Finite Group Databasebeta

← #14313235

Subgroups — #14313235

Order 1920.

560 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65987C211yesmaximal, characteristic
2D5×#834C211yesmaximal, characteristic, complemented
3D5×#833C211yesmaximal, characteristic, complemented
4#11746360C211yesmaximal, characteristic, complemented
5C5×#4539C211yesmaximal, characteristic, complemented
6#11745995C211yesmaximal, characteristic, complemented
7#11745994C211yesmaximal, characteristic, complemented
8#10599936—31nomaximal, Hall
9C2×C3×D4×D5C2211yescharacteristic
10C22×C3×D20C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C3×#4083C2211yescharacteristic
13C3×#4075C411yescharacteristic, complemented
14C3×#4041—21no—
15C3×#4040—21no—
16C3×#4030—21no—
17C3×#4028—21no—
18C3×#4028C411yescharacteristic, complemented
19C3×D5×C22⋊C4C411yescharacteristic, complemented
20D5×#217—21no—
21D5×#208—21no—
22#91118C2211yescharacteristic
23#91117C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#833C2211yescharacteristic
26#90995—21no—
27#90958—21no—
28#71847—51nomaximal, Hall
29#65987D311yescharacteristic
30D5×#100—31no—
31D5×#99—31no—
32C5×#352—31no—
33#64759—31no—
34#64695—31no—
35#64691—31no—
36C23×C3×D5C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic, complemented
38C23×C3×D5D411yescharacteristic
39C2×C3×C5×D4C2311yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic, complemented
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5C2×C411yescharacteristic
43C2×C3×C22⋊D5D411yescharacteristic
44C3×D4×D5—41no—
45C3×D4×D5—41no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—41no—
50C2×C3×D20—41no—
51C2×C3×D20D411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5D411yescharacteristic
54C2×D5×Dic3—41no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
58#6719—21no—
59#6710—21no—
60C5×#217—21no—
61C5×#208—21no—
62C3×C22⋊Dic5C2×C411yescharacteristic, complemented
63C3×#685—21no—
64C3×#685—21no—
65C3×#685—21no—
66C3×#685—21no—
67C3×#683—21no—
68#6665—41no—
69#6649—41no—
70D5×C3⋊C8—41no—
71C3×#534—51no—
72C2×#834—51no—
73C2×#833—51no—
74#4539—51no—
75#4539D511yescharacteristic, complemented
76#4536—51no—
77#4536—51no—
78C2×D4×D5C2×D311yescharacteristic
79C22×D20Dic311yescharacteristic, complemented
80C5×#123C2×D311yescharacteristic
81#4083C2×D311yescharacteristic
82#4075Dic311yescharacteristic, complemented
83D5×M16—61no—
84#4041—21no—
85#4040—21no—
86#4030—21no—
87#4028—21no—
88#4028Dic311yescharacteristic, complemented
89D5×C22⋊C4—61no—
90D5×C22⋊C4Dic311yescharacteristic, complemented
91C5×#100—31no—
92C5×#99—31no—
93#3966—31no—
94#3965—31no—
95#3955—61no—
96#3938—61no—
97#2121—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—21no—
103C22×C3×D5—21no—
104C22×C3×D5—21no—
105C22×C3×D5—41no—
106C22×C3×D5—81no—
107C22×C3×D5—81no—
108C22×C3×D5—81no—
109C22×C3×D5C22⋊C411yescharacteristic
110C22×C3×D5C22⋊C411yescharacteristic
111C22×C3×D5C22⋊C411yescharacteristic
112C3×C5×D4—41no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×Dic15—41no—
118C2×C5×Dic3—41no—
119C3×C22⋊D5—41no—
120C3×C22⋊D5—41no—
121C3×C22⋊D5—81no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5C22⋊C411yescharacteristic
124C3×D20—41no—
125C3×D20—42no—
126C3×D20—41no—
127C3×D20—41no—
128C3×D20—81no—
129C3×C4×D5—21no—
130C3×C4×D5—21no—
131C3×C4×D5—81no—
132D5×Dic3—82no—
133C3⋊#168—41no—
134C5×C3⋊C8—41no—
135C22×C3×D4—51no—
136C22×C3×D4—51no—
137C3×#123—51no—
138C3×#123—101no—
139C3×#123C2×D511yescharacteristic
140C3×#121—101no—
141C3×#121—101no—
142C3×#120—51no—
143C3×#120—51no—
144C3×#120—101no—
145C2×C3×C22⋊C4—51no—
146C2×#217—101no—
147C2×#208—101no—
148#834—51no—
149#834—101no—
150#834C2×D511yescharacteristic
151#833—51no—
152#833—101no—
153#833C2×D511yescharacteristic
154C23×D5C2×Dic311yescharacteristic
155C23×D5C2×Dic311yescharacteristic, complemented
156C23×D5#6711yescharacteristic
157C2×C5×D4C22×D311yescharacteristic
158C22×C4×C5C2×Dic311yescharacteristic, complemented
159C2×C22⋊D5—21no—
160C2×C22⋊D5C2×Dic311yescharacteristic
161C2×C22⋊D5#6711yescharacteristic
162D4×D5—41no—
163D4×D5—41no—
164C2×D20—21no—
165C2×D20—21no—
166C2×D20—21no—
167C2×D20—41no—
168C2×D20—41no—
169C2×D20#6711yescharacteristic
170C2×C4×D5—21no—
171C2×C4×D5—121no—
172C2×C4×D5#6711yescharacteristic
173C5×M16—61no—
174C5×C4⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—61no—
177C5×C22⋊C4C2×Dic311yescharacteristic, complemented
178C22⋊Dic5—61no—
179C22⋊Dic5C2×Dic311yescharacteristic, complemented
180#685—21no—
181#685—21no—
182#685—21no—
183#685—21no—
184#685—121no—
185#683—21no—
186#681—61no—
187#676—121no—
188C8×D5—121no—
189#534—51no—
190C2×#100—151no—
191C2×#99—151no—
192#352—31no—
193#352—151no—
194AΣL(1,𝔽16)—151no—
195AΣL(1,𝔽16)—151no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C2×C3×D5—21no—
202C2×C3×D5—21no—
203C2×C3×D5—41no—
204C2×C3×D5—42no—
205C2×C3×D5—41no—
206C2×C3×D5—41no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C2×C3×D5—81no—
211C2×C3×D5—81no—
212C2×C3×D5—81no—
213C2×C3×D5—82no—
214C2×C3×D5#9911yescharacteristic
215C2×C3×D5#9911yescharacteristic
216C3×C4×C5—21no—
217C3×C4×C5—41no—
218C3×C4×C5—41no—
219Dic15—81no—
220C3×Dic5—21no—
221C3×Dic5—41no—
222C5×Dic3—81no—
223C24×C3—51no—
224C24×C3—51no—
225C24×C3—51no—
226C2×C3×D4—51no—
227C2×C3×D4—51no—
228C2×C3×D4—51no—
229C2×C3×D4—101no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—201no—
234C2×C3×D4—201no—
235C2×C3×D4—201no—
236C2×C3×D4—201no—
237C2×C3×D4C22×D511yescharacteristic
238C22×C3×C4—51no—
239C22×C3×C4—101no—
240C22×C3×C4C4×D511yescharacteristic, complemented
241C22×Dic3—201no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—101no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—51no—
246C3×C22⋊C4—101no—
247C3×C22⋊C4—101no—
248C3×C22⋊C4—101no—
249C3×C22⋊C4—101no—
250C3×C22⋊C4C4×D511yescharacteristic, complemented
251#217—21no—
252#217—101no—
253#217—201no—
254#208—21no—
255#208—101no—
256#208—201no—
257C2×C3⋊C8—201no—
258C23×C5C22×Dic311yescharacteristic
259C23×C5C2×#6711yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—41no—
266C22×D5—81no—
267C22×D5—81no—
268C22×D5—81no—
269C22×D5#21711yescharacteristic
270C22×D5#21711yescharacteristic
271C22×D5#21711yescharacteristic
272C5×D4—41no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—41no—
276C2×C4×C5—121no—
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—41no—
279C22⋊D5—41no—
280C22⋊D5—81no—
281C2×Dic5—21no—
282C2×Dic5—121no—
283C2×Dic5#21711yescharacteristic
284D20—41no—
285D20—42no—
286D20—41no—
287D20—41no—
288D20—81no—
289C4×D5—21no—
290C4×D5—21no—
291C4×D5—81no—
292C4×D5—242no—
293C5×C8—121no—
294#168—121no—
295C22×D4—51no—
296C22×D4—51no—
297C2×M16—301no—
298#123—51no—
299#123—101no—
300#123D3×D511yescharacteristic
301#121—101no—
302#121—101no—
303#120—51no—
304#120—51no—
305#120—101no—
306C2×C22⋊C4—51no—
307C2×C22⋊C4—301no—
308#100—31no—
309#100—151no—
310#100—301no—
311#99—31no—
312#99—151no—
313#99—301no—
314C2×C3×C5—21no—
315C2×C3×C5—41no—
316C2×C3×C5—41no—
317C2×C3×C5C2×#9911yescharacteristic
318C3×D5—21no—
319C3×D5—21no—
320C3×D5—41no—
321C3×D5—41no—
322C3×D5—81no—
323C23×C3—51no—
324C23×C3—51no—
325C23×C3—51no—
326C23×C3—101no—
327C23×C3—101no—
328C23×C3—101no—
329C23×C3—101no—
330C23×C3—101no—
331C23×C3—201no—
332C23×C3—401no—
333C23×C3—401no—
334C23×C3—401no—
335C23×C3C2×C4×D511yescharacteristic
336C23×C3D4×D511yescharacteristic
337C3×D4—41no—
338C3×D4—201no—
339C3×D4—201no—
340C3×D4—201no—
341C3×D4—202no—
342C3×D4—201no—
343C3×D4—201no—
344C3×D4—401no—
345C3×D4—401no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—41no—
349C2×C3×C4—51no—
350C2×C3×C4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—401no—
354C2×C3×C4D4×D511yescharacteristic
355C2×Dic3—41no—
356C2×Dic3—201no—
357C2×Dic3—402no—
358C3⋊C8—41no—
359C3⋊C8—201no—
360C22×C5—21no—
361C22×C5—21no—
362C22×C5—41no—
363C22×C5—41no—
364C22×C5C2×#21711yescharacteristic
365C2×D5—21no—
366C2×D5—21no—
367C2×D5—41no—
368C2×D5—42no—
369C2×D5—41no—
370C2×D5—41no—
371C2×D5—41no—
372C2×D5—41no—
373C2×D5—41no—
374C2×D5—81no—
375C2×D5—81no—
376C2×D5—81no—
377C2×D5—82no—
378C2×D5#83411yescharacteristic
379C2×D5#83411yescharacteristic
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5—241no—
384Dic5—21no—
385Dic5—41no—
386Dic5—241no—
387C24—51no—
388C24—51no—
389C24—51no—
390C2×D4—51no—
391C2×D4—51no—
392C2×D4—51no—
393C2×D4—101no—
394C2×D4—101no—
395C2×D4—101no—
396C2×D4—101no—
397C2×D4—201no—
398C2×D4—201no—
399C2×D4—201no—
400C2×D4—201no—
401C2×D4C2×D3×D511yescharacteristic
402C22×C4—51no—
403C22×C4—101no—
404C22×C4—601no—
405C22×C4D5×Dic311yescharacteristic, complemented
406M16—61no—
407M16—301no—
408M16—601no—
409C2×C8—601no—
410C4⋊C4—21no—
411C4⋊C4—101no—
412C22⋊C4—21no—
413C22⋊C4—51no—
414C22⋊C4—61no—
415C22⋊C4—101no—
416C22⋊C4—101no—
417C22⋊C4—101no—
418C22⋊C4—101no—
419C22⋊C4—301no—
420C22⋊C4—601no—
421C22⋊C4D5×Dic311yescharacteristic, complemented
422C3×C5#212111yescharacteristic, complemented, Hall
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—51no—
428C22×C3—51no—
429C22×C3—101no—
430C22×C3—101no—
431C22×C3—201no—
432C22×C3—201no—
433C22×C3—201no—
434C22×C3—201no—
435C22×C3—201no—
436C22×C3—202no—
437C22×C3—201no—
438C22×C3—401no—
439C22×C3—401no—
440C22×C3—401no—
441C22×C3—402no—
442C22×C3D5×C22⋊C411yescharacteristic
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—101no—
447C3×C4—201no—
448Dic3—81no—
449Dic3—401no—
450C2×C5—21no—
451C2×C5—41no—
452C2×C5—41no—
453C2×C5C2×#83411yescharacteristic
454D5—21no—
455D5—21no—
456D5—41no—
457D5—41no—
458D5—81no—
459C23—51no—
460C23—51no—
461C23—51no—
462C23—101no—
463C23—101no—
464C23—101no—
465C23—101no—
466C23—101no—
467C23—201no—
468C23—401no—
469C23—401no—
470C23—401no—
471C23C2×D5×Dic311yescharacteristic
472C23D5×#6711yescharacteristic
473D4—41no—
474D4—201no—
475D4—201no—
476D4—201no—
477D4—202no—
478D4—201no—
479D4—201no—
480D4—401no—
481D4—401no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—51no—
486C2×C4—101no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—121no—
490C2×C4—401no—
491C2×C4—601no—
492C2×C4—1202no—
493C2×C4D5×#6711yescharacteristic
494C8—121no—
495C8—601no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3—101no—
500C2×C3—101no—
501C2×C3—201no—
502C2×C3—201no—
503C2×C3—401no—
504C2×C3D5×#9911yescharacteristic
505C5#7184711yescharacteristic, complemented, Sylow
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—51no—
511C22—51no—
512C22—101no—
513C22—101no—
514C22—201no—
515C22—201no—
516C22—201no—
517C22—201no—
518C22—201no—
519C22—202no—
520C22—201no—
521C22—401no—
522C22—401no—
523C22—401no—
524C22—402no—
525C22D5×#21711yescharacteristic
526C4—21no—
527C4—41no—
528C4—41no—
529C4—101no—
530C4—201no—
531C4—241no—
532C4—1201no—
533C3#1059993611yescharacteristic, complemented, Sylow
534C2—21no—
535C2—41no—
536C2—41no—
537C2—101no—
538C2—101no—
539C2—201no—
540C2—201no—
541C2—401no—
542C2D5×#83411yescharacteristic
subgroupG/H
centerC2D5×#834
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#123C22
socleC2×C3×C5C2×#99
prime radicalC3×#65987C2
cosocleC2×C3×C5×D4C23
hypercenter#123D3×D5
hypocenterC3×C5#2121
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
2. D5×#834C2semidirect
3. D5×#833C2semidirect
4. #11746360C2semidirect
5. C5×#4539C2semidirect
6. #11745995C2semidirect
7. #11745994C2semidirect
10. C22×C3×D20C4semidirect
13. C3×#4075C4semidirect
18. C3×#4028C4semidirect
19. C3×D5×C22⋊C4C4semidirect
37. C23×C3×D5C2×C4semidirect
40. C22×C3×C4×C5C2×C4semidirect
57. C3×C5×C22⋊C4C2×C4semidirect
62. C3×C22⋊Dic5C2×C4semidirect
75. #4539D5semidirect
79. C22×D20Dic3semidirect
82. #4075Dic3semidirect
88. #4028Dic3semidirect
90. D5×C22⋊C4Dic3semidirect
155. C23×D5C2×Dic3semidirect
158. C22×C4×C5C2×Dic3semidirect
177. C5×C22⋊C4C2×Dic3semidirect
179. C22⋊Dic5C2×Dic3semidirect
240. C22×C3×C4C4×D5semidirect
250. C3×C22⋊C4C4×D5semidirect
405. C22×C4D5×Dic3semidirect
421. C22⋊C4D5×Dic3semidirect
422. C3×C5#2121semidirect
505. C5#71847semidirect
533. C3#10599936semidirect

Maximal subgroups

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

subgroupindex
C3×#659872
D5×#8342
D5×#8332
#117463602
C5×#45392
#117459952
#117459942
#105999363
#718475