Finite Group Databasebeta

← #14282936

Subgroups — #14282936

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65956C211yesmaximal, characteristic
2#11748638C211yesmaximal, characteristic
3#11748316C211yesmaximal, characteristic
4#11746359C211yesmaximal, characteristic
5C5×#4538C211yesmaximal, characteristic
6#11745961C211yesmaximal, characteristic
7#11745960C211yesmaximal, characteristic
8#10599102—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C3×Q8×Dic5C411yescharacteristic, complemented
11C3×#4090C411yescharacteristic, complemented
12C3×#4070C2211yescharacteristic
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4035—21no—
15C3×#4034C411yescharacteristic, complemented
16C3×#4033—21no—
17C3×#4033C411yescharacteristic, complemented
18C3×#4024—21no—
19C3×#4023—21no—
20C2×#6668—21no—
21C2×Dic3×Dic5—21no—
22#91115C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×C3⋊#95C2211yescharacteristic
25C5×#830C2211yescharacteristic
26#90982—21no—
27Dic5×C3⋊C8—21no—
28#71835—51nomaximal, Hall
29#65956D311yescharacteristic
30#65007—31no—
31#64938—31no—
32C5×#328—31no—
33#64758—31no—
34#64687—31no—
35#64672—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C22×C3×Dic5D411yescharacteristic
41C22×C3×Dic5D411yescharacteristic
42C2×C3×Dic10—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C3×C22⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×#683—21no—
53C3×#683—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63#6668—24no—
64Dic3×Dic5—42no—
65C3×#533—51no—
66C4×C4⋊Dic3—51no—
67#4925—51no—
68#4538—51no—
69#4538—51no—
70#4538—51no—
71#4538D511yescharacteristic
72C5×C22⋊Q8C2×D311yescharacteristic
73Q8×Dic5Dic311yescharacteristic, complemented
74#4090Dic311yescharacteristic, complemented
75#4070C2×D311yescharacteristic
76C2×#683—61no—
77C2×C4×Dic5—61no—
78C2×C4×Dic5C2×D311yescharacteristic
79#4035—21no—
80#4034Dic311yescharacteristic, complemented
81#4033—21no—
82#4033Dic311yescharacteristic, complemented
83#4024—21no—
84#4023—21no—
85C5×C22⋊C8—31no—
86C5×#95—31no—
87#3963—31no—
88C22⋊#168—31no—
89#3946—61no—
90C8×Dic5—61no—
91#1503—151noSylow
92C23×C3×C5C2×D411yescharacteristic
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—22no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102C2×C5×Dic3—22no—
103C2×C5×Dic3—41no—
104C2×C5×Dic3—41no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5SD1612yes—
113C2×C3×Dic5Q1612yes—
114C3×Dic10—42no—
115C3×Dic10—41no—
116C3⋊#168—41no—
117C5×C3⋊C8—41no—
118C3×C4⋊Q8—51no—
119C3×C4⋊Q8—51no—
120C3×#125—101no—
121C3×C22⋊Q8—51no—
122C3×C22⋊Q8—101no—
123C3×C22⋊Q8C2×D511yescharacteristic
124C3×C4×Q8—51no—
125C3×C4×Q8—51no—
126C3×C4×Q8—101no—
127C3×#117—101no—
128C2×C3×C42—51no—
129C2×C4⋊Dic3—101no—
130C2×C4×Dic3—101no—
131C3⋊#95—51no—
132C3⋊#95C2×D511yescharacteristic
133#830—51no—
134#830C2×D511yescharacteristic
135C4⋊(C3⋊C8)—101no—
136C4×C3⋊C8—101no—
137C2×C5×Q8C2×Dic311yescharacteristic
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—61no—
141C22×Dic5#6711yescharacteristic
142C22×Dic5#6711yescharacteristic
143C2×Dic10—21no—
144C2×Dic10C2×Dic311yescharacteristic
145C2×C5×C8—61no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4C2×Dic311yescharacteristic
148C5×C22⋊C4—21no—
149C22⋊Dic5—21no—
150C4⋊Dic5—21no—
151C4⋊Dic5C2×Dic311yescharacteristic
152#683—21no—
153#683—21no—
154#683—21no—
155#683—21no—
156#683—21no—
157#683—64no—
158C4×Dic5—21no—
159C4×Dic5—21no—
160C4×Dic5—122no—
161C4×Dic5C2×Dic311yescharacteristic
162C4×Dic5C2×Dic311yescharacteristic
163C4×Dic5#6711yescharacteristic
164C4×Dic5#6711yescharacteristic
165C2×#168—61no—
166#533—51no—
167#431—151no—
168C4×C4⋊C4—151no—
169#328—31no—
170#328—151no—
171#328—151no—
172#328—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5C2×Q1611yescharacteristic
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182Dic15—42no—
183C3×Dic5—21no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C3×Dic5#10312yes—
187C3×Dic5#10312yes—
188C3×Dic5#10412yes—
189C5×Dic3—42no—
190C2×C3×Q8—51no—
191C2×C3×Q8—101no—
192C2×C3×Q8C4×D511yescharacteristic
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—101no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—51no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
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×C42—51no—
210C3×C42—51no—
211C3×C42—51no—
212C3×C42—51no—
213C3×C42—101no—
214C3×C42—101no—
215C4⋊Dic3—104no—
216C4×Dic3—202no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—101no—
219C23×C5C2×#6711yescharacteristic
220C5×Q8—41no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—41no—
224C2×C4×C5—62no—
225C2×C4×C5—121no—
226C2×C4×C5—121no—
227C2×C4×C5C22×Dic311yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229C2×Dic5—22no—
230C2×Dic5—21no—
231C2×Dic5—21no—
232C2×Dic5—62no—
233C2×Dic5—121no—
234C2×Dic5—121no—
235C2×Dic5#21512yes—
236C2×Dic5#21612yes—
237C2×Dic5#21711yescharacteristic
238C2×Dic5#21711yescharacteristic
239C2×Dic5#21711yescharacteristic
240C2×Dic5#21711yescharacteristic
241Dic10—42no—
242Dic10—41no—
243C5×C8—121no—
244#168—121no—
245C4⋊Q8—51no—
246C4⋊Q8—51no—
247#125—101no—
248C22⋊Q8—51no—
249C22⋊Q8—101no—
250C22⋊Q8D3×D511yescharacteristic
251C4×Q8—51no—
252C4×Q8—51no—
253C4×Q8—101no—
254#117—101no—
255C2×C4⋊C4—301no—
256C2×C42—51no—
257C2×C42—301no—
258C4⋊C8—301no—
259C22⋊C8—31no—
260C22⋊C8—151no—
261C4×C8—301no—
262#95—31no—
263#95—151no—
264C2×C3×C5—21no—
265C2×C3×C5—21no—
266C2×C3×C5#41011yescharacteristic
267C2×C3×C5C2×#10311yescharacteristic
268C2×C3×C5C2×#10411yescharacteristic
269C23×C3D4×D511yescharacteristic
270C3×Q8—41no—
271C3×Q8—201no—
272C3×Q8—202no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—51no—
279C2×C3×C4—52no—
280C2×C3×C4—52no—
281C2×C3×C4—51no—
282C2×C3×C4—102no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4C2×C4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×Dic3—22no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—102no—
291C2×Dic3—201no—
292C2×Dic3—201no—
293C3⋊C8—41no—
294C3⋊C8—201no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5C2×#21511yescharacteristic
298C22×C5C2×#21611yescharacteristic
299C22×C5C2×#21711yescharacteristic
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—41no—
303C4×C5—41no—
304C4×C5—122no—
305Dic5—21no—
306Dic5—41no—
307Dic5—41no—
308Dic5—122no—
309Dic5#83512yes—
310Dic5#83512yes—
311Dic5#83712yes—
312C2×Q8—51no—
313C2×Q8—101no—
314C2×Q8D5×Dic311yescharacteristic
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—61no—
318C22×C4—301no—
319C22×C4C2×D3×D511yescharacteristic
320C2×C8—61no—
321C2×C8—301no—
322C4⋊C4—21no—
323C4⋊C4—51no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C4⋊C4—101no—
327C4⋊C4—101no—
328C4⋊C4—101no—
329C4⋊C4—101no—
330C4⋊C4—304no—
331C4⋊C4D5×Dic311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—101no—
334C42—51no—
335C42—51no—
336C42—51no—
337C42—51no—
338C42—101no—
339C42—101no—
340C42—602no—
341C3×C5#150311yescharacteristic, complemented, Hall
342C22×C3—21no—
343C22×C3—21no—
344C22×C3D5×C22⋊C411yescharacteristic
345C22×C3D5×SD1611yescharacteristic
346C22×C3D5×Q1611yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—52no—
352C3×C4—52no—
353C3×C4—52no—
354C3×C4—101no—
355C3×C4—201no—
356C3×C4—201no—
357Dic3—42no—
358Dic3—202no—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5C2×#83511yescharacteristic
362C2×C5C2×#83711yescharacteristic
363C2×C5#524011yescharacteristic
364C23D5×#6711yescharacteristic
365Q8—41no—
366Q8—201no—
367Q8—202no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—52no—
372C2×C4—52no—
373C2×C4—51no—
374C2×C4—51no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—62no—
378C2×C4—102no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—302no—
384C2×C4—601no—
385C2×C4—601no—
386C2×C4C2×D5×Dic311yescharacteristic
387C2×C4D5×#6711yescharacteristic
388C8—121no—
389C8—601no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3#6502911yescharacteristic
393C2×C3D5×#10311yescharacteristic
394C2×C3D5×#10411yescharacteristic
395C5#7183511yescharacteristic, complemented, Sylow
396C22—21no—
397C22—21no—
398C22D5×#21511yescharacteristic
399C22D5×#21611yescharacteristic
400C22D5×#21711yescharacteristic
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—52no—
406C4—52no—
407C4—52no—
408C4—101no—
409C4—122no—
410C4—201no—
411C4—201no—
412C4—602no—
413C3#1059910211yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2#1174917211yescharacteristic
417C2D5×#83511yescharacteristic
418C2D5×#83711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1503
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
10. C3×Q8×Dic5C4semidirect
11. C3×#4090C4semidirect
15. C3×#4034C4semidirect
17. C3×#4033C4semidirect
73. Q8×Dic5Dic3semidirect
74. #4090Dic3semidirect
80. #4034Dic3semidirect
82. #4033Dic3semidirect
341. C3×C5#1503semidirect
395. C5#71835semidirect
413. C3#10599102semidirect

Maximal subgroups

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

subgroupindex
C3×#659562
#117486382
#117483162
#117463592
C5×#45382
#117459612
#117459602
#105991023
#718355