Finite Group Databasebeta

← C2×C3×#65456 #14439016

Subgroups — C2×C3×#65456 #14439016

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 452 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
3C22×C3×#689C211yesmaximal, characteristic, complemented
4C2×C3×#4082C211yesmaximal, characteristic
5C22×C3×#687C211yesmaximal, characteristic
6C22×C3×Dic20C211yesmaximal, characteristic, complemented
7C3×#65456C218yesmaximal, direct product factor
8C2×C3×#3947C211yesmaximal, characteristic, complemented
9C2×#65456C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C5×SD16—24no—
15C2×C3×C5×SD16C2214yes—
16C22×C3×C5×C8C2211yescharacteristic
17C2×C3×C22⋊Dic5—22no—
18C3×#4090—22no—
19C3×#4090C2214yescomplemented
20C2×C3×#689—24no—
21C2×C3×#689C2214yescomplemented
22C3×#4082—22no—
23C3×#4082C2214yes—
24C2×C3×#687—24no—
25C2×C3×#687C2214yes—
26C2×C3×#683—22no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C22×C3×#168C2211yescharacteristic
29C2×C3×Dic20—24no—
30C2×C3×Dic20C2214yescomplemented
31C3×#3947C2214yescomplemented
32C2×C3×#497—51nomaximal, Hall
33C22×C5×SD16C2×C311yescharacteristic
34C2×#4090C2×C311yescharacteristic, complemented
35C22×#689C2×C311yescharacteristic, complemented
36C2×#4082C2×C311yescharacteristic
37C22×#687C2×C311yescharacteristic
38C22×Dic20C2×C311yescharacteristic, complemented
39#65456C2×C318yesdirect product factor
40C2×#3947C2×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—22no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×Dic5—21no—
53C22×C3×Dic5—21no—
54C22×C3×Dic5D412yes—
55C2×C3×Dic10—22no—
56C2×C3×Dic10—22no—
57C2×C3×Dic10—22no—
58C2×C3×Dic10—22no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2312yes—
62C2×C3×Dic10C2312yes—
63C3×C5×SD16—28no—
64C2×C3×C5×C8D414yes—
65C2×C3×C5×C8C2312yes—
66C3×C22⋊Dic5—28no—
67C3×#689—28no—
68C3×#687—28no—
69C3×#683—28no—
70C3×C4×Dic5D412yes—
71C3×C4×Dic5C2312yes—
72C2×C3×#168D414yes—
73C2×C3×#168C2312yes—
74C3×Dic20—28no—
75C22×C3×Q16—51no—
76C22×C3×Q16—51no—
77C22×C3×SD16—51no—
78C22×C3×SD16D511yescharacteristic
79C2×C3×C4⋊Q8—51no—
80C2×C3×#124—51no—
81C3×#497—58no—
82C2×C3×#97—51no—
83C22×C5×Q8C22×C311yescharacteristic
84C22×C5×D4C22×C311yescharacteristic
85C22×Dic10C22×C311yescharacteristic
86C22×Dic10C22×C311yescharacteristic
87C2×C5×SD16—24no—
88C2×C5×SD16C22×C314yes—
89C22×C5×C8C22×C311yescharacteristic
90C2×C22⋊Dic5—22no—
91#4090—22no—
92#4090C22×C314yescomplemented
93C2×#689—24no—
94C2×#689C22×C314yescomplemented
95#4082—22no—
96#4082C22×C314yes—
97C2×#687—24no—
98C2×#687C22×C314yes—
99C2×#683—22no—
100C2×C4×Dic5C22×C311yescharacteristic
101C22×#168C22×C311yescharacteristic
102C2×Dic20—24no—
103C2×Dic20C22×C314yescomplemented
104#3947C22×C314yescomplemented
105C2×#497—51noSylow
106C23×C3×C5—22no—
107C23×C3×C5—42no—
108C23×C3×C5—44no—
109C23×C3×C5C2×D411yescharacteristic
110C3×C5×Q8—22no—
111C3×C5×Q8—22no—
112C3×C5×Q8—42no—
113C3×C5×D4—22no—
114C3×C5×D4—22no—
115C3×C5×D4—42no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—42no—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D412yes—
120C2×C3×C4×C5C2×D412yes—
121C2×C3×C4×C5C2411yescharacteristic
122C2×C3×Dic5—24no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—42no—
126C2×C3×Dic5—42no—
127C2×C3×Dic5C2×D414yes—
128C3×Dic10—22no—
129C3×Dic10—22no—
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—42no—
133C3×Dic10—42no—
134C3×C5×C8C2×D414yes—
135C3×#168C2×D414yes—
136C22×C3×Q8—51no—
137C22×C3×Q8—51no—
138C22×C3×Q8C2×D511yescharacteristic
139C22×C3×D4C2×D511yescharacteristic
140C2×C3×Q16—54no—
141C2×C3×Q16—54no—
142C2×C3×Q16—104no—
143C2×C3×Q16—104no—
144C2×C3×SD16—24no—
145C2×C3×SD16—54no—
146C2×C3×SD16—104no—
147C2×C3×SD16C2×D514yes—
148C22×C3×C8—51no—
149C22×C3×C8C2×D511yescharacteristic
150C3×C4⋊Q8—54no—
151C3×C4⋊Q8—102no—
152C3×#124—54no—
153C3×#124—102no—
154C2×C3×C4⋊C4—102no—
155C2×C3×C22⋊C4—102no—
156C2×C3×C42—51no—
157C3×#97—54no—
158C24×C5—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8C23×C312yes—
163C2×C5×D4—22no—
164C2×C5×D4—22no—
165C2×C5×D4—21no—
166C2×C5×D4C23×C312yes—
167C22×C4×C5—21no—
168C22×C4×C5C23×C311yescharacteristic
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5C3×D412yes—
172C2×Dic10—22no—
173C2×Dic10—22no—
174C2×Dic10—22no—
175C2×Dic10—22no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10C23×C312yes—
179C2×Dic10C23×C312yes—
180C5×SD16—28no—
181C2×C5×C8C3×D414yes—
182C2×C5×C8C23×C312yes—
183C22⋊Dic5—28no—
184#689—28no—
185#687—28no—
186#683—28no—
187C4×Dic5C3×D412yes—
188C4×Dic5C23×C312yes—
189C2×#168C3×D414yes—
190C2×#168C23×C312yes—
191Dic20—28no—
192C22×Q16—51no—
193C22×Q16—51no—
194C22×SD16—51no—
195C22×SD16C3×D511yescharacteristic
196C2×C4⋊Q8—51no—
197C2×#124—51no—
198#497—58no—
199C2×#97—51no—
200C22×C3×C5—42no—
201C22×C3×C5—44no—
202C22×C3×C5—84no—
203C22×C3×C5#12712yes—
204C22×C3×C5#13714yes—
205C22×C3×C5C22×D411yescharacteristic
206C3×C4×C5—42no—
207C3×C4×C5#12712yes—
208C3×C4×C5C22×D411yescharacteristic
209C3×C4×C5C22×D411yescharacteristic
210C3×Dic5—24no—
211C3×Dic5—42no—
212C3×Dic5—42no—
213C24×C3—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—22no—
216C2×C3×Q8—22no—
217C2×C3×Q8—52no—
218C2×C3×Q8—52no—
219C2×C3×Q8—101no—
220C2×C3×Q8—101no—
221C2×C3×Q8—102no—
222C2×C3×Q8—102no—
223C2×C3×Q8—102no—
224C2×C3×Q8—102no—
225C2×C3×Q8C22×D512yes—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4C22×D512yes—
230C22×C3×C4—21no—
231C22×C3×C4—52no—
232C22×C3×C4—101no—
233C22×C3×C4—101no—
234C22×C3×C4C22×D511yescharacteristic
235C3×Q16—108no—
236C3×Q16—108no—
237C3×SD16—28no—
238C3×SD16—108no—
239C2×C3×C8—54no—
240C2×C3×C8—52no—
241C2×C3×C8C22⋊D514yes—
242C2×C3×C8C22×D512yes—
243C3×C4⋊C4—108no—
244C3×C22⋊C4—108no—
245C3×C42—52no—
246C3×C42—52no—
247C23×C5—22no—
248C23×C5—42no—
249C23×C5—44no—
250C23×C5C2×C3×D411yescharacteristic
251C5×Q8—22no—
252C5×Q8—22no—
253C5×Q8—42no—
254C5×D4—22no—
255C5×D4—22no—
256C5×D4—42no—
257C2×C4×C5—22no—
258C2×C4×C5—42no—
259C2×C4×C5C2×C3×D411yescharacteristic
260C2×C4×C5C2×C3×D412yes—
261C2×C4×C5C2×C3×D412yes—
262C2×C4×C5C24×C311yescharacteristic
263C2×Dic5—24no—
264C2×Dic5—22no—
265C2×Dic5—22no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5C2×C3×D414yes—
269Dic10—22no—
270Dic10—22no—
271Dic10—22no—
272Dic10—22no—
273Dic10—42no—
274Dic10—42no—
275C5×C8C2×C3×D414yes—
276#168C2×C3×D414yes—
277C22×Q8—51no—
278C22×Q8—51no—
279C22×Q8C2×C3×D511yescharacteristic
280C22×D4C2×C3×D511yescharacteristic
281C2×Q16—54no—
282C2×Q16—54no—
283C2×Q16—104no—
284C2×Q16—104no—
285C2×SD16—24no—
286C2×SD16—54no—
287C2×SD16—104no—
288C2×SD16C2×C3×D514yes—
289C22×C8—51no—
290C22×C8C2×C3×D511yescharacteristic
291C4⋊Q8—54no—
292C4⋊Q8—102no—
293#124—54no—
294#124—102no—
295C2×C4⋊C4—102no—
296C2×C22⋊C4—102no—
297C2×C42—51no—
298#97—54no—
299C2×C3×C5—82no—
300C2×C3×C5#49714yescomplemented
301C2×C3×C5C2×#12711yescharacteristic
302C2×C3×C5C2×#13712yes—
303C23×C3—22no—
304C23×C3—44no—
305C23×C3—42no—
306C23×C3D4×D511yescharacteristic
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—42no—
310C3×Q8—102no—
311C3×Q8—102no—
312C3×Q8—102no—
313C3×Q8—102no—
314C3×Q8—202no—
315C3×Q8—202no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—42no—
319C2×C3×C4—22no—
320C2×C3×C4—42no—
321C2×C3×C4—54no—
322C2×C3×C4—104no—
323C2×C3×C4—102no—
324C2×C3×C4—102no—
325C2×C3×C4—202no—
326C2×C3×C4—202no—
327C2×C3×C4D4×D512yes—
328C2×C3×C4D4×D511yescharacteristic
329C2×C3×C4C2×C22⋊D512yes—
330C2×C3×C4C23×D511yescharacteristic
331C3×C8—54no—
332C3×C8C2×C22⋊D514yes—
333C22×C5—44no—
334C22×C5—42no—
335C22×C5—84no—
336C22×C5C3×#12712yes—
337C22×C5C3×#13714yes—
338C22×C5C22×C3×D411yescharacteristic
339C4×C5—42no—
340C4×C5C3×#12712yes—
341C4×C5C22×C3×D411yescharacteristic
342C4×C5C22×C3×D411yescharacteristic
343Dic5—24no—
344Dic5—42no—
345Dic5—42no—
346C24—21no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—52no—
351C2×Q8—52no—
352C2×Q8—101no—
353C2×Q8—101no—
354C2×Q8—102no—
355C2×Q8—102no—
356C2×Q8—102no—
357C2×Q8—102no—
358C2×Q8C22×C3×D512yes—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4C22×C3×D512yes—
363C22×C4—21no—
364C22×C4—52no—
365C22×C4—101no—
366C22×C4—101no—
367C22×C4C22×C3×D511yescharacteristic
368Q16—108no—
369Q16—108no—
370SD16—28no—
371SD16—108no—
372C2×C8—54no—
373C2×C8—52no—
374C2×C8C3×C22⋊D514yes—
375C2×C8C22×C3×D512yes—
376C4⋊C4—108no—
377C22⋊C4—108no—
378C42—52no—
379C42—52no—
380C3×C5C2×#49711yescharacteristic, complemented, Hall
381C22×C3—44no—
382C22×C3—42no—
383C22×C3—84no—
384C22×C3#406114yes—
385C22×C3#408612yes—
386C22×C3C2×D4×D511yescharacteristic
387C3×C4—42no—
388C3×C4—104no—
389C3×C4—202no—
390C3×C4—202no—
391C3×C4#408612yes—
392C3×C4C2×D4×D511yescharacteristic
393C3×C4C22×C22⋊D511yescharacteristic
394C2×C5—82no—
395C2×C5C3×#49714yescomplemented
396C2×C5C2×C3×#12711yescharacteristic
397C2×C5C2×C3×#13712yes—
398C23—22no—
399C23—42no—
400C23—44no—
401C23C3×D4×D511yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—42no—
405Q8—102no—
406Q8—102no—
407Q8—102no—
408Q8—102no—
409Q8—202no—
410Q8—202no—
411D4—22no—
412D4—22no—
413D4—42no—
414C2×C4—22no—
415C2×C4—42no—
416C2×C4—54no—
417C2×C4—104no—
418C2×C4—102no—
419C2×C4—102no—
420C2×C4—202no—
421C2×C4—202no—
422C2×C4C3×D4×D511yescharacteristic
423C2×C4C3×D4×D512yes—
424C2×C4C2×C3×C22⋊D512yes—
425C2×C4C23×C3×D511yescharacteristic
426C8—54no—
427C8C2×C3×C22⋊D514yes—
428C2×C3—82no—
429C2×C3#6545614yesdirect product factor
430C2×C3C2×#406112yes—
431C2×C3C2×#408611yescharacteristic
432C5C2×C3×#49711yescharacteristic, complemented, Sylow
433C22—42no—
434C22—44no—
435C22—84no—
436C22C3×#406114yes—
437C22C3×#408612yes—
438C22C2×C3×D4×D511yescharacteristic
439C4—42no—
440C4—104no—
441C4—202no—
442C4—202no—
443C4C3×#408612yes—
444C4C2×C3×D4×D511yescharacteristic
445C4C22×C3×C22⋊D511yescharacteristic
446C3C2×#6545611yescharacteristic, direct product factor, Sylow
447C2—82no—
448C2C3×#6545614yesdirect product factor
449C2C2×C3×#406112yes—
450C2C2×C3×#408611yescharacteristic
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×#497
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
3. C22×C3×#689C2semidirect
6. C22×C3×Dic20C2semidirect
7. C3×#65456C2direct (N × H)
8. C2×C3×#3947C2semidirect
9. C2×#65456C3direct (N × H)
19. C3×#4090C22semidirect
21. C2×C3×#689C22semidirect
30. C2×C3×Dic20C22semidirect
31. C3×#3947C22semidirect
34. C2×#4090C2×C3semidirect
35. C22×#689C2×C3semidirect
38. C22×Dic20C2×C3semidirect
39. #65456C2×C3direct (N × H)
40. C2×#3947C2×C3semidirect
92. #4090C22×C3semidirect
94. C2×#689C22×C3semidirect
103. C2×Dic20C22×C3semidirect
104. #3947C22×C3semidirect
300. C2×C3×C5#497semidirect
380. C3×C5C2×#497semidirect
395. C2×C5C3×#497semidirect
429. C2×C3#65456direct (N × H)
432. C5C2×C3×#497semidirect
446. C3C2×#65456direct (N × H)
448. C2C3×#65456direct (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
C22×C3×#6892
C2×C3×#40822
C22×C3×#6872
C22×C3×Dic202
C3×#654562
C2×C3×#39472
C2×#654563
C2×C3×#4975