Finite Group Databasebeta

← #14424398

Subgroups — #14424398

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×#92017C211yesmaximal, characteristic
2C2×#91798C211yesmaximal, characteristic, complemented
3#11754271C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C5×#5129C211yesmaximal, characteristic, complemented
6C3×#65420C211yesmaximal, characteristic, complemented
7#11748411C211yesmaximal, characteristic, complemented
8#11748162C214yesmaximal, complemented
9#11748120C214yesmaximal, complemented
10#10610402—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C22×Dic30C2211yescharacteristic, complemented
13C2×C5×#235C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C2×D5×#67—22no—
16#92017—24no—
17#92017—24no—
18C2×#6777—21no—
19C2×D3×D20C2212yes—
20C2×#6766—21no—
21C2×#6765C2212yes—
22C2×C3×C5×M16C2211yescharacteristic, complemented
23#91798—24no—
24C2×Dic60C2212yescomplemented
25C2×#6706C2212yescomplemented
26C22×C5×C3⋊C8C2211yescharacteristic, complemented
27C3×#4072C2211yescharacteristic, complemented
28#91543—22no—
29#91376—21no—
30#91373—21no—
31#91365C2214yescomplemented
32C2×#6657—24no—
33C2×#6657C2214yescomplemented
34C5×(C2×D3)⋊C8C2214yescomplemented
35C3×#3953C2214yescomplemented
36#90974C2212yescomplemented
37#90968C2212yescomplemented
38#78929—51nomaximal, Hall
39C2×#4149—31no—
40#66159—31no—
41C2×#4055—31no—
42C22×#677—31no—
43C5×#408—31no—
44#65420D311yescharacteristic, complemented
45#65402—31no—
46#65022—34no—
47#65020—34no—
48C23×C3×D5—21no—
49C22×D3×D5—22no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—21no—
52C22×Dic15—21no—
53#6817—22no—
54#6817D414yes—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×Dic30—22no—
58C2×Dic30—22no—
59C2×Dic30—21no—
60C2×Dic30C2312yes—
61C2×Dic30C2311yescharacteristic
62C2×C5×#67D412yes—
63C5×#235—22no—
64C5×#235—22no—
65C2×C5×D12D411yescharacteristic
66C2×C4×C5×D3C2312yes—
67C2×C5×Dic6D411yescharacteristic
68C2×C3×D20—21no—
69C2×C3×D20—22no—
70C2×C3×D20D414yes—
71C2×C3×D20C2312yes—
72D5×#67—216no—
73C2×#1202—22no—
74C2×#1201—22no—
75C2×D5×Dic3—22no—
76#6777—28no—
77D3×D20—24no—
78D3×D20—24no—
79#6766—28no—
80#6765—24no—
81#6765—24no—
82C3×C5×M16—22no—
83C2×C3×C5×C8C2312yes—
84Dic60—24no—
85#6706—24no—
86C2×C5×C3⋊C8—22no—
87C2×C5×C3⋊C8C2312yes—
88C3×C22⋊Dic5—21no—
89C3×C4⋊Dic5C2312yes—
90C3×C4×Dic5—21no—
91#6668—24no—
92(C2×D3)⋊Dic5—24no—
93#6657—28no—
94C2×#1004—51no—
95C22×#214—51no—
96C2×#909—51no—
97#5526—51no—
98C3×#418—51no—
99#5129D511yescharacteristic, complemented
100#5002—51no—
101#4783—54no—
102#4776—54no—
103C2×C5×#41—31no—
104#4149—64no—
105#4149—64no—
106C2×#713—61no—
107C2×D4×D5—61no—
108C2×D4×D5—62no—
109C2×#709—31no—
110C2×#709—32no—
111C22×D20—32no—
112C22×D20C2×D311yescharacteristic
113C22×Dic10—31no—
114C2×C5×M16C2×D311yescharacteristic, complemented
115C22×C5×C8—31no—
116#4090—61no—
117#4082—61no—
118#4081—62no—
119#4072C2×D311yescharacteristic, complemented
120#4070—34no—
121#4055—64no—
122C2×Dic20—32no—
123C2×#677—34no—
124C2×#677—32no—
125C2×#677—64no—
126C5×C22⋊C8—34no—
127#3953—32no—
128#3953C2×D314yescomplemented
129#3948—32no—
130#3009—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—21no—
133C22×C5×D3C2×D412yes—
134C22×C3×D5—22no—
135C22×C3×D5—24no—
136C22×C3×D5—82no—
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×Dic15—21no—
145C2×Dic15—22no—
146C2×Dic15—42no—
147D60—21no—
148D60C2×D412yes—
149C4×D15—24no—
150Dic30—21no—
151Dic30—22no—
152Dic30—22no—
153Dic30—42no—
154Dic30C2×D412yes—
155C5×#67—24no—
156C2×C5×Dic3C2×D412yes—
157C5×D12—22no—
158C4×C5×D3—22no—
159C4×C5×D3—22no—
160C5×Dic6—22no—
161C2×C3×Dic5—22no—
162C3×D20—24no—
163C3×D20—22no—
164C3×D20C2×D414yes—
165#1202—28no—
166#1201—28no—
167D5×Dic3—28no—
168C3×C5×C8—22no—
169C5×C3⋊C8—22no—
170C22×C3×D4—51no—
171C22×#67—102no—
172#1004—104no—
173#1004—104no—
174C2×#237—52no—
175C2×#237—101no—
176C2×D3×D4—52no—
177C2×D3×D4—101no—
178C2×#235—51no—
179C2×#235C2×D511yescharacteristic
180C22×Dic6—51no—
181C2×C3×M16C2×D511yescharacteristic, complemented
182C3×#117—51no—
183C2×#214—54no—
184C2×#214—104no—
185C22×C3⋊C8C2×D511yescharacteristic, complemented
186#909—104no—
187C2×Dic12—52no—
188C2×#204—52no—
189#897—54no—
190#886—102no—
191#875—101no—
192#869—101no—
193C3×#102—54no—
194(C2×D3)⋊C8C2×D514yescomplemented
195#810—52no—
196#809—52no—
197C23×D5—21no—
198C23×D5—62no—
199C5×#41—62no—
200C5×#41—62no—
201C2×C5×Q8—31no—
202C2×C5×D4—32no—
203C2×C5×D4—31no—
204C22×C4×C5—32no—
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—62no—
207C2×C22⋊D5—61no—
208C22×Dic5—61no—
209#713—68no—
210D4×D5—68no—
211D4×D5—616no—
212#709—34no—
213#709—64no—
214#709—62no—
215#709—64no—
216C2×D20—21no—
217C2×D20—22no—
218C2×D20—31no—
219C2×D20—64no—
220C2×D20—62no—
221C2×D20—64no—
222C2×D20D1214yes—
223C2×D20C22×D312yes—
224C2×C4×D5—62no—
225C2×C4×D5—61no—
226C2×Dic10—31no—
227C2×Dic10—32no—
228C2×Dic10—62no—
229C2×Dic10—62no—
230C2×Dic10—61no—
231C5×M16—22no—
232C2×C5×C8—32no—
233C2×C5×C8—62no—
234C2×C5×C8C22×D312yes—
235C22⋊Dic5—21no—
236C22⋊Dic5—64no—
237C4⋊Dic5C22×D312yes—
238#683—64no—
239C4×Dic5—21no—
240Dic20—64no—
241#677—64no—
242#677—68no—
243C2×H(5,𝔽2)—151no—
244C2×#137—151no—
245C22×SD16—151no—
246#536—151no—
247#452—154no—
248#450—154no—
249#418—51no—
250#416—151no—
251#408—31no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—42no—
257C2×C5×D3—22no—
258C2×C5×D3—24no—
259C2×C3×D5—24no—
260C2×C3×D5—44no—
261C2×C3×D5—84no—
262D3×D5—88no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267Dic15—42no—
268C3×Dic5—42no—
269C5×Dic3—22no—
270C24×C3—101no—
271C23×D3—102no—
272C2×C3×D4—54no—
273C2×C3×D4—52no—
274C2×C3×D4—101no—
275C2×C3×D4—102no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—1016no—
278C2×#67—101no—
279C2×#67—102no—
280C2×#67—102no—
281C2×#67D2012yes—
282C22×Dic3—102no—
283C22×Dic3—101no—
284#237—108no—
285#237—104no—
286#237—104no—
287D3×D4—104no—
288D3×D4—104no—
289D3×D4—108no—
290#235—22no—
291#235—22no—
292#235—54no—
293#235—102no—
294C2×D12—51no—
295C2×D12D2011yescharacteristic
296C2×C4×D3—101no—
297C2×C4×D3C22×D512yes—
298C2×Dic6—51no—
299C2×Dic6—52no—
300C2×Dic6—102no—
301C2×Dic6—102no—
302C2×Dic6—101no—
303C2×Dic6D2011yescharacteristic
304C3×M16—22no—
305C2×C3×C8C22×D512yes—
306C3×C4⋊C4—52no—
307C3×C22⋊C4—101no—
308C3×C42—101no—
309#214—108no—
310(C2×D3)⋊C4—104no—
311C4⋊Dic3—104no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8C22×D512yes—
314Dic12—104no—
315#204—104no—
316C23×C5—32no—
317C23×C5D3×D411yescharacteristic
318C22×D5—22no—
319C22×D5—24no—
320C22×D5—68no—
321C22×D5—61no—
322C22×D5—82no—
323C22×D5—244no—
324C5×Q8—62no—
325C5×D4—64no—
326C5×D4—62no—
327C2×C4×C5—32no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5C2×D1212yes—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5D3×D412yes—
333C2×C4×C5C23×D311yescharacteristic
334C22⋊D5—68no—
335C22⋊D5—64no—
336C2×Dic5—22no—
337C2×Dic5—61no—
338C2×Dic5—62no—
339C2×Dic5—122no—
340D20—24no—
341D20—22no—
342D20—32no—
343D20—68no—
344D20—61no—
345D20C2×D1214yes—
346C4×D5—68no—
347C4×D5—64no—
348Dic10—32no—
349Dic10—61no—
350Dic10—62no—
351Dic10—62no—
352Dic10—122no—
353C5×C8—22no—
354C5×C8—62no—
355H(5,𝔽2)—304no—
356H(5,𝔽2)—304no—
357C2×#41—31no—
358C2×#41—152no—
359C2×#41—151no—
360C2×#41—301no—
361C22×Q8—151no—
362C22×D4—51no—
363C22×D4—152no—
364C22×D4—301no—
365C22×D4—302no—
366#137—304no—
367C2×Q16—152no—
368C2×SD16—154no—
369C2×SD16—152no—
370C2×SD16—304no—
371C2×M16D3×D511yescharacteristic, complemented
372C22×C8—31no—
373C4⋊Q8—301no—
374#124—301no—
375#123—302no—
376C22⋊Q8—154no—
377#117—51no—
378#103—152no—
379#102—54no—
380#102—152no—
381C22⋊C8—34no—
382C2×C3×C5—22no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C3×D5—44no—
387C5×D3—42no—
388C23×C3—102no—
389C23×C3—104no—
390C23×C3—402no—
391C23×C3C2×D2011yescharacteristic
392C22×D3—108no—
393C22×D3—101no—
394C22×D3—404no—
395C22×D3C2×D2012yes—
396C3×D4—54no—
397C3×D4—102no—
398C3×D4—104no—
399C2×C3×C4—102no—
400C2×C3×C4C2×D2011yescharacteristic
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D512yes—
403C2×C3×C4C23×D511yescharacteristic
404#67—24no—
405#67—108no—
406#67—108no—
407#67—104no—
408C2×Dic3—108no—
409C2×Dic3—101no—
410C2×Dic3—102no—
411C2×Dic3—202no—
412C2×Dic3C2×D2012yes—
413D12—22no—
414D12—52no—
415D12—101no—
416C4×D3—22no—
417C4×D3—22no—
418C4×D3—104no—
419Dic6—22no—
420Dic6—52no—
421Dic6—101no—
422Dic6—102no—
423Dic6—102no—
424Dic6—202no—
425C3×C8—22no—
426C3⋊C8—22no—
427C22×C5—22no—
428C22×C5—62no—
429C22×C5—64no—
430C22×C5#88212yes—
431C22×C5C2×D3×D411yescharacteristic
432C2×D5—24no—
433C2×D5—44no—
434C2×D5—62no—
435C2×D5—84no—
436C2×D5—122no—
437C2×D5—248no—
438C4×C5—62no—
439C4×C5#88212yes—
440C4×C5C22×D1211yescharacteristic
441C4×C5C2×D3×D411yescharacteristic
442Dic5—42no—
443Dic5—62no—
444Dic5—122no—
445C24—101no—
446C24—302no—
447#41—62no—
448#41—62no—
449#41—154no—
450#41—304no—
451#41—304no—
452#41—308no—
453#41—302no—
454C2×Q8—31no—
455C2×Q8—151no—
456C2×Q8—152no—
457C2×Q8—301no—
458C2×Q8—302no—
459C2×Q8—302no—
460C2×D4—32no—
461C2×D4—31no—
462C2×D4—54no—
463C2×D4—52no—
464C2×D4—101no—
465C2×D4—102no—
466C2×D4—151no—
467C2×D4—302no—
468C2×D4—304no—
469C2×D4—304no—
470C2×D4—308no—
471C2×D4—3016no—
472C2×D4—302no—
473C2×D4—301no—
474C22×C4—32no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4—301no—
478C22×C4C2×D3×D511yescharacteristic
479Q16—304no—
480SD16—304no—
481SD16—308no—
482M16—22no—
483C2×C8—32no—
484C2×C8—62no—
485C2×C8C2×D3×D512yes—
486C4⋊C4—52no—
487C4⋊C4—304no—
488C22⋊C4—101no—
489C22⋊C4—304no—
490C42—101no—
491C3×C5#300911yescharacteristic, complemented, Hall
492C22×C3—22no—
493C22×C3—104no—
494C22×C3—204no—
495C22×C3—404no—
496C22×C3#402812yes—
497C22×C3C22×D2011yescharacteristic
498C2×D3—22no—
499C2×D3—24no—
500C2×D3—102no—
501C2×D3—202no—
502C2×D3—408no—
503C3×C4—202no—
504C3×C4#402812yes—
505C3×C4C2×D4×D511yescharacteristic
506C3×C4C2×D4×D511yescharacteristic
507Dic3—22no—
508Dic3—102no—
509Dic3—202no—
510C2×C5—22no—
511C2×C5—122no—
512C2×C5C2×#88211yescharacteristic
513C2×C5#577512yes—
514D5—44no—
515D5—122no—
516C23—32no—
517C23—102no—
518C23—104no—
519C23—308no—
520C23—301no—
521C23—402no—
522C23—1204no—
523C23D3×D2011yescharacteristic
524Q8—62no—
525Q8—152no—
526Q8—301no—
527Q8—302no—
528Q8—302no—
529Q8—602no—
530D4—54no—
531D4—64no—
532D4—62no—
533D4—104no—
534D4—102no—
535D4—152no—
536D4—308no—
537D4—308no—
538D4—304no—
539D4—301no—
540C2×C4—32no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—102no—
544C2×C4—308no—
545C2×C4—301no—
546C2×C4—304no—
547C2×C4—302no—
548C2×C4—602no—
549C2×C4D5×D1212yes—
550C2×C4D3×D2011yescharacteristic
551C2×C4#679012yes—
552C2×C4C22×D3×D511yescharacteristic
553C8—22no—
554C8—62no—
555C2×C3—22no—
556C2×C3—204no—
557C2×C3C2×#402811yescharacteristic
558C2×C3#6608512yes—
559D3—42no—
560D3—202no—
561C5#7892911yescharacteristic, complemented, Sylow
562C22—22no—
563C22—64no—
564C22—62no—
565C22—104no—
566C22—204no—
567C22—302no—
568C22—404no—
569C22—602no—
570C22—1208no—
571C22#9147612yes—
572C22C2×D3×D2011yescharacteristic
573C4—62no—
574C4—202no—
575C4—302no—
576C4—602no—
577C4#9147612yes—
578C4C2×D5×D1211yescharacteristic
579C4C2×#679011yescharacteristic
580C3#1061040211yescharacteristic, complemented, Sylow
581C2—22no—
582C2—122no—
583C2—204no—
584C2—602no—
585C2#1175403012yes—
586C2C2×#9147611yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#92017C2
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×#91798C2semidirect
3. #11754271C2semidirect
4. C22×#6657C2semidirect
5. C5×#5129C2semidirect
6. C3×#65420C2semidirect
7. #11748411C2semidirect
8. #11748162C2semidirect
9. #11748120C2semidirect
12. C22×Dic30C22semidirect
22. C2×C3×C5×M16C22semidirect
24. C2×Dic60C22semidirect
25. C2×#6706C22semidirect
26. C22×C5×C3⋊C8C22semidirect
27. C3×#4072C22semidirect
31. #91365C22semidirect
33. C2×#6657C22semidirect
34. C5×(C2×D3)⋊C8C22semidirect
35. C3×#3953C22semidirect
36. #90974C22semidirect
37. #90968C22semidirect
44. #65420D3semidirect
99. #5129D5semidirect
114. C2×C5×M16C2×D3semidirect
119. #4072C2×D3semidirect
128. #3953C2×D3semidirect
181. C2×C3×M16C2×D5semidirect
185. C22×C3⋊C8C2×D5semidirect
194. (C2×D3)⋊C8C2×D5semidirect
371. C2×M16D3×D5semidirect
491. C3×C5#3009semidirect
561. C5#78929semidirect
580. C3#10610402semidirect

Maximal subgroups

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

subgroupindex
C2×#920172
C2×#917982
#117542712
C22×#66572
C5×#51292
C3×#654202
#117484112
#117481622
#117481202
#106104023
#789295