Finite Group Databasebeta

← C3×#10615712 #14424097

Subgroups — C3×#10615712 #14424097

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×C3×C5×#137C211yesmaximal, characteristic, complemented
3C2×C3×#4092C211yesmaximal, characteristic, complemented
4C2×C3×#4088C211yesmaximal, characteristic, complemented
5C3×#65521C211yesmaximal, characteristic, complemented
6C3×#65476C212yesmaximal, complemented
7C3×#65475C212yesmaximal, complemented
8C3×#65462C212yesmaximal, complemented
9C3×#65458C212yesmaximal, complemented
10C3×#65422C211yesmaximal, characteristic, complemented
11C3×#65415C211yesmaximal, characteristic, complemented
12#10615712C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×C5×Q8C2211yescharacteristic, complemented
15C3×D5×#41—24no—
16C3×D5×#41—24no—
17C2×C3×#713C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic
19C2×C3×#711—21no—
20C2×C3×#711C2211yescharacteristic
21C2×C3×D4×D5—21no—
22C2×C3×D4×D5C2211yescharacteristic
23C2×C3×#709—21no—
24C2×C3×#709C2211yescharacteristic
25C22×C3×C4×D5—21no—
26C22×C3×C4×D5C2211yescharacteristic
27C3×C5×#137—24no—
28C2×C3×C5×Q16C2212yescomplemented
29C2×C3×C5×SD16C2212yescomplemented
30C2×C3×C5×M16C2211yescharacteristic, complemented
31C3×#4092—21no—
32C3×#4092—21no—
33C3×#4092C2212yes—
34C3×#4092C2212yescomplemented
35C2×C3×#689C2212yescomplemented
36C3×#4088—24no—
37C2×C3×#688C2212yescomplemented
38C2×C3×#685—21no—
39C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
40C2×C3×#683—21no—
41C2×C3×#681C2211yescharacteristic, complemented
42C3×#3967C2212yescomplemented
43C3×#3964C2212yescomplemented
44C3×#3953C2212yescomplemented
45C3×#3952C2212yes—
46C3×#3952C2212yescomplemented
47C3×#3948C2212yescomplemented
48C3×#3007—51nomaximal, Hall
49C2×D5×#41C2×C311yescharacteristic
50C2×C5×#137C2×C311yescharacteristic, complemented
51C2×#4092C2×C311yescharacteristic, complemented
52C2×#4088C2×C311yescharacteristic, complemented
53#65521C2×C311yescharacteristic, complemented
54#65476C2×C312yescomplemented
55#65475C2×C312yescomplemented
56#65462C2×C312yescomplemented
57#65458C2×C312yescomplemented
58#65422C2×C311yescharacteristic, complemented
59#65415C2×C311yescharacteristic, complemented
60C23×C3×D5—21no—
61C23×C3×D5D411yescharacteristic
62C3×C5×#41—22no—
63C3×C5×#41D414yes—
64C2×C3×C5×Q8—21no—
65C2×C3×C5×Q8—22no—
66C2×C3×C5×Q8—22no—
67C2×C3×C5×Q8C2312yes—
68C2×C3×C5×Q8C2311yescharacteristic
69C2×C3×C5×D4—21no—
70C2×C3×C5×D4C2311yescharacteristic
71C22×C3×C4×C5—21no—
72C22×C3×C4×C5—21no—
73C22×C3×C4×C5C2311yescharacteristic
74C2×C3×C22⋊D5—21no—
75C2×C3×C22⋊D5—21no—
76C2×C3×C22⋊D5—21no—
77C22×C3×Dic5—21no—
78C22×C3×Dic5—21no—
79C22×C3×Dic5D411yescharacteristic
80C3×#713—22no—
81C3×#713—22no—
82C3×Q8×D5—22no—
83C3×Q8×D5—22no—
84C3×#711—28no—
85C3×#711—22no—
86C3×#711—22no—
87C3×D4×D5—28no—
88C3×D4×D5—22no—
89C3×D4×D5—22no—
90C3×#709—28no—
91C3×#709—22no—
92C3×#709D414yes—
93C2×C3×D20—21no—
94C2×C3×D20C2311yescharacteristic
95C2×C3×C4×D5—28no—
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5D411yescharacteristic
102C2×C3×C4×D5D411yescharacteristic
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×Dic10—21no—
106C2×C3×Dic10C2311yescharacteristic
107C3×C5×Q16—24no—
108C3×C5×SD16—24no—
109C3×C5×M16—22no—
110C2×C3×C5×C8C2312yes—
111C3×#689—24no—
112C3×#688—24no—
113C3×#685—22no—
114C3×#685—22no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2312yes—
117C3×#683—22no—
118C3×#683—22no—
119C3×#681—22no—
120C2×C3×#168C2312yes—
121C22×C3×#41—51no—
122C2×C3×#137—51no—
123C2×C3×#137D511yescharacteristic, complemented
124C2×C3×C22⋊Q8—51no—
125C3×#452—52no—
126C3×#452—52no—
127C3×#451—52no—
128C3×#450—52no—
129C3×#417—51no—
130C3×#417—51no—
131C3×#407—51no—
132C2×C5×#41C22×C311yescharacteristic
133C22×C5×Q8C22×C311yescharacteristic, complemented
134D5×#41—24no—
135D5×#41—24no—
136C2×#713C22×C311yescharacteristic
137C2×Q8×D5C22×C311yescharacteristic
138C2×#711—21no—
139C2×#711C22×C311yescharacteristic
140C2×D4×D5—21no—
141C2×D4×D5C22×C311yescharacteristic
142C2×#709—21no—
143C2×#709C22×C311yescharacteristic
144C22×C4×D5—21no—
145C22×C4×D5C22×C311yescharacteristic
146C5×#137—24no—
147C2×C5×Q16C22×C312yescomplemented
148C2×C5×SD16C22×C312yescomplemented
149C2×C5×M16C22×C311yescharacteristic, complemented
150#4092—21no—
151#4092—21no—
152#4092C22×C312yes—
153#4092C22×C312yescomplemented
154C2×#689C22×C312yescomplemented
155#4088—24no—
156C2×#688C22×C312yescomplemented
157C2×#685—21no—
158C2×C4⋊Dic5C22×C311yescharacteristic, complemented
159C2×#683—21no—
160C2×#681C22×C311yescharacteristic, complemented
161#3967C22×C312yescomplemented
162#3964C22×C312yescomplemented
163#3953C22×C312yescomplemented
164#3952C22×C312yes—
165#3952C22×C312yescomplemented
166#3948C22×C312yescomplemented
167#3007—51noSylow
168C23×C3×C5—21no—
169C23×C3×C5C2×D411yescharacteristic
170C22×C3×D5—24no—
171C22×C3×D5—22no—
172C22×C3×D5—21no—
173C22×C3×D5—22no—
174C22×C3×D5—41no—
175C22×C3×D5—42no—
176C22×C3×D5—42no—
177C22×C3×D5C2×D411yescharacteristic
178C22×C3×D5C2×D411yescharacteristic
179C3×C5×Q8—21no—
180C3×C5×Q8—22no—
181C3×C5×Q8—22no—
182C3×C5×Q8—42no—
183C3×C5×Q8C2×D412yes—
184C3×C5×D4—24no—
185C3×C5×D4—21no—
186C3×C5×D4C2×D412yes—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—24no—
189C2×C3×C4×C5—22no—
190C2×C3×C4×C5—42no—
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2×D412yes—
193C2×C3×C4×C5C2×D412yes—
194C2×C3×C4×C5C2411yescharacteristic
195C3×C22⋊D5—24no—
196C3×C22⋊D5—24no—
197C3×C22⋊D5—24no—
198C2×C3×Dic5—24no—
199C2×C3×Dic5—22no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—22no—
202C2×C3×Dic5—42no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C3×D20—24no—
206C3×D20—21no—
207C3×D20C2×D412yes—
208C3×C4×D5—24no—
209C3×C4×D5—24no—
210C3×C4×D5—22no—
211C3×C4×D5—24no—
212C3×C4×D5—22no—
213C3×C4×D5—21no—
214C3×C4×D5—21no—
215C3×C4×D5—21no—
216C3×C4×D5—21no—
217C3×Dic10—24no—
218C3×Dic10—21no—
219C3×Dic10C2×D412yes—
220C3×C5×C8—22no—
221C3×#168—22no—
222C2×C3×#41—51no—
223C2×C3×#41—51no—
224C2×C3×#41—51no—
225C2×C3×#41—101no—
226C2×C3×#41—101no—
227C2×C3×#41—104no—
228C2×C3×#41—104no—
229C2×C3×#41C2×D511yescharacteristic
230C22×C3×Q8—51no—
231C22×C3×Q8C2×D511yescharacteristic, complemented
232C22×C3×D4—51no—
233C22×C3×D4—101no—
234C23×C3×C4—51no—
235C23×C3×C4—101no—
236C3×#137—24no—
237C3×#137—104no—
238C2×C3×Q16—52no—
239C2×C3×Q16C2×D512yescomplemented
240C2×C3×SD16—52no—
241C2×C3×SD16C2×D512yescomplemented
242C2×C3×M16—51no—
243C2×C3×M16C2×D511yescharacteristic, complemented
244C3×C22⋊Q8—52no—
245C3×C22⋊Q8—52no—
246C3×C22⋊Q8—101no—
247C3×C22⋊Q8—101no—
248C2×C3×C4⋊C4—51no—
249C2×C3×C4⋊C4—101no—
250C2×C3×C22⋊C4—101no—
251C3×#103—52no—
252C3×#103—52no—
253C3×#102—52no—
254C3×#102—52no—
255C3×C22⋊C8—52no—
256C3×C22⋊C8—52no—
257C23×D5—21no—
258C23×D5C3×D411yescharacteristic
259C5×#41—22no—
260C5×#41C3×D414yes—
261C2×C5×Q8—21no—
262C2×C5×Q8—22no—
263C2×C5×Q8—22no—
264C2×C5×Q8C23×C312yes—
265C2×C5×Q8C23×C311yescharacteristic
266C2×C5×D4—21no—
267C2×C5×D4C23×C311yescharacteristic
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5C23×C311yescharacteristic
271C2×C22⋊D5—21no—
272C2×C22⋊D5—21no—
273C2×C22⋊D5—21no—
274C22×Dic5—21no—
275C22×Dic5—21no—
276C22×Dic5C3×D411yescharacteristic
277#713—22no—
278#713—22no—
279Q8×D5—22no—
280Q8×D5—22no—
281#711—28no—
282#711—22no—
283#711—22no—
284D4×D5—28no—
285D4×D5—22no—
286D4×D5—22no—
287#709—28no—
288#709—22no—
289#709C3×D414yes—
290C2×D20—21no—
291C2×D20C23×C311yescharacteristic
292C2×C4×D5—28no—
293C2×C4×D5—21no—
294C2×C4×D5—21no—
295C2×C4×D5—22no—
296C2×C4×D5—22no—
297C2×C4×D5—21no—
298C2×C4×D5C3×D411yescharacteristic
299C2×C4×D5C3×D411yescharacteristic
300C2×C4×D5C23×C311yescharacteristic
301C2×C4×D5C23×C311yescharacteristic
302C2×Dic10—21no—
303C2×Dic10C23×C311yescharacteristic
304C5×Q16—24no—
305C5×SD16—24no—
306C5×M16—22no—
307C2×C5×C8C23×C312yes—
308#689—24no—
309#688—24no—
310#685—22no—
311#685—22no—
312C4⋊Dic5—21no—
313C4⋊Dic5C23×C312yes—
314#683—22no—
315#683—22no—
316#681—22no—
317C2×#168C23×C312yes—
318C22×#41—51no—
319C2×#137—51no—
320C2×#137C3×D511yescharacteristic, complemented
321C2×C22⋊Q8—51no—
322#452—52no—
323#452—52no—
324#451—52no—
325#450—52no—
326#417—51no—
327#417—51no—
328#407—51no—
329C22×C3×C5—21no—
330C22×C3×C5—21no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5#12012yes—
335C22×C3×C5C22×D411yescharacteristic
336C2×C3×D5—21no—
337C2×C3×D5—21no—
338C2×C3×D5—21no—
339C2×C3×D5—22no—
340C2×C3×D5—21no—
341C2×C3×D5—21no—
342C2×C3×D5—44no—
343C2×C3×D5—48no—
344C2×C3×D5—41no—
345C2×C3×D5—41no—
346C2×C3×D5#13712yescomplemented
347C3×C4×C5—22no—
348C3×C4×C5—42no—
349C3×C4×C5#12012yes—
350C3×C4×C5C22×D411yescharacteristic
351C3×C4×C5C22×D411yescharacteristic
352C3×Dic5—21no—
353C3×Dic5—22no—
354C3×Dic5—21no—
355C3×Dic5—42no—
356C24×C3—51no—
357C24×C3—101no—
358C3×#41—22no—
359C3×#41—54no—
360C3×#41—108no—
361C3×#41—102no—
362C3×#41—108no—
363C3×#41—102no—
364C3×#41—102no—
365C3×#41—102no—
366C3×#41—102no—
367C3×#41C22⋊D514yes—
368C2×C3×Q8—21no—
369C2×C3×Q8—22no—
370C2×C3×Q8—22no—
371C2×C3×Q8—51no—
372C2×C3×Q8—101no—
373C2×C3×Q8—102no—
374C2×C3×Q8—102no—
375C2×C3×Q8C22×D512yes—
376C2×C3×Q8C22×D511yescharacteristic
377C2×C3×D4—21no—
378C2×C3×D4—51no—
379C2×C3×D4—101no—
380C2×C3×D4—101no—
381C2×C3×D4—102no—
382C2×C3×D4—108no—
383C2×C3×D4—101no—
384C2×C3×D4—101no—
385C2×C3×D4—102no—
386C2×C3×D4C22×D511yescharacteristic
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—51no—
390C22×C3×C4—51no—
391C22×C3×C4—51no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—101no—
395C22×C3×C4—101no—
396C22×C3×C4—108no—
397C22×C3×C4—101no—
398C22×C3×C4—102no—
399C22×C3×C4—101no—
400C22×C3×C4—102no—
401C22×C3×C4—101no—
402C22×C3×C4C22×D511yescharacteristic
403C3×Q16—24no—
404C3×Q16—104no—
405C3×SD16—24no—
406C3×SD16—104no—
407C3×M16—22no—
408C3×M16—102no—
409C2×C3×C8—52no—
410C2×C3×C8C22×D512yes—
411C3×C4⋊C4—52no—
412C3×C4⋊C4—102no—
413C3×C4⋊C4—102no—
414C3×C4⋊C4—101no—
415C3×C22⋊C4—102no—
416C3×C22⋊C4—102no—
417C23×C5—21no—
418C23×C5C2×C3×D411yescharacteristic
419C22×D5—24no—
420C22×D5—22no—
421C22×D5—21no—
422C22×D5—22no—
423C22×D5—41no—
424C22×D5—42no—
425C22×D5—42no—
426C22×D5C2×C3×D411yescharacteristic
427C22×D5C2×C3×D411yescharacteristic
428C5×Q8—21no—
429C5×Q8—22no—
430C5×Q8—22no—
431C5×Q8—42no—
432C5×Q8C2×C3×D412yes—
433C5×D4—24no—
434C5×D4—21no—
435C5×D4C2×C3×D412yes—
436C2×C4×C5—21no—
437C2×C4×C5—24no—
438C2×C4×C5—22no—
439C2×C4×C5—42no—
440C2×C4×C5C2×C3×D411yescharacteristic
441C2×C4×C5C2×C3×D412yes—
442C2×C4×C5C2×C3×D412yes—
443C2×C4×C5C24×C311yescharacteristic
444C22⋊D5—24no—
445C22⋊D5—24no—
446C22⋊D5—24no—
447C2×Dic5—24no—
448C2×Dic5—22no—
449C2×Dic5—21no—
450C2×Dic5—22no—
451C2×Dic5—42no—
452C2×Dic5C2×C3×D411yescharacteristic
453C2×Dic5C2×C3×D411yescharacteristic
454D20—24no—
455D20—21no—
456D20C2×C3×D412yes—
457C4×D5—24no—
458C4×D5—24no—
459C4×D5—22no—
460C4×D5—24no—
461C4×D5—22no—
462C4×D5—21no—
463C4×D5—21no—
464C4×D5—21no—
465C4×D5—21no—
466Dic10—24no—
467Dic10—21no—
468Dic10C2×C3×D412yes—
469C5×C8—22no—
470#168—22no—
471C2×#41—51no—
472C2×#41—51no—
473C2×#41—51no—
474C2×#41—101no—
475C2×#41—101no—
476C2×#41—104no—
477C2×#41—104no—
478C2×#41C2×C3×D511yescharacteristic
479C22×Q8—51no—
480C22×Q8C2×C3×D511yescharacteristic, complemented
481C22×D4—51no—
482C22×D4—101no—
483C23×C4—51no—
484C23×C4—101no—
485#137—24no—
486#137—104no—
487C2×Q16—52no—
488C2×Q16C2×C3×D512yescomplemented
489C2×SD16—52no—
490C2×SD16C2×C3×D512yescomplemented
491C2×M16—51no—
492C2×M16C2×C3×D511yescharacteristic, complemented
493C22⋊Q8—52no—
494C22⋊Q8—52no—
495C22⋊Q8—101no—
496C22⋊Q8—101no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—101no—
499C2×C22⋊C4—101no—
500#103—52no—
501#103—52no—
502#102—52no—
503#102—52no—
504C22⋊C8—52no—
505C22⋊C8—52no—
506C2×C3×C5—22no—
507C2×C3×C5—42no—
508C2×C3×C5C2×#12011yescharacteristic
509C2×C3×C5C2×#13711yescharacteristic
510C2×C3×C5#57511yescharacteristic
511C3×D5—22no—
512C3×D5—41no—
513C3×D5—42no—
514C23×C3—21no—
515C23×C3—51no—
516C23×C3—51no—
517C23×C3—102no—
518C23×C3—104no—
519C23×C3—101no—
520C23×C3—102no—
521C23×C3—201no—
522C23×C3—202no—
523C23×C3—202no—
524C23×C3D4×D511yescharacteristic
525C3×Q8—21no—
526C3×Q8—22no—
527C3×Q8—22no—
528C3×Q8—42no—
529C3×Q8—52no—
530C3×Q8—104no—
531C3×Q8—101no—
532C3×Q8C2×C22⋊D512yes—
533C3×D4—24no—
534C3×D4—21no—
535C3×D4—52no—
536C3×D4—104no—
537C3×D4—104no—
538C3×D4—104no—
539C3×D4—104no—
540C3×D4—101no—
541C3×D4C2×C22⋊D512yes—
542C2×C3×C4—21no—
543C2×C3×C4—24no—
544C2×C3×C4—22no—
545C2×C3×C4—42no—
546C2×C3×C4—51no—
547C2×C3×C4—51no—
548C2×C3×C4—104no—
549C2×C3×C4—104no—
550C2×C3×C4—104no—
551C2×C3×C4—101no—
552C2×C3×C4—102no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—104no—
560C2×C3×C4—102no—
561C2×C3×C4—202no—
562C2×C3×C4D4×D512yes—
563C2×C3×C4D4×D511yescharacteristic
564C2×C3×C4C2×C22⋊D512yes—
565C2×C3×C4C23×D511yescharacteristic
566C3×C8—22no—
567C3×C8—102no—
568C22×C5—21no—
569C22×C5—21no—
570C22×C5—22no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5C3×#12012yes—
574C22×C5C22×C3×D411yescharacteristic
575C2×D5—21no—
576C2×D5—21no—
577C2×D5—21no—
578C2×D5—21no—
579C2×D5—21no—
580C2×D5—22no—
581C2×D5—44no—
582C2×D5—48no—
583C2×D5—41no—
584C2×D5—41no—
585C2×D5C3×#13712yescomplemented
586C4×C5—22no—
587C4×C5—42no—
588C4×C5C3×#12012yes—
589C4×C5C22×C3×D411yescharacteristic
590C4×C5C22×C3×D411yescharacteristic
591Dic5—21no—
592Dic5—22no—
593Dic5—21no—
594Dic5—42no—
595C24—51no—
596C24—101no—
597#41—22no—
598#41—54no—
599#41—108no—
600#41—102no—
601#41—108no—
602#41—102no—
603#41—102no—
604#41—102no—
605#41—102no—
606#41C3×C22⋊D514yes—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—51no—
611C2×Q8—101no—
612C2×Q8—102no—
613C2×Q8—102no—
614C2×Q8C22×C3×D512yes—
615C2×Q8C22×C3×D511yescharacteristic
616C2×D4—21no—
617C2×D4—51no—
618C2×D4—101no—
619C2×D4—101no—
620C2×D4—102no—
621C2×D4—108no—
622C2×D4—101no—
623C2×D4—101no—
624C2×D4—102no—
625C2×D4C22×C3×D511yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—108no—
636C22×C4—101no—
637C22×C4—102no—
638C22×C4—101no—
639C22×C4—102no—
640C22×C4—101no—
641C22×C4C22×C3×D511yescharacteristic
642Q16—24no—
643Q16—104no—
644SD16—24no—
645SD16—104no—
646M16—22no—
647M16—102no—
648C2×C8—52no—
649C2×C8C22×C3×D512yes—
650C4⋊C4—52no—
651C4⋊C4—102no—
652C4⋊C4—102no—
653C4⋊C4—101no—
654C22⋊C4—102no—
655C22⋊C4—102no—
656C3×C5#300711yescharacteristic, complemented, Hall
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—52no—
663C22×C3—101no—
664C22×C3—101no—
665C22×C3—101no—
666C22×C3—101no—
667C22×C3—102no—
668C22×C3—101no—
669C22×C3—204no—
670C22×C3—208no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3#408312yes—
674C22×C3C2×D4×D511yescharacteristic
675C3×C4—22no—
676C3×C4—42no—
677C3×C4—101no—
678C3×C4—101no—
679C3×C4—102no—
680C3×C4—202no—
681C3×C4#408312yes—
682C3×C4C2×D4×D511yescharacteristic
683C3×C4C22×C22⋊D511yescharacteristic
684C2×C5—22no—
685C2×C5—42no—
686C2×C5C2×C3×#12011yescharacteristic
687C2×C5C2×C3×#13711yescharacteristic
688C2×C5C3×#57511yescharacteristic
689D5—22no—
690D5—41no—
691D5—42no—
692C23—21no—
693C23—51no—
694C23—51no—
695C23—102no—
696C23—104no—
697C23—102no—
698C23—101no—
699C23—201no—
700C23—202no—
701C23—202no—
702C23C3×D4×D511yescharacteristic
703Q8—21no—
704Q8—22no—
705Q8—22no—
706Q8—42no—
707Q8—52no—
708Q8—104no—
709Q8—101no—
710Q8C2×C3×C22⋊D512yes—
711D4—24no—
712D4—21no—
713D4—52no—
714D4—104no—
715D4—104no—
716D4—104no—
717D4—104no—
718D4—101no—
719D4C2×C3×C22⋊D512yes—
720C2×C4—21no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—51no—
725C2×C4—51no—
726C2×C4—104no—
727C2×C4—104no—
728C2×C4—104no—
729C2×C4—102no—
730C2×C4—101no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—104no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—101no—
737C2×C4—101no—
738C2×C4—102no—
739C2×C4—202no—
740C2×C4C3×D4×D511yescharacteristic
741C2×C4C3×D4×D512yes—
742C2×C4C2×C3×C22⋊D512yes—
743C2×C4C23×C3×D511yescharacteristic
744C8—22no—
745C8—102no—
746C2×C3—22no—
747C2×C3—42no—
748C2×C3—102no—
749C2×C3—201no—
750C2×C3—202no—
751C2×C3D5×#13711yescharacteristic
752C2×C3#6611111yescharacteristic
753C2×C3C2×#408311yescharacteristic
754C5C3×#300711yescharacteristic, complemented, Sylow
755C22—21no—
756C22—21no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—52no—
761C22—101no—
762C22—101no—
763C22—101no—
764C22—101no—
765C22—102no—
766C22—101no—
767C22—204no—
768C22—208no—
769C22—201no—
770C22—201no—
771C22C3×#408312yes—
772C22C2×C3×D4×D511yescharacteristic
773C4—22no—
774C4—42no—
775C4—101no—
776C4—101no—
777C4—102no—
778C4—202no—
779C4C3×#408312yes—
780C4C2×C3×D4×D511yescharacteristic
781C4C22×C3×C22⋊D511yescharacteristic
782C3#1061571211yescharacteristic, direct product factor, Sylow
783C2—22no—
784C2—42no—
785C2—102no—
786C2—201no—
787C2—202no—
788C2C3×D5×#13711yescharacteristic
789C2C3×#6611111yescharacteristic
790C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×D5×#41C2
hypercenterC2×C3×#137D5
hypocenterC5C3×#3007
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#137C2semidirect
3. C2×C3×#4092C2semidirect
4. C2×C3×#4088C2semidirect
5. C3×#65521C2semidirect
6. C3×#65476C2semidirect
7. C3×#65475C2semidirect
8. C3×#65462C2semidirect
9. C3×#65458C2semidirect
10. C3×#65422C2semidirect
11. C3×#65415C2semidirect
12. #10615712C3direct (N × H)
14. C22×C3×C5×Q8C22semidirect
28. C2×C3×C5×Q16C22semidirect
29. C2×C3×C5×SD16C22semidirect
30. C2×C3×C5×M16C22semidirect
34. C3×#4092C22semidirect
35. C2×C3×#689C22semidirect
37. C2×C3×#688C22semidirect
39. C2×C3×C4⋊Dic5C22semidirect
41. C2×C3×#681C22semidirect
42. C3×#3967C22semidirect
43. C3×#3964C22semidirect
44. C3×#3953C22semidirect
46. C3×#3952C22semidirect
47. C3×#3948C22semidirect
50. C2×C5×#137C2×C3semidirect
51. C2×#4092C2×C3semidirect
52. C2×#4088C2×C3semidirect
53. #65521C2×C3semidirect
54. #65476C2×C3semidirect
55. #65475C2×C3semidirect
56. #65462C2×C3semidirect
57. #65458C2×C3semidirect
58. #65422C2×C3semidirect
59. #65415C2×C3semidirect
123. C2×C3×#137D5semidirect
133. C22×C5×Q8C22×C3semidirect
147. C2×C5×Q16C22×C3semidirect
148. C2×C5×SD16C22×C3semidirect
149. C2×C5×M16C22×C3semidirect
153. #4092C22×C3semidirect
154. C2×#689C22×C3semidirect
156. C2×#688C22×C3semidirect
158. C2×C4⋊Dic5C22×C3semidirect
160. C2×#681C22×C3semidirect
161. #3967C22×C3semidirect
162. #3964C22×C3semidirect
163. #3953C22×C3semidirect
165. #3952C22×C3semidirect
166. #3948C22×C3semidirect
231. C22×C3×Q8C2×D5semidirect
239. C2×C3×Q16C2×D5semidirect
241. C2×C3×SD16C2×D5semidirect
243. C2×C3×M16C2×D5semidirect
320. C2×#137C3×D5semidirect
346. C2×C3×D5#137semidirect
480. C22×Q8C2×C3×D5semidirect
488. C2×Q16C2×C3×D5semidirect
490. C2×SD16C2×C3×D5semidirect
492. C2×M16C2×C3×D5semidirect
585. C2×D5C3×#137semidirect
656. C3×C5#3007semidirect
754. C5C3×#3007semidirect
782. C3#10615712direct (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×#412
C2×C3×C5×#1372
C2×C3×#40922
C2×C3×#40882
C3×#655212
C3×#654762
C3×#654752
C3×#654622
C3×#654582
C3×#654222
C3×#654152
#106157123
C3×#30075