Finite Group Databasebeta

← #14453516

Subgroups — #14453516

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D4×D12C211yesmaximal, characteristic, complemented
2C3×#65886C211yesmaximal, characteristic, complemented
3C22×#6656C211yesmaximal, characteristic, complemented
4C2×#91299C211yesmaximal, characteristic, complemented
5#11751112C211yesmaximal, characteristic, complemented
6#11748548C211yesmaximal, characteristic, complemented
7#11748537C211yesmaximal, characteristic, complemented
8#11748529C211yesmaximal, characteristic, complemented
9#11748522C211yesmaximal, characteristic, complemented
10#11748516C211yesmaximal, characteristic, complemented
11#11748511C211yesmaximal, characteristic, complemented
12#11747060C211yesmaximal, characteristic, complemented
13#11747050C211yesmaximal, characteristic, complemented
14#11747042C211yesmaximal, characteristic, complemented
15#11747034C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C2×C5×D3×D4—21no—
18C22×C5×D12C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic, complemented
21C22×C3×Dic10C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic
23C2×#6710C2211yescharacteristic, complemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C5×#930C2211yescharacteristic
26C5×#930C2211yescharacteristic
27C5×#895—21no—
28C5×#882—21no—
29C5×#882—21no—
30C5×#874C2211yescharacteristic
31C4×C5×D12C2211yescharacteristic
32C3×#4085—21no—
33C3×#4076C2211yescharacteristic, complemented
34C3×#4070C2211yescharacteristic, complemented
35C3×#4042—21no—
36C3×#4031—21no—
37C3×#4027—21no—
38C3×#4021C2211yescharacteristic, complemented
39C3×C4×Dic10C2211yescharacteristic, complemented
40C2×#6656—24no—
41C2×#6656C2211yescharacteristic
42C2×#6656C2211yescharacteristic
43C2×#6656C2211yescharacteristic, complemented
44C2×#6656C2211yescharacteristic, complemented
45C2×#6656C2211yescharacteristic, complemented
46C2×#6656C2211yescharacteristic, complemented
47#91299—24no—
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×#6652C2211yescharacteristic, complemented
51#91114C2211yescharacteristic, complemented
52#91114C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90966C2211yescharacteristic
59#90966C2211yescharacteristic, complemented
60#90966C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#83542—51nomaximal, Hall
63C5×D42—31no—
64C22×#687—31no—
65C2×#4078—31no—
66#65886D311yescharacteristic, complemented
67#65507—31no—
68#65506—31no—
69#65364—31no—
70#65363—31no—
71#65331—31no—
72#65329—31no—
73#65327—31no—
74#65326—31no—
75#65307—31no—
76#65305—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4D411yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C5×#67—21no—
85C5×D3×D4—44no—
86C2×C5×D12—22no—
87C2×C5×D12—22no—
88C2×C5×D12—21no—
89C2×C5×D12—21no—
90C2×C5×D12—21no—
91C2×C5×D12—21no—
92C2×C5×D12—41no—
93C2×C5×D12—41no—
94C2×C5×D12C2311yescharacteristic
95C2×C5×D12C2311yescharacteristic
96C2×C5×D12C2311yescharacteristic
97C2×C4×C5×D3—21no—
98C2×C3×C22⋊D5—21no—
99C2×C3×C22⋊D5—21no—
100C22×C3×Dic5—21no—
101C3×#709—22no—
102C3×#709—41no—
103C2×C3×D20C2311yescharacteristic
104C2×C3×C4×D5—21no—
105C2×C3×Dic10—22no—
106C2×C3×Dic10—21no—
107C2×C3×Dic10—41no—
108C2×C3×Dic10C2311yescharacteristic
109C2×C3×Dic10C2311yescharacteristic
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C22⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C42×C5C2311yescharacteristic
114#6710—22no—
115C2×C3⋊#168—22no—
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×C4⋊Dic3C2311yescharacteristic
124C3×C22⋊Dic5—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×C4⋊Dic5C2311yescharacteristic
129C3×#683—21no—
130C3×#683—21no—
131C3×C4×Dic5—21no—
132#6656—22no—
133#6656—22no—
134#6656—22no—
135#6656—22no—
136#6656—41no—
137#6656D414yescomplemented
138#6652—22no—
139#6652—22no—
140#6652—41no—
141C3×#548—51no—
142C2×#949—51no—
143C22×#215—51no—
144D4×D12D511yescharacteristic, complemented
145#5238—51no—
146#5227—51no—
147#5058—51no—
148#5057—51no—
149#5049—51no—
150#5046—51no—
151#5038—51no—
152#5036—51no—
153#5027—51no—
154#5026—51no—
155#5011—51no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709C2×D311yescharacteristic, complemented
160C22×Dic10C2×D311yescharacteristic, complemented
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—31no—
164C5×#121—61no—
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4C2×D311yescharacteristic
169#4085—21no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—64no—
177#4078—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076C2×D311yescharacteristic, complemented
182#4070C2×D311yescharacteristic, complemented
183C2×#681—31no—
184C22×#168—31no—
185#4042—21no—
186#4031—21no—
187#4027—21no—
188#4021C2×D311yescharacteristic, complemented
189C4×Dic10C2×D311yescharacteristic, complemented
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3942—31no—
196#3942—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—42no—
208C22×C5×D3—42no—
209C22×C5×D3—42no—
210C22×C5×D3—42no—
211C22×C5×D3—81no—
212C22×C5×D3—81no—
213C22×C3×D5—21no—
214C3×C5×D4—22no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2411yescharacteristic
224C5×#67—42no—
225C5×#67—42no—
226C2×C5×Dic3—21no—
227C5×D12—21no—
228C5×D12—21no—
229C5×D12—21no—
230C5×D12—21no—
231C5×D12—21no—
232C5×D12—42no—
233C5×D12—42no—
234C5×D12—42no—
235C5×D12—81no—
236C5×D12C2×D412yes—
237C4×C5×D3—42no—
238C3×C22⋊D5—42no—
239C3×C22⋊D5—42no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—42no—
244C3×D20—21no—
245C3×D20—21no—
246C3×C4×D5—42no—
247C3×Dic10—21no—
248C3×Dic10—21no—
249C3×Dic10—21no—
250C3×Dic10—42no—
251C3×Dic10C2×D412yescomplemented
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3⋊#168—21no—
255C3⋊#168C2×D412yescomplemented
256C2×C3×#41—51no—
257C22×C3×Q8—51no—
258C2×D3×D4—21no—
259C22×D12C2×D511yescharacteristic
260C22×D12C2×D511yescharacteristic
261C3×#124—51no—
262C3×#124—101no—
263C3×C22⋊Q8—51no—
264C3×C22⋊Q8—101no—
265C3×#121—51no—
266C3×#121—101no—
267C3×C4×Q8—51no—
268C3×C4×D4—101no—
269C3×C4×D4C2×D511yescharacteristic
270#949—104no—
271C2×#215—51no—
272C2×#215—51no—
273C2×#215—51no—
274C2×#215—51no—
275C2×#215—51no—
276C2×#215—51no—
277C2×#215—104no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930C2×D511yescharacteristic
282#930C2×D511yescharacteristic
283C2×#208—51no—
284C22×C3⋊C8—51no—
285#895—21no—
286#882—21no—
287#882—21no—
288#874C2×D511yescharacteristic
289C4×D12C2×D511yescharacteristic
290#835—51no—
291#835—51no—
292#832—51no—
293#830—51no—
294#830—51no—
295#809—51no—
296#809—51no—
297#809—51no—
298#807—51no—
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C24×C5—61no—
302C24×C5—61no—
303C2×C5×D4—31no—
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—62no—
307C2×C5×D4—62no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—61no—
311C2×C5×D4—61no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—121no—
315C2×C5×D4—121no—
316C2×C5×D4—124no—
317C2×C5×D4#6711yescharacteristic
318C22×C4×C5—61no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—21no—
322C2×C22⋊D5—21no—
323C22×Dic5—21no—
324#709—22no—
325#709—41no—
326C2×D20C22×D311yescharacteristic
327C2×C4×D5—21no—
328C2×Dic10—22no—
329C2×Dic10—21no—
330C2×Dic10—41no—
331C2×Dic10C22×D311yescharacteristic
332C2×Dic10C22×D311yescharacteristic
333C5×C4⋊C4—31no—
334C5×C4⋊C4#6711yescharacteristic
335C5×C22⋊C4—61no—
336C5×C22⋊C4—61no—
337C5×C22⋊C4—61no—
338C5×C22⋊C4#6711yescharacteristic
339C5×C22⋊C4#6711yescharacteristic
340C42×C5C22×D311yescharacteristic
341C22⋊Dic5—21no—
342#687—34no—
343#687—62no—
344#687—62no—
345#687—62no—
346#687—62no—
347#687—121no—
348#686—62no—
349#686—62no—
350#686—121no—
351#685—21no—
352#685—21no—
353#685—21no—
354C4⋊Dic5C22×D311yescharacteristic
355#683—21no—
356#683—21no—
357C4×Dic5—21no—
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—31no—
362C2×#168—31no—
363C2×#168—62no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—51no—
367D42—31no—
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5AGL(1,ℤ/8)12yescomplemented
385C22×C3×C5C22×D411yescharacteristic
386C2×C5×D3—22no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—84no—
396C2×C5×D3—84no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—21no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406C3×Dic5—22no—
407C3×Dic5—41no—
408C3×Dic5—41no—
409C5×Dic3—41no—
410C23×D3—21no—
411C23×D3—21no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×Q8—51no—
416C2×C3×Q8—102no—
417C2×C3×Q8—101no—
418C2×C3×Q8—201no—
419C2×C3×D4—51no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4C22⋊D511yescharacteristic
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—21no—
428C2×#67—21no—
429D3×D4—44no—
430C2×D12—22no—
431C2×D12—22no—
432C2×D12—21no—
433C2×D12—21no—
434C2×D12—21no—
435C2×D12—21no—
436C2×D12—41no—
437C2×D12—41no—
438C2×D12C22×D511yescharacteristic
439C2×D12C22×D511yescharacteristic
440C2×D12C22×D511yescharacteristic
441C2×C4×D3—21no—
442C3×C4⋊C4—51no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4C22⋊D511yescharacteristic
446C3×C22⋊C4—101no—
447C3×C22⋊C4—101no—
448C3×C22⋊C4—101no—
449C3×C22⋊C4—101no—
450C3×C22⋊C4C22⋊D511yescharacteristic
451C3×C22⋊C4C22⋊D511yescharacteristic
452C3×C42—101no—
453C3×C42C22×D511yescharacteristic
454#215—54no—
455#215—102no—
456#215—102no—
457#215—102no—
458#215—102no—
459#215—201no—
460#213—102no—
461#213—102no—
462#213—201no—
463(C2×D3)⋊C4—21no—
464(C2×D3)⋊C4—21no—
465(C2×D3)⋊C4—21no—
466C4⋊Dic3C22×D511yescharacteristic
467#208—102no—
468C2×C3⋊C8—51no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471C2×C3⋊C8—51no—
472C2×C3⋊C8—102no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—122no—
477C23×C5—122no—
478C23×C5—122no—
479C23×C5—122no—
480C23×C5—241no—
481C23×C5—241no—
482C23×C5C2×#6711yescharacteristic
483C23×C5C2×#6711yescharacteristic
484C22×D5—21no—
485C5×D4—22no—
486C5×D4—32no—
487C5×D4—61no—
488C5×D4—61no—
489C5×D4—61no—
490C5×D4—61no—
491C5×D4—61no—
492C5×D4—122no—
493C5×D4—122no—
494C5×D4—122no—
495C5×D4—122no—
496C5×D4—122no—
497C5×D4—241no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—61no—
503C2×C4×C5—122no—
504C2×C4×C5C2×#6711yescharacteristic
505C2×C4×C5C2×#6711yescharacteristic
506C2×C4×C5C2×#6711yescharacteristic
507C2×C4×C5C2×#6711yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—42no—
510C22⋊D5—42no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—42no—
515D20—21no—
516D20—21no—
517C4×D5—42no—
518Dic10—21no—
519Dic10—21no—
520Dic10—21no—
521Dic10—42no—
522Dic10D3×D412yescomplemented
523#168—32no—
524#168—61no—
525#168—61no—
526#168—61no—
527C2×#41—51no—
528C22×Q8—51no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—61no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—151no—
545#127—31no—
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—31no—
551#121—31no—
552#121—51no—
553#121—61no—
554#121—101no—
555#120—61no—
556#120—61no—
557C4×Q8—51no—
558C4×D4—31no—
559C4×D4—101no—
560C4×D4D3×D511yescharacteristic
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—41no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577C3×D5—81no—
578C5×D3—42no—
579C5×D3—81no—
580C5×D3—81no—
581C23×C3—101no—
582C23×C3C2×C22⋊D511yescharacteristic
583C23×C3C2×C22⋊D511yescharacteristic
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—42no—
588C22×D3—42no—
589C22×D3—42no—
590C22×D3—42no—
591C22×D3—81no—
592C22×D3—81no—
593C3×Q8—52no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—22no—
599C3×D4—101no—
600C3×D4—101no—
601C3×D4—202no—
602C3×D4—202no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—202no—
611C2×C3×C4—202no—
612C2×C3×C4C2×C22⋊D511yescharacteristic
613C2×C3×C4C2×C22⋊D511yescharacteristic
614C2×C3×C4C2×C22⋊D511yescharacteristic
615C2×C3×C4C2×C22⋊D511yescharacteristic
616C2×C3×C4C23×D511yescharacteristic
617#67—42no—
618#67—42no—
619C2×Dic3—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—42no—
626D12—42no—
627D12—42no—
628D12—81no—
629D12D4×D512yes—
630C4×D3—42no—
631C3⋊C8—52no—
632C3⋊C8—101no—
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—62no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5—121no—
644C22×C5—121no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5—244no—
650C22×C5—244no—
651C22×C5#94912yescomplemented
652C22×C5C22×#6711yescharacteristic
653C2×D5—41no—
654C2×D5—41no—
655C2×D5—41no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—121no—
661C4×C5C2×D3×D411yescharacteristic
662C4×C5#100411yescharacteristic
663Dic5—22no—
664Dic5—41no—
665Dic5—41no—
666C24—61no—
667C24—61no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—51no—
672C2×Q8—102no—
673C2×Q8—101no—
674C2×Q8—201no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—51no—
679C2×D4—62no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—101no—
688C2×D4—101no—
689C2×D4—121no—
690C2×D4—121no—
691C2×D4—124no—
692C2×D4#120111yescharacteristic
693C22×C4—61no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4C2×D3×D511yescharacteristic
697C22×C4C2×D3×D511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—151no—
709C2×C8—151no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—31no—
714C4⋊C4—51no—
715C4⋊C4—101no—
716C4⋊C4—101no—
717C4⋊C4#120111yescharacteristic
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—101no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4#120111yescharacteristic
726C22⋊C4#120111yescharacteristic
727C42—101no—
728C42C2×D3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3#407812yescomplemented
739C22×C3C22×C22⋊D511yescharacteristic
740C2×D3—22no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—84no—
750C2×D3—84no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—102no—
756C3×C4—201no—
757C3×C4—201no—
758C3×C4C2×D4×D511yescharacteristic
759C3×C4#414411yescharacteristic
760Dic3—41no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—122no—
764C2×C5—241no—
765C2×C5—241no—
766C2×C5D4×#6711yescharacteristic
767C2×C5C2×#94911yescharacteristic
768C2×C5#583711yescharacteristic
769D5—81no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23—101no—
774C23—122no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23—241no—
779C23—241no—
780C23C2×#120111yescharacteristic
781C23C2×#120111yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—101no—
785Q8—101no—
786Q8—202no—
787D4—22no—
788D4—32no—
789D4—61no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—61no—
794D4—101no—
795D4—101no—
796D4—122no—
797D4—122no—
798D4—122no—
799D4—122no—
800D4—122no—
801D4—202no—
802D4—202no—
803D4—241no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—61no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—122no—
813C2×C4—202no—
814C2×C4—202no—
815C2×C4C2×#120111yescharacteristic
816C2×C4C2×#120111yescharacteristic
817C2×C4C2×#120111yescharacteristic
818C2×C4C2×#120111yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—152no—
821C8—301no—
822C8—301no—
823C8—301no—
824C2×C3—22no—
825C2×C3—41no—
826C2×C3—401no—
827C2×C3C2×#407811yescharacteristic
828C2×C3D4×C22⋊D511yescharacteristic
829C2×C3#6617011yescharacteristic
830D3—42no—
831D3—81no—
832D3—81no—
833C5#8354211yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—62no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—201no—
849C22—201no—
850C22—201no—
851C22—244no—
852C22—244no—
853C22#9129912yescomplemented
854C22C22×#120111yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—102no—
860C4—121no—
861C4—201no—
862C4—201no—
863C4D3×D4×D511yescharacteristic
864C4#9202511yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—122no—
869C2—241no—
870C2—241no—
871C2—401no—
872C2C2×#9129911yescharacteristic
873C2D4×#120111yescharacteristic
874C2#1175530411yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×D4×D12C2semidirect
2. C3×#65886C2semidirect
3. C22×#6656C2semidirect
4. C2×#91299C2semidirect
5. #11751112C2semidirect
6. #11748548C2semidirect
7. #11748537C2semidirect
8. #11748529C2semidirect
9. #11748522C2semidirect
10. #11748516C2semidirect
11. #11748511C2semidirect
12. #11747060C2semidirect
13. #11747050C2semidirect
14. #11747042C2semidirect
15. #11747034C2semidirect
20. C2×C3×#709C22semidirect
21. C22×C3×Dic10C22semidirect
23. C2×#6710C22semidirect
24. C22×C3⋊#168C22semidirect
33. C3×#4076C22semidirect
34. C3×#4070C22semidirect
38. C3×#4021C22semidirect
39. C3×C4×Dic10C22semidirect
43. C2×#6656C22semidirect
44. C2×#6656C22semidirect
45. C2×#6656C22semidirect
46. C2×#6656C22semidirect
49. C2×#6652C22semidirect
50. C2×#6652C22semidirect
51. #91114C22semidirect
52. #91114C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. #91087C22semidirect
55. #90989C22semidirect
56. #90970C22semidirect
57. #90970C22semidirect
59. #90966C22semidirect
60. #90966C22semidirect
61. #90964C22semidirect
66. #65886D3semidirect
137. #6656D4semidirect
144. D4×D12D5semidirect
159. C2×#709C2×D3semidirect
160. C22×Dic10C2×D3semidirect
181. #4076C2×D3semidirect
182. #4070C2×D3semidirect
188. #4021C2×D3semidirect
189. C4×Dic10C2×D3semidirect
251. C3×Dic10C2×D4semidirect
255. C3⋊#168C2×D4semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
522. Dic10D3×D4semidirect
651. C22×C5#949semidirect
729. C3×C5#3265semidirect
738. C22×C3#4078semidirect
833. C5#83542semidirect
853. C22#91299semidirect
865. C3#10615222semidirect

Maximal subgroups

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

subgroupindex
C5×D4×D122
C3×#658862
C22×#66562
C2×#912992
#117511122
#117485482
#117485372
#117485292
#117485222
#117485162
#117485112
#117470602
#117470502
#117470422
#117470342
#106152223
#835425