Finite Group Databasebeta

← #14460166

Subgroups — #14460166

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#11756314C211yesmaximal, characteristic, complemented
2#11752710C211yesmaximal, characteristic, complemented
3C4×C5×#213C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic, complemented
5#11749043C212yesmaximal, complemented
6#11748969C212yesmaximal, complemented
7#11747315C212yesmaximal, complemented
8#11747215C212yesmaximal, complemented
9#11747077C211yesmaximal, characteristic, complemented
10#11746994C211yesmaximal, characteristic, complemented
11#11746921C211yesmaximal, characteristic, complemented
12#10611341—31nomaximal, Hall
13C2×#6819C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91819—21no—
16C2×C4⋊Dic15—21no—
17#91786C2212yes—
18#91775—22no—
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C2×C5×#213C2211yescharacteristic
22C4×C5×D12C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91466C2212yes—
25#91460—21no—
26#91347C2212yes—
27#91338—21no—
28#91326—22no—
29C2×#6659C2212yes—
30C2×#6648C2212yes—
31C5×#832C2211yescharacteristic
32C5×#809C2211yescharacteristic
33C5×#807C2211yescharacteristic
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3964C2212yes—
36C3×#3940C2212yes—
37C3×C4⋊#168C2211yescharacteristic
38#90975C2212yes—
39#90974C2212yes—
40#90974C2212yes—
41#90957C2212yes—
42#81076—51nomaximal, Hall
43#65897—31no—
44#65889—31no—
45C4×C5×D8—31no—
46#65447—32no—
47#65308—31no—
48#65297D311yescharacteristic, complemented
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—
57C22×Dic15—22no—
58#6819—24no—
59#6819—42no—
60C2×D60D411yescharacteristic
61C2×C4×D15C2312yes—
62C2×Dic30C2312yes—
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C3×Dic10—21no—
66C2×#1203—22no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6714—22no—
71#6714D412yes—
72C4⋊Dic15—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15—22no—
75C4⋊Dic15D411yescharacteristic
76C5×#213—22no—
77C5×(C2×D3)⋊C4—21no—
78C5×C4⋊Dic3C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83C2×C3×#168C2312yes—
84#6667—22no—
85(C2×D3)⋊Dic5—22no—
86Dic3×Dic5—22no—
87#6659—42no—
88#6648—42no—
89#5734—51no—
90#5555—51no—
91C3×#476—51no—
92#5093—51no—
93C4×#213D511yescharacteristic, complemented
94#4868—52no—
95#4864—52no—
96#4841—51no—
97#4834—51no—
98#4781—52no—
99#4772—52no—
100C2×#711—32no—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4C2×D311yescharacteristic
104#4084—32no—
105C2×#687—32no—
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#3964C2×D312yes—
123#3952—32no—
124#3948—32no—
125#3948—32no—
126#3942—32no—
127#3940C2×D312yes—
128C4⋊#168C2×D311yescharacteristic
129#3303—151noSylow
130C23×C3×C5—21no—
131C22×D15C2×D412yes—
132C22×C5×D3—21no—
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
140#1220—44no—
141C2×Dic15—22no—
142C2×Dic15—44no—
143C2×Dic15C2×D412yes—
144D60—22no—
145C4×D15—22no—
146C4×D15—22no—
147Dic30—22no—
148Dic30—22no—
149C2×C5×Dic3—21no—
150C5×D12—21no—
151C5×D12—21no—
152C4×C5×D3—42no—
153C2×C3×Dic5—22no—
154C3×Dic10—81no—
155#1203—82no—
156C3×#168—22no—
157C5×C3⋊C8—21no—
158C5×C3⋊C8—21no—
159C2×#237—52no—
160C3×C4⋊Q8—51no—
161C3×C4×D4C2×D511yescharacteristic
162#947—102no—
163C2×#213C2×D511yescharacteristic
164#930—101no—
165C2×C4⋊Dic3—101no—
166C2×#204—52no—
167C2×D3×C8—52no—
168#897—52no—
169#895—52no—
170#895—101no—
171#892—52no—
172#892—101no—
173#886—102no—
174C4×D12—51no—
175C4×D12C2×D511yescharacteristic
176#869—51no—
177C3×#106—52no—
178C3×C4⋊C8—51no—
179C3×#102—52no—
180#832C2×D511yescharacteristic
181(C2×D3)⋊C8—52no—
182#816—52no—
183#810—52no—
184#810—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—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—62no—
210#687—122no—
211#685—32no—
212#685—62no—
213#685—62no—
214C4⋊Dic5—21no—
215C4⋊Dic5—31no—
216C4⋊Dic5—62no—
217C4⋊Dic5—61no—
218C4⋊Dic5—61no—
219C4⋊Dic5C22×D312yes—
220C4×Dic5—62no—
221C2×#168C22×D312yes—
222C8×D5—122no—
223#555—151no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—51no—
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×D15—22no—
239C2×D15—22no—
240C2×D15—22no—
241C2×C5×D3—41no—
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—101no—
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C2×#67—102no—
257C22×Dic3—102no—
258#237—104no—
259#237—202no—
260C2×D12—51no—
261C2×D12—102no—
262C2×D12C22×D511yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—52no—
265C2×Dic6—52no—
266C2×C3×C8—52no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—101no—
269C3×C4⋊C4C22×D511yescharacteristic
270C3×C22⋊C4—21no—
271C3×C42C22×D511yescharacteristic
272#213—22no—
273(C2×D3)⋊C4—21no—
274(C2×D3)⋊C4—52no—
275(C2×D3)⋊C4—102no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—102no—
278C4⋊Dic3—51no—
279C4⋊Dic3—102no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282C4⋊Dic3C22×D511yescharacteristic
283C4×Dic3—102no—
284C2×C3⋊C8C22×D511yescharacteristic
285C2×C3⋊C8C22×D511yescharacteristic
286#204—202no—
287D3×C8—202no—
288C23×C5—21no—
289C23×C5—61no—
290C22×D5—32no—
291C5×D4—21no—
292C5×D4—61no—
293C5×D4—61no—
294C5×D4#23912yes—
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—62no—
312Dic10—62no—
313Dic10—81no—
314C5×C8—61no—
315C5×C8—61no—
316#168—22no—
317C2×#41—152no—
318C2×SD16—152no—
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—52no—
337C4⋊C8—51no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—31no—
342#102—31no—
343#102—52no—
344C22⋊C8—152no—
345C4×C8—31no—
346C2×C3×C5—42no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—42no—
351C5×D3—81no—
352C23×C3—21no—
353C22×D3—21no—
354C22×D3—52no—
355C3×Q8—401no—
356C3×D4—21no—
357C3×D4#70912yes—
358C2×C3×C4—21no—
359C2×C3×C4—42no—
360C2×C3×C4—102no—
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4C23×D511yescharacteristic
364#67—204no—
365C2×Dic3—21no—
366C2×Dic3—52no—
367C2×Dic3—102no—
368C2×Dic3—204no—
369D12—21no—
370D12—21no—
371D12—102no—
372D12—402no—
373C4×D3—42no—
374C4×D3—102no—
375C4×D3—102no—
376Dic6—102no—
377Dic6—102no—
378C3×C8—102no—
379C3⋊C8—21no—
380C3⋊C8—21no—
381C22×C5—22no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—121no—
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×C5C2×#23911yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—42no—
398Dic5—62no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—101no—
403C2×Q8—152no—
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—602no—
414D8—62no—
415C2×C8—31no—
416C2×C8—31no—
417C2×C8—52no—
418C2×C8—602no—
419C4⋊C4—31no—
420C4⋊C4—52no—
421C4⋊C4—101no—
422C4⋊C4—151no—
423C4⋊C4—302no—
424C4⋊C4—301no—
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—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3C2×D4×D511yescharacteristic
440C2×D3—41no—
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—42no—
456C2×C5—241no—
457C2×C5#563011yescharacteristic
458C2×C5C2×#91611yescharacteristic
459C2×C5#577511yescharacteristic
460D5—122no—
461C23—21no—
462C23—61no—
463C23—152no—
464Q8—302no—
465Q8—302no—
466Q8—401no—
467D4—21no—
468D4—61no—
469D4—61no—
470D4—302no—
471D4—604no—
472D4—1202no—
473D4#676912yes—
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—42no—
491C2×C3#6588411yescharacteristic
492C2×C3C2×#405811yescharacteristic
493C2×C3#6610411yescharacteristic
494D3—81no—
495D3—202no—
496C5#8107611yescharacteristic, complemented, Sylow
497C22—22no—
498C22—41no—
499C22—41no—
500C22—121no—
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—
514C4C2×#676911yescharacteristic
515C4#9201911yescharacteristic
516C3#1061134111yescharacteristic, complemented, Sylow
517C2—42no—
518C2—241no—
519C2—602no—
520C2#1175438211yescharacteristic
521C2C2×#9149911yescharacteristic
522C2#1175533111yescharacteristic
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. #11756314C2semidirect
2. #11752710C2semidirect
3. C4×C5×#213C2semidirect
4. C3×#65297C2semidirect
5. #11749043C2semidirect
6. #11748969C2semidirect
7. #11747315C2semidirect
8. #11747215C2semidirect
9. #11747077C2semidirect
10. #11746994C2semidirect
11. #11746921C2semidirect
48. #65297D3semidirect
93. C4×#213D5semidirect
435. C3×C5#3303semidirect
496. C5#81076semidirect
516. C3#10611341semidirect

Maximal subgroups

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

subgroupindex
#117563142
#117527102
C4×C5×#2132
C3×#652972
#117490432
#117489692
#117473152
#117472152
#117470772
#117469942
#117469212
#106113413
#810765