Finite Group Databasebeta

← #14460216

Subgroups — #14460216

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
1C3×#65897C211yesmaximal, characteristic, complemented
2#11752676C211yesmaximal, characteristic, complemented
3#11751120C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic, complemented
5#11749159C212yesmaximal, complemented
6#11749046C212yesmaximal, complemented
7#11747499C212yesmaximal, complemented
8#11747170C212yesmaximal, complemented
9C3⋊C8×D20C211yesmaximal, characteristic, complemented
10#11746921C211yesmaximal, characteristic, complemented
11#11746882C211yesmaximal, characteristic, complemented
12#10611341—31nomaximal, Hall
13C2×#6772C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15C2×#6716C2212yes—
16#91758C2211yescharacteristic
17C2×C5×#213C2211yescharacteristic
18C4×C5×D12C2211yescharacteristic
19C3×#4084C2212yes—
20C3×#4076—21no—
21C3×#4072—21no—
22C3×#4038C2212yes—
23C3×#4031—22no—
24C3×C4×D20C2211yescharacteristic
25C3×#4015C2211yescharacteristic
26#91457—22no—
27#91456—21no—
28D3×C4⋊Dic5—21no—
29#91360C2212yes—
30C2×D5×C3⋊C8C2212yes—
31#91094C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#832C2211yescharacteristic
34C5×#809C2211yescharacteristic
35C5×#807C2211yescharacteristic
36C4×C5×C3⋊C8C2211yescharacteristic
37#90986C2212yes—
38#90974C2212yes—
39#90974C2212yes—
40#90966C2212yes—
41#90955C2212yes—
42#83652—51nomaximal, Hall
43#65897D311yescharacteristic, complemented
44#65889—31no—
45C4×C5×D8—31no—
46#65447—32no—
47#65308—31no—
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×Dic30C2312yes—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C3×C22⋊D5—22no—
60C2×C3×D20D411yescharacteristic
61C2×C3×C4×D5C2312yes—
62C2×C3×Dic10—21no—
63C2×#1201—22no—
64C2×D3×Dic5—22no—
65#6772—24no—
66#6772—42no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6716—42no—
71C4⋊Dic15—21no—
72C4⋊Dic15—21no—
73C2×C3⋊#168C2312yes—
74C5×#213—22no—
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C2×C5×C3⋊C8C2311yescharacteristic
79C3×C22⋊Dic5—22no—
80C3×#685—22no—
81C3×#685D412yes—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5C2312yes—
85C3×C4×Dic5—22no—
86Dic3⋊Dic5—22no—
87#6665—22no—
88D5×C3⋊C8—42no—
89C3×#555—51no—
90#5551—51no—
91#5093—51no—
92#5084—51no—
93#5041—52no—
94#5037—52no—
95#5019—51no—
96C4×#213D511yescharacteristic, complemented
97D4×C3⋊C8—51no—
98#5002—52no—
99#4996—52no—
100C2×#711—32no—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4084C2×D312yes—
105C2×#687—32no—
106#4076—21no—
107#4076—61no—
108#4072—21no—
109C2×C4⋊Dic5—61no—
110C2×C8×D5—32no—
111#4043—32no—
112#4038C2×D312yes—
113#4032—62no—
114#4031—22no—
115C4×D20C2×D311yescharacteristic
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#3942—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3303—151noSylow
130C23×C3×C5—21no—
131C22×C5×D3—21no—
132C22×C3×D5C2×D412yes—
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
140C2×Dic15—22no—
141Dic30—22no—
142Dic30—22no—
143C2×C5×Dic3—21no—
144C5×D12—21no—
145C5×D12#4112yes—
146C4×C5×D3—42no—
147C3×C22⋊D5—82no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C2×D412yes—
150C3×D20—22no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×Dic10—81no—
154#1201—44no—
155D3×Dic5—44no—
156C3⋊#168—22no—
157C5×C3⋊C8—21no—
158C5×C3⋊C8—21no—
159C2×#235—52no—
160C3×C4⋊Q8—51no—
161C3×#124—102no—
162C3×#121—52no—
163C3×#121—101no—
164C3×C4×D4—51no—
165C3×C4×D4C2×D511yescharacteristic
166C3×#117—52no—
167C3×#117—101no—
168#938—101no—
169C2×#214—52no—
170C2×#213C2×D511yescharacteristic
171#924—52no—
172C22×C3⋊C8—52no—
173D3×C4⋊C4—101no—
174#883—102no—
175C4×D12C2×D511yescharacteristic
176#869—51no—
177#832C2×D511yescharacteristic
178#830—52no—
179#810—52no—
180#810—52no—
181#810—52no—
182#809—52no—
183#809C2×D511yescharacteristic
184#808—52no—
185#807C2×D511yescharacteristic
186C4⋊(C3⋊C8)—51no—
187C4×C3⋊C8C2×D511yescharacteristic
188C2×C5×D4—31no—
189C2×C5×D4C22×D311yescharacteristic
190C22×C4×C5—21no—
191C22×C4×C5—61no—
192C2×C22⋊D5—22no—
193C2×C22⋊D5—62no—
194C22×Dic5—62no—
195#711—64no—
196#711—122no—
197C2×D20#6711yescharacteristic
198C2×C4×D5C22×D312yes—
199C2×Dic10—21no—
200C2×Dic10—32no—
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—22no—
210#687—122no—
211#685—22no—
212#685—62no—
213#685#6712yes—
214C4⋊Dic5—21no—
215C4⋊Dic5—61no—
216C4⋊Dic5—61no—
217C4⋊Dic5—62no—
218C4⋊Dic5#6711yescharacteristic
219C4⋊Dic5C22×D312yes—
220C4×Dic5—22no—
221C2×#168—32no—
222C8×D5—122no—
223#555—51no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
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×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C3×D5—22no—
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—42no—
250C3×Dic5—22no—
251C3×Dic5—42no—
252C5×Dic3—41no—
253C2×C3×Q8—101no—
254C2×C3×D4—51no—
255C2×C3×D4—102no—
256C2×C3×D4C22×D511yescharacteristic
257C22×C3×C4—21no—
258C22×C3×C4—52no—
259C2×#67—102no—
260#235—104no—
261#235—202no—
262C2×D12C22×D511yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—102no—
265C2×Dic6—52no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4C22×D511yescharacteristic
270C3×C22⋊C4—21no—
271C3×C22⋊C4—52no—
272C3×C22⋊C4—102no—
273C3×C22⋊C4—102no—
274C3×C42—102no—
275C3×C42C22×D511yescharacteristic
276#217—102no—
277#214—202no—
278#213—22no—
279(C2×D3)⋊C4—21no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282C4⋊Dic3C22×D511yescharacteristic
283Dic3⋊C4—102no—
284C2×C3⋊C8—52no—
285C2×C3⋊C8—202no—
286C2×C3⋊C8C22×D511yescharacteristic
287C2×C3⋊C8C22×D511yescharacteristic
288C23×C5—21no—
289C23×C5—61no—
290C22×D5C2×#6712yes—
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×C5C2×#6711yescharacteristic
300C2×C4×C5C2×#6711yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C22⋊D5—82no—
303C22⋊D5—124no—
304C2×Dic5—22no—
305C2×Dic5—62no—
306C2×Dic5—124no—
307C2×Dic5C2×#6712yes—
308D20—22no—
309C4×D5—22no—
310C4×D5—22no—
311Dic10—62no—
312Dic10—62no—
313Dic10—81no—
314C5×C8—61no—
315C5×C8—61no—
316#168—62no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—31no—
320C22×C8—152no—
321C4⋊Q8—51no—
322C4⋊Q8—151no—
323#124—102no—
324#123—302no—
325C22⋊Q8—152no—
326#121—52no—
327#121—101no—
328#121—301no—
329C4×D4—31no—
330C4×D4—51no—
331C4×D4D3×D511yescharacteristic
332#117—52no—
333#117—101no—
334C2×C4⋊C4—301no—
335#107—31no—
336#106—152no—
337C4⋊C8—151no—
338#103—152no—
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
350C3×D5—42no—
351C5×D3—42no—
352C23×C3—21no—
353C23×C3—52no—
354C22×D3—21no—
355C3×Q8—401no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—102no—
359C3×D4—402no—
360C2×C3×C4—21no—
361C2×C3×C4—42no—
362C2×C3×C4—52no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4—102no—
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4C23×D511yescharacteristic
369#67—204no—
370C2×Dic3—21no—
371C2×Dic3—102no—
372D12—21no—
373D12#70912yes—
374C4×D3—42no—
375C4×D3—204no—
376Dic6—102no—
377Dic6—102no—
378C3⋊C8—21no—
379C3⋊C8—21no—
380C3⋊C8—102no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—62no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C22×#6711yescharacteristic
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—22no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—121no—
394C4×C5#95012yes—
395C4×C5D3×#4111yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—22no—
398Dic5—42no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—101no—
403C2×Q8—152no—
404C2×D4—31no—
405C2×D4—51no—
406C2×D4—102no—
407C2×D4—302no—
408C2×D4C2×D3×D511yescharacteristic
409C22×C4—21no—
410C22×C4—52no—
411C22×C4—61no—
412C22×C4—302no—
413SD16—602no—
414D8—62no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—152no—
418C2×C8—602no—
419C4⋊C4—31no—
420C4⋊C4—51no—
421C4⋊C4—52no—
422C4⋊C4—101no—
423C4⋊C4—302no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C4⋊C4C2×D3×D511yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—52no—
429C22⋊C4—61no—
430C22⋊C4—102no—
431C22⋊C4—102no—
432C22⋊C4—302no—
433C42—102no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—102no—
440C22×C3—102no—
441C22×C3—102no—
442C22×C3C2×D4×D511yescharacteristic
443C2×D3—22no—
444C2×D3—41no—
445C2×D3—41no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—102no—
449C3×C4—202no—
450C3×C4#405812yes—
451C3×C4C2×#70911yescharacteristic
452C3×C4#414911yescharacteristic
453Dic3—41no—
454Dic3—202no—
455C2×C5—81no—
456C2×C5—122no—
457C2×C5C2×#95011yescharacteristic
458C2×C5#582911yescharacteristic
459C2×C5#583611yescharacteristic
460D5—42no—
461C23—21no—
462C23—52no—
463C23—61no—
464Q8—302no—
465Q8—302no—
466Q8—401no—
467D4—21no—
468D4—21no—
469D4—32no—
470D4—61no—
471D4—102no—
472D4—402no—
473D4—604no—
474C2×C4—21no—
475C2×C4—42no—
476C2×C4—52no—
477C2×C4—61no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—102no—
481C2×C4—122no—
482C2×C4—302no—
483C2×C4—604no—
484C2×C4D5×#6711yescharacteristic
485C2×C4D5×#6711yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—61no—
488C8—61no—
489C8—302no—
490C2×C3—81no—
491C2×C3—202no—
492C2×C3#6588411yescharacteristic
493C2×C3C2×#405811yescharacteristic
494C2×C3#6610411yescharacteristic
495D3—42no—
496C5#8365211yescharacteristic, complemented, Sylow
497C22—41no—
498C22—41no—
499C22—41no—
500C22—62no—
501C22—102no—
502C22—102no—
503C22—102no—
504C22—121no—
505C22—121no—
506C22C2×D5×#6711yescharacteristic
507C4—21no—
508C4—41no—
509C4—102no—
510C4—121no—
511C4—202no—
512C4—602no—
513C4#9149012yes—
514C4D3×#70911yescharacteristic
515C4#9201911yescharacteristic
516C3#1061134111yescharacteristic, complemented, Sylow
517C2—81no—
518C2—122no—
519C2—202no—
520C2#1175463811yescharacteristic
521C2C2×#9149011yescharacteristic
522C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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. C3×#65897C2semidirect
2. #11752676C2semidirect
3. #11751120C2semidirect
4. C4×C5×#213C2semidirect
5. #11749159C2semidirect
6. #11749046C2semidirect
7. #11747499C2semidirect
8. #11747170C2semidirect
9. C3⋊C8×D20C2semidirect
10. #11746921C2semidirect
11. #11746882C2semidirect
43. #65897D3semidirect
96. C4×#213D5semidirect
435. C3×C5#3303semidirect
496. C5#83652semidirect
516. C3#10611341semidirect

Maximal subgroups

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

subgroupindex
C3×#658972
#117526762
#117511202
C4×C5×#2132
#117491592
#117490462
#117474992
#117471702
C3⋊C8×D202
#117469212
#117468822
#106113413
#836525