Finite Group Databasebeta

← #14322874

Subgroups — #14322874

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91923C212yesmaximal
2C2×D5×Dic3⋊C4C211yesmaximal, characteristic
3#11752424C211yesmaximal, characteristic
4C3×#65765C211yesmaximal, characteristic
5#11752028C212yesmaximal
6#11751844C214yesmaximal, complemented
7#11751837C214yesmaximal, complemented
8#10617102—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3C2211yescharacteristic
11C22×D5×Dic3C2211yescharacteristic
12C2×#6763C2212yes—
13C2×C4⋊ΓL(1,𝔽16)C2212yes—
14C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
15C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
16C2×Dic3⋊AGL(1,𝔽5)C2214yes—
17C2×Dic3⋊AGL(1,𝔽5)C2214yes—
18#91923—28no—
19C2×Dic3×AGL(1,𝔽5)C2214yes—
20C2×#6712C411yescharacteristic, complemented
21C2×C5×Dic3⋊C4C411yescharacteristic, complemented
22C2×Dic3⋊Dic5C411yescharacteristic, complemented
23C2×#6669C411yescharacteristic, complemented
24D5×Dic3⋊C4C412yescomplemented
25D5×Dic3⋊C4C412yescomplemented
26D5×Dic3⋊C4C2212yes—
27D5×Dic3⋊C4C2212yes—
28#91235C2212yes—
29C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
30(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
31#73869—51nomaximal, Hall
32C2×#4130—32no—
33C2×D5×C4⋊C4—31no—
34#65765—31no—
35#65765—32no—
36#65765D311yescharacteristic
37#65712—34no—
38#65712—34no—
39C23×C3×D5C2311yescharacteristic
40C22×ΓL(1,𝔽16)C2314yes—
41C22×C3×AGL(1,𝔽5)C2314yes—
42C22×C3×C4×C5C2×C411yescharacteristic
43C22×Dic15C2×C411yescharacteristic
44C22×Dic15C2×C411yescharacteristic
45C22×C5×Dic3C2×C411yescharacteristic
46C22×C5×Dic3C2×C411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
48C2×C3×C4×D5—42no—
49C2×C3×C4×D5C2×C411yescharacteristic
50C2×C3×C4×D5C2×C411yescharacteristic
51C2×C3×C4×D5C2311yescharacteristic
52C2×C3×C4×D5C2311yescharacteristic
53C2×D5×Dic3—42no—
54C2×D5×Dic3C2×C412yes—
55C2×D5×Dic3C2×C412yes—
56C2×D5×Dic3D414yes—
57C2×D5×Dic3Q814yes—
58C2×D5×Dic3C2312yes—
59C2×D5×Dic3C2312yes—
60#6763—24no—
61C4⋊ΓL(1,𝔽16)—42no—
62C3×C22⋊AGL(1,𝔽5)—24no—
63C3×C4⋊AGL(1,𝔽5)—42no—
64Dic3⋊AGL(1,𝔽5)—28no—
65Dic3⋊AGL(1,𝔽5)—44no—
66Dic3×AGL(1,𝔽5)—28no—
67#6712C2×C412yes—
68#6712C2×C412yes—
69C5×Dic3⋊C4C2×C412yes—
70C5×Dic3⋊C4C2×C412yes—
71Dic3⋊Dic5C2×C412yes—
72Dic3⋊Dic5C2×C412yes—
73#6669C2×C412yes—
74#6669C2×C412yes—
75C22×Dic3⋊C4—51no—
76C2×#877—52no—
77C3×#380—51no—
78#5212—51no—
79#4976—54no—
80#4942—52no—
81#4647—54no—
82C22×C4×D5—31no—
83C22×C4×D5—31no—
84C22×C4×D5C2×D311yescharacteristic
85C2×C22⋊AGL(1,𝔽5)—32no—
86C2×C22⋊AGL(1,𝔽5)C2×D312yes—
87#4130—68no—
88C2×C4⋊AGL(1,𝔽5)—34no—
89C2×C4⋊AGL(1,𝔽5)—34no—
90C2×C4⋊AGL(1,𝔽5)—32no—
91C2×C4⋊AGL(1,𝔽5)C2×D312yes—
92C2×C4×AGL(1,𝔽5)—34no—
93C2×C5×C4⋊C4—31no—
94C2×C4⋊Dic5—31no—
95C2×#683—31no—
96C2×#683—31no—
97D5×C4⋊C4—32no—
98D5×C4⋊C4—32no—
99D5×C4⋊C4—32no—
100D5×C4⋊C4—32no—
101(C2×AGL(1,𝔽5))⋊C4—34no—
102(C2×AGL(1,𝔽5))⋊C4—32no—
103(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
104#2316—151noSylow
105C23×C3×C5C22×C411yescharacteristic
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5C22×C411yescharacteristic
109C22×C3×D5C2×D412yes—
110C22×C3×D5C2×Q812yes—
111C22×C3×D5C2411yescharacteristic
112C2×ΓL(1,𝔽16)—24no—
113C2×ΓL(1,𝔽16)—24no—
114C2×ΓL(1,𝔽16)—24no—
115C2×C3×AGL(1,𝔽5)—24no—
116C2×C3×AGL(1,𝔽5)—24no—
117C2×C3×AGL(1,𝔽5)—24no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5C22×C411yescharacteristic
120C2×C3×C4×C5C22×C411yescharacteristic
121C2×Dic15—41no—
122C2×Dic15C4⋊C414yescomplemented
123C2×Dic15C22×C412yes—
124C2×Dic15C22×C412yes—
125C2×C5×Dic3—41no—
126C2×C5×Dic3C4⋊C414yescomplemented
127C2×C5×Dic3C22×C412yes—
128C2×C5×Dic3C22×C412yes—
129C2×C3×Dic5—41no—
130C2×C3×Dic5C22×C411yescharacteristic
131C2×C3×Dic5C22×C411yescharacteristic
132C3×C4×D5—22no—
133C3×C4×D5—22no—
134C3×C4×D5—41no—
135C3×C4×D5—41no—
136D5×Dic3—24no—
137D5×Dic3—42no—
138D5×Dic3C4⋊C418yescomplemented
139D5×Dic3C2×D414yes—
140D5×Dic3C2×Q814yes—
141C23×C3×C4—51no—
142C23×Dic3—51no—
143C23×Dic3—51no—
144C2×C3×C4⋊C4—52no—
145C2×C3×C22⋊C4—52no—
146C2×#217—52no—
147C2×C4⋊Dic3—52no—
148C2×Dic3⋊C4—51no—
149C2×Dic3⋊C4—51no—
150C2×Dic3⋊C4—51no—
151C2×Dic3⋊C4—52no—
152C2×Dic3⋊C4—52no—
153C2×Dic3⋊C4—52no—
154C2×Dic3⋊C4—52no—
155C2×Dic3⋊C4—54no—
156C2×Dic3⋊C4—54no—
157C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
158C2×C4×Dic3—54no—
159#877—108no—
160C3×#95—52no—
161C3⋊#95—54no—
162C3⋊#95—52no—
163C23×D5C22×D311yescharacteristic
164C22×AGL(1,𝔽5)—34no—
165C22×AGL(1,𝔽5)C22×D314yes—
166C22×C4×C5—31no—
167C22×C4×C5—31no—
168C22×C4×C5C4×D311yescharacteristic
169C22×Dic5—31no—
170C22×Dic5—31no—
171C22×Dic5C4×D311yescharacteristic
172C2×C4×D5—32no—
173C2×C4×D5—34no—
174C2×C4×D5—34no—
175C2×C4×D5—32no—
176C2×C4×D5—32no—
177C2×C4×D5—32no—
178C2×C4×D5—42no—
179C2×C4×D5—122no—
180C2×C4×D5C4×D311yescharacteristic
181C2×C4×D5C4×D311yescharacteristic
182C2×C4×D5C22×D311yescharacteristic
183C2×C4×D5C22×D311yescharacteristic
184C22⋊AGL(1,𝔽5)—24no—
185C22⋊AGL(1,𝔽5)—64no—
186C4⋊AGL(1,𝔽5)—42no—
187C4⋊AGL(1,𝔽5)—68no—
188C4⋊AGL(1,𝔽5)—122no—
189C4⋊AGL(1,𝔽5)—124no—
190C4×AGL(1,𝔽5)—68no—
191C5×C4⋊C4—32no—
192C5×C4⋊C4—32no—
193C4⋊Dic5—32no—
194C4⋊Dic5—32no—
195#683—32no—
196#683—32no—
197#683—32no—
198#683—32no—
199C2×#117—152no—
200C22×C4⋊C4—151no—
201#389—154no—
202#389—154no—
203#380—51no—
204#380—152no—
205#380—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C2×C4⋊C412yes—
209C22×C3×C5C23×C411yescharacteristic
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—24no—
213C2×C3×D5—24no—
214C2×C3×D5C2×C4⋊C412yes—
215C2×C3×D5C22×D411yescharacteristic
216C2×C3×D5C22×Q811yescharacteristic
217C2×C3×D5H(5,𝔽2)12yes—
218C2×C3×D52−1+412yes—
219ΓL(1,𝔽16)—44no—
220C3×AGL(1,𝔽5)—44no—
221C3×C4×C5—21no—
222C3×C4×C5—21no—
223Dic15—22no—
224Dic15C2×C4⋊C414yes—
225C3×Dic5—21no—
226C3×Dic5—21no—
227C5×Dic3—22no—
228C5×Dic3C2×C4⋊C414yes—
229C24×C3—51no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—51no—
234C22×C3×C4—51no—
235C22×C3×C4—54no—
236C22×C3×C4—202no—
237C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
238C22×Dic3—51no—
239C22×Dic3—54no—
240C22×Dic3—54no—
241C22×Dic3—52no—
242C22×Dic3—52no—
243C22×Dic3—51no—
244C22×Dic3—52no—
245C22×Dic3—52no—
246C22×Dic3—54no—
247C22×Dic3—202no—
248C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
249C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
250C3×C4⋊C4—202no—
251C3×C22⋊C4—104no—
252#217—104no—
253C4⋊Dic3—202no—
254Dic3⋊C4—52no—
255Dic3⋊C4—52no—
256Dic3⋊C4—52no—
257Dic3⋊C4—52no—
258Dic3⋊C4—52no—
259Dic3⋊C4—52no—
260Dic3⋊C4—108no—
261Dic3⋊C4—204no—
262Dic3⋊C4C2×AGL(1,𝔽5)12yes—
263Dic3⋊C4C2×AGL(1,𝔽5)12yes—
264C4×Dic3—108no—
265C23×C5C2×C4×D311yescharacteristic
266C22×D5—22no—
267C22×D5—22no—
268C22×D5C2×C4×D311yescharacteristic
269C22×D5D3×D412yes—
270C22×D5D3×Q812yes—
271C22×D5C23×D311yescharacteristic
272C2×AGL(1,𝔽5)—24no—
273C2×AGL(1,𝔽5)—24no—
274C2×AGL(1,𝔽5)—24no—
275C2×AGL(1,𝔽5)—64no—
276C2×AGL(1,𝔽5)—64no—
277C2×AGL(1,𝔽5)—64no—
278C2×C4×C5—34no—
279C2×C4×C5—32no—
280C2×C4×C5—32no—
281C2×C4×C5—41no—
282C2×C4×C5—121no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5C2×C4×D311yescharacteristic
285C2×Dic5—34no—
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—41no—
289C2×Dic5—121no—
290C2×Dic5C2×C4×D311yescharacteristic
291C2×Dic5C2×C4×D311yescharacteristic
292C4×D5—22no—
293C4×D5—22no—
294C4×D5—38no—
295C4×D5—34no—
296C4×D5—34no—
297C4×D5—41no—
298C4×D5—41no—
299C4×D5—64no—
300C4×D5—122no—
301C23×C4—51no—
302C23×C4—151no—
303C23×C4—151no—
304#117—308no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—52no—
307C2×C4⋊C4—152no—
308C2×C4⋊C4—152no—
309C2×C4⋊C4—152no—
310C2×C4⋊C4—152no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C4⋊C4—151no—
314C2×C4⋊C4—154no—
315C2×C4⋊C4—154no—
316C2×C4⋊C4—152no—
317C2×C22⋊C4—52no—
318C2×C22⋊C4—152no—
319C2×C42—154no—
320#95—52no—
321#95—152no—
322#95—154no—
323C2×C3×C5—22no—
324C2×C3×C5C22×C4⋊C411yescharacteristic
325C2×C3×C5#51811yescharacteristic
326C2×C3×C5#51911yescharacteristic
327C3×D5—22no—
328C3×D5#53712yes—
329C3×D5#54412yes—
330C23×C3—51no—
331C23×C3—52no—
332C23×C3—52no—
333C23×C3—51no—
334C23×C3—102no—
335C23×C3—102no—
336C23×C3C22×AGL(1,𝔽5)11yescharacteristic
337C2×C3×C4—41no—
338C2×C3×C4—51no—
339C2×C3×C4—51no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—104no—
343C2×C3×C4—104no—
344C2×C3×C4—104no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4—201no—
348C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
349C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
350C2×Dic3—41no—
351C2×Dic3—54no—
352C2×Dic3—52no—
353C2×Dic3—58no—
354C2×Dic3—54no—
355C2×Dic3—54no—
356C2×Dic3—52no—
357C2×Dic3—104no—
358C2×Dic3—104no—
359C2×Dic3—104no—
360C2×Dic3—104no—
361C2×Dic3—202no—
362C2×Dic3—201no—
363C2×Dic3C4⋊AGL(1,𝔽5)14yescomplemented
364C2×Dic3C22×AGL(1,𝔽5)12yes—
365C2×Dic3C22×AGL(1,𝔽5)12yes—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5D3×C4⋊C412yes—
369C22×C5C22×C4×D311yescharacteristic
370C2×D5—21no—
371C2×D5—21no—
372C2×D5—24no—
373C2×D5—24no—
374C2×D5D3×C4⋊C412yes—
375C2×D5C2×D3×D411yescharacteristic
376C2×D5#100412yes—
377C2×D5C2×D3×Q811yescharacteristic
378C2×D5#101012yes—
379AGL(1,𝔽5)—44no—
380AGL(1,𝔽5)—124no—
381C4×C5—21no—
382C4×C5—21no—
383C4×C5—34no—
384C4×C5—62no—
385Dic5—21no—
386Dic5—21no—
387Dic5—34no—
388Dic5—62no—
389C24—51no—
390C22×C4—31no—
391C22×C4—31no—
392C22×C4—51no—
393C22×C4—51no—
394C22×C4—51no—
395C22×C4—51no—
396C22×C4—51no—
397C22×C4—54no—
398C22×C4—152no—
399C22×C4—152no—
400C22×C4—154no—
401C22×C4—154no—
402C22×C4—152no—
403C22×C4—152no—
404C22×C4—151no—
405C22×C4—151no—
406C22×C4—154no—
407C22×C4—202no—
408C22×C4—602no—
409C22×C4D3×AGL(1,𝔽5)11yescharacteristic
410C4⋊C4—32no—
411C4⋊C4—32no—
412C4⋊C4—152no—
413C4⋊C4—152no—
414C4⋊C4—152no—
415C4⋊C4—152no—
416C4⋊C4—152no—
417C4⋊C4—152no—
418C4⋊C4—202no—
419C4⋊C4—308no—
420C4⋊C4—604no—
421C4⋊C4—602no—
422C22⋊C4—104no—
423C22⋊C4—304no—
424C42—308no—
425C3×C5#231611yescharacteristic, complemented, Hall
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—51no—
429C22×C3—51no—
430C22×C3—52no—
431C22×C3—52no—
432C22×C3—52no—
433C22×C3—104no—
434C22×C3—104no—
435C22×C3—101no—
436C22×C3—101no—
437C22×C3C2×C4⋊AGL(1,𝔽5)12yes—
438C22×C3C23×AGL(1,𝔽5)11yescharacteristic
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—101no—
442C3×C4—101no—
443C3×C4—204no—
444Dic3—22no—
445Dic3—54no—
446Dic3—102no—
447Dic3—204no—
448Dic3C2×C4⋊AGL(1,𝔽5)14yes—
449C2×C5—22no—
450C2×C5#548611yescharacteristic
451C2×C5C2×D3×C4⋊C411yescharacteristic
452C2×C5#551611yescharacteristic
453D5—22no—
454D5#559712yes—
455D5#562312yes—
456C23—51no—
457C23—52no—
458C23—52no—
459C23—51no—
460C23—102no—
461C23—102no—
462C23C2×D3×AGL(1,𝔽5)11yescharacteristic
463C2×C4—34no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—41no—
467C2×C4—51no—
468C2×C4—51no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—104no—
472C2×C4—104no—
473C2×C4—104no—
474C2×C4—121no—
475C2×C4—154no—
476C2×C4—154no—
477C2×C4—158no—
478C2×C4—154no—
479C2×C4—152no—
480C2×C4—152no—
481C2×C4—201no—
482C2×C4—201no—
483C2×C4—201no—
484C2×C4—304no—
485C2×C4—304no—
486C2×C4—304no—
487C2×C4—304no—
488C2×C4—602no—
489C2×C4—601no—
490C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
491C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
492C2×C3—22no—
493C2×C3—52no—
494C2×C3—52no—
495C2×C3—102no—
496C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
497C2×C3#6625811yescharacteristic
498C2×C3#6626211yescharacteristic
499C5#7386911yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—52no—
503C22—51no—
504C22—51no—
505C22—52no—
506C22—52no—
507C22—104no—
508C22—104no—
509C22—101no—
510C22—101no—
511C22D3×C4⋊AGL(1,𝔽5)12yes—
512C22C22×D3×AGL(1,𝔽5)11yescharacteristic
513C4—21no—
514C4—21no—
515C4—34no—
516C4—62no—
517C4—101no—
518C4—101no—
519C4—154no—
520C4—204no—
521C4—302no—
522C4—604no—
523C3#1061710211yescharacteristic, complemented, Sylow
524C2—22no—
525C2—52no—
526C2—52no—
527C2—102no—
528C2#1175681211yescharacteristic
529C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
530C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2316
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751844C2semidirect
7. #11751837C2semidirect
20. C2×#6712C4semidirect
21. C2×C5×Dic3⋊C4C4semidirect
22. C2×Dic3⋊Dic5C4semidirect
23. C2×#6669C4semidirect
24. D5×Dic3⋊C4C4semidirect
25. D5×Dic3⋊C4C4semidirect
122. C2×Dic15C4⋊C4semidirect
126. C2×C5×Dic3C4⋊C4semidirect
138. D5×Dic3C4⋊C4semidirect
157. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
363. C2×Dic3C4⋊AGL(1,𝔽5)semidirect
425. C3×C5#2316semidirect
499. C5#73869semidirect
523. C3#10617102semidirect

Maximal subgroups

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

subgroupindex
C2×#919232
C2×D5×Dic3⋊C42
#117524242
C3×#657652
#117520282
#117518442
#117518372
#106171023
#738695