Finite Group Databasebeta

← C3×#10611972 #14453698

Subgroups — C3×#10611972 #14453698

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×#66163C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic, complemented
3C2×C3×D5×SD16C211yesmaximal, characteristic, complemented
4C3×#65966C211yesmaximal, characteristic, complemented
5C3×C5×#452C211yesmaximal, characteristic, complemented
6C3×#65479C211yesmaximal, characteristic, complemented
7C3×#65475C211yesmaximal, characteristic, complemented
8C3×#65451C211yesmaximal, characteristic, complemented
9C3×#65338C211yesmaximal, characteristic, complemented
10C3×#65102C211yesmaximal, characteristic, complemented
11C3×#65087C211yesmaximal, characteristic, complemented
12C3×#65065C211yesmaximal, characteristic, complemented
13C3×#65046C211yesmaximal, characteristic, complemented
14C3×#65027C211yesmaximal, characteristic, complemented
15C3×#65017C211yesmaximal, characteristic, complemented
16#10611972C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic
23C3×C5×C22⋊Q8C2211yescharacteristic, complemented
24C3×#4097—24no—
25C3×#4093C2211yescharacteristic
26C3×#4092C2211yescharacteristic
27C3×#4090C2211yescharacteristic, complemented
28C2×C3×#689C2211yescharacteristic, complemented
29C2×C3×#689C2211yescharacteristic, complemented
30C2×C3×#688C2211yescharacteristic
31C3×#4085—21no—
32C3×#4083—21no—
33C3×D4×Dic5C2211yescharacteristic
34C2×C3×#687C2211yescharacteristic
35C2×C3×#687C2211yescharacteristic
36C3×#4076C2211yescharacteristic
37C3×#4075—21no—
38C3×C4×C22⋊D5C2211yescharacteristic
39C2×C3×#685—21no—
40C2×C3×#681C2211yescharacteristic, complemented
41C3×D5×SD16—24no—
42C2×C3×#677C2211yescharacteristic
43C2×C3×#677C2211yescharacteristic
44C2×C3×C8×D5C2211yescharacteristic
45C3×#4043C2211yescharacteristic
46C3×#4042—21no—
47C3×#4034—21no—
48C3×#4033C2211yescharacteristic, complemented
49C3×#4027—21no—
50C3×#4024—21no—
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×#3967C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic
56C3×#3948C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3941C2211yescharacteristic
61C3×#3939C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63#66163C2×C311yescharacteristic
64C2×#4097C2×C311yescharacteristic, complemented
65C2×D5×SD16C2×C311yescharacteristic, complemented
66#65966C2×C311yescharacteristic, complemented
67C5×#452C2×C311yescharacteristic, complemented
68#65479C2×C311yescharacteristic, complemented
69#65475C2×C311yescharacteristic, complemented
70#65451C2×C311yescharacteristic, complemented
71#65338C2×C311yescharacteristic, complemented
72#65102C2×C311yescharacteristic, complemented
73#65087C2×C311yescharacteristic, complemented
74#65065C2×C311yescharacteristic, complemented
75#65046C2×C311yescharacteristic, complemented
76#65027C2×C311yescharacteristic, complemented
77#65017C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5D411yescharacteristic
90C22×C3×Dic5—21no—
91C22×C3×Dic5—21no—
92C3×Q8×D5—22no—
93C3×Q8×D5—41no—
94C3×D4×D5—22no—
95C3×D4×D5—41no—
96C2×C3×D20C2311yescharacteristic
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5C2311yescharacteristic
99C2×C3×Dic10—22no—
100C2×C3×Dic10—21no—
101C2×C3×Dic10—21no—
102C2×C3×Dic10—41no—
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×Q16—41no—
106C3×C5×SD16—22no—
107C2×C3×C5×C8C2311yescharacteristic
108C2×C3×C5×C8C2311yescharacteristic
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5D411yescharacteristic
114C3×#689—22no—
115C3×#689—22no—
116C3×#688—22no—
117C3×#687—22no—
118C3×#687D414yescomplemented
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×#683—21no—
128C3×#683—21no—
129C3×#683—21no—
130C3×#683—21no—
131C3×#683D411yescharacteristic
132C3×C4×Dic5—21no—
133C3×C4×Dic5C2311yescharacteristic
134C3×#681—22no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×#677—22no—
138C3×#677—41no—
139C3×C8×D5—22no—
140C2×C3×#137—51no—
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×#452D511yescharacteristic, complemented
150C3×#451—51no—
151C3×#450—51no—
152C3×#448—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C2×Q8×D5C22×C311yescharacteristic
157C2×D4×D5C22×C311yescharacteristic
158C22×Dic10C22×C311yescharacteristic, complemented
159C2×C5×Q16C22×C311yescharacteristic, complemented
160C2×C5×SD16C22×C311yescharacteristic
161C5×C22⋊Q8C22×C311yescharacteristic, complemented
162#4097—24no—
163#4093C22×C311yescharacteristic
164#4092C22×C311yescharacteristic
165#4090C22×C311yescharacteristic, complemented
166C2×#689C22×C311yescharacteristic, complemented
167C2×#689C22×C311yescharacteristic, complemented
168C2×#688C22×C311yescharacteristic
169#4085—21no—
170#4083—21no—
171D4×Dic5C22×C311yescharacteristic
172C2×#687C22×C311yescharacteristic
173C2×#687C22×C311yescharacteristic
174#4076C22×C311yescharacteristic
175#4075—21no—
176C4×C22⋊D5C22×C311yescharacteristic
177C2×#685—21no—
178C2×#681C22×C311yescharacteristic, complemented
179D5×SD16—24no—
180C2×#677C22×C311yescharacteristic
181C2×#677C22×C311yescharacteristic
182C2×C8×D5C22×C311yescharacteristic
183#4043C22×C311yescharacteristic
184#4042—21no—
185#4034—21no—
186#4033C22×C311yescharacteristic, complemented
187#4027—21no—
188#4024—21no—
189C5×#103C22×C311yescharacteristic, complemented
190C5×#102C22×C311yescharacteristic
191C5×C22⋊C8C22×C311yescharacteristic, complemented
192#3967C22×C311yescharacteristic, complemented
193#3952C22×C311yescharacteristic
194#3948C22×C311yescharacteristic, complemented
195#3948C22×C311yescharacteristic, complemented
196#3947C22×C311yescharacteristic, complemented
197#3946C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic
199#3939C22×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×D4—21no—
213C3×C5×D4—42no—
214C3×C5×D4C2×D412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—42no—
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2411yescharacteristic
223C3×C22⋊D5—22no—
224C3×C22⋊D5—42no—
225C3×C22⋊D5—81no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—42no—
230C2×C3×Dic5—81no—
231C2×C3×Dic5C2×D411yescharacteristic
232C2×C3×Dic5C2×D411yescharacteristic
233C2×C3×Dic5C2×D411yescharacteristic
234C3×D20—21no—
235C3×D20—21no—
236C3×C4×D5—21no—
237C3×C4×D5—21no—
238C3×C4×D5—42no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—42no—
243C3×Dic10—42no—
244C3×Dic10C2×D412yes—
245C3×C5×C8—21no—
246C3×C5×C8—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×C3×#41C2×D511yescharacteristic
250C22×C3×Q8—51no—
251C22×C3×Q8—51no—
252C22×C3×D4—51no—
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×Q16C2×D511yescharacteristic, complemented
257C2×C3×SD16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—104no—
263C2×C3×SD16C2×D511yescharacteristic
264C2×C3×M16—51no—
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—101no—
273C3×C22⋊Q8—101no—
274C3×C22⋊Q8C2×D511yescharacteristic, complemented
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×#103C2×D511yescharacteristic, complemented
289C3×#102—51no—
290C3×#102C2×D511yescharacteristic
291C3×C22⋊C8—51no—
292C3×C22⋊C8C2×D511yescharacteristic, complemented
293C3×#97—51no—
294C23×D5—21no—
295C5×#41—22no—
296C5×#41—41no—
297C2×C5×Q8C23×C311yescharacteristic
298C2×C5×Q8C23×C311yescharacteristic
299C2×C5×D4—21no—
300C2×C5×D4C23×C311yescharacteristic
301C22×C4×C5—21no—
302C22×C4×C5C23×C311yescharacteristic
303C2×C22⋊D5—21no—
304C2×C22⋊D5—21no—
305C2×C22⋊D5C3×D411yescharacteristic
306C22×Dic5—21no—
307C22×Dic5—21no—
308Q8×D5—22no—
309Q8×D5—41no—
310D4×D5—22no—
311D4×D5—41no—
312C2×D20C23×C311yescharacteristic
313C2×C4×D5—21no—
314C2×C4×D5C23×C311yescharacteristic
315C2×Dic10—22no—
316C2×Dic10—21no—
317C2×Dic10—21no—
318C2×Dic10—41no—
319C2×Dic10C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C5×Q16—41no—
322C5×SD16—22no—
323C2×C5×C8C23×C311yescharacteristic
324C2×C5×C8C23×C311yescharacteristic
325C5×C4⋊C4—21no—
326C5×C4⋊C4C23×C311yescharacteristic
327C5×C22⋊C4—21no—
328C22⋊Dic5—21no—
329C22⋊Dic5C3×D411yescharacteristic
330#689—22no—
331#689—22no—
332#688—22no—
333#687—22no—
334#687C3×D414yescomplemented
335#685—21no—
336#685—21no—
337#685—21no—
338#685—21no—
339#685—21no—
340#685C3×D411yescharacteristic
341C4⋊Dic5—21no—
342C4⋊Dic5C23×C311yescharacteristic
343#683—21no—
344#683—21no—
345#683—21no—
346#683—21no—
347#683C3×D411yescharacteristic
348C4×Dic5—21no—
349C4×Dic5C23×C311yescharacteristic
350#681—22no—
351C2×#168C23×C311yescharacteristic
352C2×#168C23×C311yescharacteristic
353#677—22no—
354#677—41no—
355C8×D5—22no—
356C2×#137—51no—
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#452C3×D511yescharacteristic, complemented
366#451—51no—
367#450—51no—
368#448—51no—
369#440—51no—
370#435—51no—
371C22×C3×C5—21no—
372C22×C3×C5—22no—
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—21no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391C3×Dic5—22no—
392C3×Dic5—21no—
393C3×Dic5—21no—
394C3×Dic5—21no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—101no—
398C3×#41—22no—
399C3×#41—41no—
400C2×C3×Q8—51no—
401C2×C3×Q8—51no—
402C2×C3×Q8—101no—
403C2×C3×Q8—102no—
404C2×C3×Q8—101no—
405C2×C3×Q8—102no—
406C2×C3×Q8—201no—
407C2×C3×Q8—201no—
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—51no—
420C22×C3×C4—101no—
421C22×C3×C4—101no—
422C22×C3×C4—101no—
423C22×C3×C4C22×D511yescharacteristic
424C3×Q16—41no—
425C3×Q16—102no—
426C3×Q16—102no—
427C3×SD16—22no—
428C3×SD16—54no—
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—102no—
437C2×C3×C8C22×D511yescharacteristic
438C2×C3×C8C22×D511yescharacteristic
439C3×C4⋊C4—21no—
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⋊C4C22×D511yescharacteristic
448C3×C22⋊C4—21no—
449C3×C22⋊C4—51no—
450C3×C22⋊C4—51no—
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×D4—21no—
471C5×D4—42no—
472C5×D4C2×C3×D412yes—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—42no—
479C2×C4×C5C2×C3×D411yescharacteristic
480C2×C4×C5C24×C311yescharacteristic
481C22⋊D5—22no—
482C22⋊D5—42no—
483C22⋊D5—81no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—42no—
488C2×Dic5—81no—
489C2×Dic5C2×C3×D411yescharacteristic
490C2×Dic5C2×C3×D411yescharacteristic
491C2×Dic5C2×C3×D411yescharacteristic
492D20—21no—
493D20—21no—
494C4×D5—21no—
495C4×D5—21no—
496C4×D5—42no—
497Dic10—21no—
498Dic10—21no—
499Dic10—21no—
500Dic10—42no—
501Dic10—42no—
502Dic10C2×C3×D412yes—
503C5×C8—21no—
504C5×C8—21no—
505#168—21no—
506#168C2×C3×D412yes—
507C2×#41C2×C3×D511yescharacteristic
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4—51no—
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
514C2×Q16C2×C3×D511yescharacteristic, complemented
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—51no—
520C2×SD16—104no—
521C2×SD16C2×C3×D511yescharacteristic
522C2×M16—51no—
523C22×C8—51no—
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124—51no—
527#123—101no—
528C22⋊Q8—51no—
529C22⋊Q8—51no—
530C22⋊Q8—101no—
531C22⋊Q8—101no—
532C22⋊Q8C2×C3×D511yescharacteristic, complemented
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#103C2×C3×D511yescharacteristic, complemented
547#102—51no—
548#102C2×C3×D511yescharacteristic
549C22⋊C8—51no—
550C22⋊C8C2×C3×D511yescharacteristic, complemented
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—52no—
571C3×Q8—101no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—202no—
575C3×Q8—202no—
576C3×D4—21no—
577C3×D4—42no—
578C3×D4—102no—
579C3×D4—101no—
580C3×D4—101no—
581C3×D4—202no—
582C3×D4—401no—
583C3×D4D4×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—51no—
591C2×C3×C4—51no—
592C2×C3×C4—51no—
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—21no—
605C3×C8—52no—
606C3×C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—22no—
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—21no—
622C4×C5—41no—
623C4×C5—41no—
624C4×C5—41no—
625C4×C5C22×C3×D411yescharacteristic
626C4×C5C3×H(5,𝔽2)11yescharacteristic
627Dic5—21no—
628Dic5—21no—
629Dic5—22no—
630Dic5—21no—
631Dic5—41no—
632Dic5—41no—
633C24—101no—
634#41—22no—
635#41—41no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—101no—
639C2×Q8—102no—
640C2×Q8—101no—
641C2×Q8—102no—
642C2×Q8—201no—
643C2×Q8—201no—
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—51no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4C22×C3×D511yescharacteristic
660Q16—41no—
661Q16—102no—
662Q16—102no—
663SD16—22no—
664SD16—54no—
665SD16—102no—
666SD16—102no—
667SD16—102no—
668SD16—201no—
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—102no—
673C2×C8C22×C3×D511yescharacteristic
674C2×C8C22×C3×D511yescharacteristic
675C4⋊C4—21no—
676C4⋊C4—51no—
677C4⋊C4—51no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4—101no—
683C4⋊C4C22×C3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—51no—
686C22⋊C4—51no—
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—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—101no—
715C3×C4—101no—
716C3×C4—101no—
717C3×C4—102no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4C2×D4×D511yescharacteristic
721C3×C4#414411yescharacteristic
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—52no—
741Q8—101no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8—202no—
746D4—21no—
747D4—42no—
748D4—102no—
749D4—101no—
750D4—101no—
751D4—202no—
752D4—401no—
753D4C3×D4×D512yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—42no—
760C2×C4—51no—
761C2×C4—51no—
762C2×C4—51no—
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—21no—
775C8—52no—
776C8—101no—
777C2×C3—41no—
778C2×C3—42no—
779C2×C3—102no—
780C2×C3—401no—
781C2×C3#6592411yescharacteristic
782C2×C3#6610411yescharacteristic
783C2×C3D5×#13711yescharacteristic
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—41no—
801C4—41no—
802C4—41no—
803C4—101no—
804C4—101no—
805C4—101no—
806C4—102no—
807C4—201no—
808C4—201no—
809C4C2×C3×D4×D511yescharacteristic
810C4C3×#414411yescharacteristic
811C3#1061197211yescharacteristic, direct product factor, Sylow
812C2—41no—
813C2—42no—
814C2—102no—
815C2—401no—
816C2C3×#6592411yescharacteristic
817C2C3×#6610411yescharacteristic
818C2C3×D5×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#452C2
socleC22×C3×C5C22×D4
prime radicalC3×#66163C2
hypercenterC3×#452D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4097C2semidirect
3. C2×C3×D5×SD16C2semidirect
4. C3×#65966C2semidirect
5. C3×C5×#452C2semidirect
6. C3×#65479C2semidirect
7. C3×#65475C2semidirect
8. C3×#65451C2semidirect
9. C3×#65338C2semidirect
10. C3×#65102C2semidirect
11. C3×#65087C2semidirect
12. C3×#65065C2semidirect
13. C3×#65046C2semidirect
14. C3×#65027C2semidirect
15. C3×#65017C2semidirect
16. #10611972C3direct (N × H)
20. C22×C3×Dic10C22semidirect
21. C2×C3×C5×Q16C22semidirect
23. C3×C5×C22⋊Q8C22semidirect
27. C3×#4090C22semidirect
28. C2×C3×#689C22semidirect
29. C2×C3×#689C22semidirect
40. C2×C3×#681C22semidirect
48. C3×#4033C22semidirect
51. C3×C5×#103C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×#3967C22semidirect
56. C3×#3948C22semidirect
57. C3×#3948C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
61. C3×#3939C22semidirect
64. C2×#4097C2×C3semidirect
65. C2×D5×SD16C2×C3semidirect
66. #65966C2×C3semidirect
67. C5×#452C2×C3semidirect
68. #65479C2×C3semidirect
69. #65475C2×C3semidirect
70. #65451C2×C3semidirect
71. #65338C2×C3semidirect
72. #65102C2×C3semidirect
73. #65087C2×C3semidirect
74. #65065C2×C3semidirect
75. #65046C2×C3semidirect
76. #65027C2×C3semidirect
77. #65017C2×C3semidirect
118. C3×#687D4semidirect
149. C3×#452D5semidirect
158. C22×Dic10C22×C3semidirect
159. C2×C5×Q16C22×C3semidirect
161. C5×C22⋊Q8C22×C3semidirect
165. #4090C22×C3semidirect
166. C2×#689C22×C3semidirect
167. C2×#689C22×C3semidirect
178. C2×#681C22×C3semidirect
186. #4033C22×C3semidirect
189. C5×#103C22×C3semidirect
191. C5×C22⋊C8C22×C3semidirect
192. #3967C22×C3semidirect
194. #3948C22×C3semidirect
195. #3948C22×C3semidirect
196. #3947C22×C3semidirect
197. #3946C22×C3semidirect
199. #3939C22×C3semidirect
256. C2×C3×Q16C2×D5semidirect
274. C3×C22⋊Q8C2×D5semidirect
288. C3×#103C2×D5semidirect
292. C3×C22⋊C8C2×D5semidirect
334. #687C3×D4semidirect
365. #452C3×D5semidirect
384. C2×C3×D5#137semidirect
514. C2×Q16C2×C3×D5semidirect
532. C22⋊Q8C2×C3×D5semidirect
546. #103C2×C3×D5semidirect
550. C22⋊C8C2×C3×D5semidirect
620. C2×D5C3×#137semidirect
695. C3×C5#3266semidirect
784. C5C3×#3266semidirect
811. C3#10611972direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661632
C2×C3×#40972
C2×C3×D5×SD162
C3×#659662
C3×C5×#4522
C3×#654792
C3×#654752
C3×#654512
C3×#653382
C3×#651022
C3×#650872
C3×#650652
C3×#650462
C3×#650272
C3×#650172
#106119723
C3×#32665