Finite Group Databasebeta

← #14284201

Subgroups — #14284201

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66002C211yesmaximal, characteristic
2D5×#803C211yesmaximal, characteristic, complemented
3#11746870C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745846C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599138—31nomaximal, Hall
9C2×C3×#713C411yescharacteristic
10C2×C3×#711C411yescharacteristic
11C3×C5×#124C2211yescharacteristic
12C3×#4090C411yescharacteristic
13C3×#4086C411yescharacteristic
14C3×#4030—21no—
15C3×#4030—21no—
16C3×#4027—21no—
17C3×#4027—21no—
18C3×#4021C2211yescharacteristic
19C3×C42×D5C2211yescharacteristic
20C2×D5×C3⋊C8—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C5×#803C2211yescharacteristic
25#90982—21no—
26#90955—21no—
27#90952—21no—
28#71798—51nomaximal, Hall
29#66002D311yescharacteristic
30#64994—31no—
31D5×#97—31no—
32C5×#329—31no—
33#64760—31no—
34#64684—31no—
35#64684—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5—21no—
42C3×#713—42no—
43C3×#711—42no—
44C2×C3×D20—21no—
45C2×C3×D20C2×C411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×Dic10C2×C411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C42×C5C2311yescharacteristic
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65D5×C3⋊C8—24no—
66C3×#532—51no—
67#4926—51no—
68C2×#803—51no—
69#4540—51no—
70#4540—51no—
71#4540—51no—
72#4540D511yescharacteristic, complemented
73C2×#713Dic311yescharacteristic
74C2×#711Dic311yescharacteristic
75C5×#124C2×D311yescharacteristic
76#4090Dic311yescharacteristic
77#4086Dic311yescharacteristic
78C2×C8×D5—61no—
79#4030—21no—
80#4030—21no—
81#4027—21no—
82#4027—21no—
83#4021C2×D311yescharacteristic
84C42×D5C2×D311yescharacteristic
85C5×#97—31no—
86C5×#97—31no—
87#3952—61no—
88#3947—61no—
89#3946—61no—
90#3935—31no—
91#3935—31no—
92#1530—151noSylow
93C23×C3×C5—21no—
94C22×C3×D5—21no—
95C22×C3×D5C22⋊C411yescharacteristic
96C3×C5×Q8—41no—
97C3×C5×D4—41no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C3×C22⋊D5—42no—
103C3×C22⋊D5—42no—
104C3×C22⋊D5—42no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—42no—
107C2×C3×Dic5C22⋊C411yescharacteristic
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C22⋊C411yescharacteristic
110C3×D20—41no—
111C3×D20—42no—
112C3×C4×D5—22no—
113C3×C4×D5—22no—
114C3×C4×D5—41no—
115C3×C4×D5—42no—
116C3×Dic10—41no—
117C3⋊#168—22no—
118C3⋊#168—41no—
119C5×C3⋊C8—22no—
120C5×C3⋊C8—41no—
121C2×C3×#41—51no—
122C2×C3×#41—51no—
123C3×C4⋊Q8—51no—
124C3×#127—51no—
125C3×#124—51no—
126C3×#124C2×D511yescharacteristic
127C3×#121—101no—
128C3×#121—101no—
129C3×C4×D4—101no—
130C3×C4×D4—101no—
131C2×C3×C42—51no—
132C22×C3⋊C8—101no—
133#830—101no—
134C4⋊(C3⋊C8)—101no—
135#803—51no—
136#803—51no—
137#803—101no—
138#803C2×D511yescharacteristic
139#803C2×D511yescharacteristic
140C2×C5×Q8C2×Dic311yescharacteristic
141C2×C5×D4C2×Dic311yescharacteristic
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144C2×C22⋊D5—21no—
145C22×Dic5—21no—
146#713—42no—
147#711—42no—
148C2×D20—21no—
149C2×D20C2×Dic311yescharacteristic
150C2×C4×D5—21no—
151C2×C4×D5C2×Dic311yescharacteristic
152C2×C4×D5#6711yescharacteristic
153C2×C4×D5#6711yescharacteristic
154C2×Dic10C2×Dic311yescharacteristic
155C2×C5×C8—61no—
156C2×C5×C8—61no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4—21no—
159C42×C5C22×D311yescharacteristic
160#685—21no—
161#685—21no—
162#683—21no—
163#683—21no—
164C4×Dic5C2×Dic311yescharacteristic
165C4×Dic5#6711yescharacteristic
166C4×Dic5#6711yescharacteristic
167C2×#168—61no—
168C2×#168—61no—
169C8×D5—64no—
170#532—51no—
171#432—151no—
172C2×#97—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#10012yes—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—41no—
191C3×Dic5—21no—
192C3×Dic5—21no—
193C3×Dic5—41no—
194C3×Dic5#10412yes—
195C3×#41—202no—
196C3×#41—202no—
197C2×C3×Q8—51no—
198C2×C3×Q8C4×D511yescharacteristic
199C2×C3×D4—51no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—101no—
204C2×C3×D4C4×D511yescharacteristic
205C22×C3×C4—51no—
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4—101no—
209C22×C3×C4—101no—
210C3×C4⋊C4—101no—
211C3×C4⋊C4—101no—
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C42—51no—
217C3×C42—51no—
218C3×C42—51no—
219C3×C42C22×D511yescharacteristic
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—104no—
223C2×C3⋊C8—101no—
224C2×C3⋊C8—101no—
225C23×C5—21no—
226C22×D5—21no—
227C22×D5#21711yescharacteristic
228C5×Q8—41no—
229C5×D4—41no—
230C2×C4×C5—21no—
231C2×C4×C5C22×Dic311yescharacteristic
232C2×C4×C5C2×#6711yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C22⋊D5—42no—
235C22⋊D5—42no—
236C22⋊D5—42no—
237C2×Dic5—21no—
238C2×Dic5—42no—
239C2×Dic5#21711yescharacteristic
240C2×Dic5#21711yescharacteristic
241C2×Dic5#21711yescharacteristic
242D20—41no—
243D20—42no—
244C4×D5—22no—
245C4×D5—22no—
246C4×D5—41no—
247C4×D5—42no—
248Dic10—41no—
249C5×C8—62no—
250C5×C8—121no—
251#168—62no—
252#168—121no—
253C2×#41—51no—
254C2×#41—51no—
255C22×C8—301no—
256C4⋊Q8—51no—
257#127—51no—
258#124—51no—
259#124D3×D511yescharacteristic
260#121—101no—
261#121—101no—
262C4×D4—101no—
263C4×D4—101no—
264C2×C42—51no—
265C4⋊C8—301no—
266C22⋊C8—301no—
267#97—31no—
268#97—31no—
269#97—151no—
270#97—151no—
271#97—301no—
272C2×C3×C5—81no—
273C2×C3×C5C2×#10011yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275C2×C3×C5#42111yescharacteristic
276C3×D5—22no—
277C3×D5—81no—
278C23×C3—21no—
279C23×C3—51no—
280C23×C3—101no—
281C3×Q8—41no—
282C3×Q8—201no—
283C3×D4—41no—
284C3×D4—201no—
285C3×D4—202no—
286C3×D4—202no—
287C3×D4—202no—
288C3×D4—202no—
289C2×C3×C4—21no—
290C2×C3×C4—51no—
291C2×C3×C4—51no—
292C2×C3×C4—51no—
293C2×C3×C4—102no—
294C2×C3×C4—102no—
295C2×C3×C4—101no—
296C2×C3×C4—201no—
297C2×C3×C4—202no—
298C2×C3×C4—202no—
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C3⋊C8—22no—
303C3⋊C8—41no—
304C3⋊C8—102no—
305C3⋊C8—201no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5C2×#21711yescharacteristic
310C2×D5—21no—
311C2×D5—21no—
312C2×D5—41no—
313C2×D5—41no—
314C2×D5—41no—
315C2×D5#83312yes—
316C4×C5—21no—
317C4×C5—21no—
318C4×C5—21no—
319C4×C5—41no—
320Dic5—21no—
321Dic5—21no—
322Dic5—41no—
323Dic5#83712yes—
324#41—202no—
325#41—202no—
326C2×Q8—51no—
327C2×Q8D5×Dic311yescharacteristic
328C2×D4—51no—
329C2×D4—101no—
330C2×D4—101no—
331C2×D4—101no—
332C2×D4—101no—
333C2×D4D5×Dic311yescharacteristic
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—101no—
338C22×C4—101no—
339C2×C8—61no—
340C2×C8—61no—
341C2×C8—304no—
342C2×C8—301no—
343C2×C8—301no—
344C4⋊C4—101no—
345C4⋊C4—101no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—101no—
349C22⋊C4—101no—
350C42—51no—
351C42—51no—
352C42—51no—
353C42C2×D3×D511yescharacteristic
354C3×C5#153011yescharacteristic, complemented, Hall
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—52no—
359C22×C3—101no—
360C22×C3—101no—
361C22×C3—201no—
362C22×C3—201no—
363C22×C3—201no—
364C22×C3D5×C22⋊C411yescharacteristic
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—52no—
370C3×C4—101no—
371C3×C4—101no—
372C3×C4—201no—
373C2×C5—81no—
374C2×C5C2×#83311yescharacteristic
375C2×C5C2×#83711yescharacteristic
376C2×C5#523611yescharacteristic
377D5—22no—
378D5—81no—
379C23—21no—
380C23—51no—
381C23—101no—
382Q8—41no—
383Q8—201no—
384D4—41no—
385D4—201no—
386D4—202no—
387D4—202no—
388D4—202no—
389D4—202no—
390C2×C4—21no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—102no—
395C2×C4—102no—
396C2×C4—101no—
397C2×C4—201no—
398C2×C4—202no—
399C2×C4—202no—
400C2×C4C2×D5×Dic311yescharacteristic
401C2×C4D5×#6711yescharacteristic
402C2×C4D5×#6711yescharacteristic
403C8—62no—
404C8—121no—
405C8—302no—
406C8—601no—
407C2×C3—81no—
408C2×C3—102no—
409C2×C3—401no—
410C2×C3D5×#10011yescharacteristic
411C2×C3D5×#10411yescharacteristic
412C2×C3#6511011yescharacteristic
413C5#7179811yescharacteristic, complemented, Sylow
414C22—41no—
415C22—41no—
416C22—41no—
417C22—52no—
418C22—101no—
419C22—101no—
420C22—201no—
421C22—201no—
422C22—201no—
423C22D5×#21711yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—52no—
429C4—101no—
430C4—101no—
431C4—201no—
432C3#1059913811yescharacteristic, complemented, Sylow
433C2—81no—
434C2—102no—
435C2—401no—
436C2D5×#83311yescharacteristic
437C2D5×#83711yescharacteristic
438C2#1174942711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66002C2
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1530
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. D5×#803C2semidirect
3. #11746870C2semidirect
4. #11746361C2semidirect
5. C5×#4540C2semidirect
6. #11745846C2semidirect
7. #11745846C2semidirect
72. #4540D5semidirect
354. C3×C5#1530semidirect
413. C5#71798semidirect
432. C3#10599138semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
D5×#8032
#117468702
#117463612
C5×#45402
#117458462
#105991383
#717985