Finite Group Databasebeta

← #14301356

Subgroups — #14301356

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×C5×#908C211yesmaximal, characteristic
2#11754513C211yesmaximal, characteristic, complemented
3#11748764C211yesmaximal, characteristic, complemented
4C2×#90979C211yesmaximal, characteristic, complemented
5#11748386C211yesmaximal, characteristic, complemented
6#11746375C211yesmaximal, characteristic, complemented
7C3×#64775C211yesmaximal, characteristic, complemented
8#10602881—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#908—22no—
15C5×#908C414yescomplemented
16C2×C5×D24—21no—
17C2×C5×#204—21no—
18C3×#4072C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20#67⋊Dic5—22no—
21C2×(C2×D3)⋊Dic5—22no—
22D3×C4⋊Dic5—21no—
23Dic5×D12—21no—
24#91338—21no—
25Dic5×Dic6—21no—
26#90979—22no—
27#90966—21no—
28#90966—21no—
29#68776—51nomaximal, Hall
30C2×C5×AGL(1,ℤ/8)—31no—
31#66161—31no—
32C2×#3969—31no—
33#65510—31no—
34#65504—31no—
35#64775D311yescharacteristic, complemented
36#64774—31no—
37C23×C5×D3—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15D412yes—
40C2×C5×#67—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235C2×C412yes—
44C5×#235D412yes—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12C2×C412yescomplemented
51C2×C5×D12D411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C5×Dic6D411yescharacteristic
54C22×C3×Dic5—21no—
55C2×D3×Dic5—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×D24—24no—
65C5×#204—24no—
66C3×C22⋊Dic5—21no—
67C3×C4⋊Dic5D411yescharacteristic
68C3×C4⋊Dic5D411yescharacteristic
69C3×C4×Dic5—21no—
70C3×C4×Dic5—21no—
71C3×C4×Dic5—21no—
72Dic3⋊Dic5—22no—
73(C2×D3)⋊Dic5—22no—
74(C2×D3)⋊Dic5—44no—
75Dic3×Dic5—22no—
76C2×#908D511yescharacteristic
77#5523—51no—
78#5001—51no—
79#4939—51no—
80C2×#805—51no—
81C3×#339—51no—
82#4554—51no—
83C2×C5×#41—31no—
84C22×C5×D4—31no—
85C5×AGL(1,ℤ/8)—34no—
86C5×AGL(1,ℤ/8)—62no—
87C2×C5×SD16—61no—
88C2×C5×D8—61no—
89C2×C5×M16C2×D311yescharacteristic
90C2×C22⋊Dic5—62no—
91Q8×Dic5—61no—
92D4×Dic5—61no—
93D4×Dic5—62no—
94#4072—61no—
95#4072C2×D311yescharacteristic
96C2×C4⋊Dic5—31no—
97C2×C4⋊Dic5—61no—
98C2×C4×Dic5C2×D311yescharacteristic
99C2×#681—31no—
100#3969—62no—
101#3964—61no—
102#3964—61no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×C5×D3—21no—
106C22×C5×D3—22no—
107C22×C5×D3—42no—
108C22×C5×D3—42no—
109C22×C5×D3—41no—
110C22×C5×D3—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—
119C5×#67—22no—
120C5×#67—22no—
121C2×C5×Dic3—21no—
122C5×D12—22no—
123C5×D12—22no—
124C5×D12—21no—
125C5×D12—41no—
126C5×D12—41no—
127C5×D12C22⋊C412yescomplemented
128C4×C5×D3—22no—
129C4×C5×D3—22no—
130C5×Dic6—21no—
131C5×Dic6C22⋊C412yescomplemented
132C2×C3×Dic5—22no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—21no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137D3×Dic5—82no—
138C3×C5×C8—22no—
139C3⋊#168—41no—
140C2×#235C2×D511yescharacteristic
141C22×D12C2×D511yescharacteristic
142C2×C3×M16C2×D511yescharacteristic
143C3×#117—51no—
144C2×C3×C42—51no—
145C2×(C2×D3)⋊C4—102no—
146C2×C4⋊Dic3—51no—
147C2×#208—51no—
148#908—22no—
149#908Dic514yescomplemented
150C2×D24—21no—
151C2×#204—21no—
152#892—101no—
153D3×C4⋊C4—101no—
154#67⋊C4—102no—
155C4×D12—101no—
156C4×Dic6—101no—
157#809—101no—
158#809—101no—
159#805—102no—
160C24×C5—61no—
161C5×#41—32no—
162C5×#41—32no—
163C5×#41—61no—
164C5×#41—61no—
165C2×C5×Q8—31no—
166C2×C5×D4—32no—
167C2×C5×D4—31no—
168C2×C5×D4—61no—
169C2×C5×D4—61no—
170C2×C5×D4—61no—
171C2×C5×D4—61no—
172C2×C5×D4—61no—
173C2×C5×D4—61no—
174C22×C4×C5—61no—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—21no—
177C22×Dic5—32no—
178C22×Dic5—62no—
179C5×SD16—64no—
180C5×D8—64no—
181C5×M16—21no—
182C5×M16C4×D312yescomplemented
183C2×C5×C8—21no—
184C22⋊Dic5—21no—
185C22⋊Dic5—62no—
186C22⋊Dic5—124no—
187C4⋊Dic5—62no—
188C4⋊Dic5—61no—
189C4⋊Dic5—61no—
190C4⋊Dic5D1211yescharacteristic
191C4⋊Dic5D1211yescharacteristic
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—62no—
196#681—61no—
197#681—61no—
198C2×#168—61no—
199C2×AGL(1,ℤ/8)—31no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—151no—
204#343—151no—
205#339—51no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×C5×D3—22no—
212C2×C5×D3—41no—
213C2×C5×D3—41no—
214C2×C5×D3—44no—
215C2×C5×D3—42no—
216C2×C5×D3—82no—
217C2×C5×D3—81no—
218C2×C5×D3—81no—
219C3×C4×C5C2×C22⋊C411yescharacteristic
220C3×C4×C5C4×D411yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5#12311yescharacteristic
223Dic15—42no—
224C3×Dic5—42no—
225C3×Dic5—41no—
226C3×Dic5—41no—
227C5×Dic3—22no—
228C23×D3—21no—
229C22×C3×C4—101no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—21no—
232C22×Dic3—52no—
233#235—21no—
234#235—21no—
235#235C2×Dic512yes—
236#235C22⋊D512yes—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12C2×Dic512yescomplemented
243C2×D12C22⋊D511yescharacteristic
244C2×C4×D3—21no—
245C2×C4×D3—102no—
246C2×Dic6C22⋊D511yescharacteristic
247C3×M16—21no—
248C3×M16C2×Dic512yescomplemented
249C2×C3×C8—21no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—51no—
252C3×C22⋊C4—101no—
253C3×C42—101no—
254C3×C42—101no—
255C3×C42—101no—
256(C2×D3)⋊C4—102no—
257(C2×D3)⋊C4—204no—
258C4⋊Dic3—101no—
259C4⋊Dic3—101no—
260Dic3⋊C4—102no—
261C4×Dic3—102no—
262#208—101no—
263#208—101no—
264C2×C3⋊C8—101no—
265D24—24no—
266#204—24no—
267C23×C5—61no—
268C23×C5—62no—
269C23×C5—122no—
270C23×C5—122no—
271C23×C5—121no—
272C23×C5—121no—
273C23×C5D3×D411yescharacteristic
274C5×Q8—32no—
275C5×Q8—61no—
276C5×D4—32no—
277C5×D4—62no—
278C5×D4—62no—
279C5×D4—62no—
280C5×D4—62no—
281C5×D4—61no—
282C5×D4—121no—
283C5×D4—121no—
284C2×C4×C5—61no—
285C2×C4×C5—62no—
286C2×C4×C5—62no—
287C2×C4×C5C2×C4×D311yescharacteristic
288C2×C4×C5C2×D1211yescharacteristic
289C2×C4×C5#23511yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5#23911yescharacteristic
293C2×Dic5—22no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—62no—
299C2×Dic5—122no—
300C2×Dic5—242no—
301C5×C8—22no—
302#168—121no—
303C2×#41—31no—
304C22×D4—31no—
305AGL(1,ℤ/8)—34no—
306AGL(1,ℤ/8)—62no—
307C2×SD16—61no—
308C2×D8—61no—
309C2×M16—151no—
310C2×M16D3×D511yescharacteristic
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—51no—
315#117—301no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—302no—
319C2×C42—51no—
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
328C5×D3—42no—
329C5×D3—82no—
330C23×C3D4×D511yescharacteristic
331C22×D3—21no—
332C22×D3—22no—
333C22×D3—42no—
334C22×D3—42no—
335C22×D3—41no—
336C22×D3—41no—
337C2×C3×C4—102no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4#71111yescharacteristic
344C2×C3×C4#71111yescharacteristic
345C2×C3×C4C22×Dic511yescharacteristic
346C2×C3×C4C2×C22⋊D511yescharacteristic
347C2×C3×C4C2×C22⋊D511yescharacteristic
348#67—22no—
349#67—22no—
350C2×Dic3—21no—
351C2×Dic3—102no—
352C2×Dic3—202no—
353D12—22no—
354D12—22no—
355D12—21no—
356D12—41no—
357D12—41no—
358D12C22⋊Dic512yescomplemented
359C4×D3—22no—
360C4×D3—22no—
361C4×D3—402no—
362Dic6—21no—
363Dic6C22⋊Dic512yescomplemented
364C3×C8—22no—
365C3⋊C8—201no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—62no—
369C22×C5—124no—
370C22×C5—121no—
371C22×C5—121no—
372C22×C5—122no—
373C22×C5—242no—
374C22×C5—241no—
375C22×C5—241no—
376C22×C5#88211yescharacteristic
377C22×C5#88411yescharacteristic
378C22×C5#89311yescharacteristic
379C4×C5—62no—
380C4×C5C4×D1211yescharacteristic
381C4×C5D3×C22⋊C411yescharacteristic
382C4×C5#89411yescharacteristic
383C4×C5#89511yescharacteristic
384Dic5—42no—
385Dic5—41no—
386Dic5—41no—
387Dic5—122no—
388C24—61no—
389#41—32no—
390#41—32no—
391#41—61no—
392#41—61no—
393C2×Q8—31no—
394C2×D4—32no—
395C2×D4—31no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C22×C4—61no—
403C22×C4—101no—
404C22×C4—152no—
405C22×C4—302no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—64no—
408D8—64no—
409M16—21no—
410M16—301no—
411M16—301no—
412M16D3×Dic512yescomplemented
413C2×C8—21no—
414C2×C8—301no—
415C4⋊C4—51no—
416C4⋊C4—51no—
417C4⋊C4—302no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C22⋊C4—101no—
421C22⋊C4—302no—
422C22⋊C4—604no—
423C42—101no—
424C42—101no—
425C42—101no—
426C42—302no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3D4×Dic511yescharacteristic
431C22×C3#408311yescharacteristic
432C22×C3#408511yescharacteristic
433C2×D3—22no—
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—44no—
437C2×D3—42no—
438C2×D3—82no—
439C2×D3—81no—
440C2×D3—81no—
441C3×C4—202no—
442C3×C4—201no—
443C3×C4—201no—
444C3×C4D4×Dic511yescharacteristic
445C3×C4#408111yescharacteristic
446C3×C4#408511yescharacteristic
447C3×C4C2×C22⋊Dic511yescharacteristic
448Dic3—22no—
449Dic3—202no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—122no—
453C2×C5—242no—
454C2×C5#466511yescharacteristic
455C2×C5#482211yescharacteristic
456C2×C5#482711yescharacteristic
457C23—61no—
458C23—62no—
459C23—122no—
460C23—122no—
461C23—121no—
462C23—121no—
463C23#677711yescharacteristic
464Q8—32no—
465Q8—61no—
466D4—32no—
467D4—62no—
468D4—62no—
469D4—62no—
470D4—61no—
471D4—62no—
472D4—121no—
473D4—121no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—102no—
478C2×C4—101no—
479C2×C4—101no—
480C2×C4—201no—
481C2×C4—201no—
482C2×C4—302no—
483C2×C4—602no—
484C2×C4—1202no—
485C2×C4#676811yescharacteristic
486C2×C4#677211yescharacteristic
487C2×C4D5×D1211yescharacteristic
488C2×C4C2×D3×Dic511yescharacteristic
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4D3×C22⋊D511yescharacteristic
491C8—22no—
492C8—601no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3#6548711yescharacteristic
496C2×C3#6549011yescharacteristic
497C2×C3#6550911yescharacteristic
498D3—42no—
499D3—82no—
500C5#6877611yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—62no—
504C22—124no—
505C22—121no—
506C22—121no—
507C22—122no—
508C22—242no—
509C22—241no—
510C22—241no—
511C22#9143511yescharacteristic
512C22#9145311yescharacteristic
513C22#9147511yescharacteristic
514C4—62no—
515C4—202no—
516C4—201no—
517C4—201no—
518C4—602no—
519C4Dic5×D1211yescharacteristic
520C4#9141611yescharacteristic
521C4#9142311yescharacteristic
522C4D3×C22⋊Dic511yescharacteristic
523C3#1060288111yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—122no—
527C2—242no—
528C2#1174824711yescharacteristic
529C2#1174825611yescharacteristic
530C2#1174890111yescharacteristic
subgroupG/H
centerC22#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C5×#908C2
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. #11754513C2semidirect
3. #11748764C2semidirect
4. C2×#90979C2semidirect
5. #11748386C2semidirect
6. #11746375C2semidirect
7. C3×#64775C2semidirect
15. C5×#908C4semidirect
35. #64775D3semidirect
50. C2×C5×D12C2×C4semidirect
57. C3×C5×M16C2×C4semidirect
127. C5×D12C22⋊C4semidirect
131. C5×Dic6C22⋊C4semidirect
149. #908Dic5semidirect
182. C5×M16C4×D3semidirect
242. C2×D12C2×Dic5semidirect
248. C3×M16C2×Dic5semidirect
358. D12C22⋊Dic5semidirect
363. Dic6C22⋊Dic5semidirect
412. M16D3×Dic5semidirect
427. C3×C5#1883semidirect
500. C5#68776semidirect
523. C3#10602881semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9082
#117545132
#117487642
C2×#909792
#117483862
#117463752
C3×#647752
#106028813
#687765