Finite Group Databasebeta

← C3×#10602458 #14299788

Subgroups — C3×#10602458 #14299788

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#520C211yesmaximal, characteristic
2C2×C3×#3969C211yesmaximal, characteristic
3C3×#65521C211yesmaximal, characteristic
4C3×#65284C211yesmaximal, characteristic, complemented
5C3×#65266C211yesmaximal, characteristic, complemented
6C3×#64752C211yesmaximal, characteristic, complemented
7C3×#64750C211yesmaximal, characteristic, complemented
8#10602458C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×C4×C5×Q8—21no—
11C3×C4×C5×D4—21no—
12C3×C4×C5×D4—22no—
13C3×C5×#117—21no—
14C3×C5×#117C2211yescharacteristic
15C2×C3×C5×C4⋊C4—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C3×#3969C414yescomplemented
22C3×#3967—21no—
23C3×#3964—21no—
24C3×#3963—22no—
25C3×#3940—21no—
26C3×#3939—21no—
27C3×#1860—51nomaximal, Hall
28C5×#520C2×C311yescharacteristic
29C2×#3969C2×C311yescharacteristic
30#65521C2×C311yescharacteristic
31#65284C2×C311yescharacteristic, complemented
32#65266C2×C311yescharacteristic, complemented
33#64752C2×C311yescharacteristic, complemented
34#64750C2×C311yescharacteristic, complemented
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×C5—22no—
44C22×C3×C4×C5D412yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×C3×Dic5—21no—
47C22×C3×Dic5—21no—
48C3×C5×C4⋊C4—22no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—22no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—22no—
56C3×C42×C5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C412yescomplemented
61C3×#681—21no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681C2×C412yescomplemented
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C3×#520D511yescharacteristic
68C3×#428—51no—
69C2×C3×#104—51no—
70C3×#417—51no—
71C3×#382—51no—
72C3×#343—51no—
73C3×#339—51no—
74C2×C5×#41C22×C311yescharacteristic
75C4×C5×Q8—21no—
76C4×C5×D4—21no—
77C4×C5×D4—22no—
78C5×#117—21no—
79C5×#117C22×C311yescharacteristic
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4C22×C311yescharacteristic
82C2×C4⋊Dic5C22×C311yescharacteristic
83C2×C4×Dic5C22×C311yescharacteristic
84C2×#681C22×C311yescharacteristic
85C2×#681C22×C311yescharacteristic
86#3969C3×C414yescomplemented
87#3967—21no—
88#3964—21no—
89#3963—22no—
90#3940—21no—
91#3939—21no—
92#1860—51noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×Q8—21no—
96C3×C5×Q8C4⋊C412yes—
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—21no—
100C3×C5×D4C4⋊C412yes—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—82no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q811yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—42no—
119C2×C3×Dic5—41no—
120C3×#168—22no—
121C3×#168—41no—
122C2×C3×#41C2×D511yescharacteristic
123C2×C3×M16—51no—
124C2×C3×M16—51no—
125C3×C4×Q8—21no—
126C3×C4×D4—21no—
127C3×C4×D4—22no—
128C3×#117—21no—
129C3×#117C2×D511yescharacteristic
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4C2×D511yescharacteristic
133C2×C3×C42—51no—
134C3×#107—101no—
135C3×#106—101no—
136C3×#104—54no—
137C3×#103—101no—
138C3×#102—101no—
139C3×#95—102no—
140C5×#41—21no—
141C5×#41—21no—
142C5×#41C2×C3×C412yes—
143C5×#41C3×Q812yes—
144C2×C5×Q8C3×D411yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4C3×D411yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5C3×D412yes—
150C22×C4×C5C23×C311yescharacteristic
151C22×Dic5—21no—
152C22×Dic5—21no—
153C5×C4⋊C4—22no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4C3×D411yescharacteristic
157C5×C4⋊C4C3×D411yescharacteristic
158C5×C22⋊C4—22no—
159C5×C22⋊C4—21no—
160C42×C5—22no—
161C42×C5—21no—
162C4⋊Dic5—21no—
163C4⋊Dic5—21no—
164C4×Dic5—21no—
165C4×Dic5C2×C3×C412yescomplemented
166#681—21no—
167#681—21no—
168#681—21no—
169#681C2×C3×C412yescomplemented
170C2×#168—21no—
171C2×#168—21no—
172#520C3×D511yescharacteristic
173#428—51no—
174C2×#104—51no—
175#417—51no—
176#382—51no—
177#343—51no—
178#339—51no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—22no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5C4×D411yescharacteristic
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C22⋊Q811yescharacteristic
187C3×C4×C5—22no—
188C3×C4×C5—41no—
189C3×C4×C5—42no—
190C3×C4×C5—41no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5#12311yescharacteristic
195C3×Dic5—42no—
196C3×Dic5—81no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41Dic1012yes—
200C3×#41C4×D512yes—
201C2×C3×Q8C22⋊D511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C22⋊D511yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—101no—
207C22×C3×C4—101no—
208C22×C3×C4C22⋊D512yes—
209C22×C3×C4C22×D511yescharacteristic
210C3×M16—52no—
211C3×M16—101no—
212C3×M16—101no—
213C3×M16—101no—
214C2×C3×C8—101no—
215C2×C3×C8—101no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4C22⋊D511yescharacteristic
222C3×C4⋊C4C22⋊D511yescharacteristic
223C3×C22⋊C4—22no—
224C3×C22⋊C4—21no—
225C3×C42—22no—
226C3×C42—21no—
227C3×C42—52no—
228C3×C42—101no—
229C23×C5—21no—
230C23×C5C2×C3×D411yescharacteristic
231C5×Q8—21no—
232C5×Q8C3×C4⋊C412yes—
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—21no—
236C5×D4C3×C4⋊C412yes—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—21no—
241C2×C4×C5—22no—
242C2×C4×C5—21no—
243C2×C4×C5—42no—
244C2×C4×C5—82no—
245C2×C4×C5C22×C3×C411yescharacteristic
246C2×C4×C5C2×C3×D411yescharacteristic
247C2×C4×C5C2×C3×D411yescharacteristic
248C2×C4×C5C2×C3×Q811yescharacteristic
249C2×C4×C5C3×#4111yescharacteristic
250C2×C4×C5C3×#4111yescharacteristic
251C2×Dic5—22no—
252C2×Dic5—41no—
253C2×Dic5—41no—
254C2×Dic5—42no—
255C2×Dic5—41no—
256#168—22no—
257#168—41no—
258C2×#41C2×C3×D511yescharacteristic
259C2×M16—51no—
260C2×M16—51no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—22no—
264#117—21no—
265#117C2×C3×D511yescharacteristic
266C2×C4⋊C4—21no—
267C2×C4⋊C4—51no—
268C2×C4⋊C4C2×C3×D511yescharacteristic
269C2×C42—51no—
270#107—101no—
271#106—101no—
272#104—54no—
273#103—101no—
274#102—101no—
275#95—102no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5—42no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C2×C3×C5#45511yescharacteristic
282C23×C3—21no—
283C23×C3C2×C22⋊D511yescharacteristic
284C3×Q8—21no—
285C3×Q8#68312yes—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—21no—
289C3×D4#68312yes—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—42no—
297C2×C3×C4—82no—
298C2×C3×C4—102no—
299C2×C3×C4—201no—
300C2×C3×C4—201no—
301C2×C3×C4—202no—
302C2×C3×C4—201no—
303C2×C3×C4C2×Dic1011yescharacteristic
304C2×C3×C4C2×C4×D511yescharacteristic
305C2×C3×C4#70911yescharacteristic
306C2×C3×C4#70911yescharacteristic
307C2×C3×C4C2×C22⋊D511yescharacteristic
308C2×C3×C4C2×C22⋊D511yescharacteristic
309C3×C8—102no—
310C3×C8—201no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—22no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5C3×C4×D411yescharacteristic
317C22×C5C3×#12011yescharacteristic
318C22×C5C3×C22⋊Q811yescharacteristic
319C4×C5—22no—
320C4×C5—41no—
321C4×C5—42no—
322C4×C5—41no—
323C4×C5C2×C3×C4⋊C411yescharacteristic
324C4×C5C3×C4×D411yescharacteristic
325C4×C5C3×C22⋊Q811yescharacteristic
326C4×C5C3×#12311yescharacteristic
327Dic5—42no—
328Dic5—81no—
329#41—21no—
330#41—21no—
331#41C3×Dic1012yes—
332#41C3×C4×D512yes—
333C2×Q8C3×C22⋊D511yescharacteristic
334C2×D4—21no—
335C2×D4C3×C22⋊D511yescharacteristic
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—101no—
339C22×C4—101no—
340C22×C4C3×C22⋊D512yes—
341C22×C4C22×C3×D511yescharacteristic
342M16—52no—
343M16—101no—
344M16—101no—
345M16—101no—
346C2×C8—101no—
347C2×C8—101no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—101no—
352C4⋊C4—101no—
353C4⋊C4C3×C22⋊D511yescharacteristic
354C4⋊C4C3×C22⋊D511yescharacteristic
355C22⋊C4—22no—
356C22⋊C4—21no—
357C42—22no—
358C42—21no—
359C42—52no—
360C42—101no—
361C3×C5#186011yescharacteristic, complemented, Hall
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3#407011yescharacteristic
368C22×C3C4×C22⋊D511yescharacteristic
369C22×C3#409911yescharacteristic
370C3×C4—22no—
371C3×C4—42no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—202no—
375C3×C4—401no—
376C3×C4C2×#68311yescharacteristic
377C3×C4#407011yescharacteristic
378C3×C4C4×C22⋊D511yescharacteristic
379C3×C4#407511yescharacteristic
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—42no—
383C2×C5C3×#38511yescharacteristic
384C2×C5C3×#45411yescharacteristic
385C2×C5C3×#45511yescharacteristic
386C23—21no—
387C23C2×C3×C22⋊D511yescharacteristic
388Q8—21no—
389Q8C3×#68312yes—
390D4—22no—
391D4—22no—
392D4—21no—
393D4C3×#68312yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—82no—
402C2×C4—102no—
403C2×C4—201no—
404C2×C4—201no—
405C2×C4—202no—
406C2×C4—201no—
407C2×C4C2×C3×Dic1011yescharacteristic
408C2×C4C2×C3×C4×D511yescharacteristic
409C2×C4C3×#70911yescharacteristic
410C2×C4C3×#70911yescharacteristic
411C2×C4C2×C3×C22⋊D511yescharacteristic
412C2×C4C2×C3×C22⋊D511yescharacteristic
413C8—102no—
414C8—201no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—42no—
418C2×C3#6549911yescharacteristic
419C2×C3#6553111yescharacteristic
420C2×C3#6553411yescharacteristic
421C5C3×#186011yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22C3×#407011yescharacteristic
428C22C3×C4×C22⋊D511yescharacteristic
429C22C3×#409911yescharacteristic
430C4—22no—
431C4—42no—
432C4—41no—
433C4—41no—
434C4—202no—
435C4—401no—
436C4C2×C3×#68311yescharacteristic
437C4C3×#407011yescharacteristic
438C4C3×C4×C22⋊D511yescharacteristic
439C4C3×#407511yescharacteristic
440C3#1060245811yescharacteristic, direct product factor, Sylow
441C2—21no—
442C2—21no—
443C2—42no—
444C2C3×#6549911yescharacteristic
445C2C3×#6553111yescharacteristic
446C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#520C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#520D5
hypocenterC5C3×#1860
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#520

Complements

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

NH ≅ G/Ntype
4. C3×#65284C2semidirect
5. C3×#65266C2semidirect
6. C3×#64752C2semidirect
7. C3×#64750C2semidirect
8. #10602458C3direct (N × H)
21. C3×#3969C4semidirect
31. #65284C2×C3semidirect
32. #65266C2×C3semidirect
33. #64752C2×C3semidirect
34. #64750C2×C3semidirect
60. C3×C4×Dic5C2×C4semidirect
64. C3×#681C2×C4semidirect
86. #3969C3×C4semidirect
165. C4×Dic5C2×C3×C4semidirect
169. #681C2×C3×C4semidirect
361. C3×C5#1860semidirect
421. C5C3×#1860semidirect
440. C3#10602458direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5202
C2×C3×#39692
C3×#655212
C3×#652842
C3×#652662
C3×#647522
C3×#647502
#106024583
C3×#18605