Finite Group Databasebeta

← #14283044

Subgroups — #14283044

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5596C211yesmaximal, characteristic
2#11748643C211yesmaximal, characteristic, complemented
3#11748337C211yesmaximal, characteristic, complemented
4#11746358C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10602605—31nomaximal, Hall
9C2×C5×#237—21no—
10C3×C5×#121C2211yescharacteristic
11C5×#940C411yescharacteristic, complemented
12C5×#939—21no—
13C5×D4×Dic3C411yescharacteristic, complemented
14C5×#930C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C5×#893C411yescharacteristic, complemented
17C5×#888C411yescharacteristic, complemented
18C5×#885—21no—
19C5×#67⋊C4—21no—
20C2×Dic3×Dic5—21no—
21#91115C2211yescharacteristic
22#91114C2211yescharacteristic
23C3×#3963C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25#90994—21no—
26Dic3⋊#168—21no—
27#90953—21no—
28#68278—51nomaximal, Hall
29C5×#532—31no—
30#65221—31no—
31#65215—31no—
32#64757—31no—
33#64757—31no—
34#64757—31no—
35#64757D311yescharacteristic, complemented
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C22×C5×Dic3—21no—
44C22×C5×Dic3D411yescharacteristic
45C22×C5×Dic3D411yescharacteristic
46C5×#237—42no—
47C5×#237—42no—
48C2×C5×D12C2×C411yescharacteristic
49C2×C4×C5×D3—21no—
50C2×C5×Dic6—21no—
51C22×C3×Dic5—21no—
52C3×C5×C4⋊C4C2×C411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C2×C3⋊#168—21no—
55C5×#217—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3C2×C411yescharacteristic
59C5×Dic3⋊C4—21no—
60C4×C5×Dic3C2×C411yescharacteristic
61C4×C5×Dic3C2×C411yescharacteristic
62C4×C5×Dic3D411yescharacteristic
63C4×C5×Dic3D411yescharacteristic
64C2×C3×#168—21no—
65Dic3×Dic5—24no—
66#5596D511yescharacteristic
67#4719—51no—
68#4648—51no—
69C3×#327—51no—
70#4537—51no—
71#4470—51no—
72#4451—51no—
73C2×C5×#41—61no—
74C5×C4⋊Q8—31no—
75C5×#127—31no—
76C5×#124—61no—
77C5×#121—31no—
78C5×#121—61no—
79C5×#121C2×D311yescharacteristic
80C4×C5×D4—31no—
81C4×C5×D4—31no—
82C4×C5×D4—61no—
83C2×C42×C5—31no—
84C2×C4×Dic5—61no—
85#3963—31no—
86#3963—61no—
87#3963C2×D311yescharacteristic
88C22⋊#168—31no—
89C22⋊#168C2×D311yescharacteristic
90C4⋊#168—61no—
91#3935—61no—
92#1505—151noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—21no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—22no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C5×#67—42no—
107C5×#67—41no—
108C5×#67—41no—
109C5×#67—42no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—22no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—42no—
115C2×C5×Dic3C22⋊C411yescharacteristic
116C2×C5×Dic3C22⋊C411yescharacteristic
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C5×D12—41no—
120C4×C5×D3—42no—
121C5×Dic6—42no—
122C2×C3×Dic5—22no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5—41no—
125C3⋊#168—41no—
126C3×#168—41no—
127C2×#237—21no—
128C3×#121C2×D511yescharacteristic
129#940Dic511yescharacteristic, complemented
130#939—21no—
131D4×Dic3Dic511yescharacteristic, complemented
132#930C2×D511yescharacteristic
133C2×C4×Dic3—101no—
134C2×C4×Dic3C2×D511yescharacteristic
135#893Dic511yescharacteristic, complemented
136#888Dic511yescharacteristic, complemented
137#885—21no—
138#67⋊C4—21no—
139C3×C22⋊C8—51no—
140C3×#95—51no—
141C3⋊#95—51no—
142C3⋊#95—101no—
143#830—51no—
144#815—101no—
145Dic3⋊C8—101no—
146C5×#41—122no—
147C5×#41—122no—
148C2×C5×Q8—61no—
149C2×C5×D4—21no—
150C2×C5×D4—31no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4C4×D311yescharacteristic
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—61no—
158C22×C4×C5—61no—
159C22×C4×C5C22×D311yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—61no—
162C5×C4⋊C4—31no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4C4×D311yescharacteristic
165C5×C22⋊C4—21no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—61no—
168C5×C22⋊C4—61no—
169C42×C5—31no—
170C42×C5—31no—
171C42×C5—31no—
172C42×C5—31no—
173C4×Dic5—64no—
174C2×#168—21no—
175C2×#168—61no—
176#532—31no—
177#432—151no—
178#376—151no—
179#327—51no—
180#327—151no—
181#327—151no—
182#327—151no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5—41no—
186C22×C3×C5—41no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
190C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
191C2×C5×D3—41no—
192C2×C5×D3—41no—
193C2×C5×D3—41no—
194C3×C4×C5—21no—
195C3×C4×C5—21no—
196C3×C4×C5—41no—
197Dic15—42no—
198C3×Dic5—42no—
199C5×Dic3—21no—
200C5×Dic3—21no—
201C5×Dic3—21no—
202C5×Dic3—41no—
203C5×Dic3#10412yes—
204C2×C3×D4—21no—
205C2×C3×D4C2×Dic511yescharacteristic
206C22×C3×C4—101no—
207C22×C3×C4C22×D511yescharacteristic
208C2×#67—21no—
209C2×#67—21no—
210C2×#67—21no—
211C22×Dic3—21no—
212C22×Dic3—101no—
213C22×Dic3C22⋊D511yescharacteristic
214C22×Dic3C22⋊D511yescharacteristic
215#237—42no—
216#237—42no—
217C2×D12C2×Dic511yescharacteristic
218C2×C4×D3—21no—
219C2×Dic6—21no—
220C2×C3×C8—101no—
221C3×C4⋊C4C2×Dic511yescharacteristic
222C3×C22⋊C4—21no—
223#217—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226C4⋊Dic3C2×Dic511yescharacteristic
227Dic3⋊C4—21no—
228C4×Dic3—104no—
229C4×Dic3C2×Dic511yescharacteristic
230C4×Dic3C2×Dic511yescharacteristic
231C4×Dic3C22⋊D511yescharacteristic
232C4×Dic3C22⋊D511yescharacteristic
233C2×C3⋊C8—101no—
234C23×C5—21no—
235C23×C5—61no—
236C23×C5D3×D411yescharacteristic
237C5×Q8—122no—
238C5×D4—41no—
239C5×D4—41no—
240C5×D4—41no—
241C5×D4—121no—
242C5×D4—122no—
243C5×D4—122no—
244C5×D4—121no—
245C5×D4—121no—
246C2×C4×C5—21no—
247C2×C4×C5—31no—
248C2×C4×C5—31no—
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—41no—
252C2×C4×C5—62no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×C4×C5—122no—
257C2×C4×C5—122no—
258C2×C4×C5C2×C4×D311yescharacteristic
259C2×C4×C5D3×D411yescharacteristic
260C2×Dic5—22no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—62no—
264C2×Dic5—121no—
265C2×Dic5—121no—
266#168—41no—
267#168—121no—
268C2×#41—61no—
269C4⋊Q8—31no—
270#127—31no—
271#124—61no—
272#121—31no—
273#121—61no—
274#121D3×D511yescharacteristic
275C4×D4—31no—
276C4×D4—31no—
277C4×D4—61no—
278C2×C42—31no—
279C2×C42—301no—
280C4⋊C8—301no—
281C22⋊C8—51no—
282C22⋊C8—151no—
283#97—301no—
284#95—51no—
285#95—151no—
286#95—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—81no—
290C2×C3×C5#41011yescharacteristic
291C2×C3×C5#41811yescharacteristic
292C2×C3×C5C2×#10411yescharacteristic
293C5×D3—81no—
294C23×C3—21no—
295C23×C3C2×C22⋊D511yescharacteristic
296C22×D3—21no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—41no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—102no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4C22×Dic511yescharacteristic
306C2×C3×C4C2×C22⋊D511yescharacteristic
307#67—42no—
308#67—41no—
309#67—41no—
310#67—42no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—22no—
314C2×Dic3—21no—
315C2×Dic3—42no—
316C2×Dic3—102no—
317C2×Dic3—201no—
318C2×Dic3—201no—
319C2×Dic3C22⋊Dic511yescharacteristic
320C2×Dic3C22⋊Dic511yescharacteristic
321C2×Dic3C22⋊Dic511yescharacteristic
322C2×Dic3C22⋊Dic511yescharacteristic
323D12—41no—
324C4×D3—42no—
325Dic6—42no—
326C3×C8—201no—
327C3⋊C8—201no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—41no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5—121no—
334C22×C5—121no—
335C22×C5—121no—
336C22×C5D3×C22⋊C411yescharacteristic
337C22×C5#91111yescharacteristic
338C22×C5#91411yescharacteristic
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—32no—
342C4×C5—41no—
343C4×C5—61no—
344C4×C5—61no—
345C4×C5—61no—
346C4×C5—121no—
347Dic5—42no—
348Dic5—122no—
349#41—122no—
350#41—122no—
351C2×Q8—61no—
352C2×D4—21no—
353C2×D4—31no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4D3×Dic511yescharacteristic
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—101no—
363C22×C4—301no—
364C22×C4C2×D3×D511yescharacteristic
365C2×C8—101no—
366C2×C8—301no—
367C4⋊C4—31no—
368C4⋊C4—61no—
369C4⋊C4D3×Dic511yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C42—31no—
375C42—31no—
376C42—31no—
377C42—31no—
378C42—304no—
379C3×C5#150511yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3#407811yescharacteristic
386C22×C3#407811yescharacteristic
387C22×C3C2×C22⋊Dic511yescharacteristic
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—41no—
394C3×C4—202no—
395Dic3—21no—
396Dic3—21no—
397Dic3—21no—
398Dic3—41no—
399Dic3—202no—
400Dic3#396912yes—
401C2×C5—21no—
402C2×C5—21no—
403C2×C5—81no—
404C2×C5—241no—
405C2×C5#474011yescharacteristic
406C2×C5#477011yescharacteristic
407C2×C5D3×#10411yescharacteristic
408C23—21no—
409C23—61no—
410C23D3×C22⋊D511yescharacteristic
411Q8—122no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—121no—
416D4—122no—
417D4—122no—
418D4—121no—
419D4—121no—
420C2×C4—21no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—41no—
426C2×C4—62no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—102no—
431C2×C4—122no—
432C2×C4—122no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—302no—
436C2×C4—601no—
437C2×C4—601no—
438C2×C4C2×D3×Dic511yescharacteristic
439C2×C4D3×C22⋊D511yescharacteristic
440C8—201no—
441C8—601no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—81no—
445C2×C3#6550411yescharacteristic
446C2×C3C2×#396911yescharacteristic
447C2×C3#6552911yescharacteristic
448D3—81no—
449C5#6827811yescharacteristic, complemented, Sylow
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22#9149411yescharacteristic
459C22#9149611yescharacteristic
460C22D3×C22⋊Dic511yescharacteristic
461C4—21no—
462C4—21no—
463C4—32no—
464C4—41no—
465C4—61no—
466C4—61no—
467C4—61no—
468C4—121no—
469C4—202no—
470C4—602no—
471C3#1060260511yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—81no—
475C2—241no—
476C2#1174896711yescharacteristic
477C2#1174917311yescharacteristic
478C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5596C2
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1505
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11748643C2semidirect
3. #11748337C2semidirect
4. #11746358C2semidirect
5. C3×#64757C2semidirect
6. #11745957C2semidirect
7. #11745956C2semidirect
11. C5×#940C4semidirect
13. C5×D4×Dic3C4semidirect
16. C5×#893C4semidirect
17. C5×#888C4semidirect
35. #64757D3semidirect
129. #940Dic5semidirect
131. D4×Dic3Dic5semidirect
135. #893Dic5semidirect
136. #888Dic5semidirect
379. C3×C5#1505semidirect
449. C5#68278semidirect
471. C3#10602605semidirect

Maximal subgroups

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

subgroupindex
C5×#55962
#117486432
#117483372
#117463582
C3×#647572
#117459572
#117459562
#106026053
#682785