Finite Group Databasebeta

← C3×#10611743 #14453188

Subgroups — C3×#10611743 #14453188

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
1C3×D4×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×C3×#4078C211yesmaximal, characteristic, complemented
3C2×C3×D5×D8C211yesmaximal, characteristic, complemented
4C3×#65946C211yesmaximal, characteristic, complemented
5C3×C5×#447C211yesmaximal, characteristic, complemented
6C3×#65445C211yesmaximal, characteristic, complemented
7C3×#65443C211yesmaximal, characteristic, complemented
8C3×#65442C211yesmaximal, characteristic, complemented
9C3×#65328C211yesmaximal, characteristic, complemented
10C3×#65075C211yesmaximal, characteristic, complemented
11C3×#65074C211yesmaximal, characteristic, complemented
12C3×#65067C211yesmaximal, characteristic, complemented
13C3×#65065C211yesmaximal, characteristic, complemented
14C3×#65023C211yesmaximal, characteristic, complemented
15C3×#65017C211yesmaximal, characteristic, complemented
16#10611743C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic, complemented
18C22×C3×C22⋊D5—21no—
19C2×C3×D4×D5C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic, complemented
21C2×C3×#709C2211yescharacteristic, complemented
22C2×C3×C5×D8C2211yescharacteristic
23C2×C3×C5×D8C2211yescharacteristic, complemented
24C3×C5×#121C2211yescharacteristic, complemented
25C3×#4099—21no—
26C3×#4086C2211yescharacteristic, complemented
27C3×#4085—21no—
28C3×#4084—21no—
29C3×#4084C2211yescharacteristic
30C3×#4083—21no—
31C3×#4083—21no—
32C3×#4082C2211yescharacteristic, complemented
33C3×D4×Dic5C2211yescharacteristic, complemented
34C2×C3×#687C2211yescharacteristic, complemented
35C2×C3×#687C2211yescharacteristic, complemented
36C3×#4078—24no—
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic, complemented
39C2×C3×#686C2211yescharacteristic, complemented
40C3×#4076C2211yescharacteristic, complemented
41C3×C4×C22⋊D5C2211yescharacteristic
42C2×C3×#681C2211yescharacteristic, complemented
43C3×D5×D8—24no—
44C2×C3×D40C2211yescharacteristic, complemented
45C2×C3×#677C2211yescharacteristic, complemented
46C2×C3×C8×D5C2211yescharacteristic, complemented
47C3×#4043C2211yescharacteristic, complemented
48C3×#4039C2211yescharacteristic, complemented
49C3×#4029—21no—
50C3×D5×C22⋊C4—21no—
51C3×C5×#102C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3952C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3941C2211yescharacteristic, complemented
61C3×#3940C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63D4×C22⋊D5C2×C311yescharacteristic, complemented
64C2×#4078C2×C311yescharacteristic, complemented
65C2×D5×D8C2×C311yescharacteristic, complemented
66#65946C2×C311yescharacteristic, complemented
67C5×#447C2×C311yescharacteristic, complemented
68#65445C2×C311yescharacteristic, complemented
69#65443C2×C311yescharacteristic, complemented
70#65442C2×C311yescharacteristic, complemented
71#65328C2×C311yescharacteristic, complemented
72#65075C2×C311yescharacteristic, complemented
73#65074C2×C311yescharacteristic, complemented
74#65067C2×C311yescharacteristic, complemented
75#65065C2×C311yescharacteristic, complemented
76#65023C2×C311yescharacteristic, complemented
77#65017C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—41no—
85C2×C3×C5×D4C2311yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—44no—
97C2×C3×C22⋊D5D411yescharacteristic
98C22×C3×Dic5—21no—
99C3×D4×D5—22no—
100C3×D4×D5—22no—
101C3×D4×D5—41no—
102C3×D4×D5—41no—
103C3×#709—22no—
104C3×#709—41no—
105C2×C3×D20C2311yescharacteristic
106C2×C3×D20C2311yescharacteristic
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5—21no—
109C2×C3×C4×D5C2311yescharacteristic
110C2×C3×Dic10C2311yescharacteristic
111C3×C5×D8—22no—
112C3×C5×D8—41no—
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C5×C22⋊C4—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5—21no—
121C3×C22⋊Dic5D411yescharacteristic
122C3×#687—22no—
123C3×#687—22no—
124C3×#686—22no—
125C3×#686—22no—
126C3×#686D414yescomplemented
127C3×#685—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685D411yescharacteristic
131C3×C4⋊Dic5—21no—
132C3×C4⋊Dic5C2311yescharacteristic
133C3×#683D411yescharacteristic
134C3×C4×Dic5C2311yescharacteristic
135C3×#681—22no—
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C3×D40—22no—
139C3×#677—41no—
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×#463—51no—
149C3×#459—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#447D511yescharacteristic, complemented
154C3×#442—51no—
155C3×#435—51no—
156C22×C5×D4C22×C311yescharacteristic, complemented
157C22×C22⋊D5—21no—
158C2×D4×D5C22×C311yescharacteristic
159C2×D4×D5C22×C311yescharacteristic, complemented
160C2×#709C22×C311yescharacteristic, complemented
161C2×C5×D8C22×C311yescharacteristic
162C2×C5×D8C22×C311yescharacteristic, complemented
163C5×#121C22×C311yescharacteristic, complemented
164#4099—21no—
165#4086C22×C311yescharacteristic, complemented
166#4085—21no—
167#4084—21no—
168#4084C22×C311yescharacteristic
169#4083—21no—
170#4083—21no—
171#4082C22×C311yescharacteristic, complemented
172D4×Dic5C22×C311yescharacteristic, complemented
173C2×#687C22×C311yescharacteristic, complemented
174C2×#687C22×C311yescharacteristic, complemented
175#4078—24no—
176C2×#686C22×C311yescharacteristic
177C2×#686C22×C311yescharacteristic, complemented
178C2×#686C22×C311yescharacteristic, complemented
179#4076C22×C311yescharacteristic, complemented
180C4×C22⋊D5C22×C311yescharacteristic
181C2×#681C22×C311yescharacteristic, complemented
182D5×D8—24no—
183C2×D40C22×C311yescharacteristic, complemented
184C2×#677C22×C311yescharacteristic, complemented
185C2×C8×D5C22×C311yescharacteristic, complemented
186#4043C22×C311yescharacteristic, complemented
187#4039C22×C311yescharacteristic, complemented
188#4029—21no—
189D5×C22⋊C4—21no—
190C5×#102C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic, complemented
192C5×C22⋊C8C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic, complemented
195#3952C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3947C22×C311yescharacteristic, complemented
198#3946C22×C311yescharacteristic, complemented
199#3941C22×C311yescharacteristic, complemented
200#3940C22×C311yescharacteristic, complemented
201#3264—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—21no—
211C22×C3×D5—42no—
212C22×C3×D5—42no—
213C22×C3×D5—42no—
214C22×C3×D5—42no—
215C22×C3×D5—81no—
216C22×C3×D5—81no—
217C22×C3×D5C2×D411yescharacteristic
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—42no—
224C3×C5×D4—81no—
225C3×C5×D4C2×D412yes—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2411yescharacteristic
231C3×C22⋊D5—22no—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—42no—
234C3×C22⋊D5—42no—
235C3×C22⋊D5—42no—
236C3×C22⋊D5—42no—
237C3×C22⋊D5—42no—
238C3×C22⋊D5—81no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—42no—
242C2×C3×Dic5C2×D411yescharacteristic
243C2×C3×Dic5C2×D411yescharacteristic
244C2×C3×Dic5C2×D411yescharacteristic
245C3×D20—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20C2×D412yescomplemented
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251C3×C4×D5—42no—
252C3×C4×D5—81no—
253C3×Dic10—21no—
254C3×Dic10—21no—
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—101no—
263C22×C3×D4C2×D511yescharacteristic, complemented
264C3×AGL(1,ℤ/8)—104no—
265C2×C3×SD16—51no—
266C2×C3×SD16—51no—
267C2×C3×SD16—51no—
268C2×C3×D8—51no—
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×D8—104no—
273C2×C3×D8C2×D511yescharacteristic
274C2×C3×D8C2×D511yescharacteristic, complemented
275C2×C3×M16—51no—
276C22×C3×C8—51no—
277C3×#127—51no—
278C3×#124—51no—
279C3×#123—101no—
280C3×C22⋊Q8—51no—
281C3×#121—51no—
282C3×#121—51no—
283C3×#121—101no—
284C3×#121—101no—
285C3×#121C2×D511yescharacteristic, complemented
286C3×#120—101no—
287C3×#120—101no—
288C3×#120—101no—
289C3×C4×D4—51no—
290C3×C4×D4—51no—
291C3×C4×D4—51no—
292C2×C3×C22⋊C4—101no—
293C3×#106—51no—
294C3×C4⋊C8—51no—
295C3×#103—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102C2×D511yescharacteristic, complemented
300C3×#102C2×D511yescharacteristic, complemented
301C3×C22⋊C8—51no—
302C3×C22⋊C8C2×D511yescharacteristic, complemented
303C3×#97—51no—
304C24×C5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C2×C5×D4—22no—
308C2×C5×D4—21no—
309C2×C5×D4—21no—
310C2×C5×D4—41no—
311C2×C5×D4C23×C311yescharacteristic
312C2×C5×D4C23×C311yescharacteristic
313C2×C5×D4C23×C311yescharacteristic
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—21no—
322C2×C22⋊D5—44no—
323C2×C22⋊D5C3×D411yescharacteristic
324C22×Dic5—21no—
325D4×D5—22no—
326D4×D5—22no—
327D4×D5—41no—
328D4×D5—41no—
329#709—22no—
330#709—41no—
331C2×D20C23×C311yescharacteristic
332C2×D20C23×C311yescharacteristic
333C2×C4×D5—21no—
334C2×C4×D5—21no—
335C2×C4×D5C23×C311yescharacteristic
336C2×Dic10C23×C311yescharacteristic
337C5×D8—22no—
338C5×D8—41no—
339C2×C5×C8C23×C311yescharacteristic
340C2×C5×C8C23×C311yescharacteristic
341C5×C4⋊C4C23×C311yescharacteristic
342C5×C22⋊C4—21no—
343C22⋊Dic5—21no—
344C22⋊Dic5—21no—
345C22⋊Dic5—21no—
346C22⋊Dic5—21no—
347C22⋊Dic5C3×D411yescharacteristic
348#687—22no—
349#687—22no—
350#686—22no—
351#686—22no—
352#686C3×D414yescomplemented
353#685—21no—
354#685—21no—
355#685—21no—
356#685C3×D411yescharacteristic
357C4⋊Dic5—21no—
358C4⋊Dic5C23×C311yescharacteristic
359#683C3×D411yescharacteristic
360C4×Dic5C23×C311yescharacteristic
361#681—22no—
362C2×#168C23×C311yescharacteristic
363C2×#168C23×C311yescharacteristic
364D40—22no—
365#677—41no—
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#463—51no—
375#459—51no—
376#450—51no—
377#449—51no—
378#447—51no—
379#447C3×D511yescharacteristic, complemented
380#442—51no—
381#435—51no—
382C22×C3×C5—21no—
383C22×C3×C5—22no—
384C22×C3×C5—21no—
385C22×C3×C5—21no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—41no—
394C22×C3×C5—84no—
395C22×C3×C5C22×D411yescharacteristic
396C2×C3×D5—21no—
397C2×C3×D5—21no—
398C2×C3×D5—22no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—84no—
405C2×C3×D5—84no—
406C2×C3×D5AGL(1,ℤ/8)12yescomplemented
407C3×C4×C5—21no—
408C3×C4×C5—41no—
409C3×C4×C5C22×D411yescharacteristic
410C3×C4×C5H(5,𝔽2)11yescharacteristic
411C3×Dic5—21no—
412C3×Dic5—21no—
413C3×Dic5—21no—
414C3×Dic5—41no—
415C3×Dic5—41no—
416C24×C3—21no—
417C24×C3—101no—
418C24×C3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8—51no—
422C2×C3×D4—22no—
423C2×C3×D4—21no—
424C2×C3×D4—21no—
425C2×C3×D4—41no—
426C2×C3×D4—51no—
427C2×C3×D4—51no—
428C2×C3×D4—51no—
429C2×C3×D4—101no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—101no—
433C2×C3×D4—102no—
434C2×C3×D4—102no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—201no—
439C2×C3×D4—201no—
440C2×C3×D4—204no—
441C2×C3×D4C22×D511yescharacteristic
442C2×C3×D4C22×D511yescharacteristic
443C2×C3×D4C22×D511yescharacteristic
444C22×C3×C4—51no—
445C22×C3×C4—101no—
446C22×C3×C4—101no—
447C22×C3×C4—101no—
448C22×C3×C4C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—102no—
451C3×SD16—201no—
452C3×D8—22no—
453C3×D8—41no—
454C3×D8—54no—
455C3×D8—102no—
456C3×D8—102no—
457C3×D8—102no—
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—51no—
470C3×C22⋊C4—51no—
471C3×C22⋊C4—101no—
472C3×C22⋊C4—101no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4—101no—
477C3×C22⋊C4—101no—
478C3×C42—51no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—42no—
483C23×C5—42no—
484C23×C5—81no—
485C23×C5C2×C3×D411yescharacteristic
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—42no—
491C22×D5—42no—
492C22×D5—81no—
493C22×D5—81no—
494C22×D5C2×C3×D411yescharacteristic
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—42no—
501C5×D4—81no—
502C5×D4C2×C3×D412yes—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5C2×C3×D411yescharacteristic
507C2×C4×C5C24×C311yescharacteristic
508C22⋊D5—22no—
509C22⋊D5—42no—
510C22⋊D5—42no—
511C22⋊D5—42no—
512C22⋊D5—42no—
513C22⋊D5—42no—
514C22⋊D5—42no—
515C22⋊D5—81no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—42no—
519C2×Dic5C2×C3×D411yescharacteristic
520C2×Dic5C2×C3×D411yescharacteristic
521C2×Dic5C2×C3×D411yescharacteristic
522D20—21no—
523D20—21no—
524D20—21no—
525D20C2×C3×D412yescomplemented
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—42no—
529C4×D5—81no—
530Dic10—21no—
531Dic10—21no—
532C5×C8—21no—
533C5×C8—21no—
534#168—21no—
535#168C2×C3×D412yescomplemented
536C2×#41—51no—
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—101no—
540C22×D4C2×C3×D511yescharacteristic, complemented
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—51no—
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—51no—
548C2×D8—51no—
549C2×D8—104no—
550C2×D8C2×C3×D511yescharacteristic
551C2×D8C2×C3×D511yescharacteristic, complemented
552C2×M16—51no—
553C22×C8—51no—
554#127—51no—
555#124—51no—
556#123—101no—
557C22⋊Q8—51no—
558#121—51no—
559#121—51no—
560#121—101no—
561#121—101no—
562#121C2×C3×D511yescharacteristic, complemented
563#120—101no—
564#120—101no—
565#120—101no—
566C4×D4—51no—
567C4×D4—51no—
568C4×D4—51no—
569C2×C22⋊C4—101no—
570#106—51no—
571C4⋊C8—51no—
572#103—51no—
573#102—51no—
574#102—51no—
575#102—51no—
576#102C2×C3×D511yescharacteristic, complemented
577#102C2×C3×D511yescharacteristic, complemented
578C22⋊C8—51no—
579C22⋊C8C2×C3×D511yescharacteristic, complemented
580#97—51no—
581C2×C3×C5—42no—
582C2×C3×C5—41no—
583C2×C3×C5—81no—
584C2×C3×C5—81no—
585C2×C3×C5D4211yescharacteristic
586C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
587C2×C3×C5#57611yescharacteristic
588C3×D5—22no—
589C3×D5—42no—
590C3×D5—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—51no—
597C23×C3—81no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—202no—
601C23×C3—202no—
602C23×C3—202no—
603C23×C3—202no—
604C23×C3—401no—
605C23×C3—401no—
606C23×C3D4×D511yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—42no—
615C3×D4—52no—
616C3×D4—81no—
617C3×D4—102no—
618C3×D4—101no—
619C3×D4—101no—
620C3×D4—101no—
621C3×D4—202no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—202no—
626C3×D4—202no—
627C3×D4—401no—
628C3×D4D4×D512yes—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—51no—
633C2×C3×C4—51no—
634C2×C3×C4—51no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—202no—
640C2×C3×C4—202no—
641C2×C3×C4—401no—
642C2×C3×C4D4×D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—52no—
647C3×C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—22no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—41no—
660C22×C5—84no—
661C22×C5C22×C3×D411yescharacteristic
662C2×D5—21no—
663C2×D5—21no—
664C2×D5—22no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—84no—
671C2×D5—84no—
672C2×D5C3×AGL(1,ℤ/8)12yescomplemented
673C4×C5—21no—
674C4×C5—41no—
675C4×C5C22×C3×D411yescharacteristic
676C4×C5C3×H(5,𝔽2)11yescharacteristic
677Dic5—21no—
678Dic5—21no—
679Dic5—21no—
680Dic5—41no—
681Dic5—41no—
682C24—21no—
683C24—101no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—41no—
692C2×D4—51no—
693C2×D4—51no—
694C2×D4—51no—
695C2×D4—101no—
696C2×D4—101no—
697C2×D4—101no—
698C2×D4—101no—
699C2×D4—102no—
700C2×D4—102no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—201no—
705C2×D4—201no—
706C2×D4—204no—
707C2×D4C22×C3×D511yescharacteristic
708C2×D4C22×C3×D511yescharacteristic
709C2×D4C22×C3×D511yescharacteristic
710C22×C4—51no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4—101no—
714C22×C4C22×C3×D511yescharacteristic
715SD16—102no—
716SD16—102no—
717SD16—201no—
718D8—22no—
719D8—41no—
720D8—54no—
721D8—102no—
722D8—102no—
723D8—102no—
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—51no—
736C22⋊C4—51no—
737C22⋊C4—101no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4—101no—
743C22⋊C4—101no—
744C42—51no—
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—52no—
759C22×C3—84no—
760C22×C3—101no—
761C22×C3—101no—
762C22×C3—102no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3—201no—
768C22×C3—404no—
769C22×C3—404no—
770C22×C3C2×D4×D511yescharacteristic
771C3×C4—21no—
772C3×C4—41no—
773C3×C4—101no—
774C3×C4—101no—
775C3×C4—101no—
776C3×C4—201no—
777C3×C4—201no—
778C3×C4C2×D4×D511yescharacteristic
779C3×C4#414411yescharacteristic
780C2×C5—42no—
781C2×C5—41no—
782C2×C5—81no—
783C2×C5—81no—
784C2×C5C3×D4211yescharacteristic
785C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
786C2×C5C3×#57611yescharacteristic
787D5—22no—
788D5—42no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—42no—
794C23—42no—
795C23—51no—
796C23—81no—
797C23—101no—
798C23—101no—
799C23—202no—
800C23—202no—
801C23—202no—
802C23—202no—
803C23—401no—
804C23—401no—
805C23C3×D4×D511yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—42no—
814D4—52no—
815D4—81no—
816D4—102no—
817D4—101no—
818D4—101no—
819D4—101no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—202no—
826D4—401no—
827D4C3×D4×D512yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—51no—
832C2×C4—51no—
833C2×C4—51no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—202no—
839C2×C4—202no—
840C2×C4—401no—
841C2×C4C3×D4×D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—21no—
845C8—52no—
846C8—101no—
847C2×C3—41no—
848C2×C3—42no—
849C2×C3—81no—
850C2×C3—81no—
851C2×C3—102no—
852C2×C3—202no—
853C2×C3—401no—
854C2×C3#6592411yescharacteristic
855C2×C3#6609111yescharacteristic
856C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—22no—
861C22—21no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—52no—
871C22—84no—
872C22—101no—
873C22—101no—
874C22—102no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—201no—
880C22—404no—
881C22—404no—
882C22C2×C3×D4×D511yescharacteristic
883C4—21no—
884C4—41no—
885C4—101no—
886C4—101no—
887C4—101no—
888C4—201no—
889C4—201no—
890C4C2×C3×D4×D511yescharacteristic
891C4C3×#414411yescharacteristic
892C3#1061174311yescharacteristic, direct product factor, Sylow
893C2—41no—
894C2—42no—
895C2—81no—
896C2—81no—
897C2—102no—
898C2—202no—
899C2—401no—
900C2C3×#6592411yescharacteristic
901C2C3×#6609111yescharacteristic
902C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#447C2
socleC22×C3×C5C22×D4
hypercenterC3×#447D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#447

Complements

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

NH ≅ G/Ntype
1. C3×D4×C22⋊D5C2semidirect
2. C2×C3×#4078C2semidirect
3. C2×C3×D5×D8C2semidirect
4. C3×#65946C2semidirect
5. C3×C5×#447C2semidirect
6. C3×#65445C2semidirect
7. C3×#65443C2semidirect
8. C3×#65442C2semidirect
9. C3×#65328C2semidirect
10. C3×#65075C2semidirect
11. C3×#65074C2semidirect
12. C3×#65067C2semidirect
13. C3×#65065C2semidirect
14. C3×#65023C2semidirect
15. C3×#65017C2semidirect
16. #10611743C3direct (N × H)
17. C22×C3×C5×D4C22semidirect
20. C2×C3×D4×D5C22semidirect
21. C2×C3×#709C22semidirect
23. C2×C3×C5×D8C22semidirect
24. C3×C5×#121C22semidirect
26. C3×#4086C22semidirect
32. C3×#4082C22semidirect
33. C3×D4×Dic5C22semidirect
34. C2×C3×#687C22semidirect
35. C2×C3×#687C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#686C22semidirect
40. C3×#4076C22semidirect
42. C2×C3×#681C22semidirect
44. C2×C3×D40C22semidirect
45. C2×C3×#677C22semidirect
46. C2×C3×C8×D5C22semidirect
47. C3×#4043C22semidirect
48. C3×#4039C22semidirect
51. C3×C5×#102C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×#3964C22semidirect
55. C3×#3953C22semidirect
56. C3×#3952C22semidirect
57. C3×#3948C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
60. C3×#3941C22semidirect
61. C3×#3940C22semidirect
63. D4×C22⋊D5C2×C3semidirect
64. C2×#4078C2×C3semidirect
65. C2×D5×D8C2×C3semidirect
66. #65946C2×C3semidirect
67. C5×#447C2×C3semidirect
68. #65445C2×C3semidirect
69. #65443C2×C3semidirect
70. #65442C2×C3semidirect
71. #65328C2×C3semidirect
72. #65075C2×C3semidirect
73. #65074C2×C3semidirect
74. #65067C2×C3semidirect
75. #65065C2×C3semidirect
76. #65023C2×C3semidirect
77. #65017C2×C3semidirect
126. C3×#686D4semidirect
153. C3×#447D5semidirect
156. C22×C5×D4C22×C3semidirect
159. C2×D4×D5C22×C3semidirect
160. C2×#709C22×C3semidirect
162. C2×C5×D8C22×C3semidirect
163. C5×#121C22×C3semidirect
165. #4086C22×C3semidirect
171. #4082C22×C3semidirect
172. D4×Dic5C22×C3semidirect
173. C2×#687C22×C3semidirect
174. C2×#687C22×C3semidirect
177. C2×#686C22×C3semidirect
178. C2×#686C22×C3semidirect
179. #4076C22×C3semidirect
181. C2×#681C22×C3semidirect
183. C2×D40C22×C3semidirect
184. C2×#677C22×C3semidirect
185. C2×C8×D5C22×C3semidirect
186. #4043C22×C3semidirect
187. #4039C22×C3semidirect
190. C5×#102C22×C3semidirect
191. C5×#102C22×C3semidirect
192. C5×C22⋊C8C22×C3semidirect
193. #3964C22×C3semidirect
194. #3953C22×C3semidirect
195. #3952C22×C3semidirect
196. #3948C22×C3semidirect
197. #3947C22×C3semidirect
198. #3946C22×C3semidirect
199. #3941C22×C3semidirect
200. #3940C22×C3semidirect
248. C3×D20C2×D4semidirect
258. C3×#168C2×D4semidirect
263. C22×C3×D4C2×D5semidirect
274. C2×C3×D8C2×D5semidirect
285. C3×#121C2×D5semidirect
299. C3×#102C2×D5semidirect
300. C3×#102C2×D5semidirect
302. C3×C22⋊C8C2×D5semidirect
352. #686C3×D4semidirect
379. #447C3×D5semidirect
406. C2×C3×D5AGL(1,ℤ/8)semidirect
525. D20C2×C3×D4semidirect
535. #168C2×C3×D4semidirect
540. C22×D4C2×C3×D5semidirect
551. C2×D8C2×C3×D5semidirect
562. #121C2×C3×D5semidirect
576. #102C2×C3×D5semidirect
577. #102C2×C3×D5semidirect
579. C22⋊C8C2×C3×D5semidirect
672. C2×D5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
857. C5C3×#3264semidirect
892. C3#10611743direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D4×C22⋊D52
C2×C3×#40782
C2×C3×D5×D82
C3×#659462
C3×C5×#4472
C3×#654452
C3×#654432
C3×#654422
C3×#653282
C3×#650752
C3×#650742
C3×#650672
C3×#650652
C3×#650232
C3×#650172
#106117433
C3×#32645