Finite Group Databasebeta

← #14282993

Subgroups — #14282993

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5791C211yesmaximal, characteristic
2C2×#91115C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4#11745963C212yesmaximal, complemented
5#11745957C212yesmaximal, complemented
6#10602501—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C23×Dic15—21no—
9C2×C5×#235C411yescharacteristic, complemented
10C5×#953—21no—
11C5×#930C411yescharacteristic, complemented
12C5×#930C2211yescharacteristic
13C5×#929—21no—
14C4×C5×#67—21no—
15C4×C5×#67—21no—
16C5×#926C411yescharacteristic, complemented
17C5×#924C411yescharacteristic, complemented
18C5×#924C2211yescharacteristic
19C2×C3×#681—21no—
20#91115—21no—
21#91115C2212yes—
22C3×C22⋊#168—21no—
23C3×C22⋊#168C2212yes—
24#69976—51nomaximal, Hall
25C5×#525—31no—
26C2×#3963—31no—
27#65496D311yescharacteristic, complemented
28#64758—32no—
29#64757—32no—
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—24no—
39C22×Dic15—22no—
40C22×Dic15—42no—
41C22×Dic15—42no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C5×#235—42no—
46C2×C5×D12C2×C411yescharacteristic, complemented
47C2×C4×C5×D3—21no—
48C2×C5×Dic6C2×C411yescharacteristic, complemented
49C5×#217—21no—
50C5×#217—21no—
51C5×#217—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×C4⋊Dic3C2×C411yescharacteristic, complemented
55C5×C4⋊Dic3C2×C411yescharacteristic, complemented
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C4×C5×Dic3—21no—
59C3×#681—42no—
60C2×C3×#168—22no—
61#5791D511yescharacteristic
62C3×#407—51no—
63C2×C3⋊#95—51no—
64#4470—52no—
65#4467—52no—
66C2×C5×#41—31no—
67C23×C4×C5C2×D311yescharacteristic
68C23×Dic5—61no—
69C5×#123—61no—
70C5×C22⋊Q8—31no—
71C5×C22⋊Q8—31no—
72C5×#121—31no—
73C5×#121—31no—
74C5×#120—61no—
75C4×C5×D4—61no—
76C4×C5×D4—61no—
77C5×#117—31no—
78C2×#681—21no—
79#3963—32no—
80#3963—61no—
81C22⋊#168—21no—
82C22⋊#168C2×D312yes—
83#1504—151noSylow
84C23×C3×C5—22no—
85C23×C3×C5—22no—
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C22⋊C411yescharacteristic
90C23×C3×C5C2×D411yescharacteristic
91C22×C5×D3—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×Dic15—24no—
103C2×Dic15—48no—
104C2×Dic15—42no—
105C2×Dic15—42no—
106C5×#67—42no—
107C5×#67—42no—
108C5×#67—41no—
109C5×#67—41no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C5×D12—41no—
114C4×C5×D3—42no—
115C5×Dic6—41no—
116C3×#168—42no—
117C23×C3×C4C2×D511yescharacteristic
118C23×Dic3—101no—
119C2×#235Dic511yescharacteristic, complemented
120C2×C3×M16—101no—
121#953—21no—
122#930Dic511yescharacteristic, complemented
123#930C2×D511yescharacteristic
124#929—21no—
125C4×#67—21no—
126C4×#67—21no—
127#926Dic511yescharacteristic, complemented
128#924Dic511yescharacteristic, complemented
129#924C2×D511yescharacteristic
130C3×C22⋊C8—52no—
131C3×C22⋊C8—101no—
132C3⋊#95—52no—
133C3⋊#95—101no—
134C24×C5D1211yescharacteristic
135C5×#41—122no—
136C2×C5×Q8—31no—
137C2×C5×D4—31no—
138C2×C5×D4—61no—
139C2×C5×D4—61no—
140C2×C5×D4—61no—
141C22×C4×C5—42no—
142C22×C4×C5—61no—
143C22×C4×C5C4×D311yescharacteristic
144C22×C4×C5C4×D311yescharacteristic
145C22×C4×C5D1211yescharacteristic
146C22×C4×C5#6711yescharacteristic
147C22×C4×C5#6711yescharacteristic
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5—64no—
150C22×Dic5—62no—
151C22×Dic5—122no—
152C22×Dic5—122no—
153C5×C4⋊C4—31no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—61no—
156C5×C4⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C5×C22⋊C4—61no—
162C42×C5—61no—
163#681—42no—
164C2×#168—22no—
165#525—31no—
166#407—51no—
167C2×#95—151no—
168#328—152no—
169#327—152no—
170C22×C3×C5—24no—
171C22×C3×C5—24no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5#9912yes—
179C22×C3×C5#10412yes—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
182C22×C3×C5#13711yescharacteristic
183C2×C5×D3—41no—
184C2×C5×D3—41no—
185C2×C5×D3—41no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190Dic15—44no—
191C5×Dic3—41no—
192C5×Dic3—41no—
193C5×Dic3—41no—
194C24×C3C22⋊D511yescharacteristic
195C22×C3×C4—42no—
196C22×C3×C4C2×Dic511yescharacteristic
197C22×C3×C4C2×Dic511yescharacteristic
198C22×C3×C4C22⋊D511yescharacteristic
199C22×C3×C4C22⋊D511yescharacteristic
200C22×C3×C4C22⋊D511yescharacteristic
201C22×C3×C4C22×D511yescharacteristic
202C2×#67—21no—
203C2×#67—21no—
204C2×#67—21no—
205C22×Dic3—104no—
206C22×Dic3—102no—
207C22×Dic3—202no—
208C22×Dic3—202no—
209#235—42no—
210C2×D12C2×Dic511yescharacteristic, complemented
211C2×C4×D3—21no—
212C2×Dic6C2×Dic511yescharacteristic, complemented
213C3×M16—202no—
214C2×C3×C8—102no—
215#217—21no—
216#217—21no—
217#217—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220C4⋊Dic3C2×Dic511yescharacteristic, complemented
221C4⋊Dic3C2×Dic511yescharacteristic, complemented
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224C4×Dic3—21no—
225C23×C5—22no—
226C23×C5—22no—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5—61no—
230C23×C5(C2×D3)⋊C411yescharacteristic
231C23×C5(C2×D3)⋊C411yescharacteristic
232C23×C5C2×D1211yescharacteristic
233C5×Q8—121no—
234C5×D4—121no—
235C5×D4—122no—
236C5×D4—122no—
237C5×D4—121no—
238C5×D4—121no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—61no—
246C2×C4×C5—61no—
247C2×C4×C5—61no—
248C2×C4×C5—122no—
249C2×C4×C5(C2×D3)⋊C411yescharacteristic
250C2×C4×C5(C2×D3)⋊C411yescharacteristic
251C2×C4×C5C2×C4×D311yescharacteristic
252C2×C4×C5C2×#6711yescharacteristic
253C2×Dic5—64no—
254C2×Dic5—128no—
255C2×Dic5—122no—
256C2×Dic5—122no—
257#168—42no—
258C2×#41—31no—
259C23×C4—301no—
260C23×C4D3×D511yescharacteristic
261C2×M16—101no—
262#123—61no—
263C22⋊Q8—31no—
264C22⋊Q8—31no—
265#121—31no—
266#121—31no—
267#120—61no—
268C4×D4—61no—
269C4×D4—61no—
270#117—31no—
271C22⋊C8—52no—
272C22⋊C8—101no—
273#95—152no—
274#95—301no—
275C2×C3×C5—21no—
276C2×C3×C5—22no—
277C2×C3×C5—22no—
278C2×C3×C5—21no—
279C2×C3×C5C2×#9911yescharacteristic
280C2×C3×C5#41711yescharacteristic
281C2×C3×C5C2×#10411yescharacteristic
282C5×D3—81no—
283C23×C3—21no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—21no—
287C23×C3C22⋊Dic511yescharacteristic
288C23×C3C22⋊Dic511yescharacteristic
289C23×C3C2×C22⋊D511yescharacteristic
290C22×D3—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4C22⋊Dic511yescharacteristic
298C2×C3×C4C22⋊Dic511yescharacteristic
299C2×C3×C4C22×Dic511yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301#67—41no—
302#67—42no—
303#67—42no—
304#67—41no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—104no—
309C2×Dic3—208no—
310C2×Dic3—202no—
311C2×Dic3—202no—
312D12—41no—
313C4×D3—42no—
314Dic6—41no—
315C3×C8—202no—
316C22×C5—24no—
317C22×C5—24no—
318C22×C5—21no—
319C22×C5—21no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5—121no—
325C22×C5—121no—
326C22×C5—121no—
327C22×C5#80612yes—
328C22×C5#82512yes—
329C22×C5#90811yescharacteristic
330C22×C5#90911yescharacteristic
331C22×C5C2×(C2×D3)⋊C411yescharacteristic
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—21no—
335C4×C5—21no—
336C4×C5—121no—
337C4×C5—121no—
338C4×C5—121no—
339Dic5—124no—
340C24#120311yescharacteristic
341#41—122no—
342C2×Q8—31no—
343C2×D4—31no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C22×C4—42no—
348C22×C4—61no—
349C22×C4—304no—
350C22×C4—302no—
351C22×C4—602no—
352C22×C4—602no—
353C22×C4D3×Dic511yescharacteristic
354C22×C4D3×Dic511yescharacteristic
355C22×C4#120111yescharacteristic
356C22×C4#120111yescharacteristic
357C22×C4#120311yescharacteristic
358C22×C4C2×D3×D511yescharacteristic
359M16—202no—
360C2×C8—102no—
361C4⋊C4—31no—
362C4⋊C4—31no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C42—61no—
371C3×C5#150411yescharacteristic, complemented, Hall
372C22×C3—24no—
373C22×C3—24no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3#396612yes—
381C22×C3#396912yes—
382C22×C3#409511yescharacteristic
383C22×C3#409711yescharacteristic
384C22×C3C2×C22⋊Dic511yescharacteristic
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392Dic3—41no—
393Dic3—41no—
394Dic3—41no—
395Dic3—204no—
396C2×C5—21no—
397C2×C5—22no—
398C2×C5—22no—
399C2×C5—21no—
400C2×C5—241no—
401C2×C5C2×#80611yescharacteristic
402C2×C5#513311yescharacteristic
403C2×C5C2×#82511yescharacteristic
404C23—22no—
405C23—22no—
406C23—21no—
407C23—21no—
408C23—61no—
409C23(C2×D3)⋊Dic511yescharacteristic
410C23(C2×D3)⋊Dic511yescharacteristic
411C23C2×#120311yescharacteristic
412Q8—121no—
413D4—121no—
414D4—122no—
415D4—122no—
416D4—121no—
417D4—121no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—122no—
428C2×C4—304no—
429C2×C4—608no—
430C2×C4—602no—
431C2×C4—602no—
432C2×C4(C2×D3)⋊Dic511yescharacteristic
433C2×C4(C2×D3)⋊Dic511yescharacteristic
434C2×C4C2×D3×Dic511yescharacteristic
435C2×C4C2×#120111yescharacteristic
436C8—202no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—22no—
440C2×C3—22no—
441C2×C3C2×#396611yescharacteristic
442C2×C3#6552111yescharacteristic
443C2×C3C2×#396911yescharacteristic
444D3—81no—
445C5#6997611yescharacteristic, complemented, Sylow
446C22—24no—
447C22—24no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22#9097812yes—
458C22#9099612yes—
459C22#9130511yescharacteristic
460C22#9132211yescharacteristic
461C22C2×(C2×D3)⋊Dic511yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—121no—
467C4—121no—
468C4—121no—
469C4—604no—
470C3#1060250111yescharacteristic, complemented, Sylow
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2—241no—
476C2#1174839011yescharacteristic
477C2C2×#9097811yescharacteristic
478C2C2×#9099611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5791C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91115C2semidirect
3. C3×#65496C2semidirect
4. #11745963C2semidirect
5. #11745957C2semidirect
9. C2×C5×#235C4semidirect
11. C5×#930C4semidirect
16. C5×#926C4semidirect
17. C5×#924C4semidirect
27. #65496D3semidirect
46. C2×C5×D12C2×C4semidirect
48. C2×C5×Dic6C2×C4semidirect
54. C5×C4⋊Dic3C2×C4semidirect
55. C5×C4⋊Dic3C2×C4semidirect
119. C2×#235Dic5semidirect
122. #930Dic5semidirect
127. #926Dic5semidirect
128. #924Dic5semidirect
210. C2×D12C2×Dic5semidirect
212. C2×Dic6C2×Dic5semidirect
220. C4⋊Dic3C2×Dic5semidirect
221. C4⋊Dic3C2×Dic5semidirect
371. C3×C5#1504semidirect
445. C5#69976semidirect
470. C3#10602501semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
C2×#911152
C3×#654962
#117459632
#117459572
#106025013
#699765