Finite Group Databasebeta

← #14439349

Subgroups — #14439349

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756591C211yesmaximal, characteristic, complemented
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C2×C3×#4095C211yesmaximal, characteristic, complemented
4C2×#91368C211yesmaximal, characteristic, complemented
5C2×#91321C211yesmaximal, characteristic, complemented
6C2×#91312C211yesmaximal, characteristic, complemented
7#11749320C212yesmaximal, complemented
8#11749318C212yesmaximal, complemented
9#11749073C212yesmaximal, complemented
10#11749072C212yesmaximal, complemented
11#11748328C211yesmaximal, characteristic, complemented
12#10615704—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91836C2211yescharacteristic, complemented
18#91833C2211yescharacteristic, complemented
19#91829C2211yescharacteristic, complemented
20#91828—22no—
21#91825C2211yescharacteristic, complemented
22C4×#1220—22no—
23C2×C4×Dic15C2211yescharacteristic
24C5×#951—24no—
25C2×C5×#216C2212yescomplemented
26C2×C5×#214C2212yescomplemented
27C2×C5×#208C2211yescharacteristic
28C3×#4095—24no—
29C2×C3×#688C2212yes—
30C2×C3×#686C2212yes—
31C2×C3×#681C2211yescharacteristic
32C2×#6665—22no—
33#91368—22no—
34#91368C2212yes—
35#91368C2212yes—
36#91321—24no—
37C2×#6663C2212yescomplemented
38C2×#6660C2212yescomplemented
39#91312—24no—
40C2×#6657C2212yes—
41C2×#6653C2212yes—
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83938—51nomaximal, Hall
45C2×C5×#137—31no—
46#66166—31no—
47C2×#4095D311yescharacteristic, complemented
48C2×#4093—31no—
49C2×#4088—31no—
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65457—32no—
55M16×Dic5—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
64C2×#1220—21no—
65C2×#1220—22no—
66C22×Dic15D412yes—
67#6817—22no—
68#6817—22no—
69C2×D60C2311yescharacteristic
70C2×C4×D15—21no—
71C2×Dic30C2311yescharacteristic
72C22×C5×Dic3—21no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6—22no—
75C2×C5×Dic6—21no—
76C2×C5×Dic6C2312yes—
77C2×C3×D20—22no—
78C2×C3×D20—22no—
79C2×C3×D20—21no—
80C2×C3×D20C2312yes—
81#6719—22no—
82#6714—22no—
83#6712—22no—
84C4×Dic15D412yes—
85C4×Dic15C2311yescharacteristic
86C4×Dic15C2311yescharacteristic
87C5×#216—24no—
88C5×#214—24no—
89C5×#208D414yescomplemented
90C2×C5×C3⋊C8C2312yes—
91C3×#688—24no—
92C3×#686—24no—
93C3×#681D414yescomplemented
94C2×C3×#168C2312yes—
95#6665—24no—
96#6665—24no—
97#6663—24no—
98#6660—24no—
99#6657—24no—
100#6653—24no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5832—51no—
103C2×#951D511yescharacteristic, complemented
104C2×#936—51no—
105C2×#932—51no—
106C2×#909—51no—
107#5168—52no—
108#5167—52no—
109#5155—52no—
110#5154—52no—
111Dic3×M16—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×D20C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4095—24no—
121#4093—31no—
122#4093—32no—
123#4093—32no—
124#4093—62no—
125#4090—31no—
126C2×#689—32no—
127#4088—64no—
128C2×#688—32no—
129C2×#688C2×D312yes—
130#4086—31no—
131#4085—62no—
132#4082—31no—
133C2×#686C2×D312yes—
134C4×C22⋊D5—62no—
135C2×#685—62no—
136C2×C4×Dic5—31no—
137C2×#681C2×D311yescharacteristic
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3153—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C3×D5—22no—
148C22×C3×D5—44no—
149C22×C3×D5—42no—
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
161#1220—44no—
162#1220—42no—
163C2×Dic15—21no—
164C2×Dic15—42no—
165C2×Dic15C2×D412yes—
166C2×Dic15C2×D412yes—
167D60—21no—
168D60—21no—
169C4×D15—42no—
170Dic30—21no—
171Dic30—21no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—42no—
174C5×Dic6—22no—
175C5×Dic6—22no—
176C5×Dic6—42no—
177C3×D20—22no—
178C3×D20—22no—
179C3×D20—42no—
180C3×#168C2×D414yes—
181C5×C3⋊C8C2×D414yes—
182C2×C3×#41C2×D511yescharacteristic
183C22×C3×D4—51no—
184C2×#235—51no—
185C22×Dic6C2×D511yescharacteristic
186C3×AGL(1,ℤ/8)—104no—
187C2×C3×SD16—52no—
188C2×C3×D8—52no—
189C2×C3×M16—51no—
190C2×#217—102no—
191#951—24no—
192#947—51no—
193#944—51no—
194C2×#216C2×D512yescomplemented
195#940—51no—
196#939—102no—
197#936—51no—
198#936—52no—
199#936—52no—
200#936—102no—
201C2×#214—52no—
202C2×#214C2×D512yescomplemented
203#932—104no—
204C2×#213—52no—
205C4×#67—102no—
206C2×C4×Dic3—51no—
207C2×#208C2×D511yescharacteristic
208#909—104no—
209C2×Dic12—52no—
210C2×#204—52no—
211#815—52no—
212C8×Dic3—52no—
213C23×D5—21no—
214C5×#41—22no—
215C5×#41—22no—
216C2×C5×Q8—32no—
217C2×C5×Q8—61no—
218C2×C5×Q8—62no—
219C2×C5×Q8—62no—
220C2×C5×Q8C22×D311yescharacteristic
221C2×C5×D4—21no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—62no—
227C2×C22⋊D5—61no—
228C22×Dic5—32no—
229#709—62no—
230#709—62no—
231C2×D20—22no—
232C2×D20—22no—
233C2×D20—21no—
234C2×D20—31no—
235C2×D20C22×D312yes—
236C2×C4×D5—61no—
237C2×Dic10—31no—
238C5×Q16—64no—
239C5×SD16—64no—
240C5×M16—34no—
241C2×C5×C8—32no—
242C22⋊Dic5—62no—
243#689—64no—
244#688—24no—
245#688—64no—
246#686—24no—
247#685—62no—
248#685—64no—
249#685—64no—
250#683—62no—
251C4×Dic5—32no—
252C4×Dic5—31no—
253C4×Dic5—31no—
254#681#6714yescomplemented
255C2×#168C22×D312yes—
256D40—64no—
257#677—64no—
258C2×#137—31no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—51no—
261C2×AGL(1,ℤ/8)—151no—
262#532—151no—
263C2×#124—151no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—151no—
269C22×C3×C5—22no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—41no—
275C2×D15—42no—
276C2×C3×D5—42no—
277C2×C3×D5—44no—
278C2×C3×D5—84no—
279C3×C4×C5—41no—
280C3×C4×C5#12712yes—
281C3×C4×C5C22×D411yescharacteristic
282C3×C4×C5C22×D411yescharacteristic
283Dic15—22no—
284Dic15—22no—
285Dic15—41no—
286C5×Dic3—42no—
287C24×C3—101no—
288C3×#41—22no—
289C3×#41—22no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4—52no—
293C2×C3×D4—102no—
294C2×C3×D4—101no—
295C2×C3×D4—102no—
296C2×C3×D4C22×D511yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—102no—
300C2×#67—101no—
301C22×Dic3—21no—
302C22×Dic3—52no—
303#235—102no—
304#235—102no—
305C2×D12—51no—
306C2×C4×D3—101no—
307C2×Dic6—22no—
308C2×Dic6—22no—
309C2×Dic6—21no—
310C2×Dic6—51no—
311C2×Dic6C22×D512yes—
312C3×SD16—104no—
313C3×D8—104no—
314C3×M16—54no—
315C2×C3×C8—52no—
316#217—104no—
317#217—104no—
318#217—102no—
319#216—24no—
320#214—24no—
321#214—104no—
322#213—104no—
323(C2×D3)⋊C4—102no—
324Dic3⋊C4—102no—
325C4×Dic3—52no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328#208C22⋊D514yescomplemented
329C2×C3⋊C8C22×D512yes—
330Dic12—104no—
331#204—104no—
332C23×C5—21no—
333C23×C5D3×D411yescharacteristic
334C22×D5—22no—
335C22×D5—44no—
336C22×D5—42no—
337C22×D5—61no—
338C5×Q8—21no—
339C5×Q8—21no—
340C5×Q8—62no—
341C5×Q8—62no—
342C5×Q8—122no—
343C5×D4—21no—
344C5×D4—21no—
345C5×D4—42no—
346C2×C4×C5—21no—
347C2×C4×C5—42no—
348C2×C4×C5—62no—
349C2×C4×C5—122no—
350C2×C4×C5D3×D412yes—
351C2×C4×C5D3×D411yescharacteristic
352C2×C4×C5C2×#6712yes—
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—124no—
355C22⋊D5—122no—
356C2×Dic5—32no—
357C2×Dic5—32no—
358C2×Dic5—61no—
359C2×Dic5—122no—
360D20—22no—
361D20—22no—
362D20—42no—
363D20—61no—
364D20—61no—
365C4×D5—122no—
366Dic10—61no—
367Dic10—61no—
368C5×C8—34no—
369#168C2×#6714yes—
370C2×#41—151no—
371C2×#41D3×D511yescharacteristic
372C22×Q8—31no—
373C22×D4—51no—
374#137—64no—
375#137—304no—
376AGL(1,ℤ/8)—104no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—32no—
379C2×Q16—152no—
380C2×SD16—32no—
381C2×SD16—52no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—52no—
385C2×D8—152no—
386C2×M16—31no—
387C2×M16—51no—
388C4⋊Q8—151no—
389#127—151no—
390#124—152no—
391#124—152no—
392#124—151no—
393#124—151no—
394#124—302no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—302no—
398C2×C42—151no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5—81no—
403C2×C3×C5C2×#12711yescharacteristic
404C2×C3×C5#57512yes—
405D15—81no—
406C3×D5—82no—
407C23×C3—21no—
408C23×C3—102no—
409C23×C3—204no—
410C23×C3—202no—
411C23×C3D4×D511yescharacteristic
412C22×D3—101no—
413C3×Q8—21no—
414C3×Q8—21no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—42no—
418C3×D4—102no—
419C3×D4—102no—
420C3×D4—202no—
421C2×C3×C4—21no—
422C2×C3×C4—42no—
423C2×C3×C4D4×D512yes—
424C2×C3×C4D4×D511yescharacteristic
425C2×C3×C4C2×C22⋊D512yes—
426C2×C3×C4C23×D511yescharacteristic
427#67—204no—
428#67—202no—
429C2×Dic3—22no—
430C2×Dic3—42no—
431C2×Dic3—52no—
432C2×Dic3—52no—
433C2×Dic3—101no—
434C2×Dic3—202no—
435D12—101no—
436D12—101no—
437C4×D3—202no—
438Dic6—22no—
439Dic6—22no—
440Dic6—42no—
441Dic6—101no—
442Dic6—101no—
443C3×C8—54no—
444C3⋊C8C2×C22⋊D514yes—
445C22×C5—22no—
446C22×C5—42no—
447C22×C5—41no—
448C22×C5#94012yes—
449C22×C5C2×D3×D411yescharacteristic
450C2×D5—44no—
451C2×D5—42no—
452C2×D5—84no—
453C2×D5—122no—
454C2×D5—121no—
455C4×C5—41no—
456C4×C5—122no—
457C4×C5#94012yes—
458C4×C5C2×D3×D411yescharacteristic
459C4×C5C22×#6711yescharacteristic
460Dic5—62no—
461Dic5—62no—
462Dic5—121no—
463C24—101no—
464#41—22no—
465#41—22no—
466#41—302no—
467#41—302no—
468C2×Q8—32no—
469C2×Q8—61no—
470C2×Q8—62no—
471C2×Q8—62no—
472C2×Q8—151no—
473C2×Q8C2×D3×D511yescharacteristic
474C2×D4—21no—
475C2×D4—52no—
476C2×D4—102no—
477C2×D4—102no—
478C2×D4—101no—
479C2×D4—151no—
480C2×D4—302no—
481C2×D4—301no—
482C2×D4C2×D3×D511yescharacteristic
483C22×C4—21no—
484C22×C4—61no—
485C22×C4—152no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—64no—
489Q16—304no—
490SD16—64no—
491SD16—104no—
492SD16—304no—
493SD16—304no—
494D8—104no—
495D8—304no—
496M16—34no—
497M16—54no—
498C2×C8—32no—
499C2×C8—52no—
500C4⋊C4—302no—
501C22⋊C4—302no—
502C22⋊C4—304no—
503C22⋊C4—304no—
504C22⋊C4—302no—
505C42—152no—
506C42—151no—
507C42—151no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—42no—
511C22×C3—41no—
512C22×C3—204no—
513C22×C3—202no—
514C22×C3—404no—
515C22×C3#408612yes—
516C22×C3C2×D4×D511yescharacteristic
517C2×D3—202no—
518C2×D3—201no—
519C3×C4—41no—
520C3×C4#408612yes—
521C3×C4C2×D4×D511yescharacteristic
522C3×C4C22×C22⋊D511yescharacteristic
523Dic3—42no—
524Dic3—102no—
525Dic3—102no—
526Dic3—201no—
527C2×C5—22no—
528C2×C5—81no—
529C2×C5#577312yes—
530C2×C5C2×#94011yescharacteristic
531D5—82no—
532D5—241no—
533C23—21no—
534C23—102no—
535C23—204no—
536C23—202no—
537C23—301no—
538C23#679011yescharacteristic
539Q8—21no—
540Q8—21no—
541Q8—62no—
542Q8—62no—
543Q8—122no—
544Q8—301no—
545Q8—301no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—102no—
550D4—102no—
551D4—202no—
552D4—301no—
553D4—301no—
554D4—604no—
555D4—602no—
556C2×C4—21no—
557C2×C4—42no—
558C2×C4—62no—
559C2×C4—122no—
560C2×C4—152no—
561C2×C4—152no—
562C2×C4—301no—
563C2×C4—602no—
564C2×C4—602no—
565C2×C4D5×#6712yes—
566C2×C4D3×C22⋊D512yes—
567C2×C4#679011yescharacteristic
568C2×C4C22×D3×D511yescharacteristic
569C8—34no—
570C8—54no—
571C2×C3—22no—
572C2×C3—81no—
573C2×C3—402no—
574C2×C3#6611112yes—
575C2×C3C2×#408611yescharacteristic
576D3—401no—
577C5#8393811yescharacteristic, complemented, Sylow
578C22—22no—
579C22—42no—
580C22—41no—
581C22—204no—
582C22—202no—
583C22—404no—
584C22—602no—
585C22—601no—
586C22#9156712yes—
587C22C2×#679011yescharacteristic
588C4—41no—
589C4—122no—
590C4—302no—
591C4—302no—
592C4—601no—
593C4#9156712yes—
594C4C2×D5×#6711yescharacteristic
595C4C2×D3×C22⋊D511yescharacteristic
596C3#1061570411yescharacteristic, complemented, Sylow
597C2—22no—
598C2—81no—
599C2—402no—
600C2—1201no—
601C2#1175534912yes—
602C2C2×#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#3153
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. #11756591C2semidirect
2. C2×C5×#951C2semidirect
3. C2×C3×#4095C2semidirect
4. C2×#91368C2semidirect
5. C2×#91321C2semidirect
6. C2×#91312C2semidirect
7. #11749320C2semidirect
8. #11749318C2semidirect
9. #11749073C2semidirect
10. #11749072C2semidirect
11. #11748328C2semidirect
17. #91836C22semidirect
18. #91833C22semidirect
19. #91829C22semidirect
21. #91825C22semidirect
25. C2×C5×#216C22semidirect
26. C2×C5×#214C22semidirect
37. C2×#6663C22semidirect
38. C2×#6660C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
47. C2×#4095D3semidirect
89. C5×#208D4semidirect
93. C3×#681D4semidirect
103. C2×#951D5semidirect
194. C2×#216C2×D5semidirect
202. C2×#214C2×D5semidirect
254. #681#67semidirect
328. #208C22⋊D5semidirect
508. C3×C5#3153semidirect
577. C5#83938semidirect
596. C3#10615704semidirect

Maximal subgroups

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

subgroupindex
#117565912
C2×C5×#9512
C2×C3×#40952
C2×#913682
C2×#913212
C2×#913122
#117493202
#117493182
#117490732
#117490722
#117483282
#106157043
#839385