Finite Group Databasebeta

← #14289713

Subgroups — #14289713

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#11756480C211yesmaximal, characteristic
2C3×#65382C211yesmaximal, characteristic
3#11746917C211yesmaximal, characteristic
4#11746917C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic
6#11745845C211yesmaximal, characteristic
7#11745845C211yesmaximal, characteristic
8#10599251—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10Q8×Dic15—21no—
11#91833—21no—
12#91779—21no—
13#91778—22no—
14#91776—21no—
15C4×Dic30C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×#3942—22no—
21C3×C4×#168C2211yescharacteristic
22#90990—21no—
23#90990—21no—
24#90974—21no—
25#90974—21no—
26#71236—51nomaximal, Hall
27#66055—31no—
28#65382D311yescharacteristic
29#65139—31no—
30#65139—31no—
31C5×#332—31no—
32#64704—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×Dic30D411yescharacteristic
37C2×C3×Dic10—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D412yes—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—22no—
42C4⋊Dic15D411yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—22no—
45#6712—22no—
46#6712—21no—
47#6712—21no—
48C4×Dic15—22no—
49C4×Dic15—21no—
50C4×Dic15—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#5721—51no—
57C3×#487—51no—
58#5091—51no—
59#5091—51no—
60#4547D511yescharacteristic
61#4456—51no—
62#4456—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64Q8×Dic5—61no—
65#4090—61no—
66#4036—61no—
67#4035—62no—
68#4033—61no—
69#4015C2×D311yescharacteristic
70C4×Dic10—31no—
71C4×Dic10—31no—
72C5×C4⋊C8—31no—
73C5×C4⋊C8—31no—
74#3950—61no—
75#3950—61no—
76#3948—61no—
77#3948—61no—
78#3942—22no—
79C4×#168C2×D311yescharacteristic
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—21no—
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30—21no—
93Dic30—21no—
94Dic30Q1612yes—
95C2×C3×Dic5—41no—
96C3×Dic10—42no—
97C3×#168—41no—
98C5×C3⋊C8—41no—
99C5×C3⋊C8—41no—
100C3×C4⋊Q8—51no—
101C3×C4⋊Q8C2×D511yescharacteristic
102Q8×Dic3—101no—
103#944—101no—
104#890—101no—
105#889—102no—
106#887—101no—
107C4×Dic6—51no—
108C4×Dic6—51no—
109C3×#103—102no—
110C3×C4×C8—51no—
111#810—101no—
112#810—101no—
113#807—101no—
114#807—101no—
115C4⋊(C3⋊C8)C2×D511yescharacteristic
116C4⋊(C3⋊C8)C2×D511yescharacteristic
117C2×C5×Q8—21no—
118C2×Dic10—21no—
119C2×Dic10—31no—
120C2×Dic10—31no—
121C2×C5×C8—61no—
122C2×C5×C8—61no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4#6712yes—
125C42×C5C22×D311yescharacteristic
126C4⋊Dic5—21no—
127C4⋊Dic5—21no—
128C4⋊Dic5—31no—
129C4⋊Dic5—31no—
130C4⋊Dic5—62no—
131#683—62no—
132#683—62no—
133#683—61no—
134#683—61no—
135C4×Dic5—62no—
136C4×Dic5—61no—
137C4×Dic5—61no—
138C2×#168—21no—
139#557—151no—
140#487—51no—
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—22no—
154Dic15—41no—
155Dic15—41no—
156Dic15—41no—
157C3×Dic5—81no—
158C2×C3×Q8—21no—
159C2×C3×Q8—101no—
160C2×Dic6—51no—
161C2×Dic6—51no—
162C2×C3×C8—101no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—101no—
165C3×C4⋊C4—101no—
166C3×C4⋊C4D2012yes—
167C3×C42C22×D511yescharacteristic
168C4⋊Dic3—51no—
169C4⋊Dic3—51no—
170C4⋊Dic3—102no—
171Dic3⋊C4—102no—
172Dic3⋊C4—102no—
173Dic3⋊C4—101no—
174Dic3⋊C4—101no—
175C4×Dic3—102no—
176C4×Dic3—101no—
177C4×Dic3—101no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C5×Q8—41no—
181C5×Q8—41no—
182C2×C4×C5—22no—
183C2×C4×C5D3×D411yescharacteristic
184C2×C4×C5D3×D411yescharacteristic
185C2×C4×C5C2×#6711yescharacteristic
186C2×Dic5—41no—
187C2×Dic5—61no—
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5—61no—
191Dic10—32no—
192Dic10—42no—
193Dic10—61no—
194Dic10—61no—
195Dic10—61no—
196C5×C8—121no—
197C5×C8—121no—
198#168—41no—
199C4⋊Q8—51no—
200C4⋊Q8—301no—
201C4⋊Q8D3×D511yescharacteristic
202#125—301no—
203#125—302no—
204C4×Q8—151no—
205C4×Q8—151no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—301no—
209#107—301no—
210C4⋊C8—31no—
211C4⋊C8—31no—
212#103—102no—
213#103—301no—
214#103—301no—
215C4×C8—51no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—202no—
222C2×C3×C4—22no—
223C2×C3×C4—201no—
224C2×C3×C4C2×D2011yescharacteristic
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4D4×D511yescharacteristic
227C2×Dic3—101no—
228C2×Dic3—101no—
229C2×Dic3—101no—
230C2×Dic3—101no—
231Dic6—52no—
232Dic6—101no—
233Dic6—101no—
234Dic6—101no—
235C3×C8—201no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C22×C5#93711yescharacteristic
239C4×C5—21no—
240C4×C5—42no—
241C4×C5#91511yescharacteristic
242C4×C5#91611yescharacteristic
243C4×C5D3×Q1611yescharacteristic
244C4×C5#91811yescharacteristic
245Dic5—62no—
246Dic5—81no—
247Dic5—121no—
248Dic5—121no—
249Dic5—121no—
250C2×Q8—21no—
251C2×Q8—101no—
252C2×Q8—151no—
253C2×Q8—151no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—101no—
257C4⋊C4—21no—
258C4⋊C4—101no—
259C4⋊C4—101no—
260C4⋊C4—151no—
261C4⋊C4—151no—
262C4⋊C4—302no—
263C4⋊C4—302no—
264C4⋊C4—302no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#120212yes—
268C42—302no—
269C42—301no—
270C42—301no—
271C42C2×D3×D511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#402811yescharacteristic
274C3×C4—21no—
275C3×C4—42no—
276C3×C4—401no—
277C3×C4#405811yescharacteristic
278C3×C4#406111yescharacteristic
279C3×C4#406111yescharacteristic
280C3×C4D5×Q1611yescharacteristic
281Dic3—102no—
282Dic3—201no—
283Dic3—201no—
284Dic3—201no—
285C2×C5#506211yescharacteristic
286C2×C5#517311yescharacteristic
287C2×C5#518611yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—152no—
291Q8—202no—
292Q8—301no—
293Q8—301no—
294Q8—301no—
295C2×C4—22no—
296C2×C4—201no—
297C2×C4—301no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—301no—
301C2×C4C2×#120211yescharacteristic
302C2×C4#679011yescharacteristic
303C2×C4#679011yescharacteristic
304C8—121no—
305C8—121no—
306C8—201no—
307C2×C3#6504211yescharacteristic
308C2×C3#6507211yescharacteristic
309C2×C3#6509711yescharacteristic
310C5#7123611yescharacteristic, complemented, Sylow
311C22#9157211yescharacteristic
312C4—21no—
313C4—42no—
314C4—302no—
315C4—401no—
316C4—601no—
317C4—601no—
318C4—601no—
319C4#9148811yescharacteristic
320C4#9149911yescharacteristic
321C4#9151111yescharacteristic
322C4#9152411yescharacteristic
323C3#1059925111yescharacteristic, complemented, Sylow
324C2#1174906311yescharacteristic
325C2#1174931011yescharacteristic
326C2#1174938811yescharacteristic
subgroupG/H
centerC22#91572
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#71236semidirect
323. C3#10599251semidirect

Maximal subgroups

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

subgroupindex
#117564802
C3×#653822
#117469172
C5×#45472
#117458452
#105992513
#712365