Finite Group Databasebeta

← #14306115

Subgroups — #14306115

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×C3×C5×#100C211yesmaximal, characteristic, complemented
3C2×#91117C211yesmaximal, characteristic, complemented
4C2×#91107C211yesmaximal, characteristic, complemented
5C2×#91107C211yesmaximal, characteristic, complemented
6#11751219C211yesmaximal, characteristic, complemented
7M16×Dic15C211yesmaximal, characteristic, complemented
8#10600857—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220C414yes—
11C22×D60C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14#91829—21no—
15#91829—22no—
16#91829—21no—
17C2×C4×Dic15C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20C3×C5×#100—22no—
21#91117—22no—
22#91107—22no—
23#91107—22no—
24#91099—21no—
25#91098—22no—
26C8×Dic15—21no—
27#70064—51nomaximal, Hall
28C2×#4086—31no—
29C2×C5×#100D311yescharacteristic, complemented
30C2×#3965—31no—
31C2×#3955—31no—
32C2×#3955—31no—
33#65407—31no—
34M16×Dic5—31no—
35C24×C3×C5C2×C412yes—
36C23×D15C2×C412yes—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C2×#1220—24no—
45C2×#1220—24no—
46C2×#1220—48no—
47C22×Dic15C2×C412yes—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60—21no—
51C2×D60—21no—
52C2×D60—21no—
53C2×D60—21no—
54C3×C5×M16—21no—
55C3×C5×M16—21no—
56C3×C5×M16—21no—
57C3×C5×M16D412yescomplemented
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C4×Dic15D411yescharacteristic
61C4×Dic15D412yes—
62C4×Dic15D411yescharacteristic
63#6710—21no—
64#6710—21no—
65#6710—21no—
66#6710D412yescomplemented
67C2×C3⋊#168—21no—
68C2×C3⋊#168—21no—
69C2×#940—51no—
70C2×C3×#100D511yescharacteristic, complemented
71C2×#833—51no—
72C2×#823—51no—
73C2×#823—51no—
74#5118—51no—
75Dic3×M16—51no—
76C22×C5×D4C2×D311yescharacteristic
77C22×C22⋊D5—34no—
78C22×D20—31no—
79C2×C5×M16C2×D311yescharacteristic
80C2×C5×M16C2×D311yescharacteristic
81#4086—61no—
82#4086—62no—
83#4086—61no—
84C2×C4×Dic5—31no—
85C2×#681—31no—
86C2×#681—31no—
87C5×#100—22no—
88#3965—62no—
89#3955—62no—
90#3955—62no—
91#3947—61no—
92#3946—62no—
93C8×Dic5—61no—
94#1965—151noSylow
95C23×C3×C5—22no—
96C23×C3×C5—22no—
97C23×C3×C5—22no—
98C23×C3×C5—44no—
99C23×C3×C5C22×C411yescharacteristic
100C22×D15—22no—
101C22×D15—22no—
102C22×D15—22no—
103C22×D15—44no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114#1220—48no—
115#1220—48no—
116C2×Dic15—24no—
117C2×Dic15C22⋊C412yes—
118C2×Dic15C22⋊C412yes—
119D60—41no—
120D60—41no—
121D60—41no—
122D60—41no—
123C3×C5×C8—22no—
124C3×C5×C8—41no—
125C3⋊#168—22no—
126C3⋊#168—41no—
127C22×C3×D4C2×D511yescharacteristic
128C22×#67—54no—
129C22×D12—51no—
130C2×C3×M16C2×D511yescharacteristic
131C2×C3×M16C2×D511yescharacteristic
132#940—101no—
133#940—102no—
134#940—101no—
135C2×C4×Dic3—51no—
136C2×#208—51no—
137C2×#208—51no—
138C3×#100—22no—
139#833—102no—
140#823—102no—
141#823—102no—
142#815—101no—
143Dic3⋊C8—102no—
144C8×Dic3—101no—
145C24×C5C4×D312yes—
146C23×D5—32no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C22×C4×C5C22×D311yescharacteristic
154C2×C22⋊D5—64no—
155C2×C22⋊D5—64no—
156C2×C22⋊D5—128no—
157C22×Dic5—32no—
158C2×D20—61no—
159C2×D20—61no—
160C2×D20—61no—
161C2×D20—61no—
162C2×D20—61no—
163C2×D20—61no—
164C5×M16—21no—
165C5×M16—21no—
166C5×M16—21no—
167C5×M16#6712yescomplemented
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C4×Dic5—31no—
171C4×Dic5—32no—
172C4×Dic5—31no—
173#681—32no—
174#681—61no—
175#681—61no—
176#681—61no—
177C2×#168—61no—
178C2×#168—61no—
179C2×#127—151no—
180#423—151no—
181C2×#100—151no—
182C2×#100—151no—
183C2×#100—151no—
184C2×#100D1511yescharacteristic, complemented
185C4×M16—151no—
186C22×C3×C5—22no—
187C22×C3×C5—42no—
188C22×C3×C5—44no—
189C22×C3×C5—82no—
190C22×C3×C5—82no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C22×C3×C5C4×D411yescharacteristic
193C22×C3×C5C4×D411yescharacteristic
194C2×D15—42no—
195C2×D15—44no—
196C2×D15—82no—
197C2×D15—82no—
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12411yescharacteristic
201C3×C4×C5#12711yescharacteristic
202Dic15—22no—
203Dic15#10014yescomplemented
204C24×C3C4×D512yes—
205C23×D3—52no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—104no—
214C2×#67—104no—
215C2×#67—208no—
216C22×Dic3—52no—
217C2×D12—101no—
218C2×D12—101no—
219C2×D12—101no—
220C2×D12—101no—
221C2×D12—101no—
222C2×D12—101no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16C22⋊D512yescomplemented
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C4×Dic3—51no—
230C4×Dic3—52no—
231C4×Dic3—51no—
232#208—52no—
233#208—101no—
234#208—101no—
235#208—101no—
236C2×C3⋊C8—101no—
237C2×C3⋊C8—101no—
238C23×C5—22no—
239C23×C5—22no—
240C23×C5—22no—
241C23×C5—44no—
242C23×C5C2×C4×D311yescharacteristic
243C22×D5—62no—
244C22×D5—62no—
245C22×D5—62no—
246C22×D5—124no—
247C5×D4—41no—
248C5×D4—41no—
249C5×D4—41no—
250C5×D4—41no—
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5#23711yescharacteristic
256C2×C4×C5C2×#6711yescharacteristic
257C22⋊D5—128no—
258C22⋊D5—128no—
259C2×Dic5—32no—
260C2×Dic5—32no—
261C2×Dic5—64no—
262D20—121no—
263D20—121no—
264D20—121no—
265D20—121no—
266C5×C8—22no—
267C5×C8—41no—
268#168—62no—
269#168—121no—
270C22×D4—154no—
271C22×D4—151no—
272C22×D4C2×D1511yescharacteristic
273C2×M16—151no—
274C2×M16—151no—
275C2×M16C2×D1511yescharacteristic
276C2×M16C2×D1511yescharacteristic
277#127—301no—
278#127—301no—
279#127—302no—
280C2×C42—151no—
281C4⋊C8—302no—
282#100—22no—
283#100—302no—
284#100—302no—
285#100—302no—
286#97—301no—
287C4×C8—301no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5—82no—
291C2×C3×C5#39011yescharacteristic
292C2×C3×C5C2×#10012yes—
293D15—82no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—44no—
298C23×C3C2×C4×D511yescharacteristic
299C22×D3—102no—
300C22×D3—102no—
301C22×D3—102no—
302C22×D3—204no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—41no—
307C2×C3×C4#70911yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4C2×C22⋊D511yescharacteristic
313#67—208no—
314#67—208no—
315C2×Dic3—52no—
316C2×Dic3—52no—
317C2×Dic3—104no—
318D12—201no—
319D12—201no—
320D12—201no—
321D12—201no—
322C3×C8—22no—
323C3×C8—41no—
324C3⋊C8—102no—
325C3⋊C8—201no—
326C22×C5—22no—
327C22×C5—42no—
328C22×C5—44no—
329C22×C5—82no—
330C22×C5—82no—
331C22×C5D3×C22⋊C411yescharacteristic
332C22×C5#67⋊C411yescharacteristic
333C22×C5C4×#6711yescharacteristic
334C2×D5—122no—
335C2×D5—124no—
336C2×D5—242no—
337C2×D5—242no—
338C4×C5#88411yescharacteristic
339C4×C5#88511yescharacteristic
340C4×C5#93911yescharacteristic
341C4×C5#94011yescharacteristic
342Dic5—34no—
343Dic5—62no—
344C24—152no—
345C24C4×D1512yes—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—304no—
353C2×D4—304no—
354C2×D4—301no—
355C2×D4—301no—
356C2×D4—301no—
357C2×D4—301no—
358C2×D4—301no—
359C2×D4—301no—
360C2×D4—608no—
361C22×C4—152no—
362C22×C4C22×D1511yescharacteristic
363M16—21no—
364M16—21no—
365M16—21no—
366M16—152no—
367M16—301no—
368M16—301no—
369M16—301no—
370M16#122012yescomplemented
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—301no—
374C2×C8—301no—
375C42—151no—
376C42—151no—
377C42—152no—
378C3×C5#196511yescharacteristic, complemented, Hall
379C22×C3—22no—
380C22×C3—44no—
381C22×C3—42no—
382C22×C3—82no—
383C22×C3—82no—
384C22×C3D5×C22⋊C411yescharacteristic
385C22×C3#402711yescharacteristic
386C22×C3C4×C22⋊D511yescharacteristic
387C2×D3—204no—
388C2×D3—202no—
389C2×D3—402no—
390C2×D3—402no—
391C3×C4#403011yescharacteristic
392C3×C4#403111yescharacteristic
393C3×C4#408511yescharacteristic
394C3×C4#408611yescharacteristic
395Dic3—54no—
396Dic3—102no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—82no—
400C2×C5D3×#10012yes—
401C2×C5#495711yescharacteristic
402D5—242no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—44no—
407C23—302no—
408C23—302no—
409C23—302no—
410C23—604no—
411C23C2×C4×D1511yescharacteristic
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—608no—
417D4—608no—
418D4—601no—
419D4—601no—
420D4—601no—
421D4—601no—
422C2×C4—152no—
423C2×C4—152no—
424C2×C4—304no—
425C2×C4#681711yescharacteristic
426C2×C4D4×D1511yescharacteristic
427C2×C4D4×D1511yescharacteristic
428C2×C4D4×D1511yescharacteristic
429C2×C4#681911yescharacteristic
430C2×C4C2×#122011yescharacteristic
431C8—22no—
432C8—41no—
433C8—302no—
434C8—601no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—82no—
438C2×C3D5×#10012yes—
439C2×C3#6524611yescharacteristic
440D3—402no—
441C5#7006411yescharacteristic, complemented, Sylow
442C22—22no—
443C22—42no—
444C22—44no—
445C22—82no—
446C22—82no—
447C22—602no—
448C22—604no—
449C22—1202no—
450C22—1202no—
451C22C22⋊C4×D1511yescharacteristic
452C22#9177011yescharacteristic
453C22C4×#122011yescharacteristic
454C4—154no—
455C4—302no—
456C4#9177311yescharacteristic
457C4#9177411yescharacteristic
458C4#9182811yescharacteristic
459C4#9182911yescharacteristic
460C3#1060085711yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—82no—
464C2—1202no—
465C2D15×#10012yes—
466C2#1175105811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#100C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91829C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#100D15
hypocenterC3×C5#1965
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#100C2semidirect
3. C2×#91117C2semidirect
4. C2×#91107C2semidirect
5. C2×#91107C2semidirect
6. #11751219C2semidirect
7. M16×Dic15C2semidirect
29. C2×C5×#100D3semidirect
57. C3×C5×M16D4semidirect
66. #6710D4semidirect
70. C2×C3×#100D5semidirect
167. C5×M16#67semidirect
184. C2×#100D15semidirect
203. Dic15#100semidirect
226. C3×M16C22⋊D5semidirect
370. M16#1220semidirect
378. C3×C5#1965semidirect
441. C5#70064semidirect
460. C3#10600857semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C3×C5×#1002
C2×#911172
C2×#911072
#117512192
M16×Dic152
#106008573
#700645