Finite Group Databasebeta

← C3×#10601185 #14307990

Subgroups — C3×#10601185 #14307990

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66167C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C2×C3×#4054C211yesmaximal, characteristic, complemented
4C2×C3×C5×#104C211yesmaximal, characteristic, complemented
5C3×#65228C211yesmaximal, characteristic, complemented
6C2×C3×#3937C211yesmaximal, characteristic, complemented
7C3×#64774C211yesmaximal, characteristic, complemented
8#10601185C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C22×C3×D20C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C3×#4095—22no—
15C3×#4095—22no—
16C3×#4092—21no—
17C2×C3×#688—21no—
18C3×#4085—22no—
19C3×#4084—21no—
20C2×C3×#686—21no—
21C3×#4076—21no—
22C2×C3×#685—22no—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C3×#4070—21no—
25C2×C3×#681C2211yescharacteristic
26C3×#4054—22no—
27C3×#4054—22no—
28C2×C3×D40—21no—
29C2×C3×#677—21no—
30C3×C5×#104—22no—
31C3×#3937—22no—
32C3×#2006—51nomaximal, Hall
33#66167C2×C311yescharacteristic, complemented
34C2×#4095C2×C311yescharacteristic, complemented
35C2×#4054C2×C311yescharacteristic, complemented
36C2×C5×#104C2×C311yescharacteristic, complemented
37#65228C2×C311yescharacteristic, complemented
38C2×#3937C2×C311yescharacteristic, complemented
39#64774C2×C311yescharacteristic, complemented
40C23×C3×D5—21no—
41C3×C5×#41—21no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41—21no—
45C2×C3×C5×Q8D411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4D411yescharacteristic
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—22no—
53C22×C3×Dic5D412yes—
54C3×#709—21no—
55C3×#709—21no—
56C3×#709—21no—
57C3×#709—21no—
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20—21no—
63C2×C3×D20D411yescharacteristic
64C2×C3×D20D412yescomplemented
65C2×C3×C4×D5—21no—
66C2×C3×Dic10D411yescharacteristic
67C3×C5×M16—21no—
68C3×C5×M16D412yescomplemented
69C2×C3×C5×C8—21no—
70C3×C42×C5—21no—
71C3×C42×C5—21no—
72C3×C22⋊Dic5—22no—
73C3×#688—24no—
74C3×#686—24no—
75C3×#685—22no—
76C3×#685—44no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5—21no—
79C3×#683—22no—
80C3×#681—21no—
81C3×#681D412yescomplemented
82C2×C3×#168—21no—
83C3×D40—24no—
84C3×#677—24no—
85C2×C3×AGL(1,ℤ/8)—51no—
86C2×C3×AGL(1,ℤ/8)—51no—
87C3×#537—51no—
88C2×C3×#104—51no—
89C2×C3×#104D511yescharacteristic, complemented
90C3×#390—51no—
91C3×#343—51no—
92C2×C5×#41C22×C311yescharacteristic
93C2×#709C22×C311yescharacteristic
94C22×D20C22×C311yescharacteristic
95C2×C5×M16C22×C311yescharacteristic
96C2×C42×C5C22×C311yescharacteristic
97#4095—22no—
98#4095—22no—
99#4092—21no—
100C2×#688—21no—
101#4085—22no—
102#4084—21no—
103C2×#686—21no—
104#4076—21no—
105C2×#685—22no—
106C2×C4⋊Dic5C22×C311yescharacteristic
107#4070—21no—
108C2×#681C22×C311yescharacteristic
109#4054—22no—
110#4054—22no—
111C2×D40—21no—
112C2×#677—21no—
113C5×#104—22no—
114#3937—22no—
115#2006—51noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D411yescharacteristic
118C22×C3×D5—21no—
119C22×C3×D5—22no—
120C22×C3×D5—42no—
121C22×C3×D5—42no—
122C22×C3×D5—41no—
123C22×C3×D5—41no—
124C3×C5×Q8—21no—
125C3×C5×Q8—21no—
126C3×C5×D4—21no—
127C3×C5×D4—21no—
128C3×C5×D4—41no—
129C3×C5×D4—41no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4111yescharacteristic
142C3×C22⋊D5—41no—
143C3×C22⋊D5—41no—
144C3×C22⋊D5—82no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—42no—
148C3×D20—22no—
149C3×D20—21no—
150C3×D20—22no—
151C3×D20—21no—
152C3×D20—41no—
153C3×D20—41no—
154C3×C4×D5—41no—
155C3×C4×D5—41no—
156C3×Dic10—21no—
157C3×Dic10—21no—
158C3×C5×C8—22no—
159C3×#168—22no—
160C2×C3×#41—51no—
161C2×C3×#41C2×D511yescharacteristic
162C22×C3×D4—51no—
163C3×AGL(1,ℤ/8)—102no—
164C3×AGL(1,ℤ/8)—102no—
165C3×AGL(1,ℤ/8)—102no—
166C3×AGL(1,ℤ/8)—102no—
167C2×C3×SD16—101no—
168C2×C3×SD16—101no—
169C2×C3×D8—101no—
170C2×C3×D8—101no—
171C2×C3×M16—51no—
172C2×C3×M16C2×D511yescharacteristic
173C3×C22⋊Q8—101no—
174C3×C22⋊Q8—101no—
175C3×#121—101no—
176C3×#121—102no—
177C3×#121—101no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C22⋊C4—102no—
180C2×C3×C42C2×D511yescharacteristic
181C3×#104—22no—
182C3×#104—102no—
183C23×D5—21no—
184C5×#41—21no—
185C5×#41—21no—
186C5×#41—21no—
187C5×#41—21no—
188C2×C5×Q8C3×D411yescharacteristic
189C2×C5×D4—21no—
190C2×C5×D4C3×D411yescharacteristic
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5C23×C311yescharacteristic
194C2×C22⋊D5—21no—
195C2×C22⋊D5—22no—
196C22×Dic5C3×D412yes—
197#709—21no—
198#709—21no—
199#709—21no—
200#709—21no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20—21no—
204C2×D20—21no—
205C2×D20—21no—
206C2×D20C3×D411yescharacteristic
207C2×D20C3×D412yescomplemented
208C2×C4×D5—21no—
209C2×Dic10C3×D411yescharacteristic
210C5×M16—21no—
211C5×M16C3×D412yescomplemented
212C2×C5×C8—21no—
213C42×C5—21no—
214C42×C5—21no—
215C22⋊Dic5—22no—
216#688—24no—
217#686—24no—
218#685—22no—
219#685—44no—
220C4⋊Dic5—21no—
221C4⋊Dic5—21no—
222#683—22no—
223#681—21no—
224#681C3×D412yescomplemented
225C2×#168—21no—
226D40—24no—
227#677—24no—
228C2×AGL(1,ℤ/8)—51no—
229C2×AGL(1,ℤ/8)—51no—
230#537—51no—
231C2×#104—51no—
232C2×#104C3×D511yescharacteristic, complemented
233#390—51no—
234#343—51no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5#12011yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5#12711yescharacteristic
243C2×C3×D5—44no—
244C2×C3×D5—41no—
245C2×C3×D5—42no—
246C2×C3×D5—41no—
247C2×C3×D5—41no—
248C2×C3×D5—82no—
249C2×C3×D5—81no—
250C2×C3×D5—81no—
251C3×C4×C5—42no—
252C3×C4×C5—41no—
253C3×C4×C5#12011yescharacteristic
254C3×C4×C5#12011yescharacteristic
255C3×C4×C5#12111yescharacteristic
256C3×C4×C5#12111yescharacteristic
257C3×Dic5—41no—
258C3×Dic5—42no—
259C24×C3—101no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—101no—
265C3×#41—101no—
266C3×#41—101no—
267C3×#41—101no—
268C2×C3×Q8—51no—
269C2×C3×Q8D2011yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4—51no—
272C2×C3×D4—52no—
273C2×C3×D4—101no—
274C2×C3×D4—102no—
275C2×C3×D4—101no—
276C2×C3×D4—101no—
277C2×C3×D4—101no—
278C2×C3×D4—101no—
279C2×C3×D4—101no—
280C2×C3×D4D2011yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—52no—
284C22×C3×C4—101no—
285C22×C3×C4C22×D511yescharacteristic
286C3×SD16—104no—
287C3×SD16—104no—
288C3×D8—104no—
289C3×D8—104no—
290C3×M16—21no—
291C3×M16—52no—
292C3×M16—101no—
293C3×M16C22⋊D512yescomplemented
294C2×C3×C8—21no—
295C2×C3×C8—101no—
296C3×C4⋊C4—102no—
297C3×C4⋊C4—101no—
298C3×C4⋊C4—101no—
299C3×C22⋊C4—102no—
300C3×C22⋊C4—102no—
301C3×C22⋊C4—204no—
302C3×C42—21no—
303C3×C42—21no—
304C23×C5—21no—
305C23×C5C2×C3×D411yescharacteristic
306C22×D5—21no—
307C22×D5—22no—
308C22×D5—42no—
309C22×D5—42no—
310C22×D5—41no—
311C22×D5—41no—
312C5×Q8—21no—
313C5×Q8—21no—
314C5×D4—21no—
315C5×D4—21no—
316C5×D4—41no—
317C5×D4—41no—
318C2×C4×C5—22no—
319C2×C4×C5—21no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5C2×C3×D411yescharacteristic
325C2×C4×C5C2×C3×D411yescharacteristic
326C2×C4×C5C2×C3×D411yescharacteristic
327C2×C4×C5C2×C3×D411yescharacteristic
328C2×C4×C5C2×C3×D411yescharacteristic
329C2×C4×C5C3×#4111yescharacteristic
330C22⋊D5—41no—
331C22⋊D5—41no—
332C22⋊D5—82no—
333C2×Dic5—21no—
334C2×Dic5—22no—
335C2×Dic5—42no—
336D20—22no—
337D20—21no—
338D20—22no—
339D20—21no—
340D20—41no—
341D20—41no—
342C4×D5—41no—
343C4×D5—41no—
344Dic10—21no—
345Dic10—21no—
346C5×C8—22no—
347#168—22no—
348C2×#41—51no—
349C2×#41C2×C3×D511yescharacteristic
350C22×D4—51no—
351AGL(1,ℤ/8)—102no—
352AGL(1,ℤ/8)—102no—
353AGL(1,ℤ/8)—102no—
354AGL(1,ℤ/8)—102no—
355C2×SD16—101no—
356C2×SD16—101no—
357C2×D8—101no—
358C2×D8—101no—
359C2×M16—51no—
360C2×M16C2×C3×D511yescharacteristic
361C22⋊Q8—101no—
362C22⋊Q8—101no—
363#121—101no—
364#121—102no—
365#121—101no—
366C2×C4⋊C4—51no—
367C2×C22⋊C4—102no—
368C2×C42C2×C3×D511yescharacteristic
369#104—22no—
370#104—102no—
371C2×C3×C5—21no—
372C2×C3×C5—21no—
373C2×C3×C5—81no—
374C2×C3×C5#39211yescharacteristic
375C2×C3×C5#45311yescharacteristic
376C2×C3×C5#45411yescharacteristic
377C3×D5—81no—
378C3×D5—82no—
379C23×C3—21no—
380C23×C3—101no—
381C23×C3—102no—
382C23×C3—202no—
383C23×C3—202no—
384C23×C3—201no—
385C23×C3—201no—
386C23×C3D4×D511yescharacteristic
387C3×Q8—21no—
388C3×Q8—21no—
389C3×Q8—101no—
390C3×Q8—101no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—102no—
396C3×D4—101no—
397C3×D4—101no—
398C3×D4—102no—
399C3×D4—201no—
400C3×D4—201no—
401C3×D4—201no—
402C3×D4—201no—
403C3×D4—402no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—102no—
411C2×C3×C4—101no—
412C2×C3×C4—201no—
413C2×C3×C4—201no—
414C2×C3×C4—202no—
415C2×C3×C4C2×D2011yescharacteristic
416C2×C3×C4#70911yescharacteristic
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4D4×D511yescharacteristic
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4C2×C22⋊D511yescharacteristic
421C3×C8—22no—
422C3×C8—102no—
423C22×C5—21no—
424C22×C5—21no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5C3×#12011yescharacteristic
429C22×C5C3×#12111yescharacteristic
430C22×C5C3×#12711yescharacteristic
431C2×D5—44no—
432C2×D5—41no—
433C2×D5—42no—
434C2×D5—41no—
435C2×D5—41no—
436C2×D5—82no—
437C2×D5—81no—
438C2×D5—81no—
439C4×C5—42no—
440C4×C5—41no—
441C4×C5C3×#12011yescharacteristic
442C4×C5C3×#12011yescharacteristic
443C4×C5C3×#12111yescharacteristic
444C4×C5C3×#12111yescharacteristic
445Dic5—41no—
446Dic5—42no—
447C24—101no—
448#41—21no—
449#41—21no—
450#41—21no—
451#41—21no—
452#41—101no—
453#41—101no—
454#41—101no—
455#41—101no—
456C2×Q8—51no—
457C2×Q8C3×D2011yescharacteristic
458C2×D4—21no—
459C2×D4—51no—
460C2×D4—52no—
461C2×D4—101no—
462C2×D4—102no—
463C2×D4—101no—
464C2×D4—101no—
465C2×D4—101no—
466C2×D4—101no—
467C2×D4—101no—
468C2×D4C3×D2011yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—52no—
472C22×C4—101no—
473C22×C4C22×C3×D511yescharacteristic
474SD16—104no—
475SD16—104no—
476D8—104no—
477D8—104no—
478M16—21no—
479M16—52no—
480M16—101no—
481M16C3×C22⋊D512yescomplemented
482C2×C8—21no—
483C2×C8—101no—
484C4⋊C4—102no—
485C4⋊C4—101no—
486C4⋊C4—101no—
487C22⋊C4—102no—
488C22⋊C4—102no—
489C22⋊C4—204no—
490C42—21no—
491C42—21no—
492C3×C5#200611yescharacteristic, complemented, Hall
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—204no—
499C22×C3—201no—
500C22×C3—201no—
501C22×C3—201no—
502C22×C3—202no—
503C22×C3—402no—
504C22×C3—401no—
505C22×C3—401no—
506C22×C3#402811yescharacteristic
507C22×C3#403011yescharacteristic
508C22×C3#408611yescharacteristic
509C3×C4—42no—
510C3×C4—41no—
511C3×C4—202no—
512C3×C4—201no—
513C3×C4#402811yescharacteristic
514C3×C4#403011yescharacteristic
515C3×C4#407611yescharacteristic
516C3×C4#408311yescharacteristic
517C2×C5—21no—
518C2×C5—21no—
519C2×C5—81no—
520C2×C5C3×#39211yescharacteristic
521C2×C5C3×#45311yescharacteristic
522C2×C5C3×#45411yescharacteristic
523D5—82no—
524D5—81no—
525C23—21no—
526C23—101no—
527C23—102no—
528C23—202no—
529C23—202no—
530C23—201no—
531C23—201no—
532C23C3×D4×D511yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—101no—
536Q8—101no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—101no—
542D4—102no—
543D4—102no—
544D4—101no—
545D4—201no—
546D4—201no—
547D4—201no—
548D4—201no—
549D4—402no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—102no—
557C2×C4—101no—
558C2×C4—201no—
559C2×C4—201no—
560C2×C4—202no—
561C2×C4C2×C3×D2011yescharacteristic
562C2×C4C3×#70911yescharacteristic
563C2×C4C3×D4×D511yescharacteristic
564C2×C4C3×D4×D511yescharacteristic
565C2×C4C3×D4×D511yescharacteristic
566C2×C4C2×C3×C22⋊D511yescharacteristic
567C8—22no—
568C8—102no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—81no—
572C2×C3—402no—
573C2×C3—401no—
574C2×C3#6511111yescharacteristic
575C2×C3#6511611yescharacteristic
576C2×C3#6524911yescharacteristic
577C5C3×#200611yescharacteristic, complemented, Sylow
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—204no—
584C22—201no—
585C22—201no—
586C22—201no—
587C22—202no—
588C22—402no—
589C22—401no—
590C22—401no—
591C22C3×#402811yescharacteristic
592C22C3×#403011yescharacteristic
593C22C3×#408611yescharacteristic
594C4—42no—
595C4—41no—
596C4—202no—
597C4—201no—
598C4C3×#402811yescharacteristic
599C4C3×#403011yescharacteristic
600C4C3×#407611yescharacteristic
601C4C3×#408311yescharacteristic
602C3#1060118511yescharacteristic, direct product factor, Sylow
603C2—21no—
604C2—21no—
605C2—81no—
606C2—402no—
607C2—401no—
608C2C3×#6511111yescharacteristic
609C2C3×#6511611yescharacteristic
610C2C3×#6524911yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
hypercenterC2×C3×#104D5
hypocenterC5C3×#2006
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
1. C3×#66167C2semidirect
2. C2×C3×#4095C2semidirect
3. C2×C3×#4054C2semidirect
4. C2×C3×C5×#104C2semidirect
5. C3×#65228C2semidirect
6. C2×C3×#3937C2semidirect
7. C3×#64774C2semidirect
8. #10601185C3direct (N × H)
33. #66167C2×C3semidirect
34. C2×#4095C2×C3semidirect
35. C2×#4054C2×C3semidirect
36. C2×C5×#104C2×C3semidirect
37. #65228C2×C3semidirect
38. C2×#3937C2×C3semidirect
39. #64774C2×C3semidirect
64. C2×C3×D20D4semidirect
68. C3×C5×M16D4semidirect
81. C3×#681D4semidirect
89. C2×C3×#104D5semidirect
207. C2×D20C3×D4semidirect
211. C5×M16C3×D4semidirect
224. #681C3×D4semidirect
232. C2×#104C3×D5semidirect
293. C3×M16C22⋊D5semidirect
481. M16C3×C22⋊D5semidirect
492. C3×C5#2006semidirect
577. C5C3×#2006semidirect
602. C3#10601185direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661672
C2×C3×#40952
C2×C3×#40542
C2×C3×C5×#1042
C3×#652282
C2×C3×#39372
C3×#647742
#106011853
C3×#20065