Finite Group Databasebeta

← #14299755

Subgroups — #14299755

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#11754496C211yesmaximal, characteristic
2#11751234C211yesmaximal, characteristic
3#11748861C211yesmaximal, characteristic, complemented
4#11748460C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic
6C5×#4555C211yesmaximal, characteristic, complemented
7C3×#64774C211yesmaximal, characteristic, complemented
8#10599564—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91552—22no—
17C2×Dic3⋊Dic5—22no—
18#91437—21no—
19#91428—21no—
20#91347—21no—
21#91340—21no—
22#91105—21no—
23#91100—21no—
24#90988—21no—
25#90985—21no—
26#90980C414yescomplemented
27#69002—51nomaximal, Hall
28#65857—31no—
29#65422—31no—
30#65284—31no—
31#65224—31no—
32C2×#3937—31no—
33C5×#339—31no—
34#64774D311yescharacteristic, complemented
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—21no—
37C22×Dic15—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×C3×Dic5D412yes—
47C2×#1200—22no—
48C3×C5×M16—21no—
49C3×C5×M16—21no—
50C2×C3×C5×C8—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C5×#217—21no—
54C5×C4⋊Dic3D411yescharacteristic
55C5×C4⋊Dic3D411yescharacteristic
56C4×C5×Dic3—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C412yescomplemented
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×#681—21no—
62C3×#681C2×C412yescomplemented
63C2×C3×#168—21no—
64Dic3⋊Dic5—44no—
65#6669—22no—
66#6667—22no—
67Dic3×Dic5—22no—
68#5504—51no—
69C2×#825—51no—
70#5133—51no—
71#5121—51no—
72#4975—51no—
73C3×#343—51no—
74#4555D511yescharacteristic, complemented
75C2×#709—31no—
76C2×C5×M16C2×D311yescharacteristic
77C5×#117—31no—
78C2×C42×C5—31no—
79C2×C4⋊Dic5—31no—
80C2×C4⋊Dic5—62no—
81C2×C4⋊Dic5C2×D311yescharacteristic
82C2×#681C2×D311yescharacteristic
83#4038—61no—
84D5×C4⋊C4—61no—
85#4027—62no—
86C4×D20—61no—
87C4×Dic10—61no—
88#3953—61no—
89#3948—61no—
90#3940—61no—
91#3939—61no—
92#3937—34no—
93#1859—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×Q811yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102#1220—22no—
103#1220—22no—
104C2×Dic15—21no—
105C2×Dic15—42no—
106C2×Dic15—41no—
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—21no—
117C2×C5×Dic3—21no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5—42no—
120#1200—82no—
121C3×C5×C8—41no—
122C3×#168—22no—
123C2×#235—51no—
124C2×C3×M16—51no—
125C2×C3×M16C2×D511yescharacteristic
126C2×C3×C4⋊C4—51no—
127C4×#67—102no—
128#926C2×D511yescharacteristic
129C2×C4⋊Dic3—51no—
130C2×Dic3⋊C4—102no—
131C2×C4×Dic3C2×D511yescharacteristic
132#893—101no—
133#892—101no—
134D3×C4⋊C4—101no—
135#887—101no—
136#825—54no—
137#821—101no—
138#818—101no—
139#817—101no—
140#816—101no—
141C22×C4×C5—61no—
142C22×C4×C5C22×D311yescharacteristic
143C2×C22⋊D5—61no—
144C22×Dic5—61no—
145C22×Dic5D1212yes—
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×M16—21no—
155C5×M16—21no—
156C2×C5×C8—21no—
157C5×C4⋊C4—31no—
158C5×C4⋊C4—31no—
159C5×C22⋊C4—61no—
160C42×C5—32no—
161C42×C5—61no—
162C42×C5—61no—
163#685—62no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C4⋊Dic5—124no—
169#683—62no—
170C4×Dic5—62no—
171#681—21no—
172#681C4×D312yescomplemented
173C2×#168—21no—
174#520—151no—
175#428—151no—
176C2×#104—151no—
177#417—151no—
178#384—151no—
179#343—51no—
180#339—31no—
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×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12311yescharacteristic
193Dic15—22no—
194Dic15—81no—
195C3×Dic5—42no—
196C5×Dic3—24no—
197C5×Dic3—41no—
198C5×Dic3—41no—
199C22×C3×C4—52no—
200C22×C3×C4C22×D511yescharacteristic
201C2×#67—101no—
202C22×Dic3—21no—
203C22×Dic3—101no—
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—21no—
213C3×M16—21no—
214C3×M16—52no—
215C3×M16—101no—
216C2×C3×C8—21no—
217C2×C3×C8—101no—
218C3×C4⋊C4—101no—
219C3×C4⋊C4—101no—
220#217—21no—
221(C2×D3)⋊C4—102no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224C4⋊Dic3D2011yescharacteristic
225C4⋊Dic3D2011yescharacteristic
226Dic3⋊C4—102no—
227Dic3⋊C4—204no—
228C4×Dic3—21no—
229C4×Dic3—21no—
230C4×Dic3—102no—
231C4×Dic3C4×D512yescomplemented
232C23×C5C2×D1211yescharacteristic
233C22×D5—61no—
234C2×C4×C5—62no—
235C2×C4×C5—62no—
236C2×C4×C5—62no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5C2×C4×D311yescharacteristic
240C2×C4×C5#23511yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243C2×C4×C5#23711yescharacteristic
244C2×C4×C5D3×Q811yescharacteristic
245C22⋊D5—62no—
246C22⋊D5—62no—
247C2×Dic5—22no—
248C2×Dic5—42no—
249C2×Dic5—61no—
250C2×Dic5—122no—
251C2×Dic5—121no—
252D20—32no—
253D20—61no—
254C4×D5—62no—
255C4×D5—62no—
256C4×D5—242no—
257Dic10—32no—
258Dic10—61no—
259C5×C8—41no—
260#168—22no—
261C2×#41—151no—
262C2×M16—51no—
263C2×M16D3×D511yescharacteristic
264C4×Q8—301no—
265C4×D4—301no—
266C4×D4—302no—
267#117—31no—
268#117—301no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4—302no—
273C2×C42—31no—
274#107—301no—
275#106—301no—
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×C3D4×D511yescharacteristic
286C22×D3—101no—
287C2×C3×C4—102no—
288C2×C3×C4—202no—
289C2×C3×C4C2×C4×D511yescharacteristic
290C2×C3×C4C2×D2011yescharacteristic
291C2×C3×C4#70911yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4#71111yescharacteristic
294C2×C3×C4Q8×D511yescharacteristic
295#67—102no—
296#67—102no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—101no—
303C2×Dic3—202no—
304C2×Dic3—201no—
305D12—52no—
306D12—101no—
307C4×D3—102no—
308C4×D3—102no—
309C4×D3—402no—
310Dic6—52no—
311Dic6—101no—
312C3×C8—41no—
313C3×C8—102no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5C4×D1211yescharacteristic
317C22×C5#88211yescharacteristic
318C22×C5#89711yescharacteristic
319C2×D5—62no—
320C2×D5—121no—
321C2×D5—121no—
322C4×C5—64no—
323C4×C5—121no—
324C4×C5—121no—
325C4×C5#67⋊C411yescharacteristic
326C4×C5#88311yescharacteristic
327C4×C5D3×C4⋊C411yescharacteristic
328C4×C5#89611yescharacteristic
329Dic5—42no—
330Dic5—62no—
331Dic5—241no—
332#41—152no—
333#41—152no—
334#41—301no—
335#41—301no—
336C2×Q8—151no—
337C2×D4—151no—
338C2×D4—301no—
339C22×C4—52no—
340C22×C4—61no—
341C22×C4—302no—
342C22×C4—301no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345M16—21no—
346M16—21no—
347M16—52no—
348M16—101no—
349C2×C8—21no—
350C2×C8—101no—
351C4⋊C4—31no—
352C4⋊C4—31no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C4⋊C4—302no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—61no—
360C22⋊C4—302no—
361C42—32no—
362C42—61no—
363C42—61no—
364C42—302no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3#402711yescharacteristic
369C22×C3#402811yescharacteristic
370C22×C3#404211yescharacteristic
371C2×D3—102no—
372C2×D3—201no—
373C2×D3—201no—
374C3×C4—202no—
375C3×C4C4×D2011yescharacteristic
376C3×C4#402911yescharacteristic
377C3×C4D5×C4⋊C411yescharacteristic
378C3×C4#404311yescharacteristic
379Dic3—24no—
380Dic3—41no—
381Dic3—41no—
382Dic3—102no—
383Dic3—401no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5#466811yescharacteristic
387C2×C5#474711yescharacteristic
388C2×C5#475211yescharacteristic
389D5—122no—
390C23—301no—
391C23D5×D1211yescharacteristic
392Q8—152no—
393Q8—301no—
394D4—152no—
395D4—302no—
396D4—302no—
397D4—301no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—102no—
404C2×C4—202no—
405C2×C4—301no—
406C2×C4—302no—
407C2×C4—302no—
408C2×C4—602no—
409C2×C4—601no—
410C2×C4—1202no—
411C2×C4D15⋊Q811yescharacteristic
412C2×C4C4×D3×D511yescharacteristic
413C2×C4D3×D2011yescharacteristic
414C2×C4#677911yescharacteristic
415C2×C4#678211yescharacteristic
416C2×C4#679011yescharacteristic
417C8—41no—
418C8—102no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3#6495711yescharacteristic
422C2×C3#6511111yescharacteristic
423C2×C3#6511511yescharacteristic
424D3—202no—
425C5#6900211yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—302no—
429C22—601no—
430C22—601no—
431C22#9140511yescharacteristic
432C22#9141911yescharacteristic
433C22#9147611yescharacteristic
434C4—64no—
435C4—121no—
436C4—121no—
437C4—202no—
438C4—302no—
439C4—1201no—
440C4#9139511yescharacteristic
441C4#9140411yescharacteristic
442C4#9142911yescharacteristic
443C4#9156211yescharacteristic
444C3#1059956411yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—602no—
448C2#1174824811yescharacteristic
449C2#1174826211yescharacteristic
450C2#1174889511yescharacteristic
subgroupG/H
centerC22#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1859
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #11748861C2semidirect
4. #11748460C2semidirect
6. C5×#4555C2semidirect
7. C3×#64774C2semidirect
26. #90980C4semidirect
34. #64774D3semidirect
58. C4×C5×Dic3C2×C4semidirect
62. C3×#681C2×C4semidirect
74. #4555D5semidirect
108. D60C4⋊C4semidirect
112. Dic30C4⋊C4semidirect
172. #681C4×D3semidirect
231. C4×Dic3C4×D5semidirect
365. C3×C5#1859semidirect
425. C5#69002semidirect
444. C3#10599564semidirect

Maximal subgroups

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

subgroupindex
#117544962
#117512342
#117488612
#117484602
C2×#909802
C5×#45552
C3×#647742
#105995643
#690025