Finite Group Databasebeta

← #14293344

Subgroups — #14293344

Order 1920.

308 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 84 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×#65131C211yesmaximal, characteristic
2#11747010C211yesmaximal, characteristic
3#11746921C211yesmaximal, characteristic, complemented
4#11746889C211yesmaximal, characteristic
5#11746307C211yesmaximal, characteristic, complemented
6C5×#4480C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10599338—31nomaximal, Hall
9#91758C2211yescharacteristic
10C3×C4×D20C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6649—21no—
13C3×C5×C4⋊C8C2211yescharacteristic
14C4⋊(C3⋊#168)C2211yescharacteristic
15C5×C4⋊(C3⋊C8)C2211yescharacteristic
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3953—21no—
18C3×#3949—21no—
19#90990—21no—
20#90974—21no—
21#90974—21no—
22#90965—21no—
23#90955—21no—
24#71139—51nomaximal, Hall
25#65135—31no—
26#65131D311yescharacteristic
27#64977—31no—
28#64970—31no—
29C5×#334—31no—
30#64706—31no—
31#64701—31no—
32C2×Dic30—21no—
33C2×C3×D20D411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C2×C3⋊#168—21no—
41C2×C5×C3⋊C8—21no—
42C2×C5×C3⋊C8D411yescharacteristic
43C2×C5×C3⋊C8D411yescharacteristic
44C3×#685—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D411yescharacteristic
48#6649—42no—
49C3×#476—51no—
50#5093—51no—
51#5012—51no—
52#5007—51no—
53#4546—51no—
54#4486—51no—
55#4480D511yescharacteristic, complemented
56C2×#676—61no—
57C4×D20C2×D311yescharacteristic
58#4015—31no—
59#4015C2×D311yescharacteristic
60C5×C4⋊C8—31no—
61C5×C4⋊C8C2×D311yescharacteristic
62C4×C5×C8—31no—
63#3953—21no—
64#3953—61no—
65#3952—61no—
66#3950—61no—
67#3949—21no—
68#3948—61no—
69#3948—61no—
70C4⋊#168—31no—
71#1703—151noSylow
72C22×C3×D5—21no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5#4111yescharacteristic
76C2×Dic15—41no—
77Dic30—41no—
78Dic30—41no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—41no—
81C3×D20—21no—
82C3×D20—21no—
83C3×C4×D5—41no—
84C3×C4×D5—41no—
85C3×Dic10—81no—
86C3×C5×C8—41no—
87C3⋊#168—41no—
88C5×C3⋊C8—21no—
89C5×C3⋊C8—21no—
90C5×C3⋊C8—41no—
91C3×C4⋊Q8—51no—
92C3×C4×D4—51no—
93C2×#208—101no—
94#869—51no—
95C3×#106—101no—
96C3×C4⋊C8C2×D511yescharacteristic
97C3×#102—101no—
98#832—101no—
99#830—101no—
100#810—101no—
101#810—101no—
102#807—101no—
103C4⋊(C3⋊C8)—51no—
104C4⋊(C3⋊C8)C2×D511yescharacteristic
105C4×C3⋊C8C2×D511yescharacteristic
106C2×D20#6711yescharacteristic
107C2×C4×D5—21no—
108C2×Dic10—21no—
109C2×Dic10—61no—
110C2×C5×C8—21no—
111C2×C5×C8—31no—
112C2×C5×C8—31no—
113C2×C5×C8—61no—
114C42×C5C22×D311yescharacteristic
115#685—21no—
116C4⋊Dic5—21no—
117C4⋊Dic5—21no—
118C4⋊Dic5—61no—
119C4⋊Dic5—61no—
120C4⋊Dic5#6711yescharacteristic
121C2×#168—61no—
122#676—122no—
123#487—151no—
124#476—51no—
125#474—151no—
126#436—151no—
127#334—31no—
128#333—151no—
129#332—151no—
130C22×C3×C5#12111yescharacteristic
131C2×C3×D5—41no—
132C2×C3×D5—41no—
133C2×C3×D5—41no—
134C3×C4×C5—21no—
135C3×C4×C5#13511yescharacteristic
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137C3×C4×C5#13711yescharacteristic
138C3×C4×C5#13711yescharacteristic
139Dic15—81no—
140C3×Dic5—41no—
141C3×Dic5—81no—
142C2×C3×Q8—101no—
143C2×C3×D4—51no—
144C22×C3×C4—101no—
145C2×Dic6—101no—
146C2×C3×C8—21no—
147C3×C4⋊C4—51no—
148C3×C4⋊C4—101no—
149C3×C4⋊C4—101no—
150C3×C22⋊C4—101no—
151C3×C42C22×D511yescharacteristic
152C4⋊Dic3—101no—
153C4⋊Dic3—101no—
154#208—202no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—101no—
157C2×C3⋊C8D2011yescharacteristic
158C2×C3⋊C8D2011yescharacteristic
159C22×D5—21no—
160C2×C4×C5D3×D411yescharacteristic
161C2×C4×C5#23711yescharacteristic
162C2×C4×C5C2×#6711yescharacteristic
163C2×Dic5—21no—
164C2×Dic5—41no—
165C2×Dic5—121no—
166D20—21no—
167D20—21no—
168C4×D5—41no—
169C4×D5—41no—
170Dic10—81no—
171Dic10—121no—
172Dic10—121no—
173C5×C8—41no—
174C5×C8—61no—
175C5×C8—61no—
176C5×C8—121no—
177#168—121no—
178C2×M16—301no—
179C4⋊Q8—51no—
180C4⋊Q8—151no—
181C4×D4—51no—
182#107—301no—
183#106—101no—
184C4⋊C8—31no—
185C4⋊C8—151no—
186C4⋊C8D3×D511yescharacteristic
187#103—301no—
188#103—301no—
189#102—101no—
190#102—301no—
191C22⋊C8—301no—
192C4×C8—31no—
193C2×C3×C5#46311yescharacteristic
194C2×C3×C5#47011yescharacteristic
195C2×C3×C5#47111yescharacteristic
196C3×D5—81no—
197C23×C3—101no—
198C3×Q8—401no—
199C3×D4—101no—
200C3×D4—101no—
201C2×C3×C4—101no—
202C2×C3×C4—201no—
203C2×C3×C4—201no—
204C2×C3×C4—201no—
205C2×C3×C4C2×D2011yescharacteristic
206C2×C3×C4D4×D511yescharacteristic
207C2×C3×C4#71311yescharacteristic
208C2×Dic3—201no—
209Dic6—201no—
210Dic6—201no—
211C3×C8—41no—
212C3⋊C8—21no—
213C3⋊C8—21no—
214C3⋊C8—41no—
215C3⋊C8—201no—
216C22×C5#93911yescharacteristic
217C2×D5—41no—
218C2×D5—41no—
219C2×D5—41no—
220C4×C5—21no—
221C4×C5#91411yescharacteristic
222C4×C5#91611yescharacteristic
223C4×C5#94211yescharacteristic
224C4×C5#95111yescharacteristic
225Dic5—41no—
226Dic5—81no—
227Dic5—241no—
228C2×Q8—101no—
229C2×Q8—301no—
230C2×D4—51no—
231C22×C4—101no—
232M16—602no—
233C2×C8—21no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8—61no—
237C2×C8—301no—
238C4⋊C4—51no—
239C4⋊C4—101no—
240C4⋊C4—101no—
241C4⋊C4—301no—
242C4⋊C4—301no—
243C22⋊C4—101no—
244C42C2×D3×D511yescharacteristic
245C3×C5#170311yescharacteristic, complemented, Hall
246C22×C3—201no—
247C22×C3—201no—
248C22×C3—201no—
249C22×C3#404111yescharacteristic
250C3×C4—21no—
251C3×C4—201no—
252C3×C4—401no—
253C3×C4#405011yescharacteristic
254C3×C4#405411yescharacteristic
255C3×C4#406111yescharacteristic
256C3×C4#406111yescharacteristic
257Dic3—401no—
258C2×C5#505211yescharacteristic
259C2×C5#516511yescharacteristic
260C2×C5#520011yescharacteristic
261D5—81no—
262C23—101no—
263Q8—401no—
264Q8—601no—
265Q8—601no—
266D4—101no—
267D4—101no—
268C2×C4—101no—
269C2×C4—201no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4—601no—
273C2×C4#676611yescharacteristic
274C2×C4D3×D2011yescharacteristic
275C2×C4D5×#6711yescharacteristic
276C8—41no—
277C8—61no—
278C8—61no—
279C8—121no—
280C8—601no—
281C2×C3—401no—
282C2×C3#6513311yescharacteristic
283C2×C3#6515711yescharacteristic
284C2×C3#6518711yescharacteristic
285C5#7113911yescharacteristic, complemented, Sylow
286C22—201no—
287C22—201no—
288C22—201no—
289C22#9140911yescharacteristic
290C4—21no—
291C4—201no—
292C4—401no—
293C4—1201no—
294C4#9125311yescharacteristic
295C4#9127211yescharacteristic
296C4#9148411yescharacteristic
297C4#9151311yescharacteristic
298C3#1059933811yescharacteristic, complemented, Sylow
299C2—401no—
300C2#1174746211yescharacteristic
301C2#1174775511yescharacteristic
302C2#1174818511yescharacteristic
subgroupG/H
centerC22#91409
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1703
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11746921C2semidirect
5. #11746307C2semidirect
6. C5×#4480C2semidirect
7. #11745861C2semidirect
55. #4480D5semidirect
245. C3×C5#1703semidirect
285. C5#71139semidirect
298. C3#10599338semidirect

Maximal subgroups

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

subgroupindex
C3×#651312
#117470102
#117469212
#117468892
#117463072
C5×#44802
#117458612
#105993383
#711395