Finite Group Databasebeta

← #14453503

Subgroups — #14453503

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×#6717C211yesmaximal, characteristic, complemented
2C3×#66151C211yesmaximal, characteristic, complemented
3C2×#91502C211yesmaximal, characteristic, complemented
4#11754647C211yesmaximal, characteristic, complemented
5C5×#5227C211yesmaximal, characteristic, complemented
6#11749397C211yesmaximal, characteristic, complemented
7#11749340C211yesmaximal, characteristic, complemented
8#11749338C211yesmaximal, characteristic, complemented
9#11749273C211yesmaximal, characteristic, complemented
10#11749272C211yesmaximal, characteristic, complemented
11#11749226C211yesmaximal, characteristic, complemented
12#11749225C211yesmaximal, characteristic, complemented
13#11748524C211yesmaximal, characteristic, complemented
14#11748522C211yesmaximal, characteristic, complemented
15#11748507C211yesmaximal, characteristic, complemented
16#10611791—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C22×D60C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic, complemented
20C2×#6790—21no—
21C2×D5×D12C2211yescharacteristic
22C2×#6717—24no—
23C2×#6717C2211yescharacteristic
24C2×#6717C2211yescharacteristic
25C2×#6717C2211yescharacteristic, complemented
26C2×#6717C2211yescharacteristic, complemented
27C22×C3⋊#168C2211yescharacteristic, complemented
28C2×C5×#215C2211yescharacteristic, complemented
29C2×C5×#215C2211yescharacteristic, complemented
30C5×#930C2211yescharacteristic
31C3×#4093—21no—
32C3×#4093C2211yescharacteristic, complemented
33C3×#4092—21no—
34C3×#4092C2211yescharacteristic, complemented
35C3×Q8×Dic5C2211yescharacteristic, complemented
36C3×#4076—21no—
37C3×#4076C2211yescharacteristic, complemented
38C3×C4×C22⋊D5—21no—
39C3×C4×C22⋊D5C2211yescharacteristic
40#91573—21no—
41#91502—24no—
42#91476—21no—
43#91451C2211yescharacteristic
44#91450C2211yescharacteristic
45#91420—21no—
46#91418C2211yescharacteristic
47C2×#6653C2211yescharacteristic
48C2×#6653C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×#6649C2211yescharacteristic, complemented
51C5×#835C2211yescharacteristic, complemented
52C5×#835C2211yescharacteristic, complemented
53C5×#830C2211yescharacteristic, complemented
54#90989C2211yescharacteristic, complemented
55#90982C2211yescharacteristic, complemented
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83542—51nomaximal, Hall
63#66151D311yescharacteristic, complemented
64C22×#688—31no—
65C2×#4060—31no—
66#65943—31no—
67C5×#448—31no—
68#65465—31no—
69#65458—31no—
70#65452—31no—
71#65327—31no—
72#65108—31no—
73#65106—31no—
74#65101—31no—
75#65100—31no—
76#65021—31no—
77#65019—31no—
78C23×D15—21no—
79C22×D3×D5—21no—
80C2×C3×C5×Q8—21no—
81C2×C3×C5×Q8—22no—
82C2×C3×C5×Q8—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×Q8C2311yescharacteristic
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×D60—22no—
88C2×D60—21no—
89C2×D60—41no—
90C2×D60C2311yescharacteristic
91C2×D60C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×D12C2311yescharacteristic
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5D411yescharacteristic
96C3×#713—22no—
97C3×#713—41no—
98C2×C3×D20—21no—
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5C2311yescharacteristic
102#6790—44no—
103C2×#1203—21no—
104C2×#1203—21no—
105C2×#1203—21no—
106C2×#1202—21no—
107C2×#1200—21no—
108D5×D12—22no—
109D5×D12—41no—
110#6717—22no—
111#6717—22no—
112#6717—22no—
113#6717D414yescomplemented
114C2×C3⋊#168—22no—
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C5×#215—22no—
118C5×#215—41no—
119C5×(C2×D3)⋊C4—21no—
120C5×C4⋊Dic3C2311yescharacteristic
121C2×C5×C3⋊C8C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C3×C22⋊Dic5D411yescharacteristic
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5C2311yescharacteristic
131C3×#683—21no—
132C3×#683D411yescharacteristic
133C3×C4×Dic5—21no—
134C3×C4×Dic5C2311yescharacteristic
135#6667—21no—
136#6667—21no—
137#6653—22no—
138#6653—41no—
139#6652—22no—
140#6649—22no—
141C3×#548—51no—
142C2×#949—51no—
143C22×#215—51no—
144D4×D12—51no—
145#5238—51no—
146#5227D511yescharacteristic, complemented
147#5058—51no—
148#5057—51no—
149#5049—51no—
150#5046—51no—
151#5038—51no—
152#5036—51no—
153#5027—51no—
154#5026—51no—
155#5011—51no—
156C22×C5×Q8C2×D311yescharacteristic, complemented
157C2×#713C2×D311yescharacteristic, complemented
158C2×D4×D5—31no—
159C2×D4×D5—61no—
160C22×D20—31no—
161C2×C5×SD16—31no—
162C2×C5×SD16—31no—
163C5×#121—31no—
164#4093—21no—
165#4093C2×D311yescharacteristic, complemented
166#4092—21no—
167#4092C2×D311yescharacteristic, complemented
168Q8×Dic5C2×D311yescharacteristic, complemented
169C2×#688—31no—
170C2×#688—31no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—64no—
174#4086—31no—
175#4083—61no—
176C2×#686—31no—
177#4076—21no—
178#4076C2×D311yescharacteristic, complemented
179C4×C22⋊D5—21no—
180C4×C22⋊D5C2×D311yescharacteristic
181C22×#168—31no—
182#4060—64no—
183C2×D40—31no—
184C2×D40—31no—
185C2×#676—31no—
186#4041—31no—
187#4039—31no—
188#4030—61no—
189#4028—61no—
190C5×#103—31no—
191C5×#103—31no—
192C5×C22⋊C8—31no—
193#3964—31no—
194#3953—31no—
195#3953—31no—
196#3952—31no—
197#3947—31no—
198#3946—31no—
199#3941—31no—
200#3939—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—81no—
208C22×C5×D3—21no—
209C22×C3×D5—21no—
210C22×C3×D5C2×D411yescharacteristic
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C3×C5×Q8—21no—
217C3×C5×Q8—42no—
218C3×C5×Q8C2×D412yescomplemented
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—42no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226D60—21no—
227D60—21no—
228D60—21no—
229D60—42no—
230D60C2×D412yes—
231C5×#67—42no—
232C2×C5×Dic3—21no—
233C5×D12—21no—
234C5×D12—21no—
235C3×C22⋊D5—22no—
236C3×C22⋊D5—42no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5C2×D411yescharacteristic
239C2×C3×Dic5C2×D411yescharacteristic
240C2×C3×Dic5C2×D411yescharacteristic
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—42no—
244C3×C4×D5—21no—
245C3×C4×D5—21no—
246C3×C4×D5—42no—
247#1203—42no—
248#1203—42no—
249#1203—81no—
250#1202—42no—
251#1200—42no—
252C3⋊#168—21no—
253C3⋊#168C2×D412yescomplemented
254C5×C3⋊C8—21no—
255C5×C3⋊C8—21no—
256C2×C3×#41—51no—
257C22×C3×Q8C2×D511yescharacteristic, complemented
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—51no—
266C3×#121—101no—
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—104no—
276C2×#215C2×D511yescharacteristic, complemented
277C2×#215C2×D511yescharacteristic, complemented
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930—51no—
282#930C2×D511yescharacteristic
283C2×#208—51no—
284C22×C3⋊C8—51no—
285#895—101no—
286#882—101no—
287#882—101no—
288#874—51no—
289C4×D12—51no—
290#835C2×D511yescharacteristic, complemented
291#835C2×D511yescharacteristic, complemented
292#832—51no—
293#830—51no—
294#830C2×D511yescharacteristic, complemented
295#809—51no—
296#809—51no—
297#809—51no—
298#807—51no—
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C23×D5—61no—
302C23×D5—61no—
303C2×C5×Q8—21no—
304C2×C5×Q8—22no—
305C2×C5×Q8—41no—
306C2×C5×Q8C22×D311yescharacteristic
307C2×C5×Q8C22×D311yescharacteristic
308C2×C5×D4—31no—
309C2×C5×D4—61no—
310C22×C4×C5—21no—
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—21no—
313C2×C22⋊D5—61no—
314C2×C22⋊D5—61no—
315C2×C22⋊D5—61no—
316C2×C22⋊D5#6711yescharacteristic
317#713—22no—
318#713—41no—
319D4×D5—62no—
320D4×D5—121no—
321D4×D5—124no—
322C2×D20—21no—
323C2×D20—31no—
324C2×D20—31no—
325C2×D20—62no—
326C2×D20—61no—
327C2×D20—61no—
328C2×D20—121no—
329C2×D20C22×D311yescharacteristic
330C2×C4×D5—21no—
331C2×C4×D5—61no—
332C2×C4×D5C22×D311yescharacteristic
333C5×SD16—62no—
334C5×SD16—121no—
335C2×C5×C8—31no—
336C2×C5×C8—31no—
337C5×C4⋊C4—31no—
338C5×C22⋊C4—61no—
339C22⋊Dic5#6711yescharacteristic
340#688—34no—
341#688—62no—
342#688—62no—
343#688—62no—
344#686—62no—
345#685—21no—
346#685—21no—
347#685—21no—
348#685—21no—
349#685—61no—
350#685—61no—
351#685#6711yescharacteristic
352C4⋊Dic5—21no—
353C4⋊Dic5C22×D311yescharacteristic
354#683—21no—
355#683#6711yescharacteristic
356C4×Dic5—21no—
357C4×Dic5C22×D311yescharacteristic
358C2×#168—31no—
359C2×#168—31no—
360C2×#168—62no—
361D40—62no—
362D40—121no—
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—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—31no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5AGL(1,ℤ/8)12yescomplemented
382C22×C3×C5C22×D411yescharacteristic
383C2×D15—22no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—84no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C3×D5—21no—
394C2×C3×D5—21no—
395C2×C3×D5—21no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399D3×D5—84no—
400C3×C4×C5—22no—
401C3×C4×C5—21no—
402C3×C4×C5—41no—
403C3×C4×C5C22×D411yescharacteristic
404C3×C4×C5H(5,𝔽2)11yescharacteristic
405C3×Dic5—21no—
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—21no—
415C2×C3×Q8—22no—
416C2×C3×Q8—41no—
417C2×C3×Q8C22×D511yescharacteristic
418C2×C3×Q8C22×D511yescharacteristic
419C2×C3×D4—51no—
420C2×C3×D4—51no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C22×C3×C4—21no—
424C22×C3×C4—51no—
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—51no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4—101no—
446C3×C22⋊C4—51no—
447C3×C22⋊C4—51no—
448C3×C22⋊C4—101no—
449C3×C22⋊C4—101no—
450C3×C22⋊C4—101no—
451C3×C22⋊C4—101no—
452C3×C42—51no—
453C3×C42—101no—
454#215—22no—
455#215—41no—
456#215—54no—
457#215—102no—
458#215—102no—
459#215—102no—
460#213—102no—
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—51no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—102no—
471C2×C3⋊C8C22×D511yescharacteristic
472C2×C3⋊C8C22×D511yescharacteristic
473C23×C5—61no—
474C23×C5C2×#6711yescharacteristic
475C22×D5—21no—
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×Q8—21no—
486C5×Q8—21no—
487C5×Q8—21no—
488C5×Q8—42no—
489C5×Q8D3×D412yescomplemented
490C5×D4—61no—
491C5×D4—61no—
492C5×D4—122no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—42no—
498C2×C4×C5—61no—
499C2×C4×C5C2×#6711yescharacteristic
500C2×C4×C5C23×D311yescharacteristic
501C22⋊D5—22no—
502C22⋊D5—42no—
503C22⋊D5—122no—
504C22⋊D5—122no—
505C22⋊D5—241no—
506C2×Dic5—21no—
507C2×Dic5C2×#6711yescharacteristic
508C2×Dic5C2×#6711yescharacteristic
509C2×Dic5C2×#6711yescharacteristic
510D20—21no—
511D20—21no—
512D20—32no—
513D20—42no—
514D20—61no—
515D20—61no—
516D20—61no—
517D20—122no—
518D20—122no—
519C4×D5—21no—
520C4×D5—21no—
521C4×D5—42no—
522C4×D5—122no—
523C5×C8—61no—
524C5×C8—61no—
525#168—32no—
526#168—61no—
527C2×#41—51no—
528C22×Q8D3×D511yescharacteristic, complemented
529C22×D4—151no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—31no—
534C2×SD16—31no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—151no—
545#127—151no—
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—31no—
551#121—51no—
552#121—101no—
553#121—151no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—51no—
558C4×D4—51no—
559C4×D4—101no—
560C4×D4—151no—
561#107—151no—
562C4⋊C8—151no—
563#103—31no—
564#103—31no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—31no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5D4211yescharacteristic
574C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
575C2×C3×C5#57711yescharacteristic
576D15—42no—
577D15—81no—
578C3×D5—41no—
579C3×D5—81no—
580C5×D3—81no—
581C23×C3—51no—
582C23×C3—101no—
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—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—42no—
597C3×Q8D4×D512yescomplemented
598C3×D4—102no—
599C3×D4—101no—
600C3×D4—101no—
601C3×D4—202no—
602C3×D4—202no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—42no—
608C2×C3×C4—51no—
609C2×C3×C4—51no—
610C2×C3×C4—51no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
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—21no—
633C3⋊C8—52no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—121no—
638C22×C5—121no—
639C22×C5—121no—
640C22×C5#94912yescomplemented
641C22×C5C22×#6711yescharacteristic
642C2×D5—21no—
643C2×D5—21no—
644C2×D5—21no—
645C2×D5—41no—
646C2×D5—41no—
647C2×D5—41no—
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—22no—
657C4×C5—21no—
658C4×C5—41no—
659C4×C5—121no—
660C4×C5C2×D3×D411yescharacteristic
661C4×C5#100411yescharacteristic
662Dic5—21no—
663Dic5—21no—
664Dic5—21no—
665Dic5—41no—
666C24—301no—
667C24—301no—
668#41—102no—
669#41—201no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—41no—
673C2×Q8C2×D3×D511yescharacteristic
674C2×Q8C2×D3×D511yescharacteristic
675C2×D4—31no—
676C2×D4—51no—
677C2×D4—51no—
678C2×D4—61no—
679C2×D4—101no—
680C2×D4—101no—
681C2×D4—151no—
682C2×D4—151no—
683C2×D4—302no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—302no—
689C2×D4—301no—
690C2×D4—601no—
691C2×D4—601no—
692C2×D4—604no—
693C22×C4—21no—
694C22×C4—51no—
695C22×C4—101no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—62no—
699SD16—121no—
700SD16—154no—
701SD16—302no—
702SD16—302no—
703SD16—302no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—31no—
714C4⋊C4—51no—
715C4⋊C4—51no—
716C4⋊C4—101no—
717C4⋊C4—101no—
718C22⋊C4—51no—
719C22⋊C4—51no—
720C22⋊C4—61no—
721C22⋊C4—101no—
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—101no—
733C22×C3—101no—
734C22×C3—101no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3#406012yescomplemented
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—22no—
753C3×C4—41no—
754C3×C4—101no—
755C3×C4—101no—
756C3×C4—101no—
757C3×C4—201no—
758C3×C4C2×D4×D511yescharacteristic
759C3×C4#414411yescharacteristic
760Dic3—41no—
761C2×C5—22no—
762C2×C5—241no—
763C2×C5D4×#6711yescharacteristic
764C2×C5C2×#94911yescharacteristic
765C2×C5#583711yescharacteristic
766D5—41no—
767D5—81no—
768D5—122no—
769D5—241no—
770C23—51no—
771C23—61no—
772C23—101no—
773C23—301no—
774C23—301no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—602no—
779C23—1201no—
780C23—1201no—
781C23D5×#6711yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—42no—
786Q8#679012yescomplemented
787D4—61no—
788D4—61no—
789D4—102no—
790D4—101no—
791D4—101no—
792D4—122no—
793D4—152no—
794D4—202no—
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—21no—
808C2×C4—42no—
809C2×C4—51no—
810C2×C4—51no—
811C2×C4—51no—
812C2×C4—61no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—202no—
817C2×C4—602no—
818C2×C4D5×#6711yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—61no—
821C8—61no—
822C8—152no—
823C8—301no—
824C2×C3—22no—
825C2×C3—201no—
826C2×C3—401no—
827C2×C3#6592411yescharacteristic
828C2×C3C2×#406011yescharacteristic
829C2×C3#6611211yescharacteristic
830D3—81no—
831D3—202no—
832D3—401no—
833C5#8354211yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—101no—
837C22—101no—
838C22—101no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—201no—
843C22—201no—
844C22—201no—
845C22—302no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9150212yescomplemented
854C22C2×D5×#6711yescharacteristic
855C4—21no—
856C4—22no—
857C4—41no—
858C4—101no—
859C4—101no—
860C4—101no—
861C4—121no—
862C4—201no—
863C4C2×#679011yescharacteristic
864C4#9204911yescharacteristic
865C3#1061179111yescharacteristic, complemented, Sylow
866C2—22no—
867C2—201no—
868C2—241no—
869C2—401no—
870C2—602no—
871C2—1201no—
872C2C2×#9150211yescharacteristic
873C2#1175508611yescharacteristic
874C2#1175543711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#6717C2semidirect
2. C3×#66151C2semidirect
3. C2×#91502C2semidirect
4. #11754647C2semidirect
5. C5×#5227C2semidirect
6. #11749397C2semidirect
7. #11749340C2semidirect
8. #11749338C2semidirect
9. #11749273C2semidirect
10. #11749272C2semidirect
11. #11749226C2semidirect
12. #11749225C2semidirect
13. #11748524C2semidirect
14. #11748522C2semidirect
15. #11748507C2semidirect
17. C22×C3×C5×Q8C22semidirect
19. C2×C3×#713C22semidirect
25. C2×#6717C22semidirect
26. C2×#6717C22semidirect
27. C22×C3⋊#168C22semidirect
28. C2×C5×#215C22semidirect
29. C2×C5×#215C22semidirect
32. C3×#4093C22semidirect
34. C3×#4092C22semidirect
35. C3×Q8×Dic5C22semidirect
37. C3×#4076C22semidirect
48. C2×#6653C22semidirect
49. C2×#6652C22semidirect
50. C2×#6649C22semidirect
51. C5×#835C22semidirect
52. C5×#835C22semidirect
53. C5×#830C22semidirect
54. #90989C22semidirect
55. #90982C22semidirect
57. #90968C22semidirect
58. #90966C22semidirect
59. #90964C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
63. #66151D3semidirect
113. #6717D4semidirect
146. #5227D5semidirect
156. C22×C5×Q8C2×D3semidirect
157. C2×#713C2×D3semidirect
165. #4093C2×D3semidirect
167. #4092C2×D3semidirect
168. Q8×Dic5C2×D3semidirect
178. #4076C2×D3semidirect
218. C3×C5×Q8C2×D4semidirect
253. C3⋊#168C2×D4semidirect
257. C22×C3×Q8C2×D5semidirect
276. C2×#215C2×D5semidirect
277. C2×#215C2×D5semidirect
290. #835C2×D5semidirect
291. #835C2×D5semidirect
294. #830C2×D5semidirect
381. C22×C3×C5AGL(1,ℤ/8)semidirect
489. C5×Q8D3×D4semidirect
528. C22×Q8D3×D5semidirect
597. C3×Q8D4×D5semidirect
640. C22×C5#949semidirect
729. C3×C5#3265semidirect
738. C22×C3#4060semidirect
786. Q8#6790semidirect
833. C5#83542semidirect
853. C22#91502semidirect
865. C3#10611791semidirect

Maximal subgroups

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

subgroupindex
C22×#67172
C3×#661512
C2×#915022
#117546472
C5×#52272
#117493972
#117493402
#117493382
#117492732
#117492722
#117492262
#117492252
#117485242
#117485222
#117485072
#106117913
#835425