Finite Group Databasebeta

← #14430237

Subgroups — #14430237

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×#66062C211yesmaximal, characteristic, complemented
2C4×#6772C211yesmaximal, characteristic
3#11751195C211yesmaximal, characteristic, complemented
4C5×#5087C211yesmaximal, characteristic, complemented
5#11747499C212yesmaximal
6#11747432C212yesmaximal, complemented
7#11747288C212yesmaximal, complemented
8#11747243C212yesmaximal, complemented
9D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#11746917C211yesmaximal, characteristic, complemented
11#11746882C211yesmaximal, characteristic, complemented
12#10612695—31nomaximal, Hall
13C2×#6772C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C3×#4092—21no—
18C3×Q8×Dic5—21no—
19C3×#4043—21no—
20C3×#4038C2212yes—
21C3×#4036C2212yes—
22C3×#4033—21no—
23C3×C42×D5C2211yescharacteristic
24C3×#4015C2211yescharacteristic
25#91440—21no—
26C4×#1201—21no—
27Dic5×D12C2211yescharacteristic
28#91398—21no—
29C4×D3×Dic5—21no—
30#91358C2211yescharacteristic
31#91333C2211yescharacteristic
32C2×D5×C3⋊C8C2212yes—
33#91094C2212yes—
34#91092C2212yes—
35C4⋊(C3⋊#168)C2211yescharacteristic
36C5×#809C2212yes—
37C5×#807C2212yes—
38C5×C4⋊(C3⋊C8)C2211yescharacteristic
39#90990C2212yes—
40#90986C2212yes—
41#90982C2212yes—
42#90974C2212yes—
43#90966C2212yes—
44#83349—51nomaximal, Hall
45#66062D311yescharacteristic, complemented
46C4×#711—31no—
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×Q8—21no—
57C2×Dic30C2311yescharacteristic
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×C4×D5D411yescharacteristic
61C2×C3×C4×D5D411yescharacteristic
62C2×C3×C4×D5C2311yescharacteristic
63C2×C3×Dic10—21no—
64C2×#1201—21no—
65C2×D3×Dic5—21no—
66C2×D3×Dic5—21no—
67#6772—22no—
68#6772Q814yescomplemented
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71C3×C42×C5C2311yescharacteristic
72C4⋊Dic15C2311yescharacteristic
73#6712—21no—
74C4×Dic15—21no—
75C2×C3⋊#168C2312yes—
76C5×(C2×D3)⋊C4—21no—
77C5×C4⋊Dic3C2311yescharacteristic
78C2×C5×C3⋊C8C2312yes—
79C3×#685—22no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5C2312yes—
83C3×#683—22no—
84C3×C4×Dic5—22no—
85C3×C4×Dic5D411yescharacteristic
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5C2311yescharacteristic
88#6669—21no—
89(C2×D3)⋊Dic5—21no—
90#6665—21no—
91Dic3×Dic5—21no—
92Dic3×Dic5—21no—
93D5×C3⋊C8—24no—
94C3×#533—51no—
95C4×#235—51no—
96#5094—51no—
97#5091—51no—
98#5087D511yescharacteristic, complemented
99#5084—51no—
100#5066—52no—
101#5063—52no—
102#5002—52no—
103#4998—52no—
104C2×C4⋊(C3⋊C8)—51no—
105C2×#711—31no—
106C5×C4⋊Q8C2×D311yescharacteristic
107C4×C5×D4—31no—
108#4092—21no—
109Q8×Dic5—21no—
110D4×Dic5—31no—
111C4×C22⋊D5—61no—
112C2×C4×Dic5—61no—
113C2×C8×D5—32no—
114#4043—21no—
115#4038—31no—
116#4038C2×D312yes—
117#4036C2×D312yes—
118#4033—21no—
119#4033—31no—
120#4027—61no—
121#4023—61no—
122C42×D5C2×D311yescharacteristic
123#4015C2×D311yescharacteristic
124C4×Dic10—31no—
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
137C22×C5×D3—21no—
138C22×C3×D5C2×D411yescharacteristic
139C3×C5×Q8—42no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146Dic30—21no—
147Dic30C2×Q812yes—
148C2×C5×Dic3—21no—
149C5×D12—21no—
150C5×D12C2×Q812yes—
151C4×C5×D3—42no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C2×D411yescharacteristic
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C3×C4×D5—22no—
157C3×C4×D5—41no—
158C3×C4×D5C2×Q812yes—
159C3×C4×D5#4112yes—
160C3×Dic10—42no—
161#1201—24no—
162D3×Dic5—24no—
163D3×Dic5—42no—
164C3⋊#168—22no—
165C5×C3⋊C8—22no—
166C2×#235—51no—
167C3×C4⋊Q8—51no—
168C3×C4⋊Q8C2×D511yescharacteristic
169C3×#125—52no—
170C3×C22⋊Q8—101no—
171C3×C22⋊Q8—101no—
172C3×C4×Q8—101no—
173C3×C4×Q8—101no—
174C3×#117—52no—
175C2×C3×C42—51no—
176C4×#67—101no—
177C4×#67—101no—
178#926—51no—
179C22×C3⋊C8—52no—
180C4×D12—51no—
181C4×D12C2×D511yescharacteristic
182#872—101no—
183C42×D3—101no—
184C4×Dic6—51no—
185C4×Dic6—51no—
186#810—52no—
187#810—52no—
188#809—52no—
189#809C2×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—21no—
198C2×C5×D4—31no—
199C22×C4×C5—61no—
200C2×C22⋊D5—61no—
201C22×Dic5—61no—
202C22×Dic5—61no—
203#711—34no—
204#711—62no—
205C2×C4×D5#6711yescharacteristic
206C2×C4×D5#6711yescharacteristic
207C2×C4×D5C22×D311yescharacteristic
208C2×Dic10—21no—
209C2×Dic10—31no—
210C2×C5×C8—32no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—31no—
213C5×C4⋊C4C22×D312yes—
214C5×C22⋊C4—61no—
215C42×C5C22×D311yescharacteristic
216C22⋊Dic5—61no—
217#685—22no—
218#685—61no—
219C4⋊Dic5—21no—
220C4⋊Dic5—22no—
221C4⋊Dic5—31no—
222C4⋊Dic5C22×D312yes—
223#683—22no—
224#683—61no—
225#683—61no—
226C4×Dic5—22no—
227C4×Dic5—61no—
228C4×Dic5—61no—
229C4×Dic5—61no—
230C4×Dic5#6711yescharacteristic
231C4×Dic5#6711yescharacteristic
232C4×Dic5C22×D311yescharacteristic
233C2×#168—32no—
234C8×D5—64no—
235#533—51no—
236C4×#41—151no—
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×C5C22×D411yescharacteristic
247C2×C5×D3—22no—
248C2×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C3×D5—21no—
251C2×C3×D5—21no—
252C2×C3×D5C22⋊Q812yes—
253C3×C4×C5—21no—
254C3×C4×C5—42no—
255C3×C4×C5#13512yes—
256C3×C4×C5C22×Q811yescharacteristic
257C3×C4×C5C2×#4111yescharacteristic
258Dic15—22no—
259Dic15—41no—
260C3×Dic5—21no—
261C3×Dic5—21no—
262C3×Dic5—42no—
263C3×Dic5C22⋊Q812yes—
264C5×Dic3—41no—
265C2×C3×Q8—21no—
266C2×C3×Q8—101no—
267C22×C3×C4—51no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C2×#67—101no—
271#235—54no—
272#235—102no—
273C2×D12C22×D511yescharacteristic
274C2×C4×D3—21no—
275C2×C4×D3—101no—
276C2×C4×D3—101no—
277C2×Dic6—51no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—52no—
280C3×C4⋊C4—102no—
281C3×C4⋊C4—102no—
282C3×C4⋊C4—101no—
283C3×C4⋊C4C22×D512yes—
284C3×C22⋊C4—102no—
285C3×C42—51no—
286C3×C42—51no—
287C3×C42—51no—
288C3×C42—102no—
289C3×C42C22×D511yescharacteristic
290#217—101no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—101no—
293C4⋊Dic3—51no—
294C4⋊Dic3C22×D511yescharacteristic
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—101no—
298C4×Dic3—101no—
299C4×Dic3—101no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—104no—
302C2×C3⋊C8C22×D512yes—
303C23×C5—61no—
304C22×D5C2×#6711yescharacteristic
305C5×Q8—42no—
306C5×D4—32no—
307C5×D4—61no—
308C2×C4×C5—22no—
309C2×C4×C5—61no—
310C2×C4×C5—122no—
311C2×C4×C5C2×#6711yescharacteristic
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—64no—
315C2×Dic5—22no—
316C2×Dic5—61no—
317C2×Dic5—64no—
318C2×Dic5—61no—
319C2×Dic5—122no—
320C2×Dic5C2×#6711yescharacteristic
321C2×Dic5C2×#6711yescharacteristic
322C2×Dic5C2×#6711yescharacteristic
323C4×D5—22no—
324C4×D5—41no—
325C4×D5D3×Q812yes—
326C4×D5#23912yes—
327Dic10—32no—
328Dic10—42no—
329Dic10—61no—
330C5×C8—62no—
331#168—62no—
332C2×#41—151no—
333C22×C8—152no—
334C4⋊Q8—51no—
335C4⋊Q8D3×D511yescharacteristic
336#125—52no—
337C22⋊Q8—101no—
338C22⋊Q8—101no—
339C4×Q8—101no—
340C4×Q8—101no—
341C4×Q8—151no—
342C4×Q8—151no—
343C4×D4—31no—
344C4×D4—151no—
345C4×D4—301no—
346C4×D4—301no—
347#117—52no—
348#117—151no—
349#117—301no—
350C2×C42—51no—
351C2×C42—301no—
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×C5C2×C22⋊Q811yescharacteristic
364C2×C3×C5C2×#13511yescharacteristic
365C2×C3×C5#57511yescharacteristic
366C3×D5—22no—
367C5×D3—42no—
368C23×C3—51no—
369C22×D3—21no—
370C3×Q8—42no—
371C3×Q8—202no—
372C2×C3×C4—22no—
373C2×C3×C4—51no—
374C2×C3×C4—52no—
375C2×C3×C4—52no—
376C2×C3×C4—51no—
377C2×C3×C4—51no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4—201no—
381C2×C3×C4D4×D511yescharacteristic
382C2×C3×C4D4×D511yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—104no—
385C2×Dic3—21no—
386C2×Dic3—101no—
387C2×Dic3—101no—
388D12—21no—
389D12Q8×D512yes—
390C4×D3—42no—
391C4×D3—104no—
392C4×D3—202no—
393Dic6—52no—
394Dic6—101no—
395C3⋊C8—22no—
396C3⋊C8—102no—
397C22×C5—62no—
398C22×C5—121no—
399C22×C5—121no—
400C22×C5C22×#6711yescharacteristic
401C2×D5—21no—
402C2×D5—21no—
403C2×D5#94612yes—
404C4×C5—21no—
405C4×C5—42no—
406C4×C5—121no—
407C4×C5#95012yes—
408C4×C5C2×D3×Q811yescharacteristic
409C4×C5C2×#23911yescharacteristic
410Dic5—21no—
411Dic5—21no—
412Dic5—42no—
413Dic5—62no—
414Dic5—121no—
415Dic5#94612yes—
416#41—154no—
417#41—302no—
418C2×Q8—21no—
419C2×Q8—101no—
420C2×Q8—151no—
421C2×D4—31no—
422C2×D4—301no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—61no—
427C22×C4—301no—
428C22×C4—301no—
429C2×C8—32no—
430C2×C8—152no—
431C2×C8—304no—
432C4⋊C4—21no—
433C4⋊C4—31no—
434C4⋊C4—52no—
435C4⋊C4—102no—
436C4⋊C4—102no—
437C4⋊C4—101no—
438C4⋊C4—151no—
439C4⋊C4—301no—
440C4⋊C4—301no—
441C4⋊C4C2×D3×D512yes—
442C22⋊C4—61no—
443C22⋊C4—102no—
444C22⋊C4—301no—
445C22⋊C4—301no—
446C42—51no—
447C42—51no—
448C42—51no—
449C42—102no—
450C42—301no—
451C42—301no—
452C42—301no—
453C42C2×D3×D511yescharacteristic
454C3×C5#307611yescharacteristic, complemented, Hall
455C22×C3—52no—
456C22×C3—101no—
457C22×C3—101no—
458C22×C3C2×D4×D511yescharacteristic
459C2×D3—22no—
460C2×D3—41no—
461C2×D3—41no—
462C3×C4—21no—
463C3×C4—42no—
464C3×C4—52no—
465C3×C4—101no—
466C3×C4—101no—
467C3×C4—202no—
468C3×C4#405812yes—
469C3×C4C2×Q8×D511yescharacteristic
470C3×C4D5×#4111yescharacteristic
471Dic3—41no—
472Dic3—102no—
473Dic3—201no—
474C2×C5—122no—
475C2×C5C2×#94611yescharacteristic
476C2×C5C2×#95011yescharacteristic
477C2×C5#582211yescharacteristic
478D5—22no—
479C23—51no—
480C23—61no—
481Q8—42no—
482Q8—152no—
483Q8—202no—
484Q8—301no—
485D4—32no—
486D4—61no—
487D4—304no—
488C2×C4—22no—
489C2×C4—51no—
490C2×C4—52no—
491C2×C4—52no—
492C2×C4—51no—
493C2×C4—51no—
494C2×C4—61no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—122no—
498C2×C4—201no—
499C2×C4—304no—
500C2×C4—301no—
501C2×C4—301no—
502C2×C4—602no—
503C2×C4D5×#6711yescharacteristic
504C2×C4D5×#6711yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—62no—
507C8—302no—
508C2×C3—102no—
509C2×C3D5×C22⋊Q811yescharacteristic
510C2×C3C2×#405811yescharacteristic
511C2×C3#6611111yescharacteristic
512D3—42no—
513C5#8334911yescharacteristic, complemented, Sylow
514C22—52no—
515C22—62no—
516C22—101no—
517C22—101no—
518C22—121no—
519C22—121no—
520C22C2×D5×#6711yescharacteristic
521C4—21no—
522C4—42no—
523C4—52no—
524C4—101no—
525C4—101no—
526C4—121no—
527C4—202no—
528C4—302no—
529C4—601no—
530C4#9149012yes—
531C4D3×Q8×D511yescharacteristic
532C4D5×#23911yescharacteristic
533C3#1061269511yescharacteristic, complemented, Sylow
534C2—102no—
535C2—122no—
536C2C2×#9149011yescharacteristic
537C2#1175508411yescharacteristic
538C2D5×#94611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6772C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66062C2semidirect
3. #11751195C2semidirect
4. C5×#5087C2semidirect
6. #11747432C2semidirect
7. #11747288C2semidirect
8. #11747243C2semidirect
9. D5×C4⋊(C3⋊C8)C2semidirect
10. #11746917C2semidirect
11. #11746882C2semidirect
45. #66062D3semidirect
68. #6772Q8semidirect
98. #5087D5semidirect
454. C3×C5#3076semidirect
513. C5#83349semidirect
533. C3#10612695semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
C4×#67722
#117511952
C5×#50872
#117474992
#117474322
#117472882
#117472432
D5×C4⋊(C3⋊C8)2
#117469172
#117468822
#106126953
#833495