Finite Group Databasebeta

← #14439487

Subgroups — #14439487

Order 1920.

1128 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
1C2×C5×#909C211yesmaximal, characteristic, complemented
2C2×C3×#4054C211yesmaximal, characteristic, complemented
3#11754600C211yesmaximal, characteristic, complemented
4#11754251C211yesmaximal, characteristic, complemented
5C22×#6655C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11751223C211yesmaximal, characteristic, complemented
8#11748015C212yesmaximal, complemented
9#11748010C212yesmaximal, complemented
10#11747981C212yesmaximal, complemented
11#11747980C212yesmaximal, complemented
12#10615705—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91815C2211yescharacteristic
19C22×C3⋊#168C2211yescharacteristic
20C5×#909—24no—
21C2×C5×Dic12C2212yescomplemented
22C2×C5×#204C2212yescomplemented
23C3×#4054—24no—
24C2×C3×D40C2212yes—
25C2×C3×#677C2212yes—
26#91563—22no—
27#91536—22no—
28#91463C2212yes—
29#91456—22no—
30#91385C2212yescomplemented
31#91368C2212yes—
32#91368C2212yescomplemented
33#91359—22no—
34C2×#6661C2211yescharacteristic, complemented
35C2×#6656C2211yescharacteristic, complemented
36C2×#6655—24no—
37C2×#6655C2212yes—
38C2×#6655C2212yes—
39C2×#6655C2211yescharacteristic, complemented
40#91297—24no—
41C2×#6652C2211yescharacteristic, complemented
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83939—51nomaximal, Hall
45C2×C5×#137—31no—
46#66164—31no—
47C2×#4096—31no—
48#66150—31no—
49C22×#688—31no—
50C2×#4054D311yescharacteristic, complemented
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65464—32no—
55#65411—31no—
56C23×C3×D5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67—21no—
59C22×C5×Dic3—21no—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12C2311yescharacteristic
63C2×C4×C5×D3—21no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6—22no—
66C2×C5×Dic6—21no—
67C2×C5×Dic6C2312yes—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20—22no—
73C2×C3×D20—22no—
74C2×C3×D20—21no—
75C2×C3×D20C2312yes—
76C2×C3×D20C2311yescharacteristic
77C2×C3×C4×D5—21no—
78C2×C3×Dic10C2311yescharacteristic
79C2×#1201—24no—
80C3×C5×M16D414yescomplemented
81C2×C3×C5×C8C2312yes—
82#6719D412yes—
83C4⋊Dic15D412yes—
84C4×Dic15C2312yes—
85C2×C3⋊#168D414yescomplemented
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88C5×Dic12—24no—
89C5×#204—24no—
90C3×D40—24no—
91C3×#677—24no—
92#6669—24no—
93#6665—24no—
94#6665—24no—
95#6661—22no—
96#6656—22no—
97#6655—22no—
98#6655—24no—
99#6655—24no—
100#6652—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5825—51no—
103C2×#950—51no—
104#5805—51no—
105C22×#214—51no—
106C2×#909D511yescharacteristic, complemented
107#5175—52no—
108#5167—52no—
109#5155—52no—
110#5154—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C22×C5×Q8—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16C2×D311yescharacteristic
120#4096—64no—
121#4093—32no—
122#4093—32no—
123#4092—62no—
124#4090—32no—
125C2×#689—31no—
126C2×#688—32no—
127C2×#688—32no—
128C2×#688—31no—
129C2×#688—64no—
130#4086—32no—
131#4083—62no—
132C2×#687—31no—
133C2×#686—31no—
134#4076—62no—
135#4075—62no—
136#4072—31no—
137C22×#168—31no—
138#4054—24no—
139C2×D40C2×D312yes—
140C2×#677C2×D312yes—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C5×D3—21no—
146C22×C3×D5—21no—
147C22×C3×D5—22no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15C2×D414yes—
155C5×#67—42no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—42no—
159C5×D12—21no—
160C5×D12—21no—
161C4×C5×D3—42no—
162C5×Dic6—21no—
163C5×Dic6—22no—
164C5×Dic6—21no—
165C5×Dic6—22no—
166C5×Dic6—42no—
167C3×C22⋊D5—42no—
168C2×C3×Dic5—21no—
169C3×D20—22no—
170C3×D20—21no—
171C3×D20—22no—
172C3×D20—21no—
173C3×D20—42no—
174C3×C4×D5—42no—
175C3×Dic10—21no—
176C3×Dic10—21no—
177#1201—84no—
178C3×C5×C8C2×D414yes—
179C3⋊#168C2×D412yes—
180C3⋊#168C2×D412yes—
181C2×C3×#41—51no—
182C22×C3×D4—51no—
183C2×#235C2×D511yescharacteristic
184C22×Dic6C2×D511yescharacteristic
185C3×AGL(1,ℤ/8)—104no—
186C2×C3×SD16—52no—
187C2×C3×D8—52no—
188C2×C3×M16C2×D511yescharacteristic
189#953—102no—
190#950—104no—
191#944—52no—
192C2×#216—51no—
193C2×#215—51no—
194#940—52no—
195#938—102no—
196#936—52no—
197#936—52no—
198#935—102no—
199C2×#214—52no—
200C2×#214—51no—
201C2×#214—52no—
202C2×#214—104no—
203C2×#213—51no—
204#926—51no—
205#924—102no—
206C22×C3⋊C8—51no—
207#909—24no—
208C2×Dic12C2×D512yescomplemented
209C2×#204C2×D512yescomplemented
210#815—52no—
211C8×Dic3—52no—
212C23×D5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—32no—
216C2×C5×Q8—31no—
217C2×C5×Q8—61no—
218C2×C5×Q8—62no—
219C2×C5×Q8—62no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—61no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C2×C22⋊D5—64no—
227#709—22no—
228#709—22no—
229C2×D20—22no—
230C2×D20—22no—
231C2×D20—21no—
232C2×D20C22×D312yes—
233C2×D20C22×D311yescharacteristic
234C2×C4×D5—21no—
235C2×Dic10C22×D311yescharacteristic
236C5×Q16—64no—
237C5×SD16—64no—
238C5×M16#6714yescomplemented
239C2×C5×C8C22×D312yes—
240C22⋊Dic5—32no—
241#689—62no—
242#688—62no—
243#688—64no—
244#688—64no—
245#687—62no—
246#686—62no—
247#685—64no—
248#685—64no—
249C4⋊Dic5—32no—
250#683—64no—
251C4×Dic5—32no—
252C2×#168—34no—
253C2×#168—31no—
254C2×#168—31no—
255D40—24no—
256#677—24no—
257C2×#137—31no—
258C2×AGL(1,ℤ/8)—51no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C2×C3×D5—41no—
274C2×C3×D5—42no—
275C2×C3×D5—44no—
276C2×C3×D5—42no—
277C2×C3×D5—84no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—24no—
282C3×Dic5—41no—
283C5×Dic3—42no—
284C5×Dic3—41no—
285C24×C3—101no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—51no—
289C2×C3×D4—51no—
290C2×C3×D4—52no—
291C2×C3×D4—101no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C2×C3×D4—102no—
295C22×C3×C4—101no—
296C22×C3×C4C22×D511yescharacteristic
297C2×#67—21no—
298C2×#67—104no—
299C22×Dic3—21no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—21no—
307C2×Dic6C22×D512yes—
308C2×Dic6C22×D511yescharacteristic
309C3×SD16—104no—
310C3×D8—104no—
311C3×M16C22⋊D514yescomplemented
312C2×C3×C8C22×D512yes—
313#217—52no—
314#217—104no—
315#217—104no—
316#216—102no—
317#215—102no—
318#214—104no—
319#214—104no—
320#214—102no—
321#213—102no—
322C4⋊Dic3—52no—
323Dic3⋊C4—104no—
324C4×Dic3—52no—
325C2×C3⋊C8—54no—
326C2×C3⋊C8—51no—
327C2×C3⋊C8—51no—
328Dic12—24no—
329#204—24no—
330C23×C5—61no—
331C23×C5D3×D411yescharacteristic
332C22×D5—21no—
333C22×D5—22no—
334C22×D5—42no—
335C22×D5—82no—
336C5×Q8—62no—
337C5×Q8—61no—
338C5×Q8—62no—
339C5×Q8—61no—
340C5×Q8—122no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—62no—
345C2×C4×C5—61no—
346C2×C4×C5—122no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D411yescharacteristic
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—42no—
353C22⋊D5—244no—
354C2×Dic5—21no—
355C2×Dic5—34no—
356D20—21no—
357D20—22no—
358D20—22no—
359D20—21no—
360D20—42no—
361C4×D5—42no—
362Dic10—21no—
363Dic10—21no—
364C5×C8C2×#6714yes—
365#168—32no—
366#168—32no—
367C2×#41—31no—
368C2×#41—51no—
369C22×Q8—31no—
370C22×D4—51no—
371#137—64no—
372AGL(1,ℤ/8)—104no—
373#135—304no—
374C2×Q16—32no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—52no—
378C2×SD16—151no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—151no—
382C2×SD16—304no—
383C2×D8—52no—
384C2×D8—151no—
385C2×M16D3×D511yescharacteristic
386C22×C8—151no—
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—151no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401C3×D5—81no—
402C3×D5—82no—
403C5×D3—81no—
404C23×C3—101no—
405C23×C3—102no—
406C23×C3—202no—
407C23×C3—402no—
408C23×C3D4×D511yescharacteristic
409C22×D3—21no—
410C3×Q8—101no—
411C3×Q8—101no—
412C3×D4—101no—
413C3×D4—102no—
414C3×D4—101no—
415C3×D4—102no—
416C3×D4—202no—
417C3×D4—202no—
418C2×C3×C4—101no—
419C2×C3×C4—202no—
420C2×C3×C4D4×D512yes—
421C2×C3×C4D4×D511yescharacteristic
422C2×C3×C4C2×C22⋊D512yes—
423C2×C3×C4C23×D511yescharacteristic
424#67—42no—
425#67—404no—
426C2×Dic3—22no—
427C2×Dic3—21no—
428C2×Dic3—42no—
429C2×Dic3—54no—
430D12—21no—
431D12—21no—
432C4×D3—42no—
433Dic6—22no—
434Dic6—21no—
435Dic6—22no—
436Dic6—21no—
437Dic6—42no—
438C3×C8C2×C22⋊D514yes—
439C3⋊C8—52no—
440C3⋊C8—52no—
441C22×C5—22no—
442C22×C5—122no—
443C22×C5—121no—
444C22×C5#94012yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—44no—
447C2×D5—42no—
448C2×D5—41no—
449C2×D5—42no—
450C2×D5—84no—
451C4×C5—121no—
452C4×C5—122no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—41no—
457Dic5—64no—
458C24—101no—
459#41—62no—
460#41—62no—
461#41—102no—
462#41—102no—
463C2×Q8—31no—
464C2×Q8—32no—
465C2×Q8—51no—
466C2×Q8—61no—
467C2×Q8—62no—
468C2×Q8—62no—
469C2×D4—31no—
470C2×D4—51no—
471C2×D4—52no—
472C2×D4—61no—
473C2×D4—101no—
474C2×D4—102no—
475C2×D4—101no—
476C2×D4—102no—
477C2×D4—304no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—64no—
483Q16—302no—
484SD16—64no—
485SD16—104no—
486SD16—302no—
487SD16—304no—
488SD16—304no—
489SD16—302no—
490D8—104no—
491D8—302no—
492M16#120114yescomplemented
493C2×C8—154no—
494C2×C8—151no—
495C2×C8—151no—
496C2×C8C2×D3×D512yes—
497C4⋊C4—152no—
498C4⋊C4—304no—
499C22⋊C4—152no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—152no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—204no—
506C22×C3—202no—
507C22×C3—201no—
508C22×C3—202no—
509C22×C3—404no—
510C22×C3#408612yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—42no—
513C2×D3—41no—
514C3×C4—201no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—42no—
519Dic3—41no—
520Dic3—104no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5#577512yes—
524C2×C5C2×#94011yescharacteristic
525D5—82no—
526D5—81no—
527C23—61no—
528C23—101no—
529C23—102no—
530C23—202no—
531C23—402no—
532C23#677711yescharacteristic
533Q8—62no—
534Q8—61no—
535Q8—62no—
536Q8—61no—
537Q8—101no—
538Q8—101no—
539Q8—122no—
540D4—61no—
541D4—61no—
542D4—101no—
543D4—102no—
544D4—101no—
545D4—102no—
546D4—122no—
547D4—202no—
548D4—202no—
549D4—1204no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—101no—
553C2×C4—122no—
554C2×C4—122no—
555C2×C4—154no—
556C2×C4—202no—
557C2×C4#677711yescharacteristic
558C2×C4#677712yes—
559C2×C4C2×#120112yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—152no—
562C8—152no—
563C8C2×#120114yes—
564C2×C3—22no—
565C2×C3—402no—
566C2×C3—401no—
567C2×C3#6611212yes—
568C2×C3C2×#408611yescharacteristic
569D3—81no—
570C5#8393911yescharacteristic, complemented, Sylow
571C22—22no—
572C22—122no—
573C22—121no—
574C22—204no—
575C22—202no—
576C22—201no—
577C22—202no—
578C22—404no—
579C22#9146312yes—
580C22C2×#677711yescharacteristic
581C4—121no—
582C4—122no—
583C4—201no—
584C4—304no—
585C4#9146312yes—
586C4C2×#677711yescharacteristic
587C4C22×#120111yescharacteristic
588C3#1061570511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—402no—
592C2—401no—
593C2#1175403712yes—
594C2C2×#9146311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5#3154
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
1. C2×C5×#909C2semidirect
2. C2×C3×#4054C2semidirect
3. #11754600C2semidirect
4. #11754251C2semidirect
5. C22×#6655C2semidirect
6. C2×#91297C2semidirect
7. #11751223C2semidirect
8. #11748015C2semidirect
9. #11748010C2semidirect
10. #11747981C2semidirect
11. #11747980C2semidirect
21. C2×C5×Dic12C22semidirect
22. C2×C5×#204C22semidirect
30. #91385C22semidirect
32. #91368C22semidirect
34. C2×#6661C22semidirect
35. C2×#6656C22semidirect
39. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
50. C2×#4054D3semidirect
80. C3×C5×M16D4semidirect
85. C2×C3⋊#168D4semidirect
106. C2×#909D5semidirect
208. C2×Dic12C2×D5semidirect
209. C2×#204C2×D5semidirect
238. C5×M16#67semidirect
311. C3×M16C22⋊D5semidirect
492. M16#1201semidirect
503. C3×C5#3154semidirect
570. C5#83939semidirect
588. C3#10615705semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9092
C2×C3×#40542
#117546002
#117542512
C22×#66552
C2×#912972
#117512232
#117480152
#117480102
#117479812
#117479802
#106157053
#839395