Finite Group Databasebeta

← #14326773

Subgroups — #14326773

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Dic3C211yesmaximal, characteristic
2C4×#6763C211yesmaximal, characteristic
3C3×#65765C211yesmaximal, characteristic
4#11752028C212yesmaximal
5Dic3×C22⋊AGL(1,𝔽5)C212yesmaximal
6#11751861C212yesmaximal, complemented
7#11751846C212yesmaximal, complemented
8#11751839C214yesmaximal, complemented
9#10617104—31nomaximal, Hall
10C22×C3×C4×D5C2211yescharacteristic
11C22×D5×Dic3C2212yes—
12C2×#6763C2211yescharacteristic
13C2×#6763C2211yescharacteristic
14C2×C4×ΓL(1,𝔽16)C2212yes—
15C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
16C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
17C2×Dic3⋊AGL(1,𝔽5)C2214yes—
18C2×Dic3×AGL(1,𝔽5)C2214yes—
19C2×C4⋊Dic15C411yescharacteristic, complemented
20C2×C5×C4⋊Dic3C411yescharacteristic, complemented
21C2×#6668C412yescomplemented
22D5×C4⋊Dic3C411yescharacteristic, complemented
23D5×C4⋊Dic3C411yescharacteristic, complemented
24D5×C4⋊Dic3C412yescomplemented
25D5×C4⋊Dic3C2212yes—
26D5×C4⋊Dic3C2211yescharacteristic
27D5×C4⋊Dic3C2211yescharacteristic
28#91235C2212yes—
29C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
30(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
31(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
32#73879—51nomaximal, Hall
33C2×D5×C4⋊C4—31no—
34#65765—32no—
35#65765D311yescharacteristic
36C4×C22⋊AGL(1,𝔽5)—31no—
37C4×C22⋊AGL(1,𝔽5)—32no—
38#65712—32no—
39#65711—34no—
40C4⋊C4×AGL(1,𝔽5)—32no—
41C23×C3×D5C2311yescharacteristic
42C22×ΓL(1,𝔽16)C2312yes—
43C22×ΓL(1,𝔽16)C2312yes—
44C22×C3×AGL(1,𝔽5)C2314yes—
45C22×C3×C4×C5C2×C411yescharacteristic
46C22×Dic15C2×C412yes—
47C22×C5×Dic3C2×C412yes—
48C22×C3×Dic5C2×C411yescharacteristic
49C2×C3×C4×D5—24no—
50C2×C3×C4×D5C2×C411yescharacteristic
51C2×C3×C4×D5C2×C411yescharacteristic
52C2×C3×C4×D5C2311yescharacteristic
53C2×C3×C4×D5C2311yescharacteristic
54C2×D5×Dic3—44no—
55C2×D5×Dic3C2×C412yes—
56C2×D5×Dic3C2×C412yes—
57C2×D5×Dic3C2312yes—
58C2×D5×Dic3C2312yes—
59#6763—22no—
60#6763Q814yes—
61C4×ΓL(1,𝔽16)—24no—
62C3×C22⋊AGL(1,𝔽5)—24no—
63C3×C4⋊AGL(1,𝔽5)—24no—
64Dic3⋊AGL(1,𝔽5)—44no—
65Dic3×AGL(1,𝔽5)—44no—
66C4⋊Dic15C2×C412yes—
67C4⋊Dic15C2×C411yescharacteristic
68C4⋊Dic15C2×C411yescharacteristic
69C5×C4⋊Dic3C2×C412yes—
70C5×C4⋊Dic3C2×C411yescharacteristic
71C5×C4⋊Dic3C2×C411yescharacteristic
72#6668C2×C412yes—
73#6668C2×C412yes—
74#6668C2×C412yes—
75#6668C2×C412yes—
76C22×C4⋊Dic3—51no—
77C3×#380—51no—
78C4×#217—51no—
79Dic3×C4⋊C4—52no—
80#4972—52no—
81#4942—52no—
82Dic3×C22⋊C4—52no—
83#4653—54no—
84C22×C4×D5—32no—
85C22×C4×D5C2×D311yescharacteristic
86C2×C22⋊AGL(1,𝔽5)—31no—
87C2×C22⋊AGL(1,𝔽5)—31no—
88C2×C22⋊AGL(1,𝔽5)C2×D312yes—
89C2×C4⋊AGL(1,𝔽5)—34no—
90C2×C4⋊AGL(1,𝔽5)C2×D312yes—
91C2×C4×AGL(1,𝔽5)—32no—
92C2×C4×AGL(1,𝔽5)—34no—
93C2×C5×C4⋊C4—31no—
94C2×C4⋊Dic5—31no—
95C2×#683—32no—
96D5×C4⋊C4—31no—
97D5×C4⋊C4—31no—
98D5×C4⋊C4—32no—
99D5×C4⋊C4—31no—
100D5×C4⋊C4—32no—
101D5×C4⋊C4—31no—
102(C2×AGL(1,𝔽5))⋊C4—34no—
103(C2×AGL(1,𝔽5))⋊C4—34no—
104(C2×AGL(1,𝔽5))⋊C4—32no—
105(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
106#2345—151noSylow
107C23×C3×C5C22×C411yescharacteristic
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5C22×C411yescharacteristic
111C22×C3×D5C2×Q812yes—
112C22×C3×D5#4112yes—
113C22×C3×D5C2411yescharacteristic
114C2×ΓL(1,𝔽16)—22no—
115C2×ΓL(1,𝔽16)—22no—
116C2×ΓL(1,𝔽16)—22no—
117C2×ΓL(1,𝔽16)—22no—
118C2×ΓL(1,𝔽16)—22no—
119C2×ΓL(1,𝔽16)C2×Q814yes—
120C2×C3×AGL(1,𝔽5)—24no—
121C2×C3×AGL(1,𝔽5)—24no—
122C2×C3×AGL(1,𝔽5)—24no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5C22×C411yescharacteristic
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×Dic15—42no—
127C2×Dic15C22×C412yes—
128C2×Dic15C22×C412yes—
129C2×C5×Dic3—42no—
130C2×C5×Dic3C22×C412yes—
131C2×C5×Dic3C22×C412yes—
132C2×C3×Dic5—22no—
133C2×C3×Dic5C22×C411yescharacteristic
134C2×C3×Dic5C22×C411yescharacteristic
135C3×C4×D5—22no—
136C3×C4×D5—22no—
137C3×C4×D5—22no—
138C3×C4×D5#4114yes—
139D5×Dic3—24no—
140D5×Dic3—24no—
141D5×Dic3—42no—
142D5×Dic3—42no—
143C23×C3×C4—51no—
144C23×Dic3—52no—
145C2×C3×C4⋊C4—52no—
146C2×C3×C22⋊C4—52no—
147C2×#217—51no—
148C2×#217—51no—
149C2×C4⋊Dic3—51no—
150C2×C4⋊Dic3—52no—
151C2×C4⋊Dic3—52no—
152C2×C4⋊Dic3—51no—
153C2×C4⋊Dic3—51no—
154C2×C4⋊Dic3—52no—
155C2×C4⋊Dic3—51no—
156C2×C4⋊Dic3—51no—
157C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic, complemented
158C2×Dic3⋊C4—54no—
159C2×C4×Dic3—52no—
160C2×C4×Dic3—54no—
161C3×#95—52no—
162C3⋊#95—54no—
163C3⋊#95—54no—
164C3⋊#95—52no—
165C23×D5C22×D311yescharacteristic
166C22×AGL(1,𝔽5)—32no—
167C22×AGL(1,𝔽5)—32no—
168C22×AGL(1,𝔽5)C22×D314yes—
169C22×C4×C5—32no—
170C22×C4×C5C4×D311yescharacteristic
171C22×Dic5—32no—
172C22×Dic5C4×D311yescharacteristic
173C2×C4×D5—24no—
174C2×C4×D5—32no—
175C2×C4×D5—32no—
176C2×C4×D5—32no—
177C2×C4×D5—32no—
178C2×C4×D5—124no—
179C2×C4×D5C4×D311yescharacteristic
180C2×C4×D5C4×D311yescharacteristic
181C2×C4×D5C22×D311yescharacteristic
182C2×C4×D5C22×D311yescharacteristic
183C22⋊AGL(1,𝔽5)—24no—
184C22⋊AGL(1,𝔽5)—34no—
185C22⋊AGL(1,𝔽5)—62no—
186C4⋊AGL(1,𝔽5)—24no—
187C4⋊AGL(1,𝔽5)—124no—
188C4×AGL(1,𝔽5)—64no—
189C4×AGL(1,𝔽5)—124no—
190C5×C4⋊C4—32no—
191C5×C4⋊C4—31no—
192C5×C4⋊C4—31no—
193C4⋊Dic5—32no—
194C4⋊Dic5—31no—
195C4⋊Dic5—31no—
196#683—32no—
197#683—32no—
198#683—32no—
199#683—32no—
200C22×C4⋊C4—151no—
201#389—152no—
202#387—154no—
203#380—51no—
204#380—152no—
205C4×C4⋊C4—152no—
206C4×C22⋊C4—152no—
207C4×C22⋊C4—151no—
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5C4×Q812yes—
211C22×C3×C5C23×C411yescharacteristic
212C2×C3×D5—21no—
213C2×C3×D5—21no—
214C2×C3×D5—24no—
215C2×C3×D5—24no—
216C2×C3×D5C4×Q812yes—
217C2×C3×D5C22×Q811yescharacteristic
218C2×C3×D5C2×#4111yescharacteristic
219C2×C3×D5C2×#4112yes—
220C2×C3×D5H(5,𝔽2)12yes—
221ΓL(1,𝔽16)—24no—
222ΓL(1,𝔽16)—42no—
223C3×AGL(1,𝔽5)—44no—
224C3×C4×C5—21no—
225C3×C4×C5#11712yes—
226Dic15—22no—
227Dic15—22no—
228C3×Dic5—21no—
229C3×Dic5#11712yes—
230C5×Dic3—22no—
231C5×Dic3—22no—
232C24×C3—51no—
233C22×C3×C4—51no—
234C22×C3×C4—51no—
235C22×C3×C4—51no—
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C22×C3×C4—54no—
239C22×C3×C4—104no—
240C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
241C22×Dic3—52no—
242C22×Dic3—52no—
243C22×Dic3—52no—
244C22×Dic3—52no—
245C22×Dic3—52no—
246C22×Dic3—52no—
247C22×Dic3—52no—
248C22×Dic3—204no—
249C22×Dic3C2×AGL(1,𝔽5)12yes—
250C3×C4⋊C4—104no—
251C3×C22⋊C4—104no—
252#217—54no—
253#217—102no—
254C4⋊Dic3—52no—
255C4⋊Dic3—51no—
256C4⋊Dic3—51no—
257C4⋊Dic3—52no—
258C4⋊Dic3—52no—
259C4⋊Dic3—52no—
260C4⋊Dic3—52no—
261C4⋊Dic3C2×AGL(1,𝔽5)12yes—
262C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
263C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
264Dic3⋊C4—204no—
265C4×Dic3—104no—
266C4×Dic3—204no—
267C23×C5C2×C4×D311yescharacteristic
268C22×D5—22no—
269C22×D5—22no—
270C22×D5C2×C4×D311yescharacteristic
271C22×D5#23712yes—
272C22×D5D3×Q812yes—
273C22×D5C23×D311yescharacteristic
274C2×AGL(1,𝔽5)—24no—
275C2×AGL(1,𝔽5)—24no—
276C2×AGL(1,𝔽5)—24no—
277C2×AGL(1,𝔽5)—34no—
278C2×AGL(1,𝔽5)—62no—
279C2×AGL(1,𝔽5)—62no—
280C2×AGL(1,𝔽5)—62no—
281C2×AGL(1,𝔽5)—62no—
282C2×AGL(1,𝔽5)—62no—
283C2×C4×C5—22no—
284C2×C4×C5—32no—
285C2×C4×C5—32no—
286C2×C4×C5—122no—
287C2×C4×C5C2×C4×D311yescharacteristic
288C2×C4×C5C2×C4×D311yescharacteristic
289C2×Dic5—22no—
290C2×Dic5—32no—
291C2×Dic5—32no—
292C2×Dic5—122no—
293C2×Dic5C2×C4×D311yescharacteristic
294C2×Dic5C2×C4×D311yescharacteristic
295C4×D5—22no—
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—64no—
299C4×D5—64no—
300C4×D5—122no—
301C4×D5—122no—
302C4×D5#23714yes—
303C23×C4—51no—
304C23×C4—152no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—52no—
307C2×C4⋊C4—151no—
308C2×C4⋊C4—152no—
309C2×C4⋊C4—151no—
310C2×C4⋊C4—152no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C4⋊C4—152no—
314C2×C4⋊C4—151no—
315C2×C4⋊C4—154no—
316C2×C22⋊C4—52no—
317C2×C22⋊C4—151no—
318C2×C22⋊C4—151no—
319C2×C42—152no—
320C2×C42—154no—
321#95—52no—
322#95—152no—
323#95—154no—
324#95—154no—
325C2×C3×C5—22no—
326C2×C3×C5C2×#11711yescharacteristic
327C2×C3×C5C2×C4×Q811yescharacteristic
328C2×C3×C5#51811yescharacteristic
329C3×D5—22no—
330C3×D5#55312yes—
331C3×D5#55412yes—
332C23×C3—51no—
333C23×C3—52no—
334C23×C3—52no—
335C23×C3—51no—
336C23×C3—102no—
337C23×C3—102no—
338C23×C3C22×AGL(1,𝔽5)11yescharacteristic
339C2×C3×C4—22no—
340C2×C3×C4—51no—
341C2×C3×C4—54no—
342C2×C3×C4—51no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—104no—
348C2×C3×C4—104no—
349C2×C3×C4—104no—
350C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
351C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
352C2×Dic3—42no—
353C2×Dic3—54no—
354C2×Dic3—52no—
355C2×Dic3—52no—
356C2×Dic3—104no—
357C2×Dic3—104no—
358C2×Dic3—102no—
359C2×Dic3—102no—
360C2×Dic3—102no—
361C2×Dic3—102no—
362C2×Dic3—102no—
363C2×Dic3—202no—
364C2×Dic3—202no—
365C2×Dic3—202no—
366C2×Dic3C22×AGL(1,𝔽5)12yes—
367C2×Dic3C22×AGL(1,𝔽5)12yes—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5#88712yes—
371C22×C5C22×C4×D311yescharacteristic
372C2×D5—21no—
373C2×D5—21no—
374C2×D5—24no—
375C2×D5—24no—
376C2×D5#88712yes—
377C2×D5C2×#23712yes—
378C2×D5C2×#23711yescharacteristic
379C2×D5C2×D3×Q811yescharacteristic
380C2×D5#100912yes—
381AGL(1,𝔽5)—44no—
382AGL(1,𝔽5)—64no—
383AGL(1,𝔽5)—122no—
384C4×C5—21no—
385C4×C5—62no—
386C4×C5—62no—
387C4×C5#87712yes—
388Dic5—21no—
389Dic5—62no—
390Dic5—62no—
391Dic5#87712yes—
392C24—51no—
393C22×C4—32no—
394C22×C4—51no—
395C22×C4—51no—
396C22×C4—51no—
397C22×C4—51no—
398C22×C4—51no—
399C22×C4—54no—
400C22×C4—104no—
401C22×C4—152no—
402C22×C4—152no—
403C22×C4—152no—
404C22×C4—152no—
405C22×C4—152no—
406C22×C4—152no—
407C22×C4—152no—
408C22×C4—604no—
409C22×C4D3×AGL(1,𝔽5)11yescharacteristic
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—104no—
414C4⋊C4—152no—
415C4⋊C4—152no—
416C4⋊C4—152no—
417C4⋊C4—152no—
418C4⋊C4—152no—
419C4⋊C4—151no—
420C4⋊C4—151no—
421C4⋊C4—604no—
422C22⋊C4—104no—
423C22⋊C4—154no—
424C22⋊C4—302no—
425C42—304no—
426C42—604no—
427C3×C5#234511yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—52no—
431C22×C3—52no—
432C22×C3—51no—
433C22×C3—51no—
434C22×C3—52no—
435C22×C3—104no—
436C22×C3—104no—
437C22×C3—101no—
438C22×C3—101no—
439C22×C3Q8×AGL(1,𝔽5)12yes—
440C22×C3C23×AGL(1,𝔽5)11yescharacteristic
441C3×C4—21no—
442C3×C4—52no—
443C3×C4—101no—
444C3×C4—204no—
445C3×C4#413012yes—
446Dic3—22no—
447Dic3—22no—
448Dic3—104no—
449Dic3—102no—
450Dic3—102no—
451Dic3—202no—
452C2×C5—22no—
453C2×C5C2×#87711yescharacteristic
454C2×C5C2×#88711yescharacteristic
455C2×C5#552111yescharacteristic
456D5—22no—
457D5#561812yes—
458D5#563512yes—
459C23—51no—
460C23—52no—
461C23—52no—
462C23—51no—
463C23—102no—
464C23—102no—
465C23C2×D3×AGL(1,𝔽5)11yescharacteristic
466C2×C4—22no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—51no—
470C2×C4—54no—
471C2×C4—51no—
472C2×C4—102no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—104no—
477C2×C4—104no—
478C2×C4—104no—
479C2×C4—122no—
480C2×C4—154no—
481C2×C4—152no—
482C2×C4—152no—
483C2×C4—304no—
484C2×C4—304no—
485C2×C4—302no—
486C2×C4—302no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4—602no—
491C2×C4—602no—
492C2×C4—602no—
493C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
494C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
495C2×C3—22no—
496C2×C3—52no—
497C2×C3—52no—
498C2×C3—102no—
499C2×C3C2×#413011yescharacteristic
500C2×C3#6625811yescharacteristic
501C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
502C5#7387911yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—51no—
506C22—51no—
507C22—52no—
508C22—52no—
509C22—52no—
510C22—104no—
511C22—104no—
512C22—101no—
513C22—101no—
514C22ΓL(1,𝔽16)⋊Q812yes—
515C22C22×D3×AGL(1,𝔽5)11yescharacteristic
516C4—21no—
517C4—52no—
518C4—62no—
519C4—62no—
520C4—101no—
521C4—204no—
522C4—304no—
523C4—302no—
524C4—302no—
525C4—602no—
526C4#9192312yes—
527C3#1061710411yescharacteristic, complemented, Sylow
528C2—22no—
529C2—52no—
530C2—52no—
531C2—102no—
532C2C2×ΓL(1,𝔽16)⋊Q811yescharacteristic
533C2#1175683711yescharacteristic
534C2C2×#9192311yescharacteristic
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#2345
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. #11751861C2semidirect
7. #11751846C2semidirect
8. #11751839C2semidirect
19. C2×C4⋊Dic15C4semidirect
20. C2×C5×C4⋊Dic3C4semidirect
21. C2×#6668C4semidirect
22. D5×C4⋊Dic3C4semidirect
23. D5×C4⋊Dic3C4semidirect
24. D5×C4⋊Dic3C4semidirect
157. C2×C4⋊Dic3AGL(1,𝔽5)semidirect
427. C3×C5#2345semidirect
502. C5#73879semidirect
527. C3#10617104semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Dic32
C4×#67632
C3×#657652
#117520282
Dic3×C22⋊AGL(1,𝔽5)2
#117518612
#117518462
#117518392
#106171043
#738795