Finite Group Databasebeta

← #14299605

Subgroups — #14299605

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754515C211yesmaximal, characteristic
2#11751040C211yesmaximal, characteristic
3#11748460C211yesmaximal, characteristic, complemented
4#11748455C211yesmaximal, characteristic, complemented
5C2×#90960C211yesmaximal, characteristic
6C5×#4523C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599551—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6714—22no—
12C2×C4⋊Dic15C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91561—22no—
18#91428—21no—
19#91428—21no—
20#91418—21no—
21#91418—21no—
22#90990—21no—
23#90988—21no—
24#90987—21no—
25#90985—21no—
26#90960C414yescomplemented
27#68758—51nomaximal, Hall
28#65855—31no—
29C2×#3955—31no—
30#65410—31no—
31#65284—31no—
32#65228—31no—
33C5×#339—31no—
34#64743D311yescharacteristic, complemented
35C23×D15D412yes—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60C2×C412yes—
44C2×D60Q812yes—
45C2×#1200—22no—
46C2×#1200—22no—
47C3×C42×C5—21no—
48C3×C42×C5—21no—
49#6714—44no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C5×#217—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C5×C4⋊Dic3D411yescharacteristic
55C4×C5×Dic3—21no—
56C5×#208—21no—
57C5×#208C2×C412yescomplemented
58C2×C5×C3⋊C8—21no—
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5D411yescharacteristic
61C3×C4⋊Dic5D411yescharacteristic
62C3×C4×Dic5—21no—
63C3×#681—21no—
64C3×#681C2×C412yescomplemented
65C2×C3×#168—21no—
66#6667—22no—
67#6667—22no—
68#5521—51no—
69C2×#823—51no—
70#5121—51no—
71#4995—51no—
72#4939—51no—
73C3×#339—51no—
74#4523D511yescharacteristic, complemented
75C22×D20—31no—
76C2×C5×M16—31no—
77C5×#117—31no—
78C2×C42×C5C2×D311yescharacteristic
79C2×#685—62no—
80#4072C2×D311yescharacteristic
81C2×C4⋊Dic5—31no—
82C2×#681C2×D311yescharacteristic
83#4039—61no—
84#4039—61no—
85D5×C22⋊C4—62no—
86C4×D20—61no—
87C4×D20—61no—
88#3955—34no—
89#3950—61no—
90#3949—61no—
91#3940—61no—
92#3939—61no—
93#1856—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—22no—
97C22×D15—42no—
98C22×D15—42no—
99C22×D15C4⋊C414yes—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—42no—
110C2×Dic15—41no—
111D60—22no—
112D60—22no—
113D60—22no—
114D60—22no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119#1200—82no—
120#1200—82no—
121C3×#168—22no—
122C5×C3⋊C8—22no—
123C22×D12—51no—
124C2×C3×M16—51no—
125C3×#117—51no—
126C2×C3×C42C2×D511yescharacteristic
127C2×(C2×D3)⋊C4—102no—
128#926C2×D511yescharacteristic
129C2×C4⋊Dic3—51no—
130C2×#208C2×D511yescharacteristic
131#893—101no—
132#893—101no—
133D3×C22⋊C4—102no—
134C4×D12—101no—
135C4×D12—101no—
136#823—54no—
137#818—101no—
138#817—101no—
139#808—101no—
140#807—101no—
141C23×D5—32no—
142C22×C4×C5—21no—
143C22×C4×C5C22×D311yescharacteristic
144C22×Dic5—61no—
145C2×D20—32no—
146C2×D20—32no—
147C2×D20—61no—
148C2×D20—61no—
149C2×D20—61no—
150C2×D20—61no—
151C2×C4×D5—62no—
152C2×C4×D5—62no—
153C5×M16—32no—
154C5×M16—61no—
155C2×C5×C8—61no—
156C5×C4⋊C4—31no—
157C5×C4⋊C4—31no—
158C5×C22⋊C4—61no—
159C42×C5—21no—
160C42×C5—21no—
161C42×C5—61no—
162C22⋊Dic5—21no—
163#685—62no—
164#685—62no—
165#685—124no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C4⋊Dic5D1211yescharacteristic
169C4⋊Dic5D1211yescharacteristic
170C4×Dic5—21no—
171#681—21no—
172#681C4×D312yescomplemented
173C2×#168—21no—
174#518—151no—
175#428—151no—
176#428—151no—
177C2×#100—151no—
178#390—151no—
179#339—31no—
180#339—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C2×C4⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×D15—24no—
187C2×D15—42no—
188C2×D15—42no—
189C2×D15—44no—
190C2×D15—82no—
191C3×C4×C5—42no—
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C4×D411yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195C3×C4×C5C22⋊Q811yescharacteristic
196Dic15—81no—
197C3×Dic5—41no—
198C3×Dic5—41no—
199C5×Dic3—41no—
200C5×Dic3—41no—
201C23×D3—52no—
202C22×C3×C4—21no—
203C22×C3×C4C22×D511yescharacteristic
204C22×Dic3—101no—
205C2×D12—52no—
206C2×D12—52no—
207C2×D12—101no—
208C2×D12—101no—
209C2×D12—101no—
210C2×D12—101no—
211C2×C4×D3—102no—
212C2×C4×D3—102no—
213C3×M16—52no—
214C3×M16—101no—
215C2×C3×C8—101no—
216C3×C4⋊C4—51no—
217C3×C4⋊C4—51no—
218C3×C22⋊C4—101no—
219C3×C42—21no—
220C3×C42—21no—
221C3×C42—101no—
222#217—21no—
223(C2×D3)⋊C4—102no—
224(C2×D3)⋊C4—102no—
225(C2×D3)⋊C4—204no—
226C4⋊Dic3—101no—
227C4⋊Dic3—101no—
228C4⋊Dic3D2011yescharacteristic
229C4⋊Dic3D2011yescharacteristic
230C4×Dic3—21no—
231#208—21no—
232#208C4×D512yescomplemented
233C2×C3⋊C8—21no—
234C23×C5D3×D411yescharacteristic
235C22×D5—34no—
236C22×D5—62no—
237C22×D5—62no—
238C22×D5—122no—
239C22×D5—122no—
240C2×C4×C5—22no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—61no—
244C2×C4×C5—61no—
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5C2×D1211yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5#23711yescharacteristic
250C2×C4×C5D3×Q811yescharacteristic
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—122no—
254C2×Dic5—121no—
255D20—62no—
256D20—62no—
257D20—62no—
258D20—62no—
259C4×D5—242no—
260C4×D5—242no—
261C5×C8—62no—
262#168—22no—
263C22×D4—151no—
264C2×M16—31no—
265C2×M16—51no—
266C4×D4—301no—
267C4×D4—301no—
268C4×D4—301no—
269C4×D4—301no—
270#117—31no—
271#117—51no—
272C2×C4⋊C4—151no—
273C2×C22⋊C4—302no—
274C2×C22⋊C4—302no—
275C2×C42D3×D511yescharacteristic
276#107—301no—
277#107—301no—
278#106—301no—
279#106—301no—
280#100—154no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38511yescharacteristic
284C2×C3×C5#45311yescharacteristic
285C2×C3×C5#45511yescharacteristic
286D15—44no—
287C23×C3D4×D511yescharacteristic
288C22×D3—54no—
289C22×D3—102no—
290C22×D3—102no—
291C22×D3—202no—
292C22×D3—202no—
293C2×C3×C4—22no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4Q8×D511yescharacteristic
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—202no—
307C2×Dic3—201no—
308D12—102no—
309D12—102no—
310D12—102no—
311D12—102no—
312C4×D3—402no—
313C4×D3—402no—
314C3×C8—102no—
315C3⋊C8—22no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5#88211yescharacteristic
319C22×C5#88311yescharacteristic
320C22×C5D3×C4⋊C411yescharacteristic
321C2×D5—64no—
322C2×D5—122no—
323C2×D5—122no—
324C2×D5—124no—
325C2×D5—242no—
326C4×C5—42no—
327C4×C5—121no—
328C4×C5—121no—
329C4×C5C4×D1211yescharacteristic
330C4×C5#67⋊C411yescharacteristic
331C4×C5#89611yescharacteristic
332C4×C5#89711yescharacteristic
333Dic5—41no—
334Dic5—41no—
335Dic5—241no—
336C24—152no—
337C2×D4—152no—
338C2×D4—152no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C22×C4—21no—
344C22×C4—302no—
345C22×C4—302no—
346C22×C4—301no—
347C22×C4C2×D3×D511yescharacteristic
348M16—32no—
349M16—52no—
350M16—61no—
351M16—101no—
352C2×C8—61no—
353C2×C8—101no—
354C4⋊C4—31no—
355C4⋊C4—31no—
356C4⋊C4—51no—
357C4⋊C4—51no—
358C4⋊C4—301no—
359C4⋊C4—301no—
360C22⋊C4—61no—
361C22⋊C4—101no—
362C22⋊C4—302no—
363C22⋊C4—302no—
364C22⋊C4—604no—
365C42—21no—
366C42—21no—
367C42—61no—
368C42—101no—
369C3×C5#185611yescharacteristic, complemented, Hall
370C22×C3—21no—
371C22×C3—21no—
372C22×C3#402811yescharacteristic
373C22×C3#402911yescharacteristic
374C22×C3D5×C4⋊C411yescharacteristic
375C2×D3—104no—
376C2×D3—202no—
377C2×D3—202no—
378C2×D3—204no—
379C2×D3—402no—
380C3×C4—42no—
381C3×C4—201no—
382C3×C4—201no—
383C3×C4C4×D2011yescharacteristic
384C3×C4#402711yescharacteristic
385C3×C4#404211yescharacteristic
386C3×C4#404311yescharacteristic
387Dic3—41no—
388Dic3—41no—
389Dic3—401no—
390C2×C5—21no—
391C2×C5—21no—
392C2×C5#466811yescharacteristic
393C2×C5#482211yescharacteristic
394C2×C5#482511yescharacteristic
395D5—124no—
396C23—154no—
397C23—302no—
398C23—302no—
399C23—602no—
400C23—602no—
401C23#679011yescharacteristic
402D4—302no—
403D4—302no—
404D4—302no—
405D4—302no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—101no—
412C2×C4—101no—
413C2×C4—602no—
414C2×C4—601no—
415C2×C4—1202no—
416C2×C4—1202no—
417C2×C4D15⋊Q811yescharacteristic
418C2×C4C4×D3×D511yescharacteristic
419C2×C4D5×D1211yescharacteristic
420C2×C4D3×D2011yescharacteristic
421C2×C4#677911yescharacteristic
422C2×C4#678211yescharacteristic
423C8—62no—
424C8—102no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3#6495711yescharacteristic
428C2×C3#6511111yescharacteristic
429C2×C3#6511411yescharacteristic
430D3—204no—
431C5#6875811yescharacteristic, complemented, Sylow
432C22—21no—
433C22—21no—
434C22—304no—
435C22—604no—
436C22—602no—
437C22—602no—
438C22—1202no—
439C22#9140411yescharacteristic
440C22#9147611yescharacteristic
441C22#9156211yescharacteristic
442C4—42no—
443C4—121no—
444C4—121no—
445C4—201no—
446C4—201no—
447C4—1201no—
448C4#9139511yescharacteristic
449C4#9140511yescharacteristic
450C4#9141911yescharacteristic
451C4#9142911yescharacteristic
452C3#1059955111yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—604no—
456C2#1174711811yescharacteristic
457C2#1174711911yescharacteristic
458C2#1174889511yescharacteristic
subgroupG/H
centerC22#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1856
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #11748460C2semidirect
4. #11748455C2semidirect
6. C5×#4523C2semidirect
7. C3×#64743C2semidirect
26. #90960C4semidirect
34. #64743D3semidirect
57. C5×#208C2×C4semidirect
64. C3×#681C2×C4semidirect
74. #4523D5semidirect
172. #681C4×D3semidirect
232. #208C4×D5semidirect
369. C3×C5#1856semidirect
431. C5#68758semidirect
452. C3#10599551semidirect

Maximal subgroups

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

subgroupindex
#117545152
#117510402
#117484602
#117484552
C2×#909602
C5×#45232
C3×#647432
#105995513
#687585