Finite Group Databasebeta

← C3×#10615688 #14425447

Subgroups — C3×#10615688 #14425447

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×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C3×#66139C211yesmaximal, characteristic, complemented
4C2×C3×#4078C211yesmaximal, characteristic, complemented
5C3×#65525C211yesmaximal, characteristic, complemented
6C3×#65490C214yesmaximal, complemented
7C3×#65487C214yesmaximal, complemented
8C3×#65428C211yesmaximal, characteristic, complemented
9C3×#65421C211yesmaximal, characteristic, complemented
10#10615688C311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic, complemented
13C3×#4150—21no—
14C3×#4150C2212yescomplemented
15C3×#4149—21no—
16C3×#4149C2212yescomplemented
17C3×D5×#41—22no—
18C3×D5×#41—22no—
19C3×#4147—21no—
20C3×#4144—21no—
21C3×#4144—22no—
22C2×C3×#709—22no—
23C2×C3×#709C2211yescharacteristic
24C2×C3×#709C2211yescharacteristic
25C3×C5×AGL(1,ℤ/8)—22no—
26C3×C5×AGL(1,ℤ/8)C2214yescomplemented
27C2×C3×C5×SD16—21no—
28C2×C3×C5×D8—21no—
29C2×C3×C5×M16C2211yescharacteristic, complemented
30C3×#4099—22no—
31C3×#4086C2212yescomplemented
32C3×#4084—22no—
33C3×#4082C2212yescomplemented
34C2×C3×#687—21no—
35C3×#4078—22no—
36C3×#4078C2214yescomplemented
37C2×C3×#686—21no—
38C3×#4072C2211yescharacteristic, complemented
39C2×C3×#681C2211yescharacteristic, complemented
40C3×#3969C2214yescomplemented
41C3×#3957C2214yescomplemented
42C3×#3956C2212yescomplemented
43C3×#3955C2212yescomplemented
44C3×#3021—51nomaximal, Hall
45#66283C2×C311yescharacteristic, complemented
46C2×C5×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
47#66139C2×C311yescharacteristic, complemented
48C2×#4078C2×C311yescharacteristic, complemented
49#65525C2×C311yescharacteristic, complemented
50#65490C2×C314yescomplemented
51#65487C2×C314yescomplemented
52#65428C2×C311yescharacteristic, complemented
53#65421C2×C311yescharacteristic, complemented
54C24×C3×C5—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×D4—21no—
62C2×C3×C5×D4—21no—
63C2×C3×C5×D4—21no—
64C2×C3×C5×D4—21no—
65C2×C3×C5×D4—21no—
66C2×C3×C5×D4D411yescharacteristic, complemented
67C2×C3×C5×D4C2312yes—
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5C2311yescharacteristic
70C2×C3×C22⋊D5—24no—
71C2×C3×C22⋊D5—21no—
72C2×C3×C22⋊D5—24no—
73C2×C3×C22⋊D5D412yes—
74C3×#713—22no—
75C3×#713—22no—
76C3×Q8×D5—22no—
77C3×Q8×D5—22no—
78C3×#711—24no—
79C3×#711—22no—
80C3×#711—22no—
81C3×#711—24no—
82C3×D4×D5—24no—
83C3×D4×D5—22no—
84C3×D4×D5—24no—
85C3×D4×D5—22no—
86C3×#709—24no—
87C3×#709—24no—
88C3×#709—21no—
89C3×#709—21no—
90C3×#709—21no—
91C3×#709—21no—
92C3×#709—21no—
93C3×#709—21no—
94C3×#709—22no—
95C3×#709—22no—
96C3×#709D412yescomplemented
97C3×#709C2312yes—
98C2×C3×D20—22no—
99C2×C3×D20D411yescharacteristic, complemented
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×SD16—24no—
108C3×C5×D8—24no—
109C3×C5×M16—21no—
110C3×C5×M16C2312yes—
111C2×C3×C5×C8—21no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5—24no—
114C3×#687—24no—
115C3×#686—24no—
116C3×C4⋊Dic5—21no—
117C3×C4×Dic5C2312yes—
118C3×#681—21no—
119C3×#681C2312yes—
120C2×C3×#168—21no—
121C3×#585—51no—
122C2×C3×AGL(1,ℤ/8)—51no—
123C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
124C3×#535—51no—
125C3×#454—54no—
126C3×#453—54no—
127C3×#421—51no—
128C3×#421—51no—
129C3×#413—51no—
130C2×C5×#41C22×C311yescharacteristic
131C22×C5×D4C22×C311yescharacteristic, complemented
132#4150—21no—
133#4150C22×C312yescomplemented
134#4149—21no—
135#4149C22×C312yescomplemented
136D5×#41—22no—
137D5×#41—22no—
138#4147—21no—
139#4144—21no—
140#4144—22no—
141C2×#709—22no—
142C2×#709C22×C311yescharacteristic
143C2×#709C22×C311yescharacteristic
144C5×AGL(1,ℤ/8)—22no—
145C5×AGL(1,ℤ/8)C22×C314yescomplemented
146C2×C5×SD16—21no—
147C2×C5×D8—21no—
148C2×C5×M16C22×C311yescharacteristic, complemented
149#4099—22no—
150#4086C22×C312yescomplemented
151#4084—22no—
152#4082C22×C312yescomplemented
153C2×#687—21no—
154#4078—22no—
155#4078C22×C314yescomplemented
156C2×#686—21no—
157#4072C22×C311yescharacteristic, complemented
158C2×#681C22×C311yescharacteristic, complemented
159#3969C22×C314yescomplemented
160#3957C22×C314yescomplemented
161#3956C22×C312yescomplemented
162#3955C22×C312yescomplemented
163#3021—51noSylow
164C23×C3×C5—21no—
165C23×C3×C5—22no—
166C23×C3×C5—41no—
167C23×C3×C5—41no—
168C23×C3×C5—82no—
169C23×C3×C5C2×D411yescharacteristic
170C22×C3×D5—24no—
171C22×C3×D5—21no—
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×D4—22no—
179C3×C5×D4—22no—
180C3×C5×D4—41no—
181C3×C5×D4—41no—
182C3×C5×D4C2×D412yes—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—22no—
185C2×C3×C4×C5—22no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2411yescharacteristic
192C3×C22⋊D5—24no—
193C3×C22⋊D5—24no—
194C3×C22⋊D5—22no—
195C3×C22⋊D5—22no—
196C3×C22⋊D5—22no—
197C3×C22⋊D5—22no—
198C3×C22⋊D5—84no—
199C2×C3×Dic5—24no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—22no—
202C2×C3×Dic5C2×D412yes—
203C3×D20—24no—
204C3×D20—21no—
205C3×D20—21no—
206C3×D20—21no—
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×D4C2×D511yescharacteristic, complemented
235C3×AGL(1,ℤ/8)—22no—
236C3×AGL(1,ℤ/8)—54no—
237C3×AGL(1,ℤ/8)—102no—
238C3×AGL(1,ℤ/8)C2×D514yescomplemented
239C2×C3×SD16—21no—
240C2×C3×SD16—101no—
241C2×C3×D8—21no—
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×#117—51no—
250C3×#104—54no—
251C3×#104—54no—
252C3×#101—52no—
253C3×#100—52no—
254C24×C5—21no—
255C5×#41—21no—
256C5×#41—21no—
257C5×#41C3×D412yescomplemented
258C5×#41C23×C312yes—
259C2×C5×Q8C3×D411yescharacteristic, complemented
260C2×C5×D4—21no—
261C2×C5×D4—21no—
262C2×C5×D4—21no—
263C2×C5×D4—21no—
264C2×C5×D4—21no—
265C2×C5×D4—21no—
266C2×C5×D4C3×D411yescharacteristic, complemented
267C2×C5×D4C23×C312yes—
268C22×C4×C5—21no—
269C22×C4×C5C23×C311yescharacteristic
270C2×C22⋊D5—24no—
271C2×C22⋊D5—21no—
272C2×C22⋊D5—24no—
273C2×C22⋊D5C3×D412yes—
274#713—22no—
275#713—22no—
276Q8×D5—22no—
277Q8×D5—22no—
278#711—24no—
279#711—22no—
280#711—22no—
281#711—24no—
282D4×D5—24no—
283D4×D5—22no—
284D4×D5—24no—
285D4×D5—22no—
286#709—24no—
287#709—24no—
288#709—21no—
289#709—21no—
290#709—21no—
291#709—21no—
292#709—21no—
293#709—21no—
294#709—22no—
295#709—22no—
296#709C3×D412yescomplemented
297#709C23×C312yes—
298C2×D20—22no—
299C2×D20C3×D411yescharacteristic, complemented
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×SD16—24no—
308C5×D8—24no—
309C5×M16—21no—
310C5×M16C23×C312yes—
311C2×C5×C8—21no—
312C22⋊Dic5—21no—
313C22⋊Dic5—24no—
314#687—24no—
315#686—24no—
316C4⋊Dic5—21no—
317C4×Dic5C23×C312yes—
318#681—21no—
319#681C23×C312yes—
320C2×#168—21no—
321#585—51no—
322C2×AGL(1,ℤ/8)—51no—
323C2×AGL(1,ℤ/8)C3×D511yescharacteristic, complemented
324#535—51no—
325#454—54no—
326#453—54no—
327#421—51no—
328#421—51no—
329#413—51no—
330C22×C3×C5—22no—
331C22×C3×C5—41no—
332C22×C3×C5—44no—
333C22×C3×C5—42no—
334C22×C3×C5—81no—
335C22×C3×C5—82no—
336C22×C3×C5—82no—
337C22×C3×C5#12011yescharacteristic
338C22×C3×C5#12011yescharacteristic
339C22×C3×C5C22×D411yescharacteristic
340C2×C3×D5—22no—
341C2×C3×D5—22no—
342C2×C3×D5—42no—
343C2×C3×D5—81no—
344C2×C3×D5—84no—
345C3×C4×C5—22no—
346C3×C4×C5#12011yescharacteristic
347C3×C4×C5#12011yescharacteristic
348C3×C4×C5C22×D411yescharacteristic
349C3×C4×C5C22×D411yescharacteristic
350C3×Dic5—22no—
351C3×Dic5—22no—
352C3×Dic5—42no—
353C24×C3—21no—
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×#41C22⋊D512yescomplemented
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×Q8C22⋊D511yescharacteristic, complemented
382C2×C3×D4—21no—
383C2×C3×D4—21no—
384C2×C3×D4—21no—
385C2×C3×D4—21no—
386C2×C3×D4—21no—
387C2×C3×D4—21no—
388C2×C3×D4—52no—
389C2×C3×D4—51no—
390C2×C3×D4—51no—
391C2×C3×D4—102no—
392C2×C3×D4—104no—
393C2×C3×D4—104no—
394C2×C3×D4—102no—
395C2×C3×D4—104no—
396C2×C3×D4—101no—
397C2×C3×D4—102no—
398C2×C3×D4—104no—
399C2×C3×D4C22⋊D511yescharacteristic, complemented
400C2×C3×D4C22×D512yes—
401C22×C3×C4—21no—
402C22×C3×C4—52no—
403C22×C3×C4—104no—
404C22×C3×C4—101no—
405C22×C3×C4C22×D511yescharacteristic
406C3×SD16—24no—
407C3×SD16—104no—
408C3×D8—24no—
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—101no—
417C3×C22⋊C4—104no—
418C3×C22⋊C4—101no—
419C3×C42—52no—
420C23×C5—21no—
421C23×C5—22no—
422C23×C5—41no—
423C23×C5—41no—
424C23×C5—82no—
425C23×C5C2×C3×D411yescharacteristic
426C22×D5—24no—
427C22×D5—21no—
428C22×D5C2×C3×D412yes—
429C5×Q8—21no—
430C5×Q8C2×C3×D412yes—
431C5×D4—22no—
432C5×D4—22no—
433C5×D4—21no—
434C5×D4—22no—
435C5×D4—22no—
436C5×D4—41no—
437C5×D4—41no—
438C5×D4C2×C3×D412yes—
439C2×C4×C5—21no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5C2×C3×D411yescharacteristic
443C2×C4×C5C2×C3×D411yescharacteristic
444C2×C4×C5C2×C3×D411yescharacteristic
445C2×C4×C5C2×C3×D411yescharacteristic
446C2×C4×C5C2×C3×D411yescharacteristic
447C2×C4×C5C24×C311yescharacteristic
448C22⋊D5—24no—
449C22⋊D5—24no—
450C22⋊D5—22no—
451C22⋊D5—22no—
452C22⋊D5—22no—
453C22⋊D5—22no—
454C22⋊D5—84no—
455C2×Dic5—24no—
456C2×Dic5—21no—
457C2×Dic5—22no—
458C2×Dic5C2×C3×D412yes—
459D20—24no—
460D20—21no—
461D20—21no—
462D20—21no—
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×D4C2×C3×D511yescharacteristic, complemented
491AGL(1,ℤ/8)—22no—
492AGL(1,ℤ/8)—54no—
493AGL(1,ℤ/8)—102no—
494AGL(1,ℤ/8)C2×C3×D514yescomplemented
495C2×SD16—21no—
496C2×SD16—101no—
497C2×D8—21no—
498C2×D8—101no—
499C2×M16—51no—
500C2×M16C2×C3×D511yescharacteristic, complemented
501#127—52no—
502#124—52no—
503#121—102no—
504#120—102no—
505#117—51no—
506#104—54no—
507#104—54no—
508#101—52no—
509#100—52no—
510C2×C3×C5—21no—
511C2×C3×C5—21no—
512C2×C3×C5—21no—
513C2×C3×C5—42no—
514C2×C3×C5—82no—
515C2×C3×C5C2×#12011yescharacteristic
516C3×D5—42no—
517C3×D5—42no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—52no—
523C23×C3—82no—
524C23×C3—104no—
525C23×C3—101no—
526C23×C3D4×D511yescharacteristic
527C3×Q8—21no—
528C3×Q8—52no—
529C3×Q8—104no—
530C3×Q8—101no—
531C3×Q8—101no—
532C3×Q8—101no—
533C3×Q8C2×C22⋊D512yes—
534C3×D4—22no—
535C3×D4—22no—
536C3×D4—22no—
537C3×D4—22no—
538C3×D4—21no—
539C3×D4—41no—
540C3×D4—41no—
541C3×D4—52no—
542C3×D4—104no—
543C3×D4—104no—
544C3×D4—104no—
545C3×D4—102no—
546C3×D4—102no—
547C3×D4—102no—
548C3×D4—102no—
549C3×D4—101no—
550C3×D4—101no—
551C3×D4—101no—
552C3×D4—404no—
553C3×D4C2×C22⋊D512yes—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—52no—
558C2×C3×C4—104no—
559C2×C3×C4—104no—
560C2×C3×C4—104no—
561C2×C3×C4—101no—
562C2×C3×C4—102no—
563C2×C3×C4—102no—
564C2×C3×C4—102no—
565C2×C3×C4—102no—
566C2×C3×C4—102no—
567C2×C3×C4D4×D511yescharacteristic
568C2×C3×C4D4×D511yescharacteristic
569C2×C3×C4D4×D511yescharacteristic
570C2×C3×C4C2×C22⋊D511yescharacteristic
571C2×C3×C4C2×C22⋊D511yescharacteristic
572C2×C3×C4C23×D511yescharacteristic
573C3×C8—22no—
574C3×C8—102no—
575C22×C5—22no—
576C22×C5—41no—
577C22×C5—44no—
578C22×C5—42no—
579C22×C5—81no—
580C22×C5—82no—
581C22×C5—82no—
582C22×C5C3×#12011yescharacteristic
583C22×C5C3×#12011yescharacteristic
584C22×C5C22×C3×D411yescharacteristic
585C2×D5—22no—
586C2×D5—22no—
587C2×D5—42no—
588C2×D5—81no—
589C2×D5—84no—
590C4×C5—22no—
591C4×C5C3×#12011yescharacteristic
592C4×C5C3×#12011yescharacteristic
593C4×C5C22×C3×D411yescharacteristic
594C4×C5C22×C3×D411yescharacteristic
595Dic5—22no—
596Dic5—22no—
597Dic5—42no—
598C24—21no—
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×C22⋊D512yescomplemented
620#41C22×C3×D512yes—
621C2×Q8—51no—
622C2×Q8—51no—
623C2×Q8—102no—
624C2×Q8—102no—
625C2×Q8—102no—
626C2×Q8C3×C22⋊D511yescharacteristic, complemented
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—52no—
634C2×D4—51no—
635C2×D4—51no—
636C2×D4—102no—
637C2×D4—104no—
638C2×D4—104no—
639C2×D4—102no—
640C2×D4—104no—
641C2×D4—101no—
642C2×D4—102no—
643C2×D4—104no—
644C2×D4C3×C22⋊D511yescharacteristic, complemented
645C2×D4C22×C3×D512yes—
646C22×C4—21no—
647C22×C4—52no—
648C22×C4—104no—
649C22×C4—101no—
650C22×C4C22×C3×D511yescharacteristic
651SD16—24no—
652SD16—104no—
653D8—24no—
654D8—104no—
655M16—21no—
656M16—52no—
657M16—101no—
658M16C22×C3×D512yes—
659C2×C8—21no—
660C2×C8—101no—
661C4⋊C4—101no—
662C22⋊C4—104no—
663C22⋊C4—101no—
664C42—52no—
665C3×C5#302111yescharacteristic, complemented, Hall
666C22×C3—22no—
667C22×C3—41no—
668C22×C3—44no—
669C22×C3—42no—
670C22×C3—81no—
671C22×C3—82no—
672C22×C3—82no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—202no—
676C22×C3—401no—
677C22×C3—404no—
678C22×C3#408311yescharacteristic
679C22×C3#408311yescharacteristic
680C22×C3C2×D4×D511yescharacteristic
681C3×C4—22no—
682C3×C4—102no—
683C3×C4—102no—
684C3×C4—202no—
685C3×C4#408311yescharacteristic
686C3×C4#408311yescharacteristic
687C3×C4C2×D4×D511yescharacteristic
688C3×C4C22×C22⋊D511yescharacteristic
689C2×C5—21no—
690C2×C5—21no—
691C2×C5—21no—
692C2×C5—42no—
693C2×C5—82no—
694C2×C5C2×C3×#12011yescharacteristic
695D5—42no—
696D5—42no—
697C23—21no—
698C23—22no—
699C23—41no—
700C23—41no—
701C23—52no—
702C23—82no—
703C23—104no—
704C23—101no—
705C23C3×D4×D511yescharacteristic
706Q8—21no—
707Q8—52no—
708Q8—104no—
709Q8—101no—
710Q8—101no—
711Q8—101no—
712Q8C2×C3×C22⋊D512yes—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—22no—
717D4—22no—
718D4—41no—
719D4—41no—
720D4—52no—
721D4—104no—
722D4—104no—
723D4—104no—
724D4—102no—
725D4—102no—
726D4—102no—
727D4—102no—
728D4—101no—
729D4—101no—
730D4—101no—
731D4—404no—
732D4C2×C3×C22⋊D512yes—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—52no—
737C2×C4—104no—
738C2×C4—104no—
739C2×C4—104no—
740C2×C4—101no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4C3×D4×D511yescharacteristic
747C2×C4C3×D4×D511yescharacteristic
748C2×C4C3×D4×D511yescharacteristic
749C2×C4C2×C3×C22⋊D511yescharacteristic
750C2×C4C2×C3×C22⋊D511yescharacteristic
751C2×C4C23×C3×D511yescharacteristic
752C8—22no—
753C8—102no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—82no—
759C2×C3—202no—
760C2×C3—202no—
761C2×C3C2×#408311yescharacteristic
762C5C3×#302111yescharacteristic, complemented, Sylow
763C22—22no—
764C22—41no—
765C22—44no—
766C22—42no—
767C22—81no—
768C22—82no—
769C22—82no—
770C22—102no—
771C22—102no—
772C22—202no—
773C22—401no—
774C22—404no—
775C22C3×#408311yescharacteristic
776C22C3×#408311yescharacteristic
777C22C2×C3×D4×D511yescharacteristic
778C4—22no—
779C4—102no—
780C4—102no—
781C4—202no—
782C4C3×#408311yescharacteristic
783C4C3×#408311yescharacteristic
784C4C2×C3×D4×D511yescharacteristic
785C4C22×C3×C22⋊D511yescharacteristic
786C3#1061568811yescharacteristic, direct product factor, Sylow
787C2—21no—
788C2—21no—
789C2—21no—
790C2—42no—
791C2—82no—
792C2—202no—
793C2—202no—
794C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC2×C3C2×#4083
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC2×C3×C5C2×#120
hypercenterC2×C3×AGL(1,ℤ/8)D5
hypocenterC5C3×#3021
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C3×#66283C2semidirect
2. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
3. C3×#66139C2semidirect
4. C2×C3×#4078C2semidirect
5. C3×#65525C2semidirect
6. C3×#65490C2semidirect
7. C3×#65487C2semidirect
8. C3×#65428C2semidirect
9. C3×#65421C2semidirect
10. #10615688C3direct (N × H)
12. C22×C3×C5×D4C22semidirect
14. C3×#4150C22semidirect
16. C3×#4149C22semidirect
26. C3×C5×AGL(1,ℤ/8)C22semidirect
29. C2×C3×C5×M16C22semidirect
31. C3×#4086C22semidirect
33. C3×#4082C22semidirect
36. C3×#4078C22semidirect
38. C3×#4072C22semidirect
39. C2×C3×#681C22semidirect
40. C3×#3969C22semidirect
41. C3×#3957C22semidirect
42. C3×#3956C22semidirect
43. C3×#3955C22semidirect
45. #66283C2×C3semidirect
46. C2×C5×AGL(1,ℤ/8)C2×C3semidirect
47. #66139C2×C3semidirect
48. C2×#4078C2×C3semidirect
49. #65525C2×C3semidirect
50. #65490C2×C3semidirect
51. #65487C2×C3semidirect
52. #65428C2×C3semidirect
53. #65421C2×C3semidirect
57. C3×C5×#41D4semidirect
59. C2×C3×C5×Q8D4semidirect
66. C2×C3×C5×D4D4semidirect
96. C3×#709D4semidirect
99. C2×C3×D20D4semidirect
105. C2×C3×Dic10D4semidirect
123. C2×C3×AGL(1,ℤ/8)D5semidirect
131. C22×C5×D4C22×C3semidirect
133. #4150C22×C3semidirect
135. #4149C22×C3semidirect
145. C5×AGL(1,ℤ/8)C22×C3semidirect
148. C2×C5×M16C22×C3semidirect
150. #4086C22×C3semidirect
152. #4082C22×C3semidirect
155. #4078C22×C3semidirect
157. #4072C22×C3semidirect
158. C2×#681C22×C3semidirect
159. #3969C22×C3semidirect
160. #3957C22×C3semidirect
161. #3956C22×C3semidirect
162. #3955C22×C3semidirect
234. C22×C3×D4C2×D5semidirect
238. C3×AGL(1,ℤ/8)C2×D5semidirect
244. C2×C3×M16C2×D5semidirect
257. C5×#41C3×D4semidirect
259. C2×C5×Q8C3×D4semidirect
266. C2×C5×D4C3×D4semidirect
296. #709C3×D4semidirect
299. C2×D20C3×D4semidirect
305. C2×Dic10C3×D4semidirect
323. C2×AGL(1,ℤ/8)C3×D5semidirect
374. C3×#41C22⋊D5semidirect
381. C2×C3×Q8C22⋊D5semidirect
399. C2×C3×D4C22⋊D5semidirect
490. C22×D4C2×C3×D5semidirect
494. AGL(1,ℤ/8)C2×C3×D5semidirect
500. C2×M16C2×C3×D5semidirect
619. #41C3×C22⋊D5semidirect
626. C2×Q8C3×C22⋊D5semidirect
644. C2×D4C3×C22⋊D5semidirect
665. C3×C5#3021semidirect
762. C5C3×#3021semidirect
786. C3#10615688direct (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×C5×AGL(1,ℤ/8)2
C3×#661392
C2×C3×#40782
C3×#655252
C3×#654902
C3×#654872
C3×#654282
C3×#654212
#106156883
C3×#30215