Finite Group Databasebeta

← #14439366

Subgroups — #14439366

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×#66059C211yesmaximal, characteristic, complemented
2C2×#91508C212yesmaximal, complemented
3C2×#91502C212yesmaximal, complemented
4D5×#875C211yesmaximal, characteristic, complemented
5#11751187C211yesmaximal, characteristic, complemented
6C5×#5086C211yesmaximal, characteristic, complemented
7#11749316C212yesmaximal, complemented
8#11749313C212yesmaximal, complemented
9#11747073C211yesmaximal, characteristic, complemented
10#11747041C211yesmaximal, characteristic, complemented
11#11747003C211yesmaximal, characteristic, complemented
12#10613602—31nomaximal, Hall
13C2×C3×#713C2212yes—
14C2×D5×D12C2211yescharacteristic
15C2×D5×Dic6C2211yescharacteristic
16C3×C5×C4⋊Q8C2211yescharacteristic, complemented
17C2×#6718C2212yescomplemented
18C2×#6717C2212yes—
19#91764C2211yescharacteristic
20C2×C5×#216C2212yescomplemented
21C2×C5×#215C2212yes—
22C5×#875C2211yescharacteristic
23C3×#4093C2212yescomplemented
24C3×#4041—22no—
25C3×#4039—22no—
26C3×#4020C2211yescharacteristic, complemented
27C3×C42×D5C2211yescharacteristic
28#91508—28no—
29#91502—28no—
30D5×(C2×D3)⋊C4—22no—
31#91375C2211yescharacteristic
32#91373C2211yescharacteristic
33#91350—22no—
34C2×#6657C2212yescomplemented
35C2×#6655C2212yescomplemented
36C2×#6653C2212yes—
37C2×#6652C2212yes—
38C2×#6649C2212yes—
39#91087C2211yescharacteristic, complemented
40C5×#803C2211yescharacteristic, complemented
41Dic5×C3⋊C8C2212yescomplemented
42#83289—51nomaximal, Hall
43C2×#4064—32no—
44C2×#4060—32no—
45#66059D311yescharacteristic, complemented
46D5×#124—31no—
47C5×#497—31no—
48#65480—32no—
49#65457—32no—
50#65375—31no—
51#65347—31no—
52#65001—31no—
53#64996—31no—
54C22×D3×D5—21no—
55C2×C3×C5×Q8C2312yes—
56C2×D60C2311yescharacteristic
57C2×Dic30C2311yescharacteristic
58C2×C5×D12C2311yescharacteristic
59C2×C5×Dic6C2311yescharacteristic
60C3×#713—24no—
61C3×#713—24no—
62C2×C3×D20—22no—
63C2×C3×D20—22no—
64C2×C3×D20C2312yes—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5D412yes—
67C2×C3×C4×D5C2311yescharacteristic
68C2×#1204—21no—
69C2×#1203—21no—
70C2×D5×Dic3—21no—
71D5×D12—24no—
72D5×Dic6—24no—
73C3×C5×C4⋊C4—22no—
74C3×C42×C5C2311yescharacteristic
75#6718—24no—
76#6717—24no—
77#6714—22no—
78C2×C3⋊#168C2312yes—
79C5×#216—24no—
80C5×#215—24no—
81C5×(C2×D3)⋊C4—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×#685—24no—
84C3×C4×Dic5D412yes—
85C3×C4×Dic5C2311yescharacteristic
86#6667—22no—
87(C2×D3)⋊Dic5—22no—
88#6657—24no—
89#6655—24no—
90#6653—24no—
91#6652—24no—
92#6649D418yescomplemented
93C3×#532—51no—
94C2×#951—52no—
95C2×#949—52no—
96C2×#875—51no—
97#5086—51no—
98#5086D511yescharacteristic, complemented
99#5074—51no—
100#5074—51no—
101#5059—52no—
102#5059—52no—
103C4×#208—51no—
104C2×#713C2×D312yes—
105C2×Q8×D5—31no—
106C2×D4×D5—31no—
107C2×C5×Q16—32no—
108C2×C5×SD16—32no—
109C5×C4⋊Q8C2×D311yescharacteristic, complemented
110C5×#124—31no—
111#4093—31no—
112#4093C2×D312yescomplemented
113C2×#689—32no—
114C2×#688—32no—
115C2×#688—32no—
116#4082—31no—
117C2×#686—32no—
118#4064—68no—
119#4060—68no—
120C2×D40—32no—
121C2×#677—32no—
122C2×#676—32no—
123#4041—22no—
124#4039—22no—
125#4031—62no—
126D5×C22⋊C4—62no—
127#4021—31no—
128#4020C2×D311yescharacteristic, complemented
129C42×D5C2×D311yescharacteristic
130C5×#97—31no—
131C8×Dic5—32no—
132#3935—31no—
133#3153—151noSylow
134C22×D15—21no—
135C22×C5×D3—21no—
136C22×C3×D5—22no—
137C22×C3×D5C2×D411yescharacteristic
138C2×D3×D5—44no—
139C2×D3×D5—42no—
140C3×C5×Q8—22no—
141C3×C5×Q8—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—21no—
146D60—22no—
147Dic30—22no—
148C2×C5×Dic3—21no—
149C5×D12—22no—
150C5×Dic6—22no—
151C2×C3×Dic5C2×D412yes—
152C2×C3×Dic5C2×D411yescharacteristic
153C3×D20—22no—
154C3×D20—22no—
155C3×D20—44no—
156C3×D20—44no—
157C3×C4×D5—42no—
158C3×C4×D5—44no—
159C3×C4×D5C2×D414yes—
160#1204—42no—
161#1203—42no—
162D5×Dic3—42no—
163C3⋊#168C2×D414yes—
164C5×C3⋊C8C2×D414yes—
165C2×C3×#41—52no—
166C22×D12—51no—
167C22×Dic6—51no—
168C3×C4⋊Q8C2×D511yescharacteristic, complemented
169C3×#127—51no—
170C3×#124—52no—
171C3×#121—102no—
172C3×C4×D4—102no—
173C2×C3×C42—51no—
174#951—108no—
175#949—108no—
176C2×#216—52no—
177C2×#216C2×D512yescomplemented
178C2×#215—52no—
179C2×#215C2×D512yes—
180C2×#214—52no—
181C2×#214—52no—
182C2×#213—52no—
183C2×#213—52no—
184C2×(C2×D3)⋊C4—102no—
185C2×#208—52no—
186#875—51no—
187#875—51no—
188#875—51no—
189#875—102no—
190#875C2×D511yescharacteristic
191#803—51no—
192#803C2×D511yescharacteristic, complemented
193C4×C3⋊C8—52no—
194C23×D5—61no—
195C2×C5×Q8—31no—
196C2×C5×Q8C22×D312yes—
197C2×C5×D4—31no—
198C2×C22⋊D5—61no—
199#713—24no—
200#713—24no—
201Q8×D5—64no—
202D4×D5—64no—
203C2×D20—22no—
204C2×D20—22no—
205C2×D20—31no—
206C2×D20C22×D312yes—
207C2×C4×D5—22no—
208C2×C4×D5—61no—
209C2×C4×D5#6712yes—
210C2×C4×D5C22×D311yescharacteristic
211C2×Dic10—31no—
212C2×Dic10—61no—
213C5×Q16—64no—
214C5×SD16—64no—
215C2×C5×C8—32no—
216C5×C4⋊C4—22no—
217C5×C22⋊C4—62no—
218C42×C5C22×D311yescharacteristic
219C22⋊Dic5—62no—
220#689—64no—
221#688—64no—
222#688—64no—
223#686—64no—
224#685—24no—
225#685—62no—
226#685—62no—
227C4×Dic5#6712yes—
228C4×Dic5C22×D311yescharacteristic
229C2×#168—32no—
230D40—64no—
231#677—64no—
232#676—38no—
233C2×#137—152no—
234C2×AGL(1,ℤ/8)—152no—
235#532—51no—
236C2×#124—151no—
237#497—31no—
238#497—151no—
239#496—151no—
240#496—151no—
241#495—152no—
242#495—152no—
243C4×M16—151no—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—41no—
246C2×D15—42no—
247C2×C5×D3—41no—
248C2×C5×D3—42no—
249C2×C3×D5—22no—
250C2×C3×D5—42no—
251C2×C3×D5—44no—
252C2×C3×D5#12712yes—
253D3×D5—84no—
254C3×C4×C5—22no—
255C3×C4×C5—42no—
256C3×C4×C5C22×D412yes—
257Dic15—41no—
258C3×Dic5—22no—
259C3×Dic5#12712yes—
260C5×Dic3—41no—
261C23×D3—101no—
262C3×#41—104no—
263C3×#41—104no—
264C2×C3×Q8C22×D512yes—
265C2×C3×D4—52no—
266C2×C3×D4—102no—
267C2×C3×D4—102no—
268C22×C3×C4—51no—
269C22×C3×C4—52no—
270C22×C3×C4—102no—
271C22×Dic3—101no—
272C2×D12—51no—
273C2×D12—104no—
274C2×D12—101no—
275C2×D12C22×D511yescharacteristic
276C2×Dic6—51no—
277C2×Dic6—104no—
278C2×Dic6—101no—
279C2×Dic6C22×D511yescharacteristic
280C3×C4⋊C4—22no—
281C3×C22⋊C4—104no—
282C3×C42—52no—
283C3×C42—51no—
284C3×C42C22×D511yescharacteristic
285#216—24no—
286#216—104no—
287#215—24no—
288#215—104no—
289#214—104no—
290#214—104no—
291#213—104no—
292#213—104no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296(C2×D3)⋊C4—102no—
297#208—58no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8C22×D512yes—
300C23×C5—61no—
301C22×D5—22no—
302C22×D5—61no—
303C22×D5—124no—
304C22×D5—122no—
305C22×D5C2×#6711yescharacteristic
306C5×Q8—22no—
307C5×Q8—22no—
308C5×Q8—62no—
309C5×D4—62no—
310C2×C4×C5—22no—
311C2×C4×C5—61no—
312C2×C4×C5C2×#6712yes—
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—122no—
315C2×Dic5—61no—
316C2×Dic5C2×#6712yes—
317C2×Dic5C2×#6711yescharacteristic
318D20—22no—
319D20—22no—
320D20—44no—
321D20—44no—
322D20—62no—
323C4×D5—42no—
324C4×D5—44no—
325C4×D5—122no—
326C4×D5D3×D414yes—
327Dic10—62no—
328Dic10—122no—
329C5×C8—34no—
330#168—34no—
331C2×#41—52no—
332C22×Q8—151no—
333C22×D4—151no—
334#137—308no—
335AGL(1,ℤ/8)—308no—
336C2×Q16—32no—
337C2×Q16—152no—
338C2×SD16—32no—
339C2×SD16—152no—
340C2×SD16—152no—
341C2×SD16—152no—
342C2×D8—152no—
343C2×D8—152no—
344C2×M16—152no—
345C4⋊Q8D3×D511yescharacteristic, complemented
346#127—51no—
347#124—31no—
348#124—52no—
349#124—151no—
350#124—151no—
351#124—151no—
352#124—302no—
353#121—102no—
354C4×D4—102no—
355C2×C22⋊C4—302no—
356C2×C42—51no—
357#97—31no—
358#97—151no—
359C4×C8—152no—
360C2×C3×C5C2×#12711yescharacteristic
361C2×C3×C5#57512yes—
362D15—81no—
363C3×D5—22no—
364C3×D5—82no—
365C5×D3—81no—
366C23×C3—51no—
367C23×C3—102no—
368C22×D3—21no—
369C22×D3—101no—
370C22×D3—202no—
371C22×D3—204no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×D4—102no—
375C3×D4—102no—
376C3×D4—204no—
377C3×D4—204no—
378C2×C3×C4—22no—
379C2×C3×C4—51no—
380C2×C3×C4—54no—
381C2×C3×C4—52no—
382C2×C3×C4—202no—
383C2×C3×C4—204no—
384C2×C3×C4D4×D512yes—
385C2×C3×C4C23×D511yescharacteristic
386C2×Dic3—21no—
387C2×Dic3—101no—
388C2×Dic3—202no—
389D12—22no—
390D12—102no—
391D12—202no—
392Dic6—22no—
393Dic6—102no—
394Dic6—202no—
395C3⋊C8—54no—
396C3⋊C8D4×D514yes—
397C22×C5—121no—
398C22×C5—122no—
399C22×C5C22×#6711yescharacteristic
400C2×D5—22no—
401C2×D5—42no—
402C2×D5—44no—
403C2×D5—121no—
404C2×D5—122no—
405C2×D5—244no—
406C2×D5#94012yes—
407C4×C5—22no—
408C4×C5—42no—
409C4×C5—121no—
410C4×C5C2×D3×D412yes—
411Dic5—22no—
412Dic5—121no—
413Dic5#94012yes—
414C24—301no—
415#41—104no—
416#41—104no—
417C2×Q8—31no—
418C2×Q8—151no—
419C2×Q8—301no—
420C2×Q8—304no—
421C2×Q8C2×D3×D512yes—
422C2×D4—31no—
423C2×D4—52no—
424C2×D4—102no—
425C2×D4—102no—
426C2×D4—151no—
427C2×D4—304no—
428C2×D4—301no—
429C22×C4—51no—
430C22×C4—52no—
431C22×C4—102no—
432C22×C4—301no—
433Q16—64no—
434Q16—304no—
435SD16—64no—
436SD16—304no—
437SD16—304no—
438SD16—304no—
439D8—304no—
440D8—304no—
441M16—158no—
442C2×C8—32no—
443C2×C8—152no—
444C4⋊C4—22no—
445C22⋊C4—62no—
446C22⋊C4—104no—
447C22⋊C4—302no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C42—52no—
451C42—51no—
452C42C2×D3×D511yescharacteristic
453C3×C5#315311yescharacteristic, complemented, Hall
454C22×C3—52no—
455C22×C3—102no—
456C22×C3—202no—
457C22×C3—204no—
458C22×C3C2×D4×D511yescharacteristic
459C2×D3—41no—
460C2×D3—42no—
461C2×D3—201no—
462C2×D3—202no—
463C2×D3—404no—
464C3×C4—22no—
465C3×C4—42no—
466C3×C4—52no—
467C3×C4—102no—
468C3×C4C2×D4×D512yes—
469Dic3—41no—
470Dic3—201no—
471C2×C5—241no—
472C2×C5C2×#94011yescharacteristic
473C2×C5#582212yes—
474D5—22no—
475D5—82no—
476D5—241no—
477C23—51no—
478C23—61no—
479C23—102no—
480C23—301no—
481C23—602no—
482C23—604no—
483Q8—22no—
484Q8—22no—
485Q8—62no—
486Q8—302no—
487Q8—602no—
488D4—62no—
489D4—102no—
490D4—102no—
491D4—204no—
492D4—204no—
493D4—302no—
494D4—602no—
495C2×C4—22no—
496C2×C4—51no—
497C2×C4—54no—
498C2×C4—52no—
499C2×C4—61no—
500C2×C4—202no—
501C2×C4—204no—
502C2×C4—301no—
503C2×C4—602no—
504C2×C4D5×#6712yes—
505C2×C4C22×D3×D511yescharacteristic
506C8—34no—
507C8—154no—
508C2×C3—102no—
509C2×C3—402no—
510C2×C3D5×#12711yescharacteristic
511C2×C3#6611112yes—
512D3—81no—
513D3—401no—
514C5#8328911yescharacteristic, complemented, Sylow
515C22—52no—
516C22—102no—
517C22—121no—
518C22—122no—
519C22—202no—
520C22—204no—
521C22—601no—
522C22—602no—
523C22—1204no—
524C22C2×D5×#6711yescharacteristic
525C4—22no—
526C4—42no—
527C4—52no—
528C4—102no—
529C4—121no—
530C4—601no—
531C4D3×D4×D512yes—
532C3#1061360211yescharacteristic, complemented, Sylow
533C2—102no—
534C2—241no—
535C2—402no—
536C2—1201no—
537C2D5×#94011yescharacteristic
538C2#1175508412yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3153
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×#66059C2semidirect
2. C2×#91508C2semidirect
3. C2×#91502C2semidirect
4. D5×#875C2semidirect
5. #11751187C2semidirect
6. C5×#5086C2semidirect
7. #11749316C2semidirect
8. #11749313C2semidirect
9. #11747073C2semidirect
10. #11747041C2semidirect
11. #11747003C2semidirect
16. C3×C5×C4⋊Q8C22semidirect
17. C2×#6718C22semidirect
20. C2×C5×#216C22semidirect
23. C3×#4093C22semidirect
26. C3×#4020C22semidirect
34. C2×#6657C22semidirect
35. C2×#6655C22semidirect
39. #91087C22semidirect
40. C5×#803C22semidirect
41. Dic5×C3⋊C8C22semidirect
45. #66059D3semidirect
92. #6649D4semidirect
98. #5086D5semidirect
109. C5×C4⋊Q8C2×D3semidirect
112. #4093C2×D3semidirect
128. #4020C2×D3semidirect
168. C3×C4⋊Q8C2×D5semidirect
177. C2×#216C2×D5semidirect
192. #803C2×D5semidirect
345. C4⋊Q8D3×D5semidirect
453. C3×C5#3153semidirect
514. C5#83289semidirect
532. C3#10613602semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
C2×#915082
C2×#915022
D5×#8752
#117511872
C5×#50862
#117493162
#117493132
#117470732
#117470412
#117470032
#106136023
#832895