Finite Group Databasebeta

← #14430267

Subgroups — #14430267

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
1C3×C4×#711C211yesmaximal, characteristic
2#11752506C211yesmaximal, characteristic, complemented
3#11751109C211yesmaximal, characteristic, complemented
4C5×#5007C211yesmaximal, characteristic, complemented
5#11749086C212yesmaximal, complemented
6#11748961C212yesmaximal
7#11747432C212yesmaximal, complemented
8#11747391C212yesmaximal, complemented
9D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#11746918C211yesmaximal, characteristic, complemented
11#11746916C211yesmaximal, characteristic, complemented
12#10612695—31nomaximal, Hall
13C2×C3×#711C2211yescharacteristic
14C3×C4×C5×D4C2211yescharacteristic
15#91758C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×D4×Dic5C2211yescharacteristic
18C3×C4×C22⋊D5—21no—
19C2×C3×C4×Dic5—21no—
20C3×#4038C2211yescharacteristic
21C3×#4033C2211yescharacteristic
22C3×#4027—21no—
23C3×#4023—21no—
24C3×C42×D5C2211yescharacteristic
25C3×C4×Dic10C2211yescharacteristic
26#91388C2212yes—
27#91360—21no—
28#91359—21no—
29#91358C2212yes—
30#91333—21no—
31Dic5×Dic6—21no—
32C2×D5×C3⋊C8C2212yes—
33#91116C2212yes—
34#91092C2212yes—
35C4⋊(C3⋊#168)C2211yescharacteristic
36C5×#832C2212yes—
37C5×#807C2212yes—
38C5×C4⋊(C3⋊C8)C2211yescharacteristic
39#90990C2212yes—
40#90986C2212yes—
41#90982C2212yes—
42#90971C2212yes—
43#90970C2212yes—
44#82507—51nomaximal, Hall
45#66062—31no—
46C4×#711D311yescharacteristic
47C5×#474—31no—
48#65383—31no—
49#65297—31no—
50#65169—32no—
51#65166—32no—
52#65139—31no—
53D5×C4⋊C8—31no—
54#65061—32no—
55#65055—32no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C2×Dic30—21no—
59C2×C5×Dic6—21no—
60C2×C3×C22⋊D5—21no—
61C22×C3×Dic5—21no—
62C22×C3×Dic5—21no—
63C3×#711—22no—
64C3×#711Q814yescomplemented
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5D411yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×C3×Dic10C2311yescharacteristic
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C22⋊C4—21no—
71C3×C42×C5C2311yescharacteristic
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74C2×C3⋊#168C2312yes—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C2×C5×C3⋊C8C2312yes—
78C3×C22⋊Dic5—21no—
79C3×#685—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×#683—21no—
82C3×#683—21no—
83C3×C4×Dic5—21no—
84C3×C4×Dic5—21no—
85C3×C4×Dic5—21no—
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5D411yescharacteristic
88C3×C4×Dic5C2311yescharacteristic
89Dic3⋊Dic5—22no—
90#6669—22no—
91#6665—22no—
92Dic3×Dic5—22no—
93D5×C3⋊C8—24no—
94C3×C4×#41—51no—
95#5470—51no—
96#5233—52no—
97#5022—52no—
98#5021—51no—
99#5020—51no—
100#5009—52no—
101#5008—51no—
102#5007D511yescharacteristic, complemented
103#4998—52no—
104C2×C4⋊(C3⋊C8)—51no—
105C2×#711C2×D311yescharacteristic
106C5×C4⋊Q8—31no—
107C4×C5×D4C2×D311yescharacteristic
108#4092—61no—
109Q8×Dic5—61no—
110D4×Dic5C2×D311yescharacteristic
111C4×C22⋊D5—21no—
112C2×C4×Dic5—21no—
113C2×C8×D5—32no—
114#4043—61no—
115#4038—32no—
116#4038C2×D311yescharacteristic
117#4036—32no—
118#4033—61no—
119#4033C2×D311yescharacteristic
120#4027—21no—
121#4023—21no—
122C42×D5C2×D311yescharacteristic
123#4015—31no—
124C4×Dic10C2×D311yescharacteristic
125C5×#107—32no—
126C5×C4⋊C8—31no—
127C5×#102—32no—
128#3964—32no—
129#3950—32no—
130#3948—32no—
131#3946—32no—
132#3942—32no—
133#3940—32no—
134#3940—32no—
135C4⋊#168—31no—
136#3076—151noSylow
137C23×C3×C5—21no—
138C22×C3×D5C2×D411yescharacteristic
139C3×C5×D4—21no—
140C3×C5×D4C2×Q812yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147Dic30—42no—
148C2×C5×Dic3—22no—
149C5×Dic6—42no—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—42no—
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C3×C4×D5—22no—
159C3×C4×D5—41no—
160C3×C4×D5C2×Q812yes—
161C3×C4×D5#4112yes—
162C3×Dic10—21no—
163C3×Dic10C2×Q812yes—
164C3⋊#168—22no—
165C5×C3⋊C8—22no—
166C2×C3×#41—51no—
167C3×C4×Q8—51no—
168C3×C4×Q8—51no—
169C3×C4×D4—51no—
170C3×C4×D4—101no—
171C3×C4×D4—101no—
172C3×C4×D4C2×D511yescharacteristic
173C3×#117—51no—
174C3×#117—101no—
175C2×C3×C42—51no—
176C2×C3×C42—101no—
177#926—52no—
178#924—101no—
179#924—101no—
180C22×C3⋊C8—52no—
181#870—52no—
182#869—51no—
183#869C2×D511yescharacteristic
184C4×Dic6—101no—
185C4×Dic6—101no—
186#835—52no—
187#835—52no—
188#832—52no—
189#832C2×D512yes—
190#808—52no—
191#808—52no—
192#807—52no—
193#807C2×D512yes—
194C4⋊(C3⋊C8)—51no—
195C4⋊(C3⋊C8)—52no—
196C4⋊(C3⋊C8)C2×D511yescharacteristic
197C2×C5×Q8—61no—
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C2×C22⋊D5—21no—
201C22×Dic5—21no—
202C22×Dic5—21no—
203#711—22no—
204#711Dic614yescomplemented
205C2×C4×D5#6711yescharacteristic
206C2×C4×D5#6711yescharacteristic
207C2×C4×D5C22×D311yescharacteristic
208C2×Dic10—61no—
209C2×Dic10C22×D311yescharacteristic
210C2×C5×C8—32no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—61no—
213C5×C4⋊C4C22×D311yescharacteristic
214C5×C22⋊C4—21no—
215C42×C5C22×D311yescharacteristic
216C22⋊Dic5—21no—
217#685—21no—
218#685—62no—
219C4⋊Dic5—32no—
220C4⋊Dic5—61no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D311yescharacteristic
223#683—21no—
224#683—21no—
225#683—62no—
226C4×Dic5—21no—
227C4×Dic5—21no—
228C4×Dic5—21no—
229C4×Dic5—62no—
230C4×Dic5#6711yescharacteristic
231C4×Dic5#6711yescharacteristic
232C4×Dic5C22×D311yescharacteristic
233C2×#168—32no—
234C8×D5—64no—
235#533—151no—
236C4×#41—51no—
237#479—152no—
238#478—152no—
239#477—151no—
240#476—151no—
241#475—151no—
242#474—31no—
243#427—152no—
244C2×C4⋊C8—151no—
245#416—152no—
246C22×C3×C5—22no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5C22×D411yescharacteristic
250C2×C3×D5—21no—
251C2×C3×D5—21no—
252C2×C3×D5C22⋊Q812yes—
253C3×C4×C5—21no—
254C3×C4×C5—41no—
255C3×C4×C5#13512yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—42no—
259C3×Dic5—22no—
260C3×Dic5—21no—
261C3×Dic5—21no—
262C3×Dic5—41no—
263C3×Dic5C22⋊Q812yes—
264C5×Dic3—42no—
265C3×#41—54no—
266C3×#41—102no—
267C2×C3×Q8—51no—
268C2×C3×D4—101no—
269C2×C3×D4C22×D511yescharacteristic
270C22×C3×C4—21no—
271C22×C3×C4—51no—
272C22×C3×C4—51no—
273C22×C3×C4—51no—
274C22×C3×C4—101no—
275C22×C3×C4—101no—
276C2×Dic6—21no—
277C2×Dic6—101no—
278C3×C4⋊C4—51no—
279C3×C4⋊C4—101no—
280C3×C4⋊C4—101no—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C22⋊C4—21no—
283C3×C22⋊C4—101no—
284C3×C22⋊C4—101no—
285C3×C42—51no—
286C3×C42—51no—
287C3×C42—51no—
288C3×C42—101no—
289C3×C42—101no—
290C3×C42—101no—
291C3×C42C22×D511yescharacteristic
292#217—102no—
293C4⋊Dic3—21no—
294C4⋊Dic3—52no—
295C4⋊Dic3—101no—
296C4⋊Dic3C22×D512yes—
297Dic3⋊C4—102no—
298Dic3⋊C4—102no—
299C4×Dic3—102no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—104no—
302C2×C3⋊C8C22×D512yes—
303C23×C5—21no—
304C22×D5C2×#6711yescharacteristic
305C5×Q8—122no—
306C5×D4—21no—
307C5×D4C2×Dic612yes—
308C2×C4×C5—21no—
309C2×C4×C5—42no—
310C2×C4×C5—62no—
311C2×C4×C5C2×#6711yescharacteristic
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—24no—
315C2×Dic5—21no—
316C2×Dic5—24no—
317C2×Dic5—21no—
318C2×Dic5—42no—
319C2×Dic5—62no—
320C2×Dic5C2×#6711yescharacteristic
321C2×Dic5C2×#6711yescharacteristic
322C2×Dic5C2×#6711yescharacteristic
323C4×D5—22no—
324C4×D5—41no—
325C4×D5C2×Dic612yes—
326C4×D5#23512yes—
327Dic10—21no—
328Dic10—122no—
329Dic10C2×Dic612yes—
330C5×C8—62no—
331#168—62no—
332C2×#41—51no—
333C22×C8—152no—
334C4⋊Q8—31no—
335C4⋊Q8—151no—
336#125—152no—
337C22⋊Q8—301no—
338C22⋊Q8—301no—
339C4×Q8—51no—
340C4×Q8—51no—
341C4×Q8—301no—
342C4×Q8—301no—
343C4×D4—51no—
344C4×D4—101no—
345C4×D4—101no—
346C4×D4D3×D511yescharacteristic
347#117—51no—
348#117—101no—
349#117—152no—
350C2×C42—51no—
351C2×C42—101no—
352#107—32no—
353#107—152no—
354#106—152no—
355#106—152no—
356C4⋊C8—31no—
357C4⋊C8—152no—
358C4⋊C8—151no—
359#103—152no—
360#103—152no—
361#102—32no—
362#102—152no—
363C2×C3×C5—42no—
364C2×C3×C5C2×C22⋊Q811yescharacteristic
365C2×C3×C5C2×#13511yescharacteristic
366C2×C3×C5#57511yescharacteristic
367C3×D5—22no—
368C23×C3—21no—
369C23×C3—51no—
370C3×Q8—52no—
371C3×Q8—101no—
372C3×D4—21no—
373C3×D4—104no—
374C3×D4Q8×D512yes—
375C2×C3×C4—21no—
376C2×C3×C4—42no—
377C2×C3×C4—51no—
378C2×C3×C4—52no—
379C2×C3×C4—52no—
380C2×C3×C4—51no—
381C2×C3×C4—51no—
382C2×C3×C4—104no—
383C2×C3×C4—101no—
384C2×C3×C4—102no—
385C2×C3×C4—101no—
386C2×C3×C4—201no—
387C2×C3×C4—202no—
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4C23×D511yescharacteristic
391C2×Dic3—22no—
392C2×Dic3—102no—
393Dic6—42no—
394Dic6—202no—
395C3⋊C8—22no—
396C3⋊C8—102no—
397C22×C5—22no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C22×#6711yescharacteristic
401C2×D5—21no—
402C2×D5—21no—
403C2×D5#92412yes—
404C4×C5—21no—
405C4×C5—41no—
406C4×C5—122no—
407C4×C5#95012yes—
408C4×C5C22×Dic611yescharacteristic
409C4×C5C2×#23511yescharacteristic
410Dic5—22no—
411Dic5—21no—
412Dic5—21no—
413Dic5—41no—
414Dic5—122no—
415Dic5#92412yes—
416#41—54no—
417#41—102no—
418C2×Q8—51no—
419C2×Q8—61no—
420C2×Q8—301no—
421C2×D4—101no—
422C2×D4C2×D3×D511yescharacteristic
423C22×C4—21no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—101no—
428C22×C4—101no—
429C2×C8—32no—
430C2×C8—152no—
431C2×C8—304no—
432C4⋊C4—32no—
433C4⋊C4—51no—
434C4⋊C4—61no—
435C4⋊C4—101no—
436C4⋊C4—101no—
437C4⋊C4—152no—
438C4⋊C4—302no—
439C4⋊C4—302no—
440C4⋊C4—301no—
441C4⋊C4C2×D3×D511yescharacteristic
442C22⋊C4—21no—
443C22⋊C4—101no—
444C22⋊C4—101no—
445C22⋊C4—302no—
446C42—51no—
447C42—51no—
448C42—51no—
449C42—101no—
450C42—101no—
451C42—101no—
452C42—302no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—22no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—52no—
459C22×C3—101no—
460C22×C3—101no—
461C22×C3C2×D4×D511yescharacteristic
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—52no—
465C3×C4—101no—
466C3×C4—101no—
467C3×C4—102no—
468C3×C4—201no—
469C3×C4#405812yes—
470C3×C4C2×Q8×D511yescharacteristic
471C3×C4D5×#4111yescharacteristic
472Dic3—42no—
473Dic3—202no—
474C2×C5—42no—
475C2×C5C2×#92411yescharacteristic
476C2×C5C2×#95011yescharacteristic
477C2×C5#582211yescharacteristic
478D5—22no—
479C23—21no—
480C23—51no—
481Q8—52no—
482Q8—101no—
483Q8—122no—
484Q8—602no—
485D4—21no—
486D4—104no—
487D4D5×Dic612yes—
488C2×C4—21no—
489C2×C4—42no—
490C2×C4—51no—
491C2×C4—52no—
492C2×C4—52no—
493C2×C4—51no—
494C2×C4—51no—
495C2×C4—62no—
496C2×C4—104no—
497C2×C4—101no—
498C2×C4—102no—
499C2×C4—101no—
500C2×C4—201no—
501C2×C4—202no—
502C2×C4—302no—
503C2×C4D5×#6711yescharacteristic
504C2×C4D5×#6711yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—62no—
507C8—302no—
508C2×C3—42no—
509C2×C3—102no—
510C2×C3D5×C22⋊Q811yescharacteristic
511C2×C3C2×#405811yescharacteristic
512C2×C3#6611111yescharacteristic
513C5#8250711yescharacteristic, complemented, Sylow
514C22—22no—
515C22—41no—
516C22—41no—
517C22—52no—
518C22—101no—
519C22—101no—
520C22C2×D5×#6711yescharacteristic
521C4—21no—
522C4—41no—
523C4—52no—
524C4—102no—
525C4—101no—
526C4—101no—
527C4—122no—
528C4—201no—
529C4—602no—
530C4#9149012yes—
531C4C2×D5×Dic611yescharacteristic
532C4D5×#23511yescharacteristic
533C3#1061269511yescharacteristic, complemented, Sylow
534C2—42no—
535C2—102no—
536C2D5×#92411yescharacteristic
537C2C2×#9149011yescharacteristic
538C2#1175534411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#711C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752506C2semidirect
3. #11751109C2semidirect
4. C5×#5007C2semidirect
5. #11749086C2semidirect
7. #11747432C2semidirect
8. #11747391C2semidirect
9. D5×C4⋊(C3⋊C8)C2semidirect
10. #11746918C2semidirect
11. #11746916C2semidirect
64. C3×#711Q8semidirect
102. #5007D5semidirect
204. #711Dic6semidirect
454. C3×C5#3076semidirect
513. C5#82507semidirect
533. C3#10612695semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7112
#117525062
#117511092
C5×#50072
#117490862
#117489612
#117474322
#117473912
D5×C4⋊(C3⋊C8)2
#117469182
#117469162
#106126953
#825075