Finite Group Databasebeta

← #14302904

Subgroups — #14302904

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756280C211yesmaximal, characteristic, complemented
2#11754609C211yesmaximal, characteristic
3C3×#65294C211yesmaximal, characteristic, complemented
4#11748420C211yesmaximal, characteristic, complemented
5C2×#90960C211yesmaximal, characteristic, complemented
6C5×#4531C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10599498—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13#91782—22no—
14C22⋊C4×D15—22no—
15C4×D60—22no—
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91572—22no—
20#91458C412yescomplemented
21#91450—22no—
22#91374C412yescomplemented
23C3×#3937—22no—
24#90976—22no—
25#90960—22no—
26#70408—51nomaximal, Hall
27#65859—31no—
28#65855—31no—
29#65428—31no—
30C2×#3955—31no—
31#65294D311yescharacteristic, complemented
32C5×H(3,ℤ/4)—31no—
33#64751—31no—
34C23×D15D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60C2×C412yes—
41C2×D60D412yes—
42C2×C4×D15—24no—
43C2×C3×C22⋊D5—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20C2×C411yescharacteristic, complemented
49C2×C3×C4×D5—21no—
50C2×C3×Dic10C2×C411yescharacteristic, complemented
51C2×#1202—24no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C42×C5D412yescomplemented
55#6719—21no—
56#6714—24no—
57C4⋊Dic15—21no—
58C4×Dic15D412yescomplemented
59C5×#217—21no—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3C2×C412yescomplemented
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68#6667—24no—
69#5830—51no—
70#5521—51no—
71C3×#421—51no—
72#5236—51no—
73C2×#823—51no—
74#4557—51no—
75#4531D511yescharacteristic, complemented
76C2×#709C2×D311yescharacteristic
77C22×D20—31no—
78C2×C5×M16—31no—
79C5×#117—31no—
80C5×#117C2×D311yescharacteristic
81#4072—31no—
82C2×#681C2×D311yescharacteristic
83#4041—62no—
84#4039—62no—
85#4028—62no—
86D5×C22⋊C4—62no—
87#4021—32no—
88#4020—32no—
89C4×D20—62no—
90#3957—62no—
91#3955—62no—
92#3937—22no—
93#1911—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—22no—
97C22×D15—82no—
98C22×D15C22⋊C414yes—
99C22×C3×D5—21no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×Dic15—22no—
108D60—22no—
109D60—22no—
110D60—22no—
111D60—22no—
112C4×D15—84no—
113C2×C5×Dic3—22no—
114C3×C22⋊D5—41no—
115C3×C22⋊D5—41no—
116C2×C3×Dic5—21no—
117C3×D20—21no—
118C3×D20—21no—
119C3×C4×D5—41no—
120C3×C4×D5—41no—
121C3×Dic10—21no—
122C3×Dic10—21no—
123#1202—84no—
124C3×#168—41no—
125C5×C3⋊C8—41no—
126C2×C3×#41—51no—
127C22×D12—51no—
128C2×C3×M16—51no—
129C3×#117C2×D511yescharacteristic
130#947—52no—
131#940—52no—
132#937—102no—
133#930—102no—
134#926—51no—
135#926C2×D511yescharacteristic
136C2×#208C2×D511yescharacteristic
137#893—102no—
138D3×C22⋊C4—102no—
139C4×D12—102no—
140C3×#104—102no—
141#837—102no—
142#823—102no—
143C23×D5—32no—
144C22×C4×C5C22×D311yescharacteristic
145C2×C22⋊D5—21no—
146#709—21no—
147#709—21no—
148#709—21no—
149#709—21no—
150C2×D20—32no—
151C2×D20—32no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20—64no—
157C2×D20C4×D311yescharacteristic, complemented
158C2×C4×D5—21no—
159C2×C4×D5—64no—
160C2×Dic10C4×D311yescharacteristic, complemented
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—61no—
166C5×C22⋊C4—21no—
167C5×C22⋊C4—61no—
168C42×C5—32no—
169C42×C5#6712yescomplemented
170C22⋊Dic5—61no—
171#685—64no—
172#685—64no—
173C4⋊Dic5—61no—
174C4×Dic5—32no—
175#681—21no—
176#681—21no—
177C2×#168—21no—
178#535—151no—
179#518—151no—
180#421—51no—
181#421—151no—
182C2×#100—151no—
183H(3,ℤ/4)—31no—
184H(3,ℤ/4)—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5#12311yescharacteristic
189C2×D15—24no—
190C2×D15—44no—
191C2×D15—44no—
192C2×D15—82no—
193C2×C3×D5—42no—
194C2×C3×D5—41no—
195C3×C4×C5—42no—
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200Dic15—42no—
201C3×Dic5—41no—
202C5×Dic3—42no—
203C23×D3—52no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C3×#41—101no—
208C2×C3×Q8—51no—
209C2×C3×D4—51no—
210C2×C3×D4—101no—
211C22×C3×C4—101no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—104no—
214C2×D12—52no—
215C2×D12—52no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12—101no—
219C2×D12—101no—
220C2×C4×D3—104no—
221C3×M16—101no—
222C3×M16—101no—
223C2×C3×C8—101no—
224C3×C4⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C42D2012yescomplemented
227#217—21no—
228#217—101no—
229(C2×D3)⋊C4—104no—
230(C2×D3)⋊C4—104no—
231C4⋊Dic3—21no—
232C4⋊Dic3—101no—
233C4×Dic3—52no—
234C4×Dic3C4×D512yescomplemented
235#208—21no—
236#208—21no—
237C2×C3⋊C8—21no—
238C23×C5D3×D411yescharacteristic
239C22×D5—21no—
240C22×D5—34no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—242no—
244C2×C4×C5—22no—
245C2×C4×C5—62no—
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C22⋊D5—41no—
253C22⋊D5—41no—
254C2×Dic5—21no—
255C2×Dic5—62no—
256D20—21no—
257D20—21no—
258D20—62no—
259D20—62no—
260D20—62no—
261D20—62no—
262D20—244no—
263C4×D5—41no—
264C4×D5—41no—
265C4×D5—244no—
266Dic10—21no—
267Dic10—21no—
268C5×C8—121no—
269#168—41no—
270C2×#41—51no—
271C22×D4—151no—
272C2×M16—31no—
273C2×M16—51no—
274#127—152no—
275#124—152no—
276#121—302no—
277#120—302no—
278C4×D4—302no—
279C4×D4—302no—
280#117—31no—
281#117—151no—
282#117D3×D511yescharacteristic
283C2×C22⋊C4—302no—
284#104—102no—
285#104—302no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—44no—
292C3×D5—81no—
293C23×C3—101no—
294C23×C3D4×D511yescharacteristic
295C22×D3—54no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—402no—
299C3×Q8—101no—
300C3×Q8—101no—
301C3×D4—101no—
302C3×D4—101no—
303C3×D4—201no—
304C3×D4—201no—
305C2×C3×C4—22no—
306C2×C3×C4—101no—
307C2×C3×C4—201no—
308C2×C3×C4—201no—
309C2×C3×C4C2×C4×D511yescharacteristic
310C2×C3×C4C2×D2011yescharacteristic
311C2×C3×C4#70911yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4#71311yescharacteristic
315#67—404no—
316C2×Dic3—22no—
317C2×Dic3—102no—
318D12—102no—
319D12—102no—
320D12—102no—
321D12—102no—
322C4×D3—404no—
323C3×C8—201no—
324C3⋊C8—41no—
325C22×C5—41no—
326C22×C5D3×C22⋊C411yescharacteristic
327C22×C5#88311yescharacteristic
328C22×C5#93711yescharacteristic
329C2×D5—42no—
330C2×D5—41no—
331C2×D5—64no—
332C2×D5—124no—
333C2×D5—124no—
334C2×D5—242no—
335C4×C5—42no—
336C4×C5—122no—
337C4×C5#67⋊C411yescharacteristic
338C4×C5#88411yescharacteristic
339C4×C5C4×#6711yescharacteristic
340C4×C5#93811yescharacteristic
341Dic5—41no—
342Dic5—122no—
343C24—152no—
344#41—101no—
345#41—101no—
346#41—101no—
347#41—101no—
348C2×Q8—51no—
349C2×D4—51no—
350C2×D4—101no—
351C2×D4—152no—
352C2×D4—152no—
353C2×D4—304no—
354C2×D4—301no—
355C2×D4—301no—
356C2×D4—301no—
357C2×D4—301no—
358C22×C4—101no—
359C22×C4—304no—
360C22×C4C2×D3×D511yescharacteristic
361M16—61no—
362M16—61no—
363M16—101no—
364M16—101no—
365C2×C8—61no—
366C2×C8—101no—
367C4⋊C4—21no—
368C4⋊C4—61no—
369C4⋊C4—301no—
370C22⋊C4—21no—
371C22⋊C4—61no—
372C22⋊C4—304no—
373C22⋊C4—304no—
374C22⋊C4—301no—
375C42—32no—
376C42—152no—
377C42#120212yescomplemented
378C3×C5#191111yescharacteristic, complemented, Hall
379C22×C3—41no—
380C22×C3—202no—
381C22×C3—201no—
382C22×C3D5×C22⋊C411yescharacteristic
383C22×C3#402811yescharacteristic
384C22×C3#404011yescharacteristic
385C2×D3—104no—
386C2×D3—204no—
387C2×D3—204no—
388C2×D3—402no—
389C3×C4—42no—
390C3×C4—201no—
391C3×C4C4×D2011yescharacteristic
392C3×C4#403011yescharacteristic
393C3×C4#403911yescharacteristic
394C3×C4#404111yescharacteristic
395Dic3—42no—
396Dic3—202no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5#495611yescharacteristic
401D5—81no—
402D5—124no—
403C23—101no—
404C23—154no—
405C23—302no—
406C23—302no—
407C23—1202no—
408C23#679011yescharacteristic
409Q8—101no—
410Q8—101no—
411D4—101no—
412D4—101no—
413D4—201no—
414D4—201no—
415D4—302no—
416D4—302no—
417D4—302no—
418D4—302no—
419D4—1204no—
420C2×C4—22no—
421C2×C4—62no—
422C2×C4—101no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—302no—
426C2×C4—1204no—
427C2×C4#676611yescharacteristic
428C2×C4#677111yescharacteristic
429C2×C4C4×D3×D511yescharacteristic
430C2×C4#677711yescharacteristic
431C2×C4C2×#120211yescharacteristic
432C2×C4#679011yescharacteristic
433C8—121no—
434C8—201no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—401no—
439C2×C3#6495411yescharacteristic
440D3—204no—
441C5#7040811yescharacteristic, complemented, Sylow
442C22—41no—
443C22—202no—
444C22—201no—
445C22—304no—
446C22—604no—
447C22—604no—
448C22—1202no—
449C22#9135411yescharacteristic
450C22#9147311yescharacteristic
451C22#9157211yescharacteristic
452C4—42no—
453C4—122no—
454C4—201no—
455C4—602no—
456C4#9139611yescharacteristic
457C4C4×#120211yescharacteristic
458C4#9146111yescharacteristic
459C4#9146511yescharacteristic
460C3#1059949811yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—401no—
465C2—604no—
466C2#1174891711yescharacteristic
subgroupG/H
centerC2#11748917
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11754609C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756280C2semidirect
3. C3×#65294C2semidirect
4. #11748420C2semidirect
5. C2×#90960C2semidirect
6. C5×#4531C2semidirect
7. #11745971C2semidirect
20. #91458C4semidirect
22. #91374C4semidirect
31. #65294D3semidirect
48. C2×C3×D20C2×C4semidirect
50. C2×C3×Dic10C2×C4semidirect
54. C3×C42×C5D4semidirect
58. C4×Dic15D4semidirect
61. C4×C5×Dic3C2×C4semidirect
75. #4531D5semidirect
157. C2×D20C4×D3semidirect
160. C2×Dic10C4×D3semidirect
169. C42×C5#67semidirect
226. C3×C42D20semidirect
234. C4×Dic3C4×D5semidirect
377. C42#1202semidirect
378. C3×C5#1911semidirect
441. C5#70408semidirect
460. C3#10599498semidirect

Maximal subgroups

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

subgroupindex
#117562802
#117546092
C3×#652942
#117484202
C2×#909602
C5×#45312
#117459712
#105994983
#704085