Finite Group Databasebeta

← #14438642

Subgroups — #14438642

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
1C5×#5668C211yesmaximal, characteristic
2D3×#4015C211yesmaximal, characteristic, complemented
3#11751156C211yesmaximal, characteristic, complemented
4C3×#65344C211yesmaximal, characteristic, complemented
5#11749201C212yesmaximal, complemented
6#11749187C212yesmaximal, complemented
7#11748955C212yesmaximal, complemented
8#11748941C212yesmaximal, complemented
9#11747005C211yesmaximal, characteristic, complemented
10#11746909C211yesmaximal, characteristic, complemented
11#11746904C211yesmaximal, characteristic, complemented
12#10615014—31nomaximal, Hall
13C2×C5×#239C2211yescharacteristic
14C2×C5×#237C2211yescharacteristic
15C2×D3×Dic10—21no—
16C3×C5×#124C2211yescharacteristic
17#91758C2211yescharacteristic
18C5×#944C2211yescharacteristic
19C5×#940C2211yescharacteristic
20C5×#884—21no—
21C5×#884—21no—
22C5×#67⋊C4—21no—
23C5×#67⋊C4—21no—
24C5×#875C2211yescharacteristic
25C42×C5×D3C2211yescharacteristic
26C3×#4015C2211yescharacteristic
27#91469—21no—
28#91469C2212yes—
29D3×C4⋊Dic5—21no—
30D3×C4⋊Dic5C2212yes—
31#91389—21no—
32C2×#6650C2212yes—
33#91119C2212yes—
34#91116C2212yes—
35#91087C2211yescharacteristic
36C3×#3967C2212yes—
37C3×#3964C2212yes—
38C3×#3935C2211yescharacteristic
39#90973C2212yes—
40#90972C2212yes—
41#90967C2212yes—
42#90966C2212yes—
43Dic3×#168C2212yes—
44#81683—51nomaximal, Hall
45C5×#532—31no—
46C2×#4015—31no—
47#65521—32no—
48#65521—32no—
49#65370—32no—
50#65359—32no—
51#65344—31no—
52#65344—31no—
53#65344—31no—
54#65344D311yescharacteristic, complemented
55C4×#681—31no—
56C2×C3×C5×Q8C2311yescharacteristic
57C2×C3×C5×D4C2311yescharacteristic
58C2×Dic30—21no—
59C2×C5×#67—21no—
60C2×C5×#67—21no—
61C2×C5×#67—21no—
62C22×C5×Dic3—21no—
63C5×#239—24no—
64C5×#237—24no—
65C2×C5×D12—21no—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C4×C5×D3D411yescharacteristic
69C2×C4×C5×D3D411yescharacteristic
70C2×C4×C5×D3C2311yescharacteristic
71C2×C5×Dic6C2311yescharacteristic
72C2×C3×Dic10—21no—
73C2×#1204—22no—
74C2×D3×Dic5—22no—
75D3×Dic10—44no—
76C3×C5×C22⋊C4—21no—
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79C4⋊Dic15—21no—
80C4⋊Dic15C2312yes—
81C2×C3⋊#168C2312yes—
82C5×(C2×D3)⋊C4—21no—
83C5×(C2×D3)⋊C4—21no—
84C5×Dic3⋊C4—21no—
85C5×Dic3⋊C4—21no—
86C4×C5×Dic3D411yescharacteristic
87C4×C5×Dic3D411yescharacteristic
88C4×C5×Dic3C2311yescharacteristic
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2312yes—
91C2×C3×#168C2312yes—
92Dic3⋊Dic5—22no—
93Dic3⋊Dic5—22no—
94#6650—24no—
95D3×C4⋊Q8—51no—
96#5668D511yescharacteristic
97C3×#489—51no—
98#5089—51no—
99#5055—51no—
100#4803—52no—
101#4792—52no—
102#4771—52no—
103#4760—52no—
104#4714—51no—
105#4707—51no—
106C2×C5×#41—31no—
107C2×C5×#41—31no—
108C22×Dic10—61no—
109C5×C4⋊Q8—31no—
110C5×#127—31no—
111C5×#124—31no—
112C5×#124C2×D311yescharacteristic
113C5×#121—61no—
114C5×#121—61no—
115C4×C5×D4—61no—
116C4×C5×D4—61no—
117C2×C42×C5—31no—
118C2×C4⋊Dic5—32no—
119C2×C4⋊Dic5—61no—
120C2×#681—32no—
121#4015—31no—
122#4015—32no—
123#4015—61no—
124#4015—61no—
125#4015C2×D311yescharacteristic
126#3967—32no—
127#3967—32no—
128#3967—32no—
129#3967C2×D312yes—
130#3964—32no—
131#3964—32no—
132#3964—32no—
133#3964C2×D312yes—
134#3935—31no—
135#3935C2×D311yescharacteristic
136C4×#168—32no—
137#3141—151noSylow
138C23×C3×C5—21no—
139C22×C5×D3—21no—
140C22×C5×D3C2×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—
149C5×#67—42no—
150C5×#67—42no—
151C5×#67—42no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—42no—
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C2×C5×Dic3C2×D411yescharacteristic
157C5×D12—22no—
158C5×D12—42no—
159C4×C5×D3—22no—
160C4×C5×D3—22no—
161C4×C5×D3—42no—
162C4×C5×D3#4114yes—
163C5×Dic6—22no—
164C2×C3×Dic5—22no—
165C3×Dic10—42no—
166#1204—44no—
167D3×Dic5—44no—
168C3⋊#168—22no—
169C3×#168—22no—
170C2×#239C2×D511yescharacteristic
171C2×D3×Q8—101no—
172C2×#237C2×D511yescharacteristic
173C3×C4⋊Q8—51no—
174C3×#124C2×D511yescharacteristic
175#944—101no—
176#944C2×D511yescharacteristic
177#940C2×D511yescharacteristic
178C2×ΓL(1,𝔽25)—52no—
179D3×C4⋊C4—52no—
180D3×C4⋊C4—101no—
181#888—52no—
182#888—101no—
183#884—21no—
184#884—21no—
185#67⋊C4—21no—
186#67⋊C4—21no—
187#875C2×D511yescharacteristic
188C42×D3C2×D511yescharacteristic
189#869—51no—
190C3×#103—52no—
191C3×#102—52no—
192C3×#97—51no—
193#835—52no—
194#832—52no—
195#821—52no—
196#816—52no—
197C8×Dic3—52no—
198#810—52no—
199#809—52no—
200#803—51no—
201C5×#41—64no—
202C5×#41—64no—
203C2×C5×Q8—31no—
204C2×C5×Q8C22×D311yescharacteristic
205C2×C5×D4—31no—
206C2×C5×D4—61no—
207C2×C5×D4—61no—
208C2×C5×D4—61no—
209C2×C5×D4—61no—
210C2×C5×D4C22×D311yescharacteristic
211C22×C4×C5—31no—
212C22×C4×C5—31no—
213C22×C4×C5—31no—
214C22×C4×C5—61no—
215C22×C4×C5—61no—
216C22×Dic5—62no—
217C2×Dic10—21no—
218C2×Dic10—62no—
219C2×Dic10—61no—
220C2×Dic10—124no—
221C5×C4⋊C4—61no—
222C5×C4⋊C4—61no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—61no—
226C5×C22⋊C4—61no—
227C42×C5—31no—
228C42×C5—31no—
229C42×C5—31no—
230C42×C5C22×D311yescharacteristic
231C4⋊Dic5—21no—
232C4⋊Dic5—32no—
233C4⋊Dic5—62no—
234C4⋊Dic5—62no—
235C4⋊Dic5—61no—
236C4⋊Dic5C22×D312yes—
237#681—64no—
238C2×#168—32no—
239C2×#168C22×D312yes—
240#532—31no—
241C2×C4⋊Q8—151no—
242#489—51no—
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×C5×D3—21no—
256C2×C5×D3—21no—
257C2×C5×D3—41no—
258C2×C5×D3—41no—
259C2×C5×D3—41no—
260C2×C5×D3#12412yes—
261C3×C4×C5—21no—
262C3×C4×C5—21no—
263C3×C4×C5—41no—
264C3×C4×C5C2×#4112yes—
265Dic15—42no—
266C3×Dic5—42no—
267C5×Dic3—41no—
268C5×Dic3#12412yes—
269C5×Dic3AGL(1,ℤ/8)12yes—
270C5×Dic3#13712yes—
271C2×C3×Q8—101no—
272C2×C3×Q8C22×D511yescharacteristic
273C2×C3×D4C22×D511yescharacteristic
274C2×#67—21no—
275C2×#67—21no—
276C2×#67—21no—
277C22×Dic3—21no—
278#239—24no—
279D3×Q8—204no—
280#237—24no—
281C2×D12—21no—
282C2×D12C22×D511yescharacteristic
283C2×C4×D3—21no—
284C2×C4×D3—102no—
285C2×C4×D3C22⋊D511yescharacteristic
286C2×C4×D3C22⋊D511yescharacteristic
287C2×C4×D3C22×D511yescharacteristic
288C2×Dic6—101no—
289C2×Dic6—102no—
290C2×Dic6C22×D511yescharacteristic
291C2×C3×C8—52no—
292C3×C4⋊C4—52no—
293C3×C4⋊C4—101no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—21no—
296C3×C42C22×D511yescharacteristic
297(C2×D3)⋊C4—21no—
298(C2×D3)⋊C4—21no—
299C4⋊Dic3—52no—
300C4⋊Dic3—101no—
301Dic3⋊C4—21no—
302Dic3⋊C4—21no—
303Dic3⋊C4—102no—
304Dic3⋊C4—102no—
305C4×Dic3C22⋊D511yescharacteristic
306C4×Dic3C22⋊D511yescharacteristic
307C4×Dic3C22×D511yescharacteristic
308C2×C3⋊C8—52no—
309ΓL(1,𝔽25)—104no—
310C23×C5—21no—
311C23×C5—31no—
312C23×C5—61no—
313C5×Q8—22no—
314C5×Q8—62no—
315C5×D4—22no—
316C5×D4—62no—
317C5×D4—122no—
318C5×D4—122no—
319C5×D4—122no—
320C5×D4—122no—
321C2×C4×C5—21no—
322C2×C4×C5—31no—
323C2×C4×C5—31no—
324C2×C4×C5—31no—
325C2×C4×C5—34no—
326C2×C4×C5—62no—
327C2×C4×C5—62no—
328C2×C4×C5—61no—
329C2×C4×C5—122no—
330C2×C4×C5—122no—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5C23×D311yescharacteristic
334C2×Dic5—22no—
335C2×Dic5—62no—
336C2×Dic5—124no—
337Dic10—42no—
338Dic10—124no—
339Dic10—122no—
340#168—22no—
341#168—62no—
342C2×#41—31no—
343C2×#41—31no—
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—31no—
353#124—31no—
354#124D3×D511yescharacteristic
355#121—61no—
356#121—61no—
357C4×D4—61no—
358C4×D4—61no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—301no—
361C2×C42—31no—
362#103—52no—
363#103—152no—
364#103—152no—
365#103—152no—
366#102—52no—
367#102—152no—
368#102—152no—
369#102—152no—
370#97—51no—
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
377C5×D3—22no—
378C5×D3—81no—
379C23×C3—21no—
380C22×D3—21no—
381C22×D3C2×C22⋊D511yescharacteristic
382C3×Q8—22no—
383C3×Q8—202no—
384C3×D4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—102no—
387C2×C3×C4C2×C22⋊D511yescharacteristic
388C2×C3×C4C2×C22⋊D511yescharacteristic
389C2×C3×C4C23×D511yescharacteristic
390#67—42no—
391#67—42no—
392#67—42no—
393C2×Dic3—21no—
394C2×Dic3—42no—
395C2×Dic3—102no—
396C2×Dic3C2×C22⋊D511yescharacteristic
397C2×Dic3C2×C22⋊D511yescharacteristic
398C2×Dic3C2×C22⋊D511yescharacteristic
399D12—22no—
400D12—42no—
401C4×D3—22no—
402C4×D3—22no—
403C4×D3—42no—
404C4×D3—204no—
405C4×D3#71114yes—
406Dic6—22no—
407Dic6—202no—
408Dic6—204no—
409C3×C8—102no—
410C3⋊C8—102no—
411C22×C5—32no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5—61no—
416C22×C5—61no—
417C22×C5—121no—
418C22×C5—121no—
419C22×C5—121no—
420C22×C5C2×D3×D411yescharacteristic
421C4×C5—21no—
422C4×C5—21no—
423C4×C5—32no—
424C4×C5—32no—
425C4×C5—32no—
426C4×C5—41no—
427C4×C5—121no—
428C4×C5D3×#4112yes—
429Dic5—42no—
430Dic5—122no—
431#41—64no—
432#41—64no—
433C2×Q8—31no—
434C2×Q8—101no—
435C2×Q8—302no—
436C2×Q8—301no—
437C2×Q8—604no—
438C2×Q8C2×D3×D511yescharacteristic
439C2×D4—31no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4C2×D3×D511yescharacteristic
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—302no—
451M16—304no—
452C2×C8—52no—
453C2×C8—152no—
454C4⋊C4—52no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—101no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—302no—
461C4⋊C4—301no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—61no—
465C22⋊C4—61no—
466C42—31no—
467C42—31no—
468C42—31no—
469C42C2×D3×D511yescharacteristic
470C3×C5#314111yescharacteristic, complemented, Hall
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3C22×C22⋊D511yescharacteristic
475C2×D3—21no—
476C2×D3—21no—
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3#408212yes—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—41no—
484C3×C4—202no—
485C3×C4C2×#71112yes—
486Dic3—41no—
487Dic3—202no—
488Dic3#408212yes—
489Dic3#409512yes—
490Dic3#409712yes—
491C2×C5—62no—
492C2×C5—81no—
493C2×C5—241no—
494C2×C5D3×#12411yescharacteristic
495C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
496C2×C5D3×#13711yescharacteristic
497C23—21no—
498C23—31no—
499C23—61no—
500Q8—22no—
501Q8—62no—
502Q8—202no—
503Q8—602no—
504Q8—604no—
505D4—22no—
506D4—62no—
507D4—122no—
508D4—122no—
509D4—122no—
510D4—122no—
511C2×C4—21no—
512C2×C4—31no—
513C2×C4—31no—
514C2×C4—31no—
515C2×C4—34no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—61no—
519C2×C4—102no—
520C2×C4—122no—
521C2×C4—122no—
522C2×C4—302no—
523C2×C4—604no—
524C2×C4D3×C22⋊D511yescharacteristic
525C2×C4D3×C22⋊D511yescharacteristic
526C2×C4C22×D3×D511yescharacteristic
527C8—102no—
528C8—302no—
529C2×C3—81no—
530C2×C3C2×#408211yescharacteristic
531C2×C3C2×#409511yescharacteristic
532C2×C3C2×#409711yescharacteristic
533D3—22no—
534D3—81no—
535C5#8168311yescharacteristic, complemented, Sylow
536C22—32no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—61no—
541C22—61no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22C2×D3×C22⋊D511yescharacteristic
546C4—21no—
547C4—21no—
548C4—32no—
549C4—32no—
550C4—32no—
551C4—41no—
552C4—121no—
553C4—202no—
554C4—602no—
555C4D3×#71112yes—
556C3#1061501411yescharacteristic, complemented, Sylow
557C2—62no—
558C2—81no—
559C2—241no—
560C2D3×#408211yescharacteristic
561C2D3×#409511yescharacteristic
562C2D3×#409711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC5×#5668C2
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. D3×#4015C2semidirect
3. #11751156C2semidirect
4. C3×#65344C2semidirect
5. #11749201C2semidirect
6. #11749187C2semidirect
7. #11748955C2semidirect
8. #11748941C2semidirect
9. #11747005C2semidirect
10. #11746909C2semidirect
11. #11746904C2semidirect
54. #65344D3semidirect
470. C3×C5#3141semidirect
535. C5#81683semidirect
556. C3#10615014semidirect

Maximal subgroups

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

subgroupindex
C5×#56682
D3×#40152
#117511562
C3×#653442
#117492012
#117491872
#117489552
#117489412
#117470052
#117469092
#117469042
#106150143
#816835