Finite Group Databasebeta

← C3×#10612089 #14453179

Subgroups — C3×#10612089 #14453179

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×#4057C211yesmaximal, characteristic, complemented
2C2×C3×D5×D8C211yesmaximal, characteristic, complemented
3C3×#66051C211yesmaximal, characteristic, complemented
4C3×#65888C211yesmaximal, characteristic, complemented
5C3×C5×#459C211yesmaximal, characteristic, complemented
6C3×#65447C211yesmaximal, characteristic, complemented
7C3×#65445C211yesmaximal, characteristic, complemented
8C3×#65363C211yesmaximal, characteristic, complemented
9C3×#65303C211yesmaximal, characteristic, complemented
10C3×#65133C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65071C211yesmaximal, characteristic, complemented
13C3×#65067C211yesmaximal, characteristic, complemented
14C3×#65065C211yesmaximal, characteristic, complemented
15C3×#65062C211yesmaximal, characteristic, complemented
16#10612089C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic, complemented
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic, complemented
21C2×C3×D4×D5C2211yescharacteristic, complemented
22C2×C3×C5×D8C2211yescharacteristic, complemented
23C2×C3×C5×D8C2211yescharacteristic, complemented
24C3×C5×#127C2211yescharacteristic, complemented
25C3×C4×C5×D4C2211yescharacteristic, complemented
26C3×#4084—21no—
27C3×#4084C2211yescharacteristic
28C3×#4084C2211yescharacteristic, complemented
29C3×#4083—21no—
30C3×#4083—21no—
31C2×C3×#687C2211yescharacteristic, complemented
32C2×C3×#687C2211yescharacteristic, complemented
33C2×C3×#686C2211yescharacteristic
34C2×C3×#686C2211yescharacteristic, complemented
35C2×C3×#686C2211yescharacteristic, complemented
36C3×#4076—21no—
37C2×C3×#685—21no—
38C3×#4057—24no—
39C3×D5×D8—24no—
40C2×C3×D40C2211yescharacteristic
41C2×C3×#677C2211yescharacteristic, complemented
42C2×C3×#676C2211yescharacteristic, complemented
43C2×C3×C8×D5C2211yescharacteristic, complemented
44C3×#4043C2211yescharacteristic, complemented
45C3×#4041C2211yescharacteristic, complemented
46C3×#4032—21no—
47C3×#4028—21no—
48C3×#4021C2211yescharacteristic, complemented
49C3×C4×D20C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3952C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic, complemented
60C3×#3940C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C2×#4057C2×C311yescharacteristic, complemented
64C2×D5×D8C2×C311yescharacteristic, complemented
65#66051C2×C311yescharacteristic, complemented
66#65888C2×C311yescharacteristic, complemented
67C5×#459C2×C311yescharacteristic, complemented
68#65447C2×C311yescharacteristic, complemented
69#65445C2×C311yescharacteristic, complemented
70#65363C2×C311yescharacteristic, complemented
71#65303C2×C311yescharacteristic, complemented
72#65133C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65071C2×C311yescharacteristic, complemented
75#65067C2×C311yescharacteristic, complemented
76#65065C2×C311yescharacteristic, complemented
77#65062C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C5×D4C2311yescharacteristic
86C22×C3×C4×C5—21no—
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—
93C22×C3×Dic5—21no—
94C3×#711—22no—
95C3×#711—41no—
96C3×D4×D5—22no—
97C3×D4×D5—22no—
98C3×D4×D5—22no—
99C3×D4×D5—41no—
100C3×D4×D5—41no—
101C3×D4×D5—41no—
102C3×D4×D5—44no—
103C2×C3×D20—21no—
104C2×C3×D20D411yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×D20C2311yescharacteristic
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5C2311yescharacteristic
109C2×C3×C4×D5C2311yescharacteristic
110C2×C3×Dic10C2311yescharacteristic
111C3×C5×D8—22no—
112C3×C5×D8—22no—
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C5×C22⋊C4—21no—
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×#687—22no—
121C3×#687—41no—
122C3×#686—22no—
123C3×#686—41no—
124C3×#686D414yescomplemented
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685D411yescharacteristic
131C3×#685D411yescharacteristic
132C3×C4⋊Dic5—21no—
133C3×C4⋊Dic5D411yescharacteristic
134C3×C4⋊Dic5C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C3×D40—22no—
138C3×#677—22no—
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×#496—51no—
146C3×#469—51no—
147C3×#465—51no—
148C3×#463—51no—
149C3×#459D511yescharacteristic, complemented
150C3×#450—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#447—51no—
154C3×#442—51no—
155C3×#435—51no—
156C2×#711C22×C311yescharacteristic, complemented
157C2×D4×D5—21no—
158C2×D4×D5C22×C311yescharacteristic
159C2×D4×D5C22×C311yescharacteristic, complemented
160C2×D4×D5C22×C311yescharacteristic, complemented
161C2×C5×D8C22×C311yescharacteristic, complemented
162C2×C5×D8C22×C311yescharacteristic, complemented
163C5×#127C22×C311yescharacteristic, complemented
164C4×C5×D4C22×C311yescharacteristic, complemented
165#4084—21no—
166#4084C22×C311yescharacteristic
167#4084C22×C311yescharacteristic, complemented
168#4083—21no—
169#4083—21no—
170C2×#687C22×C311yescharacteristic, complemented
171C2×#687C22×C311yescharacteristic, complemented
172C2×#686C22×C311yescharacteristic
173C2×#686C22×C311yescharacteristic, complemented
174C2×#686C22×C311yescharacteristic, complemented
175#4076—21no—
176C2×#685—21no—
177#4057—24no—
178D5×D8—24no—
179C2×D40C22×C311yescharacteristic
180C2×#677C22×C311yescharacteristic, complemented
181C2×#676C22×C311yescharacteristic, complemented
182C2×C8×D5C22×C311yescharacteristic, complemented
183#4043C22×C311yescharacteristic, complemented
184#4041C22×C311yescharacteristic, complemented
185#4032—21no—
186#4028—21no—
187#4021C22×C311yescharacteristic, complemented
188C4×D20C22×C311yescharacteristic
189C4×D20C22×C311yescharacteristic, complemented
190C5×C4⋊C8C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic, complemented
192C5×#102C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic, complemented
195#3952C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic, complemented
199#3940C22×C311yescharacteristic, complemented
200#3935C22×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×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—42no—
224C3×C5×D4—81no—
225C3×C5×D4C2×D412yescomplemented
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—81no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2411yescharacteristic
231C3×C22⋊D5—42no—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—42no—
234C3×C22⋊D5—42no—
235C3×C22⋊D5—42no—
236C3×C22⋊D5—42no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—42no—
240C2×C3×Dic5C2×D411yescharacteristic
241C2×C3×Dic5C2×D411yescharacteristic
242C3×D20—22no—
243C3×D20—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×D20—81no—
247C3×D20C2×D412yes—
248C3×C4×D5—21no—
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251C3×C4×D5—21no—
252C3×C4×D5—42no—
253C3×Dic10—21no—
254C3×Dic10—21no—
255C3×C5×C8—21no—
256C3×C5×C8—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
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×SD16—51no—
267C2×C3×SD16—51no—
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×#124—51no—
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×D4C2×D511yescharacteristic, complemented
292C2×C3×C22⋊C4—101no—
293C3×#106—51no—
294C3×C4⋊C8C2×D511yescharacteristic, complemented
295C3×#103—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102C2×D511yescharacteristic, complemented
300C3×#102C2×D511yescharacteristic, complemented
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97—51no—
304C23×D5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4C23×C311yescharacteristic
310C2×C5×D4C23×C311yescharacteristic
311C2×C5×D4C23×C311yescharacteristic
312C22×C4×C5—21no—
313C2×C22⋊D5—21no—
314C2×C22⋊D5—21no—
315C2×C22⋊D5—21no—
316C2×C22⋊D5—21no—
317C2×C22⋊D5—21no—
318C2×C22⋊D5—21no—
319C22×Dic5—21no—
320#711—22no—
321#711—41no—
322D4×D5—22no—
323D4×D5—22no—
324D4×D5—22no—
325D4×D5—41no—
326D4×D5—41no—
327D4×D5—41no—
328D4×D5—44no—
329C2×D20—21no—
330C2×D20C3×D411yescharacteristic
331C2×D20C23×C311yescharacteristic
332C2×D20C23×C311yescharacteristic
333C2×C4×D5—21no—
334C2×C4×D5C23×C311yescharacteristic
335C2×C4×D5C23×C311yescharacteristic
336C2×Dic10C23×C311yescharacteristic
337C5×D8—22no—
338C5×D8—22no—
339C2×C5×C8C23×C311yescharacteristic
340C2×C5×C8C23×C311yescharacteristic
341C5×C4⋊C4C23×C311yescharacteristic
342C5×C22⋊C4—21no—
343C42×C5C23×C311yescharacteristic
344C22⋊Dic5—21no—
345C22⋊Dic5—21no—
346#687—22no—
347#687—41no—
348#686—22no—
349#686—41no—
350#686C3×D414yescomplemented
351#685—21no—
352#685—21no—
353#685—21no—
354#685—21no—
355#685—21no—
356#685C3×D411yescharacteristic
357#685C3×D411yescharacteristic
358C4⋊Dic5—21no—
359C4⋊Dic5C3×D411yescharacteristic
360C4⋊Dic5C23×C311yescharacteristic
361C2×#168C23×C311yescharacteristic
362C2×#168C23×C311yescharacteristic
363D40—22no—
364#677—22no—
365#676—22no—
366C8×D5—22no—
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—51no—
369#546—51no—
370D42—51no—
371#496—51no—
372#469—51no—
373#465—51no—
374#463—51no—
375#459C3×D511yescharacteristic, complemented
376#450—51no—
377#449—51no—
378#447—51no—
379#447—51no—
380#442—51no—
381#435—51no—
382C22×C3×C5—22no—
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—21no—
397C2×C3×D5—21no—
398C2×C3×D5—41no—
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×Q8—51no—
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—21no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—101no—
448C22×C3×C4—101no—
449C3×SD16—102no—
450C3×SD16—102no—
451C3×SD16—201no—
452C3×D8—22no—
453C3×D8—22no—
454C3×D8—54no—
455C3×D8—102no—
456C3×D8—102no—
457C3×D8—201no—
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—101no—
467C3×C4⋊C4C22×D511yescharacteristic
468C3×C22⋊C4—21no—
469C3×C22⋊C4—51no—
470C3×C22⋊C4—51no—
471C3×C22⋊C4—101no—
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×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—42no—
501C5×D4—81no—
502C5×D4C2×C3×D412yescomplemented
503C2×C4×C5—21no—
504C2×C4×C5—81no—
505C2×C4×C5C2×C3×D411yescharacteristic
506C2×C4×C5C2×C3×D411yescharacteristic
507C2×C4×C5C24×C311yescharacteristic
508C22⋊D5—42no—
509C22⋊D5—42no—
510C22⋊D5—42no—
511C22⋊D5—42no—
512C22⋊D5—42no—
513C22⋊D5—42no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—42no—
517C2×Dic5C2×C3×D411yescharacteristic
518C2×Dic5C2×C3×D411yescharacteristic
519D20—22no—
520D20—21no—
521D20—21no—
522D20—21no—
523D20—81no—
524D20C2×C3×D412yes—
525C4×D5—21no—
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—21no—
529C4×D5—42no—
530Dic10—21no—
531Dic10—21no—
532C5×C8—21no—
533C5×C8—21no—
534#168—21no—
535#168C2×C3×D412yescomplemented
536C2×#41—51no—
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—51no—
540C22×D4—101no—
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—51no—
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#124—51no—
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×D4C2×C3×D511yescharacteristic, complemented
569C2×C22⋊C4—101no—
570#106—51no—
571C4⋊C8C2×C3×D511yescharacteristic, complemented
572#103—51no—
573#102—51no—
574#102—51no—
575#102—51no—
576#102C2×C3×D511yescharacteristic, complemented
577#102C2×C3×D511yescharacteristic, complemented
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97—51no—
581C2×C3×C5—42no—
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—81no—
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—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—42no—
615C3×D4—52no—
616C3×D4—81no—
617C3×D4—102no—
618C3×D4—101no—
619C3×D4—101no—
620C3×D4—101no—
621C3×D4—202no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—202no—
626C3×D4—202no—
627C3×D4—401no—
628C3×D4D4×D512yescomplemented
629C2×C3×C4—21no—
630C2×C3×C4—51no—
631C2×C3×C4—51no—
632C2×C3×C4—81no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—202no—
640C2×C3×C4—202no—
641C2×C3×C4D4×D511yescharacteristic
642C2×C3×C4D4×D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—52no—
647C3×C8—101no—
648C22×C5—22no—
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—41no—
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×Q8—51no—
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—21no—
711C22×C4—51no—
712C22×C4—51no—
713C22×C4—101no—
714C22×C4—101no—
715SD16—102no—
716SD16—102no—
717SD16—201no—
718D8—22no—
719D8—22no—
720D8—54no—
721D8—102no—
722D8—102no—
723D8—201no—
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—101no—
733C4⋊C4C22×C3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—51no—
736C22⋊C4—51no—
737C22⋊C4—101no—
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—22no—
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—101no—
760C22×C3—101no—
761C22×C3—102no—
762C22×C3—201no—
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#414911yescharacteristic
780C2×C5—42no—
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—81no—
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—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—42no—
814D4—52no—
815D4—81no—
816D4—102no—
817D4—101no—
818D4—101no—
819D4—101no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—202no—
826D4—401no—
827D4C3×D4×D512yescomplemented
828C2×C4—21no—
829C2×C4—51no—
830C2×C4—51no—
831C2×C4—81no—
832C2×C4—101no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—202no—
839C2×C4—202no—
840C2×C4C3×D4×D511yescharacteristic
841C2×C4C3×D4×D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—21no—
845C8—52no—
846C8—101no—
847C2×C3—42no—
848C2×C3—81no—
849C2×C3—81no—
850C2×C3—102no—
851C2×C3—201no—
852C2×C3—202no—
853C2×C3—401no—
854C2×C3#6594311yescharacteristic
855C2×C3#6609111yescharacteristic
856C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—22no—
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—102no—
873C22—101no—
874C22—201no—
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×#414911yescharacteristic
892C3#1061208911yescharacteristic, direct product factor, Sylow
893C2—42no—
894C2—81no—
895C2—81no—
896C2—102no—
897C2—201no—
898C2—202no—
899C2—401no—
900C2C3×#6594311yescharacteristic
901C2C3×#6609111yescharacteristic
902C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#459C2
socleC22×C3×C5C22×D4
hypercenterC3×#459D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4057C2semidirect
2. C2×C3×D5×D8C2semidirect
3. C3×#66051C2semidirect
4. C3×#65888C2semidirect
5. C3×C5×#459C2semidirect
6. C3×#65447C2semidirect
7. C3×#65445C2semidirect
8. C3×#65363C2semidirect
9. C3×#65303C2semidirect
10. C3×#65133C2semidirect
11. C3×#65125C2semidirect
12. C3×#65071C2semidirect
13. C3×#65067C2semidirect
14. C3×#65065C2semidirect
15. C3×#65062C2semidirect
16. #10612089C3direct (N × H)
17. C2×C3×#711C22semidirect
20. C2×C3×D4×D5C22semidirect
21. C2×C3×D4×D5C22semidirect
22. C2×C3×C5×D8C22semidirect
23. C2×C3×C5×D8C22semidirect
24. C3×C5×#127C22semidirect
25. C3×C4×C5×D4C22semidirect
28. C3×#4084C22semidirect
31. C2×C3×#687C22semidirect
32. C2×C3×#687C22semidirect
34. C2×C3×#686C22semidirect
35. C2×C3×#686C22semidirect
41. C2×C3×#677C22semidirect
42. C2×C3×#676C22semidirect
43. C2×C3×C8×D5C22semidirect
44. C3×#4043C22semidirect
45. C3×#4041C22semidirect
48. C3×#4021C22semidirect
50. C3×C4×D20C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×#102C22semidirect
54. C3×#3964C22semidirect
55. C3×#3953C22semidirect
56. C3×#3952C22semidirect
57. C3×#3952C22semidirect
58. C3×#3948C22semidirect
59. C3×#3941C22semidirect
60. C3×#3940C22semidirect
61. C3×#3935C22semidirect
63. C2×#4057C2×C3semidirect
64. C2×D5×D8C2×C3semidirect
65. #66051C2×C3semidirect
66. #65888C2×C3semidirect
67. C5×#459C2×C3semidirect
68. #65447C2×C3semidirect
69. #65445C2×C3semidirect
70. #65363C2×C3semidirect
71. #65303C2×C3semidirect
72. #65133C2×C3semidirect
73. #65125C2×C3semidirect
74. #65071C2×C3semidirect
75. #65067C2×C3semidirect
76. #65065C2×C3semidirect
77. #65062C2×C3semidirect
124. C3×#686D4semidirect
149. C3×#459D5semidirect
156. C2×#711C22×C3semidirect
159. C2×D4×D5C22×C3semidirect
160. C2×D4×D5C22×C3semidirect
161. C2×C5×D8C22×C3semidirect
162. C2×C5×D8C22×C3semidirect
163. C5×#127C22×C3semidirect
164. C4×C5×D4C22×C3semidirect
167. #4084C22×C3semidirect
170. C2×#687C22×C3semidirect
171. C2×#687C22×C3semidirect
173. C2×#686C22×C3semidirect
174. C2×#686C22×C3semidirect
180. C2×#677C22×C3semidirect
181. C2×#676C22×C3semidirect
182. C2×C8×D5C22×C3semidirect
183. #4043C22×C3semidirect
184. #4041C22×C3semidirect
187. #4021C22×C3semidirect
189. C4×D20C22×C3semidirect
190. C5×C4⋊C8C22×C3semidirect
191. C5×#102C22×C3semidirect
192. C5×#102C22×C3semidirect
193. #3964C22×C3semidirect
194. #3953C22×C3semidirect
195. #3952C22×C3semidirect
196. #3952C22×C3semidirect
197. #3948C22×C3semidirect
198. #3941C22×C3semidirect
199. #3940C22×C3semidirect
200. #3935C22×C3semidirect
225. C3×C5×D4C2×D4semidirect
258. C3×#168C2×D4semidirect
273. C2×C3×D8C2×D5semidirect
274. C2×C3×D8C2×D5semidirect
277. C3×#127C2×D5semidirect
291. C3×C4×D4C2×D5semidirect
294. C3×C4⋊C8C2×D5semidirect
299. C3×#102C2×D5semidirect
300. C3×#102C2×D5semidirect
350. #686C3×D4semidirect
375. #459C3×D5semidirect
406. C2×C3×D5AGL(1,ℤ/8)semidirect
502. C5×D4C2×C3×D4semidirect
535. #168C2×C3×D4semidirect
550. C2×D8C2×C3×D5semidirect
551. C2×D8C2×C3×D5semidirect
554. #127C2×C3×D5semidirect
568. C4×D4C2×C3×D5semidirect
571. C4⋊C8C2×C3×D5semidirect
576. #102C2×C3×D5semidirect
577. #102C2×C3×D5semidirect
628. C3×D4D4×D5semidirect
672. C2×D5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
827. D4C3×D4×D5semidirect
857. C5C3×#3264semidirect
892. C3#10612089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40572
C2×C3×D5×D82
C3×#660512
C3×#658882
C3×C5×#4592
C3×#654472
C3×#654452
C3×#653632
C3×#653032
C3×#651332
C3×#651252
C3×#650712
C3×#650672
C3×#650652
C3×#650622
#106120893
C3×#32645