Finite Group Databasebeta

← C3×#10600391 #14297132

Subgroups — C3×#10600391 #14297132

Order 1920.

1340 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
1C2×C3×#4144C211yesmaximal, characteristic
2C3×C5×#386C211yesmaximal, characteristic, complemented
3C2×C3×#3966C211yesmaximal, characteristic, complemented
4C3×#65502C212yesmaximal, complemented
5C2×C3×#3938C212yesmaximal, complemented
6#10600391C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic, complemented
9C22×C3×C22⋊D5—21no—
10C22×C3×C22⋊D5C2212yes—
11C3×#4144—22no—
12C3×#4144—24no—
13C3×#4144C414yescomplemented
14C2×C3×#711—22no—
15C2×C3×D4×D5—22no—
16C2×C3×#709—21no—
17C2×C3×C5×C22⋊C4—21no—
18C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
19C2×C3×C22⋊Dic5C2212yescomplemented
20C2×C3×#685—22no—
21C3×C5×#95—21no—
22C3×#3966—22no—
23C3×#3963—22no—
24C3×#3938—24no—
25C3×#1790—51nomaximal, Hall
26C2×#4144C2×C311yescharacteristic
27C5×#386C2×C311yescharacteristic, complemented
28C2×#3966C2×C311yescharacteristic, complemented
29#65502C2×C312yescomplemented
30C2×#3938C2×C312yescomplemented
31C24×C3×C5D411yescharacteristic
32C24×C3×C5C2311yescharacteristic
33C23×C3×D5—21no—
34C23×C3×D5D412yes—
35C2×C3×C5×D4—22no—
36C2×C3×C5×D4—22no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—42no—
43C22×C3×C4×C5D411yescharacteristic
44C2×C3×C22⋊D5—22no—
45C2×C3×C22⋊D5—24no—
46C2×C3×C22⋊D5—24no—
47C2×C3×C22⋊D5—22no—
48C2×C3×C22⋊D5—22no—
49C2×C3×C22⋊D5—22no—
50C2×C3×C22⋊D5—22no—
51C2×C3×C22⋊D5C2×C414yes—
52C2×C3×C22⋊D5D414yes—
53C22×C3×Dic5—21no—
54C22×C3×Dic5—22no—
55C22×C3×Dic5D412yes—
56C3×#711—28no—
57C3×#711—28no—
58C3×D4×D5—28no—
59C3×D4×D5—28no—
60C3×#709—24no—
61C3×#709—24no—
62C2×C3×D20—21no—
63C2×C3×C4×D5—22no—
64C2×C3×Dic10—21no—
65C3×C5×C22⋊C4—22no—
66C3×C5×C22⋊C4—42no—
67C3×C22⋊Dic5—22no—
68C3×C22⋊Dic5—22no—
69C3×#685—44no—
70C2×C3×H(5,𝔽2)—51no—
71C2×C3×#99—51no—
72C2×C3×#99—52no—
73C3×#386—52no—
74C3×#386D511yescharacteristic, complemented
75C22×C5×D4C22×C311yescharacteristic
76C23×C4×C5C22×C311yescharacteristic, complemented
77C22×C22⋊D5—21no—
78C22×C22⋊D5C22×C312yes—
79#4144—22no—
80#4144—24no—
81#4144C3×C414yescomplemented
82C2×#711—22no—
83C2×D4×D5—22no—
84C2×#709—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
87C2×C22⋊Dic5C22×C312yescomplemented
88C2×#685—22no—
89C5×#95—21no—
90#3966—22no—
91#3963—22no—
92#3938—24no—
93#1790—51noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5C22⋊C412yescomplemented
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D412yes—
103C23×C3×C5C2×D411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D412yes—
106C22×C3×D5—22no—
107C22×C3×D5—24no—
108C22×C3×D5—22no—
109C22×C3×D5—42no—
110C22×C3×D5—42no—
111C22×C3×D5—81no—
112C22×C3×D5—81no—
113C22×C3×D5C22⋊C414yescomplemented
114C3×C5×D4—24no—
115C3×C5×D4—24no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—24no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5C22⋊C412yescomplemented
127C3×C22⋊D5—28no—
128C3×C22⋊D5—24no—
129C3×C22⋊D5—24no—
130C3×C22⋊D5—24no—
131C3×C22⋊D5—24no—
132C2×C3×Dic5—24no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—42no—
136C2×C3×Dic5—42no—
137C2×C3×Dic5—42no—
138C2×C3×Dic5C22⋊C414yescomplemented
139C3×D20—24no—
140C3×C4×D5—28no—
141C3×Dic10—24no—
142C3×H(5,𝔽2)—54no—
143C3×H(5,𝔽2)—104no—
144C3×H(5,𝔽2)—102no—
145C2×C3×#41—102no—
146C2×C3×#41—101no—
147C22×C3×D4—52no—
148C22×C3×D4—102no—
149C22×C3×D4—101no—
150C22×C3×D4C2×D511yescharacteristic
151C23×C3×C4C2×D511yescharacteristic, complemented
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—52no—
154C2×C3×C22⋊C4—102no—
155C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
156C3×#99—104no—
157C3×#99—102no—
158C3×#95—21no—
159C3×#95—102no—
160C24×C5C3×D411yescharacteristic
161C24×C5C23×C311yescharacteristic
162C23×D5—21no—
163C23×D5C3×D412yes—
164C2×C5×D4—22no—
165C2×C5×D4—22no—
166C2×C5×D4C2×C3×C412yes—
167C2×C5×D4C3×D412yes—
168C22×C4×C5—21no—
169C22×C4×C5—22no—
170C22×C4×C5—21no—
171C22×C4×C5—42no—
172C22×C4×C5C3×D411yescharacteristic
173C2×C22⋊D5—22no—
174C2×C22⋊D5—24no—
175C2×C22⋊D5—24no—
176C2×C22⋊D5—22no—
177C2×C22⋊D5—22no—
178C2×C22⋊D5—22no—
179C2×C22⋊D5—22no—
180C2×C22⋊D5C2×C3×C414yes—
181C2×C22⋊D5C3×D414yes—
182C22×Dic5—21no—
183C22×Dic5—22no—
184C22×Dic5C3×D412yes—
185#711—28no—
186#711—28no—
187D4×D5—28no—
188D4×D5—28no—
189#709—24no—
190#709—24no—
191C2×D20—21no—
192C2×C4×D5—22no—
193C2×Dic10—21no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—42no—
196C22⋊Dic5—22no—
197C22⋊Dic5—22no—
198#685—44no—
199C2×H(5,𝔽2)—51no—
200C2×#99—51no—
201C2×#99—52no—
202#386—52no—
203#386C3×D511yescharacteristic, complemented
204C22×C3×C5—22no—
205C22×C3×C5—21no—
206C22×C3×C5—22no—
207C22×C3×C5—21no—
208C22×C3×C5—22no—
209C22×C3×C5—41no—
210C22×C3×C5—41no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—81no—
216C22×C3×C5C2×C22⋊C412yes—
217C22×C3×C5C2×C22⋊C411yescharacteristic
218C22×C3×C5#12012yes—
219C22×C3×C5#12011yescharacteristic
220C22×C3×C5#12011yescharacteristic
221C2×C3×D5—24no—
222C2×C3×D5—42no—
223C2×C3×D5—42no—
224C2×C3×D5—44no—
225C2×C3×D5—82no—
226C2×C3×D5—84no—
227C3×C4×C5—22no—
228C3×C4×C5—42no—
229C3×C4×C5—81no—
230C3×Dic5—24no—
231C3×Dic5—82no—
232C24×C3—52no—
233C24×C3—101no—
234C24×C3C22⋊D511yescharacteristic
235C24×C3C22×D511yescharacteristic
236C3×#41—104no—
237C3×#41—108no—
238C3×#41—108no—
239C3×#41—104no—
240C2×C3×Q8—101no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—54no—
244C2×C3×D4—54no—
245C2×C3×D4—101no—
246C2×C3×D4—108no—
247C2×C3×D4—108no—
248C2×C3×D4—102no—
249C2×C3×D4—104no—
250C2×C3×D4—104no—
251C2×C3×D4—102no—
252C2×C3×D4—102no—
253C2×C3×D4—102no—
254C2×C3×D4—102no—
255C2×C3×D4C4×D512yes—
256C2×C3×D4D2012yes—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—42no—
261C22×C3×C4—52no—
262C22×C3×C4—102no—
263C22×C3×C4—101no—
264C22×C3×C4—102no—
265C22×C3×C4C22⋊D511yescharacteristic
266C3×C22⋊C4—22no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—102no—
269C3×C22⋊C4—102no—
270C3×C22⋊C4—204no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5C3×C22⋊C412yescomplemented
278C23×C5C22×C3×C411yescharacteristic
279C23×C5C2×C3×D411yescharacteristic
280C23×C5C2×C3×D412yes—
281C23×C5C2×C3×D412yes—
282C23×C5C2×C3×D411yescharacteristic
283C22×D5—22no—
284C22×D5—24no—
285C22×D5—22no—
286C22×D5—42no—
287C22×D5—42no—
288C22×D5—81no—
289C22×D5—81no—
290C22×D5C3×C22⋊C414yescomplemented
291C5×D4—24no—
292C5×D4—24no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—24no—
296C2×C4×C5—22no—
297C2×C4×C5—42no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5C3×C22⋊C412yescomplemented
304C22⋊D5—28no—
305C22⋊D5—24no—
306C22⋊D5—24no—
307C22⋊D5—24no—
308C22⋊D5—24no—
309C2×Dic5—24no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—42no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5C3×C22⋊C414yescomplemented
316D20—24no—
317C4×D5—28no—
318Dic10—24no—
319H(5,𝔽2)—54no—
320H(5,𝔽2)—104no—
321H(5,𝔽2)—102no—
322C2×#41—102no—
323C2×#41—101no—
324C22×D4—52no—
325C22×D4—102no—
326C22×D4—101no—
327C22×D4C2×C3×D511yescharacteristic
328C23×C4C2×C3×D511yescharacteristic, complemented
329C2×C22⋊C4—21no—
330C2×C22⋊C4—52no—
331C2×C22⋊C4—102no—
332C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
333#99—104no—
334#99—102no—
335#95—21no—
336#95—102no—
337C2×C3×C5—22no—
338C2×C3×C5—21no—
339C2×C3×C5—22no—
340C2×C3×C5—21no—
341C2×C3×C5—42no—
342C2×C3×C5#37911yescharacteristic
343C2×C3×C5B(4,𝔽2)11yescharacteristic
344C2×C3×C5#45811yescharacteristic
345C3×D5—44no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—54no—
353C23×C3—104no—
354C23×C3—102no—
355C23×C3—102no—
356C23×C3—202no—
357C23×C3—202no—
358C23×C3—401no—
359C23×C3—401no—
360C23×C3#68512yescomplemented
361C23×C3C2×C4×D511yescharacteristic
362C23×C3C2×D2011yescharacteristic
363C23×C3D4×D512yes—
364C23×C3D4×D512yes—
365C23×C3C2×C22⋊D511yescharacteristic
366C3×Q8—104no—
367C3×D4—24no—
368C3×D4—24no—
369C3×D4—104no—
370C3×D4—108no—
371C3×D4—104no—
372C3×D4—104no—
373C3×D4—104no—
374C3×D4—104no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—54no—
386C2×C3×C4—108no—
387C2×C3×C4—104no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—202no—
391C2×C3×C4—202no—
392C2×C3×C4—202no—
393C2×C3×C4#68512yescomplemented
394C22×C5—22no—
395C22×C5—21no—
396C22×C5—22no—
397C22×C5—21no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—42no—
402C22×C5—42no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—81no—
406C22×C5C2×C3×C22⋊C412yes—
407C22×C5C2×C3×C22⋊C411yescharacteristic
408C22×C5C3×#12011yescharacteristic
409C22×C5C3×#12011yescharacteristic
410C22×C5C3×#12012yes—
411C2×D5—24no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—44no—
415C2×D5—82no—
416C2×D5—84no—
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—81no—
420Dic5—24no—
421Dic5—82no—
422C24—52no—
423C24—101no—
424C24C3×C22⋊D511yescharacteristic
425C24C22×C3×D511yescharacteristic
426#41—104no—
427#41—108no—
428#41—108no—
429#41—104no—
430C2×Q8—101no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—54no—
434C2×D4—54no—
435C2×D4—101no—
436C2×D4—108no—
437C2×D4—108no—
438C2×D4—102no—
439C2×D4—104no—
440C2×D4—104no—
441C2×D4—102no—
442C2×D4—102no—
443C2×D4—102no—
444C2×D4—102no—
445C2×D4C3×C4×D512yes—
446C2×D4C3×D2012yes—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—52no—
452C22×C4—102no—
453C22×C4—101no—
454C22×C4—102no—
455C22×C4C3×C22⋊D511yescharacteristic
456C22⋊C4—22no—
457C22⋊C4—42no—
458C22⋊C4—102no—
459C22⋊C4—102no—
460C22⋊C4—204no—
461C3×C5#179011yescharacteristic, complemented, Hall
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—81no—
474C22×C3—104no—
475C22×C3—204no—
476C22×C3—202no—
477C22×C3—202no—
478C22×C3—402no—
479C22×C3—404no—
480C22×C3D5×C22⋊C412yes—
481C22×C3#402812yes—
482C22×C3C2×#68511yescharacteristic
483C22×C3#408311yescharacteristic
484C22×C3#408311yescharacteristic
485C3×C4—22no—
486C3×C4—42no—
487C3×C4—81no—
488C3×C4—104no—
489C3×C4—402no—
490C2×C5—22no—
491C2×C5—21no—
492C2×C5—22no—
493C2×C5—21no—
494C2×C5—42no—
495C2×C5C3×#37911yescharacteristic
496C2×C5C3×B(4,𝔽2)11yescharacteristic
497C2×C5C3×#45811yescharacteristic
498D5—44no—
499C23—21no—
500C23—21no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—54no—
506C23—104no—
507C23—102no—
508C23—102no—
509C23—202no—
510C23—202no—
511C23—401no—
512C23—401no—
513C23C3×#68512yescomplemented
514C23C2×C3×C4×D511yescharacteristic
515C23C2×C3×D2011yescharacteristic
516C23C3×D4×D512yes—
517C23C3×D4×D512yes—
518C23C2×C3×C22⋊D511yescharacteristic
519Q8—104no—
520D4—24no—
521D4—24no—
522D4—104no—
523D4—108no—
524D4—104no—
525D4—104no—
526D4—104no—
527D4—104no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—54no—
539C2×C4—108no—
540C2×C4—104no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—202no—
544C2×C4—202no—
545C2×C4—202no—
546C2×C4C3×#68512yescomplemented
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—22no—
551C2×C3—42no—
552C2×C3—204no—
553C2×C3#6524411yescharacteristic
554C2×C3#6532111yescharacteristic
555C2×C3#6534211yescharacteristic
556C5C3×#179011yescharacteristic, complemented, Sylow
557C22—21no—
558C22—22no—
559C22—21no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—104no—
570C22—204no—
571C22—202no—
572C22—202no—
573C22—402no—
574C22—404no—
575C22C3×D5×C22⋊C412yes—
576C22C3×#402812yes—
577C22C2×C3×#68511yescharacteristic
578C22C3×#408311yescharacteristic
579C22C3×#408311yescharacteristic
580C4—22no—
581C4—42no—
582C4—81no—
583C4—104no—
584C4—402no—
585C3#1060039111yescharacteristic, direct product factor, Sylow
586C2—21no—
587C2—22no—
588C2—21no—
589C2—22no—
590C2—42no—
591C2—204no—
592C2C3×#6524411yescharacteristic
593C2C3×#6532111yescharacteristic
594C2C3×#6534211yescharacteristic
subgroupG/H
centerC22×C3#4083
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC3×C5×#386C2
socleC22×C3×C5#120
prime radicalC2×C3×#4144C2
cosocleC24×C5C23×C3
hypercenterC3×#386D5
hypocenterC5C3×#1790
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C3×C5×#386C2semidirect
3. C2×C3×#3966C2semidirect
4. C3×#65502C2semidirect
5. C2×C3×#3938C2semidirect
6. #10600391C3direct (N × H)
8. C23×C3×C4×C5C22semidirect
13. C3×#4144C4semidirect
18. C2×C3×C5×C22⋊C4C22semidirect
19. C2×C3×C22⋊Dic5C22semidirect
27. C5×#386C2×C3semidirect
28. C2×#3966C2×C3semidirect
29. #65502C2×C3semidirect
30. C2×#3938C2×C3semidirect
74. C3×#386D5semidirect
76. C23×C4×C5C22×C3semidirect
81. #4144C3×C4semidirect
86. C2×C5×C22⋊C4C22×C3semidirect
87. C2×C22⋊Dic5C22×C3semidirect
100. C23×C3×C5C22⋊C4semidirect
113. C22×C3×D5C22⋊C4semidirect
126. C2×C3×C4×C5C22⋊C4semidirect
138. C2×C3×Dic5C22⋊C4semidirect
151. C23×C3×C4C2×D5semidirect
155. C2×C3×C22⋊C4C2×D5semidirect
203. #386C3×D5semidirect
277. C23×C5C3×C22⋊C4semidirect
290. C22×D5C3×C22⋊C4semidirect
303. C2×C4×C5C3×C22⋊C4semidirect
315. C2×Dic5C3×C22⋊C4semidirect
328. C23×C4C2×C3×D5semidirect
332. C2×C22⋊C4C2×C3×D5semidirect
360. C23×C3#685semidirect
393. C2×C3×C4#685semidirect
461. C3×C5#1790semidirect
513. C23C3×#685semidirect
546. C2×C4C3×#685semidirect
556. C5C3×#1790semidirect
585. C3#10600391direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41442
C3×C5×#3862
C2×C3×#39662
C3×#655022
C2×C3×#39382
#106003913
C3×#17905