Finite Group Databasebeta

← C2×C3×#65459 #14423290

Subgroups — C2×C3×#65459 #14423290

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic, complemented
2C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic
4C22×C3×#687C211yesmaximal, characteristic, complemented
5C2×C3×#3967C211yesmaximal, characteristic, complemented
6C3×#65459C218yesmaximal, direct product factor
7C2×C3×#3952C211yesmaximal, characteristic, complemented
8C2×C3×#3948C211yesmaximal, characteristic, complemented
9C2×#65459C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C22⋊D5—21no—
13C2×C3×Q8×D5—24no—
14C2×C3×Q8×D5—22no—
15C2×C3×Q8×D5—24no—
16C2×C3×Q8×D5C2214yescomplemented
17C22×C3×C4×D5—21no—
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×Dic10—21no—
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×SD16—24no—
22C2×C3×C5×SD16C2214yescomplemented
23C22×C3×C5×C8C2211yescharacteristic
24C2×C3×C22⋊Dic5—21no—
25C3×#4084—22no—
26C3×#4084C2214yes—
27C2×C3×#687—24no—
28C2×C3×#687C2214yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C22×C3×#168C2211yescharacteristic
31C3×#3967C2214yescomplemented
32C3×#3952C2214yescomplemented
33C3×#3948C2214yescomplemented
34C2×C3×#448—51nomaximal, Hall
35C22×Q8×D5C2×C311yescharacteristic, complemented
36C22×C5×SD16C2×C311yescharacteristic, complemented
37C2×#4084C2×C311yescharacteristic
38C22×#687C2×C311yescharacteristic, complemented
39C2×#3967C2×C311yescharacteristic, complemented
40#65459C2×C318yesdirect product factor
41C2×#3952C2×C311yescharacteristic, complemented
42C2×#3948C2×C311yescharacteristic, complemented
43C24×C3×C5—21no—
44C23×C3×D5D411yescharacteristic
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8D414yescomplemented
48C2×C3×C5×Q8C2312yes—
49C2×C3×C5×D4—22no—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2312yes—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×C3×C22⋊D5—24no—
56C2×C3×C22⋊D5—44no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5—21no—
59C22×C3×Dic5D411yescharacteristic
60C3×Q8×D5—216no—
61C3×Q8×D5—28no—
62C3×Q8×D5—28no—
63C2×C3×C4×D5—28no—
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5D412yes—
68C2×C3×C4×D5C2312yes—
69C2×C3×Dic10—28no—
70C2×C3×Dic10—21no—
71C2×C3×Dic10—22no—
72C2×C3×Dic10—24no—
73C2×C3×Dic10D414yescomplemented
74C2×C3×Dic10C2312yes—
75C3×C5×SD16—28no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2312yes—
78C3×C22⋊Dic5—24no—
79C3×#687—28no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82C2×C3×#168—22no—
83C2×C3×#168C2312yes—
84C23×C3×Q8—51no—
85C22×C3×SD16—51no—
86C22×C3×SD16D511yescharacteristic, complemented
87C2×C3×#121—51no—
88C3×#448—58no—
89C2×C3×#103—51no—
90C2×C3×#103—51no—
91C2×C3×C22⋊C8—51no—
92C22×C5×Q8C22×C311yescharacteristic
93C22×C5×D4C22×C311yescharacteristic
94C22×C22⋊D5—21no—
95C2×Q8×D5—24no—
96C2×Q8×D5—22no—
97C2×Q8×D5—24no—
98C2×Q8×D5C22×C314yescomplemented
99C22×C4×D5—21no—
100C22×C4×D5C22×C311yescharacteristic
101C22×Dic10—21no—
102C22×Dic10C22×C311yescharacteristic
103C2×C5×SD16—24no—
104C2×C5×SD16C22×C314yescomplemented
105C22×C5×C8C22×C311yescharacteristic
106C2×C22⋊Dic5—21no—
107#4084—22no—
108#4084C22×C314yes—
109C2×#687—24no—
110C2×#687C22×C314yescomplemented
111C2×C4⋊Dic5C22×C311yescharacteristic
112C22×#168C22×C311yescharacteristic
113#3967C22×C314yescomplemented
114#3952C22×C314yescomplemented
115#3948C22×C314yescomplemented
116C2×#448—51noSylow
117C23×C3×C5—22no—
118C23×C3×C5—42no—
119C23×C3×C5—42no—
120C23×C3×C5—42no—
121C23×C3×C5C2×D411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5SD1614yescomplemented
125C22×C3×D5C2×D412yes—
126C3×C5×Q8—24no—
127C3×C5×Q8—22no—
128C3×C5×Q8C2×D414yescomplemented
129C3×C5×D4—22no—
130C3×C5×D4—22no—
131C3×C5×D4—42no—
132C2×C3×C4×C5—24no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2411yescharacteristic
138C3×C22⋊D5—48no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—24no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—42no—
144C2×C3×Dic5C2×D412yes—
145C3×C4×D5—216no—
146C3×C4×D5—24no—
147C3×C4×D5—22no—
148C3×C4×D5—22no—
149C3×Dic10—216no—
150C3×Dic10—24no—
151C3×Dic10—22no—
152C3×Dic10C2×D414yescomplemented
153C3×C5×C8—22no—
154C3×#168—22no—
155C22×C3×Q8—54no—
156C22×C3×Q8—51no—
157C22×C3×Q8—101no—
158C22×C3×Q8—102no—
159C22×C3×Q8—104no—
160C22×C3×Q8—104no—
161C22×C3×Q8C2×D511yescharacteristic
162C22×C3×D4—101no—
163C22×C3×D4C2×D511yescharacteristic
164C23×C3×C4—51no—
165C23×C3×C4—101no—
166C2×C3×SD16—24no—
167C2×C3×SD16—54no—
168C2×C3×SD16—104no—
169C2×C3×SD16C2×D514yescomplemented
170C22×C3×C8—51no—
171C22×C3×C8C2×D511yescharacteristic
172C3×#121—54no—
173C3×#121—102no—
174C2×C3×C4⋊C4—51no—
175C2×C3×C22⋊C4—101no—
176C3×#103—54no—
177C3×#103—54no—
178C3×C22⋊C8—54no—
179C24×C5—21no—
180C23×D5C3×D411yescharacteristic
181C2×C5×Q8—22no—
182C2×C5×Q8—21no—
183C2×C5×Q8C3×D414yescomplemented
184C2×C5×Q8C23×C312yes—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4—21no—
188C2×C5×D4C23×C312yes—
189C22×C4×C5—21no—
190C22×C4×C5C23×C311yescharacteristic
191C2×C22⋊D5—24no—
192C2×C22⋊D5—44no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5C3×D411yescharacteristic
196Q8×D5—216no—
197Q8×D5—28no—
198Q8×D5—28no—
199C2×C4×D5—28no—
200C2×C4×D5—24no—
201C2×C4×D5—22no—
202C2×C4×D5—22no—
203C2×C4×D5C3×D412yes—
204C2×C4×D5C23×C312yes—
205C2×Dic10—28no—
206C2×Dic10—21no—
207C2×Dic10—22no—
208C2×Dic10—24no—
209C2×Dic10C3×D414yescomplemented
210C2×Dic10C23×C312yes—
211C5×SD16—28no—
212C2×C5×C8—22no—
213C2×C5×C8C23×C312yes—
214C22⋊Dic5—24no—
215#687—28no—
216C4⋊Dic5—21no—
217C4⋊Dic5C23×C312yes—
218C2×#168—22no—
219C2×#168C23×C312yes—
220C23×Q8—51no—
221C22×SD16—51no—
222C22×SD16C3×D511yescharacteristic, complemented
223C2×#121—51no—
224#448—58no—
225C2×#103—51no—
226C2×#103—51no—
227C2×C22⋊C8—51no—
228C22×C3×C5—42no—
229C22×C3×C5—42no—
230C22×C3×C5—42no—
231C22×C3×C5—84no—
232C22×C3×C5#12012yes—
233C22×C3×C5C2×SD1612yes—
234C22×C3×C5#13712yes—
235C22×C3×C5C22×D411yescharacteristic
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5—28no—
239C2×C3×D5C2×SD1614yescomplemented
240C3×C4×C5—24no—
241C3×C4×C5#12012yes—
242C3×C4×C5C22×D411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244C3×Dic5—22no—
245C3×Dic5—24no—
246C3×Dic5—42no—
247C24×C3—21no—
248C24×C3—51no—
249C2×C3×Q8—21no—
250C2×C3×Q8—22no—
251C2×C3×Q8—54no—
252C2×C3×Q8—52no—
253C2×C3×Q8—104no—
254C2×C3×Q8—108no—
255C2×C3×Q8—108no—
256C2×C3×Q8—1016no—
257C2×C3×Q8—108no—
258C2×C3×Q8—101no—
259C2×C3×Q8—102no—
260C2×C3×Q8C22⋊D514yescomplemented
261C2×C3×Q8C22×D512yes—
262C2×C3×D4—22no—
263C2×C3×D4—21no—
264C2×C3×D4—22no—
265C2×C3×D4—104no—
266C2×C3×D4—204no—
267C2×C3×D4C22×D512yes—
268C22×C3×C4—21no—
269C22×C3×C4—51no—
270C22×C3×C4—52no—
271C22×C3×C4—52no—
272C22×C3×C4—104no—
273C22×C3×C4—108no—
274C22×C3×C4—101no—
275C22×C3×C4—102no—
276C22×C3×C4—102no—
277C22×C3×C4—101no—
278C22×C3×C4C22×D511yescharacteristic
279C3×SD16—28no—
280C3×SD16—108no—
281C2×C3×C8—22no—
282C2×C3×C8—52no—
283C2×C3×C8—102no—
284C2×C3×C8C22×D512yes—
285C3×C4⋊C4—52no—
286C3×C4⋊C4—101no—
287C3×C22⋊C4—104no—
288C23×C5—22no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—42no—
292C23×C5C2×C3×D411yescharacteristic
293C22×D5—22no—
294C22×D5—22no—
295C22×D5C3×SD1614yescomplemented
296C22×D5C2×C3×D412yes—
297C5×Q8—24no—
298C5×Q8—22no—
299C5×Q8C2×C3×D414yescomplemented
300C5×D4—22no—
301C5×D4—22no—
302C5×D4—42no—
303C2×C4×C5—24no—
304C2×C4×C5—22no—
305C2×C4×C5C2×C3×D411yescharacteristic
306C2×C4×C5C2×C3×D412yes—
307C2×C4×C5C2×C3×D412yes—
308C2×C4×C5C24×C311yescharacteristic
309C22⋊D5—48no—
310C2×Dic5—22no—
311C2×Dic5—24no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—42no—
315C2×Dic5C2×C3×D412yes—
316C4×D5—216no—
317C4×D5—24no—
318C4×D5—22no—
319C4×D5—22no—
320Dic10—216no—
321Dic10—24no—
322Dic10—22no—
323Dic10C2×C3×D414yescomplemented
324C5×C8—22no—
325#168—22no—
326C22×Q8—54no—
327C22×Q8—51no—
328C22×Q8—101no—
329C22×Q8—102no—
330C22×Q8—104no—
331C22×Q8—104no—
332C22×Q8C2×C3×D511yescharacteristic
333C22×D4—101no—
334C22×D4C2×C3×D511yescharacteristic
335C23×C4—51no—
336C23×C4—101no—
337C2×SD16—24no—
338C2×SD16—54no—
339C2×SD16—104no—
340C2×SD16C2×C3×D514yescomplemented
341C22×C8—51no—
342C22×C8C2×C3×D511yescharacteristic
343#121—54no—
344#121—102no—
345C2×C4⋊C4—51no—
346C2×C22⋊C4—101no—
347#103—54no—
348#103—54no—
349C22⋊C8—54no—
350C2×C3×C5—82no—
351C2×C3×C5#44814yescomplemented
352C2×C3×C5C2×#12011yescharacteristic
353C2×C3×C5C22×SD1611yescharacteristic
354C2×C3×C5C2×#13711yescharacteristic
355C3×D5—24no—
356C23×C3—22no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—52no—
361C23×C3—54no—
362C23×C3—102no—
363C23×C3—102no—
364C23×C3D4×D511yescharacteristic
365C3×Q8—22no—
366C3×Q8—24no—
367C3×Q8—54no—
368C3×Q8—1016no—
369C3×Q8—102no—
370C3×Q8—104no—
371C3×Q8C2×C22⋊D514yescomplemented
372C3×D4—22no—
373C3×D4—22no—
374C3×D4—42no—
375C3×D4—208no—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—52no—
379C2×C3×C4—1016no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—104no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4—104no—
386C2×C3×C4—102no—
387C2×C3×C4—202no—
388C2×C3×C4D4×D512yes—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4C2×C22⋊D512yes—
391C2×C3×C4C23×D511yescharacteristic
392C3×C8—22no—
393C3×C8—102no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—84no—
398C22×C5C3×#12012yes—
399C22×C5C2×C3×SD1612yes—
400C22×C5C3×#13712yes—
401C22×C5C22×C3×D411yescharacteristic
402C2×D5—22no—
403C2×D5—28no—
404C2×D5—22no—
405C2×D5C2×C3×SD1614yescomplemented
406C4×C5—24no—
407C4×C5C3×#12012yes—
408C4×C5C22×C3×D411yescharacteristic
409C4×C5C22×C3×D411yescharacteristic
410Dic5—22no—
411Dic5—24no—
412Dic5—42no—
413C24—21no—
414C24—51no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—54no—
418C2×Q8—52no—
419C2×Q8—104no—
420C2×Q8—108no—
421C2×Q8—108no—
422C2×Q8—1016no—
423C2×Q8—108no—
424C2×Q8—101no—
425C2×Q8—102no—
426C2×Q8C3×C22⋊D514yescomplemented
427C2×Q8C22×C3×D512yes—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—104no—
432C2×D4—204no—
433C2×D4C22×C3×D512yes—
434C22×C4—21no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—104no—
439C22×C4—108no—
440C22×C4—101no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—101no—
444C22×C4C22×C3×D511yescharacteristic
445SD16—28no—
446SD16—108no—
447C2×C8—22no—
448C2×C8—52no—
449C2×C8—102no—
450C2×C8C22×C3×D512yes—
451C4⋊C4—52no—
452C4⋊C4—101no—
453C22⋊C4—104no—
454C3×C5C2×#44811yescharacteristic, complemented, Hall
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—54no—
459C22×C3—84no—
460C22×C3—102no—
461C22×C3—102no—
462C22×C3—108no—
463C22×C3D5×SD1612yes—
464C22×C3#406112yes—
465C22×C3#408312yes—
466C22×C3C2×D4×D511yescharacteristic
467C3×C4—24no—
468C3×C4—102no—
469C3×C4—104no—
470C3×C4—202no—
471C3×C4#408312yes—
472C3×C4C2×D4×D511yescharacteristic
473C3×C4C22×C22⋊D511yescharacteristic
474C2×C5—82no—
475C2×C5C3×#44814yescomplemented
476C2×C5C2×C3×#12011yescharacteristic
477C2×C5C22×C3×SD1611yescharacteristic
478C2×C5C2×C3×#13711yescharacteristic
479D5—24no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—52no—
485C23—54no—
486C23—102no—
487C23—102no—
488C23C3×D4×D511yescharacteristic
489Q8—24no—
490Q8—22no—
491Q8—54no—
492Q8—1016no—
493Q8—104no—
494Q8—102no—
495Q8C2×C3×C22⋊D514yescomplemented
496D4—22no—
497D4—22no—
498D4—42no—
499D4—208no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—52no—
503C2×C4—1016no—
504C2×C4—102no—
505C2×C4—104no—
506C2×C4—102no—
507C2×C4—104no—
508C2×C4—102no—
509C2×C4—102no—
510C2×C4—102no—
511C2×C4—202no—
512C2×C4C3×D4×D511yescharacteristic
513C2×C4C3×D4×D512yes—
514C2×C4C2×C3×C22⋊D512yes—
515C2×C4C23×C3×D511yescharacteristic
516C8—22no—
517C8—102no—
518C2×C3—82no—
519C2×C3—104no—
520C2×C3#6545914yesdirect product factor
521C2×C3C2×D5×SD1611yescharacteristic
522C2×C3C2×#406111yescharacteristic
523C2×C3C2×#408311yescharacteristic
524C5C2×C3×#44811yescharacteristic, complemented, Sylow
525C22—42no—
526C22—42no—
527C22—42no—
528C22—54no—
529C22—84no—
530C22—102no—
531C22—108no—
532C22—102no—
533C22C3×D5×SD1612yes—
534C22C3×#406112yes—
535C22C3×#408312yes—
536C22C2×C3×D4×D511yescharacteristic
537C4—24no—
538C4—102no—
539C4—104no—
540C4—202no—
541C4C3×#408312yes—
542C4C2×C3×D4×D511yescharacteristic
543C4C22×C3×C22⋊D511yescharacteristic
544C3C2×#6545911yescharacteristic, direct product factor, Sylow
545C2—82no—
546C2—104no—
547C2C3×#6545914yesdirect product factor
548C2C2×C3×D5×SD1611yescharacteristic
549C2C2×C3×#406111yescharacteristic
550C2C2×C3×#408311yescharacteristic
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×#448
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×Q8×D5C2semidirect
2. C22×C3×C5×SD16C2semidirect
4. C22×C3×#687C2semidirect
5. C2×C3×#3967C2semidirect
6. C3×#65459C2direct (N × H)
7. C2×C3×#3952C2semidirect
8. C2×C3×#3948C2semidirect
9. C2×#65459C3direct (N × H)
16. C2×C3×Q8×D5C22semidirect
22. C2×C3×C5×SD16C22semidirect
28. C2×C3×#687C22semidirect
31. C3×#3967C22semidirect
32. C3×#3952C22semidirect
33. C3×#3948C22semidirect
35. C22×Q8×D5C2×C3semidirect
36. C22×C5×SD16C2×C3semidirect
38. C22×#687C2×C3semidirect
39. C2×#3967C2×C3semidirect
40. #65459C2×C3direct (N × H)
41. C2×#3952C2×C3semidirect
42. C2×#3948C2×C3semidirect
47. C2×C3×C5×Q8D4semidirect
73. C2×C3×Dic10D4semidirect
86. C22×C3×SD16D5semidirect
98. C2×Q8×D5C22×C3semidirect
104. C2×C5×SD16C22×C3semidirect
110. C2×#687C22×C3semidirect
113. #3967C22×C3semidirect
114. #3952C22×C3semidirect
115. #3948C22×C3semidirect
124. C22×C3×D5SD16semidirect
128. C3×C5×Q8C2×D4semidirect
152. C3×Dic10C2×D4semidirect
169. C2×C3×SD16C2×D5semidirect
183. C2×C5×Q8C3×D4semidirect
209. C2×Dic10C3×D4semidirect
222. C22×SD16C3×D5semidirect
239. C2×C3×D5C2×SD16semidirect
260. C2×C3×Q8C22⋊D5semidirect
295. C22×D5C3×SD16semidirect
299. C5×Q8C2×C3×D4semidirect
323. Dic10C2×C3×D4semidirect
340. C2×SD16C2×C3×D5semidirect
351. C2×C3×C5#448semidirect
371. C3×Q8C2×C22⋊D5semidirect
405. C2×D5C2×C3×SD16semidirect
426. C2×Q8C3×C22⋊D5semidirect
454. C3×C5C2×#448semidirect
475. C2×C5C3×#448semidirect
495. Q8C2×C3×C22⋊D5semidirect
520. C2×C3#65459direct (N × H)
524. C5C2×C3×#448semidirect
544. C3C2×#65459direct (N × H)
547. C2C3×#65459direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C22×C3×C5×SD162
C2×C3×#40842
C22×C3×#6872
C2×C3×#39672
C3×#654592
C2×C3×#39522
C2×C3×#39482
C2×#654593
C2×C3×#4485