Finite Group Databasebeta

← C3×#10613613 #14453956

Subgroups — C3×#10613613 #14453956

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
1C2×C3×#4065C211yesmaximal, characteristic, complemented
2C2×C3×#4060C211yesmaximal, characteristic, complemented
3C3×#66060C211yesmaximal, characteristic, complemented
4C3×#66010C211yesmaximal, characteristic, complemented
5C3×C5×#497C211yesmaximal, characteristic, complemented
6C3×#65478C211yesmaximal, characteristic, complemented
7C3×#65476C211yesmaximal, characteristic, complemented
8C3×#65476C211yesmaximal, characteristic, complemented
9C3×#65461C211yesmaximal, characteristic, complemented
10C3×#65460C211yesmaximal, characteristic, complemented
11C3×#65458C211yesmaximal, characteristic, complemented
12C3×#65372C211yesmaximal, characteristic, complemented
13C3×#65346C211yesmaximal, characteristic, complemented
14C3×#65000C211yesmaximal, characteristic, complemented
15C3×#64995C211yesmaximal, characteristic, complemented
16#10613613C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×Q16C2211yescharacteristic, complemented
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×SD16C2211yescharacteristic
25C3×C5×C4⋊Q8C2211yescharacteristic, complemented
26C3×C5×#124C2211yescharacteristic
27C3×#4092C2211yescharacteristic
28C3×#4092C2211yescharacteristic
29C3×#4092C2211yescharacteristic, complemented
30C2×C3×#688C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic, complemented
33C3×#4084C2211yescharacteristic
34C2×C3×#686C2211yescharacteristic
35C3×#4065—24no—
36C3×#4060—24no—
37C2×C3×D40C2211yescharacteristic
38C2×C3×#676C2211yescharacteristic
39C2×C3×C8×D5C2211yescharacteristic, complemented
40C3×#4041—21no—
41C3×#4040—21no—
42C3×#4040—21no—
43C3×D5×C4⋊C4—21no—
44C3×#4030—21no—
45C3×#4029—21no—
46C3×#4028—21no—
47C3×D5×C22⋊C4—21no—
48C3×C4×D20C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic, complemented
51C3×C5×#97C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3967C2211yescharacteristic, complemented
54C3×#3967C2211yescharacteristic, complemented
55C3×#3964C2211yescharacteristic
56C3×#3953C2211yescharacteristic
57C3×#3953C2211yescharacteristic, complemented
58C3×#3952C2211yescharacteristic
59C3×#3952C2211yescharacteristic, complemented
60C3×#3949C2211yescharacteristic, complemented
61C3×C4⋊#168C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×#4065C2×C311yescharacteristic, complemented
64C2×#4060C2×C311yescharacteristic, complemented
65#66060C2×C311yescharacteristic, complemented
66#66010C2×C311yescharacteristic, complemented
67C5×#497C2×C311yescharacteristic, complemented
68#65478C2×C311yescharacteristic, complemented
69#65476C2×C311yescharacteristic, complemented
70#65476C2×C311yescharacteristic, complemented
71#65461C2×C311yescharacteristic, complemented
72#65460C2×C311yescharacteristic, complemented
73#65458C2×C311yescharacteristic, complemented
74#65372C2×C311yescharacteristic, complemented
75#65346C2×C311yescharacteristic, complemented
76#65000C2×C311yescharacteristic, complemented
77#64995C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C3×#713—22no—
86C3×#713—22no—
87C3×#713—22no—
88C3×#713—41no—
89C3×#713—41no—
90C3×#713—41no—
91C3×D4×D5—22no—
92C3×D4×D5—41no—
93C2×C3×D20—21no—
94C2×C3×D20—21no—
95C2×C3×D20—21no—
96C2×C3×D20D411yescharacteristic
97C2×C3×D20C2311yescharacteristic
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×C4×D5C2311yescharacteristic
106C3×C5×Q16—22no—
107C3×C5×Q16—41no—
108C3×C5×SD16—22no—
109C3×C5×SD16—41no—
110C2×C3×C5×C8C2311yescharacteristic
111C2×C3×C5×C8C2311yescharacteristic
112C3×C5×C4⋊C4—21no—
113C3×C5×C4⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4—21no—
116C3×C42×C5C2311yescharacteristic
117C3×C22⋊Dic5—21no—
118C3×#688—22no—
119C3×#688—22no—
120C3×#688—22no—
121C3×#686—22no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685D411yescharacteristic
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5D411yescharacteristic
130C3×C4⋊Dic5C2311yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683—21no—
134C3×#683—21no—
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×D40D414yescomplemented
138C3×#676—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#547—51no—
143C3×#546—51no—
144C3×#497D511yescharacteristic, complemented
145C3×#470—51no—
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C2×#713C22×C311yescharacteristic
156C2×#713C22×C311yescharacteristic
157C2×#713C22×C311yescharacteristic, complemented
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×Q16C22×C311yescharacteristic, complemented
160C2×C5×Q16C22×C311yescharacteristic, complemented
161C2×C5×SD16C22×C311yescharacteristic
162C2×C5×SD16C22×C311yescharacteristic
163C5×C4⋊Q8C22×C311yescharacteristic, complemented
164C5×#124C22×C311yescharacteristic
165#4092C22×C311yescharacteristic
166#4092C22×C311yescharacteristic
167#4092C22×C311yescharacteristic, complemented
168C2×#688C22×C311yescharacteristic
169C2×#688C22×C311yescharacteristic
170C2×#688C22×C311yescharacteristic, complemented
171#4084C22×C311yescharacteristic
172C2×#686C22×C311yescharacteristic
173#4065—24no—
174#4060—24no—
175C2×D40C22×C311yescharacteristic
176C2×#676C22×C311yescharacteristic
177C2×C8×D5C22×C311yescharacteristic, complemented
178#4041—21no—
179#4040—21no—
180#4040—21no—
181D5×C4⋊C4—21no—
182#4030—21no—
183#4029—21no—
184#4028—21no—
185D5×C22⋊C4—21no—
186C4×D20C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic
188C4×D20C22×C311yescharacteristic, complemented
189C5×#97C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3967C22×C311yescharacteristic, complemented
192#3967C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic
194#3953C22×C311yescharacteristic
195#3953C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic
197#3952C22×C311yescharacteristic, complemented
198#3949C22×C311yescharacteristic, complemented
199C4⋊#168C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—42no—
205C22×C3×D5—42no—
206C22×C3×D5—81no—
207C22×C3×D5C2×D411yescharacteristic
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×Q8—21no—
214C3×C5×Q8—21no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2411yescharacteristic
223C3×C22⋊D5—42no—
224C3×C22⋊D5—81no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5C2×D411yescharacteristic
228C2×C3×Dic5C2×D411yescharacteristic
229C3×D20—21no—
230C3×D20—21no—
231C3×D20—41no—
232C3×D20—42no—
233C3×D20—42no—
234C3×D20—42no—
235C3×D20C2×D412yes—
236C3×D20C2×D412yes—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—21no—
240C3×C4×D5—21no—
241C3×C4×D5—42no—
242C3×C4×D5—42no—
243C3×C4×D5—42no—
244C3×C4×D5—42no—
245C3×C4×D5—81no—
246C3×C5×C8—21no—
247C3×C5×C8C2×D412yes—
248C3×#168—21no—
249C3×#168—21no—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41—51no—
253C22×C3×D4—51no—
254C3×AGL(1,ℤ/8)—104no—
255C3×#135—104no—
256C2×C3×Q16C2×D511yescharacteristic, complemented
257C2×C3×Q16C2×D511yescharacteristic, complemented
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16C2×D511yescharacteristic
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×D8—51no—
264C2×C3×D8—51no—
265C2×C3×M16—51no—
266C22×C3×C8—51no—
267C3×C4⋊Q8C2×D511yescharacteristic, complemented
268C3×#124C2×D511yescharacteristic
269C3×#123—101no—
270C3×#123—101no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—51no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#121—101no—
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×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97C2×D511yescharacteristic, complemented
295C23×D5—21no—
296C2×C5×Q8C23×C311yescharacteristic
297C2×C5×Q8C23×C311yescharacteristic
298C2×C5×Q8C23×C311yescharacteristic
299C2×C5×D4C23×C311yescharacteristic
300C2×C22⋊D5—21no—
301C2×C22⋊D5—21no—
302#713—22no—
303#713—22no—
304#713—22no—
305#713—41no—
306#713—41no—
307#713—41no—
308D4×D5—22no—
309D4×D5—41no—
310C2×D20—21no—
311C2×D20—21no—
312C2×D20—21no—
313C2×D20C3×D411yescharacteristic
314C2×D20C23×C311yescharacteristic
315C2×D20C23×C311yescharacteristic
316C2×C4×D5—21no—
317C2×C4×D5—21no—
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×C4×D5—21no—
321C2×C4×D5C23×C311yescharacteristic
322C2×C4×D5C23×C311yescharacteristic
323C5×Q16—22no—
324C5×Q16—41no—
325C5×SD16—22no—
326C5×SD16—41no—
327C2×C5×C8C23×C311yescharacteristic
328C2×C5×C8C23×C311yescharacteristic
329C5×C4⋊C4—21no—
330C5×C4⋊C4—21no—
331C5×C22⋊C4—21no—
332C5×C22⋊C4—21no—
333C42×C5C23×C311yescharacteristic
334C22⋊Dic5—21no—
335#688—22no—
336#688—22no—
337#688—22no—
338#686—22no—
339#685—21no—
340#685—21no—
341#685—21no—
342#685—21no—
343#685—21no—
344#685C3×D411yescharacteristic
345#685C3×D411yescharacteristic
346C4⋊Dic5C3×D411yescharacteristic
347C4⋊Dic5C23×C311yescharacteristic
348C4⋊Dic5C23×C311yescharacteristic
349#683—21no—
350#683—21no—
351#683—21no—
352C2×#168C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354D40C3×D414yescomplemented
355#676—22no—
356C8×D5—22no—
357C2×AGL(1,ℤ/8)—51no—
358C2×#135—51no—
359#547—51no—
360#546—51no—
361#497C3×D511yescharacteristic, complemented
362#470—51no—
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442—51no—
371#435—51no—
372C22×C3×C5—41no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5C22×D411yescharacteristic
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—21no—
381C2×C3×D5—21no—
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5—41no—
394C3×C4×C5C22×D411yescharacteristic
395C3×C4×C5H(5,𝔽2)11yescharacteristic
396C3×Dic5—21no—
397C3×Dic5—21no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—101no—
401C3×#41—102no—
402C3×#41—102no—
403C3×#41—102no—
404C3×#41—201no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8C22×D511yescharacteristic
408C2×C3×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—51no—
413C2×C3×D4—101no—
414C2×C3×D4—101no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—102no—
418C2×C3×D4—101no—
419C2×C3×D4—201no—
420C2×C3×D4C22×D511yescharacteristic
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4—101no—
427C22×C3×C4—101no—
428C3×Q16—22no—
429C3×Q16—41no—
430C3×SD16—22no—
431C3×SD16—41no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—102no—
435C3×D8—54no—
436C3×D8—102no—
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—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—51no—
446C3×C4⋊C4—51no—
447C3×C4⋊C4—51no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4—101no—
450C3×C4⋊C4—101no—
451C3×C22⋊C4—21no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—51no—
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×C42C22×D511yescharacteristic
462C23×C5—21no—
463C22×D5—21no—
464C22×D5—21no—
465C22×D5—42no—
466C22×D5—42no—
467C22×D5—81no—
468C22×D5C2×C3×D411yescharacteristic
469C22×D5C2×C3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—21no—
473C5×Q8—21no—
474C5×Q8—21no—
475C5×Q8—21no—
476C5×D4—21no—
477C5×D4—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5C2×C3×D411yescharacteristic
482C2×C4×C5C2×C3×D411yescharacteristic
483C2×C4×C5C24×C311yescharacteristic
484C22⋊D5—42no—
485C22⋊D5—81no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5C2×C3×D411yescharacteristic
489C2×Dic5C2×C3×D411yescharacteristic
490D20—21no—
491D20—21no—
492D20—41no—
493D20—42no—
494D20—42no—
495D20—42no—
496D20C2×C3×D412yes—
497D20C2×C3×D412yes—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—21no—
501C4×D5—21no—
502C4×D5—42no—
503C4×D5—42no—
504C4×D5—42no—
505C4×D5—42no—
506C4×D5—81no—
507C5×C8—21no—
508C5×C8C2×C3×D412yes—
509#168—21no—
510#168—21no—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41—51no—
514C22×D4—51no—
515AGL(1,ℤ/8)—104no—
516#135—104no—
517C2×Q16C2×C3×D511yescharacteristic, complemented
518C2×Q16C2×C3×D511yescharacteristic, complemented
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16C2×C3×D511yescharacteristic
523C2×SD16C2×C3×D511yescharacteristic
524C2×D8—51no—
525C2×D8—51no—
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8C2×C3×D511yescharacteristic, complemented
529#124C2×C3×D511yescharacteristic
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8—51no—
535C22⋊Q8—51no—
536#121—51no—
537#121—101no—
538#121—101no—
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#103—51no—
550#102—51no—
551#102—51no—
552#102—51no—
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97C2×C3×D511yescharacteristic, complemented
556C2×C3×C5—81no—
557C2×C3×C5D4211yescharacteristic
558C2×C3×C5#57511yescharacteristic
559C2×C3×C5#57711yescharacteristic
560C3×D5—41no—
561C3×D5—41no—
562C3×D5—42no—
563C3×D5—42no—
564C23×C3—21no—
565C23×C3—51no—
566C23×C3—51no—
567C23×C3—101no—
568C23×C3—101no—
569C23×C3—202no—
570C23×C3—202no—
571C23×C3—401no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—21no—
577C3×Q8—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—52no—
581C3×D4—52no—
582C3×D4—101no—
583C3×D4—101no—
584C3×D4—201no—
585C3×D4—202no—
586C3×D4—202no—
587C3×D4—202no—
588C3×D4—202no—
589C3×D4—401no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—51no—
594C2×C3×C4—51no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—202no—
602C2×C3×C4—202no—
603C2×C3×C4—202no—
604C2×C3×C4—202no—
605C2×C3×C4—401no—
606C2×C3×C4D4×D511yescharacteristic
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—101no—
611C3×C8—101no—
612C3×C8D4×D512yes—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5C22×C3×D411yescharacteristic
617C2×D5—21no—
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—21no—
621C2×D5—21no—
622C2×D5—21no—
623C2×D5—22no—
624C2×D5—22no—
625C2×D5—41no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—84no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5C22×C3×D411yescharacteristic
636C4×C5C3×H(5,𝔽2)11yescharacteristic
637Dic5—21no—
638Dic5—21no—
639Dic5—41no—
640Dic5—41no—
641C24—101no—
642#41—102no—
643#41—102no—
644#41—102no—
645#41—201no—
646#41—201no—
647#41—201no—
648C2×Q8C22×C3×D511yescharacteristic
649C2×Q8C22×C3×D511yescharacteristic
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—51no—
652C2×D4—51no—
653C2×D4—51no—
654C2×D4—101no—
655C2×D4—101no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—102no—
659C2×D4—101no—
660C2×D4—201no—
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669Q16—22no—
670Q16—41no—
671SD16—22no—
672SD16—41no—
673SD16—102no—
674SD16—102no—
675SD16—102no—
676D8—54no—
677D8—102no—
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—51no—
687C4⋊C4—51no—
688C4⋊C4—51no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4—101no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—51no—
695C22⋊C4—51no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4—101no—
701C22⋊C4—101no—
702C42C22×C3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—101no—
708C22×C3—101no—
709C22×C3—102no—
710C22×C3—102no—
711C22×C3—101no—
712C22×C3—101no—
713C22×C3—101no—
714C22×C3—101no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—101no—
727C3×C4—101no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414411yescharacteristic
732C2×C5—81no—
733C2×C5C3×D4211yescharacteristic
734C2×C5C3×#57511yescharacteristic
735C2×C5C3×#57711yescharacteristic
736D5—41no—
737D5—41no—
738D5—42no—
739D5—42no—
740C23—21no—
741C23—51no—
742C23—51no—
743C23—101no—
744C23—101no—
745C23—202no—
746C23—202no—
747C23—401no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—21no—
753Q8—21no—
754D4—21no—
755D4—21no—
756D4—52no—
757D4—52no—
758D4—101no—
759D4—101no—
760D4—201no—
761D4—202no—
762D4—202no—
763D4—202no—
764D4—202no—
765D4—401no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—51no—
770C2×C4—51no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—202no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—401no—
782C2×C4C3×D4×D511yescharacteristic
783C2×C4C3×D4×D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—101no—
787C8—101no—
788C8C3×D4×D512yes—
789C2×C3—81no—
790C2×C3—201no—
791C2×C3—201no—
792C2×C3—202no—
793C2×C3—202no—
794C2×C3#6605111yescharacteristic
795C2×C3#6611111yescharacteristic
796C2×C3#6611211yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—41no—
799C22—41no—
800C22—41no—
801C22—101no—
802C22—101no—
803C22—101no—
804C22—101no—
805C22—101no—
806C22—101no—
807C22—102no—
808C22—102no—
809C22—201no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—21no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—101no—
821C4—101no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414411yescharacteristic
826C3#1061361311yescharacteristic, direct product factor, Sylow
827C2—81no—
828C2—201no—
829C2—201no—
830C2—202no—
831C2—202no—
832C2C3×#6605111yescharacteristic
833C2C3×#6611111yescharacteristic
834C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#497C2
socleC22×C3×C5C22×D4
hypercenterC3×#497D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#497

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4065C2semidirect
2. C2×C3×#4060C2semidirect
3. C3×#66060C2semidirect
4. C3×#66010C2semidirect
5. C3×C5×#497C2semidirect
6. C3×#65478C2semidirect
7. C3×#65476C2semidirect
8. C3×#65476C2semidirect
9. C3×#65461C2semidirect
10. C3×#65460C2semidirect
11. C3×#65458C2semidirect
12. C3×#65372C2semidirect
13. C3×#65346C2semidirect
14. C3×#65000C2semidirect
15. C3×#64995C2semidirect
16. #10613613C3direct (N × H)
19. C2×C3×#713C22semidirect
21. C2×C3×C5×Q16C22semidirect
22. C2×C3×C5×Q16C22semidirect
25. C3×C5×C4⋊Q8C22semidirect
29. C3×#4092C22semidirect
32. C2×C3×#688C22semidirect
39. C2×C3×C8×D5C22semidirect
50. C3×C4×D20C22semidirect
51. C3×C5×#97C22semidirect
52. C3×#3967C22semidirect
53. C3×#3967C22semidirect
54. C3×#3967C22semidirect
57. C3×#3953C22semidirect
59. C3×#3952C22semidirect
60. C3×#3949C22semidirect
61. C3×C4⋊#168C22semidirect
63. C2×#4065C2×C3semidirect
64. C2×#4060C2×C3semidirect
65. #66060C2×C3semidirect
66. #66010C2×C3semidirect
67. C5×#497C2×C3semidirect
68. #65478C2×C3semidirect
69. #65476C2×C3semidirect
70. #65476C2×C3semidirect
71. #65461C2×C3semidirect
72. #65460C2×C3semidirect
73. #65458C2×C3semidirect
74. #65372C2×C3semidirect
75. #65346C2×C3semidirect
76. #65000C2×C3semidirect
77. #64995C2×C3semidirect
137. C3×D40D4semidirect
144. C3×#497D5semidirect
157. C2×#713C22×C3semidirect
159. C2×C5×Q16C22×C3semidirect
160. C2×C5×Q16C22×C3semidirect
163. C5×C4⋊Q8C22×C3semidirect
167. #4092C22×C3semidirect
170. C2×#688C22×C3semidirect
177. C2×C8×D5C22×C3semidirect
188. C4×D20C22×C3semidirect
189. C5×#97C22×C3semidirect
190. #3967C22×C3semidirect
191. #3967C22×C3semidirect
192. #3967C22×C3semidirect
195. #3953C22×C3semidirect
197. #3952C22×C3semidirect
198. #3949C22×C3semidirect
199. C4⋊#168C22×C3semidirect
256. C2×C3×Q16C2×D5semidirect
257. C2×C3×Q16C2×D5semidirect
267. C3×C4⋊Q8C2×D5semidirect
294. C3×#97C2×D5semidirect
354. D40C3×D4semidirect
361. #497C3×D5semidirect
517. C2×Q16C2×C3×D5semidirect
518. C2×Q16C2×C3×D5semidirect
528. C4⋊Q8C2×C3×D5semidirect
555. #97C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10613613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40652
C2×C3×#40602
C3×#660602
C3×#660102
C3×C5×#4972
C3×#654782
C3×#654762
C3×#654612
C3×#654602
C3×#654582
C3×#653722
C3×#653462
C3×#650002
C3×#649952
#106136133
C3×#32675