Finite Group Databasebeta

← #14302615

Subgroups — #14302615

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5748C211yesmaximal, characteristic
2#11754455C211yesmaximal, characteristic, complemented
3#11748625C211yesmaximal, characteristic, complemented
4#11748424C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7C3×#64779C211yesmaximal, characteristic, complemented
8#10602907—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C5×#909—21no—
15C5×#909C412yescomplemented
16C5×#908—21no—
17C5×#908C412yescomplemented
18C5×#904—22no—
19C3×#4072C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#67⋊Dic5—22no—
22#91435—21no—
23C4×D3×Dic5—21no—
24#91371—21no—
25#91344—21no—
26#90996—22no—
27#90978—22no—
28#90978—21no—
29#90978—21no—
30#69039—51nomaximal, Hall
31C5×#575—31no—
32#41×Dic5—31no—
33#65529—31no—
34#65525—31no—
35C2×#3969—31no—
36#64779D311yescharacteristic, complemented
37#64775—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C5×#235C2×C412yes—
49C5×#235D412yes—
50C2×C5×D12C2×C411yescharacteristic, complemented
51C2×C5×D12D411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3—21no—
54C2×C5×Dic6C2×C411yescharacteristic, complemented
55C2×C5×Dic6D411yescharacteristic
56C2×D3×Dic5—22no—
57C3×C5×M16—21no—
58C3×C5×M16C2×C412yescomplemented
59C2×C3×C5×C8—21no—
60#6719—21no—
61C4⋊Dic15—21no—
62C4×Dic15—21no—
63C4×Dic15—21no—
64C4×Dic15D411yescharacteristic
65C4×Dic15D411yescharacteristic
66C5×Dic12—22no—
67C5×D24—22no—
68C5×#204—22no—
69C5×#204—22no—
70C3×C22⋊Dic5D412yes—
71C3×C4⋊Dic5—21no—
72C3×C4×Dic5—21no—
73C3×#681—21no—
74C3×#681—21no—
75C2×C3×#168—21no—
76Dic3⋊Dic5—22no—
77(C2×D3)⋊Dic5—22no—
78Dic3×Dic5—22no—
79#5748D511yescharacteristic
80#5522—51no—
81#5139—51no—
82C2×#825—51no—
83#5006—51no—
84C3×#344—51no—
85#4555—51no—
86C2×C5×#41—31no—
87C2×C5×#41—31no—
88C5×#137—32no—
89C5×#137—61no—
90C5×AGL(1,ℤ/8)—32no—
91C5×AGL(1,ℤ/8)—61no—
92C5×#135—62no—
93C2×C5×M16C2×D311yescharacteristic
94Q8×Dic5—61no—
95D4×Dic5—61no—
96D4×Dic5—62no—
97#4072—31no—
98#4072—61no—
99#4072C2×D311yescharacteristic
100C2×C4×Dic5—31no—
101C2×C4×Dic5—61no—
102C2×#681C2×D311yescharacteristic
103#3969—61no—
104#3969—61no—
105#3969—62no—
106#3966—62no—
107#1906—151noSylow
108C23×C3×C5C2×D411yescharacteristic
109C22×C5×D3—21no—
110C22×C5×D3—21no—
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—21no—
118C2×Dic15—21no—
119C2×Dic15—42no—
120C2×Dic15—41no—
121C5×#67—22no—
122C5×#67—22no—
123C5×#67—41no—
124C5×#67—41no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—21no—
127C5×D12—21no—
128C5×D12—21no—
129C5×D12—21no—
130C5×D12C22⋊C412yes—
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C4×C5×D3—41no—
134C4×C5×D3—41no—
135C5×Dic6—21no—
136C5×Dic6—21no—
137C5×Dic6—21no—
138C5×Dic6C22⋊C412yes—
139C2×C3×Dic5—22no—
140D3×Dic5—44no—
141C3×C5×C8—22no—
142C3×#168—41no—
143C2×#235C2×D511yescharacteristic
144C2×#235C2×D511yescharacteristic
145C2×C3×M16—51no—
146C2×C3×M16C2×D511yescharacteristic
147C3×#117—51no—
148#926—51no—
149C2×C4×Dic3—51no—
150#909—21no—
151#909Dic512yescomplemented
152#908—21no—
153#908Dic512yescomplemented
154#904—22no—
155#893—101no—
156#887—101no—
157#67⋊C4—102no—
158#872—101no—
159C42×D3—101no—
160#825—101no—
161#825—101no—
162#825—102no—
163#806—102no—
164C5×#41—32no—
165C5×#41—32no—
166C5×#41—61no—
167C5×#41—61no—
168C5×#41—61no—
169C5×#41—61no—
170C5×#41—61no—
171C5×#41—61no—
172C2×C5×Q8—31no—
173C2×C5×Q8—31no—
174C2×C5×D4—31no—
175C2×C5×D4—31no—
176C2×C5×D4—61no—
177C2×C5×D4—61no—
178C22×C4×C5—61no—
179C22×C4×C5—61no—
180C22×C4×C5C22×D311yescharacteristic
181C22×Dic5—62no—
182C22×Dic5—61no—
183C5×Q16—62no—
184C5×SD16—62no—
185C5×SD16—62no—
186C5×D8—62no—
187C5×M16—21no—
188C5×M16C4×D312yescomplemented
189C2×C5×C8—21no—
190C22⋊Dic5—62no—
191C22⋊Dic5—61no—
192C22⋊Dic5D1212yes—
193C4⋊Dic5—21no—
194C4⋊Dic5—62no—
195C4⋊Dic5—61no—
196C4×Dic5—21no—
197C4×Dic5—31no—
198C4×Dic5—31no—
199C4×Dic5—62no—
200C4×Dic5—61no—
201C4×Dic5—61no—
202#681—21no—
203#681—21no—
204C2×#168—21no—
205#575—31no—
206C4×#41—151no—
207#421—151no—
208C2×#104—151no—
209#410—151no—
210#344—51no—
211#339—151no—
212C22×C3×C5—41no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C2×C5×D3—22no—
217C2×C5×D3—42no—
218C2×C5×D3—41no—
219C2×C5×D3—81no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224Dic15—22no—
225Dic15—41no—
226Dic15—81no—
227C3×Dic5—42no—
228C5×Dic3—22no—
229C5×Dic3—41no—
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—21no—
232C2×#67—21no—
233C22×Dic3—101no—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238#235—21no—
239#235—21no—
240#235C2×Dic512yes—
241#235C22⋊D512yes—
242C2×D12C2×Dic511yescharacteristic, complemented
243C2×D12C22⋊D511yescharacteristic
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—102no—
247C2×Dic6C2×Dic511yescharacteristic, complemented
248C2×Dic6C22⋊D511yescharacteristic
249C3×M16—21no—
250C3×M16—101no—
251C3×M16—101no—
252C3×M16C2×Dic512yescomplemented
253C2×C3×C8—21no—
254C2×C3×C8—101no—
255C3×C4⋊C4—101no—
256C3×C22⋊C4—52no—
257C3×C42—101no—
258#217—101no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—101no—
261Dic3⋊C4—102no—
262C4×Dic3—51no—
263C4×Dic3—51no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C4×Dic3—101no—
267Dic12—22no—
268D24—22no—
269#204—22no—
270#204—22no—
271C23×C5—61no—
272C23×C5—61no—
273C23×C5C2×D1211yescharacteristic
274C5×Q8—32no—
275C5×Q8—61no—
276C5×Q8—61no—
277C5×Q8—61no—
278C5×D4—32no—
279C5×D4—62no—
280C5×D4—62no—
281C5×D4—61no—
282C5×D4—61no—
283C5×D4—61no—
284C5×D4—121no—
285C5×D4—121no—
286C2×C4×C5—61no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—61no—
290C2×C4×C5—121no—
291C2×C4×C5—121no—
292C2×C4×C5C2×C4×D311yescharacteristic
293C2×C4×C5#23511yescharacteristic
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5#23911yescharacteristic
298C2×Dic5—22no—
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5—124no—
302C2×Dic5—122no—
303C2×Dic5—121no—
304C5×C8—22no—
305#168—41no—
306C2×#41—31no—
307C2×#41—31no—
308#137—32no—
309#137—61no—
310AGL(1,ℤ/8)—32no—
311AGL(1,ℤ/8)—61no—
312#135—62no—
313C2×M16—51no—
314C2×M16D3×D511yescharacteristic
315C4×Q8—301no—
316C4×D4—302no—
317C4×D4—301no—
318#117—51no—
319#117—151no—
320#117—301no—
321C2×C42—151no—
322C2×C42—301no—
323#104—301no—
324#104—301no—
325#104—302no—
326#99—302no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5—21no—
330C2×C3×C5#38611yescharacteristic
331C5×D3—42no—
332C5×D3—81no—
333C23×C3D4×D511yescharacteristic
334C22×D3—21no—
335C22×D3—21no—
336C2×C3×C4—102no—
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4#71111yescharacteristic
339C2×C3×C4#71111yescharacteristic
340C2×C3×C4C22×Dic511yescharacteristic
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×C3×C4C2×C22⋊D511yescharacteristic
343#67—22no—
344#67—22no—
345#67—41no—
346#67—41no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—101no—
350C2×Dic3—101no—
351C2×Dic3—202no—
352C2×Dic3—201no—
353D12—21no—
354D12—21no—
355D12—21no—
356D12C22⋊Dic512yes—
357C4×D3—22no—
358C4×D3—22no—
359C4×D3—41no—
360C4×D3—41no—
361C4×D3—204no—
362Dic6—21no—
363Dic6—21no—
364Dic6—21no—
365Dic6C22⋊Dic512yes—
366C3×C8—22no—
367C3×C8—201no—
368C22×C5—41no—
369C22×C5—62no—
370C22×C5—122no—
371C22×C5—121no—
372C22×C5—241no—
373C22×C5C4×D1211yescharacteristic
374C22×C5#88211yescharacteristic
375C22×C5#89511yescharacteristic
376C4×C5—62no—
377C4×C5—121no—
378C4×C5D3×C22⋊C411yescharacteristic
379C4×C5#88411yescharacteristic
380C4×C5#89311yescharacteristic
381C4×C5#89411yescharacteristic
382Dic5—42no—
383Dic5—62no—
384Dic5—121no—
385Dic5—241no—
386#41—32no—
387#41—32no—
388#41—61no—
389#41—61no—
390#41—61no—
391#41—61no—
392#41—61no—
393#41—61no—
394C2×Q8—31no—
395C2×Q8—31no—
396C2×D4—31no—
397C2×D4—31no—
398C2×D4—61no—
399C2×D4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—302no—
403C22×C4—301no—
404C22×C4C2×D3×D511yescharacteristic
405Q16—62no—
406SD16—62no—
407SD16—62no—
408D8—62no—
409M16—21no—
410M16—101no—
411M16—101no—
412M16D3×Dic512yescomplemented
413C2×C8—21no—
414C2×C8—101no—
415C4⋊C4—101no—
416C4⋊C4—302no—
417C4⋊C4—301no—
418C22⋊C4—52no—
419C22⋊C4—302no—
420C22⋊C4—301no—
421C42—101no—
422C42—151no—
423C42—151no—
424C42—302no—
425C42—301no—
426C42—301no—
427C3×C5#190611yescharacteristic, complemented, Hall
428C22×C3—41no—
429C22×C3D4×Dic511yescharacteristic
430C22×C3#408311yescharacteristic
431C22×C3#408511yescharacteristic
432C2×D3—22no—
433C2×D3—42no—
434C2×D3—41no—
435C2×D3—81no—
436C3×C4—202no—
437C3×C4D4×Dic511yescharacteristic
438C3×C4#408111yescharacteristic
439C3×C4#408511yescharacteristic
440C3×C4C2×C22⋊Dic511yescharacteristic
441Dic3—22no—
442Dic3—41no—
443Dic3—102no—
444Dic3—201no—
445Dic3—401no—
446C2×C5—21no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—122no—
450C2×C5—241no—
451C2×C5#466511yescharacteristic
452C23—61no—
453C23—61no—
454C23D5×D1211yescharacteristic
455Q8—32no—
456Q8—61no—
457Q8—61no—
458Q8—61no—
459D4—32no—
460D4—62no—
461D4—62no—
462D4—61no—
463D4—61no—
464D4—61no—
465D4—121no—
466D4—121no—
467C2×C4—61no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4—102no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—301no—
475C2×C4—301no—
476C2×C4—604no—
477C2×C4—602no—
478C2×C4—601no—
479C2×C4#676811yescharacteristic
480C2×C4#677211yescharacteristic
481C2×C4#677711yescharacteristic
482C2×C4C2×D3×Dic511yescharacteristic
483C2×C4D3×C22⋊D511yescharacteristic
484C2×C4D3×C22⋊D511yescharacteristic
485C8—22no—
486C8—201no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3#6550911yescharacteristic
491D3—42no—
492D3—81no—
493C5#6903911yescharacteristic, complemented, Sylow
494C22—41no—
495C22—62no—
496C22—122no—
497C22—121no—
498C22—241no—
499C22Dic5×D1211yescharacteristic
500C22#9141611yescharacteristic
501C22#9147511yescharacteristic
502C4—62no—
503C4—121no—
504C4—202no—
505C4—302no—
506C4—601no—
507C4—1201no—
508C4#9142311yescharacteristic
509C4#9143511yescharacteristic
510C4#9145311yescharacteristic
511C4D3×C22⋊Dic511yescharacteristic
512C3#1060290711yescharacteristic, complemented, Sylow
513C2—21no—
514C2—21no—
515C2—21no—
516C2—122no—
517C2—241no—
518C2#1174890111yescharacteristic
subgroupG/H
centerC4#91453
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC5×#5748C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1906
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754455C2semidirect
3. #11748625C2semidirect
4. #11748424C2semidirect
5. C2×#90978C2semidirect
6. #11746376C2semidirect
7. C3×#64779C2semidirect
15. C5×#909C4semidirect
17. C5×#908C4semidirect
36. #64779D3semidirect
50. C2×C5×D12C2×C4semidirect
54. C2×C5×Dic6C2×C4semidirect
58. C3×C5×M16C2×C4semidirect
151. #909Dic5semidirect
153. #908Dic5semidirect
188. C5×M16C4×D3semidirect
242. C2×D12C2×Dic5semidirect
247. C2×Dic6C2×Dic5semidirect
252. C3×M16C2×Dic5semidirect
412. M16D3×Dic5semidirect
427. C3×C5#1906semidirect
493. C5#69039semidirect
512. C3#10602907semidirect

Maximal subgroups

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

subgroupindex
C5×#57482
#117544552
#117486252
#117484242
C2×#909782
#117463762
C3×#647792
#106029073
#690395