Finite Group Databasebeta

← #14313232

Subgroups — #14313232

Order 1920.

560 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 86 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
1#11754952C211yesmaximal, characteristic
2C5×D3×#100C211yesmaximal, characteristic, complemented
3D3×#3966C211yesmaximal, characteristic, complemented
4#11746296C211yesmaximal, characteristic, complemented
5C3×#64696C211yesmaximal, characteristic, complemented
6#11746001C211yesmaximal, characteristic, complemented
7#11745998C211yesmaximal, characteristic, complemented
8#10600887—31nomaximal, Hall
9C2×C5×D3×D4C2211yescharacteristic
10C22×#1203C411yescharacteristic, complemented
11#91826C2211yescharacteristic
12C5×D3×M16—21no—
13C3×#4081C2211yescharacteristic
14#91573C411yescharacteristic, complemented
15#91570—21no—
16#91558—21no—
17D3×C22⋊Dic5—21no—
18D3×C22⋊Dic5C411yescharacteristic, complemented
19#91539C411yescharacteristic, complemented
20#91416—21no—
21#91351—21no—
22C3×C5×#100C2211yescharacteristic
23#91118C2211yescharacteristic
24C5×#833C2211yescharacteristic
25C5×#823—21no—
26C3×#3966C2211yescharacteristic
27#90996—21no—
28#69143—51nomaximal, Hall
29#66138—31no—
30C2×C5×#100—31no—
31C2×#3966—31no—
32#64696—31no—
33#64696D311yescharacteristic, complemented
34#64695—31no—
35#64695—31no—
36C23×D15C2×C411yescharacteristic, complemented
37C23×C5×D3C2×C411yescharacteristic
38C23×C5×D3D411yescharacteristic
39C2×C3×C5×D4C2311yescharacteristic
40C2×#1220—21no—
41C2×C5×#67C2×C411yescharacteristic
42C2×C5×#67D411yescharacteristic
43C5×D3×D4—41no—
44C5×D3×D4—41no—
45C2×C5×D12D411yescharacteristic
46C2×C4×C5×D3D411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic, complemented
48C2×#1203—21no—
49C2×#1203—21no—
50C2×#1203—21no—
51C2×#1203—41no—
52C2×#1203—41no—
53C2×D3×Dic5—21no—
54C2×D3×Dic5—41no—
55C3×C5×M16—21no—
56#6719—21no—
57#6719C2×C411yescharacteristic, complemented
58#6714—21no—
59C5×#208—21no—
60C5×ΓL(1,𝔽25)—41no—
61C5×D3×C8—41no—
62C3×C22⋊Dic5—21no—
63C3×C22⋊Dic5—21no—
64C3×C22⋊Dic5C2×C411yescharacteristic, complemented
65C3×#683—21no—
66#6669—21no—
67#6667—21no—
68(C2×D3)⋊Dic5—21no—
69(C2×D3)⋊Dic5—21no—
70(C2×D3)⋊Dic5—41no—
71#5653—51no—
72D3×#100D511yescharacteristic, complemented
73D3×#99—51no—
74C3×#352—51no—
75#4539—51no—
76#4475—51no—
77#4471—51no—
78C22×C5×D4—31no—
79C22×C22⋊D5—31no—
80C2×C5×M16—61no—
81#4099—61no—
82C2×C22⋊Dic5—31no—
83C2×C22⋊Dic5—61no—
84#4085—61no—
85#4085—61no—
86#4083—31no—
87#4083—31no—
88#4081—31no—
89#4081C2×D311yescharacteristic
90#4075—61no—
91C5×#100—31no—
92C5×#100—61no—
93C5×#100C2×D311yescharacteristic
94#3966—31no—
95#3966—61no—
96#3966C2×D311yescharacteristic
97#2121—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×D15—21no—
101C22×D15—41no—
102C22×D15—81no—
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3—21no—
106C22×C5×D3—21no—
107C22×C5×D3—81no—
108C22×C5×D3—81no—
109C22×C5×D3C22⋊C411yescharacteristic
110C22×C5×D3C22⋊C411yescharacteristic
111C22×C5×D3C22⋊C411yescharacteristic
112C3×C5×D4—41no—
113C2×C3×C4×C5C2×D411yescharacteristic
114#1220—81no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117C5×#67—41no—
118C5×#67—41no—
119C2×C5×Dic3C22⋊C411yescharacteristic
120C5×D12—41no—
121C4×C5×D3—21no—
122C4×C5×D3—21no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5—41no—
127#1203—42no—
128#1203—41no—
129#1203—41no—
130#1203—81no—
131D3×Dic5—81no—
132D3×Dic5—82no—
133C3×C5×C8—41no—
134C5×C3⋊C8—41no—
135C2×D3×D4C2×D511yescharacteristic
136C22×D12—51no—
137C3×#123—51no—
138#937—51no—
139#929—51no—
140D3×M16—21no—
141#895—101no—
142#894—101no—
143#884—101no—
144#882—51no—
145#882—101no—
146D3×C22⋊C4—51no—
147D3×C22⋊C4—101no—
148C3×#100C2×D511yescharacteristic
149C3×#99—51no—
150#834—51no—
151#833C2×D511yescharacteristic
152#823—21no—
153#806—101no—
154C24×C5—31no—
155C24×C5—31no—
156C23×D5—31no—
157C2×C5×D4—31no—
158C2×C5×D4—31no—
159C2×C5×D4—31no—
160C2×C5×D4—121no—
161C2×C5×D4—121no—
162C2×C5×D4C22×D311yescharacteristic
163C22×C4×C5—31no—
164C2×C22⋊D5—61no—
165C2×C22⋊D5—61no—
166C2×C22⋊D5—61no—
167C2×C22⋊D5—61no—
168C2×C22⋊D5—121no—
169C2×C22⋊D5—121no—
170C22×Dic5—61no—
171C22×Dic5—121no—
172C22×Dic5C4×D311yescharacteristic, complemented
173C5×M16—21no—
174C5×M16—61no—
175C5×M16—121no—
176C2×C5×C8—121no—
177C22⋊Dic5—21no—
178C22⋊Dic5—21no—
179C22⋊Dic5—31no—
180C22⋊Dic5—61no—
181C22⋊Dic5—61no—
182C22⋊Dic5—61no—
183C22⋊Dic5—121no—
184C22⋊Dic5C4×D311yescharacteristic, complemented
185#685—61no—
186#685—61no—
187#683—21no—
188#683—61no—
189#534—151no—
190C2×#100—31no—
191C2×#99—151no—
192#352—51no—
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×D15—41no—
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—82no—
205C2×C5×D3—21no—
206C2×C5×D3—21no—
207C2×C5×D3—41no—
208C2×C5×D3—42no—
209C2×C5×D3—41no—
210C2×C5×D3—41no—
211C2×C5×D3—81no—
212C2×C5×D3—81no—
213C2×C5×D3—81no—
214C2×C5×D3#9911yescharacteristic
215C2×C5×D3#9911yescharacteristic
216C3×C4×C5—21no—
217Dic15—41no—
218Dic15—81no—
219C3×Dic5—41no—
220C3×Dic5—41no—
221C3×Dic5—81no—
222C5×Dic3—21no—
223C23×D3—51no—
224C23×D3C4×D511yescharacteristic
225C23×D3D2011yescharacteristic
226C2×C3×D4C22×D511yescharacteristic
227C22×C3×C4—51no—
228C2×#67—101no—
229C2×#67C4×D511yescharacteristic
230C2×#67D2011yescharacteristic
231D3×D4—41no—
232D3×D4—41no—
233C2×D12—101no—
234C2×D12—101no—
235C2×D12—101no—
236C2×D12—201no—
237C2×D12—201no—
238C2×D12C22⋊D511yescharacteristic
239C2×C4×D3—101no—
240C2×C4×D3—201no—
241C2×C4×D3C22⋊D511yescharacteristic
242C3×M16—21no—
243C3×C4⋊C4—101no—
244C3×C22⋊C4—51no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4—101no—
247#217—51no—
248#217—101no—
249(C2×D3)⋊C4—101no—
250(C2×D3)⋊C4—101no—
251(C2×D3)⋊C4—101no—
252(C2×D3)⋊C4—101no—
253(C2×D3)⋊C4—201no—
254Dic3⋊C4—101no—
255#208—21no—
256ΓL(1,𝔽25)—41no—
257D3×C8—41no—
258C23×C5—31no—
259C23×C5—31no—
260C23×C5—31no—
261C23×C5—61no—
262C23×C5—61no—
263C23×C5—61no—
264C23×C5—61no—
265C23×C5—241no—
266C23×C5—241no—
267C23×C5C2×C4×D311yescharacteristic
268C23×C5D3×D411yescharacteristic
269C22×D5—61no—
270C22×D5—121no—
271C22×D5—241no—
272C5×D4—41no—
273C5×D4—121no—
274C5×D4—121no—
275C5×D4—121no—
276C2×C4×C5—31no—
277C2×C4×C5—61no—
278C2×C4×C5—61no—
279C2×C4×C5D3×D411yescharacteristic
280C22⋊D5—121no—
281C22⋊D5—121no—
282C22⋊D5—122no—
283C22⋊D5—241no—
284C22⋊D5—241no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—41no—
288C2×Dic5—41no—
289C2×Dic5—61no—
290C2×Dic5—121no—
291C2×Dic5—241no—
292C2×Dic5—242no—
293C5×C8—41no—
294C5×C8—121no—
295C22×D4—31no—
296C22×D4—151no—
297C2×M16—61no—
298#123—51no—
299#123—151no—
300#123—301no—
301#121—301no—
302#121—301no—
303#120—151no—
304#120—151no—
305#120—301no—
306C2×C22⋊C4—151no—
307C2×C22⋊C4—301no—
308#100—31no—
309#100—61no—
310#100D3×D511yescharacteristic
311#99—51no—
312#99—151no—
313#99—301no—
314C2×C3×C5—21no—
315C2×C3×C5—41no—
316C2×C3×C5—41no—
317C2×C3×C5C2×#9911yescharacteristic
318D15—81no—
319C5×D3—21no—
320C5×D3—21no—
321C5×D3—41no—
322C5×D3—41no—
323C23×C3C2×C4×D511yescharacteristic
324C23×C3C2×D2011yescharacteristic
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—21no—
328C22×D3—21no—
329C22×D3—81no—
330C22×D3—81no—
331C22×D3—101no—
332C22×D3—201no—
333C22×D3—401no—
334C22×D3#68511yescharacteristic
335C22×D3#68511yescharacteristic
336C22×D3#68511yescharacteristic
337C3×D4—41no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4C2×C22⋊D511yescharacteristic
343#67—41no—
344#67—41no—
345#67—401no—
346C2×Dic3—101no—
347C2×Dic3—201no—
348C2×Dic3#68511yescharacteristic
349D12—41no—
350D12—202no—
351D12—201no—
352D12—201no—
353D12—401no—
354C4×D3—21no—
355C4×D3—21no—
356C4×D3—401no—
357C4×D3—402no—
358C3×C8—41no—
359C3⋊C8—41no—
360C22×C5—21no—
361C22×C5—21no—
362C22×C5—31no—
363C22×C5—31no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—61no—
367C22×C5—61no—
368C22×C5—121no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5—122no—
372C22×C5—241no—
373C22×C5—241no—
374C22×C5—241no—
375C22×C5D3×C22⋊C411yescharacteristic
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C2×D5—242no—
380C4×C5—21no—
381C4×C5—61no—
382Dic5—41no—
383Dic5—41no—
384Dic5—81no—
385Dic5—121no—
386Dic5—241no—
387C24—31no—
388C24—31no—
389C24—151no—
390C2×D4—31no—
391C2×D4—31no—
392C2×D4—31no—
393C2×D4—121no—
394C2×D4—121no—
395C2×D4—301no—
396C2×D4—301no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4—601no—
400C2×D4—601no—
401C2×D4C2×D3×D511yescharacteristic
402C22×C4—31no—
403C22×C4—51no—
404C22×C4—301no—
405C22×C4—601no—
406M16—21no—
407M16—61no—
408M16—121no—
409C2×C8—121no—
410C4⋊C4—101no—
411C4⋊C4—301no—
412C22⋊C4—51no—
413C22⋊C4—101no—
414C22⋊C4—101no—
415C22⋊C4—151no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C22⋊C4—301no—
419C22⋊C4—301no—
420C22⋊C4—301no—
421C22⋊C4—601no—
422C3×C5#212111yescharacteristic, complemented, Hall
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3C2×#68511yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—41no—
431C2×D3—42no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—81no—
435C2×D3—81no—
436C2×D3—81no—
437C2×D3—201no—
438C2×D3—201no—
439C2×D3—201no—
440C2×D3—402no—
441C2×D3#393811yescharacteristic
442C2×D3#393811yescharacteristic
443C3×C4—21no—
444C3×C4—201no—
445C3×C4—201no—
446C3×C4—401no—
447Dic3—21no—
448Dic3—201no—
449Dic3—401no—
450C2×C5—21no—
451C2×C5—41no—
452C2×C5—41no—
453C2×C5—61no—
454C2×C5—61no—
455C2×C5—121no—
456C2×C5—121no—
457C2×C5D3×#9911yescharacteristic
458D5—241no—
459C23—31no—
460C23—31no—
461C23—31no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—241no—
467C23—241no—
468C23—301no—
469C23—601no—
470C23—1201no—
471C23C4×D3×D511yescharacteristic
472C23D3×D2011yescharacteristic
473D4—41no—
474D4—121no—
475D4—121no—
476D4—121no—
477D4—601no—
478D4—601no—
479D4—602no—
480D4—1201no—
481D4—1201no—
482C2×C4—31no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—101no—
486C2×C4—101no—
487C2×C4—201no—
488C2×C4—201no—
489C2×C4—301no—
490C2×C4—601no—
491C2×C4—1201no—
492C2×C4—1202no—
493C2×C4D3×C22⋊D511yescharacteristic
494C8—41no—
495C8—121no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3C2×#393811yescharacteristic
500D3—21no—
501D3—21no—
502D3—41no—
503D3—41no—
504D3—401no—
505C5#6914311yescharacteristic, complemented, Sylow
506C22—21no—
507C22—21no—
508C22—31no—
509C22—31no—
510C22—41no—
511C22—41no—
512C22—61no—
513C22—61no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—122no—
518C22—241no—
519C22—241no—
520C22—241no—
521C22—601no—
522C22—601no—
523C22—601no—
524C22—1202no—
525C22D3×#68511yescharacteristic
526C4—21no—
527C4—61no—
528C4—201no—
529C4—201no—
530C4—401no—
531C4—601no—
532C4—1201no—
533C3#1060088711yescharacteristic, complemented, Sylow
534C2—21no—
535C2—41no—
536C2—41no—
537C2—61no—
538C2—61no—
539C2—121no—
540C2—121no—
541C2—1201no—
542C2D3×#393811yescharacteristic
subgroupG/H
centerC2D3×#3938
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#100C22
socleC2×C3×C5C2×#99
prime radical#11754952C2
cosocleC2×C3×C5×D4C23
hypercenter#100D3×D5
hypocenterC3×C5#2121
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. C5×D3×#100C2semidirect
3. D3×#3966C2semidirect
4. #11746296C2semidirect
5. C3×#64696C2semidirect
6. #11746001C2semidirect
7. #11745998C2semidirect
10. C22×#1203C4semidirect
14. #91573C4semidirect
18. D3×C22⋊Dic5C4semidirect
19. #91539C4semidirect
33. #64696D3semidirect
36. C23×D15C2×C4semidirect
47. C22×C3×Dic5C2×C4semidirect
57. #6719C2×C4semidirect
64. C3×C22⋊Dic5C2×C4semidirect
72. D3×#100D5semidirect
172. C22×Dic5C4×D3semidirect
184. C22⋊Dic5C4×D3semidirect
422. C3×C5#2121semidirect
505. C5#69143semidirect
533. C3#10600887semidirect

Maximal subgroups

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

subgroupindex
#117549522
C5×D3×#1002
D3×#39662
#117462962
C3×#646962
#117460012
#117459982
#106008873
#691435