Finite Group Databasebeta

← C2×C3×#65063 #14431402

Subgroups — C2×C3×#65063 #14431402

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4084C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic, complemented
4C2×C3×#3964C211yesmaximal, characteristic, complemented
5C2×C3×#3952C211yesmaximal, characteristic, complemented
6C2×C3×#3950C211yesmaximal, characteristic, complemented
7C2×C3×#3939C211yesmaximal, characteristic, complemented
8C3×#65063C218yesmaximal, direct product factor
9C2×#65063C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×C3×C22⋊D5—21no—
12C22×C3×C4×D5—21no—
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×C5×C8C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C22⋊Dic5—21no—
17C3×#4084—22no—
18C3×#4084C2214yes—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×C3×#683—21no—
22C22×C3×#168C2211yescharacteristic
23C3×D5×C4⋊C4—22no—
24C3×D5×C4⋊C4C2214yescomplemented
25C3×C5×#102C2214yescomplemented
26C3×#3964C2214yescomplemented
27C3×#3952C2214yescomplemented
28C3×#3950C2214yescomplemented
29C3×#3939C2214yescomplemented
30C2×C3×#480—51nomaximal, Hall
31C2×#4084C2×C311yescharacteristic
32C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
33C2×C5×#102C2×C311yescharacteristic, complemented
34C2×#3964C2×C311yescharacteristic, complemented
35C2×#3952C2×C311yescharacteristic, complemented
36C2×#3950C2×C311yescharacteristic, complemented
37C2×#3939C2×C311yescharacteristic, complemented
38#65063C2×C318yesdirect product factor
39C24×C3×C5—21no—
40C23×C3×D5D411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4C2312yes—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×C3×C22⋊D5—24no—
48C2×C3×C22⋊D5—44no—
49C22×C3×Dic5—21no—
50C22×C3×Dic5—21no—
51C22×C3×Dic5D411yescharacteristic
52C2×C3×C4×D5—22no—
53C2×C3×C4×D5—22no—
54C2×C3×C4×D5—24no—
55C2×C3×C4×D5—44no—
56C2×C3×C4×D5D412yes—
57C2×C3×C4×D5C2312yes—
58C2×C3×C5×C8—22no—
59C2×C3×C5×C8C2312yes—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4C2312yes—
62C3×C22⋊Dic5—24no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5C2312yes—
66C3×C4⋊Dic5C2312yes—
67C3×#683—24no—
68C2×C3×#168—22no—
69C2×C3×#168C2312yes—
70C2×C3×#121—51no—
71C22×C3×C4⋊C4—51no—
72C3×#480—58no—
73C2×C3×#107—51no—
74C2×C3×#107—51no—
75C2×C3×#102—51no—
76C2×C3×#102D511yescharacteristic, complemented
77C2×C3×C22⋊C8—51no—
78C22×C5×D4C22×C311yescharacteristic
79C22×C22⋊D5—21no—
80C22×C4×D5—21no—
81C22×C4×D5C22×C311yescharacteristic
82C22×C5×C8C22×C311yescharacteristic
83C2×C5×C4⋊C4C22×C311yescharacteristic
84C2×C22⋊Dic5—21no—
85#4084—22no—
86#4084C22×C314yes—
87C2×C4⋊Dic5C22×C311yescharacteristic
88C2×C4⋊Dic5C22×C311yescharacteristic
89C2×#683—21no—
90C22×#168C22×C311yescharacteristic
91D5×C4⋊C4—22no—
92D5×C4⋊C4C22×C314yescomplemented
93C5×#102C22×C314yescomplemented
94#3964C22×C314yescomplemented
95#3952C22×C314yescomplemented
96#3950C22×C314yescomplemented
97#3939C22×C314yescomplemented
98C2×#480—51noSylow
99C23×C3×C5—22no—
100C23×C3×C5—42no—
101C23×C3×C5—42no—
102C23×C3×C5—42no—
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—22no—
105C22×C3×D5—22no—
106C22×C3×D5D814yes—
107C22×C3×D5C2×D412yes—
108C3×C5×D4—22no—
109C3×C5×D4—22no—
110C3×C5×D4—42no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—42no—
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4112yes—
115C2×C3×C4×C5#4112yes—
116C2×C3×C4×C5C2411yescharacteristic
117C3×C22⋊D5—48no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5—22no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—42no—
122C2×C3×Dic5—42no—
123C2×C3×Dic5C2×D412yes—
124C3×C4×D5—24no—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5—48no—
128C3×C5×C8—22no—
129C3×#168—22no—
130C22×C3×D4—101no—
131C22×C3×D4C2×D511yescharacteristic
132C23×C3×C4—51no—
133C23×C3×C4—101no—
134C22×C3×C8—51no—
135C22×C3×C8C2×D511yescharacteristic
136C3×#121—54no—
137C3×#121—102no—
138C2×C3×C4⋊C4—51no—
139C2×C3×C4⋊C4—51no—
140C2×C3×C4⋊C4—54no—
141C2×C3×C4⋊C4—102no—
142C2×C3×C4⋊C4—101no—
143C2×C3×C4⋊C4C2×D511yescharacteristic
144C2×C3×C22⋊C4—101no—
145C3×#107—54no—
146C3×#107—54no—
147C3×#102—54no—
148C3×#102C2×D514yescomplemented
149C3×C22⋊C8—54no—
150C24×C5—21no—
151C23×D5C3×D411yescharacteristic
152C2×C5×D4—21no—
153C2×C5×D4—22no—
154C2×C5×D4—22no—
155C2×C5×D4C23×C312yes—
156C22×C4×C5—21no—
157C22×C4×C5C23×C311yescharacteristic
158C2×C22⋊D5—24no—
159C2×C22⋊D5—44no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5C3×D411yescharacteristic
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—24no—
166C2×C4×D5—44no—
167C2×C4×D5C3×D412yes—
168C2×C4×D5C23×C312yes—
169C2×C5×C8—22no—
170C2×C5×C8C23×C312yes—
171C5×C4⋊C4—21no—
172C5×C4⋊C4C23×C312yes—
173C22⋊Dic5—24no—
174C4⋊Dic5—21no—
175C4⋊Dic5—21no—
176C4⋊Dic5C23×C312yes—
177C4⋊Dic5C23×C312yes—
178#683—24no—
179C2×#168—22no—
180C2×#168C23×C312yes—
181C2×#121—51no—
182C22×C4⋊C4—51no—
183#480—58no—
184C2×#107—51no—
185C2×#107—51no—
186C2×#102—51no—
187C2×#102C3×D511yescharacteristic, complemented
188C2×C22⋊C8—51no—
189C22×C3×C5—42no—
190C22×C3×C5—42no—
191C22×C3×C5—42no—
192C22×C3×C5—84no—
193C22×C3×C5#12312yes—
194C22×C3×C5C2×D812yes—
195C22×C3×C5#13712yes—
196C22×C3×C5C22×D411yescharacteristic
197C2×C3×D5—22no—
198C2×C3×D5—22no—
199C2×C3×D5—28no—
200C2×C3×D5C2×D814yes—
201C3×C4×C5—42no—
202C3×C4×C5#12312yes—
203C3×C4×C5C2×#4111yescharacteristic
204C3×C4×C5C2×#4111yescharacteristic
205C3×Dic5—22no—
206C3×Dic5—42no—
207C3×Dic5—42no—
208C24×C3—21no—
209C24×C3—51no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—22no—
213C2×C3×D4—104no—
214C2×C3×D4—204no—
215C2×C3×D4C22×D512yes—
216C22×C3×C4—21no—
217C22×C3×C4—51no—
218C22×C3×C4—52no—
219C22×C3×C4—52no—
220C22×C3×C4—104no—
221C22×C3×C4—102no—
222C22×C3×C4—102no—
223C22×C3×C4—101no—
224C22×C3×C4—101no—
225C22×C3×C4—204no—
226C22×C3×C4C22×D511yescharacteristic
227C2×C3×C8—22no—
228C2×C3×C8—52no—
229C2×C3×C8—102no—
230C2×C3×C8C22×D512yes—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—52no—
233C3×C4⋊C4—52no—
234C3×C4⋊C4—104no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4—101no—
237C3×C4⋊C4C22×D512yes—
238C3×C22⋊C4—104no—
239C23×C5—22no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—42no—
243C23×C5C2×C3×D411yescharacteristic
244C22×D5—22no—
245C22×D5—22no—
246C22×D5C3×D814yes—
247C22×D5C2×C3×D412yes—
248C5×D4—22no—
249C5×D4—22no—
250C5×D4—42no—
251C2×C4×C5—22no—
252C2×C4×C5—42no—
253C2×C4×C5C2×C3×D411yescharacteristic
254C2×C4×C5C3×#4112yes—
255C2×C4×C5C3×#4112yes—
256C2×C4×C5C24×C311yescharacteristic
257C22⋊D5—48no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—22no—
261C2×Dic5—42no—
262C2×Dic5—42no—
263C2×Dic5C2×C3×D412yes—
264C4×D5—24no—
265C4×D5—22no—
266C4×D5—22no—
267C4×D5—48no—
268C5×C8—22no—
269#168—22no—
270C22×D4—101no—
271C22×D4C2×C3×D511yescharacteristic
272C23×C4—51no—
273C23×C4—101no—
274C22×C8—51no—
275C22×C8C2×C3×D511yescharacteristic
276#121—54no—
277#121—102no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4—51no—
280C2×C4⋊C4—54no—
281C2×C4⋊C4—102no—
282C2×C4⋊C4—101no—
283C2×C4⋊C4C2×C3×D511yescharacteristic
284C2×C22⋊C4—101no—
285#107—54no—
286#107—54no—
287#102—54no—
288#102C2×C3×D514yescomplemented
289C22⋊C8—54no—
290C2×C3×C5—82no—
291C2×C3×C5#48014yescomplemented
292C2×C3×C5C2×#12311yescharacteristic
293C2×C3×C5C22×D811yescharacteristic
294C2×C3×C5C2×#13711yescharacteristic
295C3×D5—24no—
296C23×C3—22no—
297C23×C3—42no—
298C23×C3—42no—
299C23×C3—42no—
300C23×C3—52no—
301C23×C3—54no—
302C23×C3—102no—
303C23×C3—102no—
304C23×C3D4×D511yescharacteristic
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—42no—
308C3×D4—208no—
309C2×C3×C4—22no—
310C2×C3×C4—42no—
311C2×C3×C4—52no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4—102no—
315C2×C3×C4—104no—
316C2×C3×C4—102no—
317C2×C3×C4—102no—
318C2×C3×C4—208no—
319C2×C3×C4—202no—
320C2×C3×C4—202no—
321C2×C3×C4#70912yes—
322C2×C3×C4D4×D511yescharacteristic
323C2×C3×C4#71112yes—
324C2×C3×C4C23×D511yescharacteristic
325C3×C8—22no—
326C3×C8—102no—
327C22×C5—42no—
328C22×C5—42no—
329C22×C5—42no—
330C22×C5—84no—
331C22×C5C3×#12312yes—
332C22×C5C2×C3×D812yes—
333C22×C5C3×#13712yes—
334C22×C5C22×C3×D411yescharacteristic
335C2×D5—22no—
336C2×D5—22no—
337C2×D5—28no—
338C2×D5C2×C3×D814yes—
339C4×C5—42no—
340C4×C5C3×#12312yes—
341C4×C5C2×C3×#4111yescharacteristic
342C4×C5C2×C3×#4111yescharacteristic
343Dic5—22no—
344Dic5—42no—
345Dic5—42no—
346C24—21no—
347C24—51no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—104no—
352C2×D4—204no—
353C2×D4C22×C3×D512yes—
354C22×C4—21no—
355C22×C4—51no—
356C22×C4—52no—
357C22×C4—52no—
358C22×C4—104no—
359C22×C4—102no—
360C22×C4—102no—
361C22×C4—101no—
362C22×C4—101no—
363C22×C4—204no—
364C22×C4C22×C3×D511yescharacteristic
365C2×C8—22no—
366C2×C8—52no—
367C2×C8—102no—
368C2×C8C22×C3×D512yes—
369C4⋊C4—21no—
370C4⋊C4—52no—
371C4⋊C4—52no—
372C4⋊C4—104no—
373C4⋊C4—101no—
374C4⋊C4—101no—
375C4⋊C4C22×C3×D512yes—
376C22⋊C4—104no—
377C3×C5C2×#48011yescharacteristic, complemented, Hall
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—54no—
382C22×C3—84no—
383C22×C3—102no—
384C22×C3—108no—
385C22×C3—102no—
386C22×C3#402912yes—
387C22×C3D5×D812yes—
388C22×C3#406112yes—
389C22×C3C2×D4×D511yescharacteristic
390C3×C4—42no—
391C3×C4—102no—
392C3×C4—202no—
393C3×C4—202no—
394C3×C4#402912yes—
395C3×C4C2×#70911yescharacteristic
396C3×C4C2×#71111yescharacteristic
397C2×C5—82no—
398C2×C5C3×#48014yescomplemented
399C2×C5C2×C3×#12311yescharacteristic
400C2×C5C22×C3×D811yescharacteristic
401C2×C5C2×C3×#13711yescharacteristic
402D5—24no—
403C23—22no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—52no—
408C23—54no—
409C23—102no—
410C23—102no—
411C23C3×D4×D511yescharacteristic
412D4—22no—
413D4—22no—
414D4—42no—
415D4—208no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—52no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—102no—
422C2×C4—104no—
423C2×C4—102no—
424C2×C4—102no—
425C2×C4—208no—
426C2×C4—202no—
427C2×C4—202no—
428C2×C4C3×#70912yes—
429C2×C4C3×D4×D511yescharacteristic
430C2×C4C3×#71112yes—
431C2×C4C23×C3×D511yescharacteristic
432C8—22no—
433C8—102no—
434C2×C3—82no—
435C2×C3—104no—
436C2×C3#6506314yesdirect product factor
437C2×C3C2×#402911yescharacteristic
438C2×C3C2×D5×D811yescharacteristic
439C2×C3C2×#406111yescharacteristic
440C5C2×C3×#48011yescharacteristic, complemented, Sylow
441C22—42no—
442C22—42no—
443C22—42no—
444C22—54no—
445C22—84no—
446C22—108no—
447C22—102no—
448C22—102no—
449C22C3×#402912yes—
450C22C3×D5×D812yes—
451C22C3×#406112yes—
452C22C2×C3×D4×D511yescharacteristic
453C4—42no—
454C4—102no—
455C4—202no—
456C4—202no—
457C4C3×#402912yes—
458C4C2×C3×#70911yescharacteristic
459C4C2×C3×#71111yescharacteristic
460C3C2×#6506311yescharacteristic, direct product factor, Sylow
461C2—82no—
462C2—104no—
463C2C3×#6506314yesdirect product factor
464C2C2×C3×#402911yescharacteristic
465C2C2×C3×D5×D811yescharacteristic
466C2C2×C3×#406111yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4084C2
hypercenterC2×C3×#102D5
hypocenterC5C2×C3×#480
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C4⋊C4C2semidirect
3. C2×C3×C5×#102C2semidirect
4. C2×C3×#3964C2semidirect
5. C2×C3×#3952C2semidirect
6. C2×C3×#3950C2semidirect
7. C2×C3×#3939C2semidirect
8. C3×#65063C2direct (N × H)
9. C2×#65063C3direct (N × H)
24. C3×D5×C4⋊C4C22semidirect
25. C3×C5×#102C22semidirect
26. C3×#3964C22semidirect
27. C3×#3952C22semidirect
28. C3×#3950C22semidirect
29. C3×#3939C22semidirect
32. C2×D5×C4⋊C4C2×C3semidirect
33. C2×C5×#102C2×C3semidirect
34. C2×#3964C2×C3semidirect
35. C2×#3952C2×C3semidirect
36. C2×#3950C2×C3semidirect
37. C2×#3939C2×C3semidirect
38. #65063C2×C3direct (N × H)
76. C2×C3×#102D5semidirect
92. D5×C4⋊C4C22×C3semidirect
93. C5×#102C22×C3semidirect
94. #3964C22×C3semidirect
95. #3952C22×C3semidirect
96. #3950C22×C3semidirect
97. #3939C22×C3semidirect
148. C3×#102C2×D5semidirect
187. C2×#102C3×D5semidirect
288. #102C2×C3×D5semidirect
291. C2×C3×C5#480semidirect
377. C3×C5C2×#480semidirect
398. C2×C5C3×#480semidirect
436. C2×C3#65063direct (N × H)
440. C5C2×C3×#480semidirect
460. C3C2×#65063direct (N × H)
463. C2C3×#65063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40842
C2×C3×D5×C4⋊C42
C2×C3×C5×#1022
C2×C3×#39642
C2×C3×#39522
C2×C3×#39502
C2×C3×#39392
C3×#650632
C2×#650633
C2×C3×#4805