Finite Group Databasebeta

← #14301357

Subgroups — #14301357

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#11754492C211yesmaximal, characteristic, complemented
3#11748797C211yesmaximal, characteristic, complemented
4C2×#90978C211yesmaximal, characteristic, complemented
5#11748389C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7C3×#64774C211yesmaximal, characteristic, complemented
8#10602881—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C5×#908—22no—
15C5×#908C414yescomplemented
16C2×C5×D24—21no—
17C2×C5×#204—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20Dic5×#67—22no—
21C2×(C2×D3)⋊Dic5—22no—
22#91435—21no—
23D3×C4⋊Dic5—21no—
24#91344—21no—
25#91338—21no—
26#90978—22no—
27#90967—21no—
28#90967—21no—
29#69005—51nomaximal, Hall
30C2×C5×AGL(1,ℤ/8)—31no—
31#66161—31no—
32C2×#3969—31no—
33#65510—31no—
34#65504—31no—
35#64775—31no—
36#64774D311yescharacteristic, complemented
37C23×C5×D3—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
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×Dic5D412yes—
55C2×D3×Dic5—22no—
56C3×C5×M16—21no—
57C3×C5×M16C2×C412yescomplemented
58C2×C3×C5×C8—21no—
59#6719—21no—
60C4⋊Dic15D411yescharacteristic
61C4⋊Dic15D411yescharacteristic
62C4×Dic15—21no—
63C4×Dic15—21no—
64C4×Dic15—21no—
65C5×D24—24no—
66C5×#204—24no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×#681—21no—
70C3×#681—21no—
71C2×C3×#168—21no—
72Dic3⋊Dic5—22no—
73(C2×D3)⋊Dic5—22no—
74(C2×D3)⋊Dic5—44no—
75Dic3×Dic5—22no—
76C2×#908D511yescharacteristic
77#5504—51no—
78C2×#825—51no—
79#5131—51no—
80#4988—51no—
81C3×#343—51no—
82#4555—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—31no—
95#4072—61no—
96C2×C4⋊Dic5—61no—
97C2×C4⋊Dic5C2×D311yescharacteristic
98C2×C4×Dic5—31no—
99C2×#681C2×D311yescharacteristic
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—21no—
119C2×Dic15—21no—
120C2×Dic15—41no—
121C2×Dic15—41no—
122C5×#67—22no—
123C5×#67—22no—
124C2×C5×Dic3—21no—
125C5×D12—22no—
126C5×D12—22no—
127C5×D12—21no—
128C5×D12—41no—
129C5×D12—41no—
130C5×D12C22⋊C412yescomplemented
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C5×Dic6—21no—
134C5×Dic6C22⋊C412yescomplemented
135C2×C3×Dic5—22no—
136C2×C3×Dic5—42no—
137D3×Dic5—82no—
138C3×C5×C8—22no—
139C3×#168—41no—
140C2×#235C2×D511yescharacteristic
141C22×D12C2×D511yescharacteristic
142C2×C3×M16—51no—
143C2×C3×M16C2×D511yescharacteristic
144C2×C3×C4⋊C4—51no—
145C4×#67—102no—
146C2×(C2×D3)⋊C4—102no—
147#926—51no—
148C2×C4×Dic3—51no—
149#908—22no—
150#908Dic514yescomplemented
151C2×D24—21no—
152C2×#204—21no—
153#893—101no—
154#892—101no—
155D3×C4⋊C4—101no—
156#887—101no—
157#825—102no—
158#821—101no—
159#821—101no—
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—62no—
177C22×Dic5—61no—
178C22×Dic5D1212yes—
179C5×SD16—64no—
180C5×D8—64no—
181C5×M16—21no—
182C5×M16C4×D312yescomplemented
183C2×C5×C8—21no—
184C22⋊Dic5—62no—
185C22⋊Dic5—61no—
186C22⋊Dic5—124no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—31no—
190C4⋊Dic5—31no—
191C4⋊Dic5—62no—
192C4×Dic5—62no—
193C4×Dic5—61no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196#681—21no—
197#681—21no—
198C2×#168—21no—
199C2×AGL(1,ℤ/8)—31no—
200#520—151no—
201C2×#104—151no—
202#418—151no—
203#390—151no—
204#343—51no—
205#339—151no—
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—
224Dic15—41no—
225Dic15—41no—
226C3×Dic5—42no—
227C5×Dic3—22no—
228C23×D3—21no—
229C22×C3×C4—52no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—21no—
232C22×Dic3—101no—
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×M16—101no—
249C3×M16—101no—
250C3×M16C2×Dic512yescomplemented
251C2×C3×C8—21no—
252C2×C3×C8—101no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255#217—101no—
256(C2×D3)⋊C4—102no—
257(C2×D3)⋊C4—204no—
258C4⋊Dic3—51no—
259C4⋊Dic3—51no—
260Dic3⋊C4—102no—
261C4×Dic3—102no—
262C4×Dic3—101no—
263C4×Dic3—101no—
264C4×Dic3—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×C5C2×D1211yescharacteristic
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×C5#23511yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5#23911yescharacteristic
293C2×Dic5—22no—
294C2×Dic5—42no—
295C2×Dic5—62no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—121no—
299C2×Dic5—121no—
300C2×Dic5—242no—
301C5×C8—22no—
302#168—41no—
303C2×#41—31no—
304C22×D4—31no—
305AGL(1,ℤ/8)—34no—
306AGL(1,ℤ/8)—62no—
307C2×SD16—61no—
308C2×D8—61no—
309C2×M16—51no—
310C2×M16D3×D511yescharacteristic
311C4×Q8—301no—
312C4×D4—301no—
313C4×D4—302no—
314#117—151no—
315#117—301no—
316C2×C4⋊C4—51no—
317C2×C4⋊C4—301no—
318C2×C22⋊C4—302no—
319C2×C42—151no—
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—202no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4#71111yescharacteristic
341C2×C3×C4#71111yescharacteristic
342C2×C3×C4C22×Dic511yescharacteristic
343C2×C3×C4C2×C22⋊D511yescharacteristic
344C2×C3×C4C2×C22⋊D511yescharacteristic
345#67—22no—
346#67—22no—
347C2×Dic3—21no—
348C2×Dic3—102no—
349C2×Dic3—101no—
350C2×Dic3—101no—
351C2×Dic3—201no—
352C2×Dic3—201no—
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×C5C4×D1211yescharacteristic
377C22×C5#88211yescharacteristic
378C22×C5#89511yescharacteristic
379C4×C5—62no—
380C4×C5D3×C22⋊C411yescharacteristic
381C4×C5#88411yescharacteristic
382C4×C5#89311yescharacteristic
383C4×C5#89411yescharacteristic
384Dic5—42no—
385Dic5—122no—
386Dic5—121no—
387Dic5—121no—
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—52no—
403C22×C4—61no—
404C22×C4—302no—
405C22×C4—301no—
406C22×C4C2×D3×D511yescharacteristic
407SD16—64no—
408D8—64no—
409M16—21no—
410M16—101no—
411M16—101no—
412M16D3×Dic512yescomplemented
413C2×C8—21no—
414C2×C8—101no—
415C4⋊C4—101no—
416C4⋊C4—101no—
417C4⋊C4—151no—
418C4⋊C4—151no—
419C4⋊C4—302no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C22⋊C4—604no—
423C42—302no—
424C42—301no—
425C42—301no—
426C42—301no—
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×C4D4×Dic511yescharacteristic
443C3×C4#408111yescharacteristic
444C3×C4#408511yescharacteristic
445C3×C4C2×C22⋊Dic511yescharacteristic
446Dic3—22no—
447Dic3—202no—
448Dic3—201no—
449Dic3—201no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—122no—
453C2×C5—242no—
454C2×C5#466511yescharacteristic
455C2×C5#474711yescharacteristic
456C2×C5#475311yescharacteristic
457C23—61no—
458C23—62no—
459C23—122no—
460C23—122no—
461C23—121no—
462C23—121no—
463C23D5×D1211yescharacteristic
464Q8—32no—
465Q8—61no—
466D4—32no—
467D4—62no—
468D4—62no—
469D4—61no—
470D4—62no—
471D4—62no—
472D4—121no—
473D4—121no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—102no—
478C2×C4—202no—
479C2×C4—302no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4—1202no—
485C2×C4#676811yescharacteristic
486C2×C4#677211yescharacteristic
487C2×C4#677711yescharacteristic
488C2×C4C2×D3×Dic511yescharacteristic
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4D3×C22⋊D511yescharacteristic
491C8—22no—
492C8—201no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3#6548711yescharacteristic
496C2×C3#6549011yescharacteristic
497C2×C3#6550911yescharacteristic
498D3—42no—
499D3—82no—
500C5#6900511yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—62no—
504C22—124no—
505C22—121no—
506C22—121no—
507C22—122no—
508C22—242no—
509C22—241no—
510C22—241no—
511C22Dic5×D1211yescharacteristic
512C22#9141611yescharacteristic
513C22#9147511yescharacteristic
514C4—62no—
515C4—202no—
516C4—602no—
517C4—601no—
518C4—601no—
519C4#9142311yescharacteristic
520C4#9143511yescharacteristic
521C4#9145311yescharacteristic
522C4D3×C22⋊Dic511yescharacteristic
523C3#1060288111yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—122no—
527C2—242no—
528C2#1174824611yescharacteristic
529C2#1174825911yescharacteristic
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. #11754492C2semidirect
3. #11748797C2semidirect
4. C2×#90978C2semidirect
5. #11748389C2semidirect
6. #11746376C2semidirect
7. C3×#64774C2semidirect
15. C5×#908C4semidirect
36. #64774D3semidirect
50. C2×C5×D12C2×C4semidirect
57. C3×C5×M16C2×C4semidirect
130. C5×D12C22⋊C4semidirect
134. C5×Dic6C22⋊C4semidirect
150. #908Dic5semidirect
182. C5×M16C4×D3semidirect
242. C2×D12C2×Dic5semidirect
250. C3×M16C2×Dic5semidirect
358. D12C22⋊Dic5semidirect
363. Dic6C22⋊Dic5semidirect
412. M16D3×Dic5semidirect
427. C3×C5#1883semidirect
500. C5#69005semidirect
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
#117544922
#117487972
C2×#909782
#117483892
#117463762
C3×#647742
#106028813
#690055