Finite Group Databasebeta

← #14282996

Subgroups — #14282996

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#11754526C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3D5×C3⋊#95C211yesmaximal, characteristic, complemented
4#11746288C211yesmaximal, characteristic, complemented
5C5×#4470C211yesmaximal, characteristic, complemented
6#11745965C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10599095—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3—21no—
11C2×#6772C411yescharacteristic, complemented
12#91813C2211yescharacteristic
13C5×#930C2211yescharacteristic
14C2×C3×#676—21no—
15#91563—21no—
16Dic5×#67—21no—
17#91449C411yescharacteristic, complemented
18#91447—21no—
19#91440—21no—
20#91360C411yescharacteristic, complemented
21#91358C411yescharacteristic, complemented
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3952—21no—
27#90994—21no—
28#69976—51nomaximal, Hall
29#65940—31no—
30#65015D311yescharacteristic, complemented
31D5×#95—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30C2×C411yescharacteristic, complemented
40C2×C5×#67—21no—
41C22×C5×Dic3—21no—
42C2×C5×D12C2×C411yescharacteristic, complemented
43C22×C3×Dic5D411yescharacteristic
44C2×C3×C4×D5—42no—
45C2×C3×C4×D5C2×C411yescharacteristic
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×#1201—21no—
50C2×#1201—21no—
51C2×D3×Dic5—21no—
52C2×D5×Dic3—24no—
53C2×D5×Dic3—42no—
54C2×D5×Dic3—42no—
55#6772—42no—
56C2×C3×C5×C8—21no—
57#6719—21no—
58C4⋊Dic15C2×C411yescharacteristic, complemented
59#6712—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×C4⋊Dic3C2×C411yescharacteristic, complemented
62C2×C3×#168—21no—
63C3×#676—42no—
64Dic3⋊Dic5—21no—
65(C2×D3)⋊Dic5—21no—
66#6665—21no—
67#6665—21no—
68Dic3×Dic5—21no—
69#5791—51no—
70C3×#407—51no—
71C2×C3⋊#95—51no—
72#4470—51no—
73#4470D511yescharacteristic, complemented
74#4467—51no—
75#4467—51no—
76C2×#711—31no—
77C22×C4×D5—61no—
78C22×C4×D5C2×D311yescharacteristic
79C5×#121—31no—
80#4084—31no—
81#4083—61no—
82D4×Dic5—61no—
83#4070—31no—
84C2×#676—21no—
85#4043—31no—
86#4038—31no—
87#4029—61no—
88#4027—61no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95—31no—
91#3963—31no—
92#3963—61no—
93C22⋊#168C2×D311yescharacteristic
94#3952—21no—
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5C22⋊C411yescharacteristic
103C22×C3×D5C22⋊C411yescharacteristic
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—
113C5×#67—41no—
114C5×#67—41no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C5×D12—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5C22⋊C411yescharacteristic
122C2×C3×Dic5C22⋊C411yescharacteristic
123C3×C4×D5—22no—
124C3×C4×D5—22no—
125C3×C4×D5—41no—
126C3×C4×D5—41no—
127#1201—42no—
128#1201—42no—
129D3×Dic5—42no—
130D5×Dic3—48no—
131C3×C5×C8—41no—
132C3×#168—41no—
133C23×C3×C4—51no—
134C23×Dic3—101no—
135C2×#235—51no—
136C2×C3×M16—101no—
137#953—101no—
138#930—51no—
139#930C2×D511yescharacteristic
140#929—101no—
141C4×#67—101no—
142C4×#67—101no—
143#926—51no—
144#924—51no—
145#924—51no—
146C3×C22⋊C8—51no—
147C3×C22⋊C8—101no—
148C3×C22⋊C8C2×D511yescharacteristic
149C3⋊#95—51no—
150C3⋊#95—101no—
151C3⋊#95C2×D511yescharacteristic
152C23×D5D1211yescharacteristic
153C2×C5×D4—31no—
154C2×C5×D4—61no—
155C22×C4×C5—61no—
156C22×C4×C5C22×D311yescharacteristic
157C2×C22⋊D5—61no—
158C2×C22⋊D5—61no—
159C22×Dic5—61no—
160C22×Dic5—61no—
161C22×Dic5D1211yescharacteristic
162#711—122no—
163C2×C4×D5—42no—
164C2×C4×D5—64no—
165C2×C4×D5—122no—
166C2×C4×D5—122no—
167C2×C4×D5C4×D311yescharacteristic
168C2×C4×D5C4×D311yescharacteristic
169C2×C4×D5#6711yescharacteristic
170C2×C4×D5#6711yescharacteristic
171C2×Dic10—31no—
172C2×C5×C8—21no—
173C5×C4⋊C4—31no—
174C5×C22⋊C4—61no—
175C22⋊Dic5—61no—
176C22⋊Dic5—61no—
177#685—61no—
178#685—61no—
179C4⋊Dic5—31no—
180C4⋊Dic5—61no—
181#683—61no—
182C4×Dic5—61no—
183C2×#168—21no—
184#676—42no—
185#525—151no—
186#407—51no—
187C2×#95—151no—
188#328—151no—
189#328—151no—
190#327—31no—
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—41no—
198C2×C5×D3—41no—
199C2×C5×D3—41no—
200C2×C3×D5—24no—
201C2×C3×D5—24no—
202C2×C3×D5—21no—
203C2×C3×D5—21no—
204C2×C3×D5—21no—
205C2×C3×D5—21no—
206C2×C3×D5#9912yes—
207C2×C3×D5#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210Dic15—42no—
211Dic15—41no—
212Dic15—41no—
213C3×Dic5—21no—
214C3×Dic5—21no—
215C5×Dic3—42no—
216C5×Dic3—41no—
217C24×C3—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4—202no—
224C22×C3×C4C22×D511yescharacteristic
225C2×#67—21no—
226C2×#67—101no—
227C2×#67—101no—
228C22×Dic3—21no—
229C22×Dic3—104no—
230C22×Dic3—101no—
231C22×Dic3—202no—
232C22×Dic3—202no—
233#235—202no—
234C2×D12C4×D511yescharacteristic, complemented
235C2×C4×D3—101no—
236C2×Dic6—51no—
237C3×M16—202no—
238C2×C3×C8—21no—
239C2×C3×C8—101no—
240#217—101no—
241#217—101no—
242#217—101no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—101no—
245C4⋊Dic3—51no—
246C4⋊Dic3C4×D511yescharacteristic, complemented
247Dic3⋊C4—101no—
248Dic3⋊C4—101no—
249C4×Dic3—101no—
250C23×C5—61no—
251C23×C5C2×D1211yescharacteristic
252C22×D5—21no—
253C22×D5—21no—
254C22×D5—22no—
255C22×D5—22no—
256C22×D5(C2×D3)⋊C411yescharacteristic
257C22×D5(C2×D3)⋊C411yescharacteristic
258C5×D4—121no—
259C5×D4—121no—
260C5×D4—121no—
261C2×C4×C5—41no—
262C2×C4×C5—62no—
263C2×C4×C5—61no—
264C2×C4×C5—121no—
265C2×C4×C5—121no—
266C2×C4×C5C2×C4×D311yescharacteristic
267C2×C4×C5C2×#6711yescharacteristic
268C22⋊D5—122no—
269C22⋊D5—122no—
270C2×Dic5—41no—
271C2×Dic5—62no—
272C2×Dic5—61no—
273C2×Dic5—61no—
274C2×Dic5—122no—
275C2×Dic5—121no—
276C2×Dic5—121no—
277C2×Dic5(C2×D3)⋊C411yescharacteristic
278C2×Dic5(C2×D3)⋊C411yescharacteristic
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—41no—
282C4×D5—41no—
283C4×D5—128no—
284Dic10—121no—
285C5×C8—41no—
286#168—41no—
287C2×#41—151no—
288C23×C4—51no—
289C23×C4—301no—
290C2×M16—101no—
291#123—301no—
292C22⋊Q8—151no—
293C22⋊Q8—151no—
294#121—31no—
295#121—151no—
296#120—301no—
297C4×D4—301no—
298C4×D4—301no—
299#117—151no—
300C22⋊C8—51no—
301C22⋊C8—101no—
302C22⋊C8D3×D511yescharacteristic
303#95—31no—
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—22no—
312C3×D5—22no—
313C5×D3—81no—
314C23×C3—51no—
315C23×C3—51no—
316C23×C3—102no—
317C23×C3—102no—
318C23×C3—101no—
319C23×C3—101no—
320C23×C3D4×D511yescharacteristic
321C22×D3—21no—
322C2×C3×C4—41no—
323C2×C3×C4—51no—
324C2×C3×C4—51no—
325C2×C3×C4—102no—
326C2×C3×C4—102no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4C2×C4×D511yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332#67—41no—
333#67—41no—
334#67—202no—
335#67—202no—
336C2×Dic3—22no—
337C2×Dic3—21no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—102no—
341C2×Dic3—101no—
342C2×Dic3—101no—
343C2×Dic3—208no—
344C2×Dic3—201no—
345C2×Dic3—201no—
346D12—41no—
347C4×D3—202no—
348Dic6—201no—
349C3×C8—41no—
350C3×C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—121no—
354C22×C5—121no—
355C22×C5—121no—
356C22×C5#90811yescharacteristic
357C22×C5#90911yescharacteristic
358C22×C5C2×(C2×D3)⋊C411yescharacteristic
359C2×D5—24no—
360C2×D5—24no—
361C2×D5—21no—
362C2×D5—21no—
363C2×D5—21no—
364C2×D5—21no—
365C2×D5#80612yes—
366C2×D5#82512yes—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—122no—
370C4×C5—121no—
371Dic5—21no—
372Dic5—21no—
373Dic5—122no—
374Dic5—121no—
375Dic5—121no—
376C24—51no—
377#41—602no—
378C2×Q8—151no—
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—301no—
382C2×D4—301no—
383C22×C4—51no—
384C22×C4—51no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—61no—
389C22×C4—202no—
390C22×C4—301no—
391C22×C4—304no—
392C22×C4—301no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—202no—
397C2×C8—21no—
398C2×C8—101no—
399C4⋊C4—31no—
400C4⋊C4—151no—
401C4⋊C4—301no—
402C4⋊C4—301no—
403C22⋊C4—61no—
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—52no—
413C22×C3—52no—
414C22×C3—104no—
415C22×C3—104no—
416C22×C3—101no—
417C22×C3—101no—
418C22×C3—101no—
419C22×C3—101no—
420C22×C3D5×C22⋊C411yescharacteristic
421C22×C3#405711yescharacteristic
422C22×C3#406111yescharacteristic
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—101no—
429C3×C4—101no—
430Dic3—42no—
431Dic3—41no—
432Dic3—202no—
433Dic3—201no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—241no—
438C2×C5C2×#80611yescharacteristic
439C2×C5#513311yescharacteristic
440C2×C5C2×#82511yescharacteristic
441D5—22no—
442D5—22no—
443C23—51no—
444C23—51no—
445C23—61no—
446C23—102no—
447C23—102no—
448C23—101no—
449C23—101no—
450C23D5×D1211yescharacteristic
451Q8—601no—
452D4—121no—
453D4—121no—
454D4—121no—
455D4—602no—
456D4—602no—
457C2×C4—41no—
458C2×C4—51no—
459C2×C4—51no—
460C2×C4—62no—
461C2×C4—61no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—201no—
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×C4D5×#6711yescharacteristic
478C8—41no—
479C8—201no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—102no—
483C2×C3—102no—
484C2×C3D5×#9911yescharacteristic
485C2×C3#6506011yescharacteristic
486C2×C3D5×#10411yescharacteristic
487D3—81no—
488C5#6997611yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—52no—
492C22—52no—
493C22—104no—
494C22—104no—
495C22—101no—
496C22—101no—
497C22—101no—
498C22—101no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22#9125011yescharacteristic
503C22#9126011yescharacteristic
504C22D5×(C2×D3)⋊C411yescharacteristic
505C4—21no—
506C4—21no—
507C4—101no—
508C4—101no—
509C4—122no—
510C4—121no—
511C4—602no—
512C4—601no—
513C4—601no—
514C3#1059909511yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—102no—
518C2—102no—
519C2—241no—
520C2D5×#80611yescharacteristic
521C2#1174760511yescharacteristic
522C2D5×#82511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754526C2
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. C3×#65015C2semidirect
3. D5×C3⋊#95C2semidirect
4. #11746288C2semidirect
5. C5×#4470C2semidirect
6. #11745965C2semidirect
7. #11745957C2semidirect
11. C2×#6772C4semidirect
17. #91449C4semidirect
20. #91360C4semidirect
21. #91358C4semidirect
30. #65015D3semidirect
39. C2×Dic30C2×C4semidirect
42. C2×C5×D12C2×C4semidirect
58. C4⋊Dic15C2×C4semidirect
61. C5×C4⋊Dic3C2×C4semidirect
73. #4470D5semidirect
234. C2×D12C4×D5semidirect
246. C4⋊Dic3C4×D5semidirect
409. C3×C5#1504semidirect
488. C5#69976semidirect
514. C3#10599095semidirect

Maximal subgroups

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

subgroupindex
#117545262
C3×#650152
D5×C3⋊#952
#117462882
C5×#44702
#117459652
#117459572
#105990953
#699765