Finite Group Databasebeta

← #14285264

Subgroups — #14285264

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2#11746871C211yesmaximal, characteristic
3#11746871C211yesmaximal, characteristic
4#11746368C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599221—31nomaximal, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4090—21no—
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C412yes—
14C3×#4034—21no—
15C3×#4034C412yes—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90955—21no—
23#90955—21no—
24#90952—21no—
25#90952—21no—
26#71776—51nomaximal, Hall
27D5×C4⋊Q8D311yescharacteristic
28#65124—31no—
29#65124—31no—
30C5×#332—31no—
31#64767—31no—
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C3×Q8×D5—42no—
36C3×Q8×D5—42no—
37C2×C3×C4×D5—22no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×Dic10—21no—
42C2×C3×Dic10—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C412yes—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5C2×C412yes—
52C3×#683—22no—
53C3×#683—22no—
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57C2×C3×C4⋊Q8—51no—
58#4926—51no—
59#4926—51no—
60#4547—51no—
61#4547—51no—
62#4547—51no—
63#4547D511yescharacteristic, complemented
64C2×Q8×D5—21no—
65C5×C4⋊Q8C2×D311yescharacteristic
66#4090—21no—
67D5×C4⋊C4—21no—
68D5×C4⋊C4Dic312yes—
69#4034—21no—
70#4034Dic312yes—
71C42×D5C2×D311yescharacteristic
72#4015C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3952—61no—
77#3947—61no—
78#3947—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1556—151noSylow
82C22×C3×D5C22⋊C411yescharacteristic
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×Dic5—22no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C3×C4×D5—22no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—44no—
99C3×Dic10—44no—
100C3×Dic10—41no—
101C3×Dic10—41no—
102C3⋊#168—41no—
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C22×C3×Q8—101no—
107C3×C4⋊Q8—52no—
108C3×C4⋊Q8—51no—
109C3×C4⋊Q8—101no—
110C3×C4⋊Q8—101no—
111C3×C4⋊Q8C2×D511yescharacteristic
112C2×C3×C4⋊C4—52no—
113C2×C3×C4⋊C4—101no—
114C2×C3×C42—51no—
115#830—101no—
116#830—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121#803—101no—
122#803—101no—
123C2×C5×Q8—21no—
124Q8×D5—42no—
125Q8×D5—42no—
126C2×C4×D5—22no—
127C2×C4×D5C2×Dic311yescharacteristic
128C2×C4×D5#6711yescharacteristic
129C2×C4×D5#6711yescharacteristic
130C2×Dic10—21no—
131C2×Dic10—22no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C2×Dic312yes—
136C42×C5C22×D311yescharacteristic
137C4⋊Dic5—21no—
138C4⋊Dic5C2×Dic312yes—
139#683—22no—
140#683—22no—
141C4×Dic5C2×Dic311yescharacteristic
142C4×Dic5#6711yescharacteristic
143C4×Dic5#6711yescharacteristic
144C2×#168—61no—
145C2×#168—61no—
146C2×C4⋊Q8—51no—
147#432—151no—
148#432—151no—
149#332—31no—
150#332—151no—
151#332—151no—
152#332—151no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5#10112yes—
157C3×C4×C5—21no—
158C3×C4×C5—42no—
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—42no—
167C2×C3×Q8—21no—
168C2×C3×Q8—102no—
169C2×C3×Q8—101no—
170C2×C3×Q8—202no—
171C2×C3×Q8—202no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4—102no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—52no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4C4×D512yes—
182C3×C42—51no—
183C3×C42—51no—
184C3×C42—51no—
185C3×C42C22×D511yescharacteristic
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—101no—
189C2×C3⋊C8—101no—
190C22×D5#21711yescharacteristic
191C5×Q8—41no—
192C5×Q8—41no—
193C2×C4×C5—22no—
194C2×C4×C5C22×Dic311yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—22no—
198C2×Dic5#21711yescharacteristic
199C2×Dic5#21711yescharacteristic
200C2×Dic5#21711yescharacteristic
201C4×D5—22no—
202C4×D5—21no—
203C4×D5—21no—
204C4×D5—21no—
205C4×D5—21no—
206C4×D5—44no—
207Dic10—44no—
208Dic10—41no—
209Dic10—41no—
210C5×C8—121no—
211C5×C8—121no—
212#168—121no—
213#168—121no—
214C22×Q8—101no—
215C4⋊Q8—52no—
216C4⋊Q8—51no—
217C4⋊Q8—101no—
218C4⋊Q8—101no—
219C4⋊Q8D3×D511yescharacteristic
220C2×C4⋊C4—52no—
221C2×C4⋊C4—101no—
222C2×C42—51no—
223C4⋊C8—31no—
224C4⋊C8—31no—
225C4⋊C8—151no—
226C4⋊C8—151no—
227C22⋊C8—301no—
228C22⋊C8—301no—
229#97—301no—
230#97—301no—
231C2×C3×C5C2×#10111yescharacteristic
232C2×C3×C5#41811yescharacteristic
233C2×C3×C5#41911yescharacteristic
234C3×D5—22no—
235C23×C3—51no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×Q8—204no—
239C3×Q8—201no—
240C3×Q8—201no—
241C2×C3×C4—22no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—102no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—102no—
251C2×C3×C4—204no—
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C3⋊C8—41no—
256C3⋊C8—41no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5C2×#21711yescharacteristic
260C2×D5—21no—
261C2×D5—21no—
262C2×D5#83612yes—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5#93211yescharacteristic
266C4×C5#93211yescharacteristic
267C4×C5#94211yescharacteristic
268C4×C5#94211yescharacteristic
269Dic5—21no—
270Dic5—21no—
271Dic5—21no—
272Dic5—42no—
273C2×Q8—21no—
274C2×Q8—102no—
275C2×Q8—101no—
276C2×Q8—202no—
277C2×Q8—202no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—102no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—301no—
285C2×C8—301no—
286C4⋊C4—21no—
287C4⋊C4—52no—
288C4⋊C4—102no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4D5×Dic312yes—
292C42—51no—
293C42—51no—
294C42—51no—
295C42C2×D3×D511yescharacteristic
296C3×C5#155611yescharacteristic, complemented, Hall
297C22×C3—52no—
298C22×C3—101no—
299C22×C3—101no—
300C22×C3D5×C22⋊C411yescharacteristic
301C3×C4—21no—
302C3×C4—42no—
303C3×C4—101no—
304C3×C4—101no—
305C3×C4—101no—
306C3×C4—202no—
307C3×C4#405711yescharacteristic
308C3×C4#406011yescharacteristic
309C3×C4#406111yescharacteristic
310C3×C4#406411yescharacteristic
311C2×C5#521511yescharacteristic
312C2×C5#522511yescharacteristic
313C2×C5C2×#83611yescharacteristic
314D5—22no—
315C23—51no—
316Q8—41no—
317Q8—41no—
318Q8—204no—
319Q8—201no—
320Q8—201no—
321C2×C4—22no—
322C2×C4—51no—
323C2×C4—51no—
324C2×C4—51no—
325C2×C4—102no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—102no—
331C2×C4—204no—
332C2×C4C2×D5×Dic311yescharacteristic
333C2×C4D5×#6711yescharacteristic
334C2×C4D5×#6711yescharacteristic
335C8—121no—
336C8—121no—
337C8—601no—
338C8—601no—
339C2×C3—102no—
340C2×C3D5×#10111yescharacteristic
341C2×C3#6505911yescharacteristic
342C2×C3#6509111yescharacteristic
343C5#7177611yescharacteristic, complemented, Sylow
344C22—52no—
345C22—101no—
346C22—101no—
347C22D5×#21711yescharacteristic
348C4—21no—
349C4—42no—
350C4—101no—
351C4—101no—
352C4—101no—
353C4—202no—
354C4#9148911yescharacteristic
355C4#9149111yescharacteristic
356C4#9151311yescharacteristic
357C4#9151511yescharacteristic
358C3#1059922111yescharacteristic, complemented, Sylow
359C2—102no—
360C2#1174896211yescharacteristic
361C2#1174920811yescharacteristic
362C2D5×#83611yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1556
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746368C2semidirect
5. C5×#4547C2semidirect
6. #11745856C2semidirect
7. #11745855C2semidirect
63. #4547D5semidirect
296. C3×C5#1556semidirect
343. C5#71776semidirect
358. C3#10599221semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
#117468712
#117463682
C5×#45472
#117458562
#117458552
#105992213
#717765