Finite Group Databasebeta

← #14415532

Subgroups — #14415532

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#907C211yesmaximal, characteristic, complemented
2C2×C3×D5×M16C211yesmaximal, characteristic, complemented
3#11754563C211yesmaximal, characteristic
4#11751223C211yesmaximal, characteristic, complemented
5#11748436C211yesmaximal, characteristic, complemented
6#11748347C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747721C212yesmaximal, complemented
9#11747711C212yesmaximal, complemented
10#11747701C212yesmaximal, complemented
11C8×#1201C212yesmaximal, complemented
12#10615527—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91815C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C5×#907—24no—
20C2×C5×ΓL(1,𝔽25)C2212yescomplemented
21C2×C5×D3×C8C2212yescomplemented
22C2×C3×#681C2211yescharacteristic
23C3×D5×M16—24no—
24C2×C3×#676C2212yes—
25C2×C3×C8×D5C2212yes—
26#91563C412yes—
27#91539C412yes—
28#91449C411yescharacteristic
29#91449C411yescharacteristic
30C4×#1201C2212yes—
31C4×#1201C2212yes—
32#91359C411yescharacteristic
33#91359C411yescharacteristic
34#91099C2212yescomplemented
35C8×Dic15C2212yescomplemented
36#90983C2212yescomplemented
37#90983C2212yescomplemented
38(C2×D3)⋊#168C2212yescomplemented
39(C2×D3)⋊#168C2212yescomplemented
40#90955C2211yescharacteristic
41#90955C2211yescharacteristic
42#90955C2211yescharacteristic
43#90955C2211yescharacteristic
44#83757—51nomaximal, Hall
45C2×C5×#131—31no—
46#66162—31no—
47C2×D5×M16D311yescharacteristic, complemented
48#65523—31no—
49#65417—32no—
50#65416—32no—
51#65411—31no—
52#65400—32no—
53C8×C22⋊D5—32no—
54C2×#3952—31no—
55#65391—31no—
56C23×C3×D5C2×C411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67C2×C412yes—
59C5×#235—22no—
60C5×#235—22no—
61C2×C5×D12C2×C411yescharacteristic
62C2×C4×C5×D3C2312yes—
63C2×C5×Dic6C2×C411yescharacteristic
64C22×C3×Dic5C2×C411yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C411yescharacteristic
68C2×C3×C4×D5C2×C411yescharacteristic
69C2×C3×C4×D5C2311yescharacteristic
70C2×C3×C4×D5C2311yescharacteristic
71C2×#1201C2×C412yes—
72C2×#1201C2×C412yes—
73C3×C5×M16D414yescomplemented
74C2×C3×C5×C8C2312yes—
75#6719C2×C412yes—
76C4⋊Dic15C2×C411yescharacteristic
77C4⋊Dic15C2×C411yescharacteristic
78C4×Dic15C2312yes—
79C2×C3⋊#168—22no—
80C2×C3⋊#168C2311yescharacteristic
81C2×C3⋊#168C2311yescharacteristic
82C2×C5×C3⋊C8—22no—
83C2×C5×C3⋊C8C2311yescharacteristic
84C2×C5×C3⋊C8C2311yescharacteristic
85C5×ΓL(1,𝔽25)—24no—
86C5×D3×C8—24no—
87C3×#681—22no—
88C2×C3×#168C2312yes—
89C3×#676—24no—
90C3×C8×D5—24no—
91#6669C2×C412yes—
92#6669C2×C412yes—
93(C2×D3)⋊Dic5C2×C412yes—
94(C2×D3)⋊Dic5C2×C412yes—
95#6665C2×C412yes—
96#6665C2×C412yes—
97C22×C3×M16—51no—
98#5791—51no—
99C2×#907D511yescharacteristic, complemented
100C2×#830—51no—
101#5129—51no—
102#5128—52no—
103#5127—52no—
104#5122—51no—
105#5119—51no—
106#5111—52no—
107C8×#67—52no—
108C2×C5×#41—31no—
109C22×C4×D5C2×D311yescharacteristic
110C5×#131—64no—
111C2×C5×M16—32no—
112C2×C5×M16C2×D311yescharacteristic
113C22×C5×C8—31no—
114C22×C5×C8—32no—
115#4092—31no—
116#4092—31no—
117#4084—31no—
118#4084—31no—
119#4083—32no—
120#4081—32no—
121C4×C22⋊D5—32no—
122C4×C22⋊D5—32no—
123#4072—31no—
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126D5×M16—24no—
127C2×#676C2×D312yes—
128C2×C8×D5C2×D312yes—
129C22⋊#168—32no—
130C22⋊#168—32no—
131#3952—31no—
132#3952—31no—
133#3952—31no—
134#3952—31no—
135#3947—32no—
136#3946—32no—
137#3946—32no—
138C8×Dic5—32no—
139#2933—151noSylow
140C23×C3×C5C22×C411yescharacteristic
141C22×C5×D3C22×C412yes—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—41no—
145C22×C3×D5C22×C411yescharacteristic
146C22×C3×D5C22×C411yescharacteristic
147C2×C3×C4×C5C22×C411yescharacteristic
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15C22×C412yes—
152C2×Dic15C22×C412yes—
153C5×#67—24no—
154C2×C5×Dic3C22×C412yes—
155C5×D12—22no—
156C4×C5×D3—22no—
157C4×C5×D3—22no—
158C5×Dic6—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22×C411yescharacteristic
161C2×C3×Dic5C22×C411yescharacteristic
162C3×C4×D5—22no—
163C3×C4×D5—22no—
164C3×C4×D5—21no—
165C3×C4×D5—21no—
166C3×C4×D5—21no—
167C3×C4×D5—21no—
168#1201—24no—
169#1201—42no—
170C3×C5×C8C2×D414yes—
171C3⋊#168—21no—
172C3⋊#168—21no—
173C3×#168—22no—
174C5×C3⋊C8—21no—
175C5×C3⋊C8—21no—
176C23×C3×C4—51no—
177C2×#235C2×D511yescharacteristic
178C2×C3×M16—51no—
179C2×C3×M16—52no—
180C2×C3×M16—104no—
181C2×C3×M16C2×D511yescharacteristic
182C22×C3×C8—52no—
183#953—52no—
184#930—51no—
185#930—51no—
186#929—52no—
187C4×#67—52no—
188C4×#67—52no—
189#926—51no—
190#924—51no—
191#924—51no—
192C22×C3⋊C8—51no—
193C22×C3⋊C8C2×D511yescharacteristic
194#907—24no—
195C2×ΓL(1,𝔽25)C2×D512yescomplemented
196C2×D3×C8C2×D512yescomplemented
197#830—51no—
198#830—51no—
199#830—51no—
200#830—51no—
201(C2×D3)⋊C8—52no—
202(C2×D3)⋊C8—52no—
203#815—52no—
204Dic3⋊C8—52no—
205Dic3⋊C8—52no—
206C8×Dic3—52no—
207C23×D5C4×D311yescharacteristic
208C5×#41—62no—
209C5×#41—62no—
210C2×C5×Q8—31no—
211C2×C5×D4—32no—
212C2×C5×D4—31no—
213C22×C4×C5—32no—
214C22×C4×C5C22×D311yescharacteristic
215C2×C22⋊D5—32no—
216C2×C22⋊D5—32no—
217C22×Dic5C4×D311yescharacteristic
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5C4×D311yescharacteristic
221C2×C4×D5C4×D311yescharacteristic
222C2×C4×D5C22×D311yescharacteristic
223C2×C4×D5C22×D311yescharacteristic
224C5×M16—64no—
225C5×M16#6714yescomplemented
226C2×C5×C8—31no—
227C2×C5×C8—31no—
228C2×C5×C8—62no—
229C2×C5×C8—64no—
230C2×C5×C8C22×D312yes—
231C22⋊Dic5—32no—
232C22⋊Dic5—32no—
233C22⋊Dic5—32no—
234#685—32no—
235#685—32no—
236C4⋊Dic5—31no—
237C4⋊Dic5—31no—
238#683—32no—
239#683—32no—
240C4×Dic5—32no—
241#681—22no—
242C2×#168—31no—
243C2×#168—31no—
244C2×#168—62no—
245C2×#168C22×D312yes—
246#676—24no—
247C8×D5—24no—
248C2×#131—31no—
249C22×M16—51no—
250#525—151no—
251#436—152no—
252#435—152no—
253#435—152no—
254C8×D4—152no—
255#424—151no—
256#408—151no—
257C2×C22⋊C8—151no—
258#405—151no—
259C22×C3×C5—21no—
260C22×C3×C5—21no—
261C22×C3×C5C4×D412yes—
262C22×C3×C5C23×C411yescharacteristic
263C2×C5×D3—22no—
264C2×C5×D3—22no—
265C2×C5×D3—22no—
266C2×C3×D5—21no—
267C2×C3×D5—21no—
268C2×C3×D5—21no—
269C2×C3×D5—21no—
270C2×C3×D5—21no—
271C2×C3×D5—44no—
272C2×C3×D5#13112yescomplemented
273C3×C4×C5C4×D412yes—
274C3×C4×C5C22×D411yescharacteristic
275C3×C4×C5C2×#4111yescharacteristic
276Dic15—22no—
277Dic15—22no—
278C3×Dic5—21no—
279C3×Dic5—21no—
280C5×Dic3—22no—
281C24×C3—51no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—102no—
288C22×C3×C4—102no—
289C22×C3×C4C22×D511yescharacteristic
290C2×#67—52no—
291C2×#67—52no—
292C2×#67C4×D512yes—
293#235—22no—
294#235—22no—
295C2×D12C4×D511yescharacteristic
296C2×C4×D3C22×D512yes—
297C2×Dic6C4×D511yescharacteristic
298C3×M16—102no—
299C3×M16—104no—
300C3×M16C22⋊D514yescomplemented
301C2×C3×C8—52no—
302C2×C3×C8—104no—
303C2×C3×C8C22×D512yes—
304#217—52no—
305#217—52no—
306#217—52no—
307(C2×D3)⋊C4—52no—
308(C2×D3)⋊C4—52no—
309C4⋊Dic3—51no—
310C4⋊Dic3—51no—
311Dic3⋊C4—52no—
312Dic3⋊C4—52no—
313C4×Dic3—52no—
314C2×C3⋊C8—22no—
315C2×C3⋊C8—51no—
316C2×C3⋊C8—51no—
317C2×C3⋊C8—102no—
318C2×C3⋊C8C22×D511yescharacteristic
319C2×C3⋊C8C22×D511yescharacteristic
320ΓL(1,𝔽25)—24no—
321D3×C8—24no—
322C23×C5—32no—
323C23×C5C2×C4×D311yescharacteristic
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—41no—
327C22×D5C2×C4×D311yescharacteristic
328C22×D5C2×C4×D311yescharacteristic
329C5×Q8—62no—
330C5×D4—64no—
331C5×D4—62no—
332C2×C4×C5—32no—
333C2×C4×C5—62no—
334C2×C4×C5—62no—
335C2×C4×C5C2×C4×D311yescharacteristic
336C2×C4×C5#23512yes—
337C2×C4×C5C2×#6712yes—
338C2×C4×C5C23×D311yescharacteristic
339C22⋊D5—64no—
340C22⋊D5—122no—
341C2×Dic5—22no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5C2×C4×D311yescharacteristic
345C2×Dic5C2×C4×D311yescharacteristic
346C4×D5—22no—
347C4×D5—22no—
348C4×D5—21no—
349C4×D5—21no—
350C4×D5—21no—
351C4×D5—21no—
352C5×C8—61no—
353C5×C8—61no—
354C5×C8C2×#6714yes—
355#168—22no—
356#168—61no—
357#168—61no—
358C2×#41—31no—
359C23×C4—51no—
360#131—64no—
361C2×M16—32no—
362C2×M16—51no—
363C2×M16—52no—
364C2×M16—104no—
365C2×M16D3×D511yescharacteristic
366C22×C8—31no—
367C22×C8—32no—
368C22×C8—52no—
369C22×C8—151no—
370#123—152no—
371C22⋊Q8—151no—
372C22⋊Q8—151no—
373#121—151no—
374#121—151no—
375#120—152no—
376C4×D4—152no—
377C4×D4—152no—
378#117—151no—
379C4⋊C8—152no—
380C4⋊C8—152no—
381C22⋊C8—151no—
382C22⋊C8—151no—
383C22⋊C8—151no—
384C22⋊C8—151no—
385C22⋊C8—152no—
386C22⋊C8—152no—
387#97—152no—
388C4×C8—152no—
389C2×C3×C5—22no—
390C2×C3×C5C2×C4×D411yescharacteristic
391C2×C3×C5C2×#13111yescharacteristic
392C2×C3×C5#56811yescharacteristic
393C3×D5—22no—
394C3×D5—41no—
395C5×D3—42no—
396C23×C3—51no—
397C23×C3—51no—
398C23×C3—102no—
399C23×C3—102no—
400C23×C3—201no—
401C23×C3C2×C4×D511yescharacteristic
402C22×D3C2×C4×D512yes—
403C2×C3×C4—51no—
404C2×C3×C4—51no—
405C2×C3×C4—102no—
406C2×C3×C4—101no—
407C2×C3×C4—101no—
408C2×C3×C4—101no—
409C2×C3×C4—101no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4C2×C4×D511yescharacteristic
413C2×C3×C4#70912yes—
414C2×C3×C4C2×C22⋊D512yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—24no—
417#67—104no—
418#67—202no—
419C2×Dic3—52no—
420C2×Dic3—52no—
421C2×Dic3C2×C4×D512yes—
422D12—22no—
423C4×D3—22no—
424C4×D3—22no—
425Dic6—22no—
426C3×C8—102no—
427C3×C8C2×C22⋊D514yes—
428C3⋊C8—21no—
429C3⋊C8—21no—
430C3⋊C8—101no—
431C3⋊C8—101no—
432C22×C5—21no—
433C22×C5—21no—
434C22×C5—62no—
435C22×C5—62no—
436C22×C5—62no—
437C22×C5C4×#6712yes—
438C22×C5C22×C4×D311yescharacteristic
439C2×D5—21no—
440C2×D5—21no—
441C2×D5—21no—
442C2×D5—21no—
443C2×D5—21no—
444C2×D5—44no—
445C2×D5#90712yescomplemented
446C4×C5—62no—
447C4×C5C4×#6712yes—
448C4×C5C2×#23511yescharacteristic
449C4×C5C22×#6711yescharacteristic
450Dic5—21no—
451Dic5—21no—
452Dic5—62no—
453Dic5—62no—
454C24—51no—
455#41—62no—
456#41—62no—
457C2×Q8—31no—
458C2×D4—32no—
459C2×D4—31no—
460C2×D4—152no—
461C2×D4—152no—
462C22×C4—32no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—51no—
466C22×C4—51no—
467C22×C4—51no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4C2×D3×D511yescharacteristic
471M16—64no—
472M16—102no—
473M16—104no—
474M16#120114yescomplemented
475C2×C8—31no—
476C2×C8—31no—
477C2×C8—52no—
478C2×C8—62no—
479C2×C8—64no—
480C2×C8—104no—
481C2×C8—151no—
482C2×C8—151no—
483C2×C8—302no—
484C2×C8C2×D3×D512yes—
485C4⋊C4—152no—
486C4⋊C4—152no—
487C4⋊C4—151no—
488C4⋊C4—151no—
489C22⋊C4—152no—
490C22⋊C4—152no—
491C22⋊C4—152no—
492C22⋊C4—152no—
493C22⋊C4—152no—
494C42—152no—
495C3×C5#293311yescharacteristic, complemented, Hall
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—52no—
499C22×C3—101no—
500C22×C3—101no—
501C22×C3—101no—
502C22×C3—101no—
503C22×C3—101no—
504C22×C3—204no—
505C22×C3C4×C22⋊D512yes—
506C22×C3C22×C4×D511yescharacteristic
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—22no—
510C3×C4—101no—
511C3×C4—101no—
512C3×C4C4×C22⋊D512yes—
513C3×C4C2×#70911yescharacteristic
514C3×C4C22×C22⋊D511yescharacteristic
515Dic3—22no—
516Dic3—102no—
517Dic3—102no—
518C2×C5—22no—
519C2×C5—122no—
520C2×C5C2×#90711yescharacteristic
521C2×C5#574511yescharacteristic
522C2×C5C2×C4×#6711yescharacteristic
523D5—22no—
524D5—41no—
525C23—32no—
526C23—51no—
527C23—51no—
528C23—102no—
529C23—102no—
530C23—201no—
531C23C4×D3×D511yescharacteristic
532Q8—62no—
533D4—64no—
534D4—62no—
535D4—304no—
536D4—602no—
537C2×C4—32no—
538C2×C4—51no—
539C2×C4—51no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—152no—
550C2×C4—152no—
551C2×C4#677112yes—
552C2×C4C4×D3×D511yescharacteristic
553C2×C4C2×#120112yes—
554C2×C4C22×D3×D511yescharacteristic
555C8—61no—
556C8—61no—
557C8—102no—
558C8—301no—
559C8—301no—
560C8C2×#120114yes—
561C2×C3—22no—
562C2×C3—102no—
563C2×C3—201no—
564C2×C3D5×#13111yescharacteristic
565C2×C3#6608411yescharacteristic
566C2×C3C2×C4×C22⋊D511yescharacteristic
567D3—42no—
568C5#8375711yescharacteristic, complemented, Sylow
569C22—21no—
570C22—21no—
571C22—52no—
572C22—62no—
573C22—62no—
574C22—62no—
575C22—101no—
576C22—101no—
577C22—101no—
578C22—101no—
579C22—101no—
580C22—204no—
581C22C4×#120112yes—
582C22C2×C4×D3×D511yescharacteristic
583C4—62no—
584C4—101no—
585C4—101no—
586C4—302no—
587C4—302no—
588C4C4×#120112yes—
589C4C2×#677111yescharacteristic
590C4C22×#120111yescharacteristic
591C3#1061552711yescharacteristic, complemented, Sylow
592C2—22no—
593C2—102no—
594C2—122no—
595C2—201no—
596C2D5×#90711yescharacteristic
597C2#1175401411yescharacteristic
598C2C2×C4×#120111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×M16C22
prime radical#11754563C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C5×#907C2semidirect
2. C2×C3×D5×M16C2semidirect
4. #11751223C2semidirect
5. #11748436C2semidirect
6. #11748347C2semidirect
7. C2×#90955C2semidirect
8. #11747721C2semidirect
9. #11747711C2semidirect
10. #11747701C2semidirect
11. C8×#1201C2semidirect
20. C2×C5×ΓL(1,𝔽25)C22semidirect
21. C2×C5×D3×C8C22semidirect
34. #91099C22semidirect
35. C8×Dic15C22semidirect
36. #90983C22semidirect
37. #90983C22semidirect
38. (C2×D3)⋊#168C22semidirect
39. (C2×D3)⋊#168C22semidirect
47. C2×D5×M16D3semidirect
73. C3×C5×M16D4semidirect
99. C2×#907D5semidirect
195. C2×ΓL(1,𝔽25)C2×D5semidirect
196. C2×D3×C8C2×D5semidirect
225. C5×M16#67semidirect
272. C2×C3×D5#131semidirect
300. C3×M16C22⋊D5semidirect
445. C2×D5#907semidirect
474. M16#1201semidirect
495. C3×C5#2933semidirect
568. C5#83757semidirect
591. C3#10615527semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9072
C2×C3×D5×M162
#117545632
#117512232
#117484362
#117483472
C2×#909552
#117477212
#117477112
#117477012
C8×#12012
#106155273
#837575