Finite Group Databasebeta

← #14439457

Subgroups — #14439457

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#11756564C211yesmaximal, characteristic, complemented
2C2×C5×#932C211yesmaximal, characteristic, complemented
3C22×C3×#687C211yesmaximal, characteristic, complemented
4#11754255C211yesmaximal, characteristic, complemented
5C2×#91315C211yesmaximal, characteristic, complemented
6C2×#91303C211yesmaximal, characteristic, complemented
7#11749111C212yesmaximal, complemented
8#11749109C212yesmaximal, complemented
9#11749077C212yesmaximal, complemented
10#11749075C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615670—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91842—22no—
18#91829C2212yes—
19#91827—22no—
20#91825C2212yes—
21#91815C2211yescharacteristic
22C2×C5×#214C2212yes—
23C5×#932—24no—
24C2×C5×#213C2212yes—
25C2×C5×#208C2211yescharacteristic
26C2×C3×#687—24no—
27C2×C3×#687C2212yes—
28C2×C3×#687C2212yes—
29C22×C3×#168C2211yescharacteristic
30#91539—22no—
31#91385C2212yescomplemented
32#91370C2212yescomplemented
33#91369—22no—
34C2×#6663C2211yescharacteristic, complemented
35C2×#6662C2212yescomplemented
36C2×#6660C2211yescharacteristic, complemented
37C2×#6659C2211yescharacteristic, complemented
38#91315—24no—
39C2×#6658C2212yescomplemented
40#91303—24no—
41C2×#6654C2211yescharacteristic, complemented
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83854—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66159—31no—
47C2×#4096—31no—
48#66139—31no—
49C22×#687D311yescharacteristic, complemented
50C2×#4055—31no—
51#65464—32no—
52#65456—32no—
53#65444—32no—
54#65443—32no—
55#65411—31no—
56C24×C3×C5—21no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63C2×#1220—24no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×#67—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6C2311yescharacteristic
75C22×C3×Dic5—21no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—21no—
79C2×C3×Dic10C2312yes—
80#6719—24no—
81#6719D412yes—
82C4⋊Dic15D412yes—
83C4×Dic15C2312yes—
84C5×#214—24no—
85C5×#213—24no—
86C5×#208D414yescomplemented
87C2×C5×C3⋊C8C2312yes—
88C3×#687—24no—
89C3×#687—24no—
90C2×C3×#168D414yescomplemented
91C2×C3×#168C2311yescharacteristic
92C2×C3×#168C2311yescharacteristic
93#6669—24no—
94(C2×D3)⋊Dic5—24no—
95#6663—22no—
96#6662—24no—
97#6660—22no—
98#6659—22no—
99#6658—24no—
100#6654—22no—
101C22×C3×SD16—51no—
102#5816—51no—
103C2×#942—51no—
104#5805—51no—
105C2×#932D511yescharacteristic, complemented
106C2×#904—51no—
107#5176—52no—
108#5175—52no—
109#5168—52no—
110#5167—52no—
111#5101—51no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
120#4099—62no—
121#4096—64no—
122#4090—32no—
123C2×#689—31no—
124C2×#688—31no—
125#4086—32no—
126#4084—62no—
127#4082—32no—
128#4082—32no—
129#4081—62no—
130C2×#687—24no—
131C2×#687—31no—
132C2×#687C2×D312yes—
133C2×#687C2×D312yes—
134C2×#686—31no—
135#4072—31no—
136#4070—62no—
137C22×#168C2×D311yescharacteristic
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—21no—
149C22×C5×D3—21no—
150C3×C5×D4—22no—
151C3×C5×D4—22no—
152C3×C5×D4—42no—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157#1220—42no—
158#1220—84no—
159C2×Dic15—21no—
160C2×Dic15C2×D414yes—
161D60—21no—
162D60—21no—
163C4×D15—42no—
164Dic30—21no—
165Dic30—21no—
166C5×#67—42no—
167C2×C5×Dic3—21no—
168C5×D12—21no—
169C5×D12—21no—
170C4×C5×D3—42no—
171C5×Dic6—21no—
172C5×Dic6—21no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—42no—
175C3×Dic10—22no—
176C3×Dic10—22no—
177C3×Dic10—42no—
178C3×#168C2×D412yes—
179C3×#168C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C22×C3×Q8—51no—
182C22×C3×D4C2×D511yescharacteristic
183C2×#235—51no—
184C2×#235C2×D511yescharacteristic
185C2×C3×SD16—52no—
186C2×C3×SD16—52no—
187C2×C3×SD16—104no—
188C22×C3×C8—51no—
189#953—102no—
190#947—52no—
191#946—102no—
192#944—52no—
193C2×#216—52no—
194#942—104no—
195C2×#215—52no—
196#940—52no—
197#938—102no—
198#936—52no—
199C2×#214C2×D512yes—
200#932—24no—
201C2×#213C2×D512yes—
202#929—102no—
203#926—51no—
204C2×#208C2×D511yescharacteristic
205C2×Dic12—51no—
206#904—104no—
207C2×D24—51no—
208C2×#204—51no—
209C2×#204—51no—
210#815—52no—
211C8×Dic3—52no—
212C24×C5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—31no—
216C2×C5×D4—22no—
217C2×C5×D4—21no—
218C2×C5×D4—22no—
219C2×C5×D4—31no—
220C2×C5×D4—61no—
221C2×C5×D4C22×D312yes—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—64no—
225C2×C22⋊D5—61no—
226C22×Dic5—21no—
227#709—62no—
228#709—62no—
229C2×D20—31no—
230C2×C4×D5—61no—
231C2×Dic10—22no—
232C2×Dic10—22no—
233C2×Dic10—21no—
234C2×Dic10—31no—
235C2×Dic10C22×D312yes—
236C5×SD16—64no—
237C5×D8—64no—
238C5×M16—34no—
239C2×C5×C8—32no—
240C22⋊Dic5—32no—
241C22⋊Dic5—64no—
242C22⋊Dic5—64no—
243#689—62no—
244#688—62no—
245#687—24no—
246#687—24no—
247#687—62no—
248#686—62no—
249C4⋊Dic5—32no—
250#683—64no—
251C4×Dic5—32no—
252C2×#168#6714yescomplemented
253C2×#168C22×D311yescharacteristic
254C2×#168C22×D311yescharacteristic
255Dic20—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—31no—
259C2×#135—151no—
260C22×SD16—51no—
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—42no—
270C22×C3×C5—44no—
271C22×C3×C5—84no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—41no—
275C2×D15—42no—
276C2×C5×D3—41no—
277C2×C5×D3—42no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—24no—
282Dic15—41no—
283C3×Dic5—42no—
284C5×Dic3—41no—
285C24×C3—21no—
286C2×C3×Q8—52no—
287C2×C3×Q8—101no—
288C2×C3×Q8—102no—
289C2×C3×Q8—102no—
290C2×C3×D4—22no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4C22×D512yes—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—21no—
297C2×#67—104no—
298C2×#67—101no—
299#235—22no—
300#235—22no—
301#235—102no—
302#235—102no—
303C2×D12—51no—
304C2×D12C22×D511yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—101no—
307C2×Dic6—51no—
308C2×Dic6C22×D511yescharacteristic
309C3×SD16—104no—
310C3×SD16—104no—
311C2×C3×C8—54no—
312C2×C3×C8—51no—
313C2×C3×C8—51no—
314#217—52no—
315#217—104no—
316#216—104no—
317#215—104no—
318#214—24no—
319#213—24no—
320(C2×D3)⋊C4—104no—
321C4⋊Dic3—52no—
322Dic3⋊C4—104no—
323C4×Dic3—52no—
324#208C22⋊D514yescomplemented
325C2×C3⋊C8C22×D512yes—
326Dic12—102no—
327D24—102no—
328#204—102no—
329#204—102no—
330C23×C5—22no—
331C23×C5—42no—
332C23×C5—61no—
333C23×C5—82no—
334C23×C5D3×D411yescharacteristic
335C22×D5—61no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×D4—22no—
339C5×D4—22no—
340C5×D4—42no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—61no—
345C2×C4×C5—122no—
346C2×C4×C5D3×D412yes—
347C2×C4×C5D3×D411yescharacteristic
348C2×C4×C5C2×#6712yes—
349C2×C4×C5C23×D311yescharacteristic
350C22⋊D5—122no—
351C22⋊D5—244no—
352C2×Dic5—22no—
353C2×Dic5—34no—
354C2×Dic5—42no—
355C2×Dic5—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—22no—
360Dic10—22no—
361Dic10—42no—
362Dic10—61no—
363Dic10—61no—
364C5×C8—34no—
365#168C2×#6712yes—
366#168C2×#6712yes—
367C2×#41—31no—
368C2×#41—151no—
369C22×Q8—51no—
370C22×D4D3×D511yescharacteristic
371#137—304no—
372AGL(1,ℤ/8)—64no—
373#135—304no—
374C2×Q16—152no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—52no—
378C2×SD16—52no—
379C2×SD16—104no—
380C2×SD16—152no—
381C2×SD16—151no—
382C2×SD16—151no—
383C2×D8—32no—
384C2×D8—151no—
385C2×M16—31no—
386C22×C8—51no—
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—82no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—81no—
403C5×D3—81no—
404C23×C3—22no—
405C23×C3—42no—
406C23×C3—82no—
407C23×C3D4×D511yescharacteristic
408C22×D3—21no—
409C22×D3—101no—
410C3×Q8—102no—
411C3×Q8—102no—
412C3×Q8—202no—
413C3×D4—22no—
414C3×D4—22no—
415C3×D4—42no—
416C2×C3×C4—102no—
417C2×C3×C4—202no—
418C2×C3×C4D4×D512yes—
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4C2×C22⋊D512yes—
421C2×C3×C4C23×D511yescharacteristic
422#67—42no—
423#67—202no—
424#67—404no—
425C2×Dic3—21no—
426C2×Dic3—54no—
427C2×Dic3—101no—
428D12—21no—
429D12—21no—
430D12—101no—
431D12—101no—
432C4×D3—42no—
433C4×D3—202no—
434Dic6—21no—
435Dic6—21no—
436Dic6—101no—
437Dic6—101no—
438C3×C8—52no—
439C3×C8—52no—
440C3⋊C8C2×C22⋊D514yes—
441C22×C5—22no—
442C22×C5—44no—
443C22×C5—42no—
444C22×C5—84no—
445C22×C5—122no—
446C22×C5—121no—
447C22×C5#94012yes—
448C22×C5C2×D3×D411yescharacteristic
449C2×D5—122no—
450C2×D5—121no—
451C4×C5—121no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—42no—
456Dic5—64no—
457Dic5—121no—
458C24—21no—
459#41—62no—
460#41—62no—
461#41—302no—
462#41—302no—
463C2×Q8—31no—
464C2×Q8—52no—
465C2×Q8—101no—
466C2×Q8—102no—
467C2×Q8—102no—
468C2×Q8—151no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—31no—
473C2×D4—61no—
474C2×D4—151no—
475C2×D4—304no—
476C2×D4—301no—
477C2×D4C2×D3×D512yes—
478C22×C4—61no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—304no—
483Q16—302no—
484SD16—64no—
485SD16—104no—
486SD16—104no—
487SD16—304no—
488SD16—302no—
489SD16—302no—
490D8—64no—
491D8—302no—
492M16—34no—
493C2×C8—32no—
494C2×C8—54no—
495C2×C8—51no—
496C2×C8—51no—
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—44no—
506C22×C3—42no—
507C22×C3—84no—
508C22×C3#408612yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—42no—
511C2×D3—41no—
512C2×D3—202no—
513C2×D3—201no—
514C3×C4—202no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—41no—
519Dic3—104no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—82no—
523C2×C5—241no—
524C2×C5#576212yes—
525C2×C5C2×#94011yescharacteristic
526D5—241no—
527C23—22no—
528C23—42no—
529C23—61no—
530C23—82no—
531C23—301no—
532C23#679011yescharacteristic
533Q8—61no—
534Q8—61no—
535Q8—102no—
536Q8—102no—
537Q8—202no—
538Q8—301no—
539Q8—301no—
540D4—22no—
541D4—22no—
542D4—42no—
543D4—61no—
544D4—61no—
545D4—122no—
546D4—301no—
547D4—301no—
548D4—602no—
549D4—1204no—
550C2×C4—61no—
551C2×C4—102no—
552C2×C4—122no—
553C2×C4—154no—
554C2×C4—202no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D512yes—
559C2×C4#679011yescharacteristic
560C2×C4C22×D3×D511yescharacteristic
561C8—34no—
562C8—52no—
563C8—52no—
564C2×C3—22no—
565C2×C3—82no—
566C2×C3#6610912yes—
567C2×C3C2×#408611yescharacteristic
568D3—81no—
569D3—401no—
570C5#8385411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—44no—
574C22—84no—
575C22—121no—
576C22—122no—
577C22—601no—
578C22—602no—
579C22#9156712yes—
580C22C2×#679011yescharacteristic
581C4—121no—
582C4—202no—
583C4—304no—
584C4—601no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061567011yescharacteristic, complemented, Sylow
589C2—22no—
590C2—82no—
591C2—241no—
592C2—1201no—
593C2#1175472812yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #11756564C2semidirect
2. C2×C5×#932C2semidirect
3. C22×C3×#687C2semidirect
4. #11754255C2semidirect
5. C2×#91315C2semidirect
6. C2×#91303C2semidirect
7. #11749111C2semidirect
8. #11749109C2semidirect
9. #11749077C2semidirect
10. #11749075C2semidirect
11. #11748324C2semidirect
31. #91385C22semidirect
32. #91370C22semidirect
34. C2×#6663C22semidirect
35. C2×#6662C22semidirect
36. C2×#6660C22semidirect
37. C2×#6659C22semidirect
39. C2×#6658C22semidirect
41. C2×#6654C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
49. C22×#687D3semidirect
86. C5×#208D4semidirect
90. C2×C3×#168D4semidirect
105. C2×#932D5semidirect
252. C2×#168#67semidirect
324. #208C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83854semidirect
588. C3#10615670semidirect

Maximal subgroups

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

subgroupindex
#117565642
C2×C5×#9322
C22×C3×#6872
#117542552
C2×#913152
C2×#913032
#117491112
#117491092
#117490772
#117490752
#117483242
#106156703
#838545