Finite Group Databasebeta

← #14439359

Subgroups — #14439359

Order 1920.

1144 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×D5×#124C211yesmaximal, characteristic, complemented
2C2×#91513C212yesmaximal, complemented
3C2×#91489C212yesmaximal, complemented
4#11752672C211yesmaximal, characteristic, complemented
5#11751161C211yesmaximal, characteristic, complemented
6C5×#5058C211yesmaximal, characteristic, complemented
7#11749313C212yesmaximal, complemented
8#11749067C212yesmaximal, complemented
9#11747074C211yesmaximal, characteristic, complemented
10#11747042C211yesmaximal, characteristic, complemented
11#11747003C211yesmaximal, characteristic, complemented
12#10613577—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×C3×D4×D5C2211yescharacteristic
15C2×#6772C2212yes—
16C3×C5×#124C2211yescharacteristic
17C2×#6718C2212yescomplemented
18C2×#6716C2212yes—
19#91758C2211yescharacteristic, complemented
20C2×C5×#215C2212yescomplemented
21C2×C5×#213C2212yes—
22C5×#874C2211yescharacteristic, complemented
23C3×#4093C2211yescharacteristic
24C3×#4082C2211yescharacteristic
25C3×#4031—22no—
26C3×D5×C22⋊C4—22no—
27C3×#4021C2211yescharacteristic
28C3×C42×D5C2211yescharacteristic
29#91513—28no—
30#91489—28no—
31#91449—22no—
32Dic5×D12—22no—
33#91373C2212yescomplemented
34C2×#6662C2212yescomplemented
35C2×#6657C2212yes—
36C2×#6656C2212yescomplemented
37C2×#6652C2212yes—
38C2×#6649C2212yes—
39#91087C2211yescharacteristic, complemented
40C5×#803C2211yescharacteristic, complemented
41Dic5×C3⋊C8C2212yescomplemented
42#82943—51nomaximal, Hall
43C2×#4061—32no—
44C2×#4057—32no—
45#66050—31no—
46D5×#124D311yescharacteristic, complemented
47C5×#496—31no—
48#65457—32no—
49#65444—32no—
50#65363—31no—
51#65349—31no—
52#65004—31no—
53#64996—31no—
54C23×C3×D5—21no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×C3×C5×D4C2311yescharacteristic
57C2×Dic30C2312yes—
58C2×C5×D12—22no—
59C2×C5×D12C2312yes—
60C2×C3×C22⋊D5—21no—
61C3×Q8×D5—24no—
62C3×D4×D5—24no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×C3×C4×D5D412yes—
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×Dic10—21no—
68C2×C3×Dic10C2311yescharacteristic
69C2×#1201—22no—
70C2×D3×Dic5—22no—
71#6772—24no—
72#6772—24no—
73C3×C5×C22⋊C4—22no—
74C3×C42×C5C2311yescharacteristic
75#6718—24no—
76#6716—24no—
77C4⋊Dic15—22no—
78C2×C3⋊#168C2312yes—
79C5×#215—24no—
80C5×#213—24no—
81C2×C5×C3⋊C8C2312yes—
82C3×C22⋊Dic5—22no—
83C3×#685—22no—
84C3×#685—22no—
85C3×C4×Dic5D412yes—
86C3×C4×Dic5C2311yescharacteristic
87(C2×D3)⋊Dic5—24no—
88#6662—24no—
89#6657—24no—
90#6656—24no—
91#6652—24no—
92#6649D418yescomplemented
93C2×C3×#124—51no—
94C2×#942—52no—
95C2×#932—52no—
96#5477—51no—
97#5060—51no—
98#5060—51no—
99#5059—52no—
100#5059—52no—
101#5058—51no—
102#5058D511yescharacteristic, complemented
103C4×#208—51no—
104C2×Q8×D5C2×D311yescharacteristic
105C2×#711—32no—
106C2×D4×D5C2×D311yescharacteristic
107C2×C5×SD16—32no—
108C2×C5×D8—32no—
109C5×#127—31no—
110C5×#124C2×D311yescharacteristic
111#4093C2×D311yescharacteristic
112C2×#689—32no—
113#4084—62no—
114#4082—32no—
115#4082C2×D311yescharacteristic
116D4×Dic5—62no—
117C2×#687—32no—
118C2×#687—32no—
119C2×#686—32no—
120#4061—68no—
121#4057—68no—
122C2×Dic20—32no—
123C2×#677—32no—
124C2×#676—32no—
125#4031—22no—
126D5×C22⋊C4—22no—
127#4021C2×D311yescharacteristic
128C42×D5C2×D311yescharacteristic
129#4015—31no—
130C5×#97—31no—
131C8×Dic5—32no—
132#3935—31no—
133#3153—151noSylow
134C23×C3×C5—21no—
135C22×C5×D3—22no—
136C22×C3×D5—21no—
137C22×C3×D5—44no—
138C22×C3×D5—42no—
139C22×C3×D5C2×D411yescharacteristic
140C3×C5×Q8—22no—
141C3×C5×D4—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146Dic30—22no—
147Dic30—22no—
148C5×D12—22no—
149C5×D12—22no—
150C5×D12—44no—
151C3×C22⋊D5—42no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5C2×D412yes—
154C2×C3×Dic5C2×D411yescharacteristic
155C3×D20—22no—
156C3×C4×D5—42no—
157C3×C4×D5—42no—
158C3×C4×D5C2×D414yes—
159C3×Dic10—22no—
160C3×Dic10—42no—
161#1201—44no—
162D3×Dic5—44no—
163C3⋊#168C2×D414yes—
164C5×C3⋊C8C2×D414yes—
165C22×C3×Q8—51no—
166C22×C3×D4—51no—
167C2×#235—52no—
168C3×#124—51no—
169C3×#124—51no—
170C3×#124—51no—
171C3×#124—102no—
172C3×#124C2×D511yescharacteristic
173C2×C3×C22⋊C4—102no—
174C2×C3×C42—51no—
175C2×#216—52no—
176C2×#216—52no—
177#942—108no—
178C2×#215—52no—
179C2×#215C2×D512yescomplemented
180C2×#214—52no—
181C2×#214—52no—
182#932—108no—
183C2×#213—52no—
184C2×#213C2×D512yes—
185#930—102no—
186C2×#208—52no—
187#875—52no—
188#874C2×D511yescharacteristic, complemented
189C4×D12—102no—
190#869—51no—
191#803—51no—
192#803C2×D511yescharacteristic, complemented
193C4×C3⋊C8—52no—
194C23×D5—21no—
195C2×C5×Q8C22×D311yescharacteristic
196C2×C5×D4—32no—
197C2×C5×D4—62no—
198C2×C5×D4C22×D311yescharacteristic
199C2×C22⋊D5—21no—
200C2×C22⋊D5—62no—
201C22×Dic5—62no—
202Q8×D5—24no—
203#711—64no—
204#711—64no—
205D4×D5—24no—
206C2×D20C22×D311yescharacteristic
207C2×C4×D5—21no—
208C2×C4×D5#6712yes—
209C2×C4×D5C22×D311yescharacteristic
210C2×Dic10—21no—
211C2×Dic10—32no—
212C2×Dic10C22×D311yescharacteristic
213C5×SD16—64no—
214C5×D8—64no—
215C2×C5×C8—32no—
216C5×C22⋊C4—22no—
217C42×C5C22×D311yescharacteristic
218C22⋊Dic5—22no—
219C22⋊Dic5—64no—
220#689—64no—
221#687—64no—
222#687—64no—
223#686—64no—
224#685—22no—
225#685—22no—
226C4⋊Dic5—62no—
227C4×Dic5#6712yes—
228C4×Dic5C22×D311yescharacteristic
229C2×#168—32no—
230Dic20—64no—
231#677—64no—
232#676—38no—
233C2×#137—152no—
234C2×AGL(1,ℤ/8)—152no—
235#532—151no—
236C2×#124—51no—
237#497—151no—
238#497—151no—
239#496—31no—
240#496—151no—
241#495—152no—
242#495—152no—
243C4×M16—151no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C22×D411yescharacteristic
247C2×C5×D3—42no—
248C2×C5×D3—44no—
249C2×C3×D5—22no—
250C2×C3×D5—41no—
251C2×C3×D5—42no—
252C2×C3×D5—84no—
253C2×C3×D5#12712yes—
254C3×C4×C5—22no—
255C3×C4×C5—41no—
256C3×C4×C5C22×D412yes—
257Dic15—42no—
258C3×Dic5—22no—
259C3×Dic5—41no—
260C3×Dic5#12712yes—
261C24×C3—101no—
262C2×C3×Q8—51no—
263C2×C3×Q8—101no—
264C2×C3×Q8—104no—
265C2×C3×Q8C22×D511yescharacteristic
266C2×C3×D4—51no—
267C2×C3×D4—104no—
268C2×C3×D4—101no—
269C2×C3×D4C22×D511yescharacteristic
270C22×C3×C4—51no—
271C22×C3×C4—52no—
272C22×C3×C4—101no—
273C2×#67—102no—
274#235—104no—
275#235—104no—
276C2×D12—22no—
277C2×D12C22×D512yes—
278C2×C4×D3—102no—
279C2×Dic6—52no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—102no—
282C3×C22⋊C4—102no—
283C3×C22⋊C4—102no—
284C3×C42—52no—
285C3×C42—51no—
286C3×C42C22×D511yescharacteristic
287#216—104no—
288#216—104no—
289#215—24no—
290#215—104no—
291#214—104no—
292#214—104no—
293#213—24no—
294#213—104no—
295(C2×D3)⋊C4—104no—
296C4⋊Dic3—102no—
297#208—58no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8C22×D512yes—
300C23×C5—21no—
301C23×C5—62no—
302C22×D5—21no—
303C22×D5—44no—
304C22×D5—42no—
305C22×D5C2×#6711yescharacteristic
306C5×Q8—22no—
307C5×D4—22no—
308C5×D4—62no—
309C5×D4—62no—
310C5×D4—124no—
311C2×C4×C5—21no—
312C2×C4×C5C2×#6712yes—
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—42no—
315C22⋊D5—124no—
316C2×Dic5—21no—
317C2×Dic5—62no—
318C2×Dic5—124no—
319C2×Dic5C2×#6712yes—
320C2×Dic5C2×#6711yescharacteristic
321D20—22no—
322C4×D5—42no—
323C4×D5—42no—
324C4×D5D3×D414yes—
325Dic10—22no—
326Dic10—42no—
327Dic10—62no—
328Dic10—62no—
329C5×C8—34no—
330#168—34no—
331C2×#41—152no—
332C22×Q8—51no—
333C22×D4—51no—
334#137—308no—
335AGL(1,ℤ/8)—308no—
336C2×Q16—152no—
337C2×Q16—152no—
338C2×SD16—32no—
339C2×SD16—152no—
340C2×SD16—152no—
341C2×SD16—152no—
342C2×D8—32no—
343C2×D8—152no—
344C2×M16—152no—
345C4⋊Q8—151no—
346#127—31no—
347#124—51no—
348#124—51no—
349#124—51no—
350#124—102no—
351#124—152no—
352#124D3×D511yescharacteristic
353#121—302no—
354C4×D4—302no—
355C2×C22⋊C4—102no—
356C2×C42—51no—
357#97—31no—
358#97—151no—
359C4×C8—152no—
360C2×C3×C5—81no—
361C2×C3×C5C2×#12711yescharacteristic
362C2×C3×C5#57512yes—
363C3×D5—22no—
364C3×D5—81no—
365C5×D3—82no—
366C23×C3—21no—
367C23×C3—51no—
368C23×C3—101no—
369C23×C3—202no—
370C23×C3—204no—
371C22×D3—22no—
372C3×Q8—22no—
373C3×Q8—102no—
374C3×Q8—202no—
375C3×D4—22no—
376C3×D4—102no—
377C3×D4—202no—
378C2×C3×C4—21no—
379C2×C3×C4—51no—
380C2×C3×C4—54no—
381C2×C3×C4—52no—
382C2×C3×C4—101no—
383C2×C3×C4—202no—
384C2×C3×C4—202no—
385C2×C3×C4D4×D512yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—204no—
388C2×Dic3—102no—
389D12—22no—
390D12—22no—
391D12—44no—
392C4×D3—204no—
393Dic6—102no—
394Dic6—102no—
395C3⋊C8—54no—
396C3⋊C8D4×D514yes—
397C22×C5—41no—
398C22×C5—42no—
399C22×C5—122no—
400C22×C5—124no—
401C22×C5C22×#6711yescharacteristic
402C2×D5—22no—
403C2×D5—41no—
404C2×D5—42no—
405C2×D5—84no—
406C2×D5#94012yes—
407C4×C5—22no—
408C4×C5—41no—
409C4×C5C2×D3×D412yes—
410Dic5—22no—
411Dic5—41no—
412Dic5—122no—
413Dic5#94012yes—
414C24—101no—
415#41—304no—
416#41—304no—
417C2×Q8—51no—
418C2×Q8—101no—
419C2×Q8—104no—
420C2×Q8—152no—
421C2×Q8C2×D3×D511yescharacteristic
422C2×D4—32no—
423C2×D4—51no—
424C2×D4—62no—
425C2×D4—104no—
426C2×D4—101no—
427C2×D4—302no—
428C2×D4C2×D3×D511yescharacteristic
429C22×C4—51no—
430C22×C4—52no—
431C22×C4—101no—
432C22×C4—302no—
433Q16—304no—
434Q16—304no—
435SD16—64no—
436SD16—304no—
437SD16—304no—
438SD16—304no—
439D8—64no—
440D8—304no—
441M16—158no—
442C2×C8—32no—
443C2×C8—152no—
444C4⋊C4—302no—
445C22⋊C4—22no—
446C22⋊C4—102no—
447C22⋊C4—102no—
448C22⋊C4—102no—
449C22⋊C4—304no—
450C42—52no—
451C42—51no—
452C42C2×D3×D511yescharacteristic
453C3×C5#315311yescharacteristic, complemented, Hall
454C22×C3—41no—
455C22×C3—42no—
456C22×C3—52no—
457C22×C3—102no—
458C22×C3—201no—
459C22×C3—202no—
460C22×C3—404no—
461C22×C3C2×D4×D511yescharacteristic
462C2×D3—42no—
463C2×D3—44no—
464C3×C4—22no—
465C3×C4—41no—
466C3×C4—52no—
467C3×C4—102no—
468C3×C4—201no—
469C3×C4C2×D4×D512yes—
470Dic3—202no—
471C2×C5—81no—
472C2×C5—242no—
473C2×C5C2×#94011yescharacteristic
474C2×C5#582212yes—
475D5—22no—
476D5—81no—
477C23—21no—
478C23—51no—
479C23—62no—
480C23—101no—
481C23—202no—
482C23—204no—
483Q8—22no—
484Q8—102no—
485Q8—202no—
486Q8—302no—
487Q8—302no—
488D4—22no—
489D4—62no—
490D4—62no—
491D4—102no—
492D4—124no—
493D4—202no—
494D4—604no—
495C2×C4—21no—
496C2×C4—51no—
497C2×C4—54no—
498C2×C4—52no—
499C2×C4—101no—
500C2×C4—202no—
501C2×C4—202no—
502C2×C4—302no—
503C2×C4—604no—
504C2×C4D5×#6712yes—
505C2×C4C22×D3×D511yescharacteristic
506C8—34no—
507C8—154no—
508C2×C3—81no—
509C2×C3—102no—
510C2×C3—401no—
511C2×C3D5×#12711yescharacteristic
512C2×C3#6610712yes—
513D3—82no—
514C5#8294311yescharacteristic, complemented, Sylow
515C22—41no—
516C22—42no—
517C22—52no—
518C22—102no—
519C22—122no—
520C22—124no—
521C22—201no—
522C22—202no—
523C22—404no—
524C22C2×D5×#6711yescharacteristic
525C4—22no—
526C4—41no—
527C4—52no—
528C4—102no—
529C4—201no—
530C4—602no—
531C4D3×D4×D512yes—
532C3#1061357711yescharacteristic, complemented, Sylow
533C2—81no—
534C2—102no—
535C2—242no—
536C2—401no—
537C2D5×#94011yescharacteristic
538C2#1175534312yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5#3153
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×D5×#124C2semidirect
2. C2×#91513C2semidirect
3. C2×#91489C2semidirect
4. #11752672C2semidirect
5. #11751161C2semidirect
6. C5×#5058C2semidirect
7. #11749313C2semidirect
8. #11749067C2semidirect
9. #11747074C2semidirect
10. #11747042C2semidirect
11. #11747003C2semidirect
17. C2×#6718C22semidirect
19. #91758C22semidirect
20. C2×C5×#215C22semidirect
22. C5×#874C22semidirect
33. #91373C22semidirect
34. C2×#6662C22semidirect
36. C2×#6656C22semidirect
39. #91087C22semidirect
40. C5×#803C22semidirect
41. Dic5×C3⋊C8C22semidirect
46. D5×#124D3semidirect
92. #6649D4semidirect
102. #5058D5semidirect
179. C2×#215C2×D5semidirect
188. #874C2×D5semidirect
192. #803C2×D5semidirect
453. C3×C5#3153semidirect
514. C5#82943semidirect
532. C3#10613577semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
C2×#915132
C2×#914892
#117526722
#117511612
C5×#50582
#117493132
#117490672
#117470742
#117470422
#117470032
#106135773
#829435