Finite Group Databasebeta

← C2×C3×#65451 #14425867

Subgroups — C2×C3×#65451 #14425867

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic
2C2×C3×#4090C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic5C211yesmaximal, characteristic
4C22×C3×#687C211yesmaximal, characteristic
5C2×C3×#3967C211yesmaximal, characteristic, complemented
6C3×#65451C218yesmaximal, direct product factor
7C2×C3×#3948C211yesmaximal, characteristic, complemented
8C2×C3×#3946C211yesmaximal, characteristic, complemented
9C2×#65451C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×Dic5—21no—
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C5×SD16—24no—
15C2×C3×C5×SD16C2214yes—
16C22×C3×C5×C8C2211yescharacteristic
17C2×C3×C22⋊Dic5—21no—
18C3×#4090—22no—
19C3×#4090C2214yescomplemented
20C3×D4×Dic5—22no—
21C3×D4×Dic5C2214yes—
22C2×C3×#687—24no—
23C2×C3×#687C2214yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×#683—21no—
26C2×C3×#683—21no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C22×C3×#168C2211yescharacteristic
29C3×#3967C2214yescomplemented
30C3×#3948C2214yescomplemented
31C3×#3946C2214yescomplemented
32C2×C3×#461—51nomaximal, Hall
33C22×C5×SD16C2×C311yescharacteristic
34C2×#4090C2×C311yescharacteristic, complemented
35C2×D4×Dic5C2×C311yescharacteristic
36C22×#687C2×C311yescharacteristic
37C2×#3967C2×C311yescharacteristic, complemented
38#65451C2×C318yesdirect product factor
39C2×#3948C2×C311yescharacteristic, complemented
40C2×#3946C2×C311yescharacteristic, complemented
41C24×C3×C5—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8—22no—
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8C2312yes—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D414yes—
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×Dic5—21no—
53C22×C3×Dic5—21no—
54C22×C3×Dic5—24no—
55C22×C3×Dic5—44no—
56C22×C3×Dic5D411yescharacteristic
57C22×C3×Dic5D411yescharacteristic
58C2×C3×Dic10—22no—
59C2×C3×Dic10—22no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2312yes—
62C3×C5×SD16—28no—
63C2×C3×C5×C8—22no—
64C2×C3×C5×C8C2312yes—
65C3×C22⋊Dic5—24no—
66C3×#687—28no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5C2312yes—
69C3×#683—24no—
70C3×#683—24no—
71C3×C4×Dic5D412yes—
72C3×C4×Dic5C2312yes—
73C2×C3×#168—22no—
74C2×C3×#168C2312yes—
75C22×C3×SD16—51no—
76C22×C3×SD16D511yescharacteristic
77C2×C3×C4⋊Q8—51no—
78C2×C3×C4×D4—51no—
79C3×#461—58no—
80C2×C3×C4⋊C8—51no—
81C2×C3×#103—51no—
82C2×C3×#103—51no—
83C22×C5×Q8C22×C311yescharacteristic
84C22×C5×D4C22×C311yescharacteristic
85C23×Dic5—21no—
86C22×Dic10C22×C311yescharacteristic
87C2×C5×SD16—24no—
88C2×C5×SD16C22×C314yes—
89C22×C5×C8C22×C311yescharacteristic
90C2×C22⋊Dic5—21no—
91#4090—22no—
92#4090C22×C314yescomplemented
93D4×Dic5—22no—
94D4×Dic5C22×C314yes—
95C2×#687—24no—
96C2×#687C22×C314yes—
97C2×C4⋊Dic5C22×C311yescharacteristic
98C2×#683—21no—
99C2×#683—21no—
100C2×C4×Dic5C22×C311yescharacteristic
101C22×#168C22×C311yescharacteristic
102#3967C22×C314yescomplemented
103#3948C22×C314yescomplemented
104#3946C22×C314yescomplemented
105C2×#461—51noSylow
106C23×C3×C5—24no—
107C23×C3×C5—22no—
108C23×C3×C5—42no—
109C23×C3×C5—42no—
110C23×C3×C5C2×D411yescharacteristic
111C3×C5×Q8—22no—
112C3×C5×Q8—22no—
113C3×C5×Q8—42no—
114C3×C5×D4—24no—
115C3×C5×D4—22no—
116C3×C5×D4C2×D414yes—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—42no—
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5#4112yes—
122C2×C3×C4×C5C2411yescharacteristic
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—42no—
127C2×C3×Dic5—42no—
128C2×C3×Dic5—48no—
129C2×C3×Dic5SD1614yescomplemented
130C2×C3×Dic5C2×D412yes—
131C2×C3×Dic5C2×D412yes—
132C3×Dic10—22no—
133C3×Dic10—22no—
134C3×Dic10—42no—
135C3×C5×C8—22no—
136C3×#168—22no—
137C22×C3×Q8—51no—
138C22×C3×Q8C2×D511yescharacteristic
139C22×C3×D4C2×D511yescharacteristic
140C23×C3×C4—101no—
141C2×C3×SD16—24no—
142C2×C3×SD16—54no—
143C2×C3×SD16—104no—
144C2×C3×SD16C2×D514yes—
145C22×C3×C8—51no—
146C22×C3×C8C2×D511yescharacteristic
147C3×C4⋊Q8—54no—
148C3×C4⋊Q8—102no—
149C3×C4×D4—54no—
150C3×C4×D4—102no—
151C2×C3×C4⋊C4—51no—
152C2×C3×C4⋊C4—101no—
153C2×C3×C4⋊C4—101no—
154C2×C3×C22⋊C4—101no—
155C2×C3×C42—51no—
156C3×C4⋊C8—54no—
157C3×#103—54no—
158C3×#103—54no—
159C24×C5—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—22no—
162C2×C5×Q8—22no—
163C2×C5×Q8C23×C312yes—
164C2×C5×D4—21no—
165C2×C5×D4—22no—
166C2×C5×D4C3×D414yes—
167C2×C5×D4C23×C312yes—
168C22×C4×C5—21no—
169C22×C4×C5C23×C311yescharacteristic
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—24no—
173C22×Dic5—44no—
174C22×Dic5C3×D411yescharacteristic
175C22×Dic5C3×D411yescharacteristic
176C2×Dic10—22no—
177C2×Dic10—22no—
178C2×Dic10—21no—
179C2×Dic10C23×C312yes—
180C5×SD16—28no—
181C2×C5×C8—22no—
182C2×C5×C8C23×C312yes—
183C22⋊Dic5—24no—
184#687—28no—
185C4⋊Dic5—21no—
186C4⋊Dic5C23×C312yes—
187#683—24no—
188#683—24no—
189C4×Dic5C3×D412yes—
190C4×Dic5C23×C312yes—
191C2×#168—22no—
192C2×#168C23×C312yes—
193C22×SD16—51no—
194C22×SD16C3×D511yescharacteristic
195C2×C4⋊Q8—51no—
196C2×C4×D4—51no—
197#461—58no—
198C2×C4⋊C8—51no—
199C2×#103—51no—
200C2×#103—51no—
201C22×C3×C5—24no—
202C22×C3×C5—42no—
203C22×C3×C5—42no—
204C22×C3×C5—48no—
205C22×C3×C5#12112yes—
206C22×C3×C5C2×SD1612yes—
207C22×C3×C5#13712yes—
208C22×C3×C5C22×D411yescharacteristic
209C3×C4×C5—42no—
210C3×C4×C5#12112yes—
211C3×C4×C5C22×D411yescharacteristic
212C3×C4×C5C2×#4111yescharacteristic
213C3×Dic5—22no—
214C3×Dic5—42no—
215C3×Dic5—42no—
216C3×Dic5C2×SD1614yescomplemented
217C24×C3—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—52no—
222C2×C3×Q8—101no—
223C2×C3×Q8—102no—
224C2×C3×Q8—102no—
225C2×C3×Q8C22×D512yes—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4C22⋊D514yes—
229C2×C3×D4C22×D512yes—
230C22×C3×C4—21no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—104no—
234C22×C3×C4—101no—
235C22×C3×C4—101no—
236C22×C3×C4—204no—
237C22×C3×C4C22×D511yescharacteristic
238C3×SD16—28no—
239C3×SD16—108no—
240C2×C3×C8—22no—
241C2×C3×C8—52no—
242C2×C3×C8—102no—
243C2×C3×C8C22×D512yes—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—104no—
246C3×C4⋊C4—104no—
247C3×C4⋊C4—101no—
248C3×C22⋊C4—104no—
249C3×C42—52no—
250C3×C42—52no—
251C23×C5—24no—
252C23×C5—22no—
253C23×C5—42no—
254C23×C5—42no—
255C23×C5C2×C3×D411yescharacteristic
256C5×Q8—22no—
257C5×Q8—22no—
258C5×Q8—42no—
259C5×D4—24no—
260C5×D4—22no—
261C5×D4C2×C3×D414yes—
262C2×C4×C5—22no—
263C2×C4×C5—42no—
264C2×C4×C5C2×C3×D411yescharacteristic
265C2×C4×C5C2×C3×D412yes—
266C2×C4×C5C3×#4112yes—
267C2×C4×C5C24×C311yescharacteristic
268C2×Dic5—22no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C2×Dic5—48no—
274C2×Dic5C3×SD1614yescomplemented
275C2×Dic5C2×C3×D412yes—
276C2×Dic5C2×C3×D412yes—
277Dic10—22no—
278Dic10—22no—
279Dic10—42no—
280C5×C8—22no—
281#168—22no—
282C22×Q8—51no—
283C22×Q8C2×C3×D511yescharacteristic
284C22×D4C2×C3×D511yescharacteristic
285C23×C4—101no—
286C2×SD16—24no—
287C2×SD16—54no—
288C2×SD16—104no—
289C2×SD16C2×C3×D514yes—
290C22×C8—51no—
291C22×C8C2×C3×D511yescharacteristic
292C4⋊Q8—54no—
293C4⋊Q8—102no—
294C4×D4—54no—
295C4×D4—102no—
296C2×C4⋊C4—51no—
297C2×C4⋊C4—101no—
298C2×C4⋊C4—101no—
299C2×C22⋊C4—101no—
300C2×C42—51no—
301C4⋊C8—54no—
302#103—54no—
303#103—54no—
304C2×C3×C5—44no—
305C2×C3×C5#46114yescomplemented
306C2×C3×C5C2×#12111yescharacteristic
307C2×C3×C5C22×SD1611yescharacteristic
308C2×C3×C5C2×#13711yescharacteristic
309C23×C3—22no—
310C23×C3—24no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3D4×D511yescharacteristic
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—102no—
318C3×Q8—102no—
319C3×Q8—202no—
320C3×D4—22no—
321C3×D4—24no—
322C3×D4C2×C22⋊D514yes—
323C2×C3×C4—22no—
324C2×C3×C4—42no—
325C2×C3×C4—52no—
326C2×C3×C4—54no—
327C2×C3×C4—52no—
328C2×C3×C4—102no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4—208no—
332C2×C3×C4—202no—
333C2×C3×C4—202no—
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4#71112yes—
336C2×C3×C4C2×C22⋊D512yes—
337C2×C3×C4C23×D511yescharacteristic
338C3×C8—22no—
339C3×C8—102no—
340C22×C5—24no—
341C22×C5—42no—
342C22×C5—42no—
343C22×C5—48no—
344C22×C5C3×#12112yes—
345C22×C5C2×C3×SD1612yes—
346C22×C5C3×#13712yes—
347C22×C5C22×C3×D411yescharacteristic
348C4×C5—42no—
349C4×C5C3×#12112yes—
350C4×C5C22×C3×D411yescharacteristic
351C4×C5C2×C3×#4111yescharacteristic
352Dic5—22no—
353Dic5—42no—
354Dic5—42no—
355Dic5C2×C3×SD1614yescomplemented
356C24—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—52no—
361C2×Q8—101no—
362C2×Q8—102no—
363C2×Q8—102no—
364C2×Q8C22×C3×D512yes—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4C3×C22⋊D514yes—
368C2×D4C22×C3×D512yes—
369C22×C4—21no—
370C22×C4—51no—
371C22×C4—51no—
372C22×C4—104no—
373C22×C4—101no—
374C22×C4—101no—
375C22×C4—204no—
376C22×C4C22×C3×D511yescharacteristic
377SD16—28no—
378SD16—108no—
379C2×C8—22no—
380C2×C8—52no—
381C2×C8—102no—
382C2×C8C22×C3×D512yes—
383C4⋊C4—52no—
384C4⋊C4—104no—
385C4⋊C4—104no—
386C4⋊C4—101no—
387C22⋊C4—104no—
388C42—52no—
389C42—52no—
390C3×C5C2×#46111yescharacteristic, complemented, Hall
391C22×C3—24no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—48no—
395C22×C3D5×SD1612yes—
396C22×C3#406112yes—
397C22×C3#408512yes—
398C22×C3C2×D4×D511yescharacteristic
399C3×C4—42no—
400C3×C4—54no—
401C3×C4—102no—
402C3×C4—202no—
403C3×C4—202no—
404C3×C4#408512yes—
405C3×C4C2×#71111yescharacteristic
406C3×C4C22×C22⋊D511yescharacteristic
407C2×C5—44no—
408C2×C5C3×#46114yescomplemented
409C2×C5C2×C3×#12111yescharacteristic
410C2×C5C22×C3×SD1611yescharacteristic
411C2×C5C2×C3×#13711yescharacteristic
412C23—24no—
413C23—22no—
414C23—42no—
415C23—42no—
416C23C3×D4×D511yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—42no—
420Q8—102no—
421Q8—102no—
422Q8—202no—
423D4—24no—
424D4—22no—
425D4C2×C3×C22⋊D514yes—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—52no—
429C2×C4—54no—
430C2×C4—52no—
431C2×C4—102no—
432C2×C4—102no—
433C2×C4—102no—
434C2×C4—208no—
435C2×C4—202no—
436C2×C4—202no—
437C2×C4C3×D4×D511yescharacteristic
438C2×C4C3×#71112yes—
439C2×C4C2×C3×C22⋊D512yes—
440C2×C4C23×C3×D511yescharacteristic
441C8—22no—
442C8—102no—
443C2×C3—44no—
444C2×C3#6545114yesdirect product factor
445C2×C3C2×D5×SD1611yescharacteristic
446C2×C3C2×#406111yescharacteristic
447C2×C3C2×#408511yescharacteristic
448C5C2×C3×#46111yescharacteristic, complemented, Sylow
449C22—24no—
450C22—48no—
451C22—42no—
452C22—42no—
453C22C3×D5×SD1612yes—
454C22C3×#406112yes—
455C22C3×#408512yes—
456C22C2×C3×D4×D511yescharacteristic
457C4—42no—
458C4—54no—
459C4—102no—
460C4—202no—
461C4—202no—
462C4C3×#408512yes—
463C4C2×C3×#71111yescharacteristic
464C4C22×C3×C22⋊D511yescharacteristic
465C3C2×#6545111yescharacteristic, direct product factor, Sylow
466C2—44no—
467C2C3×#6545114yesdirect product factor
468C2C2×C3×D5×SD1611yescharacteristic
469C2C2×C3×#406111yescharacteristic
470C2C2×C3×#408511yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
hypercenterC22×C3×SD16D5
hypocenterC5C2×C3×#461
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4090C2semidirect
5. C2×C3×#3967C2semidirect
6. C3×#65451C2direct (N × H)
7. C2×C3×#3948C2semidirect
8. C2×C3×#3946C2semidirect
9. C2×#65451C3direct (N × H)
19. C3×#4090C22semidirect
29. C3×#3967C22semidirect
30. C3×#3948C22semidirect
31. C3×#3946C22semidirect
34. C2×#4090C2×C3semidirect
37. C2×#3967C2×C3semidirect
38. #65451C2×C3direct (N × H)
39. C2×#3948C2×C3semidirect
40. C2×#3946C2×C3semidirect
92. #4090C22×C3semidirect
102. #3967C22×C3semidirect
103. #3948C22×C3semidirect
104. #3946C22×C3semidirect
129. C2×C3×Dic5SD16semidirect
216. C3×Dic5C2×SD16semidirect
274. C2×Dic5C3×SD16semidirect
305. C2×C3×C5#461semidirect
355. Dic5C2×C3×SD16semidirect
390. C3×C5C2×#461semidirect
408. C2×C5C3×#461semidirect
444. C2×C3#65451direct (N × H)
448. C5C2×C3×#461semidirect
465. C3C2×#65451direct (N × H)
467. C2C3×#65451direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×SD162
C2×C3×#40902
C2×C3×D4×Dic52
C22×C3×#6872
C2×C3×#39672
C3×#654512
C2×C3×#39482
C2×C3×#39462
C2×#654513
C2×C3×#4615