Finite Group Databasebeta

← C3×#10610724 #14425309

Subgroups — C3×#10610724 #14425309

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4149C211yesmaximal, characteristic, complemented
2C3×#66156C211yesmaximal, characteristic, complemented
3C3×#66082C211yesmaximal, characteristic, complemented
4C3×#65859C211yesmaximal, characteristic, complemented
5C3×C5×#421C211yesmaximal, characteristic, complemented
6C2×C3×#3955C211yesmaximal, characteristic, complemented
7C3×#65294C211yesmaximal, characteristic, complemented
8C3×#65114C214yesmaximal, complemented
9C3×#65111C214yesmaximal, complemented
10#10610724C311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C3×#4149—22no—
13C3×#4149—22no—
14C3×#4149—22no—
15C3×#4149C2214yes—
16C2×C3×#713—21no—
17C2×C3×D4×D5—22no—
18C2×C3×D4×D5—21no—
19C2×C3×#709—21no—
20C2×C3×#709C2211yescharacteristic
21C2×C3×#709C2211yescharacteristic, complemented
22C22×C3×D20—21no—
23C22×C3×D20C2211yescharacteristic
24C2×C3×C5×M16C2211yescharacteristic, complemented
25C3×C5×#117C2211yescharacteristic, complemented
26C3×#4097C2212yescomplemented
27C3×#4096—22no—
28C3×#4095C2212yescomplemented
29C3×#4088—21no—
30C3×#4078—21no—
31C2×C3×#681C2211yescharacteristic, complemented
32C3×#4055—21no—
33C3×#4055C2212yescomplemented
34C3×#4054—21no—
35C3×#4054C2212yescomplemented
36C3×#4050—22no—
37C3×#4041—22no—
38C3×#4028—22no—
39C3×#4021C2212yescomplemented
40C3×#4020C2212yescomplemented
41C3×C5×#104C2214yescomplemented
42C3×#3955C2214yescomplemented
43C3×#3937C2214yescomplemented
44C3×#3019—51nomaximal, Hall
45C2×#4149C2×C311yescharacteristic, complemented
46#66156C2×C311yescharacteristic, complemented
47#66082C2×C311yescharacteristic, complemented
48#65859C2×C311yescharacteristic, complemented
49C5×#421C2×C311yescharacteristic, complemented
50C2×#3955C2×C311yescharacteristic, complemented
51#65294C2×C311yescharacteristic, complemented
52#65114C2×C314yescomplemented
53#65111C2×C314yescomplemented
54C23×C3×D5—22no—
55C23×C3×D5D412yes—
56C3×C5×#41—21no—
57C3×C5×#41—21no—
58C3×C5×#41D412yescomplemented
59C3×C5×#41C2312yes—
60C2×C3×C5×Q8D411yescharacteristic, complemented
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4D411yescharacteristic, complemented
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—21no—
67C2×C3×C22⋊D5—21no—
68C3×#713—24no—
69C3×#713—24no—
70C3×D4×D5—28no—
71C3×D4×D5—24no—
72C3×D4×D5—28no—
73C3×D4×D5—24no—
74C3×#709—24no—
75C3×#709—21no—
76C3×#709—21no—
77C3×#709—21no—
78C3×#709—21no—
79C3×#709—21no—
80C3×#709—21no—
81C3×#709—24no—
82C3×#709D412yescomplemented
83C3×#709C2312yes—
84C2×C3×D20—22no—
85C2×C3×D20—24no—
86C2×C3×D20—21no—
87C2×C3×D20—21no—
88C2×C3×D20—21no—
89C2×C3×D20—21no—
90C2×C3×D20—24no—
91C2×C3×D20—24no—
92C2×C3×D20D412yes—
93C2×C3×D20D411yescharacteristic, complemented
94C2×C3×D20C2312yes—
95C2×C3×D20C2311yescharacteristic, complemented
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5—21no—
99C2×C3×Dic10D411yescharacteristic, complemented
100C2×C3×Dic10C2311yescharacteristic, complemented
101C3×C5×M16—21no—
102C3×C5×M16C2312yescomplemented
103C2×C3×C5×C8—21no—
104C3×C5×C4⋊C4—21no—
105C3×C5×C22⋊C4—21no—
106C3×C42×C5C2312yescomplemented
107C3×#689—22no—
108C3×#688—22no—
109C3×#687—22no—
110C3×#686—22no—
111C3×#685—24no—
112C3×#681—21no—
113C3×#681C2312yescomplemented
114C2×C3×#168—21no—
115C3×Dic20—22no—
116C3×D40—22no—
117C3×#677—22no—
118C3×#677—22no—
119C2×C3×H(5,𝔽2)—51no—
120C3×#575—51no—
121C3×#575—51no—
122C3×#535—51no—
123C3×#455—54no—
124C3×#453—54no—
125C3×#421—51no—
126C3×#421D511yescharacteristic, complemented
127C2×C3×#100—51no—
128C2×C5×#41C22×C311yescharacteristic
129#4149—22no—
130#4149—22no—
131#4149—22no—
132#4149C22×C314yes—
133C2×#713—21no—
134C2×D4×D5—22no—
135C2×D4×D5—21no—
136C2×#709—21no—
137C2×#709C22×C311yescharacteristic
138C2×#709C22×C311yescharacteristic, complemented
139C22×D20—21no—
140C22×D20C22×C311yescharacteristic
141C2×C5×M16C22×C311yescharacteristic, complemented
142C5×#117C22×C311yescharacteristic, complemented
143#4097C22×C312yescomplemented
144#4096—22no—
145#4095C22×C312yescomplemented
146#4088—21no—
147#4078—21no—
148C2×#681C22×C311yescharacteristic, complemented
149#4055—21no—
150#4055C22×C312yescomplemented
151#4054—21no—
152#4054C22×C312yescomplemented
153#4050—22no—
154#4041—22no—
155#4028—22no—
156#4021C22×C312yescomplemented
157#4020C22×C312yescomplemented
158C5×#104C22×C314yescomplemented
159#3955C22×C314yescomplemented
160#3937C22×C314yescomplemented
161#3019—51noSylow
162C23×C3×C5—21no—
163C23×C3×C5C2×D411yescharacteristic
164C22×C3×D5—22no—
165C22×C3×D5—21no—
166C22×C3×D5—28no—
167C22×C3×D5—22no—
168C22×C3×D5—21no—
169C22×C3×D5—82no—
170C22×C3×D5—84no—
171C22×C3×D5C2×D414yes—
172C3×C5×Q8—21no—
173C3×C5×Q8C2×D412yes—
174C3×C5×D4—22no—
175C3×C5×D4—22no—
176C3×C5×D4—21no—
177C3×C5×D4C2×D412yes—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188C3×C22⋊D5—28no—
189C3×C22⋊D5—22no—
190C3×C22⋊D5—22no—
191C3×C22⋊D5—41no—
192C3×C22⋊D5—41no—
193C2×C3×Dic5—21no—
194C2×C3×Dic5—21no—
195C3×D20—28no—
196C3×D20—22no—
197C3×D20—21no—
198C3×D20—22no—
199C3×D20—22no—
200C3×D20—22no—
201C3×D20—21no—
202C3×D20—21no—
203C3×D20—84no—
204C3×D20C2×D412yes—
205C3×C4×D5—28no—
206C3×C4×D5—22no—
207C3×C4×D5—22no—
208C3×C4×D5—41no—
209C3×C4×D5—41no—
210C3×Dic10—21no—
211C3×Dic10—21no—
212C3×Dic10—21no—
213C3×Dic10C2×D412yes—
214C3×C5×C8—22no—
215C3×#168—22no—
216C3×H(5,𝔽2)—54no—
217C3×H(5,𝔽2)—102no—
218C3×H(5,𝔽2)—102no—
219C3×H(5,𝔽2)—102no—
220C2×C3×#41—51no—
221C2×C3×#41—51no—
222C2×C3×#41—101no—
223C2×C3×#41—101no—
224C2×C3×#41C2×D511yescharacteristic
225C22×C3×D4—51no—
226C22×C3×D4—101no—
227C22×C3×D4—102no—
228C22×C3×D4—101no—
229C3×#137—52no—
230C3×#137—52no—
231C3×#137—101no—
232C3×#137—101no—
233C3×AGL(1,ℤ/8)—52no—
234C3×AGL(1,ℤ/8)—52no—
235C3×AGL(1,ℤ/8)—101no—
236C3×AGL(1,ℤ/8)—101no—
237C3×#135—102no—
238C3×#135—102no—
239C2×C3×M16—51no—
240C2×C3×M16C2×D511yescharacteristic, complemented
241C3×#127—52no—
242C3×#124—52no—
243C3×#121—102no—
244C3×#120—102no—
245C3×#117C2×D511yescharacteristic, complemented
246C3×#104—54no—
247C3×#104C2×D514yescomplemented
248C3×#100—54no—
249C23×D5—22no—
250C23×D5C3×D412yes—
251C5×#41—21no—
252C5×#41—21no—
253C5×#41C3×D412yescomplemented
254C5×#41C23×C312yes—
255C2×C5×Q8C3×D411yescharacteristic, complemented
256C2×C5×D4—21no—
257C2×C5×D4C3×D411yescharacteristic, complemented
258C22×C4×C5—21no—
259C22×C4×C5C23×C311yescharacteristic
260C2×C22⋊D5—22no—
261C2×C22⋊D5—21no—
262C2×C22⋊D5—21no—
263#713—24no—
264#713—24no—
265D4×D5—28no—
266D4×D5—24no—
267D4×D5—28no—
268D4×D5—24no—
269#709—24no—
270#709—21no—
271#709—21no—
272#709—21no—
273#709—21no—
274#709—21no—
275#709—21no—
276#709—24no—
277#709C3×D412yescomplemented
278#709C23×C312yes—
279C2×D20—22no—
280C2×D20—24no—
281C2×D20—21no—
282C2×D20—21no—
283C2×D20—21no—
284C2×D20—21no—
285C2×D20—24no—
286C2×D20—24no—
287C2×D20C3×D412yes—
288C2×D20C3×D411yescharacteristic, complemented
289C2×D20C23×C312yes—
290C2×D20C23×C311yescharacteristic, complemented
291C2×C4×D5—22no—
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×Dic10C3×D411yescharacteristic, complemented
295C2×Dic10C23×C311yescharacteristic, complemented
296C5×M16—21no—
297C5×M16C23×C312yescomplemented
298C2×C5×C8—21no—
299C5×C4⋊C4—21no—
300C5×C22⋊C4—21no—
301C42×C5C23×C312yescomplemented
302#689—22no—
303#688—22no—
304#687—22no—
305#686—22no—
306#685—24no—
307#681—21no—
308#681C23×C312yescomplemented
309C2×#168—21no—
310Dic20—22no—
311D40—22no—
312#677—22no—
313#677—22no—
314C2×H(5,𝔽2)—51no—
315#575—51no—
316#575—51no—
317#535—51no—
318#455—54no—
319#453—54no—
320#421—51no—
321#421C3×D511yescharacteristic, complemented
322C2×#100—51no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—42no—
326C22×C3×C5#12011yescharacteristic
327C22×C3×C5#12011yescharacteristic
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—24no—
330C2×C3×D5—22no—
331C2×C3×D5—44no—
332C2×C3×D5—42no—
333C2×C3×D5—44no—
334C2×C3×D5—42no—
335C2×C3×D5—41no—
336C2×C3×D5—82no—
337C2×C3×D5—88no—
338C3×C4×C5—22no—
339C3×C4×C5—42no—
340C3×C4×C5#12011yescharacteristic
341C3×C4×C5#12011yescharacteristic
342C3×C4×C5C22×D411yescharacteristic
343C3×C4×C5C22×D411yescharacteristic
344C3×Dic5—22no—
345C3×Dic5—41no—
346C24×C3—52no—
347C24×C3—102no—
348C3×#41—21no—
349C3×#41—21no—
350C3×#41—52no—
351C3×#41—52no—
352C3×#41—104no—
353C3×#41—104no—
354C3×#41—104no—
355C3×#41—104no—
356C3×#41—101no—
357C3×#41—101no—
358C3×#41—101no—
359C3×#41—101no—
360C3×#41—101no—
361C3×#41—101no—
362C3×#41D2012yescomplemented
363C3×#41C22×D512yes—
364C2×C3×Q8—51no—
365C2×C3×Q8—51no—
366C2×C3×Q8D2011yescharacteristic, complemented
367C2×C3×D4—21no—
368C2×C3×D4—51no—
369C2×C3×D4—52no—
370C2×C3×D4—52no—
371C2×C3×D4—51no—
372C2×C3×D4—104no—
373C2×C3×D4—102no—
374C2×C3×D4—104no—
375C2×C3×D4—104no—
376C2×C3×D4—108no—
377C2×C3×D4—108no—
378C2×C3×D4—104no—
379C2×C3×D4—102no—
380C2×C3×D4—101no—
381C2×C3×D4—104no—
382C2×C3×D4—101no—
383C2×C3×D4—101no—
384C2×C3×D4—101no—
385C2×C3×D4—101no—
386C2×C3×D4—101no—
387C2×C3×D4D2011yescharacteristic, complemented
388C22×C3×C4—21no—
389C22×C3×C4—102no—
390C22×C3×C4—101no—
391C22×C3×C4—101no—
392C22×C3×C4C22×D511yescharacteristic
393C3×Q16—102no—
394C3×Q16—102no—
395C3×SD16—102no—
396C3×SD16—102no—
397C3×SD16—102no—
398C3×SD16—102no—
399C3×D8—102no—
400C3×D8—102no—
401C3×M16—21no—
402C3×M16—52no—
403C3×M16—101no—
404C3×M16C22×D512yescomplemented
405C2×C3×C8—21no—
406C2×C3×C8—101no—
407C3×C4⋊C4—21no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—104no—
410C3×C42C22×D512yescomplemented
411C23×C5—21no—
412C23×C5C2×C3×D411yescharacteristic
413C22×D5—22no—
414C22×D5—21no—
415C22×D5—28no—
416C22×D5—22no—
417C22×D5—21no—
418C22×D5—82no—
419C22×D5—84no—
420C22×D5C2×C3×D414yes—
421C5×Q8—21no—
422C5×Q8C2×C3×D412yes—
423C5×D4—22no—
424C5×D4—22no—
425C5×D4—21no—
426C5×D4C2×C3×D412yes—
427C2×C4×C5—21no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5C2×C3×D411yescharacteristic
432C2×C4×C5C2×C3×D411yescharacteristic
433C2×C4×C5C2×C3×D411yescharacteristic
434C2×C4×C5C2×C3×D411yescharacteristic
435C2×C4×C5C2×C3×D411yescharacteristic
436C2×C4×C5C24×C311yescharacteristic
437C22⋊D5—28no—
438C22⋊D5—22no—
439C22⋊D5—22no—
440C22⋊D5—41no—
441C22⋊D5—41no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444D20—28no—
445D20—22no—
446D20—21no—
447D20—22no—
448D20—22no—
449D20—22no—
450D20—21no—
451D20—21no—
452D20—84no—
453D20C2×C3×D412yes—
454C4×D5—28no—
455C4×D5—22no—
456C4×D5—22no—
457C4×D5—41no—
458C4×D5—41no—
459Dic10—21no—
460Dic10—21no—
461Dic10—21no—
462Dic10C2×C3×D412yes—
463C5×C8—22no—
464#168—22no—
465H(5,𝔽2)—54no—
466H(5,𝔽2)—102no—
467H(5,𝔽2)—102no—
468H(5,𝔽2)—102no—
469C2×#41—51no—
470C2×#41—51no—
471C2×#41—101no—
472C2×#41—101no—
473C2×#41C2×C3×D511yescharacteristic
474C22×D4—51no—
475C22×D4—101no—
476C22×D4—102no—
477C22×D4—101no—
478#137—52no—
479#137—52no—
480#137—101no—
481#137—101no—
482AGL(1,ℤ/8)—52no—
483AGL(1,ℤ/8)—52no—
484AGL(1,ℤ/8)—101no—
485AGL(1,ℤ/8)—101no—
486#135—102no—
487#135—102no—
488C2×M16—51no—
489C2×M16C2×C3×D511yescharacteristic, complemented
490#127—52no—
491#124—52no—
492#121—102no—
493#120—102no—
494#117C2×C3×D511yescharacteristic, complemented
495#104—54no—
496#104C2×C3×D514yescomplemented
497#100—54no—
498C2×C3×C5—21no—
499C2×C3×C5—21no—
500C2×C3×C5—21no—
501C2×C3×C5—42no—
502C2×C3×C5C2×#12011yescharacteristic
503C3×D5—44no—
504C3×D5—42no—
505C3×D5—81no—
506C23×C3—21no—
507C23×C3—54no—
508C23×C3—108no—
509C23×C3—101no—
510C23×C3—102no—
511C23×C3—102no—
512C23×C3—101no—
513C23×C3—402no—
514C23×C3—404no—
515C23×C3D4×D511yescharacteristic
516C3×Q8—21no—
517C3×Q8—52no—
518C3×Q8—101no—
519C3×Q8—101no—
520C3×Q8—101no—
521C3×Q8C2×D2012yes—
522C3×D4—22no—
523C3×D4—22no—
524C3×D4—21no—
525C3×D4—52no—
526C3×D4—108no—
527C3×D4—108no—
528C3×D4—102no—
529C3×D4—102no—
530C3×D4—102no—
531C3×D4—101no—
532C3×D4—102no—
533C3×D4—101no—
534C3×D4—101no—
535C3×D4—102no—
536C3×D4—102no—
537C3×D4—201no—
538C3×D4—201no—
539C3×D4—404no—
540C3×D4C2×D2012yes—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—108no—
546C2×C3×C4—101no—
547C2×C3×C4—102no—
548C2×C3×C4—102no—
549C2×C3×C4—101no—
550C2×C3×C4—201no—
551C2×C3×C4—201no—
552C2×C3×C4C2×D2011yescharacteristic
553C2×C3×C4C2×D2011yescharacteristic
554C2×C3×C4D4×D511yescharacteristic
555C2×C3×C4D4×D511yescharacteristic
556C2×C3×C4D4×D511yescharacteristic
557C2×C3×C4C23×D511yescharacteristic
558C3×C8—22no—
559C3×C8—102no—
560C22×C5—22no—
561C22×C5—41no—
562C22×C5—42no—
563C22×C5C3×#12011yescharacteristic
564C22×C5C3×#12011yescharacteristic
565C22×C5C22×C3×D411yescharacteristic
566C2×D5—24no—
567C2×D5—22no—
568C2×D5—44no—
569C2×D5—42no—
570C2×D5—44no—
571C2×D5—42no—
572C2×D5—41no—
573C2×D5—82no—
574C2×D5—88no—
575C4×C5—22no—
576C4×C5—42no—
577C4×C5C3×#12011yescharacteristic
578C4×C5C3×#12011yescharacteristic
579C4×C5C22×C3×D411yescharacteristic
580C4×C5C22×C3×D411yescharacteristic
581Dic5—22no—
582Dic5—41no—
583C24—52no—
584C24—102no—
585#41—21no—
586#41—21no—
587#41—52no—
588#41—52no—
589#41—104no—
590#41—104no—
591#41—104no—
592#41—104no—
593#41—101no—
594#41—101no—
595#41—101no—
596#41—101no—
597#41—101no—
598#41—101no—
599#41C3×D2012yescomplemented
600#41C22×C3×D512yes—
601C2×Q8—51no—
602C2×Q8—51no—
603C2×Q8C3×D2011yescharacteristic, complemented
604C2×D4—21no—
605C2×D4—51no—
606C2×D4—52no—
607C2×D4—52no—
608C2×D4—51no—
609C2×D4—104no—
610C2×D4—102no—
611C2×D4—104no—
612C2×D4—104no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—104no—
616C2×D4—102no—
617C2×D4—101no—
618C2×D4—104no—
619C2×D4—101no—
620C2×D4—101no—
621C2×D4—101no—
622C2×D4—101no—
623C2×D4—101no—
624C2×D4C3×D2011yescharacteristic, complemented
625C22×C4—21no—
626C22×C4—102no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4C22×C3×D511yescharacteristic
630Q16—102no—
631Q16—102no—
632SD16—102no—
633SD16—102no—
634SD16—102no—
635SD16—102no—
636D8—102no—
637D8—102no—
638M16—21no—
639M16—52no—
640M16—101no—
641M16C22×C3×D512yescomplemented
642C2×C8—21no—
643C2×C8—101no—
644C4⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—104no—
647C42C22×C3×D512yescomplemented
648C3×C5#301911yescharacteristic, complemented, Hall
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—102no—
653C22×C3—104no—
654C22×C3—204no—
655C22×C3—204no—
656C22×C3—202no—
657C22×C3—202no—
658C22×C3—201no—
659C22×C3—402no—
660C22×C3—408no—
661C22×C3#402811yescharacteristic
662C22×C3#402811yescharacteristic
663C22×C3C2×D4×D511yescharacteristic
664C3×C4—22no—
665C3×C4—42no—
666C3×C4—102no—
667C3×C4—201no—
668C3×C4#402811yescharacteristic
669C3×C4#402811yescharacteristic
670C3×C4C22×D2011yescharacteristic
671C3×C4C2×D4×D511yescharacteristic
672C2×C5—21no—
673C2×C5—21no—
674C2×C5—21no—
675C2×C5—42no—
676C2×C5C2×C3×#12011yescharacteristic
677D5—44no—
678D5—42no—
679D5—81no—
680C23—21no—
681C23—54no—
682C23—108no—
683C23—101no—
684C23—102no—
685C23—102no—
686C23—101no—
687C23—402no—
688C23—404no—
689C23C3×D4×D511yescharacteristic
690Q8—21no—
691Q8—52no—
692Q8—101no—
693Q8—101no—
694Q8—101no—
695Q8C2×C3×D2012yes—
696D4—22no—
697D4—22no—
698D4—21no—
699D4—52no—
700D4—108no—
701D4—108no—
702D4—102no—
703D4—102no—
704D4—102no—
705D4—101no—
706D4—102no—
707D4—101no—
708D4—101no—
709D4—102no—
710D4—102no—
711D4—201no—
712D4—201no—
713D4—404no—
714D4C2×C3×D2012yes—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—108no—
720C2×C4—101no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—101no—
724C2×C4—201no—
725C2×C4—201no—
726C2×C4C2×C3×D2011yescharacteristic
727C2×C4C2×C3×D2011yescharacteristic
728C2×C4C3×D4×D511yescharacteristic
729C2×C4C3×D4×D511yescharacteristic
730C2×C4C3×D4×D511yescharacteristic
731C2×C4C23×C3×D511yescharacteristic
732C8—22no—
733C8—102no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—204no—
739C2×C3—202no—
740C2×C3—401no—
741C2×C3C2×#402811yescharacteristic
742C5C3×#301911yescharacteristic, complemented, Sylow
743C22—22no—
744C22—41no—
745C22—42no—
746C22—102no—
747C22—104no—
748C22—204no—
749C22—204no—
750C22—202no—
751C22—202no—
752C22—201no—
753C22—402no—
754C22—408no—
755C22C3×#402811yescharacteristic
756C22C3×#402811yescharacteristic
757C22C2×C3×D4×D511yescharacteristic
758C4—22no—
759C4—42no—
760C4—102no—
761C4—201no—
762C4C3×#402811yescharacteristic
763C4C3×#402811yescharacteristic
764C4C22×C3×D2011yescharacteristic
765C4C2×C3×D4×D511yescharacteristic
766C3#1061072411yescharacteristic, direct product factor, Sylow
767C2—21no—
768C2—21no—
769C2—21no—
770C2—42no—
771C2—204no—
772C2—202no—
773C2—401no—
774C2C2×C3×#402811yescharacteristic
subgroupG/H
centerC2×C3C2×#4028
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5C2×#120
hypercenterC3×#421D5
hypocenterC5C3×#3019
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4149C2semidirect
2. C3×#66156C2semidirect
3. C3×#66082C2semidirect
4. C3×#65859C2semidirect
5. C3×C5×#421C2semidirect
6. C2×C3×#3955C2semidirect
7. C3×#65294C2semidirect
8. C3×#65114C2semidirect
9. C3×#65111C2semidirect
10. #10610724C3direct (N × H)
21. C2×C3×#709C22semidirect
24. C2×C3×C5×M16C22semidirect
25. C3×C5×#117C22semidirect
26. C3×#4097C22semidirect
28. C3×#4095C22semidirect
31. C2×C3×#681C22semidirect
33. C3×#4055C22semidirect
35. C3×#4054C22semidirect
39. C3×#4021C22semidirect
40. C3×#4020C22semidirect
41. C3×C5×#104C22semidirect
42. C3×#3955C22semidirect
43. C3×#3937C22semidirect
45. C2×#4149C2×C3semidirect
46. #66156C2×C3semidirect
47. #66082C2×C3semidirect
48. #65859C2×C3semidirect
49. C5×#421C2×C3semidirect
50. C2×#3955C2×C3semidirect
51. #65294C2×C3semidirect
52. #65114C2×C3semidirect
53. #65111C2×C3semidirect
58. C3×C5×#41D4semidirect
60. C2×C3×C5×Q8D4semidirect
62. C2×C3×C5×D4D4semidirect
82. C3×#709D4semidirect
93. C2×C3×D20D4semidirect
95. C2×C3×D20C23semidirect
99. C2×C3×Dic10D4semidirect
100. C2×C3×Dic10C23semidirect
102. C3×C5×M16C23semidirect
106. C3×C42×C5C23semidirect
113. C3×#681C23semidirect
126. C3×#421D5semidirect
138. C2×#709C22×C3semidirect
141. C2×C5×M16C22×C3semidirect
142. C5×#117C22×C3semidirect
143. #4097C22×C3semidirect
145. #4095C22×C3semidirect
148. C2×#681C22×C3semidirect
150. #4055C22×C3semidirect
152. #4054C22×C3semidirect
156. #4021C22×C3semidirect
157. #4020C22×C3semidirect
158. C5×#104C22×C3semidirect
159. #3955C22×C3semidirect
160. #3937C22×C3semidirect
240. C2×C3×M16C2×D5semidirect
245. C3×#117C2×D5semidirect
247. C3×#104C2×D5semidirect
253. C5×#41C3×D4semidirect
255. C2×C5×Q8C3×D4semidirect
257. C2×C5×D4C3×D4semidirect
277. #709C3×D4semidirect
288. C2×D20C3×D4semidirect
290. C2×D20C23×C3semidirect
294. C2×Dic10C3×D4semidirect
295. C2×Dic10C23×C3semidirect
297. C5×M16C23×C3semidirect
301. C42×C5C23×C3semidirect
308. #681C23×C3semidirect
321. #421C3×D5semidirect
362. C3×#41D20semidirect
366. C2×C3×Q8D20semidirect
387. C2×C3×D4D20semidirect
404. C3×M16C22×D5semidirect
410. C3×C42C22×D5semidirect
489. C2×M16C2×C3×D5semidirect
494. #117C2×C3×D5semidirect
496. #104C2×C3×D5semidirect
599. #41C3×D20semidirect
603. C2×Q8C3×D20semidirect
624. C2×D4C3×D20semidirect
641. M16C22×C3×D5semidirect
647. C42C22×C3×D5semidirect
648. C3×C5#3019semidirect
742. C5C3×#3019semidirect
766. C3#10610724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41492
C3×#661562
C3×#660822
C3×#658592
C3×C5×#4212
C2×C3×#39552
C3×#652942
C3×#651142
C3×#651112
#106107243
C3×#30195