Finite Group Databasebeta

← #14320557

Subgroups — #14320557

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×#91815C211yesmaximal, characteristic, complemented
3C22×C4×Dic15C211yesmaximal, characteristic, complemented
4#11751321C212yesmaximal
5C4×#6719C211yesmaximal, characteristic, complemented
6C4×#6719C211yesmaximal, characteristic, complemented
7#11751081C212yesmaximal, complemented
8#11751052C212yesmaximal, complemented
9#11751051C212yesmaximal, complemented
10C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
11#11751033C211yesmaximal, characteristic, complemented
12#10614049—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×Dic15C2212yes—
17C3×C4×C5×D4C418yescomplemented
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6719C2212yes—
23C2×#6719C2212yes—
24C2×#6719C2212yes—
25#91815—24no—
26C2×C4⋊Dic15C2212yes—
27C2×C4⋊Dic15C2212yes—
28C2×C4×Dic15—24no—
29C2×C4×Dic15C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31C2×C4×Dic15C2211yescharacteristic
32C2×C4×Dic15C2212yes—
33C2×C4×Dic15C2211yescharacteristic
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#82318—51nomaximal, Hall
40C2×C4×C5×D4D311yescharacteristic
41C2×#4072—31no—
42C22×C4×Dic5—31no—
43#65509—32no—
44C4×C22⋊Dic5—31no—
45C4×C22⋊Dic5—31no—
46#65270—32no—
47#65240—32no—
48#65239—32no—
49C4×C4⋊Dic5—31no—
50#65221—31no—
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4C2×C414yes—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5C2×C414yes—
60C22×C3×C4×C5C2×C414yescomplemented
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15—24no—
67C22×Dic15—24no—
68C22×Dic15—24no—
69C22×Dic15C2312yes—
70C22×Dic15C2312yes—
71C22×Dic15C2312yes—
72C22×Dic15C2312yes—
73C3×C5×C4⋊C4C2×C414yescomplemented
74C3×C5×C22⋊C4C2×C414yes—
75C3×C5×C22⋊C4C2×C414yescomplemented
76C3×C42×C5C2×C414yescomplemented
77#6719—24no—
78#6719—24no—
79#6719—24no—
80C4⋊Dic15—24no—
81C4⋊Dic15—24no—
82C4×Dic15—22no—
83C4×Dic15—22no—
84C4×Dic15—22no—
85C4×Dic15—24no—
86C4×Dic15D414yescomplemented
87C2×C3×C4×D4D511yescharacteristic
88C2×#926—51no—
89C22×C4×Dic3—51no—
90#5220—52no—
91C4×#217—51no—
92C4×#217—51no—
93#4980—52no—
94#4951—52no—
95#4950—52no—
96C4×C4⋊Dic3—51no—
97#4932—51no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5C2×D311yescharacteristic
100C23×C4×C5C2×D311yescharacteristic
101C23×Dic5—32no—
102C4×C5×D4Dic318yescomplemented
103C2×C5×C4⋊C4C2×D311yescharacteristic
104C2×C5×C22⋊C4C2×D311yescharacteristic
105C2×C5×C22⋊C4C2×D311yescharacteristic
106C2×C42×C5C2×D311yescharacteristic
107C2×C22⋊Dic5—32no—
108C2×C22⋊Dic5—32no—
109C2×C22⋊Dic5—32no—
110#4072—64no—
111C2×C4⋊Dic5—32no—
112C2×C4⋊Dic5—32no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—64no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2290—151noSylow
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—21no—
131C23×C3×C5—22no—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C22×C412yes—
134C23×C3×C5#4114yes—
135C23×C3×C5C2411yescharacteristic
136C3×C5×D4—28no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—28no—
144C2×C3×C4×C5—28no—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C22×C412yes—
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5#4112yes—
152C2×Dic15—216no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15C2×D414yes—
164C2×Dic15#4114yes—
165C22×C3×D4C2×D511yescharacteristic
166C23×C3×C4C2×D511yescharacteristic
167C23×C3×C4C2×D511yescharacteristic
168C23×Dic3—52no—
169C3×C4×D4Dic518yescomplemented
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C22⋊C4C2×D511yescharacteristic
172C2×C3×C22⋊C4C2×D511yescharacteristic
173C2×C3×C42C2×D511yescharacteristic
174C2×#217—52no—
175C2×#217—52no—
176C2×#217—52no—
177#926—104no—
178C2×C4⋊Dic3—52no—
179C2×C4⋊Dic3—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—51no—
184C2×C4×Dic3—52no—
185C2×C4×Dic3—104no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C24×C5C22×D311yescharacteristic
192C24×C5C22×D311yescharacteristic
193C2×C5×D4—24no—
194C2×C5×D4C2×Dic314yes—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5C2×Dic314yes—
200C22×C4×C5C2×Dic314yescomplemented
201C22×C4×C5C22×D311yescharacteristic
202C22×C4×C5C22×D311yescharacteristic
203C22×C4×C5C22×D311yescharacteristic
204C22×C4×C5C22×D311yescharacteristic
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—32no—
207C22×Dic5—32no—
208C22×Dic5—32no—
209C22×Dic5—32no—
210C22×Dic5—64no—
211C22×Dic5—64no—
212C22×Dic5—64no—
213C5×C4⋊C4C2×Dic314yescomplemented
214C5×C22⋊C4C2×Dic314yes—
215C5×C22⋊C4C2×Dic314yescomplemented
216C42×C5C2×Dic314yescomplemented
217C22⋊Dic5—64no—
218C22⋊Dic5—64no—
219C22⋊Dic5—64no—
220C4⋊Dic5—64no—
221C4⋊Dic5—64no—
222C4×Dic5—34no—
223C4×Dic5—64no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C2×C4×D4D1511yescharacteristic
228C2×#117—151no—
229C22×C42—151no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—151no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5—24no—
242C22×C3×C5—22no—
243C22×C3×C5—22no—
244C22×C3×C5—22no—
245C22×C3×C5—42no—
246C22×C3×C5—42no—
247C22×C3×C5#11714yescomplemented
248C22×C3×C5C23×C411yescharacteristic
249C22×C3×C5C22×D411yescharacteristic
250C22×C3×C5C2×#4112yes—
251C22×C3×C5C2×#4111yescharacteristic
252C22×C3×C5C2×#4112yes—
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255C3×C4×C5—22no—
256C3×C4×C5—22no—
257C3×C4×C5C4×D414yes—
258Dic15—24no—
259Dic15—24no—
260Dic15—42no—
261Dic15—42no—
262C24×C3C22×D511yescharacteristic
263C24×C3C22×D511yescharacteristic
264C2×C3×D4—24no—
265C2×C3×D4C2×Dic514yes—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4C2×Dic514yes—
271C22×C3×C4C2×Dic514yescomplemented
272C22×C3×C4C22×D511yescharacteristic
273C22×C3×C4C22×D511yescharacteristic
274C22×C3×C4C22×D511yescharacteristic
275C22×C3×C4C22×D511yescharacteristic
276C22×C3×C4C22×D511yescharacteristic
277C22×Dic3—52no—
278C22×Dic3—52no—
279C22×Dic3—52no—
280C22×Dic3—52no—
281C22×Dic3—104no—
282C22×Dic3—104no—
283C22×Dic3—104no—
284C3×C4⋊C4C2×Dic514yescomplemented
285C3×C22⋊C4C2×Dic514yes—
286C3×C22⋊C4C2×Dic514yescomplemented
287C3×C42C2×Dic514yescomplemented
288#217—104no—
289#217—104no—
290#217—104no—
291C4⋊Dic3—104no—
292C4⋊Dic3—104no—
293C4×Dic3—54no—
294C4×Dic3—104no—
295C4×Dic3—102no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—22no—
305C23×C5#23514yes—
306C23×C5C22×Dic312yes—
307C23×C5C22×Dic312yes—
308C23×C5C23×D311yescharacteristic
309C5×D4—28no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—22no—
316C2×C4×C5—28no—
317C2×C4×C5—28no—
318C2×C4×C5D3×D412yes—
319C2×C4×C5#23712yes—
320C2×C4×C5C22×Dic312yes—
321C2×C4×C5C22×Dic312yes—
322C2×C4×C5C22×Dic312yes—
323C2×C4×C5C22×Dic312yes—
324C2×C4×C5C22×Dic312yes—
325C2×Dic5—34no—
326C2×Dic5—34no—
327C2×Dic5—616no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—62no—
338C22×D4C2×D1511yescharacteristic
339C23×C4—152no—
340C23×C4C2×D1511yescharacteristic
341C23×C4C2×D1511yescharacteristic
342C4×D4Dic1518yescomplemented
343#117—304no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4C2×D1511yescharacteristic
347C2×C22⋊C4—152no—
348C2×C22⋊C4—152no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4C2×D1511yescharacteristic
351C2×C22⋊C4C2×D1511yescharacteristic
352C2×C42—151no—
353C2×C42—152no—
354C2×C42—151no—
355C2×C42—151no—
356C2×C42—151no—
357C2×C42—304no—
358C2×C42C2×D1511yescharacteristic
359#95—152no—
360#95—152no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5—24no—
365C2×C3×C5—42no—
366C2×C3×C5C2×#11711yescharacteristic
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5C4×#4111yescharacteristic
369C2×C3×C5#52512yes—
370C2×C3×C5#52912yes—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—22no—
378C23×C3#70914yes—
379C23×C3C22×Dic512yes—
380C23×C3C22×Dic512yes—
381C23×C3C23×D511yescharacteristic
382C3×D4—28no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—28no—
390C2×C3×C4—28no—
391C2×C3×C4D4×D512yes—
392C2×C3×C4#71112yes—
393C2×C3×C4C22×Dic512yes—
394C2×C3×C4C22×Dic512yes—
395C2×C3×C4C22×Dic512yes—
396C2×C3×C4C22×Dic512yes—
397C2×C3×C4C22×Dic512yes—
398C2×Dic3—54no—
399C2×Dic3—54no—
400C2×Dic3—1016no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—102no—
411C22×C5—24no—
412C22×C5—22no—
413C22×C5—24no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5—42no—
419C22×C5—42no—
420C22×C5#92614yescomplemented
421C22×C5C2×#23512yes—
422C22×C5C2×D3×D411yescharacteristic
423C22×C5C2×#23711yescharacteristic
424C22×C5D3×#4112yes—
425C22×C5C23×Dic311yescharacteristic
426C4×C5—22no—
427C4×C5—22no—
428C4×C5—22no—
429C4×C5—22no—
430C4×C5D4×Dic314yes—
431Dic5—64no—
432Dic5—64no—
433Dic5—122no—
434Dic5—122no—
435C24C22×D1511yescharacteristic
436C24C22×D1511yescharacteristic
437C2×D4—24no—
438C2×D4C2×Dic1514yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—152no—
444C22×C4—152no—
445C22×C4—152no—
446C22×C4—152no—
447C22×C4—304no—
448C22×C4—304no—
449C22×C4—304no—
450C22×C4C2×Dic1514yes—
451C22×C4C2×Dic1514yescomplemented
452C22×C4C22×D1511yescharacteristic
453C22×C4C22×D1511yescharacteristic
454C22×C4C22×D1511yescharacteristic
455C22×C4C22×D1511yescharacteristic
456C22×C4C22×D1511yescharacteristic
457C4⋊C4—304no—
458C4⋊C4—304no—
459C4⋊C4C2×Dic1514yescomplemented
460C22⋊C4—304no—
461C22⋊C4—304no—
462C22⋊C4—304no—
463C22⋊C4C2×Dic1514yes—
464C22⋊C4C2×Dic1514yescomplemented
465C42—154no—
466C42—304no—
467C42—302no—
468C42—302no—
469C42—302no—
470C42C2×Dic1514yescomplemented
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—24no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3#407214yescomplemented
482C22×C3C2×#70912yes—
483C22×C3C2×D4×D511yescharacteristic
484C22×C3C2×#71111yescharacteristic
485C22×C3D5×#4112yes—
486C22×C3C23×Dic511yescharacteristic
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—22no—
491C3×C4D4×Dic514yes—
492Dic3—104no—
493Dic3—104no—
494Dic3—202no—
495Dic3—202no—
496C2×C5—24no—
497C2×C5—42no—
498C2×C5#553812yes—
499C2×C5#554712yes—
500C2×C5C2×#92611yescharacteristic
501C2×C5C2×D4×Dic311yescharacteristic
502C2×C5Dic3×#4111yescharacteristic
503C23—21no—
504C23—21no—
505C23—22no—
506C23—22no—
507C23—21no—
508C23—21no—
509C23—22no—
510C23#681714yes—
511C23C22×Dic1512yes—
512C23C22×Dic1512yes—
513C23C23×D1511yescharacteristic
514D4—28no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—28no—
522C2×C4—28no—
523C2×C4—154no—
524C2×C4—154no—
525C2×C4—3016no—
526C2×C4—302no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4D4×D1512yes—
537C2×C4#681912yes—
538C2×C4C22×Dic1512yes—
539C2×C4C22×Dic1512yes—
540C2×C4C22×Dic1512yes—
541C2×C4C22×Dic1512yes—
542C2×C4C22×Dic1512yes—
543C2×C3—24no—
544C2×C3—42no—
545C2×C3#6587212yes—
546C2×C3#6588112yes—
547C2×C3C2×#407211yescharacteristic
548C2×C3C2×D4×Dic511yescharacteristic
549C2×C3#41×Dic511yescharacteristic
550C5#8231811yescharacteristic, complemented, Sylow
551C22—24no—
552C22—22no—
553C22—24no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—42no—
559C22—42no—
560C22#9181514yescomplemented
561C22C2×#681712yes—
562C22C2×D4×D1511yescharacteristic
563C22C2×#681911yescharacteristic
564C22#41×D1512yes—
565C22C23×Dic1511yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—304no—
571C4—304no—
572C4—602no—
573C4—602no—
574C4D4×Dic1514yes—
575C3#1061404911yescharacteristic, complemented, Sylow
576C2—24no—
577C2—42no—
578C2#1175629712yes—
579C2#1175630612yes—
580C2C2×#9181511yescharacteristic
581C2C2×D4×Dic1511yescharacteristic
582C2#41×Dic1511yescharacteristic
subgroupG/H
centerC22×C4C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC2×C3×C4×C5×D4C2
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×C4×D4D15
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91815C2semidirect
3. C22×C4×Dic15C2semidirect
5. C4×#6719C2semidirect
6. C4×#6719C2semidirect
7. #11751081C2semidirect
8. #11751052C2semidirect
9. #11751051C2semidirect
10. C4×C4⋊Dic15C2semidirect
11. #11751033C2semidirect
17. C3×C4×C5×D4C4semidirect
60. C22×C3×C4×C5C2×C4semidirect
73. C3×C5×C4⋊C4C2×C4semidirect
75. C3×C5×C22⋊C4C2×C4semidirect
76. C3×C42×C5C2×C4semidirect
86. C4×Dic15D4semidirect
102. C4×C5×D4Dic3semidirect
169. C3×C4×D4Dic5semidirect
200. C22×C4×C5C2×Dic3semidirect
213. C5×C4⋊C4C2×Dic3semidirect
215. C5×C22⋊C4C2×Dic3semidirect
216. C42×C5C2×Dic3semidirect
247. C22×C3×C5#117semidirect
271. C22×C3×C4C2×Dic5semidirect
284. C3×C4⋊C4C2×Dic5semidirect
286. C3×C22⋊C4C2×Dic5semidirect
287. C3×C42C2×Dic5semidirect
342. C4×D4Dic15semidirect
420. C22×C5#926semidirect
451. C22×C4C2×Dic15semidirect
459. C4⋊C4C2×Dic15semidirect
464. C22⋊C4C2×Dic15semidirect
470. C42C2×Dic15semidirect
471. C3×C5#2290semidirect
481. C22×C3#4072semidirect
550. C5#82318semidirect
560. C22#91815semidirect
575. C3#10614049semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×#918152
C22×C4×Dic152
#117513212
C4×#67192
#117510812
#117510522
#117510512
C4×C4⋊Dic152
#117510332
#106140493
#823185