Finite Group Databasebeta

← #14460061

Subgroups — #14460061

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
1#11756343C211yesmaximal, characteristic, complemented
2#11752533C211yesmaximal, characteristic
3C5×#5031C211yesmaximal, characteristic, complemented
4C3×C4×#688C211yesmaximal, characteristic, complemented
5#11749404C212yesmaximal, complemented
6#11749367C212yesmaximal, complemented
7#11747506C212yesmaximal, complemented
8#11747361C212yesmaximal, complemented
9#11746988C211yesmaximal, characteristic, complemented
10#11746929C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10612223—31nomaximal, Hall
13C2×#6766C2212yes—
14C3×C4×C5×Q8C2211yescharacteristic
15#91835C2212yes—
16#91787—22no—
17#91781C2212yes—
18#91764—21no—
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C4×Dic30—21no—
22C2×C5×#216C2212yes—
23C5×#869C2211yescharacteristic
24C2×C3×#688C2211yescharacteristic
25C3×C4×D20C2211yescharacteristic
26#91450—21no—
27#91413—22no—
28D5×C4⋊Dic3—21no—
29#91383C2212yes—
30C2×#6648C2212yes—
31C5×#810C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3967C2211yescharacteristic
34C3×#3941C2211yescharacteristic
35C3×#3940C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90990C2212yes—
38#90973C2212yes—
39#90973C2212yes—
40#90965C2212yes—
41#90957C2212yes—
42#79680—51nomaximal, Hall
43#66060—31no—
44#65918—31no—
45C5×#462—31no—
46#65477—32no—
47#65476—32no—
48#65370—31no—
49C4×#688D311yescharacteristic, complemented
50#65135—31no—
51#65123—31no—
52#65103—32no—
53#65093—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60D411yescharacteristic
56C2×C4×D15C2312yes—
57C2×Dic30—21no—
58C2×C5×Dic6C2312yes—
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×#1202—22no—
62C2×D5×Dic3—22no—
63#6766—24no—
64#6766—42no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C42×C5—21no—
68C3×C42×C5C2311yescharacteristic
69#6714—22no—
70#6714—22no—
71#6714D412yes—
72C4⋊Dic15—21no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15C2312yes—
75#6712—22no—
76C4×Dic15—22no—
77C5×#216—42no—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3—21no—
80C2×C5×C3⋊C8C2312yes—
81C3×#688—22no—
82C3×#685—21no—
83C3×C4⋊Dic5C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
86#6668—22no—
87#6667—22no—
88#6648—42no—
89#5584—51no—
90#5555—51no—
91C3×C4×SD16—51no—
92#5173—52no—
93#5031D511yescharacteristic, complemented
94#5007—51no—
95#4868—52no—
96#4813—52no—
97#4772—52no—
98C8×D12—51no—
99#4681—51no—
100C2×#713—32no—
101C2×C5×Q16—32no—
102C5×C4⋊Q8—31no—
103C4×C5×Q8C2×D311yescharacteristic
104#4092—32no—
105#4092—32no—
106C2×#688C2×D311yescharacteristic
107C2×C8×D5—32no—
108#4044—62no—
109#4041—61no—
110#4040—62no—
111#4038—32no—
112D5×C4⋊C4—61no—
113#4021—61no—
114C4×D20—31no—
115C4×D20C2×D311yescharacteristic
116#4015—31no—
117C4×Dic10—61no—
118C5×C4⋊C8—31no—
119C5×#103—32no—
120#3967—32no—
121#3967—32no—
122#3967C2×D311yescharacteristic
123#3953—32no—
124#3952—32no—
125#3950—32no—
126#3941C2×D311yescharacteristic
127#3940C2×D311yescharacteristic
128C4×#168C2×D311yescharacteristic
129#3302—151noSylow
130C22×D15C2×D412yes—
131C22×C3×D5—21no—
132C3×C5×Q8—21no—
133C3×C5×Q8—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—22no—
140C2×Dic15C2×D412yes—
141D60—22no—
142C4×D15—22no—
143C4×D15—22no—
144Dic30—42no—
145C2×C5×Dic3—22no—
146C5×Dic6—22no—
147C5×Dic6—22no—
148C2×C3×Dic5—21no—
149C3×D20—21no—
150C3×D20#4112yes—
151C3×C4×D5—42no—
152#1202—44no—
153D5×Dic3—44no—
154C3×#168—21no—
155C3×#168—21no—
156C5×C3⋊C8—22no—
157C2×#237—52no—
158C2×C3×SD16—51no—
159C3×C4×Q8C2×D511yescharacteristic
160C3×C4×D4—51no—
161#946—52no—
162C2×#216C2×D512yes—
163#930—101no—
164C2×C4⋊Dic3—101no—
165C2×D3×C8—52no—
166#898—102no—
167#897—52no—
168#892—52no—
169#886—102no—
170#875—101no—
171C4×D12—51no—
172#869—51no—
173#869C2×D511yescharacteristic
174C4×Dic6—101no—
175C3×#106—51no—
176C3×#103—51no—
177C3×#102—51no—
178C3×C4×C8—51no—
179#832—52no—
180(C2×D3)⋊C8—52no—
181#816—52no—
182#816—52no—
183#810C2×D512yes—
184#807—52no—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×Q8—32no—
187C2×C5×Q8C22×D311yescharacteristic
188#713—64no—
189#713—122no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20C22×D311yescharacteristic
193C2×C4×D5—21no—
194C2×C4×D5—32no—
195C2×C4×D5—62no—
196C2×Dic10—61no—
197C5×Q16—122no—
198C2×C5×C8—32no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4C22×D311yescharacteristic
203C42×C5—21no—
204C42×C5C22×D311yescharacteristic
205#688—22no—
206#685—21no—
207#685—32no—
208#685—62no—
209#685—62no—
210#685—62no—
211C4⋊Dic5—31no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214C4⋊Dic5C22×D311yescharacteristic
215#683—62no—
216#683—62no—
217C4×Dic5—62no—
218C2×#168C22×D311yescharacteristic
219C2×#168C22×D311yescharacteristic
220C8×D5—122no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—31no—
228#452—152no—
229C4×SD16—51no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—22no—
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—41no—
239C3×C4×C5—21no—
240C3×C4×C5—41no—
241C3×C4×C5—41no—
242C3×C4×C5#13512yes—
243C3×C4×C5C2×#4111yescharacteristic
244C3×C4×C5H(5,𝔽2)11yescharacteristic
245Dic15—22no—
246Dic15—42no—
247C3×Dic5—41no—
248C5×Dic3—42no—
249C2×C3×Q8C22×D511yescharacteristic
250C2×C3×D4—51no—
251C22×C3×C4—101no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—104no—
255#237—202no—
256C2×D12—51no—
257C2×C4×D3—52no—
258C2×Dic6—101no—
259C2×Dic6C22×D512yes—
260C3×SD16—102no—
261C2×C3×C8—51no—
262C2×C3×C8—51no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—51no—
265C3×C4⋊C4C22×D511yescharacteristic
266C3×C22⋊C4—101no—
267C3×C42—21no—
268C3×C42C22×D511yescharacteristic
269#216—42no—
270(C2×D3)⋊C4—52no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—51no—
277C4⋊Dic3—52no—
278C4⋊Dic3—102no—
279C4⋊Dic3—101no—
280Dic3⋊C4—102no—
281C4×Dic3—102no—
282C2×C3⋊C8C22×D512yes—
283D3×C8—202no—
284C22×D5—21no—
285C22×D5—32no—
286C5×Q8—21no—
287C5×Q8—21no—
288C5×Q8—62no—
289C5×Q8—62no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—62no—
293C2×C4×C5D3×D411yescharacteristic
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5C23×D311yescharacteristic
296C2×Dic5—21no—
297C2×Dic5—32no—
298C2×Dic5—62no—
299D20—21no—
300D20—62no—
301D20—124no—
302D20#23512yes—
303C4×D5—42no—
304C4×D5—62no—
305C4×D5—62no—
306C4×D5—124no—
307Dic10—122no—
308C5×C8—62no—
309#168—21no—
310#168—21no—
311C2×#41—152no—
312C2×Q16—32no—
313C2×SD16—51no—
314C22×C8—152no—
315C4⋊Q8—31no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—301no—
324C4×Q8D3×D511yescharacteristic
325C4×D4—51no—
326C4×D4—151no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—51no—
331C4⋊C8—31no—
332#103—32no—
333#103—51no—
334#103—152no—
335#103—152no—
336#102—51no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8—51no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344C3×D5—42no—
345C23×C3—101no—
346C22×D3—52no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×D4—52no—
350C3×D4—101no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—101no—
354C2×C3×C4—202no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358#67—204no—
359C2×Dic3—22no—
360C2×Dic3—52no—
361C2×Dic3—102no—
362C2×Dic3—204no—
363D12—102no—
364C4×D3—102no—
365C4×D3—102no—
366Dic6—22no—
367Dic6—22no—
368Dic6—202no—
369C3×C8—101no—
370C3×C8—101no—
371C3⋊C8—22no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—22no—
374C2×D5—41no—
375C2×D5—41no—
376C2×D5—62no—
377C2×D5—62no—
378C2×D5—62no—
379C4×C5—21no—
380C4×C5—41no—
381C4×C5—41no—
382C4×C5—122no—
383C4×C5#91612yes—
384C4×C5C2×#23511yescharacteristic
385C4×C5#100911yescharacteristic
386Dic5—41no—
387Dic5—62no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—32no—
392C2×Q8—301no—
393C2×Q8C2×D3×D511yescharacteristic
394C2×D4—51no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—101no—
398C22×C4—152no—
399C22×C4—302no—
400Q16—122no—
401SD16—102no—
402C2×C8—32no—
403C2×C8—51no—
404C2×C8—51no—
405C2×C8—602no—
406C4⋊C4—21no—
407C4⋊C4—51no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—151no—
411C4⋊C4—152no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—101no—
417C22⋊C4—152no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C42—21no—
422C42—302no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—102no—
430C2×D3—102no—
431C2×D3—102no—
432C3×C4—21no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—201no—
436C3×C4#406512yes—
437C3×C4#414411yescharacteristic
438C3×C4D5×#4111yescharacteristic
439Dic3—42no—
440Dic3—102no—
441Dic3—202no—
442C2×C5#555011yescharacteristic
443C2×C5C2×#91611yescharacteristic
444C2×C5#577111yescharacteristic
445D5—42no—
446D5—122no—
447C23—101no—
448C23—152no—
449Q8—21no—
450Q8—21no—
451Q8—62no—
452Q8—62no—
453Q8—602no—
454D4—52no—
455D4—101no—
456D4—302no—
457D4—604no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—152no—
463C2×C4—202no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—101no—
473C8—101no—
474C2×C3—202no—
475C2×C3#6594611yescharacteristic
476C2×C3C2×#406511yescharacteristic
477C2×C3#6611311yescharacteristic
478D3—202no—
479C5#7968011yescharacteristic, complemented, Sylow
480C22—102no—
481C22—201no—
482C22—201no—
483C22—302no—
484C22—302no—
485C22—302no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—41no—
489C4—41no—
490C4—122no—
491C4—201no—
492C4—302no—
493C4—602no—
494C4#9152112yes—
495C4D5×#23511yescharacteristic
496C4#9201811yescharacteristic
497C3#1061222311yescharacteristic, complemented, Sylow
498C2—202no—
499C2—602no—
500C2#1175466511yescharacteristic
501C2C2×#9152111yescharacteristic
502C2#1175535011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752533C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756343C2semidirect
3. C5×#5031C2semidirect
4. C3×C4×#688C2semidirect
5. #11749404C2semidirect
6. #11749367C2semidirect
7. #11747506C2semidirect
8. #11747361C2semidirect
9. #11746988C2semidirect
10. #11746929C2semidirect
11. #11746889C2semidirect
49. C4×#688D3semidirect
93. #5031D5semidirect
424. C3×C5#3302semidirect
479. C5#79680semidirect
497. C3#10612223semidirect

Maximal subgroups

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

subgroupindex
#117563432
#117525332
C5×#50312
C3×C4×#6882
#117494042
#117493672
#117475062
#117473612
#117469882
#117469292
#117468892
#106122233
#796805