Finite Group Databasebeta

← #14301034

Subgroups — #14301034

Order 1920.

876 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#893C211yesmaximal, characteristic, complemented
2C22×#6652C211yesmaximal, characteristic
3C2×C3×#3941C211yesmaximal, characteristic, complemented
4#11748785C211yesmaximal, characteristic, complemented
5C2×#90967C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11745967C211yesmaximal, characteristic, complemented
8#10602406—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C4×C5×D3—21no—
11C22×C3×D20C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C2×C5×(C2×D3)⋊C4—21no—
16C2×C4×C5×Dic3C2211yescharacteristic
17C5×#893—22no—
18C5×#893—22no—
19C22×C3×#168C2211yescharacteristic
20C2×#6665—21no—
21C2×#6665—21no—
22C2×#6652—22no—
23C2×#6652—22no—
24C2×#6652C414yescomplemented
25C3×#3941—22no—
26#90967—22no—
27#70208—51nomaximal, Hall
28C2×C4×C5×D4—31no—
29C22×#686—31no—
30C2×#3964—31no—
31C2×#3941D311yescharacteristic, complemented
32#65228—31no—
33#64749—31no—
34#64744—31no—
35C23×C5×D3—21no—
36C23×C3×D5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C5×D12—21no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12C2×C412yes—
46C2×C5×D12D412yes—
47C2×C5×D12D412yes—
48C2×C4×C5×D3—24no—
49C2×C4×C5×D3—42no—
50C2×C4×C5×D3—42no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20—21no—
54C2×C3×D20—21no—
55C2×C3×D20—21no—
56C2×C3×D20C2×C412yescomplemented
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4D412yes—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C2×C3⋊#168C2×C412yescomplemented
64C5×(C2×D3)⋊C4—24no—
65C4×C5×Dic3—21no—
66C4×C5×Dic3—21no—
67C2×C3×#168—21no—
68C2×C3×#168—21no—
69C2×C3×#168—21no—
70#6665—42no—
71#6665—42no—
72#6652—28no—
73C22×#213—51no—
74C2×#893D511yescharacteristic, complemented
75C2×C3×#102—51no—
76#5221—51no—
77C2×#821—51no—
78#4550—51no—
79#4529—51no—
80C22×C5×D4—31no—
81C23×C4×C5—61no—
82C22×D20C2×D311yescharacteristic
83C4×C5×D4—62no—
84C4×C5×D4—62no—
85C2×C5×C4⋊C4C2×D311yescharacteristic
86C2×C5×C22⋊C4—61no—
87C2×C42×C5—31no—
88C2×#686—34no—
89C2×#686—62no—
90C2×#686—62no—
91C2×#685—61no—
92C2×#685—61no—
93C2×C4⋊Dic5—31no—
94C22×#168—31no—
95C22×#168C2×D311yescharacteristic
96#3964—62no—
97#3941—22no—
98#1879—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3—22no—
101C22×C5×D3—22no—
102C22×C5×D3—22no—
103C22×C5×D3—41no—
104C22×C5×D3—41no—
105C22×C5×D3—41no—
106C22×C5×D3—41no—
107C22×C3×D5—22no—
108C22×C3×D5—41no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5#4111yescharacteristic
122C2×C3×C4×C5#4111yescharacteristic
123C2×Dic15—41no—
124C2×Dic15—41no—
125C2×Dic15—41no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—21no—
128C2×C5×Dic3—21no—
129C2×C5×Dic3—21no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3D812yescomplemented
132C5×D12—22no—
133C5×D12—22no—
134C5×D12—22no—
135C5×D12C22⋊C414yescomplemented
136C4×C5×D3—48no—
137C3×D20—22no—
138C3×D20—22no—
139C3×D20—41no—
140C3×D20—41no—
141C3⋊#168—22no—
142C3×#168—41no—
143C22×C3×D4—51no—
144C22×D12C2×D511yescharacteristic
145C22×C4×D3—21no—
146C22×C3×C8—51no—
147C2×C3×C4⋊C4C2×D511yescharacteristic
148C2×#217—101no—
149C2×#217—101no—
150C2×#213—54no—
151C2×#213—102no—
152C2×#213—102no—
153C2×(C2×D3)⋊C4—21no—
154C2×C4⋊Dic3—51no—
155C2×C4×Dic3C2×D511yescharacteristic
156C22×C3⋊C8—51no—
157#893—22no—
158#893—22no—
159C3×#102—102no—
160#821—102no—
161C24×C5—61no—
162C23×D5—21no—
163C2×C5×D4—32no—
164C2×C5×D4—32no—
165C2×C5×D4—32no—
166C2×C5×D4—61no—
167C2×C5×D4—61no—
168C2×C5×D4—61no—
169C22×C4×C5—21no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—64no—
173C22×C4×C5—122no—
174C22×C4×C5—122no—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—61no—
177C2×D20—21no—
178C2×D20—21no—
179C2×D20—21no—
180C2×D20—21no—
181C2×D20—21no—
182C2×D20C4×D312yescomplemented
183C5×C4⋊C4—21no—
184C5×C4⋊C4#6712yes—
185C5×C22⋊C4—64no—
186C42×C5—61no—
187C42×C5—61no—
188#686—68no—
189#685—122no—
190#685—122no—
191C4⋊Dic5—61no—
192C4⋊Dic5—61no—
193C2×#168—21no—
194C2×#168—21no—
195C2×#168—21no—
196C2×#168—32no—
197C2×#168—61no—
198C2×#168—61no—
199C22×D8—151no—
200C2×C4×D4—31no—
201C2×#102—51no—
202C2×#102—151no—
203#390—151no—
204#340—151no—
205#336—151no—
206C22×C3×C5C4×D411yescharacteristic
207C22×C3×C5#12011yescharacteristic
208C22×C3×C5#12111yescharacteristic
209C22×C3×C5C2×D811yescharacteristic
210C22×C3×C5#13511yescharacteristic
211C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
212C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
213C2×C5×D3—24no—
214C2×C5×D3—42no—
215C2×C5×D3—42no—
216C2×C5×D3—42no—
217C2×C5×D3—42no—
218C2×C5×D3—42no—
219C2×C5×D3—42no—
220C2×C3×D5—42no—
221C2×C3×D5—42no—
222C2×C3×D5—42no—
223C2×C3×D5—81no—
224C2×C3×D5—81no—
225C2×C3×D5—81no—
226C2×C3×D5—81no—
227C3×C4×C5—42no—
228C3×C4×C5C2×C22⋊C411yescharacteristic
229C3×C4×C5C4×D411yescharacteristic
230C3×C4×C5#12111yescharacteristic
231C3×C4×C5#12311yescharacteristic
232Dic15—81no—
233C5×Dic3—22no—
234C5×Dic3—41no—
235C24×C3—101no—
236C23×D3—21no—
237C2×C3×D4—52no—
238C2×C3×D4—101no—
239C2×C3×D4—101no—
240C2×C3×D4—101no—
241C2×C3×D4—101no—
242C2×C3×D4—101no—
243C22×C3×C4—21no—
244C22×C3×C4C22×D511yescharacteristic
245C22×Dic3—101no—
246C22×Dic3C22⋊D511yescharacteristic
247C22×Dic3C22⋊D511yescharacteristic
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12C4×D512yes—
252C2×D12D2012yes—
253C2×D12C22⋊D512yes—
254C2×C4×D3—24no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C3×C8—101no—
258C2×C3×C8—101no—
259C2×C3×C8—101no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4C22⋊D512yes—
262#217—202no—
263#217—202no—
264#213—108no—
265(C2×D3)⋊C4—24no—
266C4⋊Dic3—101no—
267C4⋊Dic3—101no—
268C4×Dic3—21no—
269C4×Dic3—21no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8—101no—
272C2×C3⋊C8—101no—
273C23×C5—62no—
274C23×C5—62no—
275C23×C5—62no—
276C23×C5—121no—
277C23×C5—121no—
278C23×C5—121no—
279C23×C5—121no—
280C23×C5D3×D411yescharacteristic
281C22×D5—22no—
282C22×D5—41no—
283C22×D5—41no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
287C22×D5—41no—
288C5×D4—34no—
289C5×D4—62no—
290C5×D4—62no—
291C5×D4—62no—
292C2×C4×C5—22no—
293C2×C4×C5—32no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—61no—
297C2×C4×C5—61no—
298C2×C4×C5—61no—
299C2×C4×C5—61no—
300C2×C4×C5—61no—
301C2×C4×C5—128no—
302C2×C4×C5C2×C4×D311yescharacteristic
303C2×C4×C5#23511yescharacteristic
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5#23711yescharacteristic
307C2×C4×C5C2×#6711yescharacteristic
308C2×Dic5—121no—
309C2×Dic5—121no—
310C2×Dic5—121no—
311D20—22no—
312D20—22no—
313D20—41no—
314D20—41no—
315#168—41no—
316#168—62no—
317C22×D4—31no—
318C22×D4—51no—
319C23×C4—61no—
320C2×D8—154no—
321C2×D8—302no—
322C2×D8—302no—
323C22×C8—51no—
324C22×C8—151no—
325C4×D4—62no—
326C4×D4—62no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4D3×D511yescharacteristic
329C2×C22⋊C4—61no—
330C2×C22⋊C4—301no—
331C2×C22⋊C4—301no—
332C2×C42—31no—
333#102—102no—
334#102—302no—
335C2×C3×C5#38611yescharacteristic
336C2×C3×C5C4×D811yescharacteristic
337C2×C3×C5#44211yescharacteristic
338C2×C3×C5#44711yescharacteristic
339C2×C3×C5#44911yescharacteristic
340C2×C3×C5#45911yescharacteristic
341C2×C3×C5#46311yescharacteristic
342C3×D5—82no—
343C5×D3—44no—
344C23×C3—102no—
345C23×C3—201no—
346C23×C3—201no—
347C23×C3—201no—
348C23×C3—201no—
349C23×C3—201no—
350C23×C3—201no—
351C23×C3C2×C22⋊D511yescharacteristic
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—41no—
356C22×D3—41no—
357C22×D3—41no—
358C22×D3—41no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—201no—
362C3×D4—201no—
363C2×C3×C4—22no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4C2×C4×D511yescharacteristic
367C2×C3×C4C2×D2011yescharacteristic
368C2×C3×C4#70911yescharacteristic
369C2×C3×C4#70911yescharacteristic
370C2×C3×C4C2×C22⋊D511yescharacteristic
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—201no—
378C2×Dic3—201no—
379C2×Dic3—201no—
380C2×Dic3#68612yescomplemented
381D12—22no—
382D12—22no—
383D12—22no—
384D12#68514yescomplemented
385C4×D3—48no—
386C3×C8—201no—
387C3⋊C8—102no—
388C22×C5—64no—
389C22×C5—122no—
390C22×C5—122no—
391C22×C5—122no—
392C22×C5—122no—
393C22×C5—122no—
394C22×C5—122no—
395C22×C5#67⋊C411yescharacteristic
396C22×C5#88411yescharacteristic
397C22×C5D3×D811yescharacteristic
398C22×C5#91111yescharacteristic
399C22×C5#91411yescharacteristic
400C22×C5#91611yescharacteristic
401C22×C5#93711yescharacteristic
402C2×D5—42no—
403C2×D5—42no—
404C2×D5—42no—
405C2×D5—81no—
406C2×D5—81no—
407C2×D5—81no—
408C2×D5—81no—
409C4×C5—42no—
410C4×C5—62no—
411C4×C5—121no—
412C4×C5D3×C22⋊C411yescharacteristic
413C4×C5#88311yescharacteristic
414C4×C5C4×#6711yescharacteristic
415C4×C5#93811yescharacteristic
416Dic5—241no—
417C24—61no—
418C24—101no—
419C2×D4—32no—
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—52no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—101no—
427C2×D4—101no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C22×C4—21no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—64no—
435C22×C4—122no—
436C22×C4—122no—
437C22×C4—301no—
438C22×C4C2×D3×D511yescharacteristic
439D8—308no—
440C2×C8—101no—
441C2×C8—101no—
442C2×C8—101no—
443C2×C8—152no—
444C2×C8—301no—
445C2×C8—301no—
446C4⋊C4—21no—
447C4⋊C4—301no—
448C4⋊C4—301no—
449C4⋊C4#120112yes—
450C22⋊C4—64no—
451C22⋊C4—602no—
452C22⋊C4—602no—
453C42—61no—
454C42—61no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—202no—
457C22×C3—202no—
458C22×C3—202no—
459C22×C3—401no—
460C22×C3—401no—
461C22×C3—401no—
462C22×C3—401no—
463C22×C3C4×C22⋊D511yescharacteristic
464C22×C3#407611yescharacteristic
465C22×C3C2×#68611yescharacteristic
466C22×C3#407811yescharacteristic
467C22×C3#409511yescharacteristic
468C22×C3#409611yescharacteristic
469C22×C3#409911yescharacteristic
470C2×D3—24no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—42no—
477C3×C4—42no—
478C3×C4C2×#68511yescharacteristic
479C3×C4C4×C22⋊D511yescharacteristic
480C3×C4#407511yescharacteristic
481C3×C4#407611yescharacteristic
482Dic3—22no—
483Dic3—41no—
484Dic3—401no—
485C2×C5—124no—
486C2×C5#475611yescharacteristic
487C2×C5#478511yescharacteristic
488C2×C5#478611yescharacteristic
489C2×C5#478711yescharacteristic
490C2×C5#495611yescharacteristic
491C2×C5#515611yescharacteristic
492C2×C5#517211yescharacteristic
493D5—82no—
494C23—62no—
495C23—62no—
496C23—62no—
497C23—102no—
498C23—121no—
499C23—121no—
500C23—121no—
501C23—121no—
502C23—201no—
503C23—201no—
504C23—201no—
505C23—201no—
506C23—201no—
507C23—201no—
508C23D3×C22⋊D511yescharacteristic
509D4—34no—
510D4—62no—
511D4—62no—
512D4—62no—
513D4—102no—
514D4—102no—
515D4—201no—
516D4—201no—
517C2×C4—22no—
518C2×C4—32no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—128no—
527C2×C4—601no—
528C2×C4—601no—
529C2×C4—601no—
530C2×C4#676511yescharacteristic
531C2×C4#677111yescharacteristic
532C2×C4C4×D3×D511yescharacteristic
533C2×C4D3×D2011yescharacteristic
534C2×C4C2×#120111yescharacteristic
535C2×C4D3×C22⋊D511yescharacteristic
536C8—201no—
537C8—302no—
538C2×C3—402no—
539C2×C3C4×#68611yescharacteristic
540C2×C3#6530311yescharacteristic
541C2×C3#6530411yescharacteristic
542C2×C3#6530511yescharacteristic
543C2×C3#6550211yescharacteristic
544C2×C3#6550611yescharacteristic
545C2×C3#6552711yescharacteristic
546D3—44no—
547C5#7020811yescharacteristic, complemented, Sylow
548C22—64no—
549C22—122no—
550C22—122no—
551C22—122no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—202no—
556C22—202no—
557C22—202no—
558C22—401no—
559C22—401no—
560C22—401no—
561C22—401no—
562C22#9144111yescharacteristic
563C22#9145411yescharacteristic
564C22D3×#68611yescharacteristic
565C22#9149411yescharacteristic
566C22#9150411yescharacteristic
567C22#9151711yescharacteristic
568C22#9156811yescharacteristic
569C4—42no—
570C4—62no—
571C4—121no—
572C4—1201no—
573C4C4×#120111yescharacteristic
574C4#9145211yescharacteristic
575C4#9145611yescharacteristic
576C4D3×#68511yescharacteristic
577C3#1060240611yescharacteristic, complemented, Sylow
578C2—124no—
579C2—402no—
580C2#1174721911yescharacteristic
581C2#1174722011yescharacteristic
582C2#1174737511yescharacteristic
583C2#1174740211yescharacteristic
584C2#1174891011yescharacteristic
585C2#1174903211yescharacteristic
586C2#1174928111yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6652C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1879
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#893C2semidirect
3. C2×C3×#3941C2semidirect
4. #11748785C2semidirect
5. C2×#90967C2semidirect
6. #11746350C2semidirect
7. #11745967C2semidirect
24. C2×#6652C4semidirect
31. C2×#3941D3semidirect
56. C2×C3×D20C2×C4semidirect
63. C2×C3⋊#168C2×C4semidirect
74. C2×#893D5semidirect
131. C2×C5×Dic3D8semidirect
135. C5×D12C22⋊C4semidirect
182. C2×D20C4×D3semidirect
380. C2×Dic3#686semidirect
384. D12#685semidirect
455. C3×C5#1879semidirect
547. C5#70208semidirect
577. C3#10602406semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
C22×#66522
C2×C3×#39412
#117487852
C2×#909672
#117463502
#117459672
#106024063
#702085