Finite Group Databasebeta

← C3×#10612283 #14453212

Subgroups — C3×#10612283 #14453212

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4060C211yesmaximal, characteristic, complemented
2C2×C3×D5×D8C211yesmaximal, characteristic, complemented
3C3×#66010C211yesmaximal, characteristic, complemented
4C3×D4×D20C211yesmaximal, characteristic, complemented
5C3×C5×#463C211yesmaximal, characteristic, complemented
6C3×#65458C211yesmaximal, characteristic, complemented
7C3×#65445C211yesmaximal, characteristic, complemented
8C3×#65347C211yesmaximal, characteristic, complemented
9C3×#65303C211yesmaximal, characteristic, complemented
10C3×#65132C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65100C211yesmaximal, characteristic, complemented
13C3×#65096C211yesmaximal, characteristic, complemented
14C3×#65071C211yesmaximal, characteristic, complemented
15C3×#65062C211yesmaximal, characteristic, complemented
16#10612283C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic, complemented
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic, complemented
21C22×C3×D20—21no—
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×D8C2211yescharacteristic
24C3×C5×#124C2211yescharacteristic, complemented
25C3×C4×C5×D4C2211yescharacteristic, complemented
26C3×#4092C2211yescharacteristic, complemented
27C2×C3×#688C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic, complemented
29C3×#4084C2211yescharacteristic, complemented
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic, complemented
32C2×C3×#686C2211yescharacteristic, complemented
33C3×#4076—21no—
34C3×#4060—24no—
35C3×D5×D8—24no—
36C2×C3×D40C2211yescharacteristic, complemented
37C2×C3×D40C2211yescharacteristic, complemented
38C2×C3×#676C2211yescharacteristic, complemented
39C2×C3×C8×D5C2211yescharacteristic, complemented
40C3×#4041C2211yescharacteristic
41C3×#4041C2211yescharacteristic, complemented
42C3×#4030—21no—
43C3×#4029—21no—
44C3×#4028—21no—
45C3×#4028—21no—
46C3×#4028—21no—
47C3×D5×C22⋊C4—21no—
48C3×#4020C2211yescharacteristic, complemented
49C3×C4×D20C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3952C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic, complemented
60C3×#3940C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C2×#4060C2×C311yescharacteristic, complemented
64C2×D5×D8C2×C311yescharacteristic, complemented
65#66010C2×C311yescharacteristic, complemented
66D4×D20C2×C311yescharacteristic, complemented
67C5×#463C2×C311yescharacteristic, complemented
68#65458C2×C311yescharacteristic, complemented
69#65445C2×C311yescharacteristic, complemented
70#65347C2×C311yescharacteristic, complemented
71#65303C2×C311yescharacteristic, complemented
72#65132C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65100C2×C311yescharacteristic, complemented
75#65096C2×C311yescharacteristic, complemented
76#65071C2×C311yescharacteristic, complemented
77#65062C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5—21no—
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×D4×D5—22no—
92C3×D4×D5—22no—
93C3×D4×D5—22no—
94C3×D4×D5—41no—
95C3×D4×D5—41no—
96C3×D4×D5—41no—
97C2×C3×D20—21no—
98C2×C3×D20—21no—
99C2×C3×D20—21no—
100C2×C3×D20—21no—
101C2×C3×D20—21no—
102C2×C3×D20—44no—
103C2×C3×D20D411yescharacteristic
104C2×C3×D20C2311yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×D20C2311yescharacteristic
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5—21no—
109C2×C3×C4×D5C2311yescharacteristic
110C2×C3×C4×D5C2311yescharacteristic
111C3×C5×SD16—22no—
112C3×C5×D8—22no—
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C5×C22⋊C4—21no—
117C3×C5×C22⋊C4—21no—
118C3×C5×C22⋊C4—21no—
119C3×C42×C5C2311yescharacteristic
120C3×C22⋊Dic5—21no—
121C3×#688—22no—
122C3×#688—41no—
123C3×#686—22no—
124C3×#686—41no—
125C3×#686D414yescomplemented
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685D411yescharacteristic
131C3×#685D411yescharacteristic
132C3×C4⋊Dic5D411yescharacteristic
133C3×C4⋊Dic5C2311yescharacteristic
134C3×#683—21no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×D40—22no—
138C3×D40—22no—
139C3×#676—22no—
140C3×C8×D5—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×D8—51no—
143C3×#546—51no—
144C3×D42—51no—
145C3×#496—51no—
146C3×#469—51no—
147C3×#465—51no—
148C3×#463D511yescharacteristic, complemented
149C3×#459—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#447—51no—
154C3×#442—51no—
155C3×#435—51no—
156C2×#713C22×C311yescharacteristic, complemented
157C2×D4×D5C22×C311yescharacteristic
158C2×D4×D5C22×C311yescharacteristic, complemented
159C2×D4×D5C22×C311yescharacteristic, complemented
160C22×D20—21no—
161C2×C5×SD16C22×C311yescharacteristic, complemented
162C2×C5×D8C22×C311yescharacteristic
163C5×#124C22×C311yescharacteristic, complemented
164C4×C5×D4C22×C311yescharacteristic, complemented
165#4092C22×C311yescharacteristic, complemented
166C2×#688C22×C311yescharacteristic, complemented
167C2×#688C22×C311yescharacteristic, complemented
168#4084C22×C311yescharacteristic, complemented
169C2×#686C22×C311yescharacteristic
170C2×#686C22×C311yescharacteristic, complemented
171C2×#686C22×C311yescharacteristic, complemented
172#4076—21no—
173#4060—24no—
174D5×D8—24no—
175C2×D40C22×C311yescharacteristic, complemented
176C2×D40C22×C311yescharacteristic, complemented
177C2×#676C22×C311yescharacteristic, complemented
178C2×C8×D5C22×C311yescharacteristic, complemented
179#4041C22×C311yescharacteristic
180#4041C22×C311yescharacteristic, complemented
181#4030—21no—
182#4029—21no—
183#4028—21no—
184#4028—21no—
185#4028—21no—
186D5×C22⋊C4—21no—
187#4020C22×C311yescharacteristic, complemented
188C4×D20C22×C311yescharacteristic
189C4×D20C22×C311yescharacteristic, complemented
190C5×C4⋊C8C22×C311yescharacteristic, complemented
191C5×#103C22×C311yescharacteristic, complemented
192C5×#102C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic, complemented
195#3953C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic, complemented
197#3952C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic, complemented
199#3940C22×C311yescharacteristic, complemented
200#3935C22×C311yescharacteristic, complemented
201#3264—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
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—42no—
212C22×C3×D5—42no—
213C22×C3×D5—81no—
214C22×C3×D5—81no—
215C22×C3×D5—81no—
216C22×C3×D5C2×D411yescharacteristic
217C22×C3×D5C2×D411yescharacteristic
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4C2×D412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2411yescharacteristic
230C3×C22⋊D5—42no—
231C3×C22⋊D5—42no—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—81no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—22no—
238C3×D20—21no—
239C3×D20—21no—
240C3×D20—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—42no—
244C3×D20—42no—
245C3×D20—42no—
246C3×D20—42no—
247C3×D20—81no—
248C3×D20C2×D412yescomplemented
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251C3×C4×D5—21no—
252C3×C4×D5—21no—
253C3×C4×D5—42no—
254C3×C4×D5—81no—
255C3×C5×C8—21no—
256C3×C5×C8—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C2×C3×#41—51no—
260C22×C3×D4—51no—
261C22×C3×D4—51no—
262C22×C3×D4—51no—
263C22×C3×D4—101no—
264C3×AGL(1,ℤ/8)—104no—
265C2×C3×SD16—51no—
266C2×C3×SD16—51no—
267C2×C3×SD16C2×D511yescharacteristic, complemented
268C2×C3×D8—51no—
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×D8—51no—
273C2×C3×D8—104no—
274C2×C3×D8C2×D511yescharacteristic
275C2×C3×M16—51no—
276C22×C3×C8—51no—
277C3×#127—51no—
278C3×#124C2×D511yescharacteristic, complemented
279C3×#123—101no—
280C3×C22⋊Q8—51no—
281C3×#121—51no—
282C3×#121—51no—
283C3×#121—51no—
284C3×#121—101no—
285C3×#121—101no—
286C3×#120—101no—
287C3×#120—101no—
288C3×#120—101no—
289C3×C4×D4—51no—
290C3×C4×D4—51no—
291C3×C4×D4C2×D511yescharacteristic, complemented
292C2×C3×C22⋊C4—101no—
293C3×#106—51no—
294C3×C4⋊C8C2×D511yescharacteristic, complemented
295C3×#103C2×D511yescharacteristic, complemented
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102—51no—
300C3×#102C2×D511yescharacteristic, complemented
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97—51no—
304C23×D5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C2×C5×Q8C23×C311yescharacteristic
308C2×C5×D4C23×C311yescharacteristic
309C2×C5×D4C23×C311yescharacteristic
310C22×C4×C5—21no—
311C2×C22⋊D5—21no—
312C2×C22⋊D5—21no—
313C2×C22⋊D5—21no—
314C2×C22⋊D5—21no—
315#713—22no—
316#713—41no—
317D4×D5—22no—
318D4×D5—22no—
319D4×D5—22no—
320D4×D5—41no—
321D4×D5—41no—
322D4×D5—41no—
323C2×D20—21no—
324C2×D20—21no—
325C2×D20—21no—
326C2×D20—21no—
327C2×D20—21no—
328C2×D20—44no—
329C2×D20C3×D411yescharacteristic
330C2×D20C23×C311yescharacteristic
331C2×D20C23×C311yescharacteristic
332C2×D20C23×C311yescharacteristic
333C2×C4×D5—21no—
334C2×C4×D5—21no—
335C2×C4×D5C23×C311yescharacteristic
336C2×C4×D5C23×C311yescharacteristic
337C5×SD16—22no—
338C5×D8—22no—
339C2×C5×C8C23×C311yescharacteristic
340C2×C5×C8C23×C311yescharacteristic
341C5×C4⋊C4C23×C311yescharacteristic
342C5×C22⋊C4—21no—
343C5×C22⋊C4—21no—
344C5×C22⋊C4—21no—
345C42×C5C23×C311yescharacteristic
346C22⋊Dic5—21no—
347#688—22no—
348#688—41no—
349#686—22no—
350#686—41no—
351#686C3×D414yescomplemented
352#685—21no—
353#685—21no—
354#685—21no—
355#685—21no—
356#685C3×D411yescharacteristic
357#685C3×D411yescharacteristic
358C4⋊Dic5C3×D411yescharacteristic
359C4⋊Dic5C23×C311yescharacteristic
360#683—21no—
361C2×#168C23×C311yescharacteristic
362C2×#168C23×C311yescharacteristic
363D40—22no—
364D40—22no—
365#676—22no—
366C8×D5—22no—
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—51no—
369#546—51no—
370D42—51no—
371#496—51no—
372#469—51no—
373#465—51no—
374#463C3×D511yescharacteristic, complemented
375#459—51no—
376#450—51no—
377#449—51no—
378#447—51no—
379#447—51no—
380#442—51no—
381#435—51no—
382C22×C3×C5—22no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C22×D411yescharacteristic
389C2×C3×D5—21no—
390C2×C3×D5—21no—
391C2×C3×D5—21no—
392C2×C3×D5—22no—
393C2×C3×D5—21no—
394C2×C3×D5—21no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—84no—
404C2×C3×D5—84no—
405C2×C3×D5—84no—
406C2×C3×D5AGL(1,ℤ/8)12yescomplemented
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—41no—
410C3×C4×C5—41no—
411C3×C4×C5C22×D411yescharacteristic
412C3×C4×C5H(5,𝔽2)11yescharacteristic
413C3×Dic5—21no—
414C3×Dic5—21no—
415C3×Dic5—41no—
416C24×C3—101no—
417C24×C3—101no—
418C24×C3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—51no—
425C2×C3×D4—51no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—102no—
433C2×C3×D4—102no—
434C2×C3×D4—102no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—204no—
439C2×C3×D4—201no—
440C2×C3×D4—201no—
441C2×C3×D4—201no—
442C2×C3×D4C22×D511yescharacteristic
443C2×C3×D4C22×D511yescharacteristic
444C22×C3×C4—21no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—101no—
448C22×C3×C4—101no—
449C3×SD16—22no—
450C3×SD16—102no—
451C3×SD16—201no—
452C3×D8—22no—
453C3×D8—54no—
454C3×D8—102no—
455C3×D8—102no—
456C3×D8—102no—
457C3×D8—201no—
458C3×M16—102no—
459C2×C3×C8—51no—
460C2×C3×C8—51no—
461C2×C3×C8—102no—
462C2×C3×C8C22×D511yescharacteristic
463C2×C3×C8C22×D511yescharacteristic
464C3×C4⋊C4—51no—
465C3×C4⋊C4—51no—
466C3×C4⋊C4—101no—
467C3×C4⋊C4C22×D511yescharacteristic
468C3×C22⋊C4—21no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—21no—
471C3×C22⋊C4—51no—
472C3×C22⋊C4—51no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4—101no—
477C3×C22⋊C4—101no—
478C3×C42C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—21no—
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—42no—
485C22×D5—42no—
486C22×D5—42no—
487C22×D5—42no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—81no—
491C22×D5—81no—
492C22×D5—81no—
493C22×D5C2×C3×D411yescharacteristic
494C22×D5C2×C3×D411yescharacteristic
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4C2×C3×D412yes—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—42no—
504C2×C4×C5C2×C3×D411yescharacteristic
505C2×C4×C5C2×C3×D411yescharacteristic
506C2×C4×C5C24×C311yescharacteristic
507C22⋊D5—42no—
508C22⋊D5—42no—
509C22⋊D5—42no—
510C22⋊D5—81no—
511C2×Dic5—21no—
512C2×Dic5C2×C3×D411yescharacteristic
513C2×Dic5C2×C3×D411yescharacteristic
514D20—22no—
515D20—21no—
516D20—21no—
517D20—21no—
518D20—21no—
519D20—21no—
520D20—42no—
521D20—42no—
522D20—42no—
523D20—42no—
524D20—81no—
525D20C2×C3×D412yescomplemented
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—21no—
529C4×D5—21no—
530C4×D5—42no—
531C4×D5—81no—
532C5×C8—21no—
533C5×C8—21no—
534#168—21no—
535#168C2×C3×D412yescomplemented
536C2×#41—51no—
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—51no—
540C22×D4—101no—
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16C2×C3×D511yescharacteristic, complemented
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—51no—
548C2×D8—51no—
549C2×D8—51no—
550C2×D8—104no—
551C2×D8C2×C3×D511yescharacteristic
552C2×M16—51no—
553C22×C8—51no—
554#127—51no—
555#124C2×C3×D511yescharacteristic, complemented
556#123—101no—
557C22⋊Q8—51no—
558#121—51no—
559#121—51no—
560#121—51no—
561#121—101no—
562#121—101no—
563#120—101no—
564#120—101no—
565#120—101no—
566C4×D4—51no—
567C4×D4—51no—
568C4×D4C2×C3×D511yescharacteristic, complemented
569C2×C22⋊C4—101no—
570#106—51no—
571C4⋊C8C2×C3×D511yescharacteristic, complemented
572#103C2×C3×D511yescharacteristic, complemented
573#102—51no—
574#102—51no—
575#102—51no—
576#102—51no—
577#102C2×C3×D511yescharacteristic, complemented
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97—51no—
581C2×C3×C5—42no—
582C2×C3×C5—81no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586C3×D5—22no—
587C3×D5—41no—
588C3×D5—42no—
589C3×D5—81no—
590C3×D5—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—51no—
594C23×C3—51no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—202no—
599C23×C3—202no—
600C23×C3—202no—
601C23×C3—202no—
602C23×C3—202no—
603C23×C3—202no—
604C23×C3—401no—
605C23×C3—401no—
606C23×C3—401no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—52no—
613C3×D4—102no—
614C3×D4—101no—
615C3×D4—101no—
616C3×D4—101no—
617C3×D4—101no—
618C3×D4—101no—
619C3×D4—202no—
620C3×D4—202no—
621C3×D4—202no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—202no—
626C3×D4—401no—
627C3×D4—401no—
628C3×D4D4×D512yes—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—42no—
632C2×C3×C4—51no—
633C2×C3×C4—51no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—202no—
640C2×C3×C4—401no—
641C2×C3×C4D4×D511yescharacteristic
642C2×C3×C4D4×D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—52no—
647C3×C8—101no—
648C22×C5—22no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5C22×C3×D411yescharacteristic
655C2×D5—21no—
656C2×D5—21no—
657C2×D5—21no—
658C2×D5—21no—
659C2×D5—21no—
660C2×D5—22no—
661C2×D5—41no—
662C2×D5—41no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—84no—
670C2×D5—84no—
671C2×D5—84no—
672C2×D5C3×AGL(1,ℤ/8)12yescomplemented
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—41no—
676C4×C5—41no—
677C4×C5C22×C3×D411yescharacteristic
678C4×C5C3×H(5,𝔽2)11yescharacteristic
679Dic5—21no—
680Dic5—21no—
681Dic5—41no—
682C24—101no—
683C24—101no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8C22×C3×D511yescharacteristic
688C2×D4—51no—
689C2×D4—51no—
690C2×D4—51no—
691C2×D4—51no—
692C2×D4—101no—
693C2×D4—101no—
694C2×D4—101no—
695C2×D4—101no—
696C2×D4—101no—
697C2×D4—101no—
698C2×D4—102no—
699C2×D4—102no—
700C2×D4—102no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—204no—
705C2×D4—201no—
706C2×D4—201no—
707C2×D4—201no—
708C2×D4C22×C3×D511yescharacteristic
709C2×D4C22×C3×D511yescharacteristic
710C22×C4—21no—
711C22×C4—51no—
712C22×C4—51no—
713C22×C4—101no—
714C22×C4—101no—
715SD16—22no—
716SD16—102no—
717SD16—201no—
718D8—22no—
719D8—54no—
720D8—102no—
721D8—102no—
722D8—102no—
723D8—201no—
724M16—102no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—102no—
728C2×C8C22×C3×D511yescharacteristic
729C2×C8C22×C3×D511yescharacteristic
730C4⋊C4—51no—
731C4⋊C4—51no—
732C4⋊C4—101no—
733C4⋊C4C22×C3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—51no—
738C22⋊C4—51no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4—101no—
743C22⋊C4—101no—
744C42C22×C3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—52no—
753C22×C3—101no—
754C22×C3—101no—
755C22×C3—101no—
756C22×C3—101no—
757C22×C3—101no—
758C22×C3—102no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3—201no—
762C22×C3—201no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3—404no—
768C22×C3—404no—
769C22×C3—404no—
770C22×C3C2×D4×D511yescharacteristic
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—101no—
776C3×C4—101no—
777C3×C4—201no—
778C3×C4C2×D4×D511yescharacteristic
779C3×C4#414911yescharacteristic
780C2×C5—42no—
781C2×C5—81no—
782C2×C5C3×D4211yescharacteristic
783C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
784C2×C5C3×#57611yescharacteristic
785D5—22no—
786D5—41no—
787D5—42no—
788D5—81no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—51no—
793C23—51no—
794C23—101no—
795C23—101no—
796C23—101no—
797C23—202no—
798C23—202no—
799C23—202no—
800C23—202no—
801C23—202no—
802C23—202no—
803C23—401no—
804C23—401no—
805C23—401no—
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—52no—
812D4—102no—
813D4—101no—
814D4—101no—
815D4—101no—
816D4—101no—
817D4—101no—
818D4—202no—
819D4—202no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—401no—
826D4—401no—
827D4C3×D4×D512yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—42no—
831C2×C4—51no—
832C2×C4—51no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—202no—
839C2×C4—401no—
840C2×C4C3×D4×D511yescharacteristic
841C2×C4C3×D4×D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—21no—
845C8—52no—
846C8—101no—
847C2×C3—42no—
848C2×C3—81no—
849C2×C3—102no—
850C2×C3—201no—
851C2×C3—202no—
852C2×C3—401no—
853C2×C3—401no—
854C2×C3#6594311yescharacteristic
855C2×C3#6610311yescharacteristic
856C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—52no—
865C22—101no—
866C22—101no—
867C22—101no—
868C22—101no—
869C22—101no—
870C22—102no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—404no—
880C22—404no—
881C22—404no—
882C22C2×C3×D4×D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—101no—
888C4—101no—
889C4—201no—
890C4C2×C3×D4×D511yescharacteristic
891C4C3×#414911yescharacteristic
892C3#1061228311yescharacteristic, direct product factor, Sylow
893C2—42no—
894C2—81no—
895C2—102no—
896C2—201no—
897C2—202no—
898C2—401no—
899C2—401no—
900C2C3×#6594311yescharacteristic
901C2C3×#6610311yescharacteristic
902C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#463C2
socleC22×C3×C5C22×D4
hypercenterC3×#463D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4060C2semidirect
2. C2×C3×D5×D8C2semidirect
3. C3×#66010C2semidirect
4. C3×D4×D20C2semidirect
5. C3×C5×#463C2semidirect
6. C3×#65458C2semidirect
7. C3×#65445C2semidirect
8. C3×#65347C2semidirect
9. C3×#65303C2semidirect
10. C3×#65132C2semidirect
11. C3×#65125C2semidirect
12. C3×#65100C2semidirect
13. C3×#65096C2semidirect
14. C3×#65071C2semidirect
15. C3×#65062C2semidirect
16. #10612283C3direct (N × H)
17. C2×C3×#713C22semidirect
19. C2×C3×D4×D5C22semidirect
20. C2×C3×D4×D5C22semidirect
22. C2×C3×C5×SD16C22semidirect
24. C3×C5×#124C22semidirect
25. C3×C4×C5×D4C22semidirect
26. C3×#4092C22semidirect
27. C2×C3×#688C22semidirect
28. C2×C3×#688C22semidirect
29. C3×#4084C22semidirect
31. C2×C3×#686C22semidirect
32. C2×C3×#686C22semidirect
36. C2×C3×D40C22semidirect
37. C2×C3×D40C22semidirect
38. C2×C3×#676C22semidirect
39. C2×C3×C8×D5C22semidirect
41. C3×#4041C22semidirect
48. C3×#4020C22semidirect
50. C3×C4×D20C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#102C22semidirect
54. C3×#3964C22semidirect
55. C3×#3953C22semidirect
56. C3×#3953C22semidirect
57. C3×#3952C22semidirect
58. C3×#3952C22semidirect
59. C3×#3941C22semidirect
60. C3×#3940C22semidirect
61. C3×#3935C22semidirect
63. C2×#4060C2×C3semidirect
64. C2×D5×D8C2×C3semidirect
65. #66010C2×C3semidirect
66. D4×D20C2×C3semidirect
67. C5×#463C2×C3semidirect
68. #65458C2×C3semidirect
69. #65445C2×C3semidirect
70. #65347C2×C3semidirect
71. #65303C2×C3semidirect
72. #65132C2×C3semidirect
73. #65125C2×C3semidirect
74. #65100C2×C3semidirect
75. #65096C2×C3semidirect
76. #65071C2×C3semidirect
77. #65062C2×C3semidirect
125. C3×#686D4semidirect
148. C3×#463D5semidirect
156. C2×#713C22×C3semidirect
158. C2×D4×D5C22×C3semidirect
159. C2×D4×D5C22×C3semidirect
161. C2×C5×SD16C22×C3semidirect
163. C5×#124C22×C3semidirect
164. C4×C5×D4C22×C3semidirect
165. #4092C22×C3semidirect
166. C2×#688C22×C3semidirect
167. C2×#688C22×C3semidirect
168. #4084C22×C3semidirect
170. C2×#686C22×C3semidirect
171. C2×#686C22×C3semidirect
175. C2×D40C22×C3semidirect
176. C2×D40C22×C3semidirect
177. C2×#676C22×C3semidirect
178. C2×C8×D5C22×C3semidirect
180. #4041C22×C3semidirect
187. #4020C22×C3semidirect
189. C4×D20C22×C3semidirect
190. C5×C4⋊C8C22×C3semidirect
191. C5×#103C22×C3semidirect
192. C5×#102C22×C3semidirect
193. #3964C22×C3semidirect
194. #3953C22×C3semidirect
195. #3953C22×C3semidirect
196. #3952C22×C3semidirect
197. #3952C22×C3semidirect
198. #3941C22×C3semidirect
199. #3940C22×C3semidirect
200. #3935C22×C3semidirect
248. C3×D20C2×D4semidirect
258. C3×#168C2×D4semidirect
267. C2×C3×SD16C2×D5semidirect
278. C3×#124C2×D5semidirect
291. C3×C4×D4C2×D5semidirect
294. C3×C4⋊C8C2×D5semidirect
295. C3×#103C2×D5semidirect
300. C3×#102C2×D5semidirect
351. #686C3×D4semidirect
374. #463C3×D5semidirect
406. C2×C3×D5AGL(1,ℤ/8)semidirect
525. D20C2×C3×D4semidirect
535. #168C2×C3×D4semidirect
544. C2×SD16C2×C3×D5semidirect
555. #124C2×C3×D5semidirect
568. C4×D4C2×C3×D5semidirect
571. C4⋊C8C2×C3×D5semidirect
572. #103C2×C3×D5semidirect
577. #102C2×C3×D5semidirect
672. C2×D5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
857. C5C3×#3264semidirect
892. C3#10612283direct (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×D82
C3×#660102
C3×D4×D202
C3×C5×#4632
C3×#654582
C3×#654452
C3×#653472
C3×#653032
C3×#651322
C3×#651252
C3×#651002
C3×#650962
C3×#650712
C3×#650622
#106122833
C3×#32645