Finite Group Databasebeta

← #14283286

Subgroups — #14283286

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#930C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3#11748737C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic, complemented
5C5×#4470C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10599097—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×D5×#67—21no—
11C2×D5×D12C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C5×#930C2211yescharacteristic
14C2×C3×#676—21no—
15#91566—21no—
16C2×#6665—21no—
17D5×(C2×D3)⋊C4—21no—
18#91450C411yescharacteristic, complemented
19#91449C411yescharacteristic, complemented
20#91448—21no—
21D5×C4⋊Dic3C411yescharacteristic, complemented
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23#91115C2211yescharacteristic, complemented
24C5×C3⋊#95C2211yescharacteristic, complemented
25C3×C22⋊#168C2211yescharacteristic, complemented
26C3×#3952—21no—
27#90994—21no—
28#69978—51nomaximal, Hall
29D5×#121—31no—
30#65015D311yescharacteristic, complemented
31#64953—31no—
32C5×#327—31no—
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5D411yescharacteristic
37C22×D3×D5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C2×D60C2×C411yescharacteristic
42C2×C5×#67—21no—
43C22×C5×Dic3—21no—
44C2×C5×D12C2×C411yescharacteristic
45C22×C3×Dic5D411yescharacteristic
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51D5×#67—42no—
52D5×#67—42no—
53C2×#1203—21no—
54C2×#1202—21no—
55C2×#1201—21no—
56C2×D5×Dic3—21no—
57D5×D12—42no—
58C2×C3×C5×C8—21no—
59#6714—21no—
60C4⋊Dic15C2×C411yescharacteristic
61C5×(C2×D3)⋊C4—21no—
62C5×C4⋊Dic3C2×C411yescharacteristic
63C2×C3×#168—21no—
64C3×#676—42no—
65#6668—21no—
66#6667—21no—
67(C2×D3)⋊Dic5—21no—
68#6665—42no—
69C2×#930—51no—
70C3×#407—51no—
71#5211—51no—
72#4470—51no—
73#4470—51no—
74#4470—51no—
75#4470D511yescharacteristic, complemented
76C2×D4×D5—31no—
77C2×D4×D5—61no—
78C22×C4×D5C2×D311yescharacteristic
79C5×#121—31no—
80#4085—61no—
81#4084—31no—
82#4076—31no—
83C2×#685—61no—
84C2×#676—21no—
85#4041—31no—
86D5×C4⋊C4—31no—
87#4030—61no—
88D5×C22⋊C4—61no—
89C5×C22⋊C8C2×D311yescharacteristic, complemented
90C5×#95—31no—
91#3963—31no—
92#3963—61no—
93C22⋊#168C2×D311yescharacteristic, complemented
94#3952—21no—
95#1510—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×C5×D3—21no—
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—22no—
102C22×C3×D5—41no—
103C22×C3×D5C22⋊C411yescharacteristic
104C22×C3×D5C22⋊C411yescharacteristic
105C2×D3×D5—42no—
106C2×D3×D5—42no—
107C2×D3×D5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111#1220—41no—
112#1220—41no—
113C2×Dic15—21no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117D60—41no—
118C5×#67—41no—
119C5×#67—41no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C5×D12—41no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5C22⋊C411yescharacteristic
127C2×C3×Dic5C22⋊C411yescharacteristic
128C3×C4×D5—22no—
129C3×C4×D5—22no—
130C3×C4×D5—41no—
131C3×C4×D5—41no—
132#1203—42no—
133#1202—42no—
134#1201—42no—
135D5×Dic3—42no—
136C3×C5×C8—41no—
137C3×#168—41no—
138C23×C3×C4—51no—
139C22×#67—101no—
140C22×D12—51no—
141C2×C3×M16—101no—
142C2×#217—101no—
143#930—51no—
144#930—51no—
145#930—51no—
146#930—101no—
147#930—101no—
148#930C2×D511yescharacteristic
149C2×(C2×D3)⋊C4—101no—
150C2×C4⋊Dic3—51no—
151C3×C22⋊C8—51no—
152C3×C22⋊C8—101no—
153C3×C22⋊C8C2×D511yescharacteristic, complemented
154C3⋊#95—51no—
155C3⋊#95—101no—
156C3⋊#95C2×D511yescharacteristic, complemented
157C23×D5—61no—
158C23×D5D1211yescharacteristic
159C2×C5×D4—31no—
160C2×C5×D4—61no—
161C22×C4×C5—61no—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—61no—
164C2×C22⋊D5—61no—
165C2×C22⋊D5—61no—
166C22×Dic5—61no—
167C22×Dic5D1211yescharacteristic
168D4×D5—122no—
169D4×D5—122no—
170D4×D5—122no—
171C2×D20—31no—
172C2×D20—61no—
173C2×C4×D5—42no—
174C2×C4×D5—61no—
175C2×C4×D5C4×D311yescharacteristic
176C2×C4×D5C4×D311yescharacteristic
177C2×C4×D5#6711yescharacteristic
178C2×C4×D5#6711yescharacteristic
179C2×C5×C8—21no—
180C5×C4⋊C4—31no—
181C5×C22⋊C4—61no—
182C22⋊Dic5—61no—
183#685—61no—
184#685—61no—
185#685—122no—
186C4⋊Dic5—31no—
187#683—61no—
188C2×#168—21no—
189#676—42no—
190C2×#121—151no—
191#407—51no—
192#381—151no—
193#327—31no—
194#327—151no—
195#327—151no—
196#327—151no—
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5C2×C22⋊C411yescharacteristic
200C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
201C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—41no—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C3×D5—21no—
209C2×C3×D5—21no—
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—21no—
213C2×C3×D5—42no—
214C2×C3×D5—42no—
215C2×C3×D5#9912yes—
216D3×D5—84no—
217C3×C4×C5—21no—
218C3×C4×C5—21no—
219Dic15—41no—
220Dic15—81no—
221C3×Dic5—21no—
222C3×Dic5—21no—
223C5×Dic3—41no—
224C5×Dic3—81no—
225C24×C3—51no—
226C23×D3—101no—
227C22×C3×C4—51no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—202no—
233C22×C3×C4C22×D511yescharacteristic
234C2×#67—21no—
235C2×#67—101no—
236C2×#67—101no—
237C2×#67—101no—
238C2×#67—202no—
239C2×#67—202no—
240C22×Dic3—21no—
241C22×Dic3—101no—
242C22×Dic3—101no—
243C2×D12—51no—
244C2×D12—101no—
245C2×D12—202no—
246C2×D12C4×D511yescharacteristic
247C3×M16—202no—
248C2×C3×C8—21no—
249C2×C3×C8—101no—
250#217—202no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—101no—
253(C2×D3)⋊C4—101no—
254(C2×D3)⋊C4—101no—
255C4⋊Dic3—51no—
256C4⋊Dic3—101no—
257C4⋊Dic3C4×D511yescharacteristic
258C23×C5—61no—
259C23×C5C2×D1211yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—22no—
263C22×D5—41no—
264C22×D5—61no—
265C22×D5—122no—
266C22×D5—122no—
267C22×D5—122no—
268C22×D5(C2×D3)⋊C411yescharacteristic
269C22×D5(C2×D3)⋊C411yescharacteristic
270C5×D4—121no—
271C5×D4—121no—
272C5×D4—121no—
273C2×C4×C5—41no—
274C2×C4×C5—61no—
275C2×C4×C5—121no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C22⋊D5—122no—
281C22⋊D5—122no—
282C22⋊D5—121no—
283C22⋊D5—121no—
284C2×Dic5—41no—
285C2×Dic5—61no—
286C2×Dic5—121no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289C2×Dic5(C2×D3)⋊C411yescharacteristic
290C2×Dic5(C2×D3)⋊C411yescharacteristic
291D20—121no—
292D20—122no—
293C4×D5—22no—
294C4×D5—22no—
295C4×D5—41no—
296C4×D5—41no—
297C4×D5—122no—
298C5×C8—41no—
299#168—41no—
300C22×D4—151no—
301C22×D4—301no—
302C23×C4—51no—
303C2×M16—101no—
304#121—31no—
305#121—151no—
306#121—151no—
307#121—151no—
308#121—301no—
309#121—301no—
310C2×C4⋊C4—151no—
311C2×C22⋊C4—301no—
312C2×C22⋊C4—301no—
313C22⋊C8—51no—
314C22⋊C8—101no—
315C22⋊C8D3×D511yescharacteristic, complemented
316#95—31no—
317#95—151no—
318#95—301no—
319C2×C3×C5—21no—
320C2×C3×C5—21no—
321C2×C3×C5C2×#9911yescharacteristic
322C2×C3×C5#41811yescharacteristic
323C2×C3×C5#42111yescharacteristic
324D15—81no—
325C3×D5—22no—
326C3×D5—41no—
327C5×D3—81no—
328C23×C3—51no—
329C23×C3—51no—
330C23×C3—102no—
331C23×C3—101no—
332C23×C3—101no—
333C23×C3—201no—
334C23×C3D4×D511yescharacteristic
335C22×D3—21no—
336C22×D3—101no—
337C22×D3—202no—
338C22×D3—202no—
339C22×D3—202no—
340C2×C3×C4—41no—
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4—201no—
348C2×C3×C4C2×C4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350#67—41no—
351#67—41no—
352#67—202no—
353#67—202no—
354#67—201no—
355#67—201no—
356C2×Dic3—21no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—101no—
361C2×Dic3—202no—
362C2×Dic3—201no—
363C2×Dic3—201no—
364C2×Dic3—201no—
365D12—41no—
366D12—201no—
367D12—202no—
368C3×C8—41no—
369C3×C8—201no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5#90811yescharacteristic
376C22×C5#90811yescharacteristic
377C22×C5C2×(C2×D3)⋊C411yescharacteristic
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—42no—
384C2×D5—42no—
385C2×D5—121no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—244no—
389C2×D5#80612yes—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—121no—
393C4×C5—241no—
394Dic5—21no—
395Dic5—21no—
396Dic5—121no—
397Dic5—241no—
398C24—51no—
399C24—301no—
400C2×D4—31no—
401C2×D4—61no—
402C2×D4—151no—
403C2×D4—301no—
404C2×D4—301no—
405C2×D4—301no—
406C2×D4—301no—
407C2×D4—602no—
408C2×D4—602no—
409C2×D4—602no—
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—61no—
416C22×C4—202no—
417C22×C4—301no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420M16—202no—
421C2×C8—21no—
422C2×C8—101no—
423C4⋊C4—31no—
424C4⋊C4—151no—
425C4⋊C4—301no—
426C22⋊C4—61no—
427C22⋊C4—301no—
428C22⋊C4—301no—
429C22⋊C4—301no—
430C22⋊C4—602no—
431C3×C5#151011yescharacteristic, complemented, Hall
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—52no—
435C22×C3—101no—
436C22×C3—101no—
437C22×C3—101no—
438C22×C3—101no—
439C22×C3—101no—
440C22×C3—202no—
441C22×C3—202no—
442C22×C3D5×C22⋊C411yescharacteristic
443C22×C3#405711yescharacteristic
444C22×C3#406011yescharacteristic
445C2×D3—41no—
446C2×D3—41no—
447C2×D3—41no—
448C2×D3—201no—
449C2×D3—201no—
450C2×D3—201no—
451C2×D3—404no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—101no—
455C3×C4—101no—
456Dic3—41no—
457Dic3—81no—
458Dic3—201no—
459Dic3—401no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—241no—
463C2×C5C2×#80611yescharacteristic
464C2×C5#513111yescharacteristic
465C2×C5#513911yescharacteristic
466D5—22no—
467D5—41no—
468D5—241no—
469C23—51no—
470C23—51no—
471C23—61no—
472C23—102no—
473C23—101no—
474C23—101no—
475C23—201no—
476C23—301no—
477C23—602no—
478C23—602no—
479C23—602no—
480C23D5×D1211yescharacteristic
481D4—121no—
482D4—121no—
483D4—121no—
484D4—601no—
485D4—602no—
486D4—602no—
487D4—602no—
488D4—601no—
489D4—601no—
490C2×C4—41no—
491C2×C4—51no—
492C2×C4—51no—
493C2×C4—61no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—201no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—301no—
503C2×C4—602no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4—601no—
507C2×C4C4×D3×D511yescharacteristic
508C2×C4D5×#6711yescharacteristic
509C8—41no—
510C8—201no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—102no—
514C2×C3—201no—
515C2×C3D5×#9911yescharacteristic
516C2×C3#6505911yescharacteristic
517C2×C3#6511011yescharacteristic
518D3—81no—
519D3—401no—
520C5#6997811yescharacteristic, complemented, Sylow
521C22—21no—
522C22—21no—
523C22—52no—
524C22—101no—
525C22—101no—
526C22—101no—
527C22—101no—
528C22—101no—
529C22—121no—
530C22—121no—
531C22—121no—
532C22—202no—
533C22—202no—
534C22—601no—
535C22—601no—
536C22—601no—
537C22—1204no—
538C22#9124911yescharacteristic
539C22#9125011yescharacteristic
540C22D5×(C2×D3)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—101no—
544C4—101no—
545C4—121no—
546C4—241no—
547C4—601no—
548C4—1201no—
549C3#1059909711yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—102no—
553C2—201no—
554C2—241no—
555C2—1201no—
556C2D5×#80611yescharacteristic
557C2#1174810511yescharacteristic
558C2#1174822911yescharacteristic
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 radicalD5×#930C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1510
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×#65015C2semidirect
3. #11748737C2semidirect
4. #11746291C2semidirect
5. C5×#4470C2semidirect
6. #11745959C2semidirect
7. #11745957C2semidirect
11. C2×D5×D12C4semidirect
18. #91450C4semidirect
19. #91449C4semidirect
21. D5×C4⋊Dic3C4semidirect
22. C3×C5×C22⋊C8C22semidirect
23. #91115C22semidirect
24. C5×C3⋊#95C22semidirect
25. C3×C22⋊#168C22semidirect
30. #65015D3semidirect
75. #4470D5semidirect
89. C5×C22⋊C8C2×D3semidirect
93. C22⋊#168C2×D3semidirect
153. C3×C22⋊C8C2×D5semidirect
156. C3⋊#95C2×D5semidirect
315. C22⋊C8D3×D5semidirect
431. C3×C5#1510semidirect
520. C5#69978semidirect
549. C3#10599097semidirect

Maximal subgroups

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

subgroupindex
D5×#9302
C3×#650152
#117487372
#117462912
C5×#44702
#117459592
#117459572
#105990973
#699785