Finite Group Databasebeta

← #14291450

Subgroups — #14291450

Order 1920.

376 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 87 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#11751176C211yesmaximal, characteristic, complemented
2#11751174C211yesmaximal, characteristic
3#11750949C211yesmaximal, characteristic, complemented
4#11750931C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746300C211yesmaximal, characteristic, complemented
8#10599202—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6716—21no—
11C2×#6715—21no—
12C2×#6715—21no—
13C2×#6706—21no—
14#91763C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18#91116—21no—
19#91105—21no—
20#91098—21no—
21C8×Dic15—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68409—51nomaximal, Hall
25#65364—31no—
26#65362—31no—
27#65137—31no—
28#65119—31no—
29C5×#331D311yescharacteristic, complemented
30#64705—31no—
31#64699—31no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42#6716—42no—
43#6715—42no—
44#6715—42no—
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C2×C3⋊#168D411yescharacteristic
50C2×C3⋊#168D411yescharacteristic
51#6706—42no—
52#5075—51no—
53#5073—51no—
54#4848—51no—
55#4830—51no—
56C3×#331D511yescharacteristic, complemented
57#4485—51no—
58#4479—51no—
59C5×#127C2×D311yescharacteristic
60C2×#687—61no—
61C2×#686—61no—
62C2×#686—61no—
63C2×#677—61no—
64#4020—31no—
65C4×Dic10—31no—
66C5×C4⋊C8C2×D311yescharacteristic
67C5×C4⋊C8C2×D311yescharacteristic
68#3964—61no—
69#3953—61no—
70#3946—61no—
71C8×Dic5—61no—
72C4⋊#168—31no—
73C4×#168—31no—
74#1668—151noSylow
75C23×C3×C5—41no—
76C22×D15—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—81no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87D60—41no—
88D60—41no—
89D60—41no—
90D60—41no—
91D60—81no—
92Dic30—21no—
93Dic30D812yescomplemented
94C3×C5×C8—41no—
95C3×C5×C8—41no—
96C3⋊#168—21no—
97C3⋊#168—41no—
98C3⋊#168SD1612yescomplemented
99C3×#127C2×D511yescharacteristic
100C2×#214—101no—
101C2×#213—101no—
102C2×#213—101no—
103C2×#204—101no—
104#874—51no—
105C4×Dic6—51no—
106C3×C4⋊C8C2×D511yescharacteristic
107C3×C4⋊C8C2×D511yescharacteristic
108#832—101no—
109#821—101no—
110Dic3⋊C8—101no—
111C8×Dic3—101no—
112C4⋊(C3⋊C8)—51no—
113C4×C3⋊C8—51no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×D20—61no—
118C2×D20—61no—
119C2×D20—61no—
120C2×Dic10—31no—
121C2×C5×C8—21no—
122C2×C5×C8—21no—
123C42×C5C22×D311yescharacteristic
124#687—122no—
125#686—122no—
126#686—122no—
127C4⋊Dic5—31no—
128#683—61no—
129C4×Dic5—61no—
130C2×#168—31no—
131C2×#168—31no—
132C2×#168—61no—
133#677—122no—
134#493—151no—
135#460—151no—
136#460—151no—
137C8×Q8—151no—
138#335—151no—
139#331—151no—
140#331D1511yescharacteristic, complemented
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5—81no—
144C22×C3×C5#12111yescharacteristic
145C2×D15—81no—
146C2×D15—81no—
147C2×D15—81no—
148C3×C4×C5—21no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5C2×SD1611yescharacteristic
151C3×C4×C5#13511yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153Dic15—22no—
154Dic15—41no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×D12—101no—
159C2×D12—101no—
160C2×D12—101no—
161C2×Dic6—51no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C3×C42C22×D511yescharacteristic
165#214—202no—
166#213—202no—
167#213—202no—
168C4⋊Dic3—51no—
169Dic3⋊C4—101no—
170C4×Dic3—101no—
171C2×C3⋊C8—51no—
172C2×C3⋊C8—51no—
173C2×C3⋊C8—101no—
174#204—202no—
175C23×C5—41no—
176C22×D5—121no—
177C5×D4—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—81no—
182C2×C4×C5#23511yescharacteristic
183C2×C4×C5D3×D411yescharacteristic
184C2×C4×C5D3×D411yescharacteristic
185C2×Dic5—61no—
186C2×Dic5—61no—
187D20—121no—
188D20—121no—
189D20—121no—
190D20—121no—
191D20—241no—
192Dic10—32no—
193Dic10—61no—
194C5×C8—41no—
195C5×C8—41no—
196#168—32no—
197#168—61no—
198#168—121no—
199C2×SD16—301no—
200C2×SD16—301no—
201C2×D8—301no—
202C2×D8—301no—
203#127—151no—
204#127C2×D1511yescharacteristic
205C4×Q8—151no—
206C4⋊C8—151no—
207C4⋊C8—301no—
208C4⋊C8C2×D1511yescharacteristic
209C4⋊C8C2×D1511yescharacteristic
210#102—301no—
211#102—301no—
212C4×C8—151no—
213C4×C8—301no—
214C2×C3×C5—161no—
215C2×C3×C5#46011yescharacteristic
216C2×C3×C5#46611yescharacteristic
217C2×C3×C5#47211yescharacteristic
218D15—161no—
219C23×C3—41no—
220C22×D3—201no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—81no—
226C2×C3×C4#70911yescharacteristic
227C2×C3×C4D4×D511yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×Dic3—101no—
230C2×Dic3—101no—
231D12—201no—
232D12—201no—
233D12—201no—
234D12—201no—
235D12—401no—
236Dic6—52no—
237Dic6—101no—
238C3×C8—41no—
239C3×C8—41no—
240C3⋊C8—52no—
241C3⋊C8—101no—
242C3⋊C8—201no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5#88411yescharacteristic
247C2×D5—241no—
248C2×D5—241no—
249C2×D5—241no—
250C4×C5—21no—
251C4×C5D3×D811yescharacteristic
252C4×C5#91111yescharacteristic
253C4×C5D3×SD1611yescharacteristic
254C4×C5#91611yescharacteristic
255Dic5—62no—
256Dic5—121no—
257C2×Q8—151no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—301no—
262C2×D4—301no—
263C2×D4—301no—
264SD16—602no—
265SD16—602no—
266D8—602no—
267D8—602no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—151no—
271C2×C8—151no—
272C2×C8—301no—
273C4⋊C4—151no—
274C4⋊C4—301no—
275C42—301no—
276C42C22×D1511yescharacteristic
277C3×C5#166811yescharacteristic, complemented, Hall
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3#403011yescharacteristic
282C2×D3—401no—
283C2×D3—401no—
284C2×D3—401no—
285C3×C4—21no—
286C3×C4D5×D811yescharacteristic
287C3×C4#405711yescharacteristic
288C3×C4D5×SD1611yescharacteristic
289C3×C4#406211yescharacteristic
290Dic3—102no—
291Dic3—201no—
292C2×C5—161no—
293C2×C5#474911yescharacteristic
294C2×C5#476211yescharacteristic
295C2×C5#477511yescharacteristic
296D5—481no—
297C23—41no—
298C23—601no—
299Q8—152no—
300Q8—301no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—601no—
307D4—601no—
308D4—601no—
309D4—601no—
310D4—1201no—
311C2×C4—301no—
312C2×C4—301no—
313C2×C4#681711yescharacteristic
314C2×C4D4×D1511yescharacteristic
315C2×C4D4×D1511yescharacteristic
316C8—41no—
317C8—41no—
318C8—152no—
319C8—301no—
320C8—601no—
321C2×C3—161no—
322C2×C3#6503811yescharacteristic
323C2×C3#6505111yescharacteristic
324C2×C3#6506411yescharacteristic
325D3—801no—
326C5#6840911yescharacteristic, complemented, Sylow
327C22—81no—
328C22—81no—
329C22—81no—
330C22—1201no—
331C22—1201no—
332C22—1201no—
333C22#9177311yescharacteristic
334C4—21no—
335C4—302no—
336C4—601no—
337C4D8×D1511yescharacteristic
338C4#9180011yescharacteristic
339C4SD16×D1511yescharacteristic
340C4#9180511yescharacteristic
341C3#1059920211yescharacteristic, complemented, Sylow
342C2—161no—
343C2—2401no—
344C2#1175085011yescharacteristic
345C2#1175086311yescharacteristic
346C2#1175087611yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5#121
prime radical#11751174C2
hypercenter#331D15
hypocenterC3×C5#1668
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #11751176C2semidirect
3. #11750949C2semidirect
4. #11750931C2semidirect
5. C3×C5×#331C2semidirect
6. #11746306C2semidirect
7. #11746300C2semidirect
29. C5×#331D3semidirect
56. C3×#331D5semidirect
93. Dic30D8semidirect
98. C3⋊#168SD16semidirect
140. #331D15semidirect
277. C3×C5#1668semidirect
326. C5#68409semidirect
341. C3#10599202semidirect

Maximal subgroups

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

subgroupindex
#117511762
#117511742
#117509492
#117509312
C3×C5×#3312
#117463062
#117463002
#105992023
#684095