Finite Group Databasebeta

← #14412178

Subgroups — #14412178

Order 1920.

1512 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×#92017C211yesmaximal, characteristic
2#11756504C211yesmaximal, characteristic, complemented
3#11754130C211yesmaximal, characteristic, complemented
4C5×#5132C211yesmaximal, characteristic, complemented
5C2×C3×#3955C211yesmaximal, characteristic, complemented
6#11748355C211yesmaximal, characteristic, complemented
7C2×#90958C211yesmaximal, characteristic, complemented
8#11748238C214yesmaximal, complemented
9#11748224C214yesmaximal, complemented
10#10610445—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C2×D5×#67C414yes—
15#92017—22no—
16#92017—22no—
17#92017—22no—
18#92017—22no—
19C2×#6777C2212yes—
20C2×D3×D20C412yes—
21C2×#6766C2212yes—
22C2×#6765C412yes—
23C2×C3×C5×M16C2211yescharacteristic, complemented
24C2×#6710C2211yescharacteristic, complemented
25#91796—22no—
26M16×D15C2214yescomplemented
27#91790—22no—
28C2×C5×#208C2211yescharacteristic, complemented
29C2×C3×#681C2211yescharacteristic, complemented
30#91292C2214yescomplemented
31#91291—22no—
32#91290—22no—
33C5×#824C2212yescomplemented
34C5×#823C2212yescomplemented
35C3×#3955C2214yescomplemented
36#90962C2212yescomplemented
37#90959C2212yescomplemented
38#90958C2214yescomplemented
39#78697—51nomaximal, Hall
40C2×#4149—31no—
41#66079—31no—
42#66079—31no—
43C5×#413—31no—
44#65526—31no—
45C2×#3955—31no—
46C2×#3955D311yescharacteristic, complemented
47#65040—34no—
48D5×#100—34no—
49C23×C3×D5C2×C412yes—
50C22×D3×D5C2×C414yes—
51C22×C3×C4×C5C2311yescharacteristic
52C2×#1220C2×C412yes—
53#6817D412yes—
54#6817D412yes—
55#6817D412yes—
56#6817D412yes—
57C2×D60C2×C411yescharacteristic
58C2×C4×D15C2312yes—
59C2×Dic30C2×C411yescharacteristic
60C2×C5×#67C2×C412yes—
61C5×#235—21no—
62C5×#235—21no—
63C5×#235—21no—
64C5×#235—21no—
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3C2×C412yes—
67C2×C5×Dic6C2311yescharacteristic
68C2×C3×D20—21no—
69C2×C3×D20—21no—
70C2×C3×D20—21no—
71C2×C3×D20—21no—
72C2×C3×D20C2×C412yes—
73C2×C3×D20C2312yes—
74D5×#67—28no—
75D5×#67—28no—
76C2×#1202C2×C414yes—
77C2×#1201C2×C414yes—
78C2×D5×Dic3C2×C414yes—
79#6777—24no—
80#6777—24no—
81D3×D20—24no—
82D3×D20—24no—
83#6766—24no—
84#6766—24no—
85#6765—24no—
86#6765—24no—
87C3×C5×M16—21no—
88C3×C5×M16C2312yes—
89C2×C3×C5×C8—21no—
90#6710—21no—
91#6710C2312yes—
92C2×C3⋊#168—21no—
93#6705—24no—
94C8×D15—24no—
95C5×#208—21no—
96C5×#208C2312yes—
97C2×C5×C3⋊C8—21no—
98C3×#681—21no—
99C3×#681C2312yes—
100C2×C3×#168—21no—
101#6651—24no—
102#6648—24no—
103C2×#1004—51no—
104#5745—51no—
105#5745—51no—
106C2×C3×#100—51no—
107C2×#833—51no—
108#5132—51no—
109#5132D511yescharacteristic, complemented
110#4745—54no—
111D3×#100—54no—
112C2×C5×#41—31no—
113#4149—62no—
114#4149—62no—
115#4149—62no—
116#4149—62no—
117C2×#713—32no—
118C2×D4×D5—34no—
119C2×D4×D5—32no—
120C2×#709—31no—
121C2×#709—32no—
122C22×D20—32no—
123C22×D20C2×D311yescharacteristic
124C2×C5×M16—31no—
125C2×C5×M16C2×D311yescharacteristic, complemented
126C2×#681—31no—
127C2×#681C2×D311yescharacteristic, complemented
128#4053—62no—
129#4053—62no—
130D5×M16—34no—
131D5×M16—34no—
132#4047—62no—
133#4047—62no—
134C5×#101—32no—
135C5×#100—32no—
136#3968—32no—
137#3965—32no—
138#3955—34no—
139#3955C2×D314yescomplemented
140#2888—151noSylow
141C23×C3×C5C22×C411yescharacteristic
142C22×D15C22×C412yes—
143C22×C5×D3C22×C412yes—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—82no—
147C22×C3×D5C22×C414yes—
148C2×D3×D5—28no—
149C2×D3×D5—84no—
150C2×C3×C4×C5C22×C411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2411yescharacteristic
156#1220C22⋊C414yes—
157#1220C22⋊C414yes—
158C2×Dic15C22×C412yes—
159D60C22⋊C412yes—
160D60C22⋊C412yes—
161C4×D15C2×D414yes—
162C4×D15C2×D414yes—
163Dic30C22⋊C412yes—
164Dic30C22⋊C412yes—
165C5×#67—22no—
166C5×#67—22no—
167C2×C5×Dic3C22×C412yes—
168C5×D12—21no—
169C5×D12—21no—
170C4×C5×D3—22no—
171C4×C5×D3—22no—
172C5×Dic6—21no—
173C5×Dic6—21no—
174C3×D20—22no—
175C3×D20—22no—
176C3×D20—22no—
177C3×D20—22no—
178#1202—28no—
179#1201—28no—
180D5×Dic3—28no—
181C3×C5×C8—22no—
182C3⋊#168—22no—
183C3×#168—22no—
184C5×C3⋊C8—22no—
185C22×C3×D4—51no—
186C22×#67—54no—
187#1004—102no—
188#1004—102no—
189#1004—102no—
190#1004—102no—
191C2×#237—52no—
192C2×#237—52no—
193C2×D3×D4—52no—
194C2×D3×D4—52no—
195C2×#235—51no—
196C2×#235C2×D511yescharacteristic
197C2×C3×M16—51no—
198C2×C3×M16C2×D511yescharacteristic, complemented
199C2×#208—51no—
200C2×#208C2×D511yescharacteristic, complemented
201#907—102no—
202#907—102no—
203D3×M16—54no—
204D3×M16—54no—
205#901—102no—
206#901—102no—
207C3×#100—54no—
208#833—54no—
209#824—52no—
210#824C2×D512yescomplemented
211#823—52no—
212#823C2×D512yescomplemented
213C23×D5—34no—
214C23×D5C4×D312yes—
215C5×#41—61no—
216C5×#41—61no—
217C5×#41—61no—
218C5×#41—61no—
219C2×C5×Q8—31no—
220C2×C5×D4—32no—
221C2×C5×D4—31no—
222C22×C4×C5—32no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—32no—
225C2×C22⋊D5—34no—
226#713—64no—
227#713—64no—
228D4×D5—64no—
229D4×D5—64no—
230D4×D5—68no—
231D4×D5—68no—
232#709—32no—
233#709—32no—
234#709—32no—
235#709—32no—
236#709—64no—
237#709—64no—
238C2×D20—21no—
239C2×D20—21no—
240C2×D20—21no—
241C2×D20—21no—
242C2×D20—31no—
243C2×D20—34no—
244C2×D20—64no—
245C2×D20—64no—
246C2×D20C4×D312yes—
247C2×D20C22×D312yes—
248C2×C4×D5—32no—
249C2×C4×D5—34no—
250C2×Dic10—31no—
251C5×M16—21no—
252C5×M16—32no—
253C5×M16—61no—
254C5×M16C22×D312yes—
255C2×C5×C8—21no—
256C2×C5×C8—61no—
257#681—21no—
258#681—32no—
259#681—61no—
260#681C22×D312yes—
261C2×#168—21no—
262C2×#168—61no—
263#676—64no—
264#676—64no—
265C8×D5—64no—
266C8×D5—64no—
267C2×H(5,𝔽2)—151no—
268#568—151no—
269#568—151no—
270#413—31no—
271#413—154no—
272#413—151no—
273C2×#100—51no—
274C2×#100—154no—
275C2×#100—151no—
276C22×C3×C5—41no—
277C22×C3×C5C2×C22⋊C411yescharacteristic
278C22×C3×C5C2×C22⋊C411yescharacteristic
279C22×C3×C5C23×C411yescharacteristic
280C2×D15—42no—
281C2×D15C2×C22⋊C414yes—
282C2×C5×D3—22no—
283C2×C5×D3—42no—
284C2×C3×D5—24no—
285C2×C3×D5—44no—
286C2×C3×D5—82no—
287C2×C3×D5—82no—
288D3×D5—88no—
289C3×C4×C5C2×C22⋊C411yescharacteristic
290C3×C4×C5C2×C22⋊C411yescharacteristic
291C3×C4×C5C22×D411yescharacteristic
292C3×C4×C5C22×D411yescharacteristic
293Dic15C2×C22⋊C414yes—
294C5×Dic3—22no—
295C24×C3—52no—
296C23×D3—54no—
297C2×C3×D4—52no—
298C2×C3×D4—52no—
299C2×C3×D4—101no—
300C2×C3×D4—101no—
301C2×C3×D4—101no—
302C2×C3×D4—101no—
303C22×C3×C4C22×D511yescharacteristic
304C2×#67—52no—
305C2×#67—54no—
306C2×#67—54no—
307C2×#67—108no—
308C2×#67—108no—
309C2×#67C4×D512yes—
310C22×Dic3—54no—
311#237—104no—
312#237—104no—
313#237—104no—
314#237—104no—
315D3×D4—104no—
316D3×D4—104no—
317D3×D4—104no—
318D3×D4—104no—
319#235—21no—
320#235—21no—
321#235—21no—
322#235—21no—
323#235—52no—
324#235—52no—
325#235—52no—
326#235—52no—
327C2×D12—51no—
328C2×D12C22×D511yescharacteristic
329C2×C4×D3—52no—
330C2×C4×D3C4×D512yes—
331C2×Dic6—51no—
332C2×Dic6C22×D511yescharacteristic
333C3×M16—21no—
334C3×M16—52no—
335C3×M16—101no—
336C3×M16C22×D512yes—
337C2×C3×C8—21no—
338C2×C3×C8—101no—
339#208—21no—
340#208—52no—
341#208—101no—
342#208C22×D512yes—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—101no—
345ΓL(1,𝔽25)—104no—
346ΓL(1,𝔽25)—104no—
347D3×C8—104no—
348D3×C8—104no—
349C23×C5—32no—
350C23×C5C2×C4×D311yescharacteristic
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—32no—
354C22×D5—68no—
355C22×D5—82no—
356C22×D5—244no—
357C22×D5C2×C4×D314yes—
358C5×Q8—61no—
359C5×Q8—61no—
360C5×D4—62no—
361C5×D4—62no—
362C5×D4—61no—
363C5×D4—61no—
364C2×C4×C5—32no—
365C2×C4×C5—62no—
366C2×C4×C5—62no—
367C2×C4×C5C2×C4×D311yescharacteristic
368C2×C4×C5D3×D411yescharacteristic
369C2×C4×C5D3×D411yescharacteristic
370C2×C4×C5D3×D411yescharacteristic
371C2×C4×C5D3×D411yescharacteristic
372C2×C4×C5C23×D311yescharacteristic
373C22⋊D5—34no—
374C22⋊D5—34no—
375C22⋊D5—68no—
376C2×Dic5—32no—
377D20—22no—
378D20—22no—
379D20—22no—
380D20—22no—
381D20—32no—
382D20—32no—
383D20—68no—
384C4×D5—34no—
385C4×D5—34no—
386C4×D5—68no—
387Dic10—32no—
388Dic10—32no—
389C5×C8—22no—
390C5×C8—62no—
391#168—22no—
392#168—62no—
393H(5,𝔽2)—302no—
394H(5,𝔽2)—302no—
395H(5,𝔽2)—302no—
396H(5,𝔽2)—302no—
397C2×#41—31no—
398C2×#41—152no—
399C2×#41—152no—
400C2×#41—151no—
401C22×D4—51no—
402C22×D4—152no—
403C22×D4—152no—
404C22×D4—154no—
405#131—302no—
406#131—302no—
407#131—302no—
408#131—302no—
409C2×M16—31no—
410C2×M16—51no—
411C2×M16—154no—
412C2×M16—151no—
413C2×M16—154no—
414C2×M16D3×D511yescharacteristic, complemented
415#101—32no—
416#101—152no—
417#100—32no—
418#100—54no—
419#100—154no—
420#100—152no—
421C2×C3×C5—21no—
422C2×C3×C5—21no—
423C2×C3×C5—21no—
424C2×C3×C5C22×C22⋊C411yescharacteristic
425D15—24no—
426C3×D5—44no—
427C5×D3—42no—
428C23×C3—54no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3—402no—
432C23×C3C2×C4×D511yescharacteristic
433C22×D3—52no—
434C22×D3—108no—
435C22×D3—404no—
436C22×D3C2×C4×D512yes—
437C3×D4—102no—
438C3×D4—102no—
439C3×D4—102no—
440C3×D4—102no—
441C2×C3×C4C2×C4×D511yescharacteristic
442C2×C3×C4D4×D511yescharacteristic
443C2×C3×C4D4×D511yescharacteristic
444C2×C3×C4D4×D511yescharacteristic
445C2×C3×C4D4×D511yescharacteristic
446C2×C3×C4C23×D511yescharacteristic
447#67—22no—
448#67—22no—
449#67—54no—
450#67—54no—
451#67—108no—
452#67—108no—
453C2×Dic3—52no—
454C2×Dic3—108no—
455C2×Dic3C2×C4×D512yes—
456D12—21no—
457D12—21no—
458D12—52no—
459D12—52no—
460C4×D3—22no—
461C4×D3—22no—
462C4×D3—54no—
463C4×D3—54no—
464Dic6—21no—
465Dic6—21no—
466Dic6—52no—
467Dic6—52no—
468C3×C8—22no—
469C3×C8—102no—
470C3⋊C8—22no—
471C3⋊C8—102no—
472C22×C5—41no—
473C22×C5—62no—
474C22×C5—122no—
475C22×C5D3×C22⋊C411yescharacteristic
476C22×C5D3×C22⋊C411yescharacteristic
477C22×C5C22×C4×D311yescharacteristic
478C2×D5—24no—
479C2×D5—34no—
480C2×D5—44no—
481C2×D5—82no—
482C2×D5—82no—
483C2×D5—122no—
484C2×D5—248no—
485C4×C5—62no—
486C4×C5D3×C22⋊C411yescharacteristic
487C4×C5D3×C22⋊C411yescharacteristic
488C4×C5C2×D3×D411yescharacteristic
489C4×C5C2×D3×D411yescharacteristic
490Dic5—34no—
491C24—52no—
492C24—154no—
493#41—61no—
494#41—61no—
495#41—61no—
496#41—61no—
497#41—152no—
498#41—152no—
499#41—152no—
500#41—152no—
501#41—304no—
502#41—304no—
503#41—304no—
504#41—304no—
505C2×Q8—31no—
506C2×Q8—151no—
507C2×D4—32no—
508C2×D4—31no—
509C2×D4—52no—
510C2×D4—52no—
511C2×D4—101no—
512C2×D4—101no—
513C2×D4—101no—
514C2×D4—101no—
515C2×D4—154no—
516C2×D4—152no—
517C2×D4—154no—
518C2×D4—151no—
519C2×D4—304no—
520C2×D4—304no—
521C2×D4—304no—
522C2×D4—304no—
523C2×D4—308no—
524C2×D4—308no—
525C22×C4—32no—
526C22×C4—154no—
527C22×C4—152no—
528C22×C4C2×D3×D511yescharacteristic
529M16—21no—
530M16—32no—
531M16—52no—
532M16—61no—
533M16—101no—
534M16—152no—
535M16—304no—
536M16—304no—
537M16—301no—
538M16C2×D3×D512yes—
539C2×C8—21no—
540C2×C8—61no—
541C2×C8—101no—
542C2×C8—304no—
543C2×C8—304no—
544C2×C8—301no—
545C3×C5#288811yescharacteristic, complemented, Hall
546C22×C3—41no—
547C22×C3—104no—
548C22×C3—204no—
549C22×C3—402no—
550C22×C3—402no—
551C22×C3D5×C22⋊C411yescharacteristic
552C22×C3D5×C22⋊C411yescharacteristic
553C22×C3C22×C4×D511yescharacteristic
554C2×D3—22no—
555C2×D3—42no—
556C2×D3—54no—
557C2×D3—202no—
558C2×D3—408no—
559C3×C4D5×C22⋊C411yescharacteristic
560C3×C4D5×C22⋊C411yescharacteristic
561C3×C4C2×D4×D511yescharacteristic
562C3×C4C2×D4×D511yescharacteristic
563Dic3—22no—
564Dic3—54no—
565C2×C5—21no—
566C2×C5—21no—
567C2×C5—21no—
568C2×C5—122no—
569C2×C5C2×D3×C22⋊C411yescharacteristic
570D5—44no—
571D5—64no—
572C23—32no—
573C23—54no—
574C23—102no—
575C23—102no—
576C23—152no—
577C23—308no—
578C23—402no—
579C23—1204no—
580C23C4×D3×D511yescharacteristic
581Q8—61no—
582Q8—61no—
583Q8—152no—
584Q8—152no—
585D4—62no—
586D4—62no—
587D4—61no—
588D4—61no—
589D4—102no—
590D4—102no—
591D4—102no—
592D4—102no—
593D4—154no—
594D4—154no—
595D4—152no—
596D4—152no—
597D4—308no—
598D4—308no—
599C2×C4—32no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—152no—
603C2×C4—154no—
604C2×C4—154no—
605C2×C4—308no—
606C2×C4C4×D3×D511yescharacteristic
607C2×C4#677711yescharacteristic
608C2×C4#677711yescharacteristic
609C2×C4#679011yescharacteristic
610C2×C4#679011yescharacteristic
611C2×C4C22×D3×D511yescharacteristic
612C8—22no—
613C8—62no—
614C8—102no—
615C8—302no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—204no—
620C2×C3C2×D5×C22⋊C411yescharacteristic
621D3—42no—
622D3—104no—
623C5#7869711yescharacteristic, complemented, Sylow
624C22—41no—
625C22—62no—
626C22—104no—
627C22—122no—
628C22—154no—
629C22—204no—
630C22—402no—
631C22—402no—
632C22—602no—
633C22—1208no—
634C22#9147311yescharacteristic
635C22#9147311yescharacteristic
636C22C2×C4×D3×D511yescharacteristic
637C4—62no—
638C4—154no—
639C4#9147311yescharacteristic
640C4#9147311yescharacteristic
641C4C2×#677711yescharacteristic
642C4C2×#679011yescharacteristic
643C3#1061044511yescharacteristic, complemented, Sylow
644C2—21no—
645C2—21no—
646C2—21no—
647C2—122no—
648C2—204no—
649C2—304no—
650C2C2×#9147311yescharacteristic
subgroupG/H
centerC2C2×#91473
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92017C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2888
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11756504C2semidirect
3. #11754130C2semidirect
4. C5×#5132C2semidirect
5. C2×C3×#3955C2semidirect
6. #11748355C2semidirect
7. C2×#90958C2semidirect
8. #11748238C2semidirect
9. #11748224C2semidirect
23. C2×C3×C5×M16C22semidirect
24. C2×#6710C22semidirect
26. M16×D15C22semidirect
28. C2×C5×#208C22semidirect
29. C2×C3×#681C22semidirect
30. #91292C22semidirect
33. C5×#824C22semidirect
34. C5×#823C22semidirect
35. C3×#3955C22semidirect
36. #90962C22semidirect
37. #90959C22semidirect
38. #90958C22semidirect
46. C2×#3955D3semidirect
109. #5132D5semidirect
125. C2×C5×M16C2×D3semidirect
127. C2×#681C2×D3semidirect
139. #3955C2×D3semidirect
198. C2×C3×M16C2×D5semidirect
200. C2×#208C2×D5semidirect
210. #824C2×D5semidirect
212. #823C2×D5semidirect
414. C2×M16D3×D5semidirect
545. C3×C5#2888semidirect
623. C5#78697semidirect
643. C3#10610445semidirect

Maximal subgroups

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

subgroupindex
C2×#920172
#117565042
#117541302
C5×#51322
C2×C3×#39552
#117483552
C2×#909582
#117482382
#117482242
#106104453
#786975