Finite Group Databasebeta

← #14283127

Subgroups — #14283127

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
1D3×#4076C211yesmaximal, characteristic
2C5×#4666C211yesmaximal, characteristic, complemented
3#11748505C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C3×#64671C211yesmaximal, characteristic, complemented
6#11745959C211yesmaximal, characteristic, complemented
7#11745954C211yesmaximal, characteristic, complemented
8#10600237—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×D3×C22⋊D5—21no—
11C2×D3×D20C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C2×C5×(C2×D3)⋊C4—21no—
14C2×C4×C5×Dic3—21no—
15C3×#4076C2211yescharacteristic
16#91569—21no—
17D3×#685—21no—
18#91460C411yescharacteristic, complemented
19#91456C411yescharacteristic, complemented
20#91454—21no—
21D3×C4⋊Dic5C411yescharacteristic, complemented
22C2×#6650—21no—
23C3×C5×#95C2211yescharacteristic, complemented
24#91114C2211yescharacteristic, complemented
25C5×C3⋊#95C2211yescharacteristic, complemented
26C3×C22⋊#168C2211yescharacteristic, complemented
27(C2×D3)⋊#168—21no—
28#68303—51nomaximal, Hall
29C2×#4076—31no—
30C4×C5×C22⋊C4—31no—
31#65496—31no—
32#64671—31no—
33#64671—31no—
34#64671—31no—
35#64671D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C22×D3×D5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×D60C2×C411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3D411yescharacteristic
44C2×C4×C5×D3—42no—
45C2×C4×C5×D3C2×C411yescharacteristic
46C2×C4×C5×D3C2×C411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C4×C5×D3D411yescharacteristic
49C2×C3×C22⋊D5—21no—
50C2×C3×D20C2×C411yescharacteristic
51D3×C22⋊D5—42no—
52D3×C22⋊D5—42no—
53C2×#1203—21no—
54C2×#1202—21no—
55C2×#1201—21no—
56C2×D3×Dic5—21no—
57D3×D20—42no—
58#6714—21no—
59C4⋊Dic15C2×C411yescharacteristic
60C2×C3⋊#168—21no—
61C5×(C2×D3)⋊C4—24no—
62C4×C5×Dic3—42no—
63C3×#685—21no—
64C3×C4⋊Dic5C2×C411yescharacteristic
65C2×C3×#168—21no—
66Dic3⋊Dic5—21no—
67#6667—21no—
68#6665—21no—
69#6650—42no—
70D3×#121—51no—
71#4726—51no—
72#4666D511yescharacteristic, complemented
73C3×#327—51no—
74#4537—51no—
75#4470—51no—
76#4451—51no—
77C23×C4×C5—31no—
78C22×C22⋊D5—61no—
79C22×D20—31no—
80C2×C5×C22⋊C4—61no—
81C2×C42×C5—61no—
82#4076—31no—
83#4076—31no—
84#4076—31no—
85#4076—61no—
86#4076—61no—
87#4076C2×D311yescharacteristic
88C2×#685—61no—
89C2×C4⋊Dic5—31no—
90C2×#681—61no—
91C5×#95—31no—
92C5×#95C2×D311yescharacteristic, complemented
93C22⋊#168—31no—
94C22⋊#168—61no—
95C22⋊#168C2×D311yescharacteristic, complemented
96#1507—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—21no—
99C22×C5×D3—21no—
100C22×C5×D3—21no—
101C22×C5×D3—22no—
102C22×C5×D3—41no—
103C22×C5×D3C22⋊C411yescharacteristic
104C22×C5×D3C22⋊C411yescharacteristic
105C22×C3×D5—21no—
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—
119C2×C5×Dic3—22no—
120C2×C5×Dic3—22no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3C22⋊C411yescharacteristic
124C2×C5×Dic3C22⋊C411yescharacteristic
125C4×C5×D3—22no—
126C4×C5×D3—22no—
127C4×C5×D3—41no—
128C4×C5×D3—41no—
129C3×C22⋊D5—41no—
130C3×C22⋊D5—41no—
131C2×C3×Dic5—21no—
132C3×D20—41no—
133#1203—42no—
134#1202—42no—
135#1201—42no—
136D3×Dic5—42no—
137C3⋊#168—41no—
138C3×#168—41no—
139C2×D3×D4—51no—
140C2×D3×D4—101no—
141C22×C4×D3C2×D511yescharacteristic
142C3×#121—51no—
143#939—101no—
144#938—51no—
145#930—51no—
146C2×(C2×D3)⋊C4—21no—
147C2×C4×Dic3—21no—
148C2×ΓL(1,𝔽25)—101no—
149#895—51no—
150D3×C4⋊C4—51no—
151#884—101no—
152D3×C22⋊C4—101no—
153C3×C22⋊C8—51no—
154C3×#95C2×D511yescharacteristic, complemented
155C3⋊#95C2×D511yescharacteristic, complemented
156#830—51no—
157(C2×D3)⋊C8—101no—
158C24×C5—31no—
159C23×D5—61no—
160C22×C4×C5—21no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—31no—
166C22×C4×C5—61no—
167C22×C4×C5—122no—
168C22×C4×C5C22×D311yescharacteristic
169C2×C22⋊D5—21no—
170C2×C22⋊D5—61no—
171C2×C22⋊D5—61no—
172C2×C22⋊D5—61no—
173C2×C22⋊D5—122no—
174C2×C22⋊D5—122no—
175C22×Dic5—61no—
176C2×D20—31no—
177C2×D20—61no—
178C2×D20—122no—
179C2×D20C4×D311yescharacteristic
180C5×C22⋊C4—64no—
181C42×C5—122no—
182#685—21no—
183#685—61no—
184#685—61no—
185#685—61no—
186C4⋊Dic5—31no—
187C4⋊Dic5—61no—
188C4⋊Dic5C4×D311yescharacteristic
189#681—122no—
190C2×#168—21no—
191C2×#168—61no—
192C2×#121—151no—
193#407—151no—
194C4×C22⋊C4—31no—
195#327—51no—
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—21no—
208C2×C5×D3—21no—
209C2×C5×D3—21no—
210C2×C5×D3—21no—
211C2×C5×D3—21no—
212C2×C5×D3—42no—
213C2×C5×D3—42no—
214C2×C5×D3#10412yes—
215C2×C3×D5—41no—
216C2×C3×D5—41no—
217C2×C3×D5—41no—
218D3×D5—84no—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221C3×C4×C5—42no—
222Dic15—41no—
223C3×Dic5—41no—
224C5×Dic3—21no—
225C5×Dic3—42no—
226C5×Dic3#9912yes—
227C23×D3—101no—
228C23×D3C22⋊D511yescharacteristic
229C2×C3×D4—51no—
230C2×C3×D4—101no—
231C22×C3×C4—21no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—101no—
234C2×#67—101no—
235C2×#67—101no—
236C22×Dic3—21no—
237C22×Dic3C22⋊D511yescharacteristic
238D3×D4—202no—
239D3×D4—202no—
240D3×D4—202no—
241C2×D12—51no—
242C2×D12—101no—
243C2×C4×D3—42no—
244C2×C4×D3—101no—
245C2×C4×D3C4×D511yescharacteristic
246C2×C4×D3C4×D511yescharacteristic
247C2×C4×D3D2011yescharacteristic
248C2×C4×D3D2011yescharacteristic
249C2×C3×C8—101no—
250C3×C4⋊C4—51no—
251C3×C22⋊C4—101no—
252#217—101no—
253(C2×D3)⋊C4—24no—
254(C2×D3)⋊C4—101no—
255(C2×D3)⋊C4—101no—
256C4⋊Dic3—51no—
257Dic3⋊C4—101no—
258C4×Dic3—42no—
259C2×C3⋊C8—101no—
260ΓL(1,𝔽25)—202no—
261C23×C5—31no—
262C23×C5—31no—
263C23×C5—62no—
264C23×C5—61no—
265C23×C5—61no—
266C23×C5—121no—
267C23×C5D3×D411yescharacteristic
268C22×D5—21no—
269C22×D5—61no—
270C22×D5—122no—
271C22×D5—122no—
272C22×D5—122no—
273C2×C4×C5—22no—
274C2×C4×C5—31no—
275C2×C4×C5—31no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—62no—
280C2×C4×C5—62no—
281C2×C4×C5—62no—
282C2×C4×C5—62no—
283C2×C4×C5—121no—
284C2×C4×C5—121no—
285C2×C4×C5—121no—
286C2×C4×C5—121no—
287C2×C4×C5C2×C4×D311yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C22⋊D5—41no—
290C22⋊D5—41no—
291C22⋊D5—122no—
292C22⋊D5—122no—
293C22⋊D5—121no—
294C22⋊D5—121no—
295C2×Dic5—21no—
296C2×Dic5—61no—
297C2×Dic5—122no—
298D20—41no—
299D20—121no—
300D20—122no—
301#168—41no—
302#168—121no—
303C22×D4—151no—
304C22×D4—301no—
305C23×C4—31no—
306C2×M16—301no—
307#121—51no—
308#121—151no—
309#121—151no—
310#121—151no—
311#121—301no—
312#121—301no—
313C2×C4⋊C4—151no—
314C2×C22⋊C4—61no—
315C2×C22⋊C4—301no—
316C2×C42—61no—
317C22⋊C8—51no—
318C22⋊C8—151no—
319C22⋊C8—301no—
320#95—31no—
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—81no—
329C5×D3—22no—
330C5×D3—41no—
331C23×C3—101no—
332C23×C3C2×C22⋊D511yescharacteristic
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—22no—
336C22×D3—41no—
337C22×D3—101no—
338C22×D3—202no—
339C22×D3—202no—
340C22×D3—202no—
341C22×D3#68511yescharacteristic
342C22×D3#68511yescharacteristic
343C3×D4—201no—
344C3×D4—201no—
345C3×D4—201no—
346C2×C3×C4—22no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—101no—
351C2×C3×C4C2×C4×D511yescharacteristic
352C2×C3×C4C2×D2011yescharacteristic
353#67—202no—
354#67—201no—
355#67—201no—
356#67—202no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—101no—
362C2×Dic3#68511yescharacteristic
363C2×Dic3#68511yescharacteristic
364D12—201no—
365D12—202no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3—41no—
369C4×D3—41no—
370C4×D3—202no—
371C3×C8—201no—
372C3⋊C8—201no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—32no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5—61no—
379C22×C5—61no—
380C22×C5—61no—
381C22×C5—122no—
382C22×C5—122no—
383C22×C5D3×C22⋊C411yescharacteristic
384C22×C5#91111yescharacteristic
385C22×C5#91411yescharacteristic
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—41no—
389C2×D5—121no—
390C2×D5—121no—
391C2×D5—121no—
392C2×D5—244no—
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—32no—
396C4×C5—42no—
397C4×C5—61no—
398C4×C5—122no—
399Dic5—41no—
400Dic5—121no—
401C24—31no—
402C24—301no—
403C2×D4—51no—
404C2×D4—101no—
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—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—61no—
420C22×C4—122no—
421C22×C4—301no—
422C22×C4C2×D3×D511yescharacteristic
423M16—602no—
424C2×C8—101no—
425C2×C8—301no—
426C4⋊C4—51no—
427C4⋊C4—151no—
428C4⋊C4—301no—
429C22⋊C4—64no—
430C22⋊C4—101no—
431C22⋊C4—301no—
432C22⋊C4—301no—
433C22⋊C4—301no—
434C42—122no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—201no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3C2×#68511yescharacteristic
442C22×C3#409511yescharacteristic
443C22×C3#409511yescharacteristic
444C2×D3—21no—
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—21no—
448C2×D3—21no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C2×D3—404no—
455C2×D3#393712yes—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—201no—
460Dic3—21no—
461Dic3—42no—
462Dic3—201no—
463Dic3#393812yes—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—62no—
467C2×C5—121no—
468C2×C5D3×#9911yescharacteristic
469C2×C5#477011yescharacteristic
470C2×C5D3×#10411yescharacteristic
471D5—81no—
472D5—241no—
473C23—31no—
474C23—31no—
475C23—62no—
476C23—61no—
477C23—61no—
478C23—101no—
479C23—121no—
480C23—301no—
481C23—602no—
482C23—602no—
483C23—602no—
484C23D3×C22⋊D511yescharacteristic
485D4—201no—
486D4—201no—
487D4—201no—
488D4—601no—
489D4—602no—
490D4—602no—
491D4—602no—
492D4—601no—
493D4—601no—
494C2×C4—22no—
495C2×C4—31no—
496C2×C4—31no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—101no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—301no—
510C2×C4—602no—
511C2×C4C4×D3×D511yescharacteristic
512C2×C4D3×D2011yescharacteristic
513C8—201no—
514C8—601no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—401no—
518C2×C3C2×#393711yescharacteristic
519C2×C3C2×#393811yescharacteristic
520C2×C3#6529011yescharacteristic
521D3—22no—
522D3—41no—
523D3—401no—
524C5#6830311yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—32no—
528C22—61no—
529C22—61no—
530C22—61no—
531C22—61no—
532C22—61no—
533C22—122no—
534C22—122no—
535C22—201no—
536C22—201no—
537C22—201no—
538C22—601no—
539C22—601no—
540C22—601no—
541C22—1204no—
542C22D3×#68511yescharacteristic
543C22#9148011yescharacteristic
544C22#9150411yescharacteristic
545C4—21no—
546C4—21no—
547C4—32no—
548C4—42no—
549C4—61no—
550C4—122no—
551C4—201no—
552C4—601no—
553C3#1060023711yescharacteristic, complemented, Sylow
554C2—21no—
555C2—21no—
556C2—62no—
557C2—121no—
558C2—401no—
559C2—1201no—
560C2D3×#393711yescharacteristic
561C2D3×#393811yescharacteristic
562C2#1174747711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalD3×#4076C2
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. C5×#4666C2semidirect
3. #11748505C2semidirect
4. #11746272C2semidirect
5. C3×#64671C2semidirect
6. #11745959C2semidirect
7. #11745954C2semidirect
11. C2×D3×D20C4semidirect
18. #91460C4semidirect
19. #91456C4semidirect
21. D3×C4⋊Dic5C4semidirect
23. C3×C5×#95C22semidirect
24. #91114C22semidirect
25. C5×C3⋊#95C22semidirect
26. C3×C22⋊#168C22semidirect
35. #64671D3semidirect
72. #4666D5semidirect
92. C5×#95C2×D3semidirect
95. C22⋊#168C2×D3semidirect
154. C3×#95C2×D5semidirect
155. C3⋊#95C2×D5semidirect
321. #95D3×D5semidirect
435. C3×C5#1507semidirect
524. C5#68303semidirect
553. C3#10600237semidirect

Maximal subgroups

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

subgroupindex
D3×#40762
C5×#46662
#117485052
#117462722
C3×#646712
#117459592
#117459542
#106002373
#683035