Finite Group Databasebeta

← C3×#10615718 #14453686

Subgroups — C3×#10615718 #14453686

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#137C211yesmaximal, characteristic, complemented
2C3×#66163C211yesmaximal, characteristic
3C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×C3×D5×SD16C211yesmaximal, characteristic, complemented
5C3×#65528C211yesmaximal, characteristic, complemented
6C3×#65516C211yesmaximal, characteristic, complemented
7C3×#65479C211yesmaximal, characteristic, complemented
8C3×#65477C211yesmaximal, characteristic, complemented
9C3×#65475C211yesmaximal, characteristic, complemented
10C3×#65474C211yesmaximal, characteristic, complemented
11C3×#65458C211yesmaximal, characteristic, complemented
12C3×#65453C211yesmaximal, characteristic, complemented
13C3×#65451C211yesmaximal, characteristic, complemented
14C3×#65423C211yesmaximal, characteristic, complemented
15C3×#65416C211yesmaximal, characteristic, complemented
16#10615718C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C2×C3×Q8×D5C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic
21C3×C5×#137—24no—
22C2×C3×C5×Q16C2211yescharacteristic, complemented
23C2×C3×C5×Q16C2211yescharacteristic, complemented
24C2×C3×C5×SD16C2211yescharacteristic
25C2×C3×C5×SD16C2211yescharacteristic
26C2×C3×C5×M16C2211yescharacteristic, complemented
27C3×#4093C2211yescharacteristic
28C3×#4092—21no—
29C3×#4092C2211yescharacteristic
30C3×#4092C2211yescharacteristic
31C3×Q8×Dic5C2211yescharacteristic, complemented
32C3×#4090—21no—
33C3×#4090C2211yescharacteristic, complemented
34C2×C3×#689C2211yescharacteristic, complemented
35C2×C3×#688C2211yescharacteristic
36C2×C3×#688C2211yescharacteristic
37C3×#4085—21no—
38C3×#4083—21no—
39C3×D4×Dic5C2211yescharacteristic
40C2×C3×#687C2211yescharacteristic
41C3×#4076C2211yescharacteristic
42C3×#4075—21no—
43C3×C4×C22⋊D5—21no—
44C3×C4×C22⋊D5C2211yescharacteristic
45C2×C3×#685—21no—
46C3×#4070—21no—
47C3×#4070C2211yescharacteristic, complemented
48C3×D5×SD16—24no—
49C2×C3×#677C2211yescharacteristic
50C2×C3×C8×D5C2211yescharacteristic
51C3×#3967C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3967C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic
57C3×#3952C2211yescharacteristic
58C3×#3950C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3947C2211yescharacteristic, complemented
61C3×#3946C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63C2×C5×#137C2×C311yescharacteristic, complemented
64#66163C2×C311yescharacteristic
65Q8×C22⋊D5C2×C311yescharacteristic, complemented
66C2×D5×SD16C2×C311yescharacteristic, complemented
67#65528C2×C311yescharacteristic, complemented
68#65516C2×C311yescharacteristic, complemented
69#65479C2×C311yescharacteristic, complemented
70#65477C2×C311yescharacteristic, complemented
71#65475C2×C311yescharacteristic, complemented
72#65474C2×C311yescharacteristic, complemented
73#65458C2×C311yescharacteristic, complemented
74#65453C2×C311yescharacteristic, complemented
75#65451C2×C311yescharacteristic, complemented
76#65423C2×C311yescharacteristic, complemented
77#65416C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8—21no—
82C2×C3×C5×Q8—22no—
83C2×C3×C5×Q8—41no—
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5D411yescharacteristic
95C22×C3×Dic5—21no—
96C3×Q8×D5—22no—
97C3×Q8×D5—41no—
98C3×D4×D5—22no—
99C3×D4×D5—41no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5C2311yescharacteristic
103C2×C3×Dic10—21no—
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×Q16—22no—
106C3×C5×Q16—22no—
107C3×C5×SD16—22no—
108C3×C5×SD16D414yescomplemented
109C3×C5×M16—22no—
110C2×C3×C5×C8C2311yescharacteristic
111C2×C3×C5×C8C2311yescharacteristic
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5D411yescharacteristic
115C3×#689—41no—
116C3×#688—22no—
117C3×#688—41no—
118C3×#687—22no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685D411yescharacteristic
125C3×C4⋊Dic5—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C3×C4⋊Dic5C2311yescharacteristic
128C3×#683—21no—
129C3×#683—21no—
130C3×#683—21no—
131C3×#683—21no—
132C3×#683—21no—
133C3×#683D411yescharacteristic
134C3×C4×Dic5—21no—
135C3×C4×Dic5C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C3×#677—22no—
139C3×C8×D5—22no—
140C2×C3×#137D511yescharacteristic, complemented
141C22×C3×SD16—51no—
142C3×D4×Q8—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#468—51no—
146C3×#467—51no—
147C3×#464—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#451—51no—
151C3×#450—51no—
152C3×#448—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C22×C5×Q8C22×C311yescharacteristic, complemented
157C2×Q8×D5C22×C311yescharacteristic
158C2×D4×D5C22×C311yescharacteristic
159C5×#137—24no—
160C2×C5×Q16C22×C311yescharacteristic, complemented
161C2×C5×Q16C22×C311yescharacteristic, complemented
162C2×C5×SD16C22×C311yescharacteristic
163C2×C5×SD16C22×C311yescharacteristic
164C2×C5×M16C22×C311yescharacteristic, complemented
165#4093C22×C311yescharacteristic
166#4092—21no—
167#4092C22×C311yescharacteristic
168#4092C22×C311yescharacteristic
169Q8×Dic5C22×C311yescharacteristic, complemented
170#4090—21no—
171#4090C22×C311yescharacteristic, complemented
172C2×#689C22×C311yescharacteristic, complemented
173C2×#688C22×C311yescharacteristic
174C2×#688C22×C311yescharacteristic
175#4085—21no—
176#4083—21no—
177D4×Dic5C22×C311yescharacteristic
178C2×#687C22×C311yescharacteristic
179#4076C22×C311yescharacteristic
180#4075—21no—
181C4×C22⋊D5—21no—
182C4×C22⋊D5C22×C311yescharacteristic
183C2×#685—21no—
184#4070—21no—
185#4070C22×C311yescharacteristic, complemented
186D5×SD16—24no—
187C2×#677C22×C311yescharacteristic
188C2×C8×D5C22×C311yescharacteristic
189#3967C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3967C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic
193C22⋊#168C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic
195#3952C22×C311yescharacteristic
196#3950C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3947C22×C311yescharacteristic, complemented
199#3946C22×C311yescharacteristic, complemented
200#3266—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—42no—
205C22×C3×D5—42no—
206C22×C3×D5—81no—
207C22×C3×D5C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×Q8—42no—
214C3×C5×Q8C2×D412yes—
215C3×C5×D4—21no—
216C3×C5×D4—42no—
217C3×C5×D4C2×D412yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—42no—
224C2×C3×C4×C5—42no—
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227C3×C22⋊D5—22no—
228C3×C22⋊D5—42no—
229C3×C22⋊D5—81no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—81no—
234C2×C3×Dic5C2×D411yescharacteristic
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—21no—
238C3×D20—21no—
239C3×C4×D5—21no—
240C3×C4×D5—21no—
241C3×C4×D5—42no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—42no—
245C3×C5×C8—21no—
246C3×C5×C8C2×D412yes—
247C3×#168—21no—
248C3×#168—21no—
249C2×C3×#41C2×D511yescharacteristic
250C22×C3×Q8—51no—
251C22×C3×Q8C2×D511yescharacteristic, complemented
252C22×C3×D4—51no—
253C3×#137—24no—
254C2×C3×Q16—51no—
255C2×C3×Q16C2×D511yescharacteristic, complemented
256C2×C3×Q16C2×D511yescharacteristic, complemented
257C2×C3×SD16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—104no—
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×SD16C2×D511yescharacteristic
264C2×C3×M16C2×D511yescharacteristic, complemented
265C22×C3×C8—51no—
266C3×C4⋊Q8—51no—
267C3×C4⋊Q8—101no—
268C3×#124—51no—
269C3×#123—101no—
270C3×C22⋊Q8—51no—
271C3×C22⋊Q8—51no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—101no—
274C3×C22⋊Q8—101no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#120—101no—
278C3×C4×Q8—51no—
279C3×C4×D4—51no—
280C3×C4×D4—51no—
281C3×C4×D4—101no—
282C2×C3×C22⋊C4—101no—
283C3×#107—51no—
284C3×C4⋊C8—51no—
285C3×#103—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×C22⋊C8—51no—
292C3×C22⋊C8—51no—
293C3×#97—51no—
294C23×D5—21no—
295C5×#41—22no—
296C5×#41—41no—
297C2×C5×Q8—21no—
298C2×C5×Q8—22no—
299C2×C5×Q8—41no—
300C2×C5×Q8C23×C311yescharacteristic
301C2×C5×Q8C23×C311yescharacteristic
302C2×C5×Q8C23×C311yescharacteristic
303C2×C5×D4—21no—
304C2×C5×D4C23×C311yescharacteristic
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5C23×C311yescharacteristic
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5C3×D411yescharacteristic
311C22×Dic5—21no—
312Q8×D5—22no—
313Q8×D5—41no—
314D4×D5—22no—
315D4×D5—41no—
316C2×D20C23×C311yescharacteristic
317C2×C4×D5—21no—
318C2×C4×D5C23×C311yescharacteristic
319C2×Dic10—21no—
320C2×Dic10C23×C311yescharacteristic
321C5×Q16—22no—
322C5×Q16—22no—
323C5×SD16—22no—
324C5×SD16C3×D414yescomplemented
325C5×M16—22no—
326C2×C5×C8C23×C311yescharacteristic
327C2×C5×C8C23×C311yescharacteristic
328C22⋊Dic5—21no—
329C22⋊Dic5—21no—
330C22⋊Dic5C3×D411yescharacteristic
331#689—41no—
332#688—22no—
333#688—41no—
334#687—22no—
335#685—21no—
336#685—21no—
337#685—21no—
338#685—21no—
339#685—21no—
340#685C3×D411yescharacteristic
341C4⋊Dic5—21no—
342C4⋊Dic5C23×C311yescharacteristic
343C4⋊Dic5C23×C311yescharacteristic
344#683—21no—
345#683—21no—
346#683—21no—
347#683—21no—
348#683—21no—
349#683C3×D411yescharacteristic
350C4×Dic5—21no—
351C4×Dic5C23×C311yescharacteristic
352C2×#168C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354#677—22no—
355C8×D5—22no—
356C2×#137C3×D511yescharacteristic, complemented
357C22×SD16—51no—
358D4×Q8—51no—
359#546—51no—
360#497—51no—
361#468—51no—
362#467—51no—
363#464—51no—
364#461—51no—
365#452—51no—
366#451—51no—
367#450—51no—
368#448—51no—
369#440—51no—
370#435—51no—
371C22×C3×C5—22no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5C22×D411yescharacteristic
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—84no—
384C2×C3×D5#13712yescomplemented
385C3×C4×C5—22no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391C3×Dic5—21no—
392C3×Dic5—21no—
393C3×Dic5—21no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—101no—
398C3×#41—22no—
399C3×#41—41no—
400C2×C3×Q8—21no—
401C2×C3×Q8—22no—
402C2×C3×Q8—41no—
403C2×C3×Q8—51no—
404C2×C3×Q8—101no—
405C2×C3×Q8—102no—
406C2×C3×Q8—201no—
407C2×C3×Q8C22×D511yescharacteristic
408C2×C3×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—21no—
411C2×C3×D4—51no—
412C2×C3×D4—51no—
413C2×C3×D4—101no—
414C2×C3×D4—102no—
415C2×C3×D4—101no—
416C2×C3×D4—201no—
417C2×C3×D4C22×D511yescharacteristic
418C22×C3×C4—21no—
419C22×C3×C4—21no—
420C22×C3×C4—51no—
421C22×C3×C4—101no—
422C22×C3×C4—101no—
423C22×C3×C4C22×D511yescharacteristic
424C3×Q16—22no—
425C3×Q16—22no—
426C3×Q16—201no—
427C3×SD16—22no—
428C3×SD16—102no—
429C3×SD16—102no—
430C3×SD16—102no—
431C3×SD16—201no—
432C3×SD16C22⋊D514yescomplemented
433C3×M16—22no—
434C2×C3×C8—51no—
435C2×C3×C8—51no—
436C2×C3×C8—102no—
437C2×C3×C8C22×D511yescharacteristic
438C2×C3×C8C22×D511yescharacteristic
439C3×C4⋊C4—51no—
440C3×C4⋊C4—51no—
441C3×C4⋊C4—51no—
442C3×C4⋊C4—101no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C22⋊C4—51no—
449C3×C22⋊C4—51no—
450C3×C22⋊C4—101no—
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C42—51no—
458C3×C42—101no—
459C23×C5—21no—
460C23×C5C2×C3×D411yescharacteristic
461C22×D5—21no—
462C22×D5—42no—
463C22×D5—42no—
464C22×D5—81no—
465C22×D5C2×C3×D411yescharacteristic
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—21no—
470C5×Q8—21no—
471C5×Q8—42no—
472C5×Q8C2×C3×D412yes—
473C5×D4—21no—
474C5×D4—42no—
475C5×D4C2×C3×D412yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—42no—
482C2×C4×C5—42no—
483C2×C4×C5C2×C3×D411yescharacteristic
484C2×C4×C5C24×C311yescharacteristic
485C22⋊D5—22no—
486C22⋊D5—42no—
487C22⋊D5—81no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—81no—
492C2×Dic5C2×C3×D411yescharacteristic
493C2×Dic5C2×C3×D411yescharacteristic
494C2×Dic5C2×C3×D411yescharacteristic
495D20—21no—
496D20—21no—
497C4×D5—21no—
498C4×D5—21no—
499C4×D5—42no—
500Dic10—21no—
501Dic10—21no—
502Dic10—42no—
503C5×C8—21no—
504C5×C8C2×C3×D412yes—
505#168—21no—
506#168—21no—
507C2×#41C2×C3×D511yescharacteristic
508C22×Q8—51no—
509C22×Q8C2×C3×D511yescharacteristic, complemented
510C22×D4—51no—
511#137—24no—
512C2×Q16—51no—
513C2×Q16C2×C3×D511yescharacteristic, complemented
514C2×Q16C2×C3×D511yescharacteristic, complemented
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—104no—
520C2×SD16C2×C3×D511yescharacteristic
521C2×SD16C2×C3×D511yescharacteristic
522C2×M16C2×C3×D511yescharacteristic, complemented
523C22×C8—51no—
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124—51no—
527#123—101no—
528C22⋊Q8—51no—
529C22⋊Q8—51no—
530C22⋊Q8—51no—
531C22⋊Q8—101no—
532C22⋊Q8—101no—
533#121—51no—
534#121—101no—
535#120—101no—
536C4×Q8—51no—
537C4×D4—51no—
538C4×D4—51no—
539C4×D4—101no—
540C2×C22⋊C4—101no—
541#107—51no—
542C4⋊C8—51no—
543#103—51no—
544#103—51no—
545#103—51no—
546#103—51no—
547#102—51no—
548#102—51no—
549C22⋊C8—51no—
550C22⋊C8—51no—
551#97—51no—
552C2×C3×C5—42no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557C3×D5—22no—
558C3×D5—81no—
559C23×C3—21no—
560C23×C3—51no—
561C23×C3—101no—
562C23×C3—202no—
563C23×C3—202no—
564C23×C3—401no—
565C23×C3D4×D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—42no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—202no—
575C3×Q8C2×C22⋊D512yes—
576C3×D4—21no—
577C3×D4—42no—
578C3×D4—102no—
579C3×D4—101no—
580C3×D4—101no—
581C3×D4—202no—
582C3×D4—401no—
583C3×D4C2×C22⋊D512yes—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4—51no—
592C2×C3×C4—51no—
593C2×C3×C4—51no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—202no—
600C2×C3×C4—401no—
601C2×C3×C4D4×D511yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603C3×C8—21no—
604C3×C8—101no—
605C3×C8—101no—
606C3×C8C2×C22⋊D512yes—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—22no—
610C22×C5—21no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5C22×C3×D411yescharacteristic
614C2×D5—21no—
615C2×D5—21no—
616C2×D5—41no—
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—84no—
620C2×D5C3×#13712yescomplemented
621C4×C5—22no—
622C4×C5—21no—
623C4×C5—41no—
624C4×C5—41no—
625C4×C5C22×C3×D411yescharacteristic
626C4×C5C3×H(5,𝔽2)11yescharacteristic
627Dic5—21no—
628Dic5—21no—
629Dic5—21no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—101no—
634#41—22no—
635#41—41no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—41no—
639C2×Q8—51no—
640C2×Q8—101no—
641C2×Q8—102no—
642C2×Q8—201no—
643C2×Q8C22×C3×D511yescharacteristic
644C2×Q8C22×C3×D511yescharacteristic
645C2×Q8C22×C3×D511yescharacteristic
646C2×D4—21no—
647C2×D4—51no—
648C2×D4—51no—
649C2×D4—101no—
650C2×D4—102no—
651C2×D4—101no—
652C2×D4—201no—
653C2×D4C22×C3×D511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—51no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4C22×C3×D511yescharacteristic
660Q16—22no—
661Q16—22no—
662Q16—201no—
663SD16—22no—
664SD16—102no—
665SD16—102no—
666SD16—102no—
667SD16—201no—
668SD16C3×C22⋊D514yescomplemented
669M16—22no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—102no—
673C2×C8C22×C3×D511yescharacteristic
674C2×C8C22×C3×D511yescharacteristic
675C4⋊C4—51no—
676C4⋊C4—51no—
677C4⋊C4—51no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4—101no—
683C4⋊C4—101no—
684C22⋊C4—51no—
685C22⋊C4—51no—
686C22⋊C4—101no—
687C22⋊C4—101no—
688C22⋊C4—101no—
689C22⋊C4—101no—
690C22⋊C4—101no—
691C22⋊C4—101no—
692C22⋊C4—101no—
693C42—51no—
694C42—101no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—22no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—52no—
703C22×C3—101no—
704C22×C3—101no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3—201no—
708C22×C3—404no—
709C22×C3C2×D4×D511yescharacteristic
710C3×C4—21no—
711C3×C4—22no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—101no—
715C3×C4—101no—
716C3×C4—101no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4#414411yescharacteristic
721C3×C4C22×C22⋊D511yescharacteristic
722C2×C5—42no—
723C2×C5—41no—
724C2×C5C3×D4211yescharacteristic
725C2×C5C2×C3×#13711yescharacteristic
726C2×C5C3×#57711yescharacteristic
727D5—22no—
728D5—81no—
729C23—21no—
730C23—51no—
731C23—101no—
732C23—202no—
733C23—202no—
734C23—401no—
735C23C3×D4×D511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—42no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8C2×C3×C22⋊D512yes—
746D4—21no—
747D4—42no—
748D4—102no—
749D4—101no—
750D4—101no—
751D4—202no—
752D4—401no—
753D4C2×C3×C22⋊D512yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—51no—
762C2×C4—51no—
763C2×C4—51no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—101no—
769C2×C4—202no—
770C2×C4—401no—
771C2×C4C3×D4×D511yescharacteristic
772C2×C4C23×C3×D511yescharacteristic
773C8—21no—
774C8—101no—
775C8—101no—
776C8C2×C3×C22⋊D512yes—
777C2×C3—41no—
778C2×C3—42no—
779C2×C3—102no—
780C2×C3—401no—
781C2×C3D5×#13711yescharacteristic
782C2×C3#6611211yescharacteristic
783C2×C3D4×C22⋊D511yescharacteristic
784C5C3×#326611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—52no—
792C22—101no—
793C22—101no—
794C22—201no—
795C22—201no—
796C22—201no—
797C22—404no—
798C22C2×C3×D4×D511yescharacteristic
799C4—21no—
800C4—22no—
801C4—41no—
802C4—41no—
803C4—101no—
804C4—101no—
805C4—101no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4C3×#414411yescharacteristic
810C4C22×C3×C22⋊D511yescharacteristic
811C3#1061571811yescharacteristic, direct product factor, Sylow
812C2—41no—
813C2—42no—
814C2—102no—
815C2—401no—
816C2C3×D5×#13711yescharacteristic
817C2C3×#6611211yescharacteristic
818C2C3×D4×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
prime radicalC3×#66163C2
hypercenterC2×C3×#137D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#137C2semidirect
3. C3×Q8×C22⋊D5C2semidirect
4. C2×C3×D5×SD16C2semidirect
5. C3×#65528C2semidirect
6. C3×#65516C2semidirect
7. C3×#65479C2semidirect
8. C3×#65477C2semidirect
9. C3×#65475C2semidirect
10. C3×#65474C2semidirect
11. C3×#65458C2semidirect
12. C3×#65453C2semidirect
13. C3×#65451C2semidirect
14. C3×#65423C2semidirect
15. C3×#65416C2semidirect
16. #10615718C3direct (N × H)
18. C22×C3×C5×Q8C22semidirect
22. C2×C3×C5×Q16C22semidirect
23. C2×C3×C5×Q16C22semidirect
26. C2×C3×C5×M16C22semidirect
31. C3×Q8×Dic5C22semidirect
33. C3×#4090C22semidirect
34. C2×C3×#689C22semidirect
47. C3×#4070C22semidirect
51. C3×#3967C22semidirect
52. C3×#3967C22semidirect
53. C3×#3967C22semidirect
55. C3×C22⋊#168C22semidirect
58. C3×#3950C22semidirect
59. C3×#3948C22semidirect
60. C3×#3947C22semidirect
61. C3×#3946C22semidirect
63. C2×C5×#137C2×C3semidirect
65. Q8×C22⋊D5C2×C3semidirect
66. C2×D5×SD16C2×C3semidirect
67. #65528C2×C3semidirect
68. #65516C2×C3semidirect
69. #65479C2×C3semidirect
70. #65477C2×C3semidirect
71. #65475C2×C3semidirect
72. #65474C2×C3semidirect
73. #65458C2×C3semidirect
74. #65453C2×C3semidirect
75. #65451C2×C3semidirect
76. #65423C2×C3semidirect
77. #65416C2×C3semidirect
108. C3×C5×SD16D4semidirect
140. C2×C3×#137D5semidirect
156. C22×C5×Q8C22×C3semidirect
160. C2×C5×Q16C22×C3semidirect
161. C2×C5×Q16C22×C3semidirect
164. C2×C5×M16C22×C3semidirect
169. Q8×Dic5C22×C3semidirect
171. #4090C22×C3semidirect
172. C2×#689C22×C3semidirect
185. #4070C22×C3semidirect
189. #3967C22×C3semidirect
190. #3967C22×C3semidirect
191. #3967C22×C3semidirect
193. C22⋊#168C22×C3semidirect
196. #3950C22×C3semidirect
197. #3948C22×C3semidirect
198. #3947C22×C3semidirect
199. #3946C22×C3semidirect
251. C22×C3×Q8C2×D5semidirect
255. C2×C3×Q16C2×D5semidirect
256. C2×C3×Q16C2×D5semidirect
264. C2×C3×M16C2×D5semidirect
324. C5×SD16C3×D4semidirect
356. C2×#137C3×D5semidirect
384. C2×C3×D5#137semidirect
432. C3×SD16C22⋊D5semidirect
509. C22×Q8C2×C3×D5semidirect
513. C2×Q16C2×C3×D5semidirect
514. C2×Q16C2×C3×D5semidirect
522. C2×M16C2×C3×D5semidirect
620. C2×D5C3×#137semidirect
668. SD16C3×C22⋊D5semidirect
695. C3×C5#3266semidirect
784. C5C3×#3266semidirect
811. C3#10615718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1372
C3×#661632
C3×Q8×C22⋊D52
C2×C3×D5×SD162
C3×#655282
C3×#655162
C3×#654792
C3×#654772
C3×#654752
C3×#654742
C3×#654582
C3×#654532
C3×#654512
C3×#654232
C3×#654162
#106157183
C3×#32665