Finite Group Databasebeta

← #14424239

Subgroups — #14424239

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1004C211yesmaximal, characteristic, complemented
2C2×#91480C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4#11754655C211yesmaximal, characteristic, complemented
5#11751318C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7#11749036C211yesmaximal, characteristic, complemented
8#11749035C211yesmaximal, characteristic, complemented
9#11749033C211yesmaximal, characteristic, complemented
10#11749032C211yesmaximal, characteristic, complemented
11#11748967C211yesmaximal, characteristic, complemented
12#11748965C211yesmaximal, characteristic, complemented
13#11748521C211yesmaximal, characteristic, complemented
14#11748517C211yesmaximal, characteristic, complemented
15#11748490C211yesmaximal, characteristic, complemented
16#10615832—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic, complemented
18C22×C5×#67—21no—
19C22×C5×#67—21no—
20C5×#1004—24no—
21C5×#1004—24no—
22C2×C5×#237—21no—
23C2×C5×#237C2211yescharacteristic
24C2×C5×#237C2211yescharacteristic, complemented
25C2×C5×D3×D4—21no—
26C2×C5×D3×D4C2211yescharacteristic
27C2×C5×D3×D4C2211yescharacteristic, complemented
28C2×C5×#235C2211yescharacteristic
29C2×C5×#235C2211yescharacteristic, complemented
30C2×D3×D20C2211yescharacteristic, complemented
31C2×#6715C2211yescharacteristic, complemented
32C2×#6715C2211yescharacteristic, complemented
33#91819C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic, complemented
35C2×C3×#686C2211yescharacteristic, complemented
36C3×#4076C2211yescharacteristic, complemented
37#91577—21no—
38#91567—21no—
39#91480—24no—
40D3×#686—24no—
41#91475—21no—
42#91460C2211yescharacteristic, complemented
43#91456C2211yescharacteristic, complemented
44#91455—21no—
45#91338C2211yescharacteristic, complemented
46C2×#6660C2211yescharacteristic, complemented
47C2×#6655C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C2×D3×#168C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55C3×#3964C2211yescharacteristic, complemented
56C3×#3964C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60#90967C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62(C2×D3)⋊#168C2211yescharacteristic, complemented
63(C2×D3)⋊#168C2211yescharacteristic, complemented
64#80004—51nomaximal, Hall
65C2×C5×H(5,𝔽2)—31no—
66#66164—31no—
67C2×#4095—31no—
68C22×#686—31no—
69#65527—31no—
70#65527—31no—
71#65527—31no—
72#65527—31no—
73#65523—31no—
74#65522—31no—
75#65506—31no—
76#65506—31no—
77#65506—31no—
78#65506D311yescharacteristic, complemented
79#65504—31no—
80C24×C3×C5—21no—
81C23×C5×D3—21no—
82C23×C5×D3—21no—
83C22×D3×D5—21no—
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—22no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—21no—
91C2×D60C2311yescharacteristic
92C2×C5×#67—28no—
93C2×C5×#67—28no—
94C2×C5×#67—21no—
95C2×C5×#67—21no—
96C2×C5×#67—21no—
97C2×C5×#67—21no—
98C2×C5×#67—21no—
99C2×C5×#67D411yescharacteristic
100C2×C5×#67D411yescharacteristic
101C22×C5×Dic3—21no—
102C22×C5×Dic3—21no—
103C5×#237—28no—
104C5×#237—22no—
105C5×#237—22no—
106C5×#237—22no—
107C5×#237D414yescomplemented
108C5×D3×D4—28no—
109C5×D3×D4—22no—
110C5×D3×D4—22no—
111C5×D3×D4—22no—
112C5×D3×D4D414yescomplemented
113C5×#235—22no—
114C5×#235—22no—
115C5×#235—22no—
116C5×#235—22no—
117C2×C5×D12D411yescharacteristic
118C2×C5×D12C2311yescharacteristic
119C2×C4×C5×D3—21no—
120C2×C4×C5×D3C2311yescharacteristic
121C2×C4×C5×D3C2311yescharacteristic
122C2×C5×Dic6D411yescharacteristic
123C2×C5×Dic6C2311yescharacteristic
124C2×C3×C22⋊D5—21no—
125C2×C3×D20C2311yescharacteristic
126C2×#1203—21no—
127C2×#1202—21no—
128C2×#1201—21no—
129D3×D20—22no—
130D3×D20—22no—
131#6715—22no—
132#6715—22no—
133#6714—21no—
134C4⋊Dic15C2311yescharacteristic
135C2×C3⋊#168C2311yescharacteristic
136C2×C3⋊#168C2311yescharacteristic
137C3×#686—22no—
138C3×#686—22no—
139C3×#685—21no—
140C3×C4⋊Dic5C2311yescharacteristic
141C2×C3×#168C2311yescharacteristic
142C2×C3×#168C2311yescharacteristic
143#6667—21no—
144(C2×D3)⋊Dic5—21no—
145#6665—21no—
146Dic3×Dic5—21no—
147#6660—22no—
148#6655—22no—
149#6654—22no—
150#6652—22no—
151#6650—22no—
152D3×#168—22no—
153C2×#1004D511yescharacteristic, complemented
154C2×#911—51no—
155C2×D3×D8—51no—
156#5607—51no—
157C3×#447—51no—
158#5217—51no—
159#5158—51no—
160#5156—51no—
161#5037—51no—
162#4781—51no—
163#4773—51no—
164#4772—51no—
165#4770—51no—
166#4734—51no—
167#4727—51no—
168C5×H(5,𝔽2)—64no—
169C5×H(5,𝔽2)—64no—
170C2×C5×#41—31no—
171C2×C5×#41—31no—
172C2×C5×#41—31no—
173C2×C5×#41—31no—
174C2×C5×#41—61no—
175C22×C5×D4—31no—
176C22×C5×D4—31no—
177C22×C5×D4—61no—
178C22×C5×D4—61no—
179C22×C5×D4—61no—
180C22×C5×D4C2×D311yescharacteristic, complemented
181C22×D20—31no—
182#4095—64no—
183#4093—61no—
184C2×#688—31no—
185C2×#688—31no—
186#4086—61no—
187#4083—61no—
188#4083—61no—
189C2×#686—31no—
190C2×#686—31no—
191C2×#686—31no—
192C2×#686—31no—
193C2×#686—64no—
194C2×#686C2×D311yescharacteristic, complemented
195C2×#686C2×D311yescharacteristic, complemented
196#4076—31no—
197#4076—31no—
198#4076—31no—
199#4076C2×D311yescharacteristic, complemented
200#4072—31no—
201C2×#681—31no—
202C22×#168—31no—
203#3967—31no—
204#3967—31no—
205#3964—31no—
206#3964—31no—
207#3964—31no—
208#3964—31no—
209#3964C2×D311yescharacteristic, complemented
210#3964C2×D311yescharacteristic, complemented
211C22⋊#168—31no—
212C22⋊#168—31no—
213C22⋊#168—31no—
214C22⋊#168C2×D311yescharacteristic, complemented
215#3008—151noSylow
216C23×C3×C5—24no—
217C23×C3×C5—21no—
218C23×C3×C5—21no—
219C23×C3×C5—81no—
220C23×C3×C5—81no—
221C23×C3×C5C2×D411yescharacteristic
222C22×D15—21no—
223C22×C5×D3—21no—
224C22×C5×D3—24no—
225C22×C5×D3—24no—
226C22×C5×D3—81no—
227C22×C5×D3—81no—
228C22×C5×D3—81no—
229C22×C5×D3—81no—
230C22×C5×D3C2×D411yescharacteristic
231C22×C5×D3C2×D411yescharacteristic
232C22×C3×D5—21no—
233C2×D3×D5—42no—
234C2×D3×D5—81no—
235C2×D3×D5—81no—
236C3×C5×D4—24no—
237C3×C5×D4—21no—
238C3×C5×D4—21no—
239C3×C5×D4C2×D412yes—
240C3×C5×D4C2×D412yes—
241C2×C3×C4×C5—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5C2×D411yescharacteristic
244C2×C3×C4×C5C2411yescharacteristic
245#1220—81no—
246C2×Dic15—21no—
247D60—21no—
248D60—21no—
249C5×#67—24no—
250C5×#67—24no—
251C5×#67—24no—
252C5×#67—22no—
253C5×#67—24no—
254C5×#67—22no—
255C5×#67—24no—
256C2×C5×Dic3—24no—
257C2×C5×Dic3—21no—
258C2×C5×Dic3—24no—
259C2×C5×Dic3C2×D411yescharacteristic
260C2×C5×Dic3C2×D411yescharacteristic
261C5×D12—22no—
262C5×D12—21no—
263C5×D12C2×D412yes—
264C4×C5×D3—24no—
265C4×C5×D3—21no—
266C4×C5×D3—21no—
267C4×C5×D3C2×D412yes—
268C4×C5×D3C2×D412yes—
269C5×Dic6—21no—
270C5×Dic6—22no—
271C5×Dic6C2×D412yes—
272C3×C22⋊D5—81no—
273C2×C3×Dic5—21no—
274C3×D20—21no—
275C3×D20—21no—
276#1203—81no—
277#1202—42no—
278#1201—81no—
279C3⋊#168—21no—
280C3⋊#168—21no—
281C3×#168—21no—
282C3×#168—21no—
283C22×C3×D4C2×D511yescharacteristic, complemented
284C22×#67—21no—
285C22×#67—21no—
286#1004—24no—
287#1004—24no—
288C2×#237—21no—
289C2×#237C2×D511yescharacteristic
290C2×#237C2×D511yescharacteristic, complemented
291C2×D3×D4—21no—
292C2×D3×D4—51no—
293C2×D3×D4C2×D511yescharacteristic
294C2×D3×D4C2×D511yescharacteristic, complemented
295C2×#235C2×D511yescharacteristic
296C2×#235C2×D511yescharacteristic, complemented
297C2×C3×D8—51no—
298C2×C3×D8—51no—
299C3×#121—51no—
300#940—101no—
301#938—51no—
302#937—101no—
303C2×#214—51no—
304C2×#213—51no—
305C2×#213—51no—
306C2×#213—51no—
307#930—51no—
308#911—104no—
309D3×D8—104no—
310C2×D24—51no—
311C2×#204—51no—
312C2×ΓL(1,𝔽25)—51no—
313C2×D3×C8—51no—
314#895—51no—
315#892—51no—
316#885—101no—
317#882—101no—
318C3×#102—51no—
319C3×#102—51no—
320C3×C22⋊C8—51no—
321#832—51no—
322#832—51no—
323#830—51no—
324#821—51no—
325(C2×D3)⋊C8—51no—
326(C2×D3)⋊C8—51no—
327#816—51no—
328#810—51no—
329#809—51no—
330C24×C5—21no—
331C24×C5—61no—
332C24×C5—61no—
333C23×D5—61no—
334C5×#41—34no—
335C5×#41—62no—
336C5×#41—62no—
337C5×#41—62no—
338C5×#41—62no—
339C5×#41—62no—
340C5×#41—62no—
341C5×#41—68no—
342C5×#41—62no—
343C2×C5×Q8—31no—
344C2×C5×Q8—31no—
345C2×C5×D4—22no—
346C2×C5×D4—22no—
347C2×C5×D4—21no—
348C2×C5×D4—34no—
349C2×C5×D4—31no—
350C2×C5×D4—31no—
351C2×C5×D4—31no—
352C2×C5×D4—31no—
353C2×C5×D4—62no—
354C2×C5×D4—61no—
355C2×C5×D4—61no—
356C2×C5×D4—62no—
357C2×C5×D4—68no—
358C2×C5×D4—61no—
359C2×C5×D4—61no—
360C2×C5×D4—68no—
361C2×C5×D4—68no—
362C2×C5×D4—61no—
363C2×C5×D4—62no—
364C2×C5×D4C22×D311yescharacteristic
365C2×C5×D4C22×D311yescharacteristic
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—61no—
369C22×C4×C5—61no—
370C22×C4×C5—61no—
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—21no—
373C2×C22⋊D5—61no—
374C2×C22⋊D5—61no—
375C2×C22⋊D5—61no—
376C2×D20—31no—
377C2×D20—62no—
378C2×D20—62no—
379C2×D20—61no—
380C2×D20C22×D311yescharacteristic
381C22⋊Dic5—61no—
382#688—62no—
383#688—62no—
384#686—22no—
385#686—22no—
386#686—62no—
387#686—62no—
388#686—62no—
389#686—62no—
390#685—21no—
391#685—61no—
392#685—61no—
393#685—61no—
394C4⋊Dic5—31no—
395C4⋊Dic5C22×D311yescharacteristic
396C4×Dic5—61no—
397#681—62no—
398C2×#168—31no—
399C2×#168—31no—
400C2×#168—62no—
401C2×#168C22×D311yescharacteristic
402C2×#168C22×D311yescharacteristic
403C2×H(5,𝔽2)—31no—
404C2×AGL(1,ℤ/8)—151no—
405C22×D8—151no—
406#535—151no—
407#449—151no—
408#449—151no—
409#449—151no—
410#449—151no—
411#447—51no—
412#447—151no—
413#447—151no—
414#447—151no—
415#418—151no—
416#416—151no—
417#408—151no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—21no—
421C22×C3×C5—21no—
422C22×C3×C5—21no—
423C22×C3×C5—41no—
424C22×C3×C5—41no—
425C22×C3×C5—41no—
426C22×C3×C5—41no—
427C22×C3×C5—84no—
428C22×C3×C5C22×D411yescharacteristic
429C2×D15—41no—
430C2×D15—41no—
431C2×D15—41no—
432C2×C5×D3—21no—
433C2×C5×D3—21no—
434C2×C5×D3—21no—
435C2×C5×D3—22no—
436C2×C5×D3—21no—
437C2×C5×D3—21no—
438C2×C5×D3—41no—
439C2×C5×D3—41no—
440C2×C5×D3—84no—
441C2×C5×D3—84no—
442C2×C5×D3#12012yes—
443C2×C3×D5—41no—
444C2×C3×D5—41no—
445C2×C3×D5—41no—
446D3×D5—84no—
447C3×C4×C5—21no—
448C3×C4×C5C22×D411yescharacteristic
449C3×C4×C5C22×D411yescharacteristic
450Dic15—41no—
451C3×Dic5—41no—
452C5×Dic3—21no—
453C5×Dic3—22no—
454C5×Dic3#12012yes—
455C24×C3—21no—
456C23×D3—21no—
457C23×D3—21no—
458C23×D3—101no—
459C2×C3×D4—22no—
460C2×C3×D4—22no—
461C2×C3×D4—21no—
462C2×C3×D4—51no—
463C2×C3×D4—101no—
464C2×C3×D4C22×D511yescharacteristic
465C2×C3×D4C22×D511yescharacteristic
466C22×C3×C4C22×D511yescharacteristic
467C2×#67—28no—
468C2×#67—28no—
469C2×#67—21no—
470C2×#67—21no—
471C2×#67—21no—
472C2×#67—21no—
473C2×#67—21no—
474C2×#67—101no—
475C2×#67—101no—
476C2×#67—101no—
477C2×#67C22⋊D511yescharacteristic
478C2×#67C22⋊D511yescharacteristic
479C22×Dic3—21no—
480C22×Dic3—21no—
481#237—28no—
482#237—22no—
483#237—22no—
484#237—22no—
485#237C22⋊D514yescomplemented
486D3×D4—28no—
487D3×D4—22no—
488D3×D4—22no—
489D3×D4—22no—
490D3×D4—102no—
491D3×D4—102no—
492D3×D4C22⋊D514yescomplemented
493#235—22no—
494#235—22no—
495#235—22no—
496#235—22no—
497C2×D12—51no—
498C2×D12—101no—
499C2×D12C22⋊D511yescharacteristic
500C2×D12C22×D511yescharacteristic
501C2×C4×D3—21no—
502C2×C4×D3C22×D511yescharacteristic
503C2×C4×D3C22×D511yescharacteristic
504C2×Dic6C22⋊D511yescharacteristic
505C2×Dic6C22×D511yescharacteristic
506C3×D8—102no—
507C3×D8—102no—
508C2×C3×C8—51no—
509C2×C3×C8—51no—
510C3×C4⋊C4—51no—
511C3×C22⋊C4—101no—
512#217—101no—
513#214—102no—
514#213—102no—
515#213—102no—
516#213—102no—
517(C2×D3)⋊C4—101no—
518(C2×D3)⋊C4—101no—
519(C2×D3)⋊C4—101no—
520C4⋊Dic3—51no—
521C4×Dic3—101no—
522C2×C3⋊C8—51no—
523C2×C3⋊C8—51no—
524D24—102no—
525#204—102no—
526ΓL(1,𝔽25)—102no—
527D3×C8—102no—
528C23×C5—24no—
529C23×C5—21no—
530C23×C5—21no—
531C23×C5—31no—
532C23×C5—31no—
533C23×C5—64no—
534C23×C5—64no—
535C23×C5—61no—
536C23×C5—81no—
537C23×C5—81no—
538C23×C5—241no—
539C23×C5—241no—
540C23×C5—241no—
541C23×C5—241no—
542C23×C5D3×D411yescharacteristic
543C22×D5—21no—
544C22×D5—61no—
545C22×D5—122no—
546C22×D5—241no—
547C22×D5—241no—
548C5×Q8—32no—
549C5×Q8—62no—
550C5×Q8—61no—
551C5×D4—24no—
552C5×D4—21no—
553C5×D4—21no—
554C5×D4—32no—
555C5×D4—62no—
556C5×D4—62no—
557C5×D4—64no—
558C5×D4—62no—
559C5×D4—64no—
560C5×D4—64no—
561C5×D4—64no—
562C5×D4—64no—
563C5×D4—61no—
564C5×D4D3×D412yes—
565C5×D4D3×D412yes—
566C2×C4×C5—21no—
567C2×C4×C5—21no—
568C2×C4×C5—31no—
569C2×C4×C5—32no—
570C2×C4×C5—32no—
571C2×C4×C5—31no—
572C2×C4×C5—64no—
573C2×C4×C5—64no—
574C2×C4×C5—64no—
575C2×C4×C5—61no—
576C2×C4×C5—61no—
577C2×C4×C5—61no—
578C2×C4×C5D3×D411yescharacteristic
579C2×C4×C5C23×D311yescharacteristic
580C22⋊D5—81no—
581C22⋊D5—241no—
582C22⋊D5—241no—
583C22⋊D5—241no—
584C2×Dic5—21no—
585C2×Dic5—61no—
586D20—21no—
587D20—21no—
588D20—61no—
589D20—61no—
590D20—122no—
591#168—21no—
592#168—21no—
593#168—61no—
594#168—61no—
595H(5,𝔽2)—64no—
596H(5,𝔽2)—64no—
597C2×#41—31no—
598C2×#41—31no—
599C2×#41—31no—
600C2×#41—31no—
601C2×#41—61no—
602C22×D4—31no—
603C22×D4—31no—
604C22×D4—61no—
605C22×D4—61no—
606C22×D4—61no—
607C22×D4—151no—
608C22×D4D3×D511yescharacteristic, complemented
609AGL(1,ℤ/8)—304no—
610C2×SD16—151no—
611C2×SD16—151no—
612C2×D8—51no—
613C2×D8—51no—
614C2×D8—151no—
615C2×D8—151no—
616C2×D8—151no—
617C2×D8—151no—
618C2×D8—304no—
619C2×M16—151no—
620C22×C8—151no—
621#127—301no—
622#124—301no—
623#121—51no—
624#121—151no—
625#121—151no—
626#121—151no—
627#120—301no—
628#120—301no—
629#117—151no—
630#103—151no—
631#103—151no—
632#102—51no—
633#102—51no—
634#102—151no—
635#102—151no—
636#102—151no—
637#102—151no—
638C22⋊C8—51no—
639C22⋊C8—151no—
640C22⋊C8—151no—
641C22⋊C8—151no—
642C2×C3×C5—42no—
643C2×C3×C5—42no—
644C2×C3×C5—41no—
645C2×C3×C5C2×#12011yescharacteristic
646C2×C3×C5#57611yescharacteristic
647C2×C3×C5#57611yescharacteristic
648D15—81no—
649C3×D5—81no—
650C5×D3—22no—
651C5×D3—41no—
652C5×D3—42no—
653C23×C3—24no—
654C23×C3—21no—
655C23×C3—21no—
656C23×C3—81no—
657C23×C3—81no—
658C23×C3—101no—
659C23×C3C2×C22⋊D511yescharacteristic
660C22×D3—21no—
661C22×D3—24no—
662C22×D3—24no—
663C22×D3—81no—
664C22×D3—81no—
665C22×D3—81no—
666C22×D3—81no—
667C22×D3—101no—
668C22×D3—202no—
669C22×D3—401no—
670C22×D3—401no—
671C22×D3C2×C22⋊D511yescharacteristic
672C22×D3C2×C22⋊D511yescharacteristic
673C3×D4—24no—
674C3×D4—21no—
675C3×D4—21no—
676C3×D4—101no—
677C3×D4—101no—
678C3×D4—401no—
679C3×D4C2×C22⋊D512yes—
680C3×D4C2×C22⋊D512yes—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—101no—
684C2×C3×C4C2×C22⋊D511yescharacteristic
685C2×C3×C4C23×D511yescharacteristic
686#67—24no—
687#67—24no—
688#67—24no—
689#67—22no—
690#67—24no—
691#67—22no—
692#67—24no—
693#67—202no—
694#67—401no—
695#67—401no—
696C2×Dic3—24no—
697C2×Dic3—21no—
698C2×Dic3—24no—
699C2×Dic3—101no—
700C2×Dic3C2×C22⋊D511yescharacteristic
701C2×Dic3C2×C22⋊D511yescharacteristic
702D12—22no—
703D12—21no—
704D12—101no—
705D12—101no—
706D12—401no—
707D12C2×C22⋊D512yes—
708C4×D3—24no—
709C4×D3—21no—
710C4×D3—21no—
711C4×D3C2×C22⋊D512yes—
712C4×D3C2×C22⋊D512yes—
713Dic6—21no—
714Dic6—22no—
715Dic6C2×C22⋊D512yes—
716C3×C8—101no—
717C3×C8—101no—
718C3⋊C8—101no—
719C3⋊C8—101no—
720C22×C5—21no—
721C22×C5—21no—
722C22×C5—21no—
723C22×C5—22no—
724C22×C5—22no—
725C22×C5—32no—
726C22×C5—41no—
727C22×C5—41no—
728C22×C5—41no—
729C22×C5—41no—
730C22×C5—61no—
731C22×C5—61no—
732C22×C5—61no—
733C22×C5—61no—
734C22×C5—62no—
735C22×C5—61no—
736C22×C5—84no—
737C22×C5—121no—
738C22×C5—121no—
739C22×C5—244no—
740C22×C5—244no—
741C22×C5C2×D3×D411yescharacteristic
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—121no—
746C2×D5—121no—
747C2×D5—121no—
748C2×D5—244no—
749C4×C5—21no—
750C4×C5—32no—
751C4×C5—61no—
752C4×C5—62no—
753C4×C5C2×D3×D411yescharacteristic
754C4×C5C2×D3×D411yescharacteristic
755Dic5—41no—
756Dic5—121no—
757C24—21no—
758C24—61no—
759C24—61no—
760C24—301no—
761#41—34no—
762#41—62no—
763#41—62no—
764#41—62no—
765#41—62no—
766#41—62no—
767#41—62no—
768#41—68no—
769#41—62no—
770C2×Q8—31no—
771C2×Q8—31no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—34no—
776C2×D4—31no—
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—51no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—62no—
785C2×D4—68no—
786C2×D4—61no—
787C2×D4—61no—
788C2×D4—68no—
789C2×D4—68no—
790C2×D4—61no—
791C2×D4—62no—
792C2×D4—101no—
793C2×D4—151no—
794C2×D4—302no—
795C2×D4—302no—
796C2×D4—301no—
797C2×D4—301no—
798C2×D4—301no—
799C2×D4—301no—
800C2×D4C2×D3×D511yescharacteristic
801C2×D4C2×D3×D511yescharacteristic
802C22×C4—31no—
803C22×C4—31no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4C2×D3×D511yescharacteristic
808SD16—302no—
809SD16—302no—
810D8—102no—
811D8—102no—
812D8—302no—
813D8—302no—
814D8—302no—
815D8—302no—
816M16—302no—
817C2×C8—51no—
818C2×C8—51no—
819C2×C8—151no—
820C2×C8—151no—
821C2×C8—302no—
822C4⋊C4—51no—
823C4⋊C4—151no—
824C22⋊C4—101no—
825C22⋊C4—301no—
826C22⋊C4—301no—
827C22⋊C4—301no—
828C22⋊C4—301no—
829C42—301no—
830C3×C5#300811yescharacteristic, complemented, Hall
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—84no—
841C22×C3—201no—
842C22×C3—201no—
843C22×C3—201no—
844C22×C3C22×C22⋊D511yescharacteristic
845C2×D3—21no—
846C2×D3—21no—
847C2×D3—21no—
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—22no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—84no—
854C2×D3—84no—
855C2×D3—201no—
856C2×D3—201no—
857C2×D3—201no—
858C2×D3—404no—
859C2×D3#409912yes—
860C3×C4—21no—
861C3×C4—201no—
862C3×C4C22×C22⋊D511yescharacteristic
863C3×C4C22×C22⋊D511yescharacteristic
864Dic3—21no—
865Dic3—22no—
866Dic3—201no—
867Dic3#409912yes—
868C2×C5—41no—
869C2×C5—42no—
870C2×C5—42no—
871C2×C5—62no—
872C2×C5—121no—
873C2×C5—122no—
874C2×C5D3×#12011yescharacteristic
875C2×C5#575711yescharacteristic
876C2×C5#577411yescharacteristic
877D5—81no—
878D5—241no—
879C23—24no—
880C23—21no—
881C23—21no—
882C23—31no—
883C23—31no—
884C23—64no—
885C23—64no—
886C23—61no—
887C23—81no—
888C23—81no—
889C23—101no—
890C23—241no—
891C23—241no—
892C23—241no—
893C23—241no—
894C23—301no—
895C23—602no—
896C23—1201no—
897C23—1201no—
898C23D3×C22⋊D511yescharacteristic
899Q8—32no—
900Q8—62no—
901Q8—61no—
902D4—24no—
903D4—21no—
904D4—21no—
905D4—32no—
906D4—62no—
907D4—62no—
908D4—64no—
909D4—62no—
910D4—64no—
911D4—64no—
912D4—64no—
913D4—64no—
914D4—61no—
915D4—101no—
916D4—101no—
917D4—301no—
918D4—301no—
919D4—401no—
920D4—602no—
921D4—1201no—
922D4—1201no—
923D4—1201no—
924D4D3×C22⋊D512yes—
925D4D3×C22⋊D512yes—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—31no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—31no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—64no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—101no—
939C2×C4—301no—
940C2×C4D3×C22⋊D511yescharacteristic
941C2×C4C22×D3×D511yescharacteristic
942C8—101no—
943C8—101no—
944C8—301no—
945C8—301no—
946C2×C3—42no—
947C2×C3—42no—
948C2×C3—41no—
949C2×C3—401no—
950C2×C3#6616911yescharacteristic
951C2×C3#6616911yescharacteristic
952C2×C3C2×#409911yescharacteristic
953D3—22no—
954D3—41no—
955D3—42no—
956D3—401no—
957C5#8000411yescharacteristic, complemented, Sylow
958C22—21no—
959C22—22no—
960C22—22no—
961C22—21no—
962C22—21no—
963C22—32no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—61no—
969C22—61no—
970C22—62no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—84no—
975C22—121no—
976C22—121no—
977C22—201no—
978C22—201no—
979C22—201no—
980C22—244no—
981C22—244no—
982C22—601no—
983C22—601no—
984C22—601no—
985C22—1204no—
986C22C2×D3×C22⋊D511yescharacteristic
987C4—21no—
988C4—32no—
989C4—61no—
990C4—62no—
991C4—201no—
992C4—601no—
993C4C2×D3×C22⋊D511yescharacteristic
994C4C2×D3×C22⋊D511yescharacteristic
995C3#1061583211yescharacteristic, complemented, Sylow
996C2—41no—
997C2—42no—
998C2—42no—
999C2—62no—
1000C2—121no—
1001C2—122no—
1002C2—401no—
1003C2—1201no—
1004C2#1175469711yescharacteristic
1005C2#1175469811yescharacteristic
1006C2D3×#409911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3008
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1004C2semidirect
2. C2×#91480C2semidirect
3. C2×D3×#686C2semidirect
4. #11754655C2semidirect
5. #11751318C2semidirect
6. C3×#65506C2semidirect
7. #11749036C2semidirect
8. #11749035C2semidirect
9. #11749033C2semidirect
10. #11749032C2semidirect
11. #11748967C2semidirect
12. #11748965C2semidirect
13. #11748521C2semidirect
14. #11748517C2semidirect
15. #11748490C2semidirect
17. C22×C3×C5×D4C22semidirect
24. C2×C5×#237C22semidirect
27. C2×C5×D3×D4C22semidirect
29. C2×C5×#235C22semidirect
30. C2×D3×D20C22semidirect
31. C2×#6715C22semidirect
32. C2×#6715C22semidirect
33. #91819C22semidirect
34. C2×C3×#686C22semidirect
35. C2×C3×#686C22semidirect
36. C3×#4076C22semidirect
42. #91460C22semidirect
43. #91456C22semidirect
45. #91338C22semidirect
46. C2×#6660C22semidirect
47. C2×#6655C22semidirect
48. C2×#6654C22semidirect
49. C2×#6652C22semidirect
50. C2×#6650C22semidirect
51. C2×D3×#168C22semidirect
52. #91116C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. C3×#3964C22semidirect
56. C3×#3964C22semidirect
57. C3×C22⋊#168C22semidirect
58. #90973C22semidirect
59. #90972C22semidirect
60. #90967C22semidirect
61. #90966C22semidirect
62. (C2×D3)⋊#168C22semidirect
63. (C2×D3)⋊#168C22semidirect
78. #65506D3semidirect
107. C5×#237D4semidirect
112. C5×D3×D4D4semidirect
153. C2×#1004D5semidirect
180. C22×C5×D4C2×D3semidirect
194. C2×#686C2×D3semidirect
195. C2×#686C2×D3semidirect
199. #4076C2×D3semidirect
209. #3964C2×D3semidirect
210. #3964C2×D3semidirect
214. C22⋊#168C2×D3semidirect
283. C22×C3×D4C2×D5semidirect
290. C2×#237C2×D5semidirect
294. C2×D3×D4C2×D5semidirect
296. C2×#235C2×D5semidirect
485. #237C22⋊D5semidirect
492. D3×D4C22⋊D5semidirect
608. C22×D4D3×D5semidirect
830. C3×C5#3008semidirect
957. C5#80004semidirect
995. C3#10615832semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10042
C2×#914802
C2×D3×#6862
#117546552
#117513182
C3×#655062
#117490362
#117490352
#117490332
#117490322
#117489672
#117489652
#117485212
#117485172
#117484902
#106158323
#800045