Finite Group Databasebeta

← C2×C3×#65452 #14426011

Subgroups — C2×C3×#65452 #14426011

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
2C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
3C22×C3×#688C211yesmaximal, characteristic, complemented
4C2×C3×#4086C211yesmaximal, characteristic
5C2×C3×#3964C211yesmaximal, characteristic, complemented
6C3×#65452C218yesmaximal, direct product factor
7C2×C3×#3953C211yesmaximal, characteristic, complemented
8C2×C3×#3946C211yesmaximal, characteristic, complemented
9C2×#65452C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C22⋊D5—21no—
13C22×C3×C22⋊D5—21no—
14C22×C3×D20C2211yescharacteristic
15C2×C3×C5×SD16—24no—
16C2×C3×C5×SD16C2214yescomplemented
17C22×C3×C5×C8C2211yescharacteristic
18C3×Q8×Dic5—22no—
19C3×Q8×Dic5C2214yescomplemented
20C2×C3×#688—24no—
21C2×C3×#688C2214yescomplemented
22C3×#4086—22no—
23C3×#4086C2214yes—
24C2×C3×C4⋊Dic5—21no—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5—21no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C22×C3×#168C2211yescharacteristic
29C3×#3964C2214yescomplemented
30C3×#3953C2214yescomplemented
31C3×#3946C2214yescomplemented
32C2×C3×#460—51nomaximal, Hall
33C22×C5×SD16C2×C311yescharacteristic, complemented
34C2×Q8×Dic5C2×C311yescharacteristic, complemented
35C22×#688C2×C311yescharacteristic, complemented
36C2×#4086C2×C311yescharacteristic
37C2×#3964C2×C311yescharacteristic, complemented
38#65452C2×C318yesdirect product factor
39C2×#3953C2×C311yescharacteristic, complemented
40C2×#3946C2×C311yescharacteristic, complemented
41C24×C3×C5—21no—
42C23×C3×D5—21no—
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8D414yescomplemented
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—24no—
55C2×C3×C22⋊D5—44no—
56C2×C3×C22⋊D5—44no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5D411yescharacteristic
59C22×C3×Dic5D411yescharacteristic
60C2×C3×D20—22no—
61C2×C3×D20—22no—
62C2×C3×D20—21no—
63C2×C3×D20C2312yes—
64C3×C5×SD16—28no—
65C2×C3×C5×C8—22no—
66C2×C3×C5×C8C2312yes—
67C3×#688—28no—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5—24no—
70C3×C4⋊Dic5C2312yes—
71C3×C4×Dic5—24no—
72C3×C4×Dic5D412yes—
73C3×C4×Dic5C2312yes—
74C2×C3×#168—22no—
75C2×C3×#168C2312yes—
76C22×C3×SD16—51no—
77C22×C3×SD16D511yescharacteristic, complemented
78C2×C3×#127—51no—
79C2×C3×C4×Q8—51no—
80C3×#460—58no—
81C2×C3×C4⋊C8—51no—
82C2×C3×#102—51no—
83C2×C3×#102—51no—
84C22×C5×Q8C22×C311yescharacteristic
85C22×C5×D4C22×C311yescharacteristic
86C22×C22⋊D5—21no—
87C22×C22⋊D5—21no—
88C22×D20C22×C311yescharacteristic
89C2×C5×SD16—24no—
90C2×C5×SD16C22×C314yescomplemented
91C22×C5×C8C22×C311yescharacteristic
92Q8×Dic5—22no—
93Q8×Dic5C22×C314yescomplemented
94C2×#688—24no—
95C2×#688C22×C314yescomplemented
96#4086—22no—
97#4086C22×C314yes—
98C2×C4⋊Dic5—21no—
99C2×C4⋊Dic5C22×C311yescharacteristic
100C2×C4×Dic5—21no—
101C2×C4×Dic5C22×C311yescharacteristic
102C22×#168C22×C311yescharacteristic
103#3964C22×C314yescomplemented
104#3953C22×C314yescomplemented
105#3946C22×C314yescomplemented
106C2×#460—51noSylow
107C23×C3×C5—22no—
108C23×C3×C5—42no—
109C23×C3×C5—42no—
110C23×C3×C5—42no—
111C23×C3×C5C2×D411yescharacteristic
112C22×C3×D5—22no—
113C22×C3×D5—42no—
114C22×C3×D5—42no—
115C22×C3×D5—42no—
116C3×C5×Q8—24no—
117C3×C5×Q8—22no—
118C3×C5×Q8C2×D414yescomplemented
119C3×C5×D4—22no—
120C3×C5×D4—22no—
121C3×C5×D4—42no—
122C2×C3×C4×C5—24no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5#4112yes—
127C2×C3×C4×C5C2411yescharacteristic
128C3×C22⋊D5—48no—
129C3×C22⋊D5—48no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—42no—
133C2×C3×Dic5SD1614yescomplemented
134C2×C3×Dic5C2×D412yes—
135C2×C3×Dic5C2×D412yes—
136C3×D20—22no—
137C3×D20—22no—
138C3×D20—42no—
139C3×C5×C8—22no—
140C3×#168—22no—
141C22×C3×Q8C2×D511yescharacteristic
142C22×C3×D4—51no—
143C22×C3×D4—101no—
144C22×C3×D4—101no—
145C22×C3×D4C2×D511yescharacteristic
146C2×C3×SD16—24no—
147C2×C3×SD16—54no—
148C2×C3×SD16—104no—
149C2×C3×SD16C2×D514yescomplemented
150C22×C3×C8—51no—
151C22×C3×C8C2×D511yescharacteristic
152C3×#127—54no—
153C3×#127—102no—
154C3×C4×Q8—54no—
155C3×C4×Q8—102no—
156C2×C3×C4⋊C4—51no—
157C2×C3×C4⋊C4—101no—
158C2×C3×C42—51no—
159C2×C3×C42—101no—
160C3×C4⋊C8—54no—
161C3×#102—54no—
162C3×#102—54no—
163C24×C5—21no—
164C23×D5—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—22no—
167C2×C5×Q8C3×D414yescomplemented
168C2×C5×Q8C23×C312yes—
169C2×C5×D4—22no—
170C2×C5×D4—21no—
171C2×C5×D4—22no—
172C2×C5×D4C23×C312yes—
173C22×C4×C5—21no—
174C22×C4×C5C23×C311yescharacteristic
175C2×C22⋊D5—24no—
176C2×C22⋊D5—24no—
177C2×C22⋊D5—44no—
178C2×C22⋊D5—44no—
179C22×Dic5—21no—
180C22×Dic5C3×D411yescharacteristic
181C22×Dic5C3×D411yescharacteristic
182C2×D20—22no—
183C2×D20—22no—
184C2×D20—21no—
185C2×D20C23×C312yes—
186C5×SD16—28no—
187C2×C5×C8—22no—
188C2×C5×C8C23×C312yes—
189#688—28no—
190C4⋊Dic5—21no—
191C4⋊Dic5—24no—
192C4⋊Dic5C23×C312yes—
193C4×Dic5—24no—
194C4×Dic5C3×D412yes—
195C4×Dic5C23×C312yes—
196C2×#168—22no—
197C2×#168C23×C312yes—
198C22×SD16—51no—
199C22×SD16C3×D511yescharacteristic, complemented
200C2×#127—51no—
201C2×C4×Q8—51no—
202#460—58no—
203C2×C4⋊C8—51no—
204C2×#102—51no—
205C2×#102—51no—
206C22×C3×C5—42no—
207C22×C3×C5—42no—
208C22×C3×C5—42no—
209C22×C3×C5—84no—
210C22×C3×C5#12112yes—
211C22×C3×C5C2×SD1612yes—
212C22×C3×C5AGL(1,ℤ/8)12yes—
213C22×C3×C5C22×D411yescharacteristic
214C2×C3×D5—42no—
215C2×C3×D5—42no—
216C2×C3×D5—42no—
217C2×C3×D5—84no—
218C3×C4×C5—24no—
219C3×C4×C5#12112yes—
220C3×C4×C5C22×D411yescharacteristic
221C3×C4×C5C2×#4111yescharacteristic
222C3×Dic5—22no—
223C3×Dic5—42no—
224C3×Dic5C2×SD1614yescomplemented
225C24×C3—21no—
226C24×C3—101no—
227C2×C3×Q8—21no—
228C2×C3×Q8—22no—
229C2×C3×Q8C22⋊D514yescomplemented
230C2×C3×Q8C22×D512yes—
231C2×C3×D4—21no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—52no—
235C2×C3×D4—104no—
236C2×C3×D4—104no—
237C2×C3×D4—101no—
238C2×C3×D4—102no—
239C2×C3×D4—102no—
240C2×C3×D4—204no—
241C2×C3×D4—204no—
242C2×C3×D4C22×D512yes—
243C22×C3×C4—21no—
244C22×C3×C4—51no—
245C22×C3×C4—51no—
246C22×C3×C4—101no—
247C22×C3×C4C22×D511yescharacteristic
248C3×SD16—28no—
249C3×SD16—108no—
250C2×C3×C8—22no—
251C2×C3×C8—52no—
252C2×C3×C8—102no—
253C2×C3×C8C22×D512yes—
254C3×C4⋊C4—52no—
255C3×C4⋊C4—104no—
256C3×C4⋊C4—101no—
257C3×C42—52no—
258C3×C42—52no—
259C3×C42—104no—
260C23×C5—22no—
261C23×C5—42no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5C2×C3×D411yescharacteristic
265C22×D5—22no—
266C22×D5—42no—
267C22×D5—42no—
268C22×D5—42no—
269C5×Q8—24no—
270C5×Q8—22no—
271C5×Q8C2×C3×D414yescomplemented
272C5×D4—22no—
273C5×D4—22no—
274C5×D4—42no—
275C2×C4×C5—24no—
276C2×C4×C5—22no—
277C2×C4×C5C2×C3×D411yescharacteristic
278C2×C4×C5C2×C3×D412yes—
279C2×C4×C5C3×#4112yes—
280C2×C4×C5C24×C311yescharacteristic
281C22⋊D5—48no—
282C22⋊D5—48no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—42no—
286C2×Dic5C3×SD1614yescomplemented
287C2×Dic5C2×C3×D412yes—
288C2×Dic5C2×C3×D412yes—
289D20—22no—
290D20—22no—
291D20—42no—
292C5×C8—22no—
293#168—22no—
294C22×Q8C2×C3×D511yescharacteristic
295C22×D4—51no—
296C22×D4—101no—
297C22×D4—101no—
298C22×D4C2×C3×D511yescharacteristic
299C2×SD16—24no—
300C2×SD16—54no—
301C2×SD16—104no—
302C2×SD16C2×C3×D514yescomplemented
303C22×C8—51no—
304C22×C8C2×C3×D511yescharacteristic
305#127—54no—
306#127—102no—
307C4×Q8—54no—
308C4×Q8—102no—
309C2×C4⋊C4—51no—
310C2×C4⋊C4—101no—
311C2×C42—51no—
312C2×C42—101no—
313C4⋊C8—54no—
314#102—54no—
315#102—54no—
316C2×C3×C5—82no—
317C2×C3×C5#46014yescomplemented
318C2×C3×C5C2×#12111yescharacteristic
319C2×C3×C5C22×SD1611yescharacteristic
320C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
321C3×D5—82no—
322C23×C3—22no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—102no—
327C23×C3—202no—
328C23×C3—202no—
329C23×C3—202no—
330C23×C3D4×D511yescharacteristic
331C3×Q8—22no—
332C3×Q8—24no—
333C3×Q8C2×C22⋊D514yescomplemented
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—42no—
337C3×D4—102no—
338C3×D4—102no—
339C3×D4—208no—
340C3×D4—208no—
341C3×D4—202no—
342C2×C3×C4—22no—
343C2×C3×C4—24no—
344C2×C3×C4—52no—
345C2×C3×C4—54no—
346C2×C3×C4—52no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—202no—
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4#71112yes—
352C2×C3×C4C2×C22⋊D512yes—
353C2×C3×C4C23×D511yescharacteristic
354C3×C8—22no—
355C3×C8—102no—
356C22×C5—42no—
357C22×C5—42no—
358C22×C5—42no—
359C22×C5—84no—
360C22×C5C3×#12112yes—
361C22×C5C2×C3×SD1612yes—
362C22×C5C3×AGL(1,ℤ/8)12yes—
363C22×C5C22×C3×D411yescharacteristic
364C2×D5—42no—
365C2×D5—42no—
366C2×D5—42no—
367C2×D5—84no—
368C4×C5—24no—
369C4×C5C3×#12112yes—
370C4×C5C22×C3×D411yescharacteristic
371C4×C5C2×C3×#4111yescharacteristic
372Dic5—22no—
373Dic5—42no—
374Dic5C2×C3×SD1614yescomplemented
375C24—21no—
376C24—101no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8C3×C22⋊D514yescomplemented
380C2×Q8C22×C3×D512yes—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—52no—
385C2×D4—104no—
386C2×D4—104no—
387C2×D4—101no—
388C2×D4—102no—
389C2×D4—102no—
390C2×D4—204no—
391C2×D4—204no—
392C2×D4C22×C3×D512yes—
393C22×C4—21no—
394C22×C4—51no—
395C22×C4—51no—
396C22×C4—101no—
397C22×C4C22×C3×D511yescharacteristic
398SD16—28no—
399SD16—108no—
400C2×C8—22no—
401C2×C8—52no—
402C2×C8—102no—
403C2×C8C22×C3×D512yes—
404C4⋊C4—52no—
405C4⋊C4—104no—
406C4⋊C4—101no—
407C42—52no—
408C42—52no—
409C42—104no—
410C3×C5C2×#46011yescharacteristic, complemented, Hall
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—84no—
415C22×C3—202no—
416C22×C3—202no—
417C22×C3—202no—
418C22×C3—404no—
419C22×C3D5×SD1612yes—
420C22×C3#406012yes—
421C22×C3#408512yes—
422C22×C3C2×D4×D511yescharacteristic
423C3×C4—24no—
424C3×C4—54no—
425C3×C4—102no—
426C3×C4—202no—
427C3×C4#408512yes—
428C3×C4C2×#71111yescharacteristic
429C3×C4C22×C22⋊D511yescharacteristic
430C2×C5—82no—
431C2×C5C3×#46014yescomplemented
432C2×C5C2×C3×#12111yescharacteristic
433C2×C5C22×C3×SD1611yescharacteristic
434C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
435D5—82no—
436C23—22no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—102no—
441C23—202no—
442C23—202no—
443C23—202no—
444C23C3×D4×D511yescharacteristic
445Q8—24no—
446Q8—22no—
447Q8C2×C3×C22⋊D514yescomplemented
448D4—22no—
449D4—22no—
450D4—42no—
451D4—102no—
452D4—102no—
453D4—208no—
454D4—208no—
455D4—202no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—52no—
459C2×C4—54no—
460C2×C4—52no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—202no—
464C2×C4C3×D4×D511yescharacteristic
465C2×C4C3×#71112yes—
466C2×C4C2×C3×C22⋊D512yes—
467C2×C4C23×C3×D511yescharacteristic
468C8—22no—
469C8—102no—
470C2×C3—82no—
471C2×C3—402no—
472C2×C3#6545214yesdirect product factor
473C2×C3C2×D5×SD1611yescharacteristic
474C2×C3C2×#406011yescharacteristic
475C2×C3C2×#408511yescharacteristic
476C5C2×C3×#46011yescharacteristic, complemented, Sylow
477C22—42no—
478C22—42no—
479C22—42no—
480C22—84no—
481C22—202no—
482C22—202no—
483C22—202no—
484C22—404no—
485C22C3×D5×SD1612yes—
486C22C3×#406012yes—
487C22C3×#408512yes—
488C22C2×C3×D4×D511yescharacteristic
489C4—24no—
490C4—54no—
491C4—102no—
492C4—202no—
493C4C3×#408512yes—
494C4C2×C3×#71111yescharacteristic
495C4C22×C3×C22⋊D511yescharacteristic
496C3C2×#6545211yescharacteristic, direct product factor, Sylow
497C2—82no—
498C2—402no—
499C2C3×#6545214yesdirect product factor
500C2C2×C3×D5×SD1611yescharacteristic
501C2C2×C3×#406011yescharacteristic
502C2C2×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 radicalC2×C3×#4086C2
hypercenterC22×C3×SD16D5
hypocenterC5C2×C3×#460
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×Q8×Dic5C2semidirect
3. C22×C3×#688C2semidirect
5. C2×C3×#3964C2semidirect
6. C3×#65452C2direct (N × H)
7. C2×C3×#3953C2semidirect
8. C2×C3×#3946C2semidirect
9. C2×#65452C3direct (N × H)
16. C2×C3×C5×SD16C22semidirect
19. C3×Q8×Dic5C22semidirect
21. C2×C3×#688C22semidirect
29. C3×#3964C22semidirect
30. C3×#3953C22semidirect
31. C3×#3946C22semidirect
33. C22×C5×SD16C2×C3semidirect
34. C2×Q8×Dic5C2×C3semidirect
35. C22×#688C2×C3semidirect
37. C2×#3964C2×C3semidirect
38. #65452C2×C3direct (N × H)
39. C2×#3953C2×C3semidirect
40. C2×#3946C2×C3semidirect
45. C2×C3×C5×Q8D4semidirect
77. C22×C3×SD16D5semidirect
90. C2×C5×SD16C22×C3semidirect
93. Q8×Dic5C22×C3semidirect
95. C2×#688C22×C3semidirect
103. #3964C22×C3semidirect
104. #3953C22×C3semidirect
105. #3946C22×C3semidirect
118. C3×C5×Q8C2×D4semidirect
133. C2×C3×Dic5SD16semidirect
149. C2×C3×SD16C2×D5semidirect
167. C2×C5×Q8C3×D4semidirect
199. C22×SD16C3×D5semidirect
224. C3×Dic5C2×SD16semidirect
229. C2×C3×Q8C22⋊D5semidirect
271. C5×Q8C2×C3×D4semidirect
286. C2×Dic5C3×SD16semidirect
302. C2×SD16C2×C3×D5semidirect
317. C2×C3×C5#460semidirect
333. C3×Q8C2×C22⋊D5semidirect
374. Dic5C2×C3×SD16semidirect
379. C2×Q8C3×C22⋊D5semidirect
410. C3×C5C2×#460semidirect
431. C2×C5C3×#460semidirect
447. Q8C2×C3×C22⋊D5semidirect
472. C2×C3#65452direct (N × H)
476. C5C2×C3×#460semidirect
496. C3C2×#65452direct (N × H)
499. C2C3×#65452direct (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×Q8×Dic52
C22×C3×#6882
C2×C3×#40862
C2×C3×#39642
C3×#654522
C2×C3×#39532
C2×C3×#39462
C2×#654523
C2×C3×#4605