Finite Group Databasebeta

← #14509967

Subgroups — #14509967

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757030C212yesmaximal, complemented
2C2×D8×D15C211yesmaximal, characteristic, complemented
3C5×#5757C211yesmaximal, characteristic, complemented
4C3×#66091C211yesmaximal, characteristic, complemented
5#11754701C212yesmaximal, complemented
6#11754698C212yesmaximal, complemented
7#11754692C212yesmaximal, complemented
8#11754061C212yesmaximal, complemented
9#11754059C214yesmaximal, complemented
10#11754058C212yesmaximal, complemented
11#11754053C212yesmaximal, complemented
12#11754047C214yesmaximal, complemented
13D3×D5×D8C212yesmaximal, complemented
14#11753978C211yesmaximal, characteristic, complemented
15#11753973C211yesmaximal, characteristic, complemented
16#11753963C211yesmaximal, characteristic, complemented
17#11753952C211yesmaximal, characteristic, complemented
18D5×#576—31nomaximal, Hall
19C2×D4×D15C2212yescomplemented
20C5×#1004C2212yescomplemented
21C3×#4144C2212yescomplemented
22#92049—24no—
23C2×#6790—24no—
24#92027—22no—
25#92027C2214yescomplemented
26#92026—22no—
27#92026C2214yescomplemented
28#92024—22no—
29#92024C2214yescomplemented
30D3×D4×D5—22no—
31D3×D4×D5C2214yescomplemented
32#92019C2212yescomplemented
33#92019C2212yescomplemented
34#92016C2211yescharacteristic
35#92016C2212yescomplemented
36C2×C3×C5×D8C2211yescharacteristic, complemented
37C2×#6715C2212yescomplemented
38D8×D15C2212yescomplemented
39D8×D15C2212yescomplemented
40D8×D15C2212yescomplemented
41D8×D15C2212yescomplemented
42C2×D120C2211yescharacteristic, complemented
43C2×C8×D15C2211yescharacteristic, complemented
44C5×#932C2212yescomplemented
45C5×#912C2212yescomplemented
46C5×#911C2214yescomplemented
47C5×D3×D8C2212yescomplemented
48C5×#904C2211yescharacteristic, complemented
49C5×#901C2211yescharacteristic, complemented
50C3×#4078C2212yescomplemented
51C3×#4058C2212yescomplemented
52C3×#4057C2214yescomplemented
53C3×D5×D8C2212yescomplemented
54C3×#4050C2211yescharacteristic, complemented
55C3×#4047C2211yescharacteristic, complemented
56#91500C2214yescomplemented
57#91498C2214yescomplemented
58#91496C2214yescomplemented
59#91495C2214yescomplemented
60#91492C2214yescomplemented
61#91491C2214yescomplemented
62#91487C2214yescomplemented
63#91481C2214yescomplemented
64#91480C2214yescomplemented
65D3×#686C2214yescomplemented
66#91478C2214yescomplemented
67D5×#213C2214yescomplemented
68#91305C2212yescomplemented
69#91301C2212yescomplemented
70#91297C2212yescomplemented
71#91292C2211yescharacteristic, complemented
72#91288C2211yescharacteristic, complemented
73#91284C2211yescharacteristic, complemented
74#91279C2211yescharacteristic, complemented
75#91277C2211yescharacteristic, complemented
76#91276C2212yescomplemented
77#91275C2212yescomplemented
78#91271C2212yescomplemented
79#91268C2212yescomplemented
80#91265C2212yescomplemented
81#91264C2211yescharacteristic, complemented
82#91256C2211yescharacteristic, complemented
83#91255C2212yescomplemented
84#91253C2214yescomplemented
85D3×D40C2212yescomplemented
86#91249C2214yescomplemented
87D5×D24C2212yescomplemented
88#91246C2212yescomplemented
89D3×C8×D5C2212yescomplemented
90D3×#576—51nomaximal, Hall
91D5×H(5,𝔽2)—32no—
92C5×#576—31no—
93#66169—32no—
94#66108—34no—
95#66108—32no—
96D5×AGL(1,ℤ/8)—32no—
97D5×AGL(1,ℤ/8)—34no—
98#66103—32no—
99#66103—31no—
100D5×#135—32no—
101D5×#135—31no—
102#66091—32no—
103#66091D311yescharacteristic, complemented
104C2×D5×D8—32no—
105C2×D5×D8—31no—
106#66086—31no—
107D5×#131—31no—
108C23×D15—22no—
109C22×D3×D5—24no—
110C2×C3×C5×D4C2312yescomplemented
111C2×#1220—22no—
112D4×D15—22no—
113D4×D15—22no—
114D4×D15C2314yes—
115D4×D15C2314yescomplemented
116C2×D60C2312yescomplemented
117C2×C4×D15C2311yescharacteristic
118C2×C5×#67—24no—
119C5×#237—22no—
120C5×#237C2314yescomplemented
121C5×D3×D4—22no—
122C5×D3×D4C2314yescomplemented
123C5×#235C2311yescharacteristic
124C5×#235C2312yescomplemented
125C2×C3×C22⋊D5—24no—
126C3×#711—22no—
127C3×#711C2314yescomplemented
128C3×D4×D5—22no—
129C3×D4×D5C2314yescomplemented
130C3×#709C2311yescharacteristic
131C3×#709C2312yescomplemented
132#6790—22no—
133#6790—24no—
134#6790—24no—
135#6790—24no—
136#6790—24no—
137#6790—24no—
138#6790—24no—
139#6790D412yes—
140D3×C22⋊D5—24no—
141D3×C22⋊D5—24no—
142D5×#67—24no—
143D5×#67—24no—
144C2×#1203—24no—
145C2×#1202—24no—
146C2×#1200—24no—
147#6782—24no—
148#6782—24no—
149#6780—22no—
150#6780D412yes—
151#6779—24no—
152#6779—24no—
153#6777D411yescharacteristic
154#6777C2312yes—
155D3×D20—22no—
156D3×D20C2314yescomplemented
157D5×D12—22no—
158D5×D12C2314yescomplemented
159C4×D3×D5—22no—
160C4×D3×D5C2312yes—
161#6773—22no—
162#6773C2314yescomplemented
163#6771—22no—
164#6771C2312yes—
165D15⋊Q8D411yescharacteristic
166D15⋊Q8C2312yes—
167#6769—22no—
168#6769C2314yescomplemented
169#6768D411yescharacteristic
170#6768C2312yescomplemented
171#6766D411yescharacteristic
172#6766C2312yescomplemented
173C3×C5×D8C2312yescomplemented
174C3×C5×D8C2312yescomplemented
175C2×C3×C5×C8C2311yescharacteristic, complemented
176#6715C2314yescomplemented
177#6715C2314yescomplemented
178C2×C3⋊#168C2311yescharacteristic, complemented
179D120C2312yescomplemented
180D120C2312yescomplemented
181C8×D15C2311yescharacteristic
182C8×D15C2311yescharacteristic
183C8×D15C2311yescharacteristic, complemented
184C8×D15C2311yescharacteristic, complemented
185C5×#214C2314yescomplemented
186C5×#213C2314yescomplemented
187C5×#208C2311yescharacteristic, complemented
188C5×Dic12C2311yescharacteristic, complemented
189C5×D24C2311yescharacteristic, complemented
190C5×#204C2312yescomplemented
191C5×ΓL(1,𝔽25)C2312yescomplemented
192C5×D3×C8C2312yescomplemented
193C3×#687C2314yescomplemented
194C3×#686C2314yescomplemented
195C3×#681C2311yescharacteristic, complemented
196C3×Dic20C2311yescharacteristic, complemented
197C3×D40C2311yescharacteristic, complemented
198C3×#677C2312yescomplemented
199C3×#676C2312yescomplemented
200C3×C8×D5C2312yescomplemented
201#6661C2312yescomplemented
202#6660C2314yescomplemented
203#6658C2314yescomplemented
204#6656C2312yescomplemented
205#6655C2312yescomplemented
206#6654C2314yescomplemented
207#6653C2314yescomplemented
208#6652C2312yescomplemented
209#6651C2312yescomplemented
210#6650C2312yescomplemented
211#6649C2312yescomplemented
212#6648C2312yes—
213D3×#168C2312yescomplemented
214D5×C3⋊C8C2312yescomplemented
215D3×H(5,𝔽2)—52no—
216C3×#576—51no—
217#5835—52no—
218#5774—52no—
219#5774—54no—
220D3×AGL(1,ℤ/8)—52no—
221D3×AGL(1,ℤ/8)—54no—
222#5769—52no—
223#5769—51no—
224D3×#135—52no—
225D3×#135—51no—
226#5757—52no—
227#5757D511yescharacteristic, complemented
228C2×D3×D8—51no—
229C2×D3×D8—52no—
230#5752—51no—
231D3×#131—51no—
232C5×H(5,𝔽2)—32no—
233#4149—32no—
234#4149—34no—
235#4149—32no—
236#4149—62no—
237D5×#41—31no—
238D5×#41—34no—
239D5×#41—32no—
240D5×#41—62no—
241#4144—34no—
242#4144—62no—
243#4144—64no—
244#4144C2×D312yescomplemented
245C2×D4×D5—32no—
246C2×D4×D5—34no—
247C2×D4×D5—62no—
248C2×D4×D5—64no—
249C5×AGL(1,ℤ/8)—32no—
250C5×AGL(1,ℤ/8)—34no—
251C5×#135—32no—
252C5×#135—31no—
253C2×C5×D8—32no—
254C2×C5×D8C2×D311yescharacteristic, complemented
255C5×#131—31no—
256#4096—32no—
257#4096—34no—
258#4095—34no—
259#4095—32no—
260#4094—31no—
261#4078—34no—
262#4078C2×D312yescomplemented
263C2×#686—32no—
264C2×#686—34no—
265#4065—31no—
266#4065—32no—
267D5×Q16—31no—
268#4062—34no—
269#4062—32no—
270#4060—34no—
271#4060—34no—
272#4060—34no—
273D5×SD16—34no—
274D5×SD16—32no—
275#4058—31no—
276#4058C2×D312yescomplemented
277#4057—34no—
278#4057—34no—
279#4057C2×D314yescomplemented
280D5×D8—34no—
281D5×D8—32no—
282D5×D8—32no—
283D5×D8—32no—
284D5×D8—32no—
285D5×D8—34no—
286D5×D8—31no—
287D5×D8—32no—
288D5×D8C2×D312yescomplemented
289#4054—32no—
290#4054—34no—
291#4053—31no—
292#4053—32no—
293D5×M16—31no—
294D5×M16—32no—
295#4050—32no—
296#4050C2×D311yescharacteristic, complemented
297C2×D40—31no—
298C2×D40—32no—
299#4047—32no—
300#4047C2×D311yescharacteristic, complemented
301C2×C8×D5—31no—
302C2×C8×D5—32no—
303C2×#576—151noSylow
304C23×C3×C5—22no—
305C22×D15—22no—
306C22×D15—24no—
307C22×D15—24no—
308C22×D15—84no—
309C22×D15C2×D411yescharacteristic
310C22×C5×D3—24no—
311C22×C3×D5—24no—
312C2×D3×D5—22no—
313C2×D3×D5—24no—
314C2×D3×D5—24no—
315C2×D3×D5—88no—
316C2×D3×D5C2×D412yes—
317C3×C5×D4—22no—
318C3×C5×D4C2414yes—
319C2×C3×C4×C5C2411yescharacteristic
320#1220—24no—
321#1220—24no—
322C2×Dic15C2×D411yescharacteristic
323D60—22no—
324D60C2414yes—
325C4×D15C2×D411yescharacteristic
326C4×D15C2×D411yescharacteristic
327C4×D15C2411yescharacteristic
328C4×D15C2411yescharacteristic
329C5×#67—22no—
330C5×#67—24no—
331C5×#67—24no—
332C5×#67C2×D412yes—
333C2×C5×Dic3—24no—
334C5×D12C2×D411yescharacteristic
335C5×D12C2412yes—
336C4×C5×D3—22no—
337C4×C5×D3C2412yes—
338C5×Dic6C2×D411yescharacteristic
339C5×Dic6C2412yes—
340C3×C22⋊D5—22no—
341C3×C22⋊D5—24no—
342C3×C22⋊D5—24no—
343C3×C22⋊D5C2×D412yes—
344C2×C3×Dic5—24no—
345C3×D20C2×D411yescharacteristic
346C3×D20C2412yes—
347C3×C4×D5—22no—
348C3×C4×D5C2412yes—
349C3×Dic10C2×D411yescharacteristic
350C3×Dic10C2412yes—
351#1204—22no—
352#1204C2×D412yes—
353#1203—22no—
354#1203—24no—
355#1203—24no—
356#1203C2×D412yes—
357#1202—22no—
358#1202—24no—
359#1202—24no—
360#1202C2×D412yes—
361#1201—22no—
362#1201C2×D412yes—
363#1200—22no—
364#1200—24no—
365#1200—24no—
366#1200C2×D412yes—
367D3×Dic5—22no—
368D3×Dic5C2×D412yes—
369D5×Dic3—22no—
370D5×Dic3C2×D412yes—
371C3×C5×C8C2411yescharacteristic
372C3×C5×C8C2411yescharacteristic
373C3⋊#168C2411yescharacteristic
374C3⋊#168C2411yescharacteristic
375C3×#168C2412yes—
376C5×C3⋊C8C2412yes—
377C3×H(5,𝔽2)—52no—
378#1009—52no—
379#1009—54no—
380#1009—52no—
381#1009—102no—
382D3×#41—51no—
383D3×#41—54no—
384D3×#41—52no—
385D3×#41—102no—
386#1004—54no—
387#1004—102no—
388#1004—104no—
389#1004C2×D512yescomplemented
390C2×D3×D4—52no—
391C2×D3×D4—54no—
392C2×D3×D4—102no—
393C2×D3×D4—104no—
394C3×AGL(1,ℤ/8)—52no—
395C3×AGL(1,ℤ/8)—54no—
396C3×#135—52no—
397C3×#135—51no—
398C2×C3×D8—52no—
399C2×C3×D8C2×D511yescharacteristic, complemented
400C3×#131—51no—
401#950—52no—
402#950—54no—
403#949—54no—
404#949—52no—
405#948—51no—
406#932—54no—
407#932C2×D512yescomplemented
408C2×#213—52no—
409C2×#213—54no—
410#919—51no—
411#919—52no—
412D3×Q16—51no—
413#916—54no—
414#916—52no—
415#914—54no—
416#914—54no—
417#914—54no—
418D3×SD16—54no—
419D3×SD16—52no—
420#912—51no—
421#912C2×D512yescomplemented
422#911—54no—
423#911—54no—
424#911C2×D514yescomplemented
425D3×D8—54no—
426D3×D8—52no—
427D3×D8—52no—
428D3×D8—52no—
429D3×D8—52no—
430D3×D8—54no—
431D3×D8—51no—
432D3×D8—52no—
433D3×D8C2×D512yescomplemented
434#908—52no—
435#908—54no—
436#907—51no—
437#907—52no—
438D3×M16—51no—
439D3×M16—52no—
440#904—52no—
441#904C2×D511yescharacteristic, complemented
442C2×D24—51no—
443C2×D24—52no—
444#901—52no—
445#901C2×D511yescharacteristic, complemented
446C2×D3×C8—51no—
447C2×D3×C8—52no—
448C23×D5—64no—
449C23×D5—62no—
450C5×#41—31no—
451C5×#41—34no—
452C5×#41—32no—
453C5×#41—62no—
454C2×C5×D4—34no—
455C2×C5×D4—62no—
456C2×C5×D4—64no—
457C2×C5×D4C22×D312yescomplemented
458C2×C22⋊D5—24no—
459C2×C22⋊D5—64no—
460C2×C22⋊D5—64no—
461C2×C22⋊D5—62no—
462C2×C22⋊D5—64no—
463#713—31no—
464#713—32no—
465#713—34no—
466#713—62no—
467Q8×D5—31no—
468Q8×D5—32no—
469#711—22no—
470#711—32no—
471#711—31no—
472#711—32no—
473#711—64no—
474#711—64no—
475#711—62no—
476#711C22×D314yescomplemented
477D4×D5—22no—
478D4×D5—32no—
479D4×D5—34no—
480D4×D5—34no—
481D4×D5—31no—
482D4×D5—32no—
483D4×D5—34no—
484D4×D5—62no—
485D4×D5—64no—
486D4×D5—62no—
487D4×D5—62no—
488D4×D5—64no—
489D4×D5—64no—
490D4×D5—64no—
491D4×D5—64no—
492D4×D5—62no—
493D4×D5—64no—
494D4×D5—64no—
495D4×D5—64no—
496D4×D5C22×D314yescomplemented
497#709—32no—
498#709—34no—
499#709—64no—
500#709—62no—
501#709—64no—
502#709—62no—
503#709C22×D311yescharacteristic
504#709C22×D312yescomplemented
505C2×D20—32no—
506C2×D20—34no—
507C2×D20—64no—
508C2×D20—62no—
509C2×C4×D5—31no—
510C2×C4×D5—32no—
511C2×C4×D5—62no—
512C2×C4×D5—64no—
513C5×Q16—31no—
514C5×SD16—34no—
515C5×SD16—32no—
516C5×D8—34no—
517C5×D8—31no—
518C5×D8C22×D312yescomplemented
519C5×D8C22×D312yescomplemented
520C5×M16—31no—
521C5×M16—32no—
522C2×C5×C8—32no—
523C2×C5×C8C22×D311yescharacteristic, complemented
524#689—32no—
525#688—32no—
526#688—34no—
527#687—32no—
528#687C22×D314yescomplemented
529#686—34no—
530#686—34no—
531#686—32no—
532#686—34no—
533#686C22×D314yescomplemented
534#681—32no—
535#681C22×D311yescharacteristic, complemented
536C2×#168—31no—
537C2×#168—32no—
538Dic20C22×D311yescharacteristic, complemented
539D40—34no—
540D40—32no—
541D40—32no—
542D40C22×D311yescharacteristic, complemented
543#677—34no—
544#677C22×D312yescomplemented
545#676—32no—
546#676—32no—
547#676C22×D312yescomplemented
548C8×D5—32no—
549C8×D5—31no—
550C8×D5—31no—
551C8×D5—31no—
552C8×D5—31no—
553C8×D5—32no—
554C8×D5C22×D312yescomplemented
555C2×H(5,𝔽2)—152no—
556#576—31no—
557#576—51no—
558#576—151no—
559#576—151no—
560#576—152no—
561#576—152no—
562#576—154no—
563#576—152no—
564#576—152no—
565C2×AGL(1,ℤ/8)—152no—
566C2×AGL(1,ℤ/8)—154no—
567C2×#135—152no—
568C2×#135—151no—
569C22×D8—152no—
570C22×D8—151no—
571C2×#131—151no—
572C22×C3×C5—24no—
573C22×C3×C5—82no—
574C22×C3×C5C22×D411yescharacteristic
575C2×D15—22no—
576C2×D15—24no—
577C2×D15—48no—
578C2×D15—84no—
579C2×D15—82no—
580C2×D15C22×D411yescharacteristic
581C2×D15C22×D411yescharacteristic
582C2×C5×D3—22no—
583C2×C5×D3—84no—
584C2×C5×D3C22×D412yes—
585C2×C3×D5—22no—
586C2×C3×D5—84no—
587C2×C3×D5C22×D412yes—
588D3×D5—24no—
589D3×D5—44no—
590D3×D5—84no—
591D3×D5—84no—
592C3×C4×C5C22×D411yescharacteristic
593C3×C4×C5C2511yescharacteristic
594Dic15C22×D411yescharacteristic
595Dic15C22×D411yescharacteristic
596C3×Dic5—22no—
597C3×Dic5C22×D412yes—
598C5×Dic3—22no—
599C5×Dic3C22×D412yes—
600C23×D3—104no—
601C23×D3—102no—
602C3×#41—51no—
603C3×#41—54no—
604C3×#41—52no—
605C3×#41—102no—
606C2×C3×D4—54no—
607C2×C3×D4—102no—
608C2×C3×D4—104no—
609C2×C3×D4C22×D512yescomplemented
610C2×#67—24no—
611C2×#67—104no—
612C2×#67—104no—
613C2×#67—102no—
614C2×#67—104no—
615#239—51no—
616#239—52no—
617#239—54no—
618#239—102no—
619D3×Q8—51no—
620D3×Q8—52no—
621#237—22no—
622#237—52no—
623#237—51no—
624#237—52no—
625#237—104no—
626#237—104no—
627#237—102no—
628#237C22×D514yescomplemented
629D3×D4—22no—
630D3×D4—52no—
631D3×D4—54no—
632D3×D4—54no—
633D3×D4—51no—
634D3×D4—52no—
635D3×D4—54no—
636D3×D4—102no—
637D3×D4—104no—
638D3×D4—102no—
639D3×D4—102no—
640D3×D4—104no—
641D3×D4—104no—
642D3×D4—104no—
643D3×D4—104no—
644D3×D4—102no—
645D3×D4—104no—
646D3×D4—104no—
647D3×D4—104no—
648D3×D4C22×D514yescomplemented
649#235—52no—
650#235—54no—
651#235—104no—
652#235—102no—
653#235—104no—
654#235—102no—
655#235C22×D511yescharacteristic
656#235C22×D512yescomplemented
657C2×D12—52no—
658C2×D12—54no—
659C2×D12—104no—
660C2×D12—102no—
661C2×C4×D3—51no—
662C2×C4×D3—52no—
663C2×C4×D3—102no—
664C2×C4×D3—104no—
665C3×Q16—51no—
666C3×SD16—54no—
667C3×SD16—52no—
668C3×D8—54no—
669C3×D8—51no—
670C3×D8C22×D512yescomplemented
671C3×D8C22×D512yescomplemented
672C3×M16—51no—
673C3×M16—52no—
674C2×C3×C8—52no—
675C2×C3×C8C22×D511yescharacteristic, complemented
676#216—52no—
677#215—52no—
678#215—54no—
679#214—52no—
680#214C22×D514yescomplemented
681#213—54no—
682#213—54no—
683#213—52no—
684#213—54no—
685#213C22×D514yescomplemented
686#208—52no—
687#208C22×D511yescharacteristic, complemented
688C2×C3⋊C8—51no—
689C2×C3⋊C8—52no—
690Dic12C22×D511yescharacteristic, complemented
691D24—54no—
692D24—52no—
693D24—52no—
694D24C22×D511yescharacteristic, complemented
695#204—54no—
696#204C22×D512yescomplemented
697ΓL(1,𝔽25)—52no—
698ΓL(1,𝔽25)—52no—
699ΓL(1,𝔽25)C22×D512yescomplemented
700D3×C8—52no—
701D3×C8—51no—
702D3×C8—51no—
703D3×C8—51no—
704D3×C8—51no—
705D3×C8—52no—
706D3×C8C22×D512yescomplemented
707C23×C5—22no—
708C23×C5—64no—
709C22×D5—24no—
710C22×D5—31no—
711C22×D5—32no—
712C22×D5—62no—
713C22×D5—64no—
714C22×D5—64no—
715C22×D5—64no—
716C22×D5—62no—
717C22×D5—64no—
718C22×D5—248no—
719C22×D5—244no—
720C5×Q8—31no—
721C5×Q8—32no—
722C5×D4—22no—
723C5×D4—32no—
724C5×D4—31no—
725C5×D4—32no—
726C5×D4—64no—
727C5×D4—64no—
728C5×D4—62no—
729C5×D4C23×D314yes—
730C2×C4×C5—32no—
731C2×C4×C5—64no—
732C2×C4×C5—62no—
733C2×C4×C5C23×D311yescharacteristic
734C22⋊D5—22no—
735C22⋊D5—24no—
736C22⋊D5—24no—
737C22⋊D5—32no—
738C22⋊D5—32no—
739C22⋊D5—62no—
740C22⋊D5—64no—
741C22⋊D5—62no—
742C22⋊D5—64no—
743C22⋊D5—64no—
744C22⋊D5—64no—
745C22⋊D5D3×D412yes—
746C2×Dic5—24no—
747C2×Dic5—31no—
748C2×Dic5—32no—
749C2×Dic5—62no—
750D20—32no—
751D20—34no—
752D20—64no—
753D20—62no—
754D20—64no—
755D20—62no—
756D20D3×D411yescharacteristic
757D20C23×D312yes—
758C4×D5—22no—
759C4×D5—32no—
760C4×D5—31no—
761C4×D5—31no—
762C4×D5—31no—
763C4×D5—31no—
764C4×D5—32no—
765C4×D5—64no—
766C4×D5—62no—
767C4×D5—62no—
768C4×D5—64no—
769C4×D5C23×D312yes—
770Dic10—32no—
771Dic10—62no—
772Dic10D3×D411yescharacteristic
773Dic10C23×D312yes—
774C5×C8—32no—
775C5×C8C23×D311yescharacteristic
776C5×C8C23×D311yescharacteristic
777#168—31no—
778#168—31no—
779#168C23×D312yes—
780H(5,𝔽2)—32no—
781H(5,𝔽2)—52no—
782H(5,𝔽2)—154no—
783H(5,𝔽2)—154no—
784H(5,𝔽2)—152no—
785H(5,𝔽2)—152no—
786H(5,𝔽2)—304no—
787H(5,𝔽2)—302no—
788H(5,𝔽2)—302no—
789C2×#41—151no—
790C2×#41—154no—
791C2×#41—152no—
792C2×#41—302no—
793C22×D4—154no—
794C22×D4—152no—
795C22×D4—302no—
796C22×D4—304no—
797AGL(1,ℤ/8)—32no—
798AGL(1,ℤ/8)—34no—
799AGL(1,ℤ/8)—52no—
800AGL(1,ℤ/8)—54no—
801AGL(1,ℤ/8)—154no—
802AGL(1,ℤ/8)—152no—
803AGL(1,ℤ/8)—154no—
804AGL(1,ℤ/8)—152no—
805AGL(1,ℤ/8)—154no—
806AGL(1,ℤ/8)—154no—
807AGL(1,ℤ/8)—154no—
808AGL(1,ℤ/8)—154no—
809AGL(1,ℤ/8)—154no—
810AGL(1,ℤ/8)—154no—
811#135—32no—
812#135—31no—
813#135—52no—
814#135—51no—
815#135—152no—
816#135—152no—
817#135—151no—
818#135—151no—
819#135—152no—
820#135—154no—
821#135—154no—
822#135—152no—
823C2×Q16—151no—
824C2×SD16—154no—
825C2×SD16—152no—
826C2×D8—32no—
827C2×D8—52no—
828C2×D8—152no—
829C2×D8—152no—
830C2×D8—151no—
831C2×D8—154no—
832C2×D8—154no—
833C2×D8—154no—
834C2×D8—152no—
835C2×D8—152no—
836C2×D8—152no—
837C2×D8—152no—
838C2×D8—152no—
839C2×D8—151no—
840C2×D8D3×D511yescharacteristic, complemented
841#131—31no—
842#131—51no—
843#131—152no—
844#131—152no—
845#131—151no—
846#131—151no—
847C2×M16—151no—
848C2×M16—152no—
849C22×C8—152no—
850C22×C8—151no—
851C2×C3×C5—21no—
852C2×C3×C5—44no—
853C2×C3×C5C23×D411yescharacteristic
854D15—21no—
855D15—44no—
856D15#57612yescomplemented
857C3×D5—22no—
858C3×D5—42no—
859C5×D3—22no—
860C5×D3—42no—
861C23×C3—22no—
862C23×C3—104no—
863C22×D3—24no—
864C22×D3—51no—
865C22×D3—52no—
866C22×D3—102no—
867C22×D3—104no—
868C22×D3—104no—
869C22×D3—104no—
870C22×D3—102no—
871C22×D3—104no—
872C22×D3—408no—
873C22×D3—404no—
874C3×Q8—51no—
875C3×Q8—52no—
876C3×D4—22no—
877C3×D4—52no—
878C3×D4—51no—
879C3×D4—52no—
880C3×D4—104no—
881C3×D4—104no—
882C3×D4—102no—
883C3×D4C23×D514yes—
884C2×C3×C4—52no—
885C2×C3×C4—104no—
886C2×C3×C4—102no—
887C2×C3×C4C23×D511yescharacteristic
888#67—22no—
889#67—24no—
890#67—24no—
891#67—52no—
892#67—52no—
893#67—102no—
894#67—104no—
895#67—102no—
896#67—104no—
897#67—104no—
898#67—104no—
899#67D4×D512yes—
900C2×Dic3—24no—
901C2×Dic3—51no—
902C2×Dic3—52no—
903C2×Dic3—102no—
904D12—52no—
905D12—54no—
906D12—104no—
907D12—102no—
908D12—104no—
909D12—102no—
910D12D4×D511yescharacteristic
911D12C23×D512yes—
912C4×D3—22no—
913C4×D3—52no—
914C4×D3—51no—
915C4×D3—51no—
916C4×D3—51no—
917C4×D3—51no—
918C4×D3—52no—
919C4×D3—104no—
920C4×D3—102no—
921C4×D3—102no—
922C4×D3—104no—
923C4×D3C23×D512yes—
924Dic6—52no—
925Dic6—102no—
926Dic6D4×D511yescharacteristic
927Dic6C23×D512yes—
928C3×C8—52no—
929C3×C8C23×D511yescharacteristic
930C3×C8C23×D511yescharacteristic
931C3⋊C8—51no—
932C3⋊C8—51no—
933C3⋊C8C23×D512yes—
934C22×C5—24no—
935C22×C5—32no—
936C22×C5—62no—
937C22×C5—82no—
938C22×C5—244no—
939C22×C5C2×D3×D411yescharacteristic
940C2×D5—22no—
941C2×D5—31no—
942C2×D5—31no—
943C2×D5—64no—
944C2×D5—62no—
945C2×D5—64no—
946C2×D5—84no—
947C2×D5—124no—
948C2×D5—128no—
949C2×D5—244no—
950C2×D5—244no—
951C2×D5—244no—
952C2×D5—242no—
953C2×D5C2×D3×D412yes—
954C4×C5—32no—
955C4×C5—62no—
956C4×C5C2×D3×D411yescharacteristic
957C4×C5C24×D311yescharacteristic
958Dic5—22no—
959Dic5—31no—
960Dic5—31no—
961Dic5C2×D3×D412yes—
962C24—302no—
963C24—304no—
964#41—31no—
965#41—34no—
966#41—32no—
967#41—51no—
968#41—54no—
969#41—52no—
970#41—62no—
971#41—102no—
972#41—152no—
973#41—154no—
974#41—154no—
975#41—152no—
976#41—151no—
977#41—151no—
978#41—152no—
979#41—152no—
980#41—302no—
981#41—304no—
982#41—304no—
983#41—302no—
984#41—304no—
985#41—304no—
986#41—302no—
987#41—302no—
988C2×Q8—151no—
989C2×Q8—152no—
990C2×D4—34no—
991C2×D4—54no—
992C2×D4—62no—
993C2×D4—64no—
994C2×D4—102no—
995C2×D4—104no—
996C2×D4—154no—
997C2×D4—154no—
998C2×D4—152no—
999C2×D4—151no—
1000C2×D4—152no—
1001C2×D4—154no—
1002C2×D4—154no—
1003C2×D4—152no—
1004C2×D4—302no—
1005C2×D4—304no—
1006C2×D4—302no—
1007C2×D4—304no—
1008C2×D4—302no—
1009C2×D4—302no—
1010C2×D4—304no—
1011C2×D4—304no—
1012C2×D4—304no—
1013C2×D4—302no—
1014C2×D4—304no—
1015C2×D4—304no—
1016C2×D4—304no—
1017C2×D4—304no—
1018C2×D4—304no—
1019C2×D4—302no—
1020C2×D4—304no—
1021C2×D4—304no—
1022C2×D4C2×D3×D512yescomplemented
1023C22×C4—152no—
1024C22×C4—151no—
1025C22×C4—304no—
1026C22×C4—302no—
1027Q16—31no—
1028Q16—51no—
1029Q16—152no—
1030SD16—34no—
1031SD16—32no—
1032SD16—54no—
1033SD16—52no—
1034SD16—154no—
1035SD16—154no—
1036SD16—152no—
1037SD16—152no—
1038D8—34no—
1039D8—31no—
1040D8—54no—
1041D8—51no—
1042D8—154no—
1043D8—154no—
1044D8—152no—
1045D8—154no—
1046D8—154no—
1047D8—152no—
1048D8—152no—
1049D8C2×D3×D512yescomplemented
1050D8C2×D3×D512yescomplemented
1051M16—31no—
1052M16—32no—
1053M16—51no—
1054M16—52no—
1055M16—152no—
1056M16—152no—
1057M16—152no—
1058C2×C8—32no—
1059C2×C8—52no—
1060C2×C8—152no—
1061C2×C8—152no—
1062C2×C8—152no—
1063C2×C8—151no—
1064C2×C8—151no—
1065C2×C8—151no—
1066C2×C8—151no—
1067C2×C8—151no—
1068C2×C8C2×D3×D511yescharacteristic, complemented
1069C3×C5C2×#57611yescharacteristic, complemented, Hall
1070C22×C3—24no—
1071C22×C3—52no—
1072C22×C3—82no—
1073C22×C3—102no—
1074C22×C3—404no—
1075C22×C3C2×D4×D511yescharacteristic
1076C2×D3—22no—
1077C2×D3—51no—
1078C2×D3—51no—
1079C2×D3—84no—
1080C2×D3—104no—
1081C2×D3—102no—
1082C2×D3—104no—
1083C2×D3—204no—
1084C2×D3—208no—
1085C2×D3—404no—
1086C2×D3—404no—
1087C2×D3—404no—
1088C2×D3—402no—
1089C2×D3C2×D4×D512yes—
1090C3×C4—52no—
1091C3×C4—102no—
1092C3×C4C2×D4×D511yescharacteristic
1093C3×C4C24×D511yescharacteristic
1094Dic3—22no—
1095Dic3—51no—
1096Dic3—51no—
1097Dic3C2×D4×D512yes—
1098C2×C5—21no—
1099C2×C5—44no—
1100C2×C5—62no—
1101C2×C5—122no—
1102C2×C5C22×D3×D411yescharacteristic
1103D5—22no—
1104D5—32no—
1105D5—42no—
1106D5—61no—
1107D5—124no—
1108C23—22no—
1109C23—64no—
1110C23—104no—
1111C23—152no—
1112C23—151no—
1113C23—304no—
1114C23—304no—
1115C23—304no—
1116C23—304no—
1117C23—302no—
1118C23—302no—
1119C23—1204no—
1120C23—1208no—
1121Q8—31no—
1122Q8—32no—
1123Q8—51no—
1124Q8—52no—
1125Q8—152no—
1126Q8—302no—
1127D4—22no—
1128D4—32no—
1129D4—31no—
1130D4—32no—
1131D4—52no—
1132D4—51no—
1133D4—52no—
1134D4—64no—
1135D4—64no—
1136D4—62no—
1137D4—104no—
1138D4—104no—
1139D4—102no—
1140D4—152no—
1141D4—152no—
1142D4—152no—
1143D4—154no—
1144D4—304no—
1145D4—304no—
1146D4—304no—
1147D4—302no—
1148D4—304no—
1149D4—302no—
1150D4—304no—
1151D4—304no—
1152D4—302no—
1153D4—302no—
1154D4C22×D3×D514yes—
1155C2×C4—32no—
1156C2×C4—52no—
1157C2×C4—64no—
1158C2×C4—62no—
1159C2×C4—104no—
1160C2×C4—102no—
1161C2×C4—152no—
1162C2×C4—152no—
1163C2×C4—152no—
1164C2×C4—151no—
1165C2×C4—151no—
1166C2×C4—151no—
1167C2×C4—151no—
1168C2×C4—151no—
1169C2×C4—304no—
1170C2×C4—304no—
1171C2×C4—302no—
1172C2×C4—302no—
1173C2×C4—302no—
1174C2×C4C22×D3×D511yescharacteristic
1175C8—32no—
1176C8—52no—
1177C8—151no—
1178C8—151no—
1179C8C22×D3×D511yescharacteristic
1180C8C22×D3×D511yescharacteristic
1181C2×C3—21no—
1182C2×C3—44no—
1183C2×C3—102no—
1184C2×C3—202no—
1185C2×C3C22×D4×D511yescharacteristic
1186D3—22no—
1187D3—42no—
1188D3—52no—
1189D3—101no—
1190D3—204no—
1191C5D3×#57611yescharacteristic, complemented, Sylow
1192C22—24no—
1193C22—32no—
1194C22—52no—
1195C22—62no—
1196C22—82no—
1197C22—102no—
1198C22—151no—
1199C22—151no—
1200C22—244no—
1201C22—302no—
1202C22—304no—
1203C22—304no—
1204C22—404no—
1205C22—608no—
1206C22—604no—
1207C22—1202no—
1208C22—1204no—
1209C22—1204no—
1210C22—1204no—
1211C22D3×D4×D511yescharacteristic
1212C4—32no—
1213C4—52no—
1214C4—62no—
1215C4—102no—
1216C4—151no—
1217C4—151no—
1218C4D3×D4×D511yescharacteristic
1219C4C23×D3×D511yescharacteristic
1220C3D5×#57611yescharacteristic, complemented, Sylow
1221C2—21no—
1222C2—44no—
1223C2—62no—
1224C2—102no—
1225C2—122no—
1226C2—152no—
1227C2—202no—
1228C2—301no—
1229C2—604no—
1230C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC2C2×D3×D4×D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×D8C22
socleC2×C3×C5C23×D4
hypercenterC2×D8D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #11757030C2semidirect
2. C2×D8×D15C2semidirect
3. C5×#5757C2semidirect
4. C3×#66091C2semidirect
5. #11754701C2semidirect
6. #11754698C2semidirect
7. #11754692C2semidirect
8. #11754061C2semidirect
9. #11754059C2semidirect
10. #11754058C2semidirect
11. #11754053C2semidirect
12. #11754047C2semidirect
13. D3×D5×D8C2semidirect
14. #11753978C2semidirect
15. #11753973C2semidirect
16. #11753963C2semidirect
17. #11753952C2semidirect
19. C2×D4×D15C22semidirect
20. C5×#1004C22semidirect
21. C3×#4144C22semidirect
25. #92027C22semidirect
27. #92026C22semidirect
29. #92024C22semidirect
31. D3×D4×D5C22semidirect
32. #92019C22semidirect
33. #92019C22semidirect
35. #92016C22semidirect
36. C2×C3×C5×D8C22semidirect
37. C2×#6715C22semidirect
38. D8×D15C22semidirect
39. D8×D15C22semidirect
40. D8×D15C22semidirect
41. D8×D15C22semidirect
42. C2×D120C22semidirect
43. C2×C8×D15C22semidirect
44. C5×#932C22semidirect
45. C5×#912C22semidirect
46. C5×#911C22semidirect
47. C5×D3×D8C22semidirect
48. C5×#904C22semidirect
49. C5×#901C22semidirect
50. C3×#4078C22semidirect
51. C3×#4058C22semidirect
52. C3×#4057C22semidirect
53. C3×D5×D8C22semidirect
54. C3×#4050C22semidirect
55. C3×#4047C22semidirect
56. #91500C22semidirect
57. #91498C22semidirect
58. #91496C22semidirect
59. #91495C22semidirect
60. #91492C22semidirect
61. #91491C22semidirect
62. #91487C22semidirect
63. #91481C22semidirect
64. #91480C22semidirect
65. D3×#686C22semidirect
66. #91478C22semidirect
67. D5×#213C22semidirect
68. #91305C22semidirect
69. #91301C22semidirect
70. #91297C22semidirect
71. #91292C22semidirect
72. #91288C22semidirect
73. #91284C22semidirect
74. #91279C22semidirect
75. #91277C22semidirect
76. #91276C22semidirect
77. #91275C22semidirect
78. #91271C22semidirect
79. #91268C22semidirect
80. #91265C22semidirect
81. #91264C22semidirect
82. #91256C22semidirect
83. #91255C22semidirect
84. #91253C22semidirect
85. D3×D40C22semidirect
86. #91249C22semidirect
87. D5×D24C22semidirect
88. #91246C22semidirect
89. D3×C8×D5C22semidirect
103. #66091D3semidirect
110. C2×C3×C5×D4C23semidirect
115. D4×D15C23semidirect
116. C2×D60C23semidirect
120. C5×#237C23semidirect
122. C5×D3×D4C23semidirect
124. C5×#235C23semidirect
127. C3×#711C23semidirect
129. C3×D4×D5C23semidirect
131. C3×#709C23semidirect
156. D3×D20C23semidirect
158. D5×D12C23semidirect
162. #6773C23semidirect
168. #6769C23semidirect
170. #6768C23semidirect
172. #6766C23semidirect
173. C3×C5×D8C23semidirect
174. C3×C5×D8C23semidirect
175. C2×C3×C5×C8C23semidirect
176. #6715C23semidirect
177. #6715C23semidirect
178. C2×C3⋊#168C23semidirect
179. D120C23semidirect
180. D120C23semidirect
183. C8×D15C23semidirect
184. C8×D15C23semidirect
185. C5×#214C23semidirect
186. C5×#213C23semidirect
187. C5×#208C23semidirect
188. C5×Dic12C23semidirect
189. C5×D24C23semidirect
190. C5×#204C23semidirect
191. C5×ΓL(1,𝔽25)C23semidirect
192. C5×D3×C8C23semidirect
193. C3×#687C23semidirect
194. C3×#686C23semidirect
195. C3×#681C23semidirect
196. C3×Dic20C23semidirect
197. C3×D40C23semidirect
198. C3×#677C23semidirect
199. C3×#676C23semidirect
200. C3×C8×D5C23semidirect
201. #6661C23semidirect
202. #6660C23semidirect
203. #6658C23semidirect
204. #6656C23semidirect
205. #6655C23semidirect
206. #6654C23semidirect
207. #6653C23semidirect
208. #6652C23semidirect
209. #6651C23semidirect
210. #6650C23semidirect
211. #6649C23semidirect
213. D3×#168C23semidirect
214. D5×C3⋊C8C23semidirect
227. #5757D5semidirect
244. #4144C2×D3semidirect
254. C2×C5×D8C2×D3semidirect
262. #4078C2×D3semidirect
276. #4058C2×D3semidirect
279. #4057C2×D3semidirect
288. D5×D8C2×D3semidirect
296. #4050C2×D3semidirect
300. #4047C2×D3semidirect
389. #1004C2×D5semidirect
399. C2×C3×D8C2×D5semidirect
407. #932C2×D5semidirect
421. #912C2×D5semidirect
424. #911C2×D5semidirect
433. D3×D8C2×D5semidirect
441. #904C2×D5semidirect
445. #901C2×D5semidirect
457. C2×C5×D4C22×D3semidirect
476. #711C22×D3semidirect
496. D4×D5C22×D3semidirect
504. #709C22×D3semidirect
518. C5×D8C22×D3semidirect
519. C5×D8C22×D3semidirect
523. C2×C5×C8C22×D3semidirect
528. #687C22×D3semidirect
533. #686C22×D3semidirect
535. #681C22×D3semidirect
538. Dic20C22×D3semidirect
542. D40C22×D3semidirect
544. #677C22×D3semidirect
547. #676C22×D3semidirect
554. C8×D5C22×D3semidirect
609. C2×C3×D4C22×D5semidirect
628. #237C22×D5semidirect
648. D3×D4C22×D5semidirect
656. #235C22×D5semidirect
670. C3×D8C22×D5semidirect
671. C3×D8C22×D5semidirect
675. C2×C3×C8C22×D5semidirect
680. #214C22×D5semidirect
685. #213C22×D5semidirect
687. #208C22×D5semidirect
690. Dic12C22×D5semidirect
694. D24C22×D5semidirect
696. #204C22×D5semidirect
699. ΓL(1,𝔽25)C22×D5semidirect
706. D3×C8C22×D5semidirect
840. C2×D8D3×D5semidirect
856. D15#576semidirect
1022. C2×D4C2×D3×D5semidirect
1049. D8C2×D3×D5semidirect
1050. D8C2×D3×D5semidirect
1068. C2×C8C2×D3×D5semidirect
1069. C3×C5C2×#576semidirect
1191. C5D3×#576semidirect
1220. C3D5×#576semidirect

Maximal subgroups

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

subgroupindex
#117570302
C2×D8×D152
C5×#57572
C3×#660912
#117547012
#117546982
#117546922
#117540612
#117540592
#117540582
#117540532
#117540472
D3×D5×D82
#117539782
#117539732
#117539632
#117539522
D5×#5763
D3×#5765