Finite Group Databasebeta

← #14413931

Subgroups — #14413931

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D5×Dic3C211yesmaximal, characteristic
2#11750819C211yesmaximal, characteristic, complemented
3C5×#4719C211yesmaximal, characteristic, complemented
4C3×#65015C211yesmaximal, characteristic
5#11748499C211yesmaximal, characteristic
6#11748337C211yesmaximal, characteristic, complemented
7#11748331C211yesmaximal, characteristic, complemented
8#11747601C212yesmaximal, complemented
9#11747596C212yesmaximal, complemented
10#11747587C212yesmaximal, complemented
11#11747577C212yesmaximal, complemented
12#10611062—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C411yescharacteristic
15C22×D5×Dic3C411yescharacteristic
16C2×C4×Dic15C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C3×#676C2212yes—
19C2×Dic3×Dic5C411yescharacteristic
20C2×Dic3×Dic5C411yescharacteristic
21C4×D5×Dic3C411yescharacteristic
22C4×D5×Dic3C411yescharacteristic
23C4×D5×Dic3C411yescharacteristic
24C4×D5×Dic3C411yescharacteristic
25C4×D5×Dic3C2211yescharacteristic
26C4×D5×Dic3C2211yescharacteristic
27C4×D5×Dic3C2211yescharacteristic
28C4×D5×Dic3C2211yescharacteristic
29C2×#6649C2212yes—
30C3×C5×C22⋊C8C2211yescharacteristic
31#91114C2211yescharacteristic
32#91098C2212yescomplemented
33C8×Dic15C2212yescomplemented
34C5×#830C2211yescharacteristic
35C5×#815C2212yescomplemented
36C5×Dic3⋊C8C2212yescomplemented
37C3×C22⋊#168C2211yescharacteristic
38C3×#3952C2212yes—
39Dic3⋊#168C2212yescomplemented
40#90983C2212yescomplemented
41#90955C2212yes—
42#90953C2212yescomplemented
43#90951C2212yescomplemented
44#78619—51nomaximal, Hall
45C2×C42×D5—31no—
46C5×#432—31no—
47#65215—31no—
48#65126—32no—
49#65122—32no—
50#65015—31no—
51#65015D311yescharacteristic
52#65007—31no—
53#65007—31no—
54#64996—32no—
55#64994—32no—
56C23×C3×D5C2×C411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15C2×C411yescharacteristic
59C22×Dic15C2×C411yescharacteristic
60C22×C5×Dic3C2×C411yescharacteristic
61C22×C5×Dic3C2×C411yescharacteristic
62C22×C3×Dic5C2×C411yescharacteristic
63C2×C3×C4×D5—24no—
64C2×C3×C4×D5C2×C411yescharacteristic
65C2×C3×C4×D5C2×C411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×D5×Dic3—24no—
69C2×D5×Dic3—24no—
70C2×D5×Dic3C2×C411yescharacteristic
71C2×D5×Dic3C2×C411yescharacteristic
72C2×D5×Dic3C2×C411yescharacteristic
73C2×D5×Dic3C2×C411yescharacteristic
74C2×D5×Dic3C2×C411yescharacteristic
75C2×D5×Dic3C2×C411yescharacteristic
76C2×D5×Dic3C2×C411yescharacteristic
77C2×D5×Dic3C2×C411yescharacteristic
78C2×C3×C5×C8C2312yes—
79C4×Dic15C2×C411yescharacteristic
80C4×Dic15C2×C411yescharacteristic
81C4×Dic15C2311yescharacteristic
82C4×Dic15C2311yescharacteristic
83C2×C3⋊#168C2312yes—
84C4×C5×Dic3C2×C411yescharacteristic
85C4×C5×Dic3C2×C411yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C2×C5×C3⋊C8C2312yes—
89C2×C3×#168C2312yes—
90C3×#676—24no—
91Dic3×Dic5C2×C411yescharacteristic
92Dic3×Dic5C2×C411yescharacteristic
93Dic3×Dic5C2×C411yescharacteristic
94Dic3×Dic5C2×C411yescharacteristic
95Dic3×Dic5C2×C411yescharacteristic
96Dic3×Dic5C2×C411yescharacteristic
97Dic3×Dic5C2×C411yescharacteristic
98Dic3×Dic5C2×C411yescharacteristic
99#6649—24no—
100C22×C4×Dic3—51no—
101C3×#407—51no—
102#5207—51no—
103#5118—52no—
104Dic3×M16—52no—
105#4719—51no—
106#4719—52no—
107#4719D511yescharacteristic, complemented
108#4718—51no—
109#4718—51no—
110#4718—52no—
111C22×C4×D5—31no—
112C22×C4×D5—31no—
113C22×C4×D5C2×D311yescharacteristic
114C2×C42×C5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—31no—
118C2×#676—32no—
119C2×#676C2×D312yes—
120C42×D5—31no—
121C42×D5—31no—
122C42×D5—31no—
123C42×D5—31no—
124C42×D5—31no—
125C42×D5—31no—
126C42×D5—31no—
127C42×D5—31no—
128C5×C4⋊C8—32no—
129C5×C22⋊C8—31no—
130C5×C22⋊C8C2×D311yescharacteristic
131C5×#97—32no—
132C22⋊#168—31no—
133C22⋊#168C2×D311yescharacteristic
134#3952—32no—
135#3952C2×D312yes—
136#3946—32no—
137#3946—32no—
138C8×Dic5—32no—
139C8×Dic5—32no—
140C4⋊#168—32no—
141#3935—32no—
142#2920—151noSylow
143C23×C3×C5C22×C411yescharacteristic
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5C22×C411yescharacteristic
148C22×C3×D5C22×C411yescharacteristic
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22×C411yescharacteristic
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15—22no—
153C2×Dic15M1614yescomplemented
154C2×Dic15C22×C411yescharacteristic
155C2×Dic15C22×C411yescharacteristic
156C2×Dic15C22×C411yescharacteristic
157C2×Dic15C22×C411yescharacteristic
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3C22×C411yescharacteristic
161C2×C5×Dic3C22×C411yescharacteristic
162C2×C5×Dic3C22×C411yescharacteristic
163C2×C5×Dic3C22×C411yescharacteristic
164C2×C3×Dic5—22no—
165C2×C3×Dic5C22×C411yescharacteristic
166C2×C3×Dic5C22×C411yescharacteristic
167C3×C4×D5—22no—
168C3×C4×D5—22no—
169C3×C4×D5—22no—
170C3×C4×D5#4114yes—
171D5×Dic3—22no—
172D5×Dic3—22no—
173D5×Dic3—22no—
174D5×Dic3—22no—
175D5×Dic3—22no—
176D5×Dic3—22no—
177D5×Dic3—22no—
178D5×Dic3M1614yescomplemented
179C3×C5×C8—22no—
180C3⋊#168—22no—
181C3×#168—22no—
182C5×C3⋊C8—22no—
183C23×C3×C4—51no—
184C23×Dic3—51no—
185C23×Dic3—51no—
186C2×C3×M16—52no—
187C2×C4×Dic3—51no—
188C2×C4×Dic3—51no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—51no—
191C2×C4×Dic3—51no—
192C2×C4×Dic3—51no—
193C2×C4×Dic3—51no—
194C2×C4×Dic3—51no—
195C2×C4×Dic3—51no—
196C2×C4×Dic3—51no—
197C2×C4×Dic3—51no—
198C2×C4×Dic3C2×D511yescharacteristic
199C2×#208—52no—
200C3×C22⋊C8—51no—
201C3×C22⋊C8—52no—
202C3×C22⋊C8C2×D511yescharacteristic
203#830—51no—
204#830—52no—
205#830C2×D511yescharacteristic
206#815—52no—
207#815C2×D512yescomplemented
208Dic3⋊C8—52no—
209Dic3⋊C8—52no—
210Dic3⋊C8—52no—
211Dic3⋊C8C2×D512yescomplemented
212C8×Dic3—52no—
213C8×Dic3—52no—
214C23×D5C4×D311yescharacteristic
215C22×C4×C5—31no—
216C22×C4×C5—31no—
217C22×C4×C5C22×D311yescharacteristic
218C22×Dic5—31no—
219C22×Dic5—31no—
220C22×Dic5C4×D311yescharacteristic
221C2×C4×D5—24no—
222C2×C4×D5—31no—
223C2×C4×D5—31no—
224C2×C4×D5—31no—
225C2×C4×D5—31no—
226C2×C4×D5—31no—
227C2×C4×D5—31no—
228C2×C4×D5—31no—
229C2×C4×D5—31no—
230C2×C4×D5—64no—
231C2×C4×D5—64no—
232C2×C4×D5C4×D311yescharacteristic
233C2×C4×D5C4×D311yescharacteristic
234C2×C4×D5C22×D311yescharacteristic
235C2×C4×D5C22×D311yescharacteristic
236C2×C5×C8—32no—
237C2×C5×C8C22×D312yes—
238C42×C5—31no—
239C42×C5—31no—
240C42×C5—31no—
241C42×C5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245C4×Dic5—31no—
246C4×Dic5—31no—
247C4×Dic5—31no—
248C4×Dic5—31no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C4×Dic5—31no—
252C4×Dic5—31no—
253C4×Dic5—31no—
254C2×#168—32no—
255C2×#168C22×D312yes—
256#676—24no—
257#676—64no—
258C22×C42—151no—
259#432—31no—
260#432—152no—
261#432—151no—
262#431—151no—
263#431—152no—
264#431—151no—
265#423—152no—
266#407—51no—
267#407—151no—
268C4×M16—152no—
269C22×C3×C5—21no—
270C22×C3×C5—21no—
271C22×C3×C5C2×M1612yes—
272C22×C3×C5C23×C411yescharacteristic
273C2×C3×D5—28no—
274C2×C3×D5—21no—
275C2×C3×D5—21no—
276C2×C3×D5—21no—
277C2×C3×D5—21no—
278C2×C3×D5#11712yes—
279C2×C3×D5C2×M1612yes—
280C3×C4×C5—21no—
281C3×C4×C5C2×#4112yes—
282Dic15—21no—
283Dic15C2×M1612yes—
284Dic15C2×M1612yes—
285Dic15C2×M1612yes—
286C3×Dic5—21no—
287C3×Dic5#11712yes—
288C5×Dic3—21no—
289C5×Dic3—21no—
290C5×Dic3—21no—
291C5×Dic3C2×M1612yes—
292C24×C3—51no—
293C22×C3×C4—51no—
294C22×C3×C4—51no—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—104no—
299C22×C3×C4C22×D511yescharacteristic
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—51no—
303C22×Dic3—51no—
304C22×Dic3—51no—
305C22×Dic3—51no—
306C22×Dic3—51no—
307C22×Dic3—51no—
308C22×Dic3—51no—
309C22×Dic3—51no—
310C22×Dic3—104no—
311C22×Dic3—104no—
312C22×Dic3C4×D511yescharacteristic
313C22×Dic3C4×D511yescharacteristic
314C3×M16—104no—
315C2×C3×C8—52no—
316C2×C3×C8C22×D512yes—
317C4×Dic3—51no—
318C4×Dic3—51no—
319C4×Dic3—51no—
320C4×Dic3—51no—
321C4×Dic3—51no—
322C4×Dic3—51no—
323C4×Dic3—51no—
324C4×Dic3—51no—
325C4×Dic3—51no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328C4×Dic3—51no—
329C4×Dic3C4×D511yescharacteristic
330C4×Dic3C4×D511yescharacteristic
331C4×Dic3C22×D511yescharacteristic
332C4×Dic3C22×D511yescharacteristic
333#208—104no—
334C2×C3⋊C8—52no—
335C2×C3⋊C8C22×D512yes—
336C23×C5C2×C4×D311yescharacteristic
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5C2×C4×D311yescharacteristic
341C22×D5C2×C4×D311yescharacteristic
342C2×C4×C5—22no—
343C2×C4×C5—31no—
344C2×C4×C5—31no—
345C2×C4×C5—31no—
346C2×C4×C5—31no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5C2×C4×D311yescharacteristic
350C2×C4×C5C23×D311yescharacteristic
351C2×Dic5—22no—
352C2×Dic5—34no—
353C2×Dic5—31no—
354C2×Dic5—31no—
355C2×Dic5—31no—
356C2×Dic5—31no—
357C2×Dic5—62no—
358C2×Dic5C2×C4×D311yescharacteristic
359C2×Dic5C2×C4×D311yescharacteristic
360C4×D5—22no—
361C4×D5—22no—
362C4×D5—22no—
363C4×D5—34no—
364C4×D5—62no—
365C4×D5—62no—
366C4×D5—62no—
367C4×D5—62no—
368C4×D5—62no—
369C4×D5—62no—
370C4×D5—62no—
371C4×D5#23714yes—
372C5×C8—22no—
373C5×C8—62no—
374#168—22no—
375#168—62no—
376C23×C4—51no—
377C23×C4—151no—
378C23×C4—151no—
379C2×M16—52no—
380C2×M16—152no—
381C2×C42—31no—
382C2×C42—151no—
383C2×C42—151no—
384C2×C42—151no—
385C2×C42—151no—
386C2×C42—151no—
387C2×C42—151no—
388C2×C42—151no—
389C2×C42—151no—
390C2×C42—151no—
391C2×C42—151no—
392C2×C42—151no—
393C4⋊C8—32no—
394C4⋊C8—152no—
395C4⋊C8—152no—
396C4⋊C8—152no—
397C22⋊C8—31no—
398C22⋊C8—51no—
399C22⋊C8—52no—
400C22⋊C8—152no—
401C22⋊C8—151no—
402C22⋊C8D3×D511yescharacteristic
403#97—32no—
404#97—152no—
405C4×C8—152no—
406C4×C8—152no—
407C2×C3×C5—22no—
408C2×C3×C5C2×#11711yescharacteristic
409C2×C3×C5C22×M1611yescharacteristic
410C2×C3×C5C22×M1611yescharacteristic
411C3×D5—22no—
412C3×D5—22no—
413C23×C3—51no—
414C23×C3—51no—
415C23×C3—102no—
416C23×C3—102no—
417C23×C3—102no—
418C23×C3C2×C4×D511yescharacteristic
419C2×C3×C4—22no—
420C2×C3×C4—51no—
421C2×C3×C4—54no—
422C2×C3×C4—51no—
423C2×C3×C4—102no—
424C2×C3×C4—102no—
425C2×C3×C4—102no—
426C2×C3×C4—102no—
427C2×C3×C4C2×C4×D511yescharacteristic
428C2×C3×C4C23×D511yescharacteristic
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—51no—
432C2×Dic3—51no—
433C2×Dic3—51no—
434C2×Dic3—54no—
435C2×Dic3—54no—
436C2×Dic3—51no—
437C2×Dic3—102no—
438C2×Dic3—102no—
439C2×Dic3—102no—
440C2×Dic3—102no—
441C2×Dic3—102no—
442C2×Dic3—102no—
443C2×Dic3—102no—
444C2×Dic3—102no—
445C2×Dic3C2×C4×D511yescharacteristic
446C2×Dic3C2×C4×D511yescharacteristic
447C2×Dic3C2×C4×D511yescharacteristic
448C2×Dic3C2×C4×D511yescharacteristic
449C3×C8—22no—
450C3×C8—102no—
451C3⋊C8—22no—
452C3⋊C8—102no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5D3×M1612yes—
456C22×C5C22×C4×D311yescharacteristic
457C2×D5—28no—
458C2×D5—21no—
459C2×D5—21no—
460C2×D5—21no—
461C2×D5—21no—
462C2×D5#87712yes—
463C2×D5D3×M1612yes—
464C4×C5—21no—
465C4×C5—32no—
466C4×C5—61no—
467C4×C5—61no—
468C4×C5—61no—
469C4×C5C2×#23712yes—
470Dic5—21no—
471Dic5—32no—
472Dic5—32no—
473Dic5—32no—
474Dic5—61no—
475Dic5#87712yes—
476C24—51no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—51no—
480C22×C4—51no—
481C22×C4—51no—
482C22×C4—51no—
483C22×C4—51no—
484C22×C4—104no—
485C22×C4—151no—
486C22×C4—151no—
487C22×C4—151no—
488C22×C4—151no—
489C22×C4—151no—
490C22×C4—151no—
491C22×C4—151no—
492C22×C4—151no—
493C22×C4—151no—
494C22×C4—151no—
495C22×C4—304no—
496C22×C4—304no—
497C22×C4C2×D3×D511yescharacteristic
498M16—104no—
499M16—304no—
500C2×C8—32no—
501C2×C8—52no—
502C2×C8—152no—
503C2×C8C2×D3×D512yes—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—31no—
508C42—151no—
509C42—151no—
510C42—151no—
511C42—151no—
512C42—151no—
513C42—151no—
514C42—151no—
515C42—151no—
516C42—151no—
517C42—151no—
518C42—151no—
519C42—151no—
520C3×C5#292011yescharacteristic, complemented, Hall
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—52no—
524C22×C3—52no—
525C22×C3—108no—
526C22×C3—101no—
527C22×C3—101no—
528C22×C3—101no—
529C22×C3—101no—
530C22×C3D5×M1612yes—
531C22×C3C22×C4×D511yescharacteristic
532C3×C4—21no—
533C3×C4—52no—
534C3×C4—101no—
535C3×C4D5×#4112yes—
536Dic3—21no—
537Dic3—21no—
538Dic3—21no—
539Dic3—52no—
540Dic3—52no—
541Dic3—52no—
542Dic3—101no—
543Dic3D5×M1612yes—
544C2×C5—22no—
545C2×C5C2×#87711yescharacteristic
546C2×C5C2×D3×M1611yescharacteristic
547C2×C5C2×D3×M1611yescharacteristic
548D5—22no—
549D5—22no—
550C23—51no—
551C23—51no—
552C23—102no—
553C23—102no—
554C23—102no—
555C23C4×D3×D511yescharacteristic
556C2×C4—22no—
557C2×C4—31no—
558C2×C4—31no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—51no—
562C2×C4—54no—
563C2×C4—51no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—154no—
571C2×C4—151no—
572C2×C4—151no—
573C2×C4—151no—
574C2×C4—154no—
575C2×C4—151no—
576C2×C4—302no—
577C2×C4—302no—
578C2×C4—302no—
579C2×C4—302no—
580C2×C4—302no—
581C2×C4—302no—
582C2×C4—302no—
583C2×C4—302no—
584C2×C4C4×D3×D511yescharacteristic
585C2×C4C22×D3×D511yescharacteristic
586C8—22no—
587C8—62no—
588C8—102no—
589C8—302no—
590C2×C3—22no—
591C2×C3—102no—
592C2×C3—102no—
593C2×C3D5×#11711yescharacteristic
594C2×C3C2×D5×M1611yescharacteristic
595C2×C3C2×D5×M1611yescharacteristic
596C5#7861911yescharacteristic, complemented, Sylow
597C22—21no—
598C22—21no—
599C22—52no—
600C22—52no—
601C22—108no—
602C22—101no—
603C22—101no—
604C22—101no—
605C22—101no—
606C22#9124612yes—
607C22C2×C4×D3×D511yescharacteristic
608C4—21no—
609C4—32no—
610C4—52no—
611C4—61no—
612C4—61no—
613C4—61no—
614C4—101no—
615C4—152no—
616C4—152no—
617C4—152no—
618C4—301no—
619C4D5×#23712yes—
620C3#1061106211yescharacteristic, complemented, Sylow
621C2—22no—
622C2—102no—
623C2—102no—
624C2D5×#87711yescharacteristic
625C2C2×#9124611yescharacteristic
626C2D3×D5×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C8C22
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×C4×C5C24
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#2920
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750819C2semidirect
3. C5×#4719C2semidirect
6. #11748337C2semidirect
7. #11748331C2semidirect
8. #11747601C2semidirect
9. #11747596C2semidirect
10. #11747587C2semidirect
11. #11747577C2semidirect
32. #91098C22semidirect
33. C8×Dic15C22semidirect
35. C5×#815C22semidirect
36. C5×Dic3⋊C8C22semidirect
39. Dic3⋊#168C22semidirect
40. #90983C22semidirect
42. #90953C22semidirect
43. #90951C22semidirect
107. #4719D5semidirect
153. C2×Dic15M16semidirect
178. D5×Dic3M16semidirect
207. #815C2×D5semidirect
211. Dic3⋊C8C2×D5semidirect
520. C3×C5#2920semidirect
596. C5#78619semidirect
620. C3#10611062semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×Dic32
#117508192
C5×#47192
C3×#650152
#117484992
#117483372
#117483312
#117476012
#117475962
#117475872
#117475772
#106110623
#786195