Finite Group Databasebeta

← #14289704

Subgroups — #14289704

Order 1920.

376 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#11752477C211yesmaximal, characteristic
2#11751192C211yesmaximal, characteristic
3C5×#5079C211yesmaximal, characteristic
4C3×#65380C211yesmaximal, characteristic
5#11745857C211yesmaximal, characteristic
6#11745844C211yesmaximal, characteristic
7#11745841C211yesmaximal, characteristic
8#10602029—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91384—21no—
14#91376—21no—
15#91335—22no—
16Dic5×Dic6—21no—
17#91331—21no—
18#91094—21no—
19#91091—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#835—22no—
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71158—51nomaximal, Hall
27#66055—31no—
28C5×#487—31no—
29#65380—31no—
30#65380D311yescharacteristic
31#64767—31no—
32#64676—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6—21no—
37C2×C3×Dic10D411yescharacteristic
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15D411yescharacteristic
42#6712—21no—
43C4×Dic15—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D412yes—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—21no—
50C3×C4×Dic5—21no—
51C2×C3×#168—21no—
52Dic3⋊Dic5—22no—
53#6668—22no—
54#6668—22no—
55Dic3×Dic5—22no—
56#5570—51no—
57C3×#477—51no—
58#5091—51no—
59#5079D511yescharacteristic
60#4535—51no—
61#4486—51no—
62#4484—51no—
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8C2×D311yescharacteristic
65Q8×Dic5—61no—
66#4090—61no—
67#4036—61no—
68#4035—62no—
69#4033—61no—
70C4×Dic10—31no—
71C4×Dic10C2×D311yescharacteristic
72C5×#103—62no—
73C4×C5×C8—31no—
74#3942—21no—
75#3942—61no—
76#3939—21no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1636—151noSylow
81C3×C5×Q8—42no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C2×C5×Dic3—22no—
91C5×Dic6—41no—
92C5×Dic6—41no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×Dic10—21no—
96C3×Dic10Q1612yes—
97C3⋊#168—41no—
98C3×#168—41no—
99C5×C3⋊C8—41no—
100C3×C4⋊Q8C2×D511yescharacteristic
101C3×C4×Q8—51no—
102Q8×Dic3—101no—
103#890—101no—
104#890—102no—
105#869—101no—
106#869C2×D511yescharacteristic
107C4×Dic6—51no—
108C4×Dic6—101no—
109C3×#107—101no—
110C3×C4⋊C8—51no—
111C3×#103—101no—
112#835—22no—
113#810—101no—
114#807—101no—
115C4⋊(C3⋊C8)—51no—
116C4×C3⋊C8C2×D511yescharacteristic
117C2×C5×Q8—21no—
118C2×C5×Q8—61no—
119C2×Dic10—31no—
120C2×Dic10#6711yescharacteristic
121C2×C5×C8—61no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—32no—
125C5×C4⋊C4—61no—
126C42×C5C22×D311yescharacteristic
127C4⋊Dic5—31no—
128C4⋊Dic5—62no—
129C4⋊Dic5#6711yescharacteristic
130#683—21no—
131#683—62no—
132#683—62no—
133#683—61no—
134C4×Dic5—21no—
135C4×Dic5—62no—
136C4×Dic5—61no—
137C2×#168—21no—
138C2×#168—61no—
139#557—151no—
140#487—31no—
141#477—51no—
142#477—151no—
143#332—151no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—81no—
149C3×C4×C5C2×Q1611yescharacteristic
150C3×C4×C5#13511yescharacteristic
151C3×C4×C5#13711yescharacteristic
152C3×C4×C5#13711yescharacteristic
153Dic15—41no—
154Dic15—41no—
155C3×Dic5—22no—
156C3×Dic5—41no—
157C5×Dic3—42no—
158C2×C3×Q8—21no—
159C2×C3×Q8—51no—
160C2×Dic6—21no—
161C2×Dic6—51no—
162C2×C3×C8—101no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—51no—
166C3×C4⋊C4—101no—
167C3×C42—101no—
168C3×C42C22×D511yescharacteristic
169C4⋊Dic3—21no—
170C4⋊Dic3—51no—
171C4⋊Dic3—102no—
172C4⋊Dic3—102no—
173C4⋊Dic3C22⋊D512yes—
174Dic3⋊C4—102no—
175Dic3⋊C4—101no—
176C4×Dic3—102no—
177C4×Dic3—101no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—101no—
180C5×Q8—42no—
181C5×Q8—121no—
182C5×Q8—121no—
183C2×C4×C5—41no—
184C2×C4×C5—62no—
185C2×C4×C5D3×D411yescharacteristic
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5C2×#6711yescharacteristic
188C2×Dic5—21no—
189C2×Dic5—21no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192Dic10—21no—
193Dic10—61no—
194Dic10—61no—
195Dic10#21612yes—
196C5×C8—121no—
197#168—41no—
198#168—121no—
199C4⋊Q8—31no—
200C4⋊Q8—301no—
201C4⋊Q8D3×D511yescharacteristic
202#125—302no—
203#125—301no—
204C4×Q8—51no—
205C4×Q8—151no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—101no—
209#107—301no—
210C4⋊C8—51no—
211C4⋊C8—151no—
212#103—62no—
213#103—101no—
214#103—301no—
215C4×C8—31no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—42no—
220C3×Q8—52no—
221C3×Q8—101no—
222C2×C3×C4—41no—
223C2×C3×C4—101no—
224C2×C3×C4—101no—
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4D4×D511yescharacteristic
227C2×C3×C4C2×C22⋊D511yescharacteristic
228C2×Dic3—22no—
229C2×Dic3—101no—
230C2×Dic3—101no—
231Dic6—41no—
232Dic6—41no—
233Dic6—101no—
234Dic6—101no—
235C3×C8—201no—
236C3⋊C8—41no—
237C3⋊C8—201no—
238C22×C5#93711yescharacteristic
239C4×C5—21no—
240C4×C5—81no—
241C4×C5—122no—
242C4×C5#91811yescharacteristic
243C4×C5#91911yescharacteristic
244C4×C5C2×#21611yescharacteristic
245C4×C5#95111yescharacteristic
246Dic5—22no—
247Dic5—41no—
248Dic5—121no—
249Dic5—121no—
250C2×Q8—21no—
251C2×Q8—51no—
252C2×Q8—61no—
253C2×Q8—151no—
254C2×C8—61no—
255C2×C8—101no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—32no—
260C4⋊C4—51no—
261C4⋊C4—61no—
262C4⋊C4—101no—
263C4⋊C4—151no—
264C4⋊C4—302no—
265C4⋊C4—302no—
266C4⋊C4—302no—
267C4⋊C4—301no—
268C42—101no—
269C42—302no—
270C42—301no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—81no—
276C3×C4—102no—
277C3×C4—201no—
278C3×C4#406111yescharacteristic
279C3×C4#406211yescharacteristic
280C3×C4D5×Q1611yescharacteristic
281C3×C4#406411yescharacteristic
282Dic3—42no—
283Dic3—201no—
284Dic3—201no—
285C2×C5#505011yescharacteristic
286C2×C5#518711yescharacteristic
287C2×C5#520111yescharacteristic
288Q8—42no—
289Q8—52no—
290Q8—101no—
291Q8—121no—
292Q8—121no—
293Q8—301no—
294Q8—301no—
295C2×C4—41no—
296C2×C4—62no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—301no—
300C2×C4—301no—
301C2×C4D5×#6711yescharacteristic
302C2×C4D3×C22⋊D511yescharacteristic
303C2×C4#679011yescharacteristic
304C8—121no—
305C8—201no—
306C8—601no—
307C2×C3#6535111yescharacteristic
308C2×C3#6546211yescharacteristic
309C2×C3#6547511yescharacteristic
310C5#7115811yescharacteristic, complemented, Sylow
311C22#9157711yescharacteristic
312C4—21no—
313C4—81no—
314C4—102no—
315C4—122no—
316C4—201no—
317C4—601no—
318C4—601no—
319C4D5×#21611yescharacteristic
320C4#9150811yescharacteristic
321C4#9152311yescharacteristic
322C4#9152411yescharacteristic
323C3#1060202911yescharacteristic, complemented, Sylow
324C2#1174916711yescharacteristic
325C2#1174940011yescharacteristic
326C2#1174940711yescharacteristic
subgroupG/H
centerC22#91577
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#71158semidirect
323. C3#10602029semidirect

Maximal subgroups

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

subgroupindex
#117524772
#117511922
C5×#50792
C3×#653802
#117458572
#117458442
#117458412
#106020293
#711585