Finite Group Databasebeta

← C3×#10615597 #14453704

Subgroups — C3×#10615597 #14453704

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
1C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
2C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
3C3×#66140C211yesmaximal, characteristic
4C2×C3×#4061C211yesmaximal, characteristic, complemented
5C3×#65517C211yesmaximal, characteristic, complemented
6C3×#65507C211yesmaximal, characteristic, complemented
7C3×#65463C211yesmaximal, characteristic, complemented
8C3×#65462C211yesmaximal, characteristic, complemented
9C3×#65459C211yesmaximal, characteristic, complemented
10C3×#65456C211yesmaximal, characteristic, complemented
11C3×#65455C211yesmaximal, characteristic, complemented
12C3×#65453C211yesmaximal, characteristic, complemented
13C3×#65451C211yesmaximal, characteristic, complemented
14C3×#65405C211yesmaximal, characteristic, complemented
15C3×#65400C211yesmaximal, characteristic, complemented
16#10615597C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic, complemented
20C2×C3×#711C2211yescharacteristic
21C2×C3×C5×SD16—24no—
22C2×C3×C5×SD16C2211yescharacteristic
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×SD16C2211yescharacteristic
25C2×C3×C5×SD16C2211yescharacteristic
26C22×C3×C5×C8C2211yescharacteristic
27C3×#4099—21no—
28C2×C3×C22⋊Dic5—21no—
29C3×#4092—21no—
30C3×#4092C2211yescharacteristic, complemented
31C3×Q8×Dic5C2211yescharacteristic, complemented
32C3×#4090—21no—
33C3×#4090C2211yescharacteristic, complemented
34C2×C3×#689C2211yescharacteristic, complemented
35C2×C3×#689C2211yescharacteristic, complemented
36C3×#4085—21no—
37C3×#4084C2211yescharacteristic
38C3×#4082C2211yescharacteristic
39C3×#4081—21no—
40C3×D4×Dic5C2211yescharacteristic
41C2×C3×#687C2211yescharacteristic
42C2×C3×#687C2211yescharacteristic
43C3×C4×C22⋊D5—21no—
44C3×C4×C22⋊D5C2211yescharacteristic
45C3×#4070—21no—
46C3×#4070C2211yescharacteristic
47C3×#4070C2211yescharacteristic
48C3×#4061—24no—
49C2×C3×Dic20C2211yescharacteristic, complemented
50C2×C3×#676C2211yescharacteristic, complemented
51C3×#3967C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic
54C3×#3964C2211yescharacteristic
55C3×C22⋊#168C2211yescharacteristic
56C3×#3952C2211yescharacteristic, complemented
57C3×#3950C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3947C2211yescharacteristic, complemented
61C3×#3946C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63C22×C5×SD16C2×C311yescharacteristic, complemented
64Q8×C22⋊D5C2×C311yescharacteristic, complemented
65#66140C2×C311yescharacteristic
66C2×#4061C2×C311yescharacteristic, complemented
67#65517C2×C311yescharacteristic, complemented
68#65507C2×C311yescharacteristic, complemented
69#65463C2×C311yescharacteristic, complemented
70#65462C2×C311yescharacteristic, complemented
71#65459C2×C311yescharacteristic, complemented
72#65456C2×C311yescharacteristic, complemented
73#65455C2×C311yescharacteristic, complemented
74#65453C2×C311yescharacteristic, complemented
75#65451C2×C311yescharacteristic, complemented
76#65405C2×C311yescharacteristic, complemented
77#65400C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C2×C3×C5×Q8—21no—
80C2×C3×C5×Q8—22no—
81C2×C3×C5×Q8—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5D411yescharacteristic
94C22×C3×Dic5—21no—
95C22×C3×Dic5—21no—
96C3×Q8×D5—22no—
97C3×Q8×D5—41no—
98C3×#711—22no—
99C3×#711—41no—
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5C2311yescharacteristic
102C2×C3×Dic10—21no—
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×SD16—22no—
106C3×C5×SD16—22no—
107C3×C5×SD16—22no—
108C3×C5×SD16D414yescomplemented
109C2×C3×C5×C8—22no—
110C2×C3×C5×C8C2311yescharacteristic
111C2×C3×C5×C8C2311yescharacteristic
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5—21no—
115C3×C22⋊Dic5—21no—
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5D411yescharacteristic
119C3×#689—22no—
120C3×#689—41no—
121C3×#687—22no—
122C3×#687—41no—
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×Dic20—22no—
139C3×#676—22no—
140C2×C3×#137—51no—
141C22×C3×SD16D511yescharacteristic, complemented
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—
155C22×C5×Q8C22×C311yescharacteristic
156C22×C5×D4C22×C311yescharacteristic
157C2×Q8×D5C22×C311yescharacteristic, complemented
158C2×#711C22×C311yescharacteristic
159C2×C5×SD16—24no—
160C2×C5×SD16C22×C311yescharacteristic
161C2×C5×SD16C22×C311yescharacteristic
162C2×C5×SD16C22×C311yescharacteristic
163C2×C5×SD16C22×C311yescharacteristic
164C22×C5×C8C22×C311yescharacteristic
165#4099—21no—
166C2×C22⋊Dic5—21no—
167#4092—21no—
168#4092C22×C311yescharacteristic, complemented
169Q8×Dic5C22×C311yescharacteristic, complemented
170#4090—21no—
171#4090C22×C311yescharacteristic, complemented
172C2×#689C22×C311yescharacteristic, complemented
173C2×#689C22×C311yescharacteristic, complemented
174#4085—21no—
175#4084C22×C311yescharacteristic
176#4082C22×C311yescharacteristic
177#4081—21no—
178D4×Dic5C22×C311yescharacteristic
179C2×#687C22×C311yescharacteristic
180C2×#687C22×C311yescharacteristic
181C4×C22⋊D5—21no—
182C4×C22⋊D5C22×C311yescharacteristic
183#4070—21no—
184#4070C22×C311yescharacteristic
185#4070C22×C311yescharacteristic
186#4061—24no—
187C2×Dic20C22×C311yescharacteristic, complemented
188C2×#676C22×C311yescharacteristic, complemented
189#3967C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic
192#3964C22×C311yescharacteristic
193C22⋊#168C22×C311yescharacteristic
194#3952C22×C311yescharacteristic, complemented
195#3950C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3947C22×C311yescharacteristic, complemented
199#3946C22×C311yescharacteristic, complemented
200#3266—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—42no—
204C23×C3×C5—42no—
205C23×C3×C5—81no—
206C23×C3×C5C2×D411yescharacteristic
207C22×C3×D5C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—42no—
212C3×C5×Q8C2×D412yes—
213C3×C5×D4—21no—
214C3×C5×D4—21no—
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—42no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2411yescharacteristic
225C3×C22⋊D5—22no—
226C3×C22⋊D5—42no—
227C3×C22⋊D5—81no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—42no—
233C2×C3×Dic5—81no—
234C2×C3×Dic5C2×D411yescharacteristic
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—42no—
240C3×Dic10—21no—
241C3×Dic10—21no—
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×#41—51no—
250C22×C3×Q8—51no—
251C22×C3×Q8C2×D511yescharacteristic
252C22×C3×D4C2×D511yescharacteristic
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×Q16—51no—
257C2×C3×SD16—24no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16C2×D511yescharacteristic
261C2×C3×SD16C2×D511yescharacteristic
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×SD16C2×D511yescharacteristic
264C2×C3×M16—51no—
265C22×C3×C8C2×D511yescharacteristic
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—
294C24×C5—21no—
295C2×C5×Q8—21no—
296C2×C5×Q8—22no—
297C2×C5×Q8—41no—
298C2×C5×Q8C23×C311yescharacteristic
299C2×C5×Q8C23×C311yescharacteristic
300C2×C5×D4—22no—
301C2×C5×D4—21no—
302C2×C5×D4—41no—
303C2×C5×D4C23×C311yescharacteristic
304C2×C5×D4C23×C311yescharacteristic
305C22×C4×C5—21no—
306C22×C4×C5C23×C311yescharacteristic
307C2×C22⋊D5—21no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5C3×D411yescharacteristic
310C22×Dic5—21no—
311C22×Dic5—21no—
312Q8×D5—22no—
313Q8×D5—41no—
314#711—22no—
315#711—41no—
316C2×C4×D5—21no—
317C2×C4×D5C23×C311yescharacteristic
318C2×Dic10—21no—
319C2×Dic10C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C5×SD16—22no—
322C5×SD16—22no—
323C5×SD16—22no—
324C5×SD16C3×D414yescomplemented
325C2×C5×C8—22no—
326C2×C5×C8C23×C311yescharacteristic
327C2×C5×C8C23×C311yescharacteristic
328C22⋊Dic5—21no—
329C22⋊Dic5—21no—
330C22⋊Dic5—21no—
331C22⋊Dic5—21no—
332C22⋊Dic5—21no—
333C22⋊Dic5—21no—
334C22⋊Dic5C3×D411yescharacteristic
335#689—22no—
336#689—41no—
337#687—22no—
338#687—41no—
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
354Dic20—22no—
355#676—22no—
356C2×#137—51no—
357C22×SD16C3×D511yescharacteristic, complemented
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—21no—
372C22×C3×C5—21no—
373C22×C3×C5—22no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—84no—
380C22×C3×C5#13712yescomplemented
381C22×C3×C5C22×D411yescharacteristic
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—21no—
385C3×C4×C5—22no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390C3×Dic5—21no—
391C3×Dic5—21no—
392C3×Dic5—21no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—21no—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—21no—
401C2×C3×Q8—22no—
402C2×C3×Q8—41no—
403C2×C3×Q8—51no—
404C2×C3×Q8—51no—
405C2×C3×Q8—101no—
406C2×C3×Q8—102no—
407C2×C3×Q8—201no—
408C2×C3×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—22no—
411C2×C3×D4—21no—
412C2×C3×D4—41no—
413C2×C3×D4—51no—
414C2×C3×D4—101no—
415C2×C3×D4—101no—
416C2×C3×D4C22×D511yescharacteristic
417C2×C3×D4C22×D511yescharacteristic
418C22×C3×C4—21no—
419C22×C3×C4—51no—
420C22×C3×C4—101no—
421C22×C3×C4—101no—
422C22×C3×C4—101no—
423C22×C3×C4C22×D511yescharacteristic
424C3×Q16—102no—
425C3×Q16—102no—
426C3×Q16—201no—
427C3×SD16—22no—
428C3×SD16—22no—
429C3×SD16—22no—
430C3×SD16—102no—
431C3×SD16—201no—
432C3×SD16C22⋊D514yescomplemented
433C3×M16—102no—
434C2×C3×C8—22no—
435C2×C3×C8—51no—
436C2×C3×C8—51no—
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×C5—21no—
461C23×C5—42no—
462C23×C5—42no—
463C23×C5—81no—
464C23×C5C2×C3×D411yescharacteristic
465C22×D5C2×C3×D411yescharacteristic
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—42no—
470C5×Q8C2×C3×D412yes—
471C5×D4—21no—
472C5×D4—21no—
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—42no—
481C2×C4×C5C2×C3×D411yescharacteristic
482C2×C4×C5C24×C311yescharacteristic
483C22⋊D5—22no—
484C22⋊D5—42no—
485C22⋊D5—81no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—42no—
491C2×Dic5—81no—
492C2×Dic5C2×C3×D411yescharacteristic
493C2×Dic5C2×C3×D411yescharacteristic
494C2×Dic5C2×C3×D411yescharacteristic
495C4×D5—21no—
496C4×D5—21no—
497C4×D5—42no—
498Dic10—21no—
499Dic10—21no—
500Dic10—21no—
501Dic10—21no—
502Dic10—42no—
503C5×C8—21no—
504C5×C8C2×C3×D412yes—
505#168—21no—
506#168—21no—
507C2×#41—51no—
508C22×Q8—51no—
509C22×Q8C2×C3×D511yescharacteristic
510C22×D4C2×C3×D511yescharacteristic
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
514C2×Q16—51no—
515C2×SD16—24no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16C2×C3×D511yescharacteristic
519C2×SD16C2×C3×D511yescharacteristic
520C2×SD16C2×C3×D511yescharacteristic
521C2×SD16C2×C3×D511yescharacteristic
522C2×M16—51no—
523C22×C8C2×C3×D511yescharacteristic
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—22no—
553C2×C3×C5—42no—
554C2×C3×C5—81no—
555C2×C3×C5D4211yescharacteristic
556C2×C3×C5C2×#13711yescharacteristic
557C2×C3×C5#57711yescharacteristic
558C3×D5—41no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—51no—
564C23×C3—81no—
565C23×C3D4×D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—42no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—202no—
575C3×Q8C2×C22⋊D512yes—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—42no—
580C3×D4—102no—
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—42no—
589C2×C3×C4—51no—
590C2×C3×C4—51no—
591C2×C3×C4—51no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—202no—
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—41no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—84no—
616C22×C5C3×#13712yescomplemented
617C22×C5C22×C3×D411yescharacteristic
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—21no—
621C4×C5—22no—
622C4×C5—21no—
623C4×C5—41no—
624C4×C5C22×C3×D411yescharacteristic
625C4×C5C3×H(5,𝔽2)11yescharacteristic
626Dic5—21no—
627Dic5—21no—
628Dic5—21no—
629Dic5—41no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—21no—
634#41—102no—
635#41—201no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—41no—
639C2×Q8—51no—
640C2×Q8—51no—
641C2×Q8—101no—
642C2×Q8—102no—
643C2×Q8—201no—
644C2×Q8C22×C3×D511yescharacteristic
645C2×Q8C22×C3×D511yescharacteristic
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—41no—
649C2×D4—51no—
650C2×D4—101no—
651C2×D4—101no—
652C2×D4C22×C3×D511yescharacteristic
653C2×D4C22×C3×D511yescharacteristic
654C22×C4—21no—
655C22×C4—51no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4C22×C3×D511yescharacteristic
660Q16—102no—
661Q16—102no—
662Q16—201no—
663SD16—22no—
664SD16—22no—
665SD16—22no—
666SD16—102no—
667SD16—201no—
668SD16C3×C22⋊D514yescomplemented
669M16—102no—
670C2×C8—22no—
671C2×C8—51no—
672C2×C8—51no—
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—22no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—84no—
705C22×C3—101no—
706C22×C3—101no—
707C22×C3—101no—
708C22×C3#406112yescomplemented
709C22×C3C2×D4×D511yescharacteristic
710C3×C4—21no—
711C3×C4—22no—
712C3×C4—41no—
713C3×C4—101no—
714C3×C4—101no—
715C3×C4—101no—
716C3×C4—201no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4#414411yescharacteristic
721C3×C4C22×C22⋊D511yescharacteristic
722C2×C5—22no—
723C2×C5—42no—
724C2×C5—81no—
725C2×C5C3×D4211yescharacteristic
726C2×C5C2×C3×#13711yescharacteristic
727C2×C5C3×#57711yescharacteristic
728D5—41no—
729C23—21no—
730C23—21no—
731C23—42no—
732C23—42no—
733C23—51no—
734C23—81no—
735C23C3×D4×D511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—42no—
740Q8—101no—
741Q8—101no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8C2×C3×C22⋊D512yes—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—42no—
750D4—102no—
751D4—202no—
752D4—401no—
753D4C2×C3×C22⋊D512yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—42no—
759C2×C4—51no—
760C2×C4—51no—
761C2×C4—51no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—202no—
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—22no—
778C2×C3—42no—
779C2×C3—81no—
780C2×C3—201no—
781C2×C3C2×#406111yescharacteristic
782C2×C3#6609611yescharacteristic
783C2×C3D4×C22⋊D511yescharacteristic
784C5C3×#326611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—84no—
794C22—101no—
795C22—101no—
796C22—101no—
797C22C3×#406112yescomplemented
798C22C2×C3×D4×D511yescharacteristic
799C4—21no—
800C4—22no—
801C4—41no—
802C4—101no—
803C4—101no—
804C4—101no—
805C4—201no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4C3×#414411yescharacteristic
810C4C22×C3×C22⋊D511yescharacteristic
811C3#1061559711yescharacteristic, direct product factor, Sylow
812C2—22no—
813C2—42no—
814C2—81no—
815C2—201no—
816C2C2×C3×#406111yescharacteristic
817C2C3×#6609611yescharacteristic
818C2C3×D4×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×SD16C2
socleC22×C3×C5C22×D4
prime radicalC3×#66140C2
hypercenterC22×C3×SD16D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×SD16C2semidirect
2. C3×Q8×C22⋊D5C2semidirect
4. C2×C3×#4061C2semidirect
5. C3×#65517C2semidirect
6. C3×#65507C2semidirect
7. C3×#65463C2semidirect
8. C3×#65462C2semidirect
9. C3×#65459C2semidirect
10. C3×#65456C2semidirect
11. C3×#65455C2semidirect
12. C3×#65453C2semidirect
13. C3×#65451C2semidirect
14. C3×#65405C2semidirect
15. C3×#65400C2semidirect
16. #10615597C3direct (N × H)
19. C2×C3×Q8×D5C22semidirect
30. C3×#4092C22semidirect
31. C3×Q8×Dic5C22semidirect
33. C3×#4090C22semidirect
34. C2×C3×#689C22semidirect
35. C2×C3×#689C22semidirect
49. C2×C3×Dic20C22semidirect
50. C2×C3×#676C22semidirect
51. C3×#3967C22semidirect
52. C3×#3967C22semidirect
56. C3×#3952C22semidirect
57. C3×#3950C22semidirect
58. C3×#3948C22semidirect
59. C3×#3948C22semidirect
60. C3×#3947C22semidirect
61. C3×#3946C22semidirect
63. C22×C5×SD16C2×C3semidirect
64. Q8×C22⋊D5C2×C3semidirect
66. C2×#4061C2×C3semidirect
67. #65517C2×C3semidirect
68. #65507C2×C3semidirect
69. #65463C2×C3semidirect
70. #65462C2×C3semidirect
71. #65459C2×C3semidirect
72. #65456C2×C3semidirect
73. #65455C2×C3semidirect
74. #65453C2×C3semidirect
75. #65451C2×C3semidirect
76. #65405C2×C3semidirect
77. #65400C2×C3semidirect
108. C3×C5×SD16D4semidirect
141. C22×C3×SD16D5semidirect
157. C2×Q8×D5C22×C3semidirect
168. #4092C22×C3semidirect
169. Q8×Dic5C22×C3semidirect
171. #4090C22×C3semidirect
172. C2×#689C22×C3semidirect
173. C2×#689C22×C3semidirect
187. C2×Dic20C22×C3semidirect
188. C2×#676C22×C3semidirect
189. #3967C22×C3semidirect
190. #3967C22×C3semidirect
194. #3952C22×C3semidirect
195. #3950C22×C3semidirect
196. #3948C22×C3semidirect
197. #3948C22×C3semidirect
198. #3947C22×C3semidirect
199. #3946C22×C3semidirect
324. C5×SD16C3×D4semidirect
357. C22×SD16C3×D5semidirect
380. C22×C3×C5#137semidirect
432. C3×SD16C22⋊D5semidirect
616. C22×C5C3×#137semidirect
668. SD16C3×C22⋊D5semidirect
695. C3×C5#3266semidirect
708. C22×C3#4061semidirect
784. C5C3×#3266semidirect
797. C22C3×#4061semidirect
811. C3#10615597direct (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×SD162
C3×Q8×C22⋊D52
C3×#661402
C2×C3×#40612
C3×#655172
C3×#655072
C3×#654632
C3×#654622
C3×#654592
C3×#654562
C3×#654552
C3×#654532
C3×#654512
C3×#654052
C3×#654002
#106155973
C3×#32665