Finite Group Databasebeta

← #14458305

Subgroups — #14458305

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65945C211yesmaximal, characteristic, complemented
2D12×C22⋊D5C211yesmaximal, characteristic, complemented
3#11751139C211yesmaximal, characteristic, complemented
4C5×#5036C211yesmaximal, characteristic, complemented
5#11749151C211yesmaximal, characteristic, complemented
6#11749119C211yesmaximal, characteristic, complemented
7#11749092C211yesmaximal, characteristic, complemented
8Dic5×#213C211yesmaximal, characteristic, complemented
9#11748493C211yesmaximal, characteristic, complemented
10#11748474C211yesmaximal, characteristic, complemented
11C2×#90966C211yesmaximal, characteristic, complemented
12D5×#809C211yesmaximal, characteristic, complemented
13#11747306C211yesmaximal, characteristic, complemented
14#11747237C211yesmaximal, characteristic, complemented
15#11747138C211yesmaximal, characteristic, complemented
16#10611745—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×C3×#711—21no—
19C2×D3×C22⋊D5—21no—
20C2×D5×D12C2211yescharacteristic
21C3×C5×#121C2211yescharacteristic, complemented
22C2×#6715C2211yescharacteristic, complemented
23#91819C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic, complemented
25C2×C5×#213C2211yescharacteristic
26C2×C5×#213C2211yescharacteristic, complemented
27C3×#4084C2211yescharacteristic, complemented
28C3×#4081—21no—
29C3×D4×Dic5C2211yescharacteristic, complemented
30C3×C4×C22⋊D5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
32C3×D5×C4⋊C4C2211yescharacteristic, complemented
33C3×#4034C2211yescharacteristic, complemented
34C3×#4029—21no—
35C3×#4024—21no—
36#91570—21no—
37#91475—21no—
38#91451C2211yescharacteristic
39#91449C2211yescharacteristic
40#91416—21no—
41Dic5×D12C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91116C2211yescharacteristic, complemented
44#91093C2211yescharacteristic, complemented
45#91091C2211yescharacteristic, complemented
46C5×#830C2211yescharacteristic, complemented
47C5×#809C2211yescharacteristic
48C5×#809C2211yescharacteristic, complemented
49#90990C2211yescharacteristic, complemented
50#90990C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90968C2211yescharacteristic, complemented
53#90968C2211yescharacteristic, complemented
54#90966C2211yescharacteristic
55#90966C2211yescharacteristic
56#90966C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83525—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65945D311yescharacteristic, complemented
63C5×#447—31no—
64C2×#3964—31no—
65#65446—31no—
66#65445—31no—
67#65439—31no—
68D8×Dic5—31no—
69#65327—31no—
70#65063—31no—
71D5×#102—31no—
72#65049—31no—
73#65048—31no—
74#65025—31no—
75#65014—31no—
76C23×C5×D3—21no—
77C22×D3×D5—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×D60C2311yescharacteristic
83C2×C5×D12—22no—
84C2×C5×D12—21no—
85C2×C5×D12—41no—
86C2×C5×D12C2311yescharacteristic
87C2×C5×D12C2311yescharacteristic
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5D411yescharacteristic
90C22×C3×Dic5—21no—
91C22×C3×Dic5—21no—
92C3×#711—44no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5C2311yescharacteristic
95C2×C3×Dic10—21no—
96D3×C22⋊D5—44no—
97C2×#1203—21no—
98C2×#1203—21no—
99C2×#1203—21no—
100C2×#1201—21no—
101C2×D3×Dic5—21no—
102D5×D12—22no—
103D5×D12—41no—
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106#6715—41no—
107#6714—21no—
108C4⋊Dic15C2311yescharacteristic
109C2×C3⋊#168—41no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#213—22no—
113C5×#213—41no—
114C2×C5×C3⋊C8C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5D411yescharacteristic
119C3×#685D411yescharacteristic
120C3×C4⋊Dic5—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C3×C4⋊Dic5C2311yescharacteristic
123C3×#683—21no—
124C3×#683—21no—
125C3×#683D411yescharacteristic
126C3×C4×Dic5C2311yescharacteristic
127(C2×D3)⋊Dic5—21no—
128(C2×D3)⋊Dic5—21no—
129D5×C3⋊C8—41no—
130C3×#547—51no—
131D4×D12—51no—
132#5088—51no—
133#5087—51no—
134#5038—51no—
135#5038—51no—
136#5036—51no—
137#5036D511yescharacteristic, complemented
138#5015—51no—
139C4×#213—51no—
140D4×C3⋊C8—51no—
141#4967—51no—
142#4967—51no—
143C2×#809—51no—
144C2×#809—51no—
145C22×C5×D4—31no—
146C22×C22⋊D5—61no—
147C2×#711—21no—
148C2×D4×D5—31no—
149C2×C5×D8—31no—
150C2×C5×D8—31no—
151C5×#121C2×D311yescharacteristic, complemented
152#4099—61no—
153#4086—31no—
154#4085—61no—
155#4084—31no—
156#4084C2×D311yescharacteristic, complemented
157#4083—61no—
158#4081—21no—
159D4×Dic5—31no—
160D4×Dic5C2×D311yescharacteristic, complemented
161C2×#686—31no—
162#4076—31no—
163C4×C22⋊D5C2×D311yescharacteristic
164C2×C4⋊Dic5C2×D311yescharacteristic, complemented
165C22×#168—31no—
166C2×C8×D5—31no—
167D5×C4⋊C4C2×D311yescharacteristic, complemented
168#4034C2×D311yescharacteristic, complemented
169#4029—21no—
170#4024—21no—
171C5×#102—31no—
172C5×#102—31no—
173C5×C22⋊C8—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3952—31no—
182#3950—31no—
183#3950—31no—
184#3946—31no—
185C8×Dic5—31no—
186#3941—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5C2×D411yescharacteristic
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—42no—
195C22×C5×D3—42no—
196C22×C5×D3—81no—
197C22×C3×D5C2×D411yescharacteristic
198C2×D3×D5—42no—
199C2×D3×D5—42no—
200C2×D3×D5—81no—
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—42no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2411yescharacteristic
209#1220—42no—
210C2×Dic15—21no—
211D60—21no—
212D60—21no—
213C5×D12—21no—
214C5×D12—21no—
215C5×D12—21no—
216C5×D12—42no—
217C5×D12#4112yescomplemented
218C3×C22⋊D5—42no—
219C3×C22⋊D5D814yescomplemented
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—42no—
223C2×C3×Dic5—42no—
224C2×C3×Dic5C2×D411yescharacteristic
225C2×C3×Dic5C2×D411yescharacteristic
226C2×C3×Dic5C2×D411yescharacteristic
227C3×C4×D5—21no—
228C3×C4×D5—21no—
229C3×C4×D5—42no—
230C3×Dic10—42no—
231#1203—42no—
232#1203—42no—
233#1203—81no—
234#1201—42no—
235D3×Dic5—42no—
236C3⋊#168—21no—
237C3⋊#168—21no—
238C5×C3⋊C8—21no—
239C5×C3⋊C8—21no—
240C2×C3×#41—101no—
241C2×D3×D4—101no—
242C22×D12—51no—
243C22×D12C2×D511yescharacteristic
244C3×C4⋊Q8—51no—
245C3×#123—101no—
246C3×#123—101no—
247C3×C22⋊Q8—101no—
248C3×#121—51no—
249C3×#121C2×D511yescharacteristic, complemented
250C3×C4×D4—51no—
251C3×C4×D4—51no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C4⋊C4—51no—
254C2×#213—51no—
255C2×#213C2×D511yescharacteristic
256C2×#213C2×D511yescharacteristic, complemented
257#930—51no—
258#930—51no—
259C22×C3⋊C8—51no—
260C22×C3⋊C8—51no—
261#895—101no—
262#882—101no—
263#882—101no—
264#874—51no—
265C4×D12—51no—
266#832—51no—
267#830—51no—
268#830C2×D511yescharacteristic, complemented
269#809—51no—
270#809—51no—
271#809—51no—
272#809—51no—
273#809—51no—
274#809—51no—
275#809—51no—
276#809C2×D511yescharacteristic
277#809C2×D511yescharacteristic, complemented
278#807—51no—
279#807—51no—
280#807—51no—
281C4⋊(C3⋊C8)—51no—
282C4×C3⋊C8—51no—
283C24×C5—61no—
284C23×D5—61no—
285C2×C5×D4—21no—
286C2×C5×D4—31no—
287C2×C5×D4—31no—
288C2×C5×D4—62no—
289C2×C5×D4—61no—
290C2×C5×D4—121no—
291C2×C5×D4C22×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C2×C22⋊D5—21no—
294C2×C22⋊D5—61no—
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C2×C22⋊D5—61no—
299C2×C22⋊D5—124no—
300C2×C22⋊D5#6711yescharacteristic
301C22×Dic5—21no—
302C22×Dic5—21no—
303C22×Dic5—61no—
304#711—44no—
305D4×D5—62no—
306D4×D5—121no—
307C2×D20—31no—
308C2×C4×D5—21no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—21no—
311C5×D8—62no—
312C5×D8—121no—
313C2×C5×C8—31no—
314C2×C5×C8—31no—
315C5×C4⋊C4C22×D311yescharacteristic
316C5×C22⋊C4—21no—
317C22⋊Dic5—21no—
318C22⋊Dic5—21no—
319C22⋊Dic5—61no—
320C22⋊Dic5—61no—
321C22⋊Dic5#6711yescharacteristic
322#686—121no—
323#685—61no—
324#685#6711yescharacteristic
325C4⋊Dic5—21no—
326C4⋊Dic5—31no—
327C4⋊Dic5C22×D311yescharacteristic
328C4⋊Dic5C22×D311yescharacteristic
329#683—21no—
330#683—21no—
331#683#6711yescharacteristic
332C4×Dic5C22×D311yescharacteristic
333C2×#168—31no—
334C2×#168—31no—
335C2×#168—121no—
336C8×D5—121no—
337#547—51no—
338D42—151no—
339#486—151no—
340#480—151no—
341#480—151no—
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—31no—
347#447—151no—
348C4×D8—151no—
349C8×D4—151no—
350C2×#102—151no—
351C2×#102—151no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—41no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5C2×D812yes—
358C22×C3×C5C22×D411yescharacteristic
359C2×D15—41no—
360C2×D15—41no—
361C2×D15—41no—
362C2×C5×D3—22no—
363C2×C5×D3—41no—
364C2×C5×D3—41no—
365C2×C5×D3—41no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C2×C5×D3—84no—
369C2×C3×D5—21no—
370C2×C3×D5—21no—
371C2×C3×D5C2×D812yes—
372D3×D5—84no—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5C2×#4111yescharacteristic
376C3×C4×C5H(5,𝔽2)11yescharacteristic
377Dic15—41no—
378C3×Dic5—21no—
379C3×Dic5—21no—
380C3×Dic5—41no—
381C3×Dic5—41no—
382C3×Dic5C2×D812yes—
383C23×D3—21no—
384C23×D3—101no—
385C3×#41—204no—
386C2×C3×Q8—101no—
387C2×C3×D4—21no—
388C2×C3×D4—51no—
389C2×C3×D4—101no—
390C2×C3×D4C22×D511yescharacteristic
391C22×C3×C4—51no—
392C22×C3×C4—101no—
393C22×C3×C4—101no—
394C22×C3×C4—101no—
395C22×C3×C4C22×D511yescharacteristic
396C2×#67—101no—
397C2×#67—101no—
398D3×D4—204no—
399C2×D12—22no—
400C2×D12—21no—
401C2×D12—41no—
402C2×D12—51no—
403C2×D12—102no—
404C2×D12—101no—
405C2×D12—101no—
406C2×D12—101no—
407C2×D12—201no—
408C2×D12C22×D511yescharacteristic
409C2×D12C22×D511yescharacteristic
410C2×C4×D3—101no—
411C3×C4⋊C4—51no—
412C3×C4⋊C4—51no—
413C3×C4⋊C4—51no—
414C3×C4⋊C4—101no—
415C3×C4⋊C4—101no—
416C3×C4⋊C4—101no—
417C3×C4⋊C4C22×D511yescharacteristic
418C3×C22⋊C4—21no—
419C3×C22⋊C4—51no—
420C3×C22⋊C4—51no—
421C3×C22⋊C4—101no—
422C3×C22⋊C4—101no—
423C3×C42—51no—
424#213—22no—
425#213—41no—
426#213—201no—
427(C2×D3)⋊C4—101no—
428(C2×D3)⋊C4—101no—
429(C2×D3)⋊C4—101no—
430C4⋊Dic3—51no—
431C2×C3⋊C8—51no—
432C2×C3⋊C8—51no—
433C2×C3⋊C8—201no—
434C2×C3⋊C8—201no—
435C2×C3⋊C8C22×D511yescharacteristic
436C2×C3⋊C8C22×D511yescharacteristic
437C23×C5—21no—
438C23×C5—61no—
439C23×C5—61no—
440C23×C5—122no—
441C23×C5—122no—
442C23×C5—241no—
443C23×C5C2×#6711yescharacteristic
444C22×D5—61no—
445C22×D5—122no—
446C22×D5—122no—
447C22×D5—241no—
448C22×D5C2×#6711yescharacteristic
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—32no—
452C5×D4—42no—
453C5×D4—61no—
454C5×D4—61no—
455C5×D4—61no—
456C5×D4—122no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5C2×#6711yescharacteristic
461C2×C4×C5C23×D311yescharacteristic
462C22⋊D5—42no—
463C22⋊D5—122no—
464C22⋊D5—122no—
465C22⋊D5—122no—
466C22⋊D5—122no—
467C22⋊D5—241no—
468C22⋊D5#21314yescomplemented
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—42no—
472C2×Dic5—42no—
473C2×Dic5—61no—
474C2×Dic5—122no—
475C2×Dic5C2×#6711yescharacteristic
476C2×Dic5C2×#6711yescharacteristic
477C2×Dic5C2×#6711yescharacteristic
478D20—61no—
479D20—61no—
480C4×D5—21no—
481C4×D5—21no—
482C4×D5—42no—
483Dic10—42no—
484C5×C8—61no—
485C5×C8—61no—
486#168—61no—
487#168—61no—
488C2×#41—101no—
489C22×D4—31no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—31no—
493C2×D8—31no—
494C2×D8—151no—
495C22×C8—151no—
496C22×C8—151no—
497C4⋊Q8—51no—
498#127—151no—
499#123—101no—
500#123—101no—
501C22⋊Q8—101no—
502#121—51no—
503#121—151no—
504#121—151no—
505#121—301no—
506#121D3×D511yescharacteristic, complemented
507#120—301no—
508#120—301no—
509C4×D4—51no—
510C4×D4—51no—
511C4×D4—151no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4—51no—
514#107—151no—
515#107—151no—
516#107—151no—
517C4⋊C8—151no—
518#102—31no—
519#102—31no—
520#102—151no—
521#102—151no—
522#102—151no—
523#102—151no—
524#102—151no—
525#102—151no—
526#102—151no—
527#102—151no—
528C22⋊C8—31no—
529C22⋊C8—151no—
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5—81no—
533C2×C3×C5#54611yescharacteristic
534C2×C3×C5C22×D811yescharacteristic
535C2×C3×C5#57711yescharacteristic
536D15—81no—
537C3×D5—22no—
538C5×D3—42no—
539C5×D3—81no—
540C23×C3—21no—
541C23×C3—51no—
542C23×C3D4×D511yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—81no—
548C22×D3—101no—
549C22×D3—202no—
550C22×D3—202no—
551C22×D3—401no—
552C3×Q8—202no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—42no—
556C3×D4—54no—
557C3×D4—202no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—51no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—202no—
569C2×C3×C4—202no—
570C2×C3×C4—202no—
571C2×C3×C4D4×D511yescharacteristic
572C2×C3×C4C23×D511yescharacteristic
573#67—202no—
574#67—202no—
575C2×Dic3—101no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—42no—
580D12—101no—
581D12—101no—
582D12—202no—
583D12—202no—
584D12—401no—
585D12#71112yescomplemented
586C4×D3—202no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—41no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5—62no—
597C22×C5—121no—
598C22×C5—121no—
599C22×C5—121no—
600C22×C5—121no—
601C22×C5—121no—
602C22×C5—244no—
603C22×C5C2×#21312yes—
604C22×C5C22×#6711yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—244no—
611C2×D5C2×#21312yes—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5D3×#4111yescharacteristic
615C4×C5#100911yescharacteristic
616Dic5—21no—
617Dic5—21no—
618Dic5—41no—
619Dic5—41no—
620Dic5—121no—
621Dic5C2×#21312yes—
622C24—61no—
623C24—301no—
624#41—204no—
625C2×Q8—101no—
626C2×D4—21no—
627C2×D4—31no—
628C2×D4—31no—
629C2×D4—51no—
630C2×D4—62no—
631C2×D4—61no—
632C2×D4—101no—
633C2×D4—121no—
634C2×D4—151no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—302no—
639C2×D4—301no—
640C2×D4—301no—
641C2×D4—601no—
642C2×D4—604no—
643C2×D4C2×D3×D511yescharacteristic
644C22×C4—51no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4—101no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—62no—
651D8—121no—
652D8—601no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—151no—
656C2×C8—151no—
657C2×C8—601no—
658C2×C8—601no—
659C4⋊C4—51no—
660C4⋊C4—51no—
661C4⋊C4—51no—
662C4⋊C4—101no—
663C4⋊C4—101no—
664C4⋊C4—101no—
665C4⋊C4—151no—
666C4⋊C4C2×D3×D511yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—51no—
669C22⋊C4—51no—
670C22⋊C4—101no—
671C22⋊C4—101no—
672C22⋊C4—301no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—51no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—52no—
683C22×C3—101no—
684C22×C3—101no—
685C22×C3D5×D812yes—
686C22×C3C2×D4×D511yescharacteristic
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—84no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—201no—
697C2×D3—404no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—52no—
701C3×C4—101no—
702C3×C4—101no—
703C3×C4—201no—
704C3×C4—201no—
705C3×C4C2×#71111yescharacteristic
706C3×C4#414411yescharacteristic
707Dic3—201no—
708C2×C5—22no—
709C2×C5—81no—
710C2×C5—122no—
711C2×C5—241no—
712C2×C5C22×#21311yescharacteristic
713C2×C5#582911yescharacteristic
714C2×C5#583711yescharacteristic
715D5—22no—
716D5—241no—
717C23—21no—
718C23—51no—
719C23—61no—
720C23—61no—
721C23—122no—
722C23—122no—
723C23—241no—
724C23—301no—
725C23—602no—
726C23—602no—
727C23—1201no—
728C23D5×#6711yescharacteristic
729Q8—202no—
730D4—21no—
731D4—21no—
732D4—32no—
733D4—42no—
734D4—54no—
735D4—61no—
736D4—61no—
737D4—61no—
738D4—122no—
739D4—202no—
740D4—301no—
741D4—301no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—602no—
746D4—1201no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—51no—
751C2×C4—51no—
752C2×C4—51no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—301no—
761C2×C4—602no—
762C2×C4D5×#6711yescharacteristic
763C2×C4C22×D3×D511yescharacteristic
764C8—61no—
765C8—61no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—81no—
770C2×C3—102no—
771C2×C3#6592511yescharacteristic
772C2×C3C2×D5×D811yescharacteristic
773C2×C3#6610911yescharacteristic
774D3—42no—
775D3—81no—
776D3—401no—
777C5#8352511yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—52no—
784C22—62no—
785C22—101no—
786C22—101no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—244no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22D5×#21312yes—
798C22C2×D5×#6711yescharacteristic
799C4—21no—
800C4—41no—
801C4—52no—
802C4—101no—
803C4—101no—
804C4—201no—
805C4—201no—
806C4—601no—
807C4D3×#71111yescharacteristic
808C4#9202711yescharacteristic
809C3#1061174511yescharacteristic, complemented, Sylow
810C2—22no—
811C2—81no—
812C2—102no—
813C2—122no—
814C2—241no—
815C2—1201no—
816C2C2×D5×#21311yescharacteristic
817C2#1175506311yescharacteristic
818C2#1175531711yescharacteristic
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#3294
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×#65945C2semidirect
2. D12×C22⋊D5C2semidirect
3. #11751139C2semidirect
4. C5×#5036C2semidirect
5. #11749151C2semidirect
6. #11749119C2semidirect
7. #11749092C2semidirect
8. Dic5×#213C2semidirect
9. #11748493C2semidirect
10. #11748474C2semidirect
11. C2×#90966C2semidirect
12. D5×#809C2semidirect
13. #11747306C2semidirect
14. #11747237C2semidirect
15. #11747138C2semidirect
21. C3×C5×#121C22semidirect
22. C2×#6715C22semidirect
24. C22×C3⋊#168C22semidirect
26. C2×C5×#213C22semidirect
27. C3×#4084C22semidirect
29. C3×D4×Dic5C22semidirect
31. C2×C3×C4⋊Dic5C22semidirect
32. C3×D5×C4⋊C4C22semidirect
33. C3×#4034C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91116C22semidirect
44. #91093C22semidirect
45. #91091C22semidirect
46. C5×#830C22semidirect
48. C5×#809C22semidirect
49. #90990C22semidirect
50. #90990C22semidirect
51. #90982C22semidirect
52. #90968C22semidirect
53. #90968C22semidirect
56. #90966C22semidirect
57. #90966C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
62. #65945D3semidirect
137. #5036D5semidirect
151. C5×#121C2×D3semidirect
156. #4084C2×D3semidirect
160. D4×Dic5C2×D3semidirect
164. C2×C4⋊Dic5C2×D3semidirect
167. D5×C4⋊C4C2×D3semidirect
168. #4034C2×D3semidirect
217. C5×D12#41semidirect
219. C3×C22⋊D5D8semidirect
249. C3×#121C2×D5semidirect
256. C2×#213C2×D5semidirect
268. #830C2×D5semidirect
277. #809C2×D5semidirect
468. C22⋊D5#213semidirect
506. #121D3×D5semidirect
585. D12#711semidirect
676. C3×C5#3294semidirect
777. C5#83525semidirect
809. C3#10611745semidirect

Maximal subgroups

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

subgroupindex
C3×#659452
D12×C22⋊D52
#117511392
C5×#50362
#117491512
#117491192
#117490922
Dic5×#2132
#117484932
#117484742
C2×#909662
D5×#8092
#117473062
#117472372
#117471382
#106117453
#835255