Finite Group Databasebeta

← C3×#10610725 #14425459

Subgroups — C3×#10610725 #14425459

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C2×C3×#4054C211yesmaximal, characteristic, complemented
4C3×#65859C211yesmaximal, characteristic, complemented
5C3×C5×#421C211yesmaximal, characteristic, complemented
6C3×#65421C211yesmaximal, characteristic, complemented
7C3×#65294C211yesmaximal, characteristic, complemented
8C3×#65116C214yesmaximal, complemented
9C3×#65111C214yesmaximal, complemented
10#10610725C311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C3×#4150—21no—
13C3×#4150C2212yescomplemented
14C3×#4149—21no—
15C3×#4149C2212yescomplemented
16C3×D5×#41—22no—
17C3×D5×#41—22no—
18C3×#4147—21no—
19C3×#4144—21no—
20C3×#4144—22no—
21C2×C3×#709—22no—
22C2×C3×#709C2211yescharacteristic
23C2×C3×#709C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic, complemented
25C2×C3×C5×M16C2211yescharacteristic, complemented
26C3×C5×#117C2211yescharacteristic, complemented
27C3×#4095—22no—
28C3×#4095C2214yescomplemented
29C2×C3×#688—21no—
30C2×C3×#686—21no—
31C2×C3×#681C2211yescharacteristic, complemented
32C3×#4054—22no—
33C3×#4054C2214yescomplemented
34C2×C3×D40—21no—
35C2×C3×#677—21no—
36C3×#4041—22no—
37C3×#4028—22no—
38C3×#4021C2212yescomplemented
39C3×#4020C2212yescomplemented
40C3×C5×#104C2214yescomplemented
41C3×#3956C2212yescomplemented
42C3×#3955C2212yescomplemented
43C3×#3937C2214yescomplemented
44C3×#3021—51nomaximal, Hall
45#66283C2×C311yescharacteristic, complemented
46C2×#4095C2×C311yescharacteristic, complemented
47C2×#4054C2×C311yescharacteristic, complemented
48#65859C2×C311yescharacteristic, complemented
49C5×#421C2×C311yescharacteristic, complemented
50#65421C2×C311yescharacteristic, complemented
51#65294C2×C311yescharacteristic, complemented
52#65116C2×C314yescomplemented
53#65111C2×C314yescomplemented
54C23×C3×D5—21no—
55C3×C5×#41—21no—
56C3×C5×#41—21no—
57C3×C5×#41D412yescomplemented
58C3×C5×#41C2312yes—
59C2×C3×C5×Q8D411yescharacteristic, complemented
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4D411yescharacteristic, complemented
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×C3×C22⋊D5—24no—
65C2×C3×C22⋊D5—21no—
66C2×C3×C22⋊D5D412yes—
67C3×#713—22no—
68C3×#713—22no—
69C3×Q8×D5—22no—
70C3×Q8×D5—22no—
71C3×#711—24no—
72C3×#711—22no—
73C3×#711—22no—
74C3×#711—24no—
75C3×D4×D5—24no—
76C3×D4×D5—22no—
77C3×D4×D5—24no—
78C3×D4×D5—22no—
79C3×#709—24no—
80C3×#709—24no—
81C3×#709—21no—
82C3×#709—21no—
83C3×#709—21no—
84C3×#709—21no—
85C3×#709—21no—
86C3×#709—21no—
87C3×#709—22no—
88C3×#709—22no—
89C3×#709D412yescomplemented
90C3×#709C2312yes—
91C2×C3×D20—22no—
92C2×C3×D20—21no—
93C2×C3×D20—21no—
94C2×C3×D20—21no—
95C2×C3×D20—21no—
96C2×C3×D20—21no—
97C2×C3×D20—24no—
98C2×C3×D20D411yescharacteristic, complemented
99C2×C3×D20C2312yes—
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5—24no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5D412yes—
104C2×C3×Dic10—22no—
105C2×C3×Dic10D411yescharacteristic, complemented
106C2×C3×Dic10C2311yescharacteristic
107C3×C5×M16—21no—
108C3×C5×M16C2312yes—
109C2×C3×C5×C8—21no—
110C3×C5×C4⋊C4—21no—
111C3×C5×C22⋊C4—21no—
112C3×C42×C5C2312yes—
113C3×#688—24no—
114C3×#686—24no—
115C3×#685—24no—
116C3×#681—21no—
117C3×#681C2312yes—
118C2×C3×#168—21no—
119C3×D40—24no—
120C3×#677—24no—
121C3×#585—51no—
122C2×C3×AGL(1,ℤ/8)—51no—
123C2×C3×AGL(1,ℤ/8)—51no—
124C3×#535—51no—
125C3×#454—54no—
126C3×#453—54no—
127C3×#421—51no—
128C3×#421D511yescharacteristic, complemented
129C3×#413—51no—
130C2×C5×#41C22×C311yescharacteristic
131#4150—21no—
132#4150C22×C312yescomplemented
133#4149—21no—
134#4149C22×C312yescomplemented
135D5×#41—22no—
136D5×#41—22no—
137#4147—21no—
138#4144—21no—
139#4144—22no—
140C2×#709—22no—
141C2×#709C22×C311yescharacteristic
142C2×#709C22×C311yescharacteristic
143C22×D20C22×C311yescharacteristic, complemented
144C2×C5×M16C22×C311yescharacteristic, complemented
145C5×#117C22×C311yescharacteristic, complemented
146#4095—22no—
147#4095C22×C314yescomplemented
148C2×#688—21no—
149C2×#686—21no—
150C2×#681C22×C311yescharacteristic, complemented
151#4054—22no—
152#4054C22×C314yescomplemented
153C2×D40—21no—
154C2×#677—21no—
155#4041—22no—
156#4028—22no—
157#4021C22×C312yescomplemented
158#4020C22×C312yescomplemented
159C5×#104C22×C314yescomplemented
160#3956C22×C312yescomplemented
161#3955C22×C312yescomplemented
162#3937C22×C314yescomplemented
163#3021—51noSylow
164C23×C3×C5—21no—
165C23×C3×C5C2×D411yescharacteristic
166C22×C3×D5—24no—
167C22×C3×D5—21no—
168C22×C3×D5—22no—
169C22×C3×D5—41no—
170C22×C3×D5—41no—
171C22×C3×D5—82no—
172C22×C3×D5C2×D412yes—
173C3×C5×Q8—21no—
174C3×C5×Q8C2×D412yes—
175C3×C5×D4—22no—
176C3×C5×D4—22no—
177C3×C5×D4—21no—
178C3×C5×D4C2×D412yes—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2411yescharacteristic
189C3×C22⋊D5—24no—
190C3×C22⋊D5—24no—
191C3×C22⋊D5—22no—
192C3×C22⋊D5—22no—
193C3×C22⋊D5—22no—
194C3×C22⋊D5—22no—
195C2×C3×Dic5—24no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5C2×D412yes—
198C3×D20—24no—
199C3×D20—21no—
200C3×D20—21no—
201C3×D20—21no—
202C3×D20—22no—
203C3×D20—22no—
204C3×D20—41no—
205C3×D20—41no—
206C3×D20—84no—
207C3×D20C2×D412yes—
208C3×C4×D5—24no—
209C3×C4×D5—24no—
210C3×C4×D5—22no—
211C3×C4×D5—22no—
212C3×C4×D5—22no—
213C3×C4×D5—22no—
214C3×Dic10—24no—
215C3×Dic10—21no—
216C3×Dic10—21no—
217C3×Dic10—21no—
218C3×Dic10C2×D412yes—
219C3×C5×C8—22no—
220C3×#168—22no—
221C3×2−1+4—52no—
222C3×2−1+4—101no—
223C3×2−1+4—101no—
224C3×H(5,𝔽2)—52no—
225C3×H(5,𝔽2)—102no—
226C3×H(5,𝔽2)—101no—
227C3×H(5,𝔽2)—101no—
228C2×C3×#41—51no—
229C2×C3×#41—51no—
230C2×C3×#41—102no—
231C2×C3×#41—102no—
232C2×C3×#41—102no—
233C2×C3×#41C2×D511yescharacteristic
234C22×C3×D4—51no—
235C3×AGL(1,ℤ/8)—54no—
236C3×AGL(1,ℤ/8)—54no—
237C3×AGL(1,ℤ/8)—102no—
238C3×AGL(1,ℤ/8)—102no—
239C2×C3×SD16—101no—
240C2×C3×SD16—101no—
241C2×C3×D8—101no—
242C2×C3×D8—101no—
243C2×C3×M16—51no—
244C2×C3×M16C2×D511yescharacteristic, complemented
245C3×#127—52no—
246C3×#124—52no—
247C3×#121—102no—
248C3×#120—102no—
249C3×#117C2×D511yescharacteristic, complemented
250C3×#104—54no—
251C3×#104C2×D514yescomplemented
252C3×#101—52no—
253C3×#100—52no—
254C23×D5—21no—
255C5×#41—21no—
256C5×#41—21no—
257C5×#41C3×D412yescomplemented
258C5×#41C23×C312yes—
259C2×C5×Q8C3×D411yescharacteristic, complemented
260C2×C5×D4—21no—
261C2×C5×D4C3×D411yescharacteristic, complemented
262C22×C4×C5—21no—
263C22×C4×C5C23×C311yescharacteristic
264C2×C22⋊D5—24no—
265C2×C22⋊D5—21no—
266C2×C22⋊D5C3×D412yes—
267#713—22no—
268#713—22no—
269Q8×D5—22no—
270Q8×D5—22no—
271#711—24no—
272#711—22no—
273#711—22no—
274#711—24no—
275D4×D5—24no—
276D4×D5—22no—
277D4×D5—24no—
278D4×D5—22no—
279#709—24no—
280#709—24no—
281#709—21no—
282#709—21no—
283#709—21no—
284#709—21no—
285#709—21no—
286#709—21no—
287#709—22no—
288#709—22no—
289#709C3×D412yescomplemented
290#709C23×C312yes—
291C2×D20—22no—
292C2×D20—21no—
293C2×D20—21no—
294C2×D20—21no—
295C2×D20—21no—
296C2×D20—21no—
297C2×D20—24no—
298C2×D20C3×D411yescharacteristic, complemented
299C2×D20C23×C312yes—
300C2×D20C23×C311yescharacteristic
301C2×C4×D5—24no—
302C2×C4×D5—21no—
303C2×C4×D5C3×D412yes—
304C2×Dic10—22no—
305C2×Dic10C3×D411yescharacteristic, complemented
306C2×Dic10C23×C311yescharacteristic
307C5×M16—21no—
308C5×M16C23×C312yes—
309C2×C5×C8—21no—
310C5×C4⋊C4—21no—
311C5×C22⋊C4—21no—
312C42×C5C23×C312yes—
313#688—24no—
314#686—24no—
315#685—24no—
316#681—21no—
317#681C23×C312yes—
318C2×#168—21no—
319D40—24no—
320#677—24no—
321#585—51no—
322C2×AGL(1,ℤ/8)—51no—
323C2×AGL(1,ℤ/8)—51no—
324#535—51no—
325#454—54no—
326#453—54no—
327#421—51no—
328#421C3×D511yescharacteristic, complemented
329#413—51no—
330C22×C3×C5—22no—
331C22×C3×C5—41no—
332C22×C3×C5—81no—
333C22×C3×C5#12011yescharacteristic
334C22×C3×C5#12011yescharacteristic
335C22×C3×C5C22×D411yescharacteristic
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—42no—
339C2×C3×D5—44no—
340C2×C3×D5—42no—
341C2×C3×D5—81no—
342C2×C3×D5—84no—
343C2×C3×D5—82no—
344C2×C3×D5—82no—
345C3×C4×C5—22no—
346C3×C4×C5—42no—
347C3×C4×C5#12011yescharacteristic
348C3×C4×C5#12011yescharacteristic
349C3×C4×C5C22×D411yescharacteristic
350C3×C4×C5C22×D411yescharacteristic
351C3×Dic5—22no—
352C3×Dic5—22no—
353C24×C3—101no—
354C3×#41—21no—
355C3×#41—21no—
356C3×#41—52no—
357C3×#41—52no—
358C3×#41—102no—
359C3×#41—102no—
360C3×#41—104no—
361C3×#41—104no—
362C3×#41—104no—
363C3×#41—104no—
364C3×#41—102no—
365C3×#41—102no—
366C3×#41—102no—
367C3×#41—102no—
368C3×#41—101no—
369C3×#41—101no—
370C3×#41—101no—
371C3×#41—101no—
372C3×#41—101no—
373C3×#41—101no—
374C3×#41D2012yescomplemented
375C3×#41C22×D512yes—
376C2×C3×Q8—51no—
377C2×C3×Q8—51no—
378C2×C3×Q8—102no—
379C2×C3×Q8—102no—
380C2×C3×Q8—102no—
381C2×C3×Q8D2011yescharacteristic, complemented
382C2×C3×D4—21no—
383C2×C3×D4—52no—
384C2×C3×D4—51no—
385C2×C3×D4—51no—
386C2×C3×D4—52no—
387C2×C3×D4—102no—
388C2×C3×D4—104no—
389C2×C3×D4—104no—
390C2×C3×D4—104no—
391C2×C3×D4—102no—
392C2×C3×D4—104no—
393C2×C3×D4—101no—
394C2×C3×D4—102no—
395C2×C3×D4—101no—
396C2×C3×D4—101no—
397C2×C3×D4—101no—
398C2×C3×D4—101no—
399C2×C3×D4—101no—
400C2×C3×D4D2011yescharacteristic, complemented
401C22×C3×C4—21no—
402C22×C3×C4—52no—
403C22×C3×C4—104no—
404C22×C3×C4—101no—
405C22×C3×C4C22×D511yescharacteristic
406C3×SD16—104no—
407C3×SD16—104no—
408C3×D8—104no—
409C3×D8—104no—
410C3×M16—21no—
411C3×M16—52no—
412C3×M16—101no—
413C3×M16C22×D512yes—
414C2×C3×C8—21no—
415C2×C3×C8—101no—
416C3×C4⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—104no—
419C3×C42C22×D512yes—
420C23×C5—21no—
421C23×C5C2×C3×D411yescharacteristic
422C22×D5—24no—
423C22×D5—21no—
424C22×D5—22no—
425C22×D5—41no—
426C22×D5—41no—
427C22×D5—82no—
428C22×D5C2×C3×D412yes—
429C5×Q8—21no—
430C5×Q8C2×C3×D412yes—
431C5×D4—22no—
432C5×D4—22no—
433C5×D4—21no—
434C5×D4C2×C3×D412yes—
435C2×C4×C5—21no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5C2×C3×D411yescharacteristic
440C2×C4×C5C2×C3×D411yescharacteristic
441C2×C4×C5C2×C3×D411yescharacteristic
442C2×C4×C5C2×C3×D411yescharacteristic
443C2×C4×C5C2×C3×D411yescharacteristic
444C2×C4×C5C24×C311yescharacteristic
445C22⋊D5—24no—
446C22⋊D5—24no—
447C22⋊D5—22no—
448C22⋊D5—22no—
449C22⋊D5—22no—
450C22⋊D5—22no—
451C2×Dic5—24no—
452C2×Dic5—21no—
453C2×Dic5C2×C3×D412yes—
454D20—24no—
455D20—21no—
456D20—21no—
457D20—21no—
458D20—22no—
459D20—22no—
460D20—41no—
461D20—41no—
462D20—84no—
463D20C2×C3×D412yes—
464C4×D5—24no—
465C4×D5—24no—
466C4×D5—22no—
467C4×D5—22no—
468C4×D5—22no—
469C4×D5—22no—
470Dic10—24no—
471Dic10—21no—
472Dic10—21no—
473Dic10—21no—
474Dic10C2×C3×D412yes—
475C5×C8—22no—
476#168—22no—
4772−1+4—52no—
4782−1+4—101no—
4792−1+4—101no—
480H(5,𝔽2)—52no—
481H(5,𝔽2)—102no—
482H(5,𝔽2)—101no—
483H(5,𝔽2)—101no—
484C2×#41—51no—
485C2×#41—51no—
486C2×#41—102no—
487C2×#41—102no—
488C2×#41—102no—
489C2×#41C2×C3×D511yescharacteristic
490C22×D4—51no—
491AGL(1,ℤ/8)—54no—
492AGL(1,ℤ/8)—54no—
493AGL(1,ℤ/8)—102no—
494AGL(1,ℤ/8)—102no—
495C2×SD16—101no—
496C2×SD16—101no—
497C2×D8—101no—
498C2×D8—101no—
499C2×M16—51no—
500C2×M16C2×C3×D511yescharacteristic, complemented
501#127—52no—
502#124—52no—
503#121—102no—
504#120—102no—
505#117C2×C3×D511yescharacteristic, complemented
506#104—54no—
507#104C2×C3×D514yescomplemented
508#101—52no—
509#100—52no—
510C2×C3×C5—21no—
511C2×C3×C5—21no—
512C2×C3×C5—21no—
513C2×C3×C5—42no—
514C2×C3×C5C2×#12011yescharacteristic
515C3×D5—42no—
516C3×D5—42no—
517C3×D5—82no—
518C23×C3—21no—
519C23×C3—52no—
520C23×C3—104no—
521C23×C3—101no—
522C23×C3—102no—
523C23×C3—201no—
524C23×C3—201no—
525C23×C3—402no—
526C23×C3D4×D511yescharacteristic
527C3×Q8—21no—
528C3×Q8—52no—
529C3×Q8—104no—
530C3×Q8—101no—
531C3×Q8—101no—
532C3×Q8—101no—
533C3×Q8C2×D2012yes—
534C3×D4—22no—
535C3×D4—22no—
536C3×D4—21no—
537C3×D4—52no—
538C3×D4—104no—
539C3×D4—104no—
540C3×D4—104no—
541C3×D4—102no—
542C3×D4—102no—
543C3×D4—102no—
544C3×D4—102no—
545C3×D4—101no—
546C3×D4—102no—
547C3×D4—101no—
548C3×D4—102no—
549C3×D4—101no—
550C3×D4—201no—
551C3×D4—201no—
552C3×D4—404no—
553C3×D4C2×D2012yes—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—52no—
559C2×C3×C4—104no—
560C2×C3×C4—104no—
561C2×C3×C4—104no—
562C2×C3×C4—101no—
563C2×C3×C4—102no—
564C2×C3×C4—102no—
565C2×C3×C4—102no—
566C2×C3×C4—102no—
567C2×C3×C4C2×D2011yescharacteristic
568C2×C3×C4C2×D2011yescharacteristic
569C2×C3×C4D4×D511yescharacteristic
570C2×C3×C4D4×D511yescharacteristic
571C2×C3×C4D4×D511yescharacteristic
572C2×C3×C4C23×D511yescharacteristic
573C3×C8—22no—
574C3×C8—102no—
575C22×C5—22no—
576C22×C5—41no—
577C22×C5—81no—
578C22×C5C3×#12011yescharacteristic
579C22×C5C3×#12011yescharacteristic
580C22×C5C22×C3×D411yescharacteristic
581C2×D5—22no—
582C2×D5—22no—
583C2×D5—42no—
584C2×D5—44no—
585C2×D5—42no—
586C2×D5—81no—
587C2×D5—84no—
588C2×D5—82no—
589C2×D5—82no—
590C4×C5—22no—
591C4×C5—42no—
592C4×C5C3×#12011yescharacteristic
593C4×C5C3×#12011yescharacteristic
594C4×C5C22×C3×D411yescharacteristic
595C4×C5C22×C3×D411yescharacteristic
596Dic5—22no—
597Dic5—22no—
598C24—101no—
599#41—21no—
600#41—21no—
601#41—52no—
602#41—52no—
603#41—102no—
604#41—102no—
605#41—104no—
606#41—104no—
607#41—104no—
608#41—104no—
609#41—102no—
610#41—102no—
611#41—102no—
612#41—102no—
613#41—101no—
614#41—101no—
615#41—101no—
616#41—101no—
617#41—101no—
618#41—101no—
619#41C3×D2012yescomplemented
620#41C22×C3×D512yes—
621C2×Q8—51no—
622C2×Q8—51no—
623C2×Q8—102no—
624C2×Q8—102no—
625C2×Q8—102no—
626C2×Q8C3×D2011yescharacteristic, complemented
627C2×D4—21no—
628C2×D4—52no—
629C2×D4—51no—
630C2×D4—51no—
631C2×D4—52no—
632C2×D4—102no—
633C2×D4—104no—
634C2×D4—104no—
635C2×D4—104no—
636C2×D4—102no—
637C2×D4—104no—
638C2×D4—101no—
639C2×D4—102no—
640C2×D4—101no—
641C2×D4—101no—
642C2×D4—101no—
643C2×D4—101no—
644C2×D4—101no—
645C2×D4C3×D2011yescharacteristic, complemented
646C22×C4—21no—
647C22×C4—52no—
648C22×C4—104no—
649C22×C4—101no—
650C22×C4C22×C3×D511yescharacteristic
651SD16—104no—
652SD16—104no—
653D8—104no—
654D8—104no—
655M16—21no—
656M16—52no—
657M16—101no—
658M16C22×C3×D512yes—
659C2×C8—21no—
660C2×C8—101no—
661C4⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—104no—
664C42C22×C3×D512yes—
665C3×C5#302111yescharacteristic, complemented, Hall
666C22×C3—22no—
667C22×C3—41no—
668C22×C3—81no—
669C22×C3—102no—
670C22×C3—102no—
671C22×C3—202no—
672C22×C3—204no—
673C22×C3—202no—
674C22×C3—401no—
675C22×C3—402no—
676C22×C3—402no—
677C22×C3—404no—
678C22×C3#402811yescharacteristic
679C22×C3#402811yescharacteristic
680C22×C3C2×D4×D511yescharacteristic
681C3×C4—22no—
682C3×C4—42no—
683C3×C4—102no—
684C3×C4—102no—
685C3×C4#402811yescharacteristic
686C3×C4#402811yescharacteristic
687C3×C4C22×D2011yescharacteristic
688C3×C4C2×D4×D511yescharacteristic
689C2×C5—21no—
690C2×C5—21no—
691C2×C5—21no—
692C2×C5—42no—
693C2×C5C2×C3×#12011yescharacteristic
694D5—42no—
695D5—42no—
696D5—82no—
697C23—21no—
698C23—52no—
699C23—104no—
700C23—101no—
701C23—102no—
702C23—201no—
703C23—201no—
704C23—402no—
705C23C3×D4×D511yescharacteristic
706Q8—21no—
707Q8—52no—
708Q8—104no—
709Q8—101no—
710Q8—101no—
711Q8—101no—
712Q8C2×C3×D2012yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—52no—
717D4—104no—
718D4—104no—
719D4—104no—
720D4—102no—
721D4—102no—
722D4—102no—
723D4—102no—
724D4—101no—
725D4—102no—
726D4—101no—
727D4—102no—
728D4—101no—
729D4—201no—
730D4—201no—
731D4—404no—
732D4C2×C3×D2012yes—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—52no—
738C2×C4—104no—
739C2×C4—104no—
740C2×C4—104no—
741C2×C4—101no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4C2×C3×D2011yescharacteristic
747C2×C4C2×C3×D2011yescharacteristic
748C2×C4C3×D4×D511yescharacteristic
749C2×C4C3×D4×D511yescharacteristic
750C2×C4C3×D4×D511yescharacteristic
751C2×C4C23×C3×D511yescharacteristic
752C8—22no—
753C8—102no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—202no—
759C2×C3—202no—
760C2×C3—402no—
761C2×C3C2×#402811yescharacteristic
762C5C3×#302111yescharacteristic, complemented, Sylow
763C22—22no—
764C22—41no—
765C22—81no—
766C22—102no—
767C22—102no—
768C22—202no—
769C22—204no—
770C22—202no—
771C22—401no—
772C22—402no—
773C22—402no—
774C22—404no—
775C22C3×#402811yescharacteristic
776C22C3×#402811yescharacteristic
777C22C2×C3×D4×D511yescharacteristic
778C4—22no—
779C4—42no—
780C4—102no—
781C4—102no—
782C4C3×#402811yescharacteristic
783C4C3×#402811yescharacteristic
784C4C22×C3×D2011yescharacteristic
785C4C2×C3×D4×D511yescharacteristic
786C3#1061072511yescharacteristic, direct product factor, Sylow
787C2—21no—
788C2—21no—
789C2—21no—
790C2—42no—
791C2—202no—
792C2—202no—
793C2—402no—
794C2C2×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×#3021
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. C3×#66283C2semidirect
2. C2×C3×#4095C2semidirect
3. C2×C3×#4054C2semidirect
4. C3×#65859C2semidirect
5. C3×C5×#421C2semidirect
6. C3×#65421C2semidirect
7. C3×#65294C2semidirect
8. C3×#65116C2semidirect
9. C3×#65111C2semidirect
10. #10610725C3direct (N × H)
13. C3×#4150C22semidirect
15. C3×#4149C22semidirect
24. C22×C3×D20C22semidirect
25. C2×C3×C5×M16C22semidirect
26. C3×C5×#117C22semidirect
28. C3×#4095C22semidirect
31. C2×C3×#681C22semidirect
33. C3×#4054C22semidirect
38. C3×#4021C22semidirect
39. C3×#4020C22semidirect
40. C3×C5×#104C22semidirect
41. C3×#3956C22semidirect
42. C3×#3955C22semidirect
43. C3×#3937C22semidirect
45. #66283C2×C3semidirect
46. C2×#4095C2×C3semidirect
47. C2×#4054C2×C3semidirect
48. #65859C2×C3semidirect
49. C5×#421C2×C3semidirect
50. #65421C2×C3semidirect
51. #65294C2×C3semidirect
52. #65116C2×C3semidirect
53. #65111C2×C3semidirect
57. C3×C5×#41D4semidirect
59. C2×C3×C5×Q8D4semidirect
61. C2×C3×C5×D4D4semidirect
89. C3×#709D4semidirect
98. C2×C3×D20D4semidirect
105. C2×C3×Dic10D4semidirect
128. C3×#421D5semidirect
132. #4150C22×C3semidirect
134. #4149C22×C3semidirect
143. C22×D20C22×C3semidirect
144. C2×C5×M16C22×C3semidirect
145. C5×#117C22×C3semidirect
147. #4095C22×C3semidirect
150. C2×#681C22×C3semidirect
152. #4054C22×C3semidirect
157. #4021C22×C3semidirect
158. #4020C22×C3semidirect
159. C5×#104C22×C3semidirect
160. #3956C22×C3semidirect
161. #3955C22×C3semidirect
162. #3937C22×C3semidirect
244. C2×C3×M16C2×D5semidirect
249. C3×#117C2×D5semidirect
251. C3×#104C2×D5semidirect
257. C5×#41C3×D4semidirect
259. C2×C5×Q8C3×D4semidirect
261. C2×C5×D4C3×D4semidirect
289. #709C3×D4semidirect
298. C2×D20C3×D4semidirect
305. C2×Dic10C3×D4semidirect
328. #421C3×D5semidirect
374. C3×#41D20semidirect
381. C2×C3×Q8D20semidirect
400. C2×C3×D4D20semidirect
500. C2×M16C2×C3×D5semidirect
505. #117C2×C3×D5semidirect
507. #104C2×C3×D5semidirect
619. #41C3×D20semidirect
626. C2×Q8C3×D20semidirect
645. C2×D4C3×D20semidirect
665. C3×C5#3021semidirect
762. C5C3×#3021semidirect
786. C3#10610725direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662832
C2×C3×#40952
C2×C3×#40542
C3×#658592
C3×C5×#4212
C3×#654212
C3×#652942
C3×#651162
C3×#651112
#106107253
C3×#30215