Finite Group Databasebeta

← C3×#10615273 #14453452

Subgroups — C3×#10615273 #14453452

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×#548C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C22×C3×#688C211yesmaximal, characteristic, complemented
4C3×D4×D20C211yesmaximal, characteristic, complemented
5C3×#65527C211yesmaximal, characteristic, complemented
6C3×#65516C211yesmaximal, characteristic, complemented
7C3×#65347C211yesmaximal, characteristic, complemented
8C3×#65346C211yesmaximal, characteristic, complemented
9C3×#65338C211yesmaximal, characteristic, complemented
10C3×#65335C211yesmaximal, characteristic, complemented
11C3×#65327C211yesmaximal, characteristic, complemented
12C3×#65325C211yesmaximal, characteristic, complemented
13C3×#65316C211yesmaximal, characteristic, complemented
14C3×#65315C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615273C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C3×C5×#124—21no—
23C3×C5×#124C2211yescharacteristic, complemented
24C3×C5×C22⋊Q8—21no—
25C3×C5×C22⋊Q8C2211yescharacteristic, complemented
26C3×C5×#121—21no—
27C3×C5×#121C2211yescharacteristic, complemented
28C3×C4×C5×Q8C2211yescharacteristic, complemented
29C3×C4×C5×D4—21no—
30C3×C4×C5×D4C2211yescharacteristic
31C3×#4095—24no—
32C2×C3×#688—24no—
33C2×C3×#688C2211yescharacteristic
34C2×C3×#688C2211yescharacteristic
35C2×C3×#688C2211yescharacteristic, complemented
36C2×C3×#688C2211yescharacteristic, complemented
37C2×C3×#688C2211yescharacteristic, complemented
38C2×C3×#688C2211yescharacteristic, complemented
39C2×C3×#686C2211yescharacteristic
40C2×C3×#686C2211yescharacteristic, complemented
41C2×C3×#686C2211yescharacteristic, complemented
42C3×#4076C2211yescharacteristic
43C3×#4076C2211yescharacteristic
44C2×C3×#681C2211yescharacteristic, complemented
45C22×C3×#168C2211yescharacteristic, complemented
46C3×#4041—21no—
47C3×#4028—21no—
48C3×#4028—21no—
49C3×#4020C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic
51C3×#3967C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic, complemented
58C3×#3941C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3265—51nomaximal, Hall
63C5×#548C2×C311yescharacteristic, complemented
64C2×#4095C2×C311yescharacteristic, complemented
65C22×#688C2×C311yescharacteristic, complemented
66D4×D20C2×C311yescharacteristic, complemented
67#65527C2×C311yescharacteristic, complemented
68#65516C2×C311yescharacteristic, complemented
69#65347C2×C311yescharacteristic, complemented
70#65346C2×C311yescharacteristic, complemented
71#65338C2×C311yescharacteristic, complemented
72#65335C2×C311yescharacteristic, complemented
73#65327C2×C311yescharacteristic, complemented
74#65325C2×C311yescharacteristic, complemented
75#65316C2×C311yescharacteristic, complemented
76#65315C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C2×C3×C5×Q8—21no—
83C2×C3×C5×Q8—22no—
84C2×C3×C5×Q8—41no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—21no—
89C2×C3×C5×D4D411yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5—21no—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C3×D4×D5—44no—
98C2×C3×D20—22no—
99C2×C3×D20—22no—
100C2×C3×D20—21no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—21no—
104C2×C3×D20—41no—
105C2×C3×D20—41no—
106C2×C3×D20C2311yescharacteristic
107C2×C3×D20C2311yescharacteristic
108C2×C3×D20C2311yescharacteristic
109C2×C3×C4×D5—21no—
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4—21no—
112C3×C5×C4⋊C4D411yescharacteristic
113C3×C5×C4⋊C4C2311yescharacteristic
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4—21no—
116C3×C5×C22⋊C4—21no—
117C3×C5×C22⋊C4—21no—
118C3×C5×C22⋊C4D411yescharacteristic
119C3×C5×C22⋊C4D411yescharacteristic
120C3×C42×C5—21no—
121C3×C42×C5C2311yescharacteristic
122C3×#688—22no—
123C3×#688—22no—
124C3×#688—22no—
125C3×#688—22no—
126C3×#688—41no—
127C3×#688D414yescomplemented
128C3×#686—22no—
129C3×#686—22no—
130C3×#686—41no—
131C3×#685—21no—
132C3×#685—21no—
133C3×#685—21no—
134C3×C4⋊Dic5C2311yescharacteristic
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×#548D511yescharacteristic, complemented
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×#448—51no—
153C3×#447—51no—
154C3×#440—51no—
155C3×#435—51no—
156C2×C5×#41C22×C311yescharacteristic, complemented
157C22×C5×Q8C22×C311yescharacteristic, complemented
158C2×D4×D5—21no—
159C22×D20C22×C311yescharacteristic
160C22×D20C22×C311yescharacteristic
161C5×#124—21no—
162C5×#124C22×C311yescharacteristic, complemented
163C5×C22⋊Q8—21no—
164C5×C22⋊Q8C22×C311yescharacteristic, complemented
165C5×#121—21no—
166C5×#121C22×C311yescharacteristic, complemented
167C4×C5×Q8C22×C311yescharacteristic, complemented
168C4×C5×D4—21no—
169C4×C5×D4C22×C311yescharacteristic
170#4095—24no—
171C2×#688—24no—
172C2×#688C22×C311yescharacteristic
173C2×#688C22×C311yescharacteristic
174C2×#688C22×C311yescharacteristic, complemented
175C2×#688C22×C311yescharacteristic, complemented
176C2×#688C22×C311yescharacteristic, complemented
177C2×#688C22×C311yescharacteristic, complemented
178C2×#686C22×C311yescharacteristic
179C2×#686C22×C311yescharacteristic, complemented
180C2×#686C22×C311yescharacteristic, complemented
181#4076C22×C311yescharacteristic
182#4076C22×C311yescharacteristic
183C2×#681C22×C311yescharacteristic, complemented
184C22×#168C22×C311yescharacteristic, complemented
185#4041—21no—
186#4028—21no—
187#4028—21no—
188#4020C22×C311yescharacteristic
189C4×D20C22×C311yescharacteristic
190#3967C22×C311yescharacteristic, complemented
191#3967C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic, complemented
194C22⋊#168C22×C311yescharacteristic, complemented
195#3941C22×C311yescharacteristic
196#3941C22×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×C5C2×D411yescharacteristic
204C23×C3×C5C2×D411yescharacteristic
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—42no—
211C22×C3×D5—42no—
212C22×C3×D5—81no—
213C22×C3×D5—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C3×C5×Q8—21no—
217C3×C5×Q8—42no—
218C3×C5×Q8C2×D412yescomplemented
219C3×C5×D4—22no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—42no—
223C3×C5×D4—42no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—42no—
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—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×D20—42no—
247C3×D20—42no—
248C3×D20—42no—
249C3×D20—81no—
250C3×D20C2×D412yes—
251C3×C4×D5—42no—
252C3×#168—21no—
253C3×#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×C3×#41C2×D511yescharacteristic, complemented
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—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×#127—51no—
275C3×#124—21no—
276C3×#124C2×D511yescharacteristic, complemented
277C3×C22⋊Q8—21no—
278C3×C22⋊Q8C2×D511yescharacteristic, complemented
279C3×#121—21no—
280C3×#121—51no—
281C3×#121—51no—
282C3×#121—101no—
283C3×#121C2×D511yescharacteristic, complemented
284C3×#120—101no—
285C3×#120—101no—
286C3×C4×Q8C2×D511yescharacteristic, complemented
287C3×C4×D4—21no—
288C3×C4×D4—51no—
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—
301C23×D5—21no—
302C23×D5—21no—
303C5×#41—22no—
304C5×#41—41no—
305C2×C5×Q8—21no—
306C2×C5×Q8—22no—
307C2×C5×Q8—41no—
308C2×C5×Q8C23×C311yescharacteristic
309C2×C5×Q8C23×C311yescharacteristic
310C2×C5×D4—21no—
311C2×C5×D4—21no—
312C2×C5×D4C3×D411yescharacteristic
313C2×C5×D4C23×C311yescharacteristic
314C22×C4×C5—21no—
315C22×C4×C5—21no—
316C22×C4×C5C23×C311yescharacteristic
317C22×C4×C5C23×C311yescharacteristic
318C2×C22⋊D5—21no—
319C2×C22⋊D5—21no—
320D4×D5—44no—
321C2×D20—22no—
322C2×D20—22no—
323C2×D20—21no—
324C2×D20—21no—
325C2×D20—21no—
326C2×D20—21no—
327C2×D20—41no—
328C2×D20—41no—
329C2×D20C23×C311yescharacteristic
330C2×D20C23×C311yescharacteristic
331C2×D20C23×C311yescharacteristic
332C2×C4×D5—21no—
333C5×C4⋊C4—21no—
334C5×C4⋊C4—21no—
335C5×C4⋊C4C3×D411yescharacteristic
336C5×C4⋊C4C23×C311yescharacteristic
337C5×C22⋊C4—21no—
338C5×C22⋊C4—21no—
339C5×C22⋊C4—21no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4C3×D411yescharacteristic
342C5×C22⋊C4C3×D411yescharacteristic
343C42×C5—21no—
344C42×C5C23×C311yescharacteristic
345#688—22no—
346#688—22no—
347#688—22no—
348#688—22no—
349#688—41no—
350#688C3×D414yescomplemented
351#686—22no—
352#686—22no—
353#686—41no—
354#685—21no—
355#685—21no—
356#685—21no—
357C4⋊Dic5C23×C311yescharacteristic
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#548C3×D511yescharacteristic, complemented
367D42—51no—
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—21no—
383C22×C3×C5—21no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5AGL(1,ℤ/8)12yescomplemented
388C22×C3×C5C22×D411yescharacteristic
389C2×C3×D5—22no—
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—21no—
401C3×C4×C5—21no—
402C3×C4×C5—22no—
403C3×C4×C5—21no—
404C3×C4×C5—21no—
405C3×C4×C5—41no—
406C3×C4×C5—41no—
407C3×C4×C5C22×D411yescharacteristic
408C3×C4×C5H(5,𝔽2)11yescharacteristic
409C3×Dic5—41no—
410C24×C3—101no—
411C24×C3—101no—
412C3×#41—22no—
413C3×#41—41no—
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—21no—
421C2×C3×D4—51no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—102no—
425C2×C3×D4—102no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—201no—
433C2×C3×D4—201no—
434C2×C3×D4—204no—
435C2×C3×D4C22⋊D511yescharacteristic
436C2×C3×D4C22×D511yescharacteristic
437C22×C3×C4—21no—
438C22×C3×C4—21no—
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—21no—
458C3×C4⋊C4—21no—
459C3×C4⋊C4—51no—
460C3×C4⋊C4C22⋊D511yescharacteristic
461C3×C4⋊C4C22×D511yescharacteristic
462C3×C22⋊C4—21no—
463C3×C22⋊C4—21no—
464C3×C22⋊C4—21no—
465C3×C22⋊C4—21no—
466C3×C22⋊C4—101no—
467C3×C22⋊C4—101no—
468C3×C22⋊C4—101no—
469C3×C22⋊C4C22⋊D511yescharacteristic
470C3×C22⋊C4C22⋊D511yescharacteristic
471C3×C42—21no—
472C3×C42C22×D511yescharacteristic
473C23×C5—21no—
474C23×C5C2×C3×D411yescharacteristic
475C23×C5C2×C3×D411yescharacteristic
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—42no—
480C22×D5—42no—
481C22×D5—42no—
482C22×D5—42no—
483C22×D5—81no—
484C22×D5—81no—
485C5×Q8—21no—
486C5×Q8—21no—
487C5×Q8—21no—
488C5×Q8—42no—
489C5×Q8C2×C3×D412yescomplemented
490C5×D4—22no—
491C5×D4—21no—
492C5×D4—21no—
493C5×D4—42no—
494C5×D4—42no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—42no—
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—
512D20—21no—
513D20—21no—
514D20—21no—
515D20—21no—
516D20—21no—
517D20—42no—
518D20—42no—
519D20—42no—
520D20—81no—
521D20C2×C3×D412yes—
522C4×D5—42no—
523#168—21no—
524#168—21no—
525#168—21no—
526#168C2×C3×D412yescomplemented
527C2×#41C2×C3×D511yescharacteristic, complemented
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—51no—
538C2×SD16—51no—
539C2×SD16—104no—
540C2×D8—51no—
541C2×D8—51no—
542C2×D8—51no—
543C2×M16—51no—
544C22×C8—51no—
545#127—51no—
546#124—21no—
547#124C2×C3×D511yescharacteristic, complemented
548C22⋊Q8—21no—
549C22⋊Q8C2×C3×D511yescharacteristic, complemented
550#121—21no—
551#121—51no—
552#121—51no—
553#121—101no—
554#121C2×C3×D511yescharacteristic, complemented
555#120—101no—
556#120—101no—
557C4×Q8C2×C3×D511yescharacteristic, complemented
558C4×D4—21no—
559C4×D4—51no—
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—81no—
575C2×C3×C5D4211yescharacteristic
576C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
577C2×C3×C5#57711yescharacteristic
578C3×D5—42no—
579C3×D5—81no—
580C3×D5—81no—
581C23×C3—21no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—202no—
586C23×C3—202no—
587C23×C3—202no—
588C23×C3—202no—
589C23×C3—401no—
590C23×C3—401no—
591C23×C3C2×C22⋊D511yescharacteristic
592C23×C3C2×C22⋊D511yescharacteristic
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—42no—
597C3×Q8D4×D512yescomplemented
598C3×D4—22no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—52no—
604C3×D4—101no—
605C3×D4—101no—
606C3×D4—101no—
607C3×D4—101no—
608C3×D4—101no—
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—21no—
621C2×C3×C4—21no—
622C2×C3×C4—42no—
623C2×C3×C4—42no—
624C2×C3×C4—101no—
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—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5C3×AGL(1,ℤ/8)12yescomplemented
644C22×C5C22×C3×D411yescharacteristic
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—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—22no—
661C4×C5—41no—
662C4×C5—41no—
663C4×C5C22×C3×D411yescharacteristic
664C4×C5C3×H(5,𝔽2)11yescharacteristic
665Dic5—41no—
666C24—101no—
667C24—101no—
668#41—22no—
669#41—41no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—41no—
673C2×Q8C22×C3×D511yescharacteristic
674C2×Q8C22×C3×D511yescharacteristic
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—51no—
680C2×D4—102no—
681C2×D4—102no—
682C2×D4—101no—
683C2×D4—101no—
684C2×D4—101no—
685C2×D4—101no—
686C2×D4—101no—
687C2×D4—101no—
688C2×D4—201no—
689C2×D4—201no—
690C2×D4—204no—
691C2×D4C3×C22⋊D511yescharacteristic
692C2×D4C22×C3×D511yescharacteristic
693C22×C4—21no—
694C22×C4—21no—
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—21no—
714C4⋊C4—21no—
715C4⋊C4—51no—
716C4⋊C4C3×C22⋊D511yescharacteristic
717C4⋊C4C22×C3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4C3×C22⋊D511yescharacteristic
726C22⋊C4C3×C22⋊D511yescharacteristic
727C42—21no—
728C42C22×C3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
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#409512yescomplemented
750C22×C3C22×C22⋊D511yescharacteristic
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—22no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—201no—
759C3×C4C2×D4×D511yescharacteristic
760C3×C4#414411yescharacteristic
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—81no—
764C2×C5C3×D4211yescharacteristic
765C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
766C2×C5C3×#57711yescharacteristic
767D5—42no—
768D5—81no—
769D5—81no—
770C23—21no—
771C23—101no—
772C23—101no—
773C23—101no—
774C23—202no—
775C23—202no—
776C23—202no—
777C23—202no—
778C23—401no—
779C23—401no—
780C23C2×C3×C22⋊D511yescharacteristic
781C23C2×C3×C22⋊D511yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—42no—
786Q8C3×D4×D512yescomplemented
787D4—22no—
788D4—21no—
789D4—21no—
790D4—42no—
791D4—42no—
792D4—52no—
793D4—101no—
794D4—101no—
795D4—101no—
796D4—101no—
797D4—101no—
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—21no—
810C2×C4—21no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—101no—
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—81no—
827C2×C3—202no—
828C2×C3—401no—
829C2×C3—401no—
830C2×C3D4×C22⋊D511yescharacteristic
831C2×C3C2×#409511yescharacteristic
832C2×C3#6617111yescharacteristic
833C5C3×#326511yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—102no—
843C22—201no—
844C22—201no—
845C22—201no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—201no—
850C22—201no—
851C22—404no—
852C22—404no—
853C22C3×#409512yescomplemented
854C22C22×C3×C22⋊D511yescharacteristic
855C4—21no—
856C4—21no—
857C4—22no—
858C4—21no—
859C4—21no—
860C4—41no—
861C4—41no—
862C4—201no—
863C4C2×C3×D4×D511yescharacteristic
864C4C3×#414411yescharacteristic
865C3#1061527311yescharacteristic, direct product factor, Sylow
866C2—22no—
867C2—41no—
868C2—81no—
869C2—202no—
870C2—401no—
871C2—401no—
872C2C3×D4×C22⋊D511yescharacteristic
873C2C2×C3×#409511yescharacteristic
874C2C3×#6617111yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#548C2
socleC22×C3×C5C22×D4
hypercenterC3×#548D5
hypocenterC5C3×#3265
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C3×C5×#548C2semidirect
2. C2×C3×#4095C2semidirect
3. C22×C3×#688C2semidirect
4. C3×D4×D20C2semidirect
5. C3×#65527C2semidirect
6. C3×#65516C2semidirect
7. C3×#65347C2semidirect
8. C3×#65346C2semidirect
9. C3×#65338C2semidirect
10. C3×#65335C2semidirect
11. C3×#65327C2semidirect
12. C3×#65325C2semidirect
13. C3×#65316C2semidirect
14. C3×#65315C2semidirect
15. C3×#65300C2semidirect
16. #10615273C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
23. C3×C5×#124C22semidirect
25. C3×C5×C22⋊Q8C22semidirect
27. C3×C5×#121C22semidirect
28. C3×C4×C5×Q8C22semidirect
35. C2×C3×#688C22semidirect
36. C2×C3×#688C22semidirect
37. C2×C3×#688C22semidirect
38. C2×C3×#688C22semidirect
40. C2×C3×#686C22semidirect
41. C2×C3×#686C22semidirect
44. C2×C3×#681C22semidirect
45. C22×C3×#168C22semidirect
51. C3×#3967C22semidirect
52. C3×#3967C22semidirect
53. C3×#3964C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×C22⋊#168C22semidirect
57. C3×#3941C22semidirect
58. C3×#3941C22semidirect
59. C3×#3939C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×#548C2×C3semidirect
64. C2×#4095C2×C3semidirect
65. C22×#688C2×C3semidirect
66. D4×D20C2×C3semidirect
67. #65527C2×C3semidirect
68. #65516C2×C3semidirect
69. #65347C2×C3semidirect
70. #65346C2×C3semidirect
71. #65338C2×C3semidirect
72. #65335C2×C3semidirect
73. #65327C2×C3semidirect
74. #65325C2×C3semidirect
75. #65316C2×C3semidirect
76. #65315C2×C3semidirect
77. #65300C2×C3semidirect
127. C3×#688D4semidirect
143. C3×#548D5semidirect
156. C2×C5×#41C22×C3semidirect
157. C22×C5×Q8C22×C3semidirect
162. C5×#124C22×C3semidirect
164. C5×C22⋊Q8C22×C3semidirect
166. C5×#121C22×C3semidirect
167. C4×C5×Q8C22×C3semidirect
174. C2×#688C22×C3semidirect
175. C2×#688C22×C3semidirect
176. C2×#688C22×C3semidirect
177. C2×#688C22×C3semidirect
179. C2×#686C22×C3semidirect
180. C2×#686C22×C3semidirect
183. C2×#681C22×C3semidirect
184. C22×#168C22×C3semidirect
190. #3967C22×C3semidirect
191. #3967C22×C3semidirect
192. #3964C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. C22⋊#168C22×C3semidirect
196. #3941C22×C3semidirect
197. #3941C22×C3semidirect
198. #3939C22×C3semidirect
199. C4⋊#168C22×C3semidirect
200. #3935C22×C3semidirect
218. C3×C5×Q8C2×D4semidirect
255. C3×#168C2×D4semidirect
256. C2×C3×#41C2×D5semidirect
257. C22×C3×Q8C2×D5semidirect
276. C3×#124C2×D5semidirect
278. C3×C22⋊Q8C2×D5semidirect
283. C3×#121C2×D5semidirect
286. C3×C4×Q8C2×D5semidirect
350. #688C3×D4semidirect
366. #548C3×D5semidirect
387. C22×C3×C5AGL(1,ℤ/8)semidirect
489. C5×Q8C2×C3×D4semidirect
526. #168C2×C3×D4semidirect
527. C2×#41C2×C3×D5semidirect
528. C22×Q8C2×C3×D5semidirect
547. #124C2×C3×D5semidirect
549. C22⋊Q8C2×C3×D5semidirect
554. #121C2×C3×D5semidirect
557. C4×Q8C2×C3×D5semidirect
597. C3×Q8D4×D5semidirect
643. C22×C5C3×AGL(1,ℤ/8)semidirect
729. C3×C5#3265semidirect
749. C22×C3#4095semidirect
786. Q8C3×D4×D5semidirect
833. C5C3×#3265semidirect
853. C22C3×#4095semidirect
865. C3#10615273direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5482
C2×C3×#40952
C22×C3×#6882
C3×D4×D202
C3×#655272
C3×#655162
C3×#653472
C3×#653462
C3×#653382
C3×#653352
C3×#653272
C3×#653252
C3×#653162
C3×#653152
C3×#653002
#106152733
C3×#32655