Finite Group Databasebeta

← #14453530

Subgroups — #14453530

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
1C3×#65932C211yesmaximal, characteristic, complemented
2C2×#91478C211yesmaximal, characteristic, complemented
3#11754647C211yesmaximal, characteristic, complemented
4C22×#6658C211yesmaximal, characteristic, complemented
5#11751137C211yesmaximal, characteristic, complemented
6C5×#5038C211yesmaximal, characteristic, complemented
7#11749094C211yesmaximal, characteristic, complemented
8#11749026C211yesmaximal, characteristic, complemented
9#11748980C211yesmaximal, characteristic, complemented
10#11748529C211yesmaximal, characteristic, complemented
11#11748503C211yesmaximal, characteristic, complemented
12#11747481C211yesmaximal, characteristic, complemented
13#11747460C211yesmaximal, characteristic, complemented
14#11747400C211yesmaximal, characteristic, complemented
15#11747224C211yesmaximal, characteristic, complemented
16#10612458—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic, complemented
19C22×C3×Dic10C2211yescharacteristic, complemented
20C2×#6790—21no—
21C2×D5×D12C2211yescharacteristic
22C3×C5×#121C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic
24C2×#6715C2211yescharacteristic, complemented
25C2×C5×#213C2211yescharacteristic, complemented
26C5×#930C2211yescharacteristic
27C22×C5×C3⋊C8C2211yescharacteristic, complemented
28C3×#4085—21no—
29C3×#4082C2211yescharacteristic, complemented
30C3×D4×Dic5—21no—
31C3×C4×C22⋊D5C2211yescharacteristic
32C3×#4043C2211yescharacteristic, complemented
33C3×#4033C2211yescharacteristic, complemented
34C3×#4031—21no—
35C3×#4024—21no—
36#91573—21no—
37#91478—24no—
38#91476—21no—
39#91451C2211yescharacteristic
40#91450C2211yescharacteristic
41#91420—21no—
42#91418C2211yescharacteristic
43C2×#6658—24no—
44C2×#6658C2211yescharacteristic
45C2×#6658C2211yescharacteristic
46C2×#6658C2211yescharacteristic, complemented
47C2×#6658C2211yescharacteristic, complemented
48C2×#6656C2211yescharacteristic, complemented
49C2×#6656C2211yescharacteristic, complemented
50C2×#6649C2211yescharacteristic, complemented
51#91114C2211yescharacteristic, complemented
52#91093C2211yescharacteristic
53#91093C2211yescharacteristic, complemented
54C5×#832C2211yescharacteristic, complemented
55C5×#809C2211yescharacteristic, complemented
56C5×#807C2211yescharacteristic, complemented
57#90982C2211yescharacteristic, complemented
58#90970C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83542—51nomaximal, Hall
63C2×#4057—31no—
64C22×#677—31no—
65#65943—31no—
66#65932D311yescharacteristic, complemented
67C5×#466—31no—
68#65443—31no—
69#65400—31no—
70#65329—31no—
71#65325—31no—
72#65178—31no—
73#65175—31no—
74#65076—31no—
75#65070—31no—
76#65065—31no—
77#65051—31no—
78C23×D15—21no—
79C22×D3×D5—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×D60—22no—
84C2×D60—21no—
85C2×D60—41no—
86C2×D60C2311yescharacteristic
87C2×D60C2311yescharacteristic
88C2×C5×#67—21no—
89C2×C5×D12C2311yescharacteristic
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5D411yescharacteristic
92C22×C3×Dic5—21no—
93C22×C3×Dic5—21no—
94C3×#711—22no—
95C3×#711—41no—
96C2×C3×C4×D5C2311yescharacteristic
97C2×C3×Dic10—22no—
98C2×C3×Dic10—21no—
99C2×C3×Dic10—41no—
100C2×C3×Dic10C2311yescharacteristic
101C2×C3×Dic10C2311yescharacteristic
102#6790—44no—
103C2×#1203—21no—
104C2×#1203—21no—
105C2×#1203—21no—
106C2×#1202—21no—
107C2×#1200—21no—
108D5×D12—22no—
109D5×D12—41no—
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112#6715—22no—
113#6715—41no—
114C2×C3⋊#168C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116C5×#213—22no—
117C5×(C2×D3)⋊C4—21no—
118C5×C4⋊Dic3C2311yescharacteristic
119C2×C5×C3⋊C8—22no—
120C2×C5×C3⋊C8C2311yescharacteristic
121C2×C5×C3⋊C8C2311yescharacteristic
122C3×C22⋊Dic5—21no—
123C3×C22⋊Dic5—21no—
124C3×C22⋊Dic5D411yescharacteristic
125C3×#685—21no—
126C3×#685D411yescharacteristic
127C3×C4⋊Dic5—21no—
128C3×#683—21no—
129C3×#683D411yescharacteristic
130C3×C4×Dic5—21no—
131C3×C4×Dic5C2311yescharacteristic
132#6667—21no—
133#6667—21no—
134#6658—22no—
135#6658—22no—
136#6658—22no—
137#6658D414yescomplemented
138#6656—22no—
139#6656—41no—
140#6649—22no—
141C3×#548—51no—
142C2×#949—51no—
143C22×#215—51no—
144D4×D12—51no—
145#5238—51no—
146#5227—51no—
147#5058—51no—
148#5057—51no—
149#5049—51no—
150#5046—51no—
151#5038D511yescharacteristic, complemented
152#5036—51no—
153#5027—51no—
154#5026—51no—
155#5011—51no—
156C2×#711C2×D311yescharacteristic, complemented
157C2×D4×D5—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×Dic10C2×D311yescharacteristic, complemented
161C2×C5×D8—31no—
162C22×C5×C8—31no—
163C5×#121—31no—
164C5×#121C2×D311yescharacteristic, complemented
165#4086—31no—
166#4085—21no—
167#4083—61no—
168#4082C2×D311yescharacteristic, complemented
169D4×Dic5—21no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#686—31no—
173C2×#686—31no—
174C4×C22⋊D5C2×D311yescharacteristic
175#4057—64no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—31no—
179C2×#677—31no—
180C2×#677—64no—
181C2×#676—31no—
182#4043C2×D311yescharacteristic, complemented
183#4041—31no—
184#4039—31no—
185#4033C2×D311yescharacteristic, complemented
186#4031—21no—
187#4030—61no—
188#4028—61no—
189#4024—21no—
190C5×#107—31no—
191C5×#102—31no—
192C5×#102—31no—
193C22⋊#168—31no—
194#3952—31no—
195#3947—31no—
196#3946—31no—
197#3942—31no—
198#3942—31no—
199#3941—31no—
200#3941—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—42no—
207C22×D15—42no—
208C22×D15—81no—
209C22×C5×D3—21no—
210C22×C3×D5C2×D411yescharacteristic
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—42no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222D60—21no—
223D60—21no—
224D60—21no—
225D60—42no—
226D60C2×D412yes—
227C5×#67—42no—
228C2×C5×Dic3—21no—
229C5×D12—21no—
230C5×D12—21no—
231C3×C22⋊D5—22no—
232C3×C22⋊D5—42no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—42no—
236C2×C3×Dic5—42no—
237C2×C3×Dic5C2×D411yescharacteristic
238C2×C3×Dic5C2×D411yescharacteristic
239C2×C3×Dic5C2×D411yescharacteristic
240C3×C4×D5—21no—
241C3×C4×D5—21no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—42no—
246C3×Dic10C2×D412yescomplemented
247#1203—42no—
248#1203—42no—
249#1203—81no—
250#1202—42no—
251#1200—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C5×C3⋊C8—21no—
255C5×C3⋊C8C2×D412yescomplemented
256C2×C3×#41—51no—
257C22×C3×Q8—51no—
258C2×D3×D4—101no—
259C22×D12—51no—
260C22×D12—51no—
261C3×#124—51no—
262C3×#124—101no—
263C3×C22⋊Q8—51no—
264C3×C22⋊Q8—101no—
265C3×#121—101no—
266C3×#121C2×D511yescharacteristic, complemented
267C3×C4×Q8—51no—
268C3×C4×D4—51no—
269C3×C4×D4—101no—
270#949—104no—
271C2×#215—51no—
272C2×#215—51no—
273C2×#215—51no—
274C2×#215—51no—
275C2×#215—51no—
276C2×#215—51no—
277C2×#215—104no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213C2×D511yescharacteristic, complemented
281#930—51no—
282#930C2×D511yescharacteristic
283C2×#208—51no—
284C22×C3⋊C8C2×D511yescharacteristic, complemented
285#895—101no—
286#882—101no—
287#882—101no—
288#874—51no—
289C4×D12—51no—
290#835—51no—
291#835—51no—
292#832C2×D511yescharacteristic, complemented
293#830—51no—
294#830—51no—
295#809—51no—
296#809—51no—
297#809C2×D511yescharacteristic, complemented
298#807C2×D511yescharacteristic, complemented
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C23×D5—61no—
302C23×D5—61no—
303C2×C5×D4—21no—
304C2×C5×D4—31no—
305C2×C5×D4—61no—
306C2×C5×D4C22×D311yescharacteristic
307C22×C4×C5C22×D311yescharacteristic
308C2×C22⋊D5—21no—
309C2×C22⋊D5—61no—
310C2×C22⋊D5—61no—
311C2×C22⋊D5—61no—
312C2×C22⋊D5#6711yescharacteristic
313C22×Dic5—21no—
314C22×Dic5—21no—
315#711—22no—
316#711—41no—
317D4×D5—62no—
318D4×D5—121no—
319D4×D5—124no—
320C2×D20—31no—
321C2×D20—31no—
322C2×D20—62no—
323C2×D20—61no—
324C2×D20—61no—
325C2×D20—121no—
326C2×C4×D5—61no—
327C2×C4×D5C22×D311yescharacteristic
328C2×Dic10—22no—
329C2×Dic10—21no—
330C2×Dic10—41no—
331C2×Dic10C22×D311yescharacteristic
332C2×Dic10C22×D311yescharacteristic
333C5×D8—62no—
334C2×C5×C8—31no—
335C2×C5×C8—31no—
336C2×C5×C8—62no—
337C5×C4⋊C4—31no—
338C5×C4⋊C4C22×D311yescharacteristic
339C5×C22⋊C4—21no—
340C5×C22⋊C4—61no—
341C22⋊Dic5—21no—
342C22⋊Dic5—21no—
343C22⋊Dic5#6711yescharacteristic
344#687—62no—
345#687—121no—
346#686—62no—
347#686—121no—
348#685—21no—
349#685—61no—
350#685—61no—
351#685#6711yescharacteristic
352C4⋊Dic5—21no—
353#683—21no—
354#683#6711yescharacteristic
355C4×Dic5—21no—
356C4×Dic5C22×D311yescharacteristic
357C2×#168—31no—
358C2×#168—31no—
359#677—34no—
360#677—62no—
361#677—62no—
362#677—62no—
363#676—62no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—51no—
367D42—151no—
368#496—151no—
369#468—151no—
370#466—31no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5AGL(1,ℤ/8)12yescomplemented
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—84no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C3×D5—21no—
397C2×C3×D5—21no—
398C2×C3×D5—21no—
399D3×D5—84no—
400C3×C4×C5—21no—
401C3×C4×C5—41no—
402C3×C4×C5C22×D411yescharacteristic
403C3×C4×C5H(5,𝔽2)11yescharacteristic
404C3×Dic5—21no—
405C3×Dic5—22no—
406C3×Dic5—21no—
407C3×Dic5—21no—
408C3×Dic5—41no—
409C5×Dic3—41no—
410C23×D3—101no—
411C23×D3—101no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×Q8—51no—
416C2×C3×Q8—102no—
417C2×C3×Q8—101no—
418C2×C3×Q8—201no—
419C2×C3×D4—21no—
420C2×C3×D4—51no—
421C2×C3×D4—101no—
422C2×C3×D4C22×D511yescharacteristic
423C22×C3×C4—51no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—21no—
428C2×#67—101no—
429D3×D4—204no—
430C2×D12—51no—
431C2×D12—51no—
432C2×D12—102no—
433C2×D12—102no—
434C2×D12—101no—
435C2×D12—101no—
436C2×D12—101no—
437C2×D12—101no—
438C2×D12—201no—
439C2×D12—201no—
440C2×D12C22×D511yescharacteristic
441C2×C4×D3—101no—
442C3×C4⋊C4—51no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4C22×D511yescharacteristic
446C3×C22⋊C4—21no—
447C3×C22⋊C4—51no—
448C3×C22⋊C4—51no—
449C3×C22⋊C4—101no—
450C3×C22⋊C4—101no—
451C3×C22⋊C4—101no—
452C3×C42—51no—
453C3×C42—101no—
454#215—54no—
455#215—102no—
456#215—102no—
457#215—102no—
458#215—102no—
459#215—201no—
460#213—22no—
461#213—102no—
462#213—201no—
463(C2×D3)⋊C4—21no—
464(C2×D3)⋊C4—101no—
465(C2×D3)⋊C4—101no—
466C4⋊Dic3C22×D511yescharacteristic
467#208—102no—
468C2×C3⋊C8—22no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471C2×C3⋊C8C22×D511yescharacteristic
472C2×C3⋊C8C22×D511yescharacteristic
473C23×C5—21no—
474C23×C5—61no—
475C23×C5C2×#6711yescharacteristic
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—122no—
479C22×D5—122no—
480C22×D5—122no—
481C22×D5—122no—
482C22×D5—241no—
483C22×D5—241no—
484C22×D5C2×#6711yescharacteristic
485C5×D4—21no—
486C5×D4—21no—
487C5×D4—42no—
488C5×D4—61no—
489C5×D4—61no—
490C5×D4—122no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—61no—
495C2×C4×C5C2×#6711yescharacteristic
496C2×C4×C5C23×D311yescharacteristic
497C22⋊D5—22no—
498C22⋊D5—42no—
499C22⋊D5—122no—
500C22⋊D5—122no—
501C22⋊D5—241no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5—42no—
505C2×Dic5—42no—
506C2×Dic5C2×#6711yescharacteristic
507C2×Dic5C2×#6711yescharacteristic
508C2×Dic5C2×#6711yescharacteristic
509D20—32no—
510D20—61no—
511D20—61no—
512D20—61no—
513D20—122no—
514D20—122no—
515C4×D5—21no—
516C4×D5—21no—
517C4×D5—122no—
518Dic10—21no—
519Dic10—21no—
520Dic10—21no—
521Dic10—42no—
522Dic10D3×D412yescomplemented
523C5×C8—32no—
524C5×C8—61no—
525#168—61no—
526#168—61no—
527C2×#41—51no—
528C22×Q8—51no—
529C22×D4—151no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—31no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—31no—
545#127—151no—
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—31no—
551#121—101no—
552#121—151no—
553#121—301no—
554#121D3×D511yescharacteristic, complemented
555#120—301no—
556#120—301no—
557C4×Q8—51no—
558C4×D4—51no—
559C4×D4—101no—
560C4×D4—151no—
561#107—31no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—31no—
566#102—31no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—81no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577D15—42no—
578D15—81no—
579C3×D5—41no—
580C5×D3—81no—
581C23×C3—21no—
582C23×C3—51no—
583C23×C3D4×D511yescharacteristic
584C22×D3—21no—
585C22×D3—101no—
586C22×D3—101no—
587C22×D3—202no—
588C22×D3—202no—
589C22×D3—202no—
590C22×D3—202no—
591C22×D3—401no—
592C22×D3—401no—
593C3×Q8—52no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—42no—
601C3×D4—102no—
602C3×D4—202no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—51no—
607C2×C3×C4—51no—
608C2×C3×C4—51no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—202no—
614C2×C3×C4—202no—
615C2×C3×C4D4×D511yescharacteristic
616C2×C3×C4C23×D511yescharacteristic
617#67—42no—
618#67—202no—
619C2×Dic3—21no—
620D12—21no—
621D12—21no—
622D12—52no—
623D12—101no—
624D12—101no—
625D12—101no—
626D12—202no—
627D12—202no—
628D12—202no—
629D12—401no—
630C4×D3—202no—
631C3⋊C8—21no—
632C3⋊C8—101no—
633C3⋊C8—101no—
634C3⋊C8D4×D512yescomplemented
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—121no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5#94912yescomplemented
644C22×C5C22×#6711yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—21no—
648C2×D5—62no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—41no—
658C4×C5—121no—
659C4×C5C2×D3×D411yescharacteristic
660C4×C5#100411yescharacteristic
661Dic5—22no—
662Dic5—21no—
663Dic5—21no—
664Dic5—21no—
665Dic5—41no—
666C24—301no—
667C24—301no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—51no—
672C2×Q8—102no—
673C2×Q8—101no—
674C2×Q8—201no—
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—51no—
678C2×D4—61no—
679C2×D4—101no—
680C2×D4—151no—
681C2×D4—151no—
682C2×D4—302no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—302no—
688C2×D4—301no—
689C2×D4—601no—
690C2×D4—601no—
691C2×D4—604no—
692C2×D4C2×D3×D511yescharacteristic
693C22×C4—51no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—62no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8—151no—
712C2×C8—151no—
713C4⋊C4—31no—
714C4⋊C4—51no—
715C4⋊C4—101no—
716C4⋊C4—101no—
717C4⋊C4C2×D3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—51no—
720C22⋊C4—51no—
721C22⋊C4—61no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—51no—
728C42—101no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—101no—
736C22×C3—101no—
737C22×C3—101no—
738C22×C3#405712yescomplemented
739C22×C3C2×D4×D511yescharacteristic
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—102no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—404no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—101no—
754C3×C4—101no—
755C3×C4—101no—
756C3×C4—102no—
757C3×C4—201no—
758C3×C4C2×D4×D511yescharacteristic
759C3×C4#414911yescharacteristic
760Dic3—41no—
761C2×C5—22no—
762C2×C5—81no—
763C2×C5—241no—
764C2×C5D4×#6711yescharacteristic
765C2×C5C2×#94911yescharacteristic
766C2×C5#583711yescharacteristic
767D5—41no—
768D5—122no—
769D5—241no—
770C23—21no—
771C23—51no—
772C23—61no—
773C23—301no—
774C23—301no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—602no—
779C23—1201no—
780C23—1201no—
781C23D5×#6711yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—101no—
785Q8—101no—
786Q8—202no—
787D4—21no—
788D4—21no—
789D4—42no—
790D4—61no—
791D4—61no—
792D4—102no—
793D4—122no—
794D4—152no—
795D4—202no—
796D4—301no—
797D4—301no—
798D4—301no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—51no—
808C2×C4—51no—
809C2×C4—51no—
810C2×C4—61no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—202no—
816C2×C4—202no—
817C2×C4—602no—
818C2×C4D5×#6711yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—32no—
821C8—61no—
822C8—301no—
823C8—301no—
824C2×C3—22no—
825C2×C3—81no—
826C2×C3—201no—
827C2×C3#6594311yescharacteristic
828C2×C3C2×#405711yescharacteristic
829C2×C3#6610411yescharacteristic
830D3—81no—
831D3—202no—
832D3—401no—
833C5#8354211yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—101no—
840C22—101no—
841C22—101no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—302no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9147812yescomplemented
854C22C2×D5×#6711yescharacteristic
855C4—21no—
856C4—41no—
857C4—101no—
858C4—102no—
859C4—101no—
860C4—101no—
861C4—121no—
862C4—201no—
863C4D3×D4×D511yescharacteristic
864C4#9202611yescharacteristic
865C3#1061245811yescharacteristic, complemented, Sylow
866C2—22no—
867C2—81no—
868C2—201no—
869C2—241no—
870C2—602no—
871C2—1201no—
872C2C2×#9147811yescharacteristic
873C2#1175503811yescharacteristic
874C2#1175531911yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#65932C2semidirect
2. C2×#91478C2semidirect
3. #11754647C2semidirect
4. C22×#6658C2semidirect
5. #11751137C2semidirect
6. C5×#5038C2semidirect
7. #11749094C2semidirect
8. #11749026C2semidirect
9. #11748980C2semidirect
10. #11748529C2semidirect
11. #11748503C2semidirect
12. #11747481C2semidirect
13. #11747460C2semidirect
14. #11747400C2semidirect
15. #11747224C2semidirect
18. C2×C3×#711C22semidirect
19. C22×C3×Dic10C22semidirect
22. C3×C5×#121C22semidirect
24. C2×#6715C22semidirect
25. C2×C5×#213C22semidirect
27. C22×C5×C3⋊C8C22semidirect
29. C3×#4082C22semidirect
32. C3×#4043C22semidirect
33. C3×#4033C22semidirect
46. C2×#6658C22semidirect
47. C2×#6658C22semidirect
48. C2×#6656C22semidirect
49. C2×#6656C22semidirect
50. C2×#6649C22semidirect
51. #91114C22semidirect
53. #91093C22semidirect
54. C5×#832C22semidirect
55. C5×#809C22semidirect
56. C5×#807C22semidirect
57. #90982C22semidirect
58. #90970C22semidirect
59. #90970C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
66. #65932D3semidirect
137. #6658D4semidirect
151. #5038D5semidirect
156. C2×#711C2×D3semidirect
160. C22×Dic10C2×D3semidirect
164. C5×#121C2×D3semidirect
168. #4082C2×D3semidirect
182. #4043C2×D3semidirect
185. #4033C2×D3semidirect
246. C3×Dic10C2×D4semidirect
255. C5×C3⋊C8C2×D4semidirect
266. C3×#121C2×D5semidirect
280. C2×#213C2×D5semidirect
284. C22×C3⋊C8C2×D5semidirect
292. #832C2×D5semidirect
297. #809C2×D5semidirect
298. #807C2×D5semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
522. Dic10D3×D4semidirect
554. #121D3×D5semidirect
634. C3⋊C8D4×D5semidirect
643. C22×C5#949semidirect
729. C3×C5#3265semidirect
738. C22×C3#4057semidirect
833. C5#83542semidirect
853. C22#91478semidirect
865. C3#10612458semidirect

Maximal subgroups

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

subgroupindex
C3×#659322
C2×#914782
#117546472
C22×#66582
#117511372
C5×#50382
#117490942
#117490262
#117489802
#117485292
#117485032
#117474812
#117474602
#117474002
#117472242
#106124583
#835425