Finite Group Databasebeta

← #14297662

Subgroups — #14297662

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic
2#11748834C211yesmaximal, characteristic, complemented
3C2×#90982C211yesmaximal, characteristic, complemented
4C2×#90965C211yesmaximal, characteristic
5C2×#90964C211yesmaximal, characteristic
6#11746350C211yesmaximal, characteristic, complemented
7C5×#4529C211yesmaximal, characteristic, complemented
8#10599685—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C4×D5—21no—
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×#685—21no—
17C2×C3×C4×Dic5C2211yescharacteristic
18C3×#4039—22no—
19C3×#4039C414yescomplemented
20C2×#6668—21no—
21C2×#6668—21no—
22#90982—22no—
23#90965—22no—
24#90964—22no—
25#71604—51nomaximal, Hall
26C2×#4039D311yescharacteristic
27C2×#3953—31no—
28C2×#3946—31no—
29#65265—31no—
30C2×#3941—31no—
31C5×#340—31no—
32#64749—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×C5×Dic3—21no—
38C22×C3×Dic5D411yescharacteristic
39C22×C3×Dic5D411yescharacteristic
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C2×C3×D20D412yes—
45C2×C3×D20Q812yes—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5—42no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C412yes—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C5×C4⋊Dic3—21no—
57C5×C4⋊Dic3—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61C3×#685—24no—
62C3×C4×Dic5C2×C412yes—
63C3×C4×Dic5D412yes—
64#6668—42no—
65#6668—42no—
66C2×C3×C4×D4—51no—
67C2×#832—51no—
68C2×#832—51no—
69#4935—51no—
70C2×C4⋊(C3⋊C8)—51no—
71#4529—51no—
72#4529D511yescharacteristic, complemented
73C22×D20C2×D311yescharacteristic
74C22×C4×D5—21no—
75C22×C5×C8—31no—
76C2×C5×C4⋊C4—31no—
77C2×C5×C4⋊C4C2×D311yescharacteristic
78C2×#685—21no—
79C2×C4⋊Dic5—31no—
80C2×#683—61no—
81C2×#683—61no—
82C2×C4×Dic5C2×D311yescharacteristic
83C22×#168—31no—
84#4039—22no—
85#4039Dic314yescomplemented
86#3953—62no—
87#3946—62no—
88#3941—62no—
89#1802—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5—22no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C22×C3×D5—41no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5C22⋊C412yes—
116C2×C3×Dic5C22⋊C412yes—
117C2×C3×Dic5D812yes—
118C2×C3×Dic5SD1612yes—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20—22no—
122C3×D20C4⋊C414yescomplemented
123C3×C4×D5—48no—
124C3⋊#168—41no—
125C5×C3⋊C8—41no—
126C22×C3×D4—51no—
127C23×C3×C4—101no—
128C3×C4×D4—54no—
129C3×C4×D4—102no—
130C2×C3×C4⋊C4C2×D511yescharacteristic
131C2×C3×C22⋊C4—101no—
132C2×C3×C42—51no—
133C2×C4⋊Dic3—51no—
134C2×C4⋊Dic3—101no—
135C2×C4⋊Dic3—101no—
136C2×C4⋊Dic3C2×D511yescharacteristic
137C22×C3⋊C8—51no—
138C22×C3⋊C8C2×D511yescharacteristic
139#832—102no—
140#832—102no—
141C4⋊(C3⋊C8)—102no—
142C23×D5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—61no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—61no—
147C22×Dic5#6711yescharacteristic
148C22×Dic5#6711yescharacteristic
149C2×D20—21no—
150C2×D20—21no—
151C2×D20—21no—
152C2×D20Dic612yes—
153C2×D20D1212yes—
154C2×D20C2×Dic312yes—
155C2×C4×D5—24no—
156C2×C4×D5—42no—
157C2×C4×D5—42no—
158C2×C5×C8—61no—
159C2×C5×C8—61no—
160C2×C5×C8—61no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—61no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4C2×Dic312yes—
165#685—24no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168#683—122no—
169#683—122no—
170C4×Dic5C2×Dic312yes—
171C4×Dic5#6712yes—
172C2×#168—61no—
173C2×#168—61no—
174C2×#168—61no—
175C2×C4×D4—51no—
176C2×C4⋊C8—151no—
177C2×#102—151no—
178C2×#102—151no—
179#384—151no—
180#340—31no—
181#340—151no—
182C22×C3×C5C2×C22⋊C411yescharacteristic
183C22×C3×C5#12111yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5C2×D811yescharacteristic
186C22×C3×C5C2×SD1611yescharacteristic
187C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C2×C3×D5—24no—
190C2×C3×D5—42no—
191C2×C3×D5—42no—
192C2×C3×D5—42no—
193C2×C3×D5—42no—
194C2×C3×D5—42no—
195C2×C3×D5—42no—
196C3×C4×C5—42no—
197C3×C4×C5C2×C4⋊C411yescharacteristic
198C3×C4×C5#11711yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5C22⋊Q811yescharacteristic
201Dic15—81no—
202C3×Dic5—22no—
203C3×Dic5#10214yescomplemented
204C5×Dic3—81no—
205C24×C3—101no—
206C2×C3×D4—52no—
207C2×C3×D4—52no—
208C2×C3×D4—52no—
209C2×C3×D4—101no—
210C2×C3×D4—101no—
211C2×C3×D4—101no—
212C22×C3×C4—21no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—104no—
216C22×C3×C4—202no—
217C22×C3×C4—202no—
218C22×C3×C4C22×D511yescharacteristic
219C22×Dic3—21no—
220C22×Dic3—101no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4C4×D512yes—
223C3×C22⋊C4—104no—
224C3×C42—52no—
225C3×C42—52no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228C4⋊Dic3—101no—
229C4⋊Dic3—101no—
230C4⋊Dic3—202no—
231C4⋊Dic3—202no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—101no—
236C2×C3⋊C8—101no—
237C2×C3⋊C8—101no—
238C23×C5C2×#6711yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—41no—
243C22×D5—41no—
244C22×D5—41no—
245C22×D5—41no—
246C2×C4×C5—22no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—121no—
250C2×C4×C5—121no—
251C2×C4×C5—121no—
252C2×C4×C5C2×Dic611yescharacteristic
253C2×C4×C5C2×D1211yescharacteristic
254C2×C4×C5#23511yescharacteristic
255C2×C4×C5#23511yescharacteristic
256C2×C4×C5C22×Dic311yescharacteristic
257C2×C4×C5C2×#6711yescharacteristic
258C2×Dic5—21no—
259C2×Dic5—21no—
260C2×Dic5—121no—
261C2×Dic5—121no—
262C2×Dic5—121no—
263C2×Dic5#21312yes—
264C2×Dic5#21412yes—
265C2×Dic5#21712yes—
266C2×Dic5#21712yes—
267D20—22no—
268D20—22no—
269D20—22no—
270D20C4⋊Dic314yescomplemented
271C4×D5—48no—
272C5×C8—121no—
273#168—121no—
274C22×D4—51no—
275C23×C4—101no—
276C22×C8—31no—
277C22×C8—151no—
278C4×D4—54no—
279C4×D4—102no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—151no—
282C2×C4⋊C4—301no—
283C2×C4⋊C4—301no—
284C2×C4⋊C4D3×D511yescharacteristic
285C2×C22⋊C4—101no—
286C2×C42—51no—
287C4⋊C8—302no—
288#102—302no—
289#102—302no—
290C2×C3×C5#38011yescharacteristic
291C2×C3×C5C2×#10211yescharacteristic
292C2×C3×C5#41711yescharacteristic
293C2×C3×C5#45911yescharacteristic
294C2×C3×C5#46111yescharacteristic
295C2×C3×C5#47411yescharacteristic
296C2×C3×C5#47611yescharacteristic
297C3×D5—44no—
298C23×C3—102no—
299C23×C3—102no—
300C23×C3—102no—
301C23×C3—201no—
302C23×C3—201no—
303C23×C3—201no—
304C23×C3—201no—
305C23×C3D4×D511yescharacteristic
306C3×D4—54no—
307C3×D4—102no—
308C3×D4—102no—
309C3×D4—102no—
310C2×C3×C4—22no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—52no—
314C2×C3×C4—52no—
315C2×C3×C4—52no—
316C2×C3×C4—52no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—208no—
320C2×C3×C4C2×C4×D511yescharacteristic
321C2×C3×C4#70911yescharacteristic
322C2×C3×C4#70911yescharacteristic
323C2×C3×C4D4×D511yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4Q8×D511yescharacteristic
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—201no—
330C2×Dic3—201no—
331C2×Dic3—201no—
332C3⋊C8—41no—
333C3⋊C8—201no—
334C22×C5#92411yescharacteristic
335C22×C5#93011yescharacteristic
336C22×C5C2×#21311yescharacteristic
337C22×C5C2×#21411yescharacteristic
338C22×C5#94911yescharacteristic
339C22×C5#95111yescharacteristic
340C22×C5C2×#21711yescharacteristic
341C2×D5—24no—
342C2×D5—42no—
343C2×D5—42no—
344C2×D5—42no—
345C2×D5—42no—
346C2×D5—42no—
347C2×D5—42no—
348C4×C5—42no—
349C4×C5—241no—
350C4×C5#92411yescharacteristic
351C4×C5C2×C4⋊Dic311yescharacteristic
352C4×C5#92611yescharacteristic
353C4×C5#93011yescharacteristic
354Dic5—22no—
355Dic5—241no—
356Dic5#83214yescomplemented
357C24—101no—
358C2×D4—52no—
359C2×D4—52no—
360C2×D4—52no—
361C2×D4—101no—
362C2×D4—101no—
363C2×D4—101no—
364C22×C4—21no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—61no—
368C22×C4—104no—
369C22×C4—202no—
370C22×C4—202no—
371C22×C4—301no—
372C22×C4C2×D3×D511yescharacteristic
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—301no—
377C2×C8—301no—
378C2×C8—301no—
379C4⋊C4—21no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—602no—
385C4⋊C4—602no—
386C4⋊C4D5×Dic312yes—
387C22⋊C4—104no—
388C42—52no—
389C42—52no—
390C3×C5#180211yescharacteristic, complemented, Hall
391C22×C3—104no—
392C22×C3—202no—
393C22×C3—202no—
394C22×C3—202no—
395C22×C3—202no—
396C22×C3—202no—
397C22×C3—202no—
398C22×C3D5×C22⋊C411yescharacteristic
399C22×C3#403011yescharacteristic
400C22×C3#404211yescharacteristic
401C22×C3D5×D811yescharacteristic
402C22×C3D5×SD1611yescharacteristic
403C22×C3#406011yescharacteristic
404C22×C3#406411yescharacteristic
405C3×C4—42no—
406C3×C4—54no—
407C3×C4—102no—
408C3×C4#401811yescharacteristic
409C3×C4#403011yescharacteristic
410C3×C4D5×C4⋊C411yescharacteristic
411C3×C4#404211yescharacteristic
412Dic3—81no—
413Dic3—401no—
414C2×C5#500711yescharacteristic
415C2×C5#500811yescharacteristic
416C2×C5#501511yescharacteristic
417C2×C5#501911yescharacteristic
418C2×C5#521211yescharacteristic
419C2×C5C2×#83211yescharacteristic
420C2×C5#523211yescharacteristic
421D5—44no—
422C23—102no—
423C23—102no—
424C23—102no—
425C23—201no—
426C23—201no—
427C23—201no—
428C23—201no—
429C23D5×#6711yescharacteristic
430D4—54no—
431D4—102no—
432D4—102no—
433D4—102no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—52no—
438C2×C4—52no—
439C2×C4—52no—
440C2×C4—52no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—208no—
447C2×C4—601no—
448C2×C4—601no—
449C2×C4—601no—
450C2×C4D5×Dic611yescharacteristic
451C2×C4#677111yescharacteristic
452C2×C4#677111yescharacteristic
453C2×C4D5×D1211yescharacteristic
454C2×C4C2×D5×Dic311yescharacteristic
455C2×C4D5×#6711yescharacteristic
456C8—121no—
457C8—601no—
458C2×C3—204no—
459C2×C3#6495611yescharacteristic
460C2×C3D5×#10211yescharacteristic
461C2×C3#6507511yescharacteristic
462C2×C3#6509211yescharacteristic
463C2×C3#6510711yescharacteristic
464C2×C3#6515911yescharacteristic
465C2×C3#6517911yescharacteristic
466C5#7160411yescharacteristic, complemented, Sylow
467C22—104no—
468C22—202no—
469C22—202no—
470C22—202no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22#9134911yescharacteristic
475C22#9144811yescharacteristic
476C22D5×#21311yescharacteristic
477C22D5×#21411yescharacteristic
478C22#9150211yescharacteristic
479C22#9150811yescharacteristic
480C22D5×#21711yescharacteristic
481C4—42no—
482C4—54no—
483C4—102no—
484C4—241no—
485C4—1201no—
486C4#9134911yescharacteristic
487C4#9135711yescharacteristic
488C4D5×C4⋊Dic311yescharacteristic
489C4#9144811yescharacteristic
490C3#1059968511yescharacteristic, complemented, Sylow
491C2—204no—
492C2#1174739911yescharacteristic
493C2#1174741011yescharacteristic
494C2#1174741411yescharacteristic
495C2#1174741511yescharacteristic
496C2#1174873811yescharacteristic
497C2D5×#83211yescharacteristic
498C2#1174919811yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1802
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11748834C2semidirect
3. C2×#90982C2semidirect
6. #11746350C2semidirect
7. C5×#4529C2semidirect
19. C3×#4039C4semidirect
72. #4529D5semidirect
85. #4039Dic3semidirect
122. C3×D20C4⋊C4semidirect
203. C3×Dic5#102semidirect
270. D20C4⋊Dic3semidirect
356. Dic5#832semidirect
390. C3×C5#1802semidirect
466. C5#71604semidirect
490. C3#10599685semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40392
#117488342
C2×#909822
C2×#909652
C2×#909642
#117463502
C5×#45292
#105996853
#716045