Finite Group Databasebeta

← #14283236

Subgroups — #14283236

Order 1920.

484 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
1#11754415C211yesmaximal, characteristic
2C3×#65008C211yesmaximal, characteristic, complemented
3#11748638C211yesmaximal, characteristic, complemented
4#11746291C211yesmaximal, characteristic
5C5×#4467C211yesmaximal, characteristic, complemented
6#11745963C211yesmaximal, characteristic, complemented
7#11745959C211yesmaximal, characteristic
8#10599104—31nomaximal, Hall
9#91819C2211yescharacteristic
10C5×#924C2211yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91552—21no—
13#91546—21no—
14C2×#6668—21no—
15C2×Dic3×Dic5—21no—
16#91418C411yescharacteristic, complemented
17#91402—21no—
18#91388C411yescharacteristic, complemented
19#91387—21no—
20#91375C411yescharacteristic, complemented
21Dic5×Dic6C411yescharacteristic, complemented
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3947—21no—
27C3×#3946—21no—
28#70833—51nomaximal, Hall
29#65958—31no—
30#65008D311yescharacteristic, complemented
31#64938—31no—
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—21no—
39C2×D60C2×C411yescharacteristic
40C22×C5×Dic3—21no—
41C2×C5×Dic6C2×C411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×#1200—21no—
45C2×C3×C5×C8—21no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
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—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6668—24no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—42no—
65#5479—51no—
66C3×#432—51no—
67C4×C4⋊Dic3—51no—
68#4470—51no—
69#4470—51no—
70#4467—51no—
71#4467D511yescharacteristic, complemented
72C5×C22⋊Q8—31no—
73#4093—31no—
74Q8×Dic5—31no—
75#4076—31no—
76C2×#683—61no—
77C2×C4×Dic5—61no—
78C2×C4×Dic5C2×D311yescharacteristic
79#4044—61no—
80#4039—31no—
81#4038—61no—
82#4036—31no—
83#4032—61no—
84#4027—61no—
85C5×C22⋊C8C2×D311yescharacteristic
86C5×#95—31no—
87#3963—31no—
88C22⋊#168C2×D311yescharacteristic
89#3947—21no—
90#3946—21no—
91#1509—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—21no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97#1220—41no—
98#1220—41no—
99C2×Dic15—22no—
100C2×Dic15—21no—
101C2×Dic15—41no—
102C2×Dic15—41no—
103D60—41no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C5×Dic6—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116C2×C3×Dic5C22⋊C411yescharacteristic
117#1200—42no—
118C3×C5×C8—41no—
119C3×#168—41no—
120C2×C3×C42—51no—
121#930—51no—
122#929—101no—
123C4×#67—101no—
124C2×C4⋊Dic3—101no—
125#924C2×D511yescharacteristic
126C2×C4×Dic3—101no—
127#876—101no—
128#875—51no—
129C4×D12—51no—
130#872—101no—
131#870—51no—
132C4×Dic6—51no—
133C3×C4⋊C8—101no—
134C3×C22⋊C8—51no—
135C3×C22⋊C8C2×D511yescharacteristic
136C3×#97—101no—
137C3⋊#95—51no—
138C3⋊#95C2×D511yescharacteristic
139C2×C5×Q8—31no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—61no—
143C22×Dic5—61no—
144C22×Dic5D1211yescharacteristic
145C22×Dic5D1211yescharacteristic
146C2×D20—31no—
147C2×C4×D5—61no—
148C2×C5×C8—21no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—61no—
151C5×C22⋊C4—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155#685—61no—
156C4⋊Dic5—31no—
157C4⋊Dic5—61no—
158C4⋊Dic5—61no—
159#683—64no—
160#683—61no—
161C4×Dic5—61no—
162C4×Dic5—122no—
163C4×Dic5C4×D311yescharacteristic
164C4×Dic5C4×D311yescharacteristic
165C4×Dic5#6711yescharacteristic
166C4×Dic5#6711yescharacteristic
167C2×#168—21no—
168#529—151no—
169#432—51no—
170C4×C4⋊C4—151no—
171#328—31no—
172#328—151no—
173#327—151no—
174#327—151no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×D15—41no—
181C2×D15—41no—
182C2×D15—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185Dic15—42no—
186Dic15—41no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C3×Dic5#10412yes—
191C5×Dic3—42no—
192C5×Dic3—41no—
193C5×Dic3—41no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4C22×D511yescharacteristic
197C2×#67—101no—
198C22×Dic3—21no—
199C22×Dic3—101no—
200C2×D12—51no—
201C2×C4×D3—101no—
202C2×Dic6C4×D511yescharacteristic
203C2×C3×C8—21no—
204C2×C3×C8—101no—
205C3×C42—51no—
206C3×C42—51no—
207C3×C42—51no—
208C3×C42—51no—
209#217—21no—
210(C2×D3)⋊C4—101no—
211(C2×D3)⋊C4—101no—
212(C2×D3)⋊C4—101no—
213(C2×D3)⋊C4—101no—
214C4⋊Dic3—51no—
215C4⋊Dic3—104no—
216C4⋊Dic3C4×D511yescharacteristic
217Dic3⋊C4—21no—
218Dic3⋊C4—101no—
219Dic3⋊C4—101no—
220Dic3⋊C4—101no—
221C4×Dic3—101no—
222C4×Dic3—202no—
223C23×C5C2×D1211yescharacteristic
224C22×D5—61no—
225C5×Q8—121no—
226C2×C4×C5—41no—
227C2×C4×C5—62no—
228C2×C4×C5—61no—
229C2×C4×C5—61no—
230C2×C4×C5—121no—
231C2×C4×C5—121no—
232C2×C4×C5C2×C4×D311yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C22⋊D5—121no—
235C22⋊D5—121no—
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5—22no—
239C2×Dic5—62no—
240C2×Dic5—61no—
241C2×Dic5—121no—
242C2×Dic5—121no—
243C2×Dic5(C2×D3)⋊C411yescharacteristic
244C2×Dic5(C2×D3)⋊C411yescharacteristic
245C2×Dic5(C2×D3)⋊C411yescharacteristic
246C2×Dic5(C2×D3)⋊C411yescharacteristic
247D20—121no—
248C4×D5—122no—
249C5×C8—41no—
250#168—41no—
251#126—301no—
252#125—151no—
253#124—151no—
254#123—301no—
255C22⋊Q8—31no—
256#121—151no—
257C4×Q8—151no—
258C4×D4—151no—
259C4×D4—301no—
260#117—301no—
261C2×C4⋊C4—301no—
262C2×C42—51no—
263C2×C42—301no—
264C4⋊C8—101no—
265C22⋊C8—51no—
266C22⋊C8D3×D511yescharacteristic
267#97—101no—
268#95—31no—
269#95—151no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#41011yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275D15—81no—
276C23×C3D4×D511yescharacteristic
277C22×D3—101no—
278C2×C3×C4—41no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—51no—
282C2×C3×C4—51no—
283C2×C3×C4—102no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288#67—201no—
289#67—201no—
290C2×Dic3—22no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—102no—
296C2×Dic3—101no—
297C2×Dic3—201no—
298C2×Dic3—201no—
299D12—201no—
300C4×D3—202no—
301Dic6—41no—
302C3×C8—41no—
303C3×C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5#90811yescharacteristic
307C22×C5#90911yescharacteristic
308C22×C5C2×(C2×D3)⋊C411yescharacteristic
309C2×D5—121no—
310C2×D5—121no—
311C2×D5—121no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—122no—
315C4×C5—121no—
316C4×C5—121no—
317Dic5—21no—
318Dic5—21no—
319Dic5—21no—
320Dic5—122no—
321Dic5—121no—
322Dic5#82512yes—
323C2×Q8—31no—
324C2×D4—151no—
325C2×D4—301no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—61no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332C2×C8—21no—
333C2×C8—101no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—151no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—304no—
341C22⋊C4—61no—
342C22⋊C4—301no—
343C22⋊C4—301no—
344C22⋊C4—301no—
345C22⋊C4—301no—
346C42—51no—
347C42—51no—
348C42—51no—
349C42—51no—
350C42—301no—
351C42—602no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3D5×C22⋊C411yescharacteristic
356C22×C3#406011yescharacteristic
357C22×C3#406411yescharacteristic
358C2×D3—201no—
359C2×D3—201no—
360C2×D3—201no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—52no—
364C3×C4—101no—
365C3×C4—101no—
366C3×C4—101no—
367Dic3—42no—
368Dic3—41no—
369Dic3—41no—
370Dic3—202no—
371Dic3—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#500611yescharacteristic
375C2×C5#513311yescharacteristic
376C2×C5C2×#82511yescharacteristic
377D5—241no—
378C23—301no—
379C23D5×D1211yescharacteristic
380Q8—121no—
381D4—601no—
382D4—601no—
383D4—601no—
384C2×C4—41no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—62no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—102no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—121no—
396C2×C4—121no—
397C2×C4—302no—
398C2×C4—301no—
399C2×C4—602no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C4×D3×D511yescharacteristic
403C2×C4D5×#6711yescharacteristic
404C8—41no—
405C8—201no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3#6502911yescharacteristic
409C2×C3#6509211yescharacteristic
410C2×C3D5×#10411yescharacteristic
411D3—401no—
412C5#7083311yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—601no—
416C22—601no—
417C22—601no—
418C22#9124911yescharacteristic
419C22#9126111yescharacteristic
420C22D5×(C2×D3)⋊C411yescharacteristic
421C4—21no—
422C4—21no—
423C4—52no—
424C4—101no—
425C4—101no—
426C4—101no—
427C4—122no—
428C4—121no—
429C4—121no—
430C4—602no—
431C4—601no—
432C3#1059910411yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—1201no—
436C2#1174712911yescharacteristic
437C2#1174760611yescharacteristic
438C2D5×#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 radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1509
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
2. C3×#65008C2semidirect
3. #11748638C2semidirect
5. C5×#4467C2semidirect
6. #11745963C2semidirect
16. #91418C4semidirect
18. #91388C4semidirect
20. #91375C4semidirect
21. Dic5×Dic6C4semidirect
30. #65008D3semidirect
71. #4467D5semidirect
352. C3×C5#1509semidirect
412. C5#70833semidirect
432. C3#10599104semidirect

Maximal subgroups

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

subgroupindex
#117544152
C3×#650082
#117486382
#117462912
C5×#44672
#117459632
#117459592
#105991043
#708335