Finite Group Databasebeta

← C2×C3×#65134 #14426134

Subgroups — C2×C3×#65134 #14426134

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic20C211yesmaximal, characteristic, complemented
2C22×C3×#677C211yesmaximal, characteristic
3C2×C3×#4021C211yesmaximal, characteristic
4C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
5C2×C3×C5×C4⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#3953C211yesmaximal, characteristic
7C2×C3×#3948C211yesmaximal, characteristic, complemented
8C3×#65134C218yesmaximal, direct product factor
9C2×#65134C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×D20C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C22×C3×C5×C8C2211yescharacteristic
15C2×C3×C42×C5C2211yescharacteristic
16C2×C3×#685—21no—
17C2×C3×#685—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×#683—21no—
20C2×C3×C4×Dic5—21no—
21C2×C3×Dic20—24no—
22C2×C3×Dic20C2214yescomplemented
23C2×C3×#677—24no—
24C2×C3×#677C2214yes—
25C3×#4021—22no—
26C3×#4021C2214yes—
27C3×C4×Dic10—22no—
28C3×C4×Dic10C2214yescomplemented
29C3×C5×C4⋊C8C2214yescomplemented
30C3×#3953C2214yes—
31C3×#3948C2214yescomplemented
32C2×C3×#464—51nomaximal, Hall
33C22×Dic20C2×C311yescharacteristic, complemented
34C22×#677C2×C311yescharacteristic
35C2×#4021C2×C311yescharacteristic
36C2×C4×Dic10C2×C311yescharacteristic, complemented
37C2×C5×C4⋊C8C2×C311yescharacteristic, complemented
38C2×#3953C2×C311yescharacteristic
39C2×#3948C2×C311yescharacteristic, complemented
40#65134C2×C318yesdirect product factor
41C23×C3×D5—21no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C22×C3×Dic5—21no—
46C22×C3×Dic5—21no—
47C22×C3×Dic5—21no—
48C2×C3×D20—22no—
49C2×C3×D20—22no—
50C2×C3×D20—21no—
51C2×C3×D20C2312yes—
52C2×C3×Dic10—21no—
53C2×C3×Dic10—22no—
54C2×C3×Dic10—22no—
55C2×C3×Dic10—22no—
56C2×C3×Dic10—21no—
57C2×C3×Dic10D414yes—
58C2×C3×Dic10C2312yes—
59C2×C3×Dic10C2312yes—
60C2×C3×C5×C8—22no—
61C2×C3×C5×C8—22no—
62C2×C3×C5×C8C2312yes—
63C2×C3×C5×C8C2312yes—
64C3×C42×C5D412yes—
65C3×C42×C5C2312yes—
66C3×#685—24no—
67C3×#685—24no—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5C2312yes—
70C3×#683—24no—
71C3×C4×Dic5—24no—
72C3×Dic20—28no—
73C3×#677—28no—
74C22×C3×Q16—51no—
75C22×C3×SD16—51no—
76C2×C3×#124—51no—
77C2×C3×C4×Q8—51no—
78C3×#464—58no—
79C2×C3×C4⋊C8D511yescharacteristic, complemented
80C2×C3×#103—51no—
81C2×C3×#102—51no—
82C22×D20C22×C311yescharacteristic
83C22×Dic10C22×C311yescharacteristic
84C22×Dic10C22×C311yescharacteristic
85C22×C5×C8C22×C311yescharacteristic
86C22×C5×C8C22×C311yescharacteristic
87C2×C42×C5C22×C311yescharacteristic
88C2×#685—21no—
89C2×#685—21no—
90C2×C4⋊Dic5C22×C311yescharacteristic
91C2×#683—21no—
92C2×C4×Dic5—21no—
93C2×Dic20—24no—
94C2×Dic20C22×C314yescomplemented
95C2×#677—24no—
96C2×#677C22×C314yes—
97#4021—22no—
98#4021C22×C314yes—
99C4×Dic10—22no—
100C4×Dic10C22×C314yescomplemented
101C5×C4⋊C8C22×C314yescomplemented
102#3953C22×C314yes—
103#3948C22×C314yescomplemented
104C2×#464—51noSylow
105C23×C3×C5C2×D411yescharacteristic
106C22×C3×D5—22no—
107C22×C3×D5—42no—
108C22×C3×D5—42no—
109C22×C3×D5—42no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5C2×D412yes—
113C2×C3×C4×C5C2×D412yes—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D412yes—
116C2×C3×C4×C5#4112yes—
117C2×C3×C4×C5C2411yescharacteristic
118C2×C3×Dic5—24no—
119C2×C3×Dic5—22no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5—42no—
123C2×C3×Dic5—42no—
124C3×D20—22no—
125C3×D20—22no—
126C3×D20—42no—
127C3×Dic10—24no—
128C3×Dic10—22no—
129C3×Dic10—22no—
130C3×Dic10—22no—
131C3×Dic10—42no—
132C3×Dic10C2×D414yes—
133C3×C5×C8—22no—
134C3×C5×C8—22no—
135C22×C3×Q8—51no—
136C22×C3×Q8—51no—
137C22×C3×D4—51no—
138C2×C3×Q16—54no—
139C2×C3×Q16—104no—
140C2×C3×SD16—54no—
141C2×C3×SD16—104no—
142C22×C3×C8C2×D511yescharacteristic
143C22×C3×C8C2×D511yescharacteristic
144C3×#124—54no—
145C3×#124—102no—
146C3×C4×Q8—54no—
147C3×C4×Q8—102no—
148C2×C3×C4⋊C4—51no—
149C2×C3×C4⋊C4—101no—
150C2×C3×C22⋊C4—101no—
151C2×C3×C22⋊C4—101no—
152C2×C3×C42—101no—
153C2×C3×C42C2×D511yescharacteristic
154C3×C4⋊C8C2×D514yescomplemented
155C3×#103—54no—
156C3×#102—54no—
157C23×D5—21no—
158C22×C4×C5C3×D411yescharacteristic
159C22×C4×C5C3×D411yescharacteristic
160C22×C4×C5C23×C311yescharacteristic
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C2×D20—22no—
165C2×D20—22no—
166C2×D20—21no—
167C2×D20C23×C312yes—
168C2×Dic10—21no—
169C2×Dic10—22no—
170C2×Dic10—22no—
171C2×Dic10—22no—
172C2×Dic10—21no—
173C2×Dic10C3×D414yes—
174C2×Dic10C23×C312yes—
175C2×Dic10C23×C312yes—
176C2×C5×C8—22no—
177C2×C5×C8—22no—
178C2×C5×C8C23×C312yes—
179C2×C5×C8C23×C312yes—
180C42×C5C3×D412yes—
181C42×C5C23×C312yes—
182#685—24no—
183#685—24no—
184C4⋊Dic5—21no—
185C4⋊Dic5C23×C312yes—
186#683—24no—
187C4×Dic5—24no—
188Dic20—28no—
189#677—28no—
190C22×Q16—51no—
191C22×SD16—51no—
192C2×#124—51no—
193C2×C4×Q8—51no—
194#464—58no—
195C2×C4⋊C8C3×D511yescharacteristic, complemented
196C2×#103—51no—
197C2×#102—51no—
198C22×C3×C5#12112yes—
199C22×C3×C5#13512yes—
200C22×C3×C5#13712yes—
201C22×C3×C5C22×D411yescharacteristic
202C2×C3×D5—42no—
203C2×C3×D5—42no—
204C2×C3×D5—42no—
205C2×C3×D5—84no—
206C3×C4×C5—22no—
207C3×C4×C5—22no—
208C3×C4×C5#12112yes—
209C3×C4×C5C22×D411yescharacteristic
210C3×C4×C5C2×#4111yescharacteristic
211C3×Dic5—24no—
212C3×Dic5—42no—
213C3×Dic5—42no—
214C24×C3—101no—
215C2×C3×Q8—54no—
216C2×C3×Q8—52no—
217C2×C3×Q8—52no—
218C2×C3×Q8—101no—
219C2×C3×Q8—101no—
220C2×C3×Q8—102no—
221C2×C3×Q8—102no—
222C2×C3×Q8—102no—
223C2×C3×D4—52no—
224C2×C3×D4—101no—
225C2×C3×D4—102no—
226C2×C3×D4—102no—
227C22×C3×C4—101no—
228C22×C3×C4—101no—
229C22×C3×C4—101no—
230C22×C3×C4D2011yescharacteristic
231C22×C3×C4D2011yescharacteristic
232C22×C3×C4C22×D511yescharacteristic
233C3×Q16—108no—
234C3×SD16—108no—
235C2×C3×C8—22no—
236C2×C3×C8—22no—
237C2×C3×C8C22×D512yes—
238C2×C3×C8C22×D512yes—
239C3×C4⋊C4—52no—
240C3×C4⋊C4—104no—
241C3×C4⋊C4—101no—
242C3×C22⋊C4—104no—
243C3×C22⋊C4—104no—
244C3×C42—104no—
245C3×C42D2012yes—
246C3×C42C22×D512yes—
247C23×C5C2×C3×D411yescharacteristic
248C22×D5—22no—
249C22×D5—42no—
250C22×D5—42no—
251C22×D5—42no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5C2×C3×D412yes—
255C2×C4×C5C2×C3×D412yes—
256C2×C4×C5C2×C3×D411yescharacteristic
257C2×C4×C5C2×C3×D412yes—
258C2×C4×C5C3×#4112yes—
259C2×C4×C5C24×C311yescharacteristic
260C2×Dic5—24no—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—22no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266D20—22no—
267D20—22no—
268D20—42no—
269Dic10—24no—
270Dic10—22no—
271Dic10—22no—
272Dic10—22no—
273Dic10—42no—
274Dic10C2×C3×D414yes—
275C5×C8—22no—
276C5×C8—22no—
277C22×Q8—51no—
278C22×Q8—51no—
279C22×D4—51no—
280C2×Q16—54no—
281C2×Q16—104no—
282C2×SD16—54no—
283C2×SD16—104no—
284C22×C8C2×C3×D511yescharacteristic
285C22×C8C2×C3×D511yescharacteristic
286#124—54no—
287#124—102no—
288C4×Q8—54no—
289C4×Q8—102no—
290C2×C4⋊C4—51no—
291C2×C4⋊C4—101no—
292C2×C22⋊C4—101no—
293C2×C22⋊C4—101no—
294C2×C42—101no—
295C2×C42C2×C3×D511yescharacteristic
296C4⋊C8C2×C3×D514yescomplemented
297#103—54no—
298#102—54no—
299C2×C3×C5#46414yescomplemented
300C2×C3×C5C2×#12111yescharacteristic
301C2×C3×C5C2×#13511yescharacteristic
302C2×C3×C5C2×#13711yescharacteristic
303C3×D5—82no—
304C23×C3—102no—
305C23×C3—202no—
306C23×C3—202no—
307C23×C3—202no—
308C23×C3C2×D2011yescharacteristic
309C3×Q8—54no—
310C3×Q8—102no—
311C3×Q8—104no—
312C3×Q8—102no—
313C3×Q8—102no—
314C3×Q8—202no—
315C3×D4—102no—
316C3×D4—102no—
317C3×D4—202no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—102no—
321C2×C3×C4—104no—
322C2×C3×C4—102no—
323C2×C3×C4—102no—
324C2×C3×C4—202no—
325C2×C3×C4—202no—
326C2×C3×C4C2×D2012yes—
327C2×C3×C4C2×D2012yes—
328C2×C3×C4C2×D2011yescharacteristic
329C2×C3×C4D4×D512yes—
330C2×C3×C4#71312yes—
331C2×C3×C4C23×D511yescharacteristic
332C3×C8—22no—
333C3×C8—22no—
334C22×C5C3×#12112yes—
335C22×C5C3×#13512yes—
336C22×C5C3×#13712yes—
337C22×C5C22×C3×D411yescharacteristic
338C2×D5—42no—
339C2×D5—42no—
340C2×D5—42no—
341C2×D5—84no—
342C4×C5—22no—
343C4×C5—22no—
344C4×C5C3×#12112yes—
345C4×C5C22×C3×D411yescharacteristic
346C4×C5C2×C3×#4111yescharacteristic
347Dic5—24no—
348Dic5—42no—
349Dic5—42no—
350C24—101no—
351C2×Q8—54no—
352C2×Q8—52no—
353C2×Q8—52no—
354C2×Q8—101no—
355C2×Q8—101no—
356C2×Q8—102no—
357C2×Q8—102no—
358C2×Q8—102no—
359C2×D4—52no—
360C2×D4—101no—
361C2×D4—102no—
362C2×D4—102no—
363C22×C4—101no—
364C22×C4—101no—
365C22×C4—101no—
366C22×C4C3×D2011yescharacteristic
367C22×C4C3×D2011yescharacteristic
368C22×C4C22×C3×D511yescharacteristic
369Q16—108no—
370SD16—108no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8C22×C3×D512yes—
374C2×C8C22×C3×D512yes—
375C4⋊C4—52no—
376C4⋊C4—101no—
377C4⋊C4—104no—
378C22⋊C4—104no—
379C22⋊C4—104no—
380C42—104no—
381C42C3×D2012yes—
382C42C22×C3×D512yes—
383C3×C5C2×#46411yescharacteristic, complemented, Hall
384C22×C3—202no—
385C22×C3—202no—
386C22×C3—202no—
387C22×C3—404no—
388C22×C3#404112yes—
389C22×C3#405012yes—
390C22×C3#405512yes—
391C22×C3C22×D2011yescharacteristic
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—104no—
395C3×C4—202no—
396C3×C4—202no—
397C3×C4#404112yes—
398C3×C4C2×D4×D511yescharacteristic
399C3×C4C2×#71311yescharacteristic
400C2×C5C3×#46414yescomplemented
401C2×C5C2×C3×#12111yescharacteristic
402C2×C5C2×C3×#13511yescharacteristic
403C2×C5C2×C3×#13711yescharacteristic
404D5—82no—
405C23—102no—
406C23—202no—
407C23—202no—
408C23—202no—
409C23C2×C3×D2011yescharacteristic
410Q8—54no—
411Q8—102no—
412Q8—104no—
413Q8—102no—
414Q8—102no—
415Q8—202no—
416D4—102no—
417D4—102no—
418D4—202no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—102no—
422C2×C4—104no—
423C2×C4—102no—
424C2×C4—102no—
425C2×C4—202no—
426C2×C4—202no—
427C2×C4C2×C3×D2012yes—
428C2×C4C2×C3×D2012yes—
429C2×C4C2×C3×D2011yescharacteristic
430C2×C4C3×D4×D512yes—
431C2×C4C3×#71312yes—
432C2×C4C23×C3×D511yescharacteristic
433C8—22no—
434C8—22no—
435C2×C3—402no—
436C2×C3#6513414yesdirect product factor
437C2×C3C2×#404111yescharacteristic
438C2×C3C2×#405011yescharacteristic
439C2×C3C2×#405511yescharacteristic
440C5C2×C3×#46411yescharacteristic, complemented, Sylow
441C22—202no—
442C22—202no—
443C22—202no—
444C22—404no—
445C22C3×#404112yes—
446C22C3×#405012yes—
447C22C3×#405512yes—
448C22C22×C3×D2011yescharacteristic
449C4—22no—
450C4—22no—
451C4—104no—
452C4—202no—
453C4—202no—
454C4C3×#404112yes—
455C4C2×C3×D4×D511yescharacteristic
456C4C2×C3×#71311yescharacteristic
457C3C2×#6513411yescharacteristic, direct product factor, Sylow
458C2—402no—
459C2C3×#6513414yesdirect product factor
460C2C2×C3×#404111yescharacteristic
461C2C2×C3×#405011yescharacteristic
462C2C2×C3×#405511yescharacteristic
subgroupG/H
centerC23×C3C2×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C2×C3×#464
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic20C2semidirect
4. C2×C3×C4×Dic10C2semidirect
5. C2×C3×C5×C4⋊C8C2semidirect
7. C2×C3×#3948C2semidirect
8. C3×#65134C2direct (N × H)
9. C2×#65134C3direct (N × H)
22. C2×C3×Dic20C22semidirect
28. C3×C4×Dic10C22semidirect
29. C3×C5×C4⋊C8C22semidirect
31. C3×#3948C22semidirect
33. C22×Dic20C2×C3semidirect
36. C2×C4×Dic10C2×C3semidirect
37. C2×C5×C4⋊C8C2×C3semidirect
39. C2×#3948C2×C3semidirect
40. #65134C2×C3direct (N × H)
79. C2×C3×C4⋊C8D5semidirect
94. C2×Dic20C22×C3semidirect
100. C4×Dic10C22×C3semidirect
101. C5×C4⋊C8C22×C3semidirect
103. #3948C22×C3semidirect
154. C3×C4⋊C8C2×D5semidirect
195. C2×C4⋊C8C3×D5semidirect
296. C4⋊C8C2×C3×D5semidirect
299. C2×C3×C5#464semidirect
383. C3×C5C2×#464semidirect
400. C2×C5C3×#464semidirect
436. C2×C3#65134direct (N × H)
440. C5C2×C3×#464semidirect
457. C3C2×#65134direct (N × H)
459. C2C3×#65134direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic202
C22×C3×#6772
C2×C3×#40212
C2×C3×C4×Dic102
C2×C3×C5×C4⋊C82
C2×C3×#39532
C2×C3×#39482
C3×#651342
C2×#651343
C2×C3×#4645