Finite Group Databasebeta

← C3×#41×C22⋊D5 #14483040

Subgroups — C3×#41×C22⋊D5 #14483040

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C2×C3×D5×#41C211yesmaximal, characteristic, complemented
3C3×#66168C211yesmaximal, characteristic, complemented
4C3×#66166C213yesmaximal, complemented
5C3×#66165C211yesmaximal, characteristic, complemented
6C3×#66163C213yesmaximal, complemented
7C3×#66162C213yesmaximal, complemented
8C3×#41×Dic5C211yesmaximal, characteristic, complemented
9C3×#66158C213yesmaximal, complemented
10C3×#66151C211yesmaximal, characteristic, complemented
11C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
12C3×#66140C213yesmaximal, complemented
13C3×D4×C22⋊D5C213yesmaximal, complemented
14C3×#66125C213yesmaximal, complemented
15C2×C3×C4×C22⋊D5C213yesmaximal, complemented
16#41×C22⋊D5C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41—28no—
18C2×C3×C5×#41C2211yescharacteristic
19C2×C3×C5×#41C2213yescomplemented
20C2×C3×C5×#41C2213yescomplemented
21C2×C3×C5×#41C2211yescharacteristic, complemented
22C22×C3×C5×Q8C2211yescharacteristic, complemented
23C22×C3×C5×D4C2213yescomplemented
24C23×C3×C4×C5C2213yescomplemented
25C22×C3×C22⋊D5C2213yes—
26C3×D5×#41—28no—
27C2×C3×#713C2211yescharacteristic, complemented
28C2×C3×Q8×D5C2211yescharacteristic, complemented
29C2×C3×#711C2213yescomplemented
30C2×C3×D4×D5C2213yescomplemented
31C2×C3×#709C2213yescomplemented
32C22×C3×C4×D5C2213yescomplemented
33C3×#4099C2216yescomplemented
34C2×C3×C22⋊Dic5C2213yescomplemented
35C3×#4093C2213yescomplemented
36C3×#4092C2213yescomplemented
37C3×#4092C2213yescomplemented
38C3×Q8×Dic5C2211yescharacteristic, complemented
39C3×Q8×Dic5C2211yescharacteristic, complemented
40C3×#4090C2213yescomplemented
41C3×#4086C2213yescomplemented
42C3×#4085C2216yescomplemented
43C3×#4085C2216yescomplemented
44C3×#4084C2213yescomplemented
45C3×#4084C2213yescomplemented
46C3×#4083C2216yescomplemented
47C3×#4082C2213yescomplemented
48C3×#4081C2216yescomplemented
49C3×D4×Dic5C2213yescomplemented
50C3×D4×Dic5C2213yescomplemented
51C3×#4076C2213yescomplemented
52C3×#4076C2213yescomplemented
53C3×#4075C2216yescomplemented
54C3×C4×C22⋊D5C2211yescharacteristic
55C3×C4×C22⋊D5C2213yes—
56C3×C4×C22⋊D5C2213yescomplemented
57C3×C4×C22⋊D5C2213yescomplemented
58C3×C4×C22⋊D5C2213yescomplemented
59C3×C4×C22⋊D5C2213yescomplemented
60C3×C4×C22⋊D5C2213yescomplemented
61C3×C4×C22⋊D5C2213yescomplemented
62C3×C4×C22⋊D5C2216yescomplemented
63C2×C3×#685C2213yescomplemented
64C3×#4072C2213yescomplemented
65C3×#4070C2213yescomplemented
66C3×#4070C2213yescomplemented
67C2×C3×#683C2213yescomplemented
68C2×C3×C4×Dic5C2213yescomplemented
69C3×D4×#41—51nomaximal, Hall
70C22×C5×#41C2×C311yescharacteristic, complemented
71C2×D5×#41C2×C311yescharacteristic, complemented
72#66168C2×C311yescharacteristic, complemented
73#66166C2×C313yescomplemented
74#66165C2×C311yescharacteristic, complemented
75#66163C2×C313yescomplemented
76#66162C2×C313yescomplemented
77#41×Dic5C2×C311yescharacteristic, complemented
78#66158C2×C313yescomplemented
79#66151C2×C311yescharacteristic, complemented
80Q8×C22⋊D5C2×C311yescharacteristic, complemented
81#66140C2×C313yescomplemented
82D4×C22⋊D5C2×C313yescomplemented
83#66125C2×C313yescomplemented
84C2×C4×C22⋊D5C2×C313yescomplemented
85C24×C3×C5C2313yes—
86C23×C3×D5C2313yes—
87C3×C5×#41—24no—
88C3×C5×#41—212no—
89C3×C5×#41—212no—
90C3×C5×#41D418yescomplemented
91C2×C3×C5×Q8—24no—
92C2×C3×C5×Q8C2313yes—
93C2×C3×C5×Q8C2311yescharacteristic
94C2×C3×C5×D4—212no—
95C2×C3×C5×D4C2316yes—
96C2×C3×C5×D4C2313yes—
97C2×C3×C5×D4C2313yes—
98C22×C3×C4×C5—212no—
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2313yes—
101C22×C3×C4×C5C2313yes—
102C22×C3×C4×C5C2313yes—
103C22×C3×C4×C5C2313yes—
104C22×C3×C4×C5C2313yes—
105C2×C3×C22⋊D5—212no—
106C2×C3×C22⋊D5C2313yes—
107C2×C3×C22⋊D5C2313yes—
108C2×C3×C22⋊D5C2316yes—
109C2×C3×C22⋊D5C2313yes—
110C2×C3×C22⋊D5C2316yes—
111C2×C3×C22⋊D5C2311yescharacteristic
112C22×C3×Dic5C2313yes—
113C22×C3×Dic5C2313yes—
114C22×C3×Dic5C2313yes—
115C3×#713—24no—
116C3×Q8×D5—24no—
117C3×#711—212no—
118C3×D4×D5—212no—
119C3×#709—212no—
120C2×C3×D20C2313yes—
121C2×C3×C4×D5—212no—
122C2×C3×C4×D5C2313yes—
123C2×C3×C4×D5C2313yes—
124C2×C3×C4×D5C2311yescharacteristic
125C2×C3×C4×D5C2313yes—
126C2×C3×Dic10C2313yes—
127C3×C22⋊Dic5C2316yes—
128C3×C22⋊Dic5C2313yes—
129C3×C22⋊Dic5C2316yes—
130C3×C22⋊Dic5C2313yes—
131C3×C22⋊Dic5C2311yescharacteristic
132C3×C22⋊Dic5C2313yes—
133C3×#685C2313yes—
134C3×#685C2316yes—
135C3×#685C2313yes—
136C3×#685C2311yescharacteristic
137C3×#685C2313yes—
138C3×C4⋊Dic5C2313yes—
139C3×C4⋊Dic5C2313yes—
140C3×#683C2313yes—
141C3×#683C2316yes—
142C3×#683C2313yes—
143C3×#683C2311yescharacteristic
144C3×#683C2313yes—
145C3×C4×Dic5C2313yes—
146C3×C4×Dic5C2313yes—
147C3×C4×Dic5C2311yescharacteristic
148C3×C4×Dic5C2313yes—
149C22×C3×#41—51no—
150C22×C3×#41D511yescharacteristic, complemented
151C3×#550—51no—
152C3×D4×Q8—51no—
153C3×#548—51no—
154C3×#548—51no—
155C3×#547—53no—
156C3×#546—53no—
157C3×#546—53no—
158C3×D42—53no—
159C3×#532—53no—
160C3×#525—53no—
161C3×#525—53no—
162C3×C4×#41—51no—
163C2×C3×C4×D4—53no—
164C2×C5×#41—28no—
165C2×C5×#41C22×C311yescharacteristic
166C2×C5×#41C22×C313yescomplemented
167C2×C5×#41C22×C313yescomplemented
168C2×C5×#41C22×C311yescharacteristic, complemented
169C22×C5×Q8C22×C311yescharacteristic, complemented
170C22×C5×D4C22×C313yescomplemented
171C23×C4×C5C22×C313yescomplemented
172C22×C22⋊D5C22×C313yes—
173D5×#41—28no—
174C2×#713C22×C311yescharacteristic, complemented
175C2×Q8×D5C22×C311yescharacteristic, complemented
176C2×#711C22×C313yescomplemented
177C2×D4×D5C22×C313yescomplemented
178C2×#709C22×C313yescomplemented
179C22×C4×D5C22×C313yescomplemented
180#4099C22×C316yescomplemented
181C2×C22⋊Dic5C22×C313yescomplemented
182#4093C22×C313yescomplemented
183#4092C22×C313yescomplemented
184#4092C22×C313yescomplemented
185Q8×Dic5C22×C311yescharacteristic, complemented
186Q8×Dic5C22×C311yescharacteristic, complemented
187#4090C22×C313yescomplemented
188#4086C22×C313yescomplemented
189#4085C22×C316yescomplemented
190#4085C22×C316yescomplemented
191#4084C22×C313yescomplemented
192#4084C22×C313yescomplemented
193#4083C22×C316yescomplemented
194#4082C22×C313yescomplemented
195#4081C22×C316yescomplemented
196D4×Dic5C22×C313yescomplemented
197D4×Dic5C22×C313yescomplemented
198#4076C22×C313yescomplemented
199#4076C22×C313yescomplemented
200#4075C22×C316yescomplemented
201C4×C22⋊D5C22×C311yescharacteristic
202C4×C22⋊D5C22×C313yes—
203C4×C22⋊D5C22×C313yescomplemented
204C4×C22⋊D5C22×C313yescomplemented
205C4×C22⋊D5C22×C313yescomplemented
206C4×C22⋊D5C22×C313yescomplemented
207C4×C22⋊D5C22×C313yescomplemented
208C4×C22⋊D5C22×C313yescomplemented
209C4×C22⋊D5C22×C316yescomplemented
210C2×#685C22×C313yescomplemented
211#4072C22×C313yescomplemented
212#4070C22×C313yescomplemented
213#4070C22×C313yescomplemented
214C2×#683C22×C313yescomplemented
215C2×C4×Dic5C22×C313yescomplemented
216D4×#41—51noSylow
217C23×C3×C5—26no—
218C23×C3×C5—26no—
219C23×C3×C5—43no—
220C23×C3×C5C2413yes—
221C23×C3×C5C2413yes—
222C23×C3×C5C2411yescharacteristic
223C22×C3×D5—26no—
224C22×C3×D5—26no—
225C22×C3×D5—43no—
226C22×C3×D5C2413yes—
227C22×C3×D5C2411yescharacteristic
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—212no—
231C3×C5×D4—26no—
232C3×C5×D4C2×D4112yescomplemented
233C2×C3×C4×C5—26no—
234C2×C3×C4×C5—22no—
235C2×C3×C4×C5—26no—
236C2×C3×C4×C5—26no—
237C2×C3×C4×C5—26no—
238C2×C3×C4×C5C2×D4112yescomplemented
239C2×C3×C4×C5C2411yescharacteristic
240C2×C3×C4×C5C2413yes—
241C2×C3×C4×C5C2413yes—
242C2×C3×C4×C5C2411yescharacteristic
243C3×C22⋊D5—212no—
244C3×C22⋊D5—26no—
245C3×C22⋊D5—26no—
246C3×C22⋊D5—26no—
247C3×C22⋊D5—46no—
248C3×C22⋊D5#4114yesdirect product factor
249C2×C3×Dic5—26no—
250C2×C3×Dic5—26no—
251C2×C3×Dic5—43no—
252C2×C3×Dic5C2411yescharacteristic
253C2×C3×Dic5C2413yes—
254C2×C3×Dic5C2413yes—
255C2×C3×Dic5C2413yes—
256C2×C3×Dic5C2411yescharacteristic
257C2×C3×Dic5C2411yescharacteristic
258C3×D20—26no—
259C3×C4×D5—22no—
260C3×C4×D5—26no—
261C3×C4×D5—26no—
262C3×C4×D5—26no—
263C3×Dic10—26no—
264C2×C3×#41—28no—
265C2×C3×#41—51no—
266C2×C3×#41—53no—
267C2×C3×#41—53no—
268C2×C3×#41—108no—
269C2×C3×#41C2×D511yescharacteristic
270C2×C3×#41C2×D513yescomplemented
271C2×C3×#41C2×D513yescomplemented
272C2×C3×#41C2×D511yescharacteristic, complemented
273C22×C3×Q8—51no—
274C22×C3×Q8C2×D511yescharacteristic, complemented
275C22×C3×D4—53no—
276C22×C3×D4—53no—
277C22×C3×D4C2×D513yescomplemented
278C23×C3×C4—53no—
279C23×C3×C4C2×D513yescomplemented
280C3×C4⋊Q8—53no—
281C3×#127—53no—
282C3×#124—53no—
283C3×#124—53no—
284C3×#123—56no—
285C3×#123—56no—
286C3×C22⋊Q8—53no—
287C3×C22⋊Q8—53no—
288C3×C22⋊Q8—53no—
289C3×C22⋊Q8—53no—
290C3×#121—53no—
291C3×#121—53no—
292C3×#121—56no—
293C3×#121—56no—
294C3×#121—53no—
295C3×#121—53no—
296C3×#120—56no—
297C3×#120—56no—
298C3×C4×Q8—51no—
299C3×C4×Q8—51no—
300C3×C4×D4—53no—
301C3×C4×D4—53no—
302C3×C4×D4—51no—
303C3×C4×D4—53no—
304C3×C4×D4—53no—
305C3×C4×D4—53no—
306C3×C4×D4—53no—
307C3×C4×D4—53no—
308C3×C4×D4—53no—
309C3×C4×D4—53no—
310C3×C4×D4—56no—
311C3×#117—53no—
312C2×C3×C4⋊C4—53no—
313C2×C3×C22⋊C4—53no—
314C2×C3×C22⋊C4—53no—
315C2×C3×C42—53no—
316C24×C5C23×C313yes—
317C23×D5C23×C313yes—
318C5×#41—24no—
319C5×#41—212no—
320C5×#41—212no—
321C5×#41C3×D418yescomplemented
322C2×C5×Q8—24no—
323C2×C5×Q8C23×C313yes—
324C2×C5×Q8C23×C311yescharacteristic
325C2×C5×D4—212no—
326C2×C5×D4C23×C316yes—
327C2×C5×D4C23×C313yes—
328C2×C5×D4C23×C313yes—
329C22×C4×C5—212no—
330C22×C4×C5C23×C311yescharacteristic
331C22×C4×C5C23×C313yes—
332C22×C4×C5C23×C313yes—
333C22×C4×C5C23×C313yes—
334C22×C4×C5C23×C313yes—
335C22×C4×C5C23×C313yes—
336C2×C22⋊D5—212no—
337C2×C22⋊D5C23×C313yes—
338C2×C22⋊D5C23×C316yes—
339C2×C22⋊D5C23×C313yes—
340C2×C22⋊D5C23×C313yes—
341C2×C22⋊D5C23×C316yes—
342C2×C22⋊D5C23×C311yescharacteristic
343C22×Dic5C23×C313yes—
344C22×Dic5C23×C313yes—
345C22×Dic5C23×C313yes—
346#713—24no—
347Q8×D5—24no—
348#711—212no—
349D4×D5—212no—
350#709—212no—
351C2×D20C23×C313yes—
352C2×C4×D5—212no—
353C2×C4×D5C23×C311yescharacteristic
354C2×C4×D5C23×C313yes—
355C2×C4×D5C23×C313yes—
356C2×C4×D5C23×C313yes—
357C2×Dic10C23×C313yes—
358C22⋊Dic5C23×C311yescharacteristic
359C22⋊Dic5C23×C313yes—
360C22⋊Dic5C23×C313yes—
361C22⋊Dic5C23×C313yes—
362C22⋊Dic5C23×C316yes—
363C22⋊Dic5C23×C316yes—
364#685C23×C311yescharacteristic
365#685C23×C313yes—
366#685C23×C313yes—
367#685C23×C313yes—
368#685C23×C316yes—
369C4⋊Dic5C23×C313yes—
370C4⋊Dic5C23×C313yes—
371#683C23×C311yescharacteristic
372#683C23×C313yes—
373#683C23×C313yes—
374#683C23×C313yes—
375#683C23×C316yes—
376C4×Dic5C23×C311yescharacteristic
377C4×Dic5C23×C313yes—
378C4×Dic5C23×C313yes—
379C4×Dic5C23×C313yes—
380C22×#41—51no—
381C22×#41C3×D511yescharacteristic, complemented
382#550—51no—
383D4×Q8—51no—
384#548—51no—
385#548—51no—
386#547—53no—
387#546—53no—
388#546—53no—
389D42—53no—
390#532—53no—
391#525—53no—
392#525—53no—
393C4×#41—51no—
394C2×C4×D4—53no—
395C22×C3×C5—21no—
396C22×C3×C5—23no—
397C22×C3×C5—23no—
398C22×C3×C5—21no—
399C22×C3×C5—23no—
400C22×C3×C5—23no—
401C22×C3×C5—23no—
402C22×C3×C5—412no—
403C22×C3×C5C22×D416yes—
404C22×C3×C5C2×#4112yescomplemented
405C22×C3×C5C2511yescharacteristic
406C2×C3×D5—21no—
407C2×C3×D5—21no—
408C2×C3×D5—23no—
409C2×C3×D5—23no—
410C2×C3×D5—23no—
411C2×C3×D5—412no—
412C2×C3×D5C2×#4112yescomplemented
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5C22×D416yes—
416C3×C4×C5C22×D412yes—
417C3×Dic5—23no—
418C3×Dic5—21no—
419C3×Dic5—23no—
420C3×Dic5—21no—
421C3×Dic5—23no—
422C3×Dic5C2×#4112yescomplemented
423C24×C3—53no—
424C24×C3C22×D513yes—
425C3×#41—24no—
426C3×#41—212no—
427C3×#41—212no—
428C3×#41—104no—
429C3×#41—1012no—
430C3×#41—1012no—
431C3×#41C22⋊D518yesdirect product factor
432C2×C3×Q8—24no—
433C2×C3×Q8—53no—
434C2×C3×Q8—104no—
435C2×C3×Q8C22×D513yes—
436C2×C3×Q8C22×D511yescharacteristic
437C2×C3×D4—212no—
438C2×C3×D4—51no—
439C2×C3×D4—53no—
440C2×C3×D4—53no—
441C2×C3×D4—53no—
442C2×C3×D4—56no—
443C2×C3×D4—56no—
444C2×C3×D4—53no—
445C2×C3×D4—1012no—
446C2×C3×D4—1012no—
447C2×C3×D4C22×D516yes—
448C2×C3×D4C22×D513yes—
449C2×C3×D4C22×D513yes—
450C22×C3×C4—212no—
451C22×C3×C4—53no—
452C22×C3×C4—53no—
453C22×C3×C4—53no—
454C22×C3×C4—53no—
455C22×C3×C4—53no—
456C22×C3×C4—51no—
457C22×C3×C4—53no—
458C22×C3×C4—1012no—
459C22×C3×C4C22×D513yes—
460C22×C3×C4C22×D513yes—
461C22×C3×C4C22×D513yes—
462C22×C3×C4C22×D511yescharacteristic
463C22×C3×C4C22×D513yes—
464C22×C3×C4C22×D513yes—
465C3×C4⋊C4—51no—
466C3×C4⋊C4—53no—
467C3×C4⋊C4—53no—
468C3×C4⋊C4—53no—
469C3×C4⋊C4—56no—
470C3×C4⋊C4—53no—
471C3×C4⋊C4—53no—
472C3×C22⋊C4—51no—
473C3×C22⋊C4—53no—
474C3×C22⋊C4—53no—
475C3×C22⋊C4—53no—
476C3×C22⋊C4—56no—
477C3×C22⋊C4—56no—
478C3×C22⋊C4—51no—
479C3×C22⋊C4—53no—
480C3×C22⋊C4—53no—
481C3×C22⋊C4—53no—
482C3×C22⋊C4—56no—
483C3×C42—53no—
484C3×C42—53no—
485C3×C42—51no—
486C3×C42—53no—
487C23×C5—26no—
488C23×C5—26no—
489C23×C5—43no—
490C23×C5C24×C313yes—
491C23×C5C24×C313yes—
492C23×C5C24×C311yescharacteristic
493C22×D5—26no—
494C22×D5—26no—
495C22×D5—43no—
496C22×D5C24×C313yes—
497C22×D5C24×C311yescharacteristic
498C5×Q8—26no—
499C5×Q8C2×C3×D414yescomplemented
500C5×D4—212no—
501C5×D4—26no—
502C5×D4C2×C3×D4112yescomplemented
503C2×C4×C5—26no—
504C2×C4×C5—22no—
505C2×C4×C5—26no—
506C2×C4×C5—26no—
507C2×C4×C5—26no—
508C2×C4×C5C2×C3×D4112yescomplemented
509C2×C4×C5C24×C311yescharacteristic
510C2×C4×C5C24×C313yes—
511C2×C4×C5C24×C311yescharacteristic
512C2×C4×C5C24×C313yes—
513C22⋊D5—212no—
514C22⋊D5—26no—
515C22⋊D5—26no—
516C22⋊D5—26no—
517C22⋊D5—46no—
518C22⋊D5C3×#4114yesdirect product factor
519C2×Dic5—26no—
520C2×Dic5—26no—
521C2×Dic5—43no—
522C2×Dic5C24×C311yescharacteristic
523C2×Dic5C24×C313yes—
524C2×Dic5C24×C313yes—
525C2×Dic5C24×C313yes—
526C2×Dic5C24×C311yescharacteristic
527C2×Dic5C24×C311yescharacteristic
528D20—26no—
529C4×D5—22no—
530C4×D5—26no—
531C4×D5—26no—
532C4×D5—26no—
533Dic10—26no—
534C2×#41—28no—
535C2×#41—51no—
536C2×#41—53no—
537C2×#41—53no—
538C2×#41—108no—
539C2×#41C2×C3×D511yescharacteristic
540C2×#41C2×C3×D513yescomplemented
541C2×#41C2×C3×D513yescomplemented
542C2×#41C2×C3×D511yescharacteristic, complemented
543C22×Q8—51no—
544C22×Q8C2×C3×D511yescharacteristic, complemented
545C22×D4—53no—
546C22×D4—53no—
547C22×D4C2×C3×D513yescomplemented
548C23×C4—53no—
549C23×C4C2×C3×D513yescomplemented
550C4⋊Q8—53no—
551#127—53no—
552#124—53no—
553#124—53no—
554#123—56no—
555#123—56no—
556C22⋊Q8—53no—
557C22⋊Q8—53no—
558C22⋊Q8—53no—
559C22⋊Q8—53no—
560#121—53no—
561#121—53no—
562#121—56no—
563#121—56no—
564#121—53no—
565#121—53no—
566#120—56no—
567#120—56no—
568C4×Q8—51no—
569C4×Q8—51no—
570C4×D4—53no—
571C4×D4—53no—
572C4×D4—51no—
573C4×D4—53no—
574C4×D4—53no—
575C4×D4—53no—
576C4×D4—53no—
577C4×D4—53no—
578C4×D4—53no—
579C4×D4—53no—
580C4×D4—56no—
581#117—53no—
582C2×C4⋊C4—53no—
583C2×C22⋊C4—53no—
584C2×C22⋊C4—53no—
585C2×C42—53no—
586C2×C3×C5—26no—
587C2×C3×C5—22no—
588C2×C3×C5—43no—
589C2×C3×C5C23×D411yescharacteristic
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5#58511yescharacteristic
592C3×D5—22no—
593C3×D5—43no—
594C23×C3—26no—
595C23×C3—26no—
596C23×C3—43no—
597C23×C3—51no—
598C23×C3—53no—
599C23×C3—106no—
600C23×C3—106no—
601C23×C3—203no—
602C23×C3C23×D513yes—
603C23×C3C23×D511yescharacteristic
604C23×C3C23×D513yes—
605C3×Q8—26no—
606C3×Q8—106no—
607C3×Q8C2×C22⋊D514yescomplemented
608C3×D4—212no—
609C3×D4—26no—
610C3×D4—54no—
611C3×D4—106no—
612C3×D4—106no—
613C3×D4—106no—
614C3×D4—1012no—
615C3×D4—106no—
616C3×D4—206no—
617C3×D4C2×C22⋊D5112yescomplemented
618C2×C3×C4—26no—
619C2×C3×C4—22no—
620C2×C3×C4—26no—
621C2×C3×C4—26no—
622C2×C3×C4—26no—
623C2×C3×C4—51no—
624C2×C3×C4—51no—
625C2×C3×C4—53no—
626C2×C3×C4—53no—
627C2×C3×C4—51no—
628C2×C3×C4—53no—
629C2×C3×C4—106no—
630C2×C3×C4—106no—
631C2×C3×C4—102no—
632C2×C3×C4—106no—
633C2×C3×C4—106no—
634C2×C3×C4—106no—
635C2×C3×C4—203no—
636C2×C3×C4C2×C22⋊D5112yescomplemented
637C2×C3×C4C23×D511yescharacteristic
638C2×C3×C4C23×D513yes—
639C2×C3×C4C23×D513yes—
640C2×C3×C4C23×D511yescharacteristic
641C22×C5—21no—
642C22×C5—23no—
643C22×C5—23no—
644C22×C5—21no—
645C22×C5—23no—
646C22×C5—23no—
647C22×C5—23no—
648C22×C5—412no—
649C22×C5C22×C3×D416yes—
650C22×C5C2×C3×#4112yescomplemented
651C22×C5C25×C311yescharacteristic
652C2×D5—21no—
653C2×D5—21no—
654C2×D5—23no—
655C2×D5—23no—
656C2×D5—23no—
657C2×D5—412no—
658C2×D5C2×C3×#4112yescomplemented
659C4×C5—21no—
660C4×C5—23no—
661C4×C5C22×C3×D416yes—
662C4×C5C22×C3×D412yes—
663Dic5—23no—
664Dic5—21no—
665Dic5—23no—
666Dic5—21no—
667Dic5—23no—
668Dic5C2×C3×#4112yescomplemented
669C24—53no—
670C24C22×C3×D513yes—
671#41—24no—
672#41—212no—
673#41—212no—
674#41—104no—
675#41—1012no—
676#41—1012no—
677#41C3×C22⋊D518yesdirect product factor
678C2×Q8—24no—
679C2×Q8—53no—
680C2×Q8—104no—
681C2×Q8C22×C3×D513yes—
682C2×Q8C22×C3×D511yescharacteristic
683C2×D4—212no—
684C2×D4—51no—
685C2×D4—53no—
686C2×D4—53no—
687C2×D4—53no—
688C2×D4—56no—
689C2×D4—56no—
690C2×D4—53no—
691C2×D4—1012no—
692C2×D4—1012no—
693C2×D4C22×C3×D516yes—
694C2×D4C22×C3×D513yes—
695C2×D4C22×C3×D513yes—
696C22×C4—212no—
697C22×C4—53no—
698C22×C4—53no—
699C22×C4—53no—
700C22×C4—51no—
701C22×C4—53no—
702C22×C4—53no—
703C22×C4—53no—
704C22×C4—1012no—
705C22×C4C22×C3×D513yes—
706C22×C4C22×C3×D511yescharacteristic
707C22×C4C22×C3×D513yes—
708C22×C4C22×C3×D513yes—
709C22×C4C22×C3×D513yes—
710C22×C4C22×C3×D513yes—
711C4⋊C4—51no—
712C4⋊C4—53no—
713C4⋊C4—53no—
714C4⋊C4—53no—
715C4⋊C4—53no—
716C4⋊C4—53no—
717C4⋊C4—56no—
718C22⋊C4—51no—
719C22⋊C4—53no—
720C22⋊C4—53no—
721C22⋊C4—53no—
722C22⋊C4—56no—
723C22⋊C4—56no—
724C22⋊C4—51no—
725C22⋊C4—53no—
726C22⋊C4—53no—
727C22⋊C4—53no—
728C22⋊C4—56no—
729C42—51no—
730C42—53no—
731C42—53no—
732C42—53no—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—23no—
735C22×C3—23no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—23no—
739C22×C3—23no—
740C22×C3—23no—
741C22×C3—412no—
742C22×C3—52no—
743C22×C3—101no—
744C22×C3—101no—
745C22×C3—103no—
746C22×C3—103no—
747C22×C3—103no—
748C22×C3—2012no—
749C22×C3D5×#4112yescomplemented
750C22×C3C22×C22⋊D516yes—
751C22×C3C24×D511yescharacteristic
752C3×C4—21no—
753C3×C4—23no—
754C3×C4—52no—
755C3×C4—103no—
756C3×C4—101no—
757C3×C4—103no—
758C3×C4—101no—
759C3×C4—103no—
760C3×C4C22×C22⋊D512yes—
761C3×C4C22×C22⋊D516yes—
762C2×C5—26no—
763C2×C5—22no—
764C2×C5—43no—
765C2×C5C23×C3×D411yescharacteristic
766C2×C5C22×C3×#4111yescharacteristic
767C2×C5C3×#58511yescharacteristic
768D5—22no—
769D5—43no—
770C23—26no—
771C23—26no—
772C23—43no—
773C23—51no—
774C23—53no—
775C23—106no—
776C23—106no—
777C23—203no—
778C23C23×C3×D513yes—
779C23C23×C3×D511yescharacteristic
780C23C23×C3×D513yes—
781Q8—26no—
782Q8—106no—
783Q8C2×C3×C22⋊D514yescomplemented
784D4—212no—
785D4—26no—
786D4—54no—
787D4—106no—
788D4—106no—
789D4—106no—
790D4—1012no—
791D4—106no—
792D4—206no—
793D4C2×C3×C22⋊D5112yescomplemented
794C2×C4—26no—
795C2×C4—22no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—26no—
799C2×C4—51no—
800C2×C4—51no—
801C2×C4—53no—
802C2×C4—53no—
803C2×C4—51no—
804C2×C4—53no—
805C2×C4—106no—
806C2×C4—106no—
807C2×C4—102no—
808C2×C4—106no—
809C2×C4—106no—
810C2×C4—106no—
811C2×C4—203no—
812C2×C4C2×C3×C22⋊D5112yescomplemented
813C2×C4C23×C3×D511yescharacteristic
814C2×C4C23×C3×D513yes—
815C2×C4C23×C3×D511yescharacteristic
816C2×C4C23×C3×D513yes—
817C2×C3—22no—
818C2×C3—26no—
819C2×C3—43no—
820C2×C3—102no—
821C2×C3—203no—
822C2×C3C2×D5×#4111yescharacteristic
823C2×C3#6628311yescharacteristic
824C2×C3C23×C22⋊D511yescharacteristic
825C5C3×D4×#4111yescharacteristic, complemented, Sylow
826C22—23no—
827C22—23no—
828C22—21no—
829C22—21no—
830C22—23no—
831C22—23no—
832C22—23no—
833C22—412no—
834C22—52no—
835C22—101no—
836C22—101no—
837C22—103no—
838C22—103no—
839C22—103no—
840C22—2012no—
841C22C3×D5×#4112yescomplemented
842C22C22×C3×C22⋊D516yes—
843C22C24×C3×D511yescharacteristic
844C4—21no—
845C4—23no—
846C4—52no—
847C4—103no—
848C4—101no—
849C4—103no—
850C4—101no—
851C4—103no—
852C4C22×C3×C22⋊D512yes—
853C4C22×C3×C22⋊D516yes—
854C3#41×C22⋊D511yescharacteristic, direct product factor, Sylow
855C2—22no—
856C2—26no—
857C2—43no—
858C2—102no—
859C2—203no—
860C2C2×C3×D5×#4111yescharacteristic
861C2C3×#6628311yescharacteristic
862C2C23×C3×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C3×C4C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC22×C3×C5×#41C2
socleC22×C3×C5C25
hypercenterC22×C3×#41D5
hypocenterC5C3×D4×#41
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C2×C3×D5×#41C2semidirect
3. C3×#66168C2semidirect
4. C3×#66166C2semidirect
5. C3×#66165C2semidirect
6. C3×#66163C2semidirect
7. C3×#66162C2semidirect
8. C3×#41×Dic5C2semidirect
9. C3×#66158C2semidirect
10. C3×#66151C2semidirect
11. C3×Q8×C22⋊D5C2semidirect
12. C3×#66140C2semidirect
13. C3×D4×C22⋊D5C2semidirect
14. C3×#66125C2semidirect
15. C2×C3×C4×C22⋊D5C2semidirect
16. #41×C22⋊D5C3direct (N × H)
19. C2×C3×C5×#41C22semidirect
20. C2×C3×C5×#41C22semidirect
21. C2×C3×C5×#41C22semidirect
22. C22×C3×C5×Q8C22semidirect
23. C22×C3×C5×D4C22semidirect
24. C23×C3×C4×C5C22semidirect
27. C2×C3×#713C22semidirect
28. C2×C3×Q8×D5C22semidirect
29. C2×C3×#711C22semidirect
30. C2×C3×D4×D5C22semidirect
31. C2×C3×#709C22semidirect
32. C22×C3×C4×D5C22semidirect
33. C3×#4099C22semidirect
34. C2×C3×C22⋊Dic5C22semidirect
35. C3×#4093C22semidirect
36. C3×#4092C22semidirect
37. C3×#4092C22semidirect
38. C3×Q8×Dic5C22semidirect
39. C3×Q8×Dic5C22semidirect
40. C3×#4090C22semidirect
41. C3×#4086C22semidirect
42. C3×#4085C22semidirect
43. C3×#4085C22semidirect
44. C3×#4084C22semidirect
45. C3×#4084C22semidirect
46. C3×#4083C22semidirect
47. C3×#4082C22semidirect
48. C3×#4081C22semidirect
49. C3×D4×Dic5C22semidirect
50. C3×D4×Dic5C22semidirect
51. C3×#4076C22semidirect
52. C3×#4076C22semidirect
53. C3×#4075C22semidirect
56. C3×C4×C22⋊D5C22semidirect
57. C3×C4×C22⋊D5C22semidirect
58. C3×C4×C22⋊D5C22semidirect
59. C3×C4×C22⋊D5C22semidirect
60. C3×C4×C22⋊D5C22semidirect
61. C3×C4×C22⋊D5C22semidirect
62. C3×C4×C22⋊D5C22semidirect
63. C2×C3×#685C22semidirect
64. C3×#4072C22semidirect
65. C3×#4070C22semidirect
66. C3×#4070C22semidirect
67. C2×C3×#683C22semidirect
68. C2×C3×C4×Dic5C22semidirect
70. C22×C5×#41C2×C3semidirect
71. C2×D5×#41C2×C3semidirect
72. #66168C2×C3semidirect
73. #66166C2×C3semidirect
74. #66165C2×C3semidirect
75. #66163C2×C3semidirect
76. #66162C2×C3semidirect
77. #41×Dic5C2×C3semidirect
78. #66158C2×C3semidirect
79. #66151C2×C3semidirect
80. Q8×C22⋊D5C2×C3semidirect
81. #66140C2×C3semidirect
82. D4×C22⋊D5C2×C3semidirect
83. #66125C2×C3semidirect
84. C2×C4×C22⋊D5C2×C3semidirect
90. C3×C5×#41D4semidirect
150. C22×C3×#41D5semidirect
166. C2×C5×#41C22×C3semidirect
167. C2×C5×#41C22×C3semidirect
168. C2×C5×#41C22×C3semidirect
169. C22×C5×Q8C22×C3semidirect
170. C22×C5×D4C22×C3semidirect
171. C23×C4×C5C22×C3semidirect
174. C2×#713C22×C3semidirect
175. C2×Q8×D5C22×C3semidirect
176. C2×#711C22×C3semidirect
177. C2×D4×D5C22×C3semidirect
178. C2×#709C22×C3semidirect
179. C22×C4×D5C22×C3semidirect
180. #4099C22×C3semidirect
181. C2×C22⋊Dic5C22×C3semidirect
182. #4093C22×C3semidirect
183. #4092C22×C3semidirect
184. #4092C22×C3semidirect
185. Q8×Dic5C22×C3semidirect
186. Q8×Dic5C22×C3semidirect
187. #4090C22×C3semidirect
188. #4086C22×C3semidirect
189. #4085C22×C3semidirect
190. #4085C22×C3semidirect
191. #4084C22×C3semidirect
192. #4084C22×C3semidirect
193. #4083C22×C3semidirect
194. #4082C22×C3semidirect
195. #4081C22×C3semidirect
196. D4×Dic5C22×C3semidirect
197. D4×Dic5C22×C3semidirect
198. #4076C22×C3semidirect
199. #4076C22×C3semidirect
200. #4075C22×C3semidirect
203. C4×C22⋊D5C22×C3semidirect
204. C4×C22⋊D5C22×C3semidirect
205. C4×C22⋊D5C22×C3semidirect
206. C4×C22⋊D5C22×C3semidirect
207. C4×C22⋊D5C22×C3semidirect
208. C4×C22⋊D5C22×C3semidirect
209. C4×C22⋊D5C22×C3semidirect
210. C2×#685C22×C3semidirect
211. #4072C22×C3semidirect
212. #4070C22×C3semidirect
213. #4070C22×C3semidirect
214. C2×#683C22×C3semidirect
215. C2×C4×Dic5C22×C3semidirect
229. C3×C5×Q8C2×D4semidirect
232. C3×C5×D4C2×D4semidirect
238. C2×C3×C4×C5C2×D4semidirect
248. C3×C22⋊D5#41direct (N × H)
270. C2×C3×#41C2×D5semidirect
271. C2×C3×#41C2×D5semidirect
272. C2×C3×#41C2×D5semidirect
274. C22×C3×Q8C2×D5semidirect
277. C22×C3×D4C2×D5semidirect
279. C23×C3×C4C2×D5semidirect
321. C5×#41C3×D4semidirect
381. C22×#41C3×D5semidirect
404. C22×C3×C5C2×#41semidirect
412. C2×C3×D5C2×#41semidirect
422. C3×Dic5C2×#41semidirect
431. C3×#41C22⋊D5direct (N × H)
499. C5×Q8C2×C3×D4semidirect
502. C5×D4C2×C3×D4semidirect
508. C2×C4×C5C2×C3×D4semidirect
518. C22⋊D5C3×#41direct (N × H)
540. C2×#41C2×C3×D5semidirect
541. C2×#41C2×C3×D5semidirect
542. C2×#41C2×C3×D5semidirect
544. C22×Q8C2×C3×D5semidirect
547. C22×D4C2×C3×D5semidirect
549. C23×C4C2×C3×D5semidirect
607. C3×Q8C2×C22⋊D5semidirect
617. C3×D4C2×C22⋊D5semidirect
636. C2×C3×C4C2×C22⋊D5semidirect
650. C22×C5C2×C3×#41semidirect
658. C2×D5C2×C3×#41semidirect
668. Dic5C2×C3×#41semidirect
677. #41C3×C22⋊D5direct (N × H)
733. C3×C5D4×#41semidirect
749. C22×C3D5×#41semidirect
783. Q8C2×C3×C22⋊D5semidirect
793. D4C2×C3×C22⋊D5semidirect
812. C2×C4C2×C3×C22⋊D5semidirect
825. C5C3×D4×#41semidirect
841. C22C3×D5×#41semidirect
854. C3#41×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C2×C3×D5×#412
C3×#661682
C3×#661662
C3×#661652
C3×#661632
C3×#661622
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C3×#661252
C2×C3×C4×C22⋊D52
#41×C22⋊D53
C3×D4×#415