Finite Group Databasebeta

← #14319965

Subgroups — #14319965

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic
2C2×#91923C212yesmaximal, complemented
3#11752423C211yesmaximal, characteristic, complemented
4C3×#65764C211yesmaximal, characteristic, complemented
5#11752025C212yesmaximal
6#11751854C214yesmaximal, complemented
7#11751848C214yesmaximal, complemented
8#10617480—31nomaximal, Hall
9C23×D3×D5C2211yescharacteristic
10C22×C4×D15C411yescharacteristic, complemented
11C22×C4×C5×D3C411yescharacteristic, complemented
12C22×C3×C4×D5C2211yescharacteristic
13C22×#1200C411yescharacteristic, complemented
14C22×D3×Dic5C411yescharacteristic, complemented
15C22×D5×Dic3C2211yescharacteristic
16C2×C4×D3×D5—28no—
17C2×C4×D3×D5C412yescomplemented
18C2×C4×D3×D5C412yescomplemented
19C2×C4×D3×D5C2212yes—
20C2×C4×D3×D5C2212yes—
21C2×#6763C2212yes—
22C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3⋊AGL(1,𝔽5)C2214yescomplemented
24C2×(C2×D3)⋊AGL(1,𝔽5)C2218yes—
25#91923—28no—
26C2×Dic3×AGL(1,𝔽5)C2214yescomplemented
27#91235C2214yescomplemented
28C3×(C2×AGL(1,𝔽5))⋊C4C2214yescomplemented
29#74050—51nomaximal, Hall
30C23×C4×D5—31no—
31C2×#4130—32no—
32#65800—32no—
33#65765—34no—
34#65764—31no—
35#65764D311yescharacteristic, complemented
36C4×C22⋊AGL(1,𝔽5)—34no—
37C23×D15C2×C411yescharacteristic
38C23×C5×D3C2×C411yescharacteristic
39C23×C3×D5C2311yescharacteristic
40C22×D3×D5—24no—
41C22×D3×D5—28no—
42C22×D3×D5C2×C412yes—
43C22×D3×D5C2312yes—
44C22×ΓL(1,𝔽16)C2314yes—
45C22×C3×AGL(1,𝔽5)C2314yes—
46C22×C3×C4×C5C2×C411yescharacteristic
47C22×Dic15C2×C411yescharacteristic
48C2×C4×D15—24no—
49C2×C4×D15C2×C412yes—
50C2×C4×D15C2×C412yes—
51C22×C5×Dic3C2×C411yescharacteristic
52C2×C4×C5×D3—24no—
53C2×C4×C5×D3C2×C412yes—
54C2×C4×C5×D3C2×C412yes—
55C22×C3×Dic5C2×C411yescharacteristic
56C2×C3×C4×D5—24no—
57C2×C3×C4×D5C2×C412yes—
58C2×C3×C4×D5C2312yes—
59C2×#1200—24no—
60C2×#1200C2×C412yes—
61C2×#1200C2×C412yes—
62C2×D3×Dic5—24no—
63C2×D3×Dic5C2×C412yes—
64C2×D3×Dic5C2×C412yes—
65C2×D5×Dic3C2×C411yescharacteristic
66C2×D5×Dic3C2×C411yescharacteristic
67C2×D5×Dic3D418yes—
68C2×D5×Dic3C2311yescharacteristic
69C2×D5×Dic3C2311yescharacteristic
70C4×D3×D5—28no—
71C4×D3×D5—28no—
72C4×D3×D5—28no—
73C4×D3×D5—28no—
74#6763—24no—
75C3×C22⋊AGL(1,𝔽5)—24no—
76Dic3⋊AGL(1,𝔽5)—28no—
77(C2×D3)⋊AGL(1,𝔽5)—216no—
78Dic3×AGL(1,𝔽5)—28no—
79C23×C4×D3—51no—
80C2×#877—52no—
81C3×#381—51no—
82#5211—51no—
83#4955—52no—
84#4667—54no—
85#4666—54no—
86C24×D5—31no—
87C23×C4×C5—31no—
88C23×Dic5—31no—
89C22×C4×D5—31no—
90C22×C4×D5—31no—
91C22×C4×D5—31no—
92C22×C4×D5—32no—
93C22×C4×D5—32no—
94C22×C4×D5—32no—
95C22×C4×D5—32no—
96C22×C4×D5—68no—
97C22×C4×D5C2×D311yescharacteristic
98C2×C22⋊AGL(1,𝔽5)—32no—
99C2×C22⋊AGL(1,𝔽5)—38no—
100C2×C22⋊AGL(1,𝔽5)C2×D312yes—
101#4130—68no—
102C2×C4⋊AGL(1,𝔽5)—34no—
103C2×C4×AGL(1,𝔽5)—34no—
104(C2×AGL(1,𝔽5))⋊C4—34no—
105(C2×AGL(1,𝔽5))⋊C4C2×D314yescomplemented
106#2280—151noSylow
107C23×C3×C5C22×C411yescharacteristic
108C22×D15—22no—
109C22×D15—24no—
110C22×D15C22×C412yes—
111C22×C5×D3—22no—
112C22×C5×D3—24no—
113C22×C5×D3C22×C412yes—
114C22×C3×D5—24no—
115C22×C3×D5C22×C411yescharacteristic
116C22×C3×D5C2×D414yes—
117C22×C3×D5C2411yescharacteristic
118C2×D3×D5—232no—
119C2×D3×D5—24no—
120C2×D3×D5—24no—
121C2×D3×D5—24no—
122C2×D3×D5—24no—
123C2×D3×D5—24no—
124C2×D3×D5#4118yes—
125C2×ΓL(1,𝔽16)—24no—
126C2×ΓL(1,𝔽16)—28no—
127C2×C3×AGL(1,𝔽5)—24no—
128C2×C3×AGL(1,𝔽5)—28no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15C22⋊C414yescomplemented
132C2×Dic15C22×C411yescharacteristic
133C2×Dic15C22×C411yescharacteristic
134C4×D15—24no—
135C4×D15—24no—
136C2×C5×Dic3C22⋊C414yescomplemented
137C2×C5×Dic3C22×C411yescharacteristic
138C2×C5×Dic3C22×C411yescharacteristic
139C4×C5×D3—24no—
140C4×C5×D3—24no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5C22×C412yes—
143C3×C4×D5—24no—
144C3×C4×D5—24no—
145#1200—24no—
146#1200—24no—
147D3×Dic5—24no—
148D3×Dic5—24no—
149D5×Dic3C22⋊C414yescomplemented
150D5×Dic3C22⋊C414yescomplemented
151D5×Dic3C2×D414yes—
152D5×Dic3C2×D414yes—
153C24×D3—51no—
154C23×C3×C4—51no—
155C23×Dic3—51no—
156C22×C4×D3—51no—
157C22×C4×D3—51no—
158C22×C4×D3—51no—
159C22×C4×D3—52no—
160C22×C4×D3—52no—
161C22×C4×D3—52no—
162C22×C4×D3—52no—
163C22×C4×D3—108no—
164C22×C4×D3AGL(1,𝔽5)11yescharacteristic, complemented
165C2×C3×C22⋊C4—52no—
166C2×#217—52no—
167C2×(C2×D3)⋊C4—58no—
168C2×Dic3⋊C4—54no—
169C2×C4×Dic3—54no—
170#877—108no—
171C3×#95—54no—
172C3⋊#95—54no—
173C24×C5—31no—
174C23×D5—32no—
175C23×D5—31no—
176C23×D5—32no—
177C23×D5—68no—
178C23×D5—64no—
179C23×D5C22×D311yescharacteristic
180C22×AGL(1,𝔽5)—34no—
181C22×AGL(1,𝔽5)C22×D314yes—
182C22×C4×C5—31no—
183C22×C4×C5—32no—
184C22×C4×C5—32no—
185C22×C4×C5—64no—
186C22×C4×C5C4×D311yescharacteristic
187C22×Dic5—31no—
188C22×Dic5—32no—
189C22×Dic5—32no—
190C22×Dic5—64no—
191C22×Dic5C4×D311yescharacteristic
192C2×C4×D5—24no—
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—68no—
203C2×C4×D5—68no—
204C2×C4×D5—68no—
205C2×C4×D5—68no—
206C2×C4×D5—64no—
207C2×C4×D5—64no—
208C2×C4×D5C4×D312yes—
209C2×C4×D5C22×D312yes—
210C22⋊AGL(1,𝔽5)—24no—
211C22⋊AGL(1,𝔽5)—616no—
212C22⋊AGL(1,𝔽5)—64no—
213C4⋊AGL(1,𝔽5)—68no—
214C4×AGL(1,𝔽5)—68no—
215C24×C4—151no—
216C2×#117—152no—
217#381—51no—
218#381—151no—
219#380—154no—
220#379—152no—
221C4×C22⋊C4—154no—
222C22×C3×C5—22no—
223C22×C3×C5C2×C22⋊C412yes—
224C22×C3×C5C23×C411yescharacteristic
225C2×D15—28no—
226C2×D15—22no—
227C2×D15—22no—
228C2×D15#11714yescomplemented
229C2×C5×D3—28no—
230C2×C5×D3—22no—
231C2×C5×D3—22no—
232C2×C5×D3#11714yescomplemented
233C2×C3×D5—22no—
234C2×C3×D5—28no—
235C2×C3×D5C2×C22⋊C412yes—
236C2×C3×D5C22×D412yes—
237C2×C3×D5C2×#4114yes—
238D3×D5—216no—
239D3×D5—216no—
240ΓL(1,𝔽16)—44no—
241C3×AGL(1,𝔽5)—44no—
242C3×C4×C5—22no—
243Dic15C2×C22⋊C412yes—
244Dic15C2×C22⋊C412yes—
245C3×Dic5—22no—
246C5×Dic3C2×C22⋊C412yes—
247C5×Dic3C2×C22⋊C412yes—
248C24×C3—51no—
249C23×D3—52no—
250C23×D3—51no—
251C23×D3—52no—
252C23×D3—108no—
253C23×D3—104no—
254C23×D3C2×AGL(1,𝔽5)11yescharacteristic
255C22×C3×C4—51no—
256C22×C3×C4—52no—
257C22×C3×C4—52no—
258C22×C3×C4—54no—
259C22×C3×C4—104no—
260C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
261C22×Dic3—51no—
262C22×Dic3—58no—
263C22×Dic3—51no—
264C22×Dic3—51no—
265C22×Dic3—51no—
266C22×Dic3—51no—
267C22×Dic3—54no—
268C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
269C2×C4×D3—24no—
270C2×C4×D3—52no—
271C2×C4×D3—52no—
272C2×C4×D3—52no—
273C2×C4×D3—52no—
274C2×C4×D3—52no—
275C2×C4×D3—52no—
276C2×C4×D3—108no—
277C2×C4×D3—108no—
278C2×C4×D3—108no—
279C2×C4×D3—108no—
280C2×C4×D3—104no—
281C2×C4×D3—104no—
282C2×C4×D3—104no—
283C2×C4×D3C2×AGL(1,𝔽5)12yes—
284C2×C4×D3C2×AGL(1,𝔽5)12yes—
285C3×C22⋊C4—104no—
286#217—104no—
287(C2×D3)⋊C4—1016no—
288Dic3⋊C4—108no—
289C4×Dic3—108no—
290C23×C5—32no—
291C23×C5—64no—
292C23×C5—62no—
293C23×C5C2×C4×D311yescharacteristic
294C22×D5—24no—
295C22×D5—32no—
296C22×D5—38no—
297C22×D5—64no—
298C22×D5—64no—
299C22×D5—632no—
300C22×D5—64no—
301C22×D5—62no—
302C22×D5—64no—
303C22×D5—64no—
304C22×D5—64no—
305C22×D5C2×C4×D311yescharacteristic
306C22×D5D3×D414yes—
307C22×D5C23×D311yescharacteristic
308C2×AGL(1,𝔽5)—24no—
309C2×AGL(1,𝔽5)—28no—
310C2×AGL(1,𝔽5)—64no—
311C2×AGL(1,𝔽5)—68no—
312C2×C4×C5—22no—
313C2×C4×C5—34no—
314C2×C4×C5—31no—
315C2×C4×C5—31no—
316C2×C4×C5—64no—
317C2×C4×C5—64no—
318C2×C4×C5C2×C4×D312yes—
319C2×Dic5—22no—
320C2×Dic5—34no—
321C2×Dic5—31no—
322C2×Dic5—31no—
323C2×Dic5—64no—
324C2×Dic5—64no—
325C2×Dic5C2×C4×D312yes—
326C4×D5—24no—
327C4×D5—24no—
328C4×D5—34no—
329C4×D5—34no—
330C4×D5—34no—
331C4×D5—34no—
332C4×D5—64no—
333C4×D5—64no—
334C4×D5—64no—
335C4×D5—64no—
336C25—151no—
337C23×C4—31no—
338C23×C4—51no—
339C23×C4—152no—
340C23×C4—152no—
341C23×C4—151no—
342C23×C4—152no—
343C23×C4—152no—
344C23×C4—151no—
345C23×C4—151no—
346C23×C4—151no—
347C23×C4—308no—
348#117—308no—
349C2×C4⋊C4—154no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—158no—
352C2×C22⋊C4—152no—
353C2×C42—154no—
354#95—54no—
355#95—154no—
356C2×C3×C5—22no—
357C2×C3×C5C22×C22⋊C411yescharacteristic
358C2×C3×C5C2×#11712yes—
359D15—24no—
360C3×D5—22no—
361C3×D5#52514yes—
362C5×D3—24no—
363C23×C3—51no—
364C23×C3—54no—
365C23×C3—51no—
366C23×C3—104no—
367C23×C3C22×AGL(1,𝔽5)11yescharacteristic
368C22×D3—22no—
369C22×D3—24no—
370C22×D3—52no—
371C22×D3—58no—
372C22×D3—104no—
373C22×D3—104no—
374C22×D3—104no—
375C22×D3—104no—
376C22×D3—1032no—
377C22×D3—104no—
378C22×D3—102no—
379C22×D3—104no—
380C22×D3C22×AGL(1,𝔽5)12yes—
381C2×C3×C4—22no—
382C2×C3×C4—52no—
383C2×C3×C4—104no—
384C2×C3×C4—104no—
385C2×C3×C4—102no—
386C2×C3×C4—104no—
387C2×C3×C4—108no—
388C2×C3×C4C22×AGL(1,𝔽5)12yes—
389C2×Dic3—54no—
390C2×Dic3—51no—
391C2×Dic3—51no—
392C2×Dic3—54no—
393C2×Dic3—54no—
394C2×Dic3—54no—
395C2×Dic3—54no—
396C2×Dic3—104no—
397C2×Dic3—108no—
398C2×Dic3C22⋊AGL(1,𝔽5)14yescomplemented
399C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
400C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
401C4×D3—24no—
402C4×D3—24no—
403C4×D3—104no—
404C4×D3—104no—
405C4×D3—104no—
406C4×D3—104no—
407C4×D3—104no—
408C4×D3—104no—
409C22×C5—22no—
410C22×C5—34no—
411C22×C5—68no—
412C22×C5—62no—
413C22×C5—62no—
414C22×C5D3×C22⋊C412yes—
415C22×C5C22×C4×D311yescharacteristic
416C2×D5—22no—
417C2×D5—28no—
418C2×D5—34no—
419C2×D5—616no—
420C2×D5—68no—
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—616no—
424C2×D5D3×C22⋊C412yes—
425C2×D5C2×D3×D412yes—
426C2×D5D3×#4114yes—
427AGL(1,𝔽5)—44no—
428AGL(1,𝔽5)—124no—
429C4×C5—22no—
430C4×C5—32no—
431C4×C5—32no—
432Dic5—22no—
433Dic5—32no—
434Dic5—32no—
435C24—31no—
436C24—51no—
437C24—152no—
438C24—152no—
439C24—151no—
440C24—304no—
441C24—308no—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—51no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—54no—
449C22×C4—64no—
450C22×C4—104no—
451C22×C4—152no—
452C22×C4—152no—
453C22×C4—151no—
454C22×C4—151no—
455C22×C4—158no—
456C22×C4—151no—
457C22×C4—151no—
458C22×C4—152no—
459C22×C4—152no—
460C22×C4—151no—
461C22×C4—152no—
462C22×C4—152no—
463C22×C4—154no—
464C22×C4—304no—
465C22×C4—304no—
466C22×C4—308no—
467C22×C4—308no—
468C22×C4—308no—
469C22×C4—308no—
470C22×C4—304no—
471C22×C4D3×AGL(1,𝔽5)11yescharacteristic
472C4⋊C4—308no—
473C22⋊C4—104no—
474C22⋊C4—3016no—
475C22⋊C4—304no—
476C42—308no—
477C3×C5#228011yescharacteristic, complemented, Hall
478C22×C3—22no—
479C22×C3—54no—
480C22×C3—52no—
481C22×C3—52no—
482C22×C3—108no—
483C22×C3—102no—
484C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
485C22×C3C23×AGL(1,𝔽5)11yescharacteristic
486C2×D3—28no—
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—54no—
490C2×D3—1016no—
491C2×D3—1016no—
492C2×D3—108no—
493C2×D3—102no—
494C2×D3—102no—
495C2×D3#413014yescomplemented
496C3×C4—22no—
497C3×C4—102no—
498C3×C4—204no—
499Dic3—52no—
500Dic3—52no—
501Dic3—204no—
502Dic3C2×C22⋊AGL(1,𝔽5)12yes—
503Dic3C2×C22⋊AGL(1,𝔽5)12yes—
504C2×C5—22no—
505C2×C5—64no—
506C2×C5C2×D3×C22⋊C411yescharacteristic
507C2×C5D3×#11712yes—
508D5—22no—
509D5—64no—
510D5#565614yes—
511C23—32no—
512C23—51no—
513C23—54no—
514C23—51no—
515C23—64no—
516C23—62no—
517C23—104no—
518C23—158no—
519C23—152no—
520C23—304no—
521C23—304no—
522C23—304no—
523C23—304no—
524C23—304no—
525C23—304no—
526C23—3032no—
527C23—302no—
528C23C2×D3×AGL(1,𝔽5)11yescharacteristic
529C2×C4—22no—
530C2×C4—34no—
531C2×C4—31no—
532C2×C4—31no—
533C2×C4—52no—
534C2×C4—64no—
535C2×C4—64no—
536C2×C4—104no—
537C2×C4—104no—
538C2×C4—102no—
539C2×C4—104no—
540C2×C4—108no—
541C2×C4—154no—
542C2×C4—154no—
543C2×C4—154no—
544C2×C4—154no—
545C2×C4—154no—
546C2×C4—151no—
547C2×C4—151no—
548C2×C4—304no—
549C2×C4—304no—
550C2×C4—304no—
551C2×C4—304no—
552C2×C4—304no—
553C2×C4—304no—
554C2×C4—304no—
555C2×C4—308no—
556C2×C4C2×D3×AGL(1,𝔽5)12yes—
557C2×C3—22no—
558C2×C3—54no—
559C2×C3—102no—
560C2×C3C2×#413012yes—
561C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
562D3—24no—
563D3—104no—
564C5#7405011yescharacteristic, complemented, Sylow
565C22—22no—
566C22—34no—
567C22—54no—
568C22—52no—
569C22—52no—
570C22—68no—
571C22—62no—
572C22—62no—
573C22—108no—
574C22—102no—
575C22—154no—
576C22—308no—
577C22—3016no—
578C22—3016no—
579C22—302no—
580C22—302no—
581C22D3×C22⋊AGL(1,𝔽5)12yes—
582C22C22×D3×AGL(1,𝔽5)11yescharacteristic
583C4—22no—
584C4—32no—
585C4—32no—
586C4—102no—
587C4—152no—
588C4—152no—
589C4—204no—
590C4—604no—
591C3#1061748011yescharacteristic, complemented, Sylow
592C2—22no—
593C2—54no—
594C2—64no—
595C2—102no—
596C2—304no—
597C2D3×#413012yes—
598C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×D3×D5C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91923C2semidirect
3. #11752423C2semidirect
4. C3×#65764C2semidirect
6. #11751854C2semidirect
7. #11751848C2semidirect
10. C22×C4×D15C4semidirect
11. C22×C4×C5×D3C4semidirect
13. C22×#1200C4semidirect
14. C22×D3×Dic5C4semidirect
17. C2×C4×D3×D5C4semidirect
18. C2×C4×D3×D5C4semidirect
23. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
26. C2×Dic3×AGL(1,𝔽5)C22semidirect
27. #91235C22semidirect
28. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
35. #65764D3semidirect
105. (C2×AGL(1,𝔽5))⋊C4C2×D3semidirect
131. C2×Dic15C22⋊C4semidirect
136. C2×C5×Dic3C22⋊C4semidirect
149. D5×Dic3C22⋊C4semidirect
150. D5×Dic3C22⋊C4semidirect
164. C22×C4×D3AGL(1,𝔽5)semidirect
228. C2×D15#117semidirect
232. C2×C5×D3#117semidirect
398. C2×Dic3C22⋊AGL(1,𝔽5)semidirect
477. C3×C5#2280semidirect
495. C2×D3#4130semidirect
564. C5#74050semidirect
591. C3#10617480semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C2×#919232
#117524232
C3×#657642
#117520252
#117518542
#117518482
#106174803
#740505