Finite Group Databasebeta

← #14417086

Subgroups — #14417086

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5798C211yesmaximal, characteristic, complemented
2C2×C3×#4078C211yesmaximal, characteristic
3#11754509C211yesmaximal, characteristic, complemented
4C2×#91116C211yesmaximal, characteristic, complemented
5#11749010C212yesmaximal, complemented
6Dic3×#687C212yesmaximal, complemented
7#11748988C212yesmaximal, complemented
8Dic3×#686C212yesmaximal, complemented
9#11748460C211yesmaximal, characteristic, complemented
10#11748364C211yesmaximal, characteristic, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10614268—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×#217—22no—
18C5×D4×Dic3—21no—
19C5×D4×Dic3—21no—
20C5×D4×Dic3C2212yes—
21C5×D4×Dic3C2212yes—
22C5×#926C2211yescharacteristic
23C5×#926C2211yescharacteristic
24C2×C3×#687C2212yes—
25C3×#4078C418yescomplemented
26C2×C3×#686C2212yes—
27C2×C3×#681C2211yescharacteristic
28#91559—22no—
29Dic3×D20C2212yescomplemented
30D5×C4⋊Dic3—21no—
31#91358—21no—
32Dic3×Dic10C2212yescomplemented
33#91116C2212yes—
34#91116C2212yes—
35#90988C2212yescomplemented
36#90985C2212yescomplemented
37#90970C2211yescharacteristic, complemented
38#90970C2211yescharacteristic, complemented
39#90964C2211yescharacteristic, complemented
40#90964C2211yescharacteristic, complemented
41#90953C2212yescomplemented
42Dic3×#168C2212yescomplemented
43#83930—51nomaximal, Hall
44C5×#518—31no—
45C2×#4078D311yescharacteristic
46#65857—31no—
47C2×#3964—31no—
48#65307—32no—
49C4×#687—32no—
50#65303—32no—
51C4×#686—32no—
52#65291—31no—
53#65286—31no—
54#65284—31no—
55C24×C3×C5—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4C2×C414yescomplemented
59C2×C3×C5×D4C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15—21no—
62C22×C5×Dic3—22no—
63C22×C5×Dic3—22no—
64C2×C3×C22⋊D5—21no—
65C3×#709—22no—
66C3×#709C2×C414yescomplemented
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×Dic10C2311yescharacteristic
70C2×D5×Dic3—22no—
71C4⋊Dic15—21no—
72C4⋊Dic15C2312yes—
73C2×C3⋊#168—22no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×#217—21no—
77C5×#217—22no—
78C5×#217—22no—
79C5×#217D412yes—
80C5×C4⋊Dic3D411yescharacteristic
81C5×C4⋊Dic3D411yescharacteristic
82C5×C4⋊Dic3C2311yescharacteristic
83C5×C4⋊Dic3C2311yescharacteristic
84C4×C5×Dic3—21no—
85C4×C5×Dic3C2312yes—
86C3×#687C2×C418yescomplemented
87C3×#686C2×C418yescomplemented
88C3×#681C2×C414yescomplemented
89C2×C3×#168C2312yes—
90#6668—22no—
91#6665—22no—
92Dic3×Dic5—22no—
93C2×C3×AGL(1,ℤ/8)—51no—
94#5827—51no—
95#5798D511yescharacteristic, complemented
96#5233—51no—
97C2×#832—51no—
98#5164—52no—
99Dic3×SD16—52no—
100#5152—52no—
101Dic3×D8—52no—
102#5122—51no—
103#5121—51no—
104C22×C5×D4C2×D311yescharacteristic
105C2×#709C2×D311yescharacteristic
106C4×C5×D4—32no—
107C4×C5×D4—32no—
108C4×C5×D4—61no—
109C4×C5×D4—61no—
110C5×#117—31no—
111C5×#117—31no—
112C2×C5×C22⋊C4—62no—
113C2×#687C2×D312yes—
114#4078Dic318yescomplemented
115C2×#686C2×D312yes—
116C2×C4⋊Dic5—31no—
117C2×#681C2×D311yescharacteristic
118C22×#168—31no—
119#4038—61no—
120D5×C4⋊C4—61no—
121#4027—62no—
122C4×D20—32no—
123C4×Dic10—32no—
124#3964—32no—
125#3964—32no—
126#3942—31no—
127#3942—31no—
128#3941—31no—
129#3941—31no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2946—151noSylow
135C23×C3×C5—22no—
136C23×C3×C5—24no—
137C23×C3×C5—81no—
138C23×C3×C5—81no—
139C23×C3×C5C2×D411yescharacteristic
140C22×C3×D5—21no—
141C3×C5×D4—24no—
142C3×C5×D4—22no—
143C3×C5×D4C22×C414yes—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—22no—
149C2×Dic15—81no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—82no—
153C2×C5×Dic3—82no—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3C2×D412yes—
156C3×C22⋊D5—24no—
157C2×C3×Dic5—21no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—24no—
161C3×Dic10—21no—
162C3×Dic10C22×C412yes—
163D5×Dic3—82no—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3×#168C22×C414yes—
167C2×C3×#41—51no—
168C22×C3×D4C2×D511yescharacteristic
169C3×AGL(1,ℤ/8)—58no—
170C2×C3×SD16—52no—
171C2×C3×D8—52no—
172C2×C3×M16—51no—
173C2×#217—22no—
174Q8×Dic3—52no—
175D4×Dic3—21no—
176D4×Dic3—21no—
177D4×Dic3—52no—
178D4×Dic3—102no—
179D4×Dic3C2×D512yes—
180D4×Dic3C2×D512yes—
181#926—101no—
182#926C2×D511yescharacteristic
183#926C2×D511yescharacteristic
184C2×C4⋊Dic3—51no—
185C2×C4⋊Dic3—101no—
186C22×C3⋊C8—51no—
187#835—51no—
188#835—51no—
189#832—52no—
190#832—52no—
191#832—51no—
192#832—51no—
193#818—52no—
194#817—52no—
195#815—52no—
196C8×Dic3—52no—
197C24×C5—21no—
198C2×C5×D4—21no—
199C2×C5×D4—22no—
200C2×C5×D4C2×Dic314yescomplemented
201C2×C5×D4C22×D312yes—
202C22×C4×C5—62no—
203C22×C4×C5—62no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—21no—
206C22×Dic5—61no—
207#709—22no—
208#709C2×Dic314yescomplemented
209C2×D20C22×D311yescharacteristic
210C2×C4×D5—21no—
211C2×C4×D5—62no—
212C2×Dic10C22×D311yescharacteristic
213C5×C4⋊C4—31no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4—31no—
216C5×C4⋊C4—31no—
217C5×C22⋊C4—32no—
218C5×C22⋊C4—62no—
219C5×C22⋊C4—62no—
220C5×C22⋊C4—61no—
221C42×C5—32no—
222C42×C5—61no—
223#687C2×Dic318yescomplemented
224#686C2×Dic318yescomplemented
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5—61no—
228#683—62no—
229C4×Dic5—62no—
230#681C2×Dic314yescomplemented
231C2×#168—31no—
232C2×#168—31no—
233C2×#168—62no—
234C2×#168C22×D312yes—
235C2×AGL(1,ℤ/8)—51no—
236#520—151no—
237#518—31no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—151no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—24no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5—84no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×C3×D5—22no—
255C2×C3×D5—41no—
256C2×C3×D5—41no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—42no—
261C3×Dic5—22no—
262C5×Dic3—22no—
263C5×Dic3—22no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C24×C3—21no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—22no—
271C2×C3×D4—21no—
272C2×C3×D4—51no—
273C2×C3×D4—101no—
274C2×C3×D4C4×D514yescomplemented
275C2×C3×D4C22×D512yes—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—101no—
281C22×Dic3—102no—
282C3×SD16—58no—
283C3×D8—58no—
284C3×M16—54no—
285C2×C3×C8—52no—
286#217—21no—
287#217—22no—
288#217—22no—
289#217—102no—
290#217C22⋊D512yes—
291C4⋊Dic3—52no—
292C4⋊Dic3—101no—
293C4⋊Dic3—102no—
294C4⋊Dic3C22⋊D511yescharacteristic
295C4⋊Dic3C22⋊D511yescharacteristic
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298C4×Dic3—21no—
299C4×Dic3—102no—
300C4×Dic3C22×D512yes—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—51no—
303C2×C3⋊C8—102no—
304C23×C5—22no—
305C23×C5—24no—
306C23×C5—81no—
307C23×C5—81no—
308C23×C5D3×D411yescharacteristic
309C22×D5—21no—
310C5×D4—24no—
311C5×D4—22no—
312C5×D4C22×Dic314yes—
313C2×C4×C5—32no—
314C2×C4×C5—32no—
315C2×C4×C5—61no—
316C2×C4×C5—61no—
317C2×C4×C5—242no—
318C2×C4×C5—242no—
319C2×C4×C5D3×D411yescharacteristic
320C2×C4×C5#23712yes—
321C2×C4×C5C22×Dic312yes—
322C2×C4×C5C23×D311yescharacteristic
323C22⋊D5—24no—
324C2×Dic5—21no—
325C2×Dic5—62no—
326C2×Dic5—241no—
327D20—21no—
328D20C22×Dic312yes—
329C4×D5—24no—
330C4×D5—242no—
331Dic10—21no—
332Dic10C22×Dic312yes—
333#168—61no—
334#168—61no—
335#168C22×Dic314yes—
336C2×#41—51no—
337C22×D4D3×D511yescharacteristic
338AGL(1,ℤ/8)—58no—
339C2×SD16—52no—
340C2×D8—52no—
341C2×M16—51no—
342C22×C8—151no—
343C4×Q8—152no—
344C4×D4—32no—
345C4×D4—32no—
346C4×D4—61no—
347C4×D4—61no—
348C4×D4—152no—
349C4×D4—302no—
350#117—31no—
351#117—31no—
352#117—301no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—62no—
356#107—152no—
357#106—152no—
358#103—151no—
359#103—151no—
360#102—151no—
361#102—151no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—44no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371C3×D5—42no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—81no—
375C23×C3—81no—
376C23×C3—101no—
377C23×C3C2×C22⋊D511yescharacteristic
378C3×Q8—52no—
379C3×Q8—101no—
380C3×D4—22no—
381C3×D4—24no—
382C3×D4—52no—
383C3×D4—104no—
384C3×D4—101no—
385C3×D4C2×C4×D514yes—
386C2×C3×C4—101no—
387C2×C3×C4—104no—
388C2×C3×C4C2×C4×D512yes—
389C2×C3×C4#70912yes—
390C2×C3×C4C2×C22⋊D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—82no—
395C2×Dic3—82no—
396C2×Dic3—102no—
397C2×Dic3—402no—
398C2×Dic3—401no—
399C2×Dic3C2×C22⋊D512yes—
400C2×Dic3C2×C22⋊D512yes—
401C3×C8—54no—
402C3⋊C8—101no—
403C3⋊C8—101no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—24no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—84no—
410C22×C5D4×Dic312yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—22no—
413C2×D5—41no—
414C2×D5—41no—
415C4×C5—62no—
416C4×C5—62no—
417C4×C5—121no—
418C4×C5—121no—
419C4×C5D4×Dic312yes—
420C4×C5C2×#23711yescharacteristic
421C4×C5C23×Dic311yescharacteristic
422Dic5—22no—
423Dic5—122no—
424C24—21no—
425#41—54no—
426#41—102no—
427C2×Q8—51no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—51no—
431C2×D4—101no—
432C2×D4D5×Dic314yescomplemented
433C2×D4C2×D3×D512yes—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—101no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—58no—
441D8—58no—
442M16—54no—
443C2×C8—52no—
444C2×C8—151no—
445C2×C8—151no—
446C2×C8—302no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—31no—
451C4⋊C4—152no—
452C4⋊C4—302no—
453C4⋊C4—301no—
454C22⋊C4—32no—
455C22⋊C4—62no—
456C22⋊C4—62no—
457C22⋊C4—61no—
458C22⋊C4—302no—
459C42—32no—
460C42—61no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—84no—
469C22×C3—102no—
470C22×C3—201no—
471C22×C3—201no—
472C22×C3C4×C22⋊D512yes—
473C22×C3C22×C22⋊D511yescharacteristic
474C3×C4—102no—
475C3×C4C4×C22⋊D512yes—
476C3×C4C22×C4×D511yescharacteristic
477C3×C4C2×#70911yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—41no—
481Dic3—41no—
482Dic3—202no—
483C2×C5—22no—
484C2×C5—44no—
485C2×C5#577411yescharacteristic
486C2×C5#577511yescharacteristic
487C2×C5C2×D4×Dic311yescharacteristic
488D5—42no—
489C23—22no—
490C23—24no—
491C23—81no—
492C23—81no—
493C23—101no—
494C23D3×C22⋊D511yescharacteristic
495Q8—52no—
496Q8—101no—
497D4—22no—
498D4—24no—
499D4—52no—
500D4—104no—
501D4—101no—
502D4C2×D5×Dic314yes—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—101no—
508C2×C4—104no—
509C2×C4—242no—
510C2×C4—242no—
511C2×C4—302no—
512C2×C4—1202no—
513C2×C4—1201no—
514C2×C4C2×D5×Dic312yes—
515C2×C4#677912yes—
516C2×C4D3×C22⋊D511yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—54no—
519C8—301no—
520C8—301no—
521C2×C3—22no—
522C2×C3—44no—
523C2×C3—202no—
524C2×C3C2×C4×C22⋊D511yescharacteristic
525C2×C3#6616911yescharacteristic
526C2×C3#6617011yescharacteristic
527C5#8393011yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—24no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22—102no—
535C22—201no—
536C22—201no—
537C22Dic3×C22⋊D512yes—
538C22C2×D3×C22⋊D511yescharacteristic
539C4—62no—
540C4—62no—
541C4—102no—
542C4—121no—
543C4—121no—
544C4—602no—
545C4Dic3×C22⋊D512yes—
546C4C22×D5×Dic311yescharacteristic
547C4C2×#677911yescharacteristic
548C3#1061426811yescharacteristic, complemented, Sylow
549C2—22no—
550C2—44no—
551C2—202no—
552C2#1175469811yescharacteristic
553C2#1175472011yescharacteristic
554C2C2×Dic3×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4078C2
cosocleC2×C3×C4×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5798C2semidirect
3. #11754509C2semidirect
4. C2×#91116C2semidirect
5. #11749010C2semidirect
6. Dic3×#687C2semidirect
7. #11748988C2semidirect
8. Dic3×#686C2semidirect
9. #11748460C2semidirect
10. #11748364C2semidirect
11. #11748327C2semidirect
25. C3×#4078C4semidirect
29. Dic3×D20C22semidirect
32. Dic3×Dic10C22semidirect
35. #90988C22semidirect
36. #90985C22semidirect
37. #90970C22semidirect
38. #90970C22semidirect
39. #90964C22semidirect
40. #90964C22semidirect
41. #90953C22semidirect
42. Dic3×#168C22semidirect
58. C2×C3×C5×D4C2×C4semidirect
66. C3×#709C2×C4semidirect
86. C3×#687C2×C4semidirect
87. C3×#686C2×C4semidirect
88. C3×#681C2×C4semidirect
95. #5798D5semidirect
114. #4078Dic3semidirect
200. C2×C5×D4C2×Dic3semidirect
208. #709C2×Dic3semidirect
223. #687C2×Dic3semidirect
224. #686C2×Dic3semidirect
230. #681C2×Dic3semidirect
274. C2×C3×D4C4×D5semidirect
432. C2×D4D5×Dic3semidirect
462. C3×C5#2946semidirect
527. C5#83930semidirect
548. C3#10614268semidirect

Maximal subgroups

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

subgroupindex
C5×#57982
C2×C3×#40782
#117545092
C2×#911162
#117490102
Dic3×#6872
#117489882
Dic3×#6862
#117484602
#117483642
#117483272
#106142683
#839305