Finite Group Databasebeta

← #14282945

Subgroups — #14282945

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754174C211yesmaximal, characteristic
2C3×#65007C211yesmaximal, characteristic
3#11748638C211yesmaximal, characteristic
4#11746288C211yesmaximal, characteristic
5C5×#4467C211yesmaximal, characteristic
6#11745965C211yesmaximal, characteristic
7#11745963C211yesmaximal, characteristic
8#10599102—31nomaximal, Hall
9#91813C2211yescharacteristic
10C5×#924C2211yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91574—21no—
13C2×#6668—21no—
14#91528—21no—
15C2×Dic3×Dic5—21no—
16#91468C411yescharacteristic, complemented
17#91378—21no—
18#91376C411yescharacteristic, complemented
19#91333C411yescharacteristic, complemented
20Dic5×Dic6C411yescharacteristic, complemented
21#91323—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3946—21no—
27C3×C8×Dic5—21no—
28#70792—51nomaximal, Hall
29#65956—31no—
30#65007D311yescharacteristic
31#64938—31no—
32C5×#328—31no—
33#64758—31no—
34#64687—31no—
35#64672—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×Dic30C2×C411yescharacteristic
39C22×C5×Dic3—21no—
40C2×C5×Dic6C2×C411yescharacteristic
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×#1204—21no—
44C2×C3×C5×C8—21no—
45#6719—21no—
46C4⋊Dic15C2×C411yescharacteristic
47#6712—21no—
48C5×#217—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6668—24no—
59#6668—21no—
60#6668—21no—
61#6668—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—42no—
65#5470—51no—
66C3×#431—51no—
67C4×C4⋊Dic3—51no—
68#4467—51no—
69#4467—51no—
70#4467—51no—
71#4467D511yescharacteristic
72C5×C22⋊Q8—31no—
73Q8×Dic5—31no—
74#4090—31no—
75#4070—31no—
76C2×#683—61no—
77C2×C4×Dic5—61no—
78C2×C4×Dic5C2×D311yescharacteristic
79#4035—61no—
80#4034—31no—
81#4033—31no—
82#4033—61no—
83#4024—61no—
84#4023—61no—
85C5×C22⋊C8C2×D311yescharacteristic
86C5×#95—31no—
87#3963—31no—
88C22⋊#168C2×D311yescharacteristic
89#3946—21no—
90C8×Dic5—21no—
91#1503—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—22no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101Dic30—41no—
102C2×C5×Dic3—22no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3—41no—
107C5×Dic6—41no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5SD1612yes—
114C2×C3×Dic5Q1612yes—
115#1204—42no—
116C3×C5×C8—41no—
117C3×#168—41no—
118C2×C3×C42—51no—
119#926—101no—
120C2×C4⋊Dic3—101no—
121#924—51no—
122#924—101no—
123#924C2×D511yescharacteristic
124C2×C4×Dic3—101no—
125#870—101no—
126#869—51no—
127#869—51no—
128C4×Dic6—51no—
129C4×Dic6—51no—
130C4×Dic6—101no—
131C3×C4⋊C8—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×C4×C8—101no—
135C3⋊#95—51no—
136C3⋊#95C2×D511yescharacteristic
137C2×C5×Q8—31no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—61no—
141C22×Dic5D1211yescharacteristic
142C22×Dic5D1211yescharacteristic
143C2×Dic10—31no—
144C2×Dic10—61no—
145C2×C5×C8—21no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—61no—
148C5×C22⋊C4—61no—
149C22⋊Dic5—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—61no—
152#683—64no—
153#683—61no—
154#683—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—61no—
159C4×Dic5—61no—
160C4×Dic5—122no—
161C4×Dic5C4×D311yescharacteristic
162C4×Dic5C4×D311yescharacteristic
163C4×Dic5#6711yescharacteristic
164C4×Dic5#6711yescharacteristic
165C2×#168—21no—
166#533—151no—
167#431—51no—
168C4×C4⋊C4—151no—
169#328—31no—
170#328—151no—
171#328—151no—
172#328—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5C2×Q1611yescharacteristic
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180Dic15—42no—
181Dic15—41no—
182Dic15—41no—
183C3×Dic5—21no—
184C3×Dic5#10312yes—
185C3×Dic5#10312yes—
186C3×Dic5#10412yes—
187C5×Dic3—42no—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C22×C3×C4C22×D511yescharacteristic
193C22×Dic3—21no—
194C22×Dic3—101no—
195C2×Dic6—51no—
196C2×Dic6—101no—
197C2×Dic6C4×D511yescharacteristic
198C2×C3×C8—21no—
199C2×C3×C8—101no—
200C3×C42—51no—
201C3×C42—51no—
202C3×C42—51no—
203C3×C42—51no—
204#217—21no—
205#217—101no—
206C4⋊Dic3—51no—
207C4⋊Dic3—101no—
208C4⋊Dic3—101no—
209C4⋊Dic3—101no—
210C4⋊Dic3—104no—
211C4⋊Dic3C4×D511yescharacteristic
212Dic3⋊C4—21no—
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215Dic3⋊C4—101no—
216C4×Dic3—101no—
217C4×Dic3—101no—
218C4×Dic3—202no—
219C23×C5C2×D1211yescharacteristic
220C5×Q8—121no—
221C2×C4×C5—41no—
222C2×C4×C5—62no—
223C2×C4×C5—61no—
224C2×C4×C5—61no—
225C2×C4×C5—121no—
226C2×C4×C5—121no—
227C2×C4×C5C2×C4×D311yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229C2×Dic5—22no—
230C2×Dic5—62no—
231C2×Dic5—61no—
232C2×Dic5—61no—
233C2×Dic5—121no—
234C2×Dic5—121no—
235C2×Dic5#20412yes—
236C2×Dic5Dic1212yes—
237C2×Dic5(C2×D3)⋊C411yescharacteristic
238C2×Dic5(C2×D3)⋊C411yescharacteristic
239C2×Dic5(C2×D3)⋊C411yescharacteristic
240C2×Dic5(C2×D3)⋊C411yescharacteristic
241Dic10—122no—
242Dic10—121no—
243C5×C8—41no—
244#168—41no—
245C4⋊Q8—151no—
246C4⋊Q8—151no—
247#125—301no—
248C22⋊Q8—31no—
249C22⋊Q8—151no—
250C22⋊Q8—301no—
251C4×Q8—151no—
252C4×Q8—151no—
253C4×Q8—301no—
254#117—301no—
255C2×C4⋊C4—301no—
256C2×C42—51no—
257C2×C42—301no—
258C4⋊C8—101no—
259C22⋊C8—51no—
260C22⋊C8D3×D511yescharacteristic
261C4×C8—101no—
262#95—31no—
263#95—151no—
264C2×C3×C5—21no—
265C2×C3×C5—21no—
266C2×C3×C5#41011yescharacteristic
267C2×C3×C5C2×#10311yescharacteristic
268C2×C3×C5C2×#10411yescharacteristic
269C23×C3D4×D511yescharacteristic
270C2×C3×C4—41no—
271C2×C3×C4—51no—
272C2×C3×C4—51no—
273C2×C3×C4—51no—
274C2×C3×C4—52no—
275C2×C3×C4—52no—
276C2×C3×C4—51no—
277C2×C3×C4—102no—
278C2×C3×C4C2×C4×D511yescharacteristic
279C2×C3×C4D4×D511yescharacteristic
280C2×Dic3—22no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—41no—
284C2×Dic3—41no—
285C2×Dic3—102no—
286C2×Dic3—101no—
287C2×Dic3—101no—
288C2×Dic3—201no—
289C2×Dic3—201no—
290Dic6—41no—
291Dic6—202no—
292Dic6—201no—
293C3×C8—41no—
294C3×C8—201no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5C2×#20411yescharacteristic
298C22×C5C2×Dic1211yescharacteristic
299C22×C5C2×(C2×D3)⋊C411yescharacteristic
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—122no—
303C4×C5—121no—
304C4×C5—121no—
305Dic5—21no—
306Dic5—122no—
307Dic5—121no—
308Dic5—121no—
309Dic5#81612yes—
310Dic5#81612yes—
311Dic5#82512yes—
312C2×Q8—31no—
313C2×Q8—151no—
314C2×Q8—301no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—61no—
318C22×C4—301no—
319C22×C4C2×D3×D511yescharacteristic
320C2×C8—21no—
321C2×C8—101no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—151no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—304no—
331C4⋊C4—301no—
332C22⋊C4—61no—
333C22⋊C4—301no—
334C42—51no—
335C42—51no—
336C42—51no—
337C42—51no—
338C42—301no—
339C42—301no—
340C42—602no—
341C3×C5#150311yescharacteristic, complemented, Hall
342C22×C3—21no—
343C22×C3—21no—
344C22×C3D5×C22⋊C411yescharacteristic
345C22×C3D5×SD1611yescharacteristic
346C22×C3D5×Q1611yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—52no—
350C3×C4—52no—
351C3×C4—52no—
352C3×C4—101no—
353Dic3—42no—
354Dic3—41no—
355Dic3—41no—
356Dic3—202no—
357Dic3—201no—
358Dic3—201no—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5#500611yescharacteristic
362C2×C5C2×#81611yescharacteristic
363C2×C5C2×#82511yescharacteristic
364C23D5×D1211yescharacteristic
365Q8—121no—
366Q8—601no—
367Q8—602no—
368C2×C4—41no—
369C2×C4—51no—
370C2×C4—51no—
371C2×C4—51no—
372C2×C4—52no—
373C2×C4—52no—
374C2×C4—51no—
375C2×C4—62no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—102no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—302no—
382C2×C4—301no—
383C2×C4—301no—
384C2×C4—601no—
385C2×C4—601no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4D5×#6711yescharacteristic
388C8—41no—
389C8—201no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3#6502911yescharacteristic
393C2×C3D5×#10311yescharacteristic
394C2×C3D5×#10411yescharacteristic
395C5#7079211yescharacteristic, complemented, Sylow
396C22—21no—
397C22—21no—
398C22D5×#20411yescharacteristic
399C22D5×Dic1211yescharacteristic
400C22D5×(C2×D3)⋊C411yescharacteristic
401C4—21no—
402C4—21no—
403C4—52no—
404C4—52no—
405C4—52no—
406C4—101no—
407C4—122no—
408C4—121no—
409C4—121no—
410C4—602no—
411C4—601no—
412C4—601no—
413C3#1059910211yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2#1174712911yescharacteristic
417C2D5×#81611yescharacteristic
418C2D5×#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 radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1503
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
16. #91468C4semidirect
18. #91376C4semidirect
19. #91333C4semidirect
20. Dic5×Dic6C4semidirect
341. C3×C5#1503semidirect
395. C5#70792semidirect
413. C3#10599102semidirect

Maximal subgroups

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

subgroupindex
#117541742
C3×#650072
#117486382
#117462882
C5×#44672
#117459652
#117459632
#105991023
#707925