Finite Group Databasebeta

← #14282902

Subgroups — #14282902

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754330C211yesmaximal, characteristic
2C3×#65007C211yesmaximal, characteristic, complemented
3#11748638C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic, complemented
5C5×#4470C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10599070—31nomaximal, Hall
9C2×#6782—21no—
10#91819C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C2×C3×C4×Dic5C2211yescharacteristic
13#91566—21no—
14C2×#6668—21no—
15C2×Dic3×Dic5—21no—
16#91468C411yescharacteristic, complemented
17#91451C411yescharacteristic, complemented
18#91418C411yescharacteristic, complemented
19Dic5×D12C411yescharacteristic, complemented
20#91405—21no—
21#91350—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3946—21no—
27C3×C8×Dic5—21no—
28#70789—51nomaximal, Hall
29#65930—31no—
30#65007D311yescharacteristic, complemented
31#64938—31no—
32C5×#327—31no—
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—21no—
39C2×D60C2×C411yescharacteristic
40C2×C5×#67—21no—
41C22×C5×Dic3—21no—
42C2×C5×D12C2×C411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C22×C3×Dic5D411yescharacteristic
45C2×#1204—21no—
46C2×#1203—21no—
47C2×#1203—21no—
48C2×#1200—21no—
49#6782—42no—
50#6782—42no—
51C2×D3×Dic5—21no—
52C2×C3×C5×C8—21no—
53#6714—21no—
54C4⋊Dic15C2×C411yescharacteristic
55C5×(C2×D3)⋊C4—21no—
56C5×C4⋊Dic3C2×C411yescharacteristic
57C3×C4×Dic5C2×C411yescharacteristic
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C2×C3×#168—21no—
62#6668—24no—
63#6668—21no—
64#6667—21no—
65(C2×D3)⋊Dic5—21no—
66Dic3×Dic5—42no—
67#5477—51no—
68C3×#431—51no—
69C4×C4⋊Dic3—51no—
70#4470—51no—
71#4470—51no—
72#4470—51no—
73#4470D511yescharacteristic, complemented
74C2×#711—61no—
75C5×#121—31no—
76#4086—31no—
77#4085—61no—
78D4×Dic5—31no—
79#4076—31no—
80C2×#683—61no—
81C2×C4×Dic5—61no—
82C2×C4×Dic5C2×D311yescharacteristic
83#4039—31no—
84#4034—31no—
85#4031—61no—
86#4027—61no—
87C5×C22⋊C8C2×D311yescharacteristic
88C5×#95—31no—
89#3963—31no—
90C22⋊#168C2×D311yescharacteristic
91#3946—21no—
92C8×Dic5—21no—
93#1502—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×C5×D3—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100#1220—41no—
101#1220—41no—
102C2×Dic15—22no—
103C2×Dic15—21no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106D60—41no—
107C5×#67—41no—
108C5×#67—41no—
109C2×C5×Dic3—22no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C5×D12—41no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5C22⋊C411yescharacteristic
116C2×C3×Dic5C22⋊C411yescharacteristic
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5D812yes—
120C2×C3×Dic5SD1612yes—
121#1204—42no—
122#1203—42no—
123#1203—42no—
124#1200—42no—
125D3×Dic5—42no—
126C3×C5×C8—41no—
127C3×#168—41no—
128C2×#235—101no—
129C2×C3×C42—51no—
130#930—51no—
131#930—101no—
132#930C2×D511yescharacteristic
133C2×C4⋊Dic3—101no—
134C2×C4×Dic3—101no—
135#875—101no—
136#874—51no—
137C4×D12—51no—
138C4×D12—51no—
139C4×D12—101no—
140#869—51no—
141C3×C4⋊C8—101no—
142C3×C22⋊C8—51no—
143C3×C22⋊C8C2×D511yescharacteristic
144C3×C4×C8—101no—
145C3⋊#95—51no—
146C3⋊#95C2×D511yescharacteristic
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C22×C4×C5—61no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C2×C22⋊D5—61no—
154C22×Dic5—61no—
155C22×Dic5—61no—
156C22×Dic5D1211yescharacteristic
157C22×Dic5D1211yescharacteristic
158#711—122no—
159#711—122no—
160C2×D20—31no—
161C2×C4×D5—61no—
162C2×Dic10—61no—
163C2×C5×C8—21no—
164C5×C4⋊C4—31no—
165C5×C22⋊C4—61no—
166C22⋊Dic5—61no—
167#685—61no—
168#685—61no—
169C4⋊Dic5—31no—
170#683—64no—
171#683—61no—
172C4×Dic5—122no—
173C4×Dic5C4×D311yescharacteristic
174C4×Dic5C4×D311yescharacteristic
175C4×Dic5#6711yescharacteristic
176C4×Dic5#6711yescharacteristic
177C2×#168—21no—
178#532—151no—
179#431—51no—
180C4×C4⋊C4—151no—
181#327—31no—
182#327—151no—
183#327—151no—
184#327—151no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5C2×D811yescharacteristic
189C22×C3×C5C2×SD1611yescharacteristic
190C2×D15—41no—
191C2×D15—41no—
192C2×D15—41no—
193C2×C5×D3—41no—
194C2×C5×D3—41no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198Dic15—42no—
199Dic15—41no—
200C3×Dic5—21no—
201C3×Dic5#10212yes—
202C3×Dic5#10212yes—
203C3×Dic5#10412yes—
204C5×Dic3—42no—
205C5×Dic3—41no—
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4C22×D511yescharacteristic
209C2×#67—21no—
210C2×#67—101no—
211C22×Dic3—21no—
212C22×Dic3—101no—
213#235—202no—
214#235—202no—
215C2×D12—51no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12C4×D511yescharacteristic
219C2×C4×D3—101no—
220C2×C4×D3—101no—
221C2×Dic6—101no—
222C2×C3×C8—21no—
223C2×C3×C8—101no—
224C3×C42—51no—
225C3×C42—51no—
226C3×C42—51no—
227C3×C42—51no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—101no—
230(C2×D3)⋊C4—101no—
231(C2×D3)⋊C4—101no—
232C4⋊Dic3—51no—
233C4⋊Dic3—101no—
234C4⋊Dic3—104no—
235C4⋊Dic3C4×D511yescharacteristic
236C4×Dic3—202no—
237C23×C5—61no—
238C23×C5C2×D1211yescharacteristic
239C22×D5—61no—
240C5×D4—121no—
241C5×D4—121no—
242C5×D4—121no—
243C2×C4×C5—41no—
244C2×C4×C5—62no—
245C2×C4×C5—61no—
246C2×C4×C5—121no—
247C2×C4×C5—121no—
248C2×C4×C5C2×C4×D311yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C22⋊D5—121no—
251C22⋊D5—121no—
252C22⋊D5—122no—
253C22⋊D5—122no—
254C2×Dic5—22no—
255C2×Dic5—62no—
256C2×Dic5—61no—
257C2×Dic5—121no—
258C2×Dic5—121no—
259C2×Dic5—122no—
260C2×Dic5#20412yes—
261C2×Dic5D2412yes—
262C2×Dic5(C2×D3)⋊C411yescharacteristic
263C2×Dic5(C2×D3)⋊C411yescharacteristic
264C2×Dic5(C2×D3)⋊C411yescharacteristic
265C2×Dic5(C2×D3)⋊C411yescharacteristic
266D20—121no—
267C4×D5—122no—
268Dic10—122no—
269C5×C8—41no—
270#168—41no—
271C2×#41—301no—
272C4⋊Q8—151no—
273#127—151no—
274#124—301no—
275#121—31no—
276#121—151no—
277#121—301no—
278C4×D4—151no—
279C4×D4—151no—
280C4×D4—301no—
281C2×C4⋊C4—301no—
282C2×C42—51no—
283C2×C42—301no—
284C4⋊C8—101no—
285C22⋊C8—51no—
286C22⋊C8D3×D511yescharacteristic
287C4×C8—101no—
288#95—31no—
289#95—151no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5#41011yescharacteristic
293C2×C3×C5C2×#10211yescharacteristic
294C2×C3×C5C2×#10411yescharacteristic
295D15—81no—
296C5×D3—81no—
297C23×C3D4×D511yescharacteristic
298C22×D3—21no—
299C22×D3—101no—
300C2×C3×C4—41no—
301C2×C3×C4—51no—
302C2×C3×C4—51no—
303C2×C3×C4—51no—
304C2×C3×C4—52no—
305C2×C3×C4—52no—
306C2×C3×C4—51no—
307C2×C3×C4—102no—
308C2×C3×C4C2×C4×D511yescharacteristic
309C2×C3×C4D4×D511yescharacteristic
310#67—41no—
311#67—41no—
312#67—201no—
313#67—201no—
314C2×Dic3—22no—
315C2×Dic3—21no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—102no—
319C2×Dic3—101no—
320C2×Dic3—201no—
321C2×Dic3—201no—
322D12—41no—
323D12—201no—
324D12—202no—
325D12—202no—
326C4×D3—202no—
327C4×D3—202no—
328Dic6—202no—
329C3×C8—41no—
330C3×C8—201no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—121no—
334C22×C5—121no—
335C22×C5—121no—
336C22×C5C2×#20411yescharacteristic
337C22×C5C2×D2411yescharacteristic
338C22×C5C2×(C2×D3)⋊C411yescharacteristic
339C2×D5—121no—
340C2×D5—121no—
341C2×D5—121no—
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—122no—
345C4×C5—121no—
346Dic5—21no—
347Dic5—122no—
348Dic5—121no—
349Dic5#82112yes—
350Dic5#82112yes—
351Dic5#82512yes—
352#41—602no—
353#41—602no—
354C2×Q8—301no—
355C2×D4—31no—
356C2×D4—61no—
357C2×D4—151no—
358C2×D4—301no—
359C2×D4—301no—
360C2×D4—301no—
361C22×C4—51no—
362C22×C4—51no—
363C22×C4—61no—
364C22×C4—301no—
365C22×C4—301no—
366C22×C4—301no—
367C22×C4C2×D3×D511yescharacteristic
368C2×C8—21no—
369C2×C8—101no—
370C4⋊C4—31no—
371C4⋊C4—151no—
372C4⋊C4—301no—
373C4⋊C4—304no—
374C22⋊C4—61no—
375C22⋊C4—301no—
376C22⋊C4—301no—
377C22⋊C4—301no—
378C42—51no—
379C42—51no—
380C42—51no—
381C42—51no—
382C42—602no—
383C3×C5#150211yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3D5×C22⋊C411yescharacteristic
387C22×C3D5×D811yescharacteristic
388C22×C3D5×SD1611yescharacteristic
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—41no—
392C2×D3—201no—
393C2×D3—201no—
394C2×D3—201no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—52no—
398C3×C4—52no—
399C3×C4—52no—
400C3×C4—101no—
401Dic3—42no—
402Dic3—41no—
403Dic3—202no—
404Dic3—201no—
405C2×C5—21no—
406C2×C5—21no—
407C2×C5—241no—
408C2×C5#500611yescharacteristic
409C2×C5C2×#82111yescharacteristic
410C2×C5C2×#82511yescharacteristic
411D5—241no—
412C23—61no—
413C23—301no—
414C23D5×D1211yescharacteristic
415Q8—602no—
416D4—121no—
417D4—121no—
418D4—121no—
419D4—601no—
420D4—602no—
421D4—602no—
422D4—601no—
423D4—601no—
424C2×C4—41no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—52no—
429C2×C4—52no—
430C2×C4—51no—
431C2×C4—62no—
432C2×C4—61no—
433C2×C4—102no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—302no—
437C2×C4—301no—
438C2×C4—602no—
439C2×C4—602no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4C4×D3×D511yescharacteristic
443C2×C4D5×#6711yescharacteristic
444C8—41no—
445C8—201no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3#6502911yescharacteristic
449C2×C3D5×#10211yescharacteristic
450C2×C3D5×#10411yescharacteristic
451D3—81no—
452D3—401no—
453C5#7078911yescharacteristic, complemented, Sylow
454C22—21no—
455C22—21no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—601no—
460C22—601no—
461C22—601no—
462C22D5×#20411yescharacteristic
463C22D5×D2411yescharacteristic
464C22D5×(C2×D3)⋊C411yescharacteristic
465C4—21no—
466C4—21no—
467C4—52no—
468C4—52no—
469C4—52no—
470C4—101no—
471C4—122no—
472C4—121no—
473C4—602no—
474C4—601no—
475C3#1059907011yescharacteristic, complemented, Sylow
476C2—21no—
477C2—21no—
478C2—241no—
479C2—1201no—
480C2#1174712911yescharacteristic
481C2D5×#82111yescharacteristic
482C2D5×#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#11754330C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1502
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×#65007C2semidirect
3. #11748638C2semidirect
4. #11746291C2semidirect
5. C5×#4470C2semidirect
6. #11745959C2semidirect
7. #11745957C2semidirect
16. #91468C4semidirect
17. #91451C4semidirect
18. #91418C4semidirect
19. Dic5×D12C4semidirect
30. #65007D3semidirect
73. #4470D5semidirect
383. C3×C5#1502semidirect
453. C5#70789semidirect
475. C3#10599070semidirect

Maximal subgroups

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

subgroupindex
#117543302
C3×#650072
#117486382
#117462912
C5×#44702
#117459592
#117459572
#105990703
#707895