Finite Group Databasebeta

← #14282986

Subgroups — #14282986

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#11754527C211yesmaximal, characteristic
2C3×D5×#95C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C5×#4452C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745958C211yesmaximal, characteristic, complemented
8#10599127—31nomaximal, Hall
9C22×C3×C4×D5—21no—
10C22×C3×C4×D5C2211yescharacteristic
11C2×#6773C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C5×#924C2211yescharacteristic
14#91564—21no—
15#91552—21no—
16#91450C411yescharacteristic, complemented
17#91444—21no—
18#91359C411yescharacteristic, complemented
19#91358C411yescharacteristic, complemented
20#91348—21no—
21C2×#6649—21no—
22C3×C5×#95C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×#3963—21no—
26C3×#3963C2211yescharacteristic
27#90955—21no—
28#69398—51nomaximal, Hall
29#65961—31no—
30#65015—31no—
31D5×#95D311yescharacteristic, complemented
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C2×D60C2×C411yescharacteristic, complemented
41C2×C5×Dic6C2×C411yescharacteristic, complemented
42C22×C3×Dic5—21no—
43C22×C3×Dic5D411yescharacteristic
44C2×C3×C4×D5—24no—
45C2×C3×C4×D5—42no—
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5C2×C411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C2×C3×C4×D5D411yescharacteristic
52C2×#1202—21no—
53C2×#1202—21no—
54C2×#1200—21no—
55#6773—42no—
56#6714—21no—
57C4⋊Dic15C2×C411yescharacteristic, complemented
58C2×C3⋊#168—21no—
59C5×#217—21no—
60C5×C4⋊Dic3C2×C411yescharacteristic, complemented
61C5×Dic3⋊C4—21no—
62C2×C5×C3⋊C8—21no—
63#6669—21no—
64#6667—21no—
65#6665—21no—
66#6665—21no—
67Dic3×Dic5—21no—
68#6649—42no—
69#5791—51no—
70C2×C3×#95—51no—
71#5207—51no—
72#4452—51no—
73#4452D511yescharacteristic, complemented
74#4451—51no—
75#4451—51no—
76C2×#713—31no—
77C22×C4×D5—21no—
78C22×C4×D5C2×D311yescharacteristic
79C5×C22⋊Q8—31no—
80#4092—31no—
81#4076—31no—
82C2×#676—61no—
83#4041—31no—
84#4040—61no—
85#4039—61no—
86#4038—31no—
87#4028—61no—
88#4027—61no—
89C5×C22⋊C8—31no—
90C5×#95C2×D311yescharacteristic
91#3963—21no—
92#3963C2×D311yescharacteristic
93C22⋊#168—31no—
94#3952—61no—
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—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—22no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110#1220—41no—
111#1220—41no—
112C2×Dic15—21no—
113D60—41no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C5×Dic6—41no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—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—
127C3×C4×D5—48no—
128#1202—42no—
129#1202—42no—
130#1200—42no—
131C3⋊#168—41no—
132C5×C3⋊C8—41no—
133C23×C3×C4—51no—
134C23×C3×C4—101no—
135C2×#235—51no—
136#953—101no—
137#930—51no—
138#930—51no—
139#929—101no—
140C4×#67—101no—
141C4×#67—101no—
142#926—51no—
143#924—51no—
144#924C2×D511yescharacteristic
145C2×#208—101no—
146C3×#95—51no—
147C3×#95—101no—
148C3×#95C2×D511yescharacteristic
149#830—51no—
150#830—101no—
151#830C2×D511yescharacteristic
152C23×D5#6711yescharacteristic
153C2×C5×Q8—31no—
154C22×C4×C5—21no—
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—61no—
157C22×Dic5—21no—
158C22×Dic5#6711yescharacteristic
159#713—122no—
160C2×D20—31no—
161C2×D20—61no—
162C2×D20—61no—
163C2×C4×D5—24no—
164C2×C4×D5—42no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—61no—
168C2×C4×D5C4×D311yescharacteristic
169C2×C4×D5C4×D311yescharacteristic
170C2×C4×D5D1211yescharacteristic
171C2×C4×D5D1211yescharacteristic
172C2×C5×C8—61no—
173C5×C4⋊C4—31no—
174C5×C4⋊C4—61no—
175C5×C22⋊C4—61no—
176#685—61no—
177#685—61no—
178#685—61no—
179#685—61no—
180C4⋊Dic5—31no—
181#683—61no—
182C4×Dic5—61no—
183C2×#168—61no—
184#676—122no—
185#525—151no—
186#407—151no—
187C2×#95—51no—
188#328—31no—
189#328—151no—
190#327—151no—
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×D15—41no—
198C2×D15—41no—
199C2×D15—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—
210C3×C4×C5—42no—
211Dic15—41no—
212C3×Dic5—21no—
213C3×Dic5—21no—
214C3×Dic5—42no—
215C5×Dic3—41no—
216C5×Dic3—41no—
217C24×C3—51no—
218C22×C3×C4—21no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4—51no—
224C22×C3×C4—104no—
225C22×C3×C4—101no—
226C22×C3×C4—202no—
227C22×C3×C4—202no—
228C22×C3×C4—202no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—101no—
231C2×#67—101no—
232C2×#67—101no—
233#235—202no—
234C2×D12—51no—
235C2×C4×D3—101no—
236C2×Dic6C4×D511yescharacteristic, complemented
237#217—21no—
238#217—101no—
239#217—101no—
240(C2×D3)⋊C4—101no—
241(C2×D3)⋊C4—101no—
242C4⋊Dic3—51no—
243C4⋊Dic3C4×D511yescharacteristic, complemented
244Dic3⋊C4—21no—
245Dic3⋊C4—101no—
246C4×Dic3—101no—
247#208—202no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—101no—
250C23×C5C2×#6711yescharacteristic
251C22×D5—21no—
252C22×D5—21no—
253C22×D5—22no—
254C22×D5—22no—
255C22×D5—61no—
256C22×D5(C2×D3)⋊C411yescharacteristic
257C22×D5(C2×D3)⋊C411yescharacteristic
258C5×Q8—121no—
259C2×C4×C5—22no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5C2×C4×D311yescharacteristic
266C2×C4×C5C2×D1211yescharacteristic
267C22⋊D5—121no—
268C22⋊D5—121no—
269C2×Dic5—22no—
270C2×Dic5—41no—
271C2×Dic5—41no—
272C2×Dic5—41no—
273C2×Dic5—61no—
274C2×Dic5(C2×D3)⋊C411yescharacteristic
275C2×Dic5(C2×D3)⋊C411yescharacteristic
276D20—121no—
277D20—122no—
278D20—122no—
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—41no—
282C4×D5—41no—
283C4×D5—48no—
284C4×D5—122no—
285C5×C8—121no—
286#168—121no—
287C2×#41—151no—
288C23×C4—51no—
289C23×C4—101no—
290C2×M16—301no—
291#123—301no—
292C22⋊Q8—31no—
293C22⋊Q8—151no—
294#121—151no—
295#121—151no—
296#120—301no—
297C4×D4—301no—
298C4×D4—301no—
299#117—151no—
300C22⋊C8—31no—
301C22⋊C8—151no—
302C22⋊C8—301no—
303#95—51no—
304#95—101no—
305#95D3×D511yescharacteristic
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311D15—81no—
312C3×D5—22no—
313C3×D5—22no—
314C23×C3—51no—
315C23×C3—51no—
316C23×C3—102no—
317C23×C3—102no—
318C23×C3—101no—
319C23×C3—101no—
320C23×C3D4×D511yescharacteristic
321C22×D3—101no—
322C2×C3×C4—22no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—51no—
327C2×C3×C4—51no—
328C2×C3×C4—102no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4—208no—
334C2×C3×C4—201no—
335C2×C3×C4—201no—
336C2×C3×C4—201no—
337C2×C3×C4C2×C4×D511yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339#67—202no—
340#67—202no—
341#67—201no—
342#67—201no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—101no—
346D12—201no—
347C4×D3—202no—
348Dic6—41no—
349C3⋊C8—41no—
350C3⋊C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5C2×(C2×D3)⋊C411yescharacteristic
354C22×C5#93211yescharacteristic
355C22×C5#94211yescharacteristic
356C2×D5—24no—
357C2×D5—24no—
358C2×D5—21no—
359C2×D5—21no—
360C2×D5—21no—
361C2×D5—21no—
362C2×D5—121no—
363C2×D5—121no—
364C2×D5—121no—
365C2×D5#80512yes—
366C2×D5#80612yes—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—42no—
370C4×C5—121no—
371C4×C5—121no—
372Dic5—21no—
373Dic5—21no—
374Dic5—42no—
375Dic5—121no—
376C24—51no—
377#41—602no—
378C2×Q8—31no—
379C2×D4—151no—
380C2×D4—301no—
381C2×D4—301no—
382C2×D4—301no—
383C22×C4—21no—
384C22×C4—51no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—104no—
390C22×C4—101no—
391C22×C4—202no—
392C22×C4—202no—
393C22×C4—202no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—602no—
397C2×C8—61no—
398C2×C8—301no—
399C4⋊C4—31no—
400C4⋊C4—61no—
401C4⋊C4—151no—
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#406011yescharacteristic
422C22×C3#406411yescharacteristic
423C2×D3—201no—
424C2×D3—201no—
425C2×D3—201no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—101no—
430C3×C4—101no—
431C3×C4—202no—
432Dic3—41no—
433Dic3—41no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5C2×#80511yescharacteristic
438C2×C5C2×#80611yescharacteristic
439C2×C5#496611yescharacteristic
440D5—22no—
441D5—22no—
442D5—241no—
443C23—51no—
444C23—51no—
445C23—102no—
446C23—102no—
447C23—101no—
448C23—101no—
449C23—301no—
450C23D5×#6711yescharacteristic
451Q8—121no—
452D4—601no—
453D4—602no—
454D4—602no—
455D4—601no—
456D4—601no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—51no—
462C2×C4—51no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—102no—
468C2×C4—201no—
469C2×C4—201no—
470C2×C4—208no—
471C2×C4—201no—
472C2×C4—201no—
473C2×C4—201no—
474C2×C4—301no—
475C2×C4—602no—
476C2×C4C4×D3×D511yescharacteristic
477C2×C4D5×D1211yescharacteristic
478C8—121no—
479C8—601no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—102no—
483C2×C3—102no—
484C2×C3D5×#9911yescharacteristic
485C2×C3#6509211yescharacteristic
486C2×C3D5×#10411yescharacteristic
487D3—401no—
488C5#6939811yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—52no—
492C22—52no—
493C22—104no—
494C22—104no—
495C22—101no—
496C22—101no—
497C22—101no—
498C22—101no—
499C22—601no—
500C22—601no—
501C22—601no—
502C22D5×(C2×D3)⋊C411yescharacteristic
503C22#9149111yescharacteristic
504C22#9151511yescharacteristic
505C4—21no—
506C4—21no—
507C4—42no—
508C4—101no—
509C4—101no—
510C4—121no—
511C4—121no—
512C4—202no—
513C4—601no—
514C3#1059912711yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—102no—
518C2—102no—
519C2—1201no—
520C2D5×#80511yescharacteristic
521C2D5×#80611yescharacteristic
522C2#1174750011yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754527C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×D5×#95C2semidirect
3. #11748499C2semidirect
4. #11746272C2semidirect
5. C5×#4452C2semidirect
6. #11745962C2semidirect
7. #11745958C2semidirect
11. C2×#6773C4semidirect
16. #91450C4semidirect
18. #91359C4semidirect
19. #91358C4semidirect
31. D5×#95D3semidirect
40. C2×D60C2×C4semidirect
41. C2×C5×Dic6C2×C4semidirect
57. C4⋊Dic15C2×C4semidirect
60. C5×C4⋊Dic3C2×C4semidirect
73. #4452D5semidirect
236. C2×Dic6C4×D5semidirect
243. C4⋊Dic3C4×D5semidirect
409. C3×C5#1504semidirect
488. C5#69398semidirect
514. C3#10599127semidirect

Maximal subgroups

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

subgroupindex
#117545272
C3×D5×#952
#117484992
#117462722
C5×#44522
#117459622
#117459582
#105991273
#693985