Finite Group Databasebeta

← #14283128

Subgroups — #14283128

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#121C211yesmaximal, characteristic
2#11748702C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746358C211yesmaximal, characteristic, complemented
5C5×#4537C211yesmaximal, characteristic, complemented
6#11745955C211yesmaximal, characteristic, complemented
7#11745954C211yesmaximal, characteristic, complemented
8#10599096—31nomaximal, Hall
9C2×C3×D4×D5—21no—
10C2×C3×D4×D5C411yescharacteristic, complemented
11C22×C3×C4×D5C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13C3×#4085—21no—
14C3×#4084C411yescharacteristic, complemented
15C3×#4076C2211yescharacteristic
16C3×#4041C411yescharacteristic, complemented
17C3×D5×C4⋊C4C411yescharacteristic, complemented
18C3×#4030—21no—
19C3×D5×C22⋊C4—21no—
20C2×#6665—21no—
21C2×Dic3×Dic5—21no—
22C2×#6649—21no—
23#91115C2211yescharacteristic, complemented
24#91114C2211yescharacteristic, complemented
25C5×C3⋊#95C2211yescharacteristic, complemented
26C5×#830C2211yescharacteristic, complemented
27#90955—21no—
28#71673—51nomaximal, Hall
29D5×#121D311yescharacteristic
30#65015—31no—
31#64955—31no—
32C5×#327—31no—
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5—21no—
37C23×C3×D5D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—21no—
42C22×C5×Dic3—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C2×C3×C22⋊D5—21no—
46C22×C3×Dic5D411yescharacteristic
47C3×D4×D5—42no—
48C3×D4×D5—42no—
49C3×D4×D5—42no—
50C2×C3×D20—21no—
51C2×C3×D20C2×C411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—42no—
54C2×C3×C4×D5C2×C411yescharacteristic
55C2×C3×C4×D5C2×C411yescharacteristic
56C2×C3×C4×D5D411yescharacteristic
57C2×C3×C4×D5D411yescharacteristic
58C3×C5×C4⋊C4C2×C411yescharacteristic
59C3×C5×C22⋊C4—21no—
60C2×C3⋊#168—21no—
61C2×C5×C3⋊C8—21no—
62C3×C22⋊Dic5—21no—
63C3×#685—21no—
64C3×#685—21no—
65C3×C4⋊Dic5C2×C411yescharacteristic
66C3×#683—21no—
67#6665—24no—
68Dic3×Dic5—42no—
69#6649—42no—
70C2×C3×#121—51no—
71C4×#217—51no—
72#5207—51no—
73#4537—51no—
74#4537—51no—
75#4537—51no—
76#4537D511yescharacteristic, complemented
77C2×D4×D5—21no—
78C2×D4×D5Dic311yescharacteristic, complemented
79C22×C4×D5C2×D311yescharacteristic
80C5×#121C2×D311yescharacteristic
81#4085—21no—
82#4084Dic311yescharacteristic, complemented
83#4076C2×D311yescharacteristic
84C2×#685—61no—
85C2×C4×Dic5—61no—
86C2×#676—61no—
87#4041Dic311yescharacteristic, complemented
88D5×C4⋊C4Dic311yescharacteristic, complemented
89#4030—21no—
90D5×C22⋊C4—21no—
91C5×C22⋊C8—31no—
92C5×#95—31no—
93#3963—31no—
94C22⋊#168—31no—
95#3952—61no—
96#1507—151noSylow
97C23×C3×C5—21no—
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—22no—
102C22×C3×D5—21no—
103C22×C3×D5—41no—
104C22×C3×D5—42no—
105C22×C3×D5—42no—
106C22×C3×D5—42no—
107C22×C3×D5C22⋊C411yescharacteristic
108C22×C3×D5C22⋊C411yescharacteristic
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C3×C5×D4—41no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×Dic15—22no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C3×C22⋊D5—42no—
123C3×C22⋊D5—41no—
124C3×C22⋊D5—41no—
125C3×C22⋊D5—42no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5C22⋊C411yescharacteristic
129C2×C3×Dic5C22⋊C411yescharacteristic
130C3×D20—41no—
131C3×D20—42no—
132C3×C4×D5—22no—
133C3×C4×D5—22no—
134C3×C4×D5—41no—
135C3×C4×D5—41no—
136C3×C4×D5—42no—
137C3⋊#168—41no—
138C5×C3⋊C8—41no—
139C22×C3×D4—51no—
140C22×C3×D4—101no—
141C23×C3×C4—51no—
142C3×#121—51no—
143C3×#121—51no—
144C3×#121—51no—
145C3×#121—101no—
146C3×#121—101no—
147C3×#121C2×D511yescharacteristic
148C2×C3×C4⋊C4—51no—
149C2×C3×C22⋊C4—101no—
150C2×#217—101no—
151C2×C4×Dic3—101no—
152C2×#208—101no—
153C3⋊#95—51no—
154C3⋊#95C2×D511yescharacteristic, complemented
155#830—51no—
156#830—101no—
157#830C2×D511yescharacteristic, complemented
158C23×D5—21no—
159C23×D5#6711yescharacteristic
160C2×C5×D4—21no—
161C2×C5×D4C2×Dic311yescharacteristic
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C2×C22⋊D5—21no—
165C2×C22⋊D5—21no—
166C2×C22⋊D5—21no—
167C22×Dic5—61no—
168C22×Dic5#6711yescharacteristic
169D4×D5—42no—
170D4×D5—42no—
171D4×D5—42no—
172C2×D20—21no—
173C2×D20C2×Dic311yescharacteristic
174C2×C4×D5—21no—
175C2×C4×D5—42no—
176C2×C4×D5C2×Dic311yescharacteristic
177C2×C4×D5C2×Dic311yescharacteristic
178C2×C4×D5#6711yescharacteristic
179C2×C4×D5#6711yescharacteristic
180C2×C5×C8—61no—
181C5×C4⋊C4C2×Dic311yescharacteristic
182C5×C22⋊C4—21no—
183C22⋊Dic5—21no—
184#685—21no—
185#685—21no—
186#685—64no—
187C4⋊Dic5C2×Dic311yescharacteristic
188#683—21no—
189C4×Dic5—122no—
190C2×#168—61no—
191#676—122no—
192C2×#121—51no—
193#407—151no—
194C4×C22⋊C4—151no—
195#327—31no—
196#327—151no—
197#327—151no—
198#327—151no—
199C22×C3×C5—21no—
200C22×C3×C5—21no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
206C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
207C2×C3×D5—21no—
208C2×C3×D5—21no—
209C2×C3×D5—21no—
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—42no—
213C2×C3×D5—42no—
214C2×C3×D5—41no—
215C2×C3×D5—41no—
216C2×C3×D5—41no—
217C2×C3×D5—84no—
218C2×C3×D5#10412yes—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221C3×C4×C5—41no—
222Dic15—42no—
223C3×Dic5—21no—
224C3×Dic5—41no—
225C3×Dic5#9912yes—
226C5×Dic3—42no—
227C24×C3—51no—
228C24×C3—101no—
229C2×C3×D4—21no—
230C2×C3×D4—51no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—101no—
234C2×C3×D4—101no—
235C2×C3×D4—202no—
236C2×C3×D4—202no—
237C2×C3×D4—202no—
238C2×C3×D4C4×D511yescharacteristic
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—51no—
242C22×C3×C4—51no—
243C22×C3×C4—51no—
244C22×C3×C4—101no—
245C22×C3×C4—202no—
246C22×C3×C4C22×D511yescharacteristic
247C22×Dic3—21no—
248C22×Dic3—101no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—101no—
251C3×C4⋊C4C4×D511yescharacteristic
252C3×C22⋊C4—21no—
253C3×C22⋊C4—101no—
254C3×C22⋊C4—101no—
255C3×C22⋊C4—101no—
256#217—104no—
257C4×Dic3—202no—
258#208—202no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—101no—
261C23×C5—21no—
262C23×C5C2×#6711yescharacteristic
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—22no—
266C22×D5—21no—
267C22×D5—41no—
268C22×D5—42no—
269C22×D5—42no—
270C22×D5—42no—
271C22×D5#21711yescharacteristic
272C22×D5#21711yescharacteristic
273C5×D4—41no—
274C5×D4—41no—
275C5×D4—41no—
276C2×C4×C5—21no—
277C2×C4×C5—41no—
278C2×C4×C5—62no—
279C2×C4×C5—121no—
280C2×C4×C5—121no—
281C2×C4×C5C22×Dic311yescharacteristic
282C2×C4×C5C2×#6711yescharacteristic
283C22⋊D5—42no—
284C22⋊D5—41no—
285C22⋊D5—41no—
286C22⋊D5—42no—
287C2×Dic5—22no—
288C2×Dic5—21no—
289C2×Dic5—62no—
290C2×Dic5—121no—
291C2×Dic5—121no—
292C2×Dic5#21711yescharacteristic
293C2×Dic5#21711yescharacteristic
294D20—41no—
295D20—42no—
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—41no—
299C4×D5—41no—
300C4×D5—42no—
301C5×C8—121no—
302#168—121no—
303C22×D4—51no—
304C22×D4—101no—
305C23×C4—51no—
306C2×M16—301no—
307#121—51no—
308#121—51no—
309#121—51no—
310#121—101no—
311#121—101no—
312#121D3×D511yescharacteristic
313C2×C4⋊C4—51no—
314C2×C22⋊C4—101no—
315C2×C22⋊C4—301no—
316C2×C42—301no—
317C22⋊C8—31no—
318C22⋊C8—151no—
319C22⋊C8—301no—
320#95—31no—
321#95—151no—
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5—81no—
325C2×C3×C5C2×#9911yescharacteristic
326C2×C3×C5#41811yescharacteristic
327C2×C3×C5C2×#10411yescharacteristic
328C3×D5—22no—
329C3×D5—41no—
330C3×D5—81no—
331C23×C3—21no—
332C23×C3—51no—
333C23×C3—51no—
334C23×C3—102no—
335C23×C3—101no—
336C23×C3—101no—
337C23×C3—101no—
338C23×C3—201no—
339C23×C3—202no—
340C23×C3—202no—
341C23×C3—202no—
342C23×C3D4×D511yescharacteristic
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—41no—
346C3×D4—201no—
347C3×D4—202no—
348C3×D4—202no—
349C3×D4—202no—
350C3×D4—201no—
351C3×D4—201no—
352C2×C3×C4—21no—
353C2×C3×C4—41no—
354C2×C3×C4—51no—
355C2×C3×C4—51no—
356C2×C3×C4—102no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—101no—
360C2×C3×C4—201no—
361C2×C3×C4—201no—
362C2×C3×C4—202no—
363C2×C3×C4C2×C4×D511yescharacteristic
364C2×C3×C4D4×D511yescharacteristic
365C2×Dic3—22no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—102no—
369C2×Dic3—201no—
370C2×Dic3—201no—
371C3⋊C8—41no—
372C3⋊C8—201no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5#93211yescharacteristic
379C22×C5#93211yescharacteristic
380C22×C5C2×#21711yescharacteristic
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—21no—
386C2×D5—42no—
387C2×D5—42no—
388C2×D5—41no—
389C2×D5—41no—
390C2×D5—41no—
391C2×D5—84no—
392C2×D5#83712yes—
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—41no—
396C4×C5—122no—
397Dic5—21no—
398Dic5—41no—
399Dic5—122no—
400Dic5#83412yes—
401C24—51no—
402C24—101no—
403C2×D4—21no—
404C2×D4—51no—
405C2×D4—101no—
406C2×D4—101no—
407C2×D4—101no—
408C2×D4—101no—
409C2×D4—202no—
410C2×D4—202no—
411C2×D4—202no—
412C2×D4D5×Dic311yescharacteristic
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—61no—
419C22×C4—101no—
420C22×C4—202no—
421C22×C4—301no—
422C22×C4C2×D3×D511yescharacteristic
423M16—602no—
424C2×C8—61no—
425C2×C8—301no—
426C4⋊C4—51no—
427C4⋊C4—101no—
428C4⋊C4D5×Dic311yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—101no—
431C22⋊C4—101no—
432C22⋊C4—101no—
433C22⋊C4—304no—
434C42—602no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—52no—
442C22×C3—101no—
443C22×C3—101no—
444C22×C3—101no—
445C22×C3—101no—
446C22×C3—101no—
447C22×C3—202no—
448C22×C3—202no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3—404no—
453C22×C3D5×C22⋊C411yescharacteristic
454C22×C3#405711yescharacteristic
455C22×C3#406011yescharacteristic
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—41no—
459C3×C4—52no—
460C3×C4—101no—
461C3×C4—201no—
462Dic3—42no—
463Dic3—202no—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—81no—
467C2×C5#521511yescharacteristic
468C2×C5C2×#83411yescharacteristic
469C2×C5C2×#83711yescharacteristic
470D5—22no—
471D5—41no—
472D5—81no—
473C23—21no—
474C23—51no—
475C23—51no—
476C23—102no—
477C23—101no—
478C23—101no—
479C23—101no—
480C23—201no—
481C23—202no—
482C23—202no—
483C23—202no—
484C23D5×#6711yescharacteristic
485D4—41no—
486D4—41no—
487D4—41no—
488D4—201no—
489D4—202no—
490D4—202no—
491D4—202no—
492D4—201no—
493D4—201no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—51no—
497C2×C4—51no—
498C2×C4—62no—
499C2×C4—102no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4—101no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—201no—
506C2×C4—201no—
507C2×C4—202no—
508C2×C4—302no—
509C2×C4—601no—
510C2×C4—601no—
511C2×C4C2×D5×Dic311yescharacteristic
512C2×C4D5×#6711yescharacteristic
513C8—121no—
514C8—601no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—81no—
518C2×C3—102no—
519C2×C3—201no—
520C2×C3—401no—
521C2×C3D5×#9911yescharacteristic
522C2×C3#6505911yescharacteristic
523C2×C3D5×#10411yescharacteristic
524C5#7167311yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—52no—
531C22—101no—
532C22—101no—
533C22—101no—
534C22—101no—
535C22—101no—
536C22—202no—
537C22—202no—
538C22—201no—
539C22—201no—
540C22—201no—
541C22—404no—
542C22#9148911yescharacteristic
543C22#9149111yescharacteristic
544C22D5×#21711yescharacteristic
545C4—21no—
546C4—21no—
547C4—41no—
548C4—52no—
549C4—101no—
550C4—122no—
551C4—201no—
552C4—602no—
553C3#1059909611yescharacteristic, complemented, Sylow
554C2—21no—
555C2—21no—
556C2—81no—
557C2—102no—
558C2—201no—
559C2—401no—
560C2#1174896211yescharacteristic
561C2D5×#83411yescharacteristic
562C2D5×#83711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×D5×#121C2
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1507
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. #11748702C2semidirect
3. #11748499C2semidirect
4. #11746358C2semidirect
5. C5×#4537C2semidirect
6. #11745955C2semidirect
7. #11745954C2semidirect
10. C2×C3×D4×D5C4semidirect
14. C3×#4084C4semidirect
16. C3×#4041C4semidirect
17. C3×D5×C4⋊C4C4semidirect
23. #91115C22semidirect
24. #91114C22semidirect
25. C5×C3⋊#95C22semidirect
26. C5×#830C22semidirect
76. #4537D5semidirect
78. C2×D4×D5Dic3semidirect
82. #4084Dic3semidirect
87. #4041Dic3semidirect
88. D5×C4⋊C4Dic3semidirect
154. C3⋊#95C2×D5semidirect
157. #830C2×D5semidirect
435. C3×C5#1507semidirect
524. C5#71673semidirect
553. C3#10599096semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1212
#117487022
#117484992
#117463582
C5×#45372
#117459552
#117459542
#105990963
#716735