Finite Group Databasebeta

← C3×#10611791 #14453428

Subgroups — C3×#10611791 #14453428

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66151C211yesmaximal, characteristic, complemented
2C22×C3×#688C211yesmaximal, characteristic, complemented
3C2×C3×#4060C211yesmaximal, characteristic, complemented
4C3×#65943C211yesmaximal, characteristic, complemented
5C3×C5×#448C211yesmaximal, characteristic, complemented
6C3×#65465C211yesmaximal, characteristic, complemented
7C3×#65458C211yesmaximal, characteristic, complemented
8C3×#65452C211yesmaximal, characteristic, complemented
9C3×#65327C211yesmaximal, characteristic, complemented
10C3×#65108C211yesmaximal, characteristic, complemented
11C3×#65106C211yesmaximal, characteristic, complemented
12C3×#65101C211yesmaximal, characteristic, complemented
13C3×#65100C211yesmaximal, characteristic, complemented
14C3×#65021C211yesmaximal, characteristic, complemented
15C3×#65019C211yesmaximal, characteristic, complemented
16#10611791C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×C3×#713C2211yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C2×C3×D4×D5C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C3×C5×#121C2211yescharacteristic
25C3×#4093—21no—
26C3×#4093C2211yescharacteristic, complemented
27C3×#4092—21no—
28C3×#4092C2211yescharacteristic, complemented
29C3×Q8×Dic5C2211yescharacteristic, complemented
30C2×C3×#688—24no—
31C2×C3×#688C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic
33C2×C3×#688C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic, complemented
35C3×#4086C2211yescharacteristic
36C3×#4083—21no—
37C2×C3×#686C2211yescharacteristic, complemented
38C3×#4076—21no—
39C3×#4076C2211yescharacteristic, complemented
40C3×C4×C22⋊D5—21no—
41C3×C4×C22⋊D5C2211yescharacteristic
42C22×C3×#168C2211yescharacteristic, complemented
43C3×#4060—24no—
44C2×C3×D40C2211yescharacteristic
45C2×C3×D40C2211yescharacteristic, complemented
46C2×C3×#676C2211yescharacteristic, complemented
47C3×#4041C2211yescharacteristic
48C3×#4039C2211yescharacteristic
49C3×#4030—21no—
50C3×#4028—21no—
51C3×C5×#103C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic
56C3×#3953C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×#3946C2211yescharacteristic, complemented
60C3×#3941C2211yescharacteristic, complemented
61C3×#3939C2211yescharacteristic, complemented
62C3×#3265—51nomaximal, Hall
63#66151C2×C311yescharacteristic, complemented
64C22×#688C2×C311yescharacteristic, complemented
65C2×#4060C2×C311yescharacteristic, complemented
66#65943C2×C311yescharacteristic, complemented
67C5×#448C2×C311yescharacteristic, complemented
68#65465C2×C311yescharacteristic, complemented
69#65458C2×C311yescharacteristic, complemented
70#65452C2×C311yescharacteristic, complemented
71#65327C2×C311yescharacteristic, complemented
72#65108C2×C311yescharacteristic, complemented
73#65106C2×C311yescharacteristic, complemented
74#65101C2×C311yescharacteristic, complemented
75#65100C2×C311yescharacteristic, complemented
76#65021C2×C311yescharacteristic, complemented
77#65019C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C2×C3×C5×Q8—21no—
81C2×C3×C5×Q8—22no—
82C2×C3×C5×Q8—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4C2311yescharacteristic
87C22×C3×C4×C5—21no—
88C22×C3×C4×C5C2311yescharacteristic
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5D411yescharacteristic
94C3×#713—22no—
95C3×#713—41no—
96C3×D4×D5—22no—
97C3×D4×D5—41no—
98C3×D4×D5—44no—
99C2×C3×D20—22no—
100C2×C3×D20—21no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—41no—
104C2×C3×D20C2311yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×D20C2311yescharacteristic
107C2×C3×C4×D5—21no—
108C2×C3×C4×D5—21no—
109C2×C3×C4×D5C2311yescharacteristic
110C3×C5×SD16—22no—
111C3×C5×SD16—41no—
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C3×C5×C4⋊C4C2311yescharacteristic
115C3×C5×C22⋊C4—21no—
116C3×C22⋊Dic5D411yescharacteristic
117C3×#688—22no—
118C3×#688—22no—
119C3×#688—22no—
120C3×#688D414yescomplemented
121C3×#686—22no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5C2311yescharacteristic
131C3×#683—21no—
132C3×#683D411yescharacteristic
133C3×C4×Dic5—21no—
134C3×C4×Dic5C2311yescharacteristic
135C2×C3×#168—22no—
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C3×D40—22no—
139C3×D40—41no—
140C3×#676—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×SD16—51no—
143C3×#548—51no—
144C3×D42—51no—
145C3×#496—51no—
146C3×#468—51no—
147C3×#466—51no—
148C3×#463—51no—
149C3×#460—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#448D511yescharacteristic, complemented
153C3×#447—51no—
154C3×#440—51no—
155C3×#435—51no—
156C22×C5×Q8C22×C311yescharacteristic, complemented
157C2×#713C22×C311yescharacteristic, complemented
158C2×D4×D5—21no—
159C2×D4×D5C22×C311yescharacteristic
160C22×D20C22×C311yescharacteristic
161C2×C5×SD16C22×C311yescharacteristic, complemented
162C2×C5×SD16C22×C311yescharacteristic, complemented
163C5×#121C22×C311yescharacteristic
164#4093—21no—
165#4093C22×C311yescharacteristic, complemented
166#4092—21no—
167#4092C22×C311yescharacteristic, complemented
168Q8×Dic5C22×C311yescharacteristic, complemented
169C2×#688—24no—
170C2×#688C22×C311yescharacteristic
171C2×#688C22×C311yescharacteristic
172C2×#688C22×C311yescharacteristic, complemented
173C2×#688C22×C311yescharacteristic, complemented
174#4086C22×C311yescharacteristic
175#4083—21no—
176C2×#686C22×C311yescharacteristic, complemented
177#4076—21no—
178#4076C22×C311yescharacteristic, complemented
179C4×C22⋊D5—21no—
180C4×C22⋊D5C22×C311yescharacteristic
181C22×#168C22×C311yescharacteristic, complemented
182#4060—24no—
183C2×D40C22×C311yescharacteristic
184C2×D40C22×C311yescharacteristic, complemented
185C2×#676C22×C311yescharacteristic, complemented
186#4041C22×C311yescharacteristic
187#4039C22×C311yescharacteristic
188#4030—21no—
189#4028—21no—
190C5×#103C22×C311yescharacteristic, complemented
191C5×#103C22×C311yescharacteristic, complemented
192C5×C22⋊C8C22×C311yescharacteristic, complemented
193#3964C22×C311yescharacteristic, complemented
194#3953C22×C311yescharacteristic
195#3953C22×C311yescharacteristic, complemented
196#3952C22×C311yescharacteristic, complemented
197#3947C22×C311yescharacteristic, complemented
198#3946C22×C311yescharacteristic, complemented
199#3941C22×C311yescharacteristic, complemented
200#3939C22×C311yescharacteristic, complemented
201#3265—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×C3×D5—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—81no—
212C22×C3×D5—81no—
213C22×C3×D5C2×D411yescharacteristic
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C3×C5×Q8—21no—
217C3×C5×Q8—42no—
218C3×C5×Q8C2×D412yescomplemented
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—42no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2411yescharacteristic
230C3×C22⋊D5—22no—
231C3×C22⋊D5—42no—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—42no—
234C3×C22⋊D5—81no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5C2×D411yescharacteristic
237C2×C3×Dic5C2×D411yescharacteristic
238C2×C3×Dic5C2×D411yescharacteristic
239C3×D20—21no—
240C3×D20—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—21no—
244C3×D20—42no—
245C3×D20—42no—
246C3×D20—42no—
247C3×D20C2×D412yes—
248C3×C4×D5—21no—
249C3×C4×D5—21no—
250C3×C4×D5—42no—
251C3×C4×D5—42no—
252C3×C5×C8—21no—
253C3×C5×C8—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×C3×#41—51no—
257C22×C3×Q8C2×D511yescharacteristic, complemented
258C22×C3×D4—51no—
259C22×C3×D4—51no—
260C22×C3×D4—101no—
261C3×AGL(1,ℤ/8)—104no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×SD16—51no—
265C2×C3×SD16—51no—
266C2×C3×SD16—104no—
267C2×C3×SD16C2×D511yescharacteristic, complemented
268C2×C3×SD16C2×D511yescharacteristic, complemented
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×M16—51no—
273C22×C3×C8—51no—
274C3×#127—51no—
275C3×#124—51no—
276C3×#124—101no—
277C3×C22⋊Q8—51no—
278C3×C22⋊Q8—101no—
279C3×#121—51no—
280C3×#121—51no—
281C3×#121—101no—
282C3×#121—101no—
283C3×#121C2×D511yescharacteristic
284C3×#120—101no—
285C3×#120—101no—
286C3×C4×Q8—51no—
287C3×C4×D4—51no—
288C3×C4×D4—51no—
289C3×C4×D4—101no—
290C3×#107—51no—
291C3×C4⋊C8—51no—
292C3×#103C2×D511yescharacteristic, complemented
293C3×#103C2×D511yescharacteristic, complemented
294C3×#102—51no—
295C3×#102—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×C22⋊C8—51no—
299C3×C22⋊C8C2×D511yescharacteristic, complemented
300C3×#97—51no—
301C23×D5—21no—
302C23×D5—21no—
303C2×C5×Q8—21no—
304C2×C5×Q8—22no—
305C2×C5×Q8—41no—
306C2×C5×Q8C23×C311yescharacteristic
307C2×C5×Q8C23×C311yescharacteristic
308C2×C5×D4—21no—
309C2×C5×D4C23×C311yescharacteristic
310C22×C4×C5—21no—
311C22×C4×C5C23×C311yescharacteristic
312C2×C22⋊D5—21no—
313C2×C22⋊D5—21no—
314C2×C22⋊D5—21no—
315C2×C22⋊D5—21no—
316C2×C22⋊D5C3×D411yescharacteristic
317#713—22no—
318#713—41no—
319D4×D5—22no—
320D4×D5—41no—
321D4×D5—44no—
322C2×D20—22no—
323C2×D20—21no—
324C2×D20—21no—
325C2×D20—21no—
326C2×D20—41no—
327C2×D20C23×C311yescharacteristic
328C2×D20C23×C311yescharacteristic
329C2×D20C23×C311yescharacteristic
330C2×C4×D5—21no—
331C2×C4×D5—21no—
332C2×C4×D5C23×C311yescharacteristic
333C5×SD16—22no—
334C5×SD16—41no—
335C2×C5×C8C23×C311yescharacteristic
336C2×C5×C8C23×C311yescharacteristic
337C5×C4⋊C4C23×C311yescharacteristic
338C5×C22⋊C4—21no—
339C22⋊Dic5C3×D411yescharacteristic
340#688—22no—
341#688—22no—
342#688—22no—
343#688C3×D414yescomplemented
344#686—22no—
345#685—21no—
346#685—21no—
347#685—21no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685C3×D411yescharacteristic
352C4⋊Dic5—21no—
353C4⋊Dic5C23×C311yescharacteristic
354#683—21no—
355#683C3×D411yescharacteristic
356C4×Dic5—21no—
357C4×Dic5C23×C311yescharacteristic
358C2×#168—22no—
359C2×#168C23×C311yescharacteristic
360C2×#168C23×C311yescharacteristic
361D40—22no—
362D40—41no—
363#676—22no—
364C2×AGL(1,ℤ/8)—51no—
365C22×SD16—51no—
366#548—51no—
367D42—51no—
368#496—51no—
369#468—51no—
370#466—51no—
371#463—51no—
372#460—51no—
373#450—51no—
374#449—51no—
375#448C3×D511yescharacteristic, complemented
376#447—51no—
377#440—51no—
378#435—51no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5AGL(1,ℤ/8)12yescomplemented
385C22×C3×C5C22×D411yescharacteristic
386C2×C3×D5—21no—
387C2×C3×D5—22no—
388C2×C3×D5—21no—
389C2×C3×D5—21no—
390C2×C3×D5—41no—
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—84no—
399C2×C3×D5—84no—
400C3×C4×C5—22no—
401C3×C4×C5—21no—
402C3×C4×C5—41no—
403C3×C4×C5—41no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406C3×Dic5—21no—
407C3×Dic5—21no—
408C3×Dic5—21no—
409C3×Dic5—41no—
410C24×C3—101no—
411C24×C3—101no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—21no—
415C2×C3×Q8—22no—
416C2×C3×Q8—41no—
417C2×C3×Q8C22×D511yescharacteristic
418C2×C3×Q8C22×D511yescharacteristic
419C2×C3×D4—21no—
420C2×C3×D4—51no—
421C2×C3×D4—51no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—102no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—102no—
431C2×C3×D4—101no—
432C2×C3×D4—101no—
433C2×C3×D4—201no—
434C2×C3×D4—201no—
435C2×C3×D4—204no—
436C2×C3×D4C22×D511yescharacteristic
437C22×C3×C4—21no—
438C22×C3×C4—51no—
439C22×C3×C4—101no—
440C22×C3×C4—101no—
441C22×C3×C4C22×D511yescharacteristic
442C3×SD16—22no—
443C3×SD16—41no—
444C3×SD16—54no—
445C3×SD16—102no—
446C3×SD16—102no—
447C3×SD16—102no—
448C3×D8—102no—
449C3×D8—102no—
450C3×D8—201no—
451C3×M16—102no—
452C2×C3×C8—51no—
453C2×C3×C8—51no—
454C2×C3×C8—102no—
455C2×C3×C8C22×D511yescharacteristic
456C2×C3×C8C22×D511yescharacteristic
457C3×C4⋊C4—51no—
458C3×C4⋊C4—51no—
459C3×C4⋊C4—101no—
460C3×C4⋊C4—101no—
461C3×C4⋊C4C22×D511yescharacteristic
462C3×C22⋊C4—21no—
463C3×C22⋊C4—51no—
464C3×C22⋊C4—51no—
465C3×C22⋊C4—101no—
466C3×C22⋊C4—101no—
467C3×C22⋊C4—101no—
468C3×C22⋊C4—101no—
469C3×C22⋊C4—101no—
470C3×C22⋊C4—101no—
471C3×C42—51no—
472C3×C42—101no—
473C23×C5—21no—
474C23×C5C2×C3×D411yescharacteristic
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—42no—
479C22×D5—42no—
480C22×D5—42no—
481C22×D5—42no—
482C22×D5—81no—
483C22×D5—81no—
484C22×D5C2×C3×D411yescharacteristic
485C5×Q8—21no—
486C5×Q8—21no—
487C5×Q8—21no—
488C5×Q8—42no—
489C5×Q8C2×C3×D412yescomplemented
490C5×D4—21no—
491C5×D4—21no—
492C5×D4—42no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—42no—
499C2×C4×C5C2×C3×D411yescharacteristic
500C2×C4×C5C24×C311yescharacteristic
501C22⋊D5—22no—
502C22⋊D5—42no—
503C22⋊D5—42no—
504C22⋊D5—42no—
505C22⋊D5—81no—
506C2×Dic5—21no—
507C2×Dic5C2×C3×D411yescharacteristic
508C2×Dic5C2×C3×D411yescharacteristic
509C2×Dic5C2×C3×D411yescharacteristic
510D20—21no—
511D20—21no—
512D20—21no—
513D20—21no—
514D20—21no—
515D20—42no—
516D20—42no—
517D20—42no—
518D20C2×C3×D412yes—
519C4×D5—21no—
520C4×D5—21no—
521C4×D5—42no—
522C4×D5—42no—
523C5×C8—21no—
524C5×C8—21no—
525#168—21no—
526#168C2×C3×D412yescomplemented
527C2×#41—51no—
528C22×Q8C2×C3×D511yescharacteristic, complemented
529C22×D4—51no—
530C22×D4—51no—
531C22×D4—101no—
532AGL(1,ℤ/8)—104no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—51no—
536C2×SD16—51no—
537C2×SD16—104no—
538C2×SD16C2×C3×D511yescharacteristic, complemented
539C2×SD16C2×C3×D511yescharacteristic, complemented
540C2×D8—51no—
541C2×D8—51no—
542C2×D8—51no—
543C2×M16—51no—
544C22×C8—51no—
545#127—51no—
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—51no—
551#121—51no—
552#121—101no—
553#121—101no—
554#121C2×C3×D511yescharacteristic
555#120—101no—
556#120—101no—
557C4×Q8—51no—
558C4×D4—51no—
559C4×D4—51no—
560C4×D4—101no—
561#107—51no—
562C4⋊C8—51no—
563#103C2×C3×D511yescharacteristic, complemented
564#103C2×C3×D511yescharacteristic, complemented
565#102—51no—
566#102—51no—
567#102—51no—
568#102—51no—
569C22⋊C8—51no—
570C22⋊C8C2×C3×D511yescharacteristic, complemented
571#97—51no—
572C2×C3×C5—22no—
573C2×C3×C5—81no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577C3×D5—41no—
578C3×D5—42no—
579C3×D5—81no—
580C3×D5—81no—
581C23×C3—21no—
582C23×C3—51no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3—202no—
587C23×C3—202no—
588C23×C3—202no—
589C23×C3—202no—
590C23×C3—401no—
591C23×C3—401no—
592C23×C3D4×D511yescharacteristic
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—42no—
597C3×Q8D4×D512yescomplemented
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—42no—
601C3×D4—52no—
602C3×D4—102no—
603C3×D4—101no—
604C3×D4—101no—
605C3×D4—101no—
606C3×D4—101no—
607C3×D4—101no—
608C3×D4—202no—
609C3×D4—202no—
610C3×D4—202no—
611C3×D4—202no—
612C3×D4—202no—
613C3×D4—202no—
614C3×D4—401no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—42no—
621C2×C3×C4—51no—
622C2×C3×C4—51no—
623C2×C3×C4—51no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—202no—
628C2×C3×C4—202no—
629C2×C3×C4D4×D511yescharacteristic
630C2×C3×C4C23×D511yescharacteristic
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—52no—
634C3×C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5C3×AGL(1,ℤ/8)12yescomplemented
641C22×C5C22×C3×D411yescharacteristic
642C2×D5—21no—
643C2×D5—21no—
644C2×D5—21no—
645C2×D5—22no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5—41no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—41no—
654C2×D5—84no—
655C2×D5—84no—
656C4×C5—22no—
657C4×C5—21no—
658C4×C5—41no—
659C4×C5—41no—
660C4×C5C22×C3×D411yescharacteristic
661C4×C5C3×H(5,𝔽2)11yescharacteristic
662Dic5—21no—
663Dic5—21no—
664Dic5—21no—
665Dic5—41no—
666C24—101no—
667C24—101no—
668#41—102no—
669#41—201no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—41no—
673C2×Q8C22×C3×D511yescharacteristic
674C2×Q8C22×C3×D511yescharacteristic
675C2×D4—21no—
676C2×D4—51no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—51no—
680C2×D4—102no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4—101no—
684C2×D4—101no—
685C2×D4—101no—
686C2×D4—102no—
687C2×D4—101no—
688C2×D4—101no—
689C2×D4—201no—
690C2×D4—201no—
691C2×D4—204no—
692C2×D4C22×C3×D511yescharacteristic
693C22×C4—21no—
694C22×C4—51no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4C22×C3×D511yescharacteristic
698SD16—22no—
699SD16—41no—
700SD16—54no—
701SD16—102no—
702SD16—102no—
703SD16—102no—
704D8—102no—
705D8—102no—
706D8—201no—
707M16—102no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—102no—
711C2×C8C22×C3×D511yescharacteristic
712C2×C8C22×C3×D511yescharacteristic
713C4⋊C4—51no—
714C4⋊C4—51no—
715C4⋊C4—101no—
716C4⋊C4—101no—
717C4⋊C4C22×C3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—51no—
720C22⋊C4—51no—
721C22⋊C4—101no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4—101no—
726C22⋊C4—101no—
727C42—51no—
728C42—101no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—101no—
736C22×C3—101no—
737C22×C3—101no—
738C22×C3—102no—
739C22×C3—201no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—201no—
743C22×C3—201no—
744C22×C3—201no—
745C22×C3—201no—
746C22×C3—201no—
747C22×C3—404no—
748C22×C3—404no—
749C22×C3#406012yescomplemented
750C22×C3C2×D4×D511yescharacteristic
751C3×C4—21no—
752C3×C4—22no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—101no—
756C3×C4—101no—
757C3×C4—101no—
758C3×C4—201no—
759C3×C4C2×D4×D511yescharacteristic
760C3×C4#414411yescharacteristic
761C2×C5—22no—
762C2×C5—81no—
763C2×C5C3×D4211yescharacteristic
764C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
765C2×C5C3×#57711yescharacteristic
766D5—41no—
767D5—42no—
768D5—81no—
769D5—81no—
770C23—21no—
771C23—51no—
772C23—101no—
773C23—101no—
774C23—101no—
775C23—202no—
776C23—202no—
777C23—202no—
778C23—202no—
779C23—401no—
780C23—401no—
781C23C3×D4×D511yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—42no—
786Q8C3×D4×D512yescomplemented
787D4—21no—
788D4—21no—
789D4—42no—
790D4—52no—
791D4—102no—
792D4—101no—
793D4—101no—
794D4—101no—
795D4—101no—
796D4—101no—
797D4—202no—
798D4—202no—
799D4—202no—
800D4—202no—
801D4—202no—
802D4—202no—
803D4—401no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—42no—
810C2×C4—51no—
811C2×C4—51no—
812C2×C4—51no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—202no—
817C2×C4—202no—
818C2×C4C3×D4×D511yescharacteristic
819C2×C4C23×C3×D511yescharacteristic
820C8—21no—
821C8—21no—
822C8—52no—
823C8—101no—
824C2×C3—22no—
825C2×C3—81no—
826C2×C3—201no—
827C2×C3—202no—
828C2×C3—401no—
829C2×C3—401no—
830C2×C3#6592411yescharacteristic
831C2×C3C2×#406011yescharacteristic
832C2×C3#6611211yescharacteristic
833C5C3×#326511yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—101no—
840C22—101no—
841C22—102no—
842C22—101no—
843C22—201no—
844C22—201no—
845C22—201no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—201no—
850C22—201no—
851C22—404no—
852C22—404no—
853C22C3×#406012yescomplemented
854C22C2×C3×D4×D511yescharacteristic
855C4—21no—
856C4—22no—
857C4—41no—
858C4—41no—
859C4—101no—
860C4—101no—
861C4—101no—
862C4—201no—
863C4C2×C3×D4×D511yescharacteristic
864C4C3×#414411yescharacteristic
865C3#1061179111yescharacteristic, direct product factor, Sylow
866C2—22no—
867C2—81no—
868C2—201no—
869C2—202no—
870C2—401no—
871C2—401no—
872C2C3×#6592411yescharacteristic
873C2C2×C3×#406011yescharacteristic
874C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#448C2
socleC22×C3×C5C22×D4
hypercenterC3×#448D5
hypocenterC5C3×#3265
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#448

Complements

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

NH ≅ G/Ntype
1. C3×#66151C2semidirect
2. C22×C3×#688C2semidirect
3. C2×C3×#4060C2semidirect
4. C3×#65943C2semidirect
5. C3×C5×#448C2semidirect
6. C3×#65465C2semidirect
7. C3×#65458C2semidirect
8. C3×#65452C2semidirect
9. C3×#65327C2semidirect
10. C3×#65108C2semidirect
11. C3×#65106C2semidirect
12. C3×#65101C2semidirect
13. C3×#65100C2semidirect
14. C3×#65021C2semidirect
15. C3×#65019C2semidirect
16. #10611791C3direct (N × H)
17. C22×C3×C5×Q8C22semidirect
18. C2×C3×#713C22semidirect
22. C2×C3×C5×SD16C22semidirect
23. C2×C3×C5×SD16C22semidirect
26. C3×#4093C22semidirect
28. C3×#4092C22semidirect
29. C3×Q8×Dic5C22semidirect
33. C2×C3×#688C22semidirect
34. C2×C3×#688C22semidirect
37. C2×C3×#686C22semidirect
39. C3×#4076C22semidirect
42. C22×C3×#168C22semidirect
45. C2×C3×D40C22semidirect
46. C2×C3×#676C22semidirect
51. C3×C5×#103C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×#3964C22semidirect
56. C3×#3953C22semidirect
57. C3×#3952C22semidirect
58. C3×#3947C22semidirect
59. C3×#3946C22semidirect
60. C3×#3941C22semidirect
61. C3×#3939C22semidirect
63. #66151C2×C3semidirect
64. C22×#688C2×C3semidirect
65. C2×#4060C2×C3semidirect
66. #65943C2×C3semidirect
67. C5×#448C2×C3semidirect
68. #65465C2×C3semidirect
69. #65458C2×C3semidirect
70. #65452C2×C3semidirect
71. #65327C2×C3semidirect
72. #65108C2×C3semidirect
73. #65106C2×C3semidirect
74. #65101C2×C3semidirect
75. #65100C2×C3semidirect
76. #65021C2×C3semidirect
77. #65019C2×C3semidirect
120. C3×#688D4semidirect
152. C3×#448D5semidirect
156. C22×C5×Q8C22×C3semidirect
157. C2×#713C22×C3semidirect
161. C2×C5×SD16C22×C3semidirect
162. C2×C5×SD16C22×C3semidirect
165. #4093C22×C3semidirect
167. #4092C22×C3semidirect
168. Q8×Dic5C22×C3semidirect
172. C2×#688C22×C3semidirect
173. C2×#688C22×C3semidirect
176. C2×#686C22×C3semidirect
178. #4076C22×C3semidirect
181. C22×#168C22×C3semidirect
184. C2×D40C22×C3semidirect
185. C2×#676C22×C3semidirect
190. C5×#103C22×C3semidirect
191. C5×#103C22×C3semidirect
192. C5×C22⋊C8C22×C3semidirect
193. #3964C22×C3semidirect
195. #3953C22×C3semidirect
196. #3952C22×C3semidirect
197. #3947C22×C3semidirect
198. #3946C22×C3semidirect
199. #3941C22×C3semidirect
200. #3939C22×C3semidirect
218. C3×C5×Q8C2×D4semidirect
255. C3×#168C2×D4semidirect
257. C22×C3×Q8C2×D5semidirect
267. C2×C3×SD16C2×D5semidirect
268. C2×C3×SD16C2×D5semidirect
292. C3×#103C2×D5semidirect
293. C3×#103C2×D5semidirect
299. C3×C22⋊C8C2×D5semidirect
343. #688C3×D4semidirect
375. #448C3×D5semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
489. C5×Q8C2×C3×D4semidirect
526. #168C2×C3×D4semidirect
528. C22×Q8C2×C3×D5semidirect
538. C2×SD16C2×C3×D5semidirect
539. C2×SD16C2×C3×D5semidirect
563. #103C2×C3×D5semidirect
564. #103C2×C3×D5semidirect
570. C22⋊C8C2×C3×D5semidirect
597. C3×Q8D4×D5semidirect
640. C22×C5C3×AGL(1,ℤ/8)semidirect
729. C3×C5#3265semidirect
749. C22×C3#4060semidirect
786. Q8C3×D4×D5semidirect
833. C5C3×#3265semidirect
853. C22C3×#4060semidirect
865. C3#10611791direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661512
C22×C3×#6882
C2×C3×#40602
C3×#659432
C3×C5×#4482
C3×#654652
C3×#654582
C3×#654522
C3×#653272
C3×#651082
C3×#651062
C3×#651012
C3×#651002
C3×#650212
C3×#650192
#106117913
C3×#32655