Finite Group Databasebeta

← C3×#10613587 #14453191

Subgroups — C3×#10613587 #14453191

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4060C211yesmaximal, characteristic, complemented
2C2×C3×D5×D8C211yesmaximal, characteristic, complemented
3C3×#66051C211yesmaximal, characteristic, complemented
4C3×#66010C211yesmaximal, characteristic, complemented
5C3×C5×#496C211yesmaximal, characteristic, complemented
6C3×#65461C211yesmaximal, characteristic, complemented
7C3×#65460C211yesmaximal, characteristic, complemented
8C3×#65458C211yesmaximal, characteristic, complemented
9C3×#65448C211yesmaximal, characteristic, complemented
10C3×#65445C211yesmaximal, characteristic, complemented
11C3×#65445C211yesmaximal, characteristic, complemented
12C3×#65361C211yesmaximal, characteristic, complemented
13C3×#65346C211yesmaximal, characteristic, complemented
14C3×#65000C211yesmaximal, characteristic, complemented
15C3×#64995C211yesmaximal, characteristic, complemented
16#10613587C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic, complemented
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic, complemented
21C2×C3×D4×D5C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C2×C3×C5×D8C2211yescharacteristic, complemented
25C2×C3×C5×D8C2211yescharacteristic, complemented
26C3×C5×#127C2211yescharacteristic, complemented
27C3×C5×#124C2211yescharacteristic, complemented
28C3×#4092C2211yescharacteristic, complemented
29C2×C3×#688C2211yescharacteristic, complemented
30C3×#4084—21no—
31C3×#4084C2211yescharacteristic
32C3×#4084C2211yescharacteristic, complemented
33C3×#4084C2211yescharacteristic, complemented
34C3×#4083—21no—
35C3×#4083—21no—
36C2×C3×#686C2211yescharacteristic
37C2×C3×#686C2211yescharacteristic, complemented
38C2×C3×#686C2211yescharacteristic, complemented
39C3×#4060—24no—
40C3×D5×D8—24no—
41C2×C3×D40C2211yescharacteristic
42C2×C3×#676C2211yescharacteristic, complemented
43C2×C3×C8×D5C2211yescharacteristic, complemented
44C3×#4030—21no—
45C3×#4029—21no—
46C3×#4028—21no—
47C3×D5×C22⋊C4—21no—
48C3×C4×D20C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic, complemented
50C3×C4×D20C2211yescharacteristic, complemented
51C3×C5×#97C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3964C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3953C2211yescharacteristic, complemented
58C3×#3952C2211yescharacteristic, complemented
59C3×#3952C2211yescharacteristic, complemented
60C3×#3949C2211yescharacteristic, complemented
61C3×C4⋊#168C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C2×#4060C2×C311yescharacteristic, complemented
64C2×D5×D8C2×C311yescharacteristic, complemented
65#66051C2×C311yescharacteristic, complemented
66#66010C2×C311yescharacteristic, complemented
67C5×#496C2×C311yescharacteristic, complemented
68#65461C2×C311yescharacteristic, complemented
69#65460C2×C311yescharacteristic, complemented
70#65458C2×C311yescharacteristic, complemented
71#65448C2×C311yescharacteristic, complemented
72#65445C2×C311yescharacteristic, complemented
73#65445C2×C311yescharacteristic, complemented
74#65361C2×C311yescharacteristic, complemented
75#65346C2×C311yescharacteristic, complemented
76#65000C2×C311yescharacteristic, complemented
77#64995C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C5×D4C2311yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C3×#713—22no—
94C3×#713—41no—
95C3×D4×D5—22no—
96C3×D4×D5—22no—
97C3×D4×D5—22no—
98C3×D4×D5—41no—
99C3×D4×D5—41no—
100C3×D4×D5—41no—
101C3×D4×D5—44no—
102C2×C3×D20—21no—
103C2×C3×D20D411yescharacteristic
104C2×C3×D20C2311yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5—21no—
109C2×C3×C4×D5C2311yescharacteristic
110C2×C3×C4×D5C2311yescharacteristic
111C3×C5×SD16—22no—
112C3×C5×SD16—41no—
113C3×C5×D8—22no—
114C3×C5×D8—41no—
115C2×C3×C5×C8C2311yescharacteristic
116C2×C3×C5×C8C2311yescharacteristic
117C3×C5×C22⋊C4—21no—
118C3×C5×C22⋊C4—21no—
119C3×C42×C5C2311yescharacteristic
120C3×C22⋊Dic5—21no—
121C3×C22⋊Dic5—21no—
122C3×C22⋊Dic5—21no—
123C3×#688—22no—
124C3×#686—22no—
125C3×#686—22no—
126C3×#686—22no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685D411yescharacteristic
131C3×#685D411yescharacteristic
132C3×C4⋊Dic5D411yescharacteristic
133C3×C4⋊Dic5C2311yescharacteristic
134C3×C4⋊Dic5C2311yescharacteristic
135C3×#683—21no—
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C3×D40D414yescomplemented
139C3×#676—22no—
140C3×C8×D5—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×D8—51no—
143C3×#546—51no—
144C3×D42—51no—
145C3×#496D511yescharacteristic, complemented
146C3×#469—51no—
147C3×#465—51no—
148C3×#463—51no—
149C3×#459—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#447—51no—
154C3×#442—51no—
155C3×#435—51no—
156C2×#713C22×C311yescharacteristic, complemented
157C2×D4×D5—21no—
158C2×D4×D5C22×C311yescharacteristic
159C2×D4×D5C22×C311yescharacteristic, complemented
160C2×D4×D5C22×C311yescharacteristic, complemented
161C2×C5×SD16C22×C311yescharacteristic, complemented
162C2×C5×SD16C22×C311yescharacteristic, complemented
163C2×C5×D8C22×C311yescharacteristic, complemented
164C2×C5×D8C22×C311yescharacteristic, complemented
165C5×#127C22×C311yescharacteristic, complemented
166C5×#124C22×C311yescharacteristic, complemented
167#4092C22×C311yescharacteristic, complemented
168C2×#688C22×C311yescharacteristic, complemented
169#4084—21no—
170#4084C22×C311yescharacteristic
171#4084C22×C311yescharacteristic, complemented
172#4084C22×C311yescharacteristic, complemented
173#4083—21no—
174#4083—21no—
175C2×#686C22×C311yescharacteristic
176C2×#686C22×C311yescharacteristic, complemented
177C2×#686C22×C311yescharacteristic, complemented
178#4060—24no—
179D5×D8—24no—
180C2×D40C22×C311yescharacteristic
181C2×#676C22×C311yescharacteristic, complemented
182C2×C8×D5C22×C311yescharacteristic, complemented
183#4030—21no—
184#4029—21no—
185#4028—21no—
186D5×C22⋊C4—21no—
187C4×D20C22×C311yescharacteristic
188C4×D20C22×C311yescharacteristic, complemented
189C4×D20C22×C311yescharacteristic, complemented
190C5×#97C22×C311yescharacteristic, complemented
191#3967C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194#3964C22×C311yescharacteristic, complemented
195#3953C22×C311yescharacteristic, complemented
196#3953C22×C311yescharacteristic, complemented
197#3952C22×C311yescharacteristic, complemented
198#3952C22×C311yescharacteristic, complemented
199#3949C22×C311yescharacteristic, complemented
200C4⋊#168C22×C311yescharacteristic, complemented
201#3264—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—42no—
211C22×C3×D5—42no—
212C22×C3×D5—42no—
213C22×C3×D5—81no—
214C22×C3×D5—81no—
215C22×C3×D5—81no—
216C22×C3×D5C2×D411yescharacteristic
217C22×C3×D5C2×D411yescharacteristic
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—21no—
224C3×C5×D4—21no—
225C3×C5×D4—21no—
226C3×C5×D4—42no—
227C3×C5×D4—81no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2×D411yescharacteristic
231C2×C3×C4×C5C2411yescharacteristic
232C3×C22⋊D5—42no—
233C3×C22⋊D5—42no—
234C3×C22⋊D5—42no—
235C3×C22⋊D5—42no—
236C3×C22⋊D5—42no—
237C3×C22⋊D5—81no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5C2×D411yescharacteristic
241C2×C3×Dic5C2×D411yescharacteristic
242C3×D20—22no—
243C3×D20—21no—
244C3×D20—21no—
245C3×D20—42no—
246C3×D20C2×D412yes—
247C3×D20C2×D412yescomplemented
248C3×C4×D5—21no—
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251C3×C4×D5—21no—
252C3×C4×D5—42no—
253C3×C4×D5—42no—
254C3×C4×D5—81no—
255C3×C5×C8—21no—
256C3×C5×C8C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×C3×#41—51no—
260C22×C3×D4—51no—
261C22×C3×D4—51no—
262C22×C3×D4—51no—
263C22×C3×D4—101no—
264C3×AGL(1,ℤ/8)—104no—
265C2×C3×SD16—51no—
266C2×C3×SD16C2×D511yescharacteristic, complemented
267C2×C3×SD16C2×D511yescharacteristic, complemented
268C2×C3×D8—51no—
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×D8—104no—
273C2×C3×D8C2×D511yescharacteristic, complemented
274C2×C3×D8C2×D511yescharacteristic, complemented
275C2×C3×M16—51no—
276C22×C3×C8—51no—
277C3×#127C2×D511yescharacteristic, complemented
278C3×#124C2×D511yescharacteristic, complemented
279C3×#123—101no—
280C3×C22⋊Q8—51no—
281C3×#121—51no—
282C3×#121—51no—
283C3×#121—51no—
284C3×#121—101no—
285C3×#121—101no—
286C3×#120—101no—
287C3×#120—101no—
288C3×#120—101no—
289C3×C4×D4—51no—
290C3×C4×D4—51no—
291C3×C4×D4—51no—
292C2×C3×C22⋊C4—101no—
293C3×#106—51no—
294C3×C4⋊C8—51no—
295C3×#103—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102—51no—
300C3×#102—51no—
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97C2×D511yescharacteristic, complemented
304C23×D5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C2×C5×Q8C23×C311yescharacteristic
308C2×C5×D4—21no—
309C2×C5×D4—21no—
310C2×C5×D4C23×C311yescharacteristic
311C2×C5×D4C23×C311yescharacteristic
312C2×C5×D4C23×C311yescharacteristic
313C2×C22⋊D5—21no—
314C2×C22⋊D5—21no—
315C2×C22⋊D5—21no—
316C2×C22⋊D5—21no—
317C2×C22⋊D5—21no—
318C2×C22⋊D5—21no—
319#713—22no—
320#713—41no—
321D4×D5—22no—
322D4×D5—22no—
323D4×D5—22no—
324D4×D5—41no—
325D4×D5—41no—
326D4×D5—41no—
327D4×D5—44no—
328C2×D20—21no—
329C2×D20C3×D411yescharacteristic
330C2×D20C23×C311yescharacteristic
331C2×D20C23×C311yescharacteristic
332C2×C4×D5—21no—
333C2×C4×D5—21no—
334C2×C4×D5—21no—
335C2×C4×D5C23×C311yescharacteristic
336C2×C4×D5C23×C311yescharacteristic
337C5×SD16—22no—
338C5×SD16—41no—
339C5×D8—22no—
340C5×D8—41no—
341C2×C5×C8C23×C311yescharacteristic
342C2×C5×C8C23×C311yescharacteristic
343C5×C22⋊C4—21no—
344C5×C22⋊C4—21no—
345C42×C5C23×C311yescharacteristic
346C22⋊Dic5—21no—
347C22⋊Dic5—21no—
348C22⋊Dic5—21no—
349#688—22no—
350#686—22no—
351#686—22no—
352#686—22no—
353#685—21no—
354#685—21no—
355#685—21no—
356#685C3×D411yescharacteristic
357#685C3×D411yescharacteristic
358C4⋊Dic5C3×D411yescharacteristic
359C4⋊Dic5C23×C311yescharacteristic
360C4⋊Dic5C23×C311yescharacteristic
361#683—21no—
362C2×#168C23×C311yescharacteristic
363C2×#168C23×C311yescharacteristic
364D40C3×D414yescomplemented
365#676—22no—
366C8×D5—22no—
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—51no—
369#546—51no—
370D42—51no—
371#496C3×D511yescharacteristic, complemented
372#469—51no—
373#465—51no—
374#463—51no—
375#459—51no—
376#450—51no—
377#449—51no—
378#447—51no—
379#447—51no—
380#442—51no—
381#435—51no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5C22×D411yescharacteristic
392C2×C3×D5—21no—
393C2×C3×D5—21no—
394C2×C3×D5—21no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—21no—
398C2×C3×D5—21no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—84no—
404C2×C3×D5—84no—
405C2×C3×D5—84no—
406C2×C3×D5AGL(1,ℤ/8)12yescomplemented
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—41no—
410C3×C4×C5C22×D411yescharacteristic
411C3×C4×C5H(5,𝔽2)11yescharacteristic
412C3×Dic5—21no—
413C3×Dic5—21no—
414C3×Dic5—41no—
415C3×Dic5—41no—
416C24×C3—101no—
417C24×C3—101no—
418C24×C3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—21no—
423C2×C3×D4—21no—
424C2×C3×D4—51no—
425C2×C3×D4—51no—
426C2×C3×D4—51no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—101no—
431C2×C3×D4—102no—
432C2×C3×D4—102no—
433C2×C3×D4—102no—
434C2×C3×D4—101no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—201no—
438C2×C3×D4—201no—
439C2×C3×D4—201no—
440C2×C3×D4—204no—
441C2×C3×D4C22×D511yescharacteristic
442C2×C3×D4C22×D511yescharacteristic
443C2×C3×D4C22×D511yescharacteristic
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—101no—
447C22×C3×C4—101no—
448C22×C3×C4—101no—
449C3×SD16—22no—
450C3×SD16—41no—
451C3×SD16—102no—
452C3×D8—22no—
453C3×D8—41no—
454C3×D8—54no—
455C3×D8—102no—
456C3×D8—102no—
457C3×D8—102no—
458C3×M16—102no—
459C2×C3×C8—51no—
460C2×C3×C8—51no—
461C2×C3×C8—102no—
462C2×C3×C8C22×D511yescharacteristic
463C2×C3×C8C22×D511yescharacteristic
464C3×C4⋊C4—51no—
465C3×C4⋊C4—51no—
466C3×C4⋊C4—51no—
467C3×C4⋊C4—101no—
468C3×C22⋊C4—21no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—51no—
471C3×C22⋊C4—51no—
472C3×C22⋊C4—101no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4—101no—
477C3×C22⋊C4—101no—
478C3×C42C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—42no—
485C22×D5—42no—
486C22×D5—42no—
487C22×D5—42no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—81no—
491C22×D5—81no—
492C22×D5—81no—
493C22×D5C2×C3×D411yescharacteristic
494C22×D5C2×C3×D411yescharacteristic
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—21no—
501C5×D4—21no—
502C5×D4—21no—
503C5×D4—42no—
504C5×D4—81no—
505C2×C4×C5—21no—
506C2×C4×C5C2×C3×D411yescharacteristic
507C2×C4×C5C2×C3×D411yescharacteristic
508C2×C4×C5C24×C311yescharacteristic
509C22⋊D5—42no—
510C22⋊D5—42no—
511C22⋊D5—42no—
512C22⋊D5—42no—
513C22⋊D5—42no—
514C22⋊D5—81no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5C2×C3×D411yescharacteristic
518C2×Dic5C2×C3×D411yescharacteristic
519D20—22no—
520D20—21no—
521D20—21no—
522D20—42no—
523D20C2×C3×D412yes—
524D20C2×C3×D412yescomplemented
525C4×D5—21no—
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—21no—
529C4×D5—42no—
530C4×D5—42no—
531C4×D5—81no—
532C5×C8—21no—
533C5×C8C2×C3×D412yescomplemented
534#168—21no—
535#168—21no—
536C2×#41—51no—
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—51no—
540C22×D4—101no—
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16C2×C3×D511yescharacteristic, complemented
544C2×SD16C2×C3×D511yescharacteristic, complemented
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—51no—
548C2×D8—51no—
549C2×D8—104no—
550C2×D8C2×C3×D511yescharacteristic, complemented
551C2×D8C2×C3×D511yescharacteristic, complemented
552C2×M16—51no—
553C22×C8—51no—
554#127C2×C3×D511yescharacteristic, complemented
555#124C2×C3×D511yescharacteristic, complemented
556#123—101no—
557C22⋊Q8—51no—
558#121—51no—
559#121—51no—
560#121—51no—
561#121—101no—
562#121—101no—
563#120—101no—
564#120—101no—
565#120—101no—
566C4×D4—51no—
567C4×D4—51no—
568C4×D4—51no—
569C2×C22⋊C4—101no—
570#106—51no—
571C4⋊C8—51no—
572#103—51no—
573#102—51no—
574#102—51no—
575#102—51no—
576#102—51no—
577#102—51no—
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97C2×C3×D511yescharacteristic, complemented
581C2×C3×C5—81no—
582C2×C3×C5—81no—
583C2×C3×C5—81no—
584C2×C3×C5D4211yescharacteristic
585C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
586C2×C3×C5#57611yescharacteristic
587C3×D5—22no—
588C3×D5—41no—
589C3×D5—42no—
590C3×D5—42no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—51no—
595C23×C3—51no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—202no—
599C23×C3—202no—
600C23×C3—202no—
601C23×C3—202no—
602C23×C3—202no—
603C23×C3—202no—
604C23×C3—401no—
605C23×C3—401no—
606C23×C3—401no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—42no—
616C3×D4—52no—
617C3×D4—52no—
618C3×D4—81no—
619C3×D4—102no—
620C3×D4—101no—
621C3×D4—101no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—202no—
626C3×D4—202no—
627C3×D4—202no—
628C3×D4—401no—
629C2×C3×C4—21no—
630C2×C3×C4—51no—
631C2×C3×C4—51no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—202no—
639C2×C3×C4—202no—
640C2×C3×C4—401no—
641C2×C3×C4D4×D511yescharacteristic
642C2×C3×C4D4×D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—101no—
646C3×C8—101no—
647C3×C8D4×D512yescomplemented
648C22×C5—41no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5C22×C3×D411yescharacteristic
658C2×D5—21no—
659C2×D5—21no—
660C2×D5—21no—
661C2×D5—21no—
662C2×D5—21no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—84no—
670C2×D5—84no—
671C2×D5—84no—
672C2×D5C3×AGL(1,ℤ/8)12yescomplemented
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—41no—
676C4×C5C22×C3×D411yescharacteristic
677C4×C5C3×H(5,𝔽2)11yescharacteristic
678Dic5—21no—
679Dic5—21no—
680Dic5—41no—
681Dic5—41no—
682C24—101no—
683C24—101no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8C22×C3×D511yescharacteristic
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—51no—
691C2×D4—51no—
692C2×D4—51no—
693C2×D4—101no—
694C2×D4—101no—
695C2×D4—101no—
696C2×D4—101no—
697C2×D4—102no—
698C2×D4—102no—
699C2×D4—102no—
700C2×D4—101no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—201no—
704C2×D4—201no—
705C2×D4—201no—
706C2×D4—204no—
707C2×D4C22×C3×D511yescharacteristic
708C2×D4C22×C3×D511yescharacteristic
709C2×D4C22×C3×D511yescharacteristic
710C22×C4—51no—
711C22×C4—51no—
712C22×C4—101no—
713C22×C4—101no—
714C22×C4—101no—
715SD16—22no—
716SD16—41no—
717SD16—102no—
718D8—22no—
719D8—41no—
720D8—54no—
721D8—102no—
722D8—102no—
723D8—102no—
724M16—102no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—102no—
728C2×C8C22×C3×D511yescharacteristic
729C2×C8C22×C3×D511yescharacteristic
730C4⋊C4—51no—
731C4⋊C4—51no—
732C4⋊C4—51no—
733C4⋊C4—101no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—51no—
737C22⋊C4—51no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4—101no—
743C22⋊C4—101no—
744C42C22×C3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—52no—
756C22×C3—101no—
757C22×C3—101no—
758C22×C3—101no—
759C22×C3—102no—
760C22×C3—102no—
761C22×C3—101no—
762C22×C3—101no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3—404no—
768C22×C3—404no—
769C22×C3—404no—
770C22×C3C2×D4×D511yescharacteristic
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—101no—
775C3×C4—101no—
776C3×C4—201no—
777C3×C4—201no—
778C3×C4C2×D4×D511yescharacteristic
779C3×C4#414411yescharacteristic
780C2×C5—81no—
781C2×C5—81no—
782C2×C5—81no—
783C2×C5C3×D4211yescharacteristic
784C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
785C2×C5C3×#57611yescharacteristic
786D5—22no—
787D5—41no—
788D5—42no—
789D5—42no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—51no—
794C23—51no—
795C23—101no—
796C23—101no—
797C23—202no—
798C23—202no—
799C23—202no—
800C23—202no—
801C23—202no—
802C23—202no—
803C23—401no—
804C23—401no—
805C23—401no—
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—42no—
815D4—52no—
816D4—52no—
817D4—81no—
818D4—102no—
819D4—101no—
820D4—101no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—202no—
826D4—202no—
827D4—401no—
828C2×C4—21no—
829C2×C4—51no—
830C2×C4—51no—
831C2×C4—101no—
832C2×C4—101no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—202no—
838C2×C4—202no—
839C2×C4—401no—
840C2×C4C3×D4×D511yescharacteristic
841C2×C4C3×D4×D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—101no—
845C8—101no—
846C8C3×D4×D512yescomplemented
847C2×C3—81no—
848C2×C3—81no—
849C2×C3—81no—
850C2×C3—102no—
851C2×C3—201no—
852C2×C3—202no—
853C2×C3—202no—
854C2×C3#6605111yescharacteristic
855C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
856C2×C3#6610811yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—52no—
868C22—101no—
869C22—101no—
870C22—101no—
871C22—101no—
872C22—101no—
873C22—102no—
874C22—102no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—404no—
880C22—404no—
881C22—404no—
882C22C2×C3×D4×D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—101no—
887C4—101no—
888C4—201no—
889C4—201no—
890C4C2×C3×D4×D511yescharacteristic
891C4C3×#414411yescharacteristic
892C3#1061358711yescharacteristic, direct product factor, Sylow
893C2—81no—
894C2—81no—
895C2—81no—
896C2—102no—
897C2—201no—
898C2—202no—
899C2—202no—
900C2C3×#6605111yescharacteristic
901C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
902C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#496C2
socleC22×C3×C5C22×D4
hypercenterC3×#496D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#496

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4060C2semidirect
2. C2×C3×D5×D8C2semidirect
3. C3×#66051C2semidirect
4. C3×#66010C2semidirect
5. C3×C5×#496C2semidirect
6. C3×#65461C2semidirect
7. C3×#65460C2semidirect
8. C3×#65458C2semidirect
9. C3×#65448C2semidirect
10. C3×#65445C2semidirect
11. C3×#65445C2semidirect
12. C3×#65361C2semidirect
13. C3×#65346C2semidirect
14. C3×#65000C2semidirect
15. C3×#64995C2semidirect
16. #10613587C3direct (N × H)
17. C2×C3×#713C22semidirect
20. C2×C3×D4×D5C22semidirect
21. C2×C3×D4×D5C22semidirect
22. C2×C3×C5×SD16C22semidirect
23. C2×C3×C5×SD16C22semidirect
24. C2×C3×C5×D8C22semidirect
25. C2×C3×C5×D8C22semidirect
26. C3×C5×#127C22semidirect
27. C3×C5×#124C22semidirect
28. C3×#4092C22semidirect
29. C2×C3×#688C22semidirect
32. C3×#4084C22semidirect
33. C3×#4084C22semidirect
37. C2×C3×#686C22semidirect
38. C2×C3×#686C22semidirect
42. C2×C3×#676C22semidirect
43. C2×C3×C8×D5C22semidirect
49. C3×C4×D20C22semidirect
50. C3×C4×D20C22semidirect
51. C3×C5×#97C22semidirect
52. C3×#3967C22semidirect
53. C3×#3964C22semidirect
54. C3×#3964C22semidirect
55. C3×#3964C22semidirect
56. C3×#3953C22semidirect
57. C3×#3953C22semidirect
58. C3×#3952C22semidirect
59. C3×#3952C22semidirect
60. C3×#3949C22semidirect
61. C3×C4⋊#168C22semidirect
63. C2×#4060C2×C3semidirect
64. C2×D5×D8C2×C3semidirect
65. #66051C2×C3semidirect
66. #66010C2×C3semidirect
67. C5×#496C2×C3semidirect
68. #65461C2×C3semidirect
69. #65460C2×C3semidirect
70. #65458C2×C3semidirect
71. #65448C2×C3semidirect
72. #65445C2×C3semidirect
73. #65445C2×C3semidirect
74. #65361C2×C3semidirect
75. #65346C2×C3semidirect
76. #65000C2×C3semidirect
77. #64995C2×C3semidirect
138. C3×D40D4semidirect
145. C3×#496D5semidirect
156. C2×#713C22×C3semidirect
159. C2×D4×D5C22×C3semidirect
160. C2×D4×D5C22×C3semidirect
161. C2×C5×SD16C22×C3semidirect
162. C2×C5×SD16C22×C3semidirect
163. C2×C5×D8C22×C3semidirect
164. C2×C5×D8C22×C3semidirect
165. C5×#127C22×C3semidirect
166. C5×#124C22×C3semidirect
167. #4092C22×C3semidirect
168. C2×#688C22×C3semidirect
171. #4084C22×C3semidirect
172. #4084C22×C3semidirect
176. C2×#686C22×C3semidirect
177. C2×#686C22×C3semidirect
181. C2×#676C22×C3semidirect
182. C2×C8×D5C22×C3semidirect
188. C4×D20C22×C3semidirect
189. C4×D20C22×C3semidirect
190. C5×#97C22×C3semidirect
191. #3967C22×C3semidirect
192. #3964C22×C3semidirect
193. #3964C22×C3semidirect
194. #3964C22×C3semidirect
195. #3953C22×C3semidirect
196. #3953C22×C3semidirect
197. #3952C22×C3semidirect
198. #3952C22×C3semidirect
199. #3949C22×C3semidirect
200. C4⋊#168C22×C3semidirect
247. C3×D20C2×D4semidirect
256. C3×C5×C8C2×D4semidirect
266. C2×C3×SD16C2×D5semidirect
267. C2×C3×SD16C2×D5semidirect
273. C2×C3×D8C2×D5semidirect
274. C2×C3×D8C2×D5semidirect
277. C3×#127C2×D5semidirect
278. C3×#124C2×D5semidirect
303. C3×#97C2×D5semidirect
364. D40C3×D4semidirect
371. #496C3×D5semidirect
406. C2×C3×D5AGL(1,ℤ/8)semidirect
524. D20C2×C3×D4semidirect
533. C5×C8C2×C3×D4semidirect
543. C2×SD16C2×C3×D5semidirect
544. C2×SD16C2×C3×D5semidirect
550. C2×D8C2×C3×D5semidirect
551. C2×D8C2×C3×D5semidirect
554. #127C2×C3×D5semidirect
555. #124C2×C3×D5semidirect
580. #97C2×C3×D5semidirect
647. C3×C8D4×D5semidirect
672. C2×D5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
846. C8C3×D4×D5semidirect
857. C5C3×#3264semidirect
892. C3#10613587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40602
C2×C3×D5×D82
C3×#660512
C3×#660102
C3×C5×#4962
C3×#654612
C3×#654602
C3×#654582
C3×#654482
C3×#654452
C3×#653612
C3×#653462
C3×#650002
C3×#649952
#106135873
C3×#32645