Finite Group Databasebeta

← #41×#1220 #14483041

Subgroups — #41×#1220 #14483041

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×#41×D15C211yesmaximal, characteristic, complemented
3#11756593C211yesmaximal, characteristic, complemented
4#11756591C213yesmaximal, complemented
5#11756590C211yesmaximal, characteristic, complemented
6#11756588C213yesmaximal, complemented
7#11756587C213yesmaximal, complemented
8#41×Dic15C211yesmaximal, characteristic, complemented
9#11756583C213yesmaximal, complemented
10#11756576C211yesmaximal, characteristic, complemented
11Q8×#1220C211yesmaximal, characteristic, complemented
12#11756565C213yesmaximal, complemented
13D4×#1220C213yesmaximal, complemented
14#11756550C213yesmaximal, complemented
15C2×C4×#1220C213yesmaximal, complemented
16#41×C22⋊D5—31nomaximal, 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×#1220C2213yes—
26#41×D15—28no—
27C2×#6821C2211yescharacteristic, complemented
28C2×Q8×D15C2211yescharacteristic, complemented
29C2×#6819C2213yescomplemented
30C2×D4×D15C2213yescomplemented
31C2×#6817C2213yescomplemented
32C22×C4×D15C2213yescomplemented
33#91842C2216yescomplemented
34C2×#6719C2213yescomplemented
35#91836C2213yescomplemented
36#91835C2213yescomplemented
37#91835C2213yescomplemented
38Q8×Dic15C2211yescharacteristic, complemented
39Q8×Dic15C2211yescharacteristic, complemented
40#91833C2213yescomplemented
41#91829C2213yescomplemented
42#91828C2216yescomplemented
43#91828C2216yescomplemented
44#91827C2213yescomplemented
45#91827C2213yescomplemented
46#91826C2216yescomplemented
47#91825C2213yescomplemented
48#91824C2216yescomplemented
49D4×Dic15C2213yescomplemented
50D4×Dic15C2213yescomplemented
51#91819C2213yescomplemented
52#91819C2213yescomplemented
53#91818C2216yescomplemented
54C4×#1220C2211yescharacteristic
55C4×#1220C2213yes—
56C4×#1220C2213yescomplemented
57C4×#1220C2213yescomplemented
58C4×#1220C2213yescomplemented
59C4×#1220C2213yescomplemented
60C4×#1220C2213yescomplemented
61C4×#1220C2213yescomplemented
62C4×#1220C2216yescomplemented
63C2×#6714C2213yescomplemented
64#91815C2213yescomplemented
65#91813C2213yescomplemented
66#91813C2213yescomplemented
67C2×#6712C2213yescomplemented
68C2×C4×Dic15C2213yescomplemented
69#41×#67—51nomaximal, Hall
70C22×C5×#41D311yescharacteristic, complemented
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#66151—31no—
80Q8×C22⋊D5—31no—
81#66140—33no—
82D4×C22⋊D5—33no—
83#66125—33no—
84C2×C4×C22⋊D5—33no—
85C24×C3×C5C2313yes—
86C23×D15C2313yes—
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×C5C2313yes—
100C22×C3×C4×C5C2313yes—
101C22×C3×C4×C5C2313yes—
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2313yes—
104C22×C3×C4×C5C2313yes—
105C2×#1220—212no—
106C2×#1220C2313yes—
107C2×#1220C2313yes—
108C2×#1220C2313yes—
109C2×#1220C2316yes—
110C2×#1220C2316yes—
111C2×#1220C2311yescharacteristic
112C22×Dic15C2313yes—
113C22×Dic15C2313yes—
114C22×Dic15C2313yes—
115#6821—24no—
116Q8×D15—24no—
117#6819—212no—
118D4×D15—212no—
119#6817—212no—
120C2×D60C2313yes—
121C2×C4×D15—212no—
122C2×C4×D15C2311yescharacteristic
123C2×C4×D15C2313yes—
124C2×C4×D15C2313yes—
125C2×C4×D15C2313yes—
126C2×Dic30C2313yes—
127#6719C2313yes—
128#6719C2316yes—
129#6719C2316yes—
130#6719C2311yescharacteristic
131#6719C2313yes—
132#6719C2313yes—
133#6714C2311yescharacteristic
134#6714C2313yes—
135#6714C2313yes—
136#6714C2313yes—
137#6714C2316yes—
138C4⋊Dic15C2313yes—
139C4⋊Dic15C2313yes—
140#6712C2311yescharacteristic
141#6712C2313yes—
142#6712C2313yes—
143#6712C2313yes—
144#6712C2316yes—
145C4×Dic15C2311yescharacteristic
146C4×Dic15C2313yes—
147C4×Dic15C2313yes—
148C4×Dic15C2313yes—
149C22×C3×#41D511yescharacteristic, complemented
150C2×D3×#41—51no—
151#5834—51no—
152#5832—53no—
153#5831—51no—
154#5829—53no—
155#5828—53no—
156Dic3×#41—51no—
157#5824—53no—
158#5817—51no—
159Q8×#67—51no—
160#5806—53no—
161D4×#67—53no—
162#5791—53no—
163C2×C4×#67—53no—
164C2×C5×#41—28no—
165C2×C5×#41C2×D311yescharacteristic
166C2×C5×#41C2×D313yescomplemented
167C2×C5×#41C2×D313yescomplemented
168C2×C5×#41C2×D311yescharacteristic, complemented
169C22×C5×Q8C2×D311yescharacteristic, complemented
170C22×C5×D4C2×D313yescomplemented
171C23×C4×C5C2×D313yescomplemented
172C22×C22⋊D5—33no—
173D5×#41—68no—
174C2×#713—31no—
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#4093—33no—
183#4092—33no—
184#4092—33no—
185Q8×Dic5—31no—
186Q8×Dic5—31no—
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#4076—33no—
200#4075—36no—
201C4×C22⋊D5—31no—
202C4×C22⋊D5—33no—
203C4×C22⋊D5—33no—
204C4×C22⋊D5—33no—
205C4×C22⋊D5—33no—
206C4×C22⋊D5—33no—
207C4×C22⋊D5—33no—
208C4×C22⋊D5—33no—
209C4×C22⋊D5—36no—
210C2×#685—33no—
211#4072—33no—
212#4070—33no—
213#4070—33no—
214C2×#683—33no—
215C2×C4×Dic5—33no—
216D4×#41—151noSylow
217C23×C3×C5—26no—
218C23×C3×C5—26no—
219C23×C3×C5—43no—
220C23×C3×C5C2413yes—
221C23×C3×C5C2413yes—
222C23×C3×C5C2411yescharacteristic
223C22×D15—26no—
224C22×D15—26no—
225C22×D15—43no—
226C22×D15C2413yes—
227C22×D15C2411yescharacteristic
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×C5C2411yescharacteristic
242C2×C3×C4×C5C2413yes—
243#1220—212no—
244#1220—26no—
245#1220—26no—
246#1220—26no—
247#1220—46no—
248#1220#4114yesdirect product factor
249C2×Dic15—26no—
250C2×Dic15—26no—
251C2×Dic15—43no—
252C2×Dic15C2411yescharacteristic
253C2×Dic15C2413yes—
254C2×Dic15C2413yes—
255C2×Dic15C2413yes—
256C2×Dic15C2411yescharacteristic
257C2×Dic15C2411yescharacteristic
258D60—26no—
259C4×D15—22no—
260C4×D15—26no—
261C4×D15—26no—
262C4×D15—26no—
263Dic30—26no—
264C2×C3×#41—28no—
265C2×C3×#41C2×D511yescharacteristic
266C2×C3×#41C2×D513yescomplemented
267C2×C3×#41C2×D513yescomplemented
268C2×C3×#41C2×D511yescharacteristic, complemented
269C22×C3×Q8C2×D511yescharacteristic, complemented
270C22×C3×D4C2×D513yescomplemented
271C23×C3×C4C2×D513yescomplemented
272C22×#67—53no—
273D3×#41—108no—
274C2×#239—51no—
275C2×D3×Q8—51no—
276C2×#237—53no—
277C2×D3×D4—53no—
278C2×#235—53no—
279C22×C4×D3—53no—
280#953—56no—
281C2×#217—53no—
282#947—53no—
283#946—53no—
284#946—53no—
285Q8×Dic3—51no—
286Q8×Dic3—51no—
287#944—53no—
288#940—53no—
289#939—56no—
290#939—56no—
291#938—53no—
292#938—53no—
293#937—56no—
294#936—53no—
295#935—56no—
296D4×Dic3—53no—
297D4×Dic3—53no—
298#930—53no—
299#930—53no—
300#929—56no—
301C4×#67—51no—
302C4×#67—53no—
303C4×#67—53no—
304C4×#67—53no—
305C4×#67—53no—
306C4×#67—53no—
307C4×#67—53no—
308C4×#67—53no—
309C4×#67—56no—
310C2×(C2×D3)⋊C4—53no—
311#926—53no—
312#924—53no—
313#924—53no—
314C2×Dic3⋊C4—53no—
315C2×C4×Dic3—53no—
316C24×C5C22×D313yes—
317C23×D5—33no—
318C5×#41—24no—
319C5×#41—212no—
320C5×#41—212no—
321C5×#41#6718yescomplemented
322C2×C5×Q8—24no—
323C2×C5×Q8C22×D313yes—
324C2×C5×Q8C22×D311yescharacteristic
325C2×C5×D4—212no—
326C2×C5×D4C22×D316yes—
327C2×C5×D4C22×D313yes—
328C2×C5×D4C22×D313yes—
329C22×C4×C5—212no—
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D313yes—
332C22×C4×C5C22×D313yes—
333C22×C4×C5C22×D313yes—
334C22×C4×C5C22×D313yes—
335C22×C4×C5C22×D313yes—
336C2×C22⋊D5—31no—
337C2×C22⋊D5—33no—
338C2×C22⋊D5—36no—
339C2×C22⋊D5—33no—
340C2×C22⋊D5—33no—
341C2×C22⋊D5—36no—
342C2×C22⋊D5—612no—
343C22×Dic5—33no—
344C22×Dic5—33no—
345C22×Dic5—33no—
346#713—64no—
347Q8×D5—64no—
348#711—612no—
349D4×D5—612no—
350#709—612no—
351C2×D20—33no—
352C2×C4×D5—31no—
353C2×C4×D5—33no—
354C2×C4×D5—33no—
355C2×C4×D5—33no—
356C2×C4×D5—612no—
357C2×Dic10—33no—
358C22⋊Dic5—31no—
359C22⋊Dic5—33no—
360C22⋊Dic5—33no—
361C22⋊Dic5—33no—
362C22⋊Dic5—36no—
363C22⋊Dic5—36no—
364#685—31no—
365#685—33no—
366#685—33no—
367#685—33no—
368#685—36no—
369C4⋊Dic5—33no—
370C4⋊Dic5—33no—
371#683—31no—
372#683—33no—
373#683—33no—
374#683—33no—
375#683—36no—
376C4×Dic5—31no—
377C4×Dic5—33no—
378C4×Dic5—33no—
379C4×Dic5—33no—
380C22×#41—151no—
381C22×#41D1511yescharacteristic, complemented
382#550—151no—
383D4×Q8—151no—
384#548—151no—
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—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×D15—21no—
407C2×D15—21no—
408C2×D15—23no—
409C2×D15—23no—
410C2×D15—23no—
411C2×D15—412no—
412C2×D15C2×#4112yescomplemented
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5C22×D416yes—
416C3×C4×C5C22×D412yes—
417Dic15—23no—
418Dic15—21no—
419Dic15—23no—
420Dic15—21no—
421Dic15—23no—
422Dic15C2×#4112yescomplemented
423C24×C3C22×D513yes—
424C23×D3—53no—
425C3×#41—24no—
426C3×#41—212no—
427C3×#41—212no—
428C3×#41C22⋊D518yescomplemented
429C2×C3×Q8—24no—
430C2×C3×Q8C22×D513yes—
431C2×C3×Q8C22×D511yescharacteristic
432C2×C3×D4—212no—
433C2×C3×D4C22×D516yes—
434C2×C3×D4C22×D513yes—
435C2×C3×D4C22×D513yes—
436C22×C3×C4—212no—
437C22×C3×C4C22×D513yes—
438C22×C3×C4C22×D513yes—
439C22×C3×C4C22×D513yes—
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D513yes—
442C22×C3×C4C22×D513yes—
443C2×#67—51no—
444C2×#67—53no—
445C2×#67—53no—
446C2×#67—53no—
447C2×#67—56no—
448C2×#67—56no—
449C2×#67—1012no—
450C22×Dic3—53no—
451C22×Dic3—53no—
452C22×Dic3—53no—
453#239—104no—
454D3×Q8—104no—
455#237—1012no—
456D3×D4—1012no—
457#235—1012no—
458C2×D12—53no—
459C2×C4×D3—51no—
460C2×C4×D3—53no—
461C2×C4×D3—53no—
462C2×C4×D3—53no—
463C2×C4×D3—1012no—
464C2×Dic6—53no—
465#217—53no—
466#217—56no—
467#217—56no—
468#217—51no—
469#217—53no—
470#217—53no—
471(C2×D3)⋊C4—51no—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—56no—
476C4⋊Dic3—53no—
477C4⋊Dic3—53no—
478Dic3⋊C4—51no—
479Dic3⋊C4—53no—
480Dic3⋊C4—53no—
481Dic3⋊C4—53no—
482Dic3⋊C4—56no—
483C4×Dic3—51no—
484C4×Dic3—53no—
485C4×Dic3—53no—
486C4×Dic3—53no—
487C23×C5—26no—
488C23×C5—26no—
489C23×C5—43no—
490C23×C5C23×D313yes—
491C23×C5C23×D311yescharacteristic
492C23×C5C23×D313yes—
493C22×D5—31no—
494C22×D5—33no—
495C22×D5—66no—
496C22×D5—66no—
497C22×D5—123no—
498C5×Q8—26no—
499C5×Q8C2×#6714yescomplemented
500C5×D4—212no—
501C5×D4—26no—
502C5×D4C2×#67112yescomplemented
503C2×C4×C5—26no—
504C2×C4×C5—22no—
505C2×C4×C5—26no—
506C2×C4×C5—26no—
507C2×C4×C5—26no—
508C2×C4×C5C2×#67112yescomplemented
509C2×C4×C5C23×D311yescharacteristic
510C2×C4×C5C23×D313yes—
511C2×C4×C5C23×D313yes—
512C2×C4×C5C23×D311yescharacteristic
513C22⋊D5—34no—
514C22⋊D5—66no—
515C22⋊D5—66no—
516C22⋊D5—66no—
517C22⋊D5—612no—
518C22⋊D5—126no—
519C2×Dic5—31no—
520C2×Dic5—31no—
521C2×Dic5—33no—
522C2×Dic5—33no—
523C2×Dic5—33no—
524C2×Dic5—31no—
525C2×Dic5—66no—
526C2×Dic5—66no—
527C2×Dic5—123no—
528D20—66no—
529C4×D5—62no—
530C4×D5—66no—
531C4×D5—66no—
532C4×D5—66no—
533Dic10—66no—
534C2×#41—28no—
535C2×#41—151no—
536C2×#41—153no—
537C2×#41—153no—
538C2×#41—308no—
539C2×#41C2×D1511yescharacteristic
540C2×#41C2×D1513yescomplemented
541C2×#41C2×D1513yescomplemented
542C2×#41C2×D1511yescharacteristic, complemented
543C22×Q8—151no—
544C22×Q8C2×D1511yescharacteristic, complemented
545C22×D4—153no—
546C22×D4—153no—
547C22×D4C2×D1513yescomplemented
548C23×C4—153no—
549C23×C4C2×D1513yescomplemented
550C4⋊Q8—153no—
551#127—153no—
552#124—153no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—153no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—153no—
561#121—153no—
562#121—156no—
563#121—156no—
564#121—153no—
565#121—153no—
566#120—156no—
567#120—156no—
568C4×Q8—151no—
569C4×Q8—151no—
570C4×D4—153no—
571C4×D4—153no—
572C4×D4—151no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—156no—
581#117—153no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—153no—
586C2×C3×C5—26no—
587C2×C3×C5—22no—
588C2×C3×C5—43no—
589C2×C3×C5C23×D411yescharacteristic
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5#58511yescharacteristic
592D15—22no—
593D15—43no—
594C23×C3—26no—
595C23×C3—26no—
596C23×C3—43no—
597C23×C3C23×D513yes—
598C23×C3C23×D511yescharacteristic
599C23×C3C23×D513yes—
600C22×D3—51no—
601C22×D3—53no—
602C22×D3—106no—
603C22×D3—106no—
604C22×D3—203no—
605C3×Q8—26no—
606C3×Q8C2×C22⋊D514yescomplemented
607C3×D4—212no—
608C3×D4—26no—
609C3×D4C2×C22⋊D5112yescomplemented
610C2×C3×C4—26no—
611C2×C3×C4—22no—
612C2×C3×C4—26no—
613C2×C3×C4—26no—
614C2×C3×C4—26no—
615C2×C3×C4C2×C22⋊D5112yescomplemented
616C2×C3×C4C23×D511yescharacteristic
617C2×C3×C4C23×D513yes—
618C2×C3×C4C23×D513yes—
619C2×C3×C4C23×D511yescharacteristic
620#67—54no—
621#67—106no—
622#67—106no—
623#67—106no—
624#67—1012no—
625#67—206no—
626C2×Dic3—51no—
627C2×Dic3—51no—
628C2×Dic3—53no—
629C2×Dic3—53no—
630C2×Dic3—53no—
631C2×Dic3—51no—
632C2×Dic3—106no—
633C2×Dic3—106no—
634C2×Dic3—203no—
635D12—106no—
636C4×D3—102no—
637C4×D3—106no—
638C4×D3—106no—
639C4×D3—106no—
640Dic6—106no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5—21no—
644C22×C5—21no—
645C22×C5—23no—
646C22×C5—23no—
647C22×C5—23no—
648C22×C5—412no—
649C22×C5D3×#4112yescomplemented
650C22×C5C22×#6716yes—
651C22×C5C24×D311yescharacteristic
652C2×D5—32no—
653C2×D5—61no—
654C2×D5—61no—
655C2×D5—63no—
656C2×D5—63no—
657C2×D5—63no—
658C2×D5—1212no—
659C4×C5—21no—
660C4×C5—23no—
661C4×C5C22×#6716yes—
662C4×C5C22×#6712yes—
663Dic5—32no—
664Dic5—63no—
665Dic5—61no—
666Dic5—63no—
667Dic5—63no—
668Dic5—61no—
669C24—153no—
670C24C22×D1513yes—
671#41—24no—
672#41—212no—
673#41—212no—
674#41—304no—
675#41—3012no—
676#41—3012no—
677#41#122018yesdirect product factor
678C2×Q8—24no—
679C2×Q8—153no—
680C2×Q8—304no—
681C2×Q8C22×D1513yes—
682C2×Q8C22×D1511yescharacteristic
683C2×D4—212no—
684C2×D4—151no—
685C2×D4—153no—
686C2×D4—153no—
687C2×D4—153no—
688C2×D4—156no—
689C2×D4—156no—
690C2×D4—153no—
691C2×D4—3012no—
692C2×D4—3012no—
693C2×D4C22×D1516yes—
694C2×D4C22×D1513yes—
695C2×D4C22×D1513yes—
696C22×C4—212no—
697C22×C4—153no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—151no—
703C22×C4—153no—
704C22×C4—3012no—
705C22×C4C22×D1513yes—
706C22×C4C22×D1513yes—
707C22×C4C22×D1513yes—
708C22×C4C22×D1511yescharacteristic
709C22×C4C22×D1513yes—
710C22×C4C22×D1513yes—
711C4⋊C4—151no—
712C4⋊C4—153no—
713C4⋊C4—153no—
714C4⋊C4—153no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—156no—
718C22⋊C4—151no—
719C22⋊C4—153no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—156no—
723C22⋊C4—156no—
724C22⋊C4—151no—
725C22⋊C4—153no—
726C22⋊C4—153no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—153no—
730C42—153no—
731C42—151no—
732C42—153no—
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×C3D5×#4112yescomplemented
743C22×C3C22×C22⋊D516yes—
744C22×C3C24×D511yescharacteristic
745C2×D3—52no—
746C2×D3—101no—
747C2×D3—101no—
748C2×D3—103no—
749C2×D3—103no—
750C2×D3—103no—
751C2×D3—2012no—
752C3×C4—21no—
753C3×C4—23no—
754C3×C4C22×C22⋊D516yes—
755C3×C4C22×C22⋊D512yes—
756Dic3—52no—
757Dic3—103no—
758Dic3—101no—
759Dic3—103no—
760Dic3—103no—
761Dic3—101no—
762C2×C5—26no—
763C2×C5—22no—
764C2×C5—43no—
765C2×C5C2×D3×#4111yescharacteristic
766C2×C5#596411yescharacteristic
767C2×C5C23×#6711yescharacteristic
768D5—62no—
769D5—123no—
770C23—26no—
771C23—26no—
772C23—43no—
773C23—151no—
774C23—153no—
775C23—306no—
776C23—306no—
777C23—603no—
778C23C23×D1513yes—
779C23C23×D1511yescharacteristic
780C23C23×D1513yes—
781Q8—26no—
782Q8—306no—
783Q8C2×#122014yescomplemented
784D4—212no—
785D4—26no—
786D4—154no—
787D4—306no—
788D4—306no—
789D4—306no—
790D4—3012no—
791D4—306no—
792D4—606no—
793D4C2×#1220112yescomplemented
794C2×C4—26no—
795C2×C4—22no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—26no—
799C2×C4—151no—
800C2×C4—151no—
801C2×C4—153no—
802C2×C4—153no—
803C2×C4—151no—
804C2×C4—153no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—302no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4—603no—
812C2×C4C2×#1220112yescomplemented
813C2×C4C23×D1511yescharacteristic
814C2×C4C23×D1513yes—
815C2×C4C23×D1513yes—
816C2×C4C23×D1511yescharacteristic
817C2×C3—26no—
818C2×C3—22no—
819C2×C3—43no—
820C2×C3C2×D5×#4111yescharacteristic
821C2×C3#6628311yescharacteristic
822C2×C3C23×C22⋊D511yescharacteristic
823D3—102no—
824D3—203no—
825C5#41×#6711yescharacteristic, complemented, Sylow
826C22—23no—
827C22—23no—
828C22—21no—
829C22—21no—
830C22—23no—
831C22—23no—
832C22—23no—
833C22—412no—
834C22—152no—
835C22—301no—
836C22—301no—
837C22—303no—
838C22—303no—
839C22—303no—
840C22—6012no—
841C22#41×D1512yescomplemented
842C22C22×#122016yes—
843C22C24×D1511yescharacteristic
844C4—21no—
845C4—23no—
846C4—152no—
847C4—303no—
848C4—301no—
849C4—303no—
850C4—301no—
851C4—303no—
852C4C22×#122012yes—
853C4C22×#122016yes—
854C3#41×C22⋊D511yescharacteristic, complemented, Sylow
855C2—22no—
856C2—26no—
857C2—43no—
858C2—302no—
859C2—603no—
860C2C2×#41×D1511yescharacteristic
861C2#1175714611yescharacteristic
862C2C23×#122011yescharacteristic
subgroupG/H
centerC2×C4C23×D15
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC22×C3×C5×#41C2
hypercenterC22×#41D15
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C2×#41×D15C2semidirect
3. #11756593C2semidirect
4. #11756591C2semidirect
5. #11756590C2semidirect
6. #11756588C2semidirect
7. #11756587C2semidirect
8. #41×Dic15C2semidirect
9. #11756583C2semidirect
10. #11756576C2semidirect
11. Q8×#1220C2semidirect
12. #11756565C2semidirect
13. D4×#1220C2semidirect
14. #11756550C2semidirect
15. C2×C4×#1220C2semidirect
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×#6821C22semidirect
28. C2×Q8×D15C22semidirect
29. C2×#6819C22semidirect
30. C2×D4×D15C22semidirect
31. C2×#6817C22semidirect
32. C22×C4×D15C22semidirect
33. #91842C22semidirect
34. C2×#6719C22semidirect
35. #91836C22semidirect
36. #91835C22semidirect
37. #91835C22semidirect
38. Q8×Dic15C22semidirect
39. Q8×Dic15C22semidirect
40. #91833C22semidirect
41. #91829C22semidirect
42. #91828C22semidirect
43. #91828C22semidirect
44. #91827C22semidirect
45. #91827C22semidirect
46. #91826C22semidirect
47. #91825C22semidirect
48. #91824C22semidirect
49. D4×Dic15C22semidirect
50. D4×Dic15C22semidirect
51. #91819C22semidirect
52. #91819C22semidirect
53. #91818C22semidirect
56. C4×#1220C22semidirect
57. C4×#1220C22semidirect
58. C4×#1220C22semidirect
59. C4×#1220C22semidirect
60. C4×#1220C22semidirect
61. C4×#1220C22semidirect
62. C4×#1220C22semidirect
63. C2×#6714C22semidirect
64. #91815C22semidirect
65. #91813C22semidirect
66. #91813C22semidirect
67. C2×#6712C22semidirect
68. C2×C4×Dic15C22semidirect
70. C22×C5×#41D3semidirect
90. C3×C5×#41D4semidirect
149. C22×C3×#41D5semidirect
166. C2×C5×#41C2×D3semidirect
167. C2×C5×#41C2×D3semidirect
168. C2×C5×#41C2×D3semidirect
169. C22×C5×Q8C2×D3semidirect
170. C22×C5×D4C2×D3semidirect
171. C23×C4×C5C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
232. C3×C5×D4C2×D4semidirect
238. C2×C3×C4×C5C2×D4semidirect
248. #1220#41direct (N × H)
266. C2×C3×#41C2×D5semidirect
267. C2×C3×#41C2×D5semidirect
268. C2×C3×#41C2×D5semidirect
269. C22×C3×Q8C2×D5semidirect
270. C22×C3×D4C2×D5semidirect
271. C23×C3×C4C2×D5semidirect
321. C5×#41#67semidirect
381. C22×#41D15semidirect
404. C22×C3×C5C2×#41semidirect
412. C2×D15C2×#41semidirect
422. Dic15C2×#41semidirect
428. C3×#41C22⋊D5semidirect
499. C5×Q8C2×#67semidirect
502. C5×D4C2×#67semidirect
508. C2×C4×C5C2×#67semidirect
540. C2×#41C2×D15semidirect
541. C2×#41C2×D15semidirect
542. C2×#41C2×D15semidirect
544. C22×Q8C2×D15semidirect
547. C22×D4C2×D15semidirect
549. C23×C4C2×D15semidirect
606. C3×Q8C2×C22⋊D5semidirect
609. C3×D4C2×C22⋊D5semidirect
615. C2×C3×C4C2×C22⋊D5semidirect
649. C22×C5D3×#41semidirect
677. #41#1220direct (N × H)
733. C3×C5D4×#41semidirect
742. C22×C3D5×#41semidirect
783. Q8C2×#1220semidirect
793. D4C2×#1220semidirect
812. C2×C4C2×#1220semidirect
825. C5#41×#67semidirect
841. C22#41×D15semidirect
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×C3×C5×#412
C2×#41×D152
#117565932
#117565912
#117565902
#117565882
#117565872
#41×Dic152
#117565832
#117565762
Q8×#12202
#117565652
D4×#12202
#117565502
C2×C4×#12202
#41×C22⋊D53
#41×#675