Finite Group Databasebeta

← #14283051

Subgroups — #14283051

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
1#11754330C211yesmaximal, characteristic
2C3×#65008C211yesmaximal, characteristic, complemented
3#11748635C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic, complemented
5C5×#4470C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10599071—31nomaximal, Hall
9C2×#6782—21no—
10#91819C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C2×C3×C4×Dic5C2211yescharacteristic
13#91566—21no—
14C2×Dic3×Dic5—21no—
15#91468C411yescharacteristic, complemented
16#91451C411yescharacteristic, complemented
17#91418C411yescharacteristic, complemented
18Dic5×D12C411yescharacteristic, complemented
19#91405—21no—
20#91350—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22#91115C2211yescharacteristic
23C5×C3⋊#95C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×#3947—21no—
26C3×#3946—21no—
27#90994—21no—
28#70832—51nomaximal, Hall
29#65930—31no—
30#65008D311yescharacteristic, complemented
31#64937—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—21no—
63#6667—21no—
64(C2×D3)⋊Dic5—21no—
65Dic3×Dic5—24no—
66#5477—51no—
67C3×#432—51no—
68#4932—51no—
69#4470—51no—
70#4470—51no—
71#4470—51no—
72#4470D511yescharacteristic, complemented
73C2×#711—61no—
74C5×#121—31no—
75#4086—31no—
76#4085—61no—
77D4×Dic5—31no—
78#4076—31no—
79C2×C4×Dic5—61no—
80C2×C4×Dic5C2×D311yescharacteristic
81#4039—31no—
82#4034—31no—
83#4031—61no—
84#4027—61no—
85C5×C22⋊C8C2×D311yescharacteristic
86C5×#95—31no—
87#3963—31no—
88#3963—61no—
89C22⋊#168C2×D311yescharacteristic
90#3947—21no—
91#3946—21no—
92#1505—151noSylow
93C23×C3×C5C2×D411yescharacteristic
94C22×D15—21no—
95C22×C5×D3—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99#1220—41no—
100#1220—41no—
101C2×Dic15—22no—
102C2×Dic15—21no—
103C2×Dic15—41no—
104C2×Dic15—41no—
105D60—41no—
106C5×#67—41no—
107C5×#67—41no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C5×D12—41no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5C22⋊C411yescharacteristic
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120#1204—42no—
121#1203—42no—
122#1203—42no—
123#1200—42no—
124D3×Dic5—42no—
125C3×C5×C8—41no—
126C3×#168—41no—
127C2×#235—101no—
128C2×C3×C42—51no—
129#930—51no—
130#930—101no—
131#930C2×D511yescharacteristic
132C2×C4×Dic3—101no—
133#875—101no—
134#874—51no—
135C4×D12—51no—
136C4×D12—51no—
137C4×D12—101no—
138#869—51no—
139C3×C4⋊C8—101no—
140C3×C22⋊C8—51no—
141C3×C22⋊C8C2×D511yescharacteristic
142C3×#97—101no—
143C3⋊#95—51no—
144C3⋊#95—101no—
145C3⋊#95C2×D511yescharacteristic
146C2×C5×D4—31no—
147C2×C5×D4—61no—
148C22×C4×C5—61no—
149C22×C4×C5C22×D311yescharacteristic
150C2×C22⋊D5—61no—
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C22×Dic5—61no—
154C22×Dic5—61no—
155C22×Dic5D1211yescharacteristic
156C22×Dic5D1211yescharacteristic
157#711—122no—
158#711—122no—
159C2×D20—31no—
160C2×C4×D5—61no—
161C2×Dic10—61no—
162C2×C5×C8—21no—
163C5×C4⋊C4—31no—
164C5×C22⋊C4—61no—
165C22⋊Dic5—61no—
166#685—61no—
167#685—61no—
168C4⋊Dic5—31no—
169#683—61no—
170C4×Dic5—64no—
171C4×Dic5C4×D311yescharacteristic
172C4×Dic5C4×D311yescharacteristic
173C4×Dic5#6711yescharacteristic
174C4×Dic5#6711yescharacteristic
175C2×#168—21no—
176#532—151no—
177#432—51no—
178#376—151no—
179#327—31no—
180#327—151no—
181#327—151no—
182#327—151no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
187C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
188C2×D15—41no—
189C2×D15—41no—
190C2×D15—41no—
191C2×C5×D3—41no—
192C2×C5×D3—41no—
193C2×C5×D3—41no—
194C3×C4×C5—21no—
195C3×C4×C5—21no—
196Dic15—42no—
197Dic15—41no—
198C3×Dic5—21no—
199C3×Dic5—21no—
200C3×Dic5—21no—
201C3×Dic5#10412yes—
202C5×Dic3—42no—
203C5×Dic3—41no—
204C22×C3×C4—51no—
205C22×C3×C4—51no—
206C22×C3×C4C22×D511yescharacteristic
207C2×#67—21no—
208C2×#67—101no—
209C22×Dic3—21no—
210C22×Dic3—101no—
211#235—202no—
212#235—202no—
213C2×D12—51no—
214C2×D12—101no—
215C2×D12—101no—
216C2×D12C4×D511yescharacteristic
217C2×C4×D3—101no—
218C2×C4×D3—101no—
219C2×Dic6—101no—
220C2×C3×C8—21no—
221C2×C3×C8—101no—
222C3×C42—51no—
223C3×C42—51no—
224C3×C42—51no—
225C3×C42—51no—
226(C2×D3)⋊C4—21no—
227(C2×D3)⋊C4—101no—
228(C2×D3)⋊C4—101no—
229(C2×D3)⋊C4—101no—
230C4⋊Dic3—51no—
231C4⋊Dic3—101no—
232C4⋊Dic3C4×D511yescharacteristic
233C4×Dic3—104no—
234C23×C5—61no—
235C23×C5C2×D1211yescharacteristic
236C22×D5—61no—
237C5×D4—121no—
238C5×D4—121no—
239C5×D4—121no—
240C2×C4×C5—41no—
241C2×C4×C5—62no—
242C2×C4×C5—61no—
243C2×C4×C5—121no—
244C2×C4×C5—121no—
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—122no—
248C22⋊D5—121no—
249C22⋊D5—121no—
250C22⋊D5—122no—
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—22no—
254C2×Dic5—62no—
255C2×Dic5—61no—
256C2×Dic5—122no—
257C2×Dic5—121no—
258C2×Dic5—121no—
259C2×Dic5(C2×D3)⋊C411yescharacteristic
260C2×Dic5(C2×D3)⋊C411yescharacteristic
261C2×Dic5(C2×D3)⋊C411yescharacteristic
262C2×Dic5(C2×D3)⋊C411yescharacteristic
263D20—121no—
264C4×D5—122no—
265Dic10—122no—
266C5×C8—41no—
267#168—41no—
268C2×#41—301no—
269C4⋊Q8—151no—
270#127—151no—
271#124—301no—
272#121—31no—
273#121—151no—
274#121—301no—
275C4×D4—151no—
276C4×D4—151no—
277C4×D4—301no—
278C2×C42—51no—
279C2×C42—301no—
280C4⋊C8—101no—
281C22⋊C8—51no—
282C22⋊C8D3×D511yescharacteristic
283#97—101no—
284#95—31no—
285#95—151no—
286#95—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5#41011yescharacteristic
290C2×C3×C5#41811yescharacteristic
291C2×C3×C5C2×#10411yescharacteristic
292D15—81no—
293C5×D3—81no—
294C23×C3D4×D511yescharacteristic
295C22×D3—21no—
296C22×D3—101no—
297C2×C3×C4—41no—
298C2×C3×C4—51no—
299C2×C3×C4—51no—
300C2×C3×C4—51no—
301C2×C3×C4—51no—
302C2×C3×C4—102no—
303C2×C3×C4—101no—
304C2×C3×C4—101no—
305C2×C3×C4C2×C4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307#67—41no—
308#67—41no—
309#67—201no—
310#67—201no—
311C2×Dic3—22no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—102no—
316C2×Dic3—101no—
317C2×Dic3—201no—
318C2×Dic3—201no—
319D12—41no—
320D12—201no—
321D12—202no—
322D12—202no—
323C4×D3—202no—
324C4×D3—202no—
325Dic6—202no—
326C3×C8—41no—
327C3×C8—201no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—121no—
331C22×C5—121no—
332C22×C5—121no—
333C22×C5#90811yescharacteristic
334C22×C5#90811yescharacteristic
335C22×C5C2×(C2×D3)⋊C411yescharacteristic
336C2×D5—121no—
337C2×D5—121no—
338C2×D5—121no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—122no—
342C4×C5—121no—
343Dic5—21no—
344Dic5—21no—
345Dic5—21no—
346Dic5—122no—
347Dic5—121no—
348Dic5#82512yes—
349#41—602no—
350#41—602no—
351C2×Q8—301no—
352C2×D4—31no—
353C2×D4—61no—
354C2×D4—151no—
355C2×D4—301no—
356C2×D4—301no—
357C2×D4—301no—
358C22×C4—51no—
359C22×C4—51no—
360C22×C4—61no—
361C22×C4—301no—
362C22×C4—301no—
363C22×C4—301no—
364C22×C4C2×D3×D511yescharacteristic
365C2×C8—21no—
366C2×C8—101no—
367C4⋊C4—31no—
368C4⋊C4—151no—
369C4⋊C4—301no—
370C22⋊C4—61no—
371C22⋊C4—301no—
372C22⋊C4—301no—
373C22⋊C4—301no—
374C42—51no—
375C42—51no—
376C42—51no—
377C42—51no—
378C42—304no—
379C3×C5#150511yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3D5×C22⋊C411yescharacteristic
383C22×C3#405711yescharacteristic
384C22×C3#406011yescharacteristic
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—201no—
389C2×D3—201no—
390C2×D3—201no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—52no—
394C3×C4—101no—
395C3×C4—101no—
396C3×C4—101no—
397Dic3—42no—
398Dic3—41no—
399Dic3—202no—
400Dic3—201no—
401C2×C5—21no—
402C2×C5—21no—
403C2×C5—241no—
404C2×C5#500611yescharacteristic
405C2×C5#513111yescharacteristic
406C2×C5C2×#82511yescharacteristic
407D5—241no—
408C23—61no—
409C23—301no—
410C23D5×D1211yescharacteristic
411Q8—602no—
412D4—121no—
413D4—121no—
414D4—121no—
415D4—601no—
416D4—602no—
417D4—602no—
418D4—601no—
419D4—601no—
420C2×C4—41no—
421C2×C4—51no—
422C2×C4—51no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—62no—
426C2×C4—61no—
427C2×C4—102no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4—302no—
433C2×C4—301no—
434C2×C4—602no—
435C2×C4—602no—
436C2×C4—601no—
437C2×C4—601no—
438C2×C4C4×D3×D511yescharacteristic
439C2×C4D5×#6711yescharacteristic
440C8—41no—
441C8—201no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3#6502911yescharacteristic
445C2×C3#6505911yescharacteristic
446C2×C3D5×#10411yescharacteristic
447D3—81no—
448D3—401no—
449C5#7083211yescharacteristic, complemented, Sylow
450C22—21no—
451C22—21no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—601no—
456C22—601no—
457C22—601no—
458C22#9124911yescharacteristic
459C22#9125011yescharacteristic
460C22D5×(C2×D3)⋊C411yescharacteristic
461C4—21no—
462C4—21no—
463C4—52no—
464C4—101no—
465C4—101no—
466C4—101no—
467C4—122no—
468C4—121no—
469C4—602no—
470C4—601no—
471C3#1059907111yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—241no—
475C2—1201no—
476C2#1174712911yescharacteristic
477C2#1174810511yescharacteristic
478C2D5×#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#1505
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×#65008C2semidirect
3. #11748635C2semidirect
4. #11746291C2semidirect
5. C5×#4470C2semidirect
6. #11745959C2semidirect
7. #11745957C2semidirect
15. #91468C4semidirect
16. #91451C4semidirect
17. #91418C4semidirect
18. Dic5×D12C4semidirect
30. #65008D3semidirect
72. #4470D5semidirect
379. C3×C5#1505semidirect
449. C5#70832semidirect
471. C3#10599071semidirect

Maximal subgroups

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

subgroupindex
#117543302
C3×#650082
#117486352
#117462912
C5×#44702
#117459592
#117459572
#105990713
#708325