Finite Group Databasebeta

← #14320626

Subgroups — #14320626

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×#91815C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic
3C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
4C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5#11749519C212yesmaximal
6#11749479C212yesmaximal, complemented
7#11748903C212yesmaximal, complemented
8C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
9C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
10#11748684C212yesmaximal, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10614049—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C2×#6719C2212yes—
18#91815—24no—
19C2×C4⋊Dic15C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×#217C2211yescharacteristic
23C4×C5×#67C418yescomplemented
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33C4×D3×Dic5—24no—
34C3×#3963C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73562—51nomaximal, Hall
40C2×C4×C5×D4—31no—
41C2×#4072—31no—
42C22×C4×Dic5—31no—
43#65509—32no—
44C4×C22⋊Dic5—31no—
45C4×C22⋊Dic5D311yescharacteristic, complemented
46#65270—32no—
47#65240—32no—
48#65239—32no—
49C4×C4⋊Dic5—31no—
50#65221—31no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2312yes—
60C2×C5×#67—24no—
61C2×C5×#67C2×C414yes—
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C22×C5×Dic3C2311yescharacteristic
65C2×C4×C5×D3—22no—
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3C2×C414yes—
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70C2×D3×Dic5—24no—
71C2×D3×Dic5—24no—
72C2×D3×Dic5—24no—
73#6719—24no—
74C4⋊Dic15—24no—
75C4×Dic15—22no—
76C4×Dic15D414yescomplemented
77C5×#217C2×C414yescomplemented
78C5×(C2×D3)⋊C4C2×C414yes—
79C5×Dic3⋊C4C2×C414yescomplemented
80C4×C5×Dic3C2×C414yescomplemented
81C3×C22⋊Dic5—24no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5—22no—
84Dic3⋊Dic5—24no—
85(C2×D3)⋊Dic5—24no—
86Dic3×Dic5—24no—
87C2×C4×#67D511yescharacteristic
88C2×#926—51no—
89C2×C42×D3—51no—
90C3×C4×C22⋊C4—51no—
91#4956—52no—
92#4945—52no—
93C4×(C2×D3)⋊C4—51no—
94#4932—51no—
95C4×Dic3⋊C4—51no—
96#4668—52no—
97#4655—52no—
98C22×C5×D4—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C23×Dic5—32no—
102C4×C5×D4—38no—
103C2×C5×C4⋊C4—31no—
104C2×C5×C22⋊C4—31no—
105C2×C5×C22⋊C4—31no—
106C2×C42×C5—31no—
107C2×C22⋊Dic5—32no—
108C2×C22⋊Dic5—32no—
109C2×C22⋊Dic5C2×D312yes—
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—64no—
117C2×C4×Dic5C2×D311yescharacteristic
118C2×C4×Dic5C2×D311yescharacteristic
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124#2290—151noSylow
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—21no—
129C23×C3×C5C22×C412yes—
130C23×C3×C5C2411yescharacteristic
131C22×C5×D3—21no—
132C22×C5×D3—22no—
133C22×C5×D3—21no—
134C22×C5×D3C22×C412yes—
135C22×C5×D3#4114yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—28no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5#4112yes—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15C2×D414yes—
149C5×#67—28no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3C22×C412yes—
155C2×C5×Dic3C22×C412yes—
156C2×C5×Dic3C22×C412yes—
157C4×C5×D3—28no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5#4114yes—
164D3×Dic5—216no—
165C23×C3×C4C2×D511yescharacteristic
166C22×#67C2×D511yescharacteristic
167C22×C4×D3—52no—
168C22×C4×D3C2×D511yescharacteristic
169C2×C3×C22⋊C4—52no—
170C2×C3×C42—51no—
171C2×C3×C42—51no—
172C2×#217—52no—
173C2×#217C2×D511yescharacteristic
174C4×#67Dic518yescomplemented
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4C2×D511yescharacteristic
177#926—104no—
178C2×C4⋊Dic3—52no—
179C2×Dic3⋊C4—52no—
180C2×Dic3⋊C4C2×D511yescharacteristic
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—52no—
184C2×C4×Dic3C2×D511yescharacteristic
185C42×D3—104no—
186C3×#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C24×C5—31no—
192C24×C5C22×D311yescharacteristic
193C2×C5×D4—34no—
194C2×C5×D4—64no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—31no—
198C22×C4×C5—31no—
199C22×C4×C5—31no—
200C22×C4×C5—34no—
201C22×C4×C5—62no—
202C22×C4×C5—62no—
203C22×C4×C5C4×D314yescomplemented
204C22×C4×C5C22×D311yescharacteristic
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—32no—
207C22×Dic5—32no—
208C22×Dic5—64no—
209C22×Dic5—64no—
210C22×Dic5—64no—
211C22×Dic5C22×D312yes—
212C22×Dic5C22×D312yes—
213C5×C4⋊C4—34no—
214C5×C22⋊C4—34no—
215C5×C22⋊C4—34no—
216C42×C5—34no—
217C22⋊Dic5—24no—
218C22⋊Dic5—64no—
219C22⋊Dic5—64no—
220C4⋊Dic5—64no—
221C4⋊Dic5—64no—
222C4×Dic5—22no—
223C4×Dic5—22no—
224C4×Dic5—34no—
225C4×Dic5—64no—
226C4×Dic5—62no—
227C2×C4×D4—31no—
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—51no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5C23×C411yescharacteristic
244C22×C3×C5C22×D411yescharacteristic
245C22×C3×C5C2×#4112yes—
246C22×C3×C5C2×#4111yescharacteristic
247C22×C3×C5C2×#4112yes—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3—24no—
251C2×C5×D3—24no—
252C2×C5×D3#11714yescomplemented
253C3×C4×C5—22no—
254C3×C4×C5C4×D414yes—
255Dic15—24no—
256Dic15—42no—
257C3×Dic5—24no—
258C3×Dic5—42no—
259C5×Dic3—22no—
260C5×Dic3—22no—
261C5×Dic3—22no—
262C24×C3C22×D511yescharacteristic
263C23×D3C22×D511yescharacteristic
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—52no—
267C22×C3×C4—52no—
268C22×C3×C4C2×Dic514yescomplemented
269C22×C3×C4C22×D511yescharacteristic
270C22×C3×C4C22×D511yescharacteristic
271C2×#67—24no—
272C2×#67C2×Dic514yes—
273C22×Dic3—52no—
274C22×Dic3—52no—
275C22×Dic3C22×D511yescharacteristic
276C22×Dic3C22×D511yescharacteristic
277C22×Dic3C22×D511yescharacteristic
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3—104no—
281C2×C4×D3—104no—
282C2×C4×D3—104no—
283C2×C4×D3C2×Dic514yes—
284C3×C22⋊C4—104no—
285C3×C42—102no—
286C3×C42—102no—
287#217—104no—
288#217C2×Dic514yescomplemented
289(C2×D3)⋊C4—104no—
290(C2×D3)⋊C4C2×Dic514yes—
291C4⋊Dic3—104no—
292Dic3⋊C4—104no—
293Dic3⋊C4C2×Dic514yescomplemented
294C4×Dic3—54no—
295C4×Dic3—104no—
296C4×Dic3—102no—
297C4×Dic3C2×Dic514yescomplemented
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—22no—
302C23×C5—32no—
303C23×C5—34no—
304C23×C5—62no—
305C23×C5—61no—
306C23×C5—61no—
307C23×C5C2×C4×D312yes—
308C23×C5C23×D311yescharacteristic
309C5×D4—68no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—28no—
313C2×C4×C5—32no—
314C2×C4×C5—32no—
315C2×C4×C5—32no—
316C2×C4×C5—62no—
317C2×C4×C5—61no—
318C2×C4×C5—61no—
319C2×C4×C5—62no—
320C2×C4×C5—68no—
321C2×C4×C5C2×C4×D312yes—
322C2×C4×C5C2×C4×D312yes—
323C2×C4×C5D3×D412yes—
324C2×C4×C5#23712yes—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—34no—
331C2×Dic5—616no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5#23514yes—
338C22×D4—31no—
339C23×C4—31no—
340C23×C4—152no—
341C23×C4D3×D511yescharacteristic
342C4×D4—38no—
343#117—304no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—52no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42—151no—
358C2×C42—304no—
359#95—52no—
360#95—152no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5—42no—
365C2×C3×C5C2×#11711yescharacteristic
366C2×C3×C5C2×C4×D411yescharacteristic
367C2×C3×C5C4×#4111yescharacteristic
368C2×C3×C5#52512yes—
369C2×C3×C5#52912yes—
370C5×D3—24no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—22no—
375C23×C3C22×Dic512yes—
376C23×C3C23×D511yescharacteristic
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—22no—
380C22×D3#70914yes—
381C22×D3C22×Dic512yes—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—28no—
385C2×C3×C4—54no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4D4×D512yes—
392C2×C3×C4#71112yes—
393C2×C3×C4C22×Dic512yes—
394C2×C3×C4C22×Dic512yes—
395#67—28no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—54no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3C22×Dic512yes—
407C2×Dic3C22×Dic512yes—
408C2×Dic3C22×Dic512yes—
409C4×D3—28no—
410C4×D3—1016no—
411C22×C5—22no—
412C22×C5—22no—
413C22×C5—22no—
414C22×C5—34no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—62no—
418C22×C5—62no—
419C22×C5—64no—
420C22×C5—64no—
421C22×C5C22×C4×D311yescharacteristic
422C22×C5C2×#23512yes—
423C22×C5C2×D3×D411yescharacteristic
424C22×C5C2×#23711yescharacteristic
425C22×C5D3×#4112yes—
426C4×C5—22no—
427C4×C5—62no—
428C4×C5—62no—
429C4×C5—62no—
430C4×C5#67⋊C414yes—
431Dic5—24no—
432Dic5—42no—
433Dic5—64no—
434Dic5—122no—
435C24—31no—
436C24C2×D3×D511yescharacteristic
437C2×D4—34no—
438C2×D4—64no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—34no—
445C22×C4—52no—
446C22×C4—52no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—152no—
450C22×C4—152no—
451C22×C4—304no—
452C22×C4—304no—
453C22×C4—304no—
454C22×C4D3×Dic514yescomplemented
455C22×C4C2×D3×D511yescharacteristic
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—34no—
458C4⋊C4—304no—
459C4⋊C4—304no—
460C22⋊C4—34no—
461C22⋊C4—34no—
462C22⋊C4—104no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—34no—
466C42—102no—
467C42—102no—
468C42—154no—
469C42—304no—
470C42—302no—
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3C2×#70912yes—
478C22×C3C2×D4×D511yescharacteristic
479C22×C3C2×#71111yescharacteristic
480C22×C3D5×#4112yes—
481C22×C3C23×Dic511yescharacteristic
482C2×D3—24no—
483C2×D3—22no—
484C2×D3—24no—
485C2×D3—22no—
486C2×D3#407214yescomplemented
487C3×C4—22no—
488C3×C4—104no—
489C3×C4—202no—
490C3×C4D4×Dic514yes—
491Dic3—22no—
492Dic3—22no—
493Dic3—22no—
494Dic3—104no—
495Dic3—202no—
496C2×C5—42no—
497C2×C5—64no—
498C2×C5C4×#23511yescharacteristic
499C2×C5C2×#67⋊C411yescharacteristic
500C2×C5D3×#11711yescharacteristic
501C2×C5#554712yes—
502C2×C5#555712yes—
503C23—22no—
504C23—22no—
505C23—21no—
506C23—21no—
507C23—34no—
508C23—32no—
509C23—62no—
510C23—61no—
511C23—61no—
512C23C2×D3×Dic512yes—
513C23C22×D3×D511yescharacteristic
514D4—68no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—28no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—54no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—68no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—154no—
533C2×C4—3016no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4#678012yes—
540C2×C4C2×D3×Dic512yes—
541C2×C4C2×D3×Dic512yes—
542C2×C4#679012yes—
543C2×C3—42no—
544C2×C3#6587212yes—
545C2×C3#6588112yes—
546C2×C3C2×#407211yescharacteristic
547C2×C3C2×D4×Dic511yescharacteristic
548C2×C3#41×Dic511yescharacteristic
549D3—24no—
550C5#7356211yescharacteristic, complemented, Sylow
551C22—22no—
552C22—22no—
553C22—22no—
554C22—34no—
555C22—42no—
556C22—42no—
557C22—64no—
558C22—62no—
559C22—64no—
560C22—62no—
561C22D5×#23512yes—
562C22D3×#70912yes—
563C22C2×#678011yescharacteristic
564C22C22×D3×Dic511yescharacteristic
565C22C2×#679011yescharacteristic
566C4—22no—
567C4—62no—
568C4—62no—
569C4—62no—
570C4—104no—
571C4—202no—
572C4—304no—
573C4—602no—
574C4#67⋊Dic514yes—
575C3#1061404911yescharacteristic, complemented, Sylow
576C2—42no—
577C2—64no—
578C2Dic5×#23511yescharacteristic
579C2D3×#407211yescharacteristic
580C2#1175456512yes—
581C2#1175466312yes—
582C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91815C2semidirect
3. C2×C4×D3×Dic5C2semidirect
4. C3×C4×C22⋊Dic5C2semidirect
6. #11749479C2semidirect
7. #11748903C2semidirect
8. C4×Dic3⋊Dic5C2semidirect
9. C4×(C2×D3)⋊Dic5C2semidirect
10. #11748684C2semidirect
11. #11748611C2semidirect
23. C4×C5×#67C4semidirect
45. C4×C22⋊Dic5D3semidirect
55. C22×C3×C4×C5C2×C4semidirect
76. C4×Dic15D4semidirect
77. C5×#217C2×C4semidirect
79. C5×Dic3⋊C4C2×C4semidirect
80. C4×C5×Dic3C2×C4semidirect
174. C4×#67Dic5semidirect
203. C22×C4×C5C4×D3semidirect
252. C2×C5×D3#117semidirect
268. C22×C3×C4C2×Dic5semidirect
288. #217C2×Dic5semidirect
293. Dic3⋊C4C2×Dic5semidirect
297. C4×Dic3C2×Dic5semidirect
454. C22×C4D3×Dic5semidirect
471. C3×C5#2290semidirect
486. C2×D3#4072semidirect
550. C5#73562semidirect
575. C3#10614049semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C2×C4×C5×#672
C2×C4×D3×Dic52
C3×C4×C22⋊Dic52
#117495192
#117494792
#117489032
C4×Dic3⋊Dic52
C4×(C2×D3)⋊Dic52
#117486842
#117486112
#106140493
#735625