Finite Group Databasebeta

← #14453558

Subgroups — #14453558

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
2C2×#91496C211yesmaximal, characteristic, complemented
3C2×D3×#687C211yesmaximal, characteristic, complemented
4#11752535C211yesmaximal, characteristic, complemented
5#11751117C211yesmaximal, characteristic, complemented
6C3×#65307C211yesmaximal, characteristic, complemented
7#11749056C211yesmaximal, characteristic, complemented
8#11749033C211yesmaximal, characteristic, complemented
9#11747517C211yesmaximal, characteristic, complemented
10#11747494C211yesmaximal, characteristic, complemented
11#11747464C211yesmaximal, characteristic, complemented
12#11747446C211yesmaximal, characteristic, complemented
13#11747060C211yesmaximal, characteristic, complemented
14#11747031C211yesmaximal, characteristic, complemented
15#11746987C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C22×C5×D12—21no—
20C2×#6769C2211yescharacteristic, complemented
21C2×D3×Dic10C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic
23C2×#6716C2211yescharacteristic
24C2×#6715C2211yescharacteristic
25#91764C2211yescharacteristic, complemented
26C5×#930—21no—
27C5×#895C2211yescharacteristic
28C5×#895C2211yescharacteristic
29C5×#882—21no—
30C5×#882—21no—
31C5×#874C2211yescharacteristic
32C4×C5×D12C2211yescharacteristic
33C2×C3×#687C2211yescharacteristic
34C3×C4×Dic10C2211yescharacteristic, complemented
35#91496—24no—
36D3×#687—24no—
37#91460C2211yescharacteristic, complemented
38#91419—21no—
39#91416—21no—
40#91405—21no—
41#91365C2211yescharacteristic, complemented
42#91350—21no—
43C2×#6659C2211yescharacteristic, complemented
44C2×#6659C2211yescharacteristic, complemented
45C2×#6656C2211yescharacteristic, complemented
46C2×#6656C2211yescharacteristic, complemented
47C2×#6654C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic, complemented
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91094C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic
55C3×#3942C2211yescharacteristic, complemented
56C3×#3939C2211yescharacteristic, complemented
57C3×#3935C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90966C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#79794—51nomaximal, Hall
63C5×D42—31no—
64C22×#687—31no—
65C2×#4078—31no—
66#65886—31no—
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#65307D311yescharacteristic, complemented
76#65305—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C2×D60C2311yescharacteristic
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C5×D3×D4—22no—
87C5×D3×D4—22no—
88C5×D3×D4—41no—
89C5×D3×D4—41no—
90C2×C5×D12—21no—
91C2×C5×D12—21no—
92C2×C5×D12—21no—
93C2×C5×D12—21no—
94C2×C5×D12—44no—
95C2×C5×D12D411yescharacteristic
96C2×C5×D12C2311yescharacteristic
97C2×C5×D12C2311yescharacteristic
98C2×C4×C5×D3C2311yescharacteristic
99C2×C4×C5×D3C2311yescharacteristic
100C2×C3×Dic10C2311yescharacteristic
101C2×#1204—21no—
102C2×#1203—21no—
103C2×#1203—21no—
104C2×#1200—21no—
105C2×D3×Dic5—21no—
106#6769—22no—
107#6769—41no—
108D3×Dic10—22no—
109D3×Dic10—41no—
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112C3×C42×C5C2311yescharacteristic
113#6716—22no—
114#6715—22no—
115#6714—21no—
116#6714—21no—
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×(C2×D3)⋊C4D411yescharacteristic
123C5×C4⋊Dic3D411yescharacteristic
124C3×#687D414yescomplemented
125C3×C4⋊Dic5C2311yescharacteristic
126C3×#683—21no—
127C3×C4×Dic5—21no—
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130#6668—21no—
131#6667—21no—
132(C2×D3)⋊Dic5—21no—
133#6659—22no—
134#6659—41no—
135#6656—22no—
136#6656—22no—
137#6654—22no—
138#6654—41no—
139#6650—22no—
140D3×#168—22no—
141C2×#914—51no—
142C2×D3×SD16—51no—
143#5576—51no—
144D4×D12D511yescharacteristic, complemented
145C3×#440—51no—
146#5027—51no—
147#5016—51no—
148#4886—51no—
149#4883—51no—
150#4810—51no—
151#4806—51no—
152#4776—51no—
153#4773—51no—
154#4712—51no—
155#4706—51no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709—31no—
160C22×Dic10—31no—
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—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—64no—
176C2×#687C2×D311yescharacteristic
177#4078—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4042—61no—
186#4031—61no—
187#4027—61no—
188#4021—31no—
189C4×Dic10C2×D311yescharacteristic, complemented
190#3964—31no—
191#3964—31no—
192#3964C2×D311yescharacteristic
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3942—31no—
196#3942C2×D311yescharacteristic, complemented
197#3941—31no—
198#3939C2×D311yescharacteristic, complemented
199C4⋊#168—31no—
200#3935C2×D311yescharacteristic, complemented
201#3265—151noSylow
202C23×C3×C5—21no—
203C22×D15—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—42no—
209C22×C5×D3—42no—
210C22×C5×D3—81no—
211C22×C5×D3—81no—
212C22×C5×D3C2×D411yescharacteristic
213C22×C5×D3C2×D411yescharacteristic
214C3×C5×D4—21no—
215C3×C5×D4C2×D412yes—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—42no—
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2411yescharacteristic
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224Dic30—21no—
225Dic30—21no—
226C5×#67—42no—
227C5×#67—42no—
228C2×C5×Dic3C2×D411yescharacteristic
229C2×C5×Dic3C2×D411yescharacteristic
230C5×D12—22no—
231C5×D12—21no—
232C5×D12—21no—
233C5×D12—21no—
234C5×D12—21no—
235C5×D12—42no—
236C5×D12—42no—
237C5×D12—42no—
238C5×D12—81no—
239C4×C5×D3—21no—
240C4×C5×D3—21no—
241C4×C5×D3—21no—
242C4×C5×D3—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C3×Dic10—21no—
246C3×Dic10C2×D412yescomplemented
247#1204—42no—
248#1203—42no—
249#1203—42no—
250#1200—42no—
251D3×Dic5—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×#239—51no—
257C2×D3×Q8—51no—
258C2×D3×D4C2×D511yescharacteristic
259C2×D3×D4C2×D511yescharacteristic
260C22×D12—21no—
261C2×C3×SD16—51no—
262C3×C4×Q8—51no—
263C3×C4×D4C2×D511yescharacteristic
264C2×#215—51no—
265C2×#215—51no—
266C2×#214—51no—
267C2×#213—51no—
268#930—21no—
269#914—104no—
270D3×SD16—104no—
271C2×D24—51no—
272C2×D24—51no—
273C2×#204—51no—
274C2×#204—51no—
275C2×ΓL(1,𝔽25)—51no—
276C2×D3×C8—51no—
277#897—51no—
278#897—101no—
279#895—51no—
280#895—101no—
281#895C2×D511yescharacteristic
282#895C2×D511yescharacteristic
283#882—21no—
284#882—21no—
285#875—51no—
286#875—101no—
287#874C2×D511yescharacteristic
288C4×D12—101no—
289C4×D12C2×D511yescharacteristic
290C3×#107—51no—
291C3×#103—51no—
292C3×#102—51no—
293C3×#97—51no—
294(C2×D3)⋊C8—51no—
295(C2×D3)⋊C8—51no—
296#810—51no—
297#809—51no—
298#809—51no—
299#809—51no—
300C4⋊(C3⋊C8)—51no—
301C24×C5—61no—
302C24×C5—61no—
303C2×C5×D4—31no—
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—61no—
307C2×C5×D4—61no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—62no—
311C2×C5×D4—62no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—124no—
315C2×C5×D4—121no—
316C2×C5×D4—121no—
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—21no—
319C22×C4×C5—31no—
320C22×C4×C5—31no—
321C2×C22⋊D5—61no—
322C2×C22⋊D5—61no—
323C22×Dic5—61no—
324#709—62no—
325#709—121no—
326C2×D20—31no—
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C2×Dic10—62no—
330C2×Dic10—61no—
331C2×Dic10—121no—
332C2×Dic10C22×D311yescharacteristic
333C5×C4⋊C4—31no—
334C5×C4⋊C4C22×D311yescharacteristic
335C5×C22⋊C4—21no—
336C5×C22⋊C4—31no—
337C5×C22⋊C4—31no—
338C5×C22⋊C4—61no—
339C5×C22⋊C4—61no—
340C42×C5C22×D311yescharacteristic
341C22⋊Dic5—61no—
342#687—62no—
343#687—62no—
344#687—62no—
345#687—62no—
346#687—121no—
347#687D1214yescomplemented
348#686—62no—
349#686—62no—
350#686—121no—
351#685—61no—
352#685—61no—
353#685—61no—
354C4⋊Dic5C22×D311yescharacteristic
355#683—21no—
356#683—61no—
357C4×Dic5—21no—
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—62no—
362C2×#168C22×D311yescharacteristic
363C2×#168C22×D311yescharacteristic
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—151no—
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—51no—
378#435—151no—
379C22×C3×C5—22no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5C22×D411yescharacteristic
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×C5×D3—21no—
387C2×C5×D3—21no—
388C2×C5×D3—21no—
389C2×C5×D3—21no—
390C2×C5×D3—21no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—84no—
398C2×C5×D3—84no—
399C2×C5×D3AGL(1,ℤ/8)12yescomplemented
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—41no—
403C3×C4×C5C22×D411yescharacteristic
404C3×C4×C5H(5,𝔽2)11yescharacteristic
405Dic15—41no—
406C3×Dic5—22no—
407C3×Dic5—41no—
408C5×Dic3—21no—
409C5×Dic3—21no—
410C23×D3—21no—
411C23×D3—21no—
412C2×C3×Q8—51no—
413C2×C3×D4C22×D511yescharacteristic
414C22×C3×C4—21no—
415C2×#67—21no—
416C2×#67—21no—
417#239—102no—
418#239—201no—
419D3×Q8—102no—
420D3×Q8—201no—
421D3×D4—22no—
422D3×D4—22no—
423D3×D4—41no—
424D3×D4—41no—
425C2×D12—21no—
426C2×D12—21no—
427C2×D12—21no—
428C2×D12—21no—
429C2×D12—44no—
430C2×D12—51no—
431C2×D12—101no—
432C2×D12—101no—
433C2×D12C22⋊D511yescharacteristic
434C2×D12C22×D511yescharacteristic
435C2×D12C22×D511yescharacteristic
436C2×C4×D3—101no—
437C2×C4×D3—101no—
438C2×C4×D3C22×D511yescharacteristic
439C2×C4×D3C22×D511yescharacteristic
440C2×Dic6—51no—
441C2×Dic6—101no—
442C3×SD16—54no—
443C2×C3×C8—51no—
444C2×C3×C8—51no—
445C3×C4⋊C4—51no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4C22×D511yescharacteristic
448C3×C22⋊C4—21no—
449C3×C42—101no—
450C3×C42C22×D511yescharacteristic
451#215—102no—
452#215—102no—
453#214—102no—
454#213—102no—
455(C2×D3)⋊C4—21no—
456(C2×D3)⋊C4—21no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4—101no—
461(C2×D3)⋊C4C22⋊D511yescharacteristic
462(C2×D3)⋊C4C22⋊D511yescharacteristic
463C4⋊Dic3—101no—
464C4⋊Dic3C22⋊D511yescharacteristic
465C2×C3⋊C8—51no—
466C2×C3⋊C8—51no—
467D24—102no—
468D24—201no—
469#204—102no—
470#204—201no—
471ΓL(1,𝔽25)—102no—
472D3×C8—102no—
473C23×C5—21no—
474C23×C5—31no—
475C23×C5—31no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—122no—
479C23×C5—122no—
480C23×C5—122no—
481C23×C5—122no—
482C23×C5—241no—
483C23×C5—241no—
484C22×D5—61no—
485C5×D4—21no—
486C5×D4—62no—
487C5×D4—61no—
488C5×D4—61no—
489C5×D4—61no—
490C5×D4—61no—
491C5×D4—122no—
492C5×D4—122no—
493C5×D4—122no—
494C5×D4—122no—
495C5×D4—122no—
496C5×D4—241no—
497C5×D4C2×D1212yes—
498C2×C4×C5—21no—
499C2×C4×C5—31no—
500C2×C4×C5—31no—
501C2×C4×C5—42no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5D3×D411yescharacteristic
507C2×C4×C5D3×D411yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—61no—
514C2×Dic5—122no—
515D20—61no—
516D20—61no—
517C4×D5—122no—
518Dic10—21no—
519Dic10—61no—
520Dic10—61no—
521Dic10—122no—
522Dic10C2×D1212yescomplemented
523#168—21no—
524#168—61no—
525#168—61no—
526#168C2×D1212yescomplemented
527C2×#41—151no—
528C22×Q8—151no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—61no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—51no—
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—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—31no—
551#121—31no—
552#121—61no—
553#121—151no—
554#121—301no—
555#120—61no—
556#120—61no—
557C4×Q8—51no—
558C4×D4—31no—
559C4×D4—301no—
560C4×D4D3×D511yescharacteristic
561#107—51no—
562C4⋊C8—151no—
563#103—51no—
564#103—151no—
565#102—51no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—51no—
572C2×C3×C5—42no—
573C2×C3×C5D4211yescharacteristic
574C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
575C2×C3×C5#57711yescharacteristic
576D15—81no—
577C5×D3—22no—
578C5×D3—41no—
579C5×D3—81no—
580C5×D3—81no—
581C23×C3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—42no—
585C22×D3—42no—
586C22×D3—42no—
587C22×D3—42no—
588C22×D3—81no—
589C22×D3—81no—
590C22×D3—101no—
591C22×D3C2×C22⋊D511yescharacteristic
592C22×D3C2×C22⋊D511yescharacteristic
593C3×Q8—52no—
594C3×Q8—101no—
595C3×D4—21no—
596C3×D4D4×D512yes—
597C2×C3×C4—21no—
598C2×C3×C4—42no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4C2×C22⋊D511yescharacteristic
602C2×C3×C4C2×C22⋊D511yescharacteristic
603C2×C3×C4C23×D511yescharacteristic
604#67—42no—
605#67—42no—
606C2×Dic3—101no—
607C2×Dic3C2×C22⋊D511yescharacteristic
608C2×Dic3C2×C22⋊D511yescharacteristic
609D12—22no—
610D12—21no—
611D12—21no—
612D12—21no—
613D12—21no—
614D12—42no—
615D12—42no—
616D12—42no—
617D12—81no—
618D12—101no—
619D12—101no—
620D12—202no—
621D12—202no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—202no—
627C4×D3—202no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3×C8—52no—
632C3×C8—101no—
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—22no—
636C22×C5—32no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—61no—
640C22×C5—61no—
641C22×C5—61no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5—121no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5—121no—
650C22×C5—244no—
651C22×C5—244no—
652C22×C5C2×D3×D411yescharacteristic
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—121no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—41no—
659C4×C5—61no—
660C4×C5—61no—
661C4×C5C22×D1211yescharacteristic
662C4×C5#100911yescharacteristic
663Dic5—22no—
664Dic5—41no—
665Dic5—121no—
666C24—61no—
667C24—61no—
668#41—302no—
669#41—601no—
670C2×Q8—51no—
671C2×Q8—151no—
672C2×Q8—301no—
673C2×Q8—302no—
674C2×Q8—601no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—124no—
687C2×D4—121no—
688C2×D4—121no—
689C2×D4—151no—
690C2×D4—301no—
691C2×D4—301no—
692C2×D4C2×D3×D511yescharacteristic
693C22×C4—21no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—301no—
697C22×C4—301no—
698SD16—54no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—31no—
714C4⋊C4—51no—
715C4⋊C4—101no—
716C4⋊C4—301no—
717C4⋊C4C2×D3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—31no—
720C22⋊C4—31no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—101no—
728C42C2×D3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—22no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3C22×C22⋊D511yescharacteristic
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—84no—
746C2×D3—84no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3#407812yescomplemented
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—41no—
754C3×C4—102no—
755C3×C4—201no—
756C3×C4C2×D4×D511yescharacteristic
757C3×C4#414411yescharacteristic
758Dic3—21no—
759Dic3—21no—
760Dic3—201no—
761C2×C5—42no—
762C2×C5—62no—
763C2×C5—121no—
764C2×C5—241no—
765C2×C5—241no—
766C2×C5D4×D1211yescharacteristic
767C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
768C2×C5#577811yescharacteristic
769D5—241no—
770C23—21no—
771C23—31no—
772C23—31no—
773C23—61no—
774C23—61no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23—122no—
779C23—241no—
780C23—241no—
781C23—301no—
782Q8—52no—
783Q8—101no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—21no—
788D4—62no—
789D4—61no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—122no—
794D4—122no—
795D4—122no—
796D4—122no—
797D4—122no—
798D4—241no—
799D4—301no—
800D4—301no—
801D4—602no—
802D4—602no—
803D4D5×D1212yes—
804C2×C4—21no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—42no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—301no—
815C2×C4—602no—
816C2×C4—602no—
817C2×C4D3×C22⋊D511yescharacteristic
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—52no—
821C8—101no—
822C8—301no—
823C8—301no—
824C2×C3—42no—
825C2×C3C2×#407811yescharacteristic
826C2×C3D4×C22⋊D511yescharacteristic
827C2×C3#6617011yescharacteristic
828D3—22no—
829D3—41no—
830D3—81no—
831D3—81no—
832D3—401no—
833C5#7979411yescharacteristic, complemented, Sylow
834C22—22no—
835C22—32no—
836C22—41no—
837C22—41no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—244no—
850C22—244no—
851C22—601no—
852C22—601no—
853C22—601no—
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—21no—
857C4—41no—
858C4—61no—
859C4—61no—
860C4—102no—
861C4—201no—
862C4—601no—
863C4C2×D5×D1211yescharacteristic
864C4#9201811yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—42no—
867C2—62no—
868C2—121no—
869C2—241no—
870C2—241no—
871C2—1201no—
872C2D12×C22⋊D511yescharacteristic
873C2D3×#407811yescharacteristic
874C2#1175534011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
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 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×D4×D12C2semidirect
2. C2×#91496C2semidirect
3. C2×D3×#687C2semidirect
4. #11752535C2semidirect
5. #11751117C2semidirect
6. C3×#65307C2semidirect
7. #11749056C2semidirect
8. #11749033C2semidirect
9. #11747517C2semidirect
10. #11747494C2semidirect
11. #11747464C2semidirect
12. #11747446C2semidirect
13. #11747060C2semidirect
14. #11747031C2semidirect
15. #11746987C2semidirect
20. C2×#6769C22semidirect
21. C2×D3×Dic10C22semidirect
25. #91764C22semidirect
34. C3×C4×Dic10C22semidirect
37. #91460C22semidirect
41. #91365C22semidirect
43. C2×#6659C22semidirect
44. C2×#6659C22semidirect
45. C2×#6656C22semidirect
46. C2×#6656C22semidirect
47. C2×#6654C22semidirect
48. C2×#6654C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91094C22semidirect
52. #91093C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
55. C3×#3942C22semidirect
56. C3×#3939C22semidirect
57. C3×#3935C22semidirect
58. #90966C22semidirect
59. #90966C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
75. #65307D3semidirect
124. C3×#687D4semidirect
144. D4×D12D5semidirect
189. C4×Dic10C2×D3semidirect
196. #3942C2×D3semidirect
198. #3939C2×D3semidirect
200. #3935C2×D3semidirect
246. C3×Dic10C2×D4semidirect
255. C3×#168C2×D4semidirect
347. #687D12semidirect
399. C2×C5×D3AGL(1,ℤ/8)semidirect
522. Dic10C2×D12semidirect
526. #168C2×D12semidirect
729. C3×C5#3265semidirect
750. C2×D3#4078semidirect
833. C5#79794semidirect
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
C2×#914962
C2×D3×#6872
#117525352
#117511172
C3×#653072
#117490562
#117490332
#117475172
#117474942
#117474642
#117474462
#117470602
#117470312
#117469872
#106152223
#797945