Finite Group Databasebeta

← #14299742

Subgroups — #14299742

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
1C3×#66161C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic
3C5×#5232C211yesmaximal, characteristic
4#11748866C211yesmaximal, characteristic, complemented
5#11748472C211yesmaximal, characteristic, complemented
6#11745985C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10601090—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C4×Dic15C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×C4⋊Dic3C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×Q8×Dic5—21no—
15C3×D4×Dic5—21no—
16C3×D4×Dic5—22no—
17C3×#4072—21no—
18C3×#4072C2211yescharacteristic
19C2×C3×C4⋊Dic5—21no—
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×#6669—22no—
22#91121C414yescomplemented
23C5×#835—21no—
24C5×#832—21no—
25#90989—21no—
26#90986—21no—
27#71664—51nomaximal, Hall
28#66161D311yescharacteristic
29C5×#417—31no—
30C2×#3969—31no—
31#65265—31no—
32#65253—31no—
33#64775—31no—
34#64774—31no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41C2×C412yes—
38C3×C5×#41Q812yes—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15—21no—
45C22×C5×Dic3—21no—
46C22×C3×Dic5—22no—
47C22×C3×Dic5D412yes—
48C4×Dic15—21no—
49C4×Dic15C2×C412yescomplemented
50#6710—21no—
51#6710C2×C412yescomplemented
52C2×C3⋊#168—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×#208—21no—
56C5×#208—21no—
57C2×C5×C3⋊C8—21no—
58C3×C22⋊Dic5—22no—
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5—22no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5D411yescharacteristic
64C3×C4⋊Dic5D411yescharacteristic
65C3×C4×Dic5—22no—
66C3×C4×Dic5—21no—
67#6669—44no—
68C3×#520—51no—
69C2×#837—51no—
70#5232D511yescharacteristic
71#4995—51no—
72#4975—51no—
73#4532—51no—
74#4530—51no—
75C2×C5×#41C2×D311yescharacteristic
76C2×C5×M16—31no—
77C2×C5×C4⋊C4—31no—
78Q8×Dic5—21no—
79D4×Dic5—21no—
80D4×Dic5—22no—
81#4072—21no—
82#4072C2×D311yescharacteristic
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5C2×D311yescharacteristic
85C2×#683—62no—
86C2×C4×Dic5—31no—
87C2×#681—31no—
88C5×#103—61no—
89C5×#102—61no—
90#3969—34no—
91#3940—61no—
92#3939—61no—
93#1859—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—21no—
97C3×C5×Q8C4⋊C412yescomplemented
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4—21no—
101C3×C5×D4C4⋊C412yescomplemented
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×Q811yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—22no—
113C2×Dic15—22no—
114C2×C5×Dic3—42no—
115C2×C5×Dic3—41no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—42no—
120C2×C3×Dic5—82no—
121C3⋊#168—22no—
122C5×C3⋊C8—41no—
123C2×C3×#41C2×D511yescharacteristic
124C3×C4×Q8—101no—
125C3×C4×D4—102no—
126C3×C4×D4—101no—
127C3×#117—51no—
128C3×#117—101no—
129C2×C3×C4⋊C4—51no—
130C2×C3×C4⋊C4—101no—
131C2×C4⋊Dic3C2×D511yescharacteristic
132C2×Dic3⋊C4—102no—
133C2×C4×Dic3—51no—
134C2×#208—51no—
135C2×#208C2×D511yescharacteristic
136#837—54no—
137#835—21no—
138#832—21no—
139#808—101no—
140#807—101no—
141C5×#41—21no—
142C5×#41—21no—
143C5×#41Dic612yes—
144C5×#41C4×D312yes—
145C2×C5×Q8#6711yescharacteristic
146C2×C5×D4—21no—
147C2×C5×D4#6711yescharacteristic
148C22×C4×C5—21no—
149C22×C4×C5—61no—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—22no—
152C22×Dic5—61no—
153C22×Dic5#6712yes—
154C5×M16—61no—
155C5×M16—61no—
156C2×C5×C8—61no—
157C5×C4⋊C4—61no—
158C5×C4⋊C4—61no—
159C22⋊Dic5—22no—
160C22⋊Dic5—21no—
161C4⋊Dic5—22no—
162C4⋊Dic5—21no—
163C4⋊Dic5—21no—
164C4⋊Dic5#6711yescharacteristic
165C4⋊Dic5#6711yescharacteristic
166#683—124no—
167C4×Dic5—22no—
168C4×Dic5—21no—
169C4×Dic5—32no—
170C4×Dic5—61no—
171#681—32no—
172#681—61no—
173C2×#168—61no—
174#520—51no—
175#428—151no—
176C2×#104—151no—
177#417—31no—
178#384—151no—
179#343—151no—
180#339—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—22no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5C4×D411yescharacteristic
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5C22⋊Q811yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5#12311yescharacteristic
194Dic15—24no—
195C3×Dic5—42no—
196C3×Dic5—41no—
197C3×Dic5—41no—
198C5×Dic3—81no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41Dic1012yes—
202C3×#41C4×D512yes—
203C2×C3×Q8C22⋊D511yescharacteristic
204C2×C3×D4—21no—
205C2×C3×D4C22⋊D511yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—52no—
208C22×C3×C4—102no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—101no—
212C3×C4⋊C4—51no—
213C3×C4⋊C4—51no—
214C3×C4⋊C4—102no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217C3×C22⋊C4—102no—
218C3×C22⋊C4—101no—
219C3×C42—102no—
220C3×C42—101no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223Dic3⋊C4—204no—
224C4×Dic3—52no—
225C4×Dic3—101no—
226#208—21no—
227#208—21no—
228#208—52no—
229#208—101no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—101no—
232C23×C5—21no—
233C23×C5C2×#6711yescharacteristic
234C5×Q8—21no—
235C5×Q8Dic3⋊C412yescomplemented
236C5×D4—22no—
237C5×D4—22no—
238C5×D4—21no—
239C5×D4Dic3⋊C412yescomplemented
240C2×C4×C5—21no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—122no—
244C2×C4×C5—121no—
245C2×C4×C5C2×Dic611yescharacteristic
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5#23511yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C2×Dic5—21no—
252C2×Dic5—22no—
253C2×Dic5—21no—
254C2×Dic5—42no—
255C2×Dic5—62no—
256C2×Dic5—62no—
257C2×Dic5—62no—
258C2×Dic5—82no—
259C5×C8—121no—
260#168—62no—
261C2×#41D3×D511yescharacteristic
262C2×M16—31no—
263C2×M16—151no—
264C4×Q8—101no—
265C4×D4—102no—
266C4×D4—101no—
267#117—51no—
268#117—101no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—101no—
272C2×C4⋊C4—302no—
273C2×C42—151no—
274#107—301no—
275#106—301no—
276#104—154no—
277#103—61no—
278#102—61no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5—42no—
282C2×C3×C5#38511yescharacteristic
283C2×C3×C5#45311yescharacteristic
284C2×C3×C5#45611yescharacteristic
285C23×C3—21no—
286C23×C3D4×D511yescharacteristic
287C3×Q8—21no—
288C3×Q8#68312yescomplemented
289C3×D4—22no—
290C3×D4—22no—
291C3×D4—21no—
292C3×D4#68312yescomplemented
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—102no—
299C2×C3×C4—202no—
300C2×C3×C4—402no—
301C2×C3×C4C2×Dic1011yescharacteristic
302C2×C3×C4C2×C4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×C3×C4C2×C22⋊D511yescharacteristic
307C2×Dic3—42no—
308C2×Dic3—41no—
309C2×Dic3—102no—
310C2×Dic3—102no—
311C2×Dic3—102no—
312C3⋊C8—41no—
313C3⋊C8—102no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—22no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5#92411yescharacteristic
320C22×C5C4×#6711yescharacteristic
321C22×C5#95311yescharacteristic
322C4×C5—22no—
323C4×C5—241no—
324C4×C5C2×Dic3⋊C411yescharacteristic
325C4×C5#92411yescharacteristic
326C4×C5C4×#6711yescharacteristic
327C4×C5#92911yescharacteristic
328Dic5—42no—
329Dic5—41no—
330Dic5—41no—
331Dic5—64no—
332#41—21no—
333#41—21no—
334#41#120012yes—
335#41#120412yes—
336C2×Q8#120111yescharacteristic
337C2×D4—21no—
338C2×D4#120111yescharacteristic
339C22×C4—21no—
340C22×C4—52no—
341C22×C4—61no—
342C22×C4—102no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345M16—61no—
346M16—61no—
347M16—152no—
348M16—301no—
349C2×C8—61no—
350C2×C8—301no—
351C4⋊C4—51no—
352C4⋊C4—51no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—102no—
356C4⋊C4—101no—
357C4⋊C4—101no—
358C4⋊C4—604no—
359C22⋊C4—102no—
360C22⋊C4—101no—
361C42—102no—
362C42—101no—
363C42—152no—
364C42—301no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3#402411yescharacteristic
372C22×C3#402711yescharacteristic
373C22×C3#408311yescharacteristic
374C3×C4—22no—
375C3×C4—202no—
376C3×C4—201no—
377C3×C4—201no—
378C3×C4#402411yescharacteristic
379C3×C4#402711yescharacteristic
380C3×C4C2×#68311yescharacteristic
381C3×C4#408111yescharacteristic
382Dic3—81no—
383Dic3—104no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5—42no—
387C2×C5#521011yescharacteristic
388C2×C5#524111yescharacteristic
389C2×C5#524611yescharacteristic
390C23—21no—
391C23D5×#6711yescharacteristic
392Q8—21no—
393Q8#666912yescomplemented
394D4—22no—
395D4—22no—
396D4—21no—
397D4#666912yescomplemented
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—102no—
404C2×C4—122no—
405C2×C4—121no—
406C2×C4—202no—
407C2×C4—302no—
408C2×C4—302no—
409C2×C4—302no—
410C2×C4—402no—
411C2×C4#678211yescharacteristic
412C2×C4#678211yescharacteristic
413C2×C4C2×#120011yescharacteristic
414C2×C4C2×#120111yescharacteristic
415C2×C4C2×#120411yescharacteristic
416C2×C4D5×#6711yescharacteristic
417C8—121no—
418C8—302no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—42no—
422C2×C3#6523511yescharacteristic
423C2×C3#6548711yescharacteristic
424C2×C3#6549411yescharacteristic
425C5#7166411yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—22no—
429C22—41no—
430C22—41no—
431C22#9155211yescharacteristic
432C22#9156311yescharacteristic
433C22#9157411yescharacteristic
434C4—22no—
435C4—202no—
436C4—201no—
437C4—201no—
438C4—241no—
439C4—304no—
440C4#9153911yescharacteristic
441C4C2×#666911yescharacteristic
442C4#9155211yescharacteristic
443C4#9157411yescharacteristic
444C3#1060109011yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—42no—
448C2#1174941711yescharacteristic
449C2#1174946211yescharacteristic
450C2#1174950811yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5#120
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1859
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #11748866C2semidirect
5. #11748472C2semidirect
6. #11745985C2semidirect
7. #11745973C2semidirect
22. #91121C4semidirect
49. C4×Dic15C2×C4semidirect
51. #6710C2×C4semidirect
97. C3×C5×Q8C4⋊C4semidirect
101. C3×C5×D4C4⋊C4semidirect
235. C5×Q8Dic3⋊C4semidirect
239. C5×D4Dic3⋊C4semidirect
288. C3×Q8#683semidirect
292. C3×D4#683semidirect
365. C3×C5#1859semidirect
393. Q8#6669semidirect
397. D4#6669semidirect
425. C5#71664semidirect
444. C3#10601090semidirect

Maximal subgroups

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

subgroupindex
C3×#661612
C2×#911212
C5×#52322
#117488662
#117484722
#117459852
#117459732
#106010903
#716645