Finite Group Databasebeta

← #14282846

Subgroups — #14282846

Order 1920.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66125C211yesmaximal, characteristic
2C4×#6719C211yesmaximal, characteristic, complemented
3C2×C5×#830C211yesmaximal, characteristic, complemented
4#11745960C212yesmaximal, complemented
5#11745955C212yesmaximal, complemented
6#10600735—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C411yescharacteristic, complemented
9C2×#6719—21no—
10C2×C4×Dic15—21no—
11C22×C5×C3⋊C8—21no—
12C3×#4099—21no—
13C3×#4076C411yescharacteristic, complemented
14C3×#4076C2211yescharacteristic
15C3×#4075—21no—
16C3×C4×C22⋊D5—21no—
17C3×C4×C22⋊D5—21no—
18C3×#4072C411yescharacteristic, complemented
19C3×#4070C411yescharacteristic, complemented
20C3×#4070C2211yescharacteristic
21#91115C2212yes—
22C5×#830—21no—
23C5×#830C2212yes—
24#71707—51nomaximal, Hall
25#66125D311yescharacteristic
26C2×C5×C22⋊C8—31no—
27C4×C22⋊Dic5—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
38C22×Dic15—22no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C3×#709—42no—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×Dic10C2×C411yescharacteristic
46#6719—24no—
47C4×Dic15—42no—
48C2×C5×C3⋊C8—22no—
49C2×C5×C3⋊C8—42no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—21no—
58C3×#683—21no—
59C3×C4×Dic5—21no—
60C3×#525—51no—
61C4×#217—51no—
62C2×#830D511yescharacteristic, complemented
63#4538—52no—
64#4537—52no—
65C23×C4×C5C2×D311yescharacteristic
66C2×#709Dic311yescharacteristic, complemented
67C22×C5×C8—61no—
68#4099—21no—
69C2×C22⋊Dic5—61no—
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×C4×Dic5—61no—
79C5×C22⋊C8—32no—
80C5×C22⋊C8—61no—
81#3963—32no—
82#1501—151noSylow
83C23×C3×C5—22no—
84C23×C3×C5—22no—
85C23×C3×C5—41no—
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×C3×D5—21no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×Dic15—24no—
101C2×Dic15—42no—
102C2×Dic15—42no—
103C3×C22⋊D5—42no—
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C3×D20—41no—
110C3×C4×D5—42no—
111C3×Dic10—41no—
112C5×C3⋊C8—42no—
113C2×C3×#41—51no—
114C23×C3×C4C2×D511yescharacteristic
115C3×#123—101no—
116C3×C22⋊Q8—51no—
117C3×C22⋊Q8—51no—
118C3×#121—51no—
119C3×#121—51no—
120C3×#120—101no—
121C3×C4×D4—101no—
122C3×C4×D4—101no—
123C3×#117—51no—
124C2×#217—101no—
125C2×C4×Dic3—101no—
126C22×C3⋊C8—21no—
127C3⋊#95—52no—
128#830—21no—
129#830C2×D512yes—
130C24×C5#6711yescharacteristic
131C22×C4×C5—42no—
132C22×C4×C5C2×Dic311yescharacteristic
133C22×C4×C5C2×Dic311yescharacteristic
134C22×C4×C5#6711yescharacteristic
135C22×C4×C5#6711yescharacteristic
136C22×C4×C5#6711yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C2×C22⋊D5—21no—
139C2×C22⋊D5—21no—
140C2×C22⋊D5—21no—
141C22×Dic5—62no—
142#709—42no—
143C2×D20C2×Dic311yescharacteristic
144C2×C4×D5—21no—
145C2×Dic10C2×Dic311yescharacteristic
146C2×C5×C8—62no—
147C2×C5×C8—122no—
148C22⋊Dic5—21no—
149C22⋊Dic5—21no—
150C22⋊Dic5—21no—
151C22⋊Dic5—64no—
152#685—21no—
153#685—21no—
154C4⋊Dic5C2×Dic311yescharacteristic
155C4⋊Dic5C2×Dic311yescharacteristic
156#683—21no—
157#683—21no—
158C4×Dic5—21no—
159C4×Dic5—122no—
160#525—51no—
161C2×C22⋊C8—31no—
162C4×C22⋊C4—151no—
163#328—152no—
164#327—152no—
165C22×C3×C5—21no—
166C22×C3×C5—21no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—44no—
173C22×C3×C5#10412yes—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C22×C3×C5#13512yes—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—21no—
182C3×C4×C5#9912yes—
183Dic15—44no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C3×Dic5—41no—
187C24×C3D2011yescharacteristic
188C3×#41—202no—
189C2×C3×Q8—51no—
190C2×C3×D4—51no—
191C2×C3×D4—101no—
192C2×C3×D4—101no—
193C2×C3×D4—101no—
194C22×C3×C4—42no—
195C22×C3×C4—101no—
196C22×C3×C4C4×D511yescharacteristic
197C22×C3×C4C4×D511yescharacteristic
198C22×C3×C4D2011yescharacteristic
199C22×C3×C4C22⋊D511yescharacteristic
200C22×C3×C4C22⋊D511yescharacteristic
201C22×C3×C4C22×D511yescharacteristic
202C22×Dic3—102no—
203C3×C4⋊C4—51no—
204C3×C4⋊C4—51no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C42—101no—
213#217—104no—
214C4×Dic3—202no—
215C2×C3⋊C8—22no—
216C2×C3⋊C8—42no—
217C23×C5—22no—
218C23×C5—22no—
219C23×C5—41no—
220C23×C5#21711yescharacteristic
221C23×C5#21711yescharacteristic
222C23×C5C2×#6711yescharacteristic
223C22×D5—21no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5#21711yescharacteristic
231C2×C4×C5#21711yescharacteristic
232C2×C4×C5C22×Dic311yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C22⋊D5—42no—
235C22⋊D5—42no—
236C22⋊D5—42no—
237C2×Dic5—21no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240C2×Dic5—64no—
241C2×Dic5—122no—
242C2×Dic5—122no—
243D20—41no—
244C4×D5—42no—
245Dic10—41no—
246C5×C8—122no—
247C2×#41—51no—
248C23×C4D3×D511yescharacteristic
249C22×C8—61no—
250#123—101no—
251C22⋊Q8—51no—
252C22⋊Q8—51no—
253#121—51no—
254#121—51no—
255#120—101no—
256C4×D4—101no—
257C4×D4—101no—
258#117—51no—
259C2×C22⋊C4—301no—
260C2×C42—301no—
261C22⋊C8—32no—
262C22⋊C8—61no—
263#95—152no—
264C2×C3×C5—22no—
265C2×C3×C5—22no—
266C2×C3×C5—41no—
267C2×C3×C5C2×#9911yescharacteristic
268C2×C3×C5#41611yescharacteristic
269C2×C3×C5C2×#10411yescharacteristic
270C3×D5—81no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—41no—
274C23×C3—101no—
275C23×C3#68511yescharacteristic
276C23×C3#68511yescharacteristic
277C23×C3C2×D2011yescharacteristic
278C3×Q8—201no—
279C3×D4—201no—
280C3×D4—202no—
281C3×D4—202no—
282C3×D4—202no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—202no—
293C2×C3×C4#68511yescharacteristic
294C2×C3×C4#68511yescharacteristic
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4C2×C22⋊D511yescharacteristic
297C2×Dic3—104no—
298C2×Dic3—202no—
299C2×Dic3—202no—
300C3⋊C8—42no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—44no—
309C22×C5#83712yes—
310C22×C5#95012yes—
311C22×C5C2×#21711yescharacteristic
312C2×D5—41no—
313C2×D5—41no—
314C2×D5—41no—
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—21no—
318C4×C5#83412yes—
319Dic5—41no—
320Dic5—41no—
321Dic5—41no—
322Dic5—124no—
323C24#120211yescharacteristic
324#41—202no—
325C2×Q8—51no—
326C2×D4—51no—
327C2×D4—101no—
328C2×D4—101no—
329C2×D4—101no—
330C22×C4—42no—
331C22×C4—101no—
332C22×C4—302no—
333C22×C4D5×Dic311yescharacteristic
334C22×C4D5×Dic311yescharacteristic
335C22×C4#120111yescharacteristic
336C22×C4#120111yescharacteristic
337C22×C4#120211yescharacteristic
338C22×C4C2×D3×D511yescharacteristic
339C2×C8—62no—
340C2×C8—122no—
341C4⋊C4—51no—
342C4⋊C4—51no—
343C4⋊C4—101no—
344C4⋊C4—101no—
345C22⋊C4—101no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C22⋊C4—101no—
350C22⋊C4—304no—
351C42—101no—
352C42—602no—
353C3×C5#150111yescharacteristic, complemented, Hall
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—44no—
362C22×C3—201no—
363C22×C3—201no—
364C22×C3—201no—
365C22×C3#395712yes—
366C22×C3#405012yes—
367C22×C3C2×#68511yescharacteristic
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—201no—
372C3×C4—201no—
373C3×C4—201no—
374C3×C4#393812yes—
375Dic3—204no—
376C2×C5—22no—
377C2×C5—22no—
378C2×C5—41no—
379C2×C5C2×#83411yescharacteristic
380C2×C5#523311yescharacteristic
381C2×C5C2×#83711yescharacteristic
382D5—81no—
383C23—22no—
384C23—22no—
385C23—41no—
386C23—101no—
387C23#666511yescharacteristic
388C23#666511yescharacteristic
389C23C2×#120211yescharacteristic
390Q8—201no—
391D4—201no—
392D4—202no—
393D4—202no—
394D4—202no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—202no—
405C2×C4—304no—
406C2×C4—602no—
407C2×C4—602no—
408C2×C4#666511yescharacteristic
409C2×C4#666511yescharacteristic
410C2×C4C2×D5×Dic311yescharacteristic
411C2×C4C2×#120111yescharacteristic
412C8—122no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—41no—
416C2×C3—401no—
417C2×C3C2×#393811yescharacteristic
418C2×C3#6540211yescharacteristic
419C2×C3C2×#395711yescharacteristic
420C5#7170711yescharacteristic, complemented, Sylow
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—201no—
430C22—201no—
431C22—201no—
432C22#9097612yes—
433C22#9131112yes—
434C22C2×#666511yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—201no—
439C4—201no—
440C4—201no—
441C4—604no—
442C4#9099512yes—
443C3#1060073511yescharacteristic, complemented, Sylow
444C2—22no—
445C2—22no—
446C2—41no—
447C2—401no—
448C2#1174836511yescharacteristic
449C2C2×#9097611yescharacteristic
450C2C2×#9099511yescharacteristic
subgroupG/H
centerC2×C4#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#1501
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6719C2semidirect
3. C2×C5×#830C2semidirect
4. #11745960C2semidirect
5. #11745955C2semidirect
8. C2×C3×#709C4semidirect
13. C3×#4076C4semidirect
18. C3×#4072C4semidirect
19. C3×#4070C4semidirect
62. C2×#830D5semidirect
66. C2×#709Dic3semidirect
70. #4076Dic3semidirect
75. #4072Dic3semidirect
76. #4070Dic3semidirect
353. C3×C5#1501semidirect
420. C5#71707semidirect
443. C3#10600735semidirect

Maximal subgroups

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

subgroupindex
C3×#661252
C4×#67192
C2×C5×#8302
#117459602
#117459552
#106007353
#717075