Finite Group Databasebeta

← #14439490

Subgroups — #14439490

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
1#11756584C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic, complemented
3C2×C3×#4095C211yesmaximal, characteristic, complemented
4#11754600C211yesmaximal, characteristic, complemented
5C2×#91322C211yesmaximal, characteristic, complemented
6C22×#6657C211yesmaximal, characteristic, complemented
7#11749341C212yesmaximal, complemented
8#11749320C212yesmaximal, complemented
9#11749096C212yesmaximal, complemented
10#11749072C212yesmaximal, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10615636—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91833C2212yescomplemented
18#91825C2212yescomplemented
19#91824—22no—
20#91815C2211yescharacteristic
21#91813—22no—
22C5×#950—24no—
23C2×C5×#216C2211yescharacteristic, complemented
24C2×C5×#215C2211yescharacteristic, complemented
25C2×C5×#214C2211yescharacteristic, complemented
26C2×C5×#213C2211yescharacteristic, complemented
27C22×C5×C3⋊C8C2211yescharacteristic
28C3×#4095—24no—
29C2×C3×#688C2212yes—
30C2×C3×#686C2212yes—
31C2×C3×#681C2211yescharacteristic
32#91563—22no—
33#91463C2212yes—
34#91456—22no—
35#91368C2212yes—
36#91322—24no—
37C2×#6663C2212yescomplemented
38C2×#6659C2212yescomplemented
39C2×#6657—24no—
40C2×#6657C2212yes—
41C2×#6657C2212yes—
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83939—51nomaximal, Hall
45C2×C5×#135—31no—
46#66164—31no—
47#66159—31no—
48C2×#4097—31no—
49C2×#4095D311yescharacteristic, complemented
50C22×#677—31no—
51#65479—32no—
52#65464—32no—
53#65457—32no—
54#65443—32no—
55#65390—31no—
56C23×C3×D5—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15—21no—
65C2×Dic30—22no—
66C2×Dic30—22no—
67C2×Dic30—21no—
68C2×Dic30C2312yes—
69C2×C5×#67—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6C2311yescharacteristic
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20—21no—
78C2×C3×D20C2312yes—
79C2×#1201—24no—
80#6719—24no—
81#6719D412yes—
82C4⋊Dic15D412yes—
83#6712—24no—
84C4×Dic15C2312yes—
85C5×#216—22no—
86C5×#215—22no—
87C5×#214—22no—
88C5×#213—22no—
89C2×C5×C3⋊C8D414yescomplemented
90C2×C5×C3⋊C8C2311yescharacteristic
91C2×C5×C3⋊C8C2311yescharacteristic
92C3×#688—24no—
93C3×#686—24no—
94C3×#681D414yescomplemented
95C2×C3×#168C2312yes—
96#6665—24no—
97#6663—24no—
98#6659—24no—
99#6657—24no—
100#6657—24no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5825—51no—
103C2×#950D511yescharacteristic, complemented
104#5805—51no—
105C22×#214—51no—
106C2×#909—51no—
107#5175—52no—
108#5167—52no—
109#5155—52no—
110#5154—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C2×C5×#41C2×D311yescharacteristic
114C22×D20C2×D311yescharacteristic
115C22×Dic10—31no—
116C5×#135—64no—
117C2×C5×Q16—31no—
118C2×C5×SD16—31no—
119C2×C5×SD16—31no—
120C2×C5×D8—31no—
121C22×C5×C8—31no—
122#4097—64no—
123#4095—24no—
124#4093—32no—
125#4090—32no—
126C2×#689—32no—
127C2×#688C2×D312yes—
128#4086—32no—
129#4083—62no—
130#4082—32no—
131#4081—62no—
132C2×#687—32no—
133C2×#686C2×D312yes—
134#4076—62no—
135#4072—31no—
136#4070—62no—
137C2×#681C2×D311yescharacteristic
138C2×#677—32no—
139C2×#677—32no—
140C2×#677—64no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—21no—
147C22×C3×D5—22no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161C2×Dic15—22no—
162C2×Dic15—42no—
163C2×Dic15C2×D414yes—
164Dic30—22no—
165Dic30—22no—
166Dic30—42no—
167C5×#67—42no—
168C2×C5×Dic3—21no—
169C5×D12—21no—
170C5×D12—21no—
171C4×C5×D3—42no—
172C5×Dic6—21no—
173C5×Dic6—21no—
174C3×D20—22no—
175C3×D20—22no—
176C3×D20—42no—
177#1201—84no—
178C3×#168C2×D414yes—
179C5×C3⋊C8C2×D412yes—
180C5×C3⋊C8C2×D412yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×D4—51no—
183C2×#235C2×D511yescharacteristic
184C22×Dic6—51no—
185C3×AGL(1,ℤ/8)—104no—
186C2×C3×SD16—52no—
187C2×C3×D8—52no—
188C2×C3×M16—51no—
189#953—102no—
190#950—24no—
191#944—52no—
192C2×#216C2×D511yescharacteristic, complemented
193C2×#215C2×D511yescharacteristic, complemented
194#940—52no—
195#938—102no—
196#936—52no—
197#936—52no—
198#935—102no—
199C2×#214—52no—
200C2×#214—52no—
201C2×#214—104no—
202C2×#214C2×D511yescharacteristic, complemented
203C2×#213C2×D511yescharacteristic, complemented
204#926—51no—
205#924—102no—
206C22×C3⋊C8C2×D511yescharacteristic
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C23×D5—21no—
213C5×#41—22no—
214C5×#41—22no—
215C5×#41—62no—
216C5×#41—62no—
217C2×C5×Q8—31no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—64no—
227C22×Dic5—61no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20C22×D312yes—
232C2×Dic10—32no—
233C2×Dic10—62no—
234C2×Dic10—62no—
235C2×Dic10—61no—
236C5×Q16—62no—
237C5×SD16—62no—
238C5×SD16—62no—
239C5×D8—62no—
240C2×C5×C8—34no—
241C2×C5×C8—31no—
242C2×C5×C8—31no—
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—64no—
246#688—24no—
247#687—64no—
248#686—24no—
249#685—64no—
250C4⋊Dic5—32no—
251#683—64no—
252C4×Dic5—32no—
253#681#6714yescomplemented
254C2×#168C22×D312yes—
255#677—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—51no—
259C2×#135—31no—
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—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×C5×D3—41no—
274C2×C5×D3—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5—41no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—24no—
283Dic15—42no—
284C5×Dic3—41no—
285C24×C3—101no—
286C3×#41—22no—
287C3×#41—22no—
288C2×C3×Q8C22×D511yescharacteristic
289C2×C3×D4—21no—
290C2×C3×D4—52no—
291C2×C3×D4—102no—
292C2×C3×D4—101no—
293C2×C3×D4—102no—
294C2×C3×D4C22×D511yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4C22×D511yescharacteristic
297C2×#67—21no—
298C2×#67—104no—
299C22×Dic3—101no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6—52no—
305C2×Dic6—102no—
306C2×Dic6—102no—
307C2×Dic6—101no—
308C2×Dic6C22×D511yescharacteristic
309C3×SD16—104no—
310C3×D8—104no—
311C3×M16—54no—
312C2×C3×C8—52no—
313#217—52no—
314#217—104no—
315#217—104no—
316#216—22no—
317#215—22no—
318#214—22no—
319#214—104no—
320#214—104no—
321#213—22no—
322C4⋊Dic3—52no—
323Dic3⋊C4—104no—
324C4×Dic3—52no—
325C2×C3⋊C8C22⋊D514yescomplemented
326C2×C3⋊C8C22×D511yescharacteristic
327C2×C3⋊C8C22×D511yescharacteristic
328Dic12—104no—
329#204—104no—
330C23×C5—21no—
331C23×C5—61no—
332C23×C5D3×D411yescharacteristic
333C22×D5—22no—
334C22×D5—42no—
335C22×D5—82no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×Q8—61no—
339C5×Q8—61no—
340C5×D4—21no—
341C5×D4—21no—
342C5×D4—42no—
343C5×D4—61no—
344C5×D4—61no—
345C5×D4—122no—
346C2×C4×C5—21no—
347C2×C4×C5—42no—
348C2×C4×C5—61no—
349C2×C4×C5—122no—
350C2×C4×C5D3×D412yes—
351C2×C4×C5D3×D411yescharacteristic
352C2×C4×C5C2×#6712yes—
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—244no—
355C2×Dic5—34no—
356C2×Dic5—62no—
357C2×Dic5—122no—
358D20—22no—
359D20—22no—
360D20—42no—
361Dic10—62no—
362Dic10—62no—
363Dic10—122no—
364C5×C8—32no—
365C5×C8—32no—
366#168C2×#6714yes—
367C2×#41—31no—
368C2×#41D3×D511yescharacteristic
369C22×Q8—151no—
370C22×D4—51no—
371#137—304no—
372AGL(1,ℤ/8)—104no—
373#135—64no—
374C2×Q16—31no—
375C2×Q16—152no—
376C2×SD16—31no—
377C2×SD16—31no—
378C2×SD16—52no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—31no—
384C2×D8—52no—
385C2×M16—51no—
386C22×C8—31no—
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×C5—81no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402C3×D5—82no—
403C5×D3—81no—
404C23×C3—21no—
405C23×C3—102no—
406C23×C3—202no—
407C23×C3—402no—
408C23×C3D4×D511yescharacteristic
409C22×D3—21no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×D4—21no—
413C3×D4—21no—
414C3×D4—42no—
415C3×D4—102no—
416C3×D4—102no—
417C3×D4—202no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
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—21no—
427C2×Dic3—54no—
428C2×Dic3—102no—
429C2×Dic3—202no—
430D12—21no—
431D12—21no—
432C4×D3—42no—
433Dic6—21no—
434Dic6—21no—
435Dic6—102no—
436Dic6—102no—
437Dic6—202no—
438C3×C8—54no—
439C3⋊C8C2×C22⋊D512yes—
440C3⋊C8C2×C22⋊D512yes—
441C22×C5—22no—
442C22×C5—42no—
443C22×C5—41no—
444C22×C5—122no—
445C22×C5—121no—
446C22×C5#94012yes—
447C22×C5C2×D3×D411yescharacteristic
448C2×D5—44no—
449C2×D5—42no—
450C2×D5—84no—
451C4×C5—41no—
452C4×C5—121no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—64no—
457Dic5—122no—
458C24—101no—
459#41—22no—
460#41—22no—
461#41—62no—
462#41—62no—
463C2×Q8—31no—
464C2×Q8—152no—
465C2×Q8—301no—
466C2×Q8—302no—
467C2×Q8—302no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—31no—
471C2×D4—52no—
472C2×D4—61no—
473C2×D4—102no—
474C2×D4—102no—
475C2×D4—101no—
476C2×D4—304no—
477C2×D4C2×D3×D511yescharacteristic
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—62no—
483Q16—304no—
484SD16—62no—
485SD16—62no—
486SD16—104no—
487SD16—304no—
488SD16—304no—
489SD16—304no—
490D8—62no—
491D8—104no—
492M16—54no—
493C2×C8—34no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—52no—
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—42no—
506C22×C3—41no—
507C22×C3—204no—
508C22×C3—202no—
509C22×C3—404no—
510C22×C3#408612yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—42no—
513C2×D3—41no—
514C3×C4—41no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—41no—
519Dic3—104no—
520Dic3—202no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5—241no—
524C2×C5#577512yes—
525C2×C5C2×#94011yescharacteristic
526D5—82no—
527C23—21no—
528C23—61no—
529C23—102no—
530C23—202no—
531C23—402no—
532C23#679011yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—61no—
536Q8—61no—
537Q8—302no—
538Q8—302no—
539Q8—602no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—61no—
544D4—61no—
545D4—102no—
546D4—102no—
547D4—122no—
548D4—202no—
549D4—1204no—
550C2×C4—21no—
551C2×C4—42no—
552C2×C4—61no—
553C2×C4—122no—
554C2×C4—154no—
555C2×C4—302no—
556C2×C4—602no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D512yes—
559C2×C4#679011yescharacteristic
560C2×C4C22×D3×D511yescharacteristic
561C8—32no—
562C8—32no—
563C8—54no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3—402no—
567C2×C3#6610412yes—
568C2×C3C2×#408611yescharacteristic
569D3—81no—
570C5#8393911yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—41no—
574C22—122no—
575C22—121no—
576C22—204no—
577C22—202no—
578C22—404no—
579C22#9156712yes—
580C22C2×#679011yescharacteristic
581C4—41no—
582C4—121no—
583C4—304no—
584C4—602no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061563611yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—241no—
592C2—402no—
593C2#1175533112yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756584C2semidirect
2. C2×C5×#950C2semidirect
3. C2×C3×#4095C2semidirect
4. #11754600C2semidirect
5. C2×#91322C2semidirect
6. C22×#6657C2semidirect
7. #11749341C2semidirect
8. #11749320C2semidirect
9. #11749096C2semidirect
10. #11749072C2semidirect
11. #11748326C2semidirect
17. #91833C22semidirect
18. #91825C22semidirect
23. C2×C5×#216C22semidirect
24. C2×C5×#215C22semidirect
25. C2×C5×#214C22semidirect
26. C2×C5×#213C22semidirect
37. C2×#6663C22semidirect
38. C2×#6659C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
49. C2×#4095D3semidirect
89. C2×C5×C3⋊C8D4semidirect
94. C3×#681D4semidirect
103. C2×#950D5semidirect
192. C2×#216C2×D5semidirect
193. C2×#215C2×D5semidirect
202. C2×#214C2×D5semidirect
203. C2×#213C2×D5semidirect
253. #681#67semidirect
325. C2×C3⋊C8C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83939semidirect
588. C3#10615636semidirect

Maximal subgroups

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

subgroupindex
#117565842
C2×C5×#9502
C2×C3×#40952
#117546002
C2×#913222
C22×#66572
#117493412
#117493202
#117490962
#117490722
#117483262
#106156363
#839395