Finite Group Databasebeta

← #14438049

Subgroups — #14438049

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66062C211yesmaximal, characteristic, complemented
2#11752673C211yesmaximal, characteristic
3#11751190C211yesmaximal, characteristic, complemented
4C5×#5089C211yesmaximal, characteristic, complemented
5#11747501C212yesmaximal, complemented
6#11747499C212yesmaximal, complemented
7#11747401C212yesmaximal, complemented
8#11747156C212yesmaximal, complemented
9D5×#803C211yesmaximal, characteristic, complemented
10#11746935C211yesmaximal, characteristic, complemented
11#11746904C211yesmaximal, characteristic, complemented
12#10613410—31nomaximal, Hall
13C2×#6773C2211yescharacteristic
14C2×#6772C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16#91764C2211yescharacteristic
17C5×#875C2211yescharacteristic
18C3×#4092—21no—
19C3×Q8×Dic5—21no—
20C3×#4043—21no—
21C3×#4038C2212yes—
22C3×#4036C2212yes—
23C3×#4033—21no—
24C3×C42×D5C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91451C2211yescharacteristic
27#91448—21no—
28#91448—21no—
29#91405—21no—
30#91405—21no—
31#91376C2211yescharacteristic
32C2×D5×C3⋊C8C2212yes—
33#91094C2212yes—
34#91093C2212yes—
35#91087C2211yescharacteristic
36C5×#810C2212yes—
37C5×#809C2212yes—
38C5×#803C2211yescharacteristic
39#90974C2212yes—
40#90972C2212yes—
41#90968C2212yes—
42#90966C2212yes—
43#90952C2212yes—
44#83335—51nomaximal, Hall
45#66062D311yescharacteristic, complemented
46#66002—31no—
47C5×#489—31no—
48#65378—31no—
49#65344—31no—
50#65093—32no—
51#65086—32no—
52#65061—32no—
53#65053—32no—
54#65003—31no—
55D5×#97—31no—
56C2×C3×C5×Q8—21no—
57C2×D60C2311yescharacteristic
58C2×Dic30C2311yescharacteristic
59C2×C5×D12C2311yescharacteristic
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×C4×D5D411yescharacteristic
62C2×C3×C4×D5D411yescharacteristic
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×Dic10—21no—
65C2×#1203—21no—
66C2×#1203—21no—
67C2×#1202—21no—
68C2×#1201—21no—
69C2×#1200—21no—
70C2×D3×Dic5—21no—
71#6773—24no—
72#6772—24no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—21no—
78C2×C3⋊#168C2312yes—
79C5×(C2×D3)⋊C4—21no—
80C5×(C2×D3)⋊C4—21no—
81C2×C5×C3⋊C8C2312yes—
82C3×#685—22no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—22no—
85C3×C4⋊Dic5C2312yes—
86C3×#683—22no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5C2311yescharacteristic
91#6668—21no—
92#6668—21no—
93D5×C3⋊C8—24no—
94C3×#533—51no—
95#5477—51no—
96#5089—51no—
97#5089—51no—
98#5089—51no—
99#5089D511yescharacteristic, complemented
100#5069—52no—
101#5067—52no—
102#5002—52no—
103#5002—52no—
104C2×#803—51no—
105C2×#713—31no—
106C2×#711—31no—
107C5×C4⋊Q8C2×D311yescharacteristic
108C5×#124—31no—
109#4092—21no—
110Q8×Dic5—21no—
111#4090—31no—
112#4086—31no—
113C2×C8×D5—32no—
114#4043—21no—
115#4038C2×D312yes—
116#4036C2×D312yes—
117#4033—21no—
118#4030—61no—
119#4030—61no—
120#4027—61no—
121#4027—61no—
122#4021—31no—
123C42×D5C2×D311yescharacteristic
124#4015C2×D311yescharacteristic
125C5×#103—32no—
126C5×#102—32no—
127C5×#97—31no—
128#3967—32no—
129#3964—32no—
130#3953—32no—
131#3948—32no—
132#3947—32no—
133#3942—32no—
134#3941—32no—
135#3935—31no—
136#3135—151noSylow
137C22×D15—21no—
138C22×C5×D3—21no—
139C22×C3×D5C2×D411yescharacteristic
140C3×C5×Q8—42no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—21no—
146D60—22no—
147Dic30—22no—
148C2×C5×Dic3—21no—
149C5×D12—22no—
150C5×Dic6—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5C2×D411yescharacteristic
153C2×C3×Dic5C2×D411yescharacteristic
154C2×C3×Dic5C2×D411yescharacteristic
155C3×C4×D5—41no—
156C3×C4×D5—41no—
157C3×C4×D5#4114yes—
158C3×Dic10—42no—
159#1203—42no—
160#1203—42no—
161#1202—42no—
162#1201—42no—
163#1200—42no—
164D3×Dic5—42no—
165C3⋊#168—22no—
166C5×C3⋊C8—22no—
167C2×#235—51no—
168C2×#235—51no—
169C3×C4⋊Q8—51no—
170C3×C4⋊Q8C2×D511yescharacteristic
171C3×#125—52no—
172C3×C22⋊Q8—101no—
173C3×C22⋊Q8—101no—
174C3×C4×Q8—101no—
175C3×C4×Q8—101no—
176C3×#117—52no—
177C2×C3×C42—51no—
178#930—101no—
179#930—101no—
180C22×C3⋊C8—52no—
181#875—51no—
182#875C2×D511yescharacteristic
183#874—51no—
184C4×D12—101no—
185C4×D12—101no—
186#869—51no—
187#810—52no—
188#810—52no—
189#810—52no—
190#810C2×D512yes—
191#809—52no—
192#809—52no—
193#809—52no—
194#809C2×D512yes—
195#803—51no—
196#803—52no—
197#803C2×D511yescharacteristic
198C2×C5×Q8—21no—
199C2×C5×Q8—31no—
200C2×C5×D4—31no—
201C2×C22⋊D5—61no—
202C2×C22⋊D5—61no—
203C2×C22⋊D5—61no—
204C22×Dic5—61no—
205#713—64no—
206#711—64no—
207C2×D20—31no—
208C2×D20—61no—
209C2×C4×D5—61no—
210C2×C4×D5#6711yescharacteristic
211C2×C4×D5#6711yescharacteristic
212C2×C4×D5C22×D311yescharacteristic
213C2×Dic10—21no—
214C2×Dic10—31no—
215C2×C5×C8—32no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4C22×D312yes—
218C5×C22⋊C4—61no—
219C5×C22⋊C4—61no—
220C42×C5C22×D311yescharacteristic
221#685—22no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—21no—
225C4⋊Dic5—22no—
226C4⋊Dic5C22×D312yes—
227#683—22no—
228#683—61no—
229#683—61no—
230C4×Dic5—22no—
231C4×Dic5#6711yescharacteristic
232C4×Dic5#6711yescharacteristic
233C4×Dic5C22×D311yescharacteristic
234C2×#168—32no—
235C8×D5—64no—
236#533—51no—
237#532—151no—
238#491—152no—
239#490—152no—
240#489—31no—
241#489—151no—
242#489—151no—
243#489—151no—
244#416—152no—
245#416—152no—
246C2×#97—151no—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C2×C5×D3—41no—
252C2×C5×D3—41no—
253C2×C5×D3—41no—
254C2×C3×D5—21no—
255C2×C3×D5—21no—
256C2×C3×D5#12412yes—
257C3×C4×C5—21no—
258C3×C4×C5—21no—
259C3×C4×C5—42no—
260C3×C4×C5C2×#4112yes—
261Dic15—41no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C3×Dic5—42no—
265C3×Dic5#12412yes—
266C5×Dic3—41no—
267C2×C3×Q8—21no—
268C2×C3×Q8—101no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—51no—
272C2×#67—101no—
273C2×#67—101no—
274#235—104no—
275#235—104no—
276C2×D12—51no—
277C2×D12—101no—
278C2×D12—101no—
279C2×D12C22×D511yescharacteristic
280C2×C4×D3—101no—
281C2×C4×D3—101no—
282C2×Dic6—51no—
283C2×Dic6C22×D511yescharacteristic
284C3×C4⋊C4—21no—
285C3×C4⋊C4—52no—
286C3×C4⋊C4—102no—
287C3×C4⋊C4—102no—
288C3×C4⋊C4—101no—
289C3×C4⋊C4C22×D512yes—
290C3×C22⋊C4—102no—
291C3×C42—51no—
292C3×C42—51no—
293C3×C42—51no—
294C3×C42—102no—
295C3×C42C22×D511yescharacteristic
296(C2×D3)⋊C4—21no—
297(C2×D3)⋊C4—21no—
298(C2×D3)⋊C4—101no—
299(C2×D3)⋊C4—101no—
300C4⋊Dic3—101no—
301C4⋊Dic3—101no—
302C2×C3⋊C8—52no—
303C2×C3⋊C8—104no—
304C2×C3⋊C8C22×D512yes—
305C23×C5—61no—
306C22×D5—61no—
307C22×D5C2×#6711yescharacteristic
308C5×Q8—42no—
309C5×Q8—62no—
310C5×D4—62no—
311C2×C4×C5—22no—
312C2×C4×C5—61no—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—122no—
317C22⋊D5—122no—
318C22⋊D5—122no—
319C2×Dic5—22no—
320C2×Dic5—61no—
321C2×Dic5—122no—
322C2×Dic5C2×#6711yescharacteristic
323C2×Dic5C2×#6711yescharacteristic
324C2×Dic5C2×#6711yescharacteristic
325D20—62no—
326D20—122no—
327C4×D5—41no—
328C4×D5—41no—
329C4×D5—122no—
330C4×D5#23914yes—
331Dic10—42no—
332Dic10—62no—
333C5×C8—62no—
334#168—62no—
335C2×#41—151no—
336C2×#41—151no—
337C22×C8—152no—
338C4⋊Q8—51no—
339C4⋊Q8—151no—
340C4⋊Q8D3×D511yescharacteristic
341#127—151no—
342#125—52no—
343#124—31no—
344#124—151no—
345C22⋊Q8—101no—
346C22⋊Q8—101no—
347#121—301no—
348#121—301no—
349C4×Q8—101no—
350C4×Q8—101no—
351C4×D4—301no—
352C4×D4—301no—
353#117—52no—
354C2×C42—51no—
355#103—32no—
356#103—152no—
357#103—152no—
358#103—152no—
359#102—32no—
360#102—152no—
361#102—152no—
362#102—152no—
363#97—31no—
364#97—152no—
365#97—151no—
366C2×C3×C5C2×#12411yescharacteristic
367C2×C3×C5#57511yescharacteristic
368C2×C3×C5#57511yescharacteristic
369D15—81no—
370C3×D5—22no—
371C5×D3—81no—
372C23×C3—51no—
373C22×D3—21no—
374C22×D3—101no—
375C3×Q8—42no—
376C3×Q8—202no—
377C2×C3×C4—22no—
378C2×C3×C4—51no—
379C2×C3×C4—54no—
380C2×C3×C4—51no—
381C2×C3×C4—51no—
382C2×C3×C4—102no—
383C2×C3×C4—201no—
384C2×C3×C4—201no—
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4D4×D511yescharacteristic
387C2×C3×C4C23×D511yescharacteristic
388#67—202no—
389#67—202no—
390C2×Dic3—21no—
391C2×Dic3—101no—
392D12—22no—
393D12—102no—
394D12—202no—
395D12—202no—
396C4×D3—202no—
397C4×D3—202no—
398Dic6—22no—
399Dic6—102no—
400C3⋊C8—22no—
401C3⋊C8—102no—
402C22×C5—121no—
403C22×C5—121no—
404C22×C5—121no—
405C22×C5C22×#6711yescharacteristic
406C2×D5—21no—
407C2×D5—21no—
408C2×D5—121no—
409C2×D5—121no—
410C2×D5—121no—
411C2×D5#94712yes—
412C4×C5—21no—
413C4×C5—21no—
414C4×C5—42no—
415C4×C5—121no—
416C4×C5C2×#23912yes—
417Dic5—21no—
418Dic5—21no—
419Dic5—42no—
420Dic5—121no—
421Dic5#94712yes—
422#41—304no—
423#41—304no—
424C2×Q8—21no—
425C2×Q8—31no—
426C2×Q8—101no—
427C2×Q8—151no—
428C2×D4—31no—
429C2×D4—151no—
430C2×D4—301no—
431C2×D4—301no—
432C2×D4—301no—
433C2×D4—301no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—301no—
438C22×C4—301no—
439C2×C8—32no—
440C2×C8—152no—
441C2×C8—304no—
442C4⋊C4—21no—
443C4⋊C4—52no—
444C4⋊C4—102no—
445C4⋊C4—102no—
446C4⋊C4—101no—
447C4⋊C4—301no—
448C4⋊C4—301no—
449C4⋊C4C2×D3×D512yes—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—102no—
453C22⋊C4—301no—
454C22⋊C4—301no—
455C42—51no—
456C42—51no—
457C42—51no—
458C42—102no—
459C42C2×D3×D511yescharacteristic
460C3×C5#313511yescharacteristic, complemented, Hall
461C22×C3—52no—
462C22×C3—101no—
463C22×C3—101no—
464C22×C3C2×D4×D511yescharacteristic
465C2×D3—41no—
466C2×D3—41no—
467C2×D3—41no—
468C2×D3—201no—
469C2×D3—201no—
470C2×D3—201no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—42no—
474C3×C4—52no—
475C3×C4—101no—
476C3×C4—101no—
477C3×C4—202no—
478C3×C4D5×#4112yes—
479Dic3—41no—
480Dic3—201no—
481C2×C5—241no—
482C2×C5C2×#94711yescharacteristic
483C2×C5#582211yescharacteristic
484C2×C5#582211yescharacteristic
485D5—22no—
486D5—241no—
487C23—51no—
488C23—61no—
489C23—301no—
490Q8—42no—
491Q8—62no—
492Q8—202no—
493Q8—302no—
494D4—62no—
495D4—302no—
496D4—602no—
497D4—602no—
498D4—602no—
499D4—602no—
500C2×C4—22no—
501C2×C4—51no—
502C2×C4—54no—
503C2×C4—51no—
504C2×C4—51no—
505C2×C4—61no—
506C2×C4—102no—
507C2×C4—201no—
508C2×C4—201no—
509C2×C4—301no—
510C2×C4—602no—
511C2×C4—602no—
512C2×C4D5×#6711yescharacteristic
513C2×C4D5×#6711yescharacteristic
514C2×C4C22×D3×D511yescharacteristic
515C8—62no—
516C8—302no—
517C2×C3—102no—
518C2×C3D5×#12411yescharacteristic
519C2×C3#6610711yescharacteristic
520C2×C3#6611111yescharacteristic
521D3—81no—
522D3—401no—
523C5#8333511yescharacteristic, complemented, Sylow
524C22—52no—
525C22—101no—
526C22—101no—
527C22—121no—
528C22—121no—
529C22—121no—
530C22—601no—
531C22—601no—
532C22—601no—
533C22C2×D5×#6711yescharacteristic
534C4—21no—
535C4—21no—
536C4—42no—
537C4—52no—
538C4—101no—
539C4—101no—
540C4—121no—
541C4—202no—
542C4—601no—
543C4D5×#23912yes—
544C3#1061341011yescharacteristic, complemented, Sylow
545C2—102no—
546C2—241no—
547C2—1201no—
548C2#1175469011yescharacteristic
549C2#1175508411yescharacteristic
550C2D5×#94711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752673C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3135
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. #11751190C2semidirect
4. C5×#5089C2semidirect
5. #11747501C2semidirect
6. #11747499C2semidirect
7. #11747401C2semidirect
8. #11747156C2semidirect
9. D5×#803C2semidirect
10. #11746935C2semidirect
11. #11746904C2semidirect
45. #66062D3semidirect
99. #5089D5semidirect
460. C3×C5#3135semidirect
523. C5#83335semidirect
544. C3#10613410semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
#117526732
#117511902
C5×#50892
#117475012
#117474992
#117474012
#117471562
D5×#8032
#117469352
#117469042
#106134103
#833355