Finite Group Databasebeta

← #14412666

Subgroups — #14412666

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92019C211yesmaximal, characteristic
2C2×C3×#4047C211yesmaximal, characteristic, complemented
3#11754509C211yesmaximal, characteristic, complemented
4C2×#91105C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic, complemented
6#11748396C211yesmaximal, characteristic, complemented
7#11748390C211yesmaximal, characteristic, complemented
8#11748105C212yesmaximal, complemented
9D5×#821C212yesmaximal, complemented
10#11747642C212yesmaximal, complemented
11#11747606C212yesmaximal, complemented
12#10610562—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C2×#6790—22no—
17#92019—24no—
18#92019C418yescomplemented
19C2×D3×D20—21no—
20C2×D5×D12C2212yes—
21C2×#6773C2212yes—
22C2×#6769—21no—
23C22×C3×C5×C8C2211yescharacteristic, complemented
24C2×C4⋊Dic15C2211yescharacteristic, complemented
25C5×#926C2211yescharacteristic, complemented
26C2×C3×#681C2211yescharacteristic, complemented
27C3×#4047—24no—
28C2×C3×#676C2212yescomplemented
29C2×C3×C8×D5C2212yescomplemented
30#91559—22no—
31Dic3×D20—21no—
32D5×C4⋊Dic3C2212yescomplemented
33#91358C2212yescomplemented
34Dic3×Dic10—21no—
35#91105C2212yescomplemented
36#91105C2212yescomplemented
37C5×#821C2211yescharacteristic, complemented
38C5×#821C2211yescharacteristic, complemented
39C5×#816C2211yescharacteristic, complemented
40C5×#816C2211yescharacteristic, complemented
41#90973C2212yescomplemented
42#90969C2212yescomplemented
43#90969C2212yescomplemented
44#90967C2212yescomplemented
45#83797—51nomaximal, Hall
46C2×#4149—31no—
47C2×#4047D311yescharacteristic, complemented
48#65857—31no—
49C5×#416—31no—
50#65521—31no—
51C2×#3953—31no—
52#65290—31no—
53#65093—32no—
54#65092—32no—
55#65059—32no—
56D5×#102—32no—
57C23×D15—21no—
58C22×D3×D5—22no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×Dic15—21no—
61C2×D60—21no—
62C2×D60—22no—
63C2×D60C2×C414yescomplemented
64C2×D60C2312yes—
65C2×C5×#67—21no—
66C5×#235—22no—
67C5×#235C2×C414yescomplemented
68C2×C5×D12C2311yescharacteristic
69C2×C4×C5×D3—21no—
70C2×C5×Dic6C2311yescharacteristic
71C2×C3×C22⋊D5D412yes—
72C3×#709C2×C414yes—
73C3×#709D414yes—
74C2×C3×D20D411yescharacteristic
75C2×C3×C4×D5C2312yes—
76C2×C3×Dic10D411yescharacteristic
77#6790—216no—
78C2×#1203—22no—
79C2×#1202—22no—
80C2×#1200—22no—
81C2×D5×Dic3—22no—
82D3×D20—28no—
83D5×D12—24no—
84D5×D12C2×C418yescomplemented
85#6773—24no—
86#6773C2×C418yescomplemented
87#6769—28no—
88C2×C3×C5×C8—22no—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C4⋊Dic15—21no—
92C4⋊Dic15C2312yes—
93C5×#217—21no—
94C5×C4⋊Dic3C2311yescharacteristic
95C5×C4⋊Dic3C2311yescharacteristic
96C4×C5×Dic3—21no—
97C3×#681—22no—
98C2×C3×#168C2312yes—
99C3×#676—24no—
100C3×C8×D5—24no—
101#6668—22no—
102#6665—22no—
103Dic3×Dic5—22no—
104C2×#1009—51no—
105C2×C3×#131—51no—
106#5827—51no—
107#5133—51no—
108#5133—52no—
109#5131—51no—
110#5131—52no—
111#5113—52no—
112#5113D511yescharacteristic, complemented
113C2×#821—51no—
114C2×#821—52no—
115C2×C5×#41—31no—
116#4149—38no—
117#4149—64no—
118C2×#713—32no—
119C2×D4×D5—32no—
120C2×D4×D5—62no—
121C2×#709—61no—
122C2×#709C2×D311yescharacteristic
123C22×D20—31no—
124C22×D20—61no—
125C22×C5×C8C2×D311yescharacteristic, complemented
126C5×#117—31no—
127C2×C4⋊Dic5—31no—
128C2×#681C2×D311yescharacteristic, complemented
129#4047—24no—
130C2×#676C2×D312yescomplemented
131C2×C8×D5C2×D312yescomplemented
132#4038—32no—
133D5×C4⋊C4—32no—
134#4027—62no—
135C4×D20—61no—
136C4×Dic10—61no—
137C5×#103—31no—
138C5×#103—31no—
139C5×#102—31no—
140C5×#102—31no—
141#3967—32no—
142#3964—32no—
143#3953—32no—
144#3953—32no—
145#3941—32no—
146#3941—32no—
147#2897—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—22no—
150C22×D15—24no—
151C22×D15—81no—
152C22×D15—81no—
153C22×C5×D3—21no—
154C22×C3×D5C2×D412yes—
155C2×D3×D5—28no—
156C2×D3×D5—82no—
157C2×D3×D5—82no—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5C2411yescharacteristic
162C2×Dic15—22no—
163C2×Dic15—81no—
164D60—24no—
165D60—22no—
166D60C22×C414yes—
167C5×#67—24no—
168C2×C5×Dic3—21no—
169C2×C5×Dic3—21no—
170C2×C5×Dic3—21no—
171C5×D12—21no—
172C5×D12C22×C412yes—
173C4×C5×D3—24no—
174C5×Dic6—21no—
175C5×Dic6C22×C412yes—
176C3×C22⋊D5C22⋊C418yes—
177C2×C3×Dic5C2×D412yes—
178C3×D20C22⋊C414yes—
179C3×C4×D5C22×C414yes—
180C3×C4×D5C2×D414yes—
181C3×Dic10C22⋊C414yes—
182#1203—28no—
183#1202—28no—
184#1200—28no—
185D5×Dic3—82no—
186C3×C5×C8—21no—
187C3×C5×C8—21no—
188C3×#168—22no—
189C2×C3×#41—51no—
190#1009—58no—
191#1009—104no—
192C2×#239—101no—
193C2×D3×D4—101no—
194C2×D3×D4—102no—
195C2×#235—52no—
196C2×#235C2×D511yescharacteristic
197C22×D12—51no—
198C22×D12—52no—
199C3×#131—104no—
200C2×C3×M16—51no—
201C2×C3×M16—52no—
202C22×C3×C8—52no—
203C22×C3×C8C2×D511yescharacteristic, complemented
204Q8×Dic3—101no—
205D4×Dic3—101no—
206D4×Dic3—102no—
207#926—52no—
208#926C2×D511yescharacteristic, complemented
209C2×C4⋊Dic3—51no—
210C2×C4⋊Dic3—52no—
211#821—52no—
212#821—52no—
213#821—52no—
214#821—52no—
215#821—52no—
216#821C2×D511yescharacteristic, complemented
217#821C2×D511yescharacteristic, complemented
218#816—52no—
219#816C2×D511yescharacteristic, complemented
220#816C2×D511yescharacteristic, complemented
221C23×D5—61no—
222C23×D5—62no—
223C5×#41—34no—
224C5×#41—62no—
225C2×C5×Q8—31no—
226C2×C5×D4—31no—
227C2×C5×D4—61no—
228C22×C4×C5—61no—
229C22×C4×C5C22×D311yescharacteristic
230C2×C22⋊D5—62no—
231C2×C22⋊D5D1212yes—
232C22×Dic5—61no—
233#713—38no—
234#713—64no—
235D4×D5—38no—
236D4×D5—616no—
237D4×D5—64no—
238#709—68no—
239#709C4×D314yes—
240#709#6714yes—
241C2×D20—34no—
242C2×D20—32no—
243C2×D20—62no—
244C2×D20—61no—
245C2×D20—62no—
246C2×D20—68no—
247C2×D20D1211yescharacteristic
248C2×C4×D5—62no—
249C2×C4×D5—62no—
250C2×C4×D5C22×D312yes—
251C2×Dic10D1211yescharacteristic
252C2×C5×C8—22no—
253C2×C5×C8C22×D311yescharacteristic
254C2×C5×C8C22×D311yescharacteristic
255C5×C4⋊C4—31no—
256C5×C4⋊C4—31no—
257C5×C22⋊C4—61no—
258C42×C5—61no—
259#685—62no—
260C4⋊Dic5—32no—
261C4⋊Dic5—61no—
262#683—62no—
263C4×Dic5—62no—
264#681—22no—
265C2×#168C22×D312yes—
266#676—24no—
267C8×D5—24no—
268C2×H(5,𝔽2)—151no—
269C2×#131—51no—
270#520—151no—
271#418—152no—
272#418—151no—
273#417—152no—
274#417—151no—
275#416—31no—
276#416—152no—
277C2×#102—152no—
278C2×#102—151no—
279C22×C3×C5—21no—
280C22×C3×C5—21no—
281C22×C3×C5C2×C22⋊C412yes—
282C22×C3×C5C22×D411yescharacteristic
283C2×D15—24no—
284C2×D15—42no—
285C2×D15—42no—
286C2×D15—84no—
287C2×C5×D3—22no—
288C2×C5×D3—41no—
289C2×C5×D3—41no—
290C2×C3×D5—22no—
291C2×C3×D5—22no—
292C2×C3×D5C2×C22⋊C414yes—
293D3×D5—88no—
294C3×C4×C5C2×C22⋊C412yes—
295C3×C4×C5C23×C411yescharacteristic
296C3×C4×C5C22×D411yescharacteristic
297Dic15—42no—
298C3×Dic5C2×C22⋊C414yes—
299C5×Dic3—22no—
300C5×Dic3—41no—
301C5×Dic3—41no—
302C23×D3—102no—
303C23×D3—101no—
304C3×#41—54no—
305C3×#41—54no—
306C2×C3×Q8—51no—
307C2×C3×D4—52no—
308C2×C3×D4—51no—
309C22×C3×C4—52no—
310C22×C3×C4C22×D511yescharacteristic
311C2×#67—21no—
312C2×#67—102no—
313C22×Dic3—102no—
314C22×Dic3—101no—
315#239—108no—
316D3×D4—108no—
317D3×D4—1016no—
318#235—22no—
319#235—58no—
320#235—104no—
321#235C4×D514yescomplemented
322C2×D12—54no—
323C2×D12—52no—
324C2×D12—58no—
325C2×D12—104no—
326C2×D12—102no—
327C2×D12—101no—
328C2×D12—102no—
329C2×D12C22×D511yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—102no—
332C2×Dic6C22×D511yescharacteristic
333C3×M16—104no—
334C3×M16—102no—
335C2×C3×C8—22no—
336C2×C3×C8—52no—
337C2×C3×C8—104no—
338C2×C3×C8C22×D511yescharacteristic
339C2×C3×C8C22×D511yescharacteristic
340#217—21no—
341#217—102no—
342C4⋊Dic3—52no—
343C4⋊Dic3—102no—
344C4⋊Dic3—101no—
345C4⋊Dic3C22×D511yescharacteristic
346C4⋊Dic3C22×D511yescharacteristic
347C4×Dic3—21no—
348C4×Dic3—102no—
349C23×C5—61no—
350C23×C5C2×D1211yescharacteristic
351C22×D5—62no—
352C22×D5—64no—
353C22×D5—68no—
354C22×D5—242no—
355C22×D5—242no—
356C22×D5—241no—
357C22×D5—241no—
358C22×D5C2×D1212yes—
359C5×Q8—32no—
360C5×Q8—61no—
361C5×D4—32no—
362C5×D4—64no—
363C5×D4—61no—
364C2×C4×C5—61no—
365C2×C4×C5—64no—
366C2×C4×C5—61no—
367C2×C4×C5—61no—
368C2×C4×C5C2×C4×D312yes—
369C2×C4×C5C2×D1211yescharacteristic
370C2×C4×C5C2×#6712yes—
371C2×C4×C5C23×D311yescharacteristic
372C22⋊D5—68no—
373C22⋊D5(C2×D3)⋊C418yes—
374C2×Dic5—62no—
375C2×Dic5—241no—
376C2×Dic5C2×D1212yes—
377D20—34no—
378D20—68no—
379D20—64no—
380D20—62no—
381D20(C2×D3)⋊C414yes—
382C4×D5—68no—
383C4×D5—242no—
384C4×D5C2×C4×D314yes—
385C4×D5C2×#6714yes—
386Dic10(C2×D3)⋊C414yes—
387C5×C8—21no—
388C5×C8—21no—
389#168—22no—
390H(5,𝔽2)—158no—
391H(5,𝔽2)—304no—
392C2×#41—31no—
393C2×#41—51no—
394C2×#41—152no—
395C2×#41—301no—
396C22×D4—152no—
397C22×D4—151no—
398C22×D4—301no—
399C22×D4—302no—
400#131—104no—
401C2×M16—51no—
402C2×M16—52no—
403C22×C8—52no—
404C22×C8D3×D511yescharacteristic, complemented
405C4×Q8—301no—
406C4×D4—301no—
407C4×D4—302no—
408#117—31no—
409#117—152no—
410C2×C4⋊C4—152no—
411C2×C4⋊C4—151no—
412#103—31no—
413#103—31no—
414#103—152no—
415#102—31no—
416#102—31no—
417#102—152no—
418#102—152no—
419#102—152no—
420#102—152no—
421#102—152no—
422C2×C3×C5—22no—
423C2×C3×C5C22×C22⋊C411yescharacteristic
424C2×C3×C5#57611yescharacteristic
425C2×C3×C5#57711yescharacteristic
426D15—44no—
427C3×D5—24no—
428C5×D3—42no—
429C23×C3—52no—
430C23×C3D4×D511yescharacteristic
431C22×D3—21no—
432C22×D3—108no—
433C22×D3—102no—
434C22×D3—104no—
435C22×D3—402no—
436C22×D3—402no—
437C22×D3—401no—
438C22×D3—401no—
439C3×Q8—54no—
440C3×D4—58no—
441C3×D4—54no—
442C2×C3×C4—52no—
443C2×C3×C4—54no—
444C2×C3×C4—54no—
445C2×C3×C4C2×C4×D512yes—
446C2×C3×C4D4×D511yescharacteristic
447C2×C3×C4D4×D512yes—
448C2×C3×C4C23×D511yescharacteristic
449#67—24no—
450#67—108no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—102no—
455C2×Dic3—402no—
456C2×Dic3—401no—
457D12—21no—
458D12—54no—
459D12—108no—
460D12—102no—
461D12—104no—
462D12C2×C4×D512yes—
463C4×D3—24no—
464C4×D3—108no—
465Dic6—21no—
466Dic6C2×C4×D512yes—
467C3×C8—21no—
468C3×C8—21no—
469C3×C8—102no—
470C22×C5—21no—
471C22×C5—21no—
472C22×C5—62no—
473C22×C5—121no—
474C22×C5—121no—
475C22×C5C2×(C2×D3)⋊C412yes—
476C22×C5C22×D1211yescharacteristic
477C2×D5—22no—
478C2×D5—22no—
479C2×D5—64no—
480C2×D5—122no—
481C2×D5—122no—
482C2×D5—248no—
483C2×D5—244no—
484C2×D5C2×(C2×D3)⋊C414yes—
485C4×C5—62no—
486C4×C5—121no—
487C4×C5—121no—
488C4×C5C2×(C2×D3)⋊C412yes—
489C4×C5C22×C4×D311yescharacteristic
490C4×C5C22×#6711yescharacteristic
491Dic5—122no—
492Dic5C2×(C2×D3)⋊C414yes—
493C24—302no—
494C24—301no—
495#41—34no—
496#41—54no—
497#41—54no—
498#41—62no—
499#41—158no—
500#41—304no—
501#41—308no—
502C2×Q8—31no—
503C2×Q8—51no—
504C2×D4—31no—
505C2×D4—52no—
506C2×D4—51no—
507C2×D4—61no—
508C2×D4—158no—
509C2×D4—154no—
510C2×D4—152no—
511C2×D4—304no—
512C2×D4—302no—
513C2×D4—308no—
514C2×D4—302no—
515C2×D4—3016no—
516C2×D4—301no—
517C2×D4—302no—
518C22×C4—52no—
519C22×C4—61no—
520C22×C4—302no—
521C22×C4—302no—
522C22×C4—301no—
523C22×C4C2×D3×D511yescharacteristic
524M16—104no—
525M16—102no—
526C2×C8—22no—
527C2×C8—52no—
528C2×C8—104no—
529C2×C8C2×D3×D511yescharacteristic
530C2×C8C2×D3×D511yescharacteristic
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—152no—
534C4⋊C4—302no—
535C4⋊C4—301no—
536C22⋊C4—61no—
537C22⋊C4—302no—
538C42—61no—
539C42—302no—
540C3×C5#289711yescharacteristic, complemented, Hall
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—54no—
544C22×C3—102no—
545C22×C3—102no—
546C22×C3D5×C22⋊C412yes—
547C22×C3C2×D4×D511yescharacteristic
548C2×D3—22no—
549C2×D3—41no—
550C2×D3—41no—
551C2×D3—104no—
552C2×D3—202no—
553C2×D3—202no—
554C2×D3—408no—
555C2×D3—404no—
556C3×C4—54no—
557C3×C4D5×C22⋊C412yes—
558C3×C4C22×C4×D511yescharacteristic
559C3×C4C2×D4×D511yescharacteristic
560Dic3—22no—
561Dic3—41no—
562Dic3—41no—
563Dic3—202no—
564C2×C5—22no—
565C2×C5—122no—
566C2×C5#575111yescharacteristic
567C2×C5#575211yescharacteristic
568C2×C5C22×(C2×D3)⋊C411yescharacteristic
569D5—24no—
570D5—124no—
571C23—52no—
572C23—61no—
573C23—308no—
574C23—302no—
575C23—304no—
576C23—1201no—
577C23—1201no—
578C23—1202no—
579C23—1202no—
580C23D5×D1211yescharacteristic
581Q8—32no—
582Q8—54no—
583Q8—61no—
584D4—32no—
585D4—58no—
586D4—54no—
587D4—64no—
588D4—61no—
589D4—154no—
590D4—308no—
591D4—308no—
592D4—304no—
593D4—302no—
594C2×C4—52no—
595C2×C4—54no—
596C2×C4—54no—
597C2×C4—61no—
598C2×C4—64no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—308no—
602C2×C4—302no—
603C2×C4—1202no—
604C2×C4—1201no—
605C2×C4C4×D3×D512yes—
606C2×C4D5×D1211yescharacteristic
607C2×C4D5×#6712yes—
608C2×C4C22×D3×D511yescharacteristic
609C8—21no—
610C8—21no—
611C8—102no—
612C2×C3—22no—
613C2×C3—104no—
614C2×C3C2×D5×C22⋊C411yescharacteristic
615C2×C3#6610311yescharacteristic
616C2×C3#6610411yescharacteristic
617D3—42no—
618D3—204no—
619C5#8379711yescharacteristic, complemented, Sylow
620C22—21no—
621C22—21no—
622C22—54no—
623C22—62no—
624C22—102no—
625C22—102no—
626C22—121no—
627C22—121no—
628C22—304no—
629C22—602no—
630C22—602no—
631C22—1204no—
632C22—1208no—
633C22D5×(C2×D3)⋊C412yes—
634C22C2×D5×D1211yescharacteristic
635C4—54no—
636C4—62no—
637C4—121no—
638C4—121no—
639C4—602no—
640C4D5×(C2×D3)⋊C412yes—
641C4C2×C4×D3×D511yescharacteristic
642C4C2×D5×#6711yescharacteristic
643C3#1061056211yescharacteristic, complemented, Sylow
644C2—22no—
645C2—104no—
646C2—122no—
647C2—604no—
648C2#1175396211yescharacteristic
649C2#1175396311yescharacteristic
650C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92019C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2897
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4047C2semidirect
3. #11754509C2semidirect
4. C2×#91105C2semidirect
5. C5×#5113C2semidirect
6. #11748396C2semidirect
7. #11748390C2semidirect
8. #11748105C2semidirect
9. D5×#821C2semidirect
10. #11747642C2semidirect
11. #11747606C2semidirect
18. #92019C4semidirect
23. C22×C3×C5×C8C22semidirect
24. C2×C4⋊Dic15C22semidirect
25. C5×#926C22semidirect
26. C2×C3×#681C22semidirect
28. C2×C3×#676C22semidirect
29. C2×C3×C8×D5C22semidirect
32. D5×C4⋊Dic3C22semidirect
33. #91358C22semidirect
35. #91105C22semidirect
36. #91105C22semidirect
37. C5×#821C22semidirect
38. C5×#821C22semidirect
39. C5×#816C22semidirect
40. C5×#816C22semidirect
41. #90973C22semidirect
42. #90969C22semidirect
43. #90969C22semidirect
44. #90967C22semidirect
47. C2×#4047D3semidirect
63. C2×D60C2×C4semidirect
67. C5×#235C2×C4semidirect
84. D5×D12C2×C4semidirect
86. #6773C2×C4semidirect
112. #5113D5semidirect
125. C22×C5×C8C2×D3semidirect
128. C2×#681C2×D3semidirect
130. C2×#676C2×D3semidirect
131. C2×C8×D5C2×D3semidirect
203. C22×C3×C8C2×D5semidirect
208. #926C2×D5semidirect
216. #821C2×D5semidirect
217. #821C2×D5semidirect
219. #816C2×D5semidirect
220. #816C2×D5semidirect
321. #235C4×D5semidirect
404. C22×C8D3×D5semidirect
540. C3×C5#2897semidirect
619. C5#83797semidirect
643. C3#10610562semidirect

Maximal subgroups

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

subgroupindex
C2×#920192
C2×C3×#40472
#117545092
C2×#911052
C5×#51132
#117483962
#117483902
#117481052
D5×#8212
#117476422
#117476062
#106105623
#837975