Finite Group Databasebeta

← #14313223

Subgroups — #14313223

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66138C211yesmaximal, characteristic
2C2×#91117C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4#11746000C212yesmaximal, complemented
5#11745994C212yesmaximal, complemented
6#10600808—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C3×C22⋊D5C411yescharacteristic, complemented
9C2×#6710—21no—
10C2×C5×#217—21no—
11C3×#4099—21no—
12C2×C3×C22⋊Dic5C411yescharacteristic, complemented
13C3×#4085—21no—
14C3×#4085—21no—
15C3×#4083C411yescharacteristic, complemented
16C3×#4083C2211yescharacteristic
17C3×#4081C411yescharacteristic, complemented
18C3×#4081C2211yescharacteristic
19C3×#4075—21no—
20#91117—21no—
21#91117C2212yes—
22C5×#834—21no—
23C5×#834C2212yes—
24#71847—51nomaximal, Hall
25#66138D311yescharacteristic
26C2×C5×#99—31no—
27C2×#3965—31no—
28#64692—32no—
29#64691—32no—
30C24×C3×C5C2×C411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C23×C3×D5C2×C411yescharacteristic, complemented
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4—41no—
35C2×C3×C5×D4C2×C411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×C3×C5×D4C2311yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C5×Dic3—41no—
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C2×C3×C22⋊D5—41no—
46C2×C3×C22⋊D5—41no—
47C22×C3×Dic5—21no—
48C22×C3×Dic5C2×C411yescharacteristic, complemented
49#6710—22no—
50#6710—41no—
51C2×C3⋊#168—41no—
52C5×#217—22no—
53C5×#217—41no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5C2×C411yescharacteristic, complemented
58C3×C22⋊Dic5C2×C411yescharacteristic, complemented
59C3×#685—21no—
60C3×#685—21no—
61C3×#683—21no—
62C3×#683—21no—
63C3×#534—51no—
64C2×#834D511yescharacteristic, complemented
65C2×#833—51no—
66#4539—52no—
67#4536—52no—
68C22×C5×D4C2×D311yescharacteristic
69C22×C22⋊D5Dic311yescharacteristic, complemented
70C2×C5×C22⋊C4—61no—
71#4099—21no—
72C2×C22⋊Dic5Dic311yescharacteristic, complemented
73#4085—21no—
74#4085—21no—
75#4083Dic311yescharacteristic, complemented
76#4083C2×D311yescharacteristic
77#4081Dic311yescharacteristic, complemented
78#4081C2×D311yescharacteristic
79#4075—21no—
80C2×#681—61no—
81C5×#99—32no—
82C5×#99—61no—
83#3965—32no—
84#3965—61no—
85#2121—151noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—81no—
91C23×C3×C5—81no—
92C23×C3×C5C22⋊C411yescharacteristic
93C23×C3×C5C22⋊C411yescharacteristic
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—41no—
99C22×C3×D5—81no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C5×Dic3—42no—
109C2×C5×Dic3—82no—
110C3×C22⋊D5—42no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—41no—
113C3×C22⋊D5—81no—
114C3×C22⋊D5—81no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—81no—
120C3⋊#168—42no—
121C22×C3×D4—51no—
122C22×C3×D4C2×D511yescharacteristic
123C3×#123—51no—
124C3×#123—51no—
125C3×#123—101no—
126C3×#121—101no—
127C3×#121—101no—
128C3×#120—51no—
129C3×#120—51no—
130C3×#120—101no—
131C2×C3×C22⋊C4—51no—
132C2×#217—21no—
133C2×#208—101no—
134#834—21no—
135#834C2×D512yes—
136#833—52no—
137#833—101no—
138C24×C5C2×Dic311yescharacteristic
139C24×C5#6711yescharacteristic
140C23×D5C2×Dic311yescharacteristic, complemented
141C2×C5×D4—41no—
142C2×C5×D4—41no—
143C2×C5×D4C2×Dic311yescharacteristic
144C2×C5×D4#6711yescharacteristic
145C2×C5×D4#6711yescharacteristic
146C2×C5×D4C22×D311yescharacteristic
147C22×C4×C5—121no—
148C22×C4×C5#6711yescharacteristic
149C2×C22⋊D5—21no—
150C2×C22⋊D5—21no—
151C2×C22⋊D5—21no—
152C2×C22⋊D5—21no—
153C2×C22⋊D5—41no—
154C2×C22⋊D5—41no—
155C22×Dic5—21no—
156C22×Dic5C2×Dic311yescharacteristic, complemented
157C5×C22⋊C4—62no—
158C5×C22⋊C4—121no—
159C22⋊Dic5—21no—
160C22⋊Dic5—21no—
161C22⋊Dic5—21no—
162C22⋊Dic5C2×Dic311yescharacteristic, complemented
163C22⋊Dic5C2×Dic311yescharacteristic, complemented
164#685—21no—
165#685—21no—
166#683—21no—
167#683—21no—
168#681—62no—
169#681—121no—
170C2×#168—121no—
171#534—51no—
172C2×#100—151no—
173C2×#99—31no—
174#352—152no—
175AΣL(1,𝔽16)—152no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—42no—
186C22×C3×C5—81no—
187C22×C3×C5—81no—
188C22×C3×C5—81no—
189C22×C3×C5#9911yescharacteristic
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C2×C3×D5—41no—
193C2×C3×D5—41no—
194C2×C3×D5—41no—
195C2×C3×D5—82no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C3×Dic5—41no—
199C3×Dic5—41no—
200C3×Dic5—41no—
201C5×Dic3—82no—
202C24×C3—51no—
203C24×C3C4×D511yescharacteristic
204C24×C3C22⋊D511yescharacteristic
205C2×C3×D4—41no—
206C2×C3×D4—41no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C2×C3×D4—101no—
211C2×C3×D4—201no—
212C2×C3×D4—201no—
213C2×C3×D4C4×D511yescharacteristic
214C2×C3×D4D2011yescharacteristic
215C2×C3×D4C22⋊D511yescharacteristic
216C2×C3×D4C22×D511yescharacteristic
217C22×C3×C4—51no—
218C22×C3×C4—101no—
219C22×C3×C4D2011yescharacteristic
220C22×Dic3—41no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C22⋊C4—51no—
224C3×C22⋊C4—51no—
225C3×C22⋊C4—101no—
226C3×C22⋊C4—101no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—101no—
229C3×C22⋊C4—101no—
230#217—22no—
231#217—41no—
232#208—102no—
233#208—201no—
234C2×C3⋊C8—201no—
235C23×C5—21no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—81no—
240C23×C5—81no—
241C23×C5#21711yescharacteristic
242C23×C5#21711yescharacteristic
243C23×C5#21711yescharacteristic
244C23×C5C22×Dic311yescharacteristic
245C23×C5C2×#6711yescharacteristic
246C22×D5—21no—
247C22×D5—41no—
248C22×D5—81no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—122no—
256C2×C4×C5—242no—
257C2×C4×C5#21711yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C22⋊D5—42no—
260C22⋊D5—41no—
261C22⋊D5—41no—
262C22⋊D5—81no—
263C22⋊D5—81no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5—21no—
267C2×Dic5—41no—
268C2×Dic5—81no—
269#168—122no—
270C22×D4—51no—
271C22×D4D3×D511yescharacteristic
272C2×M16—301no—
273#123—51no—
274#123—51no—
275#123—101no—
276#121—101no—
277#121—101no—
278#120—51no—
279#120—51no—
280#120—101no—
281C2×C22⋊C4—51no—
282C2×C22⋊C4—61no—
283#100—152no—
284#100—301no—
285#99—32no—
286#99—61no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5—41no—
291C2×C3×C5—41no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C3×D5—81no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—81no—
301C23×C3—81no—
302C23×C3—101no—
303C23×C3—201no—
304C23×C3—401no—
305C23×C3#68511yescharacteristic
306C23×C3#68511yescharacteristic
307C23×C3#68511yescharacteristic
308C23×C3C2×C4×D511yescharacteristic
309C23×C3C2×C22⋊D511yescharacteristic
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—202no—
315C3×D4—201no—
316C3×D4—201no—
317C3×D4—401no—
318C3×D4—401no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—201no—
325C2×C3×C4—401no—
326C2×C3×C4#68511yescharacteristic
327C2×C3×C4C2×D2011yescharacteristic
328C2×Dic3—42no—
329C2×Dic3—82no—
330C3⋊C8—202no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—81no—
342C22×C5—81no—
343C22×C5—81no—
344C22×C5#83411yescharacteristic
345C22×C5#83411yescharacteristic
346C22×C5C2×#21711yescharacteristic
347C2×D5—41no—
348C2×D5—41no—
349C2×D5—41no—
350C2×D5—82no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—242no—
354Dic5—41no—
355Dic5—41no—
356Dic5—41no—
357C24—51no—
358C24D5×Dic311yescharacteristic
359C24#120111yescharacteristic
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—101no—
363C2×D4—101no—
364C2×D4—101no—
365C2×D4—101no—
366C2×D4—201no—
367C2×D4—201no—
368C2×D4D5×Dic311yescharacteristic
369C2×D4#120111yescharacteristic
370C2×D4#120211yescharacteristic
371C2×D4C2×D3×D511yescharacteristic
372C22×C4—51no—
373C22×C4—101no—
374C22×C4—121no—
375C22×C4#120211yescharacteristic
376M16—302no—
377M16—601no—
378C2×C8—601no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C22⋊C4—51no—
382C22⋊C4—51no—
383C22⋊C4—62no—
384C22⋊C4—101no—
385C22⋊C4—101no—
386C22⋊C4—101no—
387C22⋊C4—101no—
388C22⋊C4—101no—
389C22⋊C4—121no—
390C3×C5#212111yescharacteristic, complemented, Hall
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—81no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—201no—
405C22×C3—201no—
406C22×C3—201no—
407C22×C3—402no—
408C22×C3#393811yescharacteristic
409C22×C3#393811yescharacteristic
410C22×C3C2×#68511yescharacteristic
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—201no—
414C3×C4—201no—
415C3×C4—201no—
416Dic3—82no—
417C2×C5—21no—
418C2×C5—21no—
419C2×C5—21no—
420C2×C5—41no—
421C2×C5—41no—
422C2×C5—41no—
423C2×C5—41no—
424C2×C5C2×#83411yescharacteristic
425D5—81no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—81no—
431C23—81no—
432C23—101no—
433C23—201no—
434C23—401no—
435C23#666511yescharacteristic
436C23#666511yescharacteristic
437C23#666511yescharacteristic
438C23C2×D5×Dic311yescharacteristic
439C23C2×#120111yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—202no—
445D4—201no—
446D4—201no—
447D4—401no—
448D4—401no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—101no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—122no—
455C2×C4—201no—
456C2×C4—242no—
457C2×C4—401no—
458C2×C4#666511yescharacteristic
459C2×C4C2×#120211yescharacteristic
460C8—602no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—41no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—401no—
469C2×C3C2×#393811yescharacteristic
470C5#7184711yescharacteristic, complemented, Sylow
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—201no—
485C22—201no—
486C22—201no—
487C22—402no—
488C22#9099511yescharacteristic
489C22#9099511yescharacteristic
490C22C2×#666511yescharacteristic
491C4—21no—
492C4—21no—
493C4—201no—
494C4—201no—
495C4—201no—
496C4—242no—
497C3#1060080811yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—21no—
501C2—41no—
502C2—41no—
503C2—41no—
504C2—41no—
505C2—401no—
506C2C2×#9099511yescharacteristic
subgroupG/H
centerC2C2×#90995
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5C2×#99
prime radicalC3×#66138C2
cosocleC2×C3×C5×D4C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#2121
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91117C2semidirect
3. C2×C5×#834C2semidirect
4. #11746000C2semidirect
5. #11745994C2semidirect
8. C22×C3×C22⋊D5C4semidirect
12. C2×C3×C22⋊Dic5C4semidirect
15. C3×#4083C4semidirect
17. C3×#4081C4semidirect
32. C23×C3×D5C2×C4semidirect
48. C22×C3×Dic5C2×C4semidirect
57. C3×C22⋊Dic5C2×C4semidirect
58. C3×C22⋊Dic5C2×C4semidirect
64. C2×#834D5semidirect
69. C22×C22⋊D5Dic3semidirect
72. C2×C22⋊Dic5Dic3semidirect
75. #4083Dic3semidirect
77. #4081Dic3semidirect
140. C23×D5C2×Dic3semidirect
156. C22×Dic5C2×Dic3semidirect
162. C22⋊Dic5C2×Dic3semidirect
163. C22⋊Dic5C2×Dic3semidirect
390. C3×C5#2121semidirect
470. C5#71847semidirect
497. C3#10600808semidirect

Maximal subgroups

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

subgroupindex
C3×#661382
C2×#911172
C2×C5×#8342
#117460002
#117459942
#106008083
#718475