Finite Group Databasebeta

← #14430248

Subgroups — #14430248

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6773C211yesmaximal, characteristic
2#11752506C211yesmaximal, characteristic, complemented
3#11750947C211yesmaximal, characteristic, complemented
4C5×#4850C211yesmaximal, characteristic, complemented
5C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
6#11747855C212yesmaximal, complemented
7#11747780C212yesmaximal, complemented
8#11747672C212yesmaximal, complemented
9#11747642C212yesmaximal
10#11746945C211yesmaximal, characteristic, complemented
11#11746885C211yesmaximal, characteristic, complemented
12#10612838—31nomaximal, Hall
13C2×#6773C2211yescharacteristic
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C2×C3×C8×D5C2212yes—
19C3×C42×D5C2211yescharacteristic
20#91444—21no—
21C4×#1202—21no—
22#91418C2211yescharacteristic
23#91402—21no—
24C4×#1200—21no—
25#91388C2212yes—
26#91360—21no—
27#91359—21no—
28#91358C2212yes—
29#91358C2211yescharacteristic
30#91333—21no—
31Dic5×Dic6—21no—
32Dic5×Dic6C2211yescharacteristic
33C3×C5×C4⋊C8C2211yescharacteristic
34#91105C2212yes—
35#91102C2212yes—
36C5×#818C2212yes—
37C5×#816C2212yes—
38C3×#3946C2212yes—
39C3×C4⋊#168C2211yescharacteristic
40#90985C2212yes—
41#90985C2212yes—
42#90973C2212yes—
43#90969C2212yes—
44#79025—51nomaximal, Hall
45#66062—31no—
46C4×#713—31no—
47C5×#477—31no—
48#65373—31no—
49#65309—31no—
50#65180—32no—
51#65169—32no—
52#65135—31no—
53D5×C4⋊C8D311yescharacteristic, complemented
54#65093—32no—
55#65085—32no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×Dic30—21no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×C4×D5D411yescharacteristic
62C2×C3×C4×D5D411yescharacteristic
63C2×C3×C4×D5C2311yescharacteristic
64C2×#1202—21no—
65C2×#1200—21no—
66C2×#1200—21no—
67#6773—22no—
68#6773Q814yescomplemented
69C2×C3×C5×C8C2312yes—
70C3×C42×C5C2311yescharacteristic
71#6714—21no—
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74C4⋊Dic15C2311yescharacteristic
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C5×Dic3⋊C4—21no—
79C4×C5×Dic3—21no—
80C3×C4×Dic5D411yescharacteristic
81C3×C4×Dic5D411yescharacteristic
82C3×C4×Dic5C2311yescharacteristic
83C2×C3×#168C2312yes—
84C3×C8×D5—24no—
85Dic3⋊Dic5—21no—
86Dic3⋊Dic5—22no—
87#6669—22no—
88#6667—21no—
89#6665—21no—
90#6665—22no—
91Dic3×Dic5—21no—
92Dic3×Dic5—21no—
93Dic3×Dic5—22no—
94C4×#235—51no—
95#5470—51no—
96C2×C3×C4⋊C8—51no—
97#5113—52no—
98#5106—52no—
99#4851—51no—
100#4850D511yescharacteristic, complemented
101#4847—52no—
102#4846—51no—
103#4842—51no—
104#4829—52no—
105C2×#713—31no—
106C5×C4⋊Q8—31no—
107C4×C5×Q8—31no—
108#4092—61no—
109Q8×Dic5—31no—
110Q8×Dic5—61no—
111C2×C8×D5C2×D312yes—
112#4043—61no—
113#4039—31no—
114#4039—61no—
115#4038—32no—
116#4038—31no—
117#4038—61no—
118#4036—32no—
119#4033—61no—
120C4×D20—31no—
121C4×D20—61no—
122C42×D5—61no—
123C42×D5C2×D311yescharacteristic
124#4015—31no—
125C5×#107—32no—
126C5×C4⋊C8C2×D311yescharacteristic
127C5×#103—32no—
128#3967—32no—
129#3953—32no—
130#3950—32no—
131#3946C2×D312yes—
132#3941—32no—
133#3940—32no—
134#3940—32no—
135C4⋊#168C2×D311yescharacteristic
136#3076—151noSylow
137C22×D15—21no—
138C22×C3×D5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—22no—
144D60—21no—
145D60C2×Q812yes—
146C4×D15—42no—
147Dic30—42no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C5×Dic6—21no—
152C5×Dic6—42no—
153C5×Dic6C2×Q812yes—
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C3×C4×D5—22no—
158C3×C4×D5—41no—
159C3×C4×D5C2×Q812yes—
160C3×C4×D5#4112yes—
161#1202—24no—
162#1200—24no—
163#1200—42no—
164C3×C5×C8—22no—
165C3×#168—22no—
166C2×#235—51no—
167C22×C3×C8—52no—
168C2×C3×C42—51no—
169C4×#67—101no—
170C4×#67—101no—
171#926—52no—
172#926—51no—
173#924—101no—
174#924—101no—
175C4×D12—51no—
176C4×D12—51no—
177#872—101no—
178C42×D3—101no—
179#870—52no—
180#869—51no—
181#869C2×D511yescharacteristic
182C4×Dic6—51no—
183C4×Dic6—101no—
184C4×Dic6—101no—
185C4×Dic6C2×D511yescharacteristic
186C3×C4⋊C8—52no—
187C3×C4⋊C8—51no—
188C3×C4⋊C8C2×D511yescharacteristic
189#821—52no—
190#821—52no—
191#818—52no—
192#818C2×D512yes—
193#817—52no—
194#817—52no—
195#816—52no—
196#816C2×D512yes—
197C2×C5×Q8—31no—
198C2×C5×Q8—61no—
199#713—34no—
200#713—62no—
201C2×D20—31no—
202C2×D20—61no—
203C2×C4×D5—61no—
204C2×C4×D5—61no—
205C2×C4×D5—61no—
206C2×C4×D5D1211yescharacteristic
207C2×C4×D5D1211yescharacteristic
208C2×C4×D5C22×D311yescharacteristic
209C2×Dic10—61no—
210C2×C5×C8C22×D312yes—
211C5×C4⋊C4—31no—
212C5×C4⋊C4—32no—
213C5×C4⋊C4—61no—
214C5×C4⋊C4—61no—
215C42×C5—61no—
216C42×C5C22×D311yescharacteristic
217#685—61no—
218#685—62no—
219#685—61no—
220#685—61no—
221C4⋊Dic5—31no—
222C4⋊Dic5—32no—
223C4⋊Dic5—61no—
224C4⋊Dic5—61no—
225C4⋊Dic5—62no—
226#683—62no—
227C4×Dic5—61no—
228C4×Dic5—61no—
229C4×Dic5—62no—
230C4×Dic5D1211yescharacteristic
231C4×Dic5D1211yescharacteristic
232C4×Dic5C22×D311yescharacteristic
233C2×#168C22×D312yes—
234C8×D5—24no—
235#533—151no—
236C4×#41—151no—
237#479—152no—
238#478—152no—
239#477—31no—
240#476—151no—
241#475—151no—
242#474—151no—
243#427—152no—
244C2×C4⋊C8—51no—
245#416—152no—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—22no—
248C2×D15—41no—
249C2×D15—41no—
250C2×C3×D5—21no—
251C2×C3×D5—21no—
252C2×C3×D5C22⋊Q812yes—
253C3×C4×C5—21no—
254C3×C4×C5#13512yes—
255C3×C4×C5C22×Q811yescharacteristic
256C3×C4×C5C2×#4111yescharacteristic
257Dic15—42no—
258Dic15—41no—
259C3×Dic5—21no—
260C3×Dic5—21no—
261C3×Dic5C22⋊Q812yes—
262C5×Dic3—22no—
263C5×Dic3—41no—
264C5×Dic3—42no—
265C22×C3×C4—51no—
266C22×C3×C4—51no—
267C22×C3×C4—51no—
268C2×#67—101no—
269#235—54no—
270#235—102no—
271C2×D12—51no—
272C2×C4×D3—101no—
273C2×C4×D3—101no—
274C2×C4×D3—101no—
275C2×Dic6—21no—
276C2×Dic6—101no—
277C2×Dic6C22×D511yescharacteristic
278C2×C3×C8—52no—
279C2×C3×C8—104no—
280C2×C3×C8C22×D512yes—
281C3×C42—51no—
282C3×C42—51no—
283C3×C42—51no—
284C3×C42C22×D511yescharacteristic
285#217—102no—
286#217—101no—
287(C2×D3)⋊C4—101no—
288(C2×D3)⋊C4—101no—
289C4⋊Dic3—21no—
290C4⋊Dic3—52no—
291C4⋊Dic3—51no—
292C4⋊Dic3—101no—
293C4⋊Dic3C22×D512yes—
294C4⋊Dic3C22×D511yescharacteristic
295Dic3⋊C4—21no—
296Dic3⋊C4—102no—
297Dic3⋊C4—101no—
298Dic3⋊C4—102no—
299C4×Dic3—21no—
300C4×Dic3—101no—
301C4×Dic3—102no—
302C4×Dic3—101no—
303C22×D5—61no—
304C22×D5C2×D1211yescharacteristic
305C5×Q8—32no—
306C5×Q8—61no—
307C5×Q8—122no—
308C2×C4×C5—61no—
309C2×C4×C5—62no—
310C2×C4×C5—61no—
311C2×C4×C5C2×D1211yescharacteristic
312C2×C4×C5C2×D1211yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C2×Dic5—61no—
315C2×Dic5—62no—
316C2×Dic5C2×D1211yescharacteristic
317C2×Dic5C2×D1211yescharacteristic
318C2×Dic5C2×D1211yescharacteristic
319D20—32no—
320D20—64no—
321D20—61no—
322C4×D5—22no—
323C4×D5—41no—
324C4×D5—64no—
325C4×D5—122no—
326C4×D5—122no—
327C4×D5#23712yes—
328C4×D5D3×Q812yes—
329Dic10—122no—
330C5×C8—22no—
331#168—22no—
332C2×#41—151no—
333C22×C8—52no—
334C4⋊Q8—31no—
335C4⋊Q8—151no—
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—31no—
340C4×Q8—151no—
341C4×Q8—301no—
342C4×Q8—301no—
343C4×D4—151no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—151no—
348#117—152no—
349#117—301no—
350C2×C42—51no—
351C2×C42—301no—
352#107—32no—
353#107—152no—
354#106—152no—
355#106—152no—
356C4⋊C8—52no—
357C4⋊C8—51no—
358C4⋊C8D3×D511yescharacteristic
359#103—32no—
360#103—152no—
361#102—152no—
362#102—152no—
363C2×C3×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366D15—42no—
367C3×D5—22no—
368C23×C3—51no—
369C22×D3—101no—
370C2×C3×C4—51no—
371C2×C3×C4—52no—
372C2×C3×C4—52no—
373C2×C3×C4—51no—
374C2×C3×C4—51no—
375C2×C3×C4—102no—
376C2×C3×C4—201no—
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380#67—104no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—101no—
385C2×Dic3—102no—
386D12—52no—
387D12—101no—
388C4×D3—104no—
389C4×D3—202no—
390C4×D3—202no—
391Dic6—21no—
392Dic6—42no—
393Dic6—202no—
394Dic6Q8×D512yes—
395C3×C8—22no—
396C3×C8—102no—
397C22×C5C22×D1211yescharacteristic
398C2×D5—21no—
399C2×D5—21no—
400C2×D5—62no—
401C2×D5—121no—
402C2×D5—121no—
403C2×D5#89712yes—
404C4×C5—21no—
405C4×C5—62no—
406C4×C5—121no—
407C4×C5—122no—
408C4×C5#90412yes—
409C4×C5C2×#23711yescharacteristic
410C4×C5C2×D3×Q811yescharacteristic
411Dic5—21no—
412Dic5—21no—
413Dic5—122no—
414Dic5—121no—
415Dic5#89712yes—
416#41—154no—
417#41—302no—
418C2×Q8—31no—
419C2×Q8—61no—
420C2×Q8—301no—
421C2×D4—151no—
422C2×D4—301no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—301no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—52no—
430C2×C8—104no—
431C2×C8C2×D3×D512yes—
432C4⋊C4—32no—
433C4⋊C4—31no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—152no—
437C4⋊C4—151no—
438C4⋊C4—301no—
439C4⋊C4—302no—
440C4⋊C4—302no—
441C4⋊C4—301no—
442C22⋊C4—301no—
443C22⋊C4—301no—
444C22⋊C4—302no—
445C22⋊C4—301no—
446C42—51no—
447C42—51no—
448C42—51no—
449C42—61no—
450C42—301no—
451C42—301no—
452C42—302no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—52no—
456C22×C3—101no—
457C22×C3—101no—
458C22×C3C2×D4×D511yescharacteristic
459C2×D3—102no—
460C2×D3—201no—
461C2×D3—201no—
462C3×C4—21no—
463C3×C4—52no—
464C3×C4—101no—
465C3×C4—101no—
466C3×C4#406512yes—
467C3×C4C2×Q8×D511yescharacteristic
468C3×C4D5×#4111yescharacteristic
469Dic3—22no—
470Dic3—42no—
471Dic3—41no—
472Dic3—202no—
473Dic3—201no—
474C2×C5C2×#89711yescharacteristic
475C2×C5C2×#90411yescharacteristic
476C2×C5#574811yescharacteristic
477D5—22no—
478D5—122no—
479C23—51no—
480C23—301no—
481Q8—32no—
482Q8—61no—
483Q8—122no—
484Q8—602no—
485D4—152no—
486D4—304no—
487D4—301no—
488C2×C4—51no—
489C2×C4—52no—
490C2×C4—52no—
491C2×C4—51no—
492C2×C4—51no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—62no—
496C2×C4—102no—
497C2×C4—201no—
498C2×C4—304no—
499C2×C4—301no—
500C2×C4—302no—
501C2×C4—602no—
502C2×C4—602no—
503C2×C4D5×D1211yescharacteristic
504C2×C4D5×D1211yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—22no—
507C8—102no—
508C2×C3—102no—
509C2×C3D5×C22⋊Q811yescharacteristic
510C2×C3C2×#406511yescharacteristic
511C2×C3#6610711yescharacteristic
512D3—202no—
513C5#7902511yescharacteristic, complemented, Sylow
514C22—52no—
515C22—101no—
516C22—101no—
517C22—302no—
518C22—601no—
519C22—601no—
520C22C2×D5×D1211yescharacteristic
521C4—21no—
522C4—52no—
523C4—62no—
524C4—101no—
525C4—101no—
526C4—121no—
527C4—122no—
528C4—601no—
529C4—602no—
530C4#9127112yes—
531C4D5×#23711yescharacteristic
532C4D3×Q8×D511yescharacteristic
533C3#1061283811yescharacteristic, complemented, Sylow
534C2—102no—
535C2—602no—
536C2D5×#89711yescharacteristic
537C2C2×#9127111yescharacteristic
538C2#1175402211yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6773C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752506C2semidirect
3. #11750947C2semidirect
4. C5×#4850C2semidirect
5. C3×D5×C4⋊C8C2semidirect
6. #11747855C2semidirect
7. #11747780C2semidirect
8. #11747672C2semidirect
10. #11746945C2semidirect
11. #11746885C2semidirect
53. D5×C4⋊C8D3semidirect
68. #6773Q8semidirect
100. #4850D5semidirect
454. C3×C5#3076semidirect
513. C5#79025semidirect
533. C3#10612838semidirect

Maximal subgroups

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

subgroupindex
C4×#67732
#117525062
#117509472
C5×#48502
C3×D5×C4⋊C82
#117478552
#117477802
#117476722
#117476422
#117469452
#117468852
#106128383
#790255