Finite Group Databasebeta

← #14458320

Subgroups — #14458320

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
1C5×#5507C211yesmaximal, characteristic, complemented
2#11754661C211yesmaximal, characteristic, complemented
3C2×#91093C211yesmaximal, characteristic, complemented
4C3×#65256C211yesmaximal, characteristic, complemented
5#11748525C211yesmaximal, characteristic, complemented
6#11748522C211yesmaximal, characteristic, complemented
7#67⋊#168C211yesmaximal, characteristic, complemented
8#11747482C211yesmaximal, characteristic, complemented
9D3×#3941C211yesmaximal, characteristic, complemented
10#11747446C211yesmaximal, characteristic, complemented
11#11747403C211yesmaximal, characteristic, complemented
12#11747402C211yesmaximal, characteristic, complemented
13#11747246C211yesmaximal, characteristic, complemented
14#11747230C211yesmaximal, characteristic, complemented
15#11747172C211yesmaximal, characteristic, complemented
16#10615256—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×C5×#235—21no—
19C2×#6790—21no—
20C2×D3×D20C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
22C22×C3⋊#168C2211yescharacteristic, complemented
23C5×#930C2211yescharacteristic, complemented
24C5×#929—21no—
25C4×C5×#67C2211yescharacteristic
26C5×#896—21no—
27C5×#895C2211yescharacteristic, complemented
28C5×#894—21no—
29C5×#893C2211yescharacteristic, complemented
30C5×D3×C4⋊C4C2211yescharacteristic, complemented
31C5×#888C2211yescharacteristic, complemented
32C3×#4076C2211yescharacteristic
33#91572—21no—
34#91476—21no—
35#91460C2211yescharacteristic
36#91459—21no—
37#91458C2211yescharacteristic
38#91428C2211yescharacteristic
39C2×#6654C2211yescharacteristic
40C2×#6654C2211yescharacteristic, complemented
41C2×#6652C2211yescharacteristic, complemented
42C2×D3×#168C2211yescharacteristic, complemented
43#91093C2211yescharacteristic
44#91093C2211yescharacteristic
45#91093C2211yescharacteristic, complemented
46#91093C2211yescharacteristic, complemented
47C3×C22⋊#168C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic, complemented
49C3×#3941C2211yescharacteristic, complemented
50C3×#3939C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52#90989C2211yescharacteristic, complemented
53Dic3⋊#168C2211yescharacteristic, complemented
54#90969C2211yescharacteristic
55#90969C2211yescharacteristic, complemented
56#90966C2211yescharacteristic, complemented
57#90964C2211yescharacteristic, complemented
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#81302—51nomaximal, Hall
61C5×#547—31no—
62D4×D20—31no—
63#65377—31no—
64#65376—31no—
65#65327—31no—
66#65327—31no—
67#65325—31no—
68#65325—31no—
69#65304—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65256—31no—
73#65256D311yescharacteristic, complemented
74C2×#3941—31no—
75C2×#3941—31no—
76C23×D15—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5C2311yescharacteristic
80C2×D60—22no—
81C2×D60—21no—
82C2×D60—41no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×C5×#67—21no—
86C2×C5×#67D411yescharacteristic
87C5×#235—44no—
88C2×C5×D12—21no—
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3C2311yescharacteristic
93C2×C5×Dic6—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×D20C2311yescharacteristic
96#6790—44no—
97C2×#1203—21no—
98C2×#1202—21no—
99C2×#1202—21no—
100C2×#1202—21no—
101C2×#1200—21no—
102D3×D20—22no—
103D3×D20—41no—
104C3×C5×C4⋊C4—21no—
105C3×C5×C4⋊C4C2311yescharacteristic
106C3×C5×C4⋊C4C2311yescharacteristic
107C2×C3⋊#168—41no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#217D411yescharacteristic
111C5×(C2×D3)⋊C4—21no—
112C5×(C2×D3)⋊C4—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4D411yescharacteristic
115C5×C4⋊Dic3C2311yescharacteristic
116C5×Dic3⋊C4—21no—
117C5×Dic3⋊C4—21no—
118C5×Dic3⋊C4D411yescharacteristic
119C4×C5×Dic3C2311yescharacteristic
120C3×#685—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124#6667—21no—
125#6667—21no—
126#6654—22no—
127#6654—41no—
128#6652—41no—
129D3×#168—41no—
130#5609—51no—
131#5507D511yescharacteristic, complemented
132C3×#480—51no—
133#5038—51no—
134C2×#809—51no—
135#4890—51no—
136#4883—51no—
137#4882—51no—
138#4872—51no—
139#4786—51no—
140#4773—51no—
141D3×#102—51no—
142#4760—51no—
143#4732—51no—
144#67⋊C8—51no—
145C2×C5×#41—61no—
146C2×D4×D5—61no—
147C22×D20—31no—
148C22×D20—31no—
149C5×C4⋊Q8—31no—
150C5×#123—61no—
151C5×#123—61no—
152C5×C22⋊Q8—61no—
153C5×#121—31no—
154C5×#121—31no—
155C4×C5×D4—31no—
156C4×C5×D4—31no—
157C2×C5×C4⋊C4—31no—
158C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
159C2×#686—31no—
160C2×#686—31no—
161C2×#686—31no—
162#4076—31no—
163#4076C2×D311yescharacteristic
164C22×#168—31no—
165C22×#168—31no—
166#4041—61no—
167#4028—61no—
168#4028—61no—
169#4020—31no—
170C4×D20—31no—
171#3964—31no—
172C22⋊#168—31no—
173C22⋊#168C2×D311yescharacteristic, complemented
174#3941—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941—31no—
181#3941C2×D311yescharacteristic, complemented
182#3941C2×D311yescharacteristic, complemented
183#3939—31no—
184#3939C2×D311yescharacteristic, complemented
185#3939C2×D311yescharacteristic, complemented
186C4⋊#168—31no—
187C4×#168—31no—
188#3294—151noSylow
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—42no—
193C22×D15—42no—
194C22×D15—81no—
195C22×C5×D3—21no—
196C22×C5×D3C2×D411yescharacteristic
197C22×C3×D5—21no—
198C2×D3×D5—42no—
199C2×D3×D5—42no—
200C2×D3×D5—81no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—42no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208D60—21no—
209D60—21no—
210D60—21no—
211D60—42no—
212D60#4112yescomplemented
213C5×#67—42no—
214C5×#67D814yescomplemented
215C2×C5×Dic3—21no—
216C2×C5×Dic3C2×D411yescharacteristic
217C2×C5×Dic3C2×D411yescharacteristic
218C2×C5×Dic3C2×D411yescharacteristic
219C5×D12—21no—
220C5×D12—21no—
221C5×D12—42no—
222C4×C5×D3—21no—
223C4×C5×D3—21no—
224C4×C5×D3—42no—
225C4×C5×D3—42no—
226C5×Dic6—42no—
227C3×C22⋊D5—42no—
228C2×C3×Dic5—21no—
229C3×D20—21no—
230C3×D20—21no—
231#1203—42no—
232#1202—42no—
233#1202—42no—
234#1202—81no—
235#1200—42no—
236C3⋊#168—21no—
237C3⋊#168—21no—
238C3×#168—21no—
239C3×#168—21no—
240C2×D3×D4—51no—
241C2×D3×D4—101no—
242C2×#235—21no—
243C22×D12—51no—
244C3×#121—51no—
245C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
246#940—51no—
247#937—101no—
248C2×#213—51no—
249#930C2×D511yescharacteristic, complemented
250#929—21no—
251C4×#67C2×D511yescharacteristic
252C22×C3⋊C8—51no—
253C2×D24—51no—
254C2×D24—51no—
255C2×D3×C8—51no—
256#896—21no—
257#895—51no—
258#895C2×D511yescharacteristic, complemented
259#894—21no—
260#893—51no—
261#893C2×D511yescharacteristic, complemented
262D3×C4⋊C4C2×D511yescharacteristic, complemented
263#888C2×D511yescharacteristic, complemented
264#884—101no—
265#882—101no—
266C3×#107—51no—
267C3×#107—51no—
268C3×#102—51no—
269C3×#102—51no—
270C3×C22⋊C8—51no—
271#832—51no—
272#821—51no—
273#821—51no—
274(C2×D3)⋊C8—51no—
275Dic3⋊C8—51no—
276C8×Dic3—51no—
277#809—51no—
278#809—51no—
279#809—51no—
280#809—51no—
281#809—51no—
282#807—51no—
283C23×D5—61no—
284C23×D5—61no—
285C5×#41—124no—
286C2×C5×Q8—61no—
287C2×C5×D4—31no—
288C2×C5×D4—31no—
289C2×C5×D4—61no—
290C2×C5×D4—61no—
291C22×C4×C5—21no—
292C22×C4×C5—31no—
293C22×C4×C5—61no—
294C22×C4×C5—61no—
295C22×C4×C5C22×D311yescharacteristic
296C2×C22⋊D5—21no—
297C2×C22⋊D5—61no—
298D4×D5—124no—
299C2×D20—31no—
300C2×D20—31no—
301C2×D20—62no—
302C2×D20—62no—
303C2×D20—61no—
304C2×D20—61no—
305C2×D20—61no—
306C2×D20—61no—
307C2×D20—121no—
308C2×D20—121no—
309C2×D20C22×D311yescharacteristic
310C2×C4×D5—61no—
311C5×C4⋊C4—21no—
312C5×C4⋊C4—31no—
313C5×C4⋊C4—31no—
314C5×C4⋊C4—61no—
315C5×C4⋊C4—61no—
316C5×C4⋊C4C22×D311yescharacteristic
317C5×C4⋊C4C22×D311yescharacteristic
318C5×C22⋊C4—31no—
319C5×C22⋊C4—31no—
320C5×C22⋊C4—61no—
321C5×C22⋊C4—61no—
322C5×C22⋊C4—61no—
323C42×C5—31no—
324#686—62no—
325#686—121no—
326#686—121no—
327#685—21no—
328#685—61no—
329#685—61no—
330C4⋊Dic5C22×D311yescharacteristic
331C2×#168—31no—
332C2×#168—31no—
333C2×#168—121no—
334C2×#168—121no—
335C2×#168C22×D311yescharacteristic
336C2×#168C22×D311yescharacteristic
337#547—31no—
338D42—151no—
339#486—151no—
340#480—51no—
341#480—151no—
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—151no—
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×C5C2×D812yes—
355C22×C3×C5C22×D411yescharacteristic
356C2×D15—22no—
357C2×D15—41no—
358C2×D15—41no—
359C2×D15—41no—
360C2×D15—41no—
361C2×D15—41no—
362C2×D15—84no—
363C2×C5×D3—21no—
364C2×C5×D3—21no—
365C2×C5×D3—41no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C2×C5×D3C2×D812yes—
369C2×C3×D5—41no—
370C2×C3×D5—41no—
371C2×C3×D5—41no—
372D3×D5—84no—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5—41no—
376C3×C4×C5C2×#4111yescharacteristic
377C3×C4×C5H(5,𝔽2)11yescharacteristic
378C3×Dic5—41no—
379C5×Dic3—21no—
380C5×Dic3—21no—
381C5×Dic3—41no—
382C5×Dic3C2×D812yes—
383C23×D3—101no—
384C23×D3—101no—
385C2×C3×D4—51no—
386C2×C3×D4—101no—
387C22×C3×C4—21no—
388C22×C3×C4C22×D511yescharacteristic
389C2×#67—21no—
390C2×#67—101no—
391C2×#67—101no—
392C2×#67—101no—
393C2×#67C22⋊D511yescharacteristic
394D3×D4—102no—
395D3×D4—201no—
396D3×D4—204no—
397#235—44no—
398C2×D12—21no—
399C2×D12—51no—
400C2×D12—51no—
401C2×D12—102no—
402C2×D12—101no—
403C2×D12—101no—
404C2×D12—201no—
405C2×D12C22×D511yescharacteristic
406C2×C4×D3—21no—
407C2×C4×D3—21no—
408C2×C4×D3—101no—
409C2×C4×D3C22×D511yescharacteristic
410C2×Dic6—21no—
411C2×C3×C8—51no—
412C2×C3×C8—51no—
413C3×C4⋊C4—21no—
414C3×C4⋊C4—51no—
415C3×C4⋊C4C22×D511yescharacteristic
416C3×C4⋊C4C22×D511yescharacteristic
417C3×C22⋊C4—101no—
418#217C22⋊D511yescharacteristic
419#213—201no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425(C2×D3)⋊C4C22⋊D511yescharacteristic
426C4⋊Dic3C22×D511yescharacteristic
427Dic3⋊C4—21no—
428Dic3⋊C4—21no—
429Dic3⋊C4C22⋊D511yescharacteristic
430C4×Dic3C22×D511yescharacteristic
431C2×C3⋊C8—51no—
432C2×C3⋊C8—51no—
433C2×C3⋊C8—201no—
434D24—102no—
435D24—201no—
436D3×C8—201no—
437C23×C5—31no—
438C23×C5—61no—
439C23×C5D3×D411yescharacteristic
440C22×D5—21no—
441C22×D5—61no—
442C22×D5—61no—
443C22×D5—122no—
444C22×D5—122no—
445C22×D5—122no—
446C22×D5—122no—
447C22×D5—241no—
448C22×D5—241no—
449C5×Q8—122no—
450C5×D4—34no—
451C5×D4—61no—
452C5×D4—61no—
453C5×D4—122no—
454C5×D4—122no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—31no—
460C2×C4×C5—31no—
461C2×C4×C5—31no—
462C2×C4×C5—42no—
463C2×C4×C5—61no—
464C2×C4×C5—61no—
465C2×C4×C5—61no—
466C2×C4×C5—122no—
467C2×C4×C5—122no—
468C2×C4×C5D3×D411yescharacteristic
469C2×C4×C5C23×D311yescharacteristic
470C22⋊D5—42no—
471C22⋊D5—122no—
472C2×Dic5—21no—
473D20—21no—
474D20—21no—
475D20—32no—
476D20—61no—
477D20—61no—
478D20—61no—
479D20—122no—
480D20—122no—
481D20—122no—
482D20—241no—
483C4×D5—122no—
484#168—21no—
485#168—21no—
486#168—61no—
487#168—61no—
488C2×#41—61no—
489C22×D4—151no—
490C22×D4—151no—
491C22×D4—301no—
492C2×D8—151no—
493C2×D8—151no—
494C2×D8—151no—
495C22×C8—151no—
496C22×C8—151no—
497C4⋊Q8—31no—
498#127—151no—
499#123—61no—
500#123—61no—
501C22⋊Q8—61no—
502#121—31no—
503#121—31no—
504#121—51no—
505#121—151no—
506#121—301no—
507#120—301no—
508#120—301no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—151no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4D3×D511yescharacteristic, complemented
514#107—51no—
515#107—51no—
516#107—151no—
517C4⋊C8—151no—
518#102—51no—
519#102—51no—
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—51no—
529C22⋊C8—151no—
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5#54611yescharacteristic
533C2×C3×C5C22×D811yescharacteristic
534C2×C3×C5#57711yescharacteristic
535D15—42no—
536D15—81no—
537C3×D5—81no—
538C5×D3—22no—
539C5×D3—81no—
540C23×C3—101no—
541C23×C3C2×C22⋊D511yescharacteristic
542C22×D3—21no—
543C22×D3—101no—
544C22×D3—101no—
545C22×D3—202no—
546C22×D3—202no—
547C22×D3—202no—
548C22×D3—202no—
549C22×D3—401no—
550C22×D3—401no—
551C22×D3C2×C22⋊D511yescharacteristic
552C3×D4—101no—
553C3×D4—101no—
554C3×D4—202no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—42no—
560C2×C3×C4—101no—
561C2×C3×C4C2×C22⋊D511yescharacteristic
562C2×C3×C4C23×D511yescharacteristic
563#67—42no—
564#67—202no—
565#67—202no—
566#67—401no—
567#67#68614yescomplemented
568C2×Dic3—21no—
569C2×Dic3C2×C22⋊D511yescharacteristic
570C2×Dic3C2×C22⋊D511yescharacteristic
571C2×Dic3C2×C22⋊D511yescharacteristic
572D12—21no—
573D12—21no—
574D12—42no—
575D12—52no—
576D12—101no—
577D12—101no—
578D12—101no—
579D12—202no—
580D12—202no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—42no—
584C4×D3—42no—
585C4×D3—202no—
586Dic6—42no—
587C3×C8—101no—
588C3×C8—101no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—32no—
594C22×C5—61no—
595C22×C5—61no—
596C22×C5—121no—
597C22×C5—121no—
598C22×C5—121no—
599C22×C5D3×D812yes—
600C22×C5C2×D3×D411yescharacteristic
601C2×D5—41no—
602C2×D5—41no—
603C2×D5—41no—
604C2×D5—62no—
605C2×D5—121no—
606C2×D5—121no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—244no—
611C2×D5—244no—
612C4×C5—21no—
613C4×C5—32no—
614C4×C5—41no—
615C4×C5—41no—
616C4×C5—61no—
617C4×C5—61no—
618C4×C5—121no—
619C4×C5D3×#4111yescharacteristic
620C4×C5#100911yescharacteristic
621Dic5—41no—
622C24—301no—
623C24—301no—
624#41—124no—
625C2×Q8—61no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—51no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—101no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—302no—
635C2×D4—301no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—302no—
639C2×D4—301no—
640C2×D4—301no—
641C2×D4—601no—
642C2×D4—601no—
643C2×D4—604no—
644C22×C4—21no—
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—301no—
649C22×C4C2×D3×D511yescharacteristic
650D8—302no—
651D8—601no—
652D8—601no—
653C2×C8—51no—
654C2×C8—51no—
655C2×C8—151no—
656C2×C8—151no—
657C2×C8—601no—
658C2×C8—601no—
659C4⋊C4—21no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—51no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4C2×D3×D511yescharacteristic
666C4⋊C4C2×D3×D511yescharacteristic
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—101no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—31no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—201no—
680C22×C3—201no—
681C22×C3—201no—
682C22×C3C2×#68612yes—
683C22×C3C22×C22⋊D511yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—102no—
690C2×D3—201no—
691C2×D3—201no—
692C2×D3—201no—
693C2×D3—201no—
694C2×D3—201no—
695C2×D3—404no—
696C2×D3—404no—
697C2×D3C2×#68612yes—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—201no—
702C3×C4D5×#4111yescharacteristic
703C3×C4#414911yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3C2×#68612yes—
708C2×C5—22no—
709C2×C5—62no—
710C2×C5—241no—
711C2×C5#565411yescharacteristic
712C2×C5C2×D3×D811yescharacteristic
713C2×C5#577811yescharacteristic
714D5—81no—
715D5—122no—
716D5—241no—
717C23—31no—
718C23—61no—
719C23—101no—
720C23—301no—
721C23—301no—
722C23—602no—
723C23—602no—
724C23—602no—
725C23—602no—
726C23—1201no—
727C23—1201no—
728C23D3×C22⋊D511yescharacteristic
729Q8—122no—
730D4—34no—
731D4—61no—
732D4—61no—
733D4—101no—
734D4—101no—
735D4—122no—
736D4—122no—
737D4—152no—
738D4—202no—
739D4—301no—
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—21no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—42no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—101no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—602no—
762C2×C4D3×C22⋊D511yescharacteristic
763C2×C4C22×D3×D511yescharacteristic
764C8—101no—
765C8—101no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—401no—
770C2×C3C22×#68611yescharacteristic
771C2×C3#6616311yescharacteristic
772C2×C3#6617111yescharacteristic
773D3—22no—
774D3—81no—
775D3—202no—
776D3—401no—
777C5#8130211yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—32no—
781C22—61no—
782C22—61no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—201no—
787C22—201no—
788C22—201no—
789C22—302no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—1204no—
796C22—1204no—
797C22D3×#68612yes—
798C22C2×D3×C22⋊D511yescharacteristic
799C4—21no—
800C4—32no—
801C4—41no—
802C4—41no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—201no—
807C4#9201611yescharacteristic
808C4#9201911yescharacteristic
809C3#1061525611yescharacteristic, complemented, Sylow
810C2—22no—
811C2—62no—
812C2—241no—
813C2—401no—
814C2—602no—
815C2—1201no—
816C2#1175465611yescharacteristic
817C2C2×D3×#68611yescharacteristic
818C2#1175509211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5507C2semidirect
2. #11754661C2semidirect
3. C2×#91093C2semidirect
4. C3×#65256C2semidirect
5. #11748525C2semidirect
6. #11748522C2semidirect
7. #67⋊#168C2semidirect
8. #11747482C2semidirect
9. D3×#3941C2semidirect
10. #11747446C2semidirect
11. #11747403C2semidirect
12. #11747402C2semidirect
13. #11747246C2semidirect
14. #11747230C2semidirect
15. #11747172C2semidirect
21. C2×C3×C5×C4⋊C4C22semidirect
22. C22×C3⋊#168C22semidirect
23. C5×#930C22semidirect
27. C5×#895C22semidirect
29. C5×#893C22semidirect
30. C5×D3×C4⋊C4C22semidirect
31. C5×#888C22semidirect
40. C2×#6654C22semidirect
41. C2×#6652C22semidirect
42. C2×D3×#168C22semidirect
45. #91093C22semidirect
46. #91093C22semidirect
47. C3×C22⋊#168C22semidirect
48. C3×#3941C22semidirect
49. C3×#3941C22semidirect
50. C3×#3939C22semidirect
51. C3×#3939C22semidirect
52. #90989C22semidirect
53. Dic3⋊#168C22semidirect
55. #90969C22semidirect
56. #90966C22semidirect
57. #90964C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
73. #65256D3semidirect
131. #5507D5semidirect
158. C2×C5×C4⋊C4C2×D3semidirect
173. C22⋊#168C2×D3semidirect
181. #3941C2×D3semidirect
182. #3941C2×D3semidirect
184. #3939C2×D3semidirect
185. #3939C2×D3semidirect
212. D60#41semidirect
214. C5×#67D8semidirect
245. C2×C3×C4⋊C4C2×D5semidirect
249. #930C2×D5semidirect
258. #895C2×D5semidirect
261. #893C2×D5semidirect
262. D3×C4⋊C4C2×D5semidirect
263. #888C2×D5semidirect
513. C2×C4⋊C4D3×D5semidirect
567. #67#686semidirect
676. C3×C5#3294semidirect
777. C5#81302semidirect
809. C3#10615256semidirect

Maximal subgroups

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

subgroupindex
C5×#55072
#117546612
C2×#910932
C3×#652562
#117485252
#117485222
#67⋊#1682
#117474822
D3×#39412
#117474462
#117474032
#117474022
#117472462
#117472302
#117471722
#106152563
#813025