Finite Group Databasebeta

← #14460167

Subgroups — #14460167

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×#65889C211yesmaximal, characteristic, complemented
2#11752718C211yesmaximal, characteristic, complemented
3#11751109C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic, complemented
5#11749024C212yesmaximal, complemented
6#11748961C212yesmaximal, complemented
7#11747309C212yesmaximal, complemented
8#11747204C212yesmaximal, complemented
9#11747070C211yesmaximal, characteristic, complemented
10C3⋊C8×D20C211yesmaximal, characteristic, complemented
11#11746920C211yesmaximal, characteristic, complemented
12#10611341—31nomaximal, Hall
13C2×C3×#711C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×#213C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C3×#4076—21no—
19C2×C3×C4⋊Dic5—21no—
20C3×#4043C2212yes—
21C3×#4032—22no—
22C3×C4×D20C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91462—22no—
25#91456—21no—
26#91449C2212yes—
27#91358C2212yes—
28#91338—21no—
29C2×#6656C2212yes—
30C2×D5×C3⋊C8C2212yes—
31#91116C2212yes—
32#91092C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#832C2211yescharacteristic
35C5×#809C2211yescharacteristic
36C5×#807C2211yescharacteristic
37C4×C5×C3⋊C8C2211yescharacteristic
38#90971C2212yes—
39#90971C2212yes—
40#90970C2212yes—
41#90955C2212yes—
42#83511—51nomaximal, Hall
43#65897—31no—
44#65889D311yescharacteristic, complemented
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×Dic30—21no—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C3×C22⋊D5—22no—
60C22×C3×Dic5—22no—
61C3×#711—24no—
62C3×#711—42no—
63C2×C3×D20D411yescharacteristic
64C2×C3×C4×D5C2312yes—
65C2×C3×Dic10C2312yes—
66C2×#1201—22no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15—21no—
71C4⋊Dic15C2312yes—
72C2×C3⋊#168C2312yes—
73C5×#213—22no—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×#685—22no—
79C3×#685D412yes—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5—22no—
83C3×C4⋊Dic5D411yescharacteristic
84(C2×D3)⋊Dic5—22no—
85#6665—22no—
86Dic3×Dic5—22no—
87#6656—42no—
88D5×C3⋊C8—42no—
89C3×#547—51no—
90#5563—51no—
91#5238—52no—
92#5233—52no—
93#5083—51no—
94#5079—51no—
95#5048—52no—
96#5045—52no—
97C4×#213D511yescharacteristic, complemented
98D4×C3⋊C8—51no—
99#5008—51no—
100C2×#711C2×D312yes—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4084—32no—
105C2×#687—32no—
106#4076—21no—
107#4076—61no—
108#4072—61no—
109C2×C4⋊Dic5—21no—
110C2×C8×D5—32no—
111#4043C2×D312yes—
112#4038—32no—
113#4032—22no—
114#4031—62no—
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#4112yes—
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—81no—
142C2×C5×Dic3—21no—
143C5×D12—21no—
144C5×D12—21no—
145C4×C5×D3—42no—
146C3×C22⋊D5—44no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—44no—
149C2×C3×Dic5C2×D412yes—
150C3×D20—22no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×Dic10—22no—
154C3×Dic10—22no—
155#1201—82no—
156C3⋊#168—22no—
157C5×C3⋊C8—21no—
158C5×C3⋊C8—21no—
159C2×C3×#41—52no—
160C3×C4⋊Q8—51no—
161C3×#123—102no—
162C3×C22⋊Q8—52no—
163C3×#121—101no—
164C3×C4×D4—51no—
165C3×C4×D4C2×D511yescharacteristic
166C2×C3×C4⋊C4—101no—
167C2×#215—52no—
168#938—101no—
169C2×#213C2×D511yescharacteristic
170#930—52no—
171#926—52no—
172C22×C3⋊C8—52no—
173#892—101no—
174#885—102no—
175C4×D12C2×D511yescharacteristic
176#869—51no—
177#835—52no—
178#835—52no—
179#835—52no—
180#832—52no—
181#832C2×D511yescharacteristic
182#830—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—22no—
195#711—24no—
196#711—42no—
197C2×D20#6711yescharacteristic
198C2×C4×D5C22×D312yes—
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—122no—
211#685—22no—
212#685—62no—
213#685#6712yes—
214C4⋊Dic5—21no—
215C4⋊Dic5—21no—
216C4⋊Dic5—22no—
217C4⋊Dic5—32no—
218C4⋊Dic5—61no—
219C4⋊Dic5#6711yescharacteristic
220C4×Dic5—62no—
221C2×#168—32no—
222C8×D5—122no—
223#555—151no—
224#547—51no—
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—22no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×C5×D3—41no—
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—
253C3×#41—104no—
254C3×#41—202no—
255C2×C3×Q8—52no—
256C2×C3×D4—51no—
257C2×C3×D4—102no—
258C2×C3×D4C22×D511yescharacteristic
259C22×C3×C4—21no—
260C22×C3×C4—52no—
261C22×C3×C4—102no—
262C2×#67—102no—
263C2×D12C22×D511yescharacteristic
264C2×C4×D3—21no—
265C2×Dic6—101no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—102no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4C22×D511yescharacteristic
271C3×C22⋊C4—21no—
272C3×C22⋊C4—52no—
273C3×C22⋊C4—102no—
274C3×C42C22×D511yescharacteristic
275#217—102no—
276#215—202no—
277#213—22no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—102no—
280C4⋊Dic3—52no—
281C4⋊Dic3—101no—
282C4⋊Dic3C22×D511yescharacteristic
283C4×Dic3—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—61no—
293C5×D4—61no—
294C5×D4#23712yes—
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—44no—
303C22⋊D5—242no—
304C2×Dic5—22no—
305C2×Dic5—44no—
306C2×Dic5—62no—
307C2×Dic5C2×#6712yes—
308D20—22no—
309C4×D5—22no—
310C4×D5—22no—
311Dic10—22no—
312Dic10—22no—
313Dic10—241no—
314C5×C8—61no—
315C5×C8—61no—
316#168—62no—
317C2×#41—52no—
318C2×SD16—152no—
319C2×D8—31no—
320C22×C8—152no—
321C4⋊Q8—51no—
322C4⋊Q8—151no—
323#124—302no—
324#123—102no—
325C22⋊Q8—52no—
326#121—101no—
327#121—152no—
328#121—301no—
329C4×D4—31no—
330C4×D4—51no—
331C4×D4D3×D511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—101no—
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—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350C3×D5—42no—
351C5×D3—81no—
352C23×C3—21no—
353C23×C3—52no—
354C22×D3—21no—
355C3×Q8—102no—
356C3×Q8—102no—
357C3×D4—21no—
358C3×D4—102no—
359C3×D4—204no—
360C3×D4#70912yes—
361C2×C3×C4—21no—
362C2×C3×C4—42no—
363C2×C3×C4—52no—
364C2×C3×C4—102no—
365C2×C3×C4—102no—
366C2×C3×C4—102no—
367C2×C3×C4—204no—
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4C23×D511yescharacteristic
371#67—402no—
372C2×Dic3—21no—
373C2×Dic3—102no—
374D12—21no—
375D12—21no—
376C4×D3—42no—
377Dic6—401no—
378C3⋊C8—21no—
379C3⋊C8—21no—
380C3⋊C8—102no—
381C22×C5—22no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—121no—
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×C5C2×#23711yescharacteristic
396C4×C5#100411yescharacteristic
397Dic5—22no—
398Dic5—42no—
399Dic5—122no—
400#41—104no—
401#41—202no—
402C2×Q8—52no—
403C2×Q8—301no—
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—102no—
413SD16—602no—
414D8—62no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—152no—
418C2×C8—602no—
419C4⋊C4—31no—
420C4⋊C4—51no—
421C4⋊C4—102no—
422C4⋊C4—101no—
423C4⋊C4—101no—
424C4⋊C4—152no—
425C4⋊C4—301no—
426C4⋊C4C2×D3×D511yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—52no—
429C22⋊C4—61no—
430C22⋊C4—102no—
431C22⋊C4—302no—
432C22⋊C4—302no—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—102no—
440C22×C3—102no—
441C22×C3—102no—
442C22×C3C2×D4×D511yescharacteristic
443C2×D3—41no—
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—42no—
456C2×C5—241no—
457C2×C5#580611yescharacteristic
458C2×C5C2×#95011yescharacteristic
459C2×C5#583711yescharacteristic
460D5—42no—
461C23—21no—
462C23—52no—
463C23—61no—
464Q8—102no—
465Q8—102no—
466Q8—1201no—
467D4—21no—
468D4—61no—
469D4—61no—
470D4—102no—
471D4—204no—
472D4—1202no—
473D4#676512yes—
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—204no—
483C2×C4—302no—
484C2×C4D5×#6711yescharacteristic
485C2×C4D5×#6711yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—61no—
488C8—61no—
489C8—302no—
490C2×C3—42no—
491C2×C3—202no—
492C2×C3#6588411yescharacteristic
493C2×C3C2×#405811yescharacteristic
494C2×C3#6610411yescharacteristic
495D3—81no—
496C5#8351111yescharacteristic, complemented, Sylow
497C22—22no—
498C22—41no—
499C22—41no—
500C22—102no—
501C22—102no—
502C22—102no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22C2×D5×#6711yescharacteristic
507C4—21no—
508C4—41no—
509C4—102no—
510C4—121no—
511C4—202no—
512C4—602no—
513C4#9149012yes—
514C4C2×#676511yescharacteristic
515C4#9201711yescharacteristic
516C3#1061134111yescharacteristic, complemented, Sylow
517C2—42no—
518C2—202no—
519C2—241no—
520C2#1175430511yescharacteristic
521C2C2×#9149011yescharacteristic
522C2#1175531911yescharacteristic
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×#65889C2semidirect
2. #11752718C2semidirect
3. #11751109C2semidirect
4. C4×C5×#213C2semidirect
5. #11749024C2semidirect
6. #11748961C2semidirect
7. #11747309C2semidirect
8. #11747204C2semidirect
9. #11747070C2semidirect
10. C3⋊C8×D20C2semidirect
11. #11746920C2semidirect
44. #65889D3semidirect
97. C4×#213D5semidirect
435. C3×C5#3303semidirect
496. C5#83511semidirect
516. C3#10611341semidirect

Maximal subgroups

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

subgroupindex
C3×#658892
#117527182
#117511092
C4×C5×#2132
#117490242
#117489612
#117473092
#117472042
#117470702
C3⋊C8×D202
#117469202
#106113413
#835115