Finite Group Databasebeta

← #14282998

Subgroups — #14282998

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754341C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic, complemented
3D3×#3963C211yesmaximal, characteristic, complemented
4#11746288C211yesmaximal, characteristic, complemented
5C3×#64690C211yesmaximal, characteristic, complemented
6#11745964C211yesmaximal, characteristic, complemented
7#11745955C211yesmaximal, characteristic, complemented
8#10600769—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C22×D3×Dic5—21no—
11C2×#6765C411yescharacteristic, complemented
12#91813C2211yescharacteristic
13C2×C5×ΓL(1,𝔽25)—21no—
14C3×#4076C2211yescharacteristic
15#91568—21no—
16Dic3×C22⋊D5—21no—
17#91456C411yescharacteristic, complemented
18#91452—21no—
19#91441—21no—
20#91365C411yescharacteristic, complemented
21#91338C411yescharacteristic, complemented
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×(C2×D3)⋊C8—21no—
26C3×#3963C2211yescharacteristic
27#90994—21no—
28#68302—51nomaximal, Hall
29#66125—31no—
30C5×#407—31no—
31C2×#3963—31no—
32#64690—31no—
33#64690D311yescharacteristic, complemented
34#64687—31no—
35#64687—31no—
36C23×C5×D3D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30C2×C411yescharacteristic, complemented
40C22×C5×Dic3D411yescharacteristic
41C2×C4×C5×D3—42no—
42C2×C4×C5×D3C2×C411yescharacteristic
43C2×C4×C5×D3C2×C411yescharacteristic
44C2×C4×C5×D3D411yescharacteristic
45C2×C4×C5×D3D411yescharacteristic
46C2×C3×C22⋊D5—21no—
47C22×C3×Dic5—21no—
48C2×C3×D20C2×C411yescharacteristic, complemented
49C2×#1201—21no—
50C2×#1201—21no—
51C2×D3×Dic5—24no—
52C2×D3×Dic5—42no—
53C2×D3×Dic5—42no—
54C2×D5×Dic3—21no—
55#6765—42no—
56C2×C3×C5×C8—21no—
57#6719—21no—
58C4⋊Dic15C2×C411yescharacteristic, complemented
59#6712—21no—
60C2×C5×C3⋊C8—21no—
61C5×ΓL(1,𝔽25)—42no—
62C3×#685—21no—
63C3×C4⋊Dic5C2×C411yescharacteristic, complemented
64#6668—21no—
65(C2×D3)⋊Dic5—21no—
66(C2×D3)⋊Dic5—21no—
67#6665—21no—
68Dic3×Dic5—21no—
69#5606—51no—
70#4726D511yescharacteristic, complemented
71D3×#95—51no—
72C3×#327—51no—
73#4537—51no—
74#4467—51no—
75#4452—51no—
76C23×C4×C5—31no—
77C23×Dic5—61no—
78C2×#709—31no—
79C2×C5×M16—61no—
80#4099—61no—
81#4076—31no—
82#4076C2×D311yescharacteristic
83#4075—61no—
84C4×C22⋊D5—61no—
85C4×C22⋊D5—61no—
86#4072—31no—
87#4070—31no—
88#4070—31no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92#3963—31no—
93#3963—61no—
94#3963C2×D311yescharacteristic
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—22no—
100C22×C5×D3—22no—
101C22×C5×D3C22⋊C411yescharacteristic
102C22×C5×D3C22⋊C411yescharacteristic
103C22×C3×D5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×Dic15—22no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112Dic30—41no—
113C2×C5×Dic3—41no—
114C2×C5×Dic3C22⋊C411yescharacteristic
115C2×C5×Dic3C22⋊C411yescharacteristic
116C4×C5×D3—22no—
117C4×C5×D3—22no—
118C4×C5×D3—41no—
119C4×C5×D3—41no—
120C3×C22⋊D5—41no—
121C3×C22⋊D5—41no—
122C2×C3×Dic5—22no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—41no—
125C2×C3×Dic5—41no—
126C3×D20—41no—
127#1201—42no—
128#1201—42no—
129D3×Dic5—48no—
130D5×Dic3—42no—
131C3×C5×C8—41no—
132C5×C3⋊C8—41no—
133C2×#237—51no—
134C22×C4×D3—101no—
135C22×C4×D3C2×D511yescharacteristic
136C3×#121—51no—
137#938—51no—
138#937—101no—
139D4×Dic3—101no—
140#924—51no—
141C2×ΓL(1,𝔽25)—21no—
142#897—51no—
143#892—51no—
144#883—101no—
145#67⋊C4—101no—
146C3×C22⋊C8C2×D511yescharacteristic
147C3×#95—51no—
148C3⋊#95—51no—
149C3⋊#95—101no—
150#830C2×D511yescharacteristic
151(C2×D3)⋊C8—21no—
152C24×C5—31no—
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—31no—
158C22×C4×C5—122no—
159C22×C4×C5C22×D311yescharacteristic
160C2×C22⋊D5—21no—
161C2×C22⋊D5—61no—
162C2×C22⋊D5—61no—
163C22×Dic5—21no—
164C22×Dic5—64no—
165C22×Dic5—61no—
166C22×Dic5—122no—
167C22×Dic5—122no—
168#709—122no—
169C2×D20C4×D311yescharacteristic, complemented
170C2×C4×D5—61no—
171C2×Dic10—31no—
172C5×M16—122no—
173C2×C5×C8—21no—
174C2×C5×C8—61no—
175C22⋊Dic5—61no—
176C22⋊Dic5—61no—
177C22⋊Dic5—61no—
178#685—21no—
179#685—61no—
180C4⋊Dic5—31no—
181C4⋊Dic5C4×D311yescharacteristic, complemented
182#683—61no—
183#683—61no—
184C4×Dic5—61no—
185#525—151no—
186#407—31no—
187C2×#95—151no—
188#328—151no—
189#328—151no—
190#327—51no—
191#327—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×C5×D3—24no—
198C2×C5×D3—24no—
199C2×C5×D3—21no—
200C2×C5×D3—21no—
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3#9912yes—
204C2×C5×D3#10412yes—
205C2×C3×D5—41no—
206C2×C3×D5—41no—
207C2×C3×D5—41no—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210Dic15—42no—
211Dic15—41no—
212Dic15—41no—
213C3×Dic5—42no—
214C3×Dic5—41no—
215C5×Dic3—21no—
216C5×Dic3—21no—
217C23×D3D2011yescharacteristic
218C2×C3×D4—51no—
219C2×C3×D4—101no—
220C22×C3×C4—101no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—101no—
223C2×#67—101no—
224C22×Dic3—101no—
225C22×Dic3—101no—
226C22×Dic3D2011yescharacteristic
227#237—202no—
228C2×C4×D3—42no—
229C2×C4×D3—104no—
230C2×C4×D3—202no—
231C2×C4×D3—202no—
232C2×C4×D3C4×D511yescharacteristic
233C2×C4×D3C4×D511yescharacteristic
234C2×C4×D3C22⋊D511yescharacteristic
235C2×C4×D3C22⋊D511yescharacteristic
236C2×Dic6—51no—
237C2×C3×C8—21no—
238C3×C4⋊C4—51no—
239C3×C22⋊C4—101no—
240#217—101no—
241#217—101no—
242(C2×D3)⋊C4—101no—
243(C2×D3)⋊C4—101no—
244C4⋊Dic3—51no—
245C4⋊Dic3—101no—
246Dic3⋊C4—101no—
247C4×Dic3—101no—
248C2×C3⋊C8—21no—
249ΓL(1,𝔽25)—42no—
250C23×C5—31no—
251C23×C5—31no—
252C23×C5—62no—
253C23×C5—62no—
254C23×C5—61no—
255C23×C5—61no—
256C23×C5D3×D411yescharacteristic
257C22×D5—21no—
258C2×C4×C5—31no—
259C2×C4×C5—31no—
260C2×C4×C5—41no—
261C2×C4×C5—62no—
262C2×C4×C5—62no—
263C2×C4×C5—121no—
264C2×C4×C5—121no—
265C2×C4×C5—121no—
266C2×C4×C5C2×C4×D311yescharacteristic
267C2×C4×C5D3×D411yescharacteristic
268C22⋊D5—41no—
269C22⋊D5—41no—
270C22⋊D5—122no—
271C22⋊D5—122no—
272C2×Dic5—22no—
273C2×Dic5—21no—
274C2×Dic5—41no—
275C2×Dic5—41no—
276C2×Dic5—62no—
277C2×Dic5—61no—
278C2×Dic5—61no—
279C2×Dic5—128no—
280C2×Dic5—121no—
281C2×Dic5—121no—
282D20—41no—
283C4×D5—122no—
284Dic10—121no—
285C5×C8—41no—
286C5×C8—121no—
287C2×#41—151no—
288C23×C4—31no—
289C23×C4—301no—
290C2×M16—61no—
291#123—301no—
292C22⋊Q8—151no—
293C22⋊Q8—151no—
294#121—51no—
295#121—151no—
296#120—301no—
297C4×D4—301no—
298C4×D4—301no—
299#117—151no—
300C22⋊C8—31no—
301C22⋊C8—61no—
302C22⋊C8D3×D511yescharacteristic
303#95—51no—
304#95—151no—
305#95—301no—
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311C3×D5—81no—
312C5×D3—22no—
313C5×D3—22no—
314C23×C3—101no—
315C23×C3C2×D2011yescharacteristic
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3#68511yescharacteristic
321C22×D3#68511yescharacteristic
322C3×D4—201no—
323C3×D4—201no—
324C3×D4—201no—
325C2×C3×C4—41no—
326C2×C3×C4—102no—
327C2×C3×C4—101no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4C2×C4×D511yescharacteristic
331C2×C3×C4C2×C22⋊D511yescharacteristic
332#67—202no—
333#67—202no—
334C2×Dic3—41no—
335C2×Dic3—102no—
336C2×Dic3—101no—
337C2×Dic3—101no—
338C2×Dic3—202no—
339C2×Dic3—201no—
340C2×Dic3—201no—
341C2×Dic3#68511yescharacteristic
342C2×Dic3#68511yescharacteristic
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—41no—
346C4×D3—41no—
347C4×D3—208no—
348Dic6—201no—
349C3×C8—41no—
350C3⋊C8—41no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—32no—
354C22×C5—32no—
355C22×C5—64no—
356C22×C5—64no—
357C22×C5—61no—
358C22×C5—61no—
359C22×C5—61no—
360C22×C5—61no—
361C22×C5D3×C22⋊C411yescharacteristic
362C22×C5#91111yescharacteristic
363C22×C5#91511yescharacteristic
364C2×D5—41no—
365C2×D5—41no—
366C2×D5—41no—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—61no—
370C4×C5—61no—
371Dic5—42no—
372Dic5—41no—
373Dic5—122no—
374Dic5—121no—
375Dic5—121no—
376C24—31no—
377#41—602no—
378C2×Q8—151no—
379C2×D4—51no—
380C2×D4—101no—
381C2×D4—301no—
382C2×D4—301no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—101no—
389C22×C4—122no—
390C22×C4—301no—
391C22×C4—304no—
392C22×C4—301no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—122no—
397C2×C8—21no—
398C2×C8—61no—
399C4⋊C4—51no—
400C4⋊C4—151no—
401C4⋊C4—301no—
402C4⋊C4—301no—
403C22⋊C4—101no—
404C22⋊C4—301no—
405C22⋊C4—301no—
406C22⋊C4—301no—
407C22⋊C4—301no—
408C42—301no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—201no—
413C22×C3—201no—
414C22×C3—201no—
415C22×C3#405411yescharacteristic
416C22×C3#405511yescharacteristic
417C22×C3C2×#68511yescharacteristic
418C2×D3—24no—
419C2×D3—24no—
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3#393812yes—
425C2×D3#395712yes—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—202no—
429C3×C4—201no—
430Dic3—21no—
431Dic3—21no—
432Dic3—202no—
433Dic3—201no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—62no—
438C2×C5—62no—
439C2×C5D3×#9911yescharacteristic
440C2×C5#477111yescharacteristic
441C2×C5D3×#10411yescharacteristic
442D5—81no—
443C23—31no—
444C23—31no—
445C23—62no—
446C23—62no—
447C23—61no—
448C23—61no—
449C23—101no—
450C23D3×D2011yescharacteristic
451Q8—601no—
452D4—201no—
453D4—201no—
454D4—201no—
455D4—602no—
456D4—602no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—41no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—102no—
463C2×C4—101no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—201no—
468C2×C4—201no—
469C2×C4—302no—
470C2×C4—301no—
471C2×C4—301no—
472C2×C4—602no—
473C2×C4—608no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4C4×D3×D511yescharacteristic
477C2×C4D3×C22⋊D511yescharacteristic
478C8—41no—
479C8—121no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—401no—
483C2×C3C2×#393811yescharacteristic
484C2×C3#6542211yescharacteristic
485C2×C3C2×#395711yescharacteristic
486D3—22no—
487D3—22no—
488C5#6830211yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—32no—
492C22—32no—
493C22—64no—
494C22—64no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—201no—
500C22—201no—
501C22—201no—
502C22#9125411yescharacteristic
503C22#9127411yescharacteristic
504C22D3×#68511yescharacteristic
505C4—21no—
506C4—21no—
507C4—61no—
508C4—61no—
509C4—202no—
510C4—201no—
511C4—602no—
512C4—601no—
513C4—601no—
514C3#1060076911yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—62no—
518C2—62no—
519C2—401no—
520C2D3×#393811yescharacteristic
521C2#1174813811yescharacteristic
522C2D3×#395711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754341C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4726C2semidirect
3. D3×#3963C2semidirect
4. #11746288C2semidirect
5. C3×#64690C2semidirect
6. #11745964C2semidirect
7. #11745955C2semidirect
11. C2×#6765C4semidirect
17. #91456C4semidirect
20. #91365C4semidirect
21. #91338C4semidirect
33. #64690D3semidirect
39. C2×Dic30C2×C4semidirect
48. C2×C3×D20C2×C4semidirect
58. C4⋊Dic15C2×C4semidirect
63. C3×C4⋊Dic5C2×C4semidirect
70. #4726D5semidirect
169. C2×D20C4×D3semidirect
181. C4⋊Dic5C4×D3semidirect
409. C3×C5#1504semidirect
488. C5#68302semidirect
514. C3#10600769semidirect

Maximal subgroups

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

subgroupindex
#117543412
C5×#47262
D3×#39632
#117462882
C3×#646902
#117459642
#117459552
#106007693
#683025