Finite Group Databasebeta

← C3×#10611900 #14453716

Subgroups — C3×#10611900 #14453716

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×#66140C211yesmaximal, characteristic
2C22×C3×#687C211yesmaximal, characteristic, complemented
3C2×C3×#4061C211yesmaximal, characteristic, complemented
4C3×#65966C211yesmaximal, characteristic, complemented
5C3×C5×#450C211yesmaximal, characteristic, complemented
6C3×#65459C211yesmaximal, characteristic, complemented
7C3×#65456C211yesmaximal, characteristic, complemented
8C3×#65451C211yesmaximal, characteristic, complemented
9C3×#65340C211yesmaximal, characteristic, complemented
10C3×#65072C211yesmaximal, characteristic, complemented
11C3×#65069C211yesmaximal, characteristic, complemented
12C3×#65056C211yesmaximal, characteristic, complemented
13C3×#65046C211yesmaximal, characteristic, complemented
14C3×#65028C211yesmaximal, characteristic, complemented
15C3×#65019C211yesmaximal, characteristic, complemented
16#10611900C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic, complemented
19C2×C3×#711C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×#4099—21no—
25C2×C3×C22⋊Dic5—21no—
26C3×#4090C2211yescharacteristic, complemented
27C2×C3×#689C2211yescharacteristic, complemented
28C3×#4085—21no—
29C3×#4084C2211yescharacteristic
30C3×#4082C2211yescharacteristic
31C3×#4081—21no—
32C3×D4×Dic5C2211yescharacteristic
33C2×C3×#687—24no—
34C2×C3×#687C2211yescharacteristic
35C2×C3×#687C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic
37C2×C3×#687C2211yescharacteristic
38C3×C4×C22⋊D5C2211yescharacteristic
39C3×#4070C2211yescharacteristic
40C22×C3×#168C2211yescharacteristic
41C3×#4061—24no—
42C2×C3×Dic20C2211yescharacteristic, complemented
43C2×C3×Dic20C2211yescharacteristic, complemented
44C2×C3×#676C2211yescharacteristic, complemented
45C3×#4043C2211yescharacteristic, complemented
46C3×#4042—21no—
47C3×#4034—21no—
48C3×#4033C2211yescharacteristic, complemented
49C3×#4027—21no—
50C3×#4024—21no—
51C3×C5×#102C2211yescharacteristic
52C3×C5×#102C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic
54C3×#3967C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic, complemented
56C3×#3948C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3942C2211yescharacteristic, complemented
61C3×#3939C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63#66140C2×C311yescharacteristic
64C22×#687C2×C311yescharacteristic, complemented
65C2×#4061C2×C311yescharacteristic, complemented
66#65966C2×C311yescharacteristic, complemented
67C5×#450C2×C311yescharacteristic, complemented
68#65459C2×C311yescharacteristic, complemented
69#65456C2×C311yescharacteristic, complemented
70#65451C2×C311yescharacteristic, complemented
71#65340C2×C311yescharacteristic, complemented
72#65072C2×C311yescharacteristic, complemented
73#65069C2×C311yescharacteristic, complemented
74#65056C2×C311yescharacteristic, complemented
75#65046C2×C311yescharacteristic, complemented
76#65028C2×C311yescharacteristic, complemented
77#65019C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5D411yescharacteristic
89C22×C3×Dic5—21no—
90C22×C3×Dic5—21no—
91C22×C3×Dic5—21no—
92C3×Q8×D5—22no—
93C3×Q8×D5—41no—
94C3×#711—22no—
95C3×#711—41no—
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5C2311yescharacteristic
98C2×C3×Dic10—22no—
99C2×C3×Dic10—21no—
100C2×C3×Dic10—21no—
101C2×C3×Dic10—41no—
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×SD16—22no—
106C3×C5×SD16—41no—
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⋊Dic5—21no—
114C3×C22⋊Dic5—21no—
115C3×C22⋊Dic5—21no—
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5D411yescharacteristic
118C3×#689—22no—
119C3×#687—22no—
120C3×#687—22no—
121C3×#687—22no—
122C3×#687D414yescomplemented
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
134C2×C3×#168—22no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×Dic20—22no—
138C3×Dic20—41no—
139C3×#676—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×#452—51no—
150C3×#451—51no—
151C3×#450D511yescharacteristic, complemented
152C3×#448—51no—
153C3×#440—51no—
154C3×#435—51no—
155C22×C5×D4C22×C311yescharacteristic
156C2×Q8×D5C22×C311yescharacteristic, complemented
157C2×#711C22×C311yescharacteristic
158C22×Dic10C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic
160C2×C5×SD16C22×C311yescharacteristic
161C5×C22⋊Q8C22×C311yescharacteristic
162#4099—21no—
163C2×C22⋊Dic5—21no—
164#4090C22×C311yescharacteristic, complemented
165C2×#689C22×C311yescharacteristic, complemented
166#4085—21no—
167#4084C22×C311yescharacteristic
168#4082C22×C311yescharacteristic
169#4081—21no—
170D4×Dic5C22×C311yescharacteristic
171C2×#687—24no—
172C2×#687C22×C311yescharacteristic
173C2×#687C22×C311yescharacteristic
174C2×#687C22×C311yescharacteristic
175C2×#687C22×C311yescharacteristic
176C4×C22⋊D5C22×C311yescharacteristic
177#4070C22×C311yescharacteristic
178C22×#168C22×C311yescharacteristic
179#4061—24no—
180C2×Dic20C22×C311yescharacteristic, complemented
181C2×Dic20C22×C311yescharacteristic, complemented
182C2×#676C22×C311yescharacteristic, complemented
183#4043C22×C311yescharacteristic, complemented
184#4042—21no—
185#4034—21no—
186#4033C22×C311yescharacteristic, complemented
187#4027—21no—
188#4024—21no—
189C5×#102C22×C311yescharacteristic
190C5×#102C22×C311yescharacteristic
191C5×C22⋊C8C22×C311yescharacteristic
192#3967C22×C311yescharacteristic, complemented
193#3952C22×C311yescharacteristic, complemented
194#3948C22×C311yescharacteristic, complemented
195#3948C22×C311yescharacteristic, complemented
196#3947C22×C311yescharacteristic, complemented
197#3946C22×C311yescharacteristic, complemented
198#3942C22×C311yescharacteristic, complemented
199#3939C22×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×D4—21no—
211C3×C5×D4—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×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2411yescharacteristic
221C3×C22⋊D5—22no—
222C3×C22⋊D5—42no—
223C3×C22⋊D5—81no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—42no—
229C2×C3×Dic5—42no—
230C2×C3×Dic5—81no—
231C2×C3×Dic5C2×D411yescharacteristic
232C2×C3×Dic5C2×D411yescharacteristic
233C2×C3×Dic5C2×D411yescharacteristic
234C3×C4×D5—21no—
235C3×C4×D5—21no—
236C3×C4×D5—42no—
237C3×Dic10—21no—
238C3×Dic10—21no—
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×#41—51no—
250C22×C3×Q8—51no—
251C22×C3×Q8—51no—
252C22×C3×D4C2×D511yescharacteristic
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—104no—
262C2×C3×SD16C2×D511yescharacteristic
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
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×#102C2×D511yescharacteristic
290C3×#102C2×D511yescharacteristic
291C3×C22⋊C8—51no—
292C3×C22⋊C8C2×D511yescharacteristic
293C3×#97—51no—
294C24×C5—21no—
295C2×C5×Q8C23×C311yescharacteristic
296C2×C5×D4—22no—
297C2×C5×D4—21no—
298C2×C5×D4—41no—
299C2×C5×D4C23×C311yescharacteristic
300C2×C5×D4C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C2×C22⋊D5—21no—
303C2×C22⋊D5—21no—
304C2×C22⋊D5C3×D411yescharacteristic
305C22×Dic5—21no—
306C22×Dic5—21no—
307C22×Dic5—21no—
308Q8×D5—22no—
309Q8×D5—41no—
310#711—22no—
311#711—41no—
312C2×C4×D5—21no—
313C2×C4×D5C23×C311yescharacteristic
314C2×Dic10—22no—
315C2×Dic10—21no—
316C2×Dic10—21no—
317C2×Dic10—41no—
318C2×Dic10C23×C311yescharacteristic
319C2×Dic10C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C5×SD16—22no—
322C5×SD16—41no—
323C2×C5×C8C23×C311yescharacteristic
324C2×C5×C8C23×C311yescharacteristic
325C5×C4⋊C4—21no—
326C5×C4⋊C4C23×C311yescharacteristic
327C5×C22⋊C4—21no—
328C22⋊Dic5—21no—
329C22⋊Dic5—21no—
330C22⋊Dic5—21no—
331C22⋊Dic5—21no—
332C22⋊Dic5—21no—
333C22⋊Dic5C3×D411yescharacteristic
334#689—22no—
335#687—22no—
336#687—22no—
337#687—22no—
338#687C3×D414yescomplemented
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
350C2×#168—22no—
351C2×#168C23×C311yescharacteristic
352C2×#168C23×C311yescharacteristic
353Dic20—22no—
354Dic20—41no—
355#676—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#452—51no—
366#451—51no—
367#450C3×D511yescharacteristic, complemented
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—21no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390C3×Dic5—22no—
391C3×Dic5—21no—
392C3×Dic5—21no—
393C3×Dic5—21no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—21no—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—51no—
401C2×C3×Q8—51no—
402C2×C3×Q8—51no—
403C2×C3×Q8—101no—
404C2×C3×Q8—102no—
405C2×C3×Q8—101no—
406C2×C3×Q8—102no—
407C2×C3×Q8—201no—
408C2×C3×Q8—201no—
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—51no—
419C22×C3×C4—101no—
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—41no—
429C3×SD16—54no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—102no—
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×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×D4—21no—
469C5×D4—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×C5C2×C3×D411yescharacteristic
478C2×C4×C5C24×C311yescharacteristic
479C22⋊D5—22no—
480C22⋊D5—42no—
481C22⋊D5—81no—
482C2×Dic5—21no—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—42no—
487C2×Dic5—42no—
488C2×Dic5—81no—
489C2×Dic5C2×C3×D411yescharacteristic
490C2×Dic5C2×C3×D411yescharacteristic
491C2×Dic5C2×C3×D411yescharacteristic
492C4×D5—21no—
493C4×D5—21no—
494C4×D5—42no—
495Dic10—21no—
496Dic10—21no—
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×#41—51no—
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4C2×C3×D511yescharacteristic
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—104no—
520C2×SD16C2×C3×D511yescharacteristic
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
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#102C2×C3×D511yescharacteristic
548#102C2×C3×D511yescharacteristic
549C22⋊C8—51no—
550C22⋊C8C2×C3×D511yescharacteristic
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—52no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—202no—
575C3×Q8—202no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—42no—
580C3×D4—102no—
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—51no—
589C2×C3×C4—51no—
590C2×C3×C4—51no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—202no—
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—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—21no—
622C4×C5—41no—
623C4×C5—41no—
624C4×C5C22×C3×D411yescharacteristic
625C4×C5C3×H(5,𝔽2)11yescharacteristic
626Dic5—21no—
627Dic5—21no—
628Dic5—22no—
629Dic5—21no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—21no—
634#41—102no—
635#41—201no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—101no—
640C2×Q8—102no—
641C2×Q8—101no—
642C2×Q8—102no—
643C2×Q8—201no—
644C2×Q8—201no—
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—51no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4C22×C3×D511yescharacteristic
660Q16—102no—
661Q16—102no—
662Q16—201no—
663SD16—22no—
664SD16—41no—
665SD16—54no—
666SD16—102no—
667SD16—102no—
668SD16—102no—
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—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—41no—
712C3×C4—41no—
713C3×C4—101no—
714C3×C4—101no—
715C3×C4—101no—
716C3×C4—102no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4C2×D4×D511yescharacteristic
721C3×C4#414411yescharacteristic
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—52no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8—202no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—42no—
750D4—102no—
751D4—202no—
752D4—401no—
753D4C3×D4×D512yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—51no—
759C2×C4—51no—
760C2×C4—51no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—202no—
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—22no—
778C2×C3—42no—
779C2×C3—81no—
780C2×C3—201no—
781C2×C3#6592411yescharacteristic
782C2×C3C2×#406111yescharacteristic
783C2×C3#6610911yescharacteristic
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—41no—
801C4—41no—
802C4—101no—
803C4—101no—
804C4—102no—
805C4—101no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4C2×C3×D4×D511yescharacteristic
810C4C3×#414411yescharacteristic
811C3#1061190011yescharacteristic, direct product factor, Sylow
812C2—22no—
813C2—42no—
814C2—81no—
815C2—201no—
816C2C3×#6592411yescharacteristic
817C2C2×C3×#406111yescharacteristic
818C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#450C2
socleC22×C3×C5C22×D4
prime radicalC3×#66140C2
hypercenterC3×#450D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
2. C22×C3×#687C2semidirect
3. C2×C3×#4061C2semidirect
4. C3×#65966C2semidirect
5. C3×C5×#450C2semidirect
6. C3×#65459C2semidirect
7. C3×#65456C2semidirect
8. C3×#65451C2semidirect
9. C3×#65340C2semidirect
10. C3×#65072C2semidirect
11. C3×#65069C2semidirect
12. C3×#65056C2semidirect
13. C3×#65046C2semidirect
14. C3×#65028C2semidirect
15. C3×#65019C2semidirect
16. #10611900C3direct (N × H)
18. C2×C3×Q8×D5C22semidirect
26. C3×#4090C22semidirect
27. C2×C3×#689C22semidirect
42. C2×C3×Dic20C22semidirect
43. C2×C3×Dic20C22semidirect
44. C2×C3×#676C22semidirect
45. C3×#4043C22semidirect
48. C3×#4033C22semidirect
54. C3×#3967C22semidirect
55. C3×#3952C22semidirect
56. C3×#3948C22semidirect
57. C3×#3948C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
60. C3×#3942C22semidirect
61. C3×#3939C22semidirect
64. C22×#687C2×C3semidirect
65. C2×#4061C2×C3semidirect
66. #65966C2×C3semidirect
67. C5×#450C2×C3semidirect
68. #65459C2×C3semidirect
69. #65456C2×C3semidirect
70. #65451C2×C3semidirect
71. #65340C2×C3semidirect
72. #65072C2×C3semidirect
73. #65069C2×C3semidirect
74. #65056C2×C3semidirect
75. #65046C2×C3semidirect
76. #65028C2×C3semidirect
77. #65019C2×C3semidirect
122. C3×#687D4semidirect
151. C3×#450D5semidirect
156. C2×Q8×D5C22×C3semidirect
164. #4090C22×C3semidirect
165. C2×#689C22×C3semidirect
180. C2×Dic20C22×C3semidirect
181. C2×Dic20C22×C3semidirect
182. C2×#676C22×C3semidirect
183. #4043C22×C3semidirect
186. #4033C22×C3semidirect
192. #3967C22×C3semidirect
193. #3952C22×C3semidirect
194. #3948C22×C3semidirect
195. #3948C22×C3semidirect
196. #3947C22×C3semidirect
197. #3946C22×C3semidirect
198. #3942C22×C3semidirect
199. #3939C22×C3semidirect
338. #687C3×D4semidirect
367. #450C3×D5semidirect
380. C22×C3×C5#137semidirect
616. C22×C5C3×#137semidirect
695. C3×C5#3266semidirect
708. C22×C3#4061semidirect
784. C5C3×#3266semidirect
797. C22C3×#4061semidirect
811. C3#10611900direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661402
C22×C3×#6872
C2×C3×#40612
C3×#659662
C3×C5×#4502
C3×#654592
C3×#654562
C3×#654512
C3×#653402
C3×#650722
C3×#650692
C3×#650562
C3×#650462
C3×#650282
C3×#650192
#106119003
C3×#32665