Finite Group Databasebeta

← C3×D5×#548 #14482794

Subgroups — C3×D5×#548 #14482794

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic, complemented
2C22×C3×Q8×D5C211yesmaximal, characteristic, complemented
3C3×C5×#548C211yesmaximal, characteristic, complemented
4C3×#66165C211yesmaximal, characteristic, complemented
5C3×#66151C211yesmaximal, characteristic, complemented
6C3×#66011C213yesmaximal, complemented
7C3×D5×#124C213yesmaximal, complemented
8C3×#65967C213yesmaximal, complemented
9C3×D5×C22⋊Q8C213yesmaximal, complemented
10C3×D5×#121C213yesmaximal, complemented
11C3×#65932C213yesmaximal, complemented
12C3×#65910C211yesmaximal, characteristic, complemented
13C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
14C3×#65886C213yesmaximal, complemented
15C3×C4×D4×D5C213yesmaximal, complemented
16D5×#548C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C3×D5×#41—28no—
20C2×C3×#713C2211yescharacteristic, complemented
21C2×C3×Q8×D5—28no—
22C2×C3×Q8×D5C2213yes—
23C2×C3×Q8×D5C2211yescharacteristic
24C2×C3×Q8×D5C2211yescharacteristic, complemented
25C2×C3×Q8×D5C2213yescomplemented
26C2×C3×#711C2213yescomplemented
27C2×C3×D4×D5C2213yes—
28C2×C3×D4×D5C2213yes—
29C2×C3×#709C2213yescomplemented
30C22×C3×C4×D5C2213yes—
31C22×C3×C4×D5C2213yes—
32C22×C3×Dic10C2213yescomplemented
33C3×C5×#124C2213yescomplemented
34C3×C5×C22⋊Q8C2213yescomplemented
35C3×C5×#121C2213yescomplemented
36C3×C4×C5×Q8C2211yescharacteristic, complemented
37C3×C4×C5×D4C2213yescomplemented
38C3×#4093C2213yescomplemented
39C3×#4092C2213yescomplemented
40C3×Q8×Dic5C2211yescharacteristic, complemented
41C3×#4085C2216yescomplemented
42C3×#4084C2213yescomplemented
43C3×#4082C2213yescomplemented
44C3×D4×Dic5C2213yescomplemented
45C3×#4076C2213yescomplemented
46C3×C4×C22⋊D5C2213yescomplemented
47C3×C4×C22⋊D5C2213yescomplemented
48C3×#4070C2213yescomplemented
49C3×#4043C2213yescomplemented
50C3×#4042C2216yescomplemented
51C3×#4041C2213yescomplemented
52C3×#4039C2213yescomplemented
53C3×D5×C4⋊C4C2213yes—
54C3×D5×C4⋊C4C2213yes—
55C3×#4033C2213yescomplemented
56C3×#4031C2216yescomplemented
57C3×#4031C2216yescomplemented
58C3×#4030C2216yescomplemented
59C3×#4027C2213yescomplemented
60C3×#4027C2213yescomplemented
61C3×D5×C22⋊C4C2211yescharacteristic
62C3×D5×C22⋊C4C2213yes—
63C3×D5×C22⋊C4C2216yes—
64C3×#4024C2216yescomplemented
65C3×#4021C2213yescomplemented
66C3×C4×D20C2213yescomplemented
67C3×C42×D5C2213yes—
68C3×C4×Dic10C2213yescomplemented
69C2×C3×#548—51nomaximal, Hall
70C2×D5×#41C2×C311yescharacteristic, complemented
71C22×Q8×D5C2×C311yescharacteristic, complemented
72C5×#548C2×C311yescharacteristic, complemented
73#66165C2×C311yescharacteristic, complemented
74#66151C2×C311yescharacteristic, complemented
75#66011C2×C313yescomplemented
76D5×#124C2×C313yescomplemented
77#65967C2×C313yescomplemented
78D5×C22⋊Q8C2×C313yescomplemented
79D5×#121C2×C313yescomplemented
80#65932C2×C313yescomplemented
81#65910C2×C311yescharacteristic, complemented
82C4×Q8×D5C2×C311yescharacteristic, complemented
83#65886C2×C313yescomplemented
84C4×D4×D5C2×C313yescomplemented
85C23×C3×D5C2313yes—
86C23×C3×D5C2311yescharacteristic
87C3×C5×#41—24no—
88C2×C3×C5×Q8—24no—
89C2×C3×C5×Q8C2313yes—
90C2×C3×C5×Q8C2311yescharacteristic
91C2×C3×C5×D4C2313yes—
92C2×C3×C5×D4C2313yes—
93C22×C3×C4×C5C2313yes—
94C22×C3×C4×C5C2313yes—
95C2×C3×C22⋊D5C2313yes—
96C2×C3×C22⋊D5C2313yes—
97C2×C3×C22⋊D5C2316yes—
98C22×C3×Dic5C2313yes—
99C22×C3×Dic5C2313yes—
100C3×#713—24no—
101C3×Q8×D5—24no—
102C3×Q8×D5—212no—
103C3×Q8×D5—212no—
104C3×Q8×D5D418yescomplemented
105C3×#711—212no—
106C3×D4×D5—212no—
107C3×D4×D5—212no—
108C3×#709—212no—
109C2×C3×D20C2313yes—
110C2×C3×D20C2313yes—
111C2×C3×C4×D5—212no—
112C2×C3×C4×D5—212no—
113C2×C3×C4×D5C2313yes—
114C2×C3×C4×D5C2313yes—
115C2×C3×C4×D5C2311yescharacteristic
116C2×C3×C4×D5C2313yes—
117C2×C3×C4×D5C2313yes—
118C2×C3×C4×D5C2313yes—
119C2×C3×C4×D5C2313yes—
120C2×C3×C4×D5C2311yescharacteristic
121C2×C3×C4×D5C2313yes—
122C2×C3×Dic10—212no—
123C2×C3×Dic10C2313yes—
124C2×C3×Dic10C2316yes—
125C2×C3×Dic10C2313yes—
126C3×C5×C4⋊C4C2313yes—
127C3×C5×C4⋊C4C2313yes—
128C3×C5×C22⋊C4C2311yescharacteristic
129C3×C5×C22⋊C4C2313yes—
130C3×C5×C22⋊C4C2316yes—
131C3×C42×C5C2313yes—
132C3×C22⋊Dic5C2311yescharacteristic
133C3×C22⋊Dic5C2313yes—
134C3×C22⋊Dic5C2316yes—
135C3×#685C2316yes—
136C3×#685C2316yes—
137C3×#685C2313yes—
138C3×#685C2311yescharacteristic
139C3×#685C2313yes—
140C3×#685C2311yescharacteristic
141C3×C4⋊Dic5C2313yes—
142C3×C4⋊Dic5C2313yes—
143C3×#683C2316yes—
144C3×#683C2313yes—
145C3×#683C2313yes—
146C3×C4×Dic5C2313yes—
147C3×C4×Dic5C2313yes—
148C3×C4×Dic5C2313yes—
149C22×C3×#41—51no—
150C23×C3×Q8—51no—
151C3×#548—51no—
152C3×#548—51no—
153C3×#548—53no—
154C3×#548—53no—
155C3×#548—53no—
156C3×#548—51no—
157C3×#548—53no—
158C3×#548D511yescharacteristic, direct product factor
159C2×C3×#124—53no—
160C2×C3×C22⋊Q8—53no—
161C2×C3×#121—53no—
162C2×C3×C4×Q8—51no—
163C2×C3×C4×D4—53no—
164C2×C5×#41C22×C311yescharacteristic, complemented
165C22×C5×Q8C22×C311yescharacteristic, complemented
166D5×#41—28no—
167C2×#713C22×C311yescharacteristic, complemented
168C2×Q8×D5—28no—
169C2×Q8×D5C22×C313yes—
170C2×Q8×D5C22×C311yescharacteristic
171C2×Q8×D5C22×C311yescharacteristic, complemented
172C2×Q8×D5C22×C313yescomplemented
173C2×#711C22×C313yescomplemented
174C2×D4×D5C22×C313yes—
175C2×D4×D5C22×C313yes—
176C2×#709C22×C313yescomplemented
177C22×C4×D5C22×C313yes—
178C22×C4×D5C22×C313yes—
179C22×Dic10C22×C313yescomplemented
180C5×#124C22×C313yescomplemented
181C5×C22⋊Q8C22×C313yescomplemented
182C5×#121C22×C313yescomplemented
183C4×C5×Q8C22×C311yescharacteristic, complemented
184C4×C5×D4C22×C313yescomplemented
185#4093C22×C313yescomplemented
186#4092C22×C313yescomplemented
187Q8×Dic5C22×C311yescharacteristic, complemented
188#4085C22×C316yescomplemented
189#4084C22×C313yescomplemented
190#4082C22×C313yescomplemented
191D4×Dic5C22×C313yescomplemented
192#4076C22×C313yescomplemented
193C4×C22⋊D5C22×C313yescomplemented
194C4×C22⋊D5C22×C313yescomplemented
195#4070C22×C313yescomplemented
196#4043C22×C313yescomplemented
197#4042C22×C316yescomplemented
198#4041C22×C313yescomplemented
199#4039C22×C313yescomplemented
200D5×C4⋊C4C22×C313yes—
201D5×C4⋊C4C22×C313yes—
202#4033C22×C313yescomplemented
203#4031C22×C316yescomplemented
204#4031C22×C316yescomplemented
205#4030C22×C316yescomplemented
206#4027C22×C313yescomplemented
207#4027C22×C313yescomplemented
208D5×C22⋊C4C22×C311yescharacteristic
209D5×C22⋊C4C22×C313yes—
210D5×C22⋊C4C22×C316yes—
211#4024C22×C316yescomplemented
212#4021C22×C313yescomplemented
213C4×D20C22×C313yescomplemented
214C42×D5C22×C313yes—
215C4×Dic10C22×C313yescomplemented
216C2×#548—51noSylow
217C23×C3×C5C2413yes—
218C23×C3×C5C2411yescharacteristic
219C22×C3×D5—22no—
220C22×C3×D5—22no—
221C22×C3×D5—26no—
222C22×C3×D5—26no—
223C22×C3×D5—26no—
224C22×C3×D5#4114yescomplemented
225C22×C3×D5C2413yes—
226C22×C3×D5C2411yescharacteristic
227C22×C3×D5C2411yescharacteristic
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—26no—
231C3×C5×D4—26no—
232C2×C3×C4×C5—26no—
233C2×C3×C4×C5—26no—
234C2×C3×C4×C5C2411yescharacteristic
235C2×C3×C4×C5C2413yes—
236C2×C3×C4×C5C2411yescharacteristic
237C2×C3×C4×C5C2413yes—
238C2×C3×C4×C5C2413yes—
239C3×C22⋊D5—26no—
240C3×C22⋊D5—26no—
241C3×C22⋊D5—212no—
242C2×C3×Dic5—26no—
243C2×C3×Dic5—26no—
244C2×C3×Dic5C2411yescharacteristic
245C2×C3×Dic5C2413yes—
246C2×C3×Dic5C2411yescharacteristic
247C2×C3×Dic5C2413yes—
248C2×C3×Dic5C2413yes—
249C3×D20—26no—
250C3×D20—26no—
251C3×C4×D5—22no—
252C3×C4×D5—26no—
253C3×C4×D5—26no—
254C3×C4×D5—22no—
255C3×C4×D5—26no—
256C3×C4×D5—26no—
257C3×C4×D5—26no—
258C3×C4×D5—26no—
259C3×C4×D5C2×D4112yes—
260C3×Dic10—26no—
261C3×Dic10—212no—
262C3×Dic10C2×D4112yescomplemented
263C2×C3×#41—51no—
264C2×C3×#41—53no—
265C2×C3×#41—53no—
266C2×C3×#41—108no—
267C2×C3×#41C2×D511yescharacteristic, complemented
268C22×C3×Q8—51no—
269C22×C3×Q8—53no—
270C22×C3×Q8—53no—
271C22×C3×Q8—51no—
272C22×C3×Q8—53no—
273C22×C3×Q8—108no—
274C22×C3×Q8C2×D511yescharacteristic, complemented
275C22×C3×D4—53no—
276C22×C3×D4—53no—
277C23×C3×C4—53no—
278C23×C3×C4—53no—
279C3×#124—53no—
280C3×#124—53no—
281C3×#124—56no—
282C3×#124—56no—
283C3×#124—53no—
284C3×#124C2×D513yescomplemented
285C3×C22⋊Q8—53no—
286C3×C22⋊Q8—53no—
287C3×C22⋊Q8—56no—
288C3×C22⋊Q8—53no—
289C3×C22⋊Q8—56no—
290C3×C22⋊Q8C2×D513yescomplemented
291C3×#121—53no—
292C3×#121—56no—
293C3×#121—53no—
294C3×#121—53no—
295C3×#121—56no—
296C3×#121C2×D513yescomplemented
297C3×C4×Q8—51no—
298C3×C4×Q8—53no—
299C3×C4×Q8—53no—
300C3×C4×Q8C2×D511yescharacteristic, complemented
301C3×C4×D4—53no—
302C3×C4×D4—53no—
303C3×C4×D4—53no—
304C3×C4×D4—53no—
305C3×C4×D4—53no—
306C3×C4×D4—53no—
307C3×C4×D4—53no—
308C3×C4×D4C2×D513yescomplemented
309C2×C3×C4⋊C4—53no—
310C2×C3×C4⋊C4—53no—
311C2×C3×C22⋊C4—51no—
312C2×C3×C22⋊C4—53no—
313C2×C3×C22⋊C4—56no—
314C2×C3×C42—53no—
315C23×D5C23×C313yes—
316C23×D5C23×C311yescharacteristic
317C5×#41—24no—
318C2×C5×Q8—24no—
319C2×C5×Q8C23×C313yes—
320C2×C5×Q8C23×C311yescharacteristic
321C2×C5×D4C23×C313yes—
322C2×C5×D4C23×C313yes—
323C22×C4×C5C23×C313yes—
324C22×C4×C5C23×C313yes—
325C2×C22⋊D5C23×C316yes—
326C2×C22⋊D5C23×C313yes—
327C2×C22⋊D5C23×C313yes—
328C22×Dic5C23×C313yes—
329C22×Dic5C23×C313yes—
330#713—24no—
331Q8×D5—24no—
332Q8×D5—212no—
333Q8×D5—212no—
334Q8×D5C3×D418yescomplemented
335#711—212no—
336D4×D5—212no—
337D4×D5—212no—
338#709—212no—
339C2×D20C23×C313yes—
340C2×D20C23×C313yes—
341C2×C4×D5—212no—
342C2×C4×D5—212no—
343C2×C4×D5C23×C311yescharacteristic
344C2×C4×D5C23×C313yes—
345C2×C4×D5C23×C313yes—
346C2×C4×D5C23×C313yes—
347C2×C4×D5C23×C313yes—
348C2×C4×D5C23×C313yes—
349C2×C4×D5C23×C313yes—
350C2×C4×D5C23×C311yescharacteristic
351C2×C4×D5C23×C313yes—
352C2×Dic10—212no—
353C2×Dic10C23×C313yes—
354C2×Dic10C23×C316yes—
355C2×Dic10C23×C313yes—
356C5×C4⋊C4C23×C313yes—
357C5×C4⋊C4C23×C313yes—
358C5×C22⋊C4C23×C311yescharacteristic
359C5×C22⋊C4C23×C313yes—
360C5×C22⋊C4C23×C316yes—
361C42×C5C23×C313yes—
362C22⋊Dic5C23×C316yes—
363C22⋊Dic5C23×C313yes—
364C22⋊Dic5C23×C311yescharacteristic
365#685C23×C311yescharacteristic
366#685C23×C313yes—
367#685C23×C316yes—
368#685C23×C316yes—
369#685C23×C313yes—
370#685C23×C311yescharacteristic
371C4⋊Dic5C23×C313yes—
372C4⋊Dic5C23×C313yes—
373#683C23×C316yes—
374#683C23×C313yes—
375#683C23×C313yes—
376C4×Dic5C23×C313yes—
377C4×Dic5C23×C313yes—
378C4×Dic5C23×C313yes—
379C22×#41—51no—
380C23×Q8—51no—
381#548—51no—
382#548—51no—
383#548—53no—
384#548—53no—
385#548—53no—
386#548—51no—
387#548—53no—
388#548C3×D511yescharacteristic, direct product factor
389C2×#124—53no—
390C2×C22⋊Q8—53no—
391C2×#121—53no—
392C2×C4×Q8—51no—
393C2×C4×D4—53no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5—23no—
397C22×C3×C5—23no—
398C22×C3×C5—23no—
399C22×C3×C5C2×#4112yescomplemented
400C22×C3×C5C2511yescharacteristic
401C2×C3×D5—21no—
402C2×C3×D5—21no—
403C2×C3×D5—28no—
404C2×C3×D5—23no—
405C2×C3×D5—23no—
406C2×C3×D5—23no—
407C2×C3×D5—412no—
408C2×C3×D5C22×D412yes—
409C2×C3×D5C2×#4112yes—
410C2×C3×D5C2×#4112yescomplemented
411C2×C3×D52−1+412yes—
412C3×C4×C5—23no—
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5—21no—
416C3×C4×C5C22×D416yes—
417C3×Dic5—23no—
418C3×Dic5—21no—
419C3×Dic5—23no—
420C3×Dic5—21no—
421C3×Dic5C22×D416yes—
422C24×C3—51no—
423C24×C3—53no—
424C3×#41—24no—
425C3×#41—1012no—
426C3×#41—1012no—
427C3×#41—104no—
428C2×C3×Q8—24no—
429C2×C3×Q8—58no—
430C2×C3×Q8—53no—
431C2×C3×Q8—56no—
432C2×C3×Q8—53no—
433C2×C3×Q8—1012no—
434C2×C3×Q8—1012no—
435C2×C3×Q8—1012no—
436C2×C3×Q8—104no—
437C2×C3×Q8C22×D513yes—
438C2×C3×Q8C22×D511yescharacteristic
439C2×C3×D4—53no—
440C2×C3×D4—53no—
441C2×C3×D4—56no—
442C2×C3×D4—53no—
443C2×C3×D4—53no—
444C2×C3×D4—1012no—
445C2×C3×D4—1012no—
446C2×C3×D4C22×D513yes—
447C2×C3×D4C22×D513yes—
448C22×C3×C4—53no—
449C22×C3×C4—53no—
450C22×C3×C4—53no—
451C22×C3×C4—51no—
452C22×C3×C4—53no—
453C22×C3×C4—53no—
454C22×C3×C4—51no—
455C22×C3×C4—53no—
456C22×C3×C4—53no—
457C22×C3×C4—53no—
458C22×C3×C4—53no—
459C22×C3×C4—1012no—
460C22×C3×C4—1012no—
461C22×C3×C4C22×D513yes—
462C22×C3×C4C22×D513yes—
463C3×C4⋊C4—53no—
464C3×C4⋊C4—53no—
465C3×C4⋊C4—56no—
466C3×C4⋊C4—53no—
467C3×C4⋊C4—53no—
468C3×C4⋊C4C22×D513yes—
469C3×C4⋊C4C22×D513yes—
470C3×C22⋊C4—51no—
471C3×C22⋊C4—53no—
472C3×C22⋊C4—56no—
473C3×C22⋊C4—51no—
474C3×C22⋊C4—51no—
475C3×C22⋊C4—53no—
476C3×C22⋊C4—53no—
477C3×C22⋊C4—56no—
478C3×C22⋊C4—56no—
479C3×C22⋊C4C22×D511yescharacteristic
480C3×C22⋊C4C22×D513yes—
481C3×C22⋊C4C22×D516yes—
482C3×C42—53no—
483C3×C42—53no—
484C3×C42—53no—
485C3×C42C22×D513yes—
486C23×C5C24×C313yes—
487C23×C5C24×C311yescharacteristic
488C22×D5—22no—
489C22×D5—22no—
490C22×D5—26no—
491C22×D5—26no—
492C22×D5—26no—
493C22×D5C3×#4114yescomplemented
494C22×D5C24×C313yes—
495C22×D5C24×C311yescharacteristic
496C22×D5C24×C311yescharacteristic
497C5×Q8—26no—
498C5×Q8C2×C3×D414yescomplemented
499C5×D4—26no—
500C5×D4—26no—
501C2×C4×C5—26no—
502C2×C4×C5—26no—
503C2×C4×C5C24×C311yescharacteristic
504C2×C4×C5C24×C313yes—
505C2×C4×C5C24×C311yescharacteristic
506C2×C4×C5C24×C313yes—
507C2×C4×C5C24×C313yes—
508C22⋊D5—26no—
509C22⋊D5—26no—
510C22⋊D5—212no—
511C2×Dic5—26no—
512C2×Dic5—26no—
513C2×Dic5C24×C311yescharacteristic
514C2×Dic5C24×C313yes—
515C2×Dic5C24×C311yescharacteristic
516C2×Dic5C24×C313yes—
517C2×Dic5C24×C313yes—
518D20—26no—
519D20—26no—
520C4×D5—22no—
521C4×D5—26no—
522C4×D5—26no—
523C4×D5—22no—
524C4×D5—26no—
525C4×D5—26no—
526C4×D5—26no—
527C4×D5—26no—
528C4×D5C2×C3×D4112yes—
529Dic10—26no—
530Dic10—212no—
531Dic10C2×C3×D4112yescomplemented
532C2×#41—51no—
533C2×#41—53no—
534C2×#41—53no—
535C2×#41—108no—
536C2×#41C2×C3×D511yescharacteristic, complemented
537C22×Q8—51no—
538C22×Q8—53no—
539C22×Q8—53no—
540C22×Q8—51no—
541C22×Q8—53no—
542C22×Q8—108no—
543C22×Q8C2×C3×D511yescharacteristic, complemented
544C22×D4—53no—
545C22×D4—53no—
546C23×C4—53no—
547C23×C4—53no—
548#124—53no—
549#124—53no—
550#124—56no—
551#124—56no—
552#124—53no—
553#124C2×C3×D513yescomplemented
554C22⋊Q8—53no—
555C22⋊Q8—53no—
556C22⋊Q8—56no—
557C22⋊Q8—53no—
558C22⋊Q8—56no—
559C22⋊Q8C2×C3×D513yescomplemented
560#121—53no—
561#121—56no—
562#121—53no—
563#121—53no—
564#121—56no—
565#121C2×C3×D513yescomplemented
566C4×Q8—51no—
567C4×Q8—53no—
568C4×Q8—53no—
569C4×Q8C2×C3×D511yescharacteristic, complemented
570C4×D4—53no—
571C4×D4—53no—
572C4×D4—53no—
573C4×D4—53no—
574C4×D4—53no—
575C4×D4—53no—
576C4×D4—53no—
577C4×D4C2×C3×D513yescomplemented
578C2×C4⋊C4—53no—
579C2×C4⋊C4—53no—
580C2×C22⋊C4—51no—
581C2×C22⋊C4—53no—
582C2×C22⋊C4—56no—
583C2×C42—53no—
584C2×C3×C5—22no—
585C2×C3×C5—43no—
586C2×C3×C5C23×D411yescharacteristic
587C2×C3×C5C22×#4111yescharacteristic
588C2×C3×C5C2×2−1+411yescharacteristic
589C3×D5—22no—
590C3×D5—43no—
591C3×D5#54814yesdirect product factor
592C23×C3—51no—
593C23×C3—54no—
594C23×C3—51no—
595C23×C3—53no—
596C23×C3—102no—
597C23×C3—102no—
598C23×C3—106no—
599C23×C3—106no—
600C23×C3—106no—
601C23×C3C23×D513yes—
602C23×C3C23×D511yescharacteristic
603C3×Q8—26no—
604C3×Q8—512no—
605C3×Q8—1012no—
606C3×Q8—106no—
607C3×Q8D4×D514yescomplemented
608C3×D4—26no—
609C3×D4—26no—
610C3×D4—106no—
611C3×D4—1012no—
612C3×D4—106no—
613C3×D4—106no—
614C3×D4—106no—
615C2×C3×C4—26no—
616C2×C3×C4—26no—
617C2×C3×C4—53no—
618C2×C3×C4—512no—
619C2×C3×C4—51no—
620C2×C3×C4—53no—
621C2×C3×C4—53no—
622C2×C3×C4—51no—
623C2×C3×C4—106no—
624C2×C3×C4—106no—
625C2×C3×C4—102no—
626C2×C3×C4—102no—
627C2×C3×C4—106no—
628C2×C3×C4—106no—
629C2×C3×C4—106no—
630C2×C3×C4—106no—
631C2×C3×C4—106no—
632C2×C3×C4—106no—
633C2×C3×C4C23×D511yescharacteristic
634C2×C3×C4C23×D513yes—
635C2×C3×C4C23×D513yes—
636C2×C3×C4C23×D511yescharacteristic
637C2×C3×C4C23×D513yes—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—23no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5C2×C3×#4112yescomplemented
644C22×C5C25×C311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—28no—
648C2×D5—23no—
649C2×D5—23no—
650C2×D5—23no—
651C2×D5—412no—
652C2×D5C22×C3×D412yes—
653C2×D5C2×C3×#4112yes—
654C2×D5C2×C3×#4112yescomplemented
655C2×D5C3×2−1+412yes—
656C4×C5—23no—
657C4×C5—21no—
658C4×C5—23no—
659C4×C5—21no—
660C4×C5C22×C3×D416yes—
661Dic5—23no—
662Dic5—21no—
663Dic5—23no—
664Dic5—21no—
665Dic5C22×C3×D416yes—
666C24—51no—
667C24—53no—
668#41—24no—
669#41—1012no—
670#41—1012no—
671#41—104no—
672C2×Q8—24no—
673C2×Q8—58no—
674C2×Q8—53no—
675C2×Q8—56no—
676C2×Q8—53no—
677C2×Q8—1012no—
678C2×Q8—1012no—
679C2×Q8—1012no—
680C2×Q8—104no—
681C2×Q8C22×C3×D513yes—
682C2×Q8C22×C3×D511yescharacteristic
683C2×D4—53no—
684C2×D4—53no—
685C2×D4—56no—
686C2×D4—53no—
687C2×D4—53no—
688C2×D4—1012no—
689C2×D4—1012no—
690C2×D4C22×C3×D513yes—
691C2×D4C22×C3×D513yes—
692C22×C4—53no—
693C22×C4—53no—
694C22×C4—53no—
695C22×C4—51no—
696C22×C4—53no—
697C22×C4—53no—
698C22×C4—51no—
699C22×C4—53no—
700C22×C4—53no—
701C22×C4—53no—
702C22×C4—53no—
703C22×C4—1012no—
704C22×C4—1012no—
705C22×C4C22×C3×D513yes—
706C22×C4C22×C3×D513yes—
707C4⋊C4—53no—
708C4⋊C4—53no—
709C4⋊C4—53no—
710C4⋊C4—56no—
711C4⋊C4—53no—
712C4⋊C4C22×C3×D513yes—
713C4⋊C4C22×C3×D513yes—
714C22⋊C4—51no—
715C22⋊C4—53no—
716C22⋊C4—56no—
717C22⋊C4—51no—
718C22⋊C4—51no—
719C22⋊C4—53no—
720C22⋊C4—53no—
721C22⋊C4—56no—
722C22⋊C4—56no—
723C22⋊C4C22×C3×D511yescharacteristic
724C22⋊C4C22×C3×D513yes—
725C22⋊C4C22×C3×D516yes—
726C42—53no—
727C42—53no—
728C42—53no—
729C42C22×C3×D513yes—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—23no—
734C22×C3—23no—
735C22×C3—23no—
736C22×C3—52no—
737C22×C3—52no—
738C22×C3—52no—
739C22×C3—52no—
740C22×C3—108no—
741C22×C3—101no—
742C22×C3—101no—
743C22×C3—103no—
744C22×C3—103no—
745C22×C3—103no—
746C22×C3—2012no—
747C22×C3D5×#4112yescomplemented
748C22×C3C24×D511yescharacteristic
749C3×C4—21no—
750C3×C4—23no—
751C3×C4—23no—
752C3×C4—21no—
753C3×C4—56no—
754C3×C4—101no—
755C3×C4—103no—
756C3×C4—103no—
757C3×C4—101no—
758C3×C4C2×D4×D516yes—
759C2×C5—22no—
760C2×C5—43no—
761C2×C5C23×C3×D411yescharacteristic
762C2×C5C22×C3×#4111yescharacteristic
763C2×C5C2×C3×2−1+411yescharacteristic
764D5—22no—
765D5—43no—
766D5C3×#54814yesdirect product factor
767C23—51no—
768C23—54no—
769C23—51no—
770C23—53no—
771C23—102no—
772C23—102no—
773C23—106no—
774C23—106no—
775C23—106no—
776C23C23×C3×D513yes—
777C23C23×C3×D511yescharacteristic
778Q8—26no—
779Q8—512no—
780Q8—1012no—
781Q8—106no—
782Q8C3×D4×D514yescomplemented
783D4—26no—
784D4—26no—
785D4—106no—
786D4—1012no—
787D4—106no—
788D4—106no—
789D4—106no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—53no—
793C2×C4—512no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—53no—
797C2×C4—51no—
798C2×C4—106no—
799C2×C4—106no—
800C2×C4—102no—
801C2×C4—106no—
802C2×C4—106no—
803C2×C4—102no—
804C2×C4—106no—
805C2×C4—106no—
806C2×C4—106no—
807C2×C4—106no—
808C2×C4C23×C3×D511yescharacteristic
809C2×C4C23×C3×D513yes—
810C2×C4C23×C3×D513yes—
811C2×C4C23×C3×D511yescharacteristic
812C2×C4C23×C3×D513yes—
813C2×C3—22no—
814C2×C3—43no—
815C2×C3—54no—
816C2×C3—102no—
817C2×C3—203no—
818C2×C3C22×D4×D511yescharacteristic
819C2×C3C2×D5×#4111yescharacteristic
820C2×C3D5×2−1+411yescharacteristic
821C5C2×C3×#54811yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—52no—
828C22—52no—
829C22—52no—
830C22—52no—
831C22—108no—
832C22—101no—
833C22—101no—
834C22—103no—
835C22—103no—
836C22—103no—
837C22—2012no—
838C22C3×D5×#4112yescomplemented
839C22C24×C3×D511yescharacteristic
840C4—21no—
841C4—23no—
842C4—23no—
843C4—21no—
844C4—56no—
845C4—101no—
846C4—103no—
847C4—103no—
848C4—101no—
849C4C2×C3×D4×D516yes—
850C3D5×#54811yescharacteristic, direct product factor, Sylow
851C2—22no—
852C2—43no—
853C2—54no—
854C2—102no—
855C2—203no—
856C2C22×C3×D4×D511yescharacteristic
857C2C2×C3×D5×#4111yescharacteristic
858C2C3×D5×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC3×#548D5
hypocenterC5C2×C3×#548
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×#41C2semidirect
2. C22×C3×Q8×D5C2semidirect
3. C3×C5×#548C2semidirect
4. C3×#66165C2semidirect
5. C3×#66151C2semidirect
6. C3×#66011C2semidirect
7. C3×D5×#124C2semidirect
8. C3×#65967C2semidirect
9. C3×D5×C22⋊Q8C2semidirect
10. C3×D5×#121C2semidirect
11. C3×#65932C2semidirect
12. C3×#65910C2semidirect
13. C3×C4×Q8×D5C2semidirect
14. C3×#65886C2semidirect
15. C3×C4×D4×D5C2semidirect
16. D5×#548C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
20. C2×C3×#713C22semidirect
24. C2×C3×Q8×D5C22semidirect
25. C2×C3×Q8×D5C22semidirect
26. C2×C3×#711C22semidirect
29. C2×C3×#709C22semidirect
32. C22×C3×Dic10C22semidirect
33. C3×C5×#124C22semidirect
34. C3×C5×C22⋊Q8C22semidirect
35. C3×C5×#121C22semidirect
36. C3×C4×C5×Q8C22semidirect
37. C3×C4×C5×D4C22semidirect
38. C3×#4093C22semidirect
39. C3×#4092C22semidirect
40. C3×Q8×Dic5C22semidirect
41. C3×#4085C22semidirect
42. C3×#4084C22semidirect
43. C3×#4082C22semidirect
44. C3×D4×Dic5C22semidirect
45. C3×#4076C22semidirect
46. C3×C4×C22⋊D5C22semidirect
47. C3×C4×C22⋊D5C22semidirect
48. C3×#4070C22semidirect
49. C3×#4043C22semidirect
50. C3×#4042C22semidirect
51. C3×#4041C22semidirect
52. C3×#4039C22semidirect
55. C3×#4033C22semidirect
56. C3×#4031C22semidirect
57. C3×#4031C22semidirect
58. C3×#4030C22semidirect
59. C3×#4027C22semidirect
60. C3×#4027C22semidirect
64. C3×#4024C22semidirect
65. C3×#4021C22semidirect
66. C3×C4×D20C22semidirect
68. C3×C4×Dic10C22semidirect
70. C2×D5×#41C2×C3semidirect
71. C22×Q8×D5C2×C3semidirect
72. C5×#548C2×C3semidirect
73. #66165C2×C3semidirect
74. #66151C2×C3semidirect
75. #66011C2×C3semidirect
76. D5×#124C2×C3semidirect
77. #65967C2×C3semidirect
78. D5×C22⋊Q8C2×C3semidirect
79. D5×#121C2×C3semidirect
80. #65932C2×C3semidirect
81. #65910C2×C3semidirect
82. C4×Q8×D5C2×C3semidirect
83. #65886C2×C3semidirect
84. C4×D4×D5C2×C3semidirect
104. C3×Q8×D5D4semidirect
158. C3×#548D5direct (N × H)
164. C2×C5×#41C22×C3semidirect
165. C22×C5×Q8C22×C3semidirect
167. C2×#713C22×C3semidirect
171. C2×Q8×D5C22×C3semidirect
172. C2×Q8×D5C22×C3semidirect
173. C2×#711C22×C3semidirect
176. C2×#709C22×C3semidirect
179. C22×Dic10C22×C3semidirect
180. C5×#124C22×C3semidirect
181. C5×C22⋊Q8C22×C3semidirect
182. C5×#121C22×C3semidirect
183. C4×C5×Q8C22×C3semidirect
184. C4×C5×D4C22×C3semidirect
185. #4093C22×C3semidirect
186. #4092C22×C3semidirect
187. Q8×Dic5C22×C3semidirect
188. #4085C22×C3semidirect
189. #4084C22×C3semidirect
190. #4082C22×C3semidirect
191. D4×Dic5C22×C3semidirect
192. #4076C22×C3semidirect
193. C4×C22⋊D5C22×C3semidirect
194. C4×C22⋊D5C22×C3semidirect
195. #4070C22×C3semidirect
196. #4043C22×C3semidirect
197. #4042C22×C3semidirect
198. #4041C22×C3semidirect
199. #4039C22×C3semidirect
202. #4033C22×C3semidirect
203. #4031C22×C3semidirect
204. #4031C22×C3semidirect
205. #4030C22×C3semidirect
206. #4027C22×C3semidirect
207. #4027C22×C3semidirect
211. #4024C22×C3semidirect
212. #4021C22×C3semidirect
213. C4×D20C22×C3semidirect
215. C4×Dic10C22×C3semidirect
224. C22×C3×D5#41semidirect
229. C3×C5×Q8C2×D4semidirect
262. C3×Dic10C2×D4semidirect
267. C2×C3×#41C2×D5semidirect
274. C22×C3×Q8C2×D5semidirect
284. C3×#124C2×D5semidirect
290. C3×C22⋊Q8C2×D5semidirect
296. C3×#121C2×D5semidirect
300. C3×C4×Q8C2×D5semidirect
308. C3×C4×D4C2×D5semidirect
334. Q8×D5C3×D4semidirect
388. #548C3×D5direct (N × H)
399. C22×C3×C5C2×#41semidirect
410. C2×C3×D5C2×#41semidirect
493. C22×D5C3×#41semidirect
498. C5×Q8C2×C3×D4semidirect
531. Dic10C2×C3×D4semidirect
536. C2×#41C2×C3×D5semidirect
543. C22×Q8C2×C3×D5semidirect
553. #124C2×C3×D5semidirect
559. C22⋊Q8C2×C3×D5semidirect
565. #121C2×C3×D5semidirect
569. C4×Q8C2×C3×D5semidirect
577. C4×D4C2×C3×D5semidirect
591. C3×D5#548direct (N × H)
607. C3×Q8D4×D5semidirect
643. C22×C5C2×C3×#41semidirect
654. C2×D5C2×C3×#41semidirect
730. C3×C5C2×#548semidirect
747. C22×C3D5×#41semidirect
766. D5C3×#548direct (N × H)
782. Q8C3×D4×D5semidirect
821. C5C2×C3×#548semidirect
838. C22C3×D5×#41semidirect
850. C3D5×#548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C22×C3×Q8×D52
C3×C5×#5482
C3×#661652
C3×#661512
C3×#660112
C3×D5×#1242
C3×#659672
C3×D5×C22⋊Q82
C3×D5×#1212
C3×#659322
C3×#659102
C3×C4×Q8×D52
C3×#658862
C3×C4×D4×D52
D5×#5483
C2×C3×#5485