Finite Group Databasebeta

← #14460171

Subgroups — #14460171

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
2C5×#5551C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748535C212yesmaximal, complemented
5#11748521C212yesmaximal, complemented
6#11748466C212yesmaximal, complemented
7#11748388C212yesmaximal, complemented
8#11747087C211yesmaximal, characteristic, complemented
9C4×#6654C211yesmaximal, characteristic, complemented
10#11746929C211yesmaximal, characteristic, complemented
11#11746883C211yesmaximal, characteristic, complemented
12#10615242—31nomaximal, Hall
13C2×C5×#235C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827—21no—
16#91819C2212yes—
17#91815C2212yes—
18#91781—21no—
19#91774—22no—
20C4×D60C2211yescharacteristic
21#91758C2211yescharacteristic
22C5×#938—21no—
23C5×#924C2212yes—
24C5×D3×C4⋊C4—21no—
25C5×#883—22no—
26C4×C5×D12C2211yescharacteristic
27C5×#869C2211yescharacteristic
28C22×C3×#168C2212yes—
29C2×#6660C2212yes—
30C2×#6654C2211yescharacteristic
31C3×C22⋊#168C2212yes—
32C3×C4⋊#168C2211yescharacteristic
33C3×C4×#168C2211yescharacteristic
34#90988C2211yescharacteristic
35#90985C2212yes—
36#90973C2212yes—
37#90973C2212yes—
38#90973C2212yes—
39#90969C2211yescharacteristic
40#90967C2211yescharacteristic
41#90967C2212yes—
42#79443—51nomaximal, Hall
43C5×#547—31no—
44#65897—31no—
45#65527—32no—
46#65522—32no—
47#65372—31no—
48#65370—31no—
49#65337—32no—
50#65334—32no—
51C4×#686—31no—
52D4×#168D311yescharacteristic, complemented
53#65297—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×Dic30—21no—
60C2×C5×#67—22no—
61C5×#235—24no—
62C5×#235—42no—
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C4×C5×D3—22no—
66C2×C5×Dic6C2312yes—
67C3×C5×C4⋊C4D411yescharacteristic
68C3×C5×C22⋊C4D412yes—
69C3×C42×C5C2311yescharacteristic
70#6719—22no—
71#6714—21no—
72#6714—22no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75C4⋊Dic15C2311yescharacteristic
76C4×Dic15—22no—
77C5×#217—22no—
78C5×(C2×D3)⋊C4—21no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C5×Dic3⋊C4—22no—
83C2×C3×#168—42no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2312yes—
86C2×C3×#168C2311yescharacteristic
87#6660—42no—
88#6654—22no—
89#5563—51no—
90#5551D511yescharacteristic, complemented
91C3×C8×D4—51no—
92#5114—52no—
93#5113—52no—
94#4842—51no—
95#4841—51no—
96#4734—52no—
97#4723—52no—
98C4×D24—51no—
99#4681—51no—
100C2×C5×#41—32no—
101C5×C4⋊Q8—31no—
102C5×#123—62no—
103C5×C22⋊Q8—32no—
104C5×#121—61no—
105C4×C5×D4—31no—
106C4×C5×D4C2×D311yescharacteristic
107C2×C5×C4⋊C4—61no—
108C2×#688—32no—
109#4084—61no—
110C2×#686—31no—
111#4076—32no—
112#4072—32no—
113C22×#168C2×D312yes—
114#4038—61no—
115#4031—62no—
116C4×D20—31no—
117#4015—31no—
118#3967—32no—
119#3967—32no—
120#3967—32no—
121#3964—32no—
122#3964—31no—
123C22⋊#168C2×D312yes—
124#3941—31no—
125#3940—32no—
126#3939—31no—
127C4⋊#168C2×D311yescharacteristic
128C4×#168C2×D311yescharacteristic
129#3303—151noSylow
130C23×C3×C5C2×D412yes—
131C22×D15—21no—
132C22×C5×D3—21no—
133C3×C5×D4—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140#1220—82no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143D60—21no—
144D60—21no—
145C4×D15—42no—
146Dic30—81no—
147C5×#67—44no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—22no—
150C5×D12—21no—
151C5×D12#4112yes—
152C4×C5×D3—44no—
153C4×C5×D3—42no—
154C5×Dic6—22no—
155C5×Dic6—22no—
156C3×#168—21no—
157C3×#168—22no—
158C3×#168—21no—
159C2×#235C2×D512yes—
160C22×C3×C8—52no—
161C3×C4×D4C2×D511yescharacteristic
162#938—21no—
163#938—101no—
164#930—52no—
165#926—52no—
166#924C2×D512yes—
167C2×D24—51no—
168C2×#204—52no—
169#892—101no—
170D3×C4⋊C4—21no—
171#885—102no—
172#883—22no—
173C4×D12—51no—
174C4×D12C2×D511yescharacteristic
175#869—51no—
176#869C2×D511yescharacteristic
177C3×C4⋊C8—51no—
178C3×C22⋊C8—52no—
179C3×C4×C8—51no—
180#821—51no—
181#821—52no—
182#821—51no—
183#818—51no—
184#817—52no—
185#816—52no—
186#816—52no—
187#816—52no—
188C5×#41—64no—
189C5×#41—122no—
190C2×C5×Q8—32no—
191C2×C5×D4—31no—
192C2×C5×D4—62no—
193C2×C5×D4D1211yescharacteristic
194C22×C4×C5—61no—
195C22×C4×C5—62no—
196C22×C4×C5C22×D312yes—
197C2×C22⋊D5—62no—
198C2×D20—31no—
199C2×C4×D5—61no—
200C2×Dic10—61no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—61no—
203C5×C4⋊C4—62no—
204C5×C4⋊C4—61no—
205C5×C4⋊C4D1211yescharacteristic
206C5×C22⋊C4—62no—
207C5×C22⋊C4—61no—
208C5×C22⋊C4D1212yes—
209C42×C5C22×D311yescharacteristic
210C22⋊Dic5—62no—
211#688—122no—
212#686—62no—
213#685—61no—
214#685—62no—
215C4⋊Dic5—31no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218C4×Dic5—62no—
219C2×#168—42no—
220C2×#168C22×D311yescharacteristic
221C2×#168C22×D311yescharacteristic
222C2×#168C22×D312yes—
223#555—151no—
224#547—31no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4—51no—
233#416—152no—
234C22×C3×C5—22no—
235C22×C3×C5—22no—
236C22×C3×C5—22no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—41no—
239C2×D15—41no—
240C2×D15—41no—
241C2×C5×D3—22no—
242C2×C5×D3—41no—
243C2×C5×D3—41no—
244C3×C4×C5—22no—
245C3×C4×C5—21no—
246C3×C4×C5#13512yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—41no—
250Dic15—42no—
251C5×Dic3—42no—
252C5×Dic3—41no—
253C2×C3×D4C22⋊D511yescharacteristic
254C22×C3×C4C22×D512yes—
255C2×#67—22no—
256C2×#67—102no—
257#235—24no—
258#235—42no—
259C2×D12—51no—
260C2×D12C22×D511yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—22no—
263C2×C4×D3—101no—
264C2×Dic6—101no—
265C2×Dic6C22×D512yes—
266C2×C3×C8—51no—
267C2×C3×C8—51no—
268C2×C3×C8—52no—
269C2×C3×C8—202no—
270C3×C4⋊C4C22⋊D511yescharacteristic
271C3×C22⋊C4C22⋊D512yes—
272C3×C42C22×D511yescharacteristic
273#217—22no—
274#217—102no—
275(C2×D3)⋊C4—21no—
276(C2×D3)⋊C4—101no—
277(C2×D3)⋊C4—102no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—52no—
281C4⋊Dic3—51no—
282C4⋊Dic3—101no—
283C4⋊Dic3C22×D511yescharacteristic
284Dic3⋊C4—22no—
285C4×Dic3—102no—
286D24—102no—
287#204—202no—
288C23×C5—61no—
289C23×C5C2×D1212yes—
290C22×D5—61no—
291C5×Q8—62no—
292C5×Q8—62no—
293C5×D4—22no—
294C5×D4—32no—
295C5×D4—61no—
296C5×D4—124no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—61no—
300C2×C4×C5—62no—
301C2×C4×C5—124no—
302C2×C4×C5—122no—
303C2×C4×C5C2×D1212yes—
304C2×C4×C5C2×D1211yescharacteristic
305C2×C4×C5C2×D1211yescharacteristic
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—242no—
308C2×Dic5—61no—
309C2×Dic5—62no—
310D20—61no—
311D20—61no—
312C4×D5—122no—
313Dic10—241no—
314#168—21no—
315#168—22no—
316#168—21no—
317C2×#41—32no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—52no—
321C4⋊Q8—31no—
322C4⋊Q8—151no—
323#124—302no—
324#123—62no—
325C22⋊Q8—32no—
326#121—61no—
327#121—152no—
328#121—301no—
329C4×D4—31no—
330C4×D4—151no—
331C4×D4D3×D511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—61no—
335#107—151no—
336#106—152no—
337C4⋊C8—51no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—151no—
343#102—152no—
344C22⋊C8—52no—
345C4×C8—51no—
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—81no—
351C5×D3—42no—
352C23×C3C2×C22⋊D512yes—
353C22×D3—21no—
354C22×D3—101no—
355C3×D4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4C2×C22⋊D512yes—
359C2×C3×C4C2×C22⋊D511yescharacteristic
360C2×C3×C4C2×C22⋊D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362#67—44no—
363#67—402no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—101no—
367C2×Dic3—102no—
368D12—21no—
369D12—101no—
370D12—101no—
371D12#71112yes—
372C4×D3—44no—
373C4×D3—42no—
374C4×D3—202no—
375Dic6—22no—
376Dic6—22no—
377Dic6—401no—
378C3×C8—101no—
379C3×C8—102no—
380C3×C8—101no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—62no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C22×D1211yescharacteristic
388C2×D5—121no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—21no—
392C4×C5—22no—
393C4×C5—121no—
394C4×C5—122no—
395C4×C5#90412yes—
396C4×C5#100411yescharacteristic
397C4×C5D3×#4111yescharacteristic
398Dic5—121no—
399Dic5—122no—
400#41—64no—
401#41—122no—
402C2×Q8—32no—
403C2×Q8—301no—
404C2×D4—31no—
405C2×D4—62no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4#120311yescharacteristic
409C22×C4—61no—
410C22×C4—62no—
411C22×C4—301no—
412C22×C4C2×D3×D512yes—
413SD16—602no—
414D8—302no—
415C2×C8—51no—
416C2×C8—51no—
417C2×C8—52no—
418C2×C8—202no—
419C4⋊C4—31no—
420C4⋊C4—61no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4—152no—
424C4⋊C4—151no—
425C4⋊C4—301no—
426C4⋊C4#120311yescharacteristic
427C22⋊C4—62no—
428C22⋊C4—61no—
429C22⋊C4—302no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C22⋊C4#120312yes—
433C42—302no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3C22×C22⋊D511yescharacteristic
440C2×D3—22no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—201no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4#409612yes—
449C3×C4C2×#71111yescharacteristic
450C3×C4#414411yescharacteristic
451Dic3—42no—
452Dic3—41no—
453Dic3—201no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5—122no—
457C2×C5#555411yescharacteristic
458C2×C5C2×#90411yescharacteristic
459C2×C5#575111yescharacteristic
460D5—241no—
461C23—61no—
462C23—301no—
463C23C2×#120312yes—
464Q8—62no—
465Q8—62no—
466Q8—1201no—
467D4—22no—
468D4—32no—
469D4—61no—
470D4—124no—
471D4—301no—
472D4—301no—
473D4—1202no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—124no—
479C2×C4—122no—
480C2×C4—301no—
481C2×C4—302no—
482C2×C4—602no—
483C2×C4C2×#120312yes—
484C2×C4C2×#120311yescharacteristic
485C2×C4C2×#120311yescharacteristic
486C2×C4C22×D3×D511yescharacteristic
487C8—101no—
488C8—101no—
489C8—102no—
490C2×C3—42no—
491C2×C3#6614011yescharacteristic
492C2×C3C2×#409611yescharacteristic
493C2×C3#6617111yescharacteristic
494D3—42no—
495D3—401no—
496C5#7944311yescharacteristic, complemented, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—601no—
504C22—601no—
505C22—601no—
506C22C22×#120311yescharacteristic
507C4—21no—
508C4—22no—
509C4—121no—
510C4—122no—
511C4—602no—
512C4—601no—
513C4#9130312yes—
514C4D3×#71111yescharacteristic
515C4#9202511yescharacteristic
516C3#1061524211yescharacteristic, complemented, Sylow
517C2—42no—
518C2—122no—
519C2—1201no—
520C2C2×#9130311yescharacteristic
521C2#1175497511yescharacteristic
522C2#1175530811yescharacteristic
subgroupG/H
centerC22C22×#1203
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 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756322C2semidirect
2. C5×#5551C2semidirect
3. C3×D4×#168C2semidirect
4. #11748535C2semidirect
5. #11748521C2semidirect
6. #11748466C2semidirect
7. #11748388C2semidirect
8. #11747087C2semidirect
9. C4×#6654C2semidirect
10. #11746929C2semidirect
11. #11746883C2semidirect
52. D4×#168D3semidirect
90. #5551D5semidirect
435. C3×C5#3303semidirect
496. C5#79443semidirect
516. C3#10615242semidirect

Maximal subgroups

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

subgroupindex
#117563222
C5×#55512
C3×D4×#1682
#117485352
#117485212
#117484662
#117483882
#117470872
C4×#66542
#117469292
#117468832
#106152423
#794435