Finite Group Databasebeta

← #14282278

Subgroups — #14282278

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×D15C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3C4×#6705C211yesmaximal, characteristic, complemented
4C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10598968—31nomaximal, Hall
9C2×D4×D15C411yescharacteristic
10C22×C4×D15—21no—
11C3×C4×C5×D4C2211yescharacteristic
12D4×Dic15C411yescharacteristic
13C4×#1220—21no—
14C2×#6705—21no—
15#91782C411yescharacteristic
16C4⋊C4×D15C411yescharacteristic
17#91770—21no—
18C22⋊C4×D15—21no—
19C4×D60C2211yescharacteristic
20C42×D15C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic, complemented
22C3×C4×C5×C8C2211yescharacteristic, complemented
23#91104—21no—
24#91099—21no—
25#91099—21no—
26C4⋊(C3⋊#168)C2211yescharacteristic, complemented
27C4×C3⋊#168C2211yescharacteristic, complemented
28#68175—51nomaximal, Hall
29C4×D4×D5—31no—
30#65124—31no—
31C4×#676—31no—
32C5×D4⋊C8D311yescharacteristic, complemented
33D4⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C23×D15—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×#1220—21no—
40C22×Dic15—21no—
41D4×D15—22no—
42D4×D15—22no—
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×C4×D15—21no—
46C2×C4×D15—21no—
47C2×C4×D15—42no—
48C2×C4×D15—42no—
49C2×C4×D15C2×C411yescharacteristic
50C2×C4×D15D411yescharacteristic
51C2×C4×D15D411yescharacteristic
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C42×C5C2311yescharacteristic
57#6719—21no—
58#6714—21no—
59#6714—21no—
60C4⋊Dic15C2×C411yescharacteristic
61#6712—21no—
62C4×Dic15C2×C411yescharacteristic
63C4×Dic15D411yescharacteristic
64C4×Dic15D411yescharacteristic
65C2×C3⋊#168—21no—
66C2×C3⋊#168—21no—
67#6705—24no—
68C4×D3×D4—51no—
69#4835—51no—
70C4×ΓL(1,𝔽25)—51no—
71C3×D4⋊C8D511yescharacteristic, complemented
72D4⋊(C3⋊C8)—51no—
73#4483—51no—
74#4459—51no—
75C2×D4×D5—31no—
76C22×C4×D5—61no—
77C4×C5×D4C2×D311yescharacteristic
78D4×Dic5—31no—
79C4×C22⋊D5—61no—
80C2×#676—61no—
81#4039—31no—
82D5×C4⋊C4—31no—
83#4027—61no—
84D5×C22⋊C4—61no—
85C4×D20—31no—
86C42×D5—31no—
87C5×C4⋊C8C2×D311yescharacteristic, complemented
88C4×C5×C8C2×D311yescharacteristic, complemented
89#3952—61no—
90#3947—61no—
91#3947—61no—
92C4⋊#168—31no—
93C4×#168—31no—
94#1490—151noSylow
95C23×C3×C5—21no—
96C22×D15—24no—
97C22×D15—21no—
98C22×D15—42no—
99C22×D15—42no—
100C22×D15C22⋊C411yescharacteristic
101C3×C5×D4—21no—
102C3×C5×D4M1612yescomplemented
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109#1220—24no—
110C2×Dic15—21no—
111C2×Dic15—42no—
112C2×Dic15C22⋊C411yescharacteristic
113C2×Dic15C22⋊C411yescharacteristic
114C2×Dic15C22⋊C411yescharacteristic
115D60—21no—
116D60M1612yescomplemented
117C4×D15—22no—
118C4×D15—21no—
119C4×D15—21no—
120C4×D15—21no—
121C4×D15—21no—
122C4×D15—42no—
123C4×D15—42no—
124C4×D15—41no—
125C4×D15—41no—
126C3×C5×C8—22no—
127C3×C5×C8—41no—
128C3⋊#168—22no—
129C3⋊#168—41no—
130C2×D3×D4—51no—
131C22×C4×D3—101no—
132C3×C4×D4C2×D511yescharacteristic
133D4×Dic3—51no—
134C4×#67—101no—
135C2×ΓL(1,𝔽25)—101no—
136#893—51no—
137D3×C4⋊C4—51no—
138#67⋊C4—101no—
139D3×C22⋊C4—101no—
140C4×D12—51no—
141C42×D3—51no—
142C3×C4⋊C8C2×D511yescharacteristic, complemented
143C3×C4×C8C2×D511yescharacteristic, complemented
144(C2×D3)⋊C8—101no—
145#815—101no—
146#815—101no—
147C4⋊(C3⋊C8)—51no—
148C4×C3⋊C8—51no—
149C23×D5—61no—
150C2×C5×D4C4×D311yescharacteristic
151C22×C4×C5—21no—
152C2×C22⋊D5—61no—
153C22×Dic5—61no—
154D4×D5—62no—
155D4×D5—62no—
156C2×D20—31no—
157C2×C4×D5—31no—
158C2×C4×D5—31no—
159C2×C4×D5—31no—
160C2×C4×D5—61no—
161C2×C4×D5—61no—
162C2×C4×D5—61no—
163C2×C4×D5—122no—
164C2×C4×D5—122no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C5×C4⋊C4C4×D311yescharacteristic
168C5×C22⋊C4—21no—
169C42×C5C22×D311yescharacteristic
170C22⋊Dic5—61no—
171#685—61no—
172#685—61no—
173C4⋊Dic5—31no—
174#683—61no—
175C4×Dic5—31no—
176C4×Dic5—31no—
177C4×Dic5—31no—
178C2×#168—61no—
179C2×#168—61no—
180#676—64no—
181C2×C4×D4—151no—
182#432—151no—
183C4×M16—151no—
184D4⋊C8—151no—
185D4⋊C8—151no—
186D4⋊C8—151no—
187D4⋊C8D1511yescharacteristic, complemented
188C22×C3×C5—22no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C2×D15—21no—
193C2×D15—21no—
194C2×D15—22no—
195C2×D15—48no—
196C2×D15—41no—
197C2×D15—41no—
198C2×D15#10412yes—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5C2×M1611yescharacteristic
202C3×C4×C5C2×M1611yescharacteristic
203C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
204C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
205Dic15—21no—
206Dic15—21no—
207Dic15—21no—
208Dic15—41no—
209C23×D3—101no—
210C2×C3×D4C4×D511yescharacteristic
211C22×C3×C4—21no—
212C2×#67—101no—
213C22×Dic3—101no—
214D3×D4—102no—
215D3×D4—102no—
216C2×D12—51no—
217C2×C4×D3—51no—
218C2×C4×D3—51no—
219C2×C4×D3—51no—
220C2×C4×D3—101no—
221C2×C4×D3—101no—
222C2×C4×D3—101no—
223C2×C4×D3—202no—
224C2×C4×D3—202no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C3×C4⋊C4C4×D511yescharacteristic
228C3×C22⋊C4—21no—
229C3×C42C22×D511yescharacteristic
230#217—101no—
231(C2×D3)⋊C4—101no—
232(C2×D3)⋊C4—101no—
233C4⋊Dic3—51no—
234Dic3⋊C4—101no—
235C4×Dic3—51no—
236C4×Dic3—51no—
237C4×Dic3—51no—
238C2×C3⋊C8—101no—
239C2×C3⋊C8—101no—
240ΓL(1,𝔽25)—104no—
241C23×C5—21no—
242C22×D5—31no—
243C22×D5—64no—
244C22×D5—61no—
245C22×D5—122no—
246C22×D5—122no—
247C5×D4—21no—
248C5×D4ΓL(1,𝔽25)12yescomplemented
249C2×C4×C5—21no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5C2×C4×D311yescharacteristic
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C22⋊D5—64no—
256C2×Dic5—31no—
257C2×Dic5—31no—
258C2×Dic5—31no—
259C2×Dic5—61no—
260C2×Dic5—122no—
261D20—32no—
262D20—61no—
263C4×D5—62no—
264C4×D5—61no—
265C4×D5—61no—
266C4×D5—61no—
267C4×D5—61no—
268C4×D5—122no—
269C4×D5—122no—
270C4×D5—121no—
271C4×D5—121no—
272C5×C8—22no—
273C5×C8—41no—
274#168—62no—
275#168—121no—
276C22×D4—151no—
277C23×C4—301no—
278C2×M16—301no—
279C4×D4—151no—
280C4×D4—151no—
281C4×D4—151no—
282C4×D4—301no—
283C4×D4—301no—
284C4×D4C2×D1511yescharacteristic
285C2×C4⋊C4—151no—
286C2×C22⋊C4—301no—
287C2×C42—151no—
288C4⋊C8—151no—
289C4⋊C8C2×D1511yescharacteristic, complemented
290C22⋊C8—301no—
291#97—301no—
292#97—301no—
293C4×C8—151no—
294C4×C8C2×D1511yescharacteristic, complemented
295C2×C3×C5—42no—
296C2×C3×C5#40711yescharacteristic
297C2×C3×C5#41811yescharacteristic
298C2×C3×C5C2×#10411yescharacteristic
299D15—22no—
300D15—42no—
301C23×C3—21no—
302C22×D3—51no—
303C22×D3—104no—
304C22×D3—101no—
305C22×D3—202no—
306C22×D3—202no—
307C3×D4—21no—
308C3×D4#67612yescomplemented
309C2×C3×C4—21no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4C2×C4×D511yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315#67—104no—
316C2×Dic3—51no—
317C2×Dic3—51no—
318C2×Dic3—51no—
319C2×Dic3—101no—
320C2×Dic3—202no—
321D12—52no—
322D12—101no—
323C4×D3—102no—
324C4×D3—101no—
325C4×D3—101no—
326C4×D3—101no—
327C4×D3—101no—
328C4×D3—202no—
329C4×D3—202no—
330C4×D3—201no—
331C4×D3—201no—
332C3×C8—22no—
333C3×C8—41no—
334C3⋊C8—102no—
335C3⋊C8—201no—
336C22×C5—22no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5D3×C22⋊C411yescharacteristic
340C2×D5—32no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—62no—
344C2×D5—128no—
345C2×D5—121no—
346C2×D5—121no—
347C4×C5—21no—
348C4×C5—41no—
349C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
350C4×C5D3×M1611yescharacteristic
351C4×C5#91111yescharacteristic
352C4×C5#91411yescharacteristic
353Dic5—61no—
354Dic5—61no—
355Dic5—61no—
356Dic5—121no—
357C24—301no—
358C2×D4—151no—
359C2×D4—301no—
360C2×D4—302no—
361C2×D4—302no—
362C2×D4C4×D1511yescharacteristic
363C22×C4—21no—
364C22×C4—151no—
365C22×C4—151no—
366C22×C4—151no—
367C22×C4—301no—
368C22×C4—301no—
369C22×C4—301no—
370C22×C4—301no—
371C22×C4—602no—
372C22×C4—602no—
373M16—304no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—301no—
377C2×C8—301no—
378C4⋊C4—151no—
379C4⋊C4—301no—
380C4⋊C4C4×D1511yescharacteristic
381C22⋊C4—21no—
382C22⋊C4—301no—
383C22⋊C4—301no—
384C22⋊C4—301no—
385C42—151no—
386C42—151no—
387C42—151no—
388C42C22×D1511yescharacteristic
389C3×C5#149011yescharacteristic, complemented, Hall
390C22×C3—22no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3D5×C22⋊C411yescharacteristic
394C2×D3—52no—
395C2×D3—101no—
396C2×D3—101no—
397C2×D3—102no—
398C2×D3—208no—
399C2×D3—201no—
400C2×D3—201no—
401C3×C4—21no—
402C3×C4—41no—
403C3×C4C2×#67611yescharacteristic
404C3×C4D5×M1611yescharacteristic
405C3×C4#405711yescharacteristic
406C3×C4#406011yescharacteristic
407Dic3—101no—
408Dic3—101no—
409Dic3—101no—
410Dic3—201no—
411C2×C5—42no—
412C2×C5#472611yescharacteristic
413C2×C5#477011yescharacteristic
414C2×C5D3×#10411yescharacteristic
415D5—62no—
416D5—122no—
417C23—21no—
418C23—151no—
419C23—304no—
420C23—301no—
421C23—602no—
422C23—602no—
423D4—21no—
424D4—152no—
425D4—304no—
426D4—301no—
427D4#670512yescomplemented
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—151no—
432C2×C4—151no—
433C2×C4—151no—
434C2×C4—302no—
435C2×C4—301no—
436C2×C4—301no—
437C2×C4—301no—
438C2×C4—301no—
439C2×C4—301no—
440C2×C4—602no—
441C2×C4—602no—
442C2×C4—602no—
443C2×C4—601no—
444C2×C4—601no—
445C2×C4C2×C4×D1511yescharacteristic
446C2×C4D4×D1511yescharacteristic
447C2×C4D4×D1511yescharacteristic
448C8—22no—
449C8—41no—
450C8—302no—
451C8—601no—
452C2×C3—42no—
453C2×C3#6501511yescharacteristic
454C2×C3#6505911yescharacteristic
455C2×C3D5×#10411yescharacteristic
456D3—102no—
457D3—202no—
458C5#6817511yescharacteristic, complemented, Sylow
459C22—22no—
460C22—41no—
461C22—41no—
462C22—152no—
463C22—301no—
464C22—301no—
465C22—302no—
466C22—608no—
467C22—601no—
468C22—601no—
469C22C22⋊C4×D1511yescharacteristic
470C4—21no—
471C4—41no—
472C4—301no—
473C4—301no—
474C4—301no—
475C4—601no—
476C4C2×#670511yescharacteristic
477C4M16×D1511yescharacteristic
478C4#9180011yescharacteristic
479C4#9180311yescharacteristic
480C3#1059896811yescharacteristic, complemented, Sylow
481C2—42no—
482C2—302no—
483C2—602no—
484C2#1175082711yescharacteristic
485C2#1175087111yescharacteristic
486C2D15×#10411yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D4×D15C4
cosocleC3×C42×C5C23
hypercenterD4⋊C8D15
hypocenterC3×C5#1490
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. C4×#6705C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746304C2semidirect
7. #11746280C2semidirect
21. C3×C5×C4⋊C8C22semidirect
22. C3×C4×C5×C8C22semidirect
26. C4⋊(C3⋊#168)C22semidirect
27. C4×C3⋊#168C22semidirect
32. C5×D4⋊C8D3semidirect
71. C3×D4⋊C8D5semidirect
87. C5×C4⋊C8C2×D3semidirect
88. C4×C5×C8C2×D3semidirect
102. C3×C5×D4M16semidirect
116. D60M16semidirect
142. C3×C4⋊C8C2×D5semidirect
143. C3×C4×C8C2×D5semidirect
187. D4⋊C8D15semidirect
248. C5×D4ΓL(1,𝔽25)semidirect
289. C4⋊C8C2×D15semidirect
294. C4×C8C2×D15semidirect
308. C3×D4#676semidirect
389. C3×C5#1490semidirect
427. D4#6705semidirect
458. C5#68175semidirect
480. C3#10598968semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D152
#117509362
C4×#67052
C3×C5×D4⋊C82
D4⋊(C3⋊#168)2
#117463042
#117462802
#105989683
#681755