Finite Group Databasebeta

← #14299734

Subgroups — #14299734

Order 1920.

604 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754506C211yesmaximal, characteristic
2#11751067C211yesmaximal, characteristic
3C5×#4975C211yesmaximal, characteristic, complemented
4C3×#65253C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic
6#11745986C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10600385—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×C4⋊Dic3C2211yescharacteristic
13C2×C5×Dic3⋊C4—22no—
14C2×C4×C5×Dic3C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91556—22no—
18#91437—21no—
19#91418—21no—
20#91347—21no—
21#91333—21no—
22#91094—21no—
23#91093—21no—
24C3×#3940—21no—
25C3×#3939—21no—
26#90980C414yescomplemented
27#70680—51nomaximal, Hall
28#65838—31no—
29C5×#384—31no—
30#65255—31no—
31#65253D311yescharacteristic, complemented
32C2×#3937—31no—
33#64750—31no—
34#64743—31no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38#6817—21no—
39#6817—21no—
40#6817C2×C412yes—
41#6817Q812yes—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C22×C5×Dic3—21no—
46C22×C5×Dic3D412yes—
47C2×#1200—22no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50#6710—21no—
51#6710—21no—
52C2×C3⋊#168—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×Dic3⋊C4—44no—
56C4×C5×Dic3—21no—
57C4×C5×Dic3C2×C412yescomplemented
58C3×C22⋊Dic5—21no—
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4⋊Dic5D411yescharacteristic
61C3×C4×Dic5—21no—
62C3×#681—21no—
63C3×#681C2×C412yescomplemented
64C2×C3×#168—21no—
65#6669—22no—
66#6667—22no—
67Dic3×Dic5—22no—
68#5523—51no—
69C3×#428—51no—
70C2×#825—51no—
71#4975D511yescharacteristic, complemented
72#4966—51no—
73#4554—51no—
74#4532—51no—
75C2×#709—31no—
76C2×C5×C4⋊C4—31no—
77C2×C5×C4⋊C4—62no—
78C2×C5×C4⋊C4C2×D311yescharacteristic
79C2×C42×C5—31no—
80C4×C22⋊D5—62no—
81#4072C2×D311yescharacteristic
82C2×#681—31no—
83C2×#681C2×D311yescharacteristic
84#4039—61no—
85#4038—61no—
86D5×C4⋊C4—61no—
87#4033—61no—
88#3942—61no—
89#3941—61no—
90#3940—21no—
91#3939—21no—
92#3937—34no—
93#1859—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C2×C3×C4×C5—42no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104#1220—22no—
105#1220—22no—
106C2×Dic15—21no—
107D60—21no—
108D60C4⋊C412yescomplemented
109C4×D15—22no—
110C4×D15—22no—
111Dic30—21no—
112Dic30C4⋊C412yescomplemented
113C2×C5×Dic3—22no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—42no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—21no—
120#1200—82no—
121C3⋊#168—41no—
122C3×#168—22no—
123C2×#235—51no—
124C2×C3×M16—51no—
125C3×#117—51no—
126C2×C3×C4⋊C4C2×D511yescharacteristic
127C2×C4⋊Dic3C2×D511yescharacteristic
128C2×Dic3⋊C4—22no—
129C2×C4×Dic3C2×D511yescharacteristic
130C2×#208—51no—
131#892—101no—
132D3×C4⋊C4—101no—
133#67⋊C4—102no—
134C4×D12—101no—
135C4×Dic6—101no—
136C3×#107—101no—
137C3×#106—101no—
138#825—54no—
139#810—101no—
140#809—101no—
141C22×C4×C5—21no—
142C22×C4×C5—32no—
143C22×C4×C5—61no—
144C22×C4×C5C22×D311yescharacteristic
145C2×C22⋊D5—61no—
146#709—32no—
147#709—32no—
148#709—61no—
149#709—61no—
150C2×D20—31no—
151C2×C4×D5—61no—
152C2×C4×D5—62no—
153C2×Dic10—31no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—61no—
157C5×C4⋊C4—61no—
158C5×C4⋊C4—124no—
159C42×C5—32no—
160C42×C5—61no—
161C22⋊Dic5—21no—
162#685—62no—
163C4⋊Dic5#6711yescharacteristic
164C4⋊Dic5#6711yescharacteristic
165#683—62no—
166C4×Dic5—21no—
167C4×Dic5—62no—
168#681—21no—
169#681—61no—
170#681—61no—
171#681C4×D312yescomplemented
172C2×#168—21no—
173C2×#168—61no—
174#520—151no—
175#428—51no—
176C2×#104—151no—
177#417—151no—
178#384—31no—
179#343—151no—
180#339—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C2×D15—22no—
187C2×D15—41no—
188C2×D15—41no—
189C3×C4×C5—81no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5#12311yescharacteristic
194Dic15—22no—
195C3×Dic5—41no—
196C3×Dic5—41no—
197C5×Dic3—24no—
198C5×Dic3—42no—
199C22×C3×C4—21no—
200C22×C3×C4C22×D511yescharacteristic
201C2×#67—101no—
202C22×Dic3—21no—
203C22×Dic3C22⋊D512yes—
204#235—52no—
205#235—52no—
206#235—101no—
207#235—101no—
208C2×D12—51no—
209C2×C4×D3—101no—
210C2×C4×D3—102no—
211C2×Dic6—51no—
212C3×M16—52no—
213C3×M16—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—51no—
218C3×C4⋊C4—51no—
219C3×C22⋊C4—101no—
220C3×C42—101no—
221(C2×D3)⋊C4—102no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224Dic3⋊C4—44no—
225Dic3⋊C4—102no—
226C4×Dic3—21no—
227C4×Dic3—102no—
228C4×Dic3C4×D512yescomplemented
229#208—101no—
230#208—101no—
231C2×C3⋊C8—101no—
232C23×C5D3×D411yescharacteristic
233C22×D5—61no—
234C2×C4×C5—42no—
235C2×C4×C5—41no—
236C2×C4×C5—62no—
237C2×C4×C5—62no—
238C2×C4×C5—62no—
239C2×C4×C5—62no—
240C2×C4×C5—122no—
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×Q811yescharacteristic
245C2×C4×C5#23911yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—62no—
248C22⋊D5—62no—
249C2×Dic5—21no—
250C2×Dic5—21no—
251C2×Dic5—61no—
252D20—32no—
253D20—61no—
254C4×D5—62no—
255C4×D5—62no—
256C4×D5—242no—
257Dic10—32no—
258Dic10—61no—
259#168—22no—
260#168—121no—
261C2×#41—151no—
262C2×M16—51no—
263C2×M16—151no—
264C4×Q8—301no—
265C4×D4—301no—
266C4×D4—302no—
267#117—51no—
268#117—301no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—62no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4D3×D511yescharacteristic
273C2×C42—31no—
274#107—101no—
275#106—101no—
276#104—154no—
277#103—301no—
278#102—301no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38511yescharacteristic
282C2×C3×C5#45311yescharacteristic
283C2×C3×C5#45611yescharacteristic
284D15—42no—
285C23×C3C2×C22⋊D511yescharacteristic
286C22×D3—101no—
287C2×C3×C4—42no—
288C2×C3×C4—41no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4C2×C4×D511yescharacteristic
292C2×C3×C4#70911yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4Q8×D511yescharacteristic
296C2×C3×C4#71311yescharacteristic
297#67—102no—
298#67—102no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—42no—
304C2×Dic3—101no—
305D12—52no—
306D12—101no—
307C4×D3—102no—
308C4×D3—102no—
309C4×D3—402no—
310Dic6—52no—
311Dic6—101no—
312C3×C8—102no—
313C3⋊C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5#89311yescharacteristic
317C22×C5#89611yescharacteristic
318C22×C5#93711yescharacteristic
319C2×D5—62no—
320C2×D5—121no—
321C2×D5—121no—
322C4×C5—64no—
323C4×C5—81no—
324C4×C5—122no—
325C4×C5D3×C4⋊C411yescharacteristic
326C4×C5#89411yescharacteristic
327C4×C5C4×#6711yescharacteristic
328C4×C5#94611yescharacteristic
329Dic5—41no—
330Dic5—41no—
331Dic5—62no—
332#41—152no—
333#41—152no—
334#41—301no—
335#41—301no—
336C2×Q8—151no—
337C2×D4—151no—
338C2×D4—301no—
339C22×C4—21no—
340C22×C4—32no—
341C22×C4—61no—
342C22×C4—302no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345M16—52no—
346M16—101no—
347M16—301no—
348M16—301no—
349C2×C8—101no—
350C2×C8—301no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—51no—
354C4⋊C4—51no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—124no—
358C4⋊C4—302no—
359C22⋊C4—101no—
360C22⋊C4—302no—
361C42—32no—
362C42—61no—
363C42—101no—
364C42—302no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3C4×C22⋊D511yescharacteristic
369C22×C3#408311yescharacteristic
370C22×C3#409211yescharacteristic
371C2×D3—102no—
372C2×D3—201no—
373C2×D3—201no—
374C3×C4—81no—
375C3×C4—201no—
376C3×C4—201no—
377C3×C4D5×C4⋊C411yescharacteristic
378C3×C4#403911yescharacteristic
379C3×C4#404011yescharacteristic
380C3×C4#404211yescharacteristic
381Dic3—24no—
382Dic3—42no—
383Dic3—102no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5#498911yescharacteristic
387C2×C5#519811yescharacteristic
388C2×C5#520511yescharacteristic
389D5—122no—
390C23—301no—
391C23D3×C22⋊D511yescharacteristic
392Q8—152no—
393Q8—301no—
394D4—152no—
395D4—302no—
396D4—302no—
397D4—301no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—101no—
405C2×C4—101no—
406C2×C4—122no—
407C2×C4—301no—
408C2×C4—302no—
409C2×C4—302no—
410C2×C4—1202no—
411C2×C4#676911yescharacteristic
412C2×C4D15⋊Q811yescharacteristic
413C2×C4#677311yescharacteristic
414C2×C4C4×D3×D511yescharacteristic
415C2×C4D5×#6711yescharacteristic
416C2×C4#679011yescharacteristic
417C8—102no—
418C8—601no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3#6527811yescharacteristic
422C2×C3#6536611yescharacteristic
423C2×C3#6538411yescharacteristic
424D3—202no—
425C5#7068011yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—302no—
429C22—601no—
430C22—601no—
431C22#9142411yescharacteristic
432C22#9144611yescharacteristic
433C22#9157711yescharacteristic
434C4—64no—
435C4—81no—
436C4—122no—
437C4—201no—
438C4—201no—
439C4—302no—
440C4#9140411yescharacteristic
441C4#9141111yescharacteristic
442C4#9143311yescharacteristic
443C4#9144411yescharacteristic
444C3#1060038511yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—602no—
448C2#1174889411yescharacteristic
449C2#1174916511yescharacteristic
450C2#1174941311yescharacteristic
subgroupG/H
centerC22#91577
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1859
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×#4975C2semidirect
4. C3×#65253C2semidirect
6. #11745986C2semidirect
7. #11745974C2semidirect
26. #90980C4semidirect
31. #65253D3semidirect
57. C4×C5×Dic3C2×C4semidirect
63. C3×#681C2×C4semidirect
71. #4975D5semidirect
108. D60C4⋊C4semidirect
112. Dic30C4⋊C4semidirect
171. #681C4×D3semidirect
228. C4×Dic3C4×D5semidirect
365. C3×C5#1859semidirect
425. C5#70680semidirect
444. C3#10600385semidirect

Maximal subgroups

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

subgroupindex
#117545062
#117510672
C5×#49752
C3×#652532
C2×#909802
#117459862
#117459742
#106003853
#706805