Finite Group Databasebeta

← #14279920

Subgroups — #14279920

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D5×Dic3C211yesmaximal, characteristic
2C2×#91235C211yesmaximal, characteristic
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
4C2×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal
5C2×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal
6#10604197—31nomaximal, Hall
7C23×ΓL(1,𝔽16)C2212yes—
8C23×C3×AGL(1,𝔽5)C2212yes—
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3C2211yescharacteristic
11C22×D5×Dic3C2211yescharacteristic
12C2×C4×Dic15C411yescharacteristic, complemented
13C2×C4×C5×Dic3C411yescharacteristic, complemented
14C2×Dic3×Dic5C411yescharacteristic, complemented
15C2×Dic3×Dic5C411yescharacteristic, complemented
16C4×D5×Dic3—24no—
17#91235—22no—
18C3×(C2×AGL(1,𝔽5))⋊C4—22no—
19(C2×AGL(1,𝔽5))⋊Dic3—24no—
20(C2×AGL(1,𝔽5))⋊Dic3C418yescomplemented
21#69403—51nomaximal, Hall
22C2×C42×D5—31no—
23C2×(C2×AGL(1,𝔽5))⋊C4—32no—
24C2×(C2×AGL(1,𝔽5))⋊C4—32no—
25C2×(C2×AGL(1,𝔽5))⋊C4—31no—
26C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic
27C23×C3×D5C2311yescharacteristic
28C22×ΓL(1,𝔽16)—22no—
29C22×ΓL(1,𝔽16)—22no—
30C22×ΓL(1,𝔽16)—22no—
31C22×ΓL(1,𝔽16)—22no—
32C22×ΓL(1,𝔽16)—22no—
33C22×ΓL(1,𝔽16)—22no—
34C22×ΓL(1,𝔽16)C2×C414yes—
35C22×C3×AGL(1,𝔽5)—22no—
36C22×C3×AGL(1,𝔽5)—22no—
37C22×C3×AGL(1,𝔽5)—22no—
38C22×C3×AGL(1,𝔽5)—22no—
39C22×C3×AGL(1,𝔽5)—22no—
40C22×C3×AGL(1,𝔽5)—22no—
41C22×C3×AGL(1,𝔽5)C2×C414yes—
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—22no—
49C2×C3×C4×D5—22no—
50C2×C3×C4×D5D412yes—
51C2×C3×C4×D5Q812yes—
52C2×D5×Dic3—22no—
53C2×D5×Dic3—21no—
54C2×D5×Dic3—21no—
55C2×D5×Dic3—22no—
56C2×D5×Dic3—21no—
57C2×D5×Dic3—21no—
58C2×D5×Dic3C2×C414yes—
59C2×D5×Dic3D414yes—
60C4×Dic15—22no—
61C4×C5×Dic3—22no—
62Dic3×Dic5—22no—
63Dic3×Dic5—22no—
64C22×C4×Dic3—51no—
65C2×C3×#95—51no—
66C2×C3⋊#95—52no—
67C2×C3⋊#95—52no—
68C2×C3⋊#95—51no—
69C23×AGL(1,𝔽5)—32no—
70C23×AGL(1,𝔽5)C2×D312yes—
71C22×C4×D5—31no—
72C22×C4×D5—31no—
73C22×C4×D5C2×D311yescharacteristic
74C2×C42×C5—31no—
75C2×C4×Dic5—31no—
76C2×C4×Dic5—31no—
77C2×C4×Dic5—31no—
78C42×D5—64no—
79(C2×AGL(1,𝔽5))⋊C4—22no—
80(C2×AGL(1,𝔽5))⋊C4—38no—
81(C2×AGL(1,𝔽5))⋊C4—64no—
82(C2×AGL(1,𝔽5))⋊C4—62no—
83#1434—151noSylow
84C23×C3×C5C22×C411yescharacteristic
85C22×C3×D5C22×C412yes—
86C22×C3×D5C2×D411yescharacteristic
87C22×C3×D5C2×D412yes—
88C22×C3×D5C2×Q811yescharacteristic
89C22×C3×D5#4112yes—
90C22×C3×D5#4111yescharacteristic
91C22×C3×D5#4111yescharacteristic
92C22×C3×D5#4111yescharacteristic
93C22×C3×D5#4111yescharacteristic
94C22×C3×D5#4112yes—
95C2×ΓL(1,𝔽16)—24no—
96C2×ΓL(1,𝔽16)—24no—
97C2×ΓL(1,𝔽16)—24no—
98C2×ΓL(1,𝔽16)—42no—
99C2×ΓL(1,𝔽16)—42no—
100C2×ΓL(1,𝔽16)—42no—
101C2×ΓL(1,𝔽16)—42no—
102C2×C3×AGL(1,𝔽5)—24no—
103C2×C3×AGL(1,𝔽5)—24no—
104C2×C3×AGL(1,𝔽5)—24no—
105C2×C3×AGL(1,𝔽5)—42no—
106C2×C3×AGL(1,𝔽5)—42no—
107C2×C3×AGL(1,𝔽5)—42no—
108C2×C3×AGL(1,𝔽5)—42no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5C4⋊C412yes—
112C2×Dic15—21no—
113C2×Dic15—21no—
114C2×Dic15—21no—
115C2×Dic15—21no—
116C2×Dic15C4212yes—
117C2×Dic15C22⋊C412yes—
118C2×C5×Dic3—21no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3C4212yes—
123C2×C5×Dic3C22⋊C412yes—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5C4⋊C412yes—
127C3×C4×D5—24no—
128C3×C4×D5—24no—
129D5×Dic3—24no—
130D5×Dic3—24no—
131D5×Dic3—24no—
132D5×Dic3—24no—
133C23×C3×C4—51no—
134C23×C3×C4—52no—
135C23×Dic3—51no—
136C23×Dic3—51no—
137C23×Dic3—52no—
138C2×C4×Dic3—51no—
139C2×C4×Dic3—51no—
140C2×C4×Dic3—51no—
141C2×C4×Dic3—104no—
142C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
143C3×#95—102no—
144C3⋊#95—58no—
145C3⋊#95—104no—
146C3⋊#95—102no—
147C23×D5C22×D311yescharacteristic
148C22×AGL(1,𝔽5)—22no—
149C22×AGL(1,𝔽5)—22no—
150C22×AGL(1,𝔽5)—22no—
151C22×AGL(1,𝔽5)—22no—
152C22×AGL(1,𝔽5)—22no—
153C22×AGL(1,𝔽5)—22no—
154C22×AGL(1,𝔽5)—34no—
155C22×AGL(1,𝔽5)—62no—
156C22×AGL(1,𝔽5)—62no—
157C22×AGL(1,𝔽5)—62no—
158C22×AGL(1,𝔽5)—62no—
159C22×AGL(1,𝔽5)—62no—
160C22×AGL(1,𝔽5)—62no—
161C22×AGL(1,𝔽5)C4×D314yes—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5C4×D311yescharacteristic
165C22×Dic5—31no—
166C22×Dic5—31no—
167C22×Dic5C4×D311yescharacteristic
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—34no—
171C2×C4×D5—34no—
172C2×C4×D5—62no—
173C2×C4×D5—62no—
174C2×C4×D5—61no—
175C2×C4×D5—61no—
176C2×C4×D5—61no—
177C2×C4×D5—61no—
178C2×C4×D5Dic612yes—
179C2×C4×D5#6712yes—
180C42×C5—62no—
181C4×Dic5—62no—
182C4×Dic5—62no—
183C4×Dic5—62no—
184C22×C42—151no—
185C2×#95—51no—
186C2×#95—152no—
187C2×#95—151no—
188C2×#95—152no—
189C22×C3×C5C2×C4211yescharacteristic
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C22×C3×C5C2×C4⋊C411yescharacteristic
192C22×C3×C5#11711yescharacteristic
193C22×C3×C5#11711yescharacteristic
194C22×C3×C5#11711yescharacteristic
195C22×C3×C5#11711yescharacteristic
196C2×C3×D5#11712yes—
197C2×C3×D5#11712yes—
198C2×C3×D5C4×D412yes—
199C2×C3×D5C4×D412yes—
200C2×C3×D5C4×D412yes—
201C2×C3×D5C4×Q812yes—
202C2×C3×D5#12112yes—
203C2×C3×D5C22⋊Q812yes—
204C2×C3×D5#12312yes—
205C2×C3×D5#12312yes—
206C2×C3×D5#12411yescharacteristic
207C2×C3×D5#12411yescharacteristic
208C2×C3×D5#12511yescharacteristic
209C2×C3×D5#12511yescharacteristic
210C2×C3×D5#12612yes—
211C2×C3×D5#12612yes—
212ΓL(1,𝔽16)—44no—
213C3×AGL(1,𝔽5)—44no—
214C3×C4×C5—22no—
215Dic15—22no—
216Dic15—22no—
217C3×Dic5—22no—
218C5×Dic3—22no—
219C5×Dic3—22no—
220C24×C3—51no—
221C22×C3×C4—51no—
222C22×C3×C4—52no—
223C22×C3×C4—52no—
224C22×C3×C4—54no—
225C22×C3×C4—102no—
226C22×C3×C4—102no—
227C22×C3×C4—102no—
228C22×C3×C4—102no—
229C22×C3×C4—102no—
230C22×C3×C4—102no—
231C22×C3×C4—102no—
232C22×C3×C4—102no—
233C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
234C22×Dic3—51no—
235C22×Dic3—51no—
236C22×Dic3—54no—
237C22×Dic3—54no—
238C22×Dic3—54no—
239C22×Dic3—102no—
240C22×Dic3—101no—
241C22×Dic3—101no—
242C22×Dic3—102no—
243C22×Dic3—101no—
244C22×Dic3—101no—
245C22×Dic3—102no—
246C22×Dic3—102no—
247C22×Dic3—102no—
248C22×Dic3—102no—
249C22×Dic3—102no—
250C22×Dic3—102no—
251C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
252C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
253C4×Dic3—22no—
254C4×Dic3—102no—
255C4×Dic3—102no—
256C4×Dic3—102no—
257C23×C5C2×C4×D311yescharacteristic
258C22×D5C2×Dic611yescharacteristic
259C22×D5C2×C4×D312yes—
260C22×D5#23512yes—
261C22×D5D3×D412yes—
262C22×D5#23711yescharacteristic
263C22×D5#23712yes—
264C22×D5#23711yescharacteristic
265C22×D5#23911yescharacteristic
266C22×D5#23911yescharacteristic
267C22×D5C2×#6711yescharacteristic
268C2×AGL(1,𝔽5)—24no—
269C2×AGL(1,𝔽5)—24no—
270C2×AGL(1,𝔽5)—24no—
271C2×AGL(1,𝔽5)—42no—
272C2×AGL(1,𝔽5)—42no—
273C2×AGL(1,𝔽5)—42no—
274C2×AGL(1,𝔽5)—42no—
275C2×AGL(1,𝔽5)—64no—
276C2×AGL(1,𝔽5)—64no—
277C2×AGL(1,𝔽5)—64no—
278C2×AGL(1,𝔽5)—122no—
279C2×AGL(1,𝔽5)—122no—
280C2×AGL(1,𝔽5)—122no—
281C2×AGL(1,𝔽5)—122no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—32no—
285C2×C4×C5—32no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5Dic3⋊C412yes—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—32no—
294C2×Dic5—32no—
295C2×Dic5—61no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—61no—
299C2×Dic5Dic3⋊C412yes—
300C4×D5—24no—
301C4×D5—24no—
302C4×D5—64no—
303C4×D5—64no—
304C4×D5—64no—
305C4×D5—64no—
306C23×C4—51no—
307C23×C4—52no—
308C23×C4—151no—
309C23×C4—151no—
310C23×C4—152no—
311C2×C42—31no—
312C2×C42—151no—
313C2×C42—151no—
314C2×C42—151no—
315C2×C42—304no—
316#95—102no—
317#95—158no—
318#95—302no—
319#95—304no—
320C2×C3×C5#37611yescharacteristic
321C2×C3×C5C4×C22⋊C411yescharacteristic
322C2×C3×C5C4×C4⋊C411yescharacteristic
323C2×C3×C5#38011yescharacteristic
324C2×C3×C5#38111yescharacteristic
325C2×C3×C5#38211yescharacteristic
326C2×C3×C5#38311yescharacteristic
327C3×D5#38712yes—
328C3×D5#38712yes—
329C3×D5#38812yes—
330C3×D5#38812yes—
331C23×C3—52no—
332C23×C3—51no—
333C23×C3—51no—
334C23×C3—51no—
335C23×C3—51no—
336C23×C3—52no—
337C23×C3—51no—
338C23×C3—51no—
339C23×C3—52no—
340C23×C3—52no—
341C23×C3C22×AGL(1,𝔽5)11yescharacteristic
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—52no—
345C2×C3×C4—104no—
346C2×C3×C4—104no—
347C2×C3×C4—101no—
348C2×C3×C4—101no—
349C2×C3×C4—104no—
350C2×C3×C4—104no—
351C2×C3×C4—104no—
352C2×C3×C4—202no—
353C2×C3×C4—202no—
354C2×C3×C4—202no—
355C2×C3×C4—202no—
356C2×C3×C4C4⋊AGL(1,𝔽5)12yes—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—52no—
362C2×Dic3—52no—
363C2×Dic3—104no—
364C2×Dic3—104no—
365C2×Dic3—104no—
366C2×Dic3—104no—
367C2×Dic3—101no—
368C2×Dic3—101no—
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—104no—
372C2×Dic3—104no—
373C2×Dic3—104no—
374C2×Dic3—202no—
375C2×Dic3—202no—
376C2×Dic3—202no—
377C2×Dic3—202no—
378C2×Dic3C4×AGL(1,𝔽5)12yes—
379C2×Dic3C22⋊AGL(1,𝔽5)12yes—
380C22×C5C42×D311yescharacteristic
381C22×C5#87211yescharacteristic
382C22×C5#87711yescharacteristic
383C22×C5D3×C22⋊C411yescharacteristic
384C22×C5#89211yescharacteristic
385C22×C5#89211yescharacteristic
386C22×C5C2×Dic3⋊C411yescharacteristic
387C2×D5C4×Dic612yes—
388C2×D5#87712yes—
389C2×D5#87812yes—
390C2×D5#87912yes—
391C2×D5#67⋊C412yes—
392C2×D5#88312yes—
393C2×D5#89011yescharacteristic
394C2×D5#89011yescharacteristic
395C2×D5#89212yes—
396C2×D5#89312yes—
397C2×D5#89412yes—
398C2×D5#89812yes—
399C2×D5C4×#6712yes—
400C2×D5#93611yescharacteristic
401C2×D5#93912yes—
402C2×D5#94711yescharacteristic
403AGL(1,𝔽5)—44no—
404AGL(1,𝔽5)—124no—
405C4×C5—22no—
406C4×C5—62no—
407C4×C5—62no—
408Dic5—22no—
409Dic5—62no—
410Dic5—62no—
411C24—51no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—51no—
415C22×C4—52no—
416C22×C4—52no—
417C22×C4—54no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—154no—
427C22×C4—154no—
428C22×C4—151no—
429C22×C4—151no—
430C22×C4—154no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4—301no—
434C22×C4—301no—
435C22×C4—301no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4—302no—
440C22×C4—302no—
441C22×C4—302no—
442C22×C4—302no—
443C22×C4D3×AGL(1,𝔽5)11yescharacteristic
444C42—62no—
445C42—302no—
446C42—302no—
447C42—302no—
448C3×C5#143411yescharacteristic, complemented, Hall
449C22×C3—52no—
450C22×C3—52no—
451C22×C3—52no—
452C22×C3—52no—
453C22×C3—51no—
454C22×C3—51no—
455C22×C3—51no—
456C22×C3—51no—
457C22×C3—52no—
458C22×C3—52no—
459C22×C3—52no—
460C22×C3—52no—
461C22×C3—52no—
462C22×C3—52no—
463C22×C3—52no—
464C22×C3—52no—
465C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
466C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
467C22×C3#413011yescharacteristic
468C22×C3#413011yescharacteristic
469C22×C3#413011yescharacteristic
470C22×C3#413011yescharacteristic
471C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
472C3×C4—22no—
473C3×C4—102no—
474C3×C4—204no—
475Dic3—22no—
476Dic3—22no—
477Dic3—102no—
478Dic3—102no—
479Dic3—204no—
480C2×C5#464811yescharacteristic
481C2×C5#465111yescharacteristic
482C2×C5#466411yescharacteristic
483C2×C5#466611yescharacteristic
484C2×C5C4×Dic3⋊C411yescharacteristic
485C2×C5#494211yescharacteristic
486C2×C5#497711yescharacteristic
487D5#465412yes—
488D5#465512yes—
489D5#494512yes—
490D5#499012yes—
491C23—51no—
492C23—51no—
493C23—51no—
494C23—51no—
495C23—52no—
496C23—52no—
497C23—52no—
498C23—51no—
499C23—51no—
500C23—52no—
501C23C2×D3×AGL(1,𝔽5)11yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—32no—
505C2×C4—32no—
506C2×C4—52no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—104no—
512C2×C4—104no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—104no—
516C2×C4—104no—
517C2×C4—104no—
518C2×C4—152no—
519C2×C4—152no—
520C2×C4—202no—
521C2×C4—202no—
522C2×C4—202no—
523C2×C4—202no—
524C2×C4—304no—
525C2×C4—304no—
526C2×C4—304no—
527C2×C4—304no—
528C2×C4—301no—
529C2×C4—301no—
530C2×C4—301no—
531C2×C4—301no—
532C2×C4—304no—
533C2×C4—304no—
534C2×C4—304no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4—602no—
538C2×C4—602no—
539C2×C4Dic3⋊AGL(1,𝔽5)12yes—
540C2×C3—52no—
541C2×C3—52no—
542C2×C3—52no—
543C2×C3—52no—
544C2×C3#6568611yescharacteristic
545C2×C3C4×C4⋊AGL(1,𝔽5)11yescharacteristic
546C2×C3#6568911yescharacteristic
547C2×C3#6569011yescharacteristic
548C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
549C2×C3#6576411yescharacteristic
550C2×C3#6576511yescharacteristic
551C5#6940311yescharacteristic, complemented, Sylow
552C22—52no—
553C22—52no—
554C22—51no—
555C22—51no—
556C22—51no—
557C22—51no—
558C22—52no—
559C22—52no—
560C22—52no—
561C22—52no—
562C22—52no—
563C22—52no—
564C22—52no—
565C22—52no—
566C22—52no—
567C22—52no—
568C22#9190711yescharacteristic
569C22#9190711yescharacteristic
570C22#9190911yescharacteristic
571C22C4×D3×AGL(1,𝔽5)11yescharacteristic
572C22#9192311yescharacteristic
573C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
574C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
575C4—22no—
576C4—62no—
577C4—62no—
578C4—102no—
579C4—204no—
580C4—302no—
581C4—302no—
582C4—604no—
583C3#1060419711yescharacteristic, complemented, Sylow
584C2—52no—
585C2—52no—
586C2—52no—
587C2—52no—
588C2#1175175011yescharacteristic
589C2#1175175111yescharacteristic
590C2#1175183211yescharacteristic
591C2#1175184811yescharacteristic
592C2#1175185311yescharacteristic
593C2C4×Dic3⋊AGL(1,𝔽5)11yescharacteristic
594C2#1175202811yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radical, cosocleC23×C3×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1434
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
12. C2×C4×Dic15C4semidirect
13. C2×C4×C5×Dic3C4semidirect
14. C2×Dic3×Dic5C4semidirect
15. C2×Dic3×Dic5C4semidirect
20. (C2×AGL(1,𝔽5))⋊Dic3C4semidirect
142. C2×C4×Dic3AGL(1,𝔽5)semidirect
448. C3×C5#1434semidirect
551. C5#69403semidirect
583. C3#10604197semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×Dic32
C2×#912352
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×(C2×AGL(1,𝔽5))⋊Dic32
#106041973
#694035