Finite Group Databasebeta

← #14283386

Subgroups — #14283386

Order 1920.

444 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65958C211yesmaximal, characteristic
2#11748580C211yesmaximal, characteristic, complemented
3#11748333C211yesmaximal, characteristic, complemented
4#11746359C211yesmaximal, characteristic, complemented
5C5×#4538C211yesmaximal, characteristic, complemented
6#11745955C211yesmaximal, characteristic
7#11745954C211yesmaximal, characteristic
8#10599105—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic, complemented
11C3×Q8×Dic5C411yescharacteristic, complemented
12C3×#4076C2211yescharacteristic
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4044—21no—
15C3×#4039C411yescharacteristic, complemented
16C3×#4038—21no—
17C3×#4036C411yescharacteristic, complemented
18C3×#4032—21no—
19C3×#4027—21no—
20C2×#6668—21no—
21#91115C2211yescharacteristic
22#91114C2211yescharacteristic
23C5×C3⋊#95C2211yescharacteristic
24C5×#830C2211yescharacteristic
25#90994—21no—
26#90982—21no—
27#90952—21no—
28#71756—51nomaximal, Hall
29#65958D311yescharacteristic
30#65008—31no—
31#64939—31no—
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63#6668—42no—
64C3×#529—51no—
65#4936—51no—
66#4926—51no—
67#4538—51no—
68#4538D511yescharacteristic, complemented
69#4537—51no—
70#4537—51no—
71C5×C22⋊Q8C2×D311yescharacteristic
72#4093Dic311yescharacteristic, complemented
73Q8×Dic5Dic311yescharacteristic, complemented
74#4076C2×D311yescharacteristic
75C2×#683—61no—
76C2×C4×Dic5C2×D311yescharacteristic
77#4044—21no—
78#4039Dic311yescharacteristic, complemented
79#4038—21no—
80#4036Dic311yescharacteristic, complemented
81#4032—21no—
82#4027—21no—
83C5×C22⋊C8—31no—
84C5×#95—31no—
85#3963—31no—
86#3963—61no—
87C22⋊#168—31no—
88#3947—61no—
89#3946—61no—
90#1512—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C3×C5×Q8—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—41no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102C2×C5×Dic3—41no—
103C2×C5×Dic3—41no—
104C2×C5×Dic3—41no—
105C3×C22⋊D5—41no—
106C3×C22⋊D5—41no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C3×D20—41no—
116C3×C4×D5—42no—
117C3⋊#168—41no—
118C5×C3⋊C8—41no—
119C3×#126—101no—
120C3×#125—51no—
121C3×#124—51no—
122C3×#123—101no—
123C3×C22⋊Q8C2×D511yescharacteristic
124C3×#121—51no—
125C3×C4×Q8—51no—
126C3×C4×D4—51no—
127C3×C4×D4—101no—
128C3×#117—101no—
129C2×C3×C42—51no—
130C2×C4⋊Dic3—101no—
131C3⋊#95—51no—
132C3⋊#95—101no—
133C3⋊#95C2×D511yescharacteristic
134#830—51no—
135#830C2×D511yescharacteristic
136C4⋊(C3⋊C8)—101no—
137#803—101no—
138C2×C5×Q8C2×Dic311yescharacteristic
139C22×C4×C5—61no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—21no—
142C22×Dic5—61no—
143C22×Dic5#6711yescharacteristic
144C22×Dic5#6711yescharacteristic
145C2×D20C2×Dic311yescharacteristic
146C2×C4×D5—21no—
147C2×C5×C8—61no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4C2×Dic311yescharacteristic
150C5×C22⋊C4—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—21no—
157C4⋊Dic5C2×Dic311yescharacteristic
158#683—21no—
159#683—122no—
160C4×Dic5—21no—
161C4×Dic5C2×Dic311yescharacteristic
162C4×Dic5C2×Dic311yescharacteristic
163C4×Dic5#6711yescharacteristic
164C4×Dic5#6711yescharacteristic
165C2×#168—61no—
166#529—51no—
167#432—151no—
168#382—151no—
169#328—31no—
170#328—151no—
171#327—151no—
172#327—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C2×C3×D5—41no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—41no—
184C3×C4×C5—41no—
185Dic15—81no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C3×Dic5—41no—
191C5×Dic3—81no—
192C2×C3×Q8C4×D511yescharacteristic
193C2×C3×D4—51no—
194C2×C3×D4—101no—
195C22×C3×C4—51no—
196C22×C3×C4—51no—
197C22×C3×C4—101no—
198C22×C3×C4C22×D511yescharacteristic
199C22×Dic3—21no—
200C22×Dic3—101no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—51no—
203C3×C4⋊C4—101no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4C4×D511yescharacteristic
207C3×C22⋊C4—21no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C42—51no—
213C3×C42—51no—
214C3×C42—51no—
215C3×C42—51no—
216C3×C42—101no—
217C4⋊Dic3—202no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—101no—
220C23×C5C2×#6711yescharacteristic
221C22×D5—21no—
222C5×Q8—41no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—121no—
227C2×C4×C5—121no—
228C2×C4×C5—121no—
229C2×C4×C5C22×Dic311yescharacteristic
230C2×C4×C5C2×#6711yescharacteristic
231C22⋊D5—41no—
232C22⋊D5—41no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—41no—
237C2×Dic5—121no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240C2×Dic5#21711yescharacteristic
241C2×Dic5#21711yescharacteristic
242C2×Dic5#21711yescharacteristic
243C2×Dic5#21711yescharacteristic
244D20—41no—
245C4×D5—42no—
246C5×C8—121no—
247#168—121no—
248#126—101no—
249#125—51no—
250#124—51no—
251#123—101no—
252C22⋊Q8D3×D511yescharacteristic
253#121—51no—
254C4×Q8—51no—
255C4×D4—51no—
256C4×D4—101no—
257#117—101no—
258C2×C4⋊C4—301no—
259C2×C42—51no—
260C4⋊C8—301no—
261C22⋊C8—31no—
262C22⋊C8—151no—
263#97—301no—
264#95—31no—
265#95—151no—
266#95—301no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41711yescharacteristic
271C2×C3×C5#42111yescharacteristic
272C3×D5—81no—
273C23×C3—101no—
274C23×C3D4×D511yescharacteristic
275C3×Q8—41no—
276C3×D4—201no—
277C3×D4—201no—
278C3×D4—201no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—41no—
282C2×C3×C4—51no—
283C2×C3×C4—51no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—101no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4—202no—
290C2×C3×C4—201no—
291C2×C3×C4C2×C4×D511yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—201no—
297C2×Dic3—201no—
298C2×Dic3—201no—
299C3⋊C8—41no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5#94911yescharacteristic
304C22×C5#95111yescharacteristic
305C22×C5C2×#21711yescharacteristic
306C2×D5—41no—
307C2×D5—41no—
308C2×D5—41no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—41no—
312C4×C5—41no—
313C4×C5—241no—
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—21no—
318Dic5—41no—
319Dic5—241no—
320C2×Q8D5×Dic311yescharacteristic
321C2×D4—51no—
322C2×D4—101no—
323C22×C4—51no—
324C22×C4—51no—
325C22×C4—61no—
326C22×C4—101no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—61no—
330C2×C8—301no—
331C4⋊C4—21no—
332C4⋊C4—51no—
333C4⋊C4—101no—
334C4⋊C4—101no—
335C4⋊C4—101no—
336C4⋊C4—602no—
337C4⋊C4D5×Dic311yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—101no—
340C22⋊C4—101no—
341C22⋊C4—101no—
342C22⋊C4—101no—
343C42—51no—
344C42—51no—
345C42—51no—
346C42—51no—
347C42—101no—
348C3×C5#151211yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—201no—
352C22×C3—201no—
353C22×C3—201no—
354C22×C3D5×C22⋊C411yescharacteristic
355C22×C3#406011yescharacteristic
356C22×C3#406411yescharacteristic
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—101no—
362C3×C4—101no—
363C3×C4—101no—
364C3×C4—101no—
365C3×C4—201no—
366Dic3—81no—
367Dic3—401no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5#523211yescharacteristic
371C2×C5#523611yescharacteristic
372C2×C5#524011yescharacteristic
373D5—81no—
374C23—101no—
375C23D5×#6711yescharacteristic
376Q8—41no—
377D4—201no—
378D4—201no—
379D4—201no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4—202no—
394C2×C4—201no—
395C2×C4—601no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×D5×Dic311yescharacteristic
399C2×C4D5×#6711yescharacteristic
400C8—121no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—401no—
405C2×C3#6502911yescharacteristic
406C2×C3#6509211yescharacteristic
407C2×C3#6511011yescharacteristic
408C5#7175611yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—201no—
412C22—201no—
413C22—201no—
414C22#9150211yescharacteristic
415C22#9150811yescharacteristic
416C22D5×#21711yescharacteristic
417C4—21no—
418C4—21no—
419C4—41no—
420C4—41no—
421C4—101no—
422C4—101no—
423C4—101no—
424C4—101no—
425C4—201no—
426C4—241no—
427C4—1201no—
428C3#1059910511yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—401no—
432C2#1174917211yescharacteristic
433C2#1174919811yescharacteristic
434C2#1174942711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1512
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11748580C2semidirect
3. #11748333C2semidirect
4. #11746359C2semidirect
5. C5×#4538C2semidirect
10. C3×#4093C4semidirect
11. C3×Q8×Dic5C4semidirect
15. C3×#4039C4semidirect
17. C3×#4036C4semidirect
68. #4538D5semidirect
72. #4093Dic3semidirect
73. Q8×Dic5Dic3semidirect
78. #4039Dic3semidirect
80. #4036Dic3semidirect
348. C3×C5#1512semidirect
408. C5#71756semidirect
428. C3#10599105semidirect

Maximal subgroups

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

subgroupindex
C3×#659582
#117485802
#117483332
#117463592
C5×#45382
#117459552
#117459542
#105991053
#717565