Finite Group Databasebeta

← #14282991

Subgroups — #14282991

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
2C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4#11745965C212yesmaximal, complemented
5#11745959C212yesmaximal, complemented
6#10600191—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C411yescharacteristic, complemented
9C23×C5×Dic3—21no—
10#91842—21no—
11#91819C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13#91818—21no—
14C4×#1220—21no—
15C4×#1220—21no—
16#91815C411yescharacteristic, complemented
17#91813C411yescharacteristic, complemented
18#91813C2211yescharacteristic
19C2×C3×#681—21no—
20C5×C3⋊#95—21no—
21C5×C3⋊#95C2212yes—
22C3×C22⋊#168—21no—
23C3×C22⋊#168C2212yes—
24#69976—51nomaximal, Hall
25#66125—31no—
26C2×C5×#95—31no—
27#65496D311yescharacteristic, complemented
28#64672—32no—
29#64671—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—
41#6817—42no—
42C2×D60C2×C411yescharacteristic, complemented
43C2×C4×D15—21no—
44C2×Dic30C2×C411yescharacteristic, complemented
45C22×C5×Dic3—24no—
46C22×C5×Dic3—22no—
47C22×C5×Dic3—42no—
48C22×C5×Dic3—42no—
49#6719—21no—
50#6719—21no—
51#6719—21no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15C2×C411yescharacteristic, complemented
55C4⋊Dic15C2×C411yescharacteristic, complemented
56#6712—21no—
57#6712—21no—
58C4×Dic15—21no—
59C3×#681—42no—
60C2×C3×#168—22no—
61#5791—51no—
62C3×#407—51no—
63C2×C3⋊#95D511yescharacteristic, complemented
64#4470—52no—
65#4467—52no—
66C23×C4×C5—61no—
67C23×C4×C5C2×D311yescharacteristic
68C2×#709—31no—
69#4099—61no—
70#4076—31no—
71#4076—31no—
72#4075—61no—
73C4×C22⋊D5—61no—
74C4×C22⋊D5—61no—
75#4072—31no—
76#4070—31no—
77#4070—31no—
78C2×#681—21no—
79C5×#95—32no—
80C5×#95—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×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—21no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109D60—41no—
110C4×D15—42no—
111Dic30—41no—
112C2×C5×Dic3—24no—
113C2×C5×Dic3—48no—
114C2×C5×Dic3—42no—
115C2×C5×Dic3—42no—
116C3×#168—42no—
117C23×C3×C4C2×D511yescharacteristic
118C23×Dic3—21no—
119C2×#235—51no—
120C2×C3×M16—101no—
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—52no—
131C3×C22⋊C8—101no—
132C3⋊#95—21no—
133C3⋊#95C2×D512yes—
134C24×C5D1211yescharacteristic
135C22×C4×C5—42no—
136C22×C4×C5—64no—
137C22×C4×C5—62no—
138C22×C4×C5—122no—
139C22×C4×C5—122no—
140C22×C4×C5C4×D311yescharacteristic
141C22×C4×C5C4×D311yescharacteristic
142C22×C4×C5D1211yescharacteristic
143C22×C4×C5#6711yescharacteristic
144C22×C4×C5#6711yescharacteristic
145C22×C4×C5C22×D311yescharacteristic
146C2×C22⋊D5—61no—
147C2×C22⋊D5—61no—
148C2×C22⋊D5—61no—
149#709—122no—
150C2×D20—31no—
151C2×C4×D5—61no—
152C2×Dic10—31no—
153C22⋊Dic5—61no—
154C22⋊Dic5—61no—
155C22⋊Dic5—61no—
156#685—61no—
157#685—61no—
158C4⋊Dic5—31no—
159C4⋊Dic5—31no—
160#683—61no—
161#683—61no—
162C4×Dic5—61no—
163#681—42no—
164C2×#168—22no—
165#525—151no—
166#407—51no—
167C2×#95—31no—
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—41no—
191Dic15—41no—
192Dic15—41no—
193C5×Dic3—44no—
194C24×C3C22⋊D511yescharacteristic
195C22×C3×C4—42no—
196C22×C3×C4C4×D511yescharacteristic
197C22×C3×C4C4×D511yescharacteristic
198C22×C3×C4D2011yescharacteristic
199C22×C3×C4D2011yescharacteristic
200C22×C3×C4C22⋊D511yescharacteristic
201C22×C3×C4C22×D511yescharacteristic
202C2×#67—101no—
203C2×#67—101no—
204C2×#67—101no—
205C22×Dic3—24no—
206C22×Dic3—22no—
207C22×Dic3—42no—
208C22×Dic3—42no—
209#235—202no—
210C2×D12—51no—
211C2×C4×D3—101no—
212C2×Dic6—51no—
213C3×M16—202no—
214C2×C3×C8—102no—
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—64no—
240C2×C4×C5—128no—
241C2×C4×C5—122no—
242C2×C4×C5—122no—
243C2×C4×C5(C2×D3)⋊C411yescharacteristic
244C2×C4×C5(C2×D3)⋊C411yescharacteristic
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—122no—
248C22⋊D5—122no—
249C22⋊D5—121no—
250C22⋊D5—121no—
251C2×Dic5—61no—
252C2×Dic5—61no—
253C2×Dic5—61no—
254D20—121no—
255C4×D5—122no—
256Dic10—121no—
257#168—42no—
258C2×#41—151no—
259C23×C4—61no—
260C23×C4D3×D511yescharacteristic
261C2×M16—101no—
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—52no—
272C22⋊C8—101no—
273#95—32no—
274#95—61no—
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×C22⋊D511yescharacteristic
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×D2011yescharacteristic
301#67—202no—
302#67—202no—
303#67—201no—
304#67—201no—
305C2×Dic3—24no—
306C2×Dic3—48no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—101no—
310C2×Dic3—101no—
311C2×Dic3—101no—
312D12—201no—
313C4×D3—202no—
314Dic6—201no—
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#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—
336C4×C5—124no—
337Dic5—121no—
338Dic5—121no—
339Dic5—121no—
340C24#120311yescharacteristic
341#41—602no—
342C2×Q8—151no—
343C2×D4—151no—
344C2×D4—301no—
345C2×D4—301no—
346C2×D4—301no—
347C22×C4—42no—
348C22×C4—64no—
349C22×C4—62no—
350C22×C4—122no—
351C22×C4—122no—
352C22×C4—301no—
353C22×C4#120011yescharacteristic
354C22×C4#120011yescharacteristic
355C22×C4#120211yescharacteristic
356C22×C4#120211yescharacteristic
357C22×C4#120311yescharacteristic
358C22×C4C2×D3×D511yescharacteristic
359M16—202no—
360C2×C8—102no—
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#393712yes—
381C22×C3#393812yes—
382C22×C3C2×#68511yescharacteristic
383C22×C3#407811yescharacteristic
384C22×C3#408811yescharacteristic
385C2×D3—201no—
386C2×D3—201no—
387C2×D3—201no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392Dic3—44no—
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—22no—
405C23—22no—
406C23—21no—
407C23—21no—
408C23—301no—
409C23#666711yescharacteristic
410C23#666711yescharacteristic
411C23C2×#120311yescharacteristic
412Q8—601no—
413D4—601no—
414D4—602no—
415D4—602no—
416D4—601no—
417D4—601no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—64no—
425C2×C4—128no—
426C2×C4—122no—
427C2×C4—122no—
428C2×C4—301no—
429C2×C4—301no—
430C2×C4—301no—
431C2×C4—602no—
432C2×C4#666711yescharacteristic
433C2×C4#666711yescharacteristic
434C2×C4C2×#120011yescharacteristic
435C2×C4C2×#120211yescharacteristic
436C8—202no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3C2×#393711yescharacteristic
442C2×C3C2×#393811yescharacteristic
443C2×C3#6525511yescharacteristic
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#9098012yes—
458C22#9099712yes—
459C22#9130411yescharacteristic
460C22#9132111yescharacteristic
461C22C2×#666711yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—124no—
467C4—601no—
468C4—601no—
469C4—601no—
470C3#1060019111yescharacteristic, complemented, Sylow
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2—1201no—
476C2#1174839411yescharacteristic
477C2C2×#9098011yescharacteristic
478C2C2×#9099711yescharacteristic
subgroupG/H
centerC22C2×#6667
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
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×C5×C3⋊#95C2semidirect
3. C3×#65496C2semidirect
4. #11745965C2semidirect
5. #11745959C2semidirect
8. C2×#6817C4semidirect
11. #91819C4semidirect
16. #91815C4semidirect
17. #91813C4semidirect
27. #65496D3semidirect
42. C2×D60C2×C4semidirect
44. C2×Dic30C2×C4semidirect
54. C4⋊Dic15C2×C4semidirect
55. C4⋊Dic15C2×C4semidirect
63. C2×C3⋊#95D5semidirect
371. C3×C5#1504semidirect
445. C5#69976semidirect
470. C3#10600191semidirect

Maximal subgroups

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

subgroupindex
#117565502
C2×C5×C3⋊#952
C3×#654962
#117459652
#117459592
#106001913
#699765