Finite Group Databasebeta

← #14319961

Subgroups — #14319961

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D5×Dic3C211yesmaximal, characteristic
2C2×#91923C212yesmaximal, complemented
3#11752459C211yesmaximal, characteristic
4C3×#65800C211yesmaximal, characteristic
5#11752028C214yesmaximal, complemented
6Dic3×C22⋊AGL(1,𝔽5)C214yesmaximal, complemented
7#11751984C212yesmaximal, complemented
8#10617480—31nomaximal, Hall
9C24×C3×D5C2211yescharacteristic
10C23×Dic15C411yescharacteristic, complemented
11C23×C5×Dic3C411yescharacteristic, complemented
12C22×D5×Dic3—28no—
13C22×D5×Dic3C411yescharacteristic, complemented
14C22×D5×Dic3C411yescharacteristic, complemented
15C22×D5×Dic3C412yescomplemented
16C22×D5×Dic3C412yescomplemented
17C22×D5×Dic3C2211yescharacteristic
18C22×D5×Dic3C2212yes—
19C22×D5×Dic3C2212yes—
20C22×D5×Dic3C2211yescharacteristic
21C2×#6763C2212yes—
22C2×#6763C2214yes—
23C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
24C2×C3×C22⋊AGL(1,𝔽5)C2214yes—
25C2×Dic3⋊AGL(1,𝔽5)C2214yescomplemented
26#91923—28no—
27C2×Dic3×AGL(1,𝔽5)C2214yescomplemented
28(C2×AGL(1,𝔽5))⋊Dic3C2218yescomplemented
29#73817—51nomaximal, Hall
30C23×C4×D5—31no—
31C2×#4130—32no—
32#65800—31no—
33#65800D311yescharacteristic
34#65765—34no—
35#65764—32no—
36C4×C22⋊AGL(1,𝔽5)—34no—
37C24×C3×C5C2×C411yescharacteristic
38C23×C3×D5—24no—
39C23×C3×D5—28no—
40C23×C3×D5C2×C411yescharacteristic
41C23×C3×D5C2×C412yes—
42C23×C3×D5C2311yescharacteristic
43C23×C3×D5C2312yes—
44C22×ΓL(1,𝔽16)C2314yes—
45C22×C3×AGL(1,𝔽5)C2314yes—
46C22×Dic15—24no—
47C22×Dic15C2×C411yescharacteristic
48C22×Dic15C2×C412yes—
49C22×Dic15C2×C412yes—
50C22×Dic15C2×C411yescharacteristic
51C22×C5×Dic3—24no—
52C22×C5×Dic3C2×C411yescharacteristic
53C22×C5×Dic3C2×C412yes—
54C22×C5×Dic3C2×C412yes—
55C22×C5×Dic3C2×C411yescharacteristic
56C2×D5×Dic3—24no—
57C2×D5×Dic3—24no—
58C2×D5×Dic3—24no—
59C2×D5×Dic3—28no—
60C2×D5×Dic3—28no—
61C2×D5×Dic3—28no—
62C2×D5×Dic3—28no—
63C2×D5×Dic3C2×C412yes—
64C2×D5×Dic3C2×C412yes—
65C2×D5×Dic3C2×C412yes—
66C2×D5×Dic3C2×C412yes—
67C2×D5×Dic3C2×C412yes—
68C2×D5×Dic3C2×C411yescharacteristic
69C2×D5×Dic3C2×C411yescharacteristic
70C2×D5×Dic3D418yes—
71C2×D5×Dic3C2312yes—
72C2×D5×Dic3C2311yescharacteristic
73C2×D5×Dic3C2311yescharacteristic
74#6763—24no—
75#6763—28no—
76C3×C22⋊AGL(1,𝔽5)—24no—
77C3×C22⋊AGL(1,𝔽5)—28no—
78Dic3⋊AGL(1,𝔽5)—28no—
79Dic3×AGL(1,𝔽5)—28no—
80C24×Dic3—51no—
81C2×#877—52no—
82C3×#379—51no—
83#5247—51no—
84#4943—52no—
85#4942—54no—
86Dic3×C22⋊C4—54no—
87C24×D5C2×D311yescharacteristic
88C23×C4×C5—31no—
89C23×Dic5—31no—
90C22×C4×D5—31no—
91C22×C4×D5—32no—
92C22×C4×D5—32no—
93C22×C4×D5—31no—
94C22×C4×D5—31no—
95C22×C4×D5—32no—
96C22×C4×D5—31no—
97C22×C4×D5—32no—
98C22×C4×D5—68no—
99C2×C22⋊AGL(1,𝔽5)—32no—
100C2×C22⋊AGL(1,𝔽5)—34no—
101C2×C22⋊AGL(1,𝔽5)C2×D312yes—
102C2×C22⋊AGL(1,𝔽5)C2×D314yes—
103#4130—68no—
104C2×C4⋊AGL(1,𝔽5)—34no—
105C2×C4×AGL(1,𝔽5)—34no—
106(C2×AGL(1,𝔽5))⋊C4—38no—
107#2280—151noSylow
108C23×C3×C5—22no—
109C23×C3×C5—24no—
110C23×C3×C5C22×C411yescharacteristic
111C23×C3×C5C22×C412yes—
112C22×C3×D5—232no—
113C22×C3×D5—22no—
114C22×C3×D5—24no—
115C22×C3×D5—24no—
116C22×C3×D5—24no—
117C22×C3×D5—24no—
118C22×C3×D5—24no—
119C22×C3×D5—24no—
120C22×C3×D5—24no—
121C22×C3×D5C22×C411yescharacteristic
122C22×C3×D5C22×C412yes—
123C22×C3×D5C2×D414yes—
124C22×C3×D5#4118yes—
125C22×C3×D5C2411yescharacteristic
126C2×ΓL(1,𝔽16)—24no—
127C2×ΓL(1,𝔽16)—28no—
128C2×C3×AGL(1,𝔽5)—24no—
129C2×C3×AGL(1,𝔽5)—28no—
130C2×Dic15—22no—
131C2×Dic15—24no—
132C2×Dic15—24no—
133C2×Dic15C22⋊C414yescomplemented
134C2×Dic15C22×C412yes—
135C2×Dic15C22×C411yescharacteristic
136C2×Dic15C22×C411yescharacteristic
137C2×C5×Dic3—22no—
138C2×C5×Dic3—24no—
139C2×C5×Dic3—24no—
140C2×C5×Dic3C22⋊C414yescomplemented
141C2×C5×Dic3C22×C412yes—
142C2×C5×Dic3C22×C411yescharacteristic
143C2×C5×Dic3C22×C411yescharacteristic
144D5×Dic3—24no—
145D5×Dic3—24no—
146D5×Dic3—24no—
147D5×Dic3—24no—
148D5×Dic3—24no—
149D5×Dic3—24no—
150D5×Dic3C22⋊C414yescomplemented
151D5×Dic3C22⋊C414yescomplemented
152D5×Dic3C2×D414yes—
153D5×Dic3C2×D414yes—
154C25×C3—51no—
155C23×Dic3—51no—
156C23×Dic3—51no—
157C23×Dic3—52no—
158C23×Dic3—52no—
159C23×Dic3—51no—
160C23×Dic3—51no—
161C23×Dic3—52no—
162C23×Dic3—52no—
163C23×Dic3—51no—
164C23×Dic3—108no—
165C23×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
166C2×C3×C22⋊C4—54no—
167C2×C3×C22⋊C4—52no—
168C2×#217—54no—
169C2×#217—52no—
170C2×Dic3⋊C4—54no—
171C2×C4×Dic3—54no—
172#877—108no—
173C3⋊#95—58no—
174C24×C5C4×D311yescharacteristic
175C23×D5—24no—
176C23×D5—28no—
177C23×D5C4×D312yes—
178C23×D5C4×D311yescharacteristic
179C23×D5C22×D311yescharacteristic
180C23×D5C22×D312yes—
181C22×AGL(1,𝔽5)—34no—
182C22×AGL(1,𝔽5)C22×D314yes—
183C22×C4×C5—31no—
184C22×C4×C5—32no—
185C22×C4×C5—32no—
186C22×C4×C5—31no—
187C22×C4×C5—64no—
188C22×Dic5—31no—
189C22×Dic5—32no—
190C22×Dic5—32no—
191C22×Dic5—31no—
192C22×Dic5—64no—
193C2×C4×D5—31no—
194C2×C4×D5—31no—
195C2×C4×D5—38no—
196C2×C4×D5—31no—
197C2×C4×D5—31no—
198C2×C4×D5—32no—
199C2×C4×D5—32no—
200C2×C4×D5—32no—
201C2×C4×D5—32no—
202C2×C4×D5—32no—
203C2×C4×D5—32no—
204C2×C4×D5—68no—
205C2×C4×D5—68no—
206C2×C4×D5—68no—
207C2×C4×D5—68no—
208C2×C4×D5—64no—
209C2×C4×D5—64no—
210C2×C4×D5—64no—
211C22⋊AGL(1,𝔽5)—24no—
212C22⋊AGL(1,𝔽5)—28no—
213C22⋊AGL(1,𝔽5)—64no—
214C22⋊AGL(1,𝔽5)—68no—
215C4⋊AGL(1,𝔽5)—68no—
216C4×AGL(1,𝔽5)—68no—
217C24×C4—151no—
218C2×#117—152no—
219#381—152no—
220#380—154no—
221#379—51no—
222#379—151no—
223C4×C22⋊C4—154no—
224C22×C3×C5—28no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5C2×C22⋊C412yes—
229C22×C3×C5#11714yescomplemented
230C22×C3×C5C23×C411yescharacteristic
231C2×C3×D5—216no—
232C2×C3×D5—28no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—22no—
236C2×C3×D5—28no—
237C2×C3×D5—216no—
238C2×C3×D5C2×C22⋊C412yes—
239C2×C3×D5#11714yescomplemented
240C2×C3×D5C22×D412yes—
241C2×C3×D5C2×#4114yes—
242ΓL(1,𝔽16)—44no—
243C3×AGL(1,𝔽5)—44no—
244Dic15—22no—
245Dic15C2×C22⋊C412yes—
246Dic15C2×C22⋊C412yes—
247C5×Dic3—22no—
248C5×Dic3C2×C22⋊C412yes—
249C5×Dic3C2×C22⋊C412yes—
250C24×C3—52no—
251C24×C3—51no—
252C24×C3—52no—
253C24×C3—51no—
254C24×C3—108no—
255C24×C3—104no—
256C24×C3C2×AGL(1,𝔽5)11yescharacteristic
257C22×C3×C4—54no—
258C22×Dic3—24no—
259C22×Dic3—51no—
260C22×Dic3—58no—
261C22×Dic3—51no—
262C22×Dic3—51no—
263C22×Dic3—51no—
264C22×Dic3—51no—
265C22×Dic3—52no—
266C22×Dic3—52no—
267C22×Dic3—51no—
268C22×Dic3—52no—
269C22×Dic3—52no—
270C22×Dic3—52no—
271C22×Dic3—52no—
272C22×Dic3—52no—
273C22×Dic3—52no—
274C22×Dic3—54no—
275C22×Dic3—104no—
276C22×Dic3—108no—
277C22×Dic3—108no—
278C22×Dic3—108no—
279C22×Dic3—108no—
280C22×Dic3—104no—
281C22×Dic3—104no—
282C22×Dic3—104no—
283C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
284C22×Dic3C2×AGL(1,𝔽5)12yes—
285C22×Dic3C2×AGL(1,𝔽5)12yes—
286C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
287C3×C22⋊C4—104no—
288C3×C22⋊C4—108no—
289#217—104no—
290#217—108no—
291Dic3⋊C4—108no—
292C4×Dic3—108no—
293C23×C5—24no—
294C23×C5—22no—
295C23×C5C2×C4×D312yes—
296C23×C5C2×C4×D311yescharacteristic
297C22×D5—232no—
298C22×D5—24no—
299C22×D5—22no—
300C22×D5—24no—
301C22×D5—24no—
302C22×D5—24no—
303C22×D5—24no—
304C22×D5—24no—
305C22×D5—24no—
306C22×D5C2×C4×D312yes—
307C22×D5C2×C4×D311yescharacteristic
308C22×D5D3×D414yes—
309C22×D5#23718yes—
310C22×D5C23×D311yescharacteristic
311C2×AGL(1,𝔽5)—24no—
312C2×AGL(1,𝔽5)—28no—
313C2×AGL(1,𝔽5)—64no—
314C2×AGL(1,𝔽5)—68no—
315C2×C4×C5—34no—
316C2×C4×C5—31no—
317C2×C4×C5—31no—
318C2×C4×C5—32no—
319C2×C4×C5—64no—
320C2×C4×C5—64no—
321C2×C4×C5—62no—
322C2×Dic5—34no—
323C2×Dic5—31no—
324C2×Dic5—31no—
325C2×Dic5—32no—
326C2×Dic5—64no—
327C2×Dic5—64no—
328C2×Dic5—62no—
329C4×D5—34no—
330C4×D5—34no—
331C4×D5—34no—
332C4×D5—34no—
333C4×D5—64no—
334C4×D5—64no—
335C4×D5—64no—
336C4×D5—64no—
337C4×D5—64no—
338C4×D5—64no—
339C25—51no—
340C23×C4—31no—
341C23×C4—151no—
342C23×C4—152no—
343C23×C4—152no—
344C23×C4—151no—
345C23×C4—151no—
346C23×C4—152no—
347C23×C4—152no—
348C23×C4—151no—
349C23×C4—151no—
350C23×C4—308no—
351#117—308no—
352C2×C4⋊C4—154no—
353C2×C22⋊C4—52no—
354C2×C22⋊C4—54no—
355C2×C22⋊C4—152no—
356C2×C22⋊C4—154no—
357C2×C42—154no—
358#95—158no—
359C2×C3×C5—22no—
360C2×C3×C5—24no—
361C2×C3×C5C22×C22⋊C411yescharacteristic
362C2×C3×C5C2×#11712yes—
363C3×D5—22no—
364C3×D5—24no—
365C3×D5#52514yes—
366C23×C3—24no—
367C23×C3—22no—
368C23×C3—51no—
369C23×C3—58no—
370C23×C3—54no—
371C23×C3—52no—
372C23×C3—51no—
373C23×C3—104no—
374C23×C3—104no—
375C23×C3—104no—
376C23×C3—104no—
377C23×C3—104no—
378C23×C3—104no—
379C23×C3—1032no—
380C23×C3—104no—
381C23×C3—102no—
382C23×C3C22×AGL(1,𝔽5)12yes—
383C23×C3C22×AGL(1,𝔽5)11yescharacteristic
384C2×C3×C4—104no—
385C2×C3×C4—108no—
386C2×Dic3—22no—
387C2×Dic3—24no—
388C2×Dic3—24no—
389C2×Dic3—54no—
390C2×Dic3—51no—
391C2×Dic3—51no—
392C2×Dic3—54no—
393C2×Dic3—54no—
394C2×Dic3—54no—
395C2×Dic3—54no—
396C2×Dic3—52no—
397C2×Dic3—104no—
398C2×Dic3—104no—
399C2×Dic3—104no—
400C2×Dic3—104no—
401C2×Dic3—104no—
402C2×Dic3—104no—
403C2×Dic3—102no—
404C2×Dic3—104no—
405C2×Dic3—104no—
406C2×Dic3—104no—
407C2×Dic3—108no—
408C2×Dic3C22⋊AGL(1,𝔽5)14yescomplemented
409C2×Dic3C22×AGL(1,𝔽5)12yes—
410C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
411C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
412C22×C5—28no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5#87714yescomplemented
417C22×C5D3×C22⋊C412yes—
418C22×C5C22×C4×D311yescharacteristic
419C2×D5—28no—
420C2×D5—216no—
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—22no—
424C2×D5—28no—
425C2×D5—216no—
426C2×D5#87714yescomplemented
427C2×D5D3×C22⋊C412yes—
428C2×D5C2×D3×D412yes—
429C2×D5C2×#23714yes—
430AGL(1,𝔽5)—44no—
431AGL(1,𝔽5)—124no—
432C4×C5—32no—
433C4×C5—32no—
434C4×C5—62no—
435Dic5—32no—
436Dic5—32no—
437Dic5—62no—
438C24—52no—
439C24—51no—
440C24—52no—
441C24—51no—
442C24—104no—
443C24—108no—
444C24D3×AGL(1,𝔽5)11yescharacteristic
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—31no—
449C22×C4—54no—
450C22×C4—64no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—158no—
454C22×C4—151no—
455C22×C4—151no—
456C22×C4—152no—
457C22×C4—152no—
458C22×C4—152no—
459C22×C4—152no—
460C22×C4—152no—
461C22×C4—152no—
462C22×C4—151no—
463C22×C4—152no—
464C22×C4—152no—
465C22×C4—151no—
466C22×C4—154no—
467C22×C4—304no—
468C22×C4—308no—
469C22×C4—308no—
470C22×C4—308no—
471C22×C4—308no—
472C22×C4—304no—
473C22×C4—304no—
474C22×C4—304no—
475C4⋊C4—308no—
476C22⋊C4—104no—
477C22⋊C4—108no—
478C22⋊C4—304no—
479C22⋊C4—308no—
480C42—308no—
481C3×C5#228011yescharacteristic, complemented, Hall
482C22×C3—28no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—54no—
487C22×C3—52no—
488C22×C3—54no—
489C22×C3—52no—
490C22×C3—1016no—
491C22×C3—108no—
492C22×C3—1016no—
493C22×C3—108no—
494C22×C3—102no—
495C22×C3—102no—
496C22×C3—102no—
497C22×C3#413014yescomplemented
498C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
499C22×C3C23×AGL(1,𝔽5)11yescharacteristic
500C3×C4—204no—
501Dic3—22no—
502Dic3—52no—
503Dic3—52no—
504Dic3—102no—
505Dic3—204no—
506Dic3C2×C22⋊AGL(1,𝔽5)12yes—
507Dic3C2×C22⋊AGL(1,𝔽5)12yes—
508C2×C5—24no—
509C2×C5—22no—
510C2×C5C2×#87712yes—
511C2×C5C2×D3×C22⋊C411yescharacteristic
512D5—24no—
513D5—22no—
514D5#558614yes—
515C23—24no—
516C23—22no—
517C23—51no—
518C23—58no—
519C23—54no—
520C23—52no—
521C23—51no—
522C23—104no—
523C23—104no—
524C23—104no—
525C23—104no—
526C23—104no—
527C23—104no—
528C23—1032no—
529C23—104no—
530C23—102no—
531C23C2×D3×AGL(1,𝔽5)12yes—
532C23C2×D3×AGL(1,𝔽5)11yescharacteristic
533C2×C4—34no—
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—32no—
537C2×C4—64no—
538C2×C4—64no—
539C2×C4—62no—
540C2×C4—104no—
541C2×C4—108no—
542C2×C4—154no—
543C2×C4—154no—
544C2×C4—154no—
545C2×C4—154no—
546C2×C4—154no—
547C2×C4—151no—
548C2×C4—151no—
549C2×C4—152no—
550C2×C4—304no—
551C2×C4—304no—
552C2×C4—304no—
553C2×C4—304no—
554C2×C4—304no—
555C2×C4—304no—
556C2×C4—304no—
557C2×C4—304no—
558C2×C4—302no—
559C2×C4—304no—
560C2×C4—308no—
561C2×C3—24no—
562C2×C3—22no—
563C2×C3—54no—
564C2×C3—104no—
565C2×C3—102no—
566C2×C3C2×#413012yes—
567C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
568C5#7381711yescharacteristic, complemented, Sylow
569C22—28no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—54no—
574C22—52no—
575C22—54no—
576C22—52no—
577C22—1016no—
578C22—108no—
579C22—1016no—
580C22—108no—
581C22—102no—
582C22—102no—
583C22—102no—
584C22#9192314yescomplemented
585C22D3×C22⋊AGL(1,𝔽5)12yes—
586C22C22×D3×AGL(1,𝔽5)11yescharacteristic
587C4—32no—
588C4—32no—
589C4—62no—
590C4—152no—
591C4—152no—
592C4—204no—
593C4—302no—
594C4—604no—
595C3#1061748011yescharacteristic, complemented, Sylow
596C2—24no—
597C2—22no—
598C2—54no—
599C2—104no—
600C2—102no—
601C2C2×#9192312yes—
602C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC24×C3×C5C2×C4
prime radicalC24×C3×D5C22
cosocleC22×C3×D5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#91923C2semidirect
5. #11752028C2semidirect
6. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
7. #11751984C2semidirect
10. C23×Dic15C4semidirect
11. C23×C5×Dic3C4semidirect
13. C22×D5×Dic3C4semidirect
14. C22×D5×Dic3C4semidirect
15. C22×D5×Dic3C4semidirect
16. C22×D5×Dic3C4semidirect
25. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
27. C2×Dic3×AGL(1,𝔽5)C22semidirect
28. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
133. C2×Dic15C22⋊C4semidirect
140. C2×C5×Dic3C22⋊C4semidirect
150. D5×Dic3C22⋊C4semidirect
151. D5×Dic3C22⋊C4semidirect
165. C23×Dic3AGL(1,𝔽5)semidirect
229. C22×C3×C5#117semidirect
239. C2×C3×D5#117semidirect
408. C2×Dic3C22⋊AGL(1,𝔽5)semidirect
416. C22×C5#877semidirect
426. C2×D5#877semidirect
481. C3×C5#2280semidirect
497. C22×C3#4130semidirect
568. C5#73817semidirect
584. C22#91923semidirect
595. C3#10617480semidirect

Maximal subgroups

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

subgroupindex
C23×D5×Dic32
C2×#919232
#117524592
C3×#658002
#117520282
Dic3×C22⋊AGL(1,𝔽5)2
#117519842
#106174803
#738175