Finite Group Databasebeta

← #14471529

Subgroups — #14471529

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66055C211yesmaximal, characteristic, complemented
2#11752539C211yesmaximal, characteristic
3#11751184C211yesmaximal, characteristic
4C5×#5079C211yesmaximal, characteristic, complemented
5#11749349C212yesmaximal, complemented
6#11749348C212yesmaximal, complemented
7#11749222C212yesmaximal
8#11749221C212yesmaximal
9C4×#6658C211yesmaximal, characteristic
10#11746918C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10613351—31nomaximal, Hall
13C2×D15⋊Q8—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C2×#6717C2212yes—
16C4×D60C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×Q8×Dic5C2212yes—
19C3×#4090C2212yes—
20C3×#4036—21no—
21C3×#4035—22no—
22C3×#4033—21no—
23C3×C4×Dic10C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91468C2212yes—
26#91419—22no—
27#91418C2212yes—
28#91383—21no—
29C2×#6658C2211yescharacteristic
30#91119C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C5×#835C2212yes—
33C5×#835C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35#90987C2211yescharacteristic
36#90986C2212yes—
37#90982C2212yes—
38#90971C2211yescharacteristic
39#90970C2212yes—
40#90968C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83688—51nomaximal, Hall
43#66061—31no—
44#66055D311yescharacteristic, complemented
45C5×#487—31no—
46#65383—31no—
47#65372—31no—
48#65107—32no—
49#65081—32no—
50#65080—32no—
51#65077—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2312yes—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×Dic6—21no—
58C2×C3×Dic10D411yescharacteristic
59C2×C3×Dic10C2311yescharacteristic
60C2×#1204—22no—
61C2×#1200—22no—
62D15⋊Q8—44no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66#6717—24no—
67#6714—21no—
68C4⋊Dic15C2311yescharacteristic
69C2×C3⋊#168C2312yes—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3C2312yes—
72C2×C5×C3⋊C8C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×C4⋊Dic5—22no—
75C3×C4⋊Dic5D411yescharacteristic
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#683—21no—
78C3×#683—22no—
79C3×#683—22no—
80C3×#683D412yes—
81C3×C4×Dic5—21no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5C2312yes—
84#6668—22no—
85#6667—22no—
86#6658—22no—
87C3×#557—51no—
88Q8×D12—51no—
89#5083—51no—
90#5083—52no—
91#5079—52no—
92#5079D511yescharacteristic, complemented
93C4×#215—52no—
94C4×#215—51no—
95Q8×C3⋊C8—51no—
96#5020—51no—
97#5020—52no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8—31no—
100C5×C4⋊Q8C2×D311yescharacteristic
101#4092—61no—
102Q8×Dic5C2×D312yes—
103#4090C2×D312yes—
104C2×#688—32no—
105C2×#677—31no—
106#4042—62no—
107#4039—32no—
108#4036—21no—
109#4035—22no—
110#4034—32no—
111#4033—21no—
112C4×D20—31no—
113C4×Dic10C2×D311yescharacteristic
114C4×Dic10C2×D311yescharacteristic
115C5×#103—32no—
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3359—151noSylow
128C22×D15—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136D60—21no—
137D60#4112yes—
138C4×D15—42no—
139C2×C5×Dic3—22no—
140C5×Dic6—42no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5C2×D412yes—
144C2×C3×Dic5C2×D412yes—
145C3×Dic10—21no—
146C3×Dic10—21no—
147C3×Dic10SD1614yescomplemented
148#1204—44no—
149#1200—44no—
150C3⋊#168—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—52no—
155C3×C4⋊Q8C2×D511yescharacteristic
156C3×#125—102no—
157C3×#125—101no—
158C3×C4×Q8—51no—
159C3×C4×Q8—52no—
160C3×C4×Q8—51no—
161C3×C4×Q8—101no—
162C2×#215—52no—
163C2×#215—51no—
164#897—102no—
165#897—101no—
166C4×D12—51no—
167C4×D12—52no—
168#869—52no—
169#869C2×D511yescharacteristic
170#835—52no—
171#835—52no—
172#835—51no—
173#835C2×D512yes—
174#835C2×D512yes—
175#809—51no—
176#808—52no—
177#808—51no—
178C4⋊(C3⋊C8)—51no—
179C4⋊(C3⋊C8)—52no—
180C4×C3⋊C8—52no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—61no—
183C2×C5×Q8C22×D312yes—
184Q8×D5—124no—
185C2×D20—31no—
186C2×C4×D5—61no—
187C2×C4×D5—62no—
188C2×Dic10—62no—
189C2×Dic10#6711yescharacteristic
190C2×Dic10C22×D311yescharacteristic
191C2×C5×C8—31no—
192C2×C5×C8—31no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198#688—64no—
199#685—61no—
200#685—62no—
201C4⋊Dic5—22no—
202C4⋊Dic5—31no—
203C4⋊Dic5#6711yescharacteristic
204C4⋊Dic5C22×D311yescharacteristic
205#683—21no—
206#683—22no—
207#683—22no—
208#683—62no—
209#683#6712yes—
210C4×Dic5—21no—
211C4×Dic5—22no—
212C4×Dic5C22×D312yes—
213C2×#168—32no—
214#677—62no—
215#557—51no—
216D4×Q8—151no—
217#487—31no—
218#487—152no—
219#475—152no—
220#475—151no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—41no—
236C3×Dic5—22no—
237C3×Dic5—41no—
238C3×Dic5—41no—
239C3×Dic5C2×SD1614yes—
240C5×Dic3—42no—
241C2×C3×Q8—51no—
242C2×C3×Q8—51no—
243C2×C3×Q8C22×D512yes—
244D3×Q8—204no—
245C2×D12—51no—
246C2×C4×D3—102no—
247C2×C4×D3—101no—
248C2×Dic6—21no—
249C2×Dic6—102no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—52no—
253C3×C4⋊C4—51no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—102no—
256C3×C4⋊C4—102no—
257C3×C4⋊C4—102no—
258C3×C4⋊C4—101no—
259C3×C42—52no—
260C3×C42—102no—
261C3×C42—101no—
262C3×C42C22×D511yescharacteristic
263#215—102no—
264#215—104no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—101no—
267C4⋊Dic3—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22×D512yes—
271C2×C3⋊C8—52no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274C22×D5—61no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×Q8—122no—
278C2×C4×C5—22no—
279C2×C4×C5—62no—
280C2×C4×C5C2×#6711yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—61no—
286C2×Dic5C2×#6712yes—
287C2×Dic5C2×#6712yes—
288D20—32no—
289D20—61no—
290C4×D5—122no—
291C4×D5—124no—
292Dic10—21no—
293Dic10—21no—
294Dic10—124no—
295Dic10#21514yescomplemented
296C5×C8—61no—
297C5×C8—61no—
298#168—62no—
299C22×Q8—301no—
300C2×SD16—151no—
301C2×SD16—152no—
302C4⋊Q8—31no—
303C4⋊Q8—52no—
304C4⋊Q8—152no—
305C4⋊Q8D3×D511yescharacteristic
306#125—102no—
307#125—101no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—51no—
311C4×Q8—52no—
312C4×Q8—51no—
313C4×Q8—101no—
314C4×D4—152no—
315C4×D4—151no—
316#106—152no—
317#106—151no—
318C4⋊C8—152no—
319C4⋊C8—151no—
320#103—32no—
321#103—32no—
322#103—152no—
323#103—151no—
324#103—152no—
325#102—151no—
326C4×C8—31no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331D15—42no—
332C22×D3—101no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—54no—
336C3×Q8—101no—
337C3×Q8—101no—
338C2×C3×C4—22no—
339C2×C3×C4—52no—
340C2×C3×C4—52no—
341C2×C3×C4—101no—
342C2×C3×C4—101no—
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4C23×D511yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—101no—
348D12—52no—
349D12—101no—
350C4×D3—204no—
351C4×D3—202no—
352Dic6—42no—
353Dic6—204no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—102no—
357C22×C5C22×#6711yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—122no—
364C4×C5C2×#21512yes—
365C4×C5D3×#4111yescharacteristic
366C4×C5#101011yescharacteristic
367Dic5—22no—
368Dic5—41no—
369Dic5—41no—
370Dic5—121no—
371Dic5C2×#21514yes—
372C2×Q8—51no—
373C2×Q8—51no—
374C2×Q8—61no—
375C2×Q8—302no—
376C2×Q8—604no—
377C2×Q8C2×D3×D512yes—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381SD16—302no—
382SD16—304no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—152no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—32no—
389C4⋊C4—52no—
390C4⋊C4—51no—
391C4⋊C4—51no—
392C4⋊C4—61no—
393C4⋊C4—102no—
394C4⋊C4—102no—
395C4⋊C4—102no—
396C4⋊C4—101no—
397C4⋊C4—151no—
398C4⋊C4—302no—
399C22⋊C4—302no—
400C22⋊C4—301no—
401C42—52no—
402C42—102no—
403C42—101no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—102no—
408C2×D3—201no—
409C2×D3—201no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—54no—
413C3×C4—102no—
414C3×C4—201no—
415C3×C4—201no—
416C3×C4D5×SD1612yes—
417C3×C4D5×#4111yescharacteristic
418C3×C4#415011yescharacteristic
419Dic3—42no—
420Dic3—201no—
421C2×C5C22×#21511yescharacteristic
422C2×C5#583111yescharacteristic
423C2×C5#583811yescharacteristic
424D5—122no—
425C23—301no—
426Q8—22no—
427Q8—22no—
428Q8—54no—
429Q8—101no—
430Q8—101no—
431Q8—122no—
432Q8—604no—
433D4—152no—
434D4—301no—
435C2×C4—22no—
436C2×C4—52no—
437C2×C4—52no—
438C2×C4—62no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—301no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4D5×#6711yescharacteristic
445C2×C4D5×#6711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—302no—
450C2×C3#6601111yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6610011yescharacteristic
453D3—202no—
454C5#8368811yescharacteristic, complemented, Sylow
455C22—302no—
456C22—601no—
457C22—601no—
458C22C2×D5×#6711yescharacteristic
459C4—21no—
460C4—42no—
461C4—54no—
462C4—102no—
463C4—122no—
464C4—201no—
465C4—201no—
466C4—601no—
467C4D5×#21512yes—
468C4#9202011yescharacteristic
469C4#9202411yescharacteristic
470C3#1061335111yescharacteristic, complemented, Sylow
471C2—602no—
472C2#1175493911yescharacteristic
473C2C2×D5×#21511yescharacteristic
474C2#1175510111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66055C2semidirect
4. C5×#5079C2semidirect
5. #11749349C2semidirect
6. #11749348C2semidirect
10. #11746918C2semidirect
11. C3⋊C8×Dic10C2semidirect
44. #66055D3semidirect
92. #5079D5semidirect
147. C3×Dic10SD16semidirect
295. Dic10#215semidirect
405. C3×C5#3359semidirect
454. C5#83688semidirect
470. C3#10613351semidirect

Maximal subgroups

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

subgroupindex
C3×#660552
#117525392
#117511842
C5×#50792
#117493492
#117493482
#117492222
#117492212
C4×#66582
#117469182
C3⋊C8×Dic102
#106133513
#836885