Finite Group Databasebeta

← #14460217

Subgroups — #14460217

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756322C211yesmaximal, characteristic, complemented
2#11752549C211yesmaximal, characteristic, complemented
3C4×C5×#213C211yesmaximal, characteristic, complemented
4C3×#65308C211yesmaximal, characteristic, complemented
5#11749161C212yesmaximal, complemented
6#11749053C212yesmaximal, complemented
7#11747508C212yesmaximal, complemented
8#11747364C212yesmaximal, complemented
9#11746994C211yesmaximal, characteristic, complemented
10#11746920C211yesmaximal, characteristic, complemented
11#11746883C211yesmaximal, characteristic, complemented
12#10611341—31nomaximal, Hall
13C2×#6768C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827C2212yes—
16#91819—21no—
17#91815—21no—
18#91781C2212yes—
19#91774—22no—
20C4×D60C2211yescharacteristic
21#91758C2211yescharacteristic
22C2×C5×#213C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C2×C3×#687C2212yes—
25C3×#4015C2211yescharacteristic
26#91460—21no—
27#91427—22no—
28D3×C4⋊Dic5—21no—
29#91390C2212yes—
30C2×#6648C2212yes—
31C5×#832C2211yescharacteristic
32C5×#809C2211yescharacteristic
33C5×#807C2211yescharacteristic
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3942C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37#90985C2212yes—
38#90971C2212yes—
39#90971C2212yes—
40#90967C2212yes—
41#90957C2212yes—
42#80451—51nomaximal, Hall
43#65897—31no—
44#65889—31no—
45C4×C5×D8—31no—
46#65447—32no—
47#65308D311yescharacteristic, complemented
48#65297—31no—
49#65177—32no—
50#65067—32no—
51#65061—32no—
52C8×D20—31no—
53#64970—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×#1220—22no—
57C2×D60D411yescharacteristic
58C2×C4×D15C2312yes—
59C2×Dic30—21no—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C3×Dic10C2312yes—
63C2×#1203—22no—
64C2×D3×Dic5—22no—
65#6768—24no—
66#6768—42no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6719—22no—
71#6714—22no—
72#6714D412yes—
73C4⋊Dic15—21no—
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15C2312yes—
76C4×Dic15—22no—
77C5×#213—22no—
78C5×(C2×D3)⋊C4—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C3×#687—42no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—21no—
85C2×C3×#168C2312yes—
86Dic3⋊Dic5—22no—
87#6667—22no—
88#6648—42no—
89#5726—51no—
90#5563—51no—
91C3×#461—51no—
92#5172—52no—
93#5171—52no—
94#5079—51no—
95C4×#213D511yescharacteristic, complemented
96#4842—51no—
97#4834—51no—
98#4815—52no—
99#4804—52no—
100C2×#711—32no—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4084—32no—
105C2×#687C2×D312yes—
106#4076—61no—
107#4076—61no—
108#4072—61no—
109C2×C4⋊Dic5—61no—
110C2×C8×D5—32no—
111#4043—32no—
112#4038—32no—
113#4032—62no—
114#4031—62no—
115C4×D20—31no—
116#4015—31no—
117#4015C2×D311yescharacteristic
118C5×#107—31no—
119C5×#102—31no—
120C5×#102—31no—
121C4×C5×C8—31no—
122#3964—32no—
123#3952—32no—
124#3948—32no—
125#3948—32no—
126#3942C2×D312yes—
127#3940—32no—
128C4⋊#168C2×D311yescharacteristic
129#3303—151noSylow
130C23×C3×C5—21no—
131C22×D15C2×D412yes—
132C22×C5×D3—21no—
133C3×C5×D4—21no—
134C3×C5×D4—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140#1220—82no—
141C2×Dic15—22no—
142C2×Dic15C2×D412yes—
143D60—22no—
144C4×D15—22no—
145C4×D15—22no—
146Dic30—81no—
147C2×C5×Dic3—21no—
148C5×D12—21no—
149C5×D12#4112yes—
150C4×C5×D3—42no—
151C2×C3×Dic5—22no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154#1203—44no—
155D3×Dic5—44no—
156C3×#168—22no—
157C5×C3⋊C8—21no—
158C5×C3⋊C8—21no—
159C2×#239—52no—
160C2×C3×SD16—52no—
161C3×C4⋊Q8—51no—
162C3×C4×D4C2×D511yescharacteristic
163#946—52no—
164#938—52no—
165C2×#213C2×D511yescharacteristic
166#930—101no—
167#926—101no—
168C2×D3×C8—52no—
169#895—101no—
170#894—102no—
171#892—52no—
172D3×C4⋊C4—101no—
173#885—102no—
174C4×D12—51no—
175C4×D12C2×D511yescharacteristic
176#869—51no—
177C3×C4⋊C8—51no—
178C3×#103—52no—
179#835—52no—
180#835—52no—
181#832C2×D511yescharacteristic
182#821—52no—
183(C2×D3)⋊C8—52no—
184#817—52no—
185#809C2×D511yescharacteristic
186#807C2×D511yescharacteristic
187C4×C3⋊C8C2×D511yescharacteristic
188C2×C5×D4—31no—
189C2×C5×D4C22×D311yescharacteristic
190C22×C4×C5—21no—
191C22×C4×C5—61no—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194C22×Dic5—62no—
195#711—64no—
196#711—122no—
197C2×D20—31no—
198C2×C4×D5—32no—
199C2×Dic10—61no—
200C2×Dic10C22×D312yes—
201C5×D8—62no—
202C2×C5×C8—31no—
203C2×C5×C8—31no—
204C5×C4⋊C4—31no—
205C5×C4⋊C4C22×D311yescharacteristic
206C5×C22⋊C4—21no—
207C5×C22⋊C4—61no—
208C42×C5C22×D311yescharacteristic
209C22⋊Dic5—62no—
210#687—42no—
211#685—32no—
212#685—62no—
213#685—62no—
214C4⋊Dic5—21no—
215C4⋊Dic5—21no—
216C4⋊Dic5—31no—
217C4⋊Dic5—32no—
218C4⋊Dic5—62no—
219C4⋊Dic5—61no—
220C4×Dic5—62no—
221C2×#168C22×D312yes—
222C8×D5—122no—
223#555—151no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—51no—
230#449—152no—
231C4×D8—31no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—22no—
240C2×D15—22no—
241C2×C5×D3—22no—
242C2×C5×D3—41no—
243C2×C5×D3—41no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—22no—
250Dic15—42no—
251C3×Dic5—42no—
252C5×Dic3—41no—
253C2×C3×Q8—52no—
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C2×#67—102no—
257#239—104no—
258#239—202no—
259C2×D12—51no—
260C2×D12—102no—
261C2×D12C22×D511yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—52no—
264C2×C4×D3—102no—
265C2×Dic6—101no—
266C3×SD16—202no—
267C2×C3×C8—52no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4C22×D511yescharacteristic
271C3×C22⋊C4—21no—
272C3×C42C22×D511yescharacteristic
273#217—102no—
274#213—22no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—52no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—102no—
279C4⋊Dic3—51no—
280C4⋊Dic3—52no—
281C4⋊Dic3—101no—
282C4⋊Dic3C22×D511yescharacteristic
283Dic3⋊C4—102no—
284C4×Dic3—102no—
285C2×C3⋊C8C22×D511yescharacteristic
286C2×C3⋊C8C22×D511yescharacteristic
287D3×C8—202no—
288C23×C5—21no—
289C23×C5—61no—
290C22×D5—32no—
291C5×D4—21no—
292C5×D4—21no—
293C5×D4—32no—
294C5×D4—61no—
295C2×C4×C5—21no—
296C2×C4×C5—42no—
297C2×C4×C5—61no—
298C2×C4×C5—122no—
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C22⋊D5—124no—
303C22⋊D5—242no—
304C2×Dic5—22no—
305C2×Dic5—32no—
306C2×Dic5—62no—
307C2×Dic5—124no—
308D20—62no—
309C4×D5—62no—
310C4×D5—62no—
311Dic10—22no—
312Dic10—22no—
313Dic10—241no—
314C5×C8—61no—
315C5×C8—61no—
316#168—22no—
317C2×#41—152no—
318C2×SD16—52no—
319C2×D8—31no—
320C22×C8—152no—
321C4⋊Q8—51no—
322C4⋊Q8—151no—
323#124—302no—
324#123—302no—
325C22⋊Q8—152no—
326#121—152no—
327#121—301no—
328#121—301no—
329C4×D4—31no—
330C4×D4—151no—
331C4×D4D3×D511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107—31no—
336#106—152no—
337C4⋊C8—51no—
338#103—52no—
339#103—152no—
340#103—152no—
341#102—31no—
342#102—31no—
343#102—152no—
344C22⋊C8—152no—
345C4×C8—31no—
346C2×C3×C5—81no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351C5×D3—42no—
352C23×C3—21no—
353C22×D3—21no—
354C22×D3—52no—
355C3×Q8—102no—
356C3×Q8—102no—
357C3×D4—21no—
358C3×D4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—42no—
361C2×C3×C4—102no—
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4D4×D511yescharacteristic
364C2×C3×C4C23×D511yescharacteristic
365#67—402no—
366C2×Dic3—21no—
367C2×Dic3—52no—
368C2×Dic3—102no—
369D12—21no—
370D12—102no—
371D12—204no—
372D12#70912yes—
373C4×D3—42no—
374C4×D3—102no—
375C4×D3—102no—
376C4×D3—204no—
377Dic6—401no—
378C3×C8—102no—
379C3⋊C8—21no—
380C3⋊C8—21no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—62no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C2×D3×D411yescharacteristic
388C2×D5—62no—
389C2×D5—62no—
390C2×D5—62no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—121no—
394C4×C5#91612yes—
395C4×C5#100411yescharacteristic
396C4×C5D3×#4111yescharacteristic
397Dic5—42no—
398Dic5—62no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—52no—
403C2×Q8—301no—
404C2×D4—31no—
405C2×D4—151no—
406C2×D4—302no—
407C2×D4—302no—
408C2×D4C2×D3×D511yescharacteristic
409C22×C4—21no—
410C22×C4—61no—
411C22×C4—152no—
412C22×C4—302no—
413SD16—202no—
414D8—62no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—52no—
418C2×C8—602no—
419C4⋊C4—31no—
420C4⋊C4—101no—
421C4⋊C4—101no—
422C4⋊C4—151no—
423C4⋊C4—152no—
424C4⋊C4—302no—
425C4⋊C4—301no—
426C4⋊C4C2×D3×D511yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—61no—
429C22⋊C4—152no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C22⋊C4—302no—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3C2×D4×D511yescharacteristic
440C2×D3—22no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—102no—
444C2×D3—102no—
445C2×D3—102no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—202no—
449C3×C4#405812yes—
450C3×C4C2×#70911yescharacteristic
451C3×C4#414911yescharacteristic
452Dic3—41no—
453Dic3—102no—
454Dic3—202no—
455C2×C5—81no—
456C2×C5—122no—
457C2×C5#561211yescharacteristic
458C2×C5C2×#91611yescharacteristic
459C2×C5#577811yescharacteristic
460D5—122no—
461C23—21no—
462C23—61no—
463C23—152no—
464Q8—102no—
465Q8—102no—
466Q8—1201no—
467D4—21no—
468D4—21no—
469D4—32no—
470D4—61no—
471D4—302no—
472D4—604no—
473D4—1202no—
474C2×C4—21no—
475C2×C4—42no—
476C2×C4—61no—
477C2×C4—102no—
478C2×C4—122no—
479C2×C4—152no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4—302no—
483C2×C4—604no—
484C2×C4#679011yescharacteristic
485C2×C4#679011yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—61no—
488C8—61no—
489C8—102no—
490C2×C3—81no—
491C2×C3#6588411yescharacteristic
492C2×C3C2×#405811yescharacteristic
493C2×C3#6610411yescharacteristic
494D3—42no—
495D3—202no—
496C5#8045111yescharacteristic, complemented, Sylow
497C22—41no—
498C22—41no—
499C22—41no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—302no—
504C22—302no—
505C22—302no—
506C22C2×#679011yescharacteristic
507C4—21no—
508C4—41no—
509C4—121no—
510C4—202no—
511C4—302no—
512C4—602no—
513C4#9149912yes—
514C4D3×#70911yescharacteristic
515C4#9201711yescharacteristic
516C3#1061134111yescharacteristic, complemented, Sylow
517C2—81no—
518C2—122no—
519C2—602no—
520C2#1175466711yescharacteristic
521C2C2×#9149911yescharacteristic
522C2#1175535411yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756322C2semidirect
2. #11752549C2semidirect
3. C4×C5×#213C2semidirect
4. C3×#65308C2semidirect
5. #11749161C2semidirect
6. #11749053C2semidirect
7. #11747508C2semidirect
8. #11747364C2semidirect
9. #11746994C2semidirect
10. #11746920C2semidirect
11. #11746883C2semidirect
47. #65308D3semidirect
95. C4×#213D5semidirect
435. C3×C5#3303semidirect
496. C5#80451semidirect
516. C3#10611341semidirect

Maximal subgroups

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

subgroupindex
#117563222
#117525492
C4×C5×#2132
C3×#653082
#117491612
#117490532
#117475082
#117473642
#117469942
#117469202
#117468832
#106113413
#804515