Finite Group Databasebeta

← C3×#10611853 #14453938

Subgroups — C3×#10611853 #14453938

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66158C211yesmaximal, characteristic, complemented
2C2×C3×#4096C211yesmaximal, characteristic, complemented
3C2×C3×#4057C211yesmaximal, characteristic, complemented
4C3×#65946C211yesmaximal, characteristic, complemented
5C3×C5×#449C211yesmaximal, characteristic, complemented
6C3×#65458C211yesmaximal, characteristic, complemented
7C3×#65456C211yesmaximal, characteristic, complemented
8C3×#65442C211yesmaximal, characteristic, complemented
9C3×#65330C211yesmaximal, characteristic, complemented
10C3×#65107C211yesmaximal, characteristic, complemented
11C3×#65105C211yesmaximal, characteristic, complemented
12C3×#65074C211yesmaximal, characteristic, complemented
13C3×#65072C211yesmaximal, characteristic, complemented
14C3×#65022C211yesmaximal, characteristic, complemented
15C3×#65019C211yesmaximal, characteristic, complemented
16#10611853C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×C3×#711C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic
22C2×C3×C5×D8C2211yescharacteristic
23C3×C5×#121C2211yescharacteristic
24C3×#4096—24no—
25C3×#4092C2211yescharacteristic
26C3×#4090C2211yescharacteristic, complemented
27C2×C3×#689C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic
29C3×#4085—21no—
30C3×#4084—21no—
31C3×#4083—21no—
32C3×#4082C2211yescharacteristic
33C3×#4081—21no—
34C3×D4×Dic5C2211yescharacteristic, complemented
35C2×C3×#687C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic
38C3×#4075—21no—
39C3×C4×C22⋊D5C2211yescharacteristic
40C3×#4070C2211yescharacteristic, complemented
41C2×C3×#683—21no—
42C22×C3×#168C2211yescharacteristic, complemented
43C3×#4057—24no—
44C2×C3×Dic20C2211yescharacteristic, complemented
45C2×C3×#677C2211yescharacteristic
46C2×C3×#676C2211yescharacteristic
47C3×#4043C2211yescharacteristic
48C3×#4039C2211yescharacteristic
49C3×#4029—21no—
50C3×D5×C22⋊C4—21no—
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic
55C3×#3953C2211yescharacteristic
56C3×#3952C2211yescharacteristic
57C3×#3948C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3942C2211yescharacteristic, complemented
61C3×#3940C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63#66158C2×C311yescharacteristic, complemented
64C2×#4096C2×C311yescharacteristic, complemented
65C2×#4057C2×C311yescharacteristic, complemented
66#65946C2×C311yescharacteristic, complemented
67C5×#449C2×C311yescharacteristic, complemented
68#65458C2×C311yescharacteristic, complemented
69#65456C2×C311yescharacteristic, complemented
70#65442C2×C311yescharacteristic, complemented
71#65330C2×C311yescharacteristic, complemented
72#65107C2×C311yescharacteristic, complemented
73#65105C2×C311yescharacteristic, complemented
74#65074C2×C311yescharacteristic, complemented
75#65072C2×C311yescharacteristic, complemented
76#65022C2×C311yescharacteristic, complemented
77#65019C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C5×D4C2311yescharacteristic
86C22×C3×C4×C5—21no—
87C22×C3×C4×C5C2311yescharacteristic
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5D411yescharacteristic
92C22×C3×Dic5—21no—
93C22×C3×Dic5—21no—
94C3×#711—22no—
95C3×#711—41no—
96C3×D4×D5—22no—
97C3×D4×D5—41no—
98C3×#709—22no—
99C3×#709—41no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×SD16—41no—
107C3×C5×D8—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
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⋊Dic5D411yescharacteristic
117C3×#689—22no—
118C3×#688—22no—
119C3×#687—22no—
120C3×#687—22no—
121C3×#686D414yescomplemented
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685D411yescharacteristic
126C3×C4⋊Dic5—21no—
127C3×C4⋊Dic5C2311yescharacteristic
128C3×#683—21no—
129C3×#683—21no—
130C3×#683—21no—
131C3×#683—21no—
132C3×#683D411yescharacteristic
133C3×C4×Dic5C2311yescharacteristic
134C2×C3×#168—22no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×Dic20—41no—
138C3×#677—22no—
139C3×#676—22no—
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#547—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#470—51no—
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449D511yescharacteristic, complemented
153C3×#442—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic, complemented
156C2×#711C22×C311yescharacteristic
157C2×D4×D5C22×C311yescharacteristic
158C2×#709C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic
160C2×C5×D8C22×C311yescharacteristic
161C5×#121C22×C311yescharacteristic
162#4096—24no—
163#4092C22×C311yescharacteristic
164#4090C22×C311yescharacteristic, complemented
165C2×#689C22×C311yescharacteristic, complemented
166C2×#688C22×C311yescharacteristic
167#4085—21no—
168#4084—21no—
169#4083—21no—
170#4082C22×C311yescharacteristic
171#4081—21no—
172D4×Dic5C22×C311yescharacteristic, complemented
173C2×#687C22×C311yescharacteristic
174C2×#687C22×C311yescharacteristic, complemented
175C2×#686C22×C311yescharacteristic
176#4075—21no—
177C4×C22⋊D5C22×C311yescharacteristic
178#4070C22×C311yescharacteristic, complemented
179C2×#683—21no—
180C22×#168C22×C311yescharacteristic, complemented
181#4057—24no—
182C2×Dic20C22×C311yescharacteristic, complemented
183C2×#677C22×C311yescharacteristic
184C2×#676C22×C311yescharacteristic
185#4043C22×C311yescharacteristic
186#4039C22×C311yescharacteristic
187#4029—21no—
188D5×C22⋊C4—21no—
189C5×#103C22×C311yescharacteristic, complemented
190C5×#102C22×C311yescharacteristic, complemented
191C5×C22⋊C8C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic
193#3953C22×C311yescharacteristic
194#3952C22×C311yescharacteristic
195#3948C22×C311yescharacteristic, complemented
196#3947C22×C311yescharacteristic, complemented
197#3946C22×C311yescharacteristic, complemented
198#3942C22×C311yescharacteristic, complemented
199#3940C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—81no—
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—42no—
215C3×C5×D4—81no—
216C3×C5×D4C2×D412yes—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—42no—
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2411yescharacteristic
224C3×C22⋊D5—41no—
225C3×C22⋊D5—42no—
226C3×C22⋊D5—42no—
227C3×C22⋊D5—42no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—42no—
232C2×C3×Dic5—42no—
233C2×C3×Dic5C2×D411yescharacteristic
234C2×C3×Dic5C2×D411yescharacteristic
235C2×C3×Dic5C2×D411yescharacteristic
236C3×D20—21no—
237C3×D20C2×D412yes—
238C3×C4×D5—21no—
239C3×C4×D5—21no—
240C3×C4×D5—42no—
241C3×C4×D5—81no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×#168—21no—
249C3×#168C2×D412yes—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41C2×D511yescharacteristic, complemented
253C22×C3×D4—51no—
254C3×AGL(1,ℤ/8)—104no—
255C3×#135—104no—
256C2×C3×Q16—51no—
257C2×C3×Q16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×D8—51no—
264C2×C3×D8C2×D511yescharacteristic
265C2×C3×M16—51no—
266C22×C3×C8—51no—
267C3×C4⋊Q8—51no—
268C3×#124—51no—
269C3×#123—101no—
270C3×#123—101no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—51no—
274C3×C22⋊Q8—51no—
275C3×#121—101no—
276C3×#121—101no—
277C3×#121C2×D511yescharacteristic
278C3×#120—101no—
279C3×C4×D4—51no—
280C3×C4×D4—51no—
281C3×C4×D4—51no—
282C2×C3×C4⋊C4—101no—
283C2×C3×C22⋊C4—101no—
284C3×#106—51no—
285C3×C4⋊C8—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103C2×D511yescharacteristic, complemented
289C3×#102—51no—
290C3×#102—51no—
291C3×#102C2×D511yescharacteristic, complemented
292C3×C22⋊C8—51no—
293C3×C22⋊C8C2×D511yescharacteristic, complemented
294C3×#97—51no—
295C23×D5—21no—
296C5×#41—22no—
297C5×#41—41no—
298C2×C5×Q8C23×C311yescharacteristic
299C2×C5×D4—21no—
300C2×C5×D4—21no—
301C2×C5×D4C23×C311yescharacteristic
302C2×C5×D4C23×C311yescharacteristic
303C22×C4×C5—21no—
304C22×C4×C5C23×C311yescharacteristic
305C2×C22⋊D5—21no—
306C2×C22⋊D5—21no—
307C2×C22⋊D5—21no—
308C2×C22⋊D5C3×D411yescharacteristic
309C22×Dic5—21no—
310C22×Dic5—21no—
311#711—22no—
312#711—41no—
313D4×D5—22no—
314D4×D5—41no—
315#709—22no—
316#709—41no—
317C2×D20C23×C311yescharacteristic
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×C4×D5C23×C311yescharacteristic
321C2×Dic10C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×SD16—41no—
324C5×D8—22no—
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C5×C4⋊C4C23×C311yescharacteristic
328C5×C22⋊C4—21no—
329C22⋊Dic5—21no—
330C22⋊Dic5—21no—
331C22⋊Dic5—21no—
332C22⋊Dic5—21no—
333C22⋊Dic5C3×D411yescharacteristic
334#689—22no—
335#688—22no—
336#687—22no—
337#687—22no—
338#686C3×D414yescomplemented
339#685—21no—
340#685—21no—
341#685—21no—
342#685C3×D411yescharacteristic
343C4⋊Dic5—21no—
344C4⋊Dic5C23×C311yescharacteristic
345#683—21no—
346#683—21no—
347#683—21no—
348#683—21no—
349#683C3×D411yescharacteristic
350C4×Dic5C23×C311yescharacteristic
351C2×#168—22no—
352C2×#168C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354Dic20—41no—
355#677—22no—
356#676—22no—
357C2×AGL(1,ℤ/8)—51no—
358C2×#135—51no—
359#547—51no—
360#546—51no—
361#497—51no—
362#470—51no—
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449C3×D511yescharacteristic, complemented
370#442—51no—
371#435—51no—
372C22×C3×C5—22no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C22×D411yescharacteristic
382C2×C3×D5—21no—
383C2×C3×D5—22no—
384C2×C3×D5—21no—
385C2×C3×D5—21no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5—41no—
392C3×C4×C5C22×D411yescharacteristic
393C3×C4×C5H(5,𝔽2)11yescharacteristic
394C3×Dic5—21no—
395C3×Dic5—21no—
396C3×Dic5—21no—
397C3×Dic5—41no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—101no—
401C3×#41—22no—
402C3×#41—41no—
403C3×#41—102no—
404C3×#41—102no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8—51no—
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—21no—
411C2×C3×D4—21no—
412C2×C3×D4—51no—
413C2×C3×D4—51no—
414C2×C3×D4—101no—
415C2×C3×D4—102no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4—201no—
419C2×C3×D4C22×D511yescharacteristic
420C2×C3×D4C22×D511yescharacteristic
421C22×C3×C4—21no—
422C22×C3×C4—51no—
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4—101no—
427C22×C3×C4C22×D511yescharacteristic
428C3×Q16—102no—
429C3×Q16—201no—
430C3×SD16—41no—
431C3×SD16—102no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—102no—
435C3×D8—22no—
436C3×D8—54no—
437C3×M16—102no—
438C2×C3×C8—51no—
439C2×C3×C8—51no—
440C2×C3×C8—102no—
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D511yescharacteristic
443C3×C4⋊C4—51no—
444C3×C4⋊C4—51no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4—101no—
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C42—51no—
462C23×C5—21no—
463C23×C5—21no—
464C23×C5C2×C3×D411yescharacteristic
465C22×D5—21no—
466C22×D5—42no—
467C22×D5—42no—
468C22×D5—81no—
469C22×D5C2×C3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×D4—21no—
473C5×D4—21no—
474C5×D4—21no—
475C5×D4—42no—
476C5×D4—81no—
477C5×D4C2×C3×D412yes—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—42no—
483C2×C4×C5C2×C3×D411yescharacteristic
484C2×C4×C5C24×C311yescharacteristic
485C22⋊D5—41no—
486C22⋊D5—42no—
487C22⋊D5—42no—
488C22⋊D5—42no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—42no—
493C2×Dic5—42no—
494C2×Dic5C2×C3×D411yescharacteristic
495C2×Dic5C2×C3×D411yescharacteristic
496C2×Dic5C2×C3×D411yescharacteristic
497D20—21no—
498D20C2×C3×D412yes—
499C4×D5—21no—
500C4×D5—21no—
501C4×D5—42no—
502C4×D5—81no—
503Dic10—21no—
504Dic10—21no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8—21no—
509#168—21no—
510#168C2×C3×D412yes—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41C2×C3×D511yescharacteristic, complemented
514C22×D4—51no—
515AGL(1,ℤ/8)—104no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16—51no—
523C2×SD16C2×C3×D511yescharacteristic
524C2×D8—51no—
525C2×D8C2×C3×D511yescharacteristic
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8—51no—
529#124—51no—
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8—51no—
535C22⋊Q8—51no—
536#121—101no—
537#121—101no—
538#121C2×C3×D511yescharacteristic
539#120—101no—
540C4×D4—51no—
541C4×D4—51no—
542C4×D4—51no—
543C2×C4⋊C4—101no—
544C2×C22⋊C4—101no—
545#106—51no—
546C4⋊C8—51no—
547#103—51no—
548#103—51no—
549#103C2×C3×D511yescharacteristic, complemented
550#102—51no—
551#102—51no—
552#102C2×C3×D511yescharacteristic, complemented
553C22⋊C8—51no—
554C22⋊C8C2×C3×D511yescharacteristic, complemented
555#97—51no—
556C2×C3×C5—41no—
557C2×C3×C5—42no—
558C2×C3×C5—81no—
559C2×C3×C5D4211yescharacteristic
560C2×C3×C5#57511yescharacteristic
561C2×C3×C5#57711yescharacteristic
562C3×D5—41no—
563C3×D5—42no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—51no—
567C23×C3—101no—
568C23×C3—202no—
569C23×C3—202no—
570C23×C3—401no—
571C23×C3D4×D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—42no—
582C3×D4—52no—
583C3×D4—81no—
584C3×D4—101no—
585C3×D4—201no—
586C3×D4—202no—
587C3×D4—202no—
588C3×D4—202no—
589C3×D4D4×D512yes—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—42no—
595C2×C3×C4—51no—
596C2×C3×C4—51no—
597C2×C3×C4—51no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—101no—
603C2×C3×C4—202no—
604C2×C3×C4—202no—
605C2×C3×C4—202no—
606C2×C3×C4—401no—
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—52no—
612C3×C8—101no—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—22no—
616C22×C5—21no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5C22×C3×D411yescharacteristic
623C2×D5—21no—
624C2×D5—21no—
625C2×D5—21no—
626C2×D5—22no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—84no—
630C4×C5—21no—
631C4×C5—41no—
632C4×C5—41no—
633C4×C5C22×C3×D411yescharacteristic
634C4×C5C3×H(5,𝔽2)11yescharacteristic
635Dic5—21no—
636Dic5—21no—
637Dic5—21no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641C24—101no—
642#41—22no—
643#41—41no—
644#41—102no—
645#41—102no—
646#41—201no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8—51no—
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—51no—
654C2×D4—51no—
655C2×D4—101no—
656C2×D4—102no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—201no—
660C2×D4C22×C3×D511yescharacteristic
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—51no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4C22×C3×D511yescharacteristic
669Q16—102no—
670Q16—201no—
671SD16—41no—
672SD16—102no—
673SD16—102no—
674SD16—102no—
675SD16—102no—
676D8—22no—
677D8—54no—
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—51no—
685C4⋊C4—51no—
686C4⋊C4—101no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—51no—
694C22⋊C4—51no—
695C22⋊C4—101no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4—101no—
701C22⋊C4—101no—
702C42—51no—
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—22no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—101no—
714C22×C3—101no—
715C22×C3—101no—
716C22×C3—102no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—101no—
725C3×C4—101no—
726C3×C4—101no—
727C3×C4—201no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414411yescharacteristic
732C2×C5—41no—
733C2×C5—42no—
734C2×C5—81no—
735C2×C5C3×D4211yescharacteristic
736C2×C5C3×#57511yescharacteristic
737C2×C5C3×#57711yescharacteristic
738D5—41no—
739D5—42no—
740C23—21no—
741C23—21no—
742C23—51no—
743C23—101no—
744C23—202no—
745C23—202no—
746C23—401no—
747C23C3×D4×D511yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—101no—
751Q8—101no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—52no—
759D4—81no—
760D4—101no—
761D4—201no—
762D4—202no—
763D4—202no—
764D4—202no—
765D4C3×D4×D512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—42no—
771C2×C4—51no—
772C2×C4—51no—
773C2×C4—51no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4—401no—
783C2×C4C3×D4×D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—21no—
787C8—52no—
788C8—101no—
789C2×C3—41no—
790C2×C3—42no—
791C2×C3—81no—
792C2×C3—201no—
793C2×C3—202no—
794C2×C3#6592411yescharacteristic
795C2×C3#6610211yescharacteristic
796C2×C3#6610911yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—21no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—101no—
808C22—101no—
809C22—101no—
810C22—102no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—41no—
817C4—41no—
818C4—101no—
819C4—101no—
820C4—101no—
821C4—201no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414411yescharacteristic
826C3#1061185311yescharacteristic, direct product factor, Sylow
827C2—41no—
828C2—42no—
829C2—81no—
830C2—201no—
831C2—202no—
832C2C3×#6592411yescharacteristic
833C2C3×#6610211yescharacteristic
834C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenterC3×#449D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#66158C2semidirect
2. C2×C3×#4096C2semidirect
3. C2×C3×#4057C2semidirect
4. C3×#65946C2semidirect
5. C3×C5×#449C2semidirect
6. C3×#65458C2semidirect
7. C3×#65456C2semidirect
8. C3×#65442C2semidirect
9. C3×#65330C2semidirect
10. C3×#65107C2semidirect
11. C3×#65105C2semidirect
12. C3×#65074C2semidirect
13. C3×#65072C2semidirect
14. C3×#65022C2semidirect
15. C3×#65019C2semidirect
16. #10611853C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
26. C3×#4090C22semidirect
27. C2×C3×#689C22semidirect
34. C3×D4×Dic5C22semidirect
36. C2×C3×#687C22semidirect
40. C3×#4070C22semidirect
42. C22×C3×#168C22semidirect
44. C2×C3×Dic20C22semidirect
51. C3×C5×#103C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×C22⋊C8C22semidirect
57. C3×#3948C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
60. C3×#3942C22semidirect
61. C3×#3940C22semidirect
63. #66158C2×C3semidirect
64. C2×#4096C2×C3semidirect
65. C2×#4057C2×C3semidirect
66. #65946C2×C3semidirect
67. C5×#449C2×C3semidirect
68. #65458C2×C3semidirect
69. #65456C2×C3semidirect
70. #65442C2×C3semidirect
71. #65330C2×C3semidirect
72. #65107C2×C3semidirect
73. #65105C2×C3semidirect
74. #65074C2×C3semidirect
75. #65072C2×C3semidirect
76. #65022C2×C3semidirect
77. #65019C2×C3semidirect
121. C3×#686D4semidirect
152. C3×#449D5semidirect
155. C2×C5×#41C22×C3semidirect
164. #4090C22×C3semidirect
165. C2×#689C22×C3semidirect
172. D4×Dic5C22×C3semidirect
174. C2×#687C22×C3semidirect
178. #4070C22×C3semidirect
180. C22×#168C22×C3semidirect
182. C2×Dic20C22×C3semidirect
189. C5×#103C22×C3semidirect
190. C5×#102C22×C3semidirect
191. C5×C22⋊C8C22×C3semidirect
195. #3948C22×C3semidirect
196. #3947C22×C3semidirect
197. #3946C22×C3semidirect
198. #3942C22×C3semidirect
199. #3940C22×C3semidirect
252. C2×C3×#41C2×D5semidirect
288. C3×#103C2×D5semidirect
291. C3×#102C2×D5semidirect
293. C3×C22⋊C8C2×D5semidirect
338. #686C3×D4semidirect
369. #449C3×D5semidirect
513. C2×#41C2×C3×D5semidirect
549. #103C2×C3×D5semidirect
552. #102C2×C3×D5semidirect
554. C22⋊C8C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10611853direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661582
C2×C3×#40962
C2×C3×#40572
C3×#659462
C3×C5×#4492
C3×#654582
C3×#654562
C3×#654422
C3×#653302
C3×#651072
C3×#651052
C3×#650742
C3×#650722
C3×#650222
C3×#650192
#106118533
C3×#32675