Finite Group Databasebeta

← C3×#10615737 #14425372

Subgroups — C3×#10615737 #14425372

Order 1920.

1396 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic, complemented
2C3×C5×#575C211yesmaximal, characteristic, complemented
3C3×#66159C211yesmaximal, characteristic, complemented
4C3×#66156C211yesmaximal, characteristic, complemented
5C3×#65525C211yesmaximal, characteristic, complemented
6C3×#65494C214yesmaximal, complemented
7C3×#65490C214yesmaximal, complemented
8C3×#65428C211yesmaximal, characteristic, complemented
9C2×C3×#3956C211yesmaximal, characteristic, complemented
10#10615737C311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C2×C3×C5×#41C2211yescharacteristic
13C3×#4150—22no—
14C3×#4150—22no—
15C3×#4150—22no—
16C3×#4150C2214yes—
17C2×C3×Q8×D5—21no—
18C2×C3×#711—21no—
19C2×C3×#711—22no—
20C2×C3×#709—21no—
21C2×C3×#709C2211yescharacteristic
22C22×C3×Dic10—21no—
23C22×C3×Dic10C2211yescharacteristic
24C3×C5×#137—21no—
25C3×C5×#137C2212yescomplemented
26C3×C5×AGL(1,ℤ/8)—21no—
27C3×C5×AGL(1,ℤ/8)C2212yescomplemented
28C3×C5×#135—22no—
29C2×C3×C5×M16C2211yescharacteristic
30C3×#4097—21no—
31C3×#4096—22no—
32C3×#4095—21no—
33C3×#4090C2212yescomplemented
34C3×#4088C2212yescomplemented
35C3×#4082C2212yescomplemented
36C3×#4081—22no—
37C3×#4078C2212yescomplemented
38C3×#4072C2211yescharacteristic
39C3×#4070—22no—
40C2×C3×#681C2211yescharacteristic
41C3×#3969C2214yescomplemented
42C3×#3957C2214yescomplemented
43C3×#3956C2214yescomplemented
44C3×#3020—51nomaximal, Hall
45C2×#4150C2×C311yescharacteristic, complemented
46C5×#575C2×C311yescharacteristic, complemented
47#66159C2×C311yescharacteristic, complemented
48#66156C2×C311yescharacteristic, complemented
49#65525C2×C311yescharacteristic, complemented
50#65494C2×C314yescomplemented
51#65490C2×C314yescomplemented
52#65428C2×C311yescharacteristic, complemented
53C2×#3956C2×C311yescharacteristic, complemented
54C3×C5×#41—21no—
55C3×C5×#41—21no—
56C3×C5×#41—21no—
57C3×C5×#41—21no—
58C3×C5×#41—21no—
59C3×C5×#41—21no—
60C3×C5×#41D412yes—
61C3×C5×#41C2312yes—
62C2×C3×C5×Q8D411yescharacteristic
63C2×C3×C5×Q8C2311yescharacteristic
64C2×C3×C5×D4—21no—
65C2×C3×C5×D4—21no—
66C2×C3×C5×D4D411yescharacteristic
67C2×C3×C5×D4C2311yescharacteristic
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5—21no—
70C22×C3×C4×C5C2311yescharacteristic
71C2×C3×C22⋊D5—22no—
72C2×C3×C22⋊D5—21no—
73C22×C3×Dic5—22no—
74C22×C3×Dic5D412yes—
75C3×Q8×D5—24no—
76C3×Q8×D5—24no—
77C3×#711—28no—
78C3×#711—24no—
79C3×#711—24no—
80C3×#711—28no—
81C3×#709—24no—
82C3×#709—21no—
83C3×#709—21no—
84C3×#709—24no—
85C3×#709D412yes—
86C3×#709C2312yes—
87C2×C3×D20D411yescharacteristic
88C2×C3×C4×D5—22no—
89C2×C3×C4×D5—21no—
90C2×C3×Dic10—22no—
91C2×C3×Dic10—24no—
92C2×C3×Dic10—21no—
93C2×C3×Dic10—21no—
94C2×C3×Dic10—21no—
95C2×C3×Dic10—21no—
96C2×C3×Dic10—24no—
97C2×C3×Dic10D412yes—
98C2×C3×Dic10D411yescharacteristic
99C2×C3×Dic10C2312yes—
100C3×C5×Q16—22no—
101C3×C5×SD16—22no—
102C3×C5×SD16—22no—
103C3×C5×D8—22no—
104C3×C5×M16—21no—
105C3×C5×M16C2312yes—
106C2×C3×C5×C8—21no—
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5—24no—
109C3×#689—22no—
110C3×#688—22no—
111C3×#687—22no—
112C3×#686—22no—
113C3×C4⋊Dic5—21no—
114C3×#683—24no—
115C3×C4×Dic5C2312yes—
116C3×#681—21no—
117C3×#681C2312yes—
118C2×C3×#168—21no—
119C2×C3×2−1+4—51no—
120C3×#575—51no—
121C3×#575D511yescharacteristic, complemented
122C3×#536—51no—
123C3×#456—54no—
124C3×#454—54no—
125C3×#421—51no—
126C3×#421—51no—
127C2×C3×#101—51no—
128C2×C5×#41C22×C311yescharacteristic
129C2×C5×#41C22×C311yescharacteristic
130#4150—22no—
131#4150—22no—
132#4150—22no—
133#4150C22×C314yes—
134C2×Q8×D5—21no—
135C2×#711—21no—
136C2×#711—22no—
137C2×#709—21no—
138C2×#709C22×C311yescharacteristic
139C22×Dic10—21no—
140C22×Dic10C22×C311yescharacteristic
141C5×#137—21no—
142C5×#137C22×C312yescomplemented
143C5×AGL(1,ℤ/8)—21no—
144C5×AGL(1,ℤ/8)C22×C312yescomplemented
145C5×#135—22no—
146C2×C5×M16C22×C311yescharacteristic
147#4097—21no—
148#4096—22no—
149#4095—21no—
150#4090C22×C312yescomplemented
151#4088C22×C312yescomplemented
152#4082C22×C312yescomplemented
153#4081—22no—
154#4078C22×C312yescomplemented
155#4072C22×C311yescharacteristic
156#4070—22no—
157C2×#681C22×C311yescharacteristic
158#3969C22×C314yescomplemented
159#3957C22×C314yescomplemented
160#3956C22×C314yescomplemented
161#3020—51noSylow
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5C2×D411yescharacteristic
165C22×C3×D5—21no—
166C3×C5×Q8—21no—
167C3×C5×Q8—21no—
168C3×C5×Q8—21no—
169C3×C5×Q8C2×D412yes—
170C3×C5×D4—22no—
171C3×C5×D4—22no—
172C3×C5×D4—21no—
173C3×C5×D4—21no—
174C3×C5×D4—21no—
175C3×C5×D4—41no—
176C3×C5×D4—41no—
177C3×C5×D4C2×D412yes—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—41no—
183C2×C3×C4×C5—41no—
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2411yescharacteristic
190C3×C22⋊D5—28no—
191C3×C22⋊D5—22no—
192C3×C22⋊D5—22no—
193C2×C3×Dic5—28no—
194C2×C3×Dic5—22no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—22no—
198C2×C3×Dic5C2×D414yes—
199C3×D20—21no—
200C3×D20C2×D412yes—
201C3×C4×D5—28no—
202C3×C4×D5—22no—
203C3×C4×D5—22no—
204C3×Dic10—28no—
205C3×Dic10—22no—
206C3×Dic10—21no—
207C3×Dic10—22no—
208C3×Dic10—22no—
209C3×Dic10—22no—
210C3×Dic10C2×D412yes—
211C3×C5×C8—22no—
212C3×#168—22no—
213C3×2−1+4—54no—
214C3×2−1+4—102no—
215C3×2−1+4—102no—
216C3×2−1+4—102no—
217C2×C3×#41—51no—
218C2×C3×#41—101no—
219C2×C3×#41—102no—
220C2×C3×#41—101no—
221C2×C3×#41C2×D511yescharacteristic
222C2×C3×#41C2×D511yescharacteristic
223C22×C3×Q8—51no—
224C22×C3×Q8—101no—
225C22×C3×Q8—101no—
226C3×#137—21no—
227C3×#137—52no—
228C3×#137—101no—
229C3×#137C2×D512yescomplemented
230C3×AGL(1,ℤ/8)—21no—
231C3×AGL(1,ℤ/8)—52no—
232C3×AGL(1,ℤ/8)—101no—
233C3×AGL(1,ℤ/8)C2×D512yescomplemented
234C3×#135—22no—
235C3×#135—102no—
236C2×C3×M16—51no—
237C2×C3×M16C2×D511yescharacteristic
238C3×C4⋊Q8—52no—
239C3×#124—52no—
240C3×#123—102no—
241C3×C22⋊Q8—102no—
242C3×#117—51no—
243C3×#104—54no—
244C3×#104—54no—
245C3×#101—54no—
246C5×#41—21no—
247C5×#41—21no—
248C5×#41—21no—
249C5×#41—21no—
250C5×#41—21no—
251C5×#41—21no—
252C5×#41C3×D412yes—
253C5×#41C23×C312yes—
254C2×C5×Q8C3×D411yescharacteristic
255C2×C5×Q8C23×C311yescharacteristic
256C2×C5×D4—21no—
257C2×C5×D4—21no—
258C2×C5×D4C3×D411yescharacteristic
259C2×C5×D4C23×C311yescharacteristic
260C22×C4×C5—21no—
261C22×C4×C5—21no—
262C22×C4×C5C23×C311yescharacteristic
263C2×C22⋊D5—22no—
264C2×C22⋊D5—21no—
265C22×Dic5—22no—
266C22×Dic5C3×D412yes—
267Q8×D5—24no—
268Q8×D5—24no—
269#711—28no—
270#711—24no—
271#711—24no—
272#711—28no—
273#709—24no—
274#709—21no—
275#709—21no—
276#709—24no—
277#709C3×D412yes—
278#709C23×C312yes—
279C2×D20C3×D411yescharacteristic
280C2×C4×D5—22no—
281C2×C4×D5—21no—
282C2×Dic10—22no—
283C2×Dic10—24no—
284C2×Dic10—21no—
285C2×Dic10—21no—
286C2×Dic10—21no—
287C2×Dic10—21no—
288C2×Dic10—24no—
289C2×Dic10C3×D412yes—
290C2×Dic10C3×D411yescharacteristic
291C2×Dic10C23×C312yes—
292C5×Q16—22no—
293C5×SD16—22no—
294C5×SD16—22no—
295C5×D8—22no—
296C5×M16—21no—
297C5×M16C23×C312yes—
298C2×C5×C8—21no—
299C22⋊Dic5—21no—
300C22⋊Dic5—24no—
301#689—22no—
302#688—22no—
303#687—22no—
304#686—22no—
305C4⋊Dic5—21no—
306#683—24no—
307C4×Dic5C23×C312yes—
308#681—21no—
309#681C23×C312yes—
310C2×#168—21no—
311C2×2−1+4—51no—
312#575—51no—
313#575C3×D511yescharacteristic, complemented
314#536—51no—
315#456—54no—
316#454—54no—
317#421—51no—
318#421—51no—
319C2×#101—51no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—42no—
323C22×C3×C5—42no—
324C22×C3×C5—41no—
325C22×C3×C5#12011yescharacteristic
326C22×C3×C5#12011yescharacteristic
327C22×C3×C5C22×D411yescharacteristic
328C2×C3×D5—22no—
329C2×C3×D5—42no—
330C3×C4×C5—22no—
331C3×C4×C5—41no—
332C3×C4×C5#12011yescharacteristic
333C3×C4×C5#12011yescharacteristic
334C3×C4×C5C22×D411yescharacteristic
335C3×C4×C5C22×D411yescharacteristic
336C3×Dic5—24no—
337C3×Dic5—22no—
338C3×Dic5—42no—
339C3×#41—21no—
340C3×#41—21no—
341C3×#41—21no—
342C3×#41—21no—
343C3×#41—21no—
344C3×#41—21no—
345C3×#41—52no—
346C3×#41—52no—
347C3×#41—104no—
348C3×#41—104no—
349C3×#41—108no—
350C3×#41—108no—
351C3×#41—104no—
352C3×#41—104no—
353C3×#41—101no—
354C3×#41—101no—
355C3×#41C22⋊D512yes—
356C3×#41C22×D512yes—
357C2×C3×Q8—52no—
358C2×C3×Q8—52no—
359C2×C3×Q8—51no—
360C2×C3×Q8—104no—
361C2×C3×Q8—102no—
362C2×C3×Q8—104no—
363C2×C3×Q8—104no—
364C2×C3×Q8—104no—
365C2×C3×Q8—101no—
366C2×C3×Q8—101no—
367C2×C3×Q8—101no—
368C2×C3×Q8—101no—
369C2×C3×Q8C22⋊D511yescharacteristic
370C2×C3×Q8C22×D511yescharacteristic
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4—51no—
374C2×C3×D4—102no—
375C2×C3×D4—101no—
376C2×C3×D4C22⋊D511yescharacteristic
377C2×C3×D4C22×D511yescharacteristic
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—52no—
381C22×C3×C4—102no—
382C22×C3×C4—102no—
383C22×C3×C4—101no—
384C22×C3×C4C22×D511yescharacteristic
385C3×Q16—22no—
386C3×Q16—102no—
387C3×SD16—22no—
388C3×SD16—22no—
389C3×SD16—102no—
390C3×SD16—102no—
391C3×D8—22no—
392C3×D8—102no—
393C3×M16—21no—
394C3×M16—52no—
395C3×M16—101no—
396C3×M16C22×D512yes—
397C2×C3×C8—21no—
398C2×C3×C8—101no—
399C3×C4⋊C4—104no—
400C3×C4⋊C4—101no—
401C3×C22⋊C4—104no—
402C3×C22⋊C4—101no—
403C3×C42—52no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5C2×C3×D411yescharacteristic
407C22×D5—21no—
408C5×Q8—21no—
409C5×Q8—21no—
410C5×Q8—21no—
411C5×Q8C2×C3×D412yes—
412C5×D4—22no—
413C5×D4—22no—
414C5×D4—21no—
415C5×D4—21no—
416C5×D4—21no—
417C5×D4—41no—
418C5×D4—41no—
419C5×D4C2×C3×D412yes—
420C2×C4×C5—21no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—21no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5C2×C3×D411yescharacteristic
427C2×C4×C5C2×C3×D411yescharacteristic
428C2×C4×C5C2×C3×D411yescharacteristic
429C2×C4×C5C2×C3×D411yescharacteristic
430C2×C4×C5C2×C3×D411yescharacteristic
431C2×C4×C5C24×C311yescharacteristic
432C22⋊D5—28no—
433C22⋊D5—22no—
434C22⋊D5—22no—
435C2×Dic5—28no—
436C2×Dic5—22no—
437C2×Dic5—21no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5C2×C3×D414yes—
441D20—21no—
442D20C2×C3×D412yes—
443C4×D5—28no—
444C4×D5—22no—
445C4×D5—22no—
446Dic10—28no—
447Dic10—22no—
448Dic10—21no—
449Dic10—22no—
450Dic10—22no—
451Dic10—22no—
452Dic10C2×C3×D412yes—
453C5×C8—22no—
454#168—22no—
4552−1+4—54no—
4562−1+4—102no—
4572−1+4—102no—
4582−1+4—102no—
459C2×#41—51no—
460C2×#41—101no—
461C2×#41—102no—
462C2×#41—101no—
463C2×#41C2×C3×D511yescharacteristic
464C2×#41C2×C3×D511yescharacteristic
465C22×Q8—51no—
466C22×Q8—101no—
467C22×Q8—101no—
468#137—21no—
469#137—52no—
470#137—101no—
471#137C2×C3×D512yescomplemented
472AGL(1,ℤ/8)—21no—
473AGL(1,ℤ/8)—52no—
474AGL(1,ℤ/8)—101no—
475AGL(1,ℤ/8)C2×C3×D512yescomplemented
476#135—22no—
477#135—102no—
478C2×M16—51no—
479C2×M16C2×C3×D511yescharacteristic
480C4⋊Q8—52no—
481#124—52no—
482#123—102no—
483C22⋊Q8—102no—
484#117—51no—
485#104—54no—
486#104—54no—
487#101—54no—
488C2×C3×C5—21no—
489C2×C3×C5—21no—
490C2×C3×C5—21no—
491C2×C3×C5—42no—
492C2×C3×C5—81no—
493C2×C3×C5C2×#12011yescharacteristic
494C3×D5—42no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—101no—
498C23×C3D4×D511yescharacteristic
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—52no—
503C3×Q8—108no—
504C3×Q8—102no—
505C3×Q8—102no—
506C3×Q8—102no—
507C3×Q8—102no—
508C3×Q8—101no—
509C3×Q8C2×C22⋊D512yes—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—52no—
518C3×D4—108no—
519C3×D4—102no—
520C3×D4—102no—
521C3×D4—101no—
522C3×D4C2×C22⋊D512yes—
523C2×C3×C4—21no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—54no—
530C2×C3×C4—108no—
531C2×C3×C4—108no—
532C2×C3×C4—102no—
533C2×C3×C4—102no—
534C2×C3×C4—101no—
535C2×C3×C4—102no—
536C2×C3×C4—102no—
537C2×C3×C4—102no—
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4D4×D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C2×C22⋊D511yescharacteristic
543C2×C3×C4C23×D511yescharacteristic
544C3×C8—22no—
545C3×C8—102no—
546C22×C5—22no—
547C22×C5—41no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—41no—
551C22×C5C3×#12011yescharacteristic
552C22×C5C3×#12011yescharacteristic
553C22×C5C22×C3×D411yescharacteristic
554C2×D5—22no—
555C2×D5—42no—
556C4×C5—22no—
557C4×C5—41no—
558C4×C5C3×#12011yescharacteristic
559C4×C5C3×#12011yescharacteristic
560C4×C5C22×C3×D411yescharacteristic
561C4×C5C22×C3×D411yescharacteristic
562Dic5—24no—
563Dic5—22no—
564Dic5—42no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—52no—
572#41—52no—
573#41—104no—
574#41—104no—
575#41—108no—
576#41—108no—
577#41—104no—
578#41—104no—
579#41—101no—
580#41—101no—
581#41C3×C22⋊D512yes—
582#41C22×C3×D512yes—
583C2×Q8—52no—
584C2×Q8—52no—
585C2×Q8—51no—
586C2×Q8—104no—
587C2×Q8—102no—
588C2×Q8—104no—
589C2×Q8—104no—
590C2×Q8—104no—
591C2×Q8—101no—
592C2×Q8—101no—
593C2×Q8—101no—
594C2×Q8—101no—
595C2×Q8C3×C22⋊D511yescharacteristic
596C2×Q8C22×C3×D511yescharacteristic
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—51no—
600C2×D4—102no—
601C2×D4—101no—
602C2×D4C3×C22⋊D511yescharacteristic
603C2×D4C22×C3×D511yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—52no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—101no—
610C22×C4C22×C3×D511yescharacteristic
611Q16—22no—
612Q16—102no—
613SD16—22no—
614SD16—22no—
615SD16—102no—
616SD16—102no—
617D8—22no—
618D8—102no—
619M16—21no—
620M16—52no—
621M16—101no—
622M16C22×C3×D512yes—
623C2×C8—21no—
624C2×C8—101no—
625C4⋊C4—104no—
626C4⋊C4—101no—
627C22⋊C4—104no—
628C22⋊C4—101no—
629C42—52no—
630C3×C5#302011yescharacteristic, complemented, Hall
631C22×C3—22no—
632C22×C3—41no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—41no—
636C22×C3—102no—
637C22×C3—202no—
638C22×C3#408311yescharacteristic
639C22×C3#408311yescharacteristic
640C22×C3C2×D4×D511yescharacteristic
641C3×C4—22no—
642C3×C4—41no—
643C3×C4—104no—
644C3×C4—102no—
645C3×C4—202no—
646C3×C4#408311yescharacteristic
647C3×C4#408311yescharacteristic
648C3×C4C2×D4×D511yescharacteristic
649C3×C4C22×C22⋊D511yescharacteristic
650C2×C5—21no—
651C2×C5—21no—
652C2×C5—21no—
653C2×C5—42no—
654C2×C5—81no—
655C2×C5C2×C3×#12011yescharacteristic
656D5—42no—
657C23—21no—
658C23—21no—
659C23—101no—
660C23C3×D4×D511yescharacteristic
661Q8—21no—
662Q8—21no—
663Q8—21no—
664Q8—52no—
665Q8—108no—
666Q8—102no—
667Q8—102no—
668Q8—101no—
669Q8—102no—
670Q8—102no—
671Q8C2×C3×C22⋊D512yes—
672D4—22no—
673D4—22no—
674D4—21no—
675D4—21no—
676D4—21no—
677D4—41no—
678D4—41no—
679D4—52no—
680D4—108no—
681D4—102no—
682D4—102no—
683D4—101no—
684D4C2×C3×C22⋊D512yes—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—54no—
692C2×C4—108no—
693C2×C4—108no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—101no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4C3×D4×D511yescharacteristic
701C2×C4C3×D4×D511yescharacteristic
702C2×C4C3×D4×D511yescharacteristic
703C2×C4C2×C3×C22⋊D511yescharacteristic
704C2×C4C2×C3×C22⋊D511yescharacteristic
705C2×C4C23×C3×D511yescharacteristic
706C8—22no—
707C8—102no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—42no—
712C2×C3—81no—
713C2×C3—202no—
714C2×C3C2×#408311yescharacteristic
715C5C3×#302011yescharacteristic, complemented, Sylow
716C22—22no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—102no—
722C22—202no—
723C22C3×#408311yescharacteristic
724C22C3×#408311yescharacteristic
725C22C2×C3×D4×D511yescharacteristic
726C4—22no—
727C4—41no—
728C4—104no—
729C4—102no—
730C4—202no—
731C4C3×#408311yescharacteristic
732C4C3×#408311yescharacteristic
733C4C2×C3×D4×D511yescharacteristic
734C4C22×C3×C22⋊D511yescharacteristic
735C3#1061573711yescharacteristic, direct product factor, Sylow
736C2—21no—
737C2—21no—
738C2—21no—
739C2—42no—
740C2—81no—
741C2—202no—
742C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC2×C3C2×#4083
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#575C2
socleC2×C3×C5C2×#120
hypercenterC3×#575D5
hypocenterC5C3×#3020
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#575

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4150C2semidirect
2. C3×C5×#575C2semidirect
3. C3×#66159C2semidirect
4. C3×#66156C2semidirect
5. C3×#65525C2semidirect
6. C3×#65494C2semidirect
7. C3×#65490C2semidirect
8. C3×#65428C2semidirect
9. C2×C3×#3956C2semidirect
10. #10615737C3direct (N × H)
25. C3×C5×#137C22semidirect
27. C3×C5×AGL(1,ℤ/8)C22semidirect
33. C3×#4090C22semidirect
34. C3×#4088C22semidirect
35. C3×#4082C22semidirect
37. C3×#4078C22semidirect
41. C3×#3969C22semidirect
42. C3×#3957C22semidirect
43. C3×#3956C22semidirect
45. C2×#4150C2×C3semidirect
46. C5×#575C2×C3semidirect
47. #66159C2×C3semidirect
48. #66156C2×C3semidirect
49. #65525C2×C3semidirect
50. #65494C2×C3semidirect
51. #65490C2×C3semidirect
52. #65428C2×C3semidirect
53. C2×#3956C2×C3semidirect
121. C3×#575D5semidirect
142. C5×#137C22×C3semidirect
144. C5×AGL(1,ℤ/8)C22×C3semidirect
150. #4090C22×C3semidirect
151. #4088C22×C3semidirect
152. #4082C22×C3semidirect
154. #4078C22×C3semidirect
158. #3969C22×C3semidirect
159. #3957C22×C3semidirect
160. #3956C22×C3semidirect
229. C3×#137C2×D5semidirect
233. C3×AGL(1,ℤ/8)C2×D5semidirect
313. #575C3×D5semidirect
471. #137C2×C3×D5semidirect
475. AGL(1,ℤ/8)C2×C3×D5semidirect
630. C3×C5#3020semidirect
715. C5C3×#3020semidirect
735. C3#10615737direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C3×C5×#5752
C3×#661592
C3×#661562
C3×#655252
C3×#654942
C3×#654902
C3×#654282
C2×C3×#39562
#106157373
C3×#30205