Finite Group Databasebeta

← #14302152

Subgroups — #14302152

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#208C211yesmaximal, characteristic, complemented
2C2×C3×#4030C211yesmaximal, characteristic
3C2×#91242C212yesmaximal, complemented
4#11752414C211yesmaximal, characteristic, complemented
5#11746790C212yesmaximal, complemented
6#10604249—31nomaximal, Hall
7C22×C3×C22⋊D5C411yescharacteristic
8C22×C3×C22⋊D5C2211yescharacteristic
9C22×C3×D20C411yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C2×#6762C2212yes—
12C2×#6762C2212yes—
13D5⋊#208—24no—
14C2×#6758—21no—
15C2×D5⋊(C3⋊C8)—21no—
16C2×C3×C5×C22⋊C4C411yescharacteristic
17C2×C3×#685C411yescharacteristic
18C2×C3×#683C2211yescharacteristic
19C3×#4030—21no—
20C3×#4030—21no—
21C3×#4030—21no—
22C3×#4030—21no—
23#91242—24no—
24#91232—21no—
25#91232—21no—
26#71683—51nomaximal, Hall
27C2×D5⋊M16—31no—
28C2×#4030D311yescharacteristic
29C2×#4013—32no—
30#65755—31no—
31#64919—32no—
32C24×C3×C5C2×C411yescharacteristic
33C23×C3×D5C2×C411yescharacteristic
34C23×C3×D5C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C2×C3×C22⋊D5—21no—
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—22no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—22no—
43C2×C3×C22⋊D5—42no—
44C22×C3×Dic5C2×C411yescharacteristic
45C22×C3×Dic5C2311yescharacteristic
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—42no—
49C2×C3×C4×D5—22no—
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×C4×D5D411yescharacteristic
53C2×C3×C4×D5D411yescharacteristic
54C2×C3×C4×D5D411yescharacteristic
55#6762—22no—
56#6762—22no—
57#6762—22no—
58#6762D414yescomplemented
59C2×C3⋊#170—22no—
60C2×C3⋊#170—22no—
61#6758—24no—
62D5⋊(C3⋊C8)—24no—
63C3×C5×C22⋊C4—21no—
64C3×C5×C22⋊C4—21no—
65C3×#685—21no—
66C3×#685—21no—
67C3×#683—21no—
68C3×#683—21no—
69C2×C3×#121—51no—
70C22×#208—51no—
71C2×#833—52no—
72#5207—51no—
73#4530—52no—
74C22×C22⋊D5Dic311yescharacteristic
75C22×C22⋊D5C2×D311yescharacteristic
76C22×D20Dic311yescharacteristic
77C22×C4×D5C2×D311yescharacteristic
78C2×#704—32no—
79C2×#704—32no—
80D5⋊M16—64no—
81C2×#700—61no—
82C2×D5⋊C8—61no—
83C2×C5×C22⋊C4Dic311yescharacteristic
84C2×#685Dic311yescharacteristic
85C2×#683C2×D311yescharacteristic
86#4030—21no—
87#4030—21no—
88#4030—21no—
89#4030—21no—
90#4013—64no—
91#4003—61no—
92#4003—61no—
93#1900—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5—22no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5C22×C411yescharacteristic
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5—21no—
102C22×C3×D5—22no—
103C22×C3×D5—41no—
104C22×C3×D5—41no—
105C22×C3×D5—41no—
106C22×C3×D5C22⋊C411yescharacteristic
107C22×C3×D5C22⋊C411yescharacteristic
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22⋊C411yescharacteristic
112C2×C3×C4×C5C22⋊C411yescharacteristic
113C3×C22⋊D5—42no—
114C3×C22⋊D5—42no—
115C3×C22⋊D5—41no—
116C3×C22⋊D5—42no—
117C3×C22⋊D5—41no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5C2×D412yes—
121C2×C3×Dic5C2×D411yescharacteristic
122C2×C3×Dic5C2×D411yescharacteristic
123C2×C3×Dic5#4112yes—
124C3×D20—42no—
125C3×D20—42no—
126C3×C4×D5—21no—
127C3×C4×D5—21no—
128C3×C4×D5—22no—
129C3×C4×D5—22no—
130C3×C4×D5—21no—
131C3×C4×D5—21no—
132C3⋊#170—24no—
133C3⋊#170—42no—
134C22×C3×D4—51no—
135C22×C3×D4—51no—
136C22×C3×D4—51no—
137C23×C3×C4—51no—
138C3×#121—101no—
139C3×#121—101no—
140C3×#121—101no—
141C3×#121—101no—
142C2×C3×C4⋊C4—51no—
143C2×C3×C22⋊C4—51no—
144C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
145C2×#208—52no—
146C2×#208—52no—
147C2×#208—104no—
148C2×#208—101no—
149C22×C3⋊C8—101no—
150#833—104no—
151#830—101no—
152#830—101no—
153C24×C5C2×Dic311yescharacteristic
154C23×D5C2×Dic311yescharacteristic
155C23×D5C2×Dic311yescharacteristic
156C22×C4×C5C2×Dic311yescharacteristic
157C22×C4×C5C2×Dic311yescharacteristic
158C2×C22⋊D5—21no—
159C2×C22⋊D5—21no—
160C2×C22⋊D5—22no—
161C2×C22⋊D5—22no—
162C2×C22⋊D5—21no—
163C2×C22⋊D5—21no—
164C2×C22⋊D5—42no—
165C22×Dic5C2×Dic311yescharacteristic
166C22×Dic5C22×D311yescharacteristic
167C2×D20—21no—
168C2×D20—21no—
169C2×D20—42no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5#6711yescharacteristic
173C2×C4×D5#6711yescharacteristic
174C2×C4×D5#6711yescharacteristic
175C2×C4×D5#6711yescharacteristic
176#704—34no—
177#704—62no—
178#704—62no—
179#704—62no—
180C2×#170—62no—
181C2×#170—62no—
182#700—64no—
183D5⋊C8—64no—
184C5×C22⋊C4—21no—
185C5×C22⋊C4—21no—
186#685—21no—
187#685—21no—
188#683—21no—
189#683—21no—
190C22×M16—151no—
191C2×#121—51no—
192C2×#100—152no—
193#407—151no—
194#343—152no—
195C22×C3×C5—21no—
196C22×C3×C5—21no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—82no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C22×C3×C5C4×D412yes—
203C2×C3×D5—21no—
204C2×C3×D5—21no—
205C2×C3×D5—21no—
206C2×C3×D5—21no—
207C2×C3×D5—21no—
208C2×C3×D5—44no—
209C2×C3×D5—41no—
210C2×C3×D5—41no—
211C2×C3×D5—41no—
212C2×C3×D5—82no—
213C2×C3×D5#10012yescomplemented
214C3×C4×C5—21no—
215C3×C4×C5—21no—
216C3×C4×C5—41no—
217C3×Dic5—41no—
218C3×Dic5#12011yescharacteristic
219C3×Dic5#12112yes—
220C3×Dic5#12311yescharacteristic
221C24×C3—51no—
222C24×C3—51no—
223C24×C3C2×AGL(1,𝔽5)11yescharacteristic
224C2×C3×D4—101no—
225C2×C3×D4—101no—
226C2×C3×D4—102no—
227C2×C3×D4—101no—
228C2×C3×D4—101no—
229C2×C3×D4—102no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—202no—
233C2×C3×D4—202no—
234C22×C3×C4—51no—
235C22×C3×C4—51no—
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C22×C3×C4—51no—
239C22×C3×C4—51no—
240C22×C3×C4—102no—
241C22×C3×C4—102no—
242C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
243C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
244C3×C4⋊C4—101no—
245C3×C4⋊C4—101no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—101no—
249C3×C22⋊C4—101no—
250#208—54no—
251#208—102no—
252#208—104no—
253#208—102no—
254#208—102no—
255C2×C3⋊C8—102no—
256C2×C3⋊C8—104no—
257C2×C3⋊C8—102no—
258C23×C5—21no—
259C23×C5—22no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5C22×Dic311yescharacteristic
263C22×D5—22no—
264C22×D5—22no—
265C22×D5—21no—
266C22×D5—22no—
267C22×D5—41no—
268C22×D5—41no—
269C22×D5—41no—
270C22×D5#21711yescharacteristic
271C22×D5#21711yescharacteristic
272C2×C4×C5—22no—
273C2×C4×C5—21no—
274C2×C4×C5—41no—
275C2×C4×C5#21711yescharacteristic
276C2×C4×C5#21711yescharacteristic
277C22⋊D5—42no—
278C22⋊D5—42no—
279C22⋊D5—41no—
280C22⋊D5—41no—
281C22⋊D5—42no—
282C2×Dic5—21no—
283C2×Dic5—41no—
284C2×Dic5D3×D412yes—
285C2×Dic5#23712yes—
286C2×Dic5C2×#6711yescharacteristic
287C2×Dic5C2×#6711yescharacteristic
288D20—42no—
289D20—42no—
290C4×D5—21no—
291C4×D5—21no—
292C4×D5—21no—
293C4×D5—21no—
294C4×D5—22no—
295C4×D5—22no—
296#170—64no—
297#170—122no—
298C22×D4—51no—
299C22×D4—51no—
300C22×D4—51no—
301C23×C4—51no—
302C2×M16—152no—
303C2×M16—152no—
304C2×M16—304no—
305C2×M16—301no—
306C22×C8—301no—
307#121—101no—
308#121—101no—
309#121—101no—
310#121—101no—
311C2×C4⋊C4—51no—
312C2×C22⋊C4—51no—
313C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic
314#100—304no—
315C22⋊C8—301no—
316C22⋊C8—301no—
317C2×C3×C5—22no—
318C2×C3×C5—81no—
319C2×C3×C5#38611yescharacteristic
320C2×C3×C5C2×#10011yescharacteristic
321C2×C3×C5#41311yescharacteristic
322C3×D5—22no—
323C3×D5—41no—
324C3×D5—81no—
325C23×C3—21no—
326C23×C3—22no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—51no—
330C23×C3—51no—
331C23×C3—102no—
332C23×C3—102no—
333C23×C3—101no—
334C23×C3—102no—
335C23×C3—201no—
336C23×C3—201no—
337C23×C3—201no—
338C23×C3C22×AGL(1,𝔽5)11yescharacteristic
339C3×D4—202no—
340C3×D4—202no—
341C3×D4—201no—
342C3×D4—202no—
343C3×D4—201no—
344C3×D4—202no—
345C3×D4—202no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—41no—
349C2×C3×C4—52no—
350C2×C3×C4—52no—
351C2×C3×C4—51no—
352C2×C3×C4—51no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4—101no—
358C2×C3×C4—101no—
359C2×C3×C4—101no—
360C2×C3×C4—201no—
361C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
362C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
363C3⋊C8—104no—
364C3⋊C8—202no—
365C22×C5—21no—
366C22×C5—21no—
367C22×C5—41no—
368C22×C5—41no—
369C22×C5—41no—
370C22×C5—82no—
371C22×C5D4×Dic312yes—
372C22×C5C2×#21711yescharacteristic
373C2×D5—21no—
374C2×D5—21no—
375C2×D5—21no—
376C2×D5—21no—
377C2×D5—21no—
378C2×D5—44no—
379C2×D5—41no—
380C2×D5—41no—
381C2×D5—41no—
382C2×D5—82no—
383C2×D5#83312yescomplemented
384C4×C5—21no—
385C4×C5—21no—
386C4×C5—41no—
387Dic5—41no—
388Dic5#93511yescharacteristic
389Dic5#93711yescharacteristic
390Dic5#93912yes—
391C24—51no—
392C24—51no—
393C24C2×ΓL(1,𝔽16)11yescharacteristic
394C2×D4—101no—
395C2×D4—101no—
396C2×D4—102no—
397C2×D4—101no—
398C2×D4—101no—
399C2×D4—102no—
400C2×D4—101no—
401C2×D4—101no—
402C2×D4—202no—
403C2×D4—202no—
404C22×C4—51no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—51no—
408C22×C4—51no—
409C22×C4—51no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
413C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
414M16—154no—
415M16—302no—
416M16—304no—
417M16—302no—
418M16—302no—
419C2×C8—302no—
420C2×C8—304no—
421C2×C8—302no—
422C4⋊C4—101no—
423C4⋊C4—101no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—101no—
427C22⋊C4—101no—
428C3×C5#190011yescharacteristic, complemented, Hall
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—52no—
435C22×C3—82no—
436C22×C3—101no—
437C22×C3—101no—
438C22×C3—101no—
439C22×C3—101no—
440C22×C3—101no—
441C22×C3—204no—
442C22×C3—201no—
443C22×C3—201no—
444C22×C3—201no—
445C22×C3—402no—
446C22×C3D4×AGL(1,𝔽5)12yes—
447C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—41no—
451C3×C4—51no—
452C3×C4—52no—
453C3×C4—51no—
454C3×C4—201no—
455C2×C5—22no—
456C2×C5—81no—
457C2×C5C2×#83311yescharacteristic
458C2×C5#522011yescharacteristic
459C2×C5#523711yescharacteristic
460D5—22no—
461D5—41no—
462D5—81no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—51no—
468C23—51no—
469C23—102no—
470C23—102no—
471C23—101no—
472C23—102no—
473C23—201no—
474C23—201no—
475C23—201no—
476C23C22×ΓL(1,𝔽16)11yescharacteristic
477D4—202no—
478D4—202no—
479D4—201no—
480D4—202no—
481D4—201no—
482D4—202no—
483D4—202no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—52no—
488C2×C4—52no—
489C2×C4—51no—
490C2×C4—51no—
491C2×C4—101no—
492C2×C4—101no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—101no—
496C2×C4—101no—
497C2×C4—101no—
498C2×C4—201no—
499C2×C4#676311yescharacteristic
500C2×C4#676311yescharacteristic
501C8—304no—
502C8—602no—
503C2×C3—22no—
504C2×C3—81no—
505C2×C3—102no—
506C2×C3—201no—
507C2×C3—401no—
508C2×C3#6576111yescharacteristic
509C2×C3D5⋊#10011yescharacteristic
510C2×C3#6577911yescharacteristic
511C5#7168311yescharacteristic, complemented, Sylow
512C22—21no—
513C22—21no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—52no—
518C22—82no—
519C22—101no—
520C22—101no—
521C22—101no—
522C22—101no—
523C22—101no—
524C22—204no—
525C22—201no—
526C22—201no—
527C22—201no—
528C22—402no—
529C22D4×ΓL(1,𝔽16)12yes—
530C22C2×#676311yescharacteristic
531C4—21no—
532C4—21no—
533C4—41no—
534C4—51no—
535C4—52no—
536C4—51no—
537C4—201no—
538C3#1060424911yescharacteristic, complemented, Sylow
539C2—22no—
540C2—81no—
541C2—102no—
542C2—201no—
543C2—401no—
544C2#1175242011yescharacteristic
545C2D5⋊#83311yescharacteristic
546C2#1175243811yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4030C2
cosocleC22×C3×Dic5C23
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1900
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D5⋊#208C2semidirect
3. C2×#91242C2semidirect
4. #11752414C2semidirect
5. #11746790C2semidirect
58. #6762D4semidirect
213. C2×C3×D5#100semidirect
383. C2×D5#833semidirect
428. C3×C5#1900semidirect
511. C5#71683semidirect
538. C3#10604249semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊#2082
C2×C3×#40302
C2×#912422
#117524142
#117467902
#106042493
#716835