Finite Group Databasebeta

← C3×#10615684 #14453431

Subgroups — C3×#10615684 #14453431

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 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×#66165C211yesmaximal, characteristic, complemented
3C3×D4×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×C3×D5×SD16C211yesmaximal, characteristic, complemented
5C3×#65527C211yesmaximal, characteristic, complemented
6C3×#65507C211yesmaximal, characteristic, complemented
7C3×#65459C211yesmaximal, characteristic, complemented
8C3×#65453C211yesmaximal, characteristic, complemented
9C3×#65452C211yesmaximal, characteristic, complemented
10C3×#65446C211yesmaximal, characteristic, complemented
11C3×#65445C211yesmaximal, characteristic, complemented
12C3×#65443C211yesmaximal, characteristic, complemented
13C3×#65442C211yesmaximal, characteristic, complemented
14C3×#65423C211yesmaximal, characteristic, complemented
15C3×#65416C211yesmaximal, characteristic, complemented
16#10615684C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C22⋊D5—21no—
20C2×C3×Q8×D5C2211yescharacteristic, complemented
21C2×C3×D4×D5C2211yescharacteristic
22C3×C5×AGL(1,ℤ/8)—24no—
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×SD16C2211yescharacteristic, complemented
25C2×C3×C5×D8C2211yescharacteristic
26C2×C3×C5×D8C2211yescharacteristic, complemented
27C2×C3×C5×M16C2211yescharacteristic, complemented
28C3×#4099—21no—
29C3×Q8×Dic5C2211yescharacteristic, complemented
30C2×C3×#688C2211yescharacteristic, complemented
31C3×#4086C2211yescharacteristic
32C3×#4085—21no—
33C3×#4084—21no—
34C3×#4084C2211yescharacteristic
35C3×#4084C2211yescharacteristic, complemented
36C3×#4083—21no—
37C3×#4082—21no—
38C3×#4082C2211yescharacteristic, complemented
39C3×D4×Dic5C2211yescharacteristic
40C2×C3×#687C2211yescharacteristic
41C2×C3×#687C2211yescharacteristic, complemented
42C2×C3×#686C2211yescharacteristic, complemented
43C3×#4076C2211yescharacteristic
44C3×C4×C22⋊D5—21no—
45C3×C4×C22⋊D5C2211yescharacteristic
46C3×#4070—21no—
47C3×#4070C2211yescharacteristic, complemented
48C3×D5×SD16—24no—
49C2×C3×#677C2211yescharacteristic, complemented
50C2×C3×C8×D5C2211yescharacteristic, complemented
51C3×#3967C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic
53C3×#3964C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3950C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3947C2211yescharacteristic, complemented
61C3×#3946C2211yescharacteristic, complemented
62C3×#3265—51nomaximal, Hall
63C2×C5×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
64#66165C2×C311yescharacteristic, complemented
65D4×C22⋊D5C2×C311yescharacteristic, complemented
66C2×D5×SD16C2×C311yescharacteristic, complemented
67#65527C2×C311yescharacteristic, complemented
68#65507C2×C311yescharacteristic, complemented
69#65459C2×C311yescharacteristic, complemented
70#65453C2×C311yescharacteristic, complemented
71#65452C2×C311yescharacteristic, complemented
72#65446C2×C311yescharacteristic, complemented
73#65445C2×C311yescharacteristic, complemented
74#65443C2×C311yescharacteristic, complemented
75#65442C2×C311yescharacteristic, complemented
76#65423C2×C311yescharacteristic, complemented
77#65416C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C23×C3×D5—21no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—22no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5—21no—
98C2×C3×C22⋊D5—44no—
99C2×C3×C22⋊D5D411yescharacteristic
100C22×C3×Dic5—21no—
101C3×Q8×D5—22no—
102C3×Q8×D5—41no—
103C3×D4×D5—22no—
104C3×D4×D5—41no—
105C2×C3×D20C2311yescharacteristic
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5C2311yescharacteristic
108C2×C3×Dic10—21no—
109C2×C3×Dic10C2311yescharacteristic
110C3×C5×SD16—22no—
111C3×C5×SD16D414yescomplemented
112C3×C5×D8—22no—
113C3×C5×D8—22no—
114C3×C5×M16—22no—
115C2×C3×C5×C8C2311yescharacteristic
116C2×C3×C5×C8C2311yescharacteristic
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5—21no—
121C3×C22⋊Dic5—21no—
122C3×C22⋊Dic5—21no—
123C3×C22⋊Dic5D411yescharacteristic
124C3×#688—22no—
125C3×#687—22no—
126C3×#687—41no—
127C3×#686—41no—
128C3×#685—21no—
129C3×#685D411yescharacteristic
130C3×C4⋊Dic5—21no—
131C3×C4⋊Dic5C2311yescharacteristic
132C3×C4⋊Dic5C2311yescharacteristic
133C3×#683—21no—
134C3×#683D411yescharacteristic
135C3×C4×Dic5—21no—
136C3×C4×Dic5C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C3×#677—22no—
140C3×C8×D5—22no—
141C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
142C22×C3×SD16—51no—
143C3×#548—51no—
144C3×D42—51no—
145C3×#496—51no—
146C3×#468—51no—
147C3×#466—51no—
148C3×#463—51no—
149C3×#460—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#448—51no—
153C3×#447—51no—
154C3×#440—51no—
155C3×#435—51no—
156C2×C5×#41C22×C311yescharacteristic, complemented
157C22×C5×D4C22×C311yescharacteristic
158C22×C22⋊D5—21no—
159C2×Q8×D5C22×C311yescharacteristic, complemented
160C2×D4×D5C22×C311yescharacteristic
161C5×AGL(1,ℤ/8)—24no—
162C2×C5×SD16C22×C311yescharacteristic
163C2×C5×SD16C22×C311yescharacteristic, complemented
164C2×C5×D8C22×C311yescharacteristic
165C2×C5×D8C22×C311yescharacteristic, complemented
166C2×C5×M16C22×C311yescharacteristic, complemented
167#4099—21no—
168Q8×Dic5C22×C311yescharacteristic, complemented
169C2×#688C22×C311yescharacteristic, complemented
170#4086C22×C311yescharacteristic
171#4085—21no—
172#4084—21no—
173#4084C22×C311yescharacteristic
174#4084C22×C311yescharacteristic, complemented
175#4083—21no—
176#4082—21no—
177#4082C22×C311yescharacteristic, complemented
178D4×Dic5C22×C311yescharacteristic
179C2×#687C22×C311yescharacteristic
180C2×#687C22×C311yescharacteristic, complemented
181C2×#686C22×C311yescharacteristic, complemented
182#4076C22×C311yescharacteristic
183C4×C22⋊D5—21no—
184C4×C22⋊D5C22×C311yescharacteristic
185#4070—21no—
186#4070C22×C311yescharacteristic, complemented
187D5×SD16—24no—
188C2×#677C22×C311yescharacteristic, complemented
189C2×C8×D5C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic
192#3964C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194C22⋊#168C22×C311yescharacteristic, complemented
195#3953C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic, complemented
197#3950C22×C311yescharacteristic, complemented
198#3948C22×C311yescharacteristic, complemented
199#3947C22×C311yescharacteristic, complemented
200#3946C22×C311yescharacteristic, complemented
201#3265—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—42no—
206C23×C3×C5—42no—
207C23×C3×C5—81no—
208C23×C3×C5C2×D411yescharacteristic
209C22×C3×D5—21no—
210C22×C3×D5—42no—
211C22×C3×D5—42no—
212C22×C3×D5—81no—
213C22×C3×D5C2×D411yescharacteristic
214C3×C5×Q8—21no—
215C3×C5×Q8C2×D412yescomplemented
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4—42no—
223C3×C5×D4C2×D412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—42no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2411yescharacteristic
230C3×C22⋊D5—22no—
231C3×C22⋊D5—42no—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—42no—
234C3×C22⋊D5—42no—
235C3×C22⋊D5—42no—
236C3×C22⋊D5—81no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—42no—
241C2×C3×Dic5C2×D411yescharacteristic
242C2×C3×Dic5C2×D411yescharacteristic
243C2×C3×Dic5C2×D411yescharacteristic
244C3×D20—21no—
245C3×D20—21no—
246C3×C4×D5—21no—
247C3×C4×D5—21no—
248C3×C4×D5—42no—
249C3×Dic10—21no—
250C3×Dic10—21no—
251C3×Dic10—42no—
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C3×#168—21no—
255C3×#168—21no—
256C2×C3×#41C2×D511yescharacteristic, complemented
257C22×C3×Q8—51no—
258C22×C3×D4—51no—
259C22×C3×D4—101no—
260C22×C3×D4C2×D511yescharacteristic
261C3×AGL(1,ℤ/8)—24no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×SD16—51no—
265C2×C3×SD16—51no—
266C2×C3×SD16—104no—
267C2×C3×SD16C2×D511yescharacteristic
268C2×C3×SD16C2×D511yescharacteristic, complemented
269C2×C3×D8—51no—
270C2×C3×D8C2×D511yescharacteristic
271C2×C3×D8C2×D511yescharacteristic, complemented
272C2×C3×M16C2×D511yescharacteristic, complemented
273C22×C3×C8—51no—
274C3×#127—51no—
275C3×#124—51no—
276C3×#124—101no—
277C3×C22⋊Q8—51no—
278C3×C22⋊Q8—101no—
279C3×#121—51no—
280C3×#121—51no—
281C3×#121—51no—
282C3×#121—101no—
283C3×#121—101no—
284C3×#120—101no—
285C3×#120—101no—
286C3×C4×Q8—51no—
287C3×C4×D4—51no—
288C3×C4×D4—51no—
289C3×C4×D4—101no—
290C3×#107—51no—
291C3×C4⋊C8—51no—
292C3×#103—51no—
293C3×#103—51no—
294C3×#102—51no—
295C3×#102—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×C22⋊C8—51no—
299C3×C22⋊C8—51no—
300C3×#97—51no—
301C24×C5—21no—
302C23×D5—21no—
303C5×#41—22no—
304C5×#41—41no—
305C2×C5×Q8C23×C311yescharacteristic
306C2×C5×D4—22no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—41no—
310C2×C5×D4C23×C311yescharacteristic
311C2×C5×D4C23×C311yescharacteristic
312C2×C5×D4C23×C311yescharacteristic
313C22×C4×C5—21no—
314C22×C4×C5C23×C311yescharacteristic
315C2×C22⋊D5—21no—
316C2×C22⋊D5—21no—
317C2×C22⋊D5—21no—
318C2×C22⋊D5—21no—
319C2×C22⋊D5—21no—
320C2×C22⋊D5—21no—
321C2×C22⋊D5—44no—
322C2×C22⋊D5C3×D411yescharacteristic
323C22×Dic5—21no—
324Q8×D5—22no—
325Q8×D5—41no—
326D4×D5—22no—
327D4×D5—41no—
328C2×D20C23×C311yescharacteristic
329C2×C4×D5—21no—
330C2×C4×D5C23×C311yescharacteristic
331C2×Dic10—21no—
332C2×Dic10C23×C311yescharacteristic
333C5×SD16—22no—
334C5×SD16C3×D414yescomplemented
335C5×D8—22no—
336C5×D8—22no—
337C5×M16—22no—
338C2×C5×C8C23×C311yescharacteristic
339C2×C5×C8C23×C311yescharacteristic
340C22⋊Dic5—21no—
341C22⋊Dic5—21no—
342C22⋊Dic5—21no—
343C22⋊Dic5—21no—
344C22⋊Dic5—21no—
345C22⋊Dic5—21no—
346C22⋊Dic5C3×D411yescharacteristic
347#688—22no—
348#687—22no—
349#687—41no—
350#686—41no—
351#685—21no—
352#685C3×D411yescharacteristic
353C4⋊Dic5—21no—
354C4⋊Dic5C23×C311yescharacteristic
355C4⋊Dic5C23×C311yescharacteristic
356#683—21no—
357#683C3×D411yescharacteristic
358C4×Dic5—21no—
359C4×Dic5C23×C311yescharacteristic
360C2×#168C23×C311yescharacteristic
361C2×#168C23×C311yescharacteristic
362#677—22no—
363C8×D5—22no—
364C2×AGL(1,ℤ/8)C3×D511yescharacteristic, complemented
365C22×SD16—51no—
366#548—51no—
367D42—51no—
368#496—51no—
369#468—51no—
370#466—51no—
371#463—51no—
372#460—51no—
373#450—51no—
374#449—51no—
375#448—51no—
376#447—51no—
377#440—51no—
378#435—51no—
379C22×C3×C5—22no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—84no—
392C22×C3×C5C22×D411yescharacteristic
393C2×C3×D5—21no—
394C2×C3×D5—21no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—84no—
399C2×C3×D5AGL(1,ℤ/8)12yescomplemented
400C3×C4×C5—22no—
401C3×C4×C5—21no—
402C3×C4×C5C22×D411yescharacteristic
403C3×C4×C5H(5,𝔽2)11yescharacteristic
404C3×Dic5—21no—
405C3×Dic5—21no—
406C3×Dic5—21no—
407C3×Dic5—41no—
408C3×Dic5—41no—
409C3×Dic5—41no—
410C24×C3—21no—
411C24×C3—101no—
412C3×#41—22no—
413C3×#41—41no—
414C2×C3×Q8—51no—
415C2×C3×Q8—101no—
416C2×C3×Q8—102no—
417C2×C3×Q8—201no—
418C2×C3×Q8C22×D511yescharacteristic
419C2×C3×D4—22no—
420C2×C3×D4—21no—
421C2×C3×D4—21no—
422C2×C3×D4—41no—
423C2×C3×D4—51no—
424C2×C3×D4—51no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—102no—
429C2×C3×D4—101no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—201no—
433C2×C3×D4—204no—
434C2×C3×D4C22×D511yescharacteristic
435C2×C3×D4C22×D511yescharacteristic
436C2×C3×D4C22×D511yescharacteristic
437C22×C3×C4—21no—
438C22×C3×C4—51no—
439C22×C3×C4—101no—
440C22×C3×C4—101no—
441C22×C3×C4C22×D511yescharacteristic
442C3×SD16—22no—
443C3×SD16—102no—
444C3×SD16—102no—
445C3×SD16—102no—
446C3×SD16—201no—
447C3×SD16C22⋊D514yescomplemented
448C3×D8—22no—
449C3×D8—22no—
450C3×D8—201no—
451C3×M16—22no—
452C2×C3×C8—51no—
453C2×C3×C8—51no—
454C2×C3×C8—102no—
455C2×C3×C8C22×D511yescharacteristic
456C2×C3×C8C22×D511yescharacteristic
457C3×C4⋊C4—51no—
458C3×C4⋊C4—51no—
459C3×C4⋊C4—51no—
460C3×C4⋊C4—101no—
461C3×C4⋊C4—101no—
462C3×C22⋊C4—51no—
463C3×C22⋊C4—51no—
464C3×C22⋊C4—101no—
465C3×C22⋊C4—101no—
466C3×C22⋊C4—101no—
467C3×C22⋊C4—101no—
468C3×C22⋊C4—101no—
469C3×C22⋊C4—101no—
470C3×C22⋊C4—101no—
471C3×C42—51no—
472C3×C42—101no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—42no—
477C23×C5—42no—
478C23×C5—81no—
479C23×C5C2×C3×D411yescharacteristic
480C22×D5—21no—
481C22×D5—42no—
482C22×D5—42no—
483C22×D5—81no—
484C22×D5C2×C3×D411yescharacteristic
485C5×Q8—21no—
486C5×Q8C2×C3×D412yescomplemented
487C5×D4—21no—
488C5×D4—21no—
489C5×D4—21no—
490C5×D4—21no—
491C5×D4—21no—
492C5×D4—42no—
493C5×D4—42no—
494C5×D4C2×C3×D412yes—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—42no—
499C2×C4×C5C2×C3×D411yescharacteristic
500C2×C4×C5C24×C311yescharacteristic
501C22⋊D5—22no—
502C22⋊D5—42no—
503C22⋊D5—42no—
504C22⋊D5—42no—
505C22⋊D5—42no—
506C22⋊D5—42no—
507C22⋊D5—81no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—42no—
512C2×Dic5C2×C3×D411yescharacteristic
513C2×Dic5C2×C3×D411yescharacteristic
514C2×Dic5C2×C3×D411yescharacteristic
515D20—21no—
516D20—21no—
517C4×D5—21no—
518C4×D5—21no—
519C4×D5—42no—
520Dic10—21no—
521Dic10—21no—
522Dic10—42no—
523C5×C8—21no—
524C5×C8C2×C3×D412yescomplemented
525#168—21no—
526#168—21no—
527C2×#41C2×C3×D511yescharacteristic, complemented
528C22×Q8—51no—
529C22×D4—51no—
530C22×D4—101no—
531C22×D4C2×C3×D511yescharacteristic
532AGL(1,ℤ/8)—24no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—51no—
536C2×SD16—51no—
537C2×SD16—104no—
538C2×SD16C2×C3×D511yescharacteristic
539C2×SD16C2×C3×D511yescharacteristic, complemented
540C2×D8—51no—
541C2×D8C2×C3×D511yescharacteristic
542C2×D8C2×C3×D511yescharacteristic, complemented
543C2×M16C2×C3×D511yescharacteristic, complemented
544C22×C8—51no—
545#127—51no—
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—51no—
551#121—51no—
552#121—51no—
553#121—101no—
554#121—101no—
555#120—101no—
556#120—101no—
557C4×Q8—51no—
558C4×D4—51no—
559C4×D4—51no—
560C4×D4—101no—
561#107—51no—
562C4⋊C8—51no—
563#103—51no—
564#103—51no—
565#102—51no—
566#102—51no—
567#102—51no—
568#102—51no—
569C22⋊C8—51no—
570C22⋊C8—51no—
571#97—51no—
572C2×C3×C5—42no—
573C2×C3×C5—41no—
574C2×C3×C5—81no—
575C2×C3×C5—81no—
576C2×C3×C5D4211yescharacteristic
577C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
578C2×C3×C5#57711yescharacteristic
579C3×D5—22no—
580C3×D5—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—51no—
587C23×C3—81no—
588C23×C3—101no—
589C23×C3—202no—
590C23×C3—202no—
591C23×C3—401no—
592C23×C3D4×D511yescharacteristic
593C3×Q8—21no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—202no—
597C3×Q8C2×C22⋊D512yescomplemented
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—42no—
604C3×D4—42no—
605C3×D4—102no—
606C3×D4—101no—
607C3×D4—101no—
608C3×D4—202no—
609C3×D4—202no—
610C3×D4—202no—
611C3×D4—202no—
612C3×D4—202no—
613C3×D4—401no—
614C3×D4C2×C22⋊D512yes—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—42no—
619C2×C3×C4—51no—
620C2×C3×C4—51no—
621C2×C3×C4—51no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—202no—
628C2×C3×C4—202no—
629C2×C3×C4D4×D511yescharacteristic
630C2×C3×C4C23×D511yescharacteristic
631C3×C8—21no—
632C3×C8—101no—
633C3×C8—101no—
634C3×C8C2×C22⋊D512yescomplemented
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—22no—
638C22×C5—21no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—84no—
648C22×C5C22×C3×D411yescharacteristic
649C2×D5—21no—
650C2×D5—21no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—41no—
654C2×D5—84no—
655C2×D5C3×AGL(1,ℤ/8)12yescomplemented
656C4×C5—22no—
657C4×C5—21no—
658C4×C5C22×C3×D411yescharacteristic
659C4×C5C3×H(5,𝔽2)11yescharacteristic
660Dic5—21no—
661Dic5—21no—
662Dic5—21no—
663Dic5—41no—
664Dic5—41no—
665Dic5—41no—
666C24—21no—
667C24—101no—
668#41—22no—
669#41—41no—
670C2×Q8—51no—
671C2×Q8—101no—
672C2×Q8—102no—
673C2×Q8—201no—
674C2×Q8C22×C3×D511yescharacteristic
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—51no—
680C2×D4—51no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4—101no—
684C2×D4—102no—
685C2×D4—101no—
686C2×D4—101no—
687C2×D4—101no—
688C2×D4—201no—
689C2×D4—204no—
690C2×D4C22×C3×D511yescharacteristic
691C2×D4C22×C3×D511yescharacteristic
692C2×D4C22×C3×D511yescharacteristic
693C22×C4—21no—
694C22×C4—51no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4C22×C3×D511yescharacteristic
698SD16—22no—
699SD16—102no—
700SD16—102no—
701SD16—102no—
702SD16—201no—
703SD16C3×C22⋊D514yescomplemented
704D8—22no—
705D8—22no—
706D8—201no—
707M16—22no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—102no—
711C2×C8C22×C3×D511yescharacteristic
712C2×C8C22×C3×D511yescharacteristic
713C4⋊C4—51no—
714C4⋊C4—51no—
715C4⋊C4—51no—
716C4⋊C4—101no—
717C4⋊C4—101no—
718C22⋊C4—51no—
719C22⋊C4—51no—
720C22⋊C4—101no—
721C22⋊C4—101no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4—101no—
726C22⋊C4—101no—
727C42—51no—
728C42—101no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—22no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—52no—
743C22×C3—84no—
744C22×C3—101no—
745C22×C3—101no—
746C22×C3—201no—
747C22×C3—201no—
748C22×C3—201no—
749C22×C3—404no—
750C22×C3C2×D4×D511yescharacteristic
751C3×C4—21no—
752C3×C4—22no—
753C3×C4—101no—
754C3×C4—101no—
755C3×C4—101no—
756C3×C4—201no—
757C3×C4—201no—
758C3×C4—201no—
759C3×C4#414411yescharacteristic
760C3×C4C22×C22⋊D511yescharacteristic
761C2×C5—42no—
762C2×C5—41no—
763C2×C5—81no—
764C2×C5—81no—
765C2×C5C3×D4211yescharacteristic
766C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
767C2×C5C3×#57711yescharacteristic
768D5—22no—
769D5—81no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—42no—
774C23—42no—
775C23—51no—
776C23—81no—
777C23—101no—
778C23—202no—
779C23—202no—
780C23—401no—
781C23C3×D4×D511yescharacteristic
782Q8—21no—
783Q8—101no—
784Q8—101no—
785Q8—202no—
786Q8C2×C3×C22⋊D512yescomplemented
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—42no—
793D4—42no—
794D4—102no—
795D4—101no—
796D4—101no—
797D4—202no—
798D4—202no—
799D4—202no—
800D4—202no—
801D4—202no—
802D4—401no—
803D4C2×C3×C22⋊D512yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—42no—
808C2×C4—51no—
809C2×C4—51no—
810C2×C4—51no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—202no—
817C2×C4—202no—
818C2×C4C3×D4×D511yescharacteristic
819C2×C4C23×C3×D511yescharacteristic
820C8—21no—
821C8—101no—
822C8—101no—
823C8C2×C3×C22⋊D512yescomplemented
824C2×C3—41no—
825C2×C3—42no—
826C2×C3—81no—
827C2×C3—81no—
828C2×C3—102no—
829C2×C3—401no—
830C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
831C2×C3#6610911yescharacteristic
832C2×C3D4×C22⋊D511yescharacteristic
833C5C3×#326511yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—52no—
847C22—84no—
848C22—101no—
849C22—101no—
850C22—201no—
851C22—201no—
852C22—201no—
853C22—404no—
854C22C2×C3×D4×D511yescharacteristic
855C4—21no—
856C4—22no—
857C4—101no—
858C4—101no—
859C4—101no—
860C4—201no—
861C4—201no—
862C4—201no—
863C4C3×#414411yescharacteristic
864C4C22×C3×C22⋊D511yescharacteristic
865C3#1061568411yescharacteristic, direct product factor, Sylow
866C2—41no—
867C2—42no—
868C2—81no—
869C2—81no—
870C2—102no—
871C2—401no—
872C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
873C2C3×#6610911yescharacteristic
874C2C3×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×#3265
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×#66165C2semidirect
3. C3×D4×C22⋊D5C2semidirect
4. C2×C3×D5×SD16C2semidirect
5. C3×#65527C2semidirect
6. C3×#65507C2semidirect
7. C3×#65459C2semidirect
8. C3×#65453C2semidirect
9. C3×#65452C2semidirect
10. C3×#65446C2semidirect
11. C3×#65445C2semidirect
12. C3×#65443C2semidirect
13. C3×#65442C2semidirect
14. C3×#65423C2semidirect
15. C3×#65416C2semidirect
16. #10615684C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
20. C2×C3×Q8×D5C22semidirect
24. C2×C3×C5×SD16C22semidirect
26. C2×C3×C5×D8C22semidirect
27. C2×C3×C5×M16C22semidirect
29. C3×Q8×Dic5C22semidirect
30. C2×C3×#688C22semidirect
35. C3×#4084C22semidirect
38. C3×#4082C22semidirect
41. C2×C3×#687C22semidirect
42. C2×C3×#686C22semidirect
47. C3×#4070C22semidirect
49. C2×C3×#677C22semidirect
50. C2×C3×C8×D5C22semidirect
51. C3×#3967C22semidirect
53. C3×#3964C22semidirect
54. C3×#3964C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3953C22semidirect
57. C3×#3952C22semidirect
58. C3×#3950C22semidirect
59. C3×#3948C22semidirect
60. C3×#3947C22semidirect
61. C3×#3946C22semidirect
63. C2×C5×AGL(1,ℤ/8)C2×C3semidirect
64. #66165C2×C3semidirect
65. D4×C22⋊D5C2×C3semidirect
66. C2×D5×SD16C2×C3semidirect
67. #65527C2×C3semidirect
68. #65507C2×C3semidirect
69. #65459C2×C3semidirect
70. #65453C2×C3semidirect
71. #65452C2×C3semidirect
72. #65446C2×C3semidirect
73. #65445C2×C3semidirect
74. #65443C2×C3semidirect
75. #65442C2×C3semidirect
76. #65423C2×C3semidirect
77. #65416C2×C3semidirect
111. C3×C5×SD16D4semidirect
141. C2×C3×AGL(1,ℤ/8)D5semidirect
156. C2×C5×#41C22×C3semidirect
159. C2×Q8×D5C22×C3semidirect
163. C2×C5×SD16C22×C3semidirect
165. C2×C5×D8C22×C3semidirect
166. C2×C5×M16C22×C3semidirect
168. Q8×Dic5C22×C3semidirect
169. C2×#688C22×C3semidirect
174. #4084C22×C3semidirect
177. #4082C22×C3semidirect
180. C2×#687C22×C3semidirect
181. C2×#686C22×C3semidirect
186. #4070C22×C3semidirect
188. C2×#677C22×C3semidirect
189. C2×C8×D5C22×C3semidirect
190. #3967C22×C3semidirect
192. #3964C22×C3semidirect
193. #3964C22×C3semidirect
194. C22⋊#168C22×C3semidirect
195. #3953C22×C3semidirect
196. #3952C22×C3semidirect
197. #3950C22×C3semidirect
198. #3948C22×C3semidirect
199. #3947C22×C3semidirect
200. #3946C22×C3semidirect
215. C3×C5×Q8C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
256. C2×C3×#41C2×D5semidirect
268. C2×C3×SD16C2×D5semidirect
271. C2×C3×D8C2×D5semidirect
272. C2×C3×M16C2×D5semidirect
334. C5×SD16C3×D4semidirect
364. C2×AGL(1,ℤ/8)C3×D5semidirect
399. C2×C3×D5AGL(1,ℤ/8)semidirect
447. C3×SD16C22⋊D5semidirect
486. C5×Q8C2×C3×D4semidirect
524. C5×C8C2×C3×D4semidirect
527. C2×#41C2×C3×D5semidirect
539. C2×SD16C2×C3×D5semidirect
542. C2×D8C2×C3×D5semidirect
543. C2×M16C2×C3×D5semidirect
597. C3×Q8C2×C22⋊D5semidirect
634. C3×C8C2×C22⋊D5semidirect
655. C2×D5C3×AGL(1,ℤ/8)semidirect
703. SD16C3×C22⋊D5semidirect
729. C3×C5#3265semidirect
786. Q8C2×C3×C22⋊D5semidirect
823. C8C2×C3×C22⋊D5semidirect
833. C5C3×#3265semidirect
865. C3#10615684direct (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×#661652
C3×D4×C22⋊D52
C2×C3×D5×SD162
C3×#655272
C3×#655072
C3×#654592
C3×#654532
C3×#654522
C3×#654462
C3×#654452
C3×#654432
C3×#654422
C3×#654232
C3×#654162
#106156843
C3×#32655