Finite Group Databasebeta

← C3×#10615568 #14453194

Subgroups — C3×#10615568 #14453194

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
1C22×C3×C5×D8C211yesmaximal, characteristic, complemented
2C3×#66140C211yesmaximal, characteristic, complemented
3C3×D4×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×C3×#4057C211yesmaximal, characteristic, complemented
5C3×#65507C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7C3×#65448C211yesmaximal, characteristic, complemented
8C3×#65447C211yesmaximal, characteristic, complemented
9C3×#65445C211yesmaximal, characteristic, complemented
10C3×#65443C211yesmaximal, characteristic, complemented
11C3×#65442C211yesmaximal, characteristic, complemented
12C3×#65441C211yesmaximal, characteristic, complemented
13C3×#65439C211yesmaximal, characteristic, complemented
14C3×#65403C211yesmaximal, characteristic, complemented
15C3×#65400C211yesmaximal, characteristic, complemented
16#10615568C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic, complemented
19C22×C3×C22⋊D5—21no—
20C2×C3×#711C2211yescharacteristic, complemented
21C2×C3×D4×D5C2211yescharacteristic, complemented
22C2×C3×C5×D8—24no—
23C2×C3×C5×D8C2211yescharacteristic
24C2×C3×C5×D8C2211yescharacteristic
25C2×C3×C5×D8C2211yescharacteristic, complemented
26C2×C3×C5×D8C2211yescharacteristic, complemented
27C22×C3×C5×C8C2211yescharacteristic, complemented
28C3×#4099—21no—
29C3×#4099—21no—
30C2×C3×C22⋊Dic5—21no—
31C3×#4086C2211yescharacteristic, complemented
32C3×#4085—21no—
33C3×#4085—21no—
34C3×#4084C2211yescharacteristic, complemented
35C3×#4084C2211yescharacteristic, complemented
36C3×#4083—21no—
37C3×#4082C2211yescharacteristic, complemented
38C3×#4081—21no—
39C3×D4×Dic5C2211yescharacteristic, complemented
40C3×D4×Dic5C2211yescharacteristic, complemented
41C2×C3×#687C2211yescharacteristic, complemented
42C2×C3×#687C2211yescharacteristic, complemented
43C2×C3×#686C2211yescharacteristic, complemented
44C2×C3×#686C2211yescharacteristic, complemented
45C3×#4076C2211yescharacteristic
46C3×C4×C22⋊D5C2211yescharacteristic
47C3×#4070C2211yescharacteristic, complemented
48C3×#4057—24no—
49C2×C3×#677C2211yescharacteristic, complemented
50C2×C3×#676C2211yescharacteristic, complemented
51C3×#3964C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3949C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3947C2211yescharacteristic, complemented
61C3×#3946C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C22×C5×D8C2×C311yescharacteristic, complemented
64#66140C2×C311yescharacteristic, complemented
65D4×C22⋊D5C2×C311yescharacteristic, complemented
66C2×#4057C2×C311yescharacteristic, complemented
67#65507C2×C311yescharacteristic, complemented
68#65506C2×C311yescharacteristic, complemented
69#65448C2×C311yescharacteristic, complemented
70#65447C2×C311yescharacteristic, complemented
71#65445C2×C311yescharacteristic, complemented
72#65443C2×C311yescharacteristic, complemented
73#65442C2×C311yescharacteristic, complemented
74#65441C2×C311yescharacteristic, complemented
75#65439C2×C311yescharacteristic, complemented
76#65403C2×C311yescharacteristic, complemented
77#65400C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C24×C3×C5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—22no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—41no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5—21no—
98C2×C3×C22⋊D5—21no—
99C2×C3×C22⋊D5—44no—
100C2×C3×C22⋊D5D411yescharacteristic
101C22×C3×Dic5—21no—
102C22×C3×Dic5—21no—
103C22×C3×Dic5—21no—
104C3×#711—22no—
105C3×#711—41no—
106C3×D4×D5—22no—
107C3×D4×D5—41no—
108C2×C3×D20C2311yescharacteristic
109C2×C3×C4×D5C2311yescharacteristic
110C2×C3×Dic10C2311yescharacteristic
111C3×C5×D8—22no—
112C3×C5×D8—22no—
113C3×C5×D8—22no—
114C3×C5×D8D414yescomplemented
115C2×C3×C5×C8—22no—
116C2×C3×C5×C8C2311yescharacteristic
117C2×C3×C5×C8C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5—21no—
121C3×C22⋊Dic5—21no—
122C3×C22⋊Dic5—21no—
123C3×C22⋊Dic5—21no—
124C3×C22⋊Dic5—21no—
125C3×C22⋊Dic5D411yescharacteristic
126C3×#687—22no—
127C3×#687—41no—
128C3×#686—22no—
129C3×#686—41no—
130C3×#685—21no—
131C3×#685D411yescharacteristic
132C3×C4⋊Dic5C2311yescharacteristic
133C3×C4⋊Dic5C2311yescharacteristic
134C3×#683—21no—
135C3×#683D411yescharacteristic
136C3×C4×Dic5C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C3×#677—22no—
140C3×#676—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×D8D511yescharacteristic, complemented
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×#447—51no—
154C3×#442—51no—
155C3×#435—51no—
156C22×C5×D4C22×C311yescharacteristic
157C22×C5×D4C22×C311yescharacteristic, complemented
158C22×C22⋊D5—21no—
159C2×#711C22×C311yescharacteristic, complemented
160C2×D4×D5C22×C311yescharacteristic, complemented
161C2×C5×D8—24no—
162C2×C5×D8C22×C311yescharacteristic
163C2×C5×D8C22×C311yescharacteristic
164C2×C5×D8C22×C311yescharacteristic, complemented
165C2×C5×D8C22×C311yescharacteristic, complemented
166C22×C5×C8C22×C311yescharacteristic, complemented
167#4099—21no—
168#4099—21no—
169C2×C22⋊Dic5—21no—
170#4086C22×C311yescharacteristic, complemented
171#4085—21no—
172#4085—21no—
173#4084C22×C311yescharacteristic, complemented
174#4084C22×C311yescharacteristic, complemented
175#4083—21no—
176#4082C22×C311yescharacteristic, complemented
177#4081—21no—
178D4×Dic5C22×C311yescharacteristic, complemented
179D4×Dic5C22×C311yescharacteristic, complemented
180C2×#687C22×C311yescharacteristic, complemented
181C2×#687C22×C311yescharacteristic, complemented
182C2×#686C22×C311yescharacteristic, complemented
183C2×#686C22×C311yescharacteristic, complemented
184#4076C22×C311yescharacteristic
185C4×C22⋊D5C22×C311yescharacteristic
186#4070C22×C311yescharacteristic, complemented
187#4057—24no—
188C2×#677C22×C311yescharacteristic, complemented
189C2×#676C22×C311yescharacteristic, complemented
190#3964C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194C22⋊#168C22×C311yescharacteristic, complemented
195#3953C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic, complemented
197#3949C22×C311yescharacteristic, complemented
198#3948C22×C311yescharacteristic, complemented
199#3947C22×C311yescharacteristic, complemented
200#3946C22×C311yescharacteristic, complemented
201#3264—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—21no—
206C23×C3×C5—42no—
207C23×C3×C5—42no—
208C23×C3×C5—42no—
209C23×C3×C5—42no—
210C23×C3×C5—81no—
211C23×C3×C5—81no—
212C23×C3×C5C2×D411yescharacteristic
213C22×C3×D5—21no—
214C22×C3×D5—42no—
215C22×C3×D5—42no—
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—21no—
224C3×C5×D4—42no—
225C3×C5×D4—42no—
226C3×C5×D4C2×D412yes—
227C3×C5×D4C2×D412yescomplemented
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5C2×D411yescharacteristic
231C2×C3×C4×C5C2411yescharacteristic
232C3×C22⋊D5—22no—
233C3×C22⋊D5—42no—
234C3×C22⋊D5—42no—
235C3×C22⋊D5—42no—
236C3×C22⋊D5—42no—
237C3×C22⋊D5—42no—
238C3×C22⋊D5—81no—
239C3×C22⋊D5—81no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—42no—
244C2×C3×Dic5—42no—
245C2×C3×Dic5—81no—
246C2×C3×Dic5C2×D411yescharacteristic
247C2×C3×Dic5C2×D411yescharacteristic
248C2×C3×Dic5C2×D411yescharacteristic
249C3×D20—21no—
250C3×D20—21no—
251C3×C4×D5—21no—
252C3×C4×D5—21no—
253C3×Dic10—21no—
254C3×Dic10—21no—
255C3×C5×C8—21no—
256C3×C5×C8C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×C3×#41—51no—
260C22×C3×D4—51no—
261C22×C3×D4—101no—
262C22×C3×D4C2×D511yescharacteristic
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—24no—
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8C2×D511yescharacteristic
272C2×C3×D8C2×D511yescharacteristic
273C2×C3×D8C2×D511yescharacteristic, complemented
274C2×C3×D8C2×D511yescharacteristic, complemented
275C2×C3×M16—51no—
276C22×C3×C8C2×D511yescharacteristic, complemented
277C3×#127—51no—
278C3×#124—51no—
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×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×#102—51no—
300C3×#102—51no—
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97—51no—
304C24×C5—21no—
305C24×C5—21no—
306C23×D5—21no—
307C2×C5×D4—22no—
308C2×C5×D4—22no—
309C2×C5×D4—21no—
310C2×C5×D4—21no—
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4C23×C311yescharacteristic
314C2×C5×D4C23×C311yescharacteristic
315C2×C5×D4C23×C311yescharacteristic
316C2×C5×D4C23×C311yescharacteristic
317C22×C4×C5C23×C311yescharacteristic
318C2×C22⋊D5—21no—
319C2×C22⋊D5—21no—
320C2×C22⋊D5—21no—
321C2×C22⋊D5—21no—
322C2×C22⋊D5—21no—
323C2×C22⋊D5—21no—
324C2×C22⋊D5—21no—
325C2×C22⋊D5—44no—
326C2×C22⋊D5C3×D411yescharacteristic
327C22×Dic5—21no—
328C22×Dic5—21no—
329C22×Dic5—21no—
330#711—22no—
331#711—41no—
332D4×D5—22no—
333D4×D5—41no—
334C2×D20C23×C311yescharacteristic
335C2×C4×D5C23×C311yescharacteristic
336C2×Dic10C23×C311yescharacteristic
337C5×D8—22no—
338C5×D8—22no—
339C5×D8—22no—
340C5×D8C3×D414yescomplemented
341C2×C5×C8—22no—
342C2×C5×C8C23×C311yescharacteristic
343C2×C5×C8C23×C311yescharacteristic
344C22⋊Dic5—21no—
345C22⋊Dic5—21no—
346C22⋊Dic5—21no—
347C22⋊Dic5—21no—
348C22⋊Dic5—21no—
349C22⋊Dic5—21no—
350C22⋊Dic5—21no—
351C22⋊Dic5C3×D411yescharacteristic
352#687—22no—
353#687—41no—
354#686—22no—
355#686—41no—
356#685—21no—
357#685C3×D411yescharacteristic
358C4⋊Dic5C23×C311yescharacteristic
359C4⋊Dic5C23×C311yescharacteristic
360#683—21no—
361#683C3×D411yescharacteristic
362C4×Dic5C23×C311yescharacteristic
363C2×#168C23×C311yescharacteristic
364C2×#168C23×C311yescharacteristic
365#677—22no—
366#676—22no—
367C2×AGL(1,ℤ/8)—51no—
368C22×D8C3×D511yescharacteristic, complemented
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#447—51no—
380#442—51no—
381#435—51no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—22no—
385C22×C3×C5—22no—
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—41no—
395C22×C3×C5—41no—
396C22×C3×C5—84no—
397C22×C3×C5—84no—
398C22×C3×C5AGL(1,ℤ/8)12yescomplemented
399C22×C3×C5C22×D411yescharacteristic
400C2×C3×D5—21no—
401C2×C3×D5—21no—
402C2×C3×D5—21no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5C22×D411yescharacteristic
409C3×C4×C5H(5,𝔽2)11yescharacteristic
410C3×Dic5—21no—
411C3×Dic5—21no—
412C3×Dic5—21no—
413C3×Dic5—41no—
414C3×Dic5—41no—
415C3×Dic5—41no—
416C24×C3—21no—
417C24×C3—21no—
418C24×C3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8—51no—
422C2×C3×D4—22no—
423C2×C3×D4—22no—
424C2×C3×D4—21no—
425C2×C3×D4—21no—
426C2×C3×D4—41no—
427C2×C3×D4—41no—
428C2×C3×D4—51no—
429C2×C3×D4—51no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—101no—
433C2×C3×D4—102no—
434C2×C3×D4—101no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—201no—
439C2×C3×D4—204no—
440C2×C3×D4C22×D511yescharacteristic
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—22no—
454C3×D8—22no—
455C3×D8—102no—
456C3×D8—201no—
457C3×D8C22⋊D514yescomplemented
458C3×M16—102no—
459C2×C3×C8—22no—
460C2×C3×C8—51no—
461C2×C3×C8—51no—
462C2×C3×C8C22×D511yescharacteristic
463C2×C3×C8C22×D511yescharacteristic
464C3×C4⋊C4—51no—
465C3×C4⋊C4—51no—
466C3×C4⋊C4—51no—
467C3×C4⋊C4—101no—
468C3×C22⋊C4—51no—
469C3×C22⋊C4—51no—
470C3×C22⋊C4—101no—
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—21no—
483C23×C5—42no—
484C23×C5—42no—
485C23×C5—42no—
486C23×C5—42no—
487C23×C5—81no—
488C23×C5—81no—
489C23×C5C2×C3×D411yescharacteristic
490C22×D5—21no—
491C22×D5—42no—
492C22×D5—42no—
493C22×D5—81no—
494C22×D5C2×C3×D411yescharacteristic
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—21no—
501C5×D4—42no—
502C5×D4—42no—
503C5×D4C2×C3×D412yes—
504C5×D4C2×C3×D412yescomplemented
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5C2×C3×D411yescharacteristic
508C2×C4×C5C24×C311yescharacteristic
509C22⋊D5—22no—
510C22⋊D5—42no—
511C22⋊D5—42no—
512C22⋊D5—42no—
513C22⋊D5—42no—
514C22⋊D5—42no—
515C22⋊D5—81no—
516C22⋊D5—81no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—42no—
521C2×Dic5—42no—
522C2×Dic5—81no—
523C2×Dic5C2×C3×D411yescharacteristic
524C2×Dic5C2×C3×D411yescharacteristic
525C2×Dic5C2×C3×D411yescharacteristic
526D20—21no—
527D20—21no—
528C4×D5—21no—
529C4×D5—21no—
530Dic10—21no—
531Dic10—21no—
532C5×C8—21no—
533C5×C8C2×C3×D412yescomplemented
534#168—21no—
535#168—21no—
536C2×#41—51no—
537C22×D4—51no—
538C22×D4—101no—
539C22×D4C2×C3×D511yescharacteristic
540C22×D4C2×C3×D511yescharacteristic, complemented
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—51no—
545C2×D8—24no—
546C2×D8—51no—
547C2×D8—51no—
548C2×D8C2×C3×D511yescharacteristic
549C2×D8C2×C3×D511yescharacteristic
550C2×D8C2×C3×D511yescharacteristic, complemented
551C2×D8C2×C3×D511yescharacteristic, complemented
552C2×M16—51no—
553C22×C8C2×C3×D511yescharacteristic, complemented
554#127—51no—
555#124—51no—
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×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#102—51no—
577#102—51no—
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97—51no—
581C2×C3×C5—22no—
582C2×C3×C5—42no—
583C2×C3×C5—42no—
584C2×C3×C5—81no—
585C2×C3×C5—81no—
586C2×C3×C5D4211yescharacteristic
587C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
588C2×C3×C5#57611yescharacteristic
589C3×D5—41no—
590C3×D5—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—42no—
596C23×C3—42no—
597C23×C3—42no—
598C23×C3—42no—
599C23×C3—51no—
600C23×C3—81no—
601C23×C3—81no—
602C23×C3—101no—
603C23×C3—202no—
604C23×C3—202no—
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—21no—
615C3×D4—42no—
616C3×D4—42no—
617C3×D4—102no—
618C3×D4—101no—
619C3×D4—101no—
620C3×D4—202no—
621C3×D4—202no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—401no—
626C3×D4—401no—
627C3×D4C2×C22⋊D512yes—
628C3×D4C2×C22⋊D512yescomplemented
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—51no—
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—202no—
641C2×C3×C4—401no—
642C2×C3×C4D4×D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—101no—
646C3×C8—101no—
647C3×C8C2×C22⋊D512yescomplemented
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—22no—
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—41no—
661C22×C5—41no—
662C22×C5—84no—
663C22×C5—84no—
664C22×C5C3×AGL(1,ℤ/8)12yescomplemented
665C22×C5C22×C3×D411yescharacteristic
666C2×D5—21no—
667C2×D5—21no—
668C2×D5—21no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—41no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5C22×C3×D411yescharacteristic
675C4×C5C3×H(5,𝔽2)11yescharacteristic
676Dic5—21no—
677Dic5—21no—
678Dic5—21no—
679Dic5—41no—
680Dic5—41no—
681Dic5—41no—
682C24—21no—
683C24—21no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—41no—
694C2×D4—51no—
695C2×D4—51no—
696C2×D4—101no—
697C2×D4—101no—
698C2×D4—101no—
699C2×D4—102no—
700C2×D4—101no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—201no—
705C2×D4—204no—
706C2×D4C22×C3×D511yescharacteristic
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—22no—
720D8—22no—
721D8—102no—
722D8—201no—
723D8C3×C22⋊D514yescomplemented
724M16—102no—
725C2×C8—22no—
726C2×C8—51no—
727C2×C8—51no—
728C2×C8C22×C3×D511yescharacteristic
729C2×C8C22×C3×D511yescharacteristic
730C4⋊C4—51no—
731C4⋊C4—51no—
732C4⋊C4—51no—
733C4⋊C4—101no—
734C22⋊C4—51no—
735C22⋊C4—51no—
736C22⋊C4—101no—
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—22no—
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—41no—
759C22×C3—41no—
760C22×C3—84no—
761C22×C3—84no—
762C22×C3—101no—
763C22×C3—101no—
764C22×C3—101no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3—201no—
768C22×C3—404no—
769C22×C3#405712yescomplemented
770C22×C3C2×D4×D511yescharacteristic
771C3×C4—21no—
772C3×C4—101no—
773C3×C4—101no—
774C3×C4—101no—
775C3×C4—201no—
776C3×C4—201no—
777C3×C4—201no—
778C3×C4#414411yescharacteristic
779C3×C4C22×C22⋊D511yescharacteristic
780C2×C5—22no—
781C2×C5—42no—
782C2×C5—42no—
783C2×C5—81no—
784C2×C5—81no—
785C2×C5C3×D4211yescharacteristic
786C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
787C2×C5C3×#57611yescharacteristic
788D5—41no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—51no—
799C23—81no—
800C23—81no—
801C23—101no—
802C23—202no—
803C23—202no—
804C23—401no—
805C23C3×D4×D511yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—42no—
815D4—42no—
816D4—102no—
817D4—101no—
818D4—101no—
819D4—202no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—401no—
825D4—401no—
826D4C2×C3×C22⋊D512yes—
827D4C2×C3×C22⋊D512yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—51no—
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—202no—
840C2×C4—401no—
841C2×C4C3×D4×D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—101no—
845C8—101no—
846C8C2×C3×C22⋊D512yescomplemented
847C2×C3—22no—
848C2×C3—42no—
849C2×C3—42no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—201no—
853C2×C3—401no—
854C2×C3C2×#405711yescharacteristic
855C2×C3#6609111yescharacteristic
856C2×C3D4×C22⋊D511yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—84no—
873C22—84no—
874C22—101no—
875C22—101no—
876C22—101no—
877C22—201no—
878C22—201no—
879C22—201no—
880C22—404no—
881C22C3×#405712yescomplemented
882C22C2×C3×D4×D511yescharacteristic
883C4—21no—
884C4—101no—
885C4—101no—
886C4—101no—
887C4—201no—
888C4—201no—
889C4—201no—
890C4C3×#414411yescharacteristic
891C4C22×C3×C22⋊D511yescharacteristic
892C3#1061556811yescharacteristic, direct product factor, Sylow
893C2—22no—
894C2—42no—
895C2—42no—
896C2—81no—
897C2—81no—
898C2—201no—
899C2—401no—
900C2C2×C3×#405711yescharacteristic
901C2C3×#6609111yescharacteristic
902C2C3×D4×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×D8C2
socleC22×C3×C5C22×D4
hypercenterC22×C3×D8D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×D8C2semidirect
2. C3×#66140C2semidirect
3. C3×D4×C22⋊D5C2semidirect
4. C2×C3×#4057C2semidirect
5. C3×#65507C2semidirect
6. C3×#65506C2semidirect
7. C3×#65448C2semidirect
8. C3×#65447C2semidirect
9. C3×#65445C2semidirect
10. C3×#65443C2semidirect
11. C3×#65442C2semidirect
12. C3×#65441C2semidirect
13. C3×#65439C2semidirect
14. C3×#65403C2semidirect
15. C3×#65400C2semidirect
16. #10615568C3direct (N × H)
18. C22×C3×C5×D4C22semidirect
20. C2×C3×#711C22semidirect
21. C2×C3×D4×D5C22semidirect
25. C2×C3×C5×D8C22semidirect
26. C2×C3×C5×D8C22semidirect
27. C22×C3×C5×C8C22semidirect
31. C3×#4086C22semidirect
34. C3×#4084C22semidirect
35. C3×#4084C22semidirect
37. C3×#4082C22semidirect
39. C3×D4×Dic5C22semidirect
40. C3×D4×Dic5C22semidirect
41. C2×C3×#687C22semidirect
42. C2×C3×#687C22semidirect
43. C2×C3×#686C22semidirect
44. C2×C3×#686C22semidirect
47. C3×#4070C22semidirect
49. C2×C3×#677C22semidirect
50. C2×C3×#676C22semidirect
51. C3×#3964C22semidirect
52. C3×#3964C22semidirect
53. C3×#3964C22semidirect
54. C3×#3964C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3953C22semidirect
57. C3×#3952C22semidirect
58. C3×#3949C22semidirect
59. C3×#3948C22semidirect
60. C3×#3947C22semidirect
61. C3×#3946C22semidirect
63. C22×C5×D8C2×C3semidirect
64. #66140C2×C3semidirect
65. D4×C22⋊D5C2×C3semidirect
66. C2×#4057C2×C3semidirect
67. #65507C2×C3semidirect
68. #65506C2×C3semidirect
69. #65448C2×C3semidirect
70. #65447C2×C3semidirect
71. #65445C2×C3semidirect
72. #65443C2×C3semidirect
73. #65442C2×C3semidirect
74. #65441C2×C3semidirect
75. #65439C2×C3semidirect
76. #65403C2×C3semidirect
77. #65400C2×C3semidirect
114. C3×C5×D8D4semidirect
142. C22×C3×D8D5semidirect
157. C22×C5×D4C22×C3semidirect
159. C2×#711C22×C3semidirect
160. C2×D4×D5C22×C3semidirect
164. C2×C5×D8C22×C3semidirect
165. C2×C5×D8C22×C3semidirect
166. C22×C5×C8C22×C3semidirect
170. #4086C22×C3semidirect
173. #4084C22×C3semidirect
174. #4084C22×C3semidirect
176. #4082C22×C3semidirect
178. D4×Dic5C22×C3semidirect
179. D4×Dic5C22×C3semidirect
180. C2×#687C22×C3semidirect
181. C2×#687C22×C3semidirect
182. C2×#686C22×C3semidirect
183. C2×#686C22×C3semidirect
186. #4070C22×C3semidirect
188. C2×#677C22×C3semidirect
189. C2×#676C22×C3semidirect
190. #3964C22×C3semidirect
191. #3964C22×C3semidirect
192. #3964C22×C3semidirect
193. #3964C22×C3semidirect
194. C22⋊#168C22×C3semidirect
195. #3953C22×C3semidirect
196. #3952C22×C3semidirect
197. #3949C22×C3semidirect
198. #3948C22×C3semidirect
199. #3947C22×C3semidirect
200. #3946C22×C3semidirect
227. C3×C5×D4C2×D4semidirect
256. C3×C5×C8C2×D4semidirect
263. C22×C3×D4C2×D5semidirect
273. C2×C3×D8C2×D5semidirect
274. C2×C3×D8C2×D5semidirect
276. C22×C3×C8C2×D5semidirect
340. C5×D8C3×D4semidirect
368. C22×D8C3×D5semidirect
398. C22×C3×C5AGL(1,ℤ/8)semidirect
457. C3×D8C22⋊D5semidirect
504. C5×D4C2×C3×D4semidirect
533. C5×C8C2×C3×D4semidirect
540. C22×D4C2×C3×D5semidirect
550. C2×D8C2×C3×D5semidirect
551. C2×D8C2×C3×D5semidirect
553. C22×C8C2×C3×D5semidirect
628. C3×D4C2×C22⋊D5semidirect
647. C3×C8C2×C22⋊D5semidirect
664. C22×C5C3×AGL(1,ℤ/8)semidirect
723. D8C3×C22⋊D5semidirect
745. C3×C5#3264semidirect
769. C22×C3#4057semidirect
827. D4C2×C3×C22⋊D5semidirect
846. C8C2×C3×C22⋊D5semidirect
857. C5C3×#3264semidirect
881. C22C3×#4057semidirect
892. C3#10615568direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×D82
C3×#661402
C3×D4×C22⋊D52
C2×C3×#40572
C3×#655072
C3×#655062
C3×#654482
C3×#654472
C3×#654452
C3×#654432
C3×#654422
C3×#654412
C3×#654392
C3×#654032
C3×#654002
#106155683
C3×#32645