Finite Group Databasebeta

← C3×#10615290 #14453707

Subgroups — C3×#10615290 #14453707

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
1C3×C5×D4×Q8C211yesmaximal, characteristic, complemented
2C2×C3×#4088C211yesmaximal, characteristic, complemented
3C22×C3×#688C211yesmaximal, characteristic, complemented
4C3×#65884C211yesmaximal, characteristic
5C3×#65517C211yesmaximal, characteristic, complemented
6C3×#65516C211yesmaximal, characteristic, complemented
7C3×#65375C211yesmaximal, characteristic, complemented
8C3×#65372C211yesmaximal, characteristic, complemented
9C3×#65340C211yesmaximal, characteristic, complemented
10C3×#65338C211yesmaximal, characteristic, complemented
11C3×#65336C211yesmaximal, characteristic, complemented
12C3×#65335C211yesmaximal, characteristic, complemented
13C3×#65317C211yesmaximal, characteristic, complemented
14C3×#65315C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615290C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C3×C5×C4⋊Q8—21no—
22C3×C5×C4⋊Q8C2211yescharacteristic, complemented
23C3×C5×C22⋊Q8—21no—
24C3×C5×C22⋊Q8—21no—
25C3×C5×C22⋊Q8C2211yescharacteristic
26C3×C5×C22⋊Q8C2211yescharacteristic, complemented
27C3×C4×C5×Q8C2211yescharacteristic, complemented
28C3×C4×C5×D4—21no—
29C3×C4×C5×D4C2211yescharacteristic
30C2×C3×#689C2211yescharacteristic, complemented
31C2×C3×#689C2211yescharacteristic, complemented
32C2×C3×#689C2211yescharacteristic, complemented
33C3×#4088—24no—
34C2×C3×#688—24no—
35C2×C3×#688C2211yescharacteristic
36C2×C3×#688C2211yescharacteristic
37C2×C3×#688C2211yescharacteristic
38C2×C3×#688C2211yescharacteristic
39C2×C3×#688C2211yescharacteristic
40C2×C3×#688C2211yescharacteristic
41C3×#4083—21no—
42C3×#4076C2211yescharacteristic
43C3×#4070C2211yescharacteristic
44C2×C3×#681C2211yescharacteristic, complemented
45C22×C3×#168C2211yescharacteristic
46C3×#4040—21no—
47C3×#4030—21no—
48C3×D5×C22⋊C4—21no—
49C3×#4021C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic
51C3×#3967C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3967C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3939C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63C5×D4×Q8C2×C311yescharacteristic, complemented
64C2×#4088C2×C311yescharacteristic, complemented
65C22×#688C2×C311yescharacteristic, complemented
66#65884C2×C311yescharacteristic
67#65517C2×C311yescharacteristic, complemented
68#65516C2×C311yescharacteristic, complemented
69#65375C2×C311yescharacteristic, complemented
70#65372C2×C311yescharacteristic, complemented
71#65340C2×C311yescharacteristic, complemented
72#65338C2×C311yescharacteristic, complemented
73#65336C2×C311yescharacteristic, complemented
74#65335C2×C311yescharacteristic, complemented
75#65317C2×C311yescharacteristic, complemented
76#65315C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8—21no—
80C2×C3×C5×Q8—21no—
81C2×C3×C5×Q8—22no—
82C2×C3×C5×Q8—22no—
83C2×C3×C5×Q8—41no—
84C2×C3×C5×Q8—41no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×Q8C2311yescharacteristic
88C2×C3×C5×D4D411yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C3×#709—22no—
96C3×#709—41no—
97C2×C3×D20—22no—
98C2×C3×D20—21no—
99C2×C3×D20—41no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5—21no—
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4—21no—
107C3×C5×C4⋊C4—21no—
108C3×C5×C4⋊C4—21no—
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4D411yescharacteristic
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C42×C5—21no—
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×#689—22no—
120C3×#689—22no—
121C3×#689—41no—
122C3×#688—22no—
123C3×#688—22no—
124C3×#688—22no—
125C3×#688—22no—
126C3×#688—41no—
127C3×#688D414yescomplemented
128C3×#685—21no—
129C3×#685—21no—
130C3×#685—21no—
131C3×#685—21no—
132C3×C4⋊Dic5C2311yescharacteristic
133C3×#683—21no—
134C3×#681—22no—
135C2×C3×#168—22no—
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C2×C3×#168C2311yescharacteristic
140C2×C3×#137—51no—
141C22×C3×SD16—51no—
142C3×D4×Q8D511yescharacteristic, complemented
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×Q8C22×C311yescharacteristic, complemented
157C2×#709C22×C311yescharacteristic
158C22×D20C22×C311yescharacteristic
159C5×C4⋊Q8—21no—
160C5×C4⋊Q8C22×C311yescharacteristic, complemented
161C5×C22⋊Q8—21no—
162C5×C22⋊Q8—21no—
163C5×C22⋊Q8C22×C311yescharacteristic
164C5×C22⋊Q8C22×C311yescharacteristic, complemented
165C4×C5×Q8C22×C311yescharacteristic, complemented
166C4×C5×D4—21no—
167C4×C5×D4C22×C311yescharacteristic
168C2×#689C22×C311yescharacteristic, complemented
169C2×#689C22×C311yescharacteristic, complemented
170C2×#689C22×C311yescharacteristic, complemented
171#4088—24no—
172C2×#688—24no—
173C2×#688C22×C311yescharacteristic
174C2×#688C22×C311yescharacteristic
175C2×#688C22×C311yescharacteristic
176C2×#688C22×C311yescharacteristic
177C2×#688C22×C311yescharacteristic
178C2×#688C22×C311yescharacteristic
179#4083—21no—
180#4076C22×C311yescharacteristic
181#4070C22×C311yescharacteristic
182C2×#681C22×C311yescharacteristic, complemented
183C22×#168C22×C311yescharacteristic
184#4040—21no—
185#4030—21no—
186D5×C22⋊C4—21no—
187#4021C22×C311yescharacteristic
188C4×D20C22×C311yescharacteristic
189#3967C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3967C22×C311yescharacteristic, complemented
192C22⋊#168C22×C311yescharacteristic
193C22⋊#168C22×C311yescharacteristic, complemented
194#3942C22×C311yescharacteristic, complemented
195#3941C22×C311yescharacteristic
196#3941C22×C311yescharacteristic
197#3939C22×C311yescharacteristic, complemented
198C4⋊#168C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3266—51noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—81no—
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×Q8—42no—
215C3×C5×Q8C2×D412yes—
216C3×C5×D4—22no—
217C2×C3×C4×C5—21no—
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—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—42no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2×D411yescharacteristic
231C2×C3×C4×C5C2411yescharacteristic
232C3×C22⋊D5—42no—
233C3×C22⋊D5—81no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—42no—
240C3×D20C2×D412yes—
241C3×C4×D5—42no—
242C3×C4×D5—81no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×#168—21no—
246C3×#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×C3×#41—51no—
250C22×C3×Q8C2×D511yescharacteristic
251C22×C3×Q8C2×D511yescharacteristic, complemented
252C22×C3×D4—51no—
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×Q16—51no—
257C2×C3×SD16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—104no—
264C2×C3×M16—51no—
265C22×C3×C8—51no—
266C3×C4⋊Q8—21no—
267C3×C4⋊Q8C2×D511yescharacteristic, complemented
268C3×#124—51no—
269C3×#123—101no—
270C3×C22⋊Q8—21no—
271C3×C22⋊Q8—21no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8C2×D511yescharacteristic
274C3×C22⋊Q8C2×D511yescharacteristic, complemented
275C3×#121—51no—
276C3×#121—101no—
277C3×#120—101no—
278C3×C4×Q8C2×D511yescharacteristic, complemented
279C3×C4×D4—21no—
280C3×C4×D4—51no—
281C3×C4×D4C2×D511yescharacteristic
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—
295C2×C5×Q8—21no—
296C2×C5×Q8—21no—
297C2×C5×Q8—22no—
298C2×C5×Q8—22no—
299C2×C5×Q8—41no—
300C2×C5×Q8—41no—
301C2×C5×Q8C23×C311yescharacteristic
302C2×C5×Q8C23×C311yescharacteristic
303C2×C5×Q8C23×C311yescharacteristic
304C2×C5×D4C3×D411yescharacteristic
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5C23×C311yescharacteristic
308C22×C4×C5C23×C311yescharacteristic
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311#709—22no—
312#709—41no—
313C2×D20—22no—
314C2×D20—21no—
315C2×D20—41no—
316C2×D20C23×C311yescharacteristic
317C2×D20C23×C311yescharacteristic
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×Dic10C23×C311yescharacteristic
321C5×C4⋊C4—21no—
322C5×C4⋊C4—21no—
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4C3×D411yescharacteristic
327C5×C4⋊C4C23×C311yescharacteristic
328C5×C22⋊C4—21no—
329C5×C22⋊C4—21no—
330C5×C22⋊C4C3×D411yescharacteristic
331C5×C22⋊C4C3×D411yescharacteristic
332C42×C5—21no—
333C42×C5C23×C311yescharacteristic
334C22⋊Dic5—21no—
335#689—22no—
336#689—22no—
337#689—41no—
338#688—22no—
339#688—22no—
340#688—22no—
341#688—22no—
342#688—41no—
343#688C3×D414yescomplemented
344#685—21no—
345#685—21no—
346#685—21no—
347#685—21no—
348C4⋊Dic5C23×C311yescharacteristic
349#683—21no—
350#681—22no—
351C2×#168—22no—
352C2×#168C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354C2×#168C23×C311yescharacteristic
355C2×#168C23×C311yescharacteristic
356C2×#137—51no—
357C22×SD16—51no—
358D4×Q8C3×D511yescharacteristic, complemented
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—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×C3×D5—22no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—22no—
388C3×C4×C5—21no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—101no—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—21no—
401C2×C3×Q8—21no—
402C2×C3×Q8—22no—
403C2×C3×Q8—22no—
404C2×C3×Q8—41no—
405C2×C3×Q8—41no—
406C2×C3×Q8—51no—
407C2×C3×Q8C22×D511yescharacteristic
408C2×C3×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—102no—
413C2×C3×D4—101no—
414C2×C3×D4—101no—
415C2×C3×D4—101no—
416C2×C3×D4—201no—
417C2×C3×D4C22⋊D511yescharacteristic
418C22×C3×C4—21no—
419C22×C3×C4—21no—
420C22×C3×C4—101no—
421C22×C3×C4—101no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C3×Q16—102no—
425C3×Q16—102no—
426C3×Q16—201no—
427C3×SD16—54no—
428C3×SD16—102no—
429C3×SD16—102no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—201no—
433C3×M16—102no—
434C2×C3×C8—51no—
435C2×C3×C8—51no—
436C2×C3×C8—51no—
437C2×C3×C8—51no—
438C2×C3×C8—102no—
439C3×C4⋊C4—21no—
440C3×C4⋊C4—21no—
441C3×C4⋊C4—21no—
442C3×C4⋊C4—21no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4—51no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4C22⋊D511yescharacteristic
447C3×C4⋊C4C22×D511yescharacteristic
448C3×C22⋊C4—21no—
449C3×C22⋊C4—21no—
450C3×C22⋊C4—101no—
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4C22⋊D511yescharacteristic
456C3×C22⋊C4C22⋊D511yescharacteristic
457C3×C42—21no—
458C3×C42C22×D511yescharacteristic
459C23×C5C2×C3×D411yescharacteristic
460C23×C5C2×C3×D411yescharacteristic
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—42no—
464C22×D5—42no—
465C22×D5—81no—
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—21no—
470C5×Q8—21no—
471C5×Q8—42no—
472C5×Q8—42no—
473C5×Q8C2×C3×D412yes—
474C5×D4—22no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—42no—
484C2×C4×C5—42no—
485C2×C4×C5C2×C3×D411yescharacteristic
486C2×C4×C5C2×C3×D411yescharacteristic
487C2×C4×C5C2×C3×D411yescharacteristic
488C2×C4×C5C2×C3×D411yescharacteristic
489C2×C4×C5C24×C311yescharacteristic
490C22⋊D5—42no—
491C22⋊D5—81no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494D20—21no—
495D20—21no—
496D20—21no—
497D20—42no—
498D20C2×C3×D412yes—
499C4×D5—42no—
500C4×D5—81no—
501Dic10—21no—
502Dic10—21no—
503#168—21no—
504#168—21no—
505#168—21no—
506#168C2×C3×D412yes—
507C2×#41—51no—
508C22×Q8C2×C3×D511yescharacteristic
509C22×Q8C2×C3×D511yescharacteristic, complemented
510C22×D4—51no—
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
514C2×Q16—51no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—104no—
522C2×M16—51no—
523C22×C8—51no—
524C4⋊Q8—21no—
525C4⋊Q8C2×C3×D511yescharacteristic, complemented
526#124—51no—
527#123—101no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—51no—
531C22⋊Q8C2×C3×D511yescharacteristic
532C22⋊Q8C2×C3×D511yescharacteristic, complemented
533#121—51no—
534#121—101no—
535#120—101no—
536C4×Q8C2×C3×D511yescharacteristic, complemented
537C4×D4—21no—
538C4×D4—51no—
539C4×D4C2×C3×D511yescharacteristic
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—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557C3×D5—42no—
558C3×D5—81no—
559C23×C3—101no—
560C23×C3—101no—
561C23×C3—202no—
562C23×C3—202no—
563C23×C3—401no—
564C23×C3C2×C22⋊D511yescharacteristic
565C23×C3C2×C22⋊D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—42no—
572C3×Q8—42no—
573C3×Q8—101no—
574C3×Q8—101no—
575C3×Q8D4×D512yes—
576C3×D4—22no—
577C3×D4—52no—
578C3×D4—101no—
579C3×D4—101no—
580C3×D4—101no—
581C3×D4—202no—
582C3×D4—202no—
583C3×D4—401no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—202no—
597C2×C3×C4—401no—
598C2×C3×C4C2×C22⋊D511yescharacteristic
599C2×C3×C4C2×C22⋊D511yescharacteristic
600C2×C3×C4C2×C22⋊D511yescharacteristic
601C2×C3×C4C2×C22⋊D511yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603C3×C8—52no—
604C3×C8—101no—
605C3×C8—101no—
606C3×C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5C3×#13712yescomplemented
613C22×C5C22×C3×D411yescharacteristic
614C2×D5—22no—
615C2×D5—41no—
616C2×D5—41no—
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—41no—
620C2×D5—84no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—22no—
626C4×C5—41no—
627C4×C5—41no—
628C4×C5—41no—
629C4×C5C22×C3×D411yescharacteristic
630C4×C5C3×H(5,𝔽2)11yescharacteristic
631Dic5—41no—
632Dic5—41no—
633C24—101no—
634#41—102no—
635#41—201no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—41no—
641C2×Q8—41no—
642C2×Q8—51no—
643C2×Q8C22×C3×D511yescharacteristic
644C2×Q8C22×C3×D511yescharacteristic
645C2×Q8C22×C3×D511yescharacteristic
646C2×D4—51no—
647C2×D4—51no—
648C2×D4—102no—
649C2×D4—101no—
650C2×D4—101no—
651C2×D4—101no—
652C2×D4—201no—
653C2×D4C3×C22⋊D511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4C22×C3×D511yescharacteristic
659C22×C4C22×C3×D511yescharacteristic
660Q16—102no—
661Q16—102no—
662Q16—201no—
663SD16—54no—
664SD16—102no—
665SD16—102no—
666SD16—102no—
667SD16—102no—
668SD16—201no—
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—51no—
673C2×C8—51no—
674C2×C8—102no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—51no—
681C4⋊C4—101no—
682C4⋊C4C3×C22⋊D511yescharacteristic
683C4⋊C4C22×C3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—101no—
687C22⋊C4—101no—
688C22⋊C4—101no—
689C22⋊C4—101no—
690C22⋊C4—101no—
691C22⋊C4C3×C22⋊D511yescharacteristic
692C22⋊C4C3×C22⋊D511yescharacteristic
693C42—21no—
694C42C22×C3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—102no—
702C22×C3—201no—
703C22×C3—201no—
704C22×C3—201no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3—404no—
708C22×C3#408812yescomplemented
709C22×C3C22×C22⋊D511yescharacteristic
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—22no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4C2×D4×D511yescharacteristic
721C3×C4#414411yescharacteristic
722C2×C5—22no—
723C2×C5—41no—
724C2×C5C3×D4211yescharacteristic
725C2×C5C2×C3×#13711yescharacteristic
726C2×C5C3×#57711yescharacteristic
727D5—42no—
728D5—81no—
729C23—101no—
730C23—101no—
731C23—202no—
732C23—202no—
733C23—401no—
734C23C2×C3×C22⋊D511yescharacteristic
735C23C2×C3×C22⋊D511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—42no—
742Q8—42no—
743Q8—101no—
744Q8—101no—
745Q8C3×D4×D512yes—
746D4—22no—
747D4—52no—
748D4—101no—
749D4—101no—
750D4—101no—
751D4—202no—
752D4—202no—
753D4—401no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—202no—
767C2×C4—401no—
768C2×C4C2×C3×C22⋊D511yescharacteristic
769C2×C4C2×C3×C22⋊D511yescharacteristic
770C2×C4C2×C3×C22⋊D511yescharacteristic
771C2×C4C2×C3×C22⋊D511yescharacteristic
772C2×C4C23×C3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—101no—
776C8—101no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3—202no—
780C2×C3—401no—
781C2×C3D4×C22⋊D511yescharacteristic
782C2×C3C2×#408811yescharacteristic
783C2×C3#6617111yescharacteristic
784C5C3×#326611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—102no—
791C22—201no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22—404no—
797C22C3×#408812yescomplemented
798C22C22×C3×C22⋊D511yescharacteristic
799C4—21no—
800C4—21no—
801C4—22no—
802C4—21no—
803C4—21no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—201no—
808C4—201no—
809C4C2×C3×D4×D511yescharacteristic
810C4C3×#414411yescharacteristic
811C3#1061529011yescharacteristic, direct product factor, Sylow
812C2—22no—
813C2—41no—
814C2—202no—
815C2—401no—
816C2C3×D4×C22⋊D511yescharacteristic
817C2C2×C3×#408811yescharacteristic
818C2C3×#6617111yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×D4×Q8C2
socleC22×C3×C5C22×D4
prime radicalC3×#65884C2
hypercenterC3×D4×Q8D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C5×D4×Q8C2semidirect
2. C2×C3×#4088C2semidirect
3. C22×C3×#688C2semidirect
5. C3×#65517C2semidirect
6. C3×#65516C2semidirect
7. C3×#65375C2semidirect
8. C3×#65372C2semidirect
9. C3×#65340C2semidirect
10. C3×#65338C2semidirect
11. C3×#65336C2semidirect
12. C3×#65335C2semidirect
13. C3×#65317C2semidirect
14. C3×#65315C2semidirect
15. C3×#65300C2semidirect
16. #10615290C3direct (N × H)
18. C22×C3×C5×Q8C22semidirect
22. C3×C5×C4⋊Q8C22semidirect
26. C3×C5×C22⋊Q8C22semidirect
27. C3×C4×C5×Q8C22semidirect
30. C2×C3×#689C22semidirect
31. C2×C3×#689C22semidirect
32. C2×C3×#689C22semidirect
44. C2×C3×#681C22semidirect
51. C3×#3967C22semidirect
52. C3×#3967C22semidirect
53. C3×#3967C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
59. C3×#3939C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×D4×Q8C2×C3semidirect
64. C2×#4088C2×C3semidirect
65. C22×#688C2×C3semidirect
67. #65517C2×C3semidirect
68. #65516C2×C3semidirect
69. #65375C2×C3semidirect
70. #65372C2×C3semidirect
71. #65340C2×C3semidirect
72. #65338C2×C3semidirect
73. #65336C2×C3semidirect
74. #65335C2×C3semidirect
75. #65317C2×C3semidirect
76. #65315C2×C3semidirect
77. #65300C2×C3semidirect
127. C3×#688D4semidirect
142. C3×D4×Q8D5semidirect
156. C22×C5×Q8C22×C3semidirect
160. C5×C4⋊Q8C22×C3semidirect
164. C5×C22⋊Q8C22×C3semidirect
165. C4×C5×Q8C22×C3semidirect
168. C2×#689C22×C3semidirect
169. C2×#689C22×C3semidirect
170. C2×#689C22×C3semidirect
182. C2×#681C22×C3semidirect
189. #3967C22×C3semidirect
190. #3967C22×C3semidirect
191. #3967C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. #3942C22×C3semidirect
197. #3939C22×C3semidirect
198. C4⋊#168C22×C3semidirect
199. #3935C22×C3semidirect
251. C22×C3×Q8C2×D5semidirect
267. C3×C4⋊Q8C2×D5semidirect
274. C3×C22⋊Q8C2×D5semidirect
278. C3×C4×Q8C2×D5semidirect
343. #688C3×D4semidirect
358. D4×Q8C3×D5semidirect
376. C22×C3×C5#137semidirect
509. C22×Q8C2×C3×D5semidirect
525. C4⋊Q8C2×C3×D5semidirect
532. C22⋊Q8C2×C3×D5semidirect
536. C4×Q8C2×C3×D5semidirect
612. C22×C5C3×#137semidirect
695. C3×C5#3266semidirect
708. C22×C3#4088semidirect
784. C5C3×#3266semidirect
797. C22C3×#4088semidirect
811. C3#10615290direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D4×Q82
C2×C3×#40882
C22×C3×#6882
C3×#658842
C3×#655172
C3×#655162
C3×#653752
C3×#653722
C3×#653402
C3×#653382
C3×#653362
C3×#653352
C3×#653172
C3×#653152
C3×#653002
#106152903
C3×#32665