Finite Group Databasebeta

← #14453514

Subgroups — #14453514

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×#5552C211yesmaximal, characteristic, complemented
2C3×D4×D20C211yesmaximal, characteristic, complemented
3C22×#6655C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751112C211yesmaximal, characteristic, complemented
6#11748546C211yesmaximal, characteristic, complemented
7#11748536C211yesmaximal, characteristic, complemented
8#11748527C211yesmaximal, characteristic, complemented
9#11748522C211yesmaximal, characteristic, complemented
10#11748517C211yesmaximal, characteristic, complemented
11#11748510C211yesmaximal, characteristic, complemented
12#11747068C211yesmaximal, characteristic, complemented
13#11747048C211yesmaximal, characteristic, complemented
14#11747041C211yesmaximal, characteristic, complemented
15#11747027C211yesmaximal, characteristic, complemented
16#10615273—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic, complemented
18C22×C5×Dic6C2211yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic
23C2×#6710C2211yescharacteristic, complemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C5×#939—21no—
26C5×#930C2211yescharacteristic, complemented
27C5×#924C2211yescharacteristic, complemented
28C5×#896—21no—
29C5×#885—21no—
30C5×#67⋊C4—21no—
31C5×#875C2211yescharacteristic, complemented
32C4×C5×Dic6C2211yescharacteristic, complemented
33C3×#4076C2211yescharacteristic
34C3×#4076C2211yescharacteristic
35C3×#4041—21no—
36C3×#4028—21no—
37C3×#4028—21no—
38C3×#4020C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C2×#6655—24no—
41C2×#6655C2211yescharacteristic
42C2×#6655C2211yescharacteristic
43C2×#6655C2211yescharacteristic, complemented
44C2×#6655C2211yescharacteristic, complemented
45C2×#6655C2211yescharacteristic, complemented
46C2×#6655C2211yescharacteristic, complemented
47#91298—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#90972C2211yescharacteristic, complemented
57#90972C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90964C2211yescharacteristic
60#90964C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#83491—51nomaximal, Hall
63C5×#548—31no—
64C2×#4095—31no—
65C22×#688—31no—
66D4×D20D311yescharacteristic, complemented
67#65527—31no—
68#65516—31no—
69#65347—31no—
70#65346—31no—
71#65338—31no—
72#65335—31no—
73#65327—31no—
74#65325—31no—
75#65316—31no—
76#65315—31no—
77#65300—31no—
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C2×C3×C5×D4D411yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C5×#67—21no—
85C22×C5×Dic3—21no—
86C5×#235—22no—
87C5×#235—41no—
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C5×Dic6—22no—
91C2×C5×Dic6—21no—
92C2×C5×Dic6—41no—
93C2×C5×Dic6C2311yescharacteristic
94C2×C5×Dic6C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C3×D4×D5—44no—
98C2×C3×D20—22no—
99C2×C3×D20—22no—
100C2×C3×D20—21no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—21no—
104C2×C3×D20—41no—
105C2×C3×D20—41no—
106C2×C3×D20C2311yescharacteristic
107C2×C3×D20C2311yescharacteristic
108C2×C3×D20C2311yescharacteristic
109C2×C3×C4×D5—21no—
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×#217—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4—21no—
124C5×C4⋊Dic3C2311yescharacteristic
125C5×Dic3⋊C4—21no—
126C5×Dic3⋊C4—21no—
127C4×C5×Dic3—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685—21no—
131C3×C4⋊Dic5C2311yescharacteristic
132#6655—22no—
133#6655—22no—
134#6655—22no—
135#6655—22no—
136#6655—41no—
137#6655D414yescomplemented
138#6652—22no—
139#6652—22no—
140#6652—41no—
141C3×D42—51no—
142C22×#214—51no—
143C2×#932—51no—
144#5552D511yescharacteristic, complemented
145#5218—51no—
146#5217—51no—
147#5075—51no—
148#5074—51no—
149#5042—51no—
150#5040—51no—
151#5038—51no—
152#5037—51no—
153#5018—51no—
154#5016—51no—
155#5011—51no—
156C2×C5×#41—31no—
157C22×C5×Q8—31no—
158C2×D4×D5—21no—
159C22×D20C2×D311yescharacteristic
160C22×D20C2×D311yescharacteristic
161C5×#124—31no—
162C5×#124—61no—
163C5×C22⋊Q8—31no—
164C5×C22⋊Q8—61no—
165C5×#121—31no—
166C5×#121—61no—
167C4×C5×Q8—31no—
168C4×C5×D4—61no—
169C4×C5×D4C2×D311yescharacteristic
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176C2×#688—31no—
177C2×#688—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076C2×D311yescharacteristic
182#4076C2×D311yescharacteristic
183C2×#681—31no—
184C22×#168—31no—
185#4041—21no—
186#4028—21no—
187#4028—21no—
188#4020C2×D311yescharacteristic
189C4×D20C2×D311yescharacteristic
190#3967—31no—
191#3967—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—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×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—42no—
211C22×C3×D5—42no—
212C22×C3×D5—81no—
213C22×C3×D5—81no—
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—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—42no—
230C5×D12—21no—
231C5×D12—21no—
232C4×C5×D3—42no—
233C5×Dic6—21no—
234C5×Dic6—21no—
235C5×Dic6—21no—
236C5×Dic6—42no—
237C5×Dic6C2×D412yescomplemented
238C3×C22⋊D5—42no—
239C3×C22⋊D5—42no—
240C2×C3×Dic5—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×D20—42no—
247C3×D20—42no—
248C3×D20—42no—
249C3×D20—81no—
250C3×D20C2×D412yes—
251C3×C4×D5—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3⋊#168—21no—
255C3⋊#168C2×D412yescomplemented
256C22×C3×D4—51no—
257C22×C3×D4—51no—
258C22×C3×D4—101no—
259C2×#235C2×D511yescharacteristic, complemented
260C22×Dic6C2×D511yescharacteristic, complemented
261C3×#127—51no—
262C3×#121—51no—
263C3×#121—51no—
264C3×#121—101no—
265C3×#120—101no—
266C3×#120—101no—
267C3×C4×D4—51no—
268C3×C4×D4C2×D511yescharacteristic
269#939—21no—
270C2×#214—51no—
271C2×#214—51no—
272C2×#214—51no—
273C2×#214—51no—
274C2×#214—51no—
275C2×#214—51no—
276C2×#214—104no—
277#932—104no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930C2×D511yescharacteristic, complemented
282#924C2×D511yescharacteristic, complemented
283C2×#208—51no—
284C22×C3⋊C8—51no—
285#896—21no—
286#885—21no—
287#67⋊C4—21no—
288#875C2×D511yescharacteristic, complemented
289C4×Dic6C2×D511yescharacteristic, complemented
290#832—51no—
291#832—51no—
292#832—51no—
293#830—51no—
294#830—51no—
295#810—51no—
296#810—51no—
297#809—51no—
298#807—51no—
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C23×D5—21no—
302C23×D5—21no—
303C5×#41—62no—
304C5×#41—121no—
305C2×C5×Q8—31no—
306C2×C5×Q8—31no—
307C2×C5×Q8—62no—
308C2×C5×Q8—61no—
309C2×C5×Q8—121no—
310C2×C5×D4—31no—
311C2×C5×D4—61no—
312C2×C5×D4—61no—
313C2×C5×D4#6711yescharacteristic
314C22×C4×C5—61no—
315C22×C4×C5—61no—
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—21no—
319C2×C22⋊D5—21no—
320D4×D5—44no—
321C2×D20—22no—
322C2×D20—22no—
323C2×D20—21no—
324C2×D20—21no—
325C2×D20—21no—
326C2×D20—21no—
327C2×D20—41no—
328C2×D20—41no—
329C2×D20C22×D311yescharacteristic
330C2×D20C22×D311yescharacteristic
331C2×D20C22×D311yescharacteristic
332C2×C4×D5—21no—
333C5×C4⋊C4—31no—
334C5×C4⋊C4—61no—
335C5×C4⋊C4—61no—
336C5×C4⋊C4#6711yescharacteristic
337C5×C22⋊C4—61no—
338C5×C22⋊C4—61no—
339C5×C22⋊C4—61no—
340C5×C22⋊C4—61no—
341C5×C22⋊C4#6711yescharacteristic
342C5×C22⋊C4#6711yescharacteristic
343C42×C5—61no—
344C42×C5C22×D311yescharacteristic
345#688—34no—
346#688—62no—
347#688—62no—
348#688—62no—
349#688—62no—
350#688—121no—
351#686—62no—
352#686—62no—
353#686—121no—
354#685—21no—
355#685—21no—
356#685—21no—
357C4⋊Dic5C22×D311yescharacteristic
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—31no—
367D42—51no—
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—41no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C3×D5—22no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—84no—
399C2×C3×D5—84no—
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—41no—
407C5×Dic3—22no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C24×C3—101no—
411C24×C3—101no—
412C2×C3×D4—51no—
413C2×C3×D4—51no—
414C2×C3×D4—51no—
415C2×C3×D4—102no—
416C2×C3×D4—102no—
417C2×C3×D4—101no—
418C2×C3×D4—101no—
419C2×C3×D4—101no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—201no—
424C2×C3×D4—201no—
425C2×C3×D4—204no—
426C2×C3×D4C22⋊D511yescharacteristic
427C22×C3×C4—101no—
428C22×C3×C4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C2×#67—21no—
431C2×#67—21no—
432C22×Dic3—21no—
433#235—22no—
434#235—41no—
435C2×D12C22×D511yescharacteristic
436C2×C4×D3—21no—
437C2×Dic6—22no—
438C2×Dic6—21no—
439C2×Dic6—41no—
440C2×Dic6C22×D511yescharacteristic
441C2×Dic6C22×D511yescharacteristic
442C3×C4⋊C4—51no—
443C3×C4⋊C4C22⋊D511yescharacteristic
444C3×C22⋊C4—101no—
445C3×C22⋊C4—101no—
446C3×C22⋊C4—101no—
447C3×C22⋊C4C22⋊D511yescharacteristic
448C3×C22⋊C4C22⋊D511yescharacteristic
449C3×C42C22×D511yescharacteristic
450#217—21no—
451#214—54no—
452#214—102no—
453#214—102no—
454#214—102no—
455#214—102no—
456#214—201no—
457#213—102no—
458#213—102no—
459#213—201no—
460(C2×D3)⋊C4—21no—
461(C2×D3)⋊C4—21no—
462(C2×D3)⋊C4—21no—
463C4⋊Dic3C22×D511yescharacteristic
464Dic3⋊C4—21no—
465Dic3⋊C4—21no—
466C4×Dic3—21no—
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×C5C2×#6711yescharacteristic
475C23×C5C2×#6711yescharacteristic
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—42no—
480C22×D5—42no—
481C22×D5—42no—
482C22×D5—42no—
483C22×D5—81no—
484C22×D5—81no—
485C5×Q8—32no—
486C5×Q8—61no—
487C5×Q8—61no—
488C5×Q8—61no—
489C5×Q8—122no—
490C5×D4—22no—
491C5×D4—61no—
492C5×D4—61no—
493C5×D4—122no—
494C5×D4—122no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5—122no—
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—
512D20—21no—
513D20—21no—
514D20—21no—
515D20—21no—
516D20—21no—
517D20—42no—
518D20—42no—
519D20—42no—
520D20—81no—
521D20D3×D412yes—
522C4×D5—42no—
523#168—32no—
524#168—61no—
525#168—61no—
526#168—61no—
527C2×#41—31no—
528C22×Q8—31no—
529C22×D4—51no—
530C22×D4—51no—
531C22×D4—101no—
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—51no—
546#124—31no—
547#124—61no—
548C22⋊Q8—31no—
549C22⋊Q8—61no—
550#121—31no—
551#121—51no—
552#121—51no—
553#121—61no—
554#121—101no—
555#120—101no—
556#120—101no—
557C4×Q8—31no—
558C4×D4—51no—
559C4×D4—61no—
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—42no—
578C3×D5—81no—
579C3×D5—81no—
580C5×D3—81no—
581C23×C3—101no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—202no—
585C23×C3—202no—
586C23×C3—202no—
587C23×C3—202no—
588C23×C3—401no—
589C23×C3—401no—
590C23×C3C2×C22⋊D511yescharacteristic
591C23×C3C2×C22⋊D511yescharacteristic
592C22×D3—21no—
593C3×D4—22no—
594C3×D4—52no—
595C3×D4—101no—
596C3×D4—101no—
597C3×D4—101no—
598C3×D4—101no—
599C3×D4—101no—
600C3×D4—202no—
601C3×D4—202no—
602C3×D4—202no—
603C3×D4—202no—
604C3×D4—202no—
605C3×D4—401no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—101no—
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—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—42no—
623D12—21no—
624D12—21no—
625C4×D3—42no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—42no—
630Dic6D4×D512yescomplemented
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—121no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5#93212yescomplemented
644C22×C5C22×#6711yescharacteristic
645C2×D5—22no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5—41no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—41no—
654C2×D5—84no—
655C2×D5—84no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—62no—
661C4×C5—121no—
662C4×C5—121no—
663C4×C5C2×D3×D411yescharacteristic
664C4×C5#100411yescharacteristic
665Dic5—41no—
666C24—101no—
667C24—101no—
668#41—62no—
669#41—121no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×Q8—62no—
673C2×Q8—61no—
674C2×Q8—121no—
675C2×D4—31no—
676C2×D4—51no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—102no—
682C2×D4—102no—
683C2×D4—101no—
684C2×D4—101no—
685C2×D4—101no—
686C2×D4—101no—
687C2×D4—101no—
688C2×D4—101no—
689C2×D4—201no—
690C2×D4—201no—
691C2×D4—204no—
692C2×D4#120111yescharacteristic
693C22×C4—61no—
694C22×C4—61no—
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—61no—
716C4⋊C4—61no—
717C4⋊C4#120111yescharacteristic
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4#120111yescharacteristic
726C22⋊C4#120111yescharacteristic
727C42—61no—
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—102no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3—201no—
739C22×C3—201no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—201no—
743C22×C3—201no—
744C22×C3—404no—
745C22×C3—404no—
746C22×C3#409512yescomplemented
747C22×C3C22×C22⋊D511yescharacteristic
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—201no—
756C3×C4C2×D4×D511yescharacteristic
757C3×C4#414411yescharacteristic
758Dic3—22no—
759Dic3—41no—
760Dic3—41no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—241no—
764C2×C5C2×#93211yescharacteristic
765C2×C5D4×#6711yescharacteristic
766C2×C5#583611yescharacteristic
767D5—42no—
768D5—81no—
769D5—81no—
770C23—61no—
771C23—101no—
772C23—101no—
773C23—101no—
774C23—202no—
775C23—202no—
776C23—202no—
777C23—202no—
778C23—401no—
779C23—401no—
780C23C2×#120111yescharacteristic
781C23C2×#120111yescharacteristic
782Q8—32no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—122no—
787D4—22no—
788D4—52no—
789D4—61no—
790D4—61no—
791D4—101no—
792D4—101no—
793D4—101no—
794D4—101no—
795D4—101no—
796D4—122no—
797D4—122no—
798D4—202no—
799D4—202no—
800D4—202no—
801D4—202no—
802D4—202no—
803D4—401no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—101no—
812C2×C4—122no—
813C2×C4—122no—
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—202no—
827C2×C3—401no—
828C2×C3—401no—
829C2×C3D4×C22⋊D511yescharacteristic
830C2×C3C2×#409511yescharacteristic
831C2×C3#6617111yescharacteristic
832D3—81no—
833C5#8349111yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—102no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—201no—
844C22—201no—
845C22—201no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—201no—
850C22—201no—
851C22—404no—
852C22—404no—
853C22#9129812yescomplemented
854C22C22×#120111yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—62no—
860C4—121no—
861C4—121no—
862C4—201no—
863C4D3×D4×D511yescharacteristic
864C4#9202511yescharacteristic
865C3#1061527311yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—202no—
869C2—241no—
870C2—401no—
871C2—401no—
872C2C2×#9129811yescharacteristic
873C2D4×#120111yescharacteristic
874C2#1175530311yescharacteristic
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×#5552C2semidirect
2. C3×D4×D20C2semidirect
3. C22×#6655C2semidirect
4. C2×#91298C2semidirect
5. #11751112C2semidirect
6. #11748546C2semidirect
7. #11748536C2semidirect
8. #11748527C2semidirect
9. #11748522C2semidirect
10. #11748517C2semidirect
11. #11748510C2semidirect
12. #11747068C2semidirect
13. #11747048C2semidirect
14. #11747041C2semidirect
15. #11747027C2semidirect
17. C2×C5×#235C22semidirect
18. C22×C5×Dic6C22semidirect
23. C2×#6710C22semidirect
24. C22×C3⋊#168C22semidirect
26. C5×#930C22semidirect
27. C5×#924C22semidirect
31. C5×#875C22semidirect
32. C4×C5×Dic6C22semidirect
43. C2×#6655C22semidirect
44. C2×#6655C22semidirect
45. C2×#6655C22semidirect
46. C2×#6655C22semidirect
49. C2×#6652C22semidirect
50. C2×#6652C22semidirect
51. #91114C22semidirect
52. #91114C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. #91087C22semidirect
55. #90989C22semidirect
56. #90972C22semidirect
57. #90972C22semidirect
58. #90966C22semidirect
60. #90964C22semidirect
61. #90964C22semidirect
66. D4×D20D3semidirect
137. #6655D4semidirect
144. #5552D5semidirect
237. C5×Dic6C2×D4semidirect
255. C3⋊#168C2×D4semidirect
259. C2×#235C2×D5semidirect
260. C22×Dic6C2×D5semidirect
281. #930C2×D5semidirect
282. #924C2×D5semidirect
288. #875C2×D5semidirect
289. C4×Dic6C2×D5semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
630. Dic6D4×D5semidirect
643. C22×C5#932semidirect
729. C3×C5#3265semidirect
746. C22×C3#4095semidirect
833. C5#83491semidirect
853. C22#91298semidirect
865. C3#10615273semidirect

Maximal subgroups

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

subgroupindex
C5×#55522
C3×D4×D202
C22×#66552
C2×#912982
#117511122
#117485462
#117485362
#117485272
#117485222
#117485172
#117485102
#117470682
#117470482
#117470412
#117470272
#106152733
#834915