Finite Group Databasebeta

← #14453370

Subgroups — #14453370

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5717C211yesmaximal, characteristic, complemented
2C2×#91496C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4#11752749C211yesmaximal, characteristic, complemented
5#11751173C211yesmaximal, characteristic, complemented
6C3×#65363C211yesmaximal, characteristic, complemented
7#11749162C211yesmaximal, characteristic, complemented
8#11749152C211yesmaximal, characteristic, complemented
9#11749058C211yesmaximal, characteristic, complemented
10#11749050C211yesmaximal, characteristic, complemented
11#11749032C211yesmaximal, characteristic, complemented
12#11749029C211yesmaximal, characteristic, complemented
13#11747034C211yesmaximal, characteristic, complemented
14#11747025C211yesmaximal, characteristic, complemented
15#11746987C211yesmaximal, characteristic, complemented
16#10615219—31nomaximal, Hall
17C2×C5×D3×D4—21no—
18C2×C5×D3×D4C2211yescharacteristic
19C2×C5×D3×D4C2211yescharacteristic, complemented
20C2×D3×D20C2211yescharacteristic, complemented
21C2×#6769C2211yescharacteristic, complemented
22C3×C5×#127C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24C2×#6715C2211yescharacteristic, complemented
25C4×D60C2211yescharacteristic, complemented
26C5×#938—21no—
27C5×#938C2211yescharacteristic
28C5×#938C2211yescharacteristic, complemented
29C5×#937—21no—
30C5×#937—21no—
31C4×C5×D12C2211yescharacteristic
32C4×C5×D12C2211yescharacteristic, complemented
33C2×C3×#687C2211yescharacteristic, complemented
34C2×C3×#687C2211yescharacteristic, complemented
35C2×C3×#686C2211yescharacteristic, complemented
36C2×C3×#686C2211yescharacteristic, complemented
37C3×#4021C2211yescharacteristic, complemented
38#91496—24no—
39D3×#686—24no—
40#91475—21no—
41#91473—21no—
42#91461—21no—
43#91456C2211yescharacteristic, complemented
44#91369C2211yescharacteristic, complemented
45#91356—21no—
46C2×#6656C2211yescharacteristic, complemented
47C2×#6654C2211yescharacteristic
48C2×#6652C2211yescharacteristic
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54C3×#3935C2211yescharacteristic, complemented
55#90985C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#81856—51nomaximal, Hall
63C5×D42—31no—
64C2×#4078—31no—
65C22×#686—31no—
66#65884—31no—
67#65507—31no—
68#65506—31no—
69#65363D311yescharacteristic, complemented
70#65361—31no—
71#65330—31no—
72#65328—31no—
73#65326—31no—
74#65325—31no—
75#65305—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C22×D3×D5—21no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C2×D60C2311yescharacteristic
86C2×C4×D15—21no—
87C2×C5×#67—21no—
88C2×C5×#67—21no—
89C2×C5×#67—21no—
90C2×C5×#67—21no—
91C5×D3×D4—22no—
92C5×D3×D4—22no—
93C5×D3×D4—41no—
94C5×D3×D4—41no—
95C5×D3×D4—44no—
96C2×C5×D12D411yescharacteristic
97C2×C5×D12C2311yescharacteristic
98C2×C4×C5×D3—21no—
99C2×C4×C5×D3C2311yescharacteristic
100C2×C4×C5×D3C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×Dic10C2311yescharacteristic
103C2×#1203—21no—
104C2×#1202—21no—
105C2×#1201—21no—
106C2×#1200—21no—
107D3×D20—22no—
108D3×D20—41no—
109#6769—22no—
110#6769—41no—
111C3×C42×C5C2311yescharacteristic
112#6715—22no—
113#6715—22no—
114#6714—21no—
115C4⋊Dic15C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C5×#217—21no—
119C5×#217—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×(C2×D3)⋊C4D411yescharacteristic
123C5×C4⋊Dic3D411yescharacteristic
124C5×C4⋊Dic3C2311yescharacteristic
125C3×#687—22no—
126C3×#687—41no—
127C3×#686—22no—
128C3×#686—41no—
129C3×#685—21no—
130C3×#685—21no—
131C2×C3×#168C2311yescharacteristic
132C2×C3×#168C2311yescharacteristic
133#6669—21no—
134(C2×D3)⋊Dic5—21no—
135#6665—21no—
136#6656—22no—
137#6654D414yescomplemented
138#6652—22no—
139#6650—22no—
140D3×#168—22no—
141C2×#914—51no—
142C2×D3×D8—51no—
143#5717D511yescharacteristic, complemented
144#5676—51no—
145C3×#496—51no—
146#5172—51no—
147#5171—51no—
148#5169—51no—
149#5159—51no—
150#5156—51no—
151#5156—51no—
152#5072—51no—
153#5057—51no—
154#4711—51no—
155#4706—51no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709—31no—
160C22×D20—31no—
161C5×#127C2×D311yescharacteristic, complemented
162C5×#121—31no—
163C5×#121—31no—
164C5×#121—61no—
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169#4083—61no—
170C2×#687—31no—
171C2×#687C2×D311yescharacteristic, complemented
172C2×#687C2×D311yescharacteristic, complemented
173#4078—64no—
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—64no—
179C2×#686C2×D311yescharacteristic, complemented
180C2×#686C2×D311yescharacteristic, complemented
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4040—61no—
186#4030—61no—
187D5×C22⋊C4—61no—
188#4021C2×D311yescharacteristic, complemented
189C4×D20—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3942—31no—
196#3941—31no—
197#3941—31no—
198#3940—31no—
199C4⋊#168—31no—
200#3935C2×D311yescharacteristic, complemented
201#3264—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C22×D15—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
214C22×C3×D5—21no—
215C2×D3×D5—42no—
216C2×D3×D5—42no—
217C2×D3×D5—81no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—42no—
223C3×C5×D4—81no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227C2×Dic15—21no—
228D60—21no—
229D60C2×D412yescomplemented
230C4×D15—81no—
231C5×#67—42no—
232C5×#67—42no—
233C5×#67—42no—
234C5×#67—42no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3C2×D411yescharacteristic
237C2×C5×Dic3C2×D411yescharacteristic
238C5×D12—22no—
239C5×D12—21no—
240C5×D12C2×D412yes—
241C4×C5×D3—21no—
242C4×C5×D3—21no—
243C4×C5×D3—21no—
244C4×C5×D3—21no—
245C4×C5×D3—42no—
246C2×C3×Dic5—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×Dic10—21no—
250C3×Dic10—21no—
251#1203—42no—
252#1202—42no—
253#1201—81no—
254#1200—42no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C2×#239—51no—
260C2×D3×D4—21no—
261C2×D3×D4—51no—
262C2×D3×D4C2×D511yescharacteristic
263C2×D3×D4C2×D511yescharacteristic, complemented
264C2×C3×SD16—51no—
265C2×C3×SD16—51no—
266C2×C3×D8—51no—
267C2×C3×D8—51no—
268C3×#127C2×D511yescharacteristic, complemented
269C3×#124—51no—
270#946—51no—
271C2×#215—51no—
272#938—21no—
273#938—51no—
274#938C2×D511yescharacteristic
275#938C2×D511yescharacteristic, complemented
276#937—21no—
277#937—21no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#914—104no—
282D3×D8—104no—
283C2×D24—51no—
284C2×ΓL(1,𝔽25)—51no—
285C2×D3×C8—51no—
286#884—101no—
287#883—101no—
288#882—101no—
289D3×C22⋊C4—101no—
290C4×D12—51no—
291C4×D12C2×D511yescharacteristic
292C4×D12C2×D511yescharacteristic, complemented
293C3×#97—51no—
294#835—51no—
295#832—51no—
296#832—51no—
297#832—51no—
298#821—51no—
299#821—51no—
300(C2×D3)⋊C8—51no—
301(C2×D3)⋊C8—51no—
302#817—51no—
303C4⋊(C3⋊C8)—51no—
304C24×C5—61no—
305C24×C5—61no—
306C23×D5—61no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—31no—
310C2×C5×D4—31no—
311C2×C5×D4—61no—
312C2×C5×D4—61no—
313C2×C5×D4—62no—
314C2×C5×D4—62no—
315C2×C5×D4—61no—
316C2×C5×D4—61no—
317C2×C5×D4—121no—
318C2×C5×D4—121no—
319C2×C5×D4—124no—
320C2×C5×D4C22×D311yescharacteristic
321C2×C5×D4C22×D311yescharacteristic
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—61no—
325C2×C22⋊D5—61no—
326C2×C22⋊D5—61no—
327#709—62no—
328#709—121no—
329C2×D20—31no—
330C2×D20—62no—
331C2×D20—61no—
332C2×D20—121no—
333C2×D20C22×D311yescharacteristic
334C2×C4×D5—61no—
335C2×C4×D5—61no—
336C2×Dic10C22×D311yescharacteristic
337C5×C4⋊C4—31no—
338C5×C4⋊C4—31no—
339C5×C22⋊C4—31no—
340C5×C22⋊C4—31no—
341C5×C22⋊C4—61no—
342C5×C22⋊C4—61no—
343C5×C22⋊C4—61no—
344C42×C5C22×D311yescharacteristic
345C22⋊Dic5—61no—
346#687—22no—
347#687—41no—
348#687—62no—
349#686—22no—
350#686—34no—
351#686—41no—
352#686—62no—
353#686—62no—
354#686—62no—
355#685—21no—
356#685—21no—
357#685—61no—
358#685—61no—
359C4⋊Dic5—31no—
360#683—61no—
361#681—62no—
362C2×#168—31no—
363C2×#168—31no—
364C2×#168—62no—
365C2×#168C22×D311yescharacteristic
366C2×#168C22×D311yescharacteristic
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—151no—
370D42—31no—
371#496—51no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—22no—
390C2×D15—41no—
391C2×D15—41no—
392C2×C5×D3—21no—
393C2×C5×D3—21no—
394C2×C5×D3—21no—
395C2×C5×D3—22no—
396C2×C5×D3—21no—
397C2×C5×D3—21no—
398C2×C5×D3—41no—
399C2×C5×D3—41no—
400C2×C5×D3—84no—
401C2×C5×D3—84no—
402C2×C5×D3AGL(1,ℤ/8)12yescomplemented
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5C22×D411yescharacteristic
410C3×C4×C5H(5,𝔽2)11yescharacteristic
411Dic15—41no—
412C3×Dic5—41no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C23×D3—21no—
417C23×D3—21no—
418C23×D3—101no—
419C2×C3×Q8—51no—
420C2×C3×D4—21no—
421C2×C3×D4—21no—
422C2×C3×D4—51no—
423C2×C3×D4C22×D511yescharacteristic
424C2×C3×D4C22×D511yescharacteristic
425C2×#67—21no—
426C2×#67—21no—
427C2×#67—21no—
428C2×#67—21no—
429C2×#67—101no—
430C2×#67—101no—
431#239—102no—
432#239—201no—
433D3×D4—22no—
434D3×D4—22no—
435D3×D4—41no—
436D3×D4—41no—
437D3×D4—44no—
438D3×D4—102no—
439D3×D4—201no—
440C2×D12—51no—
441C2×D12—101no—
442C2×D12C22⋊D511yescharacteristic
443C2×D12C22×D511yescharacteristic
444C2×C4×D3—21no—
445C2×C4×D3—101no—
446C2×C4×D3—101no—
447C2×C4×D3C22×D511yescharacteristic
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—201no—
451C3×D8—102no—
452C3×D8—201no—
453C2×C3×C8—51no—
454C2×C3×C8—51no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C42C22×D511yescharacteristic
458#217—21no—
459#217—21no—
460#217—101no—
461#215—102no—
462#213—102no—
463#213—102no—
464#213—102no—
465(C2×D3)⋊C4—21no—
466(C2×D3)⋊C4—101no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4C22⋊D511yescharacteristic
469(C2×D3)⋊C4C22⋊D511yescharacteristic
470C4⋊Dic3—51no—
471C4⋊Dic3C22⋊D511yescharacteristic
472C4⋊Dic3C22×D511yescharacteristic
473Dic3⋊C4—101no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476D24—54no—
477ΓL(1,𝔽25)—102no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—31no—
482C23×C5—31no—
483C23×C5—61no—
484C23×C5—122no—
485C23×C5—122no—
486C23×C5—122no—
487C23×C5—122no—
488C23×C5—241no—
489C23×C5—241no—
490C22×D5—21no—
491C22×D5—61no—
492C22×D5—122no—
493C22×D5—122no—
494C22×D5—241no—
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—32no—
500C5×D4—42no—
501C5×D4—62no—
502C5×D4—61no—
503C5×D4—81no—
504C5×D4—122no—
505C5×D4—122no—
506C5×D4—122no—
507C5×D4—122no—
508C2×C4×C5—31no—
509C2×C4×C5—31no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—122no—
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5D3×D411yescharacteristic
518C2×C4×C5C23×D311yescharacteristic
519C22⋊D5—122no—
520C22⋊D5—241no—
521C2×Dic5—21no—
522C2×Dic5—61no—
523D20—21no—
524D20—21no—
525D20—32no—
526D20—61no—
527D20—122no—
528C4×D5—122no—
529C4×D5—241no—
530Dic10—21no—
531Dic10—21no—
532#168—21no—
533#168—61no—
534#168—61no—
535#168D3×D412yescomplemented
536C2×#41—151no—
537C22×D4—31no—
538C22×D4—31no—
539C22×D4—61no—
540C22×D4—151no—
541AGL(1,ℤ/8)—304no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—151no—
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—151no—
553C22×C8—151no—
554#127D3×D511yescharacteristic, complemented
555#124—51no—
556#123—301no—
557C22⋊Q8—151no—
558#121—31no—
559#121—31no—
560#121—61no—
561#121—151no—
562#121—301no—
563#120—61no—
564#120—61no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—151no—
569C2×C22⋊C4—301no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—151no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
579C22⋊C8—151no—
580#97—51no—
581C2×C3×C5—81no—
582C2×C3×C5—81no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586D15—42no—
587C3×D5—81no—
588C5×D3—22no—
589C5×D3—41no—
590C5×D3—42no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—101no—
594C22×D3—21no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—42no—
599C22×D3—81no—
600C22×D3—81no—
601C22×D3—101no—
602C22×D3—202no—
603C22×D3—202no—
604C22×D3—401no—
605C22×D3C2×C22⋊D511yescharacteristic
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—42no—
614C3×D4—81no—
615C3×D4—101no—
616C3×D4—101no—
617C2×C3×C4—101no—
618C2×C3×C4C2×C22⋊D511yescharacteristic
619C2×C3×C4C2×C22⋊D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621#67—42no—
622#67—42no—
623#67—42no—
624#67—42no—
625#67—202no—
626#67—401no—
627C2×Dic3—21no—
628C2×Dic3—101no—
629C2×Dic3C2×C22⋊D511yescharacteristic
630C2×Dic3C2×C22⋊D511yescharacteristic
631D12—22no—
632D12—21no—
633D12—52no—
634D12—101no—
635D12—202no—
636D12D4×D512yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—42no—
642C4×D3—202no—
643C4×D3—401no—
644C3×C8—52no—
645C3×C8—101no—
646C3⋊C8—101no—
647C3⋊C8—101no—
648C22×C5—32no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—61no—
656C22×C5—61no—
657C22×C5—61no—
658C22×C5—62no—
659C22×C5—61no—
660C22×C5—61no—
661C22×C5—121no—
662C22×C5—121no—
663C22×C5—244no—
664C22×C5—244no—
665C22×C5C2×D3×D411yescharacteristic
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—62no—
670C2×D5—121no—
671C2×D5—121no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—61no—
676C4×C5—61no—
677C4×C5—121no—
678C4×C5C2×D3×D411yescharacteristic
679C4×C5#100411yescharacteristic
680Dic5—41no—
681Dic5—121no—
682C24—61no—
683C24—61no—
684C24—301no—
685#41—302no—
686#41—601no—
687C2×Q8—51no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—51no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—61no—
698C2×D4—61no—
699C2×D4—121no—
700C2×D4—121no—
701C2×D4—124no—
702C2×D4—151no—
703C2×D4—301no—
704C2×D4—302no—
705C2×D4—301no—
706C2×D4—301no—
707C2×D4—601no—
708C2×D4C2×D3×D511yescharacteristic
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—61no—
713C22×C4—301no—
714C22×C4—301no—
715SD16—102no—
716SD16—201no—
717SD16—302no—
718D8—102no—
719D8—154no—
720D8—201no—
721D8—302no—
722D8—302no—
723D8—302no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—151no—
733C4⋊C4—301no—
734C22⋊C4—31no—
735C22⋊C4—31no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42C2×D3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—201no—
753C22×C3—201no—
754C22×C3—201no—
755C22×C3C22×C22⋊D511yescharacteristic
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—22no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C2×D3—84no—
766C2×D3—102no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3#407812yescomplemented
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—201no—
774C3×C4C2×D4×D511yescharacteristic
775C3×C4#414411yescharacteristic
776Dic3—21no—
777Dic3—21no—
778Dic3—41no—
779Dic3—201no—
780C2×C5—62no—
781C2×C5—81no—
782C2×C5—81no—
783C2×C5—121no—
784C2×C5—122no—
785C2×C5#571711yescharacteristic
786C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
787C2×C5#577411yescharacteristic
788D5—81no—
789D5—122no—
790C23—21no—
791C23—21no—
792C23—31no—
793C23—31no—
794C23—61no—
795C23—101no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—122no—
800C23—241no—
801C23—241no—
802C23—301no—
803C23—602no—
804C23—602no—
805C23—1201no—
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—32no—
813D4—42no—
814D4—62no—
815D4—61no—
816D4—81no—
817D4—101no—
818D4—101no—
819D4—122no—
820D4—122no—
821D4—122no—
822D4—122no—
823D4—152no—
824D4—301no—
825D4—602no—
826D4—602no—
827D4—1201no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—101no—
836C2×C4—122no—
837C2×C4—301no—
838C2×C4—602no—
839C2×C4—1201no—
840C2×C4D3×C22⋊D511yescharacteristic
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—52no—
844C8—101no—
845C8—301no—
846C8—301no—
847C2×C3—81no—
848C2×C3—81no—
849C2×C3—401no—
850C2×C3C2×#407811yescharacteristic
851C2×C3D4×C22⋊D511yescharacteristic
852C2×C3#6616911yescharacteristic
853D3—22no—
854D3—41no—
855D3—42no—
856D3—202no—
857C5#8185611yescharacteristic, complemented, Sylow
858C22—32no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—61no—
866C22—61no—
867C22—61no—
868C22—62no—
869C22—61no—
870C22—61no—
871C22—121no—
872C22—121no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—244no—
878C22—302no—
879C22—601no—
880C22—601no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—61no—
886C4—61no—
887C4—121no—
888C4—201no—
889C4—601no—
890C4D3×D4×D511yescharacteristic
891C4#9202511yescharacteristic
892C3#1061521911yescharacteristic, complemented, Sylow
893C2—62no—
894C2—81no—
895C2—81no—
896C2—121no—
897C2—122no—
898C2—401no—
899C2—602no—
900C2D3×#407811yescharacteristic
901C2#1175469811yescharacteristic
902C2#1175505711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
hypercenter#127D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C5×#5717C2semidirect
2. C2×#91496C2semidirect
3. C2×D3×#686C2semidirect
4. #11752749C2semidirect
5. #11751173C2semidirect
6. C3×#65363C2semidirect
7. #11749162C2semidirect
8. #11749152C2semidirect
9. #11749058C2semidirect
10. #11749050C2semidirect
11. #11749032C2semidirect
12. #11749029C2semidirect
13. #11747034C2semidirect
14. #11747025C2semidirect
15. #11746987C2semidirect
19. C2×C5×D3×D4C22semidirect
20. C2×D3×D20C22semidirect
21. C2×#6769C22semidirect
22. C3×C5×#127C22semidirect
23. C2×#6715C22semidirect
24. C2×#6715C22semidirect
25. C4×D60C22semidirect
28. C5×#938C22semidirect
32. C4×C5×D12C22semidirect
33. C2×C3×#687C22semidirect
34. C2×C3×#687C22semidirect
35. C2×C3×#686C22semidirect
36. C2×C3×#686C22semidirect
37. C3×#4021C22semidirect
43. #91456C22semidirect
44. #91369C22semidirect
46. C2×#6656C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91116C22semidirect
52. #91116C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. C3×#3935C22semidirect
55. #90985C22semidirect
56. #90970C22semidirect
57. #90969C22semidirect
58. #90967C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
69. #65363D3semidirect
137. #6654D4semidirect
143. #5717D5semidirect
161. C5×#127C2×D3semidirect
171. C2×#687C2×D3semidirect
172. C2×#687C2×D3semidirect
179. C2×#686C2×D3semidirect
180. C2×#686C2×D3semidirect
188. #4021C2×D3semidirect
200. #3935C2×D3semidirect
229. D60C2×D4semidirect
258. C3×#168C2×D4semidirect
263. C2×D3×D4C2×D5semidirect
268. C3×#127C2×D5semidirect
275. #938C2×D5semidirect
292. C4×D12C2×D5semidirect
402. C2×C5×D3AGL(1,ℤ/8)semidirect
535. #168D3×D4semidirect
554. #127D3×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4078semidirect
857. C5#81856semidirect
892. C3#10615219semidirect

Maximal subgroups

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

subgroupindex
C5×#57172
C2×#914962
C2×D3×#6862
#117527492
#117511732
C3×#653632
#117491622
#117491522
#117490582
#117490502
#117490322
#117490292
#117470342
#117470252
#117469872
#106152193
#818565