Finite Group Databasebeta

← #14424494

Subgroups — #14424494

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92001C211yesmaximal, characteristic, complemented
2C22×#6706C211yesmaximal, characteristic, complemented
3#11754609C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic, complemented
6C3×#65399C211yesmaximal, characteristic, complemented
7#11748417C211yesmaximal, characteristic, complemented
8#11748163C214yesmaximal, complemented
9#11748128C214yesmaximal, complemented
10#10610567—31nomaximal, Hall
11C22×D60C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772C2212yescomplemented
17C2×D3×Dic10—21no—
18#92001—24no—
19#92001—24no—
20C2×#6765—21no—
21C2×D5×Dic6C2212yescomplemented
22C22×C3×C5×C8C2211yescharacteristic
23C2×#6706—24no—
24C2×#6706C2214yes—
25C5×#926C2211yescharacteristic
26C2×C3×#681C2211yescharacteristic
27#91572—22no—
28#91458—21no—
29#91450C2214yes—
30#91374—21no—
31C2×#6660C2212yes—
32#91305—24no—
33C2×#6654C2212yes—
34C5×#821C2212yescomplemented
35C5×#816C2212yescomplemented
36C3×#3952C2214yescomplemented
37#90975C2214yescomplemented
38#78678—51nomaximal, Hall
39C2×#4150—31no—
40C2×#4095—31no—
41C22×#677—31no—
42#65859—31no—
43C5×#416—31no—
44#65399D311yescharacteristic, complemented
45#65293—31no—
46#65095—34no—
47#65070—34no—
48C23×D15—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C2×D60—22no—
52C2×D60—22no—
53C2×D60—21no—
54C2×D60C2312yes—
55C2×Dic30—21no—
56C2×Dic30—22no—
57C2×Dic30D414yescomplemented
58C2×Dic30C2312yes—
59C2×C5×#67—21no—
60C5×#235—22no—
61C5×#235D414yescomplemented
62C2×C5×D12C2311yescharacteristic
63C2×C4×C5×D3—21no—
64C2×C5×Dic6C2311yescharacteristic
65C2×C3×C22⋊D5D412yes—
66C3×#709—22no—
67C3×#709—22no—
68C2×C3×D20D411yescharacteristic
69C2×C3×C4×D5C2312yes—
70C2×C3×Dic10D411yescharacteristic
71C2×#1204—22no—
72C2×#1202—24no—
73C2×#1201—22no—
74C2×D3×Dic5—22no—
75#6780—216no—
76C2×D5×Dic3—22no—
77#6772—24no—
78#6772—24no—
79D3×Dic10—28no—
80#6765—28no—
81D5×Dic6—24no—
82D5×Dic6—24no—
83C2×C3×C5×C8—22no—
84C2×C3×C5×C8C2312yes—
85#6706—28no—
86C5×#217—21no—
87C5×C4⋊Dic3C2312yes—
88C4×C5×Dic3—21no—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6667—24no—
92#6660—24no—
93#6654—24no—
94C2×#1010—51no—
95#5830—51no—
96C2×#908—51no—
97C22×#204—51no—
98C3×#408—51no—
99#5120—51no—
100#5113D511yescharacteristic, complemented
101#4738—54no—
102#4734—54no—
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—32no—
107C2×#711—32no—
108C2×#711—62no—
109C2×#709—61no—
110C2×#709C2×D311yescharacteristic
111C22×D20—31no—
112C22×Dic10—31no—
113C22×Dic10—61no—
114C22×C5×C8C2×D311yescharacteristic
115C5×#117—31no—
116#4095—64no—
117C2×#688—32no—
118C2×#686—32no—
119C2×#681C2×D311yescharacteristic
120C2×#677—34no—
121C2×#677—64no—
122#4041—34no—
123#4028—62no—
124#4021—61no—
125#4020—61no—
126C5×#103—32no—
127C5×#102—32no—
128#3952C2×D314yescomplemented
129#3942—34no—
130#3010—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—22no—
133C22×D15—42no—
134C22×D15—82no—
135C22×C5×D3—21no—
136C22×C3×D5C2×D412yes—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—24no—
142C2×Dic15—22no—
143D60—22no—
144D60—22no—
145D60—42no—
146Dic30—24no—
147Dic30—22no—
148Dic30C2×D414yes—
149C5×#67—24no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C5×D12—21no—
153C5×D12C2×D412yes—
154C4×C5×D3—24no—
155C5×Dic6—21no—
156C5×Dic6C2×D412yes—
157C3×C22⋊D5—24no—
158C2×C3×Dic5C2×D412yes—
159C3×D20—22no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—22no—
163#1204—28no—
164#1202—84no—
165#1201—28no—
166D3×Dic5—28no—
167D5×Dic3—28no—
168C3×C5×C8—22no—
169C3×#168—22no—
170C2×C3×#41—51no—
171#1010—104no—
172#1010—104no—
173C2×D3×Q8—101no—
174C2×#237—101no—
175C2×#237—102no—
176C2×#235—52no—
177C2×#235C2×D511yescharacteristic
178C22×D12—51no—
179C22×Dic6—51no—
180C22×Dic6—52no—
181C2×C3×M16—51no—
182C22×C3×C8C2×D511yescharacteristic
183#947—101no—
184#940—101no—
185#937—102no—
186#930—54no—
187#926C2×D511yescharacteristic
188#908—104no—
189C2×D24—52no—
190C2×#204—52no—
191C2×#204—54no—
192C2×#204—104no—
193C3×C22⋊C8—54no—
194#821C2×D512yescomplemented
195#816—54no—
196#816C2×D512yescomplemented
197C23×D5—61no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—62no—
206C2×C22⋊D5D1212yes—
207C22×Dic5—61no—
208C22×Dic5—62no—
209Q8×D5—64no—
210Q8×D5—64no—
211#711—64no—
212#711—64no—
213#711—616no—
214#709—22no—
215#709—22no—
216#709—68no—
217C2×D20—32no—
218C2×D20—62no—
219C2×D20—62no—
220C2×D20—61no—
221C2×D20—64no—
222C2×D20D1211yescharacteristic
223C2×C4×D5—62no—
224C2×C4×D5C22×D312yes—
225C2×Dic10—34no—
226C2×Dic10—32no—
227C2×Dic10—68no—
228C2×Dic10—61no—
229C2×Dic10—62no—
230C2×Dic10—62no—
231C2×Dic10D1211yescharacteristic
232C2×C5×C8—22no—
233C2×C5×C8C22×D312yes—
234C5×C4⋊C4—32no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237#688—64no—
238#686—64no—
239#685—64no—
240#681—22no—
241C2×#168C22×D312yes—
242#677—68no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—31no—
251#408—51no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—42no—
256C2×D15—44no—
257C2×D15—84no—
258C2×C5×D3—22no—
259C2×C5×D3—42no—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C3×C4×C5#12012yes—
263C3×C4×C5C22×D411yescharacteristic
264C3×C4×C5C22×D411yescharacteristic
265Dic15—24no—
266C3×Dic5—22no—
267C5×Dic3—22no—
268C5×Dic3—42no—
269C23×D3—101no—
270C3×#41—102no—
271C3×#41—102no—
272C2×C3×Q8—51no—
273C2×C3×D4—52no—
274C2×C3×D4—51no—
275C22×C3×C4—52no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—21no—
278C2×#67—104no—
279C2×#67—102no—
280C22×Dic3—102no—
281C22×Dic3—101no—
282D3×Q8—108no—
283#237—108no—
284#237—1016no—
285#235—22no—
286#235—104no—
287#235—104no—
288#235D2014yescomplemented
289C2×D12—52no—
290C2×D12—102no—
291C2×D12—102no—
292C2×D12—101no—
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—102no—
296C2×Dic6—54no—
297C2×Dic6—52no—
298C2×Dic6—104no—
299C2×Dic6—102no—
300C2×Dic6—102no—
301C2×Dic6—101no—
302C2×Dic6—104no—
303C2×Dic6C22×D511yescharacteristic
304C3×M16—102no—
305C2×C3×C8—22no—
306C2×C3×C8—52no—
307C2×C3×C8C22×D512yes—
308#217—21no—
309(C2×D3)⋊C4—104no—
310C4⋊Dic3C22×D512yes—
311C4×Dic3—21no—
312D24—104no—
313#204—108no—
314#204—104no—
315C23×C5—61no—
316C23×C5C2×D1211yescharacteristic
317C22×D5—62no—
318C22×D5—122no—
319C22×D5—242no—
320C22×D5C2×D1212yes—
321C5×Q8—32no—
322C5×Q8—61no—
323C5×D4—32no—
324C5×D4—64no—
325C5×D4—61no—
326C2×C4×C5—61no—
327C2×C4×C5—64no—
328C2×C4×C5—62no—
329C2×C4×C5C2×D1211yescharacteristic
330C2×C4×C5D3×D412yes—
331C2×C4×C5D3×D412yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—24no—
334C22⋊D5—68no—
335C2×Dic5—68no—
336C2×Dic5—64no—
337C2×Dic5—62no—
338C2×Dic5C2×D1212yes—
339D20—22no—
340D20—62no—
341D20—62no—
342D20—122no—
343D20—244no—
344C4×D5—22no—
345C4×D5—22no—
346C4×D5—68no—
347Dic10—22no—
348Dic10—34no—
349Dic10—68no—
350Dic10—64no—
351Dic10—62no—
352C5×C8—22no—
353#168—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—51no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C22×D4—151no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—152no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—51no—
371C22×C8D3×D511yescharacteristic
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—31no—
377#103—32no—
378#103—154no—
379#102—32no—
380C22⋊C8—54no—
381C2×C3×C5—22no—
382C2×C3×C5C2×#12011yescharacteristic
383C2×C3×C5#57712yes—
384D15—82no—
385C3×D5—42no—
386C5×D3—42no—
387C23×C3—52no—
388C23×C3D4×D511yescharacteristic
389C22×D3—21no—
390C22×D3—102no—
391C22×D3—202no—
392C22×D3—402no—
393C3×Q8—102no—
394C3×D4—104no—
395C3×D4—102no—
396C2×C3×C4—52no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4C2×D2012yes—
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4D4×D512yes—
402C2×C3×C4C23×D511yescharacteristic
403#67—24no—
404#67—108no—
405#67—404no—
406C2×Dic3—21no—
407C2×Dic3—22no—
408C2×Dic3—108no—
409C2×Dic3—102no—
410C2×Dic3—104no—
411D12—21no—
412D12—102no—
413D12—102no—
414D12—202no—
415D12C2×D2012yes—
416C4×D3—24no—
417C4×D3—108no—
418Dic6—21no—
419Dic6—54no—
420Dic6—108no—
421Dic6—102no—
422Dic6—104no—
423Dic6C2×D2012yes—
424C3×C8—22no—
425C3×C8—102no—
426C22×C5—22no—
427C22×C5—62no—
428C22×C5—122no—
429C22×C5#88212yes—
430C22×C5C22×D1211yescharacteristic
431C2×D5—22no—
432C2×D5—24no—
433C2×D5—122no—
434C2×D5—124no—
435C2×D5—244no—
436C4×C5—62no—
437C4×C5—122no—
438C4×C5#88212yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C2×D3×D411yescharacteristic
441Dic5—22no—
442Dic5—64no—
443C24—301no—
444#41—34no—
445#41—62no—
446#41—102no—
447#41—102no—
448#41—308no—
449#41—304no—
450#41—304no—
451#41—3016no—
452C2×Q8—31no—
453C2×Q8—51no—
454C2×Q8—154no—
455C2×Q8—152no—
456C2×Q8—302no—
457C2×Q8—308no—
458C2×Q8—304no—
459C2×Q8—304no—
460C2×Q8—301no—
461C2×Q8—302no—
462C2×D4—31no—
463C2×D4—52no—
464C2×D4—51no—
465C2×D4—61no—
466C2×D4—152no—
467C2×D4—304no—
468C2×D4—302no—
469C2×D4—301no—
470C2×D4—302no—
471C2×D4—302no—
472C22×C4—52no—
473C22×C4—61no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—102no—
482C2×C8—22no—
483C2×C8—52no—
484C2×C8C2×D3×D512yes—
485C4⋊C4—32no—
486C22⋊C4—61no—
487C22⋊C4—304no—
488C42—61no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—102no—
492C22×C3—104no—
493C22×C3#402812yes—
494C22×C3C2×D4×D511yescharacteristic
495C2×D3—22no—
496C2×D3—42no—
497C2×D3—202no—
498C2×D3—204no—
499C2×D3—404no—
500C3×C4—102no—
501C3×C4#402812yes—
502C3×C4C22×D2011yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—22no—
505Dic3—42no—
506Dic3—104no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5C2×#88211yescharacteristic
510C2×C5#575112yes—
511D5—42no—
512D5—242no—
513C23—52no—
514C23—61no—
515C23—302no—
516C23—602no—
517C23—1202no—
518C23D5×D1211yescharacteristic
519Q8—32no—
520Q8—61no—
521Q8—102no—
522Q8—154no—
523Q8—308no—
524Q8—304no—
525Q8—302no—
526D4—32no—
527D4—64no—
528D4—61no—
529D4—104no—
530D4—102no—
531D4—308no—
532D4—302no—
533D4—302no—
534D4—602no—
535D4—1204no—
536C2×C4—52no—
537C2×C4—61no—
538C2×C4—64no—
539C2×C4—62no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4—304no—
545C2×C4—302no—
546C2×C4D5×D1211yescharacteristic
547C2×C4D3×D2012yes—
548C2×C4#679012yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—22no—
551C8—102no—
552C2×C3—22no—
553C2×C3—202no—
554C2×C3C2×#402811yescharacteristic
555C2×C3#6610412yes—
556D3—42no—
557D3—402no—
558C5#7867811yescharacteristic, complemented, Sylow
559C22—22no—
560C22—62no—
561C22—102no—
562C22—104no—
563C22—122no—
564C22—602no—
565C22—604no—
566C22—1204no—
567C22#9147612yes—
568C22C2×D5×D1211yescharacteristic
569C4—62no—
570C4—102no—
571C4—122no—
572C4—304no—
573C4#9147612yes—
574C4C2×D3×D2011yescharacteristic
575C4C2×#679011yescharacteristic
576C3#1061056711yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—202no—
580C2—1202no—
581C2#1175396212yes—
582C2C2×#9147611yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#92001C2semidirect
2. C22×#6706C2semidirect
3. #11754609C2semidirect
4. C2×#91305C2semidirect
5. C5×#5113C2semidirect
6. C3×#65399C2semidirect
7. #11748417C2semidirect
8. #11748163C2semidirect
9. #11748128C2semidirect
16. C2×#6772C22semidirect
21. C2×D5×Dic6C22semidirect
34. C5×#821C22semidirect
35. C5×#816C22semidirect
36. C3×#3952C22semidirect
37. #90975C22semidirect
44. #65399D3semidirect
57. C2×Dic30D4semidirect
61. C5×#235D4semidirect
100. #5113D5semidirect
128. #3952C2×D3semidirect
194. #821C2×D5semidirect
196. #816C2×D5semidirect
288. #235D20semidirect
489. C3×C5#3010semidirect
558. C5#78678semidirect
576. C3#10610567semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C22×#67062
#117546092
C2×#913052
C5×#51132
C3×#653992
#117484172
#117481632
#117481282
#106105673
#786785