Finite Group Databasebeta

← #14438640

Subgroups — #14438640

Order 1920.

848 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
1C3×#66002C211yesmaximal, characteristic
2D5×#869C211yesmaximal, characteristic, complemented
3#11751156C211yesmaximal, characteristic, complemented
4C5×#5055C211yesmaximal, characteristic, complemented
5#11749349C212yesmaximal, complemented
6#11749198C212yesmaximal, complemented
7#11749102C212yesmaximal, complemented
8#11748951C212yesmaximal, complemented
9#11747003C211yesmaximal, characteristic, complemented
10#11746898C211yesmaximal, characteristic, complemented
11#11746893C211yesmaximal, characteristic, complemented
12#10613414—31nomaximal, Hall
13C2×C3×#713C2211yescharacteristic
14C2×C3×#711C2211yescharacteristic
15C2×D5×Dic6—21no—
16C3×C5×#124C2211yescharacteristic
17#91758C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C3×#4090C2211yescharacteristic
20C3×#4086C2211yescharacteristic
21C3×#4030—21no—
22C3×#4030—21no—
23C3×#4027—21no—
24C3×#4027—21no—
25C3×#4021C2211yescharacteristic
26C3×C42×D5C2211yescharacteristic
27#91468—21no—
28#91468C2212yes—
29D5×C4⋊Dic3—21no—
30D5×C4⋊Dic3C2212yes—
31#91376—21no—
32C2×#6649C2212yes—
33#91119C2212yes—
34#91116C2212yes—
35#91087C2211yescharacteristic
36C5×#835C2212yes—
37C5×#832C2212yes—
38C5×#803C2211yescharacteristic
39#90971C2212yes—
40#90970C2212yes—
41#90965C2212yes—
42#90964C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83283—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46#66002D311yescharacteristic
47C5×#489—31no—
48#65378—31no—
49#65344—31no—
50#65092—32no—
51#65081—32no—
52#65060—32no—
53#65049—32no—
54#65003—31no—
55#64996—31no—
56C2×C3×C5×Q8C2311yescharacteristic
57C2×C3×C5×D4C2311yescharacteristic
58C2×Dic30—21no—
59C2×C5×Dic6—21no—
60C2×C3×C22⋊D5—21no—
61C2×C3×C22⋊D5—21no—
62C2×C3×C22⋊D5—21no—
63C22×C3×Dic5—21no—
64C3×#713—24no—
65C3×#711—24no—
66C2×C3×D20—21no—
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×C4×D5D411yescharacteristic
70C2×C3×C4×D5D411yescharacteristic
71C2×C3×C4×D5C2311yescharacteristic
72C2×C3×Dic10C2311yescharacteristic
73C2×#1204—22no—
74C2×D5×Dic3—22no—
75D5×Dic6—44no—
76C3×C5×C22⋊C4—21no—
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79C4⋊Dic15—21no—
80C4⋊Dic15C2312yes—
81C2×C3⋊#168C2312yes—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3C2312yes—
84C2×C5×C3⋊C8C2312yes—
85C3×#685—21no—
86C3×#685—21no—
87C3×#683—21no—
88C3×#683—21no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92#6668—22no—
93#6668—22no—
94#6649—24no—
95C3×#532—51no—
96C2×#869—51no—
97#5232—52no—
98#5232—52no—
99#5079—52no—
100#5070—52no—
101#5055—51no—
102#5055—51no—
103#5055—51no—
104#5055D511yescharacteristic, complemented
105C4×#208—51no—
106C2×#713C2×D311yescharacteristic
107C2×Q8×D5—61no—
108C2×#711C2×D311yescharacteristic
109C5×C4⋊Q8—31no—
110C5×#124C2×D311yescharacteristic
111#4090—61no—
112#4090C2×D311yescharacteristic
113#4086C2×D311yescharacteristic
114C2×#676—32no—
115D5×C4⋊C4—32no—
116D5×C4⋊C4—61no—
117#4034—32no—
118#4034—61no—
119#4030—21no—
120#4030—21no—
121#4027—21no—
122#4027—21no—
123#4021C2×D311yescharacteristic
124C42×D5C2×D311yescharacteristic
125#4015—31no—
126C5×#103—32no—
127C5×#102—32no—
128C5×#97—31no—
129#3967—32no—
130#3964—32no—
131#3953—32no—
132#3948—32no—
133C8×Dic5—32no—
134#3942—32no—
135#3941—32no—
136#3935—31no—
137#3141—151noSylow
138C23×C3×C5—21no—
139C22×C3×D5—21no—
140C22×C3×D5C2×D411yescharacteristic
141C3×C5×Q8—22no—
142C3×C5×D4—22no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15—22no—
148Dic30—42no—
149C2×C5×Dic3—22no—
150C5×Dic6—42no—
151C3×C22⋊D5—42no—
152C3×C22⋊D5—42no—
153C3×C22⋊D5—42no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—42no—
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C3×D20—22no—
160C3×D20—42no—
161C3×C4×D5—22no—
162C3×C4×D5—22no—
163C3×C4×D5—42no—
164C3×C4×D5#4114yes—
165C3×Dic10—22no—
166#1204—44no—
167D5×Dic3—44no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C2×C3×#41—51no—
171C2×C3×#41—51no—
172C22×Dic6—101no—
173C3×C4⋊Q8—51no—
174C3×#127—51no—
175C3×#124—51no—
176C3×#124C2×D511yescharacteristic
177C3×#121—101no—
178C3×#121—101no—
179C3×C4×D4—101no—
180C3×C4×D4—101no—
181C2×C3×C42—51no—
182C2×C4⋊Dic3—52no—
183C2×C4⋊Dic3—101no—
184C2×#208—52no—
185#869—51no—
186#869—52no—
187#869—101no—
188#869—101no—
189#869C2×D511yescharacteristic
190#835—52no—
191#835—52no—
192#835—52no—
193#835C2×D512yes—
194#832—52no—
195#832—52no—
196#832—52no—
197#832C2×D512yes—
198#803—51no—
199#803C2×D511yescharacteristic
200C4×C3⋊C8—52no—
201C2×C5×Q8—61no—
202C2×C5×Q8C22×D311yescharacteristic
203C2×C5×D4C22×D311yescharacteristic
204C2×C22⋊D5—21no—
205C2×C22⋊D5—21no—
206C2×C22⋊D5—21no—
207C22×Dic5—21no—
208#713—24no—
209Q8×D5—124no—
210#711—24no—
211C2×D20—21no—
212C2×D20C22×D311yescharacteristic
213C2×C4×D5—21no—
214C2×C4×D5—62no—
215C2×C4×D5#6711yescharacteristic
216C2×C4×D5#6711yescharacteristic
217C2×C4×D5C22×D311yescharacteristic
218C2×Dic10—61no—
219C2×Dic10—62no—
220C2×Dic10C22×D311yescharacteristic
221C2×C5×C8—32no—
222C5×C4⋊C4—32no—
223C5×C4⋊C4—61no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C42×C5C22×D311yescharacteristic
227#685—21no—
228#685—21no—
229C4⋊Dic5—32no—
230C4⋊Dic5—61no—
231#683—21no—
232#683—21no—
233#683—62no—
234#683—62no—
235C4×Dic5#6711yescharacteristic
236C4×Dic5#6711yescharacteristic
237C4×Dic5C22×D311yescharacteristic
238C2×#168—32no—
239#676—64no—
240#532—51no—
241C2×C4⋊Q8—151no—
242#489—31no—
243#489—151no—
244#489—151no—
245#489—151no—
246#487—152no—
247#486—152no—
248#417—152no—
249#417—152no—
250C4×M16—151no—
251C22×C3×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5—41no—
254C22×C3×C5C22×D411yescharacteristic
255C2×C3×D5—21no—
256C2×C3×D5—21no—
257C2×C3×D5—41no—
258C2×C3×D5—41no—
259C2×C3×D5—41no—
260C2×C3×D5#12412yes—
261C3×C4×C5—21no—
262C3×C4×C5—21no—
263C3×C4×C5—41no—
264C3×C4×C5C2×#4112yes—
265Dic15—42no—
266C3×Dic5—41no—
267C3×Dic5#12412yes—
268C3×Dic5AGL(1,ℤ/8)12yes—
269C3×Dic5#13712yes—
270C5×Dic3—42no—
271C3×#41—104no—
272C3×#41—104no—
273C2×C3×Q8—51no—
274C2×C3×Q8C22×D511yescharacteristic
275C2×C3×D4—51no—
276C2×C3×D4—101no—
277C2×C3×D4—101no—
278C2×C3×D4—101no—
279C2×C3×D4—101no—
280C2×C3×D4C22×D511yescharacteristic
281C22×C3×C4—51no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—101no—
285C22×C3×C4—101no—
286C22×Dic3—102no—
287C2×Dic6—21no—
288C2×Dic6—102no—
289C2×Dic6—101no—
290C2×Dic6—204no—
291C3×C4⋊C4—101no—
292C3×C4⋊C4—101no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—101no—
296C3×C22⋊C4—101no—
297C3×C42—51no—
298C3×C42—51no—
299C3×C42—51no—
300C3×C42C22×D511yescharacteristic
301C4⋊Dic3—21no—
302C4⋊Dic3—52no—
303C4⋊Dic3—102no—
304C4⋊Dic3—102no—
305C4⋊Dic3—101no—
306C4⋊Dic3C22×D512yes—
307#208—104no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8C22×D512yes—
310C23×C5—21no—
311C22×D5—21no—
312C22×D5C2×#6711yescharacteristic
313C5×Q8—22no—
314C5×Q8—122no—
315C5×D4—22no—
316C2×C4×C5—21no—
317C2×C4×C5—62no—
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—42no—
322C22⋊D5—42no—
323C22⋊D5—42no—
324C2×Dic5—21no—
325C2×Dic5—42no—
326C2×Dic5—62no—
327C2×Dic5C2×#6711yescharacteristic
328C2×Dic5C2×#6711yescharacteristic
329C2×Dic5C2×#6711yescharacteristic
330D20—22no—
331D20—42no—
332C4×D5—22no—
333C4×D5—22no—
334C4×D5—42no—
335C4×D5—124no—
336C4×D5#23714yes—
337Dic10—22no—
338Dic10—122no—
339Dic10—124no—
340C5×C8—62no—
341#168—62no—
342C2×#41—51no—
343C2×#41—51no—
344C22×Q8—301no—
345C2×M16—152no—
346C4⋊Q8—31no—
347C4⋊Q8—51no—
348C4⋊Q8—152no—
349C4⋊Q8—151no—
350C4⋊Q8—301no—
351C4⋊Q8—301no—
352#127—51no—
353#124—51no—
354#124D3×D511yescharacteristic
355#121—101no—
356#121—101no—
357C4×D4—101no—
358C4×D4—101no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—301no—
361C2×C42—51no—
362#103—32no—
363#103—152no—
364#103—152no—
365#103—152no—
366#102—32no—
367#102—152no—
368#102—152no—
369#102—152no—
370#97—31no—
371#97—151no—
372C4×C8—152no—
373C2×C3×C5—81no—
374C2×C3×C5C2×#12411yescharacteristic
375C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C3×C5C2×#13711yescharacteristic
377C3×D5—22no—
378C3×D5—81no—
379C23×C3—21no—
380C23×C3—51no—
381C23×C3—101no—
382C3×Q8—22no—
383C3×Q8—102no—
384C3×D4—22no—
385C3×D4—102no—
386C3×D4—202no—
387C3×D4—202no—
388C3×D4—202no—
389C3×D4—202no—
390C2×C3×C4—21no—
391C2×C3×C4—51no—
392C2×C3×C4—51no—
393C2×C3×C4—51no—
394C2×C3×C4—54no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—101no—
398C2×C3×C4—202no—
399C2×C3×C4—202no—
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4C23×D511yescharacteristic
403C2×Dic3—22no—
404C2×Dic3—102no—
405C2×Dic3—204no—
406Dic6—42no—
407Dic6—204no—
408Dic6—202no—
409C3⋊C8—22no—
410C3⋊C8—102no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5C22×#6711yescharacteristic
415C2×D5—21no—
416C2×D5—21no—
417C2×D5—41no—
418C2×D5—41no—
419C2×D5—41no—
420C2×D5#93612yes—
421C4×C5—21no—
422C4×C5—21no—
423C4×C5—41no—
424C4×C5—122no—
425C4×C5C2×#23712yes—
426Dic5—41no—
427Dic5—122no—
428Dic5#93612yes—
429Dic5#94912yes—
430Dic5#95112yes—
431#41—104no—
432#41—104no—
433C2×Q8—51no—
434C2×Q8—61no—
435C2×Q8—302no—
436C2×Q8—301no—
437C2×Q8—604no—
438C2×Q8C2×D3×D511yescharacteristic
439C2×D4—51no—
440C2×D4—101no—
441C2×D4—101no—
442C2×D4—101no—
443C2×D4—101no—
444C2×D4C2×D3×D511yescharacteristic
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—302no—
451M16—304no—
452C2×C8—32no—
453C2×C8—152no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—101no—
457C4⋊C4—101no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—302no—
461C4⋊C4—301no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—101no—
465C22⋊C4—101no—
466C42—51no—
467C42—51no—
468C42—51no—
469C42C2×D3×D511yescharacteristic
470C3×C5#314111yescharacteristic, complemented, Hall
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—52no—
475C22×C3—101no—
476C22×C3—101no—
477C22×C3—201no—
478C22×C3—201no—
479C22×C3—201no—
480C22×C3C2×D4×D511yescharacteristic
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—41no—
484C3×C4—52no—
485C3×C4—52no—
486C3×C4—52no—
487C3×C4—201no—
488C3×C4D5×#4112yes—
489Dic3—42no—
490Dic3—202no—
491C2×C5—81no—
492C2×C5C2×#93611yescharacteristic
493C2×C5C2×#94911yescharacteristic
494C2×C5C2×#95111yescharacteristic
495D5—22no—
496D5—81no—
497C23—21no—
498C23—51no—
499C23—101no—
500Q8—22no—
501Q8—102no—
502Q8—122no—
503Q8—602no—
504Q8—604no—
505D4—22no—
506D4—102no—
507D4—202no—
508D4—202no—
509D4—202no—
510D4—202no—
511C2×C4—21no—
512C2×C4—51no—
513C2×C4—51no—
514C2×C4—51no—
515C2×C4—54no—
516C2×C4—62no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—101no—
520C2×C4—202no—
521C2×C4—202no—
522C2×C4—302no—
523C2×C4—604no—
524C2×C4D5×#6711yescharacteristic
525C2×C4D5×#6711yescharacteristic
526C2×C4C22×D3×D511yescharacteristic
527C8—62no—
528C8—302no—
529C2×C3—81no—
530C2×C3—102no—
531C2×C3—401no—
532C2×C3D5×#12411yescharacteristic
533C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
534C2×C3D5×#13711yescharacteristic
535C5#8328311yescharacteristic, complemented, Sylow
536C22—41no—
537C22—41no—
538C22—41no—
539C22—52no—
540C22—101no—
541C22—101no—
542C22—201no—
543C22—201no—
544C22—201no—
545C22C2×D5×#6711yescharacteristic
546C4—21no—
547C4—21no—
548C4—41no—
549C4—52no—
550C4—52no—
551C4—52no—
552C4—122no—
553C4—201no—
554C4—602no—
555C4D5×#23712yes—
556C3#1061341411yescharacteristic, complemented, Sylow
557C2—81no—
558C2—102no—
559C2—401no—
560C2D5×#93611yescharacteristic
561C2D5×#94911yescharacteristic
562C2D5×#95111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC3×#66002C2
hypercenter#124D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D5×#869C2semidirect
3. #11751156C2semidirect
4. C5×#5055C2semidirect
5. #11749349C2semidirect
6. #11749198C2semidirect
7. #11749102C2semidirect
8. #11748951C2semidirect
9. #11747003C2semidirect
10. #11746898C2semidirect
11. #11746893C2semidirect
104. #5055D5semidirect
470. C3×C5#3141semidirect
535. C5#83283semidirect
556. C3#10613414semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
D5×#8692
#117511562
C5×#50552
#117493492
#117491982
#117491022
#117489512
#117470032
#117468982
#117468932
#106134143
#832835