Finite Group Databasebeta

← #14301331

Subgroups — #14301331

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
1#11756586C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic
3C2×C5×#837C211yesmaximal, characteristic, complemented
4#11748785C211yesmaximal, characteristic, complemented
5#11748367C211yesmaximal, characteristic, complemented
6#11745987C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10601159—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11Q8×Dic15—21no—
12D4×Dic15—21no—
13D4×Dic15—22no—
14#91815—21no—
15#91815C2211yescharacteristic
16C2×C4⋊Dic15—21no—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C3×#4095—22no—
21C3×#4095C414yescomplemented
22C2×C3×#688—21no—
23C2×C3×#686—21no—
24C2×C3×#681C2211yescharacteristic
25C2×#6665—22no—
26C5×#837—22no—
27#90965—21no—
28#90965—21no—
29#72088—51nomaximal, Hall
30#66161—31no—
31C2×#4095D311yescharacteristic
32C2×C5×#104—31no—
33#65420—31no—
34#65228—31no—
35#64774—31no—
36#64743—31no—
37C23×C3×D5—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41C2×C412yes—
41C3×C5×#41D412yes—
42C2×C3×C5×Q8D411yescharacteristic
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4D411yescharacteristic
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—22no—
48C22×Dic15D412yes—
49C22×C5×Dic3—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20—21no—
54C2×C3×D20—21no—
55C2×C3×D20C2×C412yescomplemented
56#6719—22no—
57#6719—21no—
58C4⋊Dic15—22no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61C4⋊Dic15D411yescharacteristic
62C4⋊Dic15D411yescharacteristic
63C4×Dic15—22no—
64C4×Dic15—21no—
65C4×C5×Dic3—21no—
66C4×C5×Dic3—21no—
67C5×#208—21no—
68C5×#208—21no—
69C2×C5×C3⋊C8—21no—
70C3×#688—24no—
71C3×#686—24no—
72C3×#681—21no—
73C3×#681C2×C412yescomplemented
74C2×C3×#168—21no—
75#6665—44no—
76C2×C3×AGL(1,ℤ/8)—51no—
77#5827—51no—
78C2×#837D511yescharacteristic, complemented
79#5221—51no—
80#5215—51no—
81#4555—51no—
82#4554—51no—
83C2×C5×#41C2×D311yescharacteristic
84C22×D20C2×D311yescharacteristic
85C2×C5×M16—31no—
86C2×C42×C5—31no—
87#4095—22no—
88#4095Dic314yescomplemented
89Q8×Dic5—61no—
90C2×#688—21no—
91D4×Dic5—62no—
92D4×Dic5—61no—
93C2×#686—21no—
94C2×#685—62no—
95#4072—31no—
96#4072—61no—
97C2×C4⋊Dic5—31no—
98C2×C4⋊Dic5—61no—
99C2×#681C2×D311yescharacteristic
100C5×#104—62no—
101#3953—61no—
102#3953—61no—
103#1883—151noSylow
104C23×C3×C5—21no—
105C23×C3×C5C2×D411yescharacteristic
106C22×C3×D5—22no—
107C22×C3×D5—42no—
108C22×C3×D5—42no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
111C3×C5×Q8—21no—
112C3×C5×Q8C22⋊C412yescomplemented
113C3×C5×D4—22no—
114C3×C5×D4—22no—
115C3×C5×D4—21no—
116C3×C5×D4C22⋊C412yescomplemented
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5C22×C411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5#4111yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126C2×Dic15—21no—
127C2×Dic15—22no—
128C2×Dic15—21no—
129C2×Dic15—42no—
130C2×Dic15—82no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—41no—
133C2×C5×Dic3—41no—
134C3×D20—22no—
135C3×D20—22no—
136C3×D20—41no—
137C3×D20—41no—
138C3×#168—22no—
139C5×C3⋊C8—41no—
140C2×C3×#41C2×D511yescharacteristic
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×M16—51no—
147C2×#217—102no—
148Q8×Dic3—101no—
149D4×Dic3—102no—
150D4×Dic3—101no—
151#926—51no—
152#926—101no—
153C2×C4⋊Dic3—51no—
154C2×C4⋊Dic3—101no—
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208C2×D511yescharacteristic
157#837—22no—
158#832—101no—
159#832—101no—
160C23×D5—21no—
161C5×#41—21no—
162C5×#41—21no—
163C5×#41C2×Dic312yes—
164C5×#41#6712yes—
165C2×C5×Q8#6711yescharacteristic
166C2×C5×D4—21no—
167C2×C5×D4#6711yescharacteristic
168C22×C4×C5—21no—
169C22×C4×C5—61no—
170C22×C4×C5C22×D311yescharacteristic
171C22×Dic5—32no—
172C22×Dic5—62no—
173C2×D20—21no—
174C2×D20—21no—
175C2×D20—21no—
176C2×D20—21no—
177C2×D20—21no—
178C2×D20C2×Dic312yescomplemented
179C5×M16—61no—
180C5×M16—61no—
181C2×C5×C8—61no—
182C42×C5—61no—
183C42×C5—61no—
184C22⋊Dic5—62no—
185C22⋊Dic5—61no—
186#688—24no—
187#686—24no—
188#685—124no—
189C4⋊Dic5—31no—
190C4⋊Dic5—31no—
191C4⋊Dic5—62no—
192C4⋊Dic5—61no—
193C4⋊Dic5—61no—
194C4×Dic5—62no—
195C4×Dic5—61no—
196#681—21no—
197#681C2×Dic312yescomplemented
198C2×#168—21no—
199C2×AGL(1,ℤ/8)—51no—
200#520—151no—
201C2×#104—31no—
202#418—151no—
203#390—151no—
204#343—151no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5—22no—
209C22×C3×C5—41no—
210C22×C3×C5—41no—
211C22×C3×C5C4×D411yescharacteristic
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C2×C3×D5—44no—
215C2×C3×D5—42no—
216C2×C3×D5—82no—
217C2×C3×D5—81no—
218C2×C3×D5—81no—
219C3×C4×C5—22no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—42no—
225Dic15—41no—
226Dic15—41no—
227C5×Dic3—42no—
228C24×C3—101no—
229C3×#41—21no—
230C3×#41—21no—
231C3×#41C4×D512yes—
232C3×#41C22⋊D512yes—
233C2×C3×Q8D2011yescharacteristic
234C2×C3×D4—21no—
235C2×C3×D4—52no—
236C2×C3×D4—101no—
237C2×C3×D4—101no—
238C2×C3×D4—101no—
239C2×C3×D4—101no—
240C2×C3×D4—101no—
241C2×C3×D4D2011yescharacteristic
242C22×C3×C4—21no—
243C22×C3×C4C22×D511yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—52no—
246C22×Dic3—102no—
247C3×SD16—104no—
248C3×D8—104no—
249C3×M16—52no—
250C3×M16—101no—
251C2×C3×C8—101no—
252#217—102no—
253#217—101no—
254#217—204no—
255C4⋊Dic3—51no—
256C4⋊Dic3—51no—
257C4⋊Dic3—102no—
258C4⋊Dic3—101no—
259C4⋊Dic3—101no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—102no—
263C4×Dic3—101no—
264#208—21no—
265#208—21no—
266C2×C3⋊C8—21no—
267C23×C5—21no—
268C23×C5D3×D411yescharacteristic
269C22×D5—22no—
270C22×D5—42no—
271C22×D5—42no—
272C22×D5—41no—
273C22×D5—41no—
274C5×Q8—21no—
275C5×Q8#21712yescomplemented
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—21no—
279C5×D4#21712yescomplemented
280C2×C4×C5—21no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—62no—
284C2×C4×C5—121no—
285C2×C4×C5—121no—
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5#23711yescharacteristic
288C2×C4×C5#23711yescharacteristic
289C2×C4×C5C22×Dic311yescharacteristic
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×Dic5—61no—
293C2×Dic5—61no—
294C2×Dic5—62no—
295C2×Dic5—122no—
296C2×Dic5—242no—
297D20—22no—
298D20—22no—
299D20—41no—
300D20—41no—
301C5×C8—121no—
302#168—22no—
303C2×#41D3×D511yescharacteristic
304C22×D4—51no—
305AGL(1,ℤ/8)—54no—
306AGL(1,ℤ/8)—102no—
307C2×SD16—101no—
308C2×D8—101no—
309C2×M16—31no—
310C2×M16—51no—
311C4×Q8—301no—
312C4×D4—302no—
313C4×D4—301no—
314#117—151no—
315#117—301no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—302no—
319C2×C42—31no—
320#104—62no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5—42no—
326C2×C3×C5#38611yescharacteristic
327C2×C3×C5#45311yescharacteristic
328C2×C3×C5#45411yescharacteristic
329C3×D5—82no—
330C23×C3—21no—
331C23×C3—102no—
332C23×C3—202no—
333C23×C3—202no—
334C23×C3—201no—
335C23×C3—201no—
336C23×C3D4×D511yescharacteristic
337C3×Q8—21no—
338C3×Q8#68512yescomplemented
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—21no—
342C3×D4—102no—
343C3×D4—102no—
344C3×D4—201no—
345C3×D4—201no—
346C3×D4#68512yescomplemented
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4C2×C4×D511yescharacteristic
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4#71111yescharacteristic
354C2×C3×C4#71111yescharacteristic
355C2×C3×C4C2×C22⋊D511yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—102no—
362C2×Dic3—202no—
363C2×Dic3—402no—
364C3×C8—102no—
365C3⋊C8—41no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—22no—
369C22×C5—41no—
370C22×C5—41no—
371C22×C5D4×Dic311yescharacteristic
372C22×C5#93711yescharacteristic
373C22×C5#93911yescharacteristic
374C2×D5—44no—
375C2×D5—42no—
376C2×D5—82no—
377C2×D5—81no—
378C2×D5—81no—
379C4×C5—22no—
380C4×C5—122no—
381C4×C5D4×Dic311yescharacteristic
382C4×C5#93511yescharacteristic
383C4×C5#93911yescharacteristic
384C4×C5C2×#21711yescharacteristic
385Dic5—122no—
386Dic5—121no—
387Dic5—121no—
388C24—101no—
389#41—21no—
390#41—21no—
391#41D5×Dic312yes—
392#41#120112yes—
393C2×Q8#120211yescharacteristic
394C2×D4—21no—
395C2×D4—52no—
396C2×D4—101no—
397C2×D4—101no—
398C2×D4—101no—
399C2×D4—101no—
400C2×D4—101no—
401C2×D4#120211yescharacteristic
402C22×C4—21no—
403C22×C4—61no—
404C22×C4—152no—
405C22×C4—302no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—104no—
408D8—104no—
409M16—52no—
410M16—61no—
411M16—61no—
412M16—101no—
413C2×C8—61no—
414C2×C8—101no—
415C4⋊C4—151no—
416C4⋊C4—151no—
417C4⋊C4—302no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C22⋊C4—604no—
423C42—61no—
424C42—61no—
425C42—302no—
426C42—301no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—204no—
434C22×C3—202no—
435C22×C3—402no—
436C22×C3—401no—
437C22×C3—401no—
438C22×C3#402711yescharacteristic
439C22×C3#402811yescharacteristic
440C22×C3#408511yescharacteristic
441C3×C4—22no—
442C3×C4#402711yescharacteristic
443C3×C4#403211yescharacteristic
444C3×C4C2×#68511yescharacteristic
445C3×C4#408511yescharacteristic
446Dic3—42no—
447Dic3—202no—
448Dic3—201no—
449Dic3—201no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—42no—
453C2×C5#519811yescharacteristic
454C2×C5#520111yescharacteristic
455C2×C5#522011yescharacteristic
456D5—82no—
457C23—21no—
458C23—102no—
459C23—202no—
460C23—202no—
461C23—201no—
462C23—201no—
463C23#679011yescharacteristic
464Q8—21no—
465Q8#666512yescomplemented
466D4—22no—
467D4—22no—
468D4—21no—
469D4—102no—
470D4—102no—
471D4—201no—
472D4—201no—
473D4#666512yescomplemented
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—62no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4—302no—
483C2×C4—602no—
484C2×C4—1202no—
485C2×C4C2×D5×Dic311yescharacteristic
486C2×C4#678011yescharacteristic
487C2×C4#678011yescharacteristic
488C2×C4C2×#120111yescharacteristic
489C2×C4C2×#120211yescharacteristic
490C2×C4#679011yescharacteristic
491C8—102no—
492C8—121no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—42no—
496C2×C3—402no—
497C2×C3#6511111yescharacteristic
498C2×C3#6511611yescharacteristic
499C2×C3#6524711yescharacteristic
500C5#7208811yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—204no—
507C22—202no—
508C22—402no—
509C22—401no—
510C22—401no—
511C22#9155911yescharacteristic
512C22#9157111yescharacteristic
513C22#9157211yescharacteristic
514C4—22no—
515C4—122no—
516C4—602no—
517C4—601no—
518C4—601no—
519C4C2×#666511yescharacteristic
520C4#9153711yescharacteristic
521C4#9155911yescharacteristic
522C4#9157111yescharacteristic
523C3#1060115911yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—42no—
527C2—402no—
528C2#1174942111yescharacteristic
529C2#1174946011yescharacteristic
530C2#1174950011yescharacteristic
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
prime radicalC2×C3×#4095C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1883
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. #11756586C2semidirect
3. C2×C5×#837C2semidirect
4. #11748785C2semidirect
5. #11748367C2semidirect
6. #11745987C2semidirect
7. #11745976C2semidirect
21. C3×#4095C4semidirect
55. C2×C3×D20C2×C4semidirect
73. C3×#681C2×C4semidirect
78. C2×#837D5semidirect
88. #4095Dic3semidirect
112. C3×C5×Q8C22⋊C4semidirect
116. C3×C5×D4C22⋊C4semidirect
178. C2×D20C2×Dic3semidirect
197. #681C2×Dic3semidirect
275. C5×Q8#217semidirect
279. C5×D4#217semidirect
338. C3×Q8#685semidirect
346. C3×D4#685semidirect
427. C3×C5#1883semidirect
465. Q8#6665semidirect
473. D4#6665semidirect
500. C5#72088semidirect
523. C3#10601159semidirect

Maximal subgroups

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

subgroupindex
#117565862
C2×C3×#40952
C2×C5×#8372
#117487852
#117483672
#117459872
#117459762
#106011593
#720885