Finite Group Databasebeta

← C3×#10610616 #14424112

Subgroups — C3×#10610616 #14424112

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×#4097C211yesmaximal, characteristic, complemented
3C2×C3×#4055C211yesmaximal, characteristic, complemented
4C2×C3×#4043C211yesmaximal, characteristic, complemented
5C3×C5×#417C211yesmaximal, characteristic, complemented
6C3×#65415C211yesmaximal, characteristic, complemented
7C3×#65255C211yesmaximal, characteristic, complemented
8C3×#65099C212yesmaximal, complemented
9C3×#65097C212yesmaximal, complemented
10C3×#65072C212yesmaximal, complemented
11C3×#65065C212yesmaximal, complemented
12#10610616C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C3×D5×#41—24no—
15C3×D5×#41—24no—
16C2×C3×#713C2211yescharacteristic
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×#711—21no—
19C2×C3×#711C2211yescharacteristic
20C2×C3×D4×D5—21no—
21C2×C3×D4×D5C2211yescharacteristic
22C2×C3×#709—21no—
23C2×C3×#709C2211yescharacteristic
24C22×C3×C4×D5—21no—
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic, complemented
27C2×C3×C5×M16C2211yescharacteristic, complemented
28C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
29C3×#4097—24no—
30C2×C3×#689C2212yescomplemented
31C2×C3×#687C2212yescomplemented
32C2×C3×#685—21no—
33C2×C3×C4⋊Dic5—21no—
34C2×C3×#681C2211yescharacteristic, complemented
35C3×#4055—24no—
36C2×C3×Dic20C2212yescomplemented
37C2×C3×#677C2212yescomplemented
38C3×#4043—21no—
39C3×#4043—21no—
40C3×#4043C2212yes—
41C3×#4043C2212yescomplemented
42C3×C5×#103C2212yescomplemented
43C3×C5×#102C2212yescomplemented
44C3×#3952C2212yes—
45C3×#3952C2212yescomplemented
46C3×#3942C2212yescomplemented
47C3×#3941C2212yescomplemented
48C3×#3007—51nomaximal, Hall
49C2×D5×#41C2×C311yescharacteristic
50C2×#4097C2×C311yescharacteristic, complemented
51C2×#4055C2×C311yescharacteristic, complemented
52C2×#4043C2×C311yescharacteristic, complemented
53C5×#417C2×C311yescharacteristic, complemented
54#65415C2×C311yescharacteristic, complemented
55#65255C2×C311yescharacteristic, complemented
56#65099C2×C312yescomplemented
57#65097C2×C312yescomplemented
58#65072C2×C312yescomplemented
59#65065C2×C312yescomplemented
60C23×C3×D5—21no—
61C23×C3×D5D411yescharacteristic
62C3×C5×#41—22no—
63C3×C5×#41D414yes—
64C2×C3×C5×Q8C2311yescharacteristic
65C2×C3×C5×D4—21no—
66C2×C3×C5×D4C2311yescharacteristic
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5C2311yescharacteristic
70C2×C3×C22⋊D5—21no—
71C2×C3×C22⋊D5—21no—
72C2×C3×C22⋊D5—21no—
73C22×C3×Dic5—21no—
74C22×C3×Dic5—21no—
75C22×C3×Dic5D411yescharacteristic
76C3×#713—22no—
77C3×#713—22no—
78C3×Q8×D5—22no—
79C3×Q8×D5—22no—
80C3×#711—28no—
81C3×#711—22no—
82C3×#711—22no—
83C3×D4×D5—28no—
84C3×D4×D5—22no—
85C3×D4×D5—22no—
86C3×#709—28no—
87C3×#709—22no—
88C3×#709D414yes—
89C2×C3×D20—21no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×C4×D5—28no—
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5—22no—
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5D411yescharacteristic
98C2×C3×C4×D5D411yescharacteristic
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×C4×D5C2311yescharacteristic
101C2×C3×Dic10—21no—
102C2×C3×Dic10—22no—
103C2×C3×Dic10—22no—
104C2×C3×Dic10—21no—
105C2×C3×Dic10C2312yes—
106C2×C3×Dic10C2311yescharacteristic
107C3×C5×M16—22no—
108C2×C3×C5×C8C2312yes—
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4C2312yes—
111C3×#689—24no—
112C3×#687—24no—
113C3×#685—22no—
114C3×#685—22no—
115C3×C4⋊Dic5—22no—
116C3×C4⋊Dic5—22no—
117C3×#681—22no—
118C2×C3×#168C2312yes—
119C3×Dic20—24no—
120C3×#677—24no—
121C22×C3×#41—51no—
122C2×C3×#137—51no—
123C2×C3×#137—51no—
124C2×C3×C22⋊Q8—51no—
125C3×#452—52no—
126C3×#452—52no—
127C3×#451—52no—
128C3×#450—52no—
129C3×#417—51no—
130C3×#417D511yescharacteristic, complemented
131C3×#407—51no—
132C2×C5×#41C22×C311yescharacteristic
133D5×#41—24no—
134D5×#41—24no—
135C2×#713C22×C311yescharacteristic
136C2×Q8×D5C22×C311yescharacteristic
137C2×#711—21no—
138C2×#711C22×C311yescharacteristic
139C2×D4×D5—21no—
140C2×D4×D5C22×C311yescharacteristic
141C2×#709—21no—
142C2×#709C22×C311yescharacteristic
143C22×C4×D5—21no—
144C22×C4×D5C22×C311yescharacteristic
145C22×Dic10C22×C311yescharacteristic, complemented
146C2×C5×M16C22×C311yescharacteristic, complemented
147C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
148#4097—24no—
149C2×#689C22×C312yescomplemented
150C2×#687C22×C312yescomplemented
151C2×#685—21no—
152C2×C4⋊Dic5—21no—
153C2×#681C22×C311yescharacteristic, complemented
154#4055—24no—
155C2×Dic20C22×C312yescomplemented
156C2×#677C22×C312yescomplemented
157#4043—21no—
158#4043—21no—
159#4043C22×C312yes—
160#4043C22×C312yescomplemented
161C5×#103C22×C312yescomplemented
162C5×#102C22×C312yescomplemented
163#3952C22×C312yes—
164#3952C22×C312yescomplemented
165#3942C22×C312yescomplemented
166#3941C22×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×Q8C2×D412yes—
181C3×C5×D4—24no—
182C3×C5×D4—21no—
183C3×C5×D4C2×D412yes—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—24no—
186C2×C3×C4×C5—22no—
187C2×C3×C4×C5—42no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D412yes—
190C2×C3×C4×C5C2×D412yes—
191C2×C3×C4×C5C2411yescharacteristic
192C3×C22⋊D5—24no—
193C3×C22⋊D5—24no—
194C3×C22⋊D5—24no—
195C2×C3×Dic5—24no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—22no—
199C2×C3×Dic5—42no—
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C3×D20—24no—
203C3×D20—21no—
204C3×D20C2×D412yes—
205C3×C4×D5—24no—
206C3×C4×D5—24no—
207C3×C4×D5—22no—
208C3×C4×D5—24no—
209C3×C4×D5—22no—
210C3×C4×D5—21no—
211C3×C4×D5—21no—
212C3×C4×D5—21no—
213C3×C4×D5—21no—
214C3×Dic10—24no—
215C3×Dic10—21no—
216C3×Dic10—22no—
217C3×Dic10—22no—
218C3×Dic10—42no—
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×Q8—51no—
232C22×C3×D4—51no—
233C22×C3×D4—101no—
234C23×C3×C4—51no—
235C23×C3×C4—101no—
236C3×#137—104no—
237C3×#137—104no—
238C2×C3×Q16—52no—
239C2×C3×Q16—52no—
240C2×C3×SD16—52no—
241C2×C3×SD16—52no—
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—101no—
249C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
250C2×C3×C22⋊C4—101no—
251C3×#103—52no—
252C3×#103C2×D512yescomplemented
253C3×#102—52no—
254C3×#102C2×D512yescomplemented
255C3×C22⋊C8—52no—
256C3×C22⋊C8—52no—
257C23×D5—21no—
258C23×D5C3×D411yescharacteristic
259C5×#41—22no—
260C5×#41C3×D414yes—
261C2×C5×Q8C23×C311yescharacteristic
262C2×C5×D4—21no—
263C2×C5×D4C23×C311yescharacteristic
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5C23×C311yescharacteristic
267C2×C22⋊D5—21no—
268C2×C22⋊D5—21no—
269C2×C22⋊D5—21no—
270C22×Dic5—21no—
271C22×Dic5—21no—
272C22×Dic5C3×D411yescharacteristic
273#713—22no—
274#713—22no—
275Q8×D5—22no—
276Q8×D5—22no—
277#711—28no—
278#711—22no—
279#711—22no—
280D4×D5—28no—
281D4×D5—22no—
282D4×D5—22no—
283#709—28no—
284#709—22no—
285#709C3×D414yes—
286C2×D20—21no—
287C2×D20C23×C311yescharacteristic
288C2×C4×D5—28no—
289C2×C4×D5—21no—
290C2×C4×D5—21no—
291C2×C4×D5—22no—
292C2×C4×D5—22no—
293C2×C4×D5—21no—
294C2×C4×D5C3×D411yescharacteristic
295C2×C4×D5C3×D411yescharacteristic
296C2×C4×D5C23×C311yescharacteristic
297C2×C4×D5C23×C311yescharacteristic
298C2×Dic10—21no—
299C2×Dic10—22no—
300C2×Dic10—22no—
301C2×Dic10—21no—
302C2×Dic10C23×C312yes—
303C2×Dic10C23×C311yescharacteristic
304C5×M16—22no—
305C2×C5×C8C23×C312yes—
306C5×C4⋊C4—21no—
307C5×C4⋊C4C23×C312yes—
308#689—24no—
309#687—24no—
310#685—22no—
311#685—22no—
312C4⋊Dic5—22no—
313C4⋊Dic5—22no—
314#681—22no—
315C2×#168C23×C312yes—
316Dic20—24no—
317#677—24no—
318C22×#41—51no—
319C2×#137—51no—
320C2×#137—51no—
321C2×C22⋊Q8—51no—
322#452—52no—
323#452—52no—
324#451—52no—
325#450—52no—
326#417—51no—
327#417C3×D511yescharacteristic, complemented
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×#41D2014yes—
368C2×C3×Q8—51no—
369C2×C3×Q8—52no—
370C2×C3×Q8—101no—
371C2×C3×Q8—102no—
372C2×C3×Q8—102no—
373C2×C3×Q8—101no—
374C2×C3×Q8—102no—
375C2×C3×Q8—102no—
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—102no—
400C22×C3×C4—101no—
401C22×C3×C4—101no—
402C22×C3×C4C22×D511yescharacteristic
403C3×Q16—104no—
404C3×Q16—104no—
405C3×SD16—104no—
406C3×SD16—104no—
407C3×M16—22no—
408C3×M16—102no—
409C2×C3×C8—52no—
410C2×C3×C8C22×D512yes—
411C3×C4⋊C4—21no—
412C3×C4⋊C4—102no—
413C3×C4⋊C4—102no—
414C3×C4⋊C4C22×D512yes—
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×Q8C2×C3×D412yes—
430C5×D4—24no—
431C5×D4—21no—
432C5×D4C2×C3×D412yes—
433C2×C4×C5—21no—
434C2×C4×C5—24no—
435C2×C4×C5—22no—
436C2×C4×C5—42no—
437C2×C4×C5C2×C3×D412yes—
438C2×C4×C5C2×C3×D411yescharacteristic
439C2×C4×C5C2×C3×D412yes—
440C2×C4×C5C24×C311yescharacteristic
441C22⋊D5—24no—
442C22⋊D5—24no—
443C22⋊D5—24no—
444C2×Dic5—24no—
445C2×Dic5—22no—
446C2×Dic5—21no—
447C2×Dic5—22no—
448C2×Dic5—42no—
449C2×Dic5C2×C3×D411yescharacteristic
450C2×Dic5C2×C3×D411yescharacteristic
451D20—24no—
452D20—21no—
453D20C2×C3×D412yes—
454C4×D5—24no—
455C4×D5—24no—
456C4×D5—22no—
457C4×D5—24no—
458C4×D5—22no—
459C4×D5—21no—
460C4×D5—21no—
461C4×D5—21no—
462C4×D5—21no—
463Dic10—24no—
464Dic10—21no—
465Dic10—22no—
466Dic10—22no—
467Dic10—42no—
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×Q8—51no—
481C22×D4—51no—
482C22×D4—101no—
483C23×C4—51no—
484C23×C4—101no—
485#137—104no—
486#137—104no—
487C2×Q16—52no—
488C2×Q16—52no—
489C2×SD16—52no—
490C2×SD16—52no—
491C2×M16—51no—
492C2×M16C2×C3×D511yescharacteristic, complemented
493C22⋊Q8—52no—
494C22⋊Q8—52no—
495C22⋊Q8—101no—
496C22⋊Q8—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
499C2×C22⋊C4—101no—
500#103—52no—
501#103C2×C3×D512yescomplemented
502#102—52no—
503#102C2×C3×D512yescomplemented
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—52no—
527C3×Q8—104no—
528C3×Q8—101no—
529C3×Q8—102no—
530C3×Q8—102no—
531C3×Q8—202no—
532C3×Q8C2×D2012yes—
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×D2012yes—
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×C4C2×D2012yes—
563C2×C3×C4D4×D512yes—
564C2×C3×C4D4×D511yescharacteristic
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×D2014yes—
607C2×Q8—51no—
608C2×Q8—52no—
609C2×Q8—101no—
610C2×Q8—102no—
611C2×Q8—102no—
612C2×Q8—101no—
613C2×Q8—102no—
614C2×Q8—102no—
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—102no—
639C22×C4—101no—
640C22×C4—101no—
641C22×C4C22×C3×D511yescharacteristic
642Q16—104no—
643Q16—104no—
644SD16—104no—
645SD16—104no—
646M16—22no—
647M16—102no—
648C2×C8—52no—
649C2×C8C22×C3×D512yes—
650C4⋊C4—21no—
651C4⋊C4—102no—
652C4⋊C4—102no—
653C4⋊C4C22×C3×D512yes—
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—102no—
666C22×C3—101no—
667C22×C3—101no—
668C22×C3—101no—
669C22×C3—204no—
670C22×C3—208no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3#402812yes—
674C22×C3C2×D4×D511yescharacteristic
675C3×C4—22no—
676C3×C4—42no—
677C3×C4—101no—
678C3×C4—101no—
679C3×C4—102no—
680C3×C4—202no—
681C3×C4#402812yes—
682C3×C4C22×D2011yescharacteristic
683C3×C4C2×D4×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—101no—
698C23—102no—
699C23—201no—
700C23—202no—
701C23—202no—
702C23C3×D4×D511yescharacteristic
703Q8—21no—
704Q8—52no—
705Q8—104no—
706Q8—101no—
707Q8—102no—
708Q8—102no—
709Q8—202no—
710Q8C2×C3×D2012yes—
711D4—24no—
712D4—21no—
713D4—52no—
714D4—104no—
715D4—104no—
716D4—104no—
717D4—104no—
718D4—101no—
719D4C2×C3×D2012yes—
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—101no—
730C2×C4—102no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—104no—
738C2×C4—102no—
739C2×C4—202no—
740C2×C4C2×C3×D2012yes—
741C2×C4C3×D4×D512yes—
742C2×C4C3×D4×D511yescharacteristic
743C2×C4C23×C3×D511yescharacteristic
744C8—22no—
745C8—102no—
746C2×C3—22no—
747C2×C3—42no—
748C2×C3—102no—
749C2×C3—201no—
750C2×C3—202no—
751C2×C3C2×#402811yescharacteristic
752C2×C3#6610711yescharacteristic
753C2×C3D5×#13711yescharacteristic
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×#402812yes—
772C22C2×C3×D4×D511yescharacteristic
773C4—22no—
774C4—42no—
775C4—101no—
776C4—101no—
777C4—102no—
778C4—202no—
779C4C3×#402812yes—
780C4C22×C3×D2011yescharacteristic
781C4C2×C3×D4×D511yescharacteristic
782C3#1061061611yescharacteristic, direct product factor, Sylow
783C2—22no—
784C2—42no—
785C2—102no—
786C2—201no—
787C2—202no—
788C2C2×C3×#402811yescharacteristic
789C2C3×#6610711yescharacteristic
790C2C3×D5×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#417C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×D5×#41C2
hypercenterC3×#417D5
hypocenterC5C3×#3007
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4097C2semidirect
3. C2×C3×#4055C2semidirect
4. C2×C3×#4043C2semidirect
5. C3×C5×#417C2semidirect
6. C3×#65415C2semidirect
7. C3×#65255C2semidirect
8. C3×#65099C2semidirect
9. C3×#65097C2semidirect
10. C3×#65072C2semidirect
11. C3×#65065C2semidirect
12. #10610616C3direct (N × H)
26. C22×C3×Dic10C22semidirect
27. C2×C3×C5×M16C22semidirect
28. C2×C3×C5×C4⋊C4C22semidirect
30. C2×C3×#689C22semidirect
31. C2×C3×#687C22semidirect
34. C2×C3×#681C22semidirect
36. C2×C3×Dic20C22semidirect
37. C2×C3×#677C22semidirect
41. C3×#4043C22semidirect
42. C3×C5×#103C22semidirect
43. C3×C5×#102C22semidirect
45. C3×#3952C22semidirect
46. C3×#3942C22semidirect
47. C3×#3941C22semidirect
50. C2×#4097C2×C3semidirect
51. C2×#4055C2×C3semidirect
52. C2×#4043C2×C3semidirect
53. C5×#417C2×C3semidirect
54. #65415C2×C3semidirect
55. #65255C2×C3semidirect
56. #65099C2×C3semidirect
57. #65097C2×C3semidirect
58. #65072C2×C3semidirect
59. #65065C2×C3semidirect
130. C3×#417D5semidirect
145. C22×Dic10C22×C3semidirect
146. C2×C5×M16C22×C3semidirect
147. C2×C5×C4⋊C4C22×C3semidirect
149. C2×#689C22×C3semidirect
150. C2×#687C22×C3semidirect
153. C2×#681C22×C3semidirect
155. C2×Dic20C22×C3semidirect
156. C2×#677C22×C3semidirect
160. #4043C22×C3semidirect
161. C5×#103C22×C3semidirect
162. C5×#102C22×C3semidirect
164. #3952C22×C3semidirect
165. #3942C22×C3semidirect
166. #3941C22×C3semidirect
243. C2×C3×M16C2×D5semidirect
249. C2×C3×C4⋊C4C2×D5semidirect
252. C3×#103C2×D5semidirect
254. C3×#102C2×D5semidirect
327. #417C3×D5semidirect
346. C2×C3×D5#137semidirect
492. C2×M16C2×C3×D5semidirect
498. C2×C4⋊C4C2×C3×D5semidirect
501. #103C2×C3×D5semidirect
503. #102C2×C3×D5semidirect
585. C2×D5C3×#137semidirect
656. C3×C5#3007semidirect
754. C5C3×#3007semidirect
782. C3#10610616direct (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×#40972
C2×C3×#40552
C2×C3×#40432
C3×C5×#4172
C3×#654152
C3×#652552
C3×#650992
C3×#650972
C3×#650722
C3×#650652
#106106163
C3×#30075