Finite Group Databasebeta

← #14438643

Subgroups — #14438643

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
1C3×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11752673C211yesmaximal, characteristic
3#11751190C211yesmaximal, characteristic, complemented
4C5×#5089C211yesmaximal, characteristic, complemented
5#11747500C212yesmaximal, complemented
6#11747498C212yesmaximal, complemented
7#11747140C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11747003C211yesmaximal, characteristic, complemented
10#11746935C211yesmaximal, characteristic, complemented
11#11746904C211yesmaximal, characteristic, complemented
12#10613414—31nomaximal, Hall
13C2×C3×Q8×D5—21no—
14C2×#6773C2211yescharacteristic
15C2×#6772C2211yescharacteristic
16C3×C5×C4⋊Q8C2211yescharacteristic
17#91764C2211yescharacteristic
18C5×#875C2211yescharacteristic
19C3×#4090—21no—
20C3×D5×C4⋊C4—21no—
21C3×D5×C4⋊C4C2212yes—
22C3×#4034—21no—
23C3×#4034C2212yes—
24C3×C42×D5C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91451C2211yescharacteristic
27#91448—21no—
28#91448—21no—
29#91405—21no—
30#91405—21no—
31#91376C2211yescharacteristic
32C2×#6649C2212yes—
33#91094C2212yes—
34#91093C2212yes—
35#91087C2211yescharacteristic
36C5×#810C2212yes—
37C5×#809C2212yes—
38C5×#803C2211yescharacteristic
39#90974C2212yes—
40#90972C2212yes—
41#90968C2212yes—
42#90966C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83199—51nomaximal, Hall
45D5×C4⋊Q8D311yescharacteristic, complemented
46#66002—31no—
47C5×#489—31no—
48#65378—31no—
49#65344—31no—
50#65092—32no—
51#65081—32no—
52#65060—32no—
53#65049—32no—
54#65003—31no—
55#64996—31no—
56C2×C3×C5×Q8—21no—
57C2×D60C2311yescharacteristic
58C2×Dic30C2311yescharacteristic
59C2×C5×D12C2311yescharacteristic
60C2×C5×Dic6C2311yescharacteristic
61C3×Q8×D5—44no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5D411yescharacteristic
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5C2311yescharacteristic
66C2×C3×Dic10—21no—
67C2×C3×Dic10—22no—
68C2×#1203—21no—
69C2×#1203—21no—
70C2×#1202—21no—
71C2×#1201—21no—
72C2×#1200—21no—
73C2×D3×Dic5—21no—
74#6773—24no—
75#6772—24no—
76C3×C5×C4⋊C4—21no—
77C3×C5×C4⋊C4C2312yes—
78C3×C42×C5C2311yescharacteristic
79#6714—21no—
80#6714—21no—
81C2×C3⋊#168C2312yes—
82C5×(C2×D3)⋊C4—21no—
83C5×(C2×D3)⋊C4—21no—
84C2×C5×C3⋊C8C2312yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2312yes—
87C3×#683—22no—
88C3×#683—22no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92#6668—21no—
93#6668—21no—
94#6649—24no—
95C2×C3×C4⋊Q8—51no—
96#5477—51no—
97#5093—52no—
98#5089—51no—
99#5089—51no—
100#5089—51no—
101#5089D511yescharacteristic, complemented
102#5088—52no—
103#4966—52no—
104#4966—52no—
105C4×#208—51no—
106C2×#713—31no—
107C2×Q8×D5—21no—
108C2×#711—31no—
109C5×C4⋊Q8C2×D311yescharacteristic
110C5×#124—31no—
111#4090—21no—
112#4090—31no—
113#4086—31no—
114C2×#676—32no—
115D5×C4⋊C4—21no—
116D5×C4⋊C4C2×D312yes—
117#4034—21no—
118#4034C2×D312yes—
119#4030—61no—
120#4030—61no—
121#4027—61no—
122#4027—61no—
123#4021—31no—
124C42×D5C2×D311yescharacteristic
125#4015C2×D311yescharacteristic
126C5×#103—32no—
127C5×#102—32no—
128C5×#97—31no—
129#3967—32no—
130#3964—32no—
131#3953—32no—
132#3948—32no—
133C8×Dic5—32no—
134#3942—32no—
135#3941—32no—
136#3935—31no—
137#3141—151noSylow
138C22×D15—21no—
139C22×C5×D3—21no—
140C22×C3×D5C2×D411yescharacteristic
141C3×C5×Q8—42no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—21no—
147D60—22no—
148Dic30—22no—
149C2×C5×Dic3—21no—
150C5×D12—22no—
151C5×Dic6—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C2×D411yescharacteristic
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C3×C4×D5—22no—
157C3×C4×D5—22no—
158C3×C4×D5—44no—
159C3×C4×D5#4114yes—
160C3×Dic10—42no—
161C3×Dic10—44no—
162#1203—42no—
163#1203—42no—
164#1202—42no—
165#1201—42no—
166#1200—42no—
167D3×Dic5—42no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C22×C3×Q8—101no—
171C2×#235—51no—
172C2×#235—51no—
173C3×C4⋊Q8—52no—
174C3×C4⋊Q8—51no—
175C3×C4⋊Q8—101no—
176C3×C4⋊Q8—101no—
177C3×C4⋊Q8C2×D511yescharacteristic
178C2×C3×C4⋊C4—52no—
179C2×C3×C4⋊C4—101no—
180C2×C3×C42—51no—
181#930—101no—
182#930—101no—
183C2×#208—52no—
184#875—51no—
185#875C2×D511yescharacteristic
186#874—51no—
187C4×D12—101no—
188C4×D12—101no—
189#869—51no—
190#810—52no—
191#810—52no—
192#810—52no—
193#810C2×D512yes—
194#809—52no—
195#809—52no—
196#809—52no—
197#809C2×D512yes—
198#803—51no—
199#803C2×D511yescharacteristic
200C4×C3⋊C8—52no—
201C2×C5×Q8—21no—
202C2×C5×Q8—31no—
203C2×C5×D4—31no—
204C2×C22⋊D5—61no—
205C2×C22⋊D5—61no—
206C2×C22⋊D5—61no—
207C22×Dic5—61no—
208#713—64no—
209Q8×D5—44no—
210#711—64no—
211C2×D20—31no—
212C2×D20—61no—
213C2×C4×D5—22no—
214C2×C4×D5—61no—
215C2×C4×D5#6711yescharacteristic
216C2×C4×D5#6711yescharacteristic
217C2×C4×D5C22×D311yescharacteristic
218C2×Dic10—21no—
219C2×Dic10—22no—
220C2×Dic10—31no—
221C2×C5×C8—32no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4C22×D312yes—
224C5×C22⋊C4—61no—
225C5×C22⋊C4—61no—
226C42×C5C22×D311yescharacteristic
227#685—61no—
228#685—61no—
229C4⋊Dic5—21no—
230C4⋊Dic5C22×D312yes—
231#683—22no—
232#683—22no—
233#683—61no—
234#683—61no—
235C4×Dic5#6711yescharacteristic
236C4×Dic5#6711yescharacteristic
237C4×Dic5C22×D311yescharacteristic
238C2×#168—32no—
239#676—64no—
240#532—151no—
241C2×C4⋊Q8—51no—
242#489—31no—
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×C5C22×D411yescharacteristic
252C2×D15—41no—
253C2×D15—41no—
254C2×D15—41no—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C2×C5×D3—41no—
258C2×C3×D5—21no—
259C2×C3×D5—21no—
260C2×C3×D5#12412yes—
261C3×C4×C5—21no—
262C3×C4×C5—21no—
263C3×C4×C5—42no—
264C3×C4×C5C2×#4112yes—
265Dic15—41no—
266C3×Dic5—42no—
267C3×Dic5#12412yes—
268C3×Dic5AGL(1,ℤ/8)12yes—
269C3×Dic5#13712yes—
270C5×Dic3—41no—
271C2×C3×Q8—21no—
272C2×C3×Q8—102no—
273C2×C3×Q8—101no—
274C2×C3×Q8—204no—
275C22×C3×C4—51no—
276C22×C3×C4—51no—
277C22×C3×C4—51no—
278C22×C3×C4—102no—
279C2×#67—101no—
280C2×#67—101no—
281#235—104no—
282#235—104no—
283C2×D12—51no—
284C2×D12—101no—
285C2×D12—101no—
286C2×D12C22×D511yescharacteristic
287C2×C4×D3—101no—
288C2×C4×D3—101no—
289C2×Dic6—51no—
290C2×Dic6C22×D511yescharacteristic
291C3×C4⋊C4—21no—
292C3×C4⋊C4—52no—
293C3×C4⋊C4—102no—
294C3×C4⋊C4—102no—
295C3×C4⋊C4—101no—
296C3×C4⋊C4C22×D512yes—
297C3×C42—51no—
298C3×C42—51no—
299C3×C42—51no—
300C3×C42C22×D511yescharacteristic
301(C2×D3)⋊C4—21no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—101no—
304(C2×D3)⋊C4—101no—
305C4⋊Dic3—101no—
306C4⋊Dic3—101no—
307#208—104no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8C22×D512yes—
310C23×C5—61no—
311C22×D5—61no—
312C22×D5C2×#6711yescharacteristic
313C5×Q8—42no—
314C5×Q8—62no—
315C5×D4—62no—
316C2×C4×C5—22no—
317C2×C4×C5—61no—
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C23×D311yescharacteristic
321C22⋊D5—122no—
322C22⋊D5—122no—
323C22⋊D5—122no—
324C2×Dic5—22no—
325C2×Dic5—61no—
326C2×Dic5—122no—
327C2×Dic5C2×#6711yescharacteristic
328C2×Dic5C2×#6711yescharacteristic
329C2×Dic5C2×#6711yescharacteristic
330D20—62no—
331D20—122no—
332C4×D5—22no—
333C4×D5—22no—
334C4×D5—44no—
335C4×D5—122no—
336C4×D5#23914yes—
337Dic10—42no—
338Dic10—44no—
339Dic10—62no—
340C5×C8—62no—
341#168—62no—
342C2×#41—151no—
343C2×#41—151no—
344C22×Q8—101no—
345C2×M16—152no—
346C4⋊Q8—52no—
347C4⋊Q8—51no—
348C4⋊Q8—101no—
349C4⋊Q8—101no—
350C4⋊Q8—151no—
351C4⋊Q8D3×D511yescharacteristic
352#127—151no—
353#124—31no—
354#124—151no—
355#121—301no—
356#121—301no—
357C4×D4—301no—
358C4×D4—301no—
359C2×C4⋊C4—52no—
360C2×C4⋊C4—101no—
361C2×C42—51no—
362#103—32no—
363#103—152no—
364#103—152no—
365#103—152no—
366#102—32no—
367#102—152no—
368#102—152no—
369#102—152no—
370#97—31no—
371#97—151no—
372C4×C8—152no—
373C2×C3×C5C2×#12411yescharacteristic
374C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
375C2×C3×C5C2×#13711yescharacteristic
376D15—81no—
377C3×D5—22no—
378C5×D3—81no—
379C23×C3—51no—
380C22×D3—21no—
381C22×D3—101no—
382C3×Q8—42no—
383C3×Q8—202no—
384C3×Q8—204no—
385C2×C3×C4—22no—
386C2×C3×C4—51no—
387C2×C3×C4—51no—
388C2×C3×C4—51no—
389C2×C3×C4—54no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—204no—
394C2×C3×C4D4×D511yescharacteristic
395C2×C3×C4D4×D511yescharacteristic
396C2×C3×C4C23×D511yescharacteristic
397#67—202no—
398#67—202no—
399C2×Dic3—21no—
400C2×Dic3—101no—
401D12—22no—
402D12—102no—
403D12—202no—
404D12—202no—
405C4×D3—202no—
406C4×D3—202no—
407Dic6—22no—
408Dic6—102no—
409C3⋊C8—22no—
410C3⋊C8—102no—
411C22×C5—121no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5C22×#6711yescharacteristic
415C2×D5—21no—
416C2×D5—21no—
417C2×D5—121no—
418C2×D5—121no—
419C2×D5—121no—
420C2×D5#94712yes—
421C4×C5—21no—
422C4×C5—21no—
423C4×C5—42no—
424C4×C5—121no—
425C4×C5C2×#23912yes—
426Dic5—42no—
427Dic5—121no—
428Dic5#93212yes—
429Dic5#94212yes—
430Dic5#94712yes—
431#41—304no—
432#41—304no—
433C2×Q8—21no—
434C2×Q8—31no—
435C2×Q8—102no—
436C2×Q8—101no—
437C2×Q8—151no—
438C2×Q8—204no—
439C2×D4—31no—
440C2×D4—151no—
441C2×D4—301no—
442C2×D4—301no—
443C2×D4—301no—
444C2×D4—301no—
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—102no—
449C22×C4—301no—
450C22×C4—301no—
451M16—304no—
452C2×C8—32no—
453C2×C8—152no—
454C4⋊C4—21no—
455C4⋊C4—52no—
456C4⋊C4—102no—
457C4⋊C4—102no—
458C4⋊C4—101no—
459C4⋊C4—301no—
460C4⋊C4—301no—
461C4⋊C4C2×D3×D512yes—
462C22⋊C4—61no—
463C22⋊C4—61no—
464C22⋊C4—301no—
465C22⋊C4—301no—
466C42—51no—
467C42—51no—
468C42—51no—
469C42C2×D3×D511yescharacteristic
470C3×C5#314111yescharacteristic, complemented, Hall
471C22×C3—52no—
472C22×C3—101no—
473C22×C3—101no—
474C22×C3C2×D4×D511yescharacteristic
475C2×D3—41no—
476C2×D3—41no—
477C2×D3—41no—
478C2×D3—201no—
479C2×D3—201no—
480C2×D3—201no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—42no—
484C3×C4—52no—
485C3×C4—52no—
486C3×C4—52no—
487C3×C4—202no—
488C3×C4D5×#4112yes—
489Dic3—41no—
490Dic3—201no—
491C2×C5—241no—
492C2×C5C2×#93211yescharacteristic
493C2×C5C2×#94211yescharacteristic
494C2×C5C2×#94711yescharacteristic
495D5—22no—
496D5—241no—
497C23—51no—
498C23—61no—
499C23—301no—
500Q8—42no—
501Q8—62no—
502Q8—202no—
503Q8—204no—
504Q8—302no—
505D4—62no—
506D4—302no—
507D4—602no—
508D4—602no—
509D4—602no—
510D4—602no—
511C2×C4—22no—
512C2×C4—51no—
513C2×C4—51no—
514C2×C4—51no—
515C2×C4—54no—
516C2×C4—61no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—204no—
521C2×C4—301no—
522C2×C4—602no—
523C2×C4—602no—
524C2×C4D5×#6711yescharacteristic
525C2×C4D5×#6711yescharacteristic
526C2×C4C22×D3×D511yescharacteristic
527C8—62no—
528C8—302no—
529C2×C3—102no—
530C2×C3D5×#12411yescharacteristic
531C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
532C2×C3D5×#13711yescharacteristic
533D3—81no—
534D3—401no—
535C5#8319911yescharacteristic, complemented, Sylow
536C22—52no—
537C22—101no—
538C22—101no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—601no—
543C22—601no—
544C22—601no—
545C22C2×D5×#6711yescharacteristic
546C4—21no—
547C4—21no—
548C4—42no—
549C4—52no—
550C4—52no—
551C4—52no—
552C4—121no—
553C4—202no—
554C4—601no—
555C4D5×#23912yes—
556C3#1061341411yescharacteristic, complemented, Sylow
557C2—102no—
558C2—241no—
559C2—1201no—
560C2D5×#93211yescharacteristic
561C2D5×#94211yescharacteristic
562C2D5×#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#3141
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×D5×C4⋊Q8C2semidirect
3. #11751190C2semidirect
4. C5×#5089C2semidirect
5. #11747500C2semidirect
6. #11747498C2semidirect
7. #11747140C2semidirect
8. #11747138C2semidirect
9. #11747003C2semidirect
10. #11746935C2semidirect
11. #11746904C2semidirect
45. D5×C4⋊Q8D3semidirect
101. #5089D5semidirect
470. C3×C5#3141semidirect
535. C5#83199semidirect
556. C3#10613414semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
#117526732
#117511902
C5×#50892
#117475002
#117474982
#117471402
#117471382
#117470032
#117469352
#117469042
#106134143
#831995