Finite Group Databasebeta

← #14439332

Subgroups — #14439332

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
1C2×#91821C211yesmaximal, characteristic, complemented
2C2×C5×#936C211yesmaximal, characteristic, complemented
3C2×C3×#4078C211yesmaximal, characteristic, complemented
4#11754581C211yesmaximal, characteristic, complemented
5C2×#91321C211yesmaximal, characteristic, complemented
6C2×#91307C211yesmaximal, characteristic, complemented
7#11749110C212yesmaximal, complemented
8#11749098C212yesmaximal, complemented
9#11749078C212yesmaximal, complemented
10#11749074C212yesmaximal, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10614674—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6716C2212yes—
18#91821—24no—
19C2×#6715C2212yes—
20C2×#6710C2211yescharacteristic
21C2×C5×#217—22no—
22C5×#936—22no—
23C5×#936C2212yes—
24C5×#936C2212yes—
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×#687C2212yes—
27C3×#4078—24no—
28C2×C3×#686C2212yes—
29C2×C3×#681C2211yescharacteristic
30#91569—22no—
31#91458C2211yescharacteristic, complemented
32C4×#1202—22no—
33#91389C2211yescharacteristic, complemented
34#91374C2211yescharacteristic, complemented
35#91364C2211yescharacteristic, complemented
36#91321—24no—
37C2×#6663C2212yescomplemented
38C2×#6661C2212yescomplemented
39C2×#6660C2212yescomplemented
40#91307—24no—
41C2×#6655C2212yescomplemented
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83938—51nomaximal, Hall
45C2×C5×#124—31no—
46C2×#4088—31no—
47C2×#4088—31no—
48C2×#4078—31no—
49C2×#4078D311yescharacteristic, complemented
50#65811—31no—
51#65349—32no—
52#65348—32no—
53#65348—32no—
54#65347—32no—
55C4×#681—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—
63#6817—22no—
64#6817—22no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C22×C5×Dic3—21no—
69C22×C5×Dic3D412yes—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6C2312yes—
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—22no—
81#6716—24no—
82#6715—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#217—24no—
86C5×#217—24no—
87C4×C5×Dic3D412yes—
88C4×C5×Dic3C2311yescharacteristic
89C4×C5×Dic3C2311yescharacteristic
90C3×#687—24no—
91C3×#686—24no—
92C3×#681D414yescomplemented
93C2×C3×#168C2312yes—
94Dic3⋊Dic5—22no—
95#6667—22no—
96#6665—22no—
97#6663—24no—
98#6661—24no—
99#6660—24no—
100#6655—24no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5832—51no—
103C2×#951—51no—
104C2×#936D511yescharacteristic, complemented
105C2×#932—51no—
106C2×#909—51no—
107#5168—52no—
108#5167—52no—
109#5155—52no—
110#5154—52no—
111Dic3×M16—51no—
112C22×C5×Q8—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C2×#709C2×D311yescharacteristic
116C5×#124—32no—
117C5×#124—32no—
118C5×#124—62no—
119C2×C5×C22⋊C4—62no—
120C2×C42×C5—31no—
121C2×#689—32no—
122C2×#689—32no—
123#4088—64no—
124#4088—64no—
125C2×#688—32no—
126C2×#688—32no—
127C2×#687—32no—
128C2×#687C2×D312yes—
129#4078—24no—
130#4078—64no—
131C2×#686—32no—
132C2×#686C2×D312yes—
133#4076—62no—
134C2×#681—31no—
135C2×#681C2×D311yescharacteristic
136#4021—31no—
137#4021—31no—
138#4020—31no—
139C4×D20—62no—
140#4015—31no—
141#3935—32no—
142C4×#168—32no—
143#3153—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—44no—
146C23×C3×C5—42no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—21no—
149C22×C3×D5—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—
158C2×Dic15—21no—
159D60—21no—
160D60—21no—
161C4×D15—42no—
162Dic30—21no—
163Dic30—21no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—42no—
166C2×C5×Dic3—42no—
167C2×C5×Dic3C2×D412yes—
168C2×C5×Dic3C2×D412yes—
169C5×Dic6—22no—
170C5×Dic6—22no—
171C5×Dic6—42no—
172C3×C22⋊D5—42no—
173C2×C3×Dic5—21no—
174C3×D20—21no—
175C3×D20—21no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10—21no—
179#1202—44no—
180C3⋊#168C2×D414yes—
181C3×#168C2×D414yes—
182C2×C3×#41—51no—
183C22×C3×D4C2×D511yescharacteristic
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—22no—
191#951—104no—
192#947—51no—
193#944—51no—
194C2×#216—52no—
195#940—51no—
196#939—102no—
197#936—22no—
198#936—51no—
199#936C2×D512yes—
200#936C2×D512yes—
201C2×#214—52no—
202C2×#214—52no—
203#932—104no—
204C2×#213—52no—
205C4×#67—102no—
206C2×C4×Dic3C2×D511yescharacteristic
207C2×#208—51no—
208#909—104no—
209C2×Dic12—52no—
210C2×#204—52no—
211#815—52no—
212C8×Dic3—52no—
213C24×C5—21no—
214C2×C5×Q8—32no—
215C2×C5×Q8—61no—
216C2×C5×Q8—62no—
217C2×C5×Q8—62no—
218C2×C5×D4—22no—
219C2×C5×D4—21no—
220C2×C5×D4—22no—
221C2×C5×D4C22×D312yes—
222C22×C4×C5—32no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C2×C22⋊D5—61no—
227#709—22no—
228#709—22no—
229#709—62no—
230#709—62no—
231C2×D20—31no—
232C2×D20—62no—
233C2×D20C22×D311yescharacteristic
234C2×C4×D5—21no—
235C2×C4×D5—61no—
236C2×Dic10—31no—
237C2×Dic10C22×D311yescharacteristic
238C5×C22⋊C4—64no—
239C5×C22⋊C4—64no—
240C42×C5—32no—
241C42×C5—31no—
242C42×C5—31no—
243#689—64no—
244#689—64no—
245#688—64no—
246#688—64no—
247#687—24no—
248#687—64no—
249#686—24no—
250#686—64no—
251#685—62no—
252#685—62no—
253C4⋊Dic5—62no—
254#681—34no—
255#681#6714yescomplemented
256C2×#168—32no—
257C2×#168C22×D312yes—
258C2×#137—151no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—51no—
261C2×AGL(1,ℤ/8)—151no—
262#532—151no—
263C2×#124—31no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—151no—
269C22×C3×C5—22no—
270C22×C3×C5—42no—
271C22×C3×C5—44no—
272C22×C3×C5—84no—
273C22×C3×C5#12712yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×D15—41no—
276C2×D15—42no—
277C2×C3×D5—41no—
278C2×C3×D5—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—41no—
284C5×Dic3—22no—
285C5×Dic3—22no—
286C5×Dic3—42no—
287C24×C3—21no—
288C3×#41—102no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4—21no—
294C2×C3×D4—51no—
295C2×C3×D4—101no—
296C2×C3×D4C22×D512yes—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—101no—
300C2×#67—102no—
301C22×Dic3—21no—
302C22×Dic3C22⋊D512yes—
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—24no—
317#217—24no—
318#217—102no—
319#216—104no—
320#214—104no—
321#214—104no—
322#213—104no—
323(C2×D3)⋊C4—102no—
324Dic3⋊C4—102no—
325C4×Dic3C22⋊D512yes—
326C4×Dic3C22×D511yescharacteristic
327C4×Dic3C22×D511yescharacteristic
328#208—54no—
329C2×C3⋊C8—52no—
330Dic12—104no—
331#204—104no—
332C23×C5—22no—
333C23×C5—44no—
334C23×C5—42no—
335C23×C5D3×D411yescharacteristic
336C22×D5—21no—
337C22×D5—61no—
338C5×Q8—62no—
339C5×Q8—62no—
340C5×Q8—122no—
341C5×D4—22no—
342C5×D4—22no—
343C5×D4—42no—
344C2×C4×C5—32no—
345C2×C4×C5—32no—
346C2×C4×C5—62no—
347C2×C4×C5—122no—
348C2×C4×C5—122no—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5D3×D412yes—
351C2×C4×C5C2×#6712yes—
352C2×C4×C5C23×D311yescharacteristic
353C22⋊D5—42no—
354C22⋊D5—122no—
355C2×Dic5—21no—
356C2×Dic5—61no—
357D20—21no—
358D20—21no—
359D20—61no—
360D20—61no—
361D20—124no—
362C4×D5—42no—
363C4×D5—122no—
364Dic10—21no—
365Dic10—21no—
366Dic10—61no—
367Dic10—61no—
368#168—34no—
369#168C2×#6714yes—
370C2×#41—51no—
371C2×#41—151no—
372C22×Q8—31no—
373C22×D4D3×D511yescharacteristic
374#137—304no—
375#137—304no—
376AGL(1,ℤ/8)—104no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—152no—
379C2×Q16—152no—
380C2×SD16—52no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—52no—
385C2×D8—152no—
386C2×M16—51no—
387C2×M16—151no—
388C4⋊Q8—151no—
389#127—151no—
390#124—32no—
391#124—32no—
392#124—62no—
393#124—151no—
394#124—151no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—62no—
398C2×C42—31no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5—82no—
403C2×C3×C5C2×#12711yescharacteristic
404C2×C3×C5#57512yes—
405D15—81no—
406C3×D5—81no—
407C23×C3—22no—
408C23×C3—44no—
409C23×C3—42no—
410C23×C3—101no—
411C23×C3C2×C22⋊D511yescharacteristic
412C22×D3—101no—
413C3×Q8—101no—
414C3×Q8—101no—
415C3×D4—22no—
416C3×D4—22no—
417C3×D4—42no—
418C3×D4—101no—
419C3×D4—101no—
420C3×D4—202no—
421C2×C3×C4—101no—
422C2×C3×C4—202no—
423C2×C3×C4D4×D512yes—
424C2×C3×C4D4×D512yes—
425C2×C3×C4C2×C22⋊D511yescharacteristic
426C2×C3×C4C23×D511yescharacteristic
427#67—204no—
428#67—202no—
429C2×Dic3—22no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—101no—
433C2×Dic3C2×C22⋊D512yes—
434C2×Dic3C2×C22⋊D512yes—
435D12—101no—
436D12—101no—
437C4×D3—202no—
438Dic6—22no—
439Dic6—22no—
440Dic6—42no—
441Dic6—101no—
442Dic6—101no—
443C3×C8—54no—
444C3⋊C8—54no—
445C22×C5—22no—
446C22×C5—44no—
447C22×C5—42no—
448C22×C5—84no—
449C22×C5#94012yes—
450C22×C5C2×D3×D411yescharacteristic
451C2×D5—42no—
452C2×D5—41no—
453C2×D5—122no—
454C2×D5—121no—
455C4×C5—62no—
456C4×C5—62no—
457C4×C5—122no—
458C4×C5#94012yes—
459C4×C5C2×D3×D411yescharacteristic
460C4×C5C22×#6711yescharacteristic
461Dic5—41no—
462Dic5—121no—
463C24—21no—
464#41—102no—
465#41—102no—
466#41—302no—
467#41—302no—
468C2×Q8—32no—
469C2×Q8—51no—
470C2×Q8—61no—
471C2×Q8—62no—
472C2×Q8—62no—
473C2×Q8—151no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—51no—
478C2×D4—101no—
479C2×D4—151no—
480C2×D4—302no—
481C2×D4—301no—
482C2×D4C2×D3×D512yes—
483C22×C4—32no—
484C22×C4—61no—
485C22×C4—101no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—304no—
489Q16—304no—
490SD16—104no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—104no—
495D8—304no—
496M16—54no—
497M16—154no—
498C2×C8—52no—
499C2×C8—152no—
500C4⋊C4—302no—
501C22⋊C4—64no—
502C22⋊C4—64no—
503C22⋊C4—302no—
504C22⋊C4—302no—
505C42—32no—
506C42—31no—
507C42—31no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—42no—
511C22×C3—44no—
512C22×C3—84no—
513C22×C3—201no—
514C22×C3—202no—
515C22×C3#408612yes—
516C22×C3C22×C22⋊D511yescharacteristic
517C2×D3—201no—
518C2×D3—202no—
519C3×C4—201no—
520C3×C4#408612yes—
521C3×C4C2×D4×D511yescharacteristic
522C3×C4C2×D4×D511yescharacteristic
523Dic3—22no—
524Dic3—22no—
525Dic3—42no—
526Dic3—201no—
527C2×C5—22no—
528C2×C5—82no—
529C2×C5#577312yes—
530C2×C5C2×#94011yescharacteristic
531D5—81no—
532D5—241no—
533C23—22no—
534C23—44no—
535C23—42no—
536C23—101no—
537C23—301no—
538C23D3×C22⋊D511yescharacteristic
539Q8—62no—
540Q8—62no—
541Q8—101no—
542Q8—101no—
543Q8—122no—
544Q8—301no—
545Q8—301no—
546D4—22no—
547D4—22no—
548D4—42no—
549D4—101no—
550D4—101no—
551D4—202no—
552D4—301no—
553D4—301no—
554D4—604no—
555D4—602no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—62no—
559C2×C4—101no—
560C2×C4—122no—
561C2×C4—122no—
562C2×C4—202no—
563C2×C4—301no—
564C2×C4—602no—
565C2×C4D5×#6712yes—
566C2×C4D3×C22⋊D511yescharacteristic
567C2×C4#679012yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—54no—
570C8—154no—
571C2×C3—22no—
572C2×C3—82no—
573C2×C3—401no—
574C2×C3C2×#408611yescharacteristic
575C2×C3#6615612yes—
576D3—401no—
577C5#8393811yescharacteristic, complemented, Sylow
578C22—22no—
579C22—42no—
580C22—44no—
581C22—84no—
582C22—201no—
583C22—202no—
584C22—601no—
585C22—602no—
586C22#9156712yes—
587C22C2×D3×C22⋊D511yescharacteristic
588C4—62no—
589C4—62no—
590C4—122no—
591C4—201no—
592C4—601no—
593C4#9156712yes—
594C4C2×D5×#6711yescharacteristic
595C4C2×#679011yescharacteristic
596C3#1061467411yescharacteristic, complemented, Sylow
597C2—22no—
598C2—82no—
599C2—401no—
600C2—1201no—
601C2#1175469612yes—
602C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3153
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. C2×#91821C2semidirect
2. C2×C5×#936C2semidirect
3. C2×C3×#4078C2semidirect
4. #11754581C2semidirect
5. C2×#91321C2semidirect
6. C2×#91307C2semidirect
7. #11749110C2semidirect
8. #11749098C2semidirect
9. #11749078C2semidirect
10. #11749074C2semidirect
11. Dic3×#681C2semidirect
31. #91458C22semidirect
33. #91389C22semidirect
34. #91374C22semidirect
35. #91364C22semidirect
37. C2×#6663C22semidirect
38. C2×#6661C22semidirect
39. C2×#6660C22semidirect
41. C2×#6655C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
49. C2×#4078D3semidirect
83. #6710D4semidirect
92. C3×#681D4semidirect
104. C2×#936D5semidirect
255. #681#67semidirect
508. C3×C5#3153semidirect
577. C5#83938semidirect
596. C3#10614674semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C2×C5×#9362
C2×C3×#40782
#117545812
C2×#913212
C2×#913072
#117491102
#117490982
#117490782
#117490742
Dic3×#6812
#106146743
#839385