Finite Group Databasebeta

← #14302453

Subgroups — #14302453

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756280C211yesmaximal, characteristic, complemented
2C2×#91305C211yesmaximal, characteristic
3C5×#5006C211yesmaximal, characteristic, complemented
4#11748424C211yesmaximal, characteristic, complemented
5#11748396C211yesmaximal, characteristic, complemented
6C3×#64753C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10600842—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13#91782—22no—
14C22⋊C4×D15—22no—
15C4×D60—22no—
16C5×#926C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×#6660C412yescomplemented
20#91305—22no—
21#91305—22no—
22C2×#6654C412yescomplemented
23C5×#806—22no—
24#90978—22no—
25#90969—22no—
26#69027—51nomaximal, Hall
27C2×#4095—31no—
28#65855—31no—
29C5×#410—31no—
30#65525—31no—
31#65290—31no—
32#64753D311yescharacteristic, complemented
33#64751—31no—
34C23×D15—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60C2×C412yes—
40C2×D60D412yes—
41C2×D60D412yes—
42C2×C4×D15—24no—
43C2×C5×#67—21no—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C2×C5×D12C2×C411yescharacteristic, complemented
49C2×C4×C5×D3—21no—
50C2×C5×Dic6C2×C411yescharacteristic, complemented
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4D412yes—
53C3×C42×C5—21no—
54#6719—21no—
55#6714—24no—
56C4⋊Dic15—21no—
57C4×Dic15D412yes—
58C5×#217—21no—
59C5×C4⋊Dic3—21no—
60C4×C5×Dic3—21no—
61C3×#681—21no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66C2×C3×#168C2×C412yescomplemented
67#6660—24no—
68#6654—24no—
69C2×#908—51no—
70#5521—51no—
71#5139—51no—
72#5131—51no—
73#5006D511yescharacteristic, complemented
74C3×#344—51no—
75#4557—51no—
76C2×C5×#41—31no—
77C22×D20—31no—
78C5×#117—31no—
79C5×#117C2×D311yescharacteristic
80#4095—62no—
81#4095—62no—
82C2×#688—32no—
83C2×#686—32no—
84#4072—31no—
85C2×#681C2×D311yescharacteristic
86C2×#681C2×D311yescharacteristic
87#4039—62no—
88D5×C22⋊C4—62no—
89C4×D20—62no—
90C5×#99—62no—
91#3969—62no—
92#3941—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—22no—
97C22×D15—22no—
98C22×D15—82no—
99C22×C5×D3—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—
111D60C22⋊C414yes—
112C4×D15—84no—
113C5×#67—41no—
114C5×#67—41no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C5×D12—21no—
118C5×D12—21no—
119C4×C5×D3—41no—
120C4×C5×D3—41no—
121C5×Dic6—21no—
122C5×Dic6—21no—
123C3×#168—22no—
124C3×#168—41no—
125C2×#235C2×D511yescharacteristic
126C22×D12—51no—
127C2×C3×M16—51no—
128C2×C3×M16—51no—
129C3×#117C2×D511yescharacteristic
130#926—51no—
131#926C2×D511yescharacteristic
132#908—102no—
133#908—102no—
134C2×D24—52no—
135C2×#204—52no—
136#893—102no—
137D3×C22⋊C4—102no—
138C4×D12—102no—
139#825—102no—
140#821—102no—
141#806—22no—
142C23×D5—61no—
143C5×#41—61no—
144C5×#41—61no—
145C5×#41—61no—
146C5×#41—61no—
147C2×C5×Q8—31no—
148C2×C5×D4—31no—
149C2×C5×D4—61no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C2×D20—32no—
153C2×D20—32no—
154C2×D20—32no—
155C2×D20—61no—
156C2×D20—61no—
157C2×D20—61no—
158C2×C4×D5—64no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—61no—
162C5×C22⋊C4D1212yes—
163C42×C5—21no—
164C42×C5—61no—
165C22⋊Dic5—61no—
166#688—64no—
167#686—64no—
168#685—64no—
169C4⋊Dic5—61no—
170C4×Dic5—32no—
171#681—21no—
172#681—21no—
173#681—21no—
174#681—21no—
175C2×#168—21no—
176C2×#168C4×D312yescomplemented
177C2×AGL(1,ℤ/8)—151no—
178#518—151no—
179#421—151no—
180#418—151no—
181#410—31no—
182#344—51no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×D15—24no—
189C2×D15—44no—
190C2×D15—82no—
191C2×D15—82no—
192C2×C5×D3—41no—
193C2×C5×D3—81no—
194C3×C4×C5—42no—
195C3×C4×C5C2×C22⋊C411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12311yescharacteristic
199Dic15—42no—
200C5×Dic3—41no—
201C5×Dic3—81no—
202C23×D3—101no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—21no—
205#235—21no—
206#235—21no—
207#235—21no—
208#235—21no—
209C2×D12—52no—
210C2×D12—52no—
211C2×D12—52no—
212C2×D12—101no—
213C2×D12—101no—
214C2×D12—101no—
215C2×D12C4×D511yescharacteristic, complemented
216C2×C4×D3—21no—
217C2×C4×D3—104no—
218C2×Dic6C4×D511yescharacteristic, complemented
219C3×M16—101no—
220C3×M16—101no—
221C3×M16—101no—
222C3×M16—101no—
223C2×C3×C8—52no—
224C2×C3×C8—101no—
225C3×C4⋊C4—21no—
226C3×C22⋊C4C22⋊D512yes—
227C3×C42—21no—
228#217—21no—
229#217—101no—
230(C2×D3)⋊C4—104no—
231C4⋊Dic3—21no—
232C4⋊Dic3—101no—
233C4×Dic3—21no—
234C4×Dic3—52no—
235D24—104no—
236#204—104no—
237C23×C5—61no—
238C23×C5C2×D1211yescharacteristic
239C22×D5—62no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—242no—
243C5×Q8—61no—
244C5×Q8—61no—
245C5×D4—61no—
246C5×D4—61no—
247C5×D4—121no—
248C5×D4—121no—
249C2×C4×C5—22no—
250C2×C4×C5—61no—
251C2×C4×C5—121no—
252C2×C4×C5—121no—
253C2×C4×C5—121no—
254C2×C4×C5C2×C4×D311yescharacteristic
255C2×C4×C5#23511yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5D3×D411yescharacteristic
258C2×C4×C5D3×D411yescharacteristic
259C2×C4×C5#23911yescharacteristic
260C2×Dic5—62no—
261D20—34no—
262D20—62no—
263D20—62no—
264D20—62no—
265C4×D5—244no—
266#168—22no—
267#168—41no—
268C2×#41—31no—
269C22×D4—151no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—51no—
275C2×M16—51no—
276C4×D4—302no—
277C4×D4—302no—
278#117—31no—
279#117—151no—
280#117D3×D511yescharacteristic
281C2×C22⋊C4—302no—
282#104—302no—
283#102—302no—
284#99—62no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289D15—44no—
290C5×D3—81no—
291C23×C3C2×C22⋊D511yescharacteristic
292C22×D3—21no—
293C22×D3—102no—
294C22×D3—102no—
295C22×D3—102no—
296C22×D3—402no—
297C2×C3×C4—22no—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4#70911yescharacteristic
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4#71111yescharacteristic
304#67—41no—
305#67—41no—
306C2×Dic3—21no—
307C2×Dic3—41no—
308C2×Dic3—102no—
309D12—21no—
310D12—21no—
311D12—54no—
312D12—102no—
313D12—102no—
314D12—102no—
315C4×D3—41no—
316C4×D3—41no—
317C4×D3—404no—
318Dic6—21no—
319Dic6—21no—
320C3×C8—102no—
321C3×C8—201no—
322C22×C5—41no—
323C22×C5—121no—
324C22×C5—241no—
325C22×C5C4×D1211yescharacteristic
326C22×C5#88211yescharacteristic
327C22×C5#89511yescharacteristic
328C2×D5—64no—
329C2×D5—124no—
330C2×D5—242no—
331C2×D5—242no—
332C4×C5—42no—
333C4×C5—121no—
334C4×C5—241no—
335C4×C5D3×C22⋊C411yescharacteristic
336C4×C5#88411yescharacteristic
337C4×C5#89311yescharacteristic
338C4×C5#89411yescharacteristic
339Dic5—122no—
340C24—301no—
341#41—61no—
342#41—61no—
343#41—61no—
344#41—61no—
345C2×Q8—31no—
346C2×D4—31no—
347C2×D4—61no—
348C2×D4—152no—
349C2×D4—152no—
350C2×D4—152no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C22×C4—61no—
355C22×C4—304no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—101no—
360M16—101no—
361M16—101no—
362M16—101no—
363C2×C8—52no—
364C2×C8—101no—
365C4⋊C4—21no—
366C4⋊C4—61no—
367C4⋊C4—301no—
368C22⋊C4—61no—
369C22⋊C4—304no—
370C22⋊C4—301no—
371C22⋊C4#120312yes—
372C42—21no—
373C42—61no—
374C42—152no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3C4×C22⋊D511yescharacteristic
378C22×C3#408311yescharacteristic
379C22×C3#408411yescharacteristic
380C2×D3—41no—
381C2×D3—81no—
382C2×D3—104no—
383C2×D3—204no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—42no—
387C3×C4D5×C22⋊C411yescharacteristic
388C3×C4#402711yescharacteristic
389C3×C4#402911yescharacteristic
390C3×C4#403011yescharacteristic
391Dic3—41no—
392Dic3—81no—
393Dic3—202no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—241no—
398C2×C5#466511yescharacteristic
399D5—124no—
400C23—61no—
401C23—302no—
402C23—302no—
403C23—302no—
404C23—1202no—
405C23C2×#120311yescharacteristic
406Q8—61no—
407Q8—61no—
408D4—61no—
409D4—61no—
410D4—121no—
411D4—121no—
412D4—154no—
413D4—302no—
414D4—302no—
415D4—302no—
416C2×C4—22no—
417C2×C4—61no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—302no—
422C2×C4—1204no—
423C2×C4#676811yescharacteristic
424C2×C4#677111yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4#677711yescharacteristic
427C2×C4#679011yescharacteristic
428C2×C4#679011yescharacteristic
429C8—102no—
430C8—201no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3#6524511yescharacteristic
435D3—81no—
436D3—204no—
437C5#6902711yescharacteristic, complemented, Sylow
438C22—41no—
439C22—121no—
440C22—241no—
441C22—304no—
442C22—604no—
443C22—1202no—
444C22—1202no—
445C22C4×#120311yescharacteristic
446C22#9146611yescharacteristic
447C22#9157311yescharacteristic
448C4—42no—
449C4—121no—
450C4—241no—
451C4—602no—
452C4#9135511yescharacteristic
453C4#9140611yescharacteristic
454C4#9146111yescharacteristic
455C4#9147311yescharacteristic
456C3#1060084211yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—241no—
461C2—604no—
462C2#1174891811yescharacteristic
subgroupG/H
centerC2#11748918
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#91305C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1904
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. C5×#5006C2semidirect
4. #11748424C2semidirect
5. #11748396C2semidirect
6. C3×#64753C2semidirect
7. #11745971C2semidirect
19. C2×#6660C4semidirect
22. C2×#6654C4semidirect
32. #64753D3semidirect
48. C2×C5×D12C2×C4semidirect
50. C2×C5×Dic6C2×C4semidirect
66. C2×C3×#168C2×C4semidirect
73. #5006D5semidirect
176. C2×#168C4×D3semidirect
215. C2×D12C4×D5semidirect
218. C2×Dic6C4×D5semidirect
375. C3×C5#1904semidirect
437. C5#69027semidirect
456. C3#10600842semidirect

Maximal subgroups

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

subgroupindex
#117562802
C2×#913052
C5×#50062
#117484242
#117483962
C3×#647532
#117459712
#106008423
#690275