Finite Group Databasebeta

← #14453525

Subgroups — #14453525

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
1C22×C3×#677C211yesmaximal, characteristic, complemented
2#67×D20C211yesmaximal, characteristic, complemented
3#11754321C211yesmaximal, characteristic, complemented
4C2×#91253C211yesmaximal, characteristic, complemented
5#11751216C211yesmaximal, characteristic, complemented
6C5×#5111C211yesmaximal, characteristic, complemented
7#11748532C211yesmaximal, characteristic, complemented
8#11748512C211yesmaximal, characteristic, complemented
9#11748110C211yesmaximal, characteristic, complemented
10#11748007C211yesmaximal, characteristic, complemented
11#11747918C211yesmaximal, characteristic, complemented
12#11747890C211yesmaximal, characteristic, complemented
13#11747839C211yesmaximal, characteristic, complemented
14#11747795C211yesmaximal, characteristic, complemented
15#11747755C211yesmaximal, characteristic, complemented
16#10611225—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic, complemented
19C2×D5×#67—21no—
20C2×D3×D20C2211yescharacteristic
21C2×#6769C2211yescharacteristic, complemented
22C22×C3×C5×C8C2211yescharacteristic, complemented
23#91819C2211yescharacteristic
24#91819C2211yescharacteristic, complemented
25C2×D120C2211yescharacteristic, complemented
26C4×C5×#67C2211yescharacteristic
27C2×C5×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28C2×C3×#677—24no—
29C2×C3×#677C2211yescharacteristic
30C2×C3×#677C2211yescharacteristic
31C2×C3×#677C2211yescharacteristic, complemented
32C2×C3×#677C2211yescharacteristic, complemented
33#91566—21no—
34#91564—21no—
35#91552—21no—
36#91474—21no—
37#91458C2211yescharacteristic
38#91456C2211yescharacteristic
39Dic3×D20C2211yescharacteristic
40#91411—21no—
41#91409—21no—
42#91374C2211yescharacteristic, complemented
43#91369C2211yescharacteristic, complemented
44Dic3×Dic10C2211yescharacteristic, complemented
45#91326—21no—
46C2×#6658C2211yescharacteristic, complemented
47C2×#6658C2211yescharacteristic, complemented
48C2×#6653C2211yescharacteristic
49C2×#6653C2211yescharacteristic, complemented
50#91253—24no—
51#91105C2211yescharacteristic, complemented
52#91105C2211yescharacteristic, complemented
53#91102C2211yescharacteristic, complemented
54C5×#830C2211yescharacteristic, complemented
55C5×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C5×#815C2211yescharacteristic, complemented
57C5×Dic3⋊C8C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90965C2211yescharacteristic
61#90965C2211yescharacteristic, complemented
62#83864—51nomaximal, Hall
63C2×#4054—31no—
64C22×#677D311yescharacteristic, complemented
65#65886—31no—
66D4×D20—31no—
67C5×#435—31no—
68#65423—31no—
69#65404—31no—
70#65137—31no—
71#65133—31no—
72#65027—31no—
73#65023—31no—
74#65021—31no—
75#65020—31no—
76#65001—31no—
77#64999—31no—
78C23×C3×D5—21no—
79C22×D3×D5—21no—
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×#1220—21no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×C5×#67D411yescharacteristic
86C2×C4×C5×D3C2311yescharacteristic
87C22×C3×Dic5—21no—
88C2×C3×D20—22no—
89C2×C3×D20—21no—
90C2×C3×D20—41no—
91C2×C3×D20C2311yescharacteristic
92C2×C3×D20C2311yescharacteristic
93C2×C3×Dic10—22no—
94C2×C3×Dic10—21no—
95C2×C3×Dic10—41no—
96C2×C3×Dic10C2311yescharacteristic
97C2×C3×Dic10C2311yescharacteristic
98D5×#67—44no—
99C2×#1203—21no—
100C2×#1202—21no—
101C2×#1202—21no—
102C2×#1202—21no—
103C2×#1201—21no—
104C2×#1200—21no—
105C2×D5×Dic3—21no—
106D3×D20—22no—
107D3×D20—41no—
108#6769—22no—
109#6769—41no—
110C2×C3×C5×C8—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113#6714—21no—
114#6714—21no—
115C4⋊Dic15C2311yescharacteristic
116C4⋊Dic15C2311yescharacteristic
117D120—22no—
118C5×#217D411yescharacteristic
119C5×(C2×D3)⋊C4D411yescharacteristic
120C5×Dic3⋊C4D411yescharacteristic
121C4×C5×Dic3C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C5×ΓL(1,𝔽25)—22no—
125C3×#677—22no—
126C3×#677—22no—
127C3×#677—22no—
128C3×#677D414yescomplemented
129#6669—21no—
130#6668—21no—
131#6667—21no—
132#6667—21no—
133(C2×D3)⋊Dic5—21no—
134#6665—21no—
135#6665—21no—
136Dic3×Dic5—21no—
137#6658—22no—
138#6658—41no—
139#6653—22no—
140#6653—41no—
141C22×C3×SD16—51no—
142#5817—51no—
143D4×#67—51no—
144C2×#914—51no—
145#5227—51no—
146#5217—51no—
147#5176—51no—
148#5174—51no—
149#5172—51no—
150#5169—51no—
151#5165—51no—
152#5164—51no—
153#5163—51no—
154#5115—51no—
155#5111D511yescharacteristic, complemented
156C2×D4×D5—61no—
157C2×#709—31no—
158C22×D20—31no—
159C22×D20C2×D311yescharacteristic
160C22×Dic10C2×D311yescharacteristic, complemented
161C2×C5×M16—31no—
162C22×C5×C8C2×D311yescharacteristic, complemented
163C4×C5×D4—31no—
164#4085—61no—
165#4076—31no—
166#4076—31no—
167#4076—31no—
168#4070—31no—
169#4054—64no—
170C2×D40—31no—
171C2×D40—31no—
172C2×D40—31no—
173C2×#677—24no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677C2×D311yescharacteristic
177C2×#677C2×D311yescharacteristic
178C2×#677C2×D311yescharacteristic, complemented
179C2×#677C2×D311yescharacteristic, complemented
180#4042—61no—
181#4041—61no—
182#4031—61no—
183#4028—61no—
184#4028—61no—
185#4027—61no—
186#4021—31no—
187#4020—31no—
188C4×D20—31no—
189C4×Dic10—31no—
190C5×C4⋊C8—31no—
191C5×C22⋊C8—31no—
192C5×C22⋊C8—31no—
193C5×#97—31no—
194#3953—31no—
195#3953—31no—
196#3953—31no—
197#3953—31no—
198#3950—31no—
199#3948—31no—
200#3948—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×C5×D3C2×D411yescharacteristic
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—81no—
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218#1220—42no—
219#1220—42no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224D60—21no—
225D60—21no—
226C5×#67—22no—
227C2×C5×Dic3C2×D411yescharacteristic
228C2×C5×Dic3C2×D411yescharacteristic
229C2×C5×Dic3C2×D411yescharacteristic
230C4×C5×D3—21no—
231C4×C5×D3—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—42no—
235C3×D20—21no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—42no—
239C3×D20C2×D412yes—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—21no—
243C3×Dic10—42no—
244C3×Dic10C2×D412yescomplemented
245#1203—42no—
246#1202—42no—
247#1202—42no—
248#1202—81no—
249#1201—42no—
250#1200—42no—
251D5×Dic3—42no—
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C5×C3⋊C8—21no—
255C5×C3⋊C8—21no—
256C22×C3×Q8—51no—
257C22×C3×D4—51no—
258C22×#67—101no—
259C2×#239—51no—
260C2×D3×D4—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×SD16—51no—
265C2×C3×SD16—104no—
266C22×C3×C8C2×D511yescharacteristic, complemented
267#953—101no—
268#947—51no—
269#947—101no—
270#946—51no—
271#946—101no—
272Q8×Dic3—51no—
273C2×#215—51no—
274C2×#215—51no—
275#940—51no—
276#939—101no—
277#938—51no—
278#937—101no—
279D4×Dic3—51no—
280C2×#213—51no—
281C2×#213—51no—
282#930—51no—
283#930—51no—
284#930—101no—
285C4×#67—101no—
286C4×#67C2×D511yescharacteristic
287#914—104no—
288C2×D24—51no—
289C2×ΓL(1,𝔽25)C2×D511yescharacteristic, complemented
290#835—51no—
291#835—51no—
292#832—51no—
293#832—51no—
294#830C2×D511yescharacteristic, complemented
295#821—51no—
296#821—51no—
297(C2×D3)⋊C8C2×D511yescharacteristic, complemented
298#818—51no—
299#815C2×D511yescharacteristic, complemented
300Dic3⋊C8C2×D511yescharacteristic, complemented
301C23×D5—21no—
302C23×D5—61no—
303C2×C5×D4—31no—
304C22×C4×C5—31no—
305C22×C4×C5C22×D311yescharacteristic
306C2×C22⋊D5—61no—
307C2×C22⋊D5—61no—
308C2×C22⋊D5—61no—
309C2×C22⋊D5—61no—
310C22×Dic5—21no—
311D4×D5—124no—
312#709—62no—
313#709—121no—
314C2×D20—22no—
315C2×D20—21no—
316C2×D20—31no—
317C2×D20—31no—
318C2×D20—41no—
319C2×D20—62no—
320C2×D20—61no—
321C2×D20—61no—
322C2×D20—61no—
323C2×D20—121no—
324C2×D20C22×D311yescharacteristic
325C2×D20C22×D311yescharacteristic
326C2×C4×D5—61no—
327C2×C4×D5—61no—
328C2×Dic10—22no—
329C2×Dic10—21no—
330C2×Dic10—41no—
331C2×Dic10C22×D311yescharacteristic
332C2×Dic10C22×D311yescharacteristic
333C5×M16—62no—
334C2×C5×C8—22no—
335C2×C5×C8—31no—
336C2×C5×C8—31no—
337C2×C5×C8C22×D311yescharacteristic
338C2×C5×C8C22×D311yescharacteristic
339C5×C4⋊C4—31no—
340C5×C22⋊C4—31no—
341C5×C22⋊C4—31no—
342C42×C5—31no—
343C22⋊Dic5—61no—
344#685—61no—
345#685—61no—
346#685—61no—
347#685—61no—
348#685—61no—
349#685—61no—
350C4⋊Dic5—31no—
351C4⋊Dic5—31no—
352#683—61no—
353#683—61no—
354C4×Dic5—61no—
355D40—62no—
356D40—62no—
357D40—121no—
358#677—22no—
359#677—22no—
360#677—22no—
361#677—62no—
362#677—121no—
363#677#6714yescomplemented
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—51no—
366#548—151no—
367D42—151no—
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—31no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5AGL(1,ℤ/8)12yescomplemented
382C22×C3×C5C22×D411yescharacteristic
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—21no—
390C2×C5×D3—21no—
391C2×C5×D3—21no—
392C2×C3×D5—22no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—84no—
399D3×D5—84no—
400C3×C4×C5—21no—
401C3×C4×C5C22×D411yescharacteristic
402C3×C4×C5H(5,𝔽2)11yescharacteristic
403Dic15—41no—
404Dic15—41no—
405C3×Dic5—22no—
406C3×Dic5—41no—
407C5×Dic3—21no—
408C5×Dic3—21no—
409C5×Dic3—21no—
410C24×C3—101no—
411C23×D3—101no—
412C2×C3×Q8—51no—
413C2×C3×Q8—51no—
414C2×C3×Q8—102no—
415C2×C3×Q8—101no—
416C2×C3×Q8—201no—
417C2×C3×D4—51no—
418C2×C3×D4—51no—
419C2×C3×D4—102no—
420C2×C3×D4—101no—
421C2×C3×D4—201no—
422C22×C3×C4—101no—
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—101no—
425C2×#67—101no—
426C2×#67—101no—
427C2×#67—101no—
428C2×#67—101no—
429C2×#67—101no—
430C2×#67—204no—
431C2×#67D2011yescharacteristic
432C22×Dic3—101no—
433#239—102no—
434#239—201no—
435D3×D4—102no—
436D3×D4—201no—
437C2×D12—51no—
438C2×D12—51no—
439C2×D12—101no—
440C2×C4×D3—101no—
441C2×C4×D3C22×D511yescharacteristic
442C3×SD16—54no—
443C3×SD16—102no—
444C3×SD16—102no—
445C3×SD16—102no—
446C2×C3×C8—22no—
447C2×C3×C8C22×D511yescharacteristic
448C2×C3×C8C22×D511yescharacteristic
449#217—101no—
450#217—101no—
451#217D2011yescharacteristic
452#215—102no—
453#215—201no—
454#213—102no—
455#213—201no—
456(C2×D3)⋊C4—101no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4—101no—
461(C2×D3)⋊C4D2011yescharacteristic
462C4⋊Dic3—51no—
463C4⋊Dic3—51no—
464C4⋊Dic3—101no—
465Dic3⋊C4—101no—
466Dic3⋊C4D2011yescharacteristic
467C4×Dic3—101no—
468C4×Dic3C22×D511yescharacteristic
469C2×C3⋊C8C22×D511yescharacteristic
470C2×C3⋊C8C22×D511yescharacteristic
471D24—102no—
472ΓL(1,𝔽25)—22no—
473C23×C5—31no—
474C23×C5D3×D411yescharacteristic
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—42no—
478C22×D5—42no—
479C22×D5—61no—
480C22×D5—61no—
481C22×D5—81no—
482C22×D5—122no—
483C22×D5—122no—
484C22×D5—241no—
485C5×D4—62no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—31no—
489C2×C4×C5—31no—
490C2×C4×C5—31no—
491C2×C4×C5—61no—
492C2×C4×C5—61no—
493C2×C4×C5D3×D411yescharacteristic
494C2×C4×C5C23×D311yescharacteristic
495C22⋊D5—122no—
496C22⋊D5—122no—
497C22⋊D5—122no—
498C22⋊D5—122no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—42no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504D20—21no—
505D20—21no—
506D20—21no—
507D20—42no—
508D20—61no—
509D20—61no—
510D20—61no—
511D20—61no—
512D20—122no—
513D20—122no—
514D20—241no—
515D20C2×#6712yes—
516C4×D5—122no—
517C4×D5—122no—
518Dic10—21no—
519Dic10—21no—
520Dic10—21no—
521Dic10—42no—
522Dic10C2×#6712yescomplemented
523C5×C8—21no—
524C5×C8—61no—
525C5×C8—61no—
526C5×C8C2×#6712yescomplemented
527C2×#41—151no—
528C22×Q8—51no—
529C22×D4—51no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—51no—
536C2×SD16—51no—
537C2×SD16—104no—
538C2×SD16—151no—
539C2×SD16—151no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—31no—
544C22×C8D3×D511yescharacteristic, complemented
545#127—151no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—151no—
551#121—151no—
552#121—151no—
553#121—301no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—151no—
558C4×D4—31no—
559C4×D4—151no—
560C4×D4—301no—
561#107—151no—
562C4⋊C8—31no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—31no—
570C22⋊C8—31no—
571#97—31no—
572C2×C3×C5—22no—
573C2×C3×C5D4211yescharacteristic
574C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
575C2×C3×C5#57711yescharacteristic
576D15—81no—
577D15—81no—
578C3×D5—42no—
579C3×D5—81no—
580C5×D3—41no—
581C23×C3—101no—
582C23×C3—101no—
583C23×C3—202no—
584C23×C3—202no—
585C23×C3—401no—
586C23×C3C2×D2011yescharacteristic
587C22×D3—101no—
588C22×D3—101no—
589C22×D3—202no—
590C22×D3—202no—
591C22×D3—401no—
592C22×D3C2×D2011yescharacteristic
593C3×Q8—52no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—52no—
599C3×D4—101no—
600C3×D4—101no—
601C3×D4—101no—
602C3×D4—202no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—101no—
606C2×C3×C4—101no—
607C2×C3×C4—202no—
608C2×C3×C4C2×D2011yescharacteristic
609C2×C3×C4C23×D511yescharacteristic
610#67—22no—
611#67—202no—
612#67—202no—
613#67—202no—
614#67—202no—
615#67—202no—
616#67—401no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—202no—
620C2×Dic3C2×D2011yescharacteristic
621C2×Dic3C2×D2011yescharacteristic
622C2×Dic3C2×D2011yescharacteristic
623D12—101no—
624D12—101no—
625D12—101no—
626D12—101no—
627D12—202no—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—202no—
631C3×C8—21no—
632C3×C8D4×D512yescomplemented
633C3⋊C8—21no—
634C3⋊C8—21no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—61no—
638C22×C5—61no—
639C22×C5—61no—
640C22×C5#91412yescomplemented
641C22×C5C2×D3×D411yescharacteristic
642C2×D5—22no—
643C2×D5—41no—
644C2×D5—41no—
645C2×D5—41no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—84no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—61no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5#100411yescharacteristic
661C4×C5C22×#6711yescharacteristic
662Dic5—22no—
663Dic5—41no—
664Dic5—121no—
665Dic5—121no—
666C24—101no—
667C24—301no—
668#41—302no—
669#41—601no—
670C2×Q8—51no—
671C2×Q8—51no—
672C2×Q8—102no—
673C2×Q8—101no—
674C2×Q8—201no—
675C2×D4—31no—
676C2×D4—51no—
677C2×D4—51no—
678C2×D4—102no—
679C2×D4—101no—
680C2×D4—151no—
681C2×D4—151no—
682C2×D4—201no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—302no—
687C2×D4—301no—
688C2×D4—301no—
689C2×D4—301no—
690C2×D4—301no—
691C2×D4—601no—
692C2×D4—604no—
693C22×C4—31no—
694C22×C4—101no—
695C22×C4—301no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—54no—
699SD16—102no—
700SD16—102no—
701SD16—102no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—62no—
708C2×C8—22no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8C2×D3×D511yescharacteristic
712C2×C8C2×D3×D511yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—151no—
715C4⋊C4—151no—
716C4⋊C4—301no—
717C4⋊C4—301no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—301no—
721C22⋊C4—301no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—31no—
728C42—301no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—102no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3—404no—
739C22×C3#405412yescomplemented
740C22×C3C22×D2011yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—102no—
753C3×C4—201no—
754C3×C4C2×D4×D511yescharacteristic
755C3×C4#414911yescharacteristic
756Dic3—21no—
757Dic3—21no—
758Dic3—21no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—121no—
763C2×C5C2×#91411yescharacteristic
764C2×C5#576211yescharacteristic
765C2×C5D4×#6711yescharacteristic
766D5—42no—
767D5—81no—
768D5—241no—
769D5—241no—
770C23—31no—
771C23—101no—
772C23—101no—
773C23—202no—
774C23—202no—
775C23—301no—
776C23—301no—
777C23—401no—
778C23—602no—
779C23—602no—
780C23—1201no—
781C23D3×D2011yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—101no—
785Q8—101no—
786Q8—202no—
787D4—52no—
788D4—62no—
789D4—101no—
790D4—101no—
791D4—101no—
792D4—202no—
793D4—301no—
794D4—301no—
795D4—301no—
796D4—301no—
797D4—602no—
798D4—602no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—202no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—602no—
817C2×C4—602no—
818C2×C4D3×D2011yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—21no—
821C8—61no—
822C8—61no—
823C8D5×#6712yescomplemented
824C2×C3—22no—
825C2×C3—202no—
826C2×C3—401no—
827C2×C3D4×D2011yescharacteristic
828C2×C3C2×#405411yescharacteristic
829C2×C3#6608511yescharacteristic
830D3—41no—
831D3—401no—
832D3—401no—
833C5#8386411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—102no—
840C22—201no—
841C22—201no—
842C22—201no—
843C22—201no—
844C22—201no—
845C22—404no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—601no—
852C22—1204no—
853C22#9125312yescomplemented
854C22C2×D3×D2011yescharacteristic
855C4—21no—
856C4—61no—
857C4—61no—
858C4—61no—
859C4—102no—
860C4—201no—
861C4—601no—
862C4—601no—
863C4#9201711yescharacteristic
864C4C2×D5×#6711yescharacteristic
865C3#1061122511yescharacteristic, complemented, Sylow
866C2—22no—
867C2—121no—
868C2—202no—
869C2—401no—
870C2—1201no—
871C2—1201no—
872C2C2×#9125311yescharacteristic
873C2#1175397011yescharacteristic
874C2#67×D2011yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#677C2semidirect
2. #67×D20C2semidirect
3. #11754321C2semidirect
4. C2×#91253C2semidirect
5. #11751216C2semidirect
6. C5×#5111C2semidirect
7. #11748532C2semidirect
8. #11748512C2semidirect
9. #11748110C2semidirect
10. #11748007C2semidirect
11. #11747918C2semidirect
12. #11747890C2semidirect
13. #11747839C2semidirect
14. #11747795C2semidirect
15. #11747755C2semidirect
18. C22×C3×Dic10C22semidirect
21. C2×#6769C22semidirect
22. C22×C3×C5×C8C22semidirect
24. #91819C22semidirect
25. C2×D120C22semidirect
27. C2×C5×ΓL(1,𝔽25)C22semidirect
31. C2×C3×#677C22semidirect
32. C2×C3×#677C22semidirect
42. #91374C22semidirect
43. #91369C22semidirect
44. Dic3×Dic10C22semidirect
46. C2×#6658C22semidirect
47. C2×#6658C22semidirect
49. C2×#6653C22semidirect
51. #91105C22semidirect
52. #91105C22semidirect
53. #91102C22semidirect
54. C5×#830C22semidirect
55. C5×(C2×D3)⋊C8C22semidirect
56. C5×#815C22semidirect
57. C5×Dic3⋊C8C22semidirect
58. #90971C22semidirect
59. #90971C22semidirect
61. #90965C22semidirect
64. C22×#677D3semidirect
128. C3×#677D4semidirect
155. #5111D5semidirect
160. C22×Dic10C2×D3semidirect
162. C22×C5×C8C2×D3semidirect
178. C2×#677C2×D3semidirect
179. C2×#677C2×D3semidirect
244. C3×Dic10C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
266. C22×C3×C8C2×D5semidirect
289. C2×ΓL(1,𝔽25)C2×D5semidirect
294. #830C2×D5semidirect
297. (C2×D3)⋊C8C2×D5semidirect
299. #815C2×D5semidirect
300. Dic3⋊C8C2×D5semidirect
363. #677#67semidirect
381. C22×C3×C5AGL(1,ℤ/8)semidirect
522. Dic10C2×#67semidirect
526. C5×C8C2×#67semidirect
544. C22×C8D3×D5semidirect
632. C3×C8D4×D5semidirect
640. C22×C5#914semidirect
729. C3×C5#3265semidirect
739. C22×C3#4054semidirect
823. C8D5×#67semidirect
833. C5#83864semidirect
853. C22#91253semidirect
865. C3#10611225semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6772
#67×D202
#117543212
C2×#912532
#117512162
C5×#51112
#117485322
#117485122
#117481102
#117480072
#117479182
#117478902
#117478392
#117477952
#117477552
#106112253
#838645