Finite Group Databasebeta

← #14283125

Subgroups — #14283125

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#930C211yesmaximal, characteristic
2C3×#64955C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C5×#4451C211yesmaximal, characteristic, complemented
6#11745958C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10599096—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×D5×#67—21no—
11C2×D5×D12C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C5×#930C2211yescharacteristic
14C2×C3×#685—21no—
15C2×C3×C4×Dic5—21no—
16#91566—21no—
17D5×(C2×D3)⋊C4—21no—
18#91450C411yescharacteristic, complemented
19#91449C411yescharacteristic, complemented
20#91448—21no—
21D5×C4⋊Dic3C411yescharacteristic, complemented
22C2×#6649—21no—
23C3×C5×#95C2211yescharacteristic, complemented
24#91114C2211yescharacteristic, complemented
25C5×#830C2211yescharacteristic, complemented
26C3×#3963C2211yescharacteristic, complemented
27#90955—21no—
28#69444—51nomaximal, Hall
29D5×#121—31no—
30#65015—31no—
31#64955D311yescharacteristic, complemented
32C5×#327—31no—
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5D411yescharacteristic
37C22×D3×D5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×D60C2×C411yescharacteristic
42C2×C5×#67—21no—
43C2×C5×D12C2×C411yescharacteristic
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51D5×#67—42no—
52D5×#67—42no—
53C2×#1203—21no—
54C2×#1202—21no—
55C2×#1201—21no—
56C2×D5×Dic3—21no—
57D5×D12—42no—
58#6714—21no—
59C4⋊Dic15C2×C411yescharacteristic
60C2×C3⋊#168—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×C4⋊Dic3C2×C411yescharacteristic
63C2×C5×C3⋊C8—21no—
64C3×#685—24no—
65C3×C4×Dic5—42no—
66#6668—21no—
67#6667—21no—
68(C2×D3)⋊Dic5—21no—
69#6649—42no—
70C2×#930—51no—
71C3×C4×C22⋊C4—51no—
72#5207—51no—
73#4451—51no—
74#4451—51no—
75#4451—51no—
76#4451D511yescharacteristic, complemented
77C2×D4×D5—31no—
78C2×D4×D5—61no—
79C22×C4×D5C2×D311yescharacteristic
80C5×#121—31no—
81#4085—61no—
82#4084—31no—
83#4076—31no—
84C2×#685—21no—
85C2×C4×Dic5—21no—
86C2×#676—61no—
87#4041—31no—
88D5×C4⋊C4—31no—
89#4030—61no—
90D5×C22⋊C4—61no—
91C5×C22⋊C8—31no—
92C5×#95C2×D311yescharacteristic, complemented
93#3963C2×D311yescharacteristic, complemented
94C22⋊#168—31no—
95#3952—61no—
96#1507—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—21no—
99C22×C5×D3—21no—
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—22no—
103C22×C3×D5—41no—
104C22×C3×D5C22⋊C411yescharacteristic
105C22×C3×D5C22⋊C411yescharacteristic
106C2×D3×D5—42no—
107C2×D3×D5—42no—
108C2×D3×D5—42no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115#1220—41no—
116#1220—41no—
117C2×Dic15—21no—
118D60—41no—
119C5×#67—41no—
120C5×#67—41no—
121C2×C5×Dic3—21no—
122C5×D12—41no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5C22⋊C411yescharacteristic
128C2×C3×Dic5C22⋊C411yescharacteristic
129C3×C4×D5—22no—
130C3×C4×D5—22no—
131C3×C4×D5—41no—
132C3×C4×D5—41no—
133#1203—42no—
134#1202—42no—
135#1201—42no—
136D5×Dic3—42no—
137C3⋊#168—41no—
138C5×C3⋊C8—41no—
139C23×C3×C4—51no—
140C22×#67—101no—
141C22×D12—51no—
142C2×C3×C22⋊C4—101no—
143C2×C3×C42—101no—
144#930—51no—
145#930—51no—
146#930—51no—
147#930—101no—
148#930—101no—
149#930C2×D511yescharacteristic
150C2×(C2×D3)⋊C4—101no—
151C2×C4⋊Dic3—51no—
152C2×#208—101no—
153C3×#95—51no—
154C3×#95C2×D511yescharacteristic, complemented
155#830—51no—
156#830—101no—
157#830C2×D511yescharacteristic, complemented
158C23×D5—61no—
159C23×D5#6711yescharacteristic
160C2×C5×D4—31no—
161C2×C5×D4—61no—
162C22×C4×C5—21no—
163C22×C4×C5C22×D311yescharacteristic
164C2×C22⋊D5—61no—
165C2×C22⋊D5—61no—
166C2×C22⋊D5—61no—
167C22×Dic5—21no—
168C22×Dic5#6711yescharacteristic
169D4×D5—122no—
170D4×D5—122no—
171D4×D5—122no—
172C2×D20—31no—
173C2×D20—61no—
174C2×C4×D5—42no—
175C2×C4×D5—61no—
176C2×C4×D5C4×D311yescharacteristic
177C2×C4×D5C4×D311yescharacteristic
178C2×C4×D5D1211yescharacteristic
179C2×C4×D5D1211yescharacteristic
180C2×C5×C8—61no—
181C5×C4⋊C4—31no—
182C5×C22⋊C4—61no—
183C22⋊Dic5—61no—
184#685—24no—
185#685—61no—
186#685—61no—
187C4⋊Dic5—31no—
188#683—61no—
189C4×Dic5—42no—
190C2×#168—61no—
191#676—122no—
192C2×#121—151no—
193#407—151no—
194C4×C22⋊C4—51no—
195#327—31no—
196#327—151no—
197#327—151no—
198#327—151no—
199C22×C3×C5—21no—
200C22×C3×C5—21no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
203C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
204C2×D15—41no—
205C2×D15—41no—
206C2×D15—41no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—21no—
213C2×C3×D5—21no—
214C2×C3×D5—21no—
215C2×C3×D5—42no—
216C2×C3×D5—42no—
217C2×C3×D5#10412yes—
218D3×D5—84no—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221C3×C4×C5—42no—
222Dic15—41no—
223C3×Dic5—21no—
224C3×Dic5—42no—
225C3×Dic5#9912yes—
226C5×Dic3—41no—
227C24×C3—51no—
228C23×D3—101no—
229C22×C3×C4—21no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—51no—
234C22×C3×C4—51no—
235C22×C3×C4—101no—
236C22×C3×C4—202no—
237C22×C3×C4C22×D511yescharacteristic
238C2×#67—21no—
239C2×#67—101no—
240C2×#67—101no—
241C2×#67—101no—
242C2×#67—202no—
243C2×#67—202no—
244C22×Dic3—101no—
245C2×D12—51no—
246C2×D12—101no—
247C2×D12—202no—
248C2×D12C4×D511yescharacteristic
249C3×C22⋊C4—104no—
250C3×C42—202no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—101no—
253(C2×D3)⋊C4—101no—
254(C2×D3)⋊C4—101no—
255C4⋊Dic3—51no—
256C4⋊Dic3—101no—
257C4⋊Dic3C4×D511yescharacteristic
258#208—202no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—101no—
261C23×C5—61no—
262C23×C5C2×#6711yescharacteristic
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—22no—
266C22×D5—41no—
267C22×D5—61no—
268C22×D5—122no—
269C22×D5—122no—
270C22×D5—122no—
271C22×D5(C2×D3)⋊C411yescharacteristic
272C22×D5(C2×D3)⋊C411yescharacteristic
273C5×D4—121no—
274C5×D4—121no—
275C5×D4—121no—
276C2×C4×C5—22no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—61no—
281C2×C4×C5C2×C4×D311yescharacteristic
282C2×C4×C5C2×D1211yescharacteristic
283C22⋊D5—122no—
284C22⋊D5—121no—
285C22⋊D5—121no—
286C22⋊D5—122no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—41no—
290C2×Dic5—41no—
291C2×Dic5—61no—
292C2×Dic5(C2×D3)⋊C411yescharacteristic
293C2×Dic5(C2×D3)⋊C411yescharacteristic
294D20—121no—
295D20—122no—
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—41no—
299C4×D5—41no—
300C4×D5—122no—
301C5×C8—121no—
302#168—121no—
303C22×D4—151no—
304C22×D4—301no—
305C23×C4—51no—
306C2×M16—301no—
307#121—31no—
308#121—151no—
309#121—151no—
310#121—151no—
311#121—301no—
312#121—301no—
313C2×C4⋊C4—151no—
314C2×C22⋊C4—101no—
315C2×C22⋊C4—301no—
316C2×C42—101no—
317C22⋊C8—31no—
318C22⋊C8—151no—
319C22⋊C8—301no—
320#95—51no—
321#95D3×D511yescharacteristic, complemented
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5C2×#9911yescharacteristic
325C2×C3×C5#41811yescharacteristic
326C2×C3×C5C2×#10411yescharacteristic
327D15—81no—
328C3×D5—22no—
329C3×D5—41no—
330C5×D3—81no—
331C23×C3—51no—
332C23×C3—51no—
333C23×C3—102no—
334C23×C3—101no—
335C23×C3—101no—
336C23×C3—201no—
337C23×C3D4×D511yescharacteristic
338C22×D3—21no—
339C22×D3—101no—
340C22×D3—202no—
341C22×D3—202no—
342C22×D3—202no—
343C2×C3×C4—22no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—51no—
348C2×C3×C4—51no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—201no—
354C2×C3×C4—201no—
355C2×C3×C4—201no—
356C2×C3×C4—201no—
357C2×C3×C4C2×C4×D511yescharacteristic
358C2×C3×C4D4×D511yescharacteristic
359#67—41no—
360#67—41no—
361#67—202no—
362#67—202no—
363#67—201no—
364#67—201no—
365C2×Dic3—21no—
366C2×Dic3—101no—
367C2×Dic3—202no—
368D12—41no—
369D12—201no—
370D12—202no—
371C3⋊C8—41no—
372C3⋊C8—201no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—121no—
376C22×C5—121no—
377C22×C5—121no—
378C22×C5C2×(C2×D3)⋊C411yescharacteristic
379C22×C5#94911yescharacteristic
380C22×C5#94911yescharacteristic
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—21no—
386C2×D5—42no—
387C2×D5—42no—
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C2×D5—244no—
392C2×D5#80512yes—
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—42no—
396C4×C5—121no—
397Dic5—21no—
398Dic5—42no—
399Dic5—121no—
400Dic5#80612yes—
401C24—51no—
402C24—301no—
403C2×D4—31no—
404C2×D4—61no—
405C2×D4—151no—
406C2×D4—301no—
407C2×D4—301no—
408C2×D4—301no—
409C2×D4—301no—
410C2×D4—602no—
411C2×D4—602no—
412C2×D4—602no—
413C22×C4—21no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—101no—
420C22×C4—202no—
421C22×C4—301no—
422C22×C4C2×D3×D511yescharacteristic
423M16—602no—
424C2×C8—61no—
425C2×C8—301no—
426C4⋊C4—31no—
427C4⋊C4—151no—
428C4⋊C4—301no—
429C22⋊C4—61no—
430C22⋊C4—104no—
431C22⋊C4—301no—
432C22⋊C4—301no—
433C22⋊C4—301no—
434C42—202no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—52no—
439C22×C3—101no—
440C22×C3—101no—
441C22×C3—101no—
442C22×C3—101no—
443C22×C3—101no—
444C22×C3—202no—
445C22×C3—202no—
446C22×C3D5×C22⋊C411yescharacteristic
447C22×C3#405711yescharacteristic
448C22×C3#406011yescharacteristic
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—201no—
453C2×D3—201no—
454C2×D3—201no—
455C2×D3—404no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—52no—
460C3×C4—101no—
461C3×C4—202no—
462Dic3—41no—
463Dic3—201no—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—241no—
467C2×C5C2×#80511yescharacteristic
468C2×C5C2×#80611yescharacteristic
469C2×C5#500111yescharacteristic
470D5—22no—
471D5—41no—
472D5—241no—
473C23—51no—
474C23—51no—
475C23—61no—
476C23—102no—
477C23—101no—
478C23—101no—
479C23—201no—
480C23—301no—
481C23—602no—
482C23—602no—
483C23—602no—
484C23D5×#6711yescharacteristic
485D4—121no—
486D4—121no—
487D4—121no—
488D4—601no—
489D4—602no—
490D4—602no—
491D4—602no—
492D4—601no—
493D4—601no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—51no—
499C2×C4—51no—
500C2×C4—61no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—102no—
505C2×C4—201no—
506C2×C4—201no—
507C2×C4—201no—
508C2×C4—201no—
509C2×C4—301no—
510C2×C4—602no—
511C2×C4C4×D3×D511yescharacteristic
512C2×C4D5×D1211yescharacteristic
513C8—121no—
514C8—601no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—102no—
518C2×C3—201no—
519C2×C3D5×#9911yescharacteristic
520C2×C3#6505911yescharacteristic
521C2×C3D5×#10411yescharacteristic
522D3—81no—
523D3—401no—
524C5#6944411yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—52no—
528C22—101no—
529C22—101no—
530C22—101no—
531C22—101no—
532C22—101no—
533C22—121no—
534C22—121no—
535C22—121no—
536C22—202no—
537C22—202no—
538C22—601no—
539C22—601no—
540C22—601no—
541C22—1204no—
542C22D5×(C2×D3)⋊C411yescharacteristic
543C22#9147811yescharacteristic
544C22#9150211yescharacteristic
545C4—21no—
546C4—21no—
547C4—42no—
548C4—52no—
549C4—101no—
550C4—121no—
551C4—202no—
552C4—601no—
553C3#1059909611yescharacteristic, complemented, Sylow
554C2—21no—
555C2—21no—
556C2—102no—
557C2—201no—
558C2—241no—
559C2—1201no—
560C2D5×#80511yescharacteristic
561C2D5×#80611yescharacteristic
562C2#1174747511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalD5×#930C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1507
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#64955C2semidirect
3. #11748499C2semidirect
4. #11746272C2semidirect
5. C5×#4451C2semidirect
6. #11745958C2semidirect
7. #11745956C2semidirect
11. C2×D5×D12C4semidirect
18. #91450C4semidirect
19. #91449C4semidirect
21. D5×C4⋊Dic3C4semidirect
23. C3×C5×#95C22semidirect
24. #91114C22semidirect
25. C5×#830C22semidirect
26. C3×#3963C22semidirect
31. #64955D3semidirect
76. #4451D5semidirect
92. C5×#95C2×D3semidirect
93. #3963C2×D3semidirect
154. C3×#95C2×D5semidirect
157. #830C2×D5semidirect
321. #95D3×D5semidirect
435. C3×C5#1507semidirect
524. C5#69444semidirect
553. C3#10599096semidirect

Maximal subgroups

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

subgroupindex
D5×#9302
C3×#649552
#117484992
#117462722
C5×#44512
#117459582
#117459562
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