Finite Group Databasebeta

← #14439456

Subgroups — #14439456

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
1C22×#6716C211yesmaximal, characteristic, complemented
2C5×#5805C211yesmaximal, characteristic, complemented
3C2×C3×#4078C211yesmaximal, characteristic, complemented
4#11754252C211yesmaximal, characteristic, complemented
5C2×#91322C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11749110C212yesmaximal, complemented
8#11749108C212yesmaximal, complemented
9#11749074C212yesmaximal, complemented
10#11749071C212yesmaximal, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10615112—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6716—24no—
18C2×#6716C2212yes—
19C2×#6716C2212yes—
20C22×C3⋊#168C2211yescharacteristic
21C5×#953—22no—
22C5×#940C2212yes—
23C5×#938—22no—
24C5×#936C2212yes—
25C5×#926C2211yescharacteristic
26C2×C3×#687C2212yes—
27C3×#4078—24no—
28C2×C3×#686C2212yes—
29C2×C3×#681C2211yescharacteristic
30#91537—22no—
31#91389C2212yescomplemented
32#91364C2212yescomplemented
33#91360—22no—
34#91322—24no—
35C2×#6663C2212yescomplemented
36C2×#6661C2211yescharacteristic, complemented
37C2×#6659C2212yescomplemented
38C2×#6656C2211yescharacteristic, complemented
39C2×#6655C2211yescharacteristic, complemented
40#91297—24no—
41C2×#6652C2211yescharacteristic, complemented
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83939—51nomaximal, Hall
45C5×#535—31no—
46C2×#4097—31no—
47C2×#4096—31no—
48C22×#687—31no—
49C2×#4078D311yescharacteristic, complemented
50#65860—31no—
51#65365—32no—
52#65363—32no—
53#65349—32no—
54#65348—32no—
55#65286—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
62C22×Dic15—21no—
63C2×Dic30—22no—
64C2×Dic30—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C2×C5×#67—21no—
68C2×C5×#67—24no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80#6716—24no—
81#6716—24no—
82C2×C3⋊#168D414yescomplemented
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2311yescharacteristic
85C5×#217—24no—
86C5×#217D412yes—
87C5×C4⋊Dic3D412yes—
88C4×C5×Dic3C2312yes—
89C3×#687—24no—
90C3×#686—24no—
91C3×#681D414yescomplemented
92C2×C3×#168C2312yes—
93Dic3⋊Dic5—24no—
94#6665—24no—
95#6663—24no—
96#6661—22no—
97#6659—24no—
98#6656—22no—
99#6655—22no—
100#6652—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5825—51no—
103C2×#950—51no—
104#5805D511yescharacteristic, complemented
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—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709C2×D311yescharacteristic
115C22×Dic10—31no—
116C5×#127—32no—
117C5×#124—32no—
118C5×#121—62no—
119C5×#120—62no—
120C5×#117—31no—
121#4097—64no—
122#4096—64no—
123C2×#689—31no—
124C2×#689—32no—
125C2×#688—31no—
126C2×#687—32no—
127C2×#687—32no—
128C2×#687—31no—
129C2×#687—32no—
130C2×#687—64no—
131C2×#687C2×D312yes—
132#4078—24no—
133C2×#686—31no—
134C2×#686C2×D312yes—
135C2×#681C2×D311yescharacteristic
136C22×#168—31no—
137#4043—62no—
138#4032—62no—
139#4021—32no—
140#4015—32no—
141#3935—32no—
142C4×#168—32no—
143#3154—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×C5×D3—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
157C2×Dic15—22no—
158C2×Dic15—42no—
159Dic30—22no—
160Dic30—22no—
161Dic30—42no—
162C5×#67—42no—
163C5×#67—84no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3C2×D414yes—
166C5×D12—21no—
167C5×D12—21no—
168C4×C5×D3—42no—
169C5×Dic6—21no—
170C5×Dic6—21no—
171C3×C22⋊D5—42no—
172C2×C3×Dic5—21no—
173C3×D20—21no—
174C3×D20—21no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C3×#168C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×D4C2×D511yescharacteristic
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—22no—
190#950—104no—
191#944—52no—
192C2×#216—51no—
193C2×#215—51no—
194#940C2×D512yes—
195#938—22no—
196#936—52no—
197#936C2×D512yes—
198#935—102no—
199C2×#214—52no—
200C2×#214—52no—
201C2×#214—51no—
202C2×#214—104no—
203C2×#213—51no—
204#926C2×D511yescharacteristic
205#924—102no—
206C22×C3⋊C8—51no—
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
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—64no—
221C2×C5×D4—61no—
222C2×C5×D4C22×D312yes—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C22×Dic5—61no—
227#709—22no—
228#709—22no—
229C2×D20C22×D311yescharacteristic
230C2×C4×D5—21no—
231C2×Dic10—32no—
232C2×Dic10—62no—
233C2×Dic10—62no—
234C2×Dic10—61no—
235C2×Dic10C22×D311yescharacteristic
236C5×C4⋊C4—32no—
237C5×C22⋊C4—32no—
238C5×C22⋊C4—64no—
239C42×C5—32no—
240#689—62no—
241#689—64no—
242#688—62no—
243#687—24no—
244#687—62no—
245#687—64no—
246#687—64no—
247#687—64no—
248#686—24no—
249#686—62no—
250#685—64no—
251C4⋊Dic5—64no—
252#681#6714yescomplemented
253C2×#168—34no—
254C2×#168—31no—
255C2×#168—31no—
256C2×#168C22×D312yes—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—51no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—31no—
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×C5×D3—41no—
275C2×C5×D3—42no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—42no—
282C3×Dic5—41no—
283C5×Dic3—24no—
284C5×Dic3—41no—
285C24×C3—21no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—51no—
289C2×C3×D4—22no—
290C2×C3×D4—22no—
291C2×C3×D4—21no—
292C2×C3×D4—51no—
293C2×C3×D4—101no—
294C2×C3×D4C22×D512yes—
295C22×C3×C4—101no—
296C22×C3×C4C22×D511yescharacteristic
297C2×#67—21no—
298C2×#67—24no—
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—24no—
314#217—104no—
315#217C22⋊D512yes—
316#216—102no—
317#215—102no—
318#214—102no—
319#214—104no—
320#214—104no—
321#213—102no—
322C4⋊Dic3C22⋊D512yes—
323Dic3⋊C4—104no—
324C4×Dic3C22×D512yes—
325C2×C3⋊C8—54no—
326C2×C3⋊C8—51no—
327C2×C3⋊C8—51no—
328Dic12—104no—
329#204—104no—
330C23×C5—22no—
331C23×C5—42no—
332C23×C5—61no—
333C23×C5—82no—
334C23×C5D3×D411yescharacteristic
335C22×D5—21no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×D4—22no—
339C5×D4—22no—
340C5×D4—42no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C5×D4—244no—
345C2×C4×C5—34no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D411yescharacteristic
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—42no—
353C2×Dic5—21no—
354C2×Dic5—62no—
355C2×Dic5—122no—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359Dic10—21no—
360Dic10—21no—
361Dic10—62no—
362Dic10—62no—
363Dic10—122no—
364#168—32no—
365#168—32no—
366#168C2×#6714yes—
367C2×#41—31no—
368C2×#41—51no—
369C22×Q8—151no—
370C22×D4D3×D511yescharacteristic
371#137—304no—
372AGL(1,ℤ/8)—104no—
373#135—304no—
374C2×Q16—152no—
375C2×Q16—151no—
376C2×SD16—52no—
377C2×SD16—152no—
378C2×SD16—151no—
379C2×SD16—151no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—52no—
384C2×D8—151no—
385C2×M16—51no—
386C22×C8—151no—
387C4⋊Q8—152no—
388#127—32no—
389#124—32no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—62no—
394#120—62no—
395#117—31no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—82no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402C3×D5—81no—
403C5×D3—81no—
404C23×C3—22no—
405C23×C3—42no—
406C23×C3—82no—
407C23×C3—101no—
408C23×C3C2×C22⋊D511yescharacteristic
409C22×D3—21no—
410C3×Q8—101no—
411C3×Q8—101no—
412C3×D4—22no—
413C3×D4—22no—
414C3×D4—42no—
415C3×D4—101no—
416C3×D4—101no—
417C3×D4—202no—
418C2×C3×C4—101no—
419C2×C3×C4—202no—
420C2×C3×C4D4×D512yes—
421C2×C3×C4D4×D512yes—
422C2×C3×C4C2×C22⋊D511yescharacteristic
423C2×C3×C4C23×D511yescharacteristic
424#67—42no—
425#67—84no—
426C2×Dic3—21no—
427C2×Dic3—102no—
428C2×Dic3—202no—
429C2×Dic3C2×C22⋊D514yes—
430D12—21no—
431D12—21no—
432C4×D3—42no—
433Dic6—21no—
434Dic6—21no—
435Dic6—102no—
436Dic6—102no—
437Dic6—202no—
438C3×C8—54no—
439C3⋊C8—52no—
440C3⋊C8—52no—
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—42no—
450C2×D5—41no—
451C4×C5—64no—
452C4×C5—121no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—41no—
457Dic5—122no—
458C24—21no—
459#41—62no—
460#41—62no—
461#41—102no—
462#41—102no—
463C2×Q8—31no—
464C2×Q8—51no—
465C2×Q8—152no—
466C2×Q8—301no—
467C2×Q8—302no—
468C2×Q8—302no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—31no—
473C2×D4—51no—
474C2×D4—64no—
475C2×D4—61no—
476C2×D4—101no—
477C2×D4C2×D3×D512yes—
478C22×C4—61no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—304no—
483Q16—302no—
484SD16—104no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488SD16—302no—
489SD16—302no—
490D8—104no—
491D8—302no—
492M16—54no—
493C2×C8—52no—
494C2×C8—154no—
495C2×C8—151no—
496C2×C8—151no—
497C4⋊C4—32no—
498C4⋊C4—304no—
499C22⋊C4—32no—
500C22⋊C4—64no—
501C22⋊C4—304no—
502C42—32no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—42no—
506C22×C3—44no—
507C22×C3—84no—
508C22×C3—201no—
509C22×C3—202no—
510C22×C3#408612yes—
511C22×C3C22×C22⋊D511yescharacteristic
512C2×D3—41no—
513C2×D3—42no—
514C3×C4—201no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C2×D4×D511yescharacteristic
518Dic3—24no—
519Dic3—41no—
520Dic3—202no—
521C2×C5—22no—
522C2×C5—82no—
523C2×C5—241no—
524C2×C5#577512yes—
525C2×C5C2×#94011yescharacteristic
526D5—81no—
527C23—22no—
528C23—42no—
529C23—61no—
530C23—82no—
531C23—101no—
532C23D3×C22⋊D511yescharacteristic
533Q8—61no—
534Q8—61no—
535Q8—101no—
536Q8—101no—
537Q8—302no—
538Q8—302no—
539Q8—602no—
540D4—22no—
541D4—22no—
542D4—42no—
543D4—61no—
544D4—61no—
545D4—101no—
546D4—101no—
547D4—122no—
548D4—202no—
549D4—244no—
550C2×C4—34no—
551C2×C4—61no—
552C2×C4—101no—
553C2×C4—122no—
554C2×C4—202no—
555C2×C4—302no—
556C2×C4—602no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D511yescharacteristic
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—54no—
562C8—152no—
563C8—152no—
564C2×C3—22no—
565C2×C3—82no—
566C2×C3—401no—
567C2×C3C2×#408611yescharacteristic
568C2×C3#6617012yes—
569D3—81no—
570C5#8393911yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—44no—
574C22—84no—
575C22—121no—
576C22—122no—
577C22—201no—
578C22—202no—
579C22#9156712yes—
580C22C2×D3×C22⋊D511yescharacteristic
581C4—64no—
582C4—121no—
583C4—201no—
584C4—602no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061511211yescharacteristic, complemented, Sylow
589C2—22no—
590C2—82no—
591C2—241no—
592C2—401no—
593C2#1175472012yes—
594C2C2×#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#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. C22×#6716C2semidirect
2. C5×#5805C2semidirect
3. C2×C3×#4078C2semidirect
4. #11754252C2semidirect
5. C2×#91322C2semidirect
6. C2×#91297C2semidirect
7. #11749110C2semidirect
8. #11749108C2semidirect
9. #11749074C2semidirect
10. #11749071C2semidirect
11. #11748327C2semidirect
31. #91389C22semidirect
32. #91364C22semidirect
35. C2×#6663C22semidirect
36. C2×#6661C22semidirect
37. C2×#6659C22semidirect
38. C2×#6656C22semidirect
39. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
49. C2×#4078D3semidirect
82. C2×C3⋊#168D4semidirect
91. C3×#681D4semidirect
104. #5805D5semidirect
252. #681#67semidirect
503. C3×C5#3154semidirect
570. C5#83939semidirect
588. C3#10615112semidirect

Maximal subgroups

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

subgroupindex
C22×#67162
C5×#58052
C2×C3×#40782
#117542522
C2×#913222
C2×#912972
#117491102
#117491082
#117490742
#117490712
#117483272
#106151123
#839395