Finite Group Databasebeta

← C3×#10615685 #14453941

Subgroups — C3×#10615685 #14453941

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#66158C211yesmaximal, characteristic, complemented
3C3×#66140C211yesmaximal, characteristic, complemented
4C2×C3×#4058C211yesmaximal, characteristic, complemented
5C3×#65528C211yesmaximal, characteristic, complemented
6C3×#65507C211yesmaximal, characteristic, complemented
7C3×#65462C211yesmaximal, characteristic, complemented
8C3×#65460C211yesmaximal, characteristic, complemented
9C3×#65456C211yesmaximal, characteristic, complemented
10C3×#65451C211yesmaximal, characteristic, complemented
11C3×#65447C211yesmaximal, characteristic, complemented
12C3×#65442C211yesmaximal, characteristic, complemented
13C3×#65441C211yesmaximal, characteristic, complemented
14C3×#65426C211yesmaximal, characteristic, complemented
15C3×#65416C211yesmaximal, characteristic, complemented
16#10615685C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic
20C2×C3×#711C2211yescharacteristic, complemented
21C3×C5×AGL(1,ℤ/8)—24no—
22C2×C3×C5×SD16C2211yescharacteristic
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×D8C2211yescharacteristic
25C2×C3×C5×D8C2211yescharacteristic
26C2×C3×C5×M16C2211yescharacteristic
27C3×#4099—21no—
28C2×C3×C22⋊Dic5—21no—
29C3×#4092C2211yescharacteristic, complemented
30C3×#4090C2211yescharacteristic, complemented
31C2×C3×#689C2211yescharacteristic, complemented
32C3×#4085—21no—
33C3×#4085—21no—
34C3×#4084C2211yescharacteristic
35C3×#4082C2211yescharacteristic
36C3×#4081—21no—
37C3×#4081—21no—
38C3×D4×Dic5C2211yescharacteristic
39C3×D4×Dic5C2211yescharacteristic, complemented
40C2×C3×#687C2211yescharacteristic
41C2×C3×#687C2211yescharacteristic
42C2×C3×#687C2211yescharacteristic, complemented
43C3×#4075—21no—
44C3×C4×C22⋊D5C2211yescharacteristic
45C3×#4070C2211yescharacteristic
46C3×#4070C2211yescharacteristic
47C2×C3×#683—21no—
48C3×#4058—24no—
49C2×C3×Dic20C2211yescharacteristic, complemented
50C2×C3×C8×D5C2211yescharacteristic, complemented
51C3×#3967C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic
53C3×#3964C2211yescharacteristic
54C3×#3964C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic
56C3×#3952C2211yescharacteristic, complemented
57C3×#3949C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3947C2211yescharacteristic, complemented
61C3×#3946C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×C5×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
64#66158C2×C311yescharacteristic, complemented
65#66140C2×C311yescharacteristic, complemented
66C2×#4058C2×C311yescharacteristic, complemented
67#65528C2×C311yescharacteristic, complemented
68#65507C2×C311yescharacteristic, complemented
69#65462C2×C311yescharacteristic, complemented
70#65460C2×C311yescharacteristic, complemented
71#65456C2×C311yescharacteristic, complemented
72#65451C2×C311yescharacteristic, complemented
73#65447C2×C311yescharacteristic, complemented
74#65442C2×C311yescharacteristic, complemented
75#65441C2×C311yescharacteristic, complemented
76#65426C2×C311yescharacteristic, complemented
77#65416C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—22no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—41no—
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5D411yescharacteristic
95C22×C3×Dic5—21no—
96C22×C3×Dic5—21no—
97C22×C3×Dic5—21no—
98C22×C3×Dic5—21no—
99C3×#711—22no—
100C3×#711—22no—
101C3×#711—41no—
102C3×#711—41no—
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×SD16—22no—
107C3×C5×SD16—22no—
108C3×C5×D8—22no—
109C3×C5×D8D414yescomplemented
110C3×C5×M16—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5—21no—
115C3×C22⋊Dic5—21no—
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5D411yescharacteristic
121C3×#689—41no—
122C3×#687—22no—
123C3×#687—22no—
124C3×#687—41no—
125C3×#685—21no—
126C3×#685D411yescharacteristic
127C3×C4⋊Dic5C2311yescharacteristic
128C3×C4⋊Dic5C2311yescharacteristic
129C3×#683—21no—
130C3×#683—21no—
131C3×#683—21no—
132C3×#683—21no—
133C3×#683—21no—
134C3×#683D411yescharacteristic
135C3×C4×Dic5C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C3×Dic20—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
141C2×C3×#135—51no—
142C3×#547—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#470—51no—
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C22×C5×D4C22×C311yescharacteristic
157C2×#711C22×C311yescharacteristic
158C2×#711C22×C311yescharacteristic, complemented
159C5×AGL(1,ℤ/8)—24no—
160C2×C5×SD16C22×C311yescharacteristic
161C2×C5×SD16C22×C311yescharacteristic
162C2×C5×D8C22×C311yescharacteristic
163C2×C5×D8C22×C311yescharacteristic
164C2×C5×M16C22×C311yescharacteristic
165#4099—21no—
166C2×C22⋊Dic5—21no—
167#4092C22×C311yescharacteristic, complemented
168#4090C22×C311yescharacteristic, complemented
169C2×#689C22×C311yescharacteristic, complemented
170#4085—21no—
171#4085—21no—
172#4084C22×C311yescharacteristic
173#4082C22×C311yescharacteristic
174#4081—21no—
175#4081—21no—
176D4×Dic5C22×C311yescharacteristic
177D4×Dic5C22×C311yescharacteristic, complemented
178C2×#687C22×C311yescharacteristic
179C2×#687C22×C311yescharacteristic
180C2×#687C22×C311yescharacteristic, complemented
181#4075—21no—
182C4×C22⋊D5C22×C311yescharacteristic
183#4070C22×C311yescharacteristic
184#4070C22×C311yescharacteristic
185C2×#683—21no—
186#4058—24no—
187C2×Dic20C22×C311yescharacteristic, complemented
188C2×C8×D5C22×C311yescharacteristic, complemented
189#3967C22×C311yescharacteristic, complemented
190#3964C22×C311yescharacteristic
191#3964C22×C311yescharacteristic
192#3964C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic
194#3952C22×C311yescharacteristic, complemented
195#3949C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3947C22×C311yescharacteristic, complemented
199#3946C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—21no—
215C3×C5×D4—42no—
216C3×C5×D4—42no—
217C3×C5×D4C2×D412yes—
218C3×C5×D4C2×D412yes—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—42no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2411yescharacteristic
225C3×C22⋊D5—41no—
226C3×C22⋊D5—42no—
227C3×C22⋊D5—42no—
228C3×C22⋊D5—81no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—42no—
234C2×C3×Dic5—42no—
235C2×C3×Dic5—42no—
236C2×C3×Dic5—81no—
237C2×C3×Dic5C2×D411yescharacteristic
238C2×C3×Dic5C2×D411yescharacteristic
239C2×C3×Dic5C2×D411yescharacteristic
240C3×C4×D5—21no—
241C3×C4×D5—21no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8C2×D412yes—
248C3×#168—21no—
249C3×#168—21no—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41C2×D511yescharacteristic
253C22×C3×D4C2×D511yescharacteristic
254C3×AGL(1,ℤ/8)—24no—
255C3×#135—104no—
256C2×C3×Q16—51no—
257C2×C3×Q16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16C2×D511yescharacteristic
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×D8C2×D511yescharacteristic
264C2×C3×D8C2×D511yescharacteristic
265C2×C3×M16C2×D511yescharacteristic
266C22×C3×C8—51no—
267C3×C4⋊Q8—51no—
268C3×#124—51no—
269C3×#123—101no—
270C3×#123—101no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—51no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#121—101no—
278C3×#120—101no—
279C3×C4×D4—51no—
280C3×C4×D4—51no—
281C3×C4×D4—51no—
282C2×C3×C4⋊C4—101no—
283C2×C3×C22⋊C4—101no—
284C3×#106—51no—
285C3×C4⋊C8—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97—51no—
295C24×C5—21no—
296C5×#41—22no—
297C5×#41—41no—
298C2×C5×Q8C23×C311yescharacteristic
299C2×C5×D4—22no—
300C2×C5×D4—21no—
301C2×C5×D4—21no—
302C2×C5×D4—41no—
303C2×C5×D4C23×C311yescharacteristic
304C2×C5×D4C23×C311yescharacteristic
305C2×C5×D4C23×C311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5C23×C311yescharacteristic
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311C2×C22⋊D5C3×D411yescharacteristic
312C22×Dic5—21no—
313C22×Dic5—21no—
314C22×Dic5—21no—
315C22×Dic5—21no—
316#711—22no—
317#711—22no—
318#711—41no—
319#711—41no—
320C2×C4×D5C23×C311yescharacteristic
321C2×Dic10C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×SD16—22no—
324C5×SD16—22no—
325C5×D8—22no—
326C5×D8C3×D414yescomplemented
327C5×M16—22no—
328C2×C5×C8C23×C311yescharacteristic
329C2×C5×C8C23×C311yescharacteristic
330C22⋊Dic5—21no—
331C22⋊Dic5—21no—
332C22⋊Dic5—21no—
333C22⋊Dic5—21no—
334C22⋊Dic5—21no—
335C22⋊Dic5—21no—
336C22⋊Dic5—21no—
337C22⋊Dic5C3×D411yescharacteristic
338#689—41no—
339#687—22no—
340#687—22no—
341#687—41no—
342#685—21no—
343#685C3×D411yescharacteristic
344C4⋊Dic5C23×C311yescharacteristic
345C4⋊Dic5C23×C311yescharacteristic
346#683—21no—
347#683—21no—
348#683—21no—
349#683—21no—
350#683—21no—
351#683C3×D411yescharacteristic
352C4×Dic5C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354C2×#168C23×C311yescharacteristic
355Dic20—22no—
356C8×D5—22no—
357C2×AGL(1,ℤ/8)C3×D511yescharacteristic, complemented
358C2×#135—51no—
359#547—51no—
360#546—51no—
361#497—51no—
362#470—51no—
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442—51no—
371#435—51no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—84no—
385C22×C3×C5C22×D411yescharacteristic
386C2×C3×D5—21no—
387C2×C3×D5—21no—
388C2×C3×D5—21no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5C22×D411yescharacteristic
392C3×C4×C5H(5,𝔽2)11yescharacteristic
393C3×Dic5—21no—
394C3×Dic5—21no—
395C3×Dic5—21no—
396C3×Dic5—41no—
397C3×Dic5—41no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—21no—
401C3×#41—22no—
402C3×#41—41no—
403C3×#41—102no—
404C3×#41—102no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8—51no—
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—22no—
411C2×C3×D4—21no—
412C2×C3×D4—21no—
413C2×C3×D4—41no—
414C2×C3×D4—51no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4C22×D511yescharacteristic
419C2×C3×D4C22×D511yescharacteristic
420C2×C3×D4C22×D511yescharacteristic
421C22×C3×C4—21no—
422C22×C3×C4—51no—
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4—101no—
427C22×C3×C4C22×D511yescharacteristic
428C3×Q16—102no—
429C3×Q16—201no—
430C3×SD16—22no—
431C3×SD16—22no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—201no—
435C3×D8—22no—
436C3×D8C22⋊D514yescomplemented
437C3×M16—22no—
438C2×C3×C8—51no—
439C2×C3×C8—51no—
440C2×C3×C8—102no—
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D511yescharacteristic
443C3×C4⋊C4—51no—
444C3×C4⋊C4—51no—
445C3×C4⋊C4—51no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4—101no—
450C3×C4⋊C4—101no—
451C3×C22⋊C4—51no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C42—51no—
462C23×C5—21no—
463C23×C5—21no—
464C23×C5—21no—
465C23×C5—42no—
466C23×C5—42no—
467C23×C5—81no—
468C23×C5C2×C3×D411yescharacteristic
469C22×D5C2×C3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×D4—21no—
473C5×D4—21no—
474C5×D4—21no—
475C5×D4—21no—
476C5×D4—42no—
477C5×D4—42no—
478C5×D4C2×C3×D412yes—
479C5×D4C2×C3×D412yes—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—42no—
484C2×C4×C5C2×C3×D411yescharacteristic
485C2×C4×C5C24×C311yescharacteristic
486C22⋊D5—41no—
487C22⋊D5—42no—
488C22⋊D5—42no—
489C22⋊D5—81no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—42no—
495C2×Dic5—42no—
496C2×Dic5—42no—
497C2×Dic5—81no—
498C2×Dic5C2×C3×D411yescharacteristic
499C2×Dic5C2×C3×D411yescharacteristic
500C2×Dic5C2×C3×D411yescharacteristic
501C4×D5—21no—
502C4×D5—21no—
503Dic10—21no—
504Dic10—21no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8C2×C3×D412yes—
509#168—21no—
510#168—21no—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41C2×C3×D511yescharacteristic
514C22×D4C2×C3×D511yescharacteristic
515AGL(1,ℤ/8)—24no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16C2×C3×D511yescharacteristic
523C2×SD16C2×C3×D511yescharacteristic
524C2×D8C2×C3×D511yescharacteristic
525C2×D8C2×C3×D511yescharacteristic
526C2×M16C2×C3×D511yescharacteristic
527C22×C8—51no—
528C4⋊Q8—51no—
529#124—51no—
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8—51no—
535C22⋊Q8—51no—
536#121—51no—
537#121—101no—
538#121—101no—
539#120—101no—
540C4×D4—51no—
541C4×D4—51no—
542C4×D4—51no—
543C2×C4⋊C4—101no—
544C2×C22⋊C4—101no—
545#106—51no—
546C4⋊C8—51no—
547#103—51no—
548#103—51no—
549#103—51no—
550#102—51no—
551#102—51no—
552#102—51no—
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97—51no—
556C2×C3×C5—41no—
557C2×C3×C5—42no—
558C2×C3×C5—42no—
559C2×C3×C5—81no—
560C2×C3×C5D4211yescharacteristic
561C2×C3×C5#57511yescharacteristic
562C2×C3×C5#57711yescharacteristic
563C3×D5—41no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—42no—
568C23×C3—42no—
569C23×C3—51no—
570C23×C3—81no—
571C23×C3D4×D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—42no—
583C3×D4—42no—
584C3×D4—201no—
585C3×D4—202no—
586C3×D4—202no—
587C3×D4—401no—
588C3×D4C2×C22⋊D512yes—
589C3×D4C2×C22⋊D512yes—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—42no—
594C2×C3×C4—51no—
595C2×C3×C4—51no—
596C2×C3×C4—51no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—101no—
603C2×C3×C4—202no—
604C2×C3×C4—202no—
605C2×C3×C4—202no—
606C2×C3×C4—401no—
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—101no—
611C3×C8—101no—
612C3×C8C2×C22⋊D512yes—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—22no—
616C22×C5—22no—
617C22×C5—21no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5—41no—
623C22×C5—41no—
624C22×C5—41no—
625C22×C5—84no—
626C22×C5C22×C3×D411yescharacteristic
627C2×D5—21no—
628C2×D5—21no—
629C2×D5—21no—
630C4×C5—21no—
631C4×C5—41no—
632C4×C5C22×C3×D411yescharacteristic
633C4×C5C3×H(5,𝔽2)11yescharacteristic
634Dic5—21no—
635Dic5—21no—
636Dic5—21no—
637Dic5—41no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641C24—21no—
642#41—22no—
643#41—41no—
644#41—102no—
645#41—102no—
646#41—201no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8—51no—
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—41no—
655C2×D4—51no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4C22×C3×D511yescharacteristic
660C2×D4C22×C3×D511yescharacteristic
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—51no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4C22×C3×D511yescharacteristic
669Q16—102no—
670Q16—201no—
671SD16—22no—
672SD16—22no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—22no—
677D8C3×C22⋊D514yescomplemented
678M16—22no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—51no—
685C4⋊C4—51no—
686C4⋊C4—51no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4—101no—
692C22⋊C4—51no—
693C22⋊C4—51no—
694C22⋊C4—101no—
695C22⋊C4—101no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4—101no—
701C22⋊C4—101no—
702C42—51no—
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—84no—
717C22×C3—101no—
718C22×C3—101no—
719C22×C3—101no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—41no—
723C3×C4—101no—
724C3×C4—101no—
725C3×C4—101no—
726C3×C4—201no—
727C3×C4—201no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4#414411yescharacteristic
731C3×C4C22×C22⋊D511yescharacteristic
732C2×C5—41no—
733C2×C5—42no—
734C2×C5—42no—
735C2×C5—81no—
736C2×C5C3×D4211yescharacteristic
737C2×C5C3×#57511yescharacteristic
738C2×C5C3×#57711yescharacteristic
739D5—41no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—42no—
744C23—42no—
745C23—51no—
746C23—81no—
747C23C3×D4×D511yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—101no—
751Q8—101no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—201no—
761D4—202no—
762D4—202no—
763D4—401no—
764D4C2×C3×C22⋊D512yes—
765D4C2×C3×C22⋊D512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—42no—
770C2×C4—51no—
771C2×C4—51no—
772C2×C4—51no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4—401no—
783C2×C4C3×D4×D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—101no—
787C8—101no—
788C8C2×C3×C22⋊D512yes—
789C2×C3—41no—
790C2×C3—42no—
791C2×C3—42no—
792C2×C3—81no—
793C2×C3—201no—
794C2×C3#6610711yescharacteristic
795C2×C3#6610911yescharacteristic
796C2×C3D4×C22⋊D511yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—21no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—84no—
811C22—101no—
812C22—101no—
813C22—101no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—41no—
817C4—101no—
818C4—101no—
819C4—101no—
820C4—201no—
821C4—201no—
822C4—201no—
823C4—201no—
824C4C3×#414411yescharacteristic
825C4C22×C3×C22⋊D511yescharacteristic
826C3#1061568511yescharacteristic, direct product factor, Sylow
827C2—41no—
828C2—42no—
829C2—42no—
830C2—81no—
831C2—201no—
832C2C3×#6610711yescharacteristic
833C2C3×#6610911yescharacteristic
834C2C3×D4×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×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. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
2. C3×#66158C2semidirect
3. C3×#66140C2semidirect
4. C2×C3×#4058C2semidirect
5. C3×#65528C2semidirect
6. C3×#65507C2semidirect
7. C3×#65462C2semidirect
8. C3×#65460C2semidirect
9. C3×#65456C2semidirect
10. C3×#65451C2semidirect
11. C3×#65447C2semidirect
12. C3×#65442C2semidirect
13. C3×#65441C2semidirect
14. C3×#65426C2semidirect
15. C3×#65416C2semidirect
16. #10615685C3direct (N × H)
20. C2×C3×#711C22semidirect
29. C3×#4092C22semidirect
30. C3×#4090C22semidirect
31. C2×C3×#689C22semidirect
39. C3×D4×Dic5C22semidirect
42. C2×C3×#687C22semidirect
49. C2×C3×Dic20C22semidirect
50. C2×C3×C8×D5C22semidirect
51. C3×#3967C22semidirect
54. C3×#3964C22semidirect
56. C3×#3952C22semidirect
57. C3×#3949C22semidirect
58. C3×#3948C22semidirect
59. C3×#3948C22semidirect
60. C3×#3947C22semidirect
61. C3×#3946C22semidirect
63. C2×C5×AGL(1,ℤ/8)C2×C3semidirect
64. #66158C2×C3semidirect
65. #66140C2×C3semidirect
66. C2×#4058C2×C3semidirect
67. #65528C2×C3semidirect
68. #65507C2×C3semidirect
69. #65462C2×C3semidirect
70. #65460C2×C3semidirect
71. #65456C2×C3semidirect
72. #65451C2×C3semidirect
73. #65447C2×C3semidirect
74. #65442C2×C3semidirect
75. #65441C2×C3semidirect
76. #65426C2×C3semidirect
77. #65416C2×C3semidirect
109. C3×C5×D8D4semidirect
140. C2×C3×AGL(1,ℤ/8)D5semidirect
158. C2×#711C22×C3semidirect
167. #4092C22×C3semidirect
168. #4090C22×C3semidirect
169. C2×#689C22×C3semidirect
177. D4×Dic5C22×C3semidirect
180. C2×#687C22×C3semidirect
187. C2×Dic20C22×C3semidirect
188. C2×C8×D5C22×C3semidirect
189. #3967C22×C3semidirect
192. #3964C22×C3semidirect
194. #3952C22×C3semidirect
195. #3949C22×C3semidirect
196. #3948C22×C3semidirect
197. #3948C22×C3semidirect
198. #3947C22×C3semidirect
199. #3946C22×C3semidirect
326. C5×D8C3×D4semidirect
357. C2×AGL(1,ℤ/8)C3×D5semidirect
436. C3×D8C22⋊D5semidirect
677. D8C3×C22⋊D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10615685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×AGL(1,ℤ/8)2
C3×#661582
C3×#661402
C2×C3×#40582
C3×#655282
C3×#655072
C3×#654622
C3×#654602
C3×#654562
C3×#654512
C3×#654472
C3×#654422
C3×#654412
C3×#654262
C3×#654162
#106156853
C3×#32675