Finite Group Databasebeta

← #14301354

Subgroups — #14301354

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4054C211yesmaximal, characteristic
2#11754509C211yesmaximal, characteristic, complemented
3#11748785C211yesmaximal, characteristic, complemented
4C2×#90977C211yesmaximal, characteristic, complemented
5#11748366C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7C5×#4555C211yesmaximal, characteristic, complemented
8#10599569—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C3×#4054—22no—
17C3×#4054C414yescomplemented
18C2×C3×D40—21no—
19C2×C3×#677—21no—
20#91559—22no—
21C2×#6665—22no—
22Dic3×D20—21no—
23D5×C4⋊Dic3—21no—
24#91358—21no—
25Dic3×Dic10—21no—
26#90977—22no—
27#90964—21no—
28#90964—21no—
29#72088—51nomaximal, Hall
30C2×#4054D311yescharacteristic
31#65857—31no—
32#65290—31no—
33#65228—31no—
34C2×#3937—31no—
35C5×#339—31no—
36#64774—31no—
37C23×C3×D5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15D412yes—
40C22×C5×Dic3—21no—
41C2×C3×C22⋊D5—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709C2×C412yes—
45C3×#709D412yes—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20C2×C412yescomplemented
52C2×C3×D20D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×Dic10D411yescharacteristic
55C2×D5×Dic3—22no—
56C3×C5×M16—21no—
57C3×C5×M16C2×C412yescomplemented
58C2×C3×C5×C8—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61#6710—21no—
62#6710—21no—
63C2×C3⋊#168—21no—
64C5×#217—21no—
65C5×C4⋊Dic3D411yescharacteristic
66C5×C4⋊Dic3D411yescharacteristic
67C4×C5×Dic3—21no—
68C4×C5×Dic3—21no—
69C4×C5×Dic3—21no—
70C3×D40—24no—
71C3×#677—24no—
72#6668—22no—
73#6665—22no—
74#6665—44no—
75Dic3×Dic5—22no—
76C2×C3×AGL(1,ℤ/8)—51no—
77#5827—51no—
78C2×#837—51no—
79#5221—51no—
80#5215—51no—
81#4555D511yescharacteristic, complemented
82#4554—51no—
83C2×#709C2×D311yescharacteristic
84C22×D20C2×D311yescharacteristic
85C2×C5×M16C2×D311yescharacteristic
86C5×#117—31no—
87C2×C42×C5—31no—
88C2×#685—62no—
89C2×C4⋊Dic5—31no—
90C2×#681—31no—
91#4054—22no—
92#4054Dic314yescomplemented
93C2×D40—21no—
94C2×#677—21no—
95#4038—61no—
96D5×C4⋊C4—61no—
97#4027—62no—
98C4×D20—61no—
99C4×Dic10—61no—
100#3941—61no—
101#3941—61no—
102#3937—62no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×C3×D5—21no—
106C22×C3×D5—22no—
107C22×C3×D5—42no—
108C22×C3×D5—42no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×Dic15—22no—
118C2×Dic15—42no—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C3×C22⋊D5—22no—
125C3×C22⋊D5—22no—
126C2×C3×Dic5—21no—
127C3×D20—22no—
128C3×D20—22no—
129C3×D20—21no—
130C3×D20—41no—
131C3×D20—41no—
132C3×D20C22⋊C412yescomplemented
133C3×C4×D5—22no—
134C3×C4×D5—22no—
135C3×Dic10—21no—
136C3×Dic10C22⋊C412yescomplemented
137D5×Dic3—82no—
138C3×C5×C8—22no—
139C3⋊#168—41no—
140C2×C3×#41—51no—
141C22×C3×D4—51no—
142C3×AGL(1,ℤ/8)—54no—
143C3×AGL(1,ℤ/8)—102no—
144C2×C3×SD16—101no—
145C2×C3×D8—101no—
146C2×C3×M16C2×D511yescharacteristic
147C2×#217—102no—
148Q8×Dic3—101no—
149D4×Dic3—101no—
150D4×Dic3—102no—
151#926—101no—
152#926C2×D511yescharacteristic
153C2×C4⋊Dic3—51no—
154C2×C4⋊Dic3—101no—
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208—51no—
157#837—102no—
158#832—101no—
159#832—101no—
160C23×D5—21no—
161C22×C4×C5—61no—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—21no—
164C22×Dic5—32no—
165#709—21no—
166#709—21no—
167#709C2×Dic312yes—
168#709#6712yes—
169C2×D20—21no—
170C2×D20—21no—
171C2×D20—21no—
172C2×D20—21no—
173C2×D20—21no—
174C2×D20C2×Dic312yescomplemented
175C2×D20#6711yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—62no—
178C2×Dic10#6711yescharacteristic
179C5×M16—21no—
180C5×M16C2×Dic312yescomplemented
181C2×C5×C8—21no—
182C5×C4⋊C4—31no—
183C5×C4⋊C4—31no—
184C5×C22⋊C4—61no—
185C42×C5—61no—
186C42×C5—61no—
187C42×C5—61no—
188#685—62no—
189#685—124no—
190C4⋊Dic5—61no—
191C4⋊Dic5—61no—
192#683—62no—
193C4×Dic5—62no—
194#681—61no—
195#681—61no—
196C2×#168—61no—
197D40—24no—
198#677—24no—
199C2×AGL(1,ℤ/8)—51no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—151no—
204#343—151no—
205#339—31no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×C3×D5—22no—
212C2×C3×D5—41no—
213C2×C3×D5—41no—
214C2×C3×D5—44no—
215C2×C3×D5—42no—
216C2×C3×D5—82no—
217C2×C3×D5—81no—
218C2×C3×D5—81no—
219C3×C4×C5C2×C22⋊C411yescharacteristic
220C3×C4×C5C4×D411yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5#12311yescharacteristic
223Dic15—42no—
224C3×Dic5—22no—
225C5×Dic3—42no—
226C5×Dic3—41no—
227C5×Dic3—41no—
228C24×C3—101no—
229C3×#41—52no—
230C3×#41—52no—
231C3×#41—101no—
232C3×#41—101no—
233C2×C3×Q8—51no—
234C2×C3×D4—52no—
235C2×C3×D4—51no—
236C2×C3×D4—101no—
237C2×C3×D4—101no—
238C2×C3×D4—101no—
239C2×C3×D4—101no—
240C2×C3×D4—101no—
241C2×C3×D4—101no—
242C22×C3×C4—101no—
243C22×C3×C4C22×D511yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—52no—
246C22×Dic3—102no—
247C3×SD16—104no—
248C3×D8—104no—
249C3×M16—21no—
250C3×M16C4×D512yescomplemented
251C2×C3×C8—21no—
252#217—21no—
253#217—102no—
254#217—204no—
255C4⋊Dic3—102no—
256C4⋊Dic3—101no—
257C4⋊Dic3—101no—
258C4⋊Dic3D2011yescharacteristic
259C4⋊Dic3D2011yescharacteristic
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3—102no—
264#208—101no—
265#208—101no—
266C2×C3⋊C8—101no—
267C23×C5D3×D411yescharacteristic
268C22×D5—21no—
269C22×D5—22no—
270C22×D5—42no—
271C22×D5—42no—
272C22×D5—41no—
273C22×D5—41no—
274C2×C4×C5—62no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5—121no—
278C2×C4×C5—121no—
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5#23711yescharacteristic
281C2×C4×C5#23711yescharacteristic
282C2×C4×C5C22×Dic311yescharacteristic
283C2×C4×C5C2×#6711yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C22⋊D5—22no—
286C22⋊D5—22no—
287C2×Dic5—21no—
288C2×Dic5—62no—
289C2×Dic5—122no—
290D20—22no—
291D20—21no—
292D20—22no—
293D20—41no—
294D20—41no—
295D20#21712yescomplemented
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—242no—
299Dic10—21no—
300Dic10#21712yescomplemented
301C5×C8—22no—
302#168—121no—
303C2×#41—51no—
304C22×D4—51no—
305AGL(1,ℤ/8)—54no—
306AGL(1,ℤ/8)—102no—
307C2×SD16—101no—
308C2×D8—101no—
309C2×M16—151no—
310C2×M16D3×D511yescharacteristic
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—31no—
315#117—301no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—302no—
319C2×C42—31no—
320#104—302no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#38611yescharacteristic
326C2×C3×C5#45311yescharacteristic
327C2×C3×C5#45411yescharacteristic
328C3×D5—42no—
329C3×D5—82no—
330C23×C3—101no—
331C23×C3—102no—
332C23×C3—202no—
333C23×C3—202no—
334C23×C3—201no—
335C23×C3—201no—
336C23×C3D4×D511yescharacteristic
337C3×Q8—52no—
338C3×Q8—101no—
339C3×D4—52no—
340C3×D4—102no—
341C3×D4—102no—
342C3×D4—102no—
343C3×D4—102no—
344C3×D4—101no—
345C3×D4—201no—
346C3×D4—201no—
347C2×C3×C4—101no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4C2×C4×D511yescharacteristic
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4#70911yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4#71311yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—102no—
362C2×Dic3—202no—
363C2×Dic3—402no—
364C3×C8—22no—
365C3⋊C8—201no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5D4×Dic311yescharacteristic
369C22×C5#93711yescharacteristic
370C22×C5#93911yescharacteristic
371C2×D5—22no—
372C2×D5—41no—
373C2×D5—41no—
374C2×D5—44no—
375C2×D5—42no—
376C2×D5—82no—
377C2×D5—81no—
378C2×D5—81no—
379C4×C5—122no—
380C4×C5—121no—
381C4×C5—121no—
382C4×C5D4×Dic311yescharacteristic
383C4×C5#93511yescharacteristic
384C4×C5#93911yescharacteristic
385C4×C5C2×#21711yescharacteristic
386Dic5—22no—
387Dic5—122no—
388C24—101no—
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—52no—
395C2×D4—51no—
396C2×D4—101no—
397C2×D4—101no—
398C2×D4—101no—
399C2×D4—101no—
400C2×D4—101no—
401C2×D4—101no—
402C22×C4—61no—
403C22×C4—101no—
404C22×C4—152no—
405C22×C4—302no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—104no—
408D8—104no—
409M16—21no—
410M16—301no—
411M16—301no—
412M16D5×Dic312yescomplemented
413C2×C8—21no—
414C2×C8—301no—
415C4⋊C4—31no—
416C4⋊C4—31no—
417C4⋊C4—302no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C22⋊C4—61no—
421C22⋊C4—302no—
422C22⋊C4—604no—
423C42—61no—
424C42—61no—
425C42—61no—
426C42—302no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—102no—
431C22×C3—204no—
432C22×C3—201no—
433C22×C3—201no—
434C22×C3—202no—
435C22×C3—402no—
436C22×C3—401no—
437C22×C3—401no—
438C22×C3#402811yescharacteristic
439C22×C3#403011yescharacteristic
440C22×C3#403911yescharacteristic
441C3×C4—102no—
442C3×C4C4×D2011yescharacteristic
443C3×C4D5×C22⋊C411yescharacteristic
444C3×C4#404011yescharacteristic
445C3×C4#404111yescharacteristic
446Dic3—42no—
447Dic3—41no—
448Dic3—41no—
449Dic3—202no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5#519811yescharacteristic
453C2×C5#520111yescharacteristic
454C2×C5#522011yescharacteristic
455D5—42no—
456D5—82no—
457C23—101no—
458C23—102no—
459C23—202no—
460C23—202no—
461C23—201no—
462C23—201no—
463C23#677711yescharacteristic
464Q8—52no—
465Q8—101no—
466D4—52no—
467D4—102no—
468D4—102no—
469D4—101no—
470D4—102no—
471D4—102no—
472D4—201no—
473D4—201no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—101no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—302no—
483C2×C4—602no—
484C2×C4—1202no—
485C2×C4#676511yescharacteristic
486C2×C4#676611yescharacteristic
487C2×C4D3×D2011yescharacteristic
488C2×C4C2×D5×Dic311yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4D5×#6711yescharacteristic
491C8—22no—
492C8—601no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—202no—
496C2×C3—402no—
497C2×C3#6495411yescharacteristic
498C2×C3#6511111yescharacteristic
499C2×C3#6511611yescharacteristic
500C5#7208811yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—102no—
504C22—204no—
505C22—201no—
506C22—201no—
507C22—202no—
508C22—402no—
509C22—401no—
510C22—401no—
511C22#9140811yescharacteristic
512C22#9143411yescharacteristic
513C22#9147411yescharacteristic
514C4—102no—
515C4—122no—
516C4—121no—
517C4—121no—
518C4—602no—
519C4#9140711yescharacteristic
520C4#9140911yescharacteristic
521C4Dic3×D2011yescharacteristic
522C4D5×#21711yescharacteristic
523C3#1059956911yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—202no—
527C2—402no—
528C2#1174824211yescharacteristic
529C2#1174825411yescharacteristic
530C2#1174889611yescharacteristic
subgroupG/H
centerC22#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C3×#4054C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754509C2semidirect
3. #11748785C2semidirect
4. C2×#90977C2semidirect
5. #11748366C2semidirect
6. #11746375C2semidirect
7. C5×#4555C2semidirect
17. C3×#4054C4semidirect
51. C2×C3×D20C2×C4semidirect
57. C3×C5×M16C2×C4semidirect
81. #4555D5semidirect
92. #4054Dic3semidirect
132. C3×D20C22⋊C4semidirect
136. C3×Dic10C22⋊C4semidirect
174. C2×D20C2×Dic3semidirect
180. C5×M16C2×Dic3semidirect
250. C3×M16C4×D5semidirect
295. D20#217semidirect
300. Dic10#217semidirect
412. M16D5×Dic3semidirect
427. C3×C5#1883semidirect
500. C5#72088semidirect
523. C3#10599569semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40542
#117545092
#117487852
C2×#909772
#117483662
#117463752
C5×#45552
#105995693
#720885