Finite Group Databasebeta

← C3×#10612565 #14453470

Subgroups — C3×#10612565 #14453470

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×D5×SD16C211yesmaximal, characteristic, complemented
2C2×C3×#4054C211yesmaximal, characteristic, complemented
3C3×#65967C211yesmaximal, characteristic, complemented
4C3×#65943C211yesmaximal, characteristic, complemented
5C3×C5×#468C211yesmaximal, characteristic, complemented
6C3×#65465C211yesmaximal, characteristic, complemented
7C3×#65416C211yesmaximal, characteristic, complemented
8C3×#65335C211yesmaximal, characteristic, complemented
9C3×#65326C211yesmaximal, characteristic, complemented
10C3×#65178C211yesmaximal, characteristic, complemented
11C3×#65172C211yesmaximal, characteristic, complemented
12C3×#65108C211yesmaximal, characteristic, complemented
13C3×#65095C211yesmaximal, characteristic, complemented
14C3×#65062C211yesmaximal, characteristic, complemented
15C3×#65051C211yesmaximal, characteristic, complemented
16#10612565C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic, complemented
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic, complemented
21C22×C3×D20C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×M16C2211yescharacteristic, complemented
24C3×C5×C22⋊Q8C2211yescharacteristic, complemented
25C3×C5×#121C2211yescharacteristic
26C3×#4093C2211yescharacteristic, complemented
27C2×C3×#688C2211yescharacteristic
28C2×C3×#688C2211yescharacteristic, complemented
29C3×#4086C2211yescharacteristic
30C3×#4083—21no—
31C2×C3×#687C2211yescharacteristic, complemented
32C2×C3×#686C2211yescharacteristic, complemented
33C3×C4×C22⋊D5C2211yescharacteristic
34C3×D5×SD16—24no—
35C3×#4054—24no—
36C2×C3×D40C2211yescharacteristic
37C2×C3×D40C2211yescharacteristic, complemented
38C2×C3×#677C2211yescharacteristic
39C2×C3×#677C2211yescharacteristic, complemented
40C2×C3×C8×D5C2211yescharacteristic, complemented
41C3×#4042—21no—
42C3×#4041C2211yescharacteristic
43C3×#4041C2211yescharacteristic, complemented
44C3×#4039—21no—
45C3×#4039C2211yescharacteristic
46C3×#4033C2211yescharacteristic, complemented
47C3×#4031—21no—
48C3×#4030—21no—
49C3×#4030—21no—
50C3×#4028—21no—
51C3×C5×#107C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic, complemented
56C3×#3947C2211yescharacteristic, complemented
57C3×#3946C2211yescharacteristic, complemented
58C3×#3942C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic
60C3×#3941C2211yescharacteristic, complemented
61C3×#3941C2211yescharacteristic, complemented
62C3×#3265—51nomaximal, Hall
63C2×D5×SD16C2×C311yescharacteristic, complemented
64C2×#4054C2×C311yescharacteristic, complemented
65#65967C2×C311yescharacteristic, complemented
66#65943C2×C311yescharacteristic, complemented
67C5×#468C2×C311yescharacteristic, complemented
68#65465C2×C311yescharacteristic, complemented
69#65416C2×C311yescharacteristic, complemented
70#65335C2×C311yescharacteristic, complemented
71#65326C2×C311yescharacteristic, complemented
72#65178C2×C311yescharacteristic, complemented
73#65172C2×C311yescharacteristic, complemented
74#65108C2×C311yescharacteristic, complemented
75#65095C2×C311yescharacteristic, complemented
76#65062C2×C311yescharacteristic, complemented
77#65051C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5D411yescharacteristic
89C3×Q8×D5—22no—
90C3×Q8×D5—41no—
91C3×D4×D5—22no—
92C3×D4×D5—41no—
93C3×D4×D5—44no—
94C3×#709—22no—
95C3×#709—41no—
96C2×C3×D20—22no—
97C2×C3×D20—21no—
98C2×C3×D20—21no—
99C2×C3×D20—21no—
100C2×C3×D20—41no—
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103C2×C3×D20C2311yescharacteristic
104C2×C3×C4×D5—21no—
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5C2311yescharacteristic
108C2×C3×Dic10—21no—
109C2×C3×Dic10C2311yescharacteristic
110C3×C5×SD16—22no—
111C3×C5×M16—22no—
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C3×C5×C4⋊C4—21no—
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C5×C4⋊C4C2311yescharacteristic
117C3×C5×C22⋊C4—21no—
118C3×C5×C22⋊C4—21no—
119C3×C22⋊Dic5D411yescharacteristic
120C3×#688—22no—
121C3×#688—41no—
122C3×#687—22no—
123C3×#686—41no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685D411yescharacteristic
130C3×#683—21no—
131C3×#683D411yescharacteristic
132C3×C4×Dic5—21no—
133C3×C4×Dic5C2311yescharacteristic
134C2×C3×#168C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C3×D40—22no—
137C3×D40—22no—
138C3×#677—22no—
139C3×#677D414yescomplemented
140C3×C8×D5—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×SD16—51no—
143C3×#548—51no—
144C3×D42—51no—
145C3×#496—51no—
146C3×#468D511yescharacteristic, complemented
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×Q8×D5C22×C311yescharacteristic, complemented
157C2×D4×D5—21no—
158C2×D4×D5C22×C311yescharacteristic
159C2×#709C22×C311yescharacteristic, complemented
160C22×D20C22×C311yescharacteristic
161C2×C5×SD16C22×C311yescharacteristic, complemented
162C2×C5×M16C22×C311yescharacteristic, complemented
163C5×C22⋊Q8C22×C311yescharacteristic, complemented
164C5×#121C22×C311yescharacteristic
165#4093C22×C311yescharacteristic, complemented
166C2×#688C22×C311yescharacteristic
167C2×#688C22×C311yescharacteristic, complemented
168#4086C22×C311yescharacteristic
169#4083—21no—
170C2×#687C22×C311yescharacteristic, complemented
171C2×#686C22×C311yescharacteristic, complemented
172C4×C22⋊D5C22×C311yescharacteristic
173D5×SD16—24no—
174#4054—24no—
175C2×D40C22×C311yescharacteristic
176C2×D40C22×C311yescharacteristic, complemented
177C2×#677C22×C311yescharacteristic
178C2×#677C22×C311yescharacteristic, complemented
179C2×C8×D5C22×C311yescharacteristic, complemented
180#4042—21no—
181#4041C22×C311yescharacteristic
182#4041C22×C311yescharacteristic, complemented
183#4039—21no—
184#4039C22×C311yescharacteristic
185#4033C22×C311yescharacteristic, complemented
186#4031—21no—
187#4030—21no—
188#4030—21no—
189#4028—21no—
190C5×#107C22×C311yescharacteristic, complemented
191C5×#103C22×C311yescharacteristic, complemented
192C5×#102C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic, complemented
194#3952C22×C311yescharacteristic, complemented
195#3947C22×C311yescharacteristic, complemented
196#3946C22×C311yescharacteristic, complemented
197#3942C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic
199#3941C22×C311yescharacteristic, complemented
200#3941C22×C311yescharacteristic, complemented
201#3265—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—42no—
211C22×C3×D5—81no—
212C22×C3×D5—81no—
213C22×C3×D5C2×D411yescharacteristic
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—42no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226C3×C22⋊D5—22no—
227C3×C22⋊D5—42no—
228C3×C22⋊D5—42no—
229C3×C22⋊D5—42no—
230C3×C22⋊D5—81no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5C2×D411yescharacteristic
233C2×C3×Dic5C2×D411yescharacteristic
234C2×C3×Dic5C2×D411yescharacteristic
235C3×D20—21no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—21no—
240C3×D20—42no—
241C3×D20—42no—
242C3×D20—42no—
243C3×D20C2×D412yes—
244C3×C4×D5—21no—
245C3×C4×D5—21no—
246C3×C4×D5—42no—
247C3×C4×D5—42no—
248C3×C4×D5—42no—
249C3×Dic10—21no—
250C3×Dic10—42no—
251C3×Dic10C2×D412yescomplemented
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C3×#168—21no—
255C3×#168—21no—
256C2×C3×#41—51no—
257C22×C3×Q8—51no—
258C22×C3×D4—51no—
259C22×C3×D4—51no—
260C22×C3×D4—101no—
261C3×AGL(1,ℤ/8)—104no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×SD16—51no—
265C2×C3×SD16—51no—
266C2×C3×SD16—51no—
267C2×C3×SD16—104no—
268C2×C3×SD16C2×D511yescharacteristic, complemented
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×M16C2×D511yescharacteristic, complemented
273C22×C3×C8—51no—
274C3×#127—51no—
275C3×#124—51no—
276C3×#124—101no—
277C3×C22⋊Q8—101no—
278C3×C22⋊Q8C2×D511yescharacteristic, complemented
279C3×#121—51no—
280C3×#121—51no—
281C3×#121—101no—
282C3×#121—101no—
283C3×#121C2×D511yescharacteristic
284C3×#120—101no—
285C3×#120—101no—
286C3×C4×Q8—51no—
287C3×C4×D4—51no—
288C3×C4×D4—51no—
289C3×C4×D4—101no—
290C3×#107C2×D511yescharacteristic, complemented
291C3×C4⋊C8—51no—
292C3×#103—51no—
293C3×#103C2×D511yescharacteristic, complemented
294C3×#102—51no—
295C3×#102—51no—
296C3×#102—51no—
297C3×#102C2×D511yescharacteristic, complemented
298C3×C22⋊C8—51no—
299C3×C22⋊C8—51no—
300C3×#97—51no—
301C23×D5—21no—
302C23×D5—21no—
303C2×C5×Q8C23×C311yescharacteristic
304C2×C5×D4—21no—
305C2×C5×D4C23×C311yescharacteristic
306C22×C4×C5C23×C311yescharacteristic
307C2×C22⋊D5—21no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311C2×C22⋊D5C3×D411yescharacteristic
312Q8×D5—22no—
313Q8×D5—41no—
314D4×D5—22no—
315D4×D5—41no—
316D4×D5—44no—
317#709—22no—
318#709—41no—
319C2×D20—22no—
320C2×D20—21no—
321C2×D20—21no—
322C2×D20—21no—
323C2×D20—41no—
324C2×D20C23×C311yescharacteristic
325C2×D20C23×C311yescharacteristic
326C2×D20C23×C311yescharacteristic
327C2×C4×D5—21no—
328C2×C4×D5—21no—
329C2×C4×D5—21no—
330C2×C4×D5C23×C311yescharacteristic
331C2×Dic10—21no—
332C2×Dic10C23×C311yescharacteristic
333C5×SD16—22no—
334C5×M16—22no—
335C2×C5×C8C23×C311yescharacteristic
336C2×C5×C8C23×C311yescharacteristic
337C5×C4⋊C4—21no—
338C5×C4⋊C4C23×C311yescharacteristic
339C5×C4⋊C4C23×C311yescharacteristic
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C22⋊Dic5C3×D411yescharacteristic
343#688—22no—
344#688—41no—
345#687—22no—
346#686—41no—
347#685—21no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685—21no—
352#685C3×D411yescharacteristic
353#683—21no—
354#683C3×D411yescharacteristic
355C4×Dic5—21no—
356C4×Dic5C23×C311yescharacteristic
357C2×#168C23×C311yescharacteristic
358C2×#168C23×C311yescharacteristic
359D40—22no—
360D40—22no—
361#677—22no—
362#677C3×D414yescomplemented
363C8×D5—22no—
364C2×AGL(1,ℤ/8)—51no—
365C22×SD16—51no—
366#548—51no—
367D42—51no—
368#496—51no—
369#468C3×D511yescharacteristic, complemented
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—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5C22×D411yescharacteristic
386C2×C3×D5—21no—
387C2×C3×D5—21no—
388C2×C3×D5—22no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—84no—
398C2×C3×D5—84no—
399C2×C3×D5AGL(1,ℤ/8)12yescomplemented
400C3×C4×C5—21no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403C3×C4×C5—41no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406C3×Dic5—22no—
407C3×Dic5—21no—
408C3×Dic5—21no—
409C3×Dic5—21no—
410C24×C3—101no—
411C24×C3—101no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×Q8—101no—
416C2×C3×Q8—102no—
417C2×C3×Q8—201no—
418C2×C3×Q8C22×D511yescharacteristic
419C2×C3×D4—21no—
420C2×C3×D4—51no—
421C2×C3×D4—51no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—102no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—102no—
431C2×C3×D4—101no—
432C2×C3×D4—101no—
433C2×C3×D4—201no—
434C2×C3×D4—201no—
435C2×C3×D4—204no—
436C2×C3×D4C22×D511yescharacteristic
437C22×C3×C4—51no—
438C22×C3×C4—101no—
439C22×C3×C4—101no—
440C22×C3×C4—101no—
441C22×C3×C4C22×D511yescharacteristic
442C3×SD16—22no—
443C3×SD16—54no—
444C3×SD16—102no—
445C3×SD16—102no—
446C3×SD16—102no—
447C3×SD16—201no—
448C3×D8—102no—
449C3×D8—102no—
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—21no—
458C3×C4⋊C4—51no—
459C3×C4⋊C4—101no—
460C3×C4⋊C4C22×D511yescharacteristic
461C3×C4⋊C4C22×D511yescharacteristic
462C3×C22⋊C4—21no—
463C3×C22⋊C4—21no—
464C3×C22⋊C4—51no—
465C3×C22⋊C4—51no—
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×C5C2×C3×D411yescharacteristic
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—42no—
479C22×D5—42no—
480C22×D5—42no—
481C22×D5—42no—
482C22×D5—81no—
483C22×D5—81no—
484C22×D5C2×C3×D411yescharacteristic
485C5×Q8—21no—
486C5×Q8—21no—
487C5×D4—21no—
488C5×D4—21no—
489C5×D4—42no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5C2×C3×D411yescharacteristic
496C2×C4×C5C24×C311yescharacteristic
497C22⋊D5—22no—
498C22⋊D5—42no—
499C22⋊D5—42no—
500C22⋊D5—42no—
501C22⋊D5—81no—
502C2×Dic5—21no—
503C2×Dic5C2×C3×D411yescharacteristic
504C2×Dic5C2×C3×D411yescharacteristic
505C2×Dic5C2×C3×D411yescharacteristic
506D20—21no—
507D20—21no—
508D20—21no—
509D20—21no—
510D20—21no—
511D20—42no—
512D20—42no—
513D20—42no—
514D20C2×C3×D412yes—
515C4×D5—21no—
516C4×D5—21no—
517C4×D5—42no—
518C4×D5—42no—
519C4×D5—42no—
520Dic10—21no—
521Dic10—42no—
522Dic10C2×C3×D412yescomplemented
523C5×C8—21no—
524C5×C8C2×C3×D412yescomplemented
525#168—21no—
526#168—21no—
527C2×#41—51no—
528C22×Q8—51no—
529C22×D4—51no—
530C22×D4—51no—
531C22×D4—101no—
532AGL(1,ℤ/8)—104no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—51no—
536C2×SD16—51no—
537C2×SD16—51no—
538C2×SD16—104no—
539C2×SD16C2×C3×D511yescharacteristic, complemented
540C2×D8—51no—
541C2×D8—51no—
542C2×D8—51no—
543C2×M16C2×C3×D511yescharacteristic, complemented
544C22×C8—51no—
545#127—51no—
546#124—51no—
547#124—101no—
548C22⋊Q8—101no—
549C22⋊Q8C2×C3×D511yescharacteristic, complemented
550#121—51no—
551#121—51no—
552#121—101no—
553#121—101no—
554#121C2×C3×D511yescharacteristic
555#120—101no—
556#120—101no—
557C4×Q8—51no—
558C4×D4—51no—
559C4×D4—51no—
560C4×D4—101no—
561#107C2×C3×D511yescharacteristic, complemented
562C4⋊C8—51no—
563#103—51no—
564#103C2×C3×D511yescharacteristic, complemented
565#102—51no—
566#102—51no—
567#102—51no—
568#102C2×C3×D511yescharacteristic, complemented
569C22⋊C8—51no—
570C22⋊C8—51no—
571#97—51no—
572C2×C3×C5—41no—
573C2×C3×C5—81no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577C3×D5—22no—
578C3×D5—42no—
579C3×D5—81no—
580C3×D5—81no—
581C23×C3—21no—
582C23×C3—51no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3—202no—
587C23×C3—202no—
588C23×C3—202no—
589C23×C3—202no—
590C23×C3—401no—
591C23×C3—401no—
592C23×C3D4×D511yescharacteristic
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—52no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—42no—
601C3×D4—52no—
602C3×D4—102no—
603C3×D4—101no—
604C3×D4—101no—
605C3×D4—101no—
606C3×D4—101no—
607C3×D4—101no—
608C3×D4—202no—
609C3×D4—202no—
610C3×D4—202no—
611C3×D4—202no—
612C3×D4—202no—
613C3×D4—202no—
614C3×D4—401no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—51no—
621C2×C3×C4—51no—
622C2×C3×C4—51no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—202no—
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×C8D4×D512yescomplemented
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5C22×C3×D411yescharacteristic
642C2×D5—21no—
643C2×D5—21no—
644C2×D5—22no—
645C2×D5—41no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5—41no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—84no—
654C2×D5—84no—
655C2×D5C3×AGL(1,ℤ/8)12yescomplemented
656C4×C5—21no—
657C4×C5—41no—
658C4×C5—41no—
659C4×C5—41no—
660C4×C5C22×C3×D411yescharacteristic
661C4×C5C3×H(5,𝔽2)11yescharacteristic
662Dic5—21no—
663Dic5—21no—
664Dic5—22no—
665Dic5—21no—
666C24—101no—
667C24—101no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—101no—
672C2×Q8—102no—
673C2×Q8—201no—
674C2×Q8C22×C3×D511yescharacteristic
675C2×D4—21no—
676C2×D4—51no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—51no—
680C2×D4—102no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4—101no—
684C2×D4—101no—
685C2×D4—101no—
686C2×D4—102no—
687C2×D4—101no—
688C2×D4—101no—
689C2×D4—201no—
690C2×D4—201no—
691C2×D4—204no—
692C2×D4C22×C3×D511yescharacteristic
693C22×C4—51no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4C22×C3×D511yescharacteristic
698SD16—22no—
699SD16—54no—
700SD16—102no—
701SD16—102no—
702SD16—102no—
703SD16—201no—
704D8—102no—
705D8—102no—
706D8—201no—
707M16—22no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—102no—
711C2×C8C22×C3×D511yescharacteristic
712C2×C8C22×C3×D511yescharacteristic
713C4⋊C4—21no—
714C4⋊C4—51no—
715C4⋊C4—101no—
716C4⋊C4C22×C3×D511yescharacteristic
717C4⋊C4C22×C3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—51no—
721C22⋊C4—51no—
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—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—52no—
737C22×C3—101no—
738C22×C3—101no—
739C22×C3—102no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—201no—
743C22×C3—201no—
744C22×C3—201no—
745C22×C3—201no—
746C22×C3—201no—
747C22×C3—201no—
748C22×C3—404no—
749C22×C3—404no—
750C22×C3C2×D4×D511yescharacteristic
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—101no—
756C3×C4—101no—
757C3×C4—101no—
758C3×C4—102no—
759C3×C4C2×D4×D511yescharacteristic
760C3×C4#414911yescharacteristic
761C2×C5—41no—
762C2×C5—81no—
763C2×C5C3×D4211yescharacteristic
764C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
765C2×C5C3×#57711yescharacteristic
766D5—22no—
767D5—42no—
768D5—81no—
769D5—81no—
770C23—21no—
771C23—51no—
772C23—101no—
773C23—101no—
774C23—101no—
775C23—202no—
776C23—202no—
777C23—202no—
778C23—202no—
779C23—401no—
780C23—401no—
781C23C3×D4×D511yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—52no—
785Q8—101no—
786Q8—202no—
787D4—21no—
788D4—21no—
789D4—42no—
790D4—52no—
791D4—102no—
792D4—101no—
793D4—101no—
794D4—101no—
795D4—101no—
796D4—101no—
797D4—202no—
798D4—202no—
799D4—202no—
800D4—202no—
801D4—202no—
802D4—202no—
803D4—401no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—51no—
810C2×C4—51no—
811C2×C4—51no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—202no—
816C2×C4—202no—
817C2×C4—202no—
818C2×C4C3×D4×D511yescharacteristic
819C2×C4C23×C3×D511yescharacteristic
820C8—21no—
821C8—101no—
822C8—101no—
823C8C3×D4×D512yescomplemented
824C2×C3—41no—
825C2×C3—81no—
826C2×C3—102no—
827C2×C3—202no—
828C2×C3—401no—
829C2×C3—401no—
830C2×C3#6594311yescharacteristic
831C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
832C2×C3#6611211yescharacteristic
833C5C3×#326511yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—52no—
841C22—101no—
842C22—101no—
843C22—102no—
844C22—201no—
845C22—201no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—201no—
850C22—201no—
851C22—201no—
852C22—404no—
853C22—404no—
854C22C2×C3×D4×D511yescharacteristic
855C4—21no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—101no—
860C4—101no—
861C4—101no—
862C4—102no—
863C4C2×C3×D4×D511yescharacteristic
864C4C3×#414911yescharacteristic
865C3#1061256511yescharacteristic, direct product factor, Sylow
866C2—41no—
867C2—81no—
868C2—102no—
869C2—202no—
870C2—401no—
871C2—401no—
872C2C3×#6594311yescharacteristic
873C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
874C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#468C2
socleC22×C3×C5C22×D4
hypercenterC3×#468D5
hypocenterC5C3×#3265
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#468

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×SD16C2semidirect
2. C2×C3×#4054C2semidirect
3. C3×#65967C2semidirect
4. C3×#65943C2semidirect
5. C3×C5×#468C2semidirect
6. C3×#65465C2semidirect
7. C3×#65416C2semidirect
8. C3×#65335C2semidirect
9. C3×#65326C2semidirect
10. C3×#65178C2semidirect
11. C3×#65172C2semidirect
12. C3×#65108C2semidirect
13. C3×#65095C2semidirect
14. C3×#65062C2semidirect
15. C3×#65051C2semidirect
16. #10612565C3direct (N × H)
17. C2×C3×Q8×D5C22semidirect
20. C2×C3×#709C22semidirect
22. C2×C3×C5×SD16C22semidirect
23. C2×C3×C5×M16C22semidirect
24. C3×C5×C22⋊Q8C22semidirect
26. C3×#4093C22semidirect
28. C2×C3×#688C22semidirect
31. C2×C3×#687C22semidirect
32. C2×C3×#686C22semidirect
37. C2×C3×D40C22semidirect
39. C2×C3×#677C22semidirect
40. C2×C3×C8×D5C22semidirect
43. C3×#4041C22semidirect
46. C3×#4033C22semidirect
51. C3×C5×#107C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×#3952C22semidirect
56. C3×#3947C22semidirect
57. C3×#3946C22semidirect
58. C3×#3942C22semidirect
60. C3×#3941C22semidirect
61. C3×#3941C22semidirect
63. C2×D5×SD16C2×C3semidirect
64. C2×#4054C2×C3semidirect
65. #65967C2×C3semidirect
66. #65943C2×C3semidirect
67. C5×#468C2×C3semidirect
68. #65465C2×C3semidirect
69. #65416C2×C3semidirect
70. #65335C2×C3semidirect
71. #65326C2×C3semidirect
72. #65178C2×C3semidirect
73. #65172C2×C3semidirect
74. #65108C2×C3semidirect
75. #65095C2×C3semidirect
76. #65062C2×C3semidirect
77. #65051C2×C3semidirect
139. C3×#677D4semidirect
146. C3×#468D5semidirect
156. C2×Q8×D5C22×C3semidirect
159. C2×#709C22×C3semidirect
161. C2×C5×SD16C22×C3semidirect
162. C2×C5×M16C22×C3semidirect
163. C5×C22⋊Q8C22×C3semidirect
165. #4093C22×C3semidirect
167. C2×#688C22×C3semidirect
170. C2×#687C22×C3semidirect
171. C2×#686C22×C3semidirect
176. C2×D40C22×C3semidirect
178. C2×#677C22×C3semidirect
179. C2×C8×D5C22×C3semidirect
182. #4041C22×C3semidirect
185. #4033C22×C3semidirect
190. C5×#107C22×C3semidirect
191. C5×#103C22×C3semidirect
192. C5×#102C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. #3952C22×C3semidirect
195. #3947C22×C3semidirect
196. #3946C22×C3semidirect
197. #3942C22×C3semidirect
199. #3941C22×C3semidirect
200. #3941C22×C3semidirect
251. C3×Dic10C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
268. C2×C3×SD16C2×D5semidirect
272. C2×C3×M16C2×D5semidirect
278. C3×C22⋊Q8C2×D5semidirect
290. C3×#107C2×D5semidirect
293. C3×#103C2×D5semidirect
297. C3×#102C2×D5semidirect
362. #677C3×D4semidirect
369. #468C3×D5semidirect
399. C2×C3×D5AGL(1,ℤ/8)semidirect
522. Dic10C2×C3×D4semidirect
524. C5×C8C2×C3×D4semidirect
539. C2×SD16C2×C3×D5semidirect
543. C2×M16C2×C3×D5semidirect
549. C22⋊Q8C2×C3×D5semidirect
561. #107C2×C3×D5semidirect
564. #103C2×C3×D5semidirect
568. #102C2×C3×D5semidirect
634. C3×C8D4×D5semidirect
655. C2×D5C3×AGL(1,ℤ/8)semidirect
729. C3×C5#3265semidirect
823. C8C3×D4×D5semidirect
833. C5C3×#3265semidirect
865. C3#10612565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×SD162
C2×C3×#40542
C3×#659672
C3×#659432
C3×C5×#4682
C3×#654652
C3×#654162
C3×#653352
C3×#653262
C3×#651782
C3×#651722
C3×#651082
C3×#650952
C3×#650622
C3×#650512
#106125653
C3×#32655