Finite Group Databasebeta

← #14411993

Subgroups — #14411993

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92017C211yesmaximal, characteristic
2C3×#65855C211yesmaximal, characteristic, complemented
3#11754488C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5C5×#5006C211yesmaximal, characteristic, complemented
6#11748626C211yesmaximal, characteristic, complemented
7#11748625C211yesmaximal, characteristic, complemented
8D5×#806C218yesmaximal, complemented
9#10610425—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C2×C5×#235C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13C2×D5×#67C2214yes—
14#92017—22no—
15#92017—22no—
16#92017—22no—
17#92017—22no—
18C2×#6777C412yescomplemented
19C2×D3×D20C412yescomplemented
20C2×#6766C412yescomplemented
21C2×#6765C412yescomplemented
22C3×C5×#117C2211yescharacteristic, complemented
23#91815C2211yescharacteristic, complemented
24C5×#926C2211yescharacteristic, complemented
25C3×#4072C2211yescharacteristic, complemented
26C3×#4039—22no—
27C3×D5×C22⋊C4C2214yescomplemented
28C3×C4×D20—22no—
29D5×#217C2214yescomplemented
30#91434—22no—
31Dic3×D20—22no—
32#91090C2214yescomplemented
33C5×#806C2214yescomplemented
34#90997C2214yescomplemented
35#90996C2214yescomplemented
36#82546—51nomaximal, Hall
37C2×#4149—31no—
38#65855—31no—
39#65855D311yescharacteristic, complemented
40C5×#410—31no—
41#65529—31no—
42#65295—31no—
43#65295—31no—
44D5×#99—38no—
45C23×C3×D5C2312yes—
46C22×D3×D5C2×C414yescomplemented
47C22×C3×C4×C5C2311yescharacteristic
48C2×#1220C2312yes—
49#6817—21no—
50#6817—21no—
51#6817—21no—
52#6817—21no—
53C2×D60C2×C411yescharacteristic, complemented
54C2×C4×D15C2×C412yescomplemented
55C2×Dic30C2×C411yescharacteristic, complemented
56C2×C5×#67C2312yes—
57C5×#235—21no—
58C5×#235—21no—
59C5×#235—21no—
60C5×#235—21no—
61C2×C5×D12C2×C411yescharacteristic, complemented
62C2×C4×C5×D3C2×C412yescomplemented
63C2×C5×Dic6C2×C411yescharacteristic, complemented
64C2×C3×D20C2×C412yes—
65C2×C3×D20C2×C412yes—
66C2×C3×D20D412yes—
67C2×C3×D20D412yes—
68C2×C3×D20D412yes—
69C2×C3×D20D412yes—
70C2×C3×C4×D5—24no—
71D5×#67—28no—
72D5×#67—28no—
73C2×#1202C2×C414yescomplemented
74C2×#1201C2×C414yescomplemented
75C2×D5×Dic3—24no—
76C2×D5×Dic3C2×C414yescomplemented
77#6777—24no—
78#6777—24no—
79D3×D20—24no—
80D3×D20—24no—
81#6766—24no—
82#6766—24no—
83#6765—24no—
84#6765—24no—
85C3×C5×C4⋊C4—21no—
86C3×C5×C22⋊C4C2312yes—
87C3×C42×C5—21no—
88#6719C2312yes—
89C4⋊Dic15—21no—
90C4×Dic15—21no—
91C5×#217C2312yes—
92C5×C4⋊Dic3—21no—
93C4×C5×Dic3—21no—
94C3×C22⋊Dic5C2312yes—
95C3×#685—24no—
96C3×C4⋊Dic5—21no—
97C3×C4×Dic5—21no—
98#6665—24no—
99C2×#1004—51no—
100C3×#518—51no—
101#5798—51no—
102#5006—51no—
103#5006—51no—
104#5006—51no—
105#5006D511yescharacteristic, complemented
106C2×#806—58no—
107C2×C5×#41—31no—
108#4149—62no—
109#4149—62no—
110#4149—62no—
111#4149—62no—
112C2×#713—32no—
113C2×D4×D5—34no—
114C2×D4×D5—32no—
115C2×#709—31no—
116C2×#709—32no—
117C22×D20—32no—
118C22×D20C2×D311yescharacteristic
119C5×#117—31no—
120C5×#117C2×D311yescharacteristic, complemented
121#4072—31no—
122#4072C2×D311yescharacteristic, complemented
123#4039—22no—
124#4039—62no—
125D5×C22⋊C4—34no—
126D5×C22⋊C4C2×D314yescomplemented
127C4×D20—22no—
128C4×D20—62no—
129C5×#99—34no—
130#3966—34no—
131#3938—34no—
132#3938—34no—
133#2883—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×D15C22×C412yes—
136C22×C5×D3C22×C412yes—
137C22×C3×D5—82no—
138C22×C3×D5C22×C414yes—
139C22×C3×D5C2×D414yes—
140C22×C3×D5C2×D414yes—
141C2×D3×D5—28no—
142C2×D3×D5—84no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C411yescharacteristic
145C2×C3×C4×C5C22×C411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150#1220—22no—
151#1220—22no—
152C2×Dic15—22no—
153C2×Dic15C22×C412yes—
154D60—21no—
155D60—21no—
156C4×D15—22no—
157C4×D15—22no—
158Dic30—21no—
159Dic30—21no—
160C5×#67—22no—
161C5×#67—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3C22×C412yes—
164C5×D12—21no—
165C5×D12—21no—
166C4×C5×D3—22no—
167C4×C5×D3—22no—
168C5×Dic6—21no—
169C5×Dic6—21no—
170C2×C3×Dic5—22no—
171C3×D20C22⋊C414yes—
172C3×D20C22⋊C414yes—
173C3×D20C22⋊C414yes—
174C3×D20C22⋊C414yes—
175C3×C4×D5—84no—
176#1202—28no—
177#1201—28no—
178D5×Dic3—28no—
179D5×Dic3—84no—
180C22×C3×D4—51no—
181C22×#67—54no—
182#1004—102no—
183#1004—102no—
184#1004—102no—
185#1004—102no—
186C2×#237—52no—
187C2×#237—52no—
188C2×D3×D4—52no—
189C2×D3×D4—52no—
190C2×#235—51no—
191C2×#235C2×D511yescharacteristic
192C3×C4×D4—102no—
193C3×C4×D4—102no—
194C3×#117—51no—
195C3×#117C2×D511yescharacteristic, complemented
196C2×C3×C22⋊C4—54no—
197C2×#217—54no—
198D4×Dic3—102no—
199D4×Dic3—102no—
200#926—51no—
201#926C2×D511yescharacteristic, complemented
202#806—54no—
203#806—54no—
204#806—54no—
205#806C2×D514yescomplemented
206C23×D5—34no—
207C23×D5C22×D312yes—
208C5×#41—61no—
209C5×#41—61no—
210C5×#41—61no—
211C5×#41—61no—
212C2×C5×Q8—31no—
213C2×C5×D4—32no—
214C2×C5×D4—31no—
215C22×C4×C5—32no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—32no—
218C2×C22⋊D5—34no—
219#713—64no—
220#713—64no—
221D4×D5—68no—
222D4×D5—68no—
223D4×D5—64no—
224D4×D5—64no—
225#709—61no—
226#709—61no—
227#709—61no—
228#709—61no—
229#709—64no—
230#709—64no—
231C2×D20—34no—
232C2×D20—31no—
233C2×D20—64no—
234C2×D20—64no—
235C2×D20C4×D312yes—
236C2×D20C4×D312yes—
237C2×D20D1212yes—
238C2×D20D1212yes—
239C2×D20#6712yes—
240C2×D20#6712yes—
241C2×C4×D5—24no—
242C2×C4×D5—34no—
243C2×C4×D5—32no—
244C2×C4×D5—64no—
245C2×Dic10—31no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—61no—
248C5×C22⋊C4—32no—
249C5×C22⋊C4C22×D312yes—
250C42×C5—21no—
251C42×C5—61no—
252C22⋊Dic5—32no—
253C22⋊Dic5C22×D312yes—
254#685—24no—
255#685—64no—
256C4⋊Dic5—21no—
257C4⋊Dic5—61no—
258C4×Dic5—21no—
259C4×Dic5—61no—
260C2×H(5,𝔽2)—151no—
261#518—51no—
262#518—151no—
263#410—31no—
264#410—151no—
265#410—151no—
266#410—151no—
267C2×#99—158no—
268C22×C3×C5—41no—
269C22×C3×C5C23×C411yescharacteristic
270C22×C3×C5C22×D411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—22no—
273C2×D15—42no—
274C2×C5×D3—22no—
275C2×C5×D3—42no—
276C2×C3×D5—44no—
277C2×C3×D5—44no—
278C2×C3×D5—44no—
279C2×C3×D5C2×C22⋊C418yes—
280D3×D5—88no—
281C3×C4×C5—42no—
282C3×C4×C5C2×C22⋊C411yescharacteristic
283C3×C4×C5C2×C22⋊C411yescharacteristic
284C3×C4×C5C2×C22⋊C411yescharacteristic
285C3×C4×C5C2×C22⋊C411yescharacteristic
286Dic15—22no—
287Dic15—42no—
288C3×Dic5—42no—
289C5×Dic3—22no—
290C5×Dic3—42no—
291C24×C3—52no—
292C23×D3—54no—
293C2×C3×D4—52no—
294C2×C3×D4—52no—
295C2×C3×D4—52no—
296C2×C3×D4—52no—
297C2×C3×D4—52no—
298C2×C3×D4—52no—
299C22×C3×C4—104no—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—52no—
302C2×#67—54no—
303C2×#67—54no—
304C2×#67—108no—
305C2×#67—108no—
306C2×#67C22×D512yes—
307C22×Dic3—54no—
308C22×Dic3—104no—
309#237—104no—
310#237—104no—
311#237—104no—
312#237—104no—
313D3×D4—104no—
314D3×D4—104no—
315D3×D4—104no—
316D3×D4—104no—
317#235—21no—
318#235—21no—
319#235—21no—
320#235—21no—
321#235—101no—
322#235—101no—
323#235—101no—
324#235—101no—
325C2×D12—51no—
326C2×D12C4×D511yescharacteristic, complemented
327C2×C4×D3—52no—
328C2×C4×D3C4×D512yescomplemented
329C2×Dic6—51no—
330C2×Dic6C4×D511yescharacteristic, complemented
331C3×C4⋊C4—21no—
332C3×C4⋊C4—101no—
333C3×C22⋊C4—52no—
334C3×C22⋊C4—104no—
335C3×C22⋊C4C22×D512yes—
336C3×C42—21no—
337C3×C42—101no—
338#217—52no—
339#217—104no—
340#217C22×D512yes—
341C4⋊Dic3—21no—
342C4⋊Dic3—101no—
343C4×Dic3—21no—
344C4×Dic3—101no—
345C23×C5—32no—
346C23×C5C23×D311yescharacteristic
347C22×D5—32no—
348C22×D5—68no—
349C22×D5—82no—
350C22×D5—244no—
351C22×D5C2×C4×D314yes—
352C22×D5C2×D1214yes—
353C22×D5C2×#6714yes—
354C5×Q8—61no—
355C5×Q8—61no—
356C5×D4—62no—
357C5×D4—62no—
358C5×D4—61no—
359C5×D4—61no—
360C2×C4×C5—22no—
361C2×C4×C5—32no—
362C2×C4×C5—62no—
363C2×C4×C5—62no—
364C2×C4×C5—62no—
365C2×C4×C5C2×C4×D311yescharacteristic
366C2×C4×C5C2×C4×D311yescharacteristic
367C2×C4×C5C2×D1211yescharacteristic
368C2×C4×C5C2×D1211yescharacteristic
369C2×C4×C5C2×#6711yescharacteristic
370C2×C4×C5C2×#6711yescharacteristic
371C22⋊D5—62no—
372C22⋊D5—62no—
373C22⋊D5—68no—
374C2×Dic5—22no—
375C2×Dic5—32no—
376C2×Dic5—62no—
377D20—68no—
378D20—61no—
379D20—61no—
380D20(C2×D3)⋊C414yes—
381D20(C2×D3)⋊C414yes—
382D20(C2×D3)⋊C414yes—
383D20(C2×D3)⋊C414yes—
384C4×D5—68no—
385C4×D5—62no—
386C4×D5—62no—
387C4×D5—84no—
388C4×D5—244no—
389Dic10—61no—
390Dic10—61no—
391H(5,𝔽2)—302no—
392H(5,𝔽2)—302no—
393H(5,𝔽2)—302no—
394H(5,𝔽2)—302no—
395C2×#41—31no—
396C2×#41—152no—
397C2×#41—152no—
398C2×#41—151no—
399C22×D4—51no—
400C22×D4—152no—
401C22×D4—152no—
402C22×D4—154no—
403C4×D4—102no—
404C4×D4—102no—
405C4×D4—302no—
406C4×D4—302no—
407#117—31no—
408#117—51no—
409#117—151no—
410#117D3×D511yescharacteristic, complemented
411C2×C22⋊C4—54no—
412C2×C22⋊C4—154no—
413#99—34no—
414#99—154no—
415#99—154no—
416#99—154no—
417C2×C3×C5—21no—
418C2×C3×C5—21no—
419C2×C3×C5—21no—
420C2×C3×C5C22×C22⋊C411yescharacteristic
421D15—42no—
422C3×D5—28no—
423C5×D3—42no—
424C23×C3—54no—
425C23×C3—54no—
426C23×C3—54no—
427C23×C3—402no—
428C23×C3C23×D511yescharacteristic
429C22×D3—52no—
430C22×D3—108no—
431C22×D3—404no—
432C22×D3C2×C4×D512yes—
433C3×D4—54no—
434C3×D4—54no—
435C3×D4—54no—
436C3×D4—54no—
437C2×C3×C4—22no—
438C2×C3×C4—102no—
439C2×C3×C4—404no—
440C2×C3×C4C2×C4×D511yescharacteristic
441C2×C3×C4C2×C4×D511yescharacteristic
442C2×C3×C4D4×D511yescharacteristic
443C2×C3×C4D4×D511yescharacteristic
444C2×C3×C4D4×D511yescharacteristic
445C2×C3×C4D4×D511yescharacteristic
446#67—22no—
447#67—22no—
448#67—108no—
449#67—108no—
450#67—102no—
451#67—102no—
452C2×Dic3—22no—
453C2×Dic3—52no—
454C2×Dic3—108no—
455C2×Dic3—102no—
456C2×Dic3—404no—
457C2×Dic3C2×C4×D512yes—
458D12—21no—
459D12—21no—
460D12—101no—
461D12—101no—
462C4×D3—22no—
463C4×D3—22no—
464C4×D3—102no—
465C4×D3—102no—
466Dic6—21no—
467Dic6—21no—
468Dic6—101no—
469Dic6—101no—
470C22×C5—41no—
471C22×C5—62no—
472C22×C5—122no—
473C22×C5C22×C4×D311yescharacteristic
474C22×C5C22×D1211yescharacteristic
475C22×C5C22×#6711yescharacteristic
476C2×D5—44no—
477C2×D5—44no—
478C2×D5—44no—
479C2×D5—62no—
480C2×D5—122no—
481C2×D5—248no—
482C2×D5C2×(C2×D3)⋊C418yes—
483C4×C5—42no—
484C4×C5—62no—
485C4×C5—122no—
486C4×C5C2×(C2×D3)⋊C411yescharacteristic
487C4×C5C2×(C2×D3)⋊C411yescharacteristic
488C4×C5C2×(C2×D3)⋊C411yescharacteristic
489C4×C5C2×(C2×D3)⋊C411yescharacteristic
490Dic5—42no—
491Dic5—62no—
492Dic5—122no—
493C24—52no—
494C24—154no—
495#41—61no—
496#41—61no—
497#41—61no—
498#41—61no—
499#41—304no—
500#41—304no—
501#41—304no—
502#41—304no—
503#41—301no—
504#41—301no—
505#41—301no—
506#41—301no—
507C2×Q8—31no—
508C2×Q8—151no—
509C2×D4—32no—
510C2×D4—31no—
511C2×D4—52no—
512C2×D4—52no—
513C2×D4—52no—
514C2×D4—52no—
515C2×D4—52no—
516C2×D4—52no—
517C2×D4—154no—
518C2×D4—154no—
519C2×D4—152no—
520C2×D4—151no—
521C2×D4—304no—
522C2×D4—304no—
523C2×D4—304no—
524C2×D4—304no—
525C2×D4—308no—
526C2×D4—308no—
527C22×C4—32no—
528C22×C4—104no—
529C22×C4—154no—
530C22×C4—152no—
531C22×C4—304no—
532C22×C4C2×D3×D511yescharacteristic
533C4⋊C4—21no—
534C4⋊C4—61no—
535C4⋊C4—101no—
536C4⋊C4—301no—
537C22⋊C4—32no—
538C22⋊C4—52no—
539C22⋊C4—104no—
540C22⋊C4—152no—
541C22⋊C4—304no—
542C22⋊C4C2×D3×D512yes—
543C42—21no—
544C42—61no—
545C42—101no—
546C42—301no—
547C3×C5#288311yescharacteristic, complemented, Hall
548C22×C3—41no—
549C22×C3—58no—
550C22×C3—204no—
551C22×C3—204no—
552C22×C3—204no—
553C22×C3C22×C4×D511yescharacteristic
554C22×C3C2×D4×D511yescharacteristic
555C22×C3C2×D4×D511yescharacteristic
556C2×D3—22no—
557C2×D3—42no—
558C2×D3—102no—
559C2×D3—202no—
560C2×D3—408no—
561C3×C4—42no—
562C3×C4—202no—
563C3×C4D5×C22⋊C411yescharacteristic
564C3×C4D5×C22⋊C411yescharacteristic
565C3×C4D5×C22⋊C411yescharacteristic
566C3×C4D5×C22⋊C411yescharacteristic
567Dic3—22no—
568Dic3—42no—
569Dic3—102no—
570Dic3—202no—
571C2×C5—21no—
572C2×C5—21no—
573C2×C5—21no—
574C2×C5—122no—
575C2×C5C22×(C2×D3)⋊C411yescharacteristic
576D5—28no—
577D5—122no—
578C23—32no—
579C23—54no—
580C23—54no—
581C23—54no—
582C23—152no—
583C23—308no—
584C23—402no—
585C23—1204no—
586C23C22×D3×D511yescharacteristic
587Q8—61no—
588Q8—61no—
589Q8—301no—
590Q8—301no—
591D4—54no—
592D4—54no—
593D4—54no—
594D4—54no—
595D4—62no—
596D4—62no—
597D4—61no—
598D4—61no—
599D4—308no—
600D4—308no—
601D4—302no—
602D4—302no—
603D4—301no—
604D4—301no—
605C2×C4—22no—
606C2×C4—32no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—102no—
611C2×C4—152no—
612C2×C4—308no—
613C2×C4—302no—
614C2×C4—302no—
615C2×C4—302no—
616C2×C4—404no—
617C2×C4—1204no—
618C2×C4C4×D3×D511yescharacteristic
619C2×C4C4×D3×D511yescharacteristic
620C2×C4D5×D1211yescharacteristic
621C2×C4D5×D1211yescharacteristic
622C2×C4D5×#6711yescharacteristic
623C2×C4D5×#6711yescharacteristic
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—108no—
628C2×C3C2×D5×C22⋊C411yescharacteristic
629D3—42no—
630D3—202no—
631C5#8254611yescharacteristic, complemented, Sylow
632C22—41no—
633C22—58no—
634C22—62no—
635C22—122no—
636C22—204no—
637C22—204no—
638C22—204no—
639C22—302no—
640C22—602no—
641C22—1208no—
642C22C2×C4×D3×D511yescharacteristic
643C22C2×D5×D1211yescharacteristic
644C22C2×D5×#6711yescharacteristic
645C4—42no—
646C4—62no—
647C4—122no—
648C4—202no—
649C4—302no—
650C4—602no—
651C4D5×(C2×D3)⋊C411yescharacteristic
652C4D5×(C2×D3)⋊C411yescharacteristic
653C4D5×(C2×D3)⋊C411yescharacteristic
654C4D5×(C2×D3)⋊C411yescharacteristic
655C3#1061042511yescharacteristic, complemented, Sylow
656C2—21no—
657C2—21no—
658C2—21no—
659C2—108no—
660C2—122no—
661C2—602no—
662C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2C2×D5×(C2×D3)⋊C4
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92017C2
cosocleC23×C3×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2883
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65855C2semidirect
3. #11754488C2semidirect
4. #11751107C2semidirect
5. C5×#5006C2semidirect
6. #11748626C2semidirect
7. #11748625C2semidirect
8. D5×#806C2semidirect
18. C2×#6777C4semidirect
19. C2×D3×D20C4semidirect
20. C2×#6766C4semidirect
21. C2×#6765C4semidirect
22. C3×C5×#117C22semidirect
23. #91815C22semidirect
24. C5×#926C22semidirect
25. C3×#4072C22semidirect
27. C3×D5×C22⋊C4C22semidirect
29. D5×#217C22semidirect
32. #91090C22semidirect
33. C5×#806C22semidirect
34. #90997C22semidirect
35. #90996C22semidirect
39. #65855D3semidirect
46. C22×D3×D5C2×C4semidirect
53. C2×D60C2×C4semidirect
54. C2×C4×D15C2×C4semidirect
55. C2×Dic30C2×C4semidirect
61. C2×C5×D12C2×C4semidirect
62. C2×C4×C5×D3C2×C4semidirect
63. C2×C5×Dic6C2×C4semidirect
73. C2×#1202C2×C4semidirect
74. C2×#1201C2×C4semidirect
76. C2×D5×Dic3C2×C4semidirect
105. #5006D5semidirect
120. C5×#117C2×D3semidirect
122. #4072C2×D3semidirect
126. D5×C22⋊C4C2×D3semidirect
195. C3×#117C2×D5semidirect
201. #926C2×D5semidirect
205. #806C2×D5semidirect
326. C2×D12C4×D5semidirect
328. C2×C4×D3C4×D5semidirect
330. C2×Dic6C4×D5semidirect
410. #117D3×D5semidirect
547. C3×C5#2883semidirect
631. C5#82546semidirect
655. C3#10610425semidirect

Maximal subgroups

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

subgroupindex
C2×#920172
C3×#658552
#117544882
#117511072
C5×#50062
#117486262
#117486252
D5×#8062
#106104253
#825465