Finite Group Databasebeta

← #14460169

Subgroups — #14460169

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#11756310C211yesmaximal, characteristic, complemented
2C5×#5563C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748533C212yesmaximal, complemented
5#11748526C212yesmaximal, complemented
6#11748463C212yesmaximal, complemented
7#11748393C212yesmaximal, complemented
8#11747077C211yesmaximal, characteristic, complemented
9C4×#6654C211yesmaximal, characteristic, complemented
10#11746930C211yesmaximal, characteristic, complemented
11#11746885C211yesmaximal, characteristic, complemented
12#10615383—31nomaximal, Hall
13C2×#6817C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827—21no—
16#91813C2212yes—
17C4⋊C4×D15—21no—
18#91772—22no—
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C5×#938—21no—
22C5×#930C2212yes—
23C5×#926C2212yes—
24C5×#892—21no—
25C5×#885—22no—
26C4×C5×D12C2211yescharacteristic
27C5×#869C2211yescharacteristic
28C22×C3×#168C2212yes—
29C2×#6659C2212yes—
30C2×#6654C2211yescharacteristic
31C3×C22⋊#168C2212yes—
32C3×C4⋊#168C2211yescharacteristic
33C3×C4×#168C2211yescharacteristic
34#90988C2211yescharacteristic
35#90985C2212yes—
36#90975C2212yes—
37#90975C2212yes—
38#90975C2212yes—
39#90969C2211yescharacteristic
40#90969C2212yes—
41#90967C2211yescharacteristic
42#79443—51nomaximal, Hall
43C5×#555—31no—
44#65885—31no—
45#65382—31no—
46#65373—31no—
47#65330—32no—
48#65326—32no—
49#65308—31no—
50C4×#686—31no—
51D4×#168D311yescharacteristic, complemented
52#65291—32no—
53#65285—32no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57#6817—24no—
58#6817—42no—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×Dic30C2312yes—
63C2×C5×#67—22no—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6—21no—
67C3×C5×C4⋊C4D411yescharacteristic
68C3×C5×C22⋊C4D412yes—
69C3×C42×C5C2311yescharacteristic
70#6719—22no—
71#6714—21no—
72C4⋊Dic15—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2311yescharacteristic
75#6712—22no—
76C5×#217—22no—
77C5×(C2×D3)⋊C4—21no—
78C5×(C2×D3)⋊C4—22no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C5×C4⋊Dic3C2311yescharacteristic
82C4×C5×Dic3—22no—
83C2×C3×#168—42no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2312yes—
86C2×C3×#168C2311yescharacteristic
87#6659—42no—
88#6654—22no—
89#5563D511yescharacteristic, complemented
90#5551—51no—
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×#709—32no—
101C5×C4⋊Q8—31no—
102C5×#124—62no—
103C5×#121—32no—
104C5×#121—61no—
105C4×C5×D4—31no—
106C4×C5×D4C2×D311yescharacteristic
107C5×#117—32no—
108C5×#117—61no—
109#4084—61no—
110C2×#687—32no—
111C2×#686—31no—
112#4070—32no—
113C22×#168C2×D312yes—
114D5×C4⋊C4—61no—
115#4029—62no—
116C4×D20—31no—
117#4015—31no—
118#3964—31no—
119C22⋊#168C2×D312yes—
120#3942—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3941—32no—
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—44no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143D60—21no—
144D60#4112yes—
145C4×D15—44no—
146C4×D15—42no—
147Dic30—22no—
148Dic30—22no—
149C5×#67—82no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C5×D12—21no—
153C5×D12—21no—
154C4×C5×D3—42no—
155C5×Dic6—81no—
156C3×#168—21no—
157C3×#168—22no—
158C3×#168—21no—
159C2×#235—52no—
160C22×C3×C8—52no—
161C3×C4×D4C2×D511yescharacteristic
162#938—21no—
163#938—101no—
164#930C2×D512yes—
165#926C2×D512yes—
166#924—52no—
167C2×D24—51no—
168C2×#204—52no—
169#892—21no—
170D3×C4⋊C4—101no—
171#885—22no—
172#883—102no—
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—51no—
182#821—52no—
183#818—51no—
184#817—52no—
185#816—52no—
186#816—52no—
187#816—52no—
188C2×C5×Q8—61no—
189C2×C5×D4—31no—
190C2×C5×D4—62no—
191C2×C5×D4D1211yescharacteristic
192C22×C4×C5—61no—
193C22×C4×C5C22×D312yes—
194C2×C22⋊D5—62no—
195#709—64no—
196#709—122no—
197C2×D20—31no—
198C2×C4×D5—62no—
199C2×C4×D5—61no—
200C2×Dic10—32no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—32no—
203C5×C4⋊C4—61no—
204C5×C4⋊C4D1211yescharacteristic
205C5×C22⋊C4—62no—
206C5×C22⋊C4—62no—
207C5×C22⋊C4—61no—
208C5×C22⋊C4D1212yes—
209C42×C5—62no—
210C42×C5C22×D311yescharacteristic
211C22⋊Dic5—62no—
212#687—122no—
213#686—62no—
214#685—61no—
215C4⋊Dic5—31no—
216C4⋊Dic5—61no—
217C4⋊Dic5—61no—
218#683—62no—
219C2×#168—42no—
220C2×#168C22×D311yescharacteristic
221C2×#168C22×D311yescharacteristic
222C2×#168C22×D312yes—
223#555—31no—
224#547—151no—
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—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×C5×D3—41no—
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—42no—
250Dic15—41no—
251C5×Dic3—41no—
252C5×Dic3—42no—
253C2×C3×D4C22⋊D511yescharacteristic
254C22×C3×C4C22×D512yes—
255C2×#67—22no—
256C2×#67—102no—
257#235—104no—
258#235—202no—
259C2×D12—51no—
260C2×D12C22×D511yescharacteristic
261C2×C4×D3—21no—
262C2×C4×D3—101no—
263C2×C4×D3—102no—
264C2×Dic6—21no—
265C2×Dic6—52no—
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—22no—
277(C2×D3)⋊C4—101no—
278C4⋊Dic3—21no—
279C4⋊Dic3—51no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282C4⋊Dic3C22×D512yes—
283C4⋊Dic3C22×D511yescharacteristic
284Dic3⋊C4—102no—
285C4×Dic3—22no—
286D24—102no—
287#204—202no—
288C23×C5—61no—
289C23×C5C2×D1212yes—
290C22×D5—61no—
291C5×Q8—241no—
292C5×D4—22no—
293C5×D4—61no—
294C5×D4—61no—
295C5×D4—242no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—61no—
299C2×C4×C5—62no—
300C2×C4×C5—122no—
301C2×C4×C5C2×D1212yes—
302C2×C4×C5C2×D1211yescharacteristic
303C2×C4×C5C2×D1211yescharacteristic
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—124no—
306C2×Dic5—61no—
307C2×Dic5—62no—
308D20—32no—
309D20—61no—
310C4×D5—124no—
311C4×D5—122no—
312Dic10—62no—
313Dic10—62no—
314#168—21no—
315#168—22no—
316#168—21no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—52no—
321C4⋊Q8—31no—
322C4⋊Q8—151no—
323#124—62no—
324#123—302no—
325C22⋊Q8—152no—
326#121—32no—
327#121—61no—
328#121—301no—
329C4×D4—31no—
330C4×D4—151no—
331C4×D4D3×D511yescharacteristic
332#117—32no—
333#117—61no—
334C2×C4⋊C4—301no—
335#107—151no—
336#106—152no—
337C4⋊C8—51no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—152no—
343#102—151no—
344C22⋊C8—52no—
345C4×C8—51no—
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351C5×D3—81no—
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—82no—
363#67—204no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—101no—
367C2×Dic3—102no—
368D12—21no—
369D12—21no—
370D12—52no—
371D12—101no—
372C4×D3—42no—
373C4×D3—204no—
374C4×D3—202no—
375Dic6—81no—
376Dic6—102no—
377Dic6—102no—
378C3×C8—101no—
379C3×C8—102no—
380C3×C8—101no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—121no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5C22×D1211yescharacteristic
388C2×D5—62no—
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—304no—
401#41—602no—
402C2×Q8—61no—
403C2×Q8—152no—
404C2×D4—31no—
405C2×D4—62no—
406C2×D4—151no—
407C2×D4—302no—
408C2×D4#120311yescharacteristic
409C22×C4—61no—
410C22×C4—301no—
411C22×C4—302no—
412C22×C4C2×D3×D512yes—
413SD16—602no—
414D8—302no—
415C2×C8—51no—
416C2×C8—51no—
417C2×C8—52no—
418C2×C8—202no—
419C4⋊C4—32no—
420C4⋊C4—31no—
421C4⋊C4—61no—
422C4⋊C4—151no—
423C4⋊C4—301no—
424C4⋊C4—302no—
425C4⋊C4—301no—
426C4⋊C4#120311yescharacteristic
427C22⋊C4—62no—
428C22⋊C4—62no—
429C22⋊C4—61no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C22⋊C4#120312yes—
433C42—62no—
434C42C2×D3×D511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3C22×C22⋊D511yescharacteristic
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—102no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4#409612yes—
449C3×C4D5×#4111yescharacteristic
450C3×C4#414911yescharacteristic
451Dic3—41no—
452Dic3—42no—
453Dic3—201no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5—241no—
457C2×C5#555411yescharacteristic
458C2×C5C2×#90411yescharacteristic
459C2×C5#575111yescharacteristic
460D5—122no—
461C23—61no—
462C23—301no—
463C23C2×#120312yes—
464Q8—241no—
465Q8—302no—
466Q8—302no—
467D4—22no—
468D4—61no—
469D4—61no—
470D4—152no—
471D4—242no—
472D4—301no—
473D4—604no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—61no—
477C2×C4—62no—
478C2×C4—122no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—604no—
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×C3C2×#409611yescharacteristic
492C2×C3#6616311yescharacteristic
493C2×C3#6617011yescharacteristic
494D3—81no—
495D3—202no—
496C5#7944311yescharacteristic, complemented, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22—302no—
504C22—601no—
505C22—601no—
506C22C22×#120311yescharacteristic
507C4—21no—
508C4—22no—
509C4—122no—
510C4—121no—
511C4—601no—
512C4—602no—
513C4#9130312yes—
514C4#9202411yescharacteristic
515C4#9202611yescharacteristic
516C3#1061538311yescharacteristic, complemented, Sylow
517C2—42no—
518C2—241no—
519C2—602no—
520C2C2×#9130311yescharacteristic
521C2#1175498211yescharacteristic
522C2#1175530711yescharacteristic
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. #11756310C2semidirect
2. C5×#5563C2semidirect
3. C3×D4×#168C2semidirect
4. #11748533C2semidirect
5. #11748526C2semidirect
6. #11748463C2semidirect
7. #11748393C2semidirect
8. #11747077C2semidirect
9. C4×#6654C2semidirect
10. #11746930C2semidirect
11. #11746885C2semidirect
51. D4×#168D3semidirect
89. #5563D5semidirect
435. C3×C5#3303semidirect
496. C5#79443semidirect
516. C3#10615383semidirect

Maximal subgroups

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

subgroupindex
#117563102
C5×#55632
C3×D4×#1682
#117485332
#117485262
#117484632
#117483932
#117470772
C4×#66542
#117469302
#117468852
#106153833
#794435