C22×D12—101no—
180C22×D12C2×D511yescharacteristic
181C3×#137—104no—
182C2×C3×Q16—52no—
183C2×C3×SD16—52no—
184C2×C3×M16C2×D511yescharacteristic, complemented
185#947—101no—
186#946—54no—
187#944—101no—
188C2×#215—54no—
189C2×#215—104no—
190#929—102no—
191#926C2×D511yescharacteristic, complemented
192C22×C3⋊C8—51no—
193#835—52no—
194#832—52no—
195#821C2×D514yescomplemented
196(C2×D3)⋊C8—54no—
197C24×C5—61no—
198C23×D5—62no—
199C2×C5×D4—34no—
200C2×C5×D4—32no—
201C2×C5×D4—61no—
202C2×C5×D4—62no—
203C22×C4×C5C22×D311yescharacteristic
204C2×C22⋊D5—21no—
205C2×C22⋊D5—32no—
206C2×C22⋊D5—62no—
207C2×C22⋊D5—62no—
208C2×C22⋊D5—616no—
209C22×Dic5—21no—
210C22×Dic5—62no—
211#711—64no—
212#711—68no—
213#711—64no—
214D4×D5—68no—
215D4×D5—64no—
216D4×D5—64no—
217#709—22no—
218#709—62no—
219#709—62no—
220#709#6714yes—
221C2×D20—31no—
222C2×D20C22×D311yescharacteristic
223C2×C4×D5—21no—
224C2×C4×D5—32no—
225C2×Dic10—22no—
226C2×Dic10—22no—
227C2×Dic10—21no—
228C2×Dic10—31no—
229C2×Dic10C22×D312yes—
230C2×Dic10C22×D311yescharacteristic
231C5×M16—22no—
232C2×C5×C8C22×D312yes—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236#687—68no—
237#685—64no—
238C4⋊Dic5—64no—
239C2×#168—32no—
240C2×#168—62no—
241Dic20—24no—
242#677—24no—
243C2×H(5,𝔽2)—151no—
244C2×#137—51no—
245C22×SD16—151no—
246#536—151no—
247#452—154no—
248#450—154no—
249#418—31no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—24no—
257C2×C5×D3—24no—
258C2×C5×D3—44no—
259C2×C5×D3—84no—
260C2×C3×D5—22no—
261C2×C3×D5—42no—
262D3×D5—88no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267C3×Dic5—22no—
268C3×Dic5—42no—
269C5×Dic3—42no—
270C23×D3—21no—
271C23×D3—102no—
272C3×#41—54no—
273C3×#41—102no—
274C2×C3×Q8—51no—
275C2×C3×Q8—52no—
276C2×C3×Q8—101no—
277C2×C3×Q8—102no—
278C2×C3×Q8—102no—
279C2×C3×D4—51no—
280C2×C3×D4—101no—
281C22×C3×C4—101no—
282C22×C3×C4—101no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—52no—
285C2×#67—102no—
286#239—104no—
287#239—104no—
288D3×D4—104no—
289D3×D4—1016no—
290D3×D4—104no—
291#235—108no—
292#235—102no—
293#235—102no—
294C2×D12—21no—
295C2×D12—22no—
296C2×D12—51no—
297C2×D12—108no—
298C2×D12—102no—
299C2×D12D2014yes—
300C2×D12C22×D512yes—
301C2×C4×D3—52no—
302C2×C4×D3—102no—
303C2×Dic6—51no—
304C3×Q16—104no—
305C3×SD16—104no—
306C3×M16—22no—
307C2×C3×C8C22×D512yes—
308#217—21no—
309#215—108no—
310(C2×D3)⋊C4—104no—
311C4⋊Dic3C22×D512yes—
312Dic3⋊C4—104no—
313C4×Dic3—21no—
314C2×C3⋊C8—52no—
315C2×C3⋊C8—102no—
316C23×C5—62no—
317C23×C5—64no—
318C23×C5—242no—
319C23×C5D3×D411yescharacteristic
320C22×D5—21no—
321C22×D5—32no—
322C22×D5—68no—
323C22×D5—244no—
324C5×D4—34no—
325C5×D4—64no—
326C5×D4—62no—
327C2×C4×C5—62no—
328C2×C4×C5D3×D412yes—
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5C2×#6712yes—
331C2×C4×C5C23×D311yescharacteristic
332C22⋊D5—24no—
333C22⋊D5—68no—
334C22⋊D5—68no—
335C22⋊D5—64no—
336C2×Dic5—21no—
337C2×Dic5—22no—
338C2×Dic5—32no—
339C2×Dic5—42no—
340C2×Dic5—68no—
341D20—21no—
342D20—62no—
343D20C2×#6712yes—
344C4×D5—24no—
345C4×D5—62no—
346C4×D5—62no—
347Dic10—21no—
348Dic10—22no—
349Dic10—22no—
350Dic10—42no—
351Dic10—62no—
352Dic10C2×#6712yes—
353C5×C8—22no—
354#168—62no—
355H(5,𝔽2)—304no—
356H(5,𝔽2)—304no—
357C2×#41—51no—
358C2×#41—151no—
359C2×#41—152no—
360C2×#41—301no—
361C22×Q8—51no—
362C22×D4—31no—
363C22×D4—152no—
364C22×D4—301no—
365C22×D4—302no—
366#137—104no—
367C2×Q16—52no—
368C2×SD16—52no—
369C2×SD16—154no—
370C2×SD16—304no—
371C2×M16D3×D511yescharacteristic, complemented
372C22×C8—151no—
373C4⋊Q8—301no—
374#124—301no—
375#123—302no—
376C22⋊Q8—154no—
377#117—31no—
378#103—152no—
379#102—34no—
380#102—152no—
381C22⋊C8—154no—
382C2×C3×C5—22no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C3×D5—42no—
387C5×D3—44no—
388C23×C3—101no—
389C23×C3D4×D511yescharacteristic
390C22×D3—22no—
391C22×D3—24no—
392C22×D3—52no—
393C22×D3—82no—
394C22×D3—108no—
395C22×D3—404no—
396C3×Q8—52no—
397C3×Q8—101no—
398C3×Q8—102no—
399C3×Q8—102no—
400C3×Q8—202no—
401C3×D4—52no—
402C3×D4—104no—
403C3×D4—101no—
404C2×C3×C4—101no—
405C2×C3×C4—104no—
406C2×C3×C4—102no—
407C2×C3×C4—202no—
408C2×C3×C4C2×D2012yes—
409C2×C3×C4D4×D511yescharacteristic
410C2×C3×C4D4×D512yes—
411C2×C3×C4C23×D511yescharacteristic
412#67—108no—
413#67—104no—
414C2×Dic3—22no—
415C2×Dic3—52no—
416D12—22no—
417D12—24no—
418D12—108no—
419D12—102no—
420D12C2×D2014yes—
421C4×D3—108no—
422C4×D3—102no—
423C4×D3—102no—
424Dic6—102no—
425C3×C8—22no—
426C3⋊C8—102no—
427C22×C5—22no—
428C22×C5—64no—
429C22×C5—124no—
430C22×C5—244no—
431C22×C5#93712yes—
432C22×C5C2×D3×D411yescharacteristic
433C2×D5—22no—
434C2×D5—42no—
435C2×D5—64no—
436C2×D5—62no—
437C2×D5—248no—
438C4×C5—122no—
439C4×C5#93712yes—
440C4×C5C2×D3×D411yescharacteristic
441C4×C5C22×#6711yescharacteristic
442Dic5—22no—
443Dic5—42no—
444Dic5—62no—
445C24—61no—
446C24—302no—
447#41—54no—
448#41—102no—
449#41—308no—
450#41—304no—
451#41—304no—
452#41—302no—
453#41—302no—
454C2×Q8—51no—
455C2×Q8—52no—
456C2×Q8—101no—
457C2×Q8—102no—
458C2×Q8—102no—
459C2×Q8—151no—
460C2×D4—34no—
461C2×D4—32no—
462C2×D4—51no—
463C2×D4—61no—
464C2×D4—62no—
465C2×D4—101no—
466C2×D4—152no—
467C2×D4—151no—
468C2×D4—308no—
469C2×D4—302no—
470C2×D4—302no—
471C2×D4—304no—
472C2×D4—304no—
473C2×D4—3016no—
474C22×C4—101no—
475C22×C4—101no—
476C22×C4—152no—
477C22×C4—302no—
478C22×C4C2×D3×D511yescharacteristic
479Q16—104no—
480SD16—104no—
481SD16—308no—
482M16—22no—
483C2×C8—152no—
484C2×C8—302no—
485C2×C8C2×D3×D512yes—
486C4⋊C4—32no—
487C4⋊C4—304no—
488C22⋊C4—61no—
489C22⋊C4—304no—
490C42—61no—
491C3×C5#300911yescharacteristic, complemented, Hall
492C22×C3—22no—
493C22×C3—102no—
494C22×C3—202no—
495C22×C3#402812yes—
496C22×C3C2×D4×D511yescharacteristic
497C2×D3—24no—
498C2×D3—44no—
499C2×D3—84no—
500C2×D3—102no—
501C2×D3—104no—
502C2×D3—408no—
503C3×C4—102no—
504C3×C4—202no—
505C3×C4#402812yes—
506C3×C4C22×D2011yescharacteristic
507C3×C4C2×D4×D511yescharacteristic
508Dic3—42no—
509Dic3—102no—
510C2×C5—22no—
511C2×C5—124no—
512C2×C5#577812yes—
513C2×C5C2×#93711yescharacteristic
514D5—42no—
515D5—122no—
516C23—62no—
517C23—64no—
518C23—101no—
519C23—152no—
520C23—242no—
521C23—308no—
522C23—1204no—
523C23#677711yescharacteristic
524Q8—52no—
525Q8—101no—
526Q8—102no—
527Q8—102no—
528Q8—202no—
529Q8—302no—
530D4—34no—
531D4—52no—
532D4—64no—
533D4—62no—
534D4—104no—
535D4—101no—
536D4—308no—
537D4—308no—
538D4—304no—
539D4—302no—
540C2×C4—62no—
541C2×C4—101no—
542C2×C4—104no—
543C2×C4—102no—
544C2×C4—152no—
545C2×C4—202no—
546C2×C4—308no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4D3×D2012yes—
550C2×C4#677711yescharacteristic
551C2×C4D5×#6712yes—
552C2×C4C22×D3×D511yescharacteristic
553C8—22no—
554C8—302no—
555C2×C3—22no—
556C2×C3—202no—
557C2×C3C2×#402811yescharacteristic
558C2×C3#6610912yes—
559D3—44no—
560D3—202no—
561C5#8398211yescharacteristic, complemented, Sylow
562C22—22no—
563C22—64no—
564C22—102no—
565C22—124no—
566C22—202no—
567C22—244no—
568C22—304no—
569C22—302no—
570C22—1208no—
571C22#9147412yes—
572C22C2×#677711yescharacteristic
573C4—102no—
574C4—122no—
575C4—202no—
576C4—302no—
577C4#9147412yes—
578C4C2×D3×D2011yescharacteristic
579C4C2×D5×#6711yescharacteristic
580C3#1061066011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—124no—
583C2—202no—
584C2—602no—
585C2#1175403912yes—
586C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#92018C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3009
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4055C2semidirect
3. #11754278C2semidirect
4. C22×#6656C2semidirect
5. #11751230C2semidirect
6. C5×#5131C2semidirect
7. #11748364C2semidirect
8. #11748151C2semidirect
9. #11748111C2semidirect
14. C22×C3×Dic10C22semidirect
22. C2×C3×C5×M16C22semidirect
23. C22×C3⋊#168C22semidirect
24. C5×#926C22semidirect
26. C2×C3×Dic20C22semidirect
27. C2×C3×#677C22semidirect
29. #91390C22semidirect
33. C2×#6656C22semidirect
34. #91104C22semidirect
35. C5×#821C22semidirect
36. #90970C22semidirect
37. #90964C22semidirect
41. C2×#4055D3semidirect
101. #5131D5semidirect
113. C22×Dic10C2×D3semidirect
114. C2×C5×M16C2×D3semidirect
120. C2×Dic20C2×D3semidirect
121. C2×#677C2×D3semidirect
184. C2×C3×M16C2×D5semidirect
191. #926C2×D5semidirect
195. #821C2×D5semidirect
371. C2×M16D3×D5semidirect
491. C3×C5#3009semidirect
561. C5#83982semidirect
580. C3#10610660semidirect

Maximal subgroups

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

subgroupindex
C2×#920182
C2×C3×#40552
#117542782
C22×#66562
#117512302
C5×#51312
#117483642
#117481512
#117481112
#106106603
#839825