Finite Group Databasebeta

← C3×#10610371 #14424115

Subgroups — C3×#10610371 #14424115

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×#709C211yesmaximal, characteristic
2C2×C3×#4070C211yesmaximal, characteristic, complemented
3C2×C3×#4055C212yesmaximal, complemented
4C3×C5×#407C211yesmaximal, characteristic, complemented
5C3×#65422C212yesmaximal, complemented
6C3×#65028C212yesmaximal, complemented
7C3×#65022C214yesmaximal, complemented
8C3×#65020C212yesmaximal, complemented
9#10610371C311yesmaximal, characteristic, direct product factor, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C3×C22⋊D5—21no—
12C2×C3×#709—21no—
13C2×C3×#709—21no—
14C2×C3×#709—28no—
15C2×C3×#709C2212yes—
16C2×C3×#709C2212yes—
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5—21no—
19C22×C3×Dic10C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C2×C3×C5×M16C2212yescomplemented
22C2×C3×C22⋊Dic5—21no—
23C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
24C3×#4070—21no—
25C3×#4070—21no—
26C3×#4070C2212yes—
27C3×#4070C2212yescomplemented
28C2×C3×#683—21no—
29C3×#4055—28no—
30C2×C3×Dic20C2214yescomplemented
31C2×C3×#677C2214yescomplemented
32C3×C5×C22⋊C8C2212yes—
33C3×C5×C22⋊C8C2212yescomplemented
34C3×#3953C2214yescomplemented
35C3×#3948C2214yescomplemented
36C3×#3007—51nomaximal, Hall
37C22×#709C2×C311yescharacteristic
38C2×#4070C2×C311yescharacteristic, complemented
39C2×#4055C2×C312yescomplemented
40C5×#407C2×C311yescharacteristic, complemented
41#65422C2×C312yescomplemented
42#65028C2×C312yescomplemented
43#65022C2×C314yescomplemented
44#65020C2×C312yescomplemented
45C24×C3×C5D411yescharacteristic
46C23×C3×D5—21no—
47C22×C3×C4×C5—24no—
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5D411yescharacteristic
50C22×C3×C4×C5D411yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C2×C3×C22⋊D5—28no—
55C2×C3×C22⋊D5—22no—
56C2×C3×C22⋊D5—22no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5—21no—
59C22×C3×Dic5—21no—
60C3×#709—28no—
61C3×#709—28no—
62C3×#709—24no—
63C3×#709—24no—
64C3×#709—24no—
65C3×#709D418yes—
66C2×C3×D20—21no—
67C2×C3×D20—24no—
68C2×C3×D20C2312yes—
69C2×C3×C4×D5—28no—
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5—22no—
72C2×C3×Dic10—21no—
73C2×C3×Dic10—24no—
74C2×C3×Dic10—24no—
75C2×C3×Dic10—21no—
76C2×C3×Dic10C2312yes—
77C2×C3×Dic10C2312yes—
78C3×C5×M16—24no—
79C2×C3×C5×C8C2314yes—
80C3×C22⋊Dic5—22no—
81C3×C22⋊Dic5—22no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×#683—22no—
85C3×#683—22no—
86C3×Dic20—28no—
87C3×#677—28no—
88C22×C3×#41—51no—
89C2×C3×#137—52no—
90C2×C3×C22⋊Q8—51no—
91C3×#452—54no—
92C3×#451—52no—
93C3×#450—52no—
94C3×#417—52no—
95C3×#407D511yescharacteristic, complemented
96C23×C4×C5C22×C311yescharacteristic
97C22×C22⋊D5—21no—
98C2×#709—21no—
99C2×#709—21no—
100C2×#709—28no—
101C2×#709C22×C312yes—
102C2×#709C22×C312yes—
103C22×D20C22×C311yescharacteristic
104C22×C4×D5—21no—
105C22×Dic10C22×C311yescharacteristic
106C22×Dic10C22×C311yescharacteristic, complemented
107C2×C5×M16C22×C312yescomplemented
108C2×C22⋊Dic5—21no—
109C2×C4⋊Dic5C22×C311yescharacteristic, complemented
110#4070—21no—
111#4070—21no—
112#4070C22×C312yes—
113#4070C22×C312yescomplemented
114C2×#683—21no—
115#4055—28no—
116C2×Dic20C22×C314yescomplemented
117C2×#677C22×C314yescomplemented
118C5×C22⋊C8C22×C312yes—
119C5×C22⋊C8C22×C312yescomplemented
120#3953C22×C314yescomplemented
121#3948C22×C314yescomplemented
122#3007—51noSylow
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—41no—
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C22×C3×D5—24no—
130C22×C3×D5—22no—
131C22×C3×D5—42no—
132C22×C3×D5—42no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D414yes—
142C2×C3×C4×C5C2411yescharacteristic
143C3×C22⋊D5—28no—
144C3×C22⋊D5—28no—
145C2×C3×Dic5—24no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—42no—
150C2×C3×Dic5—42no—
151C3×D20—24no—
152C3×D20—22no—
153C3×D20C2×D414yes—
154C3×C4×D5—28no—
155C3×C4×D5—28no—
156C3×Dic10—24no—
157C3×Dic10—22no—
158C3×Dic10—24no—
159C3×Dic10—42no—
160C3×Dic10C2×D414yes—
161C3×C5×C8—24no—
162C2×C3×#41—52no—
163C2×C3×#41—52no—
164C2×C3×#41—108no—
165C2×C3×#41—101no—
166C2×C3×#41—101no—
167C22×C3×Q8—51no—
168C22×C3×Q8—51no—
169C22×C3×D4—51no—
170C22×C3×D4—101no—
171C23×C3×C4—101no—
172C23×C3×C4C2×D511yescharacteristic
173C3×#137—108no—
174C2×C3×Q16—54no—
175C2×C3×SD16—54no—
176C2×C3×M16C2×D512yescomplemented
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⋊C8C2×D512yes—
187C3×C22⋊C8C2×D512yescomplemented
188C24×C5C3×D411yescharacteristic
189C23×D5—21no—
190C22×C4×C5—24no—
191C22×C4×C5C3×D411yescharacteristic
192C22×C4×C5C3×D411yescharacteristic
193C22×C4×C5C3×D411yescharacteristic
194C22×C4×C5C23×C311yescharacteristic
195C22×C4×C5C23×C311yescharacteristic
196C22×C4×C5C23×C311yescharacteristic
197C2×C22⋊D5—28no—
198C2×C22⋊D5—22no—
199C2×C22⋊D5—22no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—21no—
203#709—28no—
204#709—28no—
205#709—24no—
206#709—24no—
207#709—24no—
208#709C3×D418yes—
209C2×D20—21no—
210C2×D20—24no—
211C2×D20C23×C312yes—
212C2×C4×D5—28no—
213C2×C4×D5—22no—
214C2×C4×D5—22no—
215C2×Dic10—21no—
216C2×Dic10—24no—
217C2×Dic10—24no—
218C2×Dic10—21no—
219C2×Dic10C23×C312yes—
220C2×Dic10C23×C312yes—
221C5×M16—24no—
222C2×C5×C8C23×C314yes—
223C22⋊Dic5—22no—
224C22⋊Dic5—22no—
225C4⋊Dic5—21no—
226C4⋊Dic5C23×C312yes—
227#683—22no—
228#683—22no—
229Dic20—28no—
230#677—28no—
231C22×#41—51no—
232C2×#137—52no—
233C2×C22⋊Q8—51no—
234#452—54no—
235#451—52no—
236#450—52no—
237#417—52no—
238#407C3×D511yescharacteristic, complemented
239C22×C3×C5—21no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5—44no—
247C22×C3×C5#12012yes—
248C22×C3×C5#13712yescomplemented
249C22×C3×C5C22×D411yescharacteristic
250C2×C3×D5—24no—
251C2×C3×D5—48no—
252C2×C3×D5—42no—
253C2×C3×D5—42no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5#12012yes—
257C3×C4×C5C22×D412yes—
258C3×Dic5—24no—
259C3×Dic5—42no—
260C3×Dic5—42no—
261C24×C3—101no—
262C24×C3D2011yescharacteristic
263C3×#41—58no—
264C3×#41—104no—
265C3×#41—104no—
266C3×#41—108no—
267C3×#41—108no—
268C3×#41—104no—
269C2×C3×Q8—52no—
270C2×C3×Q8—52no—
271C2×C3×Q8—104no—
272C2×C3×Q8—101no—
273C2×C3×Q8—101no—
274C2×C3×Q8—104no—
275C2×C3×D4—52no—
276C2×C3×D4—104no—
277C2×C3×D4—108no—
278C2×C3×D4—102no—
279C2×C3×D4—102no—
280C2×C3×D4—101no—
281C22×C3×C4—24no—
282C22×C3×C4—108no—
283C22×C3×C4—101no—
284C22×C3×C4—102no—
285C22×C3×C4—102no—
286C22×C3×C4—101no—
287C22×C3×C4—101no—
288C22×C3×C4D2011yescharacteristic
289C22×C3×C4D2011yescharacteristic
290C22×C3×C4D2011yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D511yescharacteristic
294C3×Q16—108no—
295C3×SD16—108no—
296C3×M16—24no—
297C2×C3×C8C22×D514yes—
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—22no—
305C23×C5—22no—
306C23×C5—41no—
307C23×C5C2×C3×D411yescharacteristic
308C23×C5C2×C3×D411yescharacteristic
309C23×C5C2×C3×D411yescharacteristic
310C22×D5—24no—
311C22×D5—22no—
312C22×D5—42no—
313C22×D5—42no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5C2×C3×D411yescharacteristic
320C2×C4×C5C2×C3×D411yescharacteristic
321C2×C4×C5C2×C3×D411yescharacteristic
322C2×C4×C5C2×C3×D414yes—
323C2×C4×C5C24×C311yescharacteristic
324C22⋊D5—28no—
325C22⋊D5—28no—
326C2×Dic5—24no—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—42no—
331C2×Dic5—42no—
332D20—24no—
333D20—22no—
334D20C2×C3×D414yes—
335C4×D5—28no—
336C4×D5—28no—
337Dic10—24no—
338Dic10—22no—
339Dic10—24no—
340Dic10—42no—
341Dic10C2×C3×D414yes—
342C5×C8—24no—
343C2×#41—52no—
344C2×#41—52no—
345C2×#41—108no—
346C2×#41—101no—
347C2×#41—101no—
348C22×Q8—51no—
349C22×Q8—51no—
350C22×D4—51no—
351C22×D4—101no—
352C23×C4—101no—
353C23×C4C2×C3×D511yescharacteristic
354#137—108no—
355C2×Q16—54no—
356C2×SD16—54no—
357C2×M16C2×C3×D512yescomplemented
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⋊C8C2×C3×D512yes—
368C22⋊C8C2×C3×D512yescomplemented
369C2×C3×C5—22no—
370C2×C3×C5—22no—
371C2×C3×C5—41no—
372C2×C3×C5C2×#12011yescharacteristic
373C2×C3×C5C2×#13711yescharacteristic
374C2×C3×C5#57511yescharacteristic
375C3×D5—44no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3—104no—
380C23×C3—102no—
381C23×C3—202no—
382C23×C3—202no—
383C23×C3C2×D2011yescharacteristic
384C23×C3C2×D2011yescharacteristic
385C23×C3C2×D2011yescharacteristic
386C3×Q8—54no—
387C3×Q8—104no—
388C3×Q8—102no—
389C3×Q8—104no—
390C3×Q8—202no—
391C3×D4—54no—
392C3×D4—104no—
393C3×D4—108no—
394C3×D4—108no—
395C3×D4—102no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—108no—
402C2×C3×C4—104no—
403C2×C3×C4—102no—
404C2×C3×C4—108no—
405C2×C3×C4—102no—
406C2×C3×C4—102no—
407C2×C3×C4—202no—
408C2×C3×C4—202no—
409C2×C3×C4C2×D2011yescharacteristic
410C2×C3×C4C2×D2011yescharacteristic
411C2×C3×C4C2×D2011yescharacteristic
412C2×C3×C4D4×D514yes—
413C2×C3×C4C23×D511yescharacteristic
414C3×C8—24no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—44no—
423C22×C5C3×#12012yes—
424C22×C5C3×#13712yescomplemented
425C22×C5C22×C3×D411yescharacteristic
426C2×D5—24no—
427C2×D5—48no—
428C2×D5—42no—
429C2×D5—42no—
430C4×C5—21no—
431C4×C5—21no—
432C4×C5C3×#12012yes—
433C4×C5C22×C3×D412yes—
434Dic5—24no—
435Dic5—42no—
436Dic5—42no—
437C24—101no—
438C24C3×D2011yescharacteristic
439#41—58no—
440#41—104no—
441#41—104no—
442#41—108no—
443#41—108no—
444#41—104no—
445C2×Q8—52no—
446C2×Q8—52no—
447C2×Q8—104no—
448C2×Q8—101no—
449C2×Q8—101no—
450C2×Q8—104no—
451C2×D4—52no—
452C2×D4—104no—
453C2×D4—108no—
454C2×D4—102no—
455C2×D4—102no—
456C2×D4—101no—
457C22×C4—24no—
458C22×C4—108no—
459C22×C4—101no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4C3×D2011yescharacteristic
465C22×C4C3×D2011yescharacteristic
466C22×C4C3×D2011yescharacteristic
467C22×C4C22×C3×D511yescharacteristic
468C22×C4C22×C3×D511yescharacteristic
469C22×C4C22×C3×D511yescharacteristic
470Q16—108no—
471SD16—108no—
472M16—24no—
473C2×C8C22×C3×D514yes—
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—44no—
489C22×C3—104no—
490C22×C3—208no—
491C22×C3—202no—
492C22×C3—202no—
493C22×C3#402812yes—
494C22×C3#405512yescomplemented
495C22×C3C22×D2011yescharacteristic
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—104no—
499C3×C4—202no—
500C3×C4—202no—
501C3×C4#402812yes—
502C3×C4C2×D4×D512yes—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5C2×C3×#12011yescharacteristic
507C2×C5C2×C3×#13711yescharacteristic
508C2×C5C3×#57511yescharacteristic
509D5—44no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—104no—
514C23—102no—
515C23—202no—
516C23—202no—
517C23C2×C3×D2011yescharacteristic
518C23C2×C3×D2011yescharacteristic
519C23C2×C3×D2011yescharacteristic
520Q8—54no—
521Q8—104no—
522Q8—102no—
523Q8—104no—
524Q8—202no—
525D4—54no—
526D4—104no—
527D4—108no—
528D4—108no—
529D4—102no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—108no—
536C2×C4—104no—
537C2×C4—102no—
538C2×C4—108no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—202no—
542C2×C4—202no—
543C2×C4C2×C3×D2011yescharacteristic
544C2×C4C2×C3×D2011yescharacteristic
545C2×C4C2×C3×D2011yescharacteristic
546C2×C4C3×D4×D514yes—
547C2×C4C23×C3×D511yescharacteristic
548C8—24no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3—204no—
553C2×C3C2×#402811yescharacteristic
554C2×C3C2×#405511yescharacteristic
555C2×C3#6608211yescharacteristic
556C5C3×#300711yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—44no—
565C22—104no—
566C22—208no—
567C22—202no—
568C22—202no—
569C22C3×#402812yes—
570C22C3×#405512yescomplemented
571C22C22×C3×D2011yescharacteristic
572C4—21no—
573C4—21no—
574C4—104no—
575C4—202no—
576C4—202no—
577C4C3×#402812yes—
578C4C2×C3×D4×D512yes—
579C3#1061037111yescharacteristic, direct product factor, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—204no—
584C2C2×C3×#402811yescharacteristic
585C2C2×C3×#405511yescharacteristic
586C2C3×#6608211yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#407C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×#709C2
hypercenterC3×#407D5
hypocenterC5C3×#3007
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4070C2semidirect
3. C2×C3×#4055C2semidirect
4. C3×C5×#407C2semidirect
5. C3×#65422C2semidirect
6. C3×#65028C2semidirect
7. C3×#65022C2semidirect
8. C3×#65020C2semidirect
9. #10610371C3direct (N × H)
20. C22×C3×Dic10C22semidirect
21. C2×C3×C5×M16C22semidirect
23. C2×C3×C4⋊Dic5C22semidirect
27. C3×#4070C22semidirect
30. C2×C3×Dic20C22semidirect
31. C2×C3×#677C22semidirect
33. C3×C5×C22⋊C8C22semidirect
34. C3×#3953C22semidirect
35. C3×#3948C22semidirect
38. C2×#4070C2×C3semidirect
39. C2×#4055C2×C3semidirect
40. C5×#407C2×C3semidirect
41. #65422C2×C3semidirect
42. #65028C2×C3semidirect
43. #65022C2×C3semidirect
44. #65020C2×C3semidirect
95. C3×#407D5semidirect
106. C22×Dic10C22×C3semidirect
107. C2×C5×M16C22×C3semidirect
109. C2×C4⋊Dic5C22×C3semidirect
113. #4070C22×C3semidirect
116. C2×Dic20C22×C3semidirect
117. C2×#677C22×C3semidirect
119. C5×C22⋊C8C22×C3semidirect
120. #3953C22×C3semidirect
121. #3948C22×C3semidirect
176. C2×C3×M16C2×D5semidirect
187. C3×C22⋊C8C2×D5semidirect
238. #407C3×D5semidirect
248. C22×C3×C5#137semidirect
357. C2×M16C2×C3×D5semidirect
368. C22⋊C8C2×C3×D5semidirect
424. C22×C5C3×#137semidirect
480. C3×C5#3007semidirect
494. C22×C3#4055semidirect
556. C5C3×#3007semidirect
570. C22C3×#4055semidirect
579. C3#10610371direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×C3×#40702
C2×C3×#40552
C3×C5×#4072
C3×#654222
C3×#650282
C3×#650222
C3×#650202
#106103713
C3×#30075