Finite Group Databasebeta

← C3×#10612135 #14453434

Subgroups — C3×#10612135 #14453434

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×#4060C211yesmaximal, characteristic, complemented
2C2×C3×D5×SD16C211yesmaximal, characteristic, complemented
3C3×#66051C211yesmaximal, characteristic, complemented
4C3×#65910C211yesmaximal, characteristic, complemented
5C3×C5×#460C211yesmaximal, characteristic, complemented
6C3×#65461C211yesmaximal, characteristic, complemented
7C3×#65459C211yesmaximal, characteristic, complemented
8C3×#65363C211yesmaximal, characteristic, complemented
9C3×#65315C211yesmaximal, characteristic, complemented
10C3×#65133C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65069C211yesmaximal, characteristic, complemented
13C3×#65065C211yesmaximal, characteristic, complemented
14C3×#65064C211yesmaximal, characteristic, complemented
15C3×#65062C211yesmaximal, characteristic, complemented
16#10612135C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic, complemented
18C2×C3×Q8×D5C2211yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×D4×D5C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C3×C5×#127C2211yescharacteristic
25C3×C4×C5×Q8C2211yescharacteristic, complemented
26C2×C3×#688C2211yescharacteristic
27C3×#4084—21no—
28C3×#4084C2211yescharacteristic
29C3×#4084C2211yescharacteristic
30C3×#4083—21no—
31C3×#4083—21no—
32C2×C3×#687C2211yescharacteristic, complemented
33C2×C3×#687C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic, complemented
35C2×C3×#686C2211yescharacteristic, complemented
36C3×#4060—24no—
37C3×D5×SD16—24no—
38C2×C3×D40C2211yescharacteristic
39C2×C3×#677C2211yescharacteristic
40C2×C3×#676C2211yescharacteristic, complemented
41C2×C3×C8×D5C2211yescharacteristic, complemented
42C3×#4043—21no—
43C3×#4043C2211yescharacteristic, complemented
44C3×#4041—21no—
45C3×#4041C2211yescharacteristic, complemented
46C3×#4021—21no—
47C3×#4021C2211yescharacteristic, complemented
48C3×C4×D20—21no—
49C3×C4×D20C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×#3967C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3952C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic
60C3×#3939C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3265—51nomaximal, Hall
63C2×#4060C2×C311yescharacteristic, complemented
64C2×D5×SD16C2×C311yescharacteristic, complemented
65#66051C2×C311yescharacteristic, complemented
66#65910C2×C311yescharacteristic, complemented
67C5×#460C2×C311yescharacteristic, complemented
68#65461C2×C311yescharacteristic, complemented
69#65459C2×C311yescharacteristic, complemented
70#65363C2×C311yescharacteristic, complemented
71#65315C2×C311yescharacteristic, complemented
72#65133C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65069C2×C311yescharacteristic, complemented
75#65065C2×C311yescharacteristic, complemented
76#65064C2×C311yescharacteristic, complemented
77#65062C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C3×#713—22no—
90C3×#713—41no—
91C3×Q8×D5—22no—
92C3×Q8×D5—41no—
93C3×D4×D5—22no—
94C3×D4×D5—22no—
95C3×D4×D5—41no—
96C3×D4×D5—41no—
97C3×D4×D5—44no—
98C2×C3×D20—21no—
99C2×C3×D20—21no—
100C2×C3×D20D411yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5—21no—
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5C2311yescharacteristic
107C2×C3×C4×D5C2311yescharacteristic
108C2×C3×Dic10—21no—
109C2×C3×Dic10C2311yescharacteristic
110C3×C5×SD16—22no—
111C3×C5×SD16—22no—
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C3×C5×C4⋊C4—21no—
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C42×C5—21no—
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×#688D414yescomplemented
121C3×#687—22no—
122C3×#687—41no—
123C3×#686—22no—
124C3×#686—41no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685D411yescharacteristic
131C3×#685D411yescharacteristic
132C3×C4⋊Dic5—21no—
133C3×C4⋊Dic5D411yescharacteristic
134C3×C4⋊Dic5C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×D40—22no—
138C3×#677—22no—
139C3×#676—22no—
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×#468—51no—
147C3×#466—51no—
148C3×#463—51no—
149C3×#460D511yescharacteristic, complemented
150C3×#450—51no—
151C3×#449—51no—
152C3×#448—51no—
153C3×#447—51no—
154C3×#440—51no—
155C3×#435—51no—
156C2×#713C22×C311yescharacteristic, complemented
157C2×Q8×D5C22×C311yescharacteristic, complemented
158C2×D4×D5—21no—
159C2×D4×D5C22×C311yescharacteristic
160C2×D4×D5C22×C311yescharacteristic
161C2×C5×SD16C22×C311yescharacteristic, complemented
162C2×C5×SD16C22×C311yescharacteristic, complemented
163C5×#127C22×C311yescharacteristic
164C4×C5×Q8C22×C311yescharacteristic, complemented
165C2×#688C22×C311yescharacteristic
166#4084—21no—
167#4084C22×C311yescharacteristic
168#4084C22×C311yescharacteristic
169#4083—21no—
170#4083—21no—
171C2×#687C22×C311yescharacteristic, complemented
172C2×#687C22×C311yescharacteristic, complemented
173C2×#686C22×C311yescharacteristic, complemented
174C2×#686C22×C311yescharacteristic, complemented
175#4060—24no—
176D5×SD16—24no—
177C2×D40C22×C311yescharacteristic
178C2×#677C22×C311yescharacteristic
179C2×#676C22×C311yescharacteristic, complemented
180C2×C8×D5C22×C311yescharacteristic, complemented
181#4043—21no—
182#4043C22×C311yescharacteristic, complemented
183#4041—21no—
184#4041C22×C311yescharacteristic, complemented
185#4021—21no—
186#4021C22×C311yescharacteristic, complemented
187C4×D20—21no—
188C4×D20C22×C311yescharacteristic
189C4×D20C22×C311yescharacteristic
190C5×C4⋊C8C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic, complemented
192C5×#102C22×C311yescharacteristic, complemented
193#3967C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic, complemented
195#3952C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic
199#3939C22×C311yescharacteristic, complemented
200#3935C22×C311yescharacteristic, complemented
201#3265—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—42no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—81no—
211C22×C3×D5—81no—
212C22×C3×D5C2×D411yescharacteristic
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—42no—
221C3×C5×D4—81no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227C3×C22⋊D5—42no—
228C3×C22⋊D5—42no—
229C3×C22⋊D5—42no—
230C3×C22⋊D5—42no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5C2×D411yescharacteristic
234C2×C3×Dic5C2×D411yescharacteristic
235C3×D20—22no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—42no—
240C3×D20—42no—
241C3×D20C2×D412yes—
242C3×C4×D5—21no—
243C3×C4×D5—21no—
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—21no—
251C3×Dic10—42no—
252C3×C5×C8—21no—
253C3×C5×C8—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
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—104no—
267C2×C3×SD16C2×D511yescharacteristic, complemented
268C2×C3×SD16C2×D511yescharacteristic, complemented
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×M16—51no—
273C22×C3×C8—51no—
274C3×#127C2×D511yescharacteristic
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×Q8C2×D511yescharacteristic, complemented
287C3×C4×D4—51no—
288C3×C4×D4—51no—
289C3×C4×D4—101no—
290C3×#107—51no—
291C3×C4⋊C8C2×D511yescharacteristic, complemented
292C3×#103—51no—
293C3×#103—51no—
294C3×#102—51no—
295C3×#102—51no—
296C3×#102C2×D511yescharacteristic, complemented
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×D4—21no—
306C2×C5×D4C23×C311yescharacteristic
307C2×C5×D4C23×C311yescharacteristic
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311C2×C22⋊D5—21no—
312#713—22no—
313#713—41no—
314Q8×D5—22no—
315Q8×D5—41no—
316D4×D5—22no—
317D4×D5—22no—
318D4×D5—41no—
319D4×D5—41no—
320D4×D5—44no—
321C2×D20—21no—
322C2×D20—21no—
323C2×D20C3×D411yescharacteristic
324C2×D20C23×C311yescharacteristic
325C2×D20C23×C311yescharacteristic
326C2×C4×D5—21no—
327C2×C4×D5—21no—
328C2×C4×D5—21no—
329C2×C4×D5C23×C311yescharacteristic
330C2×C4×D5C23×C311yescharacteristic
331C2×Dic10—21no—
332C2×Dic10C23×C311yescharacteristic
333C5×SD16—22no—
334C5×SD16—22no—
335C2×C5×C8C23×C311yescharacteristic
336C2×C5×C8C23×C311yescharacteristic
337C5×C4⋊C4—21no—
338C5×C4⋊C4C23×C311yescharacteristic
339C42×C5—21no—
340C42×C5C23×C311yescharacteristic
341C22⋊Dic5—21no—
342C22⋊Dic5—21no—
343#688C3×D414yescomplemented
344#687—22no—
345#687—41no—
346#686—22no—
347#686—41no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685—21no—
352#685—21no—
353#685C3×D411yescharacteristic
354#685C3×D411yescharacteristic
355C4⋊Dic5—21no—
356C4⋊Dic5C3×D411yescharacteristic
357C4⋊Dic5C23×C311yescharacteristic
358C2×#168C23×C311yescharacteristic
359C2×#168C23×C311yescharacteristic
360D40—22no—
361#677—22no—
362#676—22no—
363C8×D5—22no—
364C2×AGL(1,ℤ/8)—51no—
365C22×SD16—51no—
366#548—51no—
367D42—51no—
368#496—51no—
369#468—51no—
370#466—51no—
371#463—51no—
372#460C3×D511yescharacteristic, complemented
373#450—51no—
374#449—51no—
375#448—51no—
376#447—51no—
377#440—51no—
378#435—51no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
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—21no—
389C2×C3×D5—22no—
390C2×C3×D5—21no—
391C2×C3×D5—21no—
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—22no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—41no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406C3×Dic5—21no—
407C3×Dic5—21no—
408C3×Dic5—41no—
409C3×Dic5—41no—
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—21no—
421C2×C3×D4—51no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—102no—
429C2×C3×D4—102no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—201no—
433C2×C3×D4—201no—
434C2×C3×D4—204no—
435C2×C3×D4C22×D511yescharacteristic
436C2×C3×D4C22×D511yescharacteristic
437C22×C3×C4—51no—
438C22×C3×C4—51no—
439C22×C3×C4—101no—
440C22×C3×C4—101no—
441C22×C3×C4—101no—
442C3×SD16—22no—
443C3×SD16—22no—
444C3×SD16—54no—
445C3×SD16—102no—
446C3×SD16—102no—
447C3×SD16—201no—
448C3×D8—102no—
449C3×D8—102no—
450C3×D8—201no—
451C3×M16—102no—
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—51no—
460C3×C4⋊C4—101no—
461C3×C4⋊C4C22×D511yescharacteristic
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—21no—
472C3×C42C22×D511yescharacteristic
473C23×C5—21no—
474C23×C5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—42no—
478C22×D5—42no—
479C22×D5—42no—
480C22×D5—42no—
481C22×D5—81no—
482C22×D5—81no—
483C22×D5C2×C3×D411yescharacteristic
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—42no—
492C5×D4—81no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5C2×C3×D411yescharacteristic
496C2×C4×C5C2×C3×D411yescharacteristic
497C2×C4×C5C24×C311yescharacteristic
498C22⋊D5—42no—
499C22⋊D5—42no—
500C22⋊D5—42no—
501C22⋊D5—42no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5C2×C3×D411yescharacteristic
505C2×Dic5C2×C3×D411yescharacteristic
506D20—22no—
507D20—21no—
508D20—21no—
509D20—21no—
510D20—42no—
511D20—42no—
512D20C2×C3×D412yes—
513C4×D5—21no—
514C4×D5—21no—
515C4×D5—21no—
516C4×D5—21no—
517C4×D5—42no—
518C4×D5—42no—
519C4×D5—42no—
520Dic10—21no—
521Dic10—21no—
522Dic10—42no—
523C5×C8—21no—
524C5×C8—21no—
525#168—21no—
526#168C2×C3×D412yescomplemented
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—104no—
538C2×SD16C2×C3×D511yescharacteristic, complemented
539C2×SD16C2×C3×D511yescharacteristic, complemented
540C2×D8—51no—
541C2×D8—51no—
542C2×D8—51no—
543C2×M16—51no—
544C22×C8—51no—
545#127C2×C3×D511yescharacteristic
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×Q8C2×C3×D511yescharacteristic, complemented
558C4×D4—51no—
559C4×D4—51no—
560C4×D4—101no—
561#107—51no—
562C4⋊C8C2×C3×D511yescharacteristic, complemented
563#103—51no—
564#103—51no—
565#102—51no—
566#102—51no—
567#102C2×C3×D511yescharacteristic, complemented
568#102C2×C3×D511yescharacteristic, complemented
569C22⋊C8—51no—
570C22⋊C8—51no—
571#97—51no—
572C2×C3×C5—81no—
573C2×C3×C5—81no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577C3×D5—22no—
578C3×D5—41no—
579C3×D5—42no—
580C3×D5—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—51no—
584C23×C3—51no—
585C23×C3—101no—
586C23×C3—101no—
587C23×C3—202no—
588C23×C3—202no—
589C23×C3—202no—
590C23×C3—202no—
591C23×C3—401no—
592C23×C3—401no—
593C3×Q8—21no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—202no—
597C3×Q8D4×D512yescomplemented
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—42no—
603C3×D4—52no—
604C3×D4—81no—
605C3×D4—102no—
606C3×D4—101no—
607C3×D4—101no—
608C3×D4—101no—
609C3×D4—202no—
610C3×D4—202no—
611C3×D4—202no—
612C3×D4—202no—
613C3×D4—202no—
614C3×D4—202no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—51no—
618C2×C3×C4—51no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—202no—
626C2×C3×C4—202no—
627C2×C3×C4—202no—
628C2×C3×C4D4×D511yescharacteristic
629C2×C3×C4D4×D511yescharacteristic
630C2×C3×C4C23×D511yescharacteristic
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—52no—
634C3×C8—101no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5C22×C3×D411yescharacteristic
642C2×D5—21no—
643C2×D5—21no—
644C2×D5—21no—
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—22no—
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—21no—
658C4×C5—22no—
659C4×C5—41no—
660C4×C5C22×C3×D411yescharacteristic
661C4×C5C3×H(5,𝔽2)11yescharacteristic
662Dic5—21no—
663Dic5—21no—
664Dic5—41no—
665Dic5—41no—
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—21no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—51no—
680C2×D4—101no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4—101no—
684C2×D4—102no—
685C2×D4—102no—
686C2×D4—101no—
687C2×D4—101no—
688C2×D4—201no—
689C2×D4—201no—
690C2×D4—204no—
691C2×D4C22×C3×D511yescharacteristic
692C2×D4C22×C3×D511yescharacteristic
693C22×C4—51no—
694C22×C4—51no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4—101no—
698SD16—22no—
699SD16—22no—
700SD16—54no—
701SD16—102no—
702SD16—102no—
703SD16—201no—
704D8—102no—
705D8—102no—
706D8—201no—
707M16—102no—
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—51no—
716C4⋊C4—101no—
717C4⋊C4C22×C3×D511yescharacteristic
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—21no—
728C42C22×C3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—52no—
737C22×C3—101no—
738C22×C3—101no—
739C22×C3—101no—
740C22×C3—101no—
741C22×C3—101no—
742C22×C3—102no—
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—21no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—101no—
756C3×C4—101no—
757C3×C4—201no—
758C3×C4—201no—
759C3×C4C2×D4×D511yescharacteristic
760C3×C4#414911yescharacteristic
761C2×C5—81no—
762C2×C5—81no—
763C2×C5C3×D4211yescharacteristic
764C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
765C2×C5C3×#57711yescharacteristic
766D5—22no—
767D5—41no—
768D5—42no—
769D5—81no—
770C23—21no—
771C23—21no—
772C23—51no—
773C23—51no—
774C23—101no—
775C23—101no—
776C23—202no—
777C23—202no—
778C23—202no—
779C23—202no—
780C23—401no—
781C23—401no—
782Q8—21no—
783Q8—101no—
784Q8—101no—
785Q8—202no—
786Q8C3×D4×D512yescomplemented
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—42no—
792D4—52no—
793D4—81no—
794D4—102no—
795D4—101no—
796D4—101no—
797D4—101no—
798D4—202no—
799D4—202no—
800D4—202no—
801D4—202no—
802D4—202no—
803D4—202no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—51no—
807C2×C4—51no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—202no—
815C2×C4—202no—
816C2×C4—202no—
817C2×C4C3×D4×D511yescharacteristic
818C2×C4C3×D4×D511yescharacteristic
819C2×C4C23×C3×D511yescharacteristic
820C8—21no—
821C8—21no—
822C8—52no—
823C8—101no—
824C2×C3—81no—
825C2×C3—81no—
826C2×C3—102no—
827C2×C3—201no—
828C2×C3—202no—
829C2×C3—401no—
830C2×C3#6594311yescharacteristic
831C2×C3#6609611yescharacteristic
832C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
833C5C3×#326511yescharacteristic, complemented, Sylow
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—52no—
841C22—101no—
842C22—101no—
843C22—101no—
844C22—101no—
845C22—102no—
846C22—101no—
847C22—201no—
848C22—201no—
849C22—201no—
850C22—201no—
851C22—201no—
852C22—404no—
853C22—404no—
854C22C2×C3×D4×D511yescharacteristic
855C4—21no—
856C4—22no—
857C4—21no—
858C4—41no—
859C4—101no—
860C4—101no—
861C4—201no—
862C4—201no—
863C4C2×C3×D4×D511yescharacteristic
864C4C3×#414911yescharacteristic
865C3#1061213511yescharacteristic, direct product factor, Sylow
866C2—81no—
867C2—81no—
868C2—102no—
869C2—201no—
870C2—202no—
871C2—401no—
872C2C3×#6594311yescharacteristic
873C2C3×#6609611yescharacteristic
874C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#460C2
socleC22×C3×C5C22×D4
hypercenterC3×#460D5
hypocenterC5C3×#3265
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4060C2semidirect
2. C2×C3×D5×SD16C2semidirect
3. C3×#66051C2semidirect
4. C3×#65910C2semidirect
5. C3×C5×#460C2semidirect
6. C3×#65461C2semidirect
7. C3×#65459C2semidirect
8. C3×#65363C2semidirect
9. C3×#65315C2semidirect
10. C3×#65133C2semidirect
11. C3×#65125C2semidirect
12. C3×#65069C2semidirect
13. C3×#65065C2semidirect
14. C3×#65064C2semidirect
15. C3×#65062C2semidirect
16. #10612135C3direct (N × H)
17. C2×C3×#713C22semidirect
18. C2×C3×Q8×D5C22semidirect
22. C2×C3×C5×SD16C22semidirect
23. C2×C3×C5×SD16C22semidirect
25. C3×C4×C5×Q8C22semidirect
32. C2×C3×#687C22semidirect
33. C2×C3×#687C22semidirect
34. C2×C3×#686C22semidirect
35. C2×C3×#686C22semidirect
40. C2×C3×#676C22semidirect
41. C2×C3×C8×D5C22semidirect
43. C3×#4043C22semidirect
45. C3×#4041C22semidirect
47. C3×#4021C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×#102C22semidirect
54. C3×#3967C22semidirect
55. C3×#3953C22semidirect
56. C3×#3952C22semidirect
57. C3×#3952C22semidirect
58. C3×#3948C22semidirect
60. C3×#3939C22semidirect
61. C3×#3935C22semidirect
63. C2×#4060C2×C3semidirect
64. C2×D5×SD16C2×C3semidirect
65. #66051C2×C3semidirect
66. #65910C2×C3semidirect
67. C5×#460C2×C3semidirect
68. #65461C2×C3semidirect
69. #65459C2×C3semidirect
70. #65363C2×C3semidirect
71. #65315C2×C3semidirect
72. #65133C2×C3semidirect
73. #65125C2×C3semidirect
74. #65069C2×C3semidirect
75. #65065C2×C3semidirect
76. #65064C2×C3semidirect
77. #65062C2×C3semidirect
120. C3×#688D4semidirect
149. C3×#460D5semidirect
156. C2×#713C22×C3semidirect
157. C2×Q8×D5C22×C3semidirect
161. C2×C5×SD16C22×C3semidirect
162. C2×C5×SD16C22×C3semidirect
164. C4×C5×Q8C22×C3semidirect
171. C2×#687C22×C3semidirect
172. C2×#687C22×C3semidirect
173. C2×#686C22×C3semidirect
174. C2×#686C22×C3semidirect
179. C2×#676C22×C3semidirect
180. C2×C8×D5C22×C3semidirect
182. #4043C22×C3semidirect
184. #4041C22×C3semidirect
186. #4021C22×C3semidirect
190. C5×C4⋊C8C22×C3semidirect
191. C5×#102C22×C3semidirect
192. C5×#102C22×C3semidirect
193. #3967C22×C3semidirect
194. #3953C22×C3semidirect
195. #3952C22×C3semidirect
196. #3952C22×C3semidirect
197. #3948C22×C3semidirect
199. #3939C22×C3semidirect
200. #3935C22×C3semidirect
215. C3×C5×Q8C2×D4semidirect
255. C3×#168C2×D4semidirect
267. C2×C3×SD16C2×D5semidirect
268. C2×C3×SD16C2×D5semidirect
286. C3×C4×Q8C2×D5semidirect
291. C3×C4⋊C8C2×D5semidirect
296. C3×#102C2×D5semidirect
297. C3×#102C2×D5semidirect
343. #688C3×D4semidirect
372. #460C3×D5semidirect
399. C2×C3×D5AGL(1,ℤ/8)semidirect
486. C5×Q8C2×C3×D4semidirect
526. #168C2×C3×D4semidirect
538. C2×SD16C2×C3×D5semidirect
539. C2×SD16C2×C3×D5semidirect
557. C4×Q8C2×C3×D5semidirect
562. C4⋊C8C2×C3×D5semidirect
567. #102C2×C3×D5semidirect
568. #102C2×C3×D5semidirect
597. C3×Q8D4×D5semidirect
655. C2×D5C3×AGL(1,ℤ/8)semidirect
729. C3×C5#3265semidirect
786. Q8C3×D4×D5semidirect
833. C5C3×#3265semidirect
865. C3#10612135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40602
C2×C3×D5×SD162
C3×#660512
C3×#659102
C3×C5×#4602
C3×#654612
C3×#654592
C3×#653632
C3×#653152
C3×#651332
C3×#651252
C3×#650692
C3×#650652
C3×#650642
C3×#650622
#106121353
C3×#32655