Finite Group Databasebeta

← #14289714

Subgroups — #14289714

Order 1920.

376 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66055C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic
3#11746916C211yesmaximal, characteristic
4#11746916C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic
6#11745840C211yesmaximal, characteristic
7#11745840C211yesmaximal, characteristic
8#10599251—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×Q8×Dic5—21no—
12C3×#4090—21no—
13C3×#4036—21no—
14C3×#4035—22no—
15C3×#4033—21no—
16C3×C4×Dic10C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18#91094—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90990—21no—
23#90990—21no—
24#90971—21no—
25#90971—21no—
26#71936—51nomaximal, Hall
27#66055D311yescharacteristic
28#65382—31no—
29#65139—31no—
30#65139—31no—
31C5×#332—31no—
32#64704—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C3×Dic10D411yescharacteristic
37C2×C3×Dic10D411yescharacteristic
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D412yes—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C2×C3⋊#168—21no—
44C2×C5×C3⋊C8—21no—
45C2×C5×C3⋊C8—21no—
46C3×C4⋊Dic5—22no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—22no—
50C3×#683—22no—
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5—21no—
56C3×#557—51no—
57#5093—51no—
58#5021—51no—
59#5021—51no—
60#4547D511yescharacteristic
61#4535—51no—
62#4535—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64Q8×Dic5—21no—
65#4090—21no—
66#4036—21no—
67#4035—22no—
68#4033—21no—
69#4015—31no—
70C4×Dic10C2×D311yescharacteristic
71C4×Dic10C2×D311yescharacteristic
72C5×C4⋊C8—31no—
73C5×C4⋊C8—31no—
74#3950—61no—
75#3950—61no—
76#3948—61no—
77#3948—61no—
78#3942—62no—
79C4×#168—31no—
80#1636—151noSylow
81C3×C5×Q8—41no—
82C3×C5×Q8—41no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—41no—
88Dic30—42no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×Dic10—21no—
94C3×Dic10—21no—
95C3×Dic10—21no—
96C3×Dic10Q1612yes—
97C3⋊#168—41no—
98C5×C3⋊C8—41no—
99C5×C3⋊C8—41no—
100C3×C4⋊Q8—101no—
101C3×C4⋊Q8C2×D511yescharacteristic
102C3×#125—101no—
103C3×#125—102no—
104C3×C4×Q8—51no—
105C3×C4×Q8—51no—
106C3×C4×Q8—101no—
107C3×C4×Q8—101no—
108#869—51no—
109#835—101no—
110#835—101no—
111#810—102no—
112#807—101no—
113#807—101no—
114C4⋊(C3⋊C8)C2×D511yescharacteristic
115C4⋊(C3⋊C8)C2×D511yescharacteristic
116C4×C3⋊C8—51no—
117C2×C5×Q8—21no—
118C2×Dic10—61no—
119C2×Dic10#6711yescharacteristic
120C2×Dic10#6711yescharacteristic
121C2×C5×C8—61no—
122C2×C5×C8—61no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4#6712yes—
125C42×C5C22×D311yescharacteristic
126C4⋊Dic5—22no—
127C4⋊Dic5—61no—
128C4⋊Dic5—61no—
129C4⋊Dic5#6711yescharacteristic
130C4⋊Dic5#6711yescharacteristic
131#683—22no—
132#683—22no—
133#683—21no—
134#683—21no—
135C4×Dic5—22no—
136C4×Dic5—21no—
137C4×Dic5—21no—
138C2×#168—61no—
139#557—51no—
140#487—151no—
141#477—151no—
142#477—151no—
143#332—31no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—42no—
149C3×C4×C5C2×Q1611yescharacteristic
150C3×C4×C5#13511yescharacteristic
151C3×C4×C5#13711yescharacteristic
152C3×C4×C5#13711yescharacteristic
153Dic15—81no—
154C3×Dic5—22no—
155C3×Dic5—41no—
156C3×Dic5—41no—
157C3×Dic5—41no—
158C2×C3×Q8—21no—
159C2×C3×Q8—51no—
160C2×C3×Q8—51no—
161C2×Dic6—101no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—51no—
164C3×C4⋊C4—51no—
165C3×C4⋊C4—102no—
166C3×C4⋊C4—102no—
167C3×C4⋊C4—102no—
168C3×C4⋊C4—101no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4D2012yes—
171C3×C42—102no—
172C3×C42—101no—
173C3×C42—101no—
174C3×C42C22×D511yescharacteristic
175C4⋊Dic3—101no—
176C4⋊Dic3—101no—
177C2×C3⋊C8—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—101no—
180C5×Q8—41no—
181C5×Q8—41no—
182C2×C4×C5—22no—
183C2×C4×C5C2×#6711yescharacteristic
184C2×C4×C5C2×#6711yescharacteristic
185C2×C4×C5C2×#6711yescharacteristic
186C2×Dic5—21no—
187C2×Dic5—21no—
188C2×Dic5—21no—
189C2×Dic5—21no—
190C2×Dic5—121no—
191Dic10—21no—
192Dic10—21no—
193Dic10—21no—
194Dic10—122no—
195Dic10#21612yes—
196C5×C8—121no—
197C5×C8—121no—
198#168—121no—
199C4⋊Q8—101no—
200C4⋊Q8—151no—
201C4⋊Q8D3×D511yescharacteristic
202#125—101no—
203#125—102no—
204C4×Q8—51no—
205C4×Q8—51no—
206C4×Q8—101no—
207C4×Q8—101no—
208#107—301no—
209#107—301no—
210C4⋊C8—31no—
211C4⋊C8—31no—
212#103—301no—
213#103—301no—
214#103—302no—
215C4×C8—151no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—52no—
222C3×Q8—101no—
223C3×Q8—101no—
224C3×Q8—101no—
225C2×C3×C4—22no—
226C2×C3×C4—101no—
227C2×C3×C4—101no—
228C2×C3×C4—101no—
229C2×C3×C4—101no—
230C2×C3×C4C2×D2011yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×Dic3—201no—
234Dic6—202no—
235C3⋊C8—41no—
236C3⋊C8—41no—
237C3⋊C8—201no—
238C22×C5#95311yescharacteristic
239C4×C5—21no—
240C4×C5—42no—
241C4×C5#94211yescharacteristic
242C4×C5C2×#21611yescharacteristic
243C4×C5#95011yescharacteristic
244C4×C5#95111yescharacteristic
245Dic5—22no—
246Dic5—41no—
247Dic5—41no—
248Dic5—41no—
249Dic5—241no—
250C2×Q8—21no—
251C2×Q8—51no—
252C2×Q8—51no—
253C2×Q8—301no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—51no—
259C4⋊C4—51no—
260C4⋊C4—102no—
261C4⋊C4—102no—
262C4⋊C4—102no—
263C4⋊C4—101no—
264C4⋊C4—101no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#120212yes—
268C42—102no—
269C42—101no—
270C42—101no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#402811yescharacteristic
274C3×C4—21no—
275C3×C4—42no—
276C3×C4—102no—
277C3×C4—201no—
278C3×C4—201no—
279C3×C4—201no—
280C3×C4#405811yescharacteristic
281C3×C4#406111yescharacteristic
282C3×C4#406111yescharacteristic
283C3×C4D5×Q1611yescharacteristic
284Dic3—401no—
285C2×C5#522811yescharacteristic
286C2×C5#523911yescharacteristic
287C2×C5#524511yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—52no—
291Q8—101no—
292Q8—101no—
293Q8—101no—
294Q8—602no—
295C2×C4—22no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—601no—
301C2×C4C2×#120211yescharacteristic
302C2×C4D5×#6711yescharacteristic
303C2×C4D5×#6711yescharacteristic
304C8—121no—
305C8—121no—
306C8—601no—
307C2×C3#6504211yescharacteristic
308C2×C3#6507211yescharacteristic
309C2×C3#6509711yescharacteristic
310C5#7193611yescharacteristic, complemented, Sylow
311C22#9156411yescharacteristic
312C4—21no—
313C4—42no—
314C4—102no—
315C4—201no—
316C4—201no—
317C4—201no—
318C4—1201no—
319C4#9148411yescharacteristic
320C4#9149011yescharacteristic
321C4D5×#21611yescharacteristic
322C4#9151311yescharacteristic
323C3#1059925111yescharacteristic, complemented, Sylow
324C2#1174904911yescharacteristic
325C2#1174929111yescharacteristic
326C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1636
LCSG ▷ C3×C42×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
272. C3×C5#1636semidirect
310. C5#71936semidirect
323. C3#10599251semidirect

Maximal subgroups

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

subgroupindex
C3×#660552
#117511942
#117469162
C5×#45472
#117458402
#105992513
#719365