Finite Group Databasebeta

← C2×C3×#65463 #14427889

Subgroups — C2×C3×#65463 #14427889

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
2C2×C3×#4092C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic
4C22×C3×#676C211yesmaximal, characteristic, complemented
5C2×C3×#3967C211yesmaximal, characteristic, complemented
6C2×C3×#3964C211yesmaximal, characteristic, complemented
7C3×#65463C218yesmaximal, direct product factor
8C2×C3×#3950C211yesmaximal, characteristic, complemented
9C2×#65463C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C22⋊D5—21no—
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C5×SD16—24no—
15C2×C3×C5×SD16C2214yescomplemented
16C22×C3×C5×C8C2211yescharacteristic
17C2×C3×C22⋊Dic5—21no—
18C3×#4092—22no—
19C3×#4092C2214yescomplemented
20C3×#4084—22no—
21C3×#4084C2214yes—
22C2×C3×#685—21no—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×#683—21no—
26C22×C3×#168C2211yescharacteristic
27C2×C3×#676—24no—
28C2×C3×#676C2214yescomplemented
29C3×#3967C2214yescomplemented
30C3×#3964C2214yescomplemented
31C3×#3950C2214yescomplemented
32C2×C3×#468—51nomaximal, Hall
33C22×C5×SD16C2×C311yescharacteristic, complemented
34C2×#4092C2×C311yescharacteristic, complemented
35C2×#4084C2×C311yescharacteristic
36C22×#676C2×C311yescharacteristic, complemented
37C2×#3967C2×C311yescharacteristic, complemented
38C2×#3964C2×C311yescharacteristic, complemented
39#65463C2×C318yesdirect product factor
40C2×#3950C2×C311yescharacteristic, complemented
41C24×C3×C5—21no—
42C23×C3×D5D411yescharacteristic
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8C2312yes—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4—22no—
50C2×C3×C5×D4C2312yes—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C2×C3×C22⋊D5—24no—
54C2×C3×C22⋊D5—44no—
55C22×C3×Dic5—21no—
56C22×C3×Dic5—21no—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×C4×D5—22no—
59C2×C3×C4×D5—22no—
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5C2312yes—
62C3×C5×SD16—28no—
63C2×C3×C5×C8D414yescomplemented
64C2×C3×C5×C8C2312yes—
65C3×C22⋊Dic5—24no—
66C3×#685—24no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5C2312yes—
70C3×C4⋊Dic5C2312yes—
71C3×#683—24no—
72C2×C3×#168—22no—
73C2×C3×#168C2312yes—
74C3×#676—28no—
75C22×C3×SD16D511yescharacteristic, complemented
76C22×C3×M16—51no—
77C2×C3×C22⋊Q8—51no—
78C2×C3×#121—51no—
79C3×#468—58no—
80C2×C3×#107—51no—
81C2×C3×#103—51no—
82C2×C3×#102—51no—
83C22×C5×Q8C22×C311yescharacteristic
84C22×C5×D4C22×C311yescharacteristic
85C22×C22⋊D5—21no—
86C22×C4×D5C22×C311yescharacteristic
87C2×C5×SD16—24no—
88C2×C5×SD16C22×C314yescomplemented
89C22×C5×C8C22×C311yescharacteristic
90C2×C22⋊Dic5—21no—
91#4092—22no—
92#4092C22×C314yescomplemented
93#4084—22no—
94#4084C22×C314yes—
95C2×#685—21no—
96C2×C4⋊Dic5C22×C311yescharacteristic
97C2×C4⋊Dic5C22×C311yescharacteristic
98C2×#683—21no—
99C22×#168C22×C311yescharacteristic
100C2×#676—24no—
101C2×#676C22×C314yescomplemented
102#3967C22×C314yescomplemented
103#3964C22×C314yescomplemented
104#3950C22×C314yescomplemented
105C2×#468—51noSylow
106C23×C3×C5—22no—
107C23×C3×C5—42no—
108C23×C3×C5—42no—
109C23×C3×C5—42no—
110C23×C3×C5C2×D411yescharacteristic
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5C2×D412yes—
115C3×C5×Q8—22no—
116C3×C5×Q8—22no—
117C3×C5×Q8—42no—
118C3×C5×D4—22no—
119C3×C5×D4—22no—
120C3×C5×D4—42no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—42no—
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5#4112yes—
126C2×C3×C4×C5C2411yescharacteristic
127C3×C22⋊D5—48no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—42no—
132C2×C3×Dic5—42no—
133C2×C3×Dic5C2×D412yes—
134C3×C4×D5—24no—
135C3×C4×D5—22no—
136C3×C4×D5—22no—
137C3×C5×C8C2×D414yescomplemented
138C3×#168—22no—
139C22×C3×Q8C2×D511yescharacteristic
140C22×C3×D4—101no—
141C22×C3×D4C2×D511yescharacteristic
142C23×C3×C4—51no—
143C2×C3×SD16—24no—
144C2×C3×SD16C2×D514yescomplemented
145C2×C3×M16—54no—
146C2×C3×M16—104no—
147C22×C3×C8—51no—
148C22×C3×C8C2×D511yescharacteristic
149C3×C22⋊Q8—54no—
150C3×C22⋊Q8—102no—
151C3×#121—54no—
152C3×#121—102no—
153C2×C3×C4⋊C4—51no—
154C2×C3×C4⋊C4—51no—
155C2×C3×C4⋊C4—101no—
156C2×C3×C22⋊C4—101no—
157C2×C3×C22⋊C4—101no—
158C3×#107—54no—
159C3×#103—54no—
160C3×#102—54no—
161C24×C5—21no—
162C23×D5C3×D411yescharacteristic
163C2×C5×Q8—21no—
164C2×C5×Q8—22no—
165C2×C5×Q8—22no—
166C2×C5×Q8C23×C312yes—
167C2×C5×D4—22no—
168C2×C5×D4—21no—
169C2×C5×D4—22no—
170C2×C5×D4C23×C312yes—
171C22×C4×C5—21no—
172C22×C4×C5C23×C311yescharacteristic
173C2×C22⋊D5—24no—
174C2×C22⋊D5—44no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5C3×D411yescharacteristic
178C2×C4×D5—22no—
179C2×C4×D5—22no—
180C2×C4×D5C3×D412yes—
181C2×C4×D5C23×C312yes—
182C5×SD16—28no—
183C2×C5×C8C3×D414yescomplemented
184C2×C5×C8C23×C312yes—
185C22⋊Dic5—24no—
186#685—24no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5C23×C312yes—
190C4⋊Dic5C23×C312yes—
191#683—24no—
192C2×#168—22no—
193C2×#168C23×C312yes—
194#676—28no—
195C22×SD16C3×D511yescharacteristic, complemented
196C22×M16—51no—
197C2×C22⋊Q8—51no—
198C2×#121—51no—
199#468—58no—
200C2×#107—51no—
201C2×#103—51no—
202C2×#102—51no—
203C22×C3×C5—42no—
204C22×C3×C5—42no—
205C22×C3×C5—42no—
206C22×C3×C5—84no—
207C22×C3×C5#12112yes—
208C22×C3×C5AGL(1,ℤ/8)12yes—
209C22×C3×C5#13712yes—
210C22×C3×C5C22×D411yescharacteristic
211C2×C3×D5—22no—
212C2×C3×D5—22no—
213C2×C3×D5—22no—
214C2×C3×D5—44no—
215C3×C4×C5—42no—
216C3×C4×C5#12112yes—
217C3×C4×C5C22×D411yescharacteristic
218C3×C4×C5C2×#4111yescharacteristic
219C3×Dic5—22no—
220C3×Dic5—42no—
221C3×Dic5—42no—
222C24×C3—21no—
223C24×C3—51no—
224C2×C3×Q8—21no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C2×C3×Q8C22×D512yes—
228C2×C3×D4—21no—
229C2×C3×D4—22no—
230C2×C3×D4—22no—
231C2×C3×D4—104no—
232C2×C3×D4—204no—
233C2×C3×D4C22×D512yes—
234C22×C3×C4—21no—
235C22×C3×C4—51no—
236C22×C3×C4—52no—
237C22×C3×C4—52no—
238C22×C3×C4—102no—
239C22×C3×C4—102no—
240C22×C3×C4—101no—
241C22×C3×C4—101no—
242C22×C3×C4C22×D511yescharacteristic
243C3×SD16—28no—
244C3×M16—108no—
245C2×C3×C8—52no—
246C2×C3×C8—102no—
247C2×C3×C8C22⋊D514yescomplemented
248C2×C3×C8C22×D512yes—
249C3×C4⋊C4—52no—
250C3×C4⋊C4—52no—
251C3×C4⋊C4—104no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C22⋊C4—104no—
255C3×C22⋊C4—104no—
256C23×C5—22no—
257C23×C5—42no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5C2×C3×D411yescharacteristic
261C22×D5—22no—
262C22×D5—22no—
263C22×D5—22no—
264C22×D5C2×C3×D412yes—
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8—42no—
268C5×D4—22no—
269C5×D4—22no—
270C5×D4—42no—
271C2×C4×C5—22no—
272C2×C4×C5—42no—
273C2×C4×C5C2×C3×D411yescharacteristic
274C2×C4×C5C2×C3×D412yes—
275C2×C4×C5C3×#4112yes—
276C2×C4×C5C24×C311yescharacteristic
277C22⋊D5—48no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5C2×C3×D412yes—
284C4×D5—24no—
285C4×D5—22no—
286C4×D5—22no—
287C5×C8C2×C3×D414yescomplemented
288#168—22no—
289C22×Q8C2×C3×D511yescharacteristic
290C22×D4—101no—
291C22×D4C2×C3×D511yescharacteristic
292C23×C4—51no—
293C2×SD16—24no—
294C2×SD16C2×C3×D514yescomplemented
295C2×M16—54no—
296C2×M16—104no—
297C22×C8—51no—
298C22×C8C2×C3×D511yescharacteristic
299C22⋊Q8—54no—
300C22⋊Q8—102no—
301#121—54no—
302#121—102no—
303C2×C4⋊C4—51no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—101no—
306C2×C22⋊C4—101no—
307C2×C22⋊C4—101no—
308#107—54no—
309#103—54no—
310#102—54no—
311C2×C3×C5—82no—
312C2×C3×C5#46814yescomplemented
313C2×C3×C5C2×#12111yescharacteristic
314C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
315C2×C3×C5C2×#13711yescharacteristic
316C3×D5—42no—
317C23×C3—22no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—52no—
322C23×C3—102no—
323C23×C3—102no—
324C23×C3—102no—
325C23×C3D4×D511yescharacteristic
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—42no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—42no—
332C3×D4—208no—
333C2×C3×C4—22no—
334C2×C3×C4—42no—
335C2×C3×C4—52no—
336C2×C3×C4—102no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4—104no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—202no—
343C2×C3×C4—202no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4#71112yes—
346C2×C3×C4C2×C22⋊D512yes—
347C2×C3×C4C23×D511yescharacteristic
348C3×C8—102no—
349C3×C8C2×C22⋊D514yescomplemented
350C22×C5—42no—
351C22×C5—42no—
352C22×C5—42no—
353C22×C5—84no—
354C22×C5C3×#12112yes—
355C22×C5C3×AGL(1,ℤ/8)12yes—
356C22×C5C3×#13712yes—
357C22×C5C22×C3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—22no—
360C2×D5—22no—
361C2×D5—44no—
362C4×C5—42no—
363C4×C5C3×#12112yes—
364C4×C5C22×C3×D411yescharacteristic
365C4×C5C2×C3×#4111yescharacteristic
366Dic5—22no—
367Dic5—42no—
368Dic5—42no—
369C24—21no—
370C24—51no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8C22×C3×D512yes—
375C2×D4—21no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—104no—
379C2×D4—204no—
380C2×D4C22×C3×D512yes—
381C22×C4—21no—
382C22×C4—51no—
383C22×C4—52no—
384C22×C4—52no—
385C22×C4—102no—
386C22×C4—102no—
387C22×C4—101no—
388C22×C4—101no—
389C22×C4C22×C3×D511yescharacteristic
390SD16—28no—
391M16—108no—
392C2×C8—52no—
393C2×C8—102no—
394C2×C8C3×C22⋊D514yescomplemented
395C2×C8C22×C3×D512yes—
396C4⋊C4—52no—
397C4⋊C4—52no—
398C4⋊C4—104no—
399C4⋊C4—101no—
400C4⋊C4—101no—
401C22⋊C4—104no—
402C22⋊C4—104no—
403C3×C5C2×#46811yescharacteristic, complemented, Hall
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—84no—
408C22×C3—102no—
409C22×C3—102no—
410C22×C3—102no—
411C22×C3—204no—
412C22×C3#406012yes—
413C22×C3#406112yes—
414C22×C3#408412yes—
415C22×C3C2×D4×D511yescharacteristic
416C3×C4—42no—
417C3×C4—102no—
418C3×C4—202no—
419C3×C4—202no—
420C3×C4#408412yes—
421C3×C4C2×#71111yescharacteristic
422C3×C4C22×C22⋊D511yescharacteristic
423C2×C5—82no—
424C2×C5C3×#46814yescomplemented
425C2×C5C2×C3×#12111yescharacteristic
426C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
427C2×C5C2×C3×#13711yescharacteristic
428D5—42no—
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—52no—
434C23—102no—
435C23—102no—
436C23—102no—
437C23C3×D4×D511yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—42no—
441D4—22no—
442D4—22no—
443D4—42no—
444D4—208no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—52no—
448C2×C4—102no—
449C2×C4—104no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—102no—
453C2×C4—102no—
454C2×C4—202no—
455C2×C4—202no—
456C2×C4C3×D4×D511yescharacteristic
457C2×C4C3×#71112yes—
458C2×C4C2×C3×C22⋊D512yes—
459C2×C4C23×C3×D511yescharacteristic
460C8—102no—
461C8C2×C3×C22⋊D514yescomplemented
462C2×C3—82no—
463C2×C3—202no—
464C2×C3#6546314yesdirect product factor
465C2×C3C2×#406011yescharacteristic
466C2×C3C2×#406111yescharacteristic
467C2×C3C2×#408411yescharacteristic
468C5C2×C3×#46811yescharacteristic, complemented, Sylow
469C22—42no—
470C22—42no—
471C22—42no—
472C22—84no—
473C22—102no—
474C22—102no—
475C22—102no—
476C22—204no—
477C22C3×#406012yes—
478C22C3×#406112yes—
479C22C3×#408412yes—
480C22C2×C3×D4×D511yescharacteristic
481C4—42no—
482C4—102no—
483C4—202no—
484C4—202no—
485C4C3×#408412yes—
486C4C2×C3×#71111yescharacteristic
487C4C22×C3×C22⋊D511yescharacteristic
488C3C2×#6546311yescharacteristic, direct product factor, Sylow
489C2—82no—
490C2—202no—
491C2C3×#6546314yesdirect product factor
492C2C2×C3×#406011yescharacteristic
493C2C2×C3×#406111yescharacteristic
494C2C2×C3×#408411yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4084C2
hypercenterC22×C3×SD16D5
hypocenterC5C2×C3×#468
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
1. C22×C3×C5×SD16C2semidirect
2. C2×C3×#4092C2semidirect
4. C22×C3×#676C2semidirect
5. C2×C3×#3967C2semidirect
6. C2×C3×#3964C2semidirect
7. C3×#65463C2direct (N × H)
8. C2×C3×#3950C2semidirect
9. C2×#65463C3direct (N × H)
15. C2×C3×C5×SD16C22semidirect
19. C3×#4092C22semidirect
28. C2×C3×#676C22semidirect
29. C3×#3967C22semidirect
30. C3×#3964C22semidirect
31. C3×#3950C22semidirect
33. C22×C5×SD16C2×C3semidirect
34. C2×#4092C2×C3semidirect
36. C22×#676C2×C3semidirect
37. C2×#3967C2×C3semidirect
38. C2×#3964C2×C3semidirect
39. #65463C2×C3direct (N × H)
40. C2×#3950C2×C3semidirect
63. C2×C3×C5×C8D4semidirect
75. C22×C3×SD16D5semidirect
88. C2×C5×SD16C22×C3semidirect
92. #4092C22×C3semidirect
101. C2×#676C22×C3semidirect
102. #3967C22×C3semidirect
103. #3964C22×C3semidirect
104. #3950C22×C3semidirect
137. C3×C5×C8C2×D4semidirect
144. C2×C3×SD16C2×D5semidirect
183. C2×C5×C8C3×D4semidirect
195. C22×SD16C3×D5semidirect
247. C2×C3×C8C22⋊D5semidirect
287. C5×C8C2×C3×D4semidirect
294. C2×SD16C2×C3×D5semidirect
312. C2×C3×C5#468semidirect
349. C3×C8C2×C22⋊D5semidirect
394. C2×C8C3×C22⋊D5semidirect
403. C3×C5C2×#468semidirect
424. C2×C5C3×#468semidirect
461. C8C2×C3×C22⋊D5semidirect
464. C2×C3#65463direct (N × H)
468. C5C2×C3×#468semidirect
488. C3C2×#65463direct (N × H)
491. C2C3×#65463direct (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×#40922
C2×C3×#40842
C22×C3×#6762
C2×C3×#39672
C2×C3×#39642
C3×#654632
C2×C3×#39502
C2×#654633
C2×C3×#4685