Finite Group Databasebeta

← #14284052

Subgroups — #14284052

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#124C211yesmaximal, characteristic
2#11747003C211yesmaximal, characteristic, complemented
3#11746870C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745846C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599136—31nomaximal, Hall
9C2×C3×Q8×D5C411yescharacteristic
10C2×C3×D4×D5C411yescharacteristic
11C3×C5×#124C2211yescharacteristic
12C3×#4093C411yescharacteristic
13C3×#4082C411yescharacteristic
14C3×#4031—21no—
15C3×#4031—21no—
16C3×D5×C22⋊C4—21no—
17C3×D5×C22⋊C4—21no—
18C3×#4021C2211yescharacteristic
19C3×C42×D5C2211yescharacteristic
20C2×#6649—21no—
21#91087C2211yescharacteristic, complemented
22#91087C2211yescharacteristic, complemented
23C5×#803C2211yescharacteristic, complemented
24C5×#803C2211yescharacteristic, complemented
25#90982—21no—
26#90955—21no—
27Dic5×C3⋊C8—21no—
28#71718—51nomaximal, Hall
29D5×#124D311yescharacteristic
30#64996—31no—
31#64994—31no—
32C5×#329—31no—
33#64760—31no—
34#64684—31no—
35#64684—31no—
36C23×C3×D5—21no—
37C2×C3×C5×Q8C2×C411yescharacteristic
38C2×C3×C5×D4C2×C411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C3×Q8×D5—42no—
41C3×D4×D5—42no—
42C2×C3×D20C2×C411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2×C411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×Dic10—21no—
48C2×C3×Dic10C2×C411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×#685—21no—
61C3×#685—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65#6649—24no—
66C2×C3×#124—51no—
67#4926—51no—
68C4×#208—51no—
69#4540—51no—
70#4540—51no—
71#4540—51no—
72#4540D511yescharacteristic, complemented
73C2×Q8×D5Dic311yescharacteristic
74C2×D4×D5Dic311yescharacteristic
75C5×#124C2×D311yescharacteristic
76#4093Dic311yescharacteristic
77#4082Dic311yescharacteristic
78C2×#676—61no—
79#4031—21no—
80#4031—21no—
81D5×C22⋊C4—21no—
82D5×C22⋊C4—21no—
83#4021C2×D311yescharacteristic
84C42×D5C2×D311yescharacteristic
85C5×#97—31no—
86C5×#97—31no—
87#3952—61no—
88#3946—61no—
89C8×Dic5—61no—
90#3935—31no—
91#3935—31no—
92#1527—151noSylow
93C23×C3×C5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—42no—
96C22×C3×D5—42no—
97C22×C3×D5—42no—
98C22×C3×D5C22⋊C411yescharacteristic
99C3×C5×Q8—41no—
100C3×C5×D4—41no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C3×C22⋊D5—42no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5C22⋊C411yescharacteristic
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C22⋊C411yescharacteristic
110C3×D20—41no—
111C3×C4×D5—22no—
112C3×C4×D5—22no—
113C3×C4×D5—41no—
114C3×C4×D5—42no—
115C3×Dic10—42no—
116C3×Dic10—41no—
117C3⋊#168—22no—
118C3⋊#168—41no—
119C5×C3⋊C8—22no—
120C5×C3⋊C8—41no—
121C22×C3×Q8—51no—
122C22×C3×D4—51no—
123C3×#124—51no—
124C3×#124—51no—
125C3×#124—51no—
126C3×#124—101no—
127C3×#124—101no—
128C3×#124C2×D511yescharacteristic
129C2×C3×C22⋊C4—101no—
130C2×C3×C22⋊C4—101no—
131C2×C3×C42—51no—
132C2×#208—101no—
133#830—101no—
134C4⋊(C3⋊C8)—101no—
135#803—51no—
136#803—51no—
137#803C2×D511yescharacteristic, complemented
138#803C2×D511yescharacteristic, complemented
139C4×C3⋊C8—101no—
140C23×D5—21no—
141C2×C5×Q8C2×Dic311yescharacteristic
142C2×C5×D4C2×Dic311yescharacteristic
143C2×C22⋊D5—21no—
144Q8×D5—42no—
145D4×D5—42no—
146C2×D20C2×Dic311yescharacteristic
147C2×C4×D5—21no—
148C2×C4×D5C2×Dic311yescharacteristic
149C2×C4×D5#6711yescharacteristic
150C2×C4×D5#6711yescharacteristic
151C2×Dic10—21no—
152C2×Dic10C2×Dic311yescharacteristic
153C2×C5×C8—61no—
154C2×C5×C8—61no—
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C42×C5C22×D311yescharacteristic
158C22⋊Dic5—21no—
159C22⋊Dic5—21no—
160#685—21no—
161#685—21no—
162#685—21no—
163#685—21no—
164C4×Dic5C2×Dic311yescharacteristic
165C4×Dic5#6711yescharacteristic
166C4×Dic5#6711yescharacteristic
167C2×#168—61no—
168C2×#168—61no—
169#676—64no—
170C2×#124—51no—
171#432—151no—
172C4×M16—151no—
173#329—31no—
174#329—151no—
175#329—151no—
176#329—151no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C2×C3×D5—84no—
187C2×C3×D5#10412yes—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×Dic5—21no—
193C3×Dic5—21no—
194C3×Dic5—41no—
195C3×Dic5#10012yes—
196C24×C3—101no—
197C2×C3×Q8—51no—
198C2×C3×Q8—101no—
199C2×C3×Q8—202no—
200C2×C3×Q8C4×D511yescharacteristic
201C2×C3×D4—51no—
202C2×C3×D4—101no—
203C2×C3×D4—202no—
204C2×C3×D4C4×D511yescharacteristic
205C22×C3×C4—51no—
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4—101no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C42—51no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42C22×D511yescharacteristic
221#208—104no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C23×C5—21no—
227C22×D5—21no—
228C22×D5—42no—
229C22×D5—42no—
230C22×D5—42no—
231C22×D5#21711yescharacteristic
232C5×Q8—41no—
233C5×D4—41no—
234C2×C4×C5—21no—
235C2×C4×C5C22×Dic311yescharacteristic
236C2×C4×C5C2×#6711yescharacteristic
237C2×C4×C5C2×#6711yescharacteristic
238C22⋊D5—42no—
239C2×Dic5—21no—
240C2×Dic5#21711yescharacteristic
241C2×Dic5#21711yescharacteristic
242C2×Dic5#21711yescharacteristic
243D20—41no—
244C4×D5—22no—
245C4×D5—22no—
246C4×D5—41no—
247C4×D5—42no—
248Dic10—42no—
249Dic10—41no—
250C5×C8—62no—
251C5×C8—121no—
252#168—62no—
253#168—121no—
254C22×Q8—51no—
255C22×D4—51no—
256C2×M16—301no—
257#124—51no—
258#124—51no—
259#124—51no—
260#124—101no—
261#124—101no—
262#124D3×D511yescharacteristic
263C2×C22⋊C4—101no—
264C2×C22⋊C4—101no—
265C2×C42—51no—
266C4⋊C8—301no—
267C22⋊C8—301no—
268#97—31no—
269#97—31no—
270#97—151no—
271#97—151no—
272C4×C8—301no—
273C2×C3×C5—81no—
274C2×C3×C5C2×#10011yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C2×C3×C5#42111yescharacteristic
277C3×D5—22no—
278C3×D5—81no—
279C23×C3—21no—
280C23×C3—51no—
281C23×C3—101no—
282C23×C3—202no—
283C23×C3—202no—
284C23×C3—202no—
285C3×Q8—41no—
286C3×Q8—201no—
287C3×Q8—202no—
288C3×D4—41no—
289C3×D4—201no—
290C3×D4—202no—
291C2×C3×C4—21no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—51no—
295C2×C3×C4—102no—
296C2×C3×C4—102no—
297C2×C3×C4—101no—
298C2×C3×C4—201no—
299C2×C3×C4—202no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C3⋊C8—22no—
304C3⋊C8—41no—
305C3⋊C8—102no—
306C3⋊C8—201no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5C2×#21711yescharacteristic
311C2×D5—21no—
312C2×D5—21no—
313C2×D5—41no—
314C2×D5—41no—
315C2×D5—41no—
316C2×D5—84no—
317C2×D5#83712yes—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—41no—
322Dic5—21no—
323Dic5—21no—
324Dic5—41no—
325Dic5#83312yes—
326C24—101no—
327C2×Q8—51no—
328C2×Q8—101no—
329C2×Q8—202no—
330C2×Q8D5×Dic311yescharacteristic
331C2×D4—51no—
332C2×D4—101no—
333C2×D4—202no—
334C2×D4D5×Dic311yescharacteristic
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—101no—
339M16—304no—
340C2×C8—61no—
341C2×C8—61no—
342C2×C8—301no—
343C2×C8—301no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C22⋊C4—101no—
350C22⋊C4—101no—
351C22⋊C4—101no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42C2×D3×D511yescharacteristic
356C3×C5#152711yescharacteristic, complemented, Hall
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—52no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3—201no—
364C22×C3—201no—
365C22×C3—201no—
366C22×C3—404no—
367C22×C3D5×C22⋊C411yescharacteristic
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372C3×C4—52no—
373C3×C4—101no—
374C3×C4—101no—
375C3×C4—201no—
376C2×C5—81no—
377C2×C5C2×#83311yescharacteristic
378C2×C5C2×#83711yescharacteristic
379C2×C5#523611yescharacteristic
380D5—22no—
381D5—81no—
382C23—21no—
383C23—51no—
384C23—101no—
385C23—202no—
386C23—202no—
387C23—202no—
388Q8—41no—
389Q8—201no—
390Q8—202no—
391D4—41no—
392D4—201no—
393D4—202no—
394C2×C4—21no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—101no—
401C2×C4—201no—
402C2×C4—202no—
403C2×C4C2×D5×Dic311yescharacteristic
404C2×C4D5×#6711yescharacteristic
405C2×C4D5×#6711yescharacteristic
406C8—62no—
407C8—121no—
408C8—302no—
409C8—601no—
410C2×C3—81no—
411C2×C3—102no—
412C2×C3—401no—
413C2×C3D5×#10011yescharacteristic
414C2×C3D5×#10411yescharacteristic
415C2×C3#6511011yescharacteristic
416C5#7171811yescharacteristic, complemented, Sylow
417C22—41no—
418C22—41no—
419C22—41no—
420C22—52no—
421C22—101no—
422C22—101no—
423C22—201no—
424C22—201no—
425C22—201no—
426C22—404no—
427C22D5×#21711yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—52no—
433C4—101no—
434C4—101no—
435C4—201no—
436C3#1059913611yescharacteristic, complemented, Sylow
437C2—81no—
438C2—102no—
439C2—401no—
440C2D5×#83311yescharacteristic
441C2D5×#83711yescharacteristic
442C2#1174942711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1527
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11747003C2semidirect
3. #11746870C2semidirect
4. #11746361C2semidirect
5. C5×#4540C2semidirect
6. #11745846C2semidirect
7. #11745846C2semidirect
21. #91087C22semidirect
22. #91087C22semidirect
23. C5×#803C22semidirect
24. C5×#803C22semidirect
72. #4540D5semidirect
137. #803C2×D5semidirect
138. #803C2×D5semidirect
356. C3×C5#1527semidirect
416. C5#71718semidirect
436. C3#10599136semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
#117470032
#117468702
#117463612
C5×#45402
#117458462
#105991363
#717185