Finite Group Databasebeta

← #14483204

Subgroups — #14483204

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×C5×#239C211yesmaximal, characteristic, complemented
2C2×#92034C211yesmaximal, characteristic, complemented
3Q8×#1220C211yesmaximal, characteristic, complemented
4C3×#66151C211yesmaximal, characteristic, complemented
5#11755280C213yesmaximal, complemented
6#11755276C213yesmaximal, complemented
7#11755254C211yesmaximal, characteristic, complemented
8#11755233C213yesmaximal, complemented
9Dic5×#239C211yesmaximal, characteristic, complemented
10#11755160C213yesmaximal, complemented
11#11755134C211yesmaximal, characteristic, complemented
12#11754657C213yesmaximal, complemented
13C4×D3×C22⋊D5C213yesmaximal, complemented
14#11754540C213yesmaximal, complemented
15#11754341C213yesmaximal, complemented
16#41×C22⋊D5—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×#239—28no—
20C2×C5×#239C2211yescharacteristic
21C2×C5×#239C2213yescomplemented
22C2×C5×#239C2213yescomplemented
23C2×C5×#239C2211yescharacteristic, complemented
24C22×C5×D12C2213yescomplemented
25C22×C4×C5×D3C2213yescomplemented
26C2×C3×#713C2211yescharacteristic, complemented
27C2×D3×C22⋊D5C2213yes—
28#92034—28no—
29C2×#6777C2213yescomplemented
30C2×C4×D3×D5C2213yescomplemented
31C2×#6772C2213yescomplemented
32C2×#6765C2213yescomplemented
33#91835C2213yescomplemented
34Q8×Dic15C2211yescharacteristic, complemented
35#91833C2213yescomplemented
36C4×#1220C2213yes—
37#91813C2213yescomplemented
38C3×#4093C2213yescomplemented
39C3×#4092C2213yescomplemented
40C3×Q8×Dic5C2211yescharacteristic, complemented
41C3×#4076C2213yescomplemented
42C3×C4×C22⋊D5C2213yescomplemented
43#91568C2216yescomplemented
44#91556C2211yescharacteristic
45D3×C22⋊Dic5C2213yescomplemented
46Dic3×C22⋊D5C2213yescomplemented
47#91475C2216yescomplemented
48D3×#685C2213yescomplemented
49#91466C2213yescomplemented
50#91463C2213yescomplemented
51#91456C2213yescomplemented
52#91453C2216yescomplemented
53#91453C2216yescomplemented
54#91452C2216yescomplemented
55#91449C2213yescomplemented
56#91446C2213yescomplemented
57C4×#1203C2213yescomplemented
58#91441C2216yescomplemented
59#91441C2213yescomplemented
60C4×#1201C2213yescomplemented
61#91435C2213yescomplemented
62#91423C2216yescomplemented
63Dic5×D12C2213yescomplemented
64D3×#683C2213yescomplemented
65C4×D3×Dic5C2213yescomplemented
66#91373C2213yescomplemented
67#91365C2213yescomplemented
68#91338C2213yescomplemented
69#86710—51nomaximal, Hall
70C22×C5×#41—31no—
71C2×D5×#41—31no—
72#66168—31no—
73#66166—33no—
74#66165—31no—
75#66163—33no—
76#66162—33no—
77#41×Dic5—31no—
78#66158—33no—
79#66151D311yescharacteristic, complemented
80Q8×C22⋊D5—31no—
81#66140—33no—
82D4×C22⋊D5—33no—
83#66125—33no—
84C2×C4×C22⋊D5—33no—
85C23×C5×D3C2313yes—
86C22×D3×D5C2313yes—
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C2×#1220C2311yescharacteristic
92Q8×D15—24no—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C22×C5×Dic3C2311yescharacteristic
96C5×#239—24no—
97C5×#239—212no—
98C5×#239—212no—
99C5×#239D418yescomplemented
100C2×C5×D12—212no—
101C2×C5×D12C2316yes—
102C2×C5×D12C2313yes—
103C2×C5×D12C2313yes—
104C2×C4×C5×D3—212no—
105C2×C4×C5×D3C2313yes—
106C2×C4×C5×D3C2313yes—
107C2×C4×C5×D3C2313yes—
108C2×C4×C5×D3C2313yes—
109C2×C3×C22⋊D5C2313yes—
110C3×#713—24no—
111C2×C3×D20C2313yes—
112C2×C3×C4×D5C2313yes—
113D3×C22⋊D5—212no—
114C2×#1203C2313yes—
115C2×#1201C2313yes—
116C2×#1201C2316yes—
117C2×#1201C2316yes—
118C2×#1200C2311yescharacteristic
119C2×D3×Dic5C2313yes—
120C2×D3×Dic5C2313yes—
121C2×D3×Dic5C2313yes—
122C2×D5×Dic3C2313yes—
123#6777—212no—
124C4×D3×D5—212no—
125#6772—212no—
126#6765—212no—
127#6719C2313yes—
128#6714C2313yes—
129C4⋊Dic15C2313yes—
130#6712C2313yes—
131#6712C2316yes—
132C4×Dic15C2313yes—
133C3×C22⋊Dic5C2311yescharacteristic
134C3×#685C2316yes—
135C3×#685C2313yes—
136C3×C4⋊Dic5C2313yes—
137C3×#683C2313yes—
138C3×C4×Dic5C2313yes—
139#6669C2311yescharacteristic
140#6668C2313yes—
141#6667C2311yescharacteristic
142(C2×D3)⋊Dic5C2316yes—
143(C2×D3)⋊Dic5C2313yes—
144(C2×D3)⋊Dic5C2316yes—
145(C2×D3)⋊Dic5C2313yes—
146#6665C2313yes—
147Dic3×Dic5C2311yescharacteristic
148Dic3×Dic5C2313yes—
149C2×D3×#41—51no—
150C22×#239D511yescharacteristic, complemented
151C3×#548—51no—
152#5834—51no—
153Q8×#67—51no—
154#5676—53no—
155#5668—53no—
156#5631—53no—
157#5627—53no—
158#5609—53no—
159#5606—53no—
160#5576—51no—
161C4×#239—51no—
162#5550—53no—
163C4×D3×D4—53no—
164C2×C5×#41—31no—
165C2×C5×#41—33no—
166C2×C5×#41—33no—
167C2×C5×#41—31no—
168C2×C5×#41—68no—
169C22×C5×Q8C2×D311yescharacteristic, complemented
170C22×C5×D4—33no—
171C23×C4×C5—33no—
172C22×C22⋊D5—33no—
173D5×#41—68no—
174C2×#713C2×D311yescharacteristic, complemented
175C2×Q8×D5—31no—
176C2×#711—33no—
177C2×D4×D5—33no—
178C2×#709—33no—
179C22×C4×D5—33no—
180#4099—36no—
181C2×C22⋊Dic5—33no—
182#4093C2×D313yescomplemented
183#4092—33no—
184#4092C2×D313yescomplemented
185Q8×Dic5—31no—
186Q8×Dic5C2×D311yescharacteristic, complemented
187#4090—33no—
188#4086—33no—
189#4085—36no—
190#4085—36no—
191#4084—33no—
192#4084—33no—
193#4083—36no—
194#4082—33no—
195#4081—36no—
196D4×Dic5—33no—
197D4×Dic5—33no—
198#4076—33no—
199#4076C2×D313yescomplemented
200#4075—36no—
201C4×C22⋊D5—33no—
202C4×C22⋊D5—33no—
203C4×C22⋊D5—33no—
204C4×C22⋊D5—31no—
205C4×C22⋊D5—33no—
206C4×C22⋊D5—36no—
207C4×C22⋊D5—33no—
208C4×C22⋊D5—33no—
209C4×C22⋊D5C2×D313yescomplemented
210C2×#685—33no—
211#4072—33no—
212#4070—33no—
213#4070—33no—
214C2×#683—33no—
215C2×C4×Dic5—33no—
216D4×#41—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15C2411yescharacteristic
219C22×C5×D3—26no—
220C22×C5×D3—26no—
221C22×C5×D3—43no—
222C22×C5×D3C2413yes—
223C22×C5×D3C2413yes—
224C22×C3×D5C2413yes—
225C2×D3×D5—26no—
226C2×D3×D5—26no—
227C2×D3×D5—43no—
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2413yes—
232C2×C3×C4×C5C2413yes—
233#1220#4114yescomplemented
234C2×Dic15C2413yes—
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237C4×D15—26no—
238Dic30—26no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3C2411yescharacteristic
241C2×C5×Dic3C2411yescharacteristic
242C5×D12—212no—
243C5×D12—26no—
244C5×D12C2×D4112yescomplemented
245C4×C5×D3—26no—
246C4×C5×D3—26no—
247C4×C5×D3—26no—
248C4×C5×D3C2×D4112yescomplemented
249C3×C22⋊D5—26no—
250C2×C3×Dic5C2413yes—
251C2×C3×Dic5C2411yescharacteristic
252C2×C3×Dic5C2411yescharacteristic
253C3×D20—26no—
254C3×C4×D5—26no—
255#1203—26no—
256#1201—212no—
257#1201—26no—
258#1201—46no—
259#1200—22no—
260D3×Dic5—26no—
261D3×Dic5—26no—
262D3×Dic5—43no—
263D5×Dic3—26no—
264C2×C3×#41—51no—
265C22×C3×Q8C2×D511yescharacteristic, complemented
266D3×#41—108no—
267C2×#239—28no—
268C2×#239C2×D511yescharacteristic
269C2×#239C2×D513yescomplemented
270C2×#239C2×D513yescomplemented
271C2×#239C2×D511yescharacteristic, complemented
272C2×D3×Q8—51no—
273C2×#237—53no—
274C2×D3×D4—53no—
275C2×D3×D4—53no—
276C2×#235—53no—
277C22×D12C2×D513yescomplemented
278C22×C4×D3—53no—
279C22×C4×D3C2×D513yescomplemented
280C3×#124—53no—
281C3×C22⋊Q8—53no—
282C3×#121—53no—
283C3×C4×Q8—51no—
284C3×C4×D4—53no—
285#946—53no—
286Q8×Dic3—51no—
287#944—53no—
288#940—53no—
289#938—53no—
290#937—56no—
291D4×Dic3—53no—
292#930—53no—
293C4×#67—53no—
294C4×#67—53no—
295#924—53no—
296#897—53no—
297#895—53no—
298#894—56no—
299#893—53no—
300#893—53no—
301#892—53no—
302D3×C4⋊C4—53no—
303#884—56no—
304#884—56no—
305#883—56no—
306#882—56no—
307#67⋊C4—51no—
308#67⋊C4—53no—
309#67⋊C4—56no—
310D3×C22⋊C4—53no—
311D3×C22⋊C4—53no—
312#875—53no—
313C4×D12—53no—
314C4×D12—53no—
315C42×D3—53no—
316C24×C5—33no—
317C23×D5—33no—
318C5×#41—38no—
319C5×#41—612no—
320C5×#41—612no—
321C5×#41—64no—
322C2×C5×Q8—24no—
323C2×C5×Q8C22×D313yes—
324C2×C5×Q8C22×D311yescharacteristic
325C2×C5×D4—33no—
326C2×C5×D4—36no—
327C2×C5×D4—33no—
328C2×C5×D4—612no—
329C22×C4×C5—33no—
330C22×C4×C5—31no—
331C22×C4×C5—33no—
332C22×C4×C5—33no—
333C22×C4×C5—33no—
334C22×C4×C5—612no—
335C22×C4×C5C22×D313yes—
336C2×C22⋊D5—31no—
337C2×C22⋊D5—36no—
338C2×C22⋊D5—33no—
339C2×C22⋊D5—36no—
340C2×C22⋊D5—33no—
341C2×C22⋊D5—612no—
342C2×C22⋊D5C22×D313yes—
343C22×Dic5—33no—
344C22×Dic5—33no—
345C22×Dic5—33no—
346#713—24no—
347Q8×D5—64no—
348#711—612no—
349D4×D5—612no—
350#709—612no—
351C2×D20C22×D313yes—
352C2×C4×D5—33no—
353C2×C4×D5—33no—
354C2×C4×D5—31no—
355C2×C4×D5—612no—
356C2×C4×D5C22×D313yes—
357C2×Dic10—33no—
358C22⋊Dic5—33no—
359C22⋊Dic5—33no—
360C22⋊Dic5—33no—
361C22⋊Dic5—36no—
362C22⋊Dic5—36no—
363C22⋊Dic5C22×D311yescharacteristic
364#685—33no—
365#685—33no—
366#685—31no—
367#685C22×D313yes—
368#685C22×D316yes—
369C4⋊Dic5—33no—
370C4⋊Dic5C22×D313yes—
371#683—33no—
372#683—36no—
373#683—33no—
374#683—31no—
375#683C22×D313yes—
376C4×Dic5—33no—
377C4×Dic5—31no—
378C4×Dic5—33no—
379C4×Dic5C22×D313yes—
380C22×#41—31no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—151no—
384#548—51no—
385#548—151no—
386#547—153no—
387#546—153no—
388#546—153no—
389D42—153no—
390#532—153no—
391#525—153no—
392#525—153no—
393C4×#41—151no—
394C2×C4×D4—153no—
395C22×C3×C5—21no—
396C22×C3×C5—21no—
397C22×C3×C5C2×#4112yescomplemented
398C22×C3×C5C2511yescharacteristic
399C2×D15—21no—
400C2×D15—21no—
401C2×D15C2×#4112yescomplemented
402C2×C5×D3—23no—
403C2×C5×D3—23no—
404C2×C5×D3—23no—
405C2×C5×D3—23no—
406C2×C5×D3—23no—
407C2×C5×D3—412no—
408C2×C5×D3C22×D416yes—
409C2×C3×D5—23no—
410C2×C3×D5—23no—
411C2×C3×D5—23no—
412D3×D5—412no—
413C3×C4×C5—23no—
414C3×C4×C5C22×D416yes—
415Dic15—23no—
416Dic15—23no—
417Dic15C2×#4112yescomplemented
418C3×Dic5—21no—
419C3×Dic5—23no—
420C3×Dic5—21no—
421C5×Dic3—21no—
422C5×Dic3C22×D412yes—
423C23×D3—53no—
424C23×D3C22×D513yes—
425C3×#41—104no—
426C2×C3×Q8—24no—
427C2×C3×Q8C22×D513yes—
428C2×C3×Q8C22×D511yescharacteristic
429C2×C3×D4—53no—
430C2×C3×D4—53no—
431C22×C3×C4—53no—
432C22×C3×C4C22×D513yes—
433C2×#67—51no—
434C2×#67—53no—
435C2×#67—56no—
436C2×#67—56no—
437C22×Dic3—53no—
438C22×Dic3C22×D511yescharacteristic
439#239—24no—
440#239—212no—
441#239—212no—
442#239C22⋊D518yescomplemented
443D3×Q8—104no—
444#237—1012no—
445D3×D4—1012no—
446D3×D4—1012no—
447#235—1012no—
448C2×D12—212no—
449C2×D12—53no—
450C2×D12C22×D513yes—
451C2×D12C22×D516yes—
452C2×D12C22×D513yes—
453C2×C4×D3—212no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—51no—
458C2×C4×D3—53no—
459C2×C4×D3—1012no—
460C2×C4×D3C22×D513yes—
461C2×C4×D3C22×D513yes—
462C2×C4×D3C22×D513yes—
463C2×C4×D3C22×D513yes—
464C2×Dic6—53no—
465C3×C4⋊C4—53no—
466C3×C4⋊C4—53no—
467C3×C22⋊C4—51no—
468C3×C22⋊C4—53no—
469C3×C22⋊C4—56no—
470C3×C42—53no—
471#217—53no—
472#217—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—56no—
475(C2×D3)⋊C4—56no—
476(C2×D3)⋊C4—53no—
477(C2×D3)⋊C4—53no—
478(C2×D3)⋊C4—51no—
479C4⋊Dic3—53no—
480C4⋊Dic3—53no—
481Dic3⋊C4—56no—
482Dic3⋊C4—53no—
483Dic3⋊C4—51no—
484C4×Dic3—53no—
485C4×Dic3—51no—
486C4×Dic3—53no—
487C23×C5—33no—
488C23×C5—33no—
489C23×C5—66no—
490C23×C5—66no—
491C23×C5—123no—
492C23×C5C23×D311yescharacteristic
493C22×D5—31no—
494C22×D5—66no—
495C22×D5—66no—
496C22×D5—123no—
497C22×D5C23×D313yes—
498C5×Q8—26no—
499C5×Q8D3×D414yescomplemented
500C5×D4—312no—
501C5×D4—612no—
502C5×D4—66no—
503C2×C4×C5—26no—
504C2×C4×C5—31no—
505C2×C4×C5—312no—
506C2×C4×C5—31no—
507C2×C4×C5—66no—
508C2×C4×C5—66no—
509C2×C4×C5—62no—
510C2×C4×C5—66no—
511C2×C4×C5C23×D313yes—
512C2×C4×C5C23×D313yes—
513C22⋊D5—26no—
514C22⋊D5—34no—
515C22⋊D5—66no—
516C22⋊D5—66no—
517C22⋊D5—612no—
518C22⋊D5—126no—
519C2×Dic5—31no—
520C2×Dic5—33no—
521C2×Dic5—33no—
522C2×Dic5—66no—
523C2×Dic5—66no—
524C2×Dic5—123no—
525C2×Dic5C23×D311yescharacteristic
526C2×Dic5C23×D313yes—
527C2×Dic5C23×D311yescharacteristic
528D20—26no—
529C4×D5—26no—
530C4×D5—62no—
531C4×D5—66no—
532C4×D5—66no—
533Dic10—66no—
534C2×#41—31no—
535C2×#41—33no—
536C2×#41—33no—
537C2×#41—31no—
538C2×#41—51no—
539C2×#41—68no—
540C2×#41—153no—
541C2×#41—153no—
542C2×#41—308no—
543C22×Q8—151no—
544C22×Q8D3×D511yescharacteristic, complemented
545C22×D4—33no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—33no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—53no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—53no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—53no—
561#121—156no—
562#121—156no—
563#121—153no—
564#121—153no—
565#121—153no—
566#120—156no—
567#120—156no—
568C4×Q8—51no—
569C4×Q8—151no—
570C4×D4—53no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—151no—
574C4×D4—153no—
575C4×D4—156no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—153no—
581#117—153no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—153no—
586C2×C3×C5—22no—
587C2×C3×C5C23×D411yescharacteristic
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5#58511yescharacteristic
590D15—22no—
591C3×D5—43no—
592C5×D3—26no—
593C5×D3—43no—
594C23×C3—53no—
595C23×C3C23×D511yescharacteristic
596C22×D3—26no—
597C22×D3—26no—
598C22×D3—43no—
599C22×D3—51no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3—203no—
603C22×D3C23×D513yes—
604C22×D3C23×D513yes—
605C3×Q8—26no—
606C3×Q8C2×C22⋊D514yescomplemented
607C3×D4—106no—
608C3×D4—106no—
609C2×C3×C4—26no—
610C2×C3×C4—53no—
611C2×C3×C4—51no—
612C2×C3×C4—51no—
613C2×C3×C4—106no—
614C2×C3×C4C23×D513yes—
615C2×C3×C4C23×D513yes—
616#67—54no—
617#67—106no—
618#67—1012no—
619#67—206no—
620C2×Dic3—22no—
621C2×Dic3—51no—
622C2×Dic3—53no—
623C2×Dic3—53no—
624C2×Dic3—106no—
625C2×Dic3C23×D511yescharacteristic
626C2×Dic3C23×D511yescharacteristic
627D12—212no—
628D12—26no—
629D12—106no—
630D12C2×C22⋊D5112yescomplemented
631C4×D3—26no—
632C4×D3—26no—
633C4×D3—26no—
634C4×D3—106no—
635C4×D3—106no—
636C4×D3—106no—
637C4×D3—102no—
638C4×D3—203no—
639C4×D3C2×C22⋊D5112yescomplemented
640Dic6—106no—
641C22×C5—21no—
642C22×C5—21no—
643C22×C5—36no—
644C22×C5—63no—
645C22×C5—63no—
646C22×C5—63no—
647C22×C5—63no—
648C22×C5—63no—
649C22×C5—1212no—
650C22×C5D3×#4112yescomplemented
651C22×C5C24×D311yescharacteristic
652C2×D5—23no—
653C2×D5—23no—
654C2×D5—23no—
655C2×D5—32no—
656C2×D5—61no—
657C2×D5—61no—
658C2×D5—1212no—
659C4×C5—23no—
660C4×C5—32no—
661C4×C5—61no—
662C4×C5C2×D3×D416yes—
663Dic5—21no—
664Dic5—23no—
665Dic5—21no—
666Dic5—32no—
667Dic5—63no—
668Dic5—63no—
669C24—33no—
670C24—153no—
671#41—38no—
672#41—612no—
673#41—612no—
674#41—64no—
675#41—104no—
676#41—3012no—
677#41—3012no—
678C2×Q8—24no—
679C2×Q8—153no—
680C2×Q8—304no—
681C2×Q8C2×D3×D513yes—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—36no—
685C2×D4—33no—
686C2×D4—53no—
687C2×D4—53no—
688C2×D4—612no—
689C2×D4—153no—
690C2×D4—151no—
691C2×D4—153no—
692C2×D4—156no—
693C2×D4—156no—
694C2×D4—3012no—
695C2×D4—3012no—
696C22×C4—33no—
697C22×C4—31no—
698C22×C4—33no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—53no—
702C22×C4—612no—
703C22×C4—151no—
704C22×C4—153no—
705C22×C4—153no—
706C22×C4—153no—
707C22×C4—153no—
708C22×C4—153no—
709C22×C4—3012no—
710C22×C4C2×D3×D513yes—
711C4⋊C4—53no—
712C4⋊C4—53no—
713C4⋊C4—151no—
714C4⋊C4—153no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—156no—
718C22⋊C4—51no—
719C22⋊C4—53no—
720C22⋊C4—56no—
721C22⋊C4—151no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—153no—
725C22⋊C4—156no—
726C22⋊C4—156no—
727C22⋊C4—153no—
728C22⋊C4—153no—
729C42—53no—
730C42—151no—
731C42—153no—
732C42—153no—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—103no—
737C22×C3—103no—
738C22×C3—103no—
739C22×C3D5×#4112yescomplemented
740C22×C3C24×D511yescharacteristic
741C2×D3—23no—
742C2×D3—23no—
743C2×D3—23no—
744C2×D3—23no—
745C2×D3—23no—
746C2×D3—412no—
747C2×D3—52no—
748C2×D3—101no—
749C2×D3—101no—
750C2×D3—2012no—
751C2×D3C22×C22⋊D516yes—
752C3×C4—23no—
753C3×C4—103no—
754C3×C4—101no—
755C3×C4—101no—
756C3×C4C22×C22⋊D516yes—
757Dic3—21no—
758Dic3—52no—
759Dic3—103no—
760Dic3—103no—
761Dic3C22×C22⋊D512yes—
762C2×C5—22no—
763C2×C5—66no—
764C2×C5—123no—
765C2×C5C22×D3×D411yescharacteristic
766C2×C5C2×D3×#4111yescharacteristic
767C2×C5#596811yescharacteristic
768D5—43no—
769D5—62no—
770C23—33no—
771C23—33no—
772C23—53no—
773C23—66no—
774C23—66no—
775C23—123no—
776C23—151no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23C22×D3×D511yescharacteristic
781Q8—26no—
782Q8—306no—
783Q8D3×C22⋊D514yescomplemented
784D4—312no—
785D4—612no—
786D4—66no—
787D4—106no—
788D4—106no—
789D4—154no—
790D4—306no—
791D4—306no—
792D4—3012no—
793D4—606no—
794C2×C4—26no—
795C2×C4—31no—
796C2×C4—312no—
797C2×C4—31no—
798C2×C4—51no—
799C2×C4—53no—
800C2×C4—51no—
801C2×C4—66no—
802C2×C4—66no—
803C2×C4—62no—
804C2×C4—66no—
805C2×C4—106no—
806C2×C4—151no—
807C2×C4—153no—
808C2×C4—153no—
809C2×C4—302no—
810C2×C4—306no—
811C2×C4—306no—
812C2×C4—306no—
813C2×C4—306no—
814C2×C4—603no—
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D513yes—
817C2×C3—22no—
818C2×C3—203no—
819C2×C3C2×D5×#4111yescharacteristic
820C2×C3#6628311yescharacteristic
821C2×C3C23×C22⋊D511yescharacteristic
822D3—26no—
823D3—43no—
824D3—102no—
825C5#8671011yescharacteristic, complemented, Sylow
826C22—21no—
827C22—21no—
828C22—36no—
829C22—63no—
830C22—63no—
831C22—63no—
832C22—63no—
833C22—63no—
834C22—103no—
835C22—103no—
836C22—103no—
837C22—1212no—
838C22—152no—
839C22—301no—
840C22—301no—
841C22—6012no—
842C22#9203412yescomplemented
843C22C23×D3×D511yescharacteristic
844C4—23no—
845C4—32no—
846C4—61no—
847C4—101no—
848C4—103no—
849C4—101no—
850C4—152no—
851C4—303no—
852C4—303no—
853C4C2×D3×C22⋊D516yes—
854C3#41×C22⋊D511yescharacteristic, complemented, Sylow
855C2—22no—
856C2—66no—
857C2—123no—
858C2—203no—
859C2—302no—
860C2C2×#9203411yescharacteristic
861C2#1175704911yescharacteristic
862C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×#239C2semidirect
2. C2×#92034C2semidirect
3. Q8×#1220C2semidirect
4. C3×#66151C2semidirect
5. #11755280C2semidirect
6. #11755276C2semidirect
7. #11755254C2semidirect
8. #11755233C2semidirect
9. Dic5×#239C2semidirect
10. #11755160C2semidirect
11. #11755134C2semidirect
12. #11754657C2semidirect
13. C4×D3×C22⋊D5C2semidirect
14. #11754540C2semidirect
15. #11754341C2semidirect
17. C22×C3×C5×Q8C22semidirect
18. C2×Q8×D15C22semidirect
21. C2×C5×#239C22semidirect
22. C2×C5×#239C22semidirect
23. C2×C5×#239C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
26. C2×C3×#713C22semidirect
29. C2×#6777C22semidirect
30. C2×C4×D3×D5C22semidirect
31. C2×#6772C22semidirect
32. C2×#6765C22semidirect
33. #91835C22semidirect
34. Q8×Dic15C22semidirect
35. #91833C22semidirect
37. #91813C22semidirect
38. C3×#4093C22semidirect
39. C3×#4092C22semidirect
40. C3×Q8×Dic5C22semidirect
41. C3×#4076C22semidirect
42. C3×C4×C22⋊D5C22semidirect
43. #91568C22semidirect
45. D3×C22⋊Dic5C22semidirect
46. Dic3×C22⋊D5C22semidirect
47. #91475C22semidirect
48. D3×#685C22semidirect
49. #91466C22semidirect
50. #91463C22semidirect
51. #91456C22semidirect
52. #91453C22semidirect
53. #91453C22semidirect
54. #91452C22semidirect
55. #91449C22semidirect
56. #91446C22semidirect
57. C4×#1203C22semidirect
58. #91441C22semidirect
59. #91441C22semidirect
60. C4×#1201C22semidirect
61. #91435C22semidirect
62. #91423C22semidirect
63. Dic5×D12C22semidirect
64. D3×#683C22semidirect
65. C4×D3×Dic5C22semidirect
66. #91373C22semidirect
67. #91365C22semidirect
68. #91338C22semidirect
79. #66151D3semidirect
99. C5×#239D4semidirect
150. C22×#239D5semidirect
169. C22×C5×Q8C2×D3semidirect
174. C2×#713C2×D3semidirect
182. #4093C2×D3semidirect
184. #4092C2×D3semidirect
186. Q8×Dic5C2×D3semidirect
199. #4076C2×D3semidirect
209. C4×C22⋊D5C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
233. #1220#41semidirect
244. C5×D12C2×D4semidirect
248. C4×C5×D3C2×D4semidirect
265. C22×C3×Q8C2×D5semidirect
269. C2×#239C2×D5semidirect
270. C2×#239C2×D5semidirect
271. C2×#239C2×D5semidirect
277. C22×D12C2×D5semidirect
279. C22×C4×D3C2×D5semidirect
397. C22×C3×C5C2×#41semidirect
401. C2×D15C2×#41semidirect
417. Dic15C2×#41semidirect
442. #239C22⋊D5semidirect
499. C5×Q8D3×D4semidirect
544. C22×Q8D3×D5semidirect
606. C3×Q8C2×C22⋊D5semidirect
630. D12C2×C22⋊D5semidirect
639. C4×D3C2×C22⋊D5semidirect
650. C22×C5D3×#41semidirect
733. C3×C5D4×#41semidirect
739. C22×C3D5×#41semidirect
783. Q8D3×C22⋊D5semidirect
825. C5#86710semidirect
842. C22#92034semidirect
854. C3#41×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2392
C2×#920342
Q8×#12202
C3×#661512
#117552802
#117552762
#117552542
#117552332
Dic5×#2392
#117551602
#117551342
#117546572
C4×D3×C22⋊D52
#117545402
#117543412
#41×C22⋊D53
#867105