Finite Group Databasebeta

← C3×#10615219 #14453182

Subgroups — C3×#10615219 #14453182

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
1C3×C5×D42C211yesmaximal, characteristic, complemented
2C2×C3×#4078C211yesmaximal, characteristic, complemented
3C22×C3×#686C211yesmaximal, characteristic, complemented
4C3×#65884C211yesmaximal, characteristic, complemented
5C3×#65507C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7C3×#65363C211yesmaximal, characteristic, complemented
8C3×#65361C211yesmaximal, characteristic, complemented
9C3×#65330C211yesmaximal, characteristic, complemented
10C3×#65328C211yesmaximal, characteristic, complemented
11C3×#65326C211yesmaximal, characteristic, complemented
12C3×#65325C211yesmaximal, characteristic, complemented
13C3×#65305C211yesmaximal, characteristic, complemented
14C3×#65303C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615219C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4—21no—
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic, complemented
20C2×C3×#709C2211yescharacteristic, complemented
21C22×C3×D20C2211yescharacteristic, complemented
22C3×C5×#127C2211yescharacteristic, complemented
23C3×C5×#121—21no—
24C3×C5×#121C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic, complemented
26C3×C5×#120—21no—
27C3×C5×#120—21no—
28C3×C4×C5×D4C2211yescharacteristic
29C3×C4×C5×D4C2211yescharacteristic, complemented
30C3×#4083—21no—
31C2×C3×#687C2211yescharacteristic, complemented
32C2×C3×#687C2211yescharacteristic, complemented
33C2×C3×#687C2211yescharacteristic, complemented
34C3×#4078—24no—
35C2×C3×#686—24no—
36C2×C3×#686C2211yescharacteristic
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic, complemented
39C2×C3×#686C2211yescharacteristic, complemented
40C2×C3×#686C2211yescharacteristic, complemented
41C2×C3×#686C2211yescharacteristic, complemented
42C3×#4076C2211yescharacteristic, complemented
43C3×#4070C2211yescharacteristic, complemented
44C2×C3×#681C2211yescharacteristic, complemented
45C22×C3×#168C2211yescharacteristic, complemented
46C3×#4040—21no—
47C3×#4030—21no—
48C3×D5×C22⋊C4—21no—
49C3×#4021C2211yescharacteristic, complemented
50C3×C4×D20C2211yescharacteristic, complemented
51C3×#3964C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic, complemented
58C3×#3941C2211yescharacteristic, complemented
59C3×#3940C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C5×D42C2×C311yescharacteristic, complemented
64C2×#4078C2×C311yescharacteristic, complemented
65C22×#686C2×C311yescharacteristic, complemented
66#65884C2×C311yescharacteristic, complemented
67#65507C2×C311yescharacteristic, complemented
68#65506C2×C311yescharacteristic, complemented
69#65363C2×C311yescharacteristic, complemented
70#65361C2×C311yescharacteristic, complemented
71#65330C2×C311yescharacteristic, complemented
72#65328C2×C311yescharacteristic, complemented
73#65326C2×C311yescharacteristic, complemented
74#65325C2×C311yescharacteristic, complemented
75#65305C2×C311yescharacteristic, complemented
76#65303C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C24×C3×C5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—22no—
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—21no—
89C2×C3×C5×D4—41no—
90C2×C3×C5×D4—41no—
91C2×C3×C5×D4—44no—
92C2×C3×C5×D4D411yescharacteristic
93C2×C3×C5×D4C2311yescharacteristic
94C2×C3×C5×D4C2311yescharacteristic
95C2×C3×C5×D4C2311yescharacteristic
96C22×C3×C4×C5—21no—
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C2×C3×C22⋊D5—21no—
100C2×C3×C22⋊D5—21no—
101C3×#709—22no—
102C3×#709—41no—
103C2×C3×D20—22no—
104C2×C3×D20—21no—
105C2×C3×D20—41no—
106C2×C3×D20C2311yescharacteristic
107C2×C3×D20C2311yescharacteristic
108C2×C3×C4×D5—21no—
109C2×C3×C4×D5—21no—
110C2×C3×Dic10C2311yescharacteristic
111C3×C5×C4⋊C4D411yescharacteristic
112C3×C5×C4⋊C4C2311yescharacteristic
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4—21no—
116C3×C5×C22⋊C4D411yescharacteristic
117C3×C5×C22⋊C4D411yescharacteristic
118C3×C42×C5C2311yescharacteristic
119C3×C22⋊Dic5—21no—
120C3×#687—22no—
121C3×#687—22no—
122C3×#687—41no—
123C3×#686—22no—
124C3×#686—22no—
125C3×#686—22no—
126C3×#686—22no—
127C3×#686—41no—
128C3×#686D414yescomplemented
129C3×#685—21no—
130C3×#685—21no—
131C3×#685—21no—
132C3×#685—21no—
133C3×C4⋊Dic5C2311yescharacteristic
134C3×#683—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×D8—51no—
143C3×#546—51no—
144C3×D42D511yescharacteristic, complemented
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×#435—51no—
156C22×C5×D4—21no—
157C22×C5×D4C22×C311yescharacteristic
158C22×C5×D4C22×C311yescharacteristic, complemented
159C2×#709C22×C311yescharacteristic, complemented
160C22×D20C22×C311yescharacteristic, complemented
161C5×#127C22×C311yescharacteristic, complemented
162C5×#121—21no—
163C5×#121C22×C311yescharacteristic
164C5×#121C22×C311yescharacteristic, complemented
165C5×#120—21no—
166C5×#120—21no—
167C4×C5×D4C22×C311yescharacteristic
168C4×C5×D4C22×C311yescharacteristic, complemented
169#4083—21no—
170C2×#687C22×C311yescharacteristic, complemented
171C2×#687C22×C311yescharacteristic, complemented
172C2×#687C22×C311yescharacteristic, complemented
173#4078—24no—
174C2×#686—24no—
175C2×#686C22×C311yescharacteristic
176C2×#686C22×C311yescharacteristic
177C2×#686C22×C311yescharacteristic, complemented
178C2×#686C22×C311yescharacteristic, complemented
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#4040—21no—
186#4030—21no—
187D5×C22⋊C4—21no—
188#4021C22×C311yescharacteristic, complemented
189C4×D20C22×C311yescharacteristic, complemented
190#3964C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic, complemented
194C22⋊#168C22×C311yescharacteristic, complemented
195#3942C22×C311yescharacteristic, complemented
196#3941C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic, complemented
198#3940C22×C311yescharacteristic, complemented
199C4⋊#168C22×C311yescharacteristic, complemented
200#3935C22×C311yescharacteristic, complemented
201#3264—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—
214C22×C3×D5—21no—
215C22×C3×D5—42no—
216C22×C3×D5—42no—
217C22×C3×D5—81no—
218C3×C5×D4—22no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—21no—
224C3×C5×D4—42no—
225C3×C5×D4—42no—
226C3×C5×D4—42no—
227C3×C5×D4—42no—
228C3×C5×D4—42no—
229C3×C5×D4—81no—
230C3×C5×D4C2×D412yes—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—42no—
237C2×C3×C4×C5C2×D411yescharacteristic
238C2×C3×C4×C5C2×D411yescharacteristic
239C2×C3×C4×C5C2×D411yescharacteristic
240C2×C3×C4×C5C2×D411yescharacteristic
241C2×C3×C4×C5C2411yescharacteristic
242C3×C22⋊D5—42no—
243C3×C22⋊D5—81no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×D20—42no—
250C3×D20C2×D412yescomplemented
251C3×C4×D5—42no—
252C3×C4×D5—81no—
253C3×Dic10—21no—
254C3×Dic10—21no—
255C3×#168—21no—
256C3×#168—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C2×C3×#41—51no—
260C22×C3×D4—21no—
261C22×C3×D4—51no—
262C22×C3×D4C2×D511yescharacteristic
263C22×C3×D4C2×D511yescharacteristic, complemented
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×M16—51no—
276C22×C3×C8—51no—
277C3×#127C2×D511yescharacteristic, complemented
278C3×#124—51no—
279C3×#123—101no—
280C3×C22⋊Q8—51no—
281C3×#121—21no—
282C3×#121—51no—
283C3×#121—101no—
284C3×#121C2×D511yescharacteristic
285C3×#121C2×D511yescharacteristic, complemented
286C3×#120—21no—
287C3×#120—21no—
288C3×#120—101no—
289C3×C4×D4—51no—
290C3×C4×D4C2×D511yescharacteristic
291C3×C4×D4C2×D511yescharacteristic, complemented
292C2×C3×C22⋊C4—101no—
293C3×#106—51no—
294C3×C4⋊C8—51no—
295C3×#103—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102—51no—
300C3×#102—51no—
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97—51no—
304C24×C5—21no—
305C24×C5—21no—
306C23×D5—21no—
307C2×C5×D4—22no—
308C2×C5×D4—22no—
309C2×C5×D4—21no—
310C2×C5×D4—21no—
311C2×C5×D4—21no—
312C2×C5×D4—21no—
313C2×C5×D4—21no—
314C2×C5×D4—21no—
315C2×C5×D4—41no—
316C2×C5×D4—41no—
317C2×C5×D4—44no—
318C2×C5×D4C3×D411yescharacteristic
319C2×C5×D4C23×C311yescharacteristic
320C2×C5×D4C23×C311yescharacteristic
321C2×C5×D4C23×C311yescharacteristic
322C22×C4×C5—21no—
323C22×C4×C5C23×C311yescharacteristic
324C22×C4×C5C23×C311yescharacteristic
325C2×C22⋊D5—21no—
326C2×C22⋊D5—21no—
327#709—22no—
328#709—41no—
329C2×D20—22no—
330C2×D20—21no—
331C2×D20—41no—
332C2×D20C23×C311yescharacteristic
333C2×D20C23×C311yescharacteristic
334C2×C4×D5—21no—
335C2×C4×D5—21no—
336C2×Dic10C23×C311yescharacteristic
337C5×C4⋊C4C3×D411yescharacteristic
338C5×C4⋊C4C23×C311yescharacteristic
339C5×C22⋊C4—21no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4C3×D411yescharacteristic
343C5×C22⋊C4C3×D411yescharacteristic
344C42×C5C23×C311yescharacteristic
345C22⋊Dic5—21no—
346#687—22no—
347#687—22no—
348#687—41no—
349#686—22no—
350#686—22no—
351#686—22no—
352#686—22no—
353#686—41no—
354#686C3×D414yescomplemented
355#685—21no—
356#685—21no—
357#685—21no—
358#685—21no—
359C4⋊Dic5C23×C311yescharacteristic
360#683—21no—
361#681—22no—
362C2×#168—22no—
363C2×#168C23×C311yescharacteristic
364C2×#168C23×C311yescharacteristic
365C2×#168C23×C311yescharacteristic
366C2×#168C23×C311yescharacteristic
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—51no—
369#546—51no—
370D42C3×D511yescharacteristic, complemented
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#435—51no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
385C22×C3×C5—22no—
386C22×C3×C5—21no—
387C22×C3×C5—21no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—41no—
394C22×C3×C5—41no—
395C22×C3×C5—41no—
396C22×C3×C5—84no—
397C22×C3×C5—84no—
398C22×C3×C5AGL(1,ℤ/8)12yescomplemented
399C22×C3×C5C22×D411yescharacteristic
400C2×C3×D5—22no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—21no—
410C3×C4×C5—21no—
411C3×C4×C5—41no—
412C3×C4×C5C22×D411yescharacteristic
413C3×C4×C5H(5,𝔽2)11yescharacteristic
414C3×Dic5—41no—
415C3×Dic5—41no—
416C24×C3—21no—
417C24×C3—21no—
418C24×C3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8—51no—
422C2×C3×D4—22no—
423C2×C3×D4—22no—
424C2×C3×D4—21no—
425C2×C3×D4—21no—
426C2×C3×D4—21no—
427C2×C3×D4—21no—
428C2×C3×D4—21no—
429C2×C3×D4—21no—
430C2×C3×D4—41no—
431C2×C3×D4—41no—
432C2×C3×D4—44no—
433C2×C3×D4—51no—
434C2×C3×D4—51no—
435C2×C3×D4—102no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—101no—
439C2×C3×D4—201no—
440C2×C3×D4C22⋊D511yescharacteristic
441C2×C3×D4C22×D511yescharacteristic
442C2×C3×D4C22×D511yescharacteristic
443C2×C3×D4C22×D511yescharacteristic
444C22×C3×C4—21no—
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—102no—
459C2×C3×C8—51no—
460C2×C3×C8—51no—
461C2×C3×C8—51no—
462C2×C3×C8—51no—
463C2×C3×C8—102no—
464C3×C4⋊C4—51no—
465C3×C4⋊C4—101no—
466C3×C4⋊C4C22⋊D511yescharacteristic
467C3×C4⋊C4C22×D511yescharacteristic
468C3×C22⋊C4—21no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—21no—
471C3×C22⋊C4—101no—
472C3×C22⋊C4—101no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4C22⋊D511yescharacteristic
477C3×C22⋊C4C22⋊D511yescharacteristic
478C3×C42C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—42no—
483C23×C5—42no—
484C23×C5—42no—
485C23×C5—42no—
486C23×C5—81no—
487C23×C5—81no—
488C23×C5C2×C3×D411yescharacteristic
489C23×C5C2×C3×D411yescharacteristic
490C22×D5—21no—
491C22×D5—21no—
492C22×D5—42no—
493C22×D5—42no—
494C22×D5—81no—
495C5×D4—22no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—21no—
501C5×D4—42no—
502C5×D4—42no—
503C5×D4—42no—
504C5×D4—42no—
505C5×D4—42no—
506C5×D4—81no—
507C5×D4C2×C3×D412yes—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—21no—
513C2×C4×C5—42no—
514C2×C4×C5C2×C3×D411yescharacteristic
515C2×C4×C5C2×C3×D411yescharacteristic
516C2×C4×C5C2×C3×D411yescharacteristic
517C2×C4×C5C2×C3×D411yescharacteristic
518C2×C4×C5C24×C311yescharacteristic
519C22⋊D5—42no—
520C22⋊D5—81no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523D20—21no—
524D20—21no—
525D20—21no—
526D20—42no—
527D20C2×C3×D412yescomplemented
528C4×D5—42no—
529C4×D5—81no—
530Dic10—21no—
531Dic10—21no—
532#168—21no—
533#168—21no—
534#168—21no—
535#168C2×C3×D412yescomplemented
536C2×#41—51no—
537C22×D4—21no—
538C22×D4—51no—
539C22×D4C2×C3×D511yescharacteristic
540C22×D4C2×C3×D511yescharacteristic, complemented
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×M16—51no—
553C22×C8—51no—
554#127C2×C3×D511yescharacteristic, complemented
555#124—51no—
556#123—101no—
557C22⋊Q8—51no—
558#121—21no—
559#121—51no—
560#121—101no—
561#121C2×C3×D511yescharacteristic
562#121C2×C3×D511yescharacteristic, complemented
563#120—21no—
564#120—21no—
565#120—101no—
566C4×D4—51no—
567C4×D4C2×C3×D511yescharacteristic
568C4×D4C2×C3×D511yescharacteristic, complemented
569C2×C22⋊C4—101no—
570#106—51no—
571C4⋊C8—51no—
572#103—51no—
573#102—51no—
574#102—51no—
575#102—51no—
576#102—51no—
577#102—51no—
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97—51no—
581C2×C3×C5—22no—
582C2×C3×C5—41no—
583C2×C3×C5—42no—
584C2×C3×C5—81no—
585C2×C3×C5—81no—
586C2×C3×C5D4211yescharacteristic
587C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
588C2×C3×C5#57611yescharacteristic
589C3×D5—42no—
590C3×D5—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—42no—
597C23×C3—42no—
598C23×C3—81no—
599C23×C3—81no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—202no—
603C23×C3—202no—
604C23×C3—401no—
605C23×C3C2×C22⋊D511yescharacteristic
606C23×C3C2×C22⋊D511yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—22no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—42no—
616C3×D4—42no—
617C3×D4—42no—
618C3×D4—42no—
619C3×D4—42no—
620C3×D4—52no—
621C3×D4—81no—
622C3×D4—101no—
623C3×D4—101no—
624C3×D4—101no—
625C3×D4—202no—
626C3×D4—202no—
627C3×D4—401no—
628C3×D4D4×D512yes—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—42no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—202no—
638C2×C3×C4—401no—
639C2×C3×C4C2×C22⋊D511yescharacteristic
640C2×C3×C4C2×C22⋊D511yescharacteristic
641C2×C3×C4C2×C22⋊D511yescharacteristic
642C2×C3×C4C2×C22⋊D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—52no—
645C3×C8—101no—
646C3×C8—101no—
647C3×C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—21no—
653C22×C5—22no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—41no—
660C22×C5—41no—
661C22×C5—41no—
662C22×C5—84no—
663C22×C5—84no—
664C22×C5C3×AGL(1,ℤ/8)12yescomplemented
665C22×C5C22×C3×D411yescharacteristic
666C2×D5—22no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—41no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—21no—
676C4×C5—21no—
677C4×C5—41no—
678C4×C5C22×C3×D411yescharacteristic
679C4×C5C3×H(5,𝔽2)11yescharacteristic
680Dic5—41no—
681Dic5—41no—
682C24—21no—
683C24—21no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—44no—
699C2×D4—51no—
700C2×D4—51no—
701C2×D4—102no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—101no—
705C2×D4—201no—
706C2×D4C3×C22⋊D511yescharacteristic
707C2×D4C22×C3×D511yescharacteristic
708C2×D4C22×C3×D511yescharacteristic
709C2×D4C22×C3×D511yescharacteristic
710C22×C4—21no—
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—102no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—51no—
728C2×C8—51no—
729C2×C8—102no—
730C4⋊C4—51no—
731C4⋊C4—101no—
732C4⋊C4C3×C22⋊D511yescharacteristic
733C4⋊C4C22×C3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—101no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4C3×C22⋊D511yescharacteristic
743C22⋊C4C3×C22⋊D511yescharacteristic
744C42C22×C3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—84no—
761C22×C3—84no—
762C22×C3—102no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3—201no—
768C22×C3—404no—
769C22×C3#407812yescomplemented
770C22×C3C22×C22⋊D511yescharacteristic
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—201no—
777C3×C4—201no—
778C3×C4C2×D4×D511yescharacteristic
779C3×C4#414411yescharacteristic
780C2×C5—22no—
781C2×C5—41no—
782C2×C5—42no—
783C2×C5—81no—
784C2×C5—81no—
785C2×C5C3×D4211yescharacteristic
786C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
787C2×C5C3×#57611yescharacteristic
788D5—42no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—101no—
800C23—101no—
801C23—202no—
802C23—202no—
803C23—401no—
804C23C2×C3×C22⋊D511yescharacteristic
805C23C2×C3×C22⋊D511yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—22no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—42no—
815D4—42no—
816D4—42no—
817D4—42no—
818D4—42no—
819D4—52no—
820D4—81no—
821D4—101no—
822D4—101no—
823D4—101no—
824D4—202no—
825D4—202no—
826D4—401no—
827D4C3×D4×D512yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—42no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—202no—
837C2×C4—401no—
838C2×C4C2×C3×C22⋊D511yescharacteristic
839C2×C4C2×C3×C22⋊D511yescharacteristic
840C2×C4C2×C3×C22⋊D511yescharacteristic
841C2×C4C2×C3×C22⋊D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—52no—
844C8—101no—
845C8—101no—
846C8—101no—
847C2×C3—22no—
848C2×C3—41no—
849C2×C3—42no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—202no—
853C2×C3—401no—
854C2×C3C2×#407811yescharacteristic
855C2×C3D4×C22⋊D511yescharacteristic
856C2×C3#6616911yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—22no—
863C22—21no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—84no—
873C22—84no—
874C22—102no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—201no—
880C22—404no—
881C22C3×#407812yescomplemented
882C22C22×C3×C22⋊D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—41no—
888C4—201no—
889C4—201no—
890C4C2×C3×D4×D511yescharacteristic
891C4C3×#414411yescharacteristic
892C3#1061521911yescharacteristic, direct product factor, Sylow
893C2—22no—
894C2—41no—
895C2—42no—
896C2—81no—
897C2—81no—
898C2—202no—
899C2—401no—
900C2C2×C3×#407811yescharacteristic
901C2C3×D4×C22⋊D511yescharacteristic
902C2C3×#6616911yescharacteristic
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×#3264
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. C2×C3×#4078C2semidirect
3. C22×C3×#686C2semidirect
4. C3×#65884C2semidirect
5. C3×#65507C2semidirect
6. C3×#65506C2semidirect
7. C3×#65363C2semidirect
8. C3×#65361C2semidirect
9. C3×#65330C2semidirect
10. C3×#65328C2semidirect
11. C3×#65326C2semidirect
12. C3×#65325C2semidirect
13. C3×#65305C2semidirect
14. C3×#65303C2semidirect
15. C3×#65300C2semidirect
16. #10615219C3direct (N × H)
19. C22×C3×C5×D4C22semidirect
20. C2×C3×#709C22semidirect
21. C22×C3×D20C22semidirect
22. C3×C5×#127C22semidirect
25. C3×C5×#121C22semidirect
29. C3×C4×C5×D4C22semidirect
31. C2×C3×#687C22semidirect
32. C2×C3×#687C22semidirect
33. C2×C3×#687C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#686C22semidirect
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×D20C22semidirect
51. C3×#3964C22semidirect
52. C3×#3964C22semidirect
53. C3×#3964C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
57. C3×#3941C22semidirect
58. C3×#3941C22semidirect
59. C3×#3940C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×D42C2×C3semidirect
64. C2×#4078C2×C3semidirect
65. C22×#686C2×C3semidirect
66. #65884C2×C3semidirect
67. #65507C2×C3semidirect
68. #65506C2×C3semidirect
69. #65363C2×C3semidirect
70. #65361C2×C3semidirect
71. #65330C2×C3semidirect
72. #65328C2×C3semidirect
73. #65326C2×C3semidirect
74. #65325C2×C3semidirect
75. #65305C2×C3semidirect
76. #65303C2×C3semidirect
77. #65300C2×C3semidirect
128. C3×#686D4semidirect
144. C3×D42D5semidirect
158. C22×C5×D4C22×C3semidirect
159. C2×#709C22×C3semidirect
160. C22×D20C22×C3semidirect
161. C5×#127C22×C3semidirect
164. C5×#121C22×C3semidirect
168. C4×C5×D4C22×C3semidirect
170. C2×#687C22×C3semidirect
171. C2×#687C22×C3semidirect
172. C2×#687C22×C3semidirect
177. C2×#686C22×C3semidirect
178. C2×#686C22×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×D20C22×C3semidirect
190. #3964C22×C3semidirect
191. #3964C22×C3semidirect
192. #3964C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. C22⋊#168C22×C3semidirect
195. #3942C22×C3semidirect
196. #3941C22×C3semidirect
197. #3941C22×C3semidirect
198. #3940C22×C3semidirect
199. C4⋊#168C22×C3semidirect
200. #3935C22×C3semidirect
250. C3×D20C2×D4semidirect
258. C3×#168C2×D4semidirect
263. C22×C3×D4C2×D5semidirect
277. C3×#127C2×D5semidirect
285. C3×#121C2×D5semidirect
291. C3×C4×D4C2×D5semidirect
354. #686C3×D4semidirect
370. D42C3×D5semidirect
398. C22×C3×C5AGL(1,ℤ/8)semidirect
527. D20C2×C3×D4semidirect
535. #168C2×C3×D4semidirect
540. C22×D4C2×C3×D5semidirect
554. #127C2×C3×D5semidirect
562. #121C2×C3×D5semidirect
568. C4×D4C2×C3×D5semidirect
664. C22×C5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
769. C22×C3#4078semidirect
857. C5C3×#3264semidirect
881. C22C3×#4078semidirect
892. C3#10615219direct (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
C2×C3×#40782
C22×C3×#6862
C3×#658842
C3×#655072
C3×#655062
C3×#653632
C3×#653612
C3×#653302
C3×#653282
C3×#653262
C3×#653252
C3×#653052
C3×#653032
C3×#653002
#106152193
C3×#32645