Finite Group Databasebeta

← C3×#10599785 #14302141

Subgroups — C3×#10599785 #14302141

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×M16C211yesmaximal, characteristic, complemented
2C2×C3×#4041C211yesmaximal, characteristic
3C2×C3×#3955C211yesmaximal, characteristic, complemented
4C2×C3×#3955C211yesmaximal, characteristic, complemented
5C3×#65415C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7C3×#64750C211yesmaximal, characteristic, complemented
8#10599785C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C412yes—
10C22×C3×D20C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×#685C412yes—
16C2×C3×#681C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18C3×D5×M16—22no—
19C3×D5×M16—22no—
20C2×C3×#676—21no—
21C2×C3×C8×D5—21no—
22C3×#4041—21no—
23C3×#4041—21no—
24C3×#4041—21no—
25C3×#4041—21no—
26C3×#3955—22no—
27C3×#3955—22no—
28C3×#3952—21no—
29C3×#3952—21no—
30C3×#1900—51nomaximal, Hall
31C2×D5×M16C2×C311yescharacteristic, complemented
32C2×#4041C2×C311yescharacteristic
33C2×#3955C2×C311yescharacteristic, complemented
34C2×#3955C2×C311yescharacteristic, complemented
35#65415C2×C311yescharacteristic, complemented
36C5×#343C2×C311yescharacteristic, complemented
37#64750C2×C311yescharacteristic, complemented
38C23×C3×D5C2×C411yescharacteristic
39C23×C3×D5C2×C412yes—
40C22×C3×C4×C5C2×C412yes—
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×D20—22no—
44C2×C3×D20—22no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20—44no—
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5D411yescharacteristic
57C2×C3×C4×D5D411yescharacteristic
58C2×C3×C4×D5D411yescharacteristic
59C2×C3×C4×D5D411yescharacteristic
60C3×C5×M16—21no—
61C3×C5×M16—21no—
62C3×C5×M16—21no—
63C3×C5×M16D412yescomplemented
64C2×C3×C5×C8—21no—
65C2×C3×C5×C8—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4—21no—
68C3×#685—22no—
69C3×#685—22no—
70C3×#681—21no—
71C3×#681—21no—
72C3×#681—21no—
73C3×#681D412yescomplemented
74C2×C3×#168—21no—
75C2×C3×#168—21no—
76C3×#676—24no—
77C3×C8×D5—24no—
78C22×C3×M16—51no—
79C2×C3×#121—51no—
80C2×C3×#100—51no—
81C2×C3×#100—51no—
82C3×#407—51no—
83C3×#343—51no—
84C3×#343D511yescharacteristic, complemented
85C22×D20C3×C412yes—
86C22×D20C22×C311yescharacteristic
87C22×C4×D5C22×C311yescharacteristic
88C2×C5×M16C22×C311yescharacteristic
89C2×C5×M16C22×C311yescharacteristic
90C2×C5×C4⋊C4C22×C311yescharacteristic
91C2×#685C3×C412yes—
92C2×#681C22×C311yescharacteristic
93C2×#681C22×C311yescharacteristic
94D5×M16—22no—
95D5×M16—22no—
96C2×#676—21no—
97C2×C8×D5—21no—
98#4041—21no—
99#4041—21no—
100#4041—21no—
101#4041—21no—
102#3955—22no—
103#3955—22no—
104#3952—21no—
105#3952—21no—
106#1900—51noSylow
107C23×C3×C5C22×C411yescharacteristic
108C22×C3×D5—21no—
109C22×C3×D5—21no—
110C22×C3×D5—22no—
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—41no—
115C22×C3×D5—42no—
116C22×C3×D5—42no—
117C22×C3×D5C22⋊C411yescharacteristic
118C22×C3×D5C22⋊C411yescharacteristic
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127C2×C3×Dic5—21no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5C22⋊C411yescharacteristic
130C2×C3×Dic5C22⋊C411yescharacteristic
131C3×D20—44no—
132C3×D20—44no—
133C3×D20—41no—
134C3×D20—41no—
135C3×D20—41no—
136C3×D20—41no—
137C3×C4×D5—21no—
138C3×C4×D5—21no—
139C3×C4×D5—21no—
140C3×C4×D5—21no—
141C3×C4×D5—21no—
142C3×C4×D5—21no—
143C3×C4×D5—21no—
144C3×C4×D5—21no—
145C3×C5×C8—22no—
146C3×C5×C8—41no—
147C3×#168—22no—
148C3×#168—41no—
149C22×C3×D4—52no—
150C22×C3×D4—51no—
151C23×C3×C4—51no—
152C2×C3×M16—51no—
153C2×C3×M16—51no—
154C2×C3×M16—101no—
155C2×C3×M16—102no—
156C2×C3×M16—102no—
157C2×C3×M16C2×D511yescharacteristic
158C2×C3×M16C2×D511yescharacteristic
159C22×C3×C8—101no—
160C3×#121—101no—
161C3×#121—101no—
162C3×#121—101no—
163C3×#121—101no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×C3×C22⋊C4—52no—
166C3×#100—102no—
167C3×#100—102no—
168C3×C22⋊C8—101no—
169C3×C22⋊C8—101no—
170C23×D5C2×C3×C411yescharacteristic
171C23×D5C2×C3×C412yes—
172C22×C4×C5C2×C3×C412yes—
173C22×C4×C5C23×C311yescharacteristic
174C22×Dic5C2×C3×C411yescharacteristic
175C2×D20—22no—
176C2×D20—22no—
177C2×D20—21no—
178C2×D20—21no—
179C2×D20—21no—
180C2×D20—21no—
181C2×D20—21no—
182C2×D20—21no—
183C2×D20—44no—
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×C4×D5—21no—
187C2×C4×D5—21no—
188C2×C4×D5C3×D411yescharacteristic
189C2×C4×D5C3×D411yescharacteristic
190C2×C4×D5C3×D411yescharacteristic
191C2×C4×D5C3×D411yescharacteristic
192C5×M16—21no—
193C5×M16—21no—
194C5×M16—21no—
195C5×M16C3×D412yescomplemented
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200#685—22no—
201#685—22no—
202#681—21no—
203#681—21no—
204#681—21no—
205#681C3×D412yescomplemented
206C2×#168—21no—
207C2×#168—21no—
208#676—24no—
209C8×D5—24no—
210C22×M16—51no—
211C2×#121—51no—
212C2×#100—51no—
213C2×#100—51no—
214#407—51no—
215#343—51no—
216#343C3×D511yescharacteristic, complemented
217C22×C3×C5—21no—
218C22×C3×C5—21no—
219C22×C3×C5C2×C22⋊C411yescharacteristic
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5C4×D411yescharacteristic
222C2×C3×D5—21no—
223C2×C3×D5—21no—
224C2×C3×D5—21no—
225C2×C3×D5—21no—
226C2×C3×D5—21no—
227C2×C3×D5—42no—
228C2×C3×D5—42no—
229C2×C3×D5—42no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—82no—
233C2×C3×D5—82no—
234C2×C3×D5#10012yescomplemented
235C3×C4×C5—42no—
236C3×C4×C5#12011yescharacteristic
237C3×C4×C5#12111yescharacteristic
238C3×C4×C5#12111yescharacteristic
239C3×C4×C5#12311yescharacteristic
240C3×Dic5—21no—
241C3×Dic5—21no—
242C24×C3—51no—
243C24×C3—52no—
244C2×C3×D4—102no—
245C2×C3×D4—102no—
246C2×C3×D4—101no—
247C2×C3×D4—101no—
248C2×C3×D4—101no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×C3×D4—101no—
252C2×C3×D4—204no—
253C22×C3×C4—51no—
254C22×C3×C4—51no—
255C22×C3×C4—51no—
256C22×C3×C4—51no—
257C22×C3×C4—51no—
258C22×C3×C4—101no—
259C22×C3×C4—101no—
260C22×C3×C4—101no—
261C22×C3×C4—101no—
262C22×C3×C4C4×D512yes—
263C22×C3×C4C22×D511yescharacteristic
264C3×M16—21no—
265C3×M16—21no—
266C3×M16—21no—
267C3×M16—52no—
268C3×M16—104no—
269C3×M16—101no—
270C3×M16—101no—
271C3×M16—101no—
272C3×M16D2012yescomplemented
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—104no—
276C2×C3×C8—101no—
277C2×C3×C8—101no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C22⋊C4—102no—
281C3×C22⋊C4—102no—
282C23×C5C22×C3×C411yescharacteristic
283C22×D5—21no—
284C22×D5—21no—
285C22×D5—22no—
286C22×D5—22no—
287C22×D5—22no—
288C22×D5—22no—
289C22×D5—41no—
290C22×D5—42no—
291C22×D5—42no—
292C22×D5C3×C22⋊C411yescharacteristic
293C22×D5C3×C22⋊C411yescharacteristic
294C2×C4×C5—22no—
295C2×C4×C5—42no—
296C2×C4×C5C2×C3×D411yescharacteristic
297C2×C4×C5C2×C3×D411yescharacteristic
298C2×C4×C5C2×C3×D411yescharacteristic
299C2×C4×C5C2×C3×D411yescharacteristic
300C2×C4×C5C3×#4111yescharacteristic
301C2×C4×C5C3×#4111yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5C3×C22⋊C411yescharacteristic
305C2×Dic5C3×C22⋊C411yescharacteristic
306D20—44no—
307D20—44no—
308D20—41no—
309D20—41no—
310D20—41no—
311D20—41no—
312C4×D5—21no—
313C4×D5—21no—
314C4×D5—21no—
315C4×D5—21no—
316C4×D5—21no—
317C4×D5—21no—
318C4×D5—21no—
319C4×D5—21no—
320C5×C8—22no—
321C5×C8—41no—
322#168—22no—
323#168—41no—
324C22×D4—52no—
325C22×D4—51no—
326C23×C4—51no—
327C2×M16—51no—
328C2×M16—51no—
329C2×M16—101no—
330C2×M16—102no—
331C2×M16—102no—
332C2×M16C2×C3×D511yescharacteristic
333C2×M16C2×C3×D511yescharacteristic
334C22×C8—101no—
335#121—101no—
336#121—101no—
337#121—101no—
338#121—101no—
339C2×C4⋊C4C2×C3×D511yescharacteristic
340C2×C22⋊C4—52no—
341#100—102no—
342#100—102no—
343C22⋊C8—101no—
344C22⋊C8—101no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5#38611yescharacteristic
348C2×C3×C5C2×#10011yescharacteristic
349C2×C3×C5#41311yescharacteristic
350C3×D5—22no—
351C3×D5—41no—
352C3×D5—82no—
353C23×C3—51no—
354C23×C3—51no—
355C23×C3—102no—
356C23×C3—101no—
357C23×C3—101no—
358C23×C3—102no—
359C23×C3—102no—
360C23×C3—102no—
361C23×C3—201no—
362C23×C3—202no—
363C23×C3—202no—
364C23×C3C2×C4×D511yescharacteristic
365C3×D4—204no—
366C3×D4—204no—
367C3×D4—201no—
368C3×D4—201no—
369C3×D4—201no—
370C3×D4—201no—
371C2×C3×C4—22no—
372C2×C3×C4—42no—
373C2×C3×C4—51no—
374C2×C3×C4—51no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—101no—
379C2×C3×C4—101no—
380C2×C3×C4—101no—
381C2×C3×C4—101no—
382C2×C3×C4—101no—
383C2×C3×C4—101no—
384C2×C3×C4—101no—
385C2×C3×C4C2×D2011yescharacteristic
386C2×C3×C4#70911yescharacteristic
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4#71311yescharacteristic
391C3×C8—22no—
392C3×C8—41no—
393C3×C8—102no—
394C3×C8—201no—
395C22×C5—21no—
396C22×C5—21no—
397C22×C5C2×C3×C22⋊C411yescharacteristic
398C22×C5C3×C4×D411yescharacteristic
399C22×C5C3×C4×D411yescharacteristic
400C2×D5—21no—
401C2×D5—21no—
402C2×D5—21no—
403C2×D5—21no—
404C2×D5—21no—
405C2×D5—42no—
406C2×D5—42no—
407C2×D5—42no—
408C2×D5—42no—
409C2×D5—42no—
410C2×D5—82no—
411C2×D5—82no—
412C2×D5C3×#10012yescomplemented
413C4×C5—42no—
414C4×C5C3×#12011yescharacteristic
415C4×C5C3×#12111yescharacteristic
416C4×C5C3×#12111yescharacteristic
417C4×C5C3×#12311yescharacteristic
418Dic5—21no—
419Dic5—21no—
420C24—51no—
421C24—52no—
422C2×D4—102no—
423C2×D4—102no—
424C2×D4—101no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—204no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4C3×C4×D512yes—
441C22×C4C22×C3×D511yescharacteristic
442M16—21no—
443M16—21no—
444M16—21no—
445M16—52no—
446M16—104no—
447M16—101no—
448M16—101no—
449M16—101no—
450M16C3×D2012yescomplemented
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—104no—
454C2×C8—101no—
455C2×C8—101no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C22⋊C4—102no—
459C22⋊C4—102no—
460C3×C5#190011yescharacteristic, complemented, Hall
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—52no—
464C22×C3—101no—
465C22×C3—101no—
466C22×C3—101no—
467C22×C3—101no—
468C22×C3—101no—
469C22×C3—202no—
470C22×C3—202no—
471C22×C3—202no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—402no—
475C22×C3—402no—
476C22×C3C4×D2011yescharacteristic
477C22×C3D5×C22⋊C411yescharacteristic
478C22×C3#403911yescharacteristic
479C3×C4—42no—
480C3×C4—101no—
481C3×C4—101no—
482C3×C4#402811yescharacteristic
483C3×C4#403011yescharacteristic
484C3×C4#404011yescharacteristic
485C3×C4#404111yescharacteristic
486C2×C5—21no—
487C2×C5—21no—
488C2×C5C3×#38611yescharacteristic
489C2×C5C2×C3×#10011yescharacteristic
490C2×C5C3×#41311yescharacteristic
491D5—22no—
492D5—41no—
493D5—82no—
494C23—51no—
495C23—51no—
496C23—102no—
497C23—101no—
498C23—101no—
499C23—102no—
500C23—102no—
501C23—102no—
502C23—201no—
503C23—202no—
504C23—202no—
505C23C2×C3×C4×D511yescharacteristic
506D4—204no—
507D4—204no—
508D4—201no—
509D4—201no—
510D4—201no—
511D4—201no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—51no—
515C2×C4—51no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4C2×C3×D2011yescharacteristic
527C2×C4C3×#70911yescharacteristic
528C2×C4C3×D4×D511yescharacteristic
529C2×C4C3×D4×D511yescharacteristic
530C2×C4C3×D4×D511yescharacteristic
531C2×C4C3×#71311yescharacteristic
532C8—22no—
533C8—41no—
534C8—102no—
535C8—201no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—102no—
539C2×C3—201no—
540C2×C3—402no—
541C2×C3#6495411yescharacteristic
542C2×C3D5×#10011yescharacteristic
543C2×C3#6504011yescharacteristic
544C5C3×#190011yescharacteristic, complemented, Sylow
545C22—21no—
546C22—21no—
547C22—52no—
548C22—101no—
549C22—101no—
550C22—101no—
551C22—101no—
552C22—101no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—202no—
557C22—202no—
558C22—402no—
559C22—402no—
560C22C3×C4×D2011yescharacteristic
561C22C3×D5×C22⋊C411yescharacteristic
562C22C3×#403911yescharacteristic
563C4—42no—
564C4—101no—
565C4—101no—
566C4C3×#402811yescharacteristic
567C4C3×#403011yescharacteristic
568C4C3×#404011yescharacteristic
569C4C3×#404111yescharacteristic
570C3#1059978511yescharacteristic, direct product factor, Sylow
571C2—21no—
572C2—21no—
573C2—102no—
574C2—201no—
575C2—402no—
576C2C3×#6495411yescharacteristic
577C2C3×D5×#10011yescharacteristic
578C2C3×#6504011yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#343C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4041C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#343D5
hypocenterC5C3×#1900
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×M16C2semidirect
3. C2×C3×#3955C2semidirect
4. C2×C3×#3955C2semidirect
5. C3×#65415C2semidirect
6. C3×C5×#343C2semidirect
7. C3×#64750C2semidirect
8. #10599785C3direct (N × H)
31. C2×D5×M16C2×C3semidirect
33. C2×#3955C2×C3semidirect
34. C2×#3955C2×C3semidirect
35. #65415C2×C3semidirect
36. C5×#343C2×C3semidirect
37. #64750C2×C3semidirect
63. C3×C5×M16D4semidirect
73. C3×#681D4semidirect
84. C3×#343D5semidirect
195. C5×M16C3×D4semidirect
205. #681C3×D4semidirect
216. #343C3×D5semidirect
234. C2×C3×D5#100semidirect
272. C3×M16D20semidirect
412. C2×D5C3×#100semidirect
450. M16C3×D20semidirect
460. C3×C5#1900semidirect
544. C5C3×#1900semidirect
570. C3#10599785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×M162
C2×C3×#40412
C2×C3×#39552
C3×#654152
C3×C5×#3432
C3×#647502
#105997853
C3×#19005