Finite Group Databasebeta

← C3×#10601473 #14299708

Subgroups — C3×#10601473 #14299708

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×#65857C211yesmaximal, characteristic
2C3×C5×#428C211yesmaximal, characteristic, complemented
3C2×C3×#3957C211yesmaximal, characteristic
4C3×#65265C211yesmaximal, characteristic, complemented
5C3×#65255C211yesmaximal, characteristic
6C3×#64774C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10601473C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C2×C3×#683—22no—
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4038—21no—
18C3×D5×C4⋊C4—21no—
19C3×#4027—22no—
20C3×C4×D20—21no—
21C3×C4×Dic10—21no—
22C3×C5×#107—21no—
23C3×C5×#106—21no—
24C3×#3957C414yescomplemented
25C3×#3942—21no—
26C3×#3941—21no—
27C3×#1859—51nomaximal, Hall
28#65857C2×C311yescharacteristic
29C5×#428C2×C311yescharacteristic, complemented
30C2×#3957C2×C311yescharacteristic
31#65265C2×C311yescharacteristic, complemented
32#65255C2×C311yescharacteristic
33#64774C2×C311yescharacteristic, complemented
34#64752C2×C311yescharacteristic, complemented
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C3×C22⋊D5—21no—
38C22×C3×Dic5—21no—
39C22×C3×Dic5D412yes—
40C3×#709—21no—
41C3×#709—21no—
42C3×#709C2×C412yes—
43C3×#709Q812yes—
44C2×C3×D20D411yescharacteristic
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—22no—
47C2×C3×Dic10D411yescharacteristic
48C3×C5×M16—21no—
49C3×C5×M16C2×C412yescomplemented
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C4⋊C4D411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C42×C5—21no—
57C3×#685—22no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5—21no—
60C3×#683—22no—
61C3×#683—44no—
62C3×C4×Dic5—22no—
63C3×C4×Dic5—21no—
64C3×C4×Dic5C2×C412yescomplemented
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68C3×#520—51no—
69C3×#428D511yescharacteristic, complemented
70C2×C3×#104—51no—
71C3×#417—51no—
72C3×#384—51no—
73C3×#343—51no—
74C3×#339—51no—
75C2×#709C22×C311yescharacteristic
76C2×C5×M16C22×C311yescharacteristic
77C5×#117C22×C311yescharacteristic
78C2×C5×C4⋊C4C22×C311yescharacteristic
79C2×C4⋊Dic5C22×C311yescharacteristic
80C2×#683—22no—
81C2×C4×Dic5C22×C311yescharacteristic
82C2×#681C22×C311yescharacteristic
83#4038—21no—
84D5×C4⋊C4—21no—
85#4027—22no—
86C4×D20—21no—
87C4×Dic10—21no—
88C5×#107—21no—
89C5×#106—21no—
90#3957C3×C414yescomplemented
91#3942—21no—
92#3941—21no—
93#1859—51noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—42no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×Q811yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C3×C22⋊D5—22no—
107C3×C22⋊D5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—42no—
114C3×D20—21no—
115C3×D20C4⋊C412yescomplemented
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×C4×D5—82no—
119C3×Dic10—21no—
120C3×Dic10C4⋊C412yescomplemented
121C3×C5×C8—22no—
122C3×#168—41no—
123C2×C3×#41—51no—
124C2×C3×M16—51no—
125C2×C3×M16C2×D511yescharacteristic
126C3×C4×Q8—101no—
127C3×C4×D4—101no—
128C3×C4×D4—102no—
129C3×#117—101no—
130C3×#117C2×D511yescharacteristic
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—101no—
133C2×C3×C4⋊C4—102no—
134C2×C3×C4⋊C4C2×D511yescharacteristic
135C2×C3×C42—51no—
136C3×#107—21no—
137C3×#106—21no—
138C3×#104—54no—
139C3×#103—101no—
140C3×#102—101no—
141C22×C4×C5—21no—
142C22×C4×C5C23×C311yescharacteristic
143C2×C22⋊D5—21no—
144C22×Dic5—21no—
145C22×Dic5C3×D412yes—
146#709—21no—
147#709—21no—
148#709C2×C3×C412yes—
149#709C3×Q812yes—
150C2×D20C3×D411yescharacteristic
151C2×C4×D5—21no—
152C2×C4×D5—22no—
153C2×Dic10C3×D411yescharacteristic
154C5×M16—21no—
155C5×M16C2×C3×C412yescomplemented
156C2×C5×C8—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4C3×D411yescharacteristic
160C5×C4⋊C4C3×D411yescharacteristic
161C5×C22⋊C4—21no—
162C42×C5—21no—
163#685—22no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166#683—22no—
167#683—44no—
168C4×Dic5—22no—
169C4×Dic5—21no—
170C4×Dic5C2×C3×C412yescomplemented
171#681—21no—
172#681—21no—
173C2×#168—21no—
174#520—51no—
175#428C3×D511yescharacteristic, complemented
176C2×#104—51no—
177#417—51no—
178#384—51no—
179#343—51no—
180#339—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5—41no—
190C3×C4×C5—41no—
191C3×C4×C5—81no—
192C3×C4×C5C2×C4⋊C411yescharacteristic
193C3×C4×C5C4×D411yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195C3×C4×C5#12311yescharacteristic
196C3×Dic5—24no—
197C3×Dic5—22no—
198C3×Dic5—42no—
199C3×#41—52no—
200C3×#41—52no—
201C3×#41—101no—
202C3×#41—101no—
203C2×C3×Q8—51no—
204C2×C3×D4—51no—
205C2×C3×D4—101no—
206C22×C3×C4—21no—
207C22×C3×C4—52no—
208C22×C3×C4—102no—
209C22×C3×C4—101no—
210C22×C3×C4—101no—
211C22×C3×C4C22×D511yescharacteristic
212C3×M16—21no—
213C3×M16—101no—
214C3×M16—101no—
215C3×M16C4×D512yescomplemented
216C2×C3×C8—21no—
217C2×C3×C8—101no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—102no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—204no—
224C3×C4⋊C4C22⋊D511yescharacteristic
225C3×C4⋊C4C22⋊D511yescharacteristic
226C3×C22⋊C4—21no—
227C3×C22⋊C4—102no—
228C3×C42—21no—
229C3×C42—52no—
230C3×C42—102no—
231C3×C42—101no—
232C23×C5C2×C3×D411yescharacteristic
233C22×D5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—42no—
237C2×C4×C5—41no—
238C2×C4×C5C22×C3×C411yescharacteristic
239C2×C4×C5C2×C3×D411yescharacteristic
240C2×C4×C5C2×C3×D411yescharacteristic
241C2×C4×C5C2×C3×Q811yescharacteristic
242C2×C4×C5C3×#4111yescharacteristic
243C2×C4×C5C3×#4111yescharacteristic
244C22⋊D5—22no—
245C22⋊D5—22no—
246C2×Dic5—22no—
247C2×Dic5—22no—
248C2×Dic5—22no—
249C2×Dic5—21no—
250C2×Dic5—22no—
251C2×Dic5—42no—
252D20—21no—
253D20C3×C4⋊C412yescomplemented
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—82no—
257Dic10—21no—
258Dic10C3×C4⋊C412yescomplemented
259C5×C8—22no—
260#168—41no—
261C2×#41—51no—
262C2×M16—51no—
263C2×M16C2×C3×D511yescharacteristic
264C4×Q8—101no—
265C4×D4—101no—
266C4×D4—102no—
267#117—101no—
268#117C2×C3×D511yescharacteristic
269C2×C4⋊C4—51no—
270C2×C4⋊C4—101no—
271C2×C4⋊C4—102no—
272C2×C4⋊C4C2×C3×D511yescharacteristic
273C2×C42—51no—
274#107—21no—
275#106—21no—
276#104—54no—
277#103—101no—
278#102—101no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38511yescharacteristic
282C2×C3×C5#45311yescharacteristic
283C2×C3×C5#45611yescharacteristic
284C3×D5—42no—
285C23×C3—101no—
286C23×C3D4×D511yescharacteristic
287C3×Q8—52no—
288C3×Q8—101no—
289C3×D4—52no—
290C3×D4—102no—
291C3×D4—102no—
292C3×D4—101no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—42no—
296C2×C3×C4—41no—
297C2×C3×C4—102no—
298C2×C3×C4—102no—
299C2×C3×C4—102no—
300C2×C3×C4—101no—
301C2×C3×C4—102no—
302C2×C3×C4—102no—
303C2×C3×C4—102no—
304C2×C3×C4—202no—
305C2×C3×C4—402no—
306C2×C3×C4C2×C4×D511yescharacteristic
307C2×C3×C4#70911yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4Q8×D511yescharacteristic
310C2×C3×C4#71311yescharacteristic
311C2×C3×C4C2×C22⋊D511yescharacteristic
312C3×C8—22no—
313C3×C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5C3×C4×D411yescharacteristic
317C22×C5C3×#12011yescharacteristic
318C22×C5C3×C22⋊Q811yescharacteristic
319C2×D5—22no—
320C2×D5—41no—
321C2×D5—41no—
322C4×C5—41no—
323C4×C5—41no—
324C4×C5—81no—
325C4×C5C2×C3×C4⋊C411yescharacteristic
326C4×C5C3×C4×D411yescharacteristic
327C4×C5C3×C22⋊Q811yescharacteristic
328C4×C5C3×#12311yescharacteristic
329Dic5—24no—
330Dic5—22no—
331Dic5—42no—
332#41—52no—
333#41—52no—
334#41—101no—
335#41—101no—
336C2×Q8—51no—
337C2×D4—51no—
338C2×D4—101no—
339C22×C4—21no—
340C22×C4—52no—
341C22×C4—102no—
342C22×C4—101no—
343C22×C4—101no—
344C22×C4C22×C3×D511yescharacteristic
345M16—21no—
346M16—101no—
347M16—101no—
348M16C3×C4×D512yescomplemented
349C2×C8—21no—
350C2×C8—101no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—102no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C4⋊C4—204no—
357C4⋊C4C3×C22⋊D511yescharacteristic
358C4⋊C4C3×C22⋊D511yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—102no—
361C42—21no—
362C42—52no—
363C42—102no—
364C42—101no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—102no—
369C22×C3—201no—
370C22×C3—201no—
371C22×C3#403911yescharacteristic
372C22×C3#404211yescharacteristic
373C22×C3#408311yescharacteristic
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—81no—
377C3×C4—104no—
378C3×C4—102no—
379C3×C4—202no—
380C3×C4D5×C4⋊C411yescharacteristic
381C3×C4#404011yescharacteristic
382C3×C4C4×C22⋊D511yescharacteristic
383C3×C4#409211yescharacteristic
384C2×C5—21no—
385C2×C5—21no—
386C2×C5C3×#38511yescharacteristic
387C2×C5C3×#45311yescharacteristic
388C2×C5C3×#45611yescharacteristic
389D5—42no—
390C23—101no—
391C23C3×D4×D511yescharacteristic
392Q8—52no—
393Q8—101no—
394D4—52no—
395D4—102no—
396D4—102no—
397D4—101no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—102no—
403C2×C4—102no—
404C2×C4—101no—
405C2×C4—102no—
406C2×C4—102no—
407C2×C4—102no—
408C2×C4—102no—
409C2×C4—202no—
410C2×C4—402no—
411C2×C4C2×C3×C4×D511yescharacteristic
412C2×C4C3×#70911yescharacteristic
413C2×C4C3×D4×D511yescharacteristic
414C2×C4C3×Q8×D511yescharacteristic
415C2×C4C3×#71311yescharacteristic
416C2×C4C2×C3×C22⋊D511yescharacteristic
417C8—22no—
418C8—201no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—202no—
422C2×C3#6527811yescharacteristic
423C2×C3#6548711yescharacteristic
424C2×C3#6549411yescharacteristic
425C5C3×#185911yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—102no—
429C22—201no—
430C22—201no—
431C22C3×#403911yescharacteristic
432C22C3×#404211yescharacteristic
433C22C3×#408311yescharacteristic
434C4—41no—
435C4—41no—
436C4—81no—
437C4—104no—
438C4—102no—
439C4—202no—
440C4C3×D5×C4⋊C411yescharacteristic
441C4C3×#404011yescharacteristic
442C4C3×C4×C22⋊D511yescharacteristic
443C4C3×#409211yescharacteristic
444C3#1060147311yescharacteristic, direct product factor, Sylow
445C2—21no—
446C2—21no—
447C2—202no—
448C2C3×#6527811yescharacteristic
449C2C3×#6548711yescharacteristic
450C2C3×#6549411yescharacteristic
subgroupG/H
centerC22×C3#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#428C2
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#428D5
hypocenterC5C3×#1859
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
2. C3×C5×#428C2semidirect
4. C3×#65265C2semidirect
6. C3×#64774C2semidirect
7. C3×#64752C2semidirect
8. #10601473C3direct (N × H)
24. C3×#3957C4semidirect
29. C5×#428C2×C3semidirect
31. #65265C2×C3semidirect
33. #64774C2×C3semidirect
34. #64752C2×C3semidirect
49. C3×C5×M16C2×C4semidirect
64. C3×C4×Dic5C2×C4semidirect
69. C3×#428D5semidirect
90. #3957C3×C4semidirect
115. C3×D20C4⋊C4semidirect
120. C3×Dic10C4⋊C4semidirect
155. C5×M16C2×C3×C4semidirect
170. C4×Dic5C2×C3×C4semidirect
175. #428C3×D5semidirect
215. C3×M16C4×D5semidirect
253. D20C3×C4⋊C4semidirect
258. Dic10C3×C4⋊C4semidirect
348. M16C3×C4×D5semidirect
365. C3×C5#1859semidirect
425. C5C3×#1859semidirect
444. C3#10601473direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658572
C3×C5×#4282
C2×C3×#39572
C3×#652652
C3×#652552
C3×#647742
C3×#647522
#106014733
C3×#18595