Finite Group Databasebeta

← #14282990

Subgroups — #14282990

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
1C3×#66125C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic, complemented
3C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
4#11745961C212yesmaximal, complemented
5#11745954C212yesmaximal, complemented
6#10600191—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C23×C5×Dic3—21no—
9C2×C3×#709C411yescharacteristic, complemented
10C2×#6710—21no—
11C3×#4099—21no—
12C3×#4076C411yescharacteristic, complemented
13C3×#4076C2211yescharacteristic
14C3×#4075—21no—
15C3×C4×C22⋊D5—21no—
16C3×C4×C22⋊D5—21no—
17C3×#4072C411yescharacteristic, complemented
18C3×#4070C411yescharacteristic, complemented
19C3×#4070C2211yescharacteristic
20#91114—21no—
21#91114C2212yes—
22C5×C3⋊#95—21no—
23C5×C3⋊#95C2212yes—
24#71708—51nomaximal, Hall
25#66125D311yescharacteristic
26C2×C5×#95—31no—
27#65496—31no—
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
38C22×C5×Dic3—24no—
39C22×C5×Dic3—22no—
40C22×C5×Dic3—42no—
41C22×C5×Dic3—42no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C3×#709—42no—
46C2×C3×D20C2×C411yescharacteristic, complemented
47C2×C3×C4×D5—21no—
48C2×C3×Dic10C2×C411yescharacteristic, complemented
49#6710—42no—
50C2×C3⋊#168—22no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5—21no—
53C3×C22⋊Dic5—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic, complemented
57C3×C4⋊Dic5C2×C411yescharacteristic, complemented
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C3×#525—51no—
62C2×C3⋊#95D511yescharacteristic, complemented
63#5207—51no—
64#4538—52no—
65#4537—52no—
66C23×C4×C5—61no—
67C23×C4×C5C2×D311yescharacteristic
68C2×#709Dic311yescharacteristic, complemented
69#4099—21no—
70#4076Dic311yescharacteristic, complemented
71#4076C2×D311yescharacteristic
72#4075—21no—
73C4×C22⋊D5—21no—
74C4×C22⋊D5—21no—
75#4072Dic311yescharacteristic, complemented
76#4070Dic311yescharacteristic, complemented
77#4070C2×D311yescharacteristic
78C2×#681—61no—
79C5×#95—32no—
80C5×#95—61no—
81C22⋊#168—32no—
82C22⋊#168—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×C3×D5—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×C5×Dic3—24no—
103C2×C5×Dic3—48no—
104C2×C5×Dic3—42no—
105C2×C5×Dic3—42no—
106C3×C22⋊D5—42no—
107C3×C22⋊D5—42no—
108C3×C22⋊D5—41no—
109C3×C22⋊D5—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C3×D20—41no—
114C3×C4×D5—42no—
115C3×Dic10—41no—
116C3⋊#168—42no—
117C2×C3×#41—51no—
118C23×C3×C4C2×D511yescharacteristic
119C23×Dic3—21no—
120C3×#123—101no—
121C3×C22⋊Q8—51no—
122C3×C22⋊Q8—51no—
123C3×#121—51no—
124C3×#121—51no—
125C3×#120—101no—
126C3×C4×D4—101no—
127C3×C4×D4—101no—
128C3×#117—51no—
129C2×#208—101no—
130C3⋊#95—21no—
131C3⋊#95C2×D512yes—
132#830—52no—
133#830—101no—
134C24×C5#6711yescharacteristic
135C22×C4×C5—42no—
136C22×C4×C5—64no—
137C22×C4×C5—62no—
138C22×C4×C5—122no—
139C22×C4×C5—122no—
140C22×C4×C5C2×Dic311yescharacteristic
141C22×C4×C5C2×Dic311yescharacteristic
142C22×C4×C5#6711yescharacteristic
143C22×C4×C5#6711yescharacteristic
144C22×C4×C5#6711yescharacteristic
145C22×C4×C5C22×D311yescharacteristic
146C2×C22⋊D5—21no—
147C2×C22⋊D5—21no—
148C2×C22⋊D5—21no—
149#709—42no—
150C2×D20C2×Dic311yescharacteristic, complemented
151C2×C4×D5—21no—
152C2×Dic10C2×Dic311yescharacteristic, complemented
153C22⋊Dic5—21no—
154C22⋊Dic5—21no—
155C22⋊Dic5—21no—
156#685—21no—
157#685—21no—
158C4⋊Dic5C2×Dic311yescharacteristic, complemented
159C4⋊Dic5C2×Dic311yescharacteristic, complemented
160#683—21no—
161#683—21no—
162C4×Dic5—21no—
163#681—122no—
164C2×#168—62no—
165#525—51no—
166#407—151no—
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×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×Dic5—41no—
191C3×Dic5—41no—
192C3×Dic5—41no—
193C5×Dic3—44no—
194C24×C3C22⋊D511yescharacteristic
195C3×#41—202no—
196C2×C3×Q8—51no—
197C2×C3×D4—51no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C22×C3×C4—42no—
202C22×C3×C4—101no—
203C22×C3×C4C4×D511yescharacteristic
204C22×C3×C4C4×D511yescharacteristic
205C22×C3×C4D2011yescharacteristic
206C22×C3×C4D2011yescharacteristic
207C22×C3×C4C22⋊D511yescharacteristic
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—24no—
210C22×Dic3—22no—
211C22×Dic3—42no—
212C22×Dic3—42no—
213C3×C4⋊C4—51no—
214C3×C4⋊C4—51no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C22⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C42—101no—
223#208—202no—
224C2×C3⋊C8—102no—
225C23×C5—22no—
226C23×C5—22no—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5#21711yescharacteristic
230C23×C5#21711yescharacteristic
231C23×C5C2×#6711yescharacteristic
232C22×D5—21no—
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#21711yescharacteristic
244C2×C4×C5#21711yescharacteristic
245C2×C4×C5C22×Dic311yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—42no—
248C22⋊D5—42no—
249C22⋊D5—41no—
250C22⋊D5—41no—
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—21no—
254D20—41no—
255C4×D5—42no—
256Dic10—41no—
257#168—122no—
258C2×#41—51no—
259C23×C4—61no—
260C23×C4D3×D511yescharacteristic
261C2×M16—301no—
262#123—101no—
263C22⋊Q8—51no—
264C22⋊Q8—51no—
265#121—51no—
266#121—51no—
267#120—101no—
268C4×D4—101no—
269C4×D4—101no—
270#117—51no—
271C22⋊C8—152no—
272C22⋊C8—301no—
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
282C3×D5—81no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—101no—
288C23×C3#68511yescharacteristic
289C23×C3#68511yescharacteristic
290C23×C3C2×C22⋊D511yescharacteristic
291C3×Q8—201no—
292C3×D4—201no—
293C3×D4—202no—
294C3×D4—202no—
295C3×D4—201no—
296C3×D4—201no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—101no—
304C2×C3×C4—101no—
305C2×C3×C4—101no—
306C2×C3×C4—202no—
307C2×C3×C4#68511yescharacteristic
308C2×C3×C4#68511yescharacteristic
309C2×C3×C4C2×C4×D511yescharacteristic
310C2×C3×C4C2×D2011yescharacteristic
311C2×Dic3—24no—
312C2×Dic3—48no—
313C2×Dic3—42no—
314C2×Dic3—42no—
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#83412yes—
325C22×C5#83712yes—
326C22×C5#94911yescharacteristic
327C22×C5#95111yescharacteristic
328C22×C5C2×#21711yescharacteristic
329C2×D5—41no—
330C2×D5—41no—
331C2×D5—41no—
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—21no—
335C4×C5—21no—
336C4×C5—124no—
337Dic5—41no—
338Dic5—41no—
339Dic5—41no—
340C24#120111yescharacteristic
341#41—202no—
342C2×Q8—51no—
343C2×D4—51no—
344C2×D4—101no—
345C2×D4—101no—
346C2×D4—101no—
347C22×C4—42no—
348C22×C4—64no—
349C22×C4—62no—
350C22×C4—101no—
351C22×C4—122no—
352C22×C4—122no—
353C22×C4D5×Dic311yescharacteristic
354C22×C4D5×Dic311yescharacteristic
355C22×C4#120111yescharacteristic
356C22×C4#120211yescharacteristic
357C22×C4#120211yescharacteristic
358C22×C4C2×D3×D511yescharacteristic
359M16—602no—
360C2×C8—302no—
361C4⋊C4—51no—
362C4⋊C4—51no—
363C4⋊C4—101no—
364C4⋊C4—101no—
365C22⋊C4—101no—
366C22⋊C4—101no—
367C22⋊C4—101no—
368C22⋊C4—101no—
369C22⋊C4—101no—
370C42—101no—
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—201no—
381C22×C3—201no—
382C22×C3—201no—
383C22×C3#393712yes—
384C22×C3#393812yes—
385C22×C3C2×#68511yescharacteristic
386C22×C3#407811yescharacteristic
387C22×C3#408811yescharacteristic
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—201no—
393C3×C4—201no—
394C3×C4—201no—
395Dic3—44no—
396C2×C5—21no—
397C2×C5—22no—
398C2×C5—22no—
399C2×C5—21no—
400C2×C5C2×#83411yescharacteristic
401C2×C5#523211yescharacteristic
402C2×C5C2×#83711yescharacteristic
403D5—81no—
404C23—22no—
405C23—22no—
406C23—21no—
407C23—21no—
408C23—101no—
409C23#666511yescharacteristic
410C23#666511yescharacteristic
411C23C2×#120111yescharacteristic
412Q8—201no—
413D4—201no—
414D4—202no—
415D4—202no—
416D4—201no—
417D4—201no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—64no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—128no—
429C2×C4—122no—
430C2×C4—122no—
431C2×C4—202no—
432C2×C4#666511yescharacteristic
433C2×C4#666511yescharacteristic
434C2×C4C2×D5×Dic311yescharacteristic
435C2×C4C2×#120211yescharacteristic
436C8—602no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3—401no—
442C2×C3C2×#393711yescharacteristic
443C2×C3C2×#393811yescharacteristic
444C2×C3#6525511yescharacteristic
445C5#7170811yescharacteristic, complemented, Sylow
446C22—24no—
447C22—24no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—201no—
455C22—201no—
456C22—201no—
457C22#9097712yes—
458C22#9099512yes—
459C22#9129911yescharacteristic
460C22#9130711yescharacteristic
461C22C2×#666511yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—124no—
467C4—201no—
468C4—201no—
469C4—201no—
470C3#1060019111yescharacteristic, complemented, Sylow
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2—401no—
476C2#1174836811yescharacteristic
477C2C2×#9097711yescharacteristic
478C2C2×#9099511yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
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. #11751308C2semidirect
3. C2×C5×C3⋊#95C2semidirect
4. #11745961C2semidirect
5. #11745954C2semidirect
9. C2×C3×#709C4semidirect
12. C3×#4076C4semidirect
17. C3×#4072C4semidirect
18. C3×#4070C4semidirect
46. C2×C3×D20C2×C4semidirect
48. C2×C3×Dic10C2×C4semidirect
56. C3×C4⋊Dic5C2×C4semidirect
57. C3×C4⋊Dic5C2×C4semidirect
62. C2×C3⋊#95D5semidirect
68. C2×#709Dic3semidirect
70. #4076Dic3semidirect
75. #4072Dic3semidirect
76. #4070Dic3semidirect
150. C2×D20C2×Dic3semidirect
152. C2×Dic10C2×Dic3semidirect
158. C4⋊Dic5C2×Dic3semidirect
159. C4⋊Dic5C2×Dic3semidirect
371. C3×C5#1504semidirect
445. C5#71708semidirect
470. C3#10600191semidirect

Maximal subgroups

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

subgroupindex
C3×#661252
#117513082
C2×C5×C3⋊#952
#117459612
#117459542
#106001913
#717085