Finite Group Databasebeta

← C3×#10615222 #14453437

Subgroups — C3×#10615222 #14453437

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×C5×D42C211yesmaximal, characteristic, complemented
2C22×C3×#687C211yesmaximal, characteristic, complemented
3C2×C3×#4078C211yesmaximal, characteristic, complemented
4C3×#65886C211yesmaximal, characteristic, complemented
5C3×#65507C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7C3×#65364C211yesmaximal, characteristic, complemented
8C3×#65363C211yesmaximal, characteristic, complemented
9C3×#65331C211yesmaximal, characteristic, complemented
10C3×#65329C211yesmaximal, characteristic, complemented
11C3×#65327C211yesmaximal, characteristic, complemented
12C3×#65326C211yesmaximal, characteristic, complemented
13C3×#65307C211yesmaximal, characteristic, complemented
14C3×#65305C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615222C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4—21no—
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic, complemented
21C22×C3×Dic10C2211yescharacteristic, complemented
22C3×C5×#127C2211yescharacteristic
23C3×C5×#121—21no—
24C3×C5×#121C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic
26C3×C5×#120—21no—
27C3×C5×#120—21no—
28C3×C4×C5×D4C2211yescharacteristic
29C3×C4×C5×D4C2211yescharacteristic
30C3×#4085—21no—
31C2×C3×#687—24no—
32C2×C3×#687C2211yescharacteristic
33C2×C3×#687C2211yescharacteristic
34C2×C3×#687C2211yescharacteristic, complemented
35C2×C3×#687C2211yescharacteristic, complemented
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#687C2211yescharacteristic, complemented
38C3×#4078—24no—
39C2×C3×#686C2211yescharacteristic
40C2×C3×#686C2211yescharacteristic, complemented
41C2×C3×#686C2211yescharacteristic, complemented
42C3×#4076C2211yescharacteristic, complemented
43C3×#4070C2211yescharacteristic, complemented
44C2×C3×#681C2211yescharacteristic, complemented
45C22×C3×#168C2211yescharacteristic, complemented
46C3×#4042—21no—
47C3×#4031—21no—
48C3×#4027—21no—
49C3×#4021C2211yescharacteristic, complemented
50C3×C4×Dic10C2211yescharacteristic, complemented
51C3×#3964C2211yescharacteristic
52C3×#3964C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58C3×#3941C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3265—51nomaximal, Hall
63C5×D42C2×C311yescharacteristic, complemented
64C22×#687C2×C311yescharacteristic, complemented
65C2×#4078C2×C311yescharacteristic, complemented
66#65886C2×C311yescharacteristic, complemented
67#65507C2×C311yescharacteristic, complemented
68#65506C2×C311yescharacteristic, complemented
69#65364C2×C311yescharacteristic, complemented
70#65363C2×C311yescharacteristic, complemented
71#65331C2×C311yescharacteristic, complemented
72#65329C2×C311yescharacteristic, complemented
73#65327C2×C311yescharacteristic, complemented
74#65326C2×C311yescharacteristic, complemented
75#65307C2×C311yescharacteristic, complemented
76#65305C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C24×C3×C5—21no—
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—41no—
89C2×C3×C5×D4—41no—
90C2×C3×C5×D4—44no—
91C2×C3×C5×D4D411yescharacteristic
92C2×C3×C5×D4C2311yescharacteristic
93C2×C3×C5×D4C2311yescharacteristic
94C2×C3×C5×D4C2311yescharacteristic
95C22×C3×C4×C5—21no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C2×C3×C22⋊D5—21no—
99C2×C3×C22⋊D5—21no—
100C22×C3×Dic5—21no—
101C3×#709—22no—
102C3×#709—41no—
103C2×C3×D20C2311yescharacteristic
104C2×C3×C4×D5—21no—
105C2×C3×Dic10—22no—
106C2×C3×Dic10—21no—
107C2×C3×Dic10—41no—
108C2×C3×Dic10C2311yescharacteristic
109C2×C3×Dic10C2311yescharacteristic
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C5×C22⋊C4D411yescharacteristic
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×#687—22no—
120C3×#687—22no—
121C3×#687—22no—
122C3×#687—22no—
123C3×#687—41no—
124C3×#687D414yescomplemented
125C3×#686—22no—
126C3×#686—22no—
127C3×#686—41no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685—21no—
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683—21no—
134C3×C4×Dic5—21no—
135C3×#681—22no—
136C2×C3×#168—22no—
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C2×C3×#168C2311yescharacteristic
140C2×C3×#168C2311yescharacteristic
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×SD16—51no—
143C3×#548—51no—
144C3×D42D511yescharacteristic, complemented
145C3×#496—51no—
146C3×#468—51no—
147C3×#466—51no—
148C3×#463—51no—
149C3×#460—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#448—51no—
153C3×#447—51no—
154C3×#440—51no—
155C3×#435—51no—
156C22×C5×D4—21no—
157C22×C5×D4C22×C311yescharacteristic
158C22×C5×D4C22×C311yescharacteristic
159C2×#709C22×C311yescharacteristic, complemented
160C22×Dic10C22×C311yescharacteristic, complemented
161C5×#127C22×C311yescharacteristic
162C5×#121—21no—
163C5×#121C22×C311yescharacteristic
164C5×#121C22×C311yescharacteristic
165C5×#120—21no—
166C5×#120—21no—
167C4×C5×D4C22×C311yescharacteristic
168C4×C5×D4C22×C311yescharacteristic
169#4085—21no—
170C2×#687—24no—
171C2×#687C22×C311yescharacteristic
172C2×#687C22×C311yescharacteristic
173C2×#687C22×C311yescharacteristic, complemented
174C2×#687C22×C311yescharacteristic, complemented
175C2×#687C22×C311yescharacteristic, complemented
176C2×#687C22×C311yescharacteristic, complemented
177#4078—24no—
178C2×#686C22×C311yescharacteristic
179C2×#686C22×C311yescharacteristic, complemented
180C2×#686C22×C311yescharacteristic, complemented
181#4076C22×C311yescharacteristic, complemented
182#4070C22×C311yescharacteristic, complemented
183C2×#681C22×C311yescharacteristic, complemented
184C22×#168C22×C311yescharacteristic, complemented
185#4042—21no—
186#4031—21no—
187#4027—21no—
188#4021C22×C311yescharacteristic, complemented
189C4×Dic10C22×C311yescharacteristic, complemented
190#3964C22×C311yescharacteristic
191#3964C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic, complemented
194C22⋊#168C22×C311yescharacteristic, complemented
195#3942C22×C311yescharacteristic, complemented
196#3942C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic, complemented
198#3939C22×C311yescharacteristic, complemented
199C4⋊#168C22×C311yescharacteristic, complemented
200#3935C22×C311yescharacteristic, complemented
201#3265—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—42no—
206C23×C3×C5—42no—
207C23×C3×C5—42no—
208C23×C3×C5—42no—
209C23×C3×C5—81no—
210C23×C3×C5—81no—
211C23×C3×C5C2×D411yescharacteristic
212C23×C3×C5C2×D411yescharacteristic
213C22×C3×D5—21no—
214C3×C5×D4—22no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—42no—
221C3×C5×D4—42no—
222C3×C5×D4—42no—
223C3×C5×D4—42no—
224C3×C5×D4—42no—
225C3×C5×D4—81no—
226C3×C5×D4C2×D412yes—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—42no—
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2×D411yescharacteristic
236C2×C3×C4×C5C2×D411yescharacteristic
237C2×C3×C4×C5C2411yescharacteristic
238C3×C22⋊D5—42no—
239C3×C22⋊D5—42no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—42no—
244C3×D20—21no—
245C3×D20—21no—
246C3×C4×D5—42no—
247C3×Dic10—21no—
248C3×Dic10—21no—
249C3×Dic10—21no—
250C3×Dic10—42no—
251C3×Dic10C2×D412yescomplemented
252C3×#168—21no—
253C3×#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×C3×#41—51no—
257C22×C3×Q8—51no—
258C22×C3×D4—21no—
259C22×C3×D4C2×D511yescharacteristic
260C22×C3×D4C2×D511yescharacteristic
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—51no—
267C2×C3×SD16—51no—
268C2×C3×SD16—104no—
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×M16—51no—
273C22×C3×C8—51no—
274C3×#127C2×D511yescharacteristic
275C3×#124—51no—
276C3×#124—101no—
277C3×C22⋊Q8—51no—
278C3×C22⋊Q8—101no—
279C3×#121—21no—
280C3×#121—51no—
281C3×#121—101no—
282C3×#121C2×D511yescharacteristic
283C3×#121C2×D511yescharacteristic
284C3×#120—21no—
285C3×#120—21no—
286C3×C4×Q8—51no—
287C3×C4×D4—101no—
288C3×C4×D4C2×D511yescharacteristic
289C3×C4×D4C2×D511yescharacteristic
290C3×#107—51no—
291C3×C4⋊C8—51no—
292C3×#103—51no—
293C3×#103—51no—
294C3×#102—51no—
295C3×#102—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×C22⋊C8—51no—
299C3×C22⋊C8—51no—
300C3×#97—51no—
301C24×C5—21no—
302C24×C5—21no—
303C2×C5×D4—22no—
304C2×C5×D4—22no—
305C2×C5×D4—21no—
306C2×C5×D4—21no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—21no—
310C2×C5×D4—21no—
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4—44no—
314C2×C5×D4C3×D411yescharacteristic
315C2×C5×D4C23×C311yescharacteristic
316C2×C5×D4C23×C311yescharacteristic
317C2×C5×D4C23×C311yescharacteristic
318C22×C4×C5—21no—
319C22×C4×C5C23×C311yescharacteristic
320C22×C4×C5C23×C311yescharacteristic
321C2×C22⋊D5—21no—
322C2×C22⋊D5—21no—
323C22×Dic5—21no—
324#709—22no—
325#709—41no—
326C2×D20C23×C311yescharacteristic
327C2×C4×D5—21no—
328C2×Dic10—22no—
329C2×Dic10—21no—
330C2×Dic10—41no—
331C2×Dic10C23×C311yescharacteristic
332C2×Dic10C23×C311yescharacteristic
333C5×C4⋊C4C3×D411yescharacteristic
334C5×C4⋊C4C23×C311yescharacteristic
335C5×C22⋊C4—21no—
336C5×C22⋊C4—21no—
337C5×C22⋊C4—21no—
338C5×C22⋊C4C3×D411yescharacteristic
339C5×C22⋊C4C3×D411yescharacteristic
340C42×C5C23×C311yescharacteristic
341C22⋊Dic5—21no—
342#687—22no—
343#687—22no—
344#687—22no—
345#687—22no—
346#687—41no—
347#687C3×D414yescomplemented
348#686—22no—
349#686—22no—
350#686—41no—
351#685—21no—
352#685—21no—
353#685—21no—
354C4⋊Dic5C23×C311yescharacteristic
355#683—21no—
356#683—21no—
357C4×Dic5—21no—
358#681—22no—
359C2×#168—22no—
360C2×#168C23×C311yescharacteristic
361C2×#168C23×C311yescharacteristic
362C2×#168C23×C311yescharacteristic
363C2×#168C23×C311yescharacteristic
364C2×AGL(1,ℤ/8)—51no—
365C22×SD16—51no—
366#548—51no—
367D42C3×D511yescharacteristic, complemented
368#496—51no—
369#468—51no—
370#466—51no—
371#463—51no—
372#460—51no—
373#450—51no—
374#449—51no—
375#448—51no—
376#447—51no—
377#440—51no—
378#435—51no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—22no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
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×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—84no—
394C22×C3×C5—84no—
395C22×C3×C5AGL(1,ℤ/8)12yescomplemented
396C22×C3×C5C22×D411yescharacteristic
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—21no—
404C3×C4×C5—41no—
405C3×C4×C5C22×D411yescharacteristic
406C3×C4×C5H(5,𝔽2)11yescharacteristic
407C3×Dic5—22no—
408C3×Dic5—41no—
409C3×Dic5—41no—
410C24×C3—21no—
411C24×C3—21no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×Q8—51no—
416C2×C3×Q8—102no—
417C2×C3×Q8—101no—
418C2×C3×Q8—201no—
419C2×C3×D4—22no—
420C2×C3×D4—22no—
421C2×C3×D4—21no—
422C2×C3×D4—21no—
423C2×C3×D4—21no—
424C2×C3×D4—21no—
425C2×C3×D4—21no—
426C2×C3×D4—21no—
427C2×C3×D4—41no—
428C2×C3×D4—41no—
429C2×C3×D4—44no—
430C2×C3×D4—51no—
431C2×C3×D4—101no—
432C2×C3×D4—101no—
433C2×C3×D4C22⋊D511yescharacteristic
434C2×C3×D4C22×D511yescharacteristic
435C2×C3×D4C22×D511yescharacteristic
436C2×C3×D4C22×D511yescharacteristic
437C22×C3×C4—21no—
438C22×C3×C4—101no—
439C22×C3×C4—101no—
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C3×SD16—54no—
443C3×SD16—102no—
444C3×SD16—102no—
445C3×SD16—102no—
446C3×SD16—102no—
447C3×SD16—201no—
448C3×D8—102no—
449C3×D8—102no—
450C3×D8—201no—
451C3×M16—102no—
452C2×C3×C8—51no—
453C2×C3×C8—51no—
454C2×C3×C8—51no—
455C2×C3×C8—51no—
456C2×C3×C8—102no—
457C3×C4⋊C4—51no—
458C3×C4⋊C4—101no—
459C3×C4⋊C4—101no—
460C3×C4⋊C4C22⋊D511yescharacteristic
461C3×C4⋊C4C22×D511yescharacteristic
462C3×C22⋊C4—21no—
463C3×C22⋊C4—21no—
464C3×C22⋊C4—21no—
465C3×C22⋊C4—101no—
466C3×C22⋊C4—101no—
467C3×C22⋊C4—101no—
468C3×C22⋊C4—101no—
469C3×C22⋊C4C22⋊D511yescharacteristic
470C3×C22⋊C4C22⋊D511yescharacteristic
471C3×C42—101no—
472C3×C42C22×D511yescharacteristic
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—42no—
477C23×C5—42no—
478C23×C5—42no—
479C23×C5—42no—
480C23×C5—81no—
481C23×C5—81no—
482C23×C5C2×C3×D411yescharacteristic
483C23×C5C2×C3×D411yescharacteristic
484C22×D5—21no—
485C5×D4—22no—
486C5×D4—21no—
487C5×D4—21no—
488C5×D4—21no—
489C5×D4—21no—
490C5×D4—21no—
491C5×D4—42no—
492C5×D4—42no—
493C5×D4—42no—
494C5×D4—42no—
495C5×D4—42no—
496C5×D4—81no—
497C5×D4C2×C3×D412yes—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—42no—
504C2×C4×C5C2×C3×D411yescharacteristic
505C2×C4×C5C2×C3×D411yescharacteristic
506C2×C4×C5C2×C3×D411yescharacteristic
507C2×C4×C5C2×C3×D411yescharacteristic
508C2×C4×C5C24×C311yescharacteristic
509C22⋊D5—42no—
510C22⋊D5—42no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—42no—
515D20—21no—
516D20—21no—
517C4×D5—42no—
518Dic10—21no—
519Dic10—21no—
520Dic10—21no—
521Dic10—42no—
522Dic10C2×C3×D412yescomplemented
523#168—21no—
524#168—21no—
525#168—21no—
526#168C2×C3×D412yescomplemented
527C2×#41—51no—
528C22×Q8—51no—
529C22×D4—21no—
530C22×D4C2×C3×D511yescharacteristic
531C22×D4C2×C3×D511yescharacteristic
532AGL(1,ℤ/8)—104no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—51no—
536C2×SD16—51no—
537C2×SD16—51no—
538C2×SD16—51no—
539C2×SD16—104no—
540C2×D8—51no—
541C2×D8—51no—
542C2×D8—51no—
543C2×M16—51no—
544C22×C8—51no—
545#127C2×C3×D511yescharacteristic
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—21no—
551#121—51no—
552#121—101no—
553#121C2×C3×D511yescharacteristic
554#121C2×C3×D511yescharacteristic
555#120—21no—
556#120—21no—
557C4×Q8—51no—
558C4×D4—101no—
559C4×D4C2×C3×D511yescharacteristic
560C4×D4C2×C3×D511yescharacteristic
561#107—51no—
562C4⋊C8—51no—
563#103—51no—
564#103—51no—
565#102—51no—
566#102—51no—
567#102—51no—
568#102—51no—
569C22⋊C8—51no—
570C22⋊C8—51no—
571#97—51no—
572C2×C3×C5—22no—
573C2×C3×C5—41no—
574C2×C3×C5—42no—
575C2×C3×C5—81no—
576C2×C3×C5—81no—
577C2×C3×C5D4211yescharacteristic
578C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
579C2×C3×C5#57711yescharacteristic
580C3×D5—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3—81no—
589C23×C3—81no—
590C23×C3—101no—
591C23×C3C2×C22⋊D511yescharacteristic
592C23×C3C2×C22⋊D511yescharacteristic
593C3×Q8—52no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—22no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—21no—
604C3×D4—42no—
605C3×D4—42no—
606C3×D4—42no—
607C3×D4—42no—
608C3×D4—42no—
609C3×D4—81no—
610C3×D4—101no—
611C3×D4—101no—
612C3×D4—202no—
613C3×D4—202no—
614C3×D4D4×D512yes—
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—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—202no—
625C2×C3×C4—202no—
626C2×C3×C4C2×C22⋊D511yescharacteristic
627C2×C3×C4C2×C22⋊D511yescharacteristic
628C2×C3×C4C2×C22⋊D511yescharacteristic
629C2×C3×C4C2×C22⋊D511yescharacteristic
630C2×C3×C4C23×D511yescharacteristic
631C3×C8—52no—
632C3×C8—101no—
633C3×C8—101no—
634C3×C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—22no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
649C22×C5—84no—
650C22×C5—84no—
651C22×C5C3×AGL(1,ℤ/8)12yescomplemented
652C22×C5C22×C3×D411yescharacteristic
653C2×D5—41no—
654C2×D5—41no—
655C2×D5—41no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—41no—
661C4×C5C22×C3×D411yescharacteristic
662C4×C5C3×H(5,𝔽2)11yescharacteristic
663Dic5—22no—
664Dic5—41no—
665Dic5—41no—
666C24—21no—
667C24—21no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—51no—
672C2×Q8—102no—
673C2×Q8—101no—
674C2×Q8—201no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—41no—
684C2×D4—41no—
685C2×D4—44no—
686C2×D4—51no—
687C2×D4—101no—
688C2×D4—101no—
689C2×D4C3×C22⋊D511yescharacteristic
690C2×D4C22×C3×D511yescharacteristic
691C2×D4C22×C3×D511yescharacteristic
692C2×D4C22×C3×D511yescharacteristic
693C22×C4—21no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4C22×C3×D511yescharacteristic
697C22×C4C22×C3×D511yescharacteristic
698SD16—54no—
699SD16—102no—
700SD16—102no—
701SD16—102no—
702SD16—102no—
703SD16—201no—
704D8—102no—
705D8—102no—
706D8—201no—
707M16—102no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—51no—
711C2×C8—51no—
712C2×C8—102no—
713C4⋊C4—51no—
714C4⋊C4—101no—
715C4⋊C4—101no—
716C4⋊C4C3×C22⋊D511yescharacteristic
717C4⋊C4C22×C3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—101no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4C3×C22⋊D511yescharacteristic
726C22⋊C4C3×C22⋊D511yescharacteristic
727C42—101no—
728C42C22×C3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—84no—
745C22×C3—84no—
746C22×C3—201no—
747C22×C3—201no—
748C22×C3—201no—
749C22×C3#407812yescomplemented
750C22×C3C22×C22⋊D511yescharacteristic
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—102no—
757C3×C4—201no—
758C3×C4—201no—
759C3×C4C2×D4×D511yescharacteristic
760C3×C4#414411yescharacteristic
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—42no—
764C2×C5—81no—
765C2×C5—81no—
766C2×C5C3×D4211yescharacteristic
767C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
768C2×C5C3×#57711yescharacteristic
769D5—81no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—81no—
778C23—81no—
779C23—101no—
780C23C2×C3×C22⋊D511yescharacteristic
781C23C2×C3×C22⋊D511yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—101no—
785Q8—101no—
786Q8—202no—
787D4—22no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—81no—
799D4—101no—
800D4—101no—
801D4—202no—
802D4—202no—
803D4C3×D4×D512yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—42no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—202no—
814C2×C4—202no—
815C2×C4C2×C3×C22⋊D511yescharacteristic
816C2×C4C2×C3×C22⋊D511yescharacteristic
817C2×C4C2×C3×C22⋊D511yescharacteristic
818C2×C4C2×C3×C22⋊D511yescharacteristic
819C2×C4C23×C3×D511yescharacteristic
820C8—52no—
821C8—101no—
822C8—101no—
823C8—101no—
824C2×C3—22no—
825C2×C3—41no—
826C2×C3—42no—
827C2×C3—81no—
828C2×C3—81no—
829C2×C3—401no—
830C2×C3C2×#407811yescharacteristic
831C2×C3D4×C22⋊D511yescharacteristic
832C2×C3#6617011yescharacteristic
833C5C3×#326511yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—22no—
839C22—21no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—84no—
849C22—84no—
850C22—201no—
851C22—201no—
852C22—201no—
853C22C3×#407812yescomplemented
854C22C22×C3×C22⋊D511yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—41no—
860C4—102no—
861C4—201no—
862C4—201no—
863C4C2×C3×D4×D511yescharacteristic
864C4C3×#414411yescharacteristic
865C3#1061522211yescharacteristic, direct product factor, Sylow
866C2—22no—
867C2—41no—
868C2—42no—
869C2—81no—
870C2—81no—
871C2—401no—
872C2C2×C3×#407811yescharacteristic
873C2C3×D4×C22⋊D511yescharacteristic
874C2C3×#6617011yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×D42C2
socleC22×C3×C5C22×D4
hypercenterC3×D42D5
hypocenterC5C3×#3265
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×D42

Complements

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

NH ≅ G/Ntype
1. C3×C5×D42C2semidirect
2. C22×C3×#687C2semidirect
3. C2×C3×#4078C2semidirect
4. C3×#65886C2semidirect
5. C3×#65507C2semidirect
6. C3×#65506C2semidirect
7. C3×#65364C2semidirect
8. C3×#65363C2semidirect
9. C3×#65331C2semidirect
10. C3×#65329C2semidirect
11. C3×#65327C2semidirect
12. C3×#65326C2semidirect
13. C3×#65307C2semidirect
14. C3×#65305C2semidirect
15. C3×#65300C2semidirect
16. #10615222C3direct (N × H)
20. C2×C3×#709C22semidirect
21. C22×C3×Dic10C22semidirect
34. C2×C3×#687C22semidirect
35. C2×C3×#687C22semidirect
36. C2×C3×#687C22semidirect
37. C2×C3×#687C22semidirect
40. C2×C3×#686C22semidirect
41. C2×C3×#686C22semidirect
42. C3×#4076C22semidirect
43. C3×#4070C22semidirect
44. C2×C3×#681C22semidirect
45. C22×C3×#168C22semidirect
49. C3×#4021C22semidirect
50. C3×C4×Dic10C22semidirect
52. C3×#3964C22semidirect
53. C3×#3964C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
57. C3×#3942C22semidirect
58. C3×#3941C22semidirect
59. C3×#3939C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×D42C2×C3semidirect
64. C22×#687C2×C3semidirect
65. C2×#4078C2×C3semidirect
66. #65886C2×C3semidirect
67. #65507C2×C3semidirect
68. #65506C2×C3semidirect
69. #65364C2×C3semidirect
70. #65363C2×C3semidirect
71. #65331C2×C3semidirect
72. #65329C2×C3semidirect
73. #65327C2×C3semidirect
74. #65326C2×C3semidirect
75. #65307C2×C3semidirect
76. #65305C2×C3semidirect
77. #65300C2×C3semidirect
124. C3×#687D4semidirect
144. C3×D42D5semidirect
159. C2×#709C22×C3semidirect
160. C22×Dic10C22×C3semidirect
173. C2×#687C22×C3semidirect
174. C2×#687C22×C3semidirect
175. C2×#687C22×C3semidirect
176. C2×#687C22×C3semidirect
179. C2×#686C22×C3semidirect
180. C2×#686C22×C3semidirect
181. #4076C22×C3semidirect
182. #4070C22×C3semidirect
183. C2×#681C22×C3semidirect
184. C22×#168C22×C3semidirect
188. #4021C22×C3semidirect
189. C4×Dic10C22×C3semidirect
191. #3964C22×C3semidirect
192. #3964C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. C22⋊#168C22×C3semidirect
195. #3942C22×C3semidirect
196. #3942C22×C3semidirect
197. #3941C22×C3semidirect
198. #3939C22×C3semidirect
199. C4⋊#168C22×C3semidirect
200. #3935C22×C3semidirect
251. C3×Dic10C2×D4semidirect
255. C3×#168C2×D4semidirect
347. #687C3×D4semidirect
367. D42C3×D5semidirect
395. C22×C3×C5AGL(1,ℤ/8)semidirect
522. Dic10C2×C3×D4semidirect
526. #168C2×C3×D4semidirect
651. C22×C5C3×AGL(1,ℤ/8)semidirect
729. C3×C5#3265semidirect
749. C22×C3#4078semidirect
833. C5C3×#3265semidirect
853. C22C3×#4078semidirect
865. C3#10615222direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D422
C22×C3×#6872
C2×C3×#40782
C3×#658862
C3×#655072
C3×#655062
C3×#653642
C3×#653632
C3×#653312
C3×#653292
C3×#653272
C3×#653262
C3×#653072
C3×#653052
C3×#653002
#106152223
C3×#32655