Finite Group Databasebeta

← #14424708

Subgroups — #14424708

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1009C211yesmaximal, characteristic, complemented
2C2×#91519C211yesmaximal, characteristic, complemented
3C2×#91496C211yesmaximal, characteristic, complemented
4#11754353C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6C3×#65528C211yesmaximal, characteristic, complemented
7#11749305C211yesmaximal, characteristic, complemented
8#11749282C211yesmaximal, characteristic, complemented
9#11749201C211yesmaximal, characteristic, complemented
10#11749058C211yesmaximal, characteristic, complemented
11#11749033C211yesmaximal, characteristic, complemented
12D3×#3964C211yesmaximal, characteristic, complemented
13#11748537C211yesmaximal, characteristic, complemented
14#11748520C211yesmaximal, characteristic, complemented
15#11748490C211yesmaximal, characteristic, complemented
16#10615833—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C5×#1009—24no—
19C5×#1009—24no—
20C2×C5×#239C2211yescharacteristic
21C2×C5×#239C2211yescharacteristic
22C2×C5×D3×D4—21no—
23C2×C5×D3×D4—21no—
24C2×C5×D3×D4C2211yescharacteristic
25C2×C5×D3×D4C2211yescharacteristic
26C2×C5×#235—21no—
27C2×C5×#235C2211yescharacteristic
28C22×C5×D12—21no—
29C22×C5×D12C2211yescharacteristic
30C2×#6769C2211yescharacteristic, complemented
31C2×#6717C2211yescharacteristic, complemented
32C2×#6715C2211yescharacteristic, complemented
33#91819C2211yescharacteristic, complemented
34C2×C3×#689C2211yescharacteristic, complemented
35C2×C3×#687C2211yescharacteristic, complemented
36C3×#4070C2211yescharacteristic, complemented
37#91558—21no—
38#91557—21no—
39#91519—24no—
40#91496—24no—
41#91460C2211yescharacteristic, complemented
42D3×C4⋊Dic5C2211yescharacteristic, complemented
43#91424—21no—
44#91416—21no—
45#91369C2211yescharacteristic, complemented
46C2×#6656C2211yescharacteristic, complemented
47C2×#6656C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic, complemented
49C2×#6654C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C2×D3×#168C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55C3×#3967C2211yescharacteristic, complemented
56C3×#3964C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#90966C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62(C2×D3)⋊#168C2211yescharacteristic, complemented
63(C2×D3)⋊#168C2211yescharacteristic, complemented
64#80231—51nomaximal, Hall
65C2×C5×H(5,𝔽2)—31no—
66#66167—31no—
67C2×#4096—31no—
68C2×#4078—31no—
69#65528—31no—
70#65528D311yescharacteristic, complemented
71#65527—31no—
72#65527—31no—
73#65523—31no—
74#65521—31no—
75#65507—31no—
76#65507—31no—
77#65506—31no—
78#65506—31no—
79C2×#3964—31no—
80C23×C5×D3—21no—
81C23×C5×D3—21no—
82C23×C5×D3—21no—
83C3×C5×#41—22no—
84C3×C5×#41—22no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—21no—
91C2×D60C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×#67—21no—
94C2×C5×#67D411yescharacteristic
95C2×C5×#67D411yescharacteristic
96C5×#239—22no—
97C5×#239—22no—
98C5×#239—22no—
99C5×#239D414yescomplemented
100C5×D3×D4—28no—
101C5×D3×D4—28no—
102C5×D3×D4—22no—
103C5×D3×D4—22no—
104C5×D3×D4—22no—
105C5×D3×D4D414yescomplemented
106C5×#235—28no—
107C5×#235—22no—
108C5×#235—22no—
109C2×C5×D12—28no—
110C2×C5×D12—21no—
111C2×C5×D12—21no—
112C2×C5×D12—21no—
113C2×C5×D12—22no—
114C2×C5×D12—22no—
115C2×C5×D12D411yescharacteristic
116C2×C5×D12C2311yescharacteristic
117C2×C5×D12C2311yescharacteristic
118C2×C4×C5×D3—21no—
119C2×C4×C5×D3—21no—
120C2×C4×C5×D3C2311yescharacteristic
121C2×C4×C5×D3C2311yescharacteristic
122C2×C5×Dic6D411yescharacteristic
123C2×C3×Dic10C2311yescharacteristic
124C2×#1203—21no—
125C2×#1203—21no—
126C2×#1200—21no—
127C2×D3×Dic5—21no—
128#6769—22no—
129#6769—22no—
130#6717—22no—
131#6715—22no—
132#6714—21no—
133C4⋊Dic15C2311yescharacteristic
134C2×C3⋊#168C2311yescharacteristic
135C2×C3⋊#168C2311yescharacteristic
136C3×C22⋊Dic5—21no—
137C3×#689—22no—
138C3×#687—22no—
139C3×C4⋊Dic5C2311yescharacteristic
140C3×#683—21no—
141C2×C3×#168C2311yescharacteristic
142C2×C3×#168C2311yescharacteristic
143Dic3⋊Dic5—21no—
144#6669—21no—
145#6667—21no—
146(C2×D3)⋊Dic5—21no—
147#6656—22no—
148#6656—22no—
149#6654—22no—
150#6654—22no—
151#6650—22no—
152D3×#168—22no—
153C2×#1009D511yescharacteristic, complemented
154C2×#919—51no—
155C2×#914—51no—
156#5629—51no—
157C3×#452—51no—
158#5238—51no—
159#5187—51no—
160#5169—51no—
161#5046—51no—
162#4810—51no—
163#4803—51no—
164#4773—51no—
165D3×#102—51no—
166#4732—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—61no—
174C2×C5×#41C2×D311yescharacteristic
175C22×C5×D4—31no—
176C22×C5×D4—31no—
177C22×C5×D4—31no—
178C22×C5×D4—61no—
179C22×C5×D4—61no—
180C22×C5×D4—61no—
181C2×#709—31no—
182#4096—64no—
183#4092—61no—
184C2×#689C2×D311yescharacteristic, complemented
185C2×#688—31no—
186#4085—61no—
187#4085—61no—
188#4084—61no—
189C2×#687—31no—
190C2×#687—31no—
191C2×#687C2×D311yescharacteristic, complemented
192#4078—64no—
193C2×#686—31no—
194C2×#686—31no—
195C2×#686—31no—
196#4076—31no—
197#4076—31no—
198C2×C4⋊Dic5—31no—
199#4070—31no—
200#4070C2×D311yescharacteristic, complemented
201C2×#681—31no—
202C22×#168—31no—
203#3967—31no—
204#3967C2×D311yescharacteristic, complemented
205#3964—31no—
206#3964—31no—
207#3964—31no—
208#3964—31no—
209#3964—31no—
210#3964C2×D311yescharacteristic, complemented
211C22⋊#168—31no—
212C22⋊#168—31no—
213C22⋊#168—31no—
214C22⋊#168C2×D311yescharacteristic, complemented
215#3012—151noSylow
216C23×C3×C5—21no—
217C23×C3×C5C2×D411yescharacteristic
218C22×D15—21no—
219C22×C5×D3—21no—
220C22×C5×D3—21no—
221C22×C5×D3—24no—
222C22×C5×D3—24no—
223C22×C5×D3—24no—
224C22×C5×D3—81no—
225C22×C5×D3—81no—
226C22×C5×D3—81no—
227C22×C5×D3—81no—
228C22×C5×D3—81no—
229C22×C5×D3—81no—
230C22×C5×D3C2×D411yescharacteristic
231C22×C5×D3C2×D411yescharacteristic
232C3×C5×Q8—21no—
233C3×C5×Q8C2×D412yes—
234C3×C5×D4—24no—
235C3×C5×D4—21no—
236C3×C5×D4C2×D412yes—
237C2×C3×C4×C5—24no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5C2×D411yescharacteristic
242C2×C3×C4×C5C2411yescharacteristic
243#1220—81no—
244C2×Dic15—21no—
245D60—21no—
246D60—21no—
247C5×#67—24no—
248C5×#67—22no—
249C5×#67—22no—
250C5×#67—24no—
251C2×C5×Dic3C2×D411yescharacteristic
252C2×C5×Dic3C2×D411yescharacteristic
253C5×D12—24no—
254C5×D12—24no—
255C5×D12—22no—
256C5×D12—24no—
257C5×D12—21no—
258C5×D12—21no—
259C5×D12C2×D412yes—
260C5×D12C2×D412yes—
261C4×C5×D3—24no—
262C4×C5×D3—21no—
263C4×C5×D3—21no—
264C4×C5×D3—24no—
265C4×C5×D3C2×D412yes—
266C4×C5×D3C2×D412yes—
267C5×Dic6—22no—
268C2×C3×Dic5—21no—
269C2×C3×Dic5—21no—
270C3×Dic10—21no—
271C3×Dic10—21no—
272#1203—42no—
273#1203—81no—
274#1200—42no—
275D3×Dic5—81no—
276C3⋊#168—21no—
277C3⋊#168—21no—
278C3×#168—21no—
279C3×#168—21no—
280C2×C3×#41C2×D511yescharacteristic
281#1009—24no—
282#1009—24no—
283C2×#239—51no—
284C2×#239C2×D511yescharacteristic
285C2×#239C2×D511yescharacteristic
286C2×D3×D4—21no—
287C2×D3×D4—21no—
288C2×D3×D4C2×D511yescharacteristic
289C2×D3×D4C2×D511yescharacteristic
290C2×#235—21no—
291C2×#235C2×D511yescharacteristic
292C22×D12—21no—
293C22×D12C2×D511yescharacteristic
294C2×C3×Q16—51no—
295C2×C3×SD16—51no—
296C3×C22⋊Q8—51no—
297#946—51no—
298C2×#215—51no—
299C2×#215—51no—
300C2×#215—51no—
301C2×#213—51no—
302#930—51no—
303#919—104no—
304#914—104no—
305C2×D24—51no—
306C2×D24—51no—
307C2×ΓL(1,𝔽25)—51no—
308C2×D3×C8—51no—
309#896—101no—
310#895—51no—
311#895—101no—
312D3×C4⋊C4—51no—
313#884—101no—
314#884—101no—
315C3×#103—51no—
316C3×#102—51no—
317C3×C22⋊C8—51no—
318#835—51no—
319#832—51no—
320#830—51no—
321#821—51no—
322#821—51no—
323(C2×D3)⋊C8—51no—
324(C2×D3)⋊C8—51no—
325#809—51no—
326#809—51no—
327C24×C5—61no—
328C24×C5—61no—
329C24×C5—61no—
330C5×#41—22no—
331C5×#41—22no—
332C5×#41—34no—
333C5×#41—62no—
334C5×#41—62no—
335C5×#41—68no—
336C5×#41—62no—
337C5×#41—62no—
338C5×#41—62no—
339C2×C5×Q8—31no—
340C2×C5×Q8C22×D311yescharacteristic
341C2×C5×D4—21no—
342C2×C5×D4—34no—
343C2×C5×D4—31no—
344C2×C5×D4—31no—
345C2×C5×D4—31no—
346C2×C5×D4—31no—
347C2×C5×D4—31no—
348C2×C5×D4—62no—
349C2×C5×D4—62no—
350C2×C5×D4—61no—
351C2×C5×D4—61no—
352C2×C5×D4—68no—
353C2×C5×D4—62no—
354C2×C5×D4—61no—
355C2×C5×D4—61no—
356C2×C5×D4—62no—
357C2×C5×D4—68no—
358C2×C5×D4—68no—
359C2×C5×D4—62no—
360C2×C5×D4—61no—
361C2×C5×D4C22×D311yescharacteristic
362C22×C4×C5—21no—
363C22×C4×C5—31no—
364C22×C4×C5—31no—
365C22×C4×C5—61no—
366C22×C4×C5—61no—
367C22×C4×C5C22×D311yescharacteristic
368C2×C22⋊D5—61no—
369C2×C22⋊D5—61no—
370C2×C22⋊D5—61no—
371C22×Dic5—61no—
372#709—62no—
373#709—62no—
374C2×D20—31no—
375C2×C4×D5—61no—
376C2×Dic10C22×D311yescharacteristic
377C22⋊Dic5—21no—
378C22⋊Dic5—61no—
379#689—22no—
380#688—62no—
381#687—22no—
382#687—62no—
383#687—62no—
384#686—62no—
385#686—62no—
386#686—62no—
387#685—61no—
388#685—61no—
389C4⋊Dic5—31no—
390C4⋊Dic5—61no—
391C4⋊Dic5C22×D311yescharacteristic
392#683—21no—
393#683—61no—
394#681—62no—
395C2×#168—31no—
396C2×#168—31no—
397C2×#168—62no—
398C2×#168C22×D311yescharacteristic
399C2×#168C22×D311yescharacteristic
400C2×H(5,𝔽2)—31no—
401C2×AGL(1,ℤ/8)—151no—
402C2×#135—151no—
403#537—151no—
404#452—51no—
405#452—151no—
406#450—151no—
407#450—151no—
408#449—151no—
409#449—151no—
410#447—151no—
411#447—151no—
412#417—151no—
413C2×#102—151no—
414#408—151no—
415C22×C3×C5—21no—
416C22×C3×C5—22no—
417C22×C3×C5—21no—
418C22×C3×C5—21no—
419C22×C3×C5—41no—
420C22×C3×C5—41no—
421C22×C3×C5C22×D411yescharacteristic
422C2×D15—41no—
423C2×D15—41no—
424C2×D15—41no—
425C2×C5×D3—21no—
426C2×C5×D3—21no—
427C2×C5×D3—21no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—21no—
431C2×C5×D3—21no—
432C2×C5×D3—41no—
433C2×C5×D3—41no—
434C2×C5×D3—41no—
435C2×C5×D3—41no—
436C2×C5×D3—84no—
437C2×C5×D3—84no—
438C2×C5×D3—84no—
439C2×C5×D3#12012yes—
440C3×C4×C5—21no—
441C3×C4×C5—22no—
442C3×C4×C5C22×D411yescharacteristic
443C3×C4×C5C22×D411yescharacteristic
444Dic15—41no—
445C3×Dic5—41no—
446C3×Dic5—41no—
447C5×Dic3—21no—
448C5×Dic3#12012yes—
449C23×D3—21no—
450C23×D3—21no—
451C23×D3—21no—
452C3×#41—22no—
453C3×#41—22no—
454C2×C3×Q8—51no—
455C2×C3×Q8C22×D511yescharacteristic
456C2×C3×D4—21no—
457C2×C3×D4C22×D511yescharacteristic
458C22×C3×C4—21no—
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—21no—
461C2×#67—21no—
462C2×#67—101no—
463C2×#67C22⋊D511yescharacteristic
464C2×#67C22⋊D511yescharacteristic
465#239—22no—
466#239—22no—
467#239—22no—
468#239—102no—
469#239—102no—
470#239C22⋊D514yescomplemented
471D3×D4—28no—
472D3×D4—28no—
473D3×D4—22no—
474D3×D4—22no—
475D3×D4—22no—
476D3×D4C22⋊D514yescomplemented
477#235—28no—
478#235—22no—
479#235—22no—
480C2×D12—28no—
481C2×D12—21no—
482C2×D12—21no—
483C2×D12—21no—
484C2×D12—22no—
485C2×D12—22no—
486C2×D12—51no—
487C2×D12—101no—
488C2×D12—101no—
489C2×D12C22⋊D511yescharacteristic
490C2×D12C22×D511yescharacteristic
491C2×D12C22×D511yescharacteristic
492C2×C4×D3—21no—
493C2×C4×D3—21no—
494C2×C4×D3—101no—
495C2×C4×D3—101no—
496C2×C4×D3C22×D511yescharacteristic
497C2×C4×D3C22×D511yescharacteristic
498C2×Dic6C22⋊D511yescharacteristic
499C3×Q16—102no—
500C3×SD16—102no—
501C2×C3×C8—51no—
502C2×C3×C8—51no—
503C3×C4⋊C4—51no—
504C3×C4⋊C4—101no—
505C3×C22⋊C4—101no—
506#215—102no—
507#215—102no—
508#215—102no—
509#213—102no—
510(C2×D3)⋊C4—101no—
511(C2×D3)⋊C4—101no—
512(C2×D3)⋊C4—101no—
513C4⋊Dic3—51no—
514Dic3⋊C4—101no—
515Dic3⋊C4—101no—
516C2×C3⋊C8—51no—
517C2×C3⋊C8—51no—
518D24—102no—
519D24—102no—
520ΓL(1,𝔽25)—102no—
521D3×C8—102no—
522C23×C5—21no—
523C23×C5—31no—
524C23×C5—31no—
525C23×C5—64no—
526C23×C5—64no—
527C23×C5—64no—
528C23×C5—61no—
529C23×C5—61no—
530C23×C5—241no—
531C23×C5—241no—
532C23×C5—241no—
533C23×C5—241no—
534C23×C5—241no—
535C23×C5—241no—
536C23×C5D3×D411yescharacteristic
537C22×D5—61no—
538C5×Q8—21no—
539C5×Q8—62no—
540C5×Q8D3×D412yes—
541C5×D4—24no—
542C5×D4—21no—
543C5×D4—32no—
544C5×D4—32no—
545C5×D4—62no—
546C5×D4—64no—
547C5×D4—64no—
548C5×D4—64no—
549C5×D4—62no—
550C5×D4—64no—
551C5×D4—62no—
552C5×D4—64no—
553C5×D4—61no—
554C5×D4—61no—
555C5×D4D3×D412yes—
556C2×C4×C5—24no—
557C2×C4×C5—21no—
558C2×C4×C5—21no—
559C2×C4×C5—21no—
560C2×C4×C5—31no—
561C2×C4×C5—32no—
562C2×C4×C5—32no—
563C2×C4×C5—31no—
564C2×C4×C5—64no—
565C2×C4×C5—64no—
566C2×C4×C5—61no—
567C2×C4×C5—61no—
568C2×C4×C5D3×D411yescharacteristic
569C2×C4×C5C23×D311yescharacteristic
570C22⋊D5—122no—
571C22⋊D5—241no—
572C22⋊D5—241no—
573C2×Dic5—21no—
574C2×Dic5—21no—
575C2×Dic5—61no—
576C2×Dic5—241no—
577D20—61no—
578D20—61no—
579C4×D5—122no—
580Dic10—21no—
581Dic10—21no—
582#168—21no—
583#168—21no—
584#168—61no—
585#168—61no—
586H(5,𝔽2)—64no—
587H(5,𝔽2)—64no—
588C2×#41—31no—
589C2×#41—31no—
590C2×#41—31no—
591C2×#41—61no—
592C2×#41—151no—
593C2×#41D3×D511yescharacteristic
594C22×D4—31no—
595C22×D4—31no—
596C22×D4—31no—
597C22×D4—61no—
598C22×D4—61no—
599C22×D4—61no—
600AGL(1,ℤ/8)—304no—
601#135—304no—
602C2×Q16—51no—
603C2×SD16—51no—
604C2×SD16—151no—
605C2×SD16—151no—
606C2×SD16—151no—
607C2×D8—151no—
608C2×D8—151no—
609C2×D8—151no—
610C2×M16—151no—
611C22×C8—151no—
612C22⋊Q8—51no—
613C22⋊Q8—151no—
614C22⋊Q8—301no—
615#121—151no—
616#121—151no—
617#121—301no—
618#121—301no—
619#121—301no—
620C2×C4⋊C4—151no—
621#103—51no—
622#103—151no—
623#102—51no—
624#102—151no—
625#102—151no—
626#102—151no—
627#102—151no—
628#102—151no—
629C22⋊C8—51no—
630C22⋊C8—151no—
631C22⋊C8—151no—
632C22⋊C8—151no—
633C2×C3×C5—41no—
634C2×C3×C5—42no—
635C2×C3×C5C2×#12011yescharacteristic
636C2×C3×C5#57611yescharacteristic
637C2×C3×C5#57711yescharacteristic
638D15—81no—
639C5×D3—22no—
640C5×D3—41no—
641C5×D3—42no—
642C5×D3—42no—
643C23×C3—21no—
644C23×C3C2×C22⋊D511yescharacteristic
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—24no—
648C22×D3—24no—
649C22×D3—24no—
650C22×D3—81no—
651C22×D3—81no—
652C22×D3—81no—
653C22×D3—81no—
654C22×D3—81no—
655C22×D3—81no—
656C22×D3—101no—
657C22×D3C2×C22⋊D511yescharacteristic
658C22×D3C2×C22⋊D511yescharacteristic
659C3×Q8—21no—
660C3×Q8—101no—
661C3×Q8—101no—
662C3×Q8C2×C22⋊D512yes—
663C3×D4—24no—
664C3×D4—21no—
665C3×D4C2×C22⋊D512yes—
666C2×C3×C4—24no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4C2×C22⋊D511yescharacteristic
673C2×C3×C4C23×D511yescharacteristic
674#67—24no—
675#67—22no—
676#67—22no—
677#67—24no—
678#67—401no—
679C2×Dic3—101no—
680C2×Dic3C2×C22⋊D511yescharacteristic
681C2×Dic3C2×C22⋊D511yescharacteristic
682D12—24no—
683D12—24no—
684D12—22no—
685D12—24no—
686D12—21no—
687D12—21no—
688D12—101no—
689D12—101no—
690D12—202no—
691D12—401no—
692D12C2×C22⋊D512yes—
693D12C2×C22⋊D512yes—
694C4×D3—24no—
695C4×D3—21no—
696C4×D3—21no—
697C4×D3—24no—
698C4×D3—202no—
699C4×D3—401no—
700C4×D3C2×C22⋊D512yes—
701C4×D3C2×C22⋊D512yes—
702Dic6—22no—
703C3×C8—101no—
704C3×C8—101no—
705C3⋊C8—101no—
706C3⋊C8—101no—
707C22×C5—21no—
708C22×C5—21no—
709C22×C5—21no—
710C22×C5—22no—
711C22×C5—32no—
712C22×C5—41no—
713C22×C5—41no—
714C22×C5—61no—
715C22×C5—61no—
716C22×C5—61no—
717C22×C5—61no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—61no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5—121no—
725C22×C5—244no—
726C22×C5—244no—
727C22×C5—244no—
728C22×C5C2×D3×D411yescharacteristic
729C2×D5—121no—
730C2×D5—121no—
731C2×D5—121no—
732C4×C5—21no—
733C4×C5—22no—
734C4×C5—32no—
735C4×C5—61no—
736C4×C5C2×D3×D411yescharacteristic
737C4×C5C2×D3×D411yescharacteristic
738Dic5—41no—
739Dic5—41no—
740Dic5—121no—
741C24—61no—
742C24—61no—
743C24—61no—
744#41—22no—
745#41—22no—
746#41—34no—
747#41—62no—
748#41—62no—
749#41—68no—
750#41—62no—
751#41—62no—
752#41—62no—
753#41—302no—
754#41—302no—
755C2×Q8—31no—
756C2×Q8—51no—
757C2×Q8C2×D3×D511yescharacteristic
758C2×D4—21no—
759C2×D4—34no—
760C2×D4—31no—
761C2×D4—31no—
762C2×D4—31no—
763C2×D4—31no—
764C2×D4—31no—
765C2×D4—62no—
766C2×D4—62no—
767C2×D4—61no—
768C2×D4—61no—
769C2×D4—68no—
770C2×D4—62no—
771C2×D4—61no—
772C2×D4—61no—
773C2×D4—62no—
774C2×D4—68no—
775C2×D4—68no—
776C2×D4—62no—
777C2×D4—61no—
778C2×D4—151no—
779C2×D4—301no—
780C2×D4—301no—
781C2×D4—301no—
782C2×D4C2×D3×D511yescharacteristic
783C22×C4—21no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—301no—
789C22×C4—301no—
790C22×C4C2×D3×D511yescharacteristic
791Q16—102no—
792SD16—102no—
793SD16—302no—
794SD16—302no—
795SD16—302no—
796D8—302no—
797D8—302no—
798D8—302no—
799M16—302no—
800C2×C8—51no—
801C2×C8—51no—
802C2×C8—151no—
803C2×C8—151no—
804C2×C8—302no—
805C4⋊C4—51no—
806C4⋊C4—101no—
807C4⋊C4—151no—
808C4⋊C4—301no—
809C4⋊C4—301no—
810C22⋊C4—101no—
811C22⋊C4—301no—
812C22⋊C4—301no—
813C22⋊C4—301no—
814C3×C5#301211yescharacteristic, complemented, Hall
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—22no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3C22×C22⋊D511yescharacteristic
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—84no—
834C2×D3—84no—
835C2×D3—84no—
836C2×D3—201no—
837C2×D3—201no—
838C2×D3—201no—
839C2×D3#409912yes—
840C3×C4—21no—
841C3×C4—22no—
842C3×C4—201no—
843C3×C4—201no—
844C3×C4C22×C22⋊D511yescharacteristic
845C3×C4C22×C22⋊D511yescharacteristic
846Dic3—21no—
847Dic3—201no—
848Dic3#409912yes—
849C2×C5—41no—
850C2×C5—42no—
851C2×C5—62no—
852C2×C5—121no—
853C2×C5—122no—
854C2×C5—122no—
855C2×C5D3×#12011yescharacteristic
856C2×C5#576911yescharacteristic
857C2×C5#577811yescharacteristic
858D5—241no—
859C23—21no—
860C23—31no—
861C23—31no—
862C23—64no—
863C23—64no—
864C23—64no—
865C23—61no—
866C23—61no—
867C23—241no—
868C23—241no—
869C23—241no—
870C23—241no—
871C23—241no—
872C23—241no—
873C23—301no—
874C23D3×C22⋊D511yescharacteristic
875Q8—21no—
876Q8—62no—
877Q8—101no—
878Q8—101no—
879Q8D3×C22⋊D512yes—
880D4—24no—
881D4—21no—
882D4—32no—
883D4—32no—
884D4—62no—
885D4—64no—
886D4—64no—
887D4—64no—
888D4—62no—
889D4—64no—
890D4—62no—
891D4—64no—
892D4—61no—
893D4—61no—
894D4—301no—
895D4—301no—
896D4—602no—
897D4—1201no—
898D4—1201no—
899D4D3×C22⋊D512yes—
900C2×C4—24no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—31no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—31no—
908C2×C4—64no—
909C2×C4—64no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—101no—
913C2×C4—101no—
914C2×C4—301no—
915C2×C4—602no—
916C2×C4—1201no—
917C2×C4D3×C22⋊D511yescharacteristic
918C2×C4C22×D3×D511yescharacteristic
919C8—101no—
920C8—101no—
921C8—301no—
922C8—301no—
923C2×C3—41no—
924C2×C3—42no—
925C2×C3#6616911yescharacteristic
926C2×C3#6617011yescharacteristic
927C2×C3C2×#409911yescharacteristic
928D3—22no—
929D3—41no—
930D3—42no—
931D3—42no—
932D3—401no—
933C5#8023111yescharacteristic, complemented, Sylow
934C22—21no—
935C22—21no—
936C22—21no—
937C22—22no—
938C22—32no—
939C22—41no—
940C22—41no—
941C22—61no—
942C22—61no—
943C22—61no—
944C22—61no—
945C22—62no—
946C22—62no—
947C22—61no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—121no—
952C22—244no—
953C22—244no—
954C22—244no—
955C22—601no—
956C22—601no—
957C22—601no—
958C22C2×D3×C22⋊D511yescharacteristic
959C4—21no—
960C4—22no—
961C4—32no—
962C4—61no—
963C4—201no—
964C4—201no—
965C4—601no—
966C4C2×D3×C22⋊D511yescharacteristic
967C4C2×D3×C22⋊D511yescharacteristic
968C3#1061583311yescharacteristic, complemented, Sylow
969C2—41no—
970C2—42no—
971C2—62no—
972C2—121no—
973C2—122no—
974C2—122no—
975C2—1201no—
976C2#1175532511yescharacteristic
977C2#1175534011yescharacteristic
978C2D3×#409911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3012
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1009C2semidirect
2. C2×#91519C2semidirect
3. C2×#91496C2semidirect
4. #11754353C2semidirect
5. #11751339C2semidirect
6. C3×#65528C2semidirect
7. #11749305C2semidirect
8. #11749282C2semidirect
9. #11749201C2semidirect
10. #11749058C2semidirect
11. #11749033C2semidirect
12. D3×#3964C2semidirect
13. #11748537C2semidirect
14. #11748520C2semidirect
15. #11748490C2semidirect
30. C2×#6769C22semidirect
31. C2×#6717C22semidirect
32. C2×#6715C22semidirect
33. #91819C22semidirect
34. C2×C3×#689C22semidirect
35. C2×C3×#687C22semidirect
36. C3×#4070C22semidirect
41. #91460C22semidirect
42. D3×C4⋊Dic5C22semidirect
45. #91369C22semidirect
46. C2×#6656C22semidirect
47. C2×#6656C22semidirect
48. C2×#6654C22semidirect
49. C2×#6654C22semidirect
50. C2×#6650C22semidirect
51. C2×D3×#168C22semidirect
52. #91119C22semidirect
53. #91116C22semidirect
54. #91114C22semidirect
55. C3×#3967C22semidirect
56. C3×#3964C22semidirect
57. C3×C22⋊#168C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
60. #90966C22semidirect
61. #90966C22semidirect
62. (C2×D3)⋊#168C22semidirect
63. (C2×D3)⋊#168C22semidirect
70. #65528D3semidirect
99. C5×#239D4semidirect
105. C5×D3×D4D4semidirect
153. C2×#1009D5semidirect
184. C2×#689C2×D3semidirect
191. C2×#687C2×D3semidirect
200. #4070C2×D3semidirect
204. #3967C2×D3semidirect
210. #3964C2×D3semidirect
214. C22⋊#168C2×D3semidirect
470. #239C22⋊D5semidirect
476. D3×D4C22⋊D5semidirect
814. C3×C5#3012semidirect
933. C5#80231semidirect
968. C3#10615833semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C2×#915192
C2×#914962
#117543532
#117513392
C3×#655282
#117493052
#117492822
#117492012
#117490582
#117490332
D3×#39642
#117485372
#117485202
#117484902
#106158333
#802315