Finite Group Databasebeta

← #14425691

Subgroups — #14425691

Order 1920.

1532 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5964C211yesmaximal, characteristic, complemented
2C3×#66162C211yesmaximal, characteristic, complemented
3#11754563C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11749183C214yesmaximal, complemented
6#11749177C214yesmaximal, complemented
7#11748625C212yesmaximal, complemented
8#10615856—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×#1010—22no—
11C5×#1009—22no—
12C5×D3×#41—24no—
13C5×#1007—21no—
14C5×#1004—21no—
15C5×#1004C2214yes—
16C2×C5×#235—22no—
17C2×C5×#235C2212yes—
18C22×C3×C4×D5C2211yescharacteristic, complemented
19#91815C2212yescomplemented
20C3×#4092—21no—
21C3×#4084—21no—
22C3×#4083C2212yescomplemented
23C3×#4081C2212yescomplemented
24C3×C4×C22⋊D5—22no—
25C3×#4072C2211yescharacteristic, complemented
26#91563C2214yescomplemented
27#91539C2214yescomplemented
28#91449—22no—
29C4×#1201—24no—
30#91359—22no—
31#91118C2214yescomplemented
32#90996C2218yescomplemented
33#82936—51nomaximal, Hall
34C5×#585—31no—
35#66162—32no—
36#66162D311yescharacteristic, complemented
37#65533—34no—
38#65532—34no—
39#65529—32no—
40#65529—31no—
41C23×C3×D5C2311yescharacteristic
42C3×C5×#41—22no—
43C3×C5×#41—22no—
44C2×C3×C5×Q8D411yescharacteristic, complemented
45C2×C3×C5×D4D411yescharacteristic, complemented
46C2×C3×C5×D4C2312yes—
47C22×C3×C4×C5D412yescomplemented
48C22×C3×C4×C5C2311yescharacteristic
49C2×C5×#67—24no—
50C2×C5×#67C2314yes—
51C5×#239—24no—
52C5×D3×Q8—24no—
53C5×#237—24no—
54C5×#237—28no—
55C5×D3×D4—24no—
56C5×D3×D4—28no—
57C5×#235—24no—
58C5×#235—24no—
59C5×#235—22no—
60C5×#235—24no—
61C5×#235—22no—
62C5×#235—22no—
63C5×#235—22no—
64C2×C5×D12—22no—
65C2×C5×D12D412yescomplemented
66C2×C4×C5×D3—24no—
67C2×C4×C5×D3D414yescomplemented
68C2×C5×Dic6—22no—
69C2×C5×Dic6D412yescomplemented
70C2×C3×C22⋊D5—22no—
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—21no—
76C2×#1201—24no—
77#6719C2314yes—
78C4⋊Dic15—22no—
79C4×Dic15—22no—
80C3×C22⋊Dic5—22no—
81C3×C22⋊Dic5C2312yes—
82C3×#685—22no—
83C3×C4⋊Dic5—21no—
84C3×#683—22no—
85C3×C4×Dic5—21no—
86#6669—24no—
87(C2×D3)⋊Dic5—24no—
88#6665—24no—
89#5964D511yescharacteristic, complemented
90C3×#525—51no—
91#5791—52no—
92#5240—51no—
93#5053—54no—
94#5032—54no—
95#5006—52no—
96C5×2−1+4—62no—
97C5×2−1+4—61no—
98C5×H(5,𝔽2)—34no—
99C5×H(5,𝔽2)—62no—
100C5×H(5,𝔽2)—61no—
101C2×C5×#41—32no—
102C2×C5×#41—64no—
103C2×C5×#41—62no—
104C2×C5×#41C2×D311yescharacteristic
105C22×C4×D5C2×D311yescharacteristic, complemented
106#4092—21no—
107#4092—62no—
108#4084—21no—
109#4084—62no—
110#4083—34no—
111#4083C2×D312yescomplemented
112#4081—34no—
113#4081C2×D312yescomplemented
114C4×C22⋊D5—22no—
115C4×C22⋊D5—64no—
116#4072—32no—
117#4072C2×D311yescharacteristic, complemented
118#3966—34no—
119#3966—38no—
120#3025—151noSylow
121C23×C3×C5C2×D412yes—
122C23×C3×C5C2411yescharacteristic
123C22×C5×D3—24no—
124C22×C5×D3C2×D414yes—
125C22×C3×D5—22no—
126C22×C3×D5—21no—
127C22×C3×D5—42no—
128C3×C5×Q8—22no—
129C3×C5×D4—24no—
130C3×C5×D4—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×Dic15—24no—
139C5×#67—28no—
140C5×#67—24no—
141C5×#67—24no—
142C2×C5×Dic3—24no—
143C2×C5×Dic3C2×D414yes—
144C5×D12—24no—
145C5×D12—22no—
146C5×D12—22no—
147C4×C5×D3—28no—
148C4×C5×D3—24no—
149C4×C5×D3—24no—
150C5×Dic6—24no—
151C5×Dic6—22no—
152C5×Dic6—22no—
153C3×C22⋊D5—44no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—21no—
157C3×C4×D5—41no—
158C3×C4×D5—42no—
159C3×C4×D5—41no—
160#1201—48no—
161C2×C3×#41C2×D511yescharacteristic
162C23×C3×C4—51no—
163#1010—22no—
164#1009—22no—
165D3×#41—24no—
166#1007—21no—
167#1004—21no—
168#1004C2×D514yes—
169C2×#235—22no—
170C2×#235C2×D512yes—
171C3×#123—52no—
172C3×C22⋊Q8—101no—
173C3×#121—101no—
174C3×#120—52no—
175C3×C4×D4—102no—
176C3×#117—51no—
177#953—54no—
178#930—102no—
179#929—54no—
180C4×#67—104no—
181#926—52no—
182#924—102no—
183#834—54no—
184#806—58no—
185C23×D5C22×D311yescharacteristic
186C5×#41—22no—
187C5×#41—22no—
188C5×#41—64no—
189C5×#41—64no—
190C5×#41—68no—
191C5×#41—64no—
192C5×#41—64no—
193C5×#41—62no—
194C5×#41—62no—
195C5×#41—62no—
196C5×#41—62no—
197C5×#41—64no—
198C2×C5×Q8—32no—
199C2×C5×Q8—62no—
200C2×C5×Q8—64no—
201C2×C5×Q8#6711yescharacteristic, complemented
202C2×C5×D4—34no—
203C2×C5×D4—32no—
204C2×C5×D4—62no—
205C2×C5×D4—68no—
206C2×C5×D4—64no—
207C2×C5×D4—64no—
208C2×C5×D4#6711yescharacteristic, complemented
209C2×C5×D4C22×D312yes—
210C22×C4×C5—34no—
211C22×C4×C5—64no—
212C22×C4×C5#6712yescomplemented
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—22no—
215C2×C22⋊D5—64no—
216C22×Dic5C22×D311yescharacteristic
217C2×C4×D5—22no—
218C2×C4×D5—22no—
219C2×C4×D5—21no—
220C2×C4×D5—21no—
221C22⋊Dic5—22no—
222C22⋊Dic5—34no—
223C22⋊Dic5—64no—
224C22⋊Dic5C22×D312yes—
225#685—22no—
226#685—64no—
227C4⋊Dic5—21no—
228C4⋊Dic5—62no—
229#683—22no—
230#683—64no—
231C4×Dic5—21no—
232C4×Dic5—62no—
233#585—31no—
234#525—51no—
235#525—152no—
236#458—154no—
237B(4,𝔽2)—154no—
238#410—152no—
239#410—151no—
240C22×C3×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—42no—
243C22×C3×C5C22×D412yes—
244C22×C3×C5C22×D411yescharacteristic
245C2×C5×D3—24no—
246C2×C5×D3—44no—
247C2×C5×D3—84no—
248C2×C3×D5—24no—
249C2×C3×D5—22no—
250C2×C3×D5—41no—
251C2×C3×D5—42no—
252C2×C3×D5—41no—
253C3×C4×C5—22no—
254C3×C4×C5#12011yescharacteristic
255C3×C4×C5#12012yes—
256C3×C4×C5#12011yescharacteristic
257Dic15—44no—
258C3×Dic5—42no—
259C3×Dic5—41no—
260C5×Dic3—24no—
261C24×C3—51no—
262C3×#41—22no—
263C3×#41—22no—
264C2×C3×Q8C22⋊D511yescharacteristic, complemented
265C2×C3×D4—102no—
266C2×C3×D4C22⋊D511yescharacteristic, complemented
267C2×C3×D4C22×D512yes—
268C22×C3×C4—51no—
269C22×C3×C4—102no—
270C22×C3×C4—102no—
271C22×C3×C4—101no—
272C22×C3×C4—101no—
273C22×C3×C4C22⋊D512yescomplemented
274C22×C3×C4C22×D511yescharacteristic
275C2×#67—24no—
276C2×#67—104no—
277C2×#67C22×D514yes—
278#239—24no—
279D3×Q8—24no—
280#237—24no—
281#237—28no—
282D3×D4—24no—
283D3×D4—28no—
284#235—24no—
285#235—24no—
286#235—22no—
287#235—24no—
288#235—22no—
289#235—22no—
290#235—22no—
291C2×D12—22no—
292C2×D12C22⋊D512yescomplemented
293C2×C4×D3—24no—
294C2×C4×D3C22⋊D514yescomplemented
295C2×Dic6—22no—
296C2×Dic6C22⋊D512yescomplemented
297C3×C4⋊C4—102no—
298C3×C4⋊C4—101no—
299C3×C22⋊C4—52no—
300C3×C22⋊C4—102no—
301C3×C22⋊C4—102no—
302C3×C42—101no—
303#217—54no—
304#217—104no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—102no—
307Dic3⋊C4—104no—
308C4×Dic3—102no—
309C23×C5—34no—
310C23×C5—64no—
311C23×C5C2×#6712yes—
312C23×C5C23×D311yescharacteristic
313C22×D5—22no—
314C22×D5—21no—
315C22×D5—42no—
316C5×Q8—22no—
317C5×Q8—64no—
318C5×Q8—62no—
319C5×Q8—62no—
320C5×D4—24no—
321C5×D4—22no—
322C5×D4—64no—
323C5×D4—68no—
324C5×D4—64no—
325C5×D4—64no—
326C5×D4—62no—
327C5×D4—62no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—34no—
331C2×C4×C5—68no—
332C2×C4×C5—64no—
333C2×C4×C5—64no—
334C2×C4×C5—64no—
335C2×C4×C5D3×D412yes—
336C2×C4×C5D3×D412yes—
337C2×C4×C5C2×#6712yes—
338C2×C4×C5C2×#6711yescharacteristic
339C2×C4×C5C2×#6711yescharacteristic
340C22⋊D5—44no—
341C22⋊D5—128no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—21no—
345C2×Dic5—64no—
346C4×D5—41no—
347C4×D5—42no—
348C4×D5—41no—
3492−1+4—62no—
3502−1+4—61no—
351H(5,𝔽2)—34no—
352H(5,𝔽2)—62no—
353H(5,𝔽2)—61no—
354C2×#41—32no—
355C2×#41—64no—
356C2×#41—62no—
357C2×#41D3×D511yescharacteristic
358C23×C4—51no—
359#123—52no—
360#123—154no—
361C22⋊Q8—101no—
362C22⋊Q8—302no—
363#121—101no—
364#121—302no—
365#120—52no—
366#120—154no—
367C4×D4—102no—
368C4×D4—304no—
369#117—51no—
370#117—152no—
371#99—158no—
372#99—154no—
373C2×C3×C5—21no—
374C2×C3×C5—22no—
375C2×C3×C5—42no—
376C2×C3×C5C2×#12011yescharacteristic
377C3×D5—42no—
378C5×D3—44no—
379C23×C3—102no—
380C23×C3—101no—
381C23×C3—202no—
382C23×C3C2×C22⋊D512yes—
383C23×C3C23×D511yescharacteristic
384C22×D3—24no—
385C22×D3C2×C22⋊D514yes—
386C3×Q8—22no—
387C3×D4—24no—
388C3×D4—22no—
389C3×D4—204no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—102no—
393C2×C3×C4—102no—
394C2×C3×C4—101no—
395C2×C3×C4—201no—
396C2×C3×C4—202no—
397C2×C3×C4—201no—
398C2×C3×C4C2×C22⋊D512yes—
399C2×C3×C4C2×C22⋊D511yescharacteristic
400C2×C3×C4C2×C22⋊D511yescharacteristic
401C2×C3×C4C2×C22⋊D512yes—
402C2×C3×C4C2×C22⋊D512yes—
403#67—28no—
404#67—24no—
405#67—24no—
406#67—208no—
407C2×Dic3—24no—
408C2×Dic3—104no—
409C2×Dic3C2×C22⋊D514yes—
410D12—24no—
411D12—22no—
412D12—22no—
413C4×D3—28no—
414C4×D3—24no—
415C4×D3—24no—
416Dic6—24no—
417Dic6—22no—
418Dic6—22no—
419C22×C5—22no—
420C22×C5—41no—
421C22×C5—42no—
422C22×C5—64no—
423C22×C5—124no—
424C22×C5—244no—
425C22×C5C2×D3×D412yes—
426C22×C5C22×#6711yescharacteristic
427C2×D5—22no—
428C2×D5—24no—
429C2×D5—41no—
430C2×D5—42no—
431C2×D5—41no—
432C4×C5—22no—
433C4×C5—64no—
434C4×C5#93711yescharacteristic
435C4×C5#93712yes—
436C4×C5#93711yescharacteristic
437Dic5—42no—
438Dic5—41no—
439Dic5—124no—
440C24—51no—
441#41—22no—
442#41—22no—
443#41—64no—
444#41—64no—
445#41—68no—
446#41—64no—
447#41—64no—
448#41—62no—
449#41—62no—
450#41—64no—
451#41—62no—
452#41—62no—
453C2×Q8—32no—
454C2×Q8—62no—
455C2×Q8—64no—
456C2×Q8#120111yescharacteristic, complemented
457C2×D4—34no—
458C2×D4—32no—
459C2×D4—62no—
460C2×D4—68no—
461C2×D4—64no—
462C2×D4—64no—
463C2×D4—102no—
464C2×D4—304no—
465C2×D4#120111yescharacteristic, complemented
466C2×D4C2×D3×D512yes—
467C22×C4—34no—
468C22×C4—51no—
469C22×C4—64no—
470C22×C4—101no—
471C22×C4—101no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4#120112yescomplemented
475C22×C4C2×D3×D511yescharacteristic
476C4⋊C4—101no—
477C4⋊C4—102no—
478C4⋊C4—304no—
479C4⋊C4—302no—
480C22⋊C4—52no—
481C22⋊C4—102no—
482C22⋊C4—102no—
483C22⋊C4—154no—
484C22⋊C4—304no—
485C22⋊C4—304no—
486C42—101no—
487C42—302no—
488C3×C5#302511yescharacteristic, complemented, Hall
489C22×C3—22no—
490C22×C3—41no—
491C22×C3—42no—
492C22×C3—104no—
493C22×C3—102no—
494C22×C3—202no—
495C22×C3—201no—
496C22×C3—201no—
497C22×C3C22×C22⋊D511yescharacteristic
498C22×C3C22×C22⋊D512yes—
499C2×D3—24no—
500C2×D3—44no—
501C2×D3—84no—
502C3×C4—22no—
503C3×C4—202no—
504C3×C4—201no—
505C3×C4#409911yescharacteristic
506C3×C4#409912yes—
507C3×C4#409911yescharacteristic
508Dic3—24no—
509Dic3—204no—
510C2×C5—21no—
511C2×C5—22no—
512C2×C5—42no—
513C2×C5—124no—
514C2×C5C2×#93711yescharacteristic
515D5—42no—
516C23—34no—
517C23—64no—
518C23—101no—
519C23—102no—
520C23—202no—
521C23C2×#120112yes—
522C23C22×D3×D511yescharacteristic
523Q8—22no—
524Q8—64no—
525Q8—62no—
526Q8—62no—
527D4—24no—
528D4—22no—
529D4—64no—
530D4—68no—
531D4—64no—
532D4—64no—
533D4—62no—
534D4—62no—
535D4—204no—
536D4—608no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—34no—
540C2×C4—68no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—64no—
544C2×C4—102no—
545C2×C4—101no—
546C2×C4—102no—
547C2×C4—201no—
548C2×C4—202no—
549C2×C4—201no—
550C2×C4—304no—
551C2×C4C2×#120112yes—
552C2×C4C2×#120111yescharacteristic
553C2×C4C2×#120111yescharacteristic
554C2×C4D3×C22⋊D512yes—
555C2×C4D3×C22⋊D512yes—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—42no—
559C2×C3—202no—
560C2×C3C2×#409911yescharacteristic
561D3—44no—
562C5#8293611yescharacteristic, complemented, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—64no—
567C22—102no—
568C22—104no—
569C22—124no—
570C22—201no—
571C22—202no—
572C22—201no—
573C22—244no—
574C22C22×#120111yescharacteristic
575C22C2×D3×C22⋊D512yes—
576C4—22no—
577C4—64no—
578C4—202no—
579C4—201no—
580C4—604no—
581C4#9156811yescharacteristic
582C4#9156812yes—
583C4#9156811yescharacteristic
584C3#1061585611yescharacteristic, complemented, Sylow
585C2—21no—
586C2—22no—
587C2—42no—
588C2—124no—
589C2—202no—
590C2C2×#9156811yescharacteristic
subgroupG/H
centerC4#91568
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3025
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C5×#5964C2semidirect
2. C3×#66162C2semidirect
3. #11754563C2semidirect
4. #11751341C2semidirect
5. #11749183C2semidirect
6. #11749177C2semidirect
7. #11748625C2semidirect
18. C22×C3×C4×D5C22semidirect
19. #91815C22semidirect
22. C3×#4083C22semidirect
23. C3×#4081C22semidirect
25. C3×#4072C22semidirect
26. #91563C22semidirect
27. #91539C22semidirect
31. #91118C22semidirect
32. #90996C22semidirect
36. #66162D3semidirect
44. C2×C3×C5×Q8D4semidirect
45. C2×C3×C5×D4D4semidirect
47. C22×C3×C4×C5D4semidirect
65. C2×C5×D12D4semidirect
67. C2×C4×C5×D3D4semidirect
69. C2×C5×Dic6D4semidirect
89. #5964D5semidirect
105. C22×C4×D5C2×D3semidirect
111. #4083C2×D3semidirect
113. #4081C2×D3semidirect
117. #4072C2×D3semidirect
201. C2×C5×Q8#67semidirect
208. C2×C5×D4#67semidirect
212. C22×C4×C5#67semidirect
264. C2×C3×Q8C22⋊D5semidirect
266. C2×C3×D4C22⋊D5semidirect
273. C22×C3×C4C22⋊D5semidirect
292. C2×D12C22⋊D5semidirect
294. C2×C4×D3C22⋊D5semidirect
296. C2×Dic6C22⋊D5semidirect
456. C2×Q8#1201semidirect
465. C2×D4#1201semidirect
474. C22×C4#1201semidirect
488. C3×C5#3025semidirect
562. C5#82936semidirect
584. C3#10615856semidirect

Maximal subgroups

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

subgroupindex
C5×#59642
C3×#661622
#117545632
#117513412
#117491832
#117491772
#117486252
#106158563
#829365