Finite Group Databasebeta

← C3×#10610687 #14412544

Subgroups — C3×#10610687 #14412544

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#713C211yesmaximal, characteristic
2C2×C3×D5×M16C211yesmaximal, characteristic, complemented
3C3×D5×#117C211yesmaximal, characteristic, complemented
4C3×C5×#419C211yesmaximal, characteristic, complemented
5C3×#65514C211yesmaximal, characteristic, complemented
6C3×#65420C211yesmaximal, characteristic, complemented
7C3×#65290C211yesmaximal, characteristic, complemented
8C3×#65093C214yesmaximal, complemented
9C3×#65092C214yesmaximal, complemented
10#10610687C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C2×C3×#713—24no—
13C2×C3×#713—21no—
14C2×C3×#713—21no—
15C2×C3×#713C418yescomplemented
16C2×C3×#713C2212yes—
17C2×C3×#713C2212yes—
18C22×C3×D20—21no—
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5—21no—
21C22×C3×C4×D5C2211yescharacteristic
22C2×C3×C5×M16C2211yescharacteristic
23C3×C5×#117C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26C3×D5×M16—24no—
27C2×C3×#676C2212yescomplemented
28C2×C3×C8×D5C2212yescomplemented
29C3×#4038C2212yescomplemented
30C3×D5×C4⋊C4C2212yescomplemented
31C3×D5×C22⋊C4—21no—
32C3×#4023—21no—
33C3×#4018—21no—
34C3×C42×D5—21no—
35C3×C5×#103C2214yescomplemented
36C3×#3967C2214yescomplemented
37C3×#3953C2214yescomplemented
38C3×#3941C2214yescomplemented
39C3×#2896—51nomaximal, Hall
40C22×#713C2×C311yescharacteristic
41C2×D5×M16C2×C311yescharacteristic, complemented
42D5×#117C2×C311yescharacteristic, complemented
43C5×#419C2×C311yescharacteristic, complemented
44#65514C2×C311yescharacteristic, complemented
45#65420C2×C311yescharacteristic, complemented
46#65290C2×C311yescharacteristic, complemented
47#65093C2×C314yescomplemented
48#65092C2×C314yescomplemented
49C23×C3×D5—21no—
50C23×C3×D5D411yescharacteristic
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—21no—
53C2×C3×C5×Q8C2×C414yescomplemented
54C2×C3×C5×Q8C2312yes—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×Dic5D411yescharacteristic
58C3×#713—28no—
59C3×#713—28no—
60C3×#713—24no—
61C3×#713—24no—
62C3×#713C2×C418yes—
63C3×#713C2×C418yescomplemented
64C2×C3×D20—28no—
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20—21no—
68C2×C3×D20—22no—
69C2×C3×D20C2×C414yescomplemented
70C2×C3×D20C2312yes—
71C2×C3×C4×D5—28no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2×C414yes—
76C2×C3×C4×D5D411yescharacteristic
77C2×C3×C4×D5D411yescharacteristic
78C2×C3×C4×D5D414yes—
79C2×C3×C4×D5C2311yescharacteristic
80C2×C3×C4×D5C2311yescharacteristic
81C3×C5×M16—22no—
82C2×C3×C5×C8C2312yes—
83C3×C5×C4⋊C4C2312yes—
84C3×C5×C22⋊C4—21no—
85C3×C42×C5—21no—
86C3×C22⋊Dic5—21no—
87C3×#685—22no—
88C3×C4⋊Dic5C2312yes—
89C3×#683—22no—
90C3×C4×Dic5—21no—
91C3×C4×Dic5—22no—
92C3×#681—22no—
93C2×C3×#168C2312yes—
94C3×#676—24no—
95C3×C8×D5—24no—
96C22×C3×#41—51no—
97C22×C3×M16—51no—
98C2×C3×#117—51no—
99C3×#419—51no—
100C3×#419D511yescharacteristic, complemented
101C3×#418—51no—
102C3×#418—51no—
103C3×#417—54no—
104C3×#416—54no—
105C22×C5×Q8C22×C311yescharacteristic
106C2×#713—24no—
107C2×#713—21no—
108C2×#713—21no—
109C2×#713C3×C418yescomplemented
110C2×#713C22×C312yes—
111C2×#713C22×C312yes—
112C22×D20—21no—
113C22×D20C22×C311yescharacteristic
114C22×C4×D5—21no—
115C22×C4×D5C22×C311yescharacteristic
116C2×C5×M16C22×C311yescharacteristic
117C5×#117C22×C311yescharacteristic
118#4072C22×C311yescharacteristic
119C2×#681C22×C311yescharacteristic
120D5×M16—24no—
121C2×#676C22×C312yescomplemented
122C2×C8×D5C22×C312yescomplemented
123#4038C22×C312yescomplemented
124D5×C4⋊C4C22×C312yescomplemented
125D5×C22⋊C4—21no—
126#4023—21no—
127#4018—21no—
128C42×D5—21no—
129C5×#103C22×C314yescomplemented
130#3967C22×C314yescomplemented
131#3953C22×C314yescomplemented
132#3941C22×C314yescomplemented
133#2896—51noSylow
134C23×C3×C5C2×D411yescharacteristic
135C22×C3×D5—24no—
136C22×C3×D5—22no—
137C22×C3×D5—42no—
138C22×C3×D5—44no—
139C22×C3×D5C22⋊C414yes—
140C22×C3×D5C2×D411yescharacteristic
141C22×C3×D5C2×D411yescharacteristic
142C3×C5×Q8—24no—
143C3×C5×Q8—22no—
144C3×C5×Q8C22×C414yes—
145C2×C3×C4×C5—24no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5C2411yescharacteristic
152C2×C3×Dic5—22no—
153C2×C3×Dic5C22⋊C414yes—
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C3×D20—28no—
157C3×D20—28no—
158C3×D20—24no—
159C3×D20—22no—
160C3×D20C22×C414yes—
161C3×C4×D5—28no—
162C3×C4×D5—28no—
163C3×C4×D5—44no—
164C3×C4×D5C22⋊C414yes—
165C3×C4×D5C22⋊C414yes—
166C3×C4×D5C22×C412yes—
167C3×C4×D5C22×C412yes—
168C3×C4×D5C2×D412yes—
169C3×C4×D5C2×D412yes—
170C3×C5×C8—22no—
171C3×#168—22no—
172C2×C3×#41—58no—
173C2×C3×#41—52no—
174C2×C3×#41—52no—
175C2×C3×#41—101no—
176C2×C3×#41—101no—
177C2×C3×#41—104no—
178C22×C3×Q8C2×D511yescharacteristic
179C22×C3×D4—51no—
180C22×C3×D4—101no—
181C23×C3×C4—51no—
182C23×C3×C4—101no—
183C2×C3×M16—51no—
184C2×C3×M16—52no—
185C2×C3×M16—104no—
186C2×C3×M16C2×D511yescharacteristic
187C22×C3×C8—52no—
188C3×#117—51no—
189C3×#117—52no—
190C3×#117—101no—
191C3×#117—101no—
192C3×#117C2×D511yescharacteristic
193C2×C3×C4⋊C4—52no—
194C2×C3×C22⋊C4—101no—
195C2×C3×C42—101no—
196C3×#103—54no—
197C3×#103C2×D514yescomplemented
198C3×#102—54no—
199C3×#102—54no—
200C23×D5—21no—
201C23×D5C3×D411yescharacteristic
202C2×C5×Q8—22no—
203C2×C5×Q8—21no—
204C2×C5×Q8C2×C3×C414yescomplemented
205C2×C5×Q8C23×C312yes—
206C22×C4×C5—21no—
207C22×C4×C5C23×C311yescharacteristic
208C22×Dic5C3×D411yescharacteristic
209#713—28no—
210#713—28no—
211#713—24no—
212#713—24no—
213#713C2×C3×C418yes—
214#713C2×C3×C418yescomplemented
215C2×D20—28no—
216C2×D20—22no—
217C2×D20—22no—
218C2×D20—21no—
219C2×D20—22no—
220C2×D20C2×C3×C414yescomplemented
221C2×D20C23×C312yes—
222C2×C4×D5—28no—
223C2×C4×D5—22no—
224C2×C4×D5—22no—
225C2×C4×D5—22no—
226C2×C4×D5C2×C3×C414yes—
227C2×C4×D5C3×D411yescharacteristic
228C2×C4×D5C3×D411yescharacteristic
229C2×C4×D5C3×D414yes—
230C2×C4×D5C23×C311yescharacteristic
231C2×C4×D5C23×C311yescharacteristic
232C5×M16—22no—
233C2×C5×C8C23×C312yes—
234C5×C4⋊C4C23×C312yes—
235C5×C22⋊C4—21no—
236C42×C5—21no—
237C22⋊Dic5—21no—
238#685—22no—
239C4⋊Dic5C23×C312yes—
240#683—22no—
241C4×Dic5—21no—
242C4×Dic5—22no—
243#681—22no—
244C2×#168C23×C312yes—
245#676—24no—
246C8×D5—24no—
247C22×#41—51no—
248C22×M16—51no—
249C2×#117—51no—
250#419—51no—
251#419C3×D511yescharacteristic, complemented
252#418—51no—
253#418—51no—
254#417—54no—
255#416—54no—
256C22×C3×C5—22no—
257C22×C3×C5C2×C22⋊C412yes—
258C22×C3×C5C22×D411yescharacteristic
259C2×C3×D5—22no—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C2×C3×D5—44no—
263C2×C3×D5—48no—
264C2×C3×D5—44no—
265C2×C3×D5C2×C22⋊C412yes—
266C2×C3×D5C2×C22⋊C412yes—
267C3×C4×C5—24no—
268C3×C4×C5—42no—
269C3×C4×C5C2×C22⋊C412yes—
270C3×C4×C5C23×C411yescharacteristic
271C3×C4×C5C22×D411yescharacteristic
272C3×Dic5—42no—
273C3×Dic5C2×C22⋊C412yes—
274C3×Dic5C2×C22⋊C412yes—
275C24×C3—51no—
276C24×C3—101no—
277C3×#41—58no—
278C3×#41—58no—
279C3×#41—104no—
280C3×#41—104no—
281C3×#41—108no—
282C3×#41—108no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8C4×D514yescomplemented
286C2×C3×Q8C22×D512yes—
287C2×C3×D4—54no—
288C2×C3×D4—52no—
289C2×C3×D4—102no—
290C2×C3×D4—102no—
291C2×C3×D4—108no—
292C2×C3×D4—102no—
293C2×C3×D4—101no—
294C22×C3×C4—21no—
295C22×C3×C4—51no—
296C22×C3×C4—54no—
297C22×C3×C4—51no—
298C22×C3×C4—51no—
299C22×C3×C4—54no—
300C22×C3×C4—51no—
301C22×C3×C4—51no—
302C22×C3×C4—102no—
303C22×C3×C4—102no—
304C22×C3×C4—108no—
305C22×C3×C4—102no—
306C22×C3×C4C22×D511yescharacteristic
307C3×M16—22no—
308C3×M16—104no—
309C3×M16—102no—
310C2×C3×C8—52no—
311C2×C3×C8—104no—
312C2×C3×C8C22×D512yes—
313C3×C4⋊C4—52no—
314C3×C4⋊C4—102no—
315C3×C4⋊C4C22×D512yes—
316C3×C22⋊C4—21no—
317C3×C22⋊C4—102no—
318C3×C22⋊C4—101no—
319C3×C42—21no—
320C3×C42—102no—
321C3×C42—101no—
322C23×C5C2×C3×D411yescharacteristic
323C22×D5—24no—
324C22×D5—22no—
325C22×D5—42no—
326C22×D5—44no—
327C22×D5C3×C22⋊C414yes—
328C22×D5C2×C3×D411yescharacteristic
329C22×D5C2×C3×D411yescharacteristic
330C5×Q8—24no—
331C5×Q8—22no—
332C5×Q8C22×C3×C414yes—
333C2×C4×C5—24no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5C22×C3×C412yes—
337C2×C4×C5C2×C3×D411yescharacteristic
338C2×C4×C5C2×C3×D412yes—
339C2×C4×C5C24×C311yescharacteristic
340C2×Dic5—22no—
341C2×Dic5C3×C22⋊C414yes—
342C2×Dic5C2×C3×D411yescharacteristic
343C2×Dic5C2×C3×D411yescharacteristic
344D20—28no—
345D20—28no—
346D20—24no—
347D20—22no—
348D20C22×C3×C414yes—
349C4×D5—28no—
350C4×D5—28no—
351C4×D5—44no—
352C4×D5C3×C22⋊C414yes—
353C4×D5C3×C22⋊C414yes—
354C4×D5C22×C3×C412yes—
355C4×D5C22×C3×C412yes—
356C4×D5C2×C3×D412yes—
357C4×D5C2×C3×D412yes—
358C5×C8—22no—
359#168—22no—
360C2×#41—58no—
361C2×#41—52no—
362C2×#41—52no—
363C2×#41—101no—
364C2×#41—101no—
365C2×#41—104no—
366C22×Q8C2×C3×D511yescharacteristic
367C22×D4—51no—
368C22×D4—101no—
369C23×C4—51no—
370C23×C4—101no—
371C2×M16—51no—
372C2×M16—52no—
373C2×M16—104no—
374C2×M16C2×C3×D511yescharacteristic
375C22×C8—52no—
376#117—51no—
377#117—52no—
378#117—101no—
379#117—101no—
380#117C2×C3×D511yescharacteristic
381C2×C4⋊C4—52no—
382C2×C22⋊C4—101no—
383C2×C42—101no—
384#103—54no—
385#103C2×C3×D514yescomplemented
386#102—54no—
387#102—54no—
388C2×C3×C5—22no—
389C2×C3×C5C22×C22⋊C411yescharacteristic
390C2×C3×C5#57512yes—
391C3×D5—22no—
392C3×D5—22no—
393C3×D5—44no—
394C23×C3—51no—
395C23×C3—51no—
396C23×C3—54no—
397C23×C3—102no—
398C23×C3—104no—
399C23×C3—202no—
400C23×C3—204no—
401C23×C3D4×D511yescharacteristic
402C3×Q8—22no—
403C3×Q8—24no—
404C3×Q8C2×C4×D514yes—
405C3×D4—54no—
406C3×D4—108no—
407C3×D4—108no—
408C3×D4—102no—
409C3×D4—104no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—51no—
414C2×C3×C4—51no—
415C2×C3×C4—54no—
416C2×C3×C4—52no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—54no—
421C2×C3×C4—54no—
422C2×C3×C4—108no—
423C2×C3×C4—108no—
424C2×C3×C4—102no—
425C2×C3×C4—204no—
426C2×C3×C4C2×C4×D512yes—
427C2×C3×C4D4×D512yes—
428C2×C3×C4D4×D511yescharacteristic
429C2×C3×C4C23×D511yescharacteristic
430C3×C8—22no—
431C3×C8—102no—
432C22×C5—22no—
433C22×C5C2×C3×C22⋊C412yes—
434C22×C5C22×C3×D411yescharacteristic
435C2×D5—22no—
436C2×D5—22no—
437C2×D5—24no—
438C2×D5—44no—
439C2×D5—48no—
440C2×D5—44no—
441C2×D5C2×C3×C22⋊C412yes—
442C2×D5C2×C3×C22⋊C412yes—
443C4×C5—24no—
444C4×C5—42no—
445C4×C5C2×C3×C22⋊C412yes—
446C4×C5C23×C3×C411yescharacteristic
447C4×C5C22×C3×D411yescharacteristic
448Dic5—42no—
449Dic5C2×C3×C22⋊C412yes—
450Dic5C2×C3×C22⋊C412yes—
451C24—51no—
452C24—101no—
453#41—58no—
454#41—58no—
455#41—104no—
456#41—104no—
457#41—108no—
458#41—108no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8C3×C4×D514yescomplemented
462C2×Q8C22×C3×D512yes—
463C2×D4—54no—
464C2×D4—52no—
465C2×D4—102no—
466C2×D4—102no—
467C2×D4—108no—
468C2×D4—102no—
469C2×D4—101no—
470C22×C4—21no—
471C22×C4—51no—
472C22×C4—54no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—54no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—108no—
481C22×C4—102no—
482C22×C4C22×C3×D511yescharacteristic
483M16—22no—
484M16—104no—
485M16—102no—
486C2×C8—52no—
487C2×C8—104no—
488C2×C8C22×C3×D512yes—
489C4⋊C4—52no—
490C4⋊C4—102no—
491C4⋊C4C22×C3×D512yes—
492C22⋊C4—21no—
493C22⋊C4—102no—
494C22⋊C4—101no—
495C42—21no—
496C42—102no—
497C42—101no—
498C3×C5#289611yescharacteristic, complemented, Hall
499C22×C3—22no—
500C22×C3—52no—
501C22×C3—52no—
502C22×C3—102no—
503C22×C3—102no—
504C22×C3—104no—
505C22×C3—204no—
506C22×C3—208no—
507C22×C3—204no—
508C22×C3D5×C22⋊C412yes—
509C22×C3C2×D4×D511yescharacteristic
510C3×C4—24no—
511C3×C4—42no—
512C3×C4—52no—
513C3×C4—52no—
514C3×C4—202no—
515C3×C4D5×C22⋊C412yes—
516C3×C4C22×C4×D511yescharacteristic
517C3×C4C2×D4×D511yescharacteristic
518C2×C5—22no—
519C2×C5C22×C3×C22⋊C411yescharacteristic
520C2×C5C3×#57512yes—
521D5—22no—
522D5—22no—
523D5—44no—
524C23—51no—
525C23—51no—
526C23—54no—
527C23—102no—
528C23—104no—
529C23—202no—
530C23—204no—
531C23C3×D4×D511yescharacteristic
532Q8—22no—
533Q8—24no—
534Q8C2×C3×C4×D514yes—
535D4—54no—
536D4—108no—
537D4—108no—
538D4—102no—
539D4—104no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—51no—
544C2×C4—51no—
545C2×C4—54no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—52no—
549C2×C4—52no—
550C2×C4—54no—
551C2×C4—54no—
552C2×C4—108no—
553C2×C4—108no—
554C2×C4—102no—
555C2×C4—204no—
556C2×C4C2×C3×C4×D512yes—
557C2×C4C3×D4×D512yes—
558C2×C4C3×D4×D511yescharacteristic
559C2×C4C23×C3×D511yescharacteristic
560C8—22no—
561C8—102no—
562C2×C3—22no—
563C2×C3—102no—
564C2×C3—102no—
565C2×C3—204no—
566C2×C3C2×D5×C22⋊C411yescharacteristic
567C2×C3#6611112yes—
568C5C3×#289611yescharacteristic, complemented, Sylow
569C22—22no—
570C22—52no—
571C22—52no—
572C22—102no—
573C22—102no—
574C22—104no—
575C22—204no—
576C22—208no—
577C22—204no—
578C22C3×D5×C22⋊C412yes—
579C22C2×C3×D4×D511yescharacteristic
580C4—24no—
581C4—42no—
582C4—52no—
583C4—52no—
584C4—202no—
585C4C3×D5×C22⋊C412yes—
586C4C22×C3×C4×D511yescharacteristic
587C4C2×C3×D4×D511yescharacteristic
588C3#1061068711yescharacteristic, direct product factor, Sylow
589C2—22no—
590C2—102no—
591C2—102no—
592C2—204no—
593C2C2×C3×D5×C22⋊C411yescharacteristic
594C2C3×#6611112yes—
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#419C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×#713C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#419D5
hypocenterC5C3×#2896
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×M16C2semidirect
3. C3×D5×#117C2semidirect
4. C3×C5×#419C2semidirect
5. C3×#65514C2semidirect
6. C3×#65420C2semidirect
7. C3×#65290C2semidirect
8. C3×#65093C2semidirect
9. C3×#65092C2semidirect
10. #10610687C3direct (N × H)
15. C2×C3×#713C4semidirect
27. C2×C3×#676C22semidirect
28. C2×C3×C8×D5C22semidirect
29. C3×#4038C22semidirect
30. C3×D5×C4⋊C4C22semidirect
35. C3×C5×#103C22semidirect
36. C3×#3967C22semidirect
37. C3×#3953C22semidirect
38. C3×#3941C22semidirect
41. C2×D5×M16C2×C3semidirect
42. D5×#117C2×C3semidirect
43. C5×#419C2×C3semidirect
44. #65514C2×C3semidirect
45. #65420C2×C3semidirect
46. #65290C2×C3semidirect
47. #65093C2×C3semidirect
48. #65092C2×C3semidirect
53. C2×C3×C5×Q8C2×C4semidirect
63. C3×#713C2×C4semidirect
69. C2×C3×D20C2×C4semidirect
100. C3×#419D5semidirect
109. C2×#713C3×C4semidirect
121. C2×#676C22×C3semidirect
122. C2×C8×D5C22×C3semidirect
123. #4038C22×C3semidirect
124. D5×C4⋊C4C22×C3semidirect
129. C5×#103C22×C3semidirect
130. #3967C22×C3semidirect
131. #3953C22×C3semidirect
132. #3941C22×C3semidirect
197. C3×#103C2×D5semidirect
204. C2×C5×Q8C2×C3×C4semidirect
214. #713C2×C3×C4semidirect
220. C2×D20C2×C3×C4semidirect
251. #419C3×D5semidirect
285. C2×C3×Q8C4×D5semidirect
385. #103C2×C3×D5semidirect
461. C2×Q8C3×C4×D5semidirect
498. C3×C5#2896semidirect
568. C5C3×#2896semidirect
588. C3#10610687direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C2×C3×D5×M162
C3×D5×#1172
C3×C5×#4192
C3×#655142
C3×#654202
C3×#652902
C3×#650932
C3×#650922
#106106873
C3×#28965