Finite Group Databasebeta

← #14282972

Subgroups — #14282972

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
1#11756550C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic, complemented
3C2×#91115C211yesmaximal, characteristic, complemented
4#11746291C212yesmaximal, complemented
5#11746288C212yesmaximal, complemented
6#10600769—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C23×Dic15—21no—
9C2×#6817C411yescharacteristic, complemented
10C2×C3×C5×M16—21no—
11#91842—21no—
12#91819C411yescharacteristic, complemented
13#91819C2211yescharacteristic
14#91818—21no—
15C4×#1220—21no—
16C4×#1220—21no—
17#91815C411yescharacteristic, complemented
18#91813C411yescharacteristic, complemented
19#91813C2211yescharacteristic
20C3×C5×C22⋊C8—21no—
21C3×C5×C22⋊C8C2212yes—
22#91115—21no—
23#91115C2212yes—
24#69976—51nomaximal, Hall
25#66125—31no—
26C5×#407D311yescharacteristic, complemented
27C2×#3963—31no—
28#64690—32no—
29#64687—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
38C2×#1220—21no—
39C2×#1220—21no—
40C2×#1220—21no—
41C22×Dic15—24no—
42C22×Dic15—22no—
43C22×Dic15—42no—
44C22×Dic15—42no—
45#6817—42no—
46C2×D60C2×C411yescharacteristic, complemented
47C2×C4×D15—21no—
48C2×Dic30C2×C411yescharacteristic, complemented
49C3×C5×M16—42no—
50C2×C3×C5×C8—22no—
51#6719—21no—
52#6719—21no—
53#6719—21no—
54#6714—21no—
55#6714—21no—
56C4⋊Dic15C2×C411yescharacteristic, complemented
57C4⋊Dic15C2×C411yescharacteristic, complemented
58#6712—21no—
59#6712—21no—
60C4×Dic15—21no—
61#5791—51no—
62C3×#407D511yescharacteristic, complemented
63C2×C3⋊#95—51no—
64#4470—52no—
65#4467—52no—
66C23×C4×C5C2×D311yescharacteristic
67C23×Dic5—61no—
68C2×#709—31no—
69C2×C5×M16—21no—
70#4099—61no—
71#4076—31no—
72#4076—31no—
73#4075—61no—
74C4×C22⋊D5—61no—
75C4×C22⋊D5—61no—
76#4072—31no—
77#4070—31no—
78#4070—31no—
79C5×C22⋊C8—21no—
80C5×C22⋊C8C2×D312yes—
81#3963—32no—
82#3963—61no—
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×D15—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
102#1220—42no—
103#1220—42no—
104#1220—41no—
105#1220—41no—
106C2×Dic15—24no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—48no—
111C2×Dic15—42no—
112C2×Dic15—42no—
113D60—41no—
114C4×D15—42no—
115Dic30—41no—
116C3×C5×C8—42no—
117C23×C3×C4C2×D511yescharacteristic
118C23×Dic3—101no—
119C2×#235—51no—
120C2×C3×M16—21no—
121#953—101no—
122#930—51no—
123#930—51no—
124#929—101no—
125C4×#67—101no—
126C4×#67—101no—
127#926—51no—
128#924—51no—
129#924—51no—
130C3×C22⋊C8—21no—
131C3×C22⋊C8C2×D512yes—
132C3⋊#95—52no—
133C3⋊#95—101no—
134C24×C5D1211yescharacteristic
135C22×C4×C5—42no—
136C22×C4×C5C4×D311yescharacteristic
137C22×C4×C5C4×D311yescharacteristic
138C22×C4×C5D1211yescharacteristic
139C22×C4×C5#6711yescharacteristic
140C22×C4×C5#6711yescharacteristic
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—61no—
143C2×C22⋊D5—61no—
144C2×C22⋊D5—61no—
145C22×Dic5—64no—
146C22×Dic5—62no—
147C22×Dic5—122no—
148C22×Dic5—122no—
149#709—122no—
150C2×D20—31no—
151C2×C4×D5—61no—
152C2×Dic10—31no—
153C5×M16—42no—
154C2×C5×C8—22no—
155C22⋊Dic5—61no—
156C22⋊Dic5—61no—
157C22⋊Dic5—61no—
158#685—61no—
159#685—61no—
160C4⋊Dic5—31no—
161C4⋊Dic5—31no—
162#683—61no—
163#683—61no—
164C4×Dic5—61no—
165#525—151no—
166#407D1511yescharacteristic, complemented
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×D15—41no—
184C2×D15—41no—
185C2×D15—41no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190Dic15—44no—
191Dic15—41no—
192Dic15—41no—
193Dic15—41no—
194C24×C3D2011yescharacteristic
195C22×C3×C4—42no—
196C22×C3×C4C4×D511yescharacteristic
197C22×C3×C4C4×D511yescharacteristic
198C22×C3×C4D2011yescharacteristic
199C22×C3×C4C22⋊D511yescharacteristic
200C22×C3×C4C22⋊D511yescharacteristic
201C22×C3×C4C22×D511yescharacteristic
202C2×#67—101no—
203C2×#67—101no—
204C2×#67—101no—
205C22×Dic3—104no—
206C22×Dic3—102no—
207C22×Dic3—202no—
208C22×Dic3—202no—
209#235—202no—
210C2×D12—51no—
211C2×C4×D3—101no—
212C2×Dic6—51no—
213C3×M16—42no—
214C2×C3×C8—22no—
215#217—101no—
216#217—101no—
217#217—101no—
218(C2×D3)⋊C4—101no—
219(C2×D3)⋊C4—101no—
220C4⋊Dic3—51no—
221C4⋊Dic3—51no—
222Dic3⋊C4—101no—
223Dic3⋊C4—101no—
224C4×Dic3—101no—
225C23×C5—22no—
226C23×C5—22no—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5(C2×D3)⋊C411yescharacteristic
230C23×C5(C2×D3)⋊C411yescharacteristic
231C23×C5C2×D1211yescharacteristic
232C22×D5—61no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5(C2×D3)⋊C411yescharacteristic
240C2×C4×C5(C2×D3)⋊C411yescharacteristic
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5C2×#6711yescharacteristic
243C22⋊D5—122no—
244C22⋊D5—122no—
245C22⋊D5—121no—
246C22⋊D5—121no—
247C2×Dic5—64no—
248C2×Dic5—61no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—128no—
252C2×Dic5—122no—
253C2×Dic5—122no—
254D20—121no—
255C4×D5—122no—
256Dic10—121no—
257C5×C8—42no—
258C2×#41—151no—
259C23×C4—301no—
260C23×C4C2×D1511yescharacteristic
261C2×M16—21no—
262#123—301no—
263C22⋊Q8—151no—
264C22⋊Q8—151no—
265#121—151no—
266#121—151no—
267#120—301no—
268C4×D4—301no—
269C4×D4—301no—
270#117—151no—
271C22⋊C8—21no—
272C22⋊C8C2×D1512yes—
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
282D15—81no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3#68511yescharacteristic
288C23×C3#68511yescharacteristic
289C23×C3C2×D2011yescharacteristic
290C22×D3—101no—
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×C4#68511yescharacteristic
298C2×C3×C4#68511yescharacteristic
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301#67—202no—
302#67—202no—
303#67—201no—
304#67—201no—
305C2×Dic3—104no—
306C2×Dic3—101no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309C2×Dic3—208no—
310C2×Dic3—202no—
311C2×Dic3—202no—
312D12—201no—
313C4×D3—202no—
314Dic6—201no—
315C3×C8—42no—
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#80612yes—
325C22×C5#82512yes—
326C22×C5#90811yescharacteristic
327C22×C5#90911yescharacteristic
328C22×C5C2×(C2×D3)⋊C411yescharacteristic
329C2×D5—121no—
330C2×D5—121no—
331C2×D5—121no—
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—21no—
335C4×C5—21no—
336Dic5—124no—
337Dic5—121no—
338Dic5—121no—
339Dic5—121no—
340C24D6011yescharacteristic
341#41—602no—
342C2×Q8—151no—
343C2×D4—151no—
344C2×D4—301no—
345C2×D4—301no—
346C2×D4—301no—
347C22×C4—42no—
348C22×C4—304no—
349C22×C4—302no—
350C22×C4—301no—
351C22×C4—602no—
352C22×C4—602no—
353C22×C4C4×D1511yescharacteristic
354C22×C4C4×D1511yescharacteristic
355C22×C4D6011yescharacteristic
356C22×C4#122011yescharacteristic
357C22×C4#122011yescharacteristic
358C22×C4C22×D1511yescharacteristic
359M16—42no—
360C2×C8—22no—
361C4⋊C4—151no—
362C4⋊C4—151no—
363C4⋊C4—301no—
364C4⋊C4—301no—
365C22⋊C4—301no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C22⋊C4—301no—
370C42—301no—
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#393812yes—
381C22×C3#395712yes—
382C22×C3#405411yescharacteristic
383C22×C3#405511yescharacteristic
384C22×C3C2×#68511yescharacteristic
385C2×D3—201no—
386C2×D3—201no—
387C2×D3—201no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392Dic3—204no—
393Dic3—201no—
394Dic3—201no—
395Dic3—201no—
396C2×C5—21no—
397C2×C5—22no—
398C2×C5—22no—
399C2×C5—21no—
400C2×C5C2×#80611yescharacteristic
401C2×C5#513311yescharacteristic
402C2×C5C2×#82511yescharacteristic
403D5—241no—
404C23—21no—
405C23—21no—
406C23—22no—
407C23—22no—
408C23—301no—
409C23#671411yescharacteristic
410C23#671411yescharacteristic
411C23C2×D6011yescharacteristic
412Q8—601no—
413D4—601no—
414D4—601no—
415D4—601no—
416D4—602no—
417D4—602no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—304no—
425C2×C4—301no—
426C2×C4—301no—
427C2×C4—301no—
428C2×C4—602no—
429C2×C4—608no—
430C2×C4—602no—
431C2×C4—602no—
432C2×C4#671411yescharacteristic
433C2×C4#671411yescharacteristic
434C2×C4C2×C4×D1511yescharacteristic
435C2×C4C2×#122011yescharacteristic
436C8—42no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3C2×#393811yescharacteristic
442C2×C3#6542211yescharacteristic
443C2×C3C2×#395711yescharacteristic
444D3—401no—
445C5#6997611yescharacteristic, complemented, Sylow
446C22—24no—
447C22—24no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—601no—
455C22—601no—
456C22—601no—
457C22#9109012yes—
458C22#9110912yes—
459C22#9179711yescharacteristic
460C22#9179811yescharacteristic
461C22C2×#671411yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—604no—
467C4—601no—
468C4—601no—
469C4—601no—
470C3#1060076911yescharacteristic, complemented, Sylow
471C2—21no—
472C2—21no—
473C2—22no—
474C2—22no—
475C2—1201no—
476C2C2×#9109011yescharacteristic
477C2#1175123411yescharacteristic
478C2C2×#9110911yescharacteristic
subgroupG/H
centerC22C2×#6714
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
cosocleC22×C3×C4×C5C23
hypercenter#407D15
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C3×C5×#407C2semidirect
3. C2×#91115C2semidirect
4. #11746291C2semidirect
5. #11746288C2semidirect
9. C2×#6817C4semidirect
12. #91819C4semidirect
17. #91815C4semidirect
18. #91813C4semidirect
26. C5×#407D3semidirect
46. C2×D60C2×C4semidirect
48. C2×Dic30C2×C4semidirect
56. C4⋊Dic15C2×C4semidirect
57. C4⋊Dic15C2×C4semidirect
62. C3×#407D5semidirect
166. #407D15semidirect
371. C3×C5#1504semidirect
445. C5#69976semidirect
470. C3#10600769semidirect

Maximal subgroups

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

subgroupindex
#117565502
C3×C5×#4072
C2×#911152
#117462912
#117462882
#106007693
#699765