Finite Group Databasebeta

← #14460011

Subgroups — #14460011

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5551C211yesmaximal, characteristic
2C3×#65876C211yesmaximal, characteristic, complemented
3D4×C3⋊#168C211yesmaximal, characteristic, complemented
4#11748562C212yesmaximal, complemented
5#11748538C212yesmaximal, complemented
6#11748404C212yesmaximal, complemented
7#11748382C212yesmaximal, complemented
8#11747094C211yesmaximal, characteristic, complemented
9C4×#6656C211yesmaximal, characteristic, complemented
10#11746923C211yesmaximal, characteristic, complemented
11#11746900C211yesmaximal, characteristic, complemented
12#10615241—31nomaximal, Hall
13C2×C5×#235C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15C22×C3⋊#168C2212yes—
16C5×#938—21no—
17C5×#924C2212yes—
18C5×D3×C4⋊C4—21no—
19C5×#883—22no—
20C4×C5×D12C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C3×#4082—21no—
23C3×#4072C2212yes—
24C3×#4070C2212yes—
25C3×#4033—21no—
26C3×#4025—22no—
27C3×#4015C2211yescharacteristic
28C3×C4×Dic10C2211yescharacteristic
29C2×#6661C2212yes—
30C2×#6656C2211yescharacteristic
31#91114C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34#90989C2212yes—
35#90986C2211yescharacteristic
36#90972C2212yes—
37#90972C2212yes—
38#90972C2212yes—
39#90970C2211yescharacteristic
40#90966C2211yescharacteristic
41#90966C2212yes—
42#83664—51nomaximal, Hall
43C5×#547—31no—
44#65876D311yescharacteristic, complemented
45#65528—32no—
46#65522—32no—
47#65379—31no—
48#65370—31no—
49#65340—32no—
50#65334—32no—
51C4×#687—31no—
52D4×#168—31no—
53#65296—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×C5×#67—22no—
57C5×#235—24no—
58C5×#235—42no—
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C4×C5×D3—22no—
62C2×C5×Dic6C2312yes—
63C2×C3×Dic10—21no—
64C2×C3×Dic10C2311yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2311yescharacteristic
68C2×C3⋊#168—42no—
69C2×C3⋊#168C2311yescharacteristic
70C2×C3⋊#168C2312yes—
71C2×C3⋊#168C2311yescharacteristic
72C5×#217—22no—
73C5×(C2×D3)⋊C4—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×Dic3⋊C4—22no—
78C3×C22⋊Dic5—22no—
79C3×C22⋊Dic5—22no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2312yes—
83C3×#683—21no—
84C3×#683—22no—
85C3×C4×Dic5—21no—
86C3×C4×Dic5—22no—
87#6661—42no—
88#6656—22no—
89C3×#556—51no—
90#5551D511yescharacteristic
91#5093—51no—
92#5087—51no—
93#5051—52no—
94#5047—52no—
95#5031—51no—
96C4×#215—51no—
97D4×C3⋊C8—51no—
98#5002—52no—
99#4996—52no—
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×#689—32no—
109#4082—21no—
110C2×#687—31no—
111#4072C2×D312yes—
112#4070C2×D312yes—
113C22×#168—32no—
114#4033—21no—
115#4025—22no—
116#4015C2×D311yescharacteristic
117C4×Dic10C2×D311yescharacteristic
118#3967—32no—
119#3967—32no—
120#3967—32no—
121#3964—32no—
122#3964—31no—
123C22⋊#168—32no—
124#3942—31no—
125#3940—31no—
126#3939—32no—
127C4⋊#168—31no—
128C4×#168—31no—
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×C5×D3—21no—
132C3×C5×D4—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C5×#67—44no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—22no—
142C5×D12—21no—
143C5×D12#4112yes—
144C4×C5×D3—44no—
145C4×C5×D3—42no—
146C5×Dic6—22no—
147C5×Dic6—22no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C3×Dic10—21no—
152C3×Dic10—21no—
153C3×Dic10—42no—
154C3⋊#168—21no—
155C3⋊#168—22no—
156C3⋊#168—21no—
157C2×#235C2×D512yes—
158C3×C4⋊Q8—51no—
159C3×#126—102no—
160C3×#124—101no—
161C3×C22⋊Q8—52no—
162C3×C4×Q8—51no—
163C3×C4×Q8—101no—
164C3×C4×D4C2×D511yescharacteristic
165C3×#117—52no—
166C2×#216—52no—
167C2×#215—51no—
168#938—21no—
169#924C2×D512yes—
170C22×C3⋊C8—52no—
171D3×C4⋊C4—21no—
172#883—22no—
173C4×D12C2×D511yescharacteristic
174#869C2×D511yescharacteristic
175#835—51no—
176#830—52no—
177#810—52no—
178#810—52no—
179#810—52no—
180#809—51no—
181#809—52no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)—51no—
185C4×C3⋊C8—51no—
186C5×#41—64no—
187C5×#41—122no—
188C2×C5×Q8—32no—
189C2×C5×D4—31no—
190C2×C5×D4—62no—
191C2×C5×D4#6711yescharacteristic
192C22×C4×C5—61no—
193C22×C4×C5—62no—
194C22×C4×C5C22×D312yes—
195C2×Dic10—21no—
196C2×Dic10C22×D311yescharacteristic
197C5×C4⋊C4—31no—
198C5×C4⋊C4—61no—
199C5×C4⋊C4—62no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4#6711yescharacteristic
202C5×C22⋊C4—62no—
203C5×C22⋊C4—61no—
204C5×C22⋊C4#6712yes—
205C42×C5C22×D311yescharacteristic
206C22⋊Dic5—22no—
207C22⋊Dic5—22no—
208#689—122no—
209#687—62no—
210C4⋊Dic5—21no—
211C4⋊Dic5C22×D312yes—
212C4⋊Dic5C22×D311yescharacteristic
213#683—21no—
214#683—22no—
215C4×Dic5—21no—
216C4×Dic5—22no—
217C2×#168—31no—
218C2×#168—31no—
219C2×#168—32no—
220C2×#168—122no—
221#556—51no—
222#547—31no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×C5×D3—22no—
237C2×C5×D3—41no—
238C2×C5×D3—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244C3×Dic5—41no—
245C3×Dic5—42no—
246C3×Dic5—41no—
247C5×Dic3—42no—
248C5×Dic3—41no—
249C2×C3×Q8—51no—
250C2×C3×Q8—101no—
251C2×C3×D4C22⋊D511yescharacteristic
252C22×C3×C4C22×D512yes—
253C2×#67—22no—
254#235—24no—
255#235—42no—
256C2×D12C22×D511yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—22no—
259C2×Dic6C22×D512yes—
260C3×C4⋊C4—52no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4—101no—
265C3×C4⋊C4C22⋊D511yescharacteristic
266C3×C22⋊C4—102no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4C22⋊D512yes—
269C3×C42—102no—
270C3×C42—101no—
271C3×C42C22×D511yescharacteristic
272#217—22no—
273#216—202no—
274#215—102no—
275(C2×D3)⋊C4—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3C22×D511yescharacteristic
279Dic3⋊C4—22no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—202no—
284C23×C5—61no—
285C23×C5C2×#6712yes—
286C5×Q8—62no—
287C5×Q8—62no—
288C5×D4—22no—
289C5×D4—32no—
290C5×D4—61no—
291C5×D4—124no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—61no—
295C2×C4×C5—62no—
296C2×C4×C5—124no—
297C2×C4×C5—122no—
298C2×C4×C5C2×#6712yes—
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C2×#6711yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—22no—
305Dic10—21no—
306Dic10—21no—
307Dic10—42no—
308#168—61no—
309#168—61no—
310#168—62no—
311C2×#41—32no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—31no—
316C4⋊Q8—51no—
317#126—102no—
318#124—101no—
319#123—62no—
320C22⋊Q8—32no—
321C22⋊Q8—52no—
322#121—61no—
323C4×Q8—51no—
324C4×Q8—101no—
325C4×D4—31no—
326C4×D4D3×D511yescharacteristic
327#117—52no—
328C2×C4⋊C4—61no—
329#107—152no—
330#106—151no—
331C4⋊C8—151no—
332#103—151no—
333#103—152no—
334#103—152no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8—151no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344C5×D3—42no—
345C23×C3C2×C22⋊D512yes—
346C22×D3—21no—
347C3×Q8—101no—
348C3×Q8—101no—
349C3×Q8—202no—
350C3×D4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—101no—
354C2×C3×C4—102no—
355C2×C3×C4—101no—
356C2×C3×C4C2×C22⋊D512yes—
357C2×C3×C4C2×C22⋊D511yescharacteristic
358C2×C3×C4C2×C22⋊D511yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—44no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363D12—21no—
364D12#71112yes—
365C4×D3—44no—
366C4×D3—42no—
367Dic6—22no—
368Dic6—22no—
369C3⋊C8—101no—
370C3⋊C8—101no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5—62no—
376C22×C5—121no—
377C22×C5—121no—
378C22×C5C22×#6711yescharacteristic
379C4×C5—22no—
380C4×C5—21no—
381C4×C5—121no—
382C4×C5—122no—
383C4×C5#95012yes—
384C4×C5D3×#4111yescharacteristic
385C4×C5#100911yescharacteristic
386Dic5—42no—
387Dic5—41no—
388Dic5—41no—
389#41—64no—
390#41—122no—
391C2×Q8—32no—
392C2×Q8—51no—
393C2×Q8—101no—
394C2×D4—31no—
395C2×D4—62no—
396C2×D4#120111yescharacteristic
397C22×C4—61no—
398C22×C4—62no—
399C22×C4C2×D3×D512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—151no—
403C2×C8—151no—
404C2×C8—152no—
405C2×C8—602no—
406C4⋊C4—31no—
407C4⋊C4—51no—
408C4⋊C4—52no—
409C4⋊C4—61no—
410C4⋊C4—62no—
411C4⋊C4—61no—
412C4⋊C4—101no—
413C4⋊C4—102no—
414C4⋊C4—101no—
415C4⋊C4#120111yescharacteristic
416C22⋊C4—62no—
417C22⋊C4—61no—
418C22⋊C4—102no—
419C22⋊C4—102no—
420C22⋊C4#120112yes—
421C42—102no—
422C42—101no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3C22×C22⋊D511yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—201no—
435C3×C4—202no—
436C3×C4—201no—
437C3×C4#409612yes—
438C3×C4C2×#71111yescharacteristic
439C3×C4#414411yescharacteristic
440Dic3—42no—
441Dic3—41no—
442C2×C5—42no—
443C2×C5—122no—
444C2×C5C2×#95011yescharacteristic
445C2×C5#582911yescharacteristic
446C2×C5#583811yescharacteristic
447C23—61no—
448C23C2×#120112yes—
449Q8—62no—
450Q8—62no—
451Q8—101no—
452Q8—101no—
453Q8—202no—
454D4—22no—
455D4—32no—
456D4—61no—
457D4—124no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—101no—
463C2×C4—102no—
464C2×C4—101no—
465C2×C4—124no—
466C2×C4—122no—
467C2×C4C2×#120112yes—
468C2×C4C2×#120111yescharacteristic
469C2×C4C2×#120111yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—301no—
472C8—301no—
473C8—302no—
474C2×C3—42no—
475C2×C3#6614011yescharacteristic
476C2×C3C2×#409611yescharacteristic
477C2×C3#6617211yescharacteristic
478D3—42no—
479C5#8366411yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—62no—
484C22—121no—
485C22—121no—
486C22C22×#120111yescharacteristic
487C4—21no—
488C4—22no—
489C4—121no—
490C4—122no—
491C4—201no—
492C4—202no—
493C4—201no—
494C4#9129712yes—
495C4D3×#71111yescharacteristic
496C4#9202711yescharacteristic
497C3#1061524111yescharacteristic, complemented, Sylow
498C2—42no—
499C2—122no—
500C2C2×#9129711yescharacteristic
501C2#1175496811yescharacteristic
502C2#1175530211yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5551C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3302
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
2. C3×#65876C2semidirect
3. D4×C3⋊#168C2semidirect
4. #11748562C2semidirect
5. #11748538C2semidirect
6. #11748404C2semidirect
7. #11748382C2semidirect
8. #11747094C2semidirect
9. C4×#6656C2semidirect
10. #11746923C2semidirect
11. #11746900C2semidirect
44. #65876D3semidirect
424. C3×C5#3302semidirect
479. C5#83664semidirect
497. C3#10615241semidirect

Maximal subgroups

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

subgroupindex
C5×#55512
C3×#658762
D4×C3⋊#1682
#117485622
#117485382
#117484042
#117483822
#117470942
C4×#66562
#117469232
#117469002
#106152413
#836645