Finite Group Databasebeta

← C3×#10611224 #14453209

Subgroups — C3×#10611224 #14453209

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×#4054C211yesmaximal, characteristic, complemented
2C22×C3×D40C211yesmaximal, characteristic, complemented
3C3×#65884C211yesmaximal, characteristic, complemented
4C3×D4×D20C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6C3×#65424C211yesmaximal, characteristic, complemented
7C3×#65403C211yesmaximal, characteristic, complemented
8C3×#65133C211yesmaximal, characteristic, complemented
9C3×#65132C211yesmaximal, characteristic, complemented
10C3×#65023C211yesmaximal, characteristic, complemented
11C3×#65021C211yesmaximal, characteristic, complemented
12C3×#65021C211yesmaximal, characteristic, complemented
13C3×#65020C211yesmaximal, characteristic, complemented
14C3×#65001C211yesmaximal, characteristic, complemented
15C3×#65000C211yesmaximal, characteristic, complemented
16#10611224C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×D4×D5—21no—
18C2×C3×#709C2211yescharacteristic, complemented
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic, complemented
21C22×C3×D20C2211yescharacteristic, complemented
22C2×C3×C5×M16C2211yescharacteristic, complemented
23C22×C3×C5×C8C2211yescharacteristic, complemented
24C3×C4×C5×D4C2211yescharacteristic
25C3×#4083—21no—
26C3×#4076C2211yescharacteristic
27C3×#4076C2211yescharacteristic, complemented
28C3×#4076C2211yescharacteristic, complemented
29C3×#4070C2211yescharacteristic, complemented
30C3×#4054—24no—
31C2×C3×D40—24no—
32C2×C3×D40C2211yescharacteristic
33C2×C3×D40C2211yescharacteristic
34C2×C3×D40C2211yescharacteristic, complemented
35C2×C3×D40C2211yescharacteristic, complemented
36C2×C3×D40C2211yescharacteristic, complemented
37C2×C3×D40C2211yescharacteristic, complemented
38C2×C3×#677C2211yescharacteristic, complemented
39C2×C3×#677C2211yescharacteristic, complemented
40C2×C3×#677C2211yescharacteristic, complemented
41C3×#4041—21no—
42C3×#4040—21no—
43C3×#4030—21no—
44C3×#4028—21no—
45C3×#4028—21no—
46C3×D5×C22⋊C4—21no—
47C3×#4021C2211yescharacteristic, complemented
48C3×#4020C2211yescharacteristic, complemented
49C3×C4×D20C2211yescharacteristic, complemented
50C3×C4×D20C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3953C2211yescharacteristic, complemented
58C3×#3953C2211yescharacteristic, complemented
59C3×#3953C2211yescharacteristic, complemented
60C3×#3949C2211yescharacteristic, complemented
61C3×#3948C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C2×#4054C2×C311yescharacteristic, complemented
64C22×D40C2×C311yescharacteristic, complemented
65#65884C2×C311yescharacteristic, complemented
66D4×D20C2×C311yescharacteristic, complemented
67C5×#435C2×C311yescharacteristic, complemented
68#65424C2×C311yescharacteristic, complemented
69#65403C2×C311yescharacteristic, complemented
70#65133C2×C311yescharacteristic, complemented
71#65132C2×C311yescharacteristic, complemented
72#65023C2×C311yescharacteristic, complemented
73#65021C2×C311yescharacteristic, complemented
74#65021C2×C311yescharacteristic, complemented
75#65020C2×C311yescharacteristic, complemented
76#65001C2×C311yescharacteristic, complemented
77#65000C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4D411yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C3×D4×D5—44no—
89C3×#709—22no—
90C3×#709—41no—
91C2×C3×D20—22no—
92C2×C3×D20—22no—
93C2×C3×D20—22no—
94C2×C3×D20—21no—
95C2×C3×D20—21no—
96C2×C3×D20—21no—
97C2×C3×D20—21no—
98C2×C3×D20—21no—
99C2×C3×D20—41no—
100C2×C3×D20—41no—
101C2×C3×D20—41no—
102C2×C3×D20C2311yescharacteristic
103C2×C3×D20C2311yescharacteristic
104C2×C3×D20C2311yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×D20C2311yescharacteristic
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5—21no—
109C2×C3×C4×D5—21no—
110C2×C3×Dic10C2311yescharacteristic
111C3×C5×M16—22no—
112C2×C3×C5×C8—22no—
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C2×C3×C5×C8C2311yescharacteristic
116C2×C3×C5×C8C2311yescharacteristic
117C3×C5×C4⋊C4D411yescharacteristic
118C3×C5×C22⋊C4D411yescharacteristic
119C3×C5×C22⋊C4D411yescharacteristic
120C3×C42×C5C2311yescharacteristic
121C3×C22⋊Dic5—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×C4⋊Dic5C2311yescharacteristic
130C3×C4⋊Dic5C2311yescharacteristic
131C3×#683—21no—
132C3×D40—22no—
133C3×D40—22no—
134C3×D40—22no—
135C3×D40—22no—
136C3×D40—41no—
137C3×D40D414yescomplemented
138C3×#677—22no—
139C3×#677—22no—
140C3×#677—41no—
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×#459—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#447—51no—
154C3×#442—51no—
155C3×#435D511yescharacteristic, complemented
156C2×D4×D5—21no—
157C2×#709C22×C311yescharacteristic, complemented
158C22×D20C22×C311yescharacteristic
159C22×D20C22×C311yescharacteristic, complemented
160C22×D20C22×C311yescharacteristic, complemented
161C2×C5×M16C22×C311yescharacteristic, complemented
162C22×C5×C8C22×C311yescharacteristic, complemented
163C4×C5×D4C22×C311yescharacteristic
164#4083—21no—
165#4076C22×C311yescharacteristic
166#4076C22×C311yescharacteristic, complemented
167#4076C22×C311yescharacteristic, complemented
168#4070C22×C311yescharacteristic, complemented
169#4054—24no—
170C2×D40—24no—
171C2×D40C22×C311yescharacteristic
172C2×D40C22×C311yescharacteristic
173C2×D40C22×C311yescharacteristic, complemented
174C2×D40C22×C311yescharacteristic, complemented
175C2×D40C22×C311yescharacteristic, complemented
176C2×D40C22×C311yescharacteristic, complemented
177C2×#677C22×C311yescharacteristic, complemented
178C2×#677C22×C311yescharacteristic, complemented
179C2×#677C22×C311yescharacteristic, complemented
180#4041—21no—
181#4040—21no—
182#4030—21no—
183#4028—21no—
184#4028—21no—
185D5×C22⋊C4—21no—
186#4021C22×C311yescharacteristic, complemented
187#4020C22×C311yescharacteristic, complemented
188C4×D20C22×C311yescharacteristic, complemented
189C4×D20C22×C311yescharacteristic, complemented
190C5×C4⋊C8C22×C311yescharacteristic, complemented
191C5×C22⋊C8C22×C311yescharacteristic, complemented
192C5×C22⋊C8C22×C311yescharacteristic, complemented
193C5×#97C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic, complemented
195#3953C22×C311yescharacteristic, complemented
196#3953C22×C311yescharacteristic, complemented
197#3953C22×C311yescharacteristic, complemented
198#3953C22×C311yescharacteristic, complemented
199#3949C22×C311yescharacteristic, complemented
200#3948C22×C311yescharacteristic, complemented
201#3264—51noSylow
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—42no—
210C22×C3×D5—42no—
211C22×C3×D5—42no—
212C22×C3×D5—42no—
213C22×C3×D5—42no—
214C22×C3×D5—42no—
215C22×C3×D5—81no—
216C22×C3×D5—81no—
217C22×C3×D5—81no—
218C3×C5×D4—22no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2×D411yescharacteristic
227C2×C3×C4×C5C2411yescharacteristic
228C3×C22⋊D5—42no—
229C3×C22⋊D5—42no—
230C3×C22⋊D5—42no—
231C3×C22⋊D5—81no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C3×D20—21no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—21no—
240C3×D20—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—42no—
244C3×D20—42no—
245C3×D20—42no—
246C3×D20—42no—
247C3×D20—81no—
248C3×D20C2×D412yes—
249C3×D20C2×D412yescomplemented
250C3×C4×D5—42no—
251C3×C4×D5—42no—
252C3×C4×D5—81no—
253C3×Dic10—21no—
254C3×Dic10—21no—
255C3×C5×C8—21no—
256C3×C5×C8—21no—
257C3×C5×C8—21no—
258C3×C5×C8C2×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—51no—
273C2×C3×D8—51no—
274C2×C3×D8—104no—
275C2×C3×M16C2×D511yescharacteristic, complemented
276C22×C3×C8C2×D511yescharacteristic, complemented
277C3×#127—51no—
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
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×#102—51no—
300C3×#102—51no—
301C3×C22⋊C8C2×D511yescharacteristic, complemented
302C3×C22⋊C8C2×D511yescharacteristic, complemented
303C3×#97C2×D511yescharacteristic, complemented
304C23×D5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C2×C5×D4C3×D411yescharacteristic
308C22×C4×C5C23×C311yescharacteristic
309C22×C4×C5C23×C311yescharacteristic
310C2×C22⋊D5—21no—
311C2×C22⋊D5—21no—
312C2×C22⋊D5—21no—
313C2×C22⋊D5—21no—
314D4×D5—44no—
315#709—22no—
316#709—41no—
317C2×D20—22no—
318C2×D20—22no—
319C2×D20—22no—
320C2×D20—21no—
321C2×D20—21no—
322C2×D20—21no—
323C2×D20—21no—
324C2×D20—21no—
325C2×D20—41no—
326C2×D20—41no—
327C2×D20—41no—
328C2×D20C23×C311yescharacteristic
329C2×D20C23×C311yescharacteristic
330C2×D20C23×C311yescharacteristic
331C2×D20C23×C311yescharacteristic
332C2×D20C23×C311yescharacteristic
333C2×C4×D5—21no—
334C2×C4×D5—21no—
335C2×C4×D5—21no—
336C2×Dic10C23×C311yescharacteristic
337C5×M16—22no—
338C2×C5×C8—22no—
339C2×C5×C8C23×C311yescharacteristic
340C2×C5×C8C23×C311yescharacteristic
341C2×C5×C8C23×C311yescharacteristic
342C2×C5×C8C23×C311yescharacteristic
343C5×C4⋊C4C3×D411yescharacteristic
344C5×C22⋊C4C3×D411yescharacteristic
345C5×C22⋊C4C3×D411yescharacteristic
346C42×C5C23×C311yescharacteristic
347C22⋊Dic5—21no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685—21no—
352#685—21no—
353#685—21no—
354#685—21no—
355C4⋊Dic5C23×C311yescharacteristic
356C4⋊Dic5C23×C311yescharacteristic
357#683—21no—
358D40—22no—
359D40—22no—
360D40—22no—
361D40—22no—
362D40—41no—
363D40C3×D414yescomplemented
364#677—22no—
365#677—22no—
366#677—41no—
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#459—51no—
376#450—51no—
377#449—51no—
378#447—51no—
379#447—51no—
380#442—51no—
381#435C3×D511yescharacteristic, complemented
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
385C22×C3×C5—21no—
386C22×C3×C5—21no—
387C22×C3×C5AGL(1,ℤ/8)12yescomplemented
388C22×C3×C5C22×D411yescharacteristic
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—84no—
405C2×C3×D5—84no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—21no—
410C3×C4×C5—21no—
411C3×C4×C5C22×D411yescharacteristic
412C3×C4×C5H(5,𝔽2)11yescharacteristic
413C3×Dic5—41no—
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—51no—
423C2×C3×D4—51no—
424C2×C3×D4—51no—
425C2×C3×D4—51no—
426C2×C3×D4—51no—
427C2×C3×D4—102no—
428C2×C3×D4—102no—
429C2×C3×D4—102no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—101no—
433C2×C3×D4—101no—
434C2×C3×D4—101no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—101no—
439C2×C3×D4—201no—
440C2×C3×D4—201no—
441C2×C3×D4—201no—
442C2×C3×D4—204no—
443C2×C3×D4D2011yescharacteristic
444C22×C3×C4—101no—
445C22×C3×C4—101no—
446C22×C3×C4—101no—
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—102no—
451C3×SD16—201no—
452C3×D8—54no—
453C3×D8—102no—
454C3×D8—102no—
455C3×D8—102no—
456C3×D8—102no—
457C3×D8—201no—
458C3×M16—22no—
459C2×C3×C8—22no—
460C2×C3×C8C22×D511yescharacteristic
461C2×C3×C8C22×D511yescharacteristic
462C2×C3×C8C22×D511yescharacteristic
463C2×C3×C8C22×D511yescharacteristic
464C3×C4⋊C4—51no—
465C3×C4⋊C4—51no—
466C3×C4⋊C4—101no—
467C3×C4⋊C4D2011yescharacteristic
468C3×C22⋊C4—101no—
469C3×C22⋊C4—101no—
470C3×C22⋊C4—101no—
471C3×C22⋊C4—101no—
472C3×C22⋊C4—101no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4D2011yescharacteristic
477C3×C22⋊C4D2011yescharacteristic
478C3×C42C22×D511yescharacteristic
479C23×C5C2×C3×D411yescharacteristic
480C23×C5C2×C3×D411yescharacteristic
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—42no—
487C22×D5—42no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—42no—
491C22×D5—42no—
492C22×D5—81no—
493C22×D5—81no—
494C22×D5—81no—
495C5×D4—22no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5C2×C3×D411yescharacteristic
501C2×C4×C5C2×C3×D411yescharacteristic
502C2×C4×C5C2×C3×D411yescharacteristic
503C2×C4×C5C2×C3×D411yescharacteristic
504C2×C4×C5C24×C311yescharacteristic
505C22⋊D5—42no—
506C22⋊D5—42no—
507C22⋊D5—42no—
508C22⋊D5—81no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512D20—21no—
513D20—21no—
514D20—21no—
515D20—21no—
516D20—21no—
517D20—21no—
518D20—21no—
519D20—21no—
520D20—42no—
521D20—42no—
522D20—42no—
523D20—42no—
524D20—81no—
525D20C2×C3×D412yes—
526D20C2×C3×D412yescomplemented
527C4×D5—42no—
528C4×D5—42no—
529C4×D5—81no—
530Dic10—21no—
531Dic10—21no—
532C5×C8—21no—
533C5×C8—21no—
534C5×C8—21no—
535C5×C8C2×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—51no—
550C2×D8—51no—
551C2×D8—104no—
552C2×M16C2×C3×D511yescharacteristic, complemented
553C22×C8C2×C3×D511yescharacteristic, complemented
554#127—51no—
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
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#102—51no—
577#102—51no—
578C22⋊C8C2×C3×D511yescharacteristic, complemented
579C22⋊C8C2×C3×D511yescharacteristic, complemented
580#97C2×C3×D511yescharacteristic, complemented
581C2×C3×C5—22no—
582C2×C3×C5—41no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586C3×D5—42no—
587C3×D5—42no—
588C3×D5—81no—
589C3×D5—81no—
590C3×D5—81no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3—202no—
597C23×C3—202no—
598C23×C3—202no—
599C23×C3—202no—
600C23×C3—202no—
601C23×C3—202no—
602C23×C3—401no—
603C23×C3—401no—
604C23×C3—401no—
605C23×C3C2×D2011yescharacteristic
606C23×C3C2×D2011yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—22no—
610C3×D4—52no—
611C3×D4—52no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—101no—
615C3×D4—101no—
616C3×D4—101no—
617C3×D4—101no—
618C3×D4—101no—
619C3×D4—101no—
620C3×D4—202no—
621C3×D4—202no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—202no—
626C3×D4—202no—
627C3×D4—401no—
628C3×D4—401no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—202no—
637C2×C3×C4—202no—
638C2×C3×C4—401no—
639C2×C3×C4C2×D2011yescharacteristic
640C2×C3×C4C2×D2011yescharacteristic
641C2×C3×C4C2×D2011yescharacteristic
642C2×C3×C4C2×D2011yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8D4×D512yescomplemented
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—21no—
653C22×C5C3×AGL(1,ℤ/8)12yescomplemented
654C22×C5C22×C3×D411yescharacteristic
655C2×D5—22no—
656C2×D5—22no—
657C2×D5—41no—
658C2×D5—41no—
659C2×D5—41no—
660C2×D5—41no—
661C2×D5—41no—
662C2×D5—41no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—84no—
671C2×D5—84no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—21no—
676C4×C5—21no—
677C4×C5C22×C3×D411yescharacteristic
678C4×C5C3×H(5,𝔽2)11yescharacteristic
679Dic5—41no—
680Dic5—41no—
681Dic5—41no—
682C24—101no—
683C24—101no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—51no—
689C2×D4—51no—
690C2×D4—51no—
691C2×D4—51no—
692C2×D4—51no—
693C2×D4—102no—
694C2×D4—102no—
695C2×D4—102no—
696C2×D4—101no—
697C2×D4—101no—
698C2×D4—101no—
699C2×D4—101no—
700C2×D4—101no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—101no—
705C2×D4—201no—
706C2×D4—201no—
707C2×D4—201no—
708C2×D4—204no—
709C2×D4C3×D2011yescharacteristic
710C22×C4—101no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715SD16—102no—
716SD16—102no—
717SD16—201no—
718D8—54no—
719D8—102no—
720D8—102no—
721D8—102no—
722D8—102no—
723D8—201no—
724M16—22no—
725C2×C8—22no—
726C2×C8C22×C3×D511yescharacteristic
727C2×C8C22×C3×D511yescharacteristic
728C2×C8C22×C3×D511yescharacteristic
729C2×C8C22×C3×D511yescharacteristic
730C4⋊C4—51no—
731C4⋊C4—51no—
732C4⋊C4—101no—
733C4⋊C4C3×D2011yescharacteristic
734C22⋊C4—101no—
735C22⋊C4—101no—
736C22⋊C4—101no—
737C22⋊C4—101no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4C3×D2011yescharacteristic
743C22⋊C4C3×D2011yescharacteristic
744C42C22×C3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—201no—
754C22×C3—201no—
755C22×C3—201no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3—201no—
762C22×C3—201no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—404no—
767C22×C3—404no—
768C22×C3—404no—
769C22×C3#405412yescomplemented
770C22×C3C22×D2011yescharacteristic
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—201no—
776C3×C4—201no—
777C3×C4—201no—
778C3×C4C2×D4×D511yescharacteristic
779C3×C4#414911yescharacteristic
780C2×C5—22no—
781C2×C5—41no—
782C2×C5C3×D4211yescharacteristic
783C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
784C2×C5C3×#57611yescharacteristic
785D5—42no—
786D5—42no—
787D5—81no—
788D5—81no—
789D5—81no—
790C23—101no—
791C23—101no—
792C23—101no—
793C23—101no—
794C23—101no—
795C23—202no—
796C23—202no—
797C23—202no—
798C23—202no—
799C23—202no—
800C23—202no—
801C23—401no—
802C23—401no—
803C23—401no—
804C23C2×C3×D2011yescharacteristic
805C23C2×C3×D2011yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—22no—
809D4—52no—
810D4—52no—
811D4—101no—
812D4—101no—
813D4—101no—
814D4—101no—
815D4—101no—
816D4—101no—
817D4—101no—
818D4—101no—
819D4—202no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—202no—
826D4—401no—
827D4—401no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—101no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—202no—
836C2×C4—202no—
837C2×C4—401no—
838C2×C4C2×C3×D2011yescharacteristic
839C2×C4C2×C3×D2011yescharacteristic
840C2×C4C2×C3×D2011yescharacteristic
841C2×C4C2×C3×D2011yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—21no—
845C8—21no—
846C8C3×D4×D512yescomplemented
847C2×C3—22no—
848C2×C3—41no—
849C2×C3—202no—
850C2×C3—202no—
851C2×C3—401no—
852C2×C3—401no—
853C2×C3—401no—
854C2×C3D4×D2011yescharacteristic
855C2×C3C2×#405411yescharacteristic
856C2×C3#6608611yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—102no—
864C22—102no—
865C22—201no—
866C22—201no—
867C22—201no—
868C22—201no—
869C22—201no—
870C22—201no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—404no—
879C22—404no—
880C22—404no—
881C22C3×#405412yescomplemented
882C22C22×C3×D2011yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—201no—
888C4—201no—
889C4—201no—
890C4C2×C3×D4×D511yescharacteristic
891C4C3×#414911yescharacteristic
892C3#1061122411yescharacteristic, direct product factor, Sylow
893C2—22no—
894C2—41no—
895C2—202no—
896C2—202no—
897C2—401no—
898C2—401no—
899C2—401no—
900C2C3×D4×D2011yescharacteristic
901C2C2×C3×#405411yescharacteristic
902C2C3×#6608611yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
hypercenterC3×#435D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4054C2semidirect
2. C22×C3×D40C2semidirect
3. C3×#65884C2semidirect
4. C3×D4×D20C2semidirect
5. C3×C5×#435C2semidirect
6. C3×#65424C2semidirect
7. C3×#65403C2semidirect
8. C3×#65133C2semidirect
9. C3×#65132C2semidirect
10. C3×#65023C2semidirect
11. C3×#65021C2semidirect
12. C3×#65021C2semidirect
13. C3×#65020C2semidirect
14. C3×#65001C2semidirect
15. C3×#65000C2semidirect
16. #10611224C3direct (N × H)
18. C2×C3×#709C22semidirect
20. C22×C3×D20C22semidirect
21. C22×C3×D20C22semidirect
22. C2×C3×C5×M16C22semidirect
23. C22×C3×C5×C8C22semidirect
27. C3×#4076C22semidirect
28. C3×#4076C22semidirect
29. C3×#4070C22semidirect
34. C2×C3×D40C22semidirect
35. C2×C3×D40C22semidirect
36. C2×C3×D40C22semidirect
37. C2×C3×D40C22semidirect
38. C2×C3×#677C22semidirect
39. C2×C3×#677C22semidirect
40. C2×C3×#677C22semidirect
47. C3×#4021C22semidirect
48. C3×#4020C22semidirect
49. C3×C4×D20C22semidirect
50. C3×C4×D20C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×C22⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
55. C3×#3953C22semidirect
56. C3×#3953C22semidirect
57. C3×#3953C22semidirect
58. C3×#3953C22semidirect
59. C3×#3953C22semidirect
60. C3×#3949C22semidirect
61. C3×#3948C22semidirect
63. C2×#4054C2×C3semidirect
64. C22×D40C2×C3semidirect
65. #65884C2×C3semidirect
66. D4×D20C2×C3semidirect
67. C5×#435C2×C3semidirect
68. #65424C2×C3semidirect
69. #65403C2×C3semidirect
70. #65133C2×C3semidirect
71. #65132C2×C3semidirect
72. #65023C2×C3semidirect
73. #65021C2×C3semidirect
74. #65021C2×C3semidirect
75. #65020C2×C3semidirect
76. #65001C2×C3semidirect
77. #65000C2×C3semidirect
137. C3×D40D4semidirect
155. C3×#435D5semidirect
157. C2×#709C22×C3semidirect
159. C22×D20C22×C3semidirect
160. C22×D20C22×C3semidirect
161. C2×C5×M16C22×C3semidirect
162. C22×C5×C8C22×C3semidirect
166. #4076C22×C3semidirect
167. #4076C22×C3semidirect
168. #4070C22×C3semidirect
173. C2×D40C22×C3semidirect
174. C2×D40C22×C3semidirect
175. C2×D40C22×C3semidirect
176. C2×D40C22×C3semidirect
177. C2×#677C22×C3semidirect
178. C2×#677C22×C3semidirect
179. C2×#677C22×C3semidirect
186. #4021C22×C3semidirect
187. #4020C22×C3semidirect
188. C4×D20C22×C3semidirect
189. C4×D20C22×C3semidirect
190. C5×C4⋊C8C22×C3semidirect
191. C5×C22⋊C8C22×C3semidirect
192. C5×C22⋊C8C22×C3semidirect
193. C5×#97C22×C3semidirect
194. #3953C22×C3semidirect
195. #3953C22×C3semidirect
196. #3953C22×C3semidirect
197. #3953C22×C3semidirect
198. #3953C22×C3semidirect
199. #3949C22×C3semidirect
200. #3948C22×C3semidirect
249. C3×D20C2×D4semidirect
258. C3×C5×C8C2×D4semidirect
275. C2×C3×M16C2×D5semidirect
276. C22×C3×C8C2×D5semidirect
294. C3×C4⋊C8C2×D5semidirect
301. C3×C22⋊C8C2×D5semidirect
302. C3×C22⋊C8C2×D5semidirect
303. C3×#97C2×D5semidirect
363. D40C3×D4semidirect
381. #435C3×D5semidirect
387. C22×C3×C5AGL(1,ℤ/8)semidirect
526. D20C2×C3×D4semidirect
535. C5×C8C2×C3×D4semidirect
552. C2×M16C2×C3×D5semidirect
553. C22×C8C2×C3×D5semidirect
571. C4⋊C8C2×C3×D5semidirect
578. C22⋊C8C2×C3×D5semidirect
579. C22⋊C8C2×C3×D5semidirect
580. #97C2×C3×D5semidirect
647. C3×C8D4×D5semidirect
653. C22×C5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
769. C22×C3#4054semidirect
846. C8C3×D4×D5semidirect
857. C5C3×#3264semidirect
881. C22C3×#4054semidirect
892. C3#10611224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40542
C22×C3×D402
C3×#658842
C3×D4×D202
C3×C5×#4352
C3×#654242
C3×#654032
C3×#651332
C3×#651322
C3×#650232
C3×#650212
C3×#650202
C3×#650012
C3×#650002
#106112243
C3×#32645