Finite Group Databasebeta

← C3×#10615815 #14424109

Subgroups — C3×#10615815 #14424109

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic
2C2×C3×#4097C212yesmaximal, complemented
3C2×C3×#4070C211yesmaximal, characteristic, complemented
4C3×#65528C214yesmaximal, complemented
5C3×#65521C212yesmaximal, complemented
6C3×#65517C212yesmaximal, complemented
7C3×#65507C212yesmaximal, complemented
8C3×#65496C211yesmaximal, characteristic, complemented
9#10615815C311yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×#41—28no—
11C2×C3×C5×#41—21no—
12C2×C3×C5×#41—21no—
13C2×C3×C5×#41C2212yes—
14C2×C3×C5×#41C2212yes—
15C22×C3×C5×Q8C2211yescharacteristic
16C22×C3×C5×D4—21no—
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5—21no—
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C2×C3×C22⋊Dic5—21no—
22C3×#4097—28no—
23C2×C3×#689C2214yescomplemented
24C2×C3×#687C2214yescomplemented
25C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
26C3×#4070—21no—
27C3×#4070—21no—
28C3×#4070C2212yes—
29C3×#4070C2212yescomplemented
30C2×C3×#683—21no—
31C2×C3×#681C2212yescomplemented
32C3×#3967C2214yescomplemented
33C3×#3964C2214yescomplemented
34C3×C22⋊#168C2212yes—
35C3×C22⋊#168C2212yescomplemented
36C3×#3007—51nomaximal, Hall
37C22×C5×#41C2×C311yescharacteristic
38C2×#4097C2×C312yescomplemented
39C2×#4070C2×C311yescharacteristic, complemented
40#65528C2×C314yescomplemented
41#65521C2×C312yescomplemented
42#65517C2×C312yescomplemented
43#65507C2×C312yescomplemented
44#65496C2×C311yescharacteristic, complemented
45C24×C3×C5—21no—
46C24×C3×C5D411yescharacteristic
47C3×C5×#41—28no—
48C3×C5×#41—28no—
49C3×C5×#41—24no—
50C3×C5×#41—24no—
51C3×C5×#41—24no—
52C3×C5×#41D418yes—
53C2×C3×C5×Q8—24no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56C2×C3×C5×D4—28no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—24no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5—28no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—22no—
66C22×C3×C4×C5—24no—
67C22×C3×C4×C5D411yescharacteristic
68C22×C3×C4×C5D411yescharacteristic
69C22×C3×C4×C5D411yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×Dic5—21no—
74C22×C3×Dic5—21no—
75C2×C3×Dic10—24no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10C2312yes—
78C3×C22⋊Dic5—22no—
79C3×C22⋊Dic5—22no—
80C3×#689—28no—
81C3×#687—28no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×#683—22no—
85C3×#683—22no—
86C3×#681—24no—
87C2×C3×#168C2314yes—
88C22×C3×#41D511yescharacteristic
89C2×C3×#137—52no—
90C2×C3×C22⋊Q8—51no—
91C3×#452—54no—
92C3×#451—52no—
93C3×#450—52no—
94C3×#417—52no—
95C3×#407—51no—
96C2×C5×#41—28no—
97C2×C5×#41—21no—
98C2×C5×#41—21no—
99C2×C5×#41C22×C312yes—
100C2×C5×#41C22×C312yes—
101C22×C5×Q8C22×C311yescharacteristic
102C22×C5×D4—21no—
103C22×C5×D4C22×C311yescharacteristic
104C23×C4×C5—21no—
105C23×C4×C5C22×C311yescharacteristic
106C22×Dic10C22×C311yescharacteristic, complemented
107C2×C22⋊Dic5—21no—
108#4097—28no—
109C2×#689C22×C314yescomplemented
110C2×#687C22×C314yescomplemented
111C2×C4⋊Dic5C22×C311yescharacteristic, complemented
112#4070—21no—
113#4070—21no—
114#4070C22×C312yes—
115#4070C22×C312yescomplemented
116C2×#683—21no—
117C2×#681C22×C312yescomplemented
118#3967C22×C314yescomplemented
119#3964C22×C314yescomplemented
120C22⋊#168C22×C312yes—
121C22⋊#168C22×C312yescomplemented
122#3007—51noSylow
123C23×C3×C5—24no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—41no—
128C23×C3×C5—42no—
129C23×C3×C5—42no—
130C23×C3×C5C2×D411yescharacteristic
131C23×C3×C5C2×D411yescharacteristic
132C23×C3×C5C2×D411yescharacteristic
133C3×C5×Q8—24no—
134C3×C5×Q8—22no—
135C3×C5×Q8C2×D414yes—
136C3×C5×D4—28no—
137C3×C5×D4—24no—
138C3×C5×D4—28no—
139C3×C5×D4—22no—
140C3×C5×D4C2×D414yes—
141C2×C3×C4×C5—24no—
142C2×C3×C4×C5—28no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—28no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D414yes—
154C2×C3×C4×C5C2411yescharacteristic
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—42no—
158C2×C3×Dic5—42no—
159C3×Dic10—24no—
160C3×Dic10—42no—
161C3×#168—24no—
162C2×C3×#41—28no—
163C2×C3×#41—21no—
164C2×C3×#41—21no—
165C2×C3×#41C2×D512yes—
166C2×C3×#41C2×D512yes—
167C22×C3×Q8—51no—
168C22×C3×Q8C2×D511yescharacteristic
169C22×C3×D4—21no—
170C22×C3×D4C2×D511yescharacteristic
171C23×C3×C4—21no—
172C23×C3×C4C2×D511yescharacteristic
173C3×#137—108no—
174C2×C3×Q16—54no—
175C2×C3×SD16—54no—
176C2×C3×M16—52no—
177C3×C22⋊Q8—52no—
178C3×C22⋊Q8—52no—
179C3×C22⋊Q8—101no—
180C3×C22⋊Q8—101no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—101no—
183C2×C3×C22⋊C4—101no—
184C3×#103—54no—
185C3×#102—54no—
186C3×C22⋊C8—52no—
187C3×C22⋊C8—52no—
188C24×C5—21no—
189C24×C5C3×D411yescharacteristic
190C5×#41—28no—
191C5×#41—28no—
192C5×#41—24no—
193C5×#41—24no—
194C5×#41—24no—
195C5×#41C3×D418yes—
196C2×C5×Q8—24no—
197C2×C5×Q8—21no—
198C2×C5×Q8C23×C312yes—
199C2×C5×D4—28no—
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4—24no—
203C2×C5×D4—21no—
204C2×C5×D4C23×C312yes—
205C22×C4×C5—28no—
206C22×C4×C5—21no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—24no—
210C22×C4×C5C3×D411yescharacteristic
211C22×C4×C5C3×D411yescharacteristic
212C22×C4×C5C3×D411yescharacteristic
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C311yescharacteristic
215C22×C4×C5C23×C311yescharacteristic
216C22×Dic5—21no—
217C22×Dic5—21no—
218C2×Dic10—24no—
219C2×Dic10—21no—
220C2×Dic10C23×C312yes—
221C22⋊Dic5—22no—
222C22⋊Dic5—22no—
223#689—28no—
224#687—28no—
225C4⋊Dic5—21no—
226C4⋊Dic5C23×C312yes—
227#683—22no—
228#683—22no—
229#681—24no—
230C2×#168C23×C314yes—
231C22×#41C3×D511yescharacteristic
232C2×#137—52no—
233C2×C22⋊Q8—51no—
234#452—54no—
235#451—52no—
236#450—52no—
237#417—52no—
238#407—51no—
239C22×C3×C5—21no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—24no—
245C22×C3×C5—21no—
246C22×C3×C5—21no—
247C22×C3×C5—44no—
248C22×C3×C5—48no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5#12012yes—
252C22×C3×C5#13712yescomplemented
253C22×C3×C5C22×D411yescharacteristic
254C3×C4×C5—21no—
255C3×C4×C5—24no—
256C3×C4×C5—21no—
257C3×C4×C5#12012yes—
258C3×C4×C5C22×D412yes—
259C3×Dic5—42no—
260C3×Dic5—42no—
261C24×C3—21no—
262C24×C3C22⋊D511yescharacteristic
263C3×#41—28no—
264C3×#41—28no—
265C3×#41—24no—
266C3×#41—24no—
267C3×#41—24no—
268C3×#41C22⋊D518yes—
269C2×C3×Q8—24no—
270C2×C3×Q8—21no—
271C2×C3×Q8—52no—
272C2×C3×Q8—101no—
273C2×C3×Q8—104no—
274C2×C3×Q8C22×D512yes—
275C2×C3×D4—28no—
276C2×C3×D4—22no—
277C2×C3×D4—22no—
278C2×C3×D4—24no—
279C2×C3×D4—21no—
280C2×C3×D4C22×D512yes—
281C22×C3×C4—28no—
282C22×C3×C4—21no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—24no—
286C22×C3×C4—101no—
287C22×C3×C4—101no—
288C22×C3×C4C22⋊D511yescharacteristic
289C22×C3×C4C22⋊D511yescharacteristic
290C22×C3×C4C22⋊D511yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D511yescharacteristic
294C3×Q16—108no—
295C3×SD16—108no—
296C3×M16—104no—
297C2×C3×C8—54no—
298C3×C4⋊C4—52no—
299C3×C4⋊C4—102no—
300C3×C4⋊C4—102no—
301C3×C4⋊C4—101no—
302C3×C22⋊C4—102no—
303C3×C22⋊C4—102no—
304C23×C5—24no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—41no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5C2×C3×D411yescharacteristic
312C23×C5C2×C3×D411yescharacteristic
313C23×C5C2×C3×D411yescharacteristic
314C5×Q8—24no—
315C5×Q8—22no—
316C5×Q8C2×C3×D414yes—
317C5×D4—28no—
318C5×D4—24no—
319C5×D4—28no—
320C5×D4—22no—
321C5×D4C2×C3×D414yes—
322C2×C4×C5—24no—
323C2×C4×C5—28no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—28no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5C2×C3×D411yescharacteristic
332C2×C4×C5C2×C3×D411yescharacteristic
333C2×C4×C5C2×C3×D411yescharacteristic
334C2×C4×C5C2×C3×D414yes—
335C2×C4×C5C24×C311yescharacteristic
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—42no—
339C2×Dic5—42no—
340Dic10—24no—
341Dic10—42no—
342#168—24no—
343C2×#41—28no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41C2×C3×D512yes—
347C2×#41C2×C3×D512yes—
348C22×Q8—51no—
349C22×Q8C2×C3×D511yescharacteristic
350C22×D4—21no—
351C22×D4C2×C3×D511yescharacteristic
352C23×C4—21no—
353C23×C4C2×C3×D511yescharacteristic
354#137—108no—
355C2×Q16—54no—
356C2×SD16—54no—
357C2×M16—52no—
358C22⋊Q8—52no—
359C22⋊Q8—52no—
360C22⋊Q8—101no—
361C22⋊Q8—101no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—101no—
364C2×C22⋊C4—101no—
365#103—54no—
366#102—54no—
367C22⋊C8—52no—
368C22⋊C8—52no—
369C2×C3×C5—22no—
370C2×C3×C5—22no—
371C2×C3×C5—41no—
372C2×C3×C5—44no—
373C2×C3×C5C2×#12011yescharacteristic
374C2×C3×C5C2×#13711yescharacteristic
375C2×C3×C5#57511yescharacteristic
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—41no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3C2×C22⋊D511yescharacteristic
384C23×C3C2×C22⋊D511yescharacteristic
385C23×C3C2×C22⋊D511yescharacteristic
386C3×Q8—24no—
387C3×Q8—22no—
388C3×Q8—104no—
389C3×Q8—202no—
390C3×Q8C2×C22⋊D514yes—
391C3×D4—28no—
392C3×D4—24no—
393C3×D4—28no—
394C3×D4—22no—
395C3×D4C2×C22⋊D514yes—
396C2×C3×C4—24no—
397C2×C3×C4—28no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—28no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—102no—
406C2×C3×C4—102no—
407C2×C3×C4—202no—
408C2×C3×C4—202no—
409C2×C3×C4C2×C22⋊D511yescharacteristic
410C2×C3×C4C2×C22⋊D511yescharacteristic
411C2×C3×C4C2×C22⋊D511yescharacteristic
412C2×C3×C4C2×C22⋊D514yes—
413C2×C3×C4C23×D511yescharacteristic
414C3×C8—104no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—24no—
423C22×C5—44no—
424C22×C5—48no—
425C22×C5—42no—
426C22×C5—42no—
427C22×C5C3×#12012yes—
428C22×C5C3×#13712yescomplemented
429C22×C5C22×C3×D411yescharacteristic
430C4×C5—21no—
431C4×C5—24no—
432C4×C5—21no—
433C4×C5C3×#12012yes—
434C4×C5C22×C3×D412yes—
435Dic5—42no—
436Dic5—42no—
437C24—21no—
438C24C3×C22⋊D511yescharacteristic
439#41—28no—
440#41—28no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41C3×C22⋊D518yes—
445C2×Q8—24no—
446C2×Q8—21no—
447C2×Q8—52no—
448C2×Q8—101no—
449C2×Q8—104no—
450C2×Q8C22×C3×D512yes—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—21no—
456C2×D4C22×C3×D512yes—
457C22×C4—28no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4C3×C22⋊D511yescharacteristic
465C22×C4C3×C22⋊D511yescharacteristic
466C22×C4C3×C22⋊D511yescharacteristic
467C22×C4C22×C3×D511yescharacteristic
468C22×C4C22×C3×D511yescharacteristic
469C22×C4C22×C3×D511yescharacteristic
470Q16—108no—
471SD16—108no—
472M16—104no—
473C2×C8—54no—
474C4⋊C4—52no—
475C4⋊C4—101no—
476C4⋊C4—102no—
477C4⋊C4—102no—
478C22⋊C4—102no—
479C22⋊C4—102no—
480C3×C5#300711yescharacteristic, complemented, Hall
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—24no—
489C22×C3—44no—
490C22×C3—48no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3#409712yescomplemented
494C22×C3#409912yes—
495C22×C3C22×C22⋊D511yescharacteristic
496C3×C4—21no—
497C3×C4—24no—
498C3×C4—21no—
499C3×C4—202no—
500C3×C4—202no—
501C3×C4#409912yes—
502C3×C4C22×C22⋊D512yes—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5—44no—
507C2×C5C2×C3×#12011yescharacteristic
508C2×C5C2×C3×#13711yescharacteristic
509C2×C5C3×#57511yescharacteristic
510C23—24no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23C2×C3×C22⋊D511yescharacteristic
518C23C2×C3×C22⋊D511yescharacteristic
519C23C2×C3×C22⋊D511yescharacteristic
520Q8—24no—
521Q8—22no—
522Q8—104no—
523Q8—202no—
524Q8C2×C3×C22⋊D514yes—
525D4—28no—
526D4—24no—
527D4—28no—
528D4—22no—
529D4C2×C3×C22⋊D514yes—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—28no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—202no—
542C2×C4—202no—
543C2×C4C2×C3×C22⋊D511yescharacteristic
544C2×C4C2×C3×C22⋊D511yescharacteristic
545C2×C4C2×C3×C22⋊D511yescharacteristic
546C2×C4C2×C3×C22⋊D514yes—
547C2×C4C23×C3×D511yescharacteristic
548C8—104no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3—44no—
553C2×C3#6615611yescharacteristic
554C2×C3C2×#409711yescharacteristic
555C2×C3C2×#409911yescharacteristic
556C5C3×#300711yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—44no—
566C22—48no—
567C22—42no—
568C22—42no—
569C22C3×#409712yescomplemented
570C22C3×#409912yes—
571C22C22×C3×C22⋊D511yescharacteristic
572C4—21no—
573C4—24no—
574C4—21no—
575C4—202no—
576C4—202no—
577C4C3×#409912yes—
578C4C22×C3×C22⋊D512yes—
579C3#1061581511yescharacteristic, direct product factor, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—44no—
584C2C3×#6615611yescharacteristic
585C2C2×C3×#409711yescharacteristic
586C2C2×C3×#409911yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC22×C3×C5×#41C2
socleC22×C3×C5C22×D4
hypercenterC22×C3×#41D5
hypocenterC5C3×#3007
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4097C2semidirect
3. C2×C3×#4070C2semidirect
4. C3×#65528C2semidirect
5. C3×#65521C2semidirect
6. C3×#65517C2semidirect
7. C3×#65507C2semidirect
8. C3×#65496C2semidirect
9. #10615815C3direct (N × H)
20. C22×C3×Dic10C22semidirect
23. C2×C3×#689C22semidirect
24. C2×C3×#687C22semidirect
25. C2×C3×C4⋊Dic5C22semidirect
29. C3×#4070C22semidirect
31. C2×C3×#681C22semidirect
32. C3×#3967C22semidirect
33. C3×#3964C22semidirect
35. C3×C22⋊#168C22semidirect
38. C2×#4097C2×C3semidirect
39. C2×#4070C2×C3semidirect
40. #65528C2×C3semidirect
41. #65521C2×C3semidirect
42. #65517C2×C3semidirect
43. #65507C2×C3semidirect
44. #65496C2×C3semidirect
106. C22×Dic10C22×C3semidirect
109. C2×#689C22×C3semidirect
110. C2×#687C22×C3semidirect
111. C2×C4⋊Dic5C22×C3semidirect
115. #4070C22×C3semidirect
117. C2×#681C22×C3semidirect
118. #3967C22×C3semidirect
119. #3964C22×C3semidirect
121. C22⋊#168C22×C3semidirect
252. C22×C3×C5#137semidirect
428. C22×C5C3×#137semidirect
480. C3×C5#3007semidirect
493. C22×C3#4097semidirect
556. C5C3×#3007semidirect
569. C22C3×#4097semidirect
579. C3#10615815direct (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×#412
C2×C3×#40972
C2×C3×#40702
C3×#655282
C3×#655212
C3×#655172
C3×#655072
C3×#654962
#106158153
C3×#30075