Finite Group Databasebeta

← #14292452

Subgroups — #14292452

Order 1920.

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

normal subgroups only

This group has 336 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
1#11751186C211yesmaximal, characteristic
2C3×#65383C211yesmaximal, characteristic, complemented
3#11747064C211yesmaximal, characteristic
4#11746862C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745868C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic
8#10599265—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6717—21no—
11C2×#6717—21no—
12#91763C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14C2×#6658—21no—
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×#3942—21no—
19C3×#3940—21no—
20C3×C4⋊#168C2211yescharacteristic
21#90982—21no—
22#90968—21no—
23#90952—21no—
24#71120—51nomaximal, Hall
25#65383D311yescharacteristic, complemented
26#65374—31no—
27#65137—31no—
28#65120—31no—
29C5×#332—31no—
30#64705—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×C3×Dic10D411yescharacteristic
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C42×C5C2311yescharacteristic
40#6717—42no—
41#6717—42no—
42C2×C3⋊#168D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44C2×C5×C3⋊C8—21no—
45C2×C5×C3⋊C8—21no—
46C3×C4⋊Dic5D411yescharacteristic
47C3×#683—21no—
48C3×C4×Dic5—21no—
49C2×C3×#168—21no—
50#6658—42no—
51C3×#475—51no—
52#5085—51no—
53#5027—51no—
54#5024—51no—
55#4547D511yescharacteristic, complemented
56#4485—51no—
57#4479—51no—
58C5×C4⋊Q8C2×D311yescharacteristic
59C2×#688—61no—
60C2×#688—61no—
61C2×#677—61no—
62#4020—31no—
63C4×Dic10C2×D311yescharacteristic
64C5×C4⋊C8—31no—
65C5×C4⋊C8—31no—
66#3953—61no—
67#3947—61no—
68#3946—61no—
69#3942—21no—
70#3940—21no—
71C4⋊#168C2×D311yescharacteristic
72C4×#168—31no—
73#1686—151noSylow
74C22×D15—41no—
75C3×C5×Q8—41no—
76C3×C5×Q8—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5#4111yescharacteristic
81D60—41no—
82D60—41no—
83D60—41no—
84D60—41no—
85D60—81no—
86C2×C3×Dic5—21no—
87C2×C3×Dic5—21no—
88C3×Dic10—21no—
89C3×Dic10—21no—
90C3⋊#168—21no—
91C3⋊#168SD1612yescomplemented
92C3×#168—41no—
93C5×C3⋊C8—41no—
94C5×C3⋊C8—41no—
95C3×C4⋊Q8C2×D511yescharacteristic
96C3×C4×Q8—51no—
97C2×#215—101no—
98C2×#215—101no—
99C2×#215—101no—
100#874—51no—
101C3×#106—101no—
102C3×C4⋊C8—51no—
103C3×#103—101no—
104#809—101no—
105C4⋊(C3⋊C8)—101no—
106C4⋊(C3⋊C8)C2×D511yescharacteristic
107C4⋊(C3⋊C8)C2×D511yescharacteristic
108#803—101no—
109C4×C3⋊C8—51no—
110C2×C5×Q8—21no—
111C2×D20—61no—
112C2×D20—61no—
113C2×D20—61no—
114C2×Dic10#6711yescharacteristic
115C2×C5×C8—61no—
116C2×C5×C8—61no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C42×C5C22×D311yescharacteristic
120#688—122no—
121#688—122no—
122C4⋊Dic5#6711yescharacteristic
123#683—21no—
124C4×Dic5—21no—
125C2×#168—21no—
126C2×#168—31no—
127C2×#168—31no—
128#677—122no—
129#492—151no—
130#475—51no—
131#460—151no—
132#446—151no—
133#335—151no—
134#332—31no—
135#331—151no—
136C22×C3×C5#12111yescharacteristic
137C2×D15—81no—
138C2×D15—81no—
139C2×D15—81no—
140C3×C4×C5—21no—
141C3×C4×C5—81no—
142C3×C4×C5C2×SD1611yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
145C3×C4×C5#13711yescharacteristic
146C3×Dic5—41no—
147C3×Dic5—41no—
148C2×C3×Q8—21no—
149C2×C3×Q8—51no—
150C2×D12—101no—
151C2×D12—101no—
152C2×D12—101no—
153C2×C3×C8—101no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—51no—
157C3×C4⋊C4—101no—
158C3×C42—101no—
159C3×C42C22×D511yescharacteristic
160#215—202no—
161#215—202no—
162#215—202no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—51no—
166C2×C3⋊C8—51no—
167C22×D5—121no—
168C5×Q8—41no—
169C5×Q8—41no—
170C2×C4×C5—41no—
171C2×C4×C5D3×D411yescharacteristic
172C2×C4×C5#23711yescharacteristic
173C2×C4×C5C2×#6711yescharacteristic
174C2×Dic5—21no—
175C2×Dic5—21no—
176D20—121no—
177D20—121no—
178D20—121no—
179D20—121no—
180D20—241no—
181Dic10—21no—
182Dic10—21no—
183C5×C8—121no—
184C5×C8—121no—
185#168—32no—
186#168—41no—
187#168—61no—
188C2×SD16—301no—
189C2×SD16—301no—
190C2×SD16—301no—
191C4⋊Q8D3×D511yescharacteristic
192#127—151no—
193C4×Q8—51no—
194#106—101no—
195C4⋊C8—31no—
196C4⋊C8—31no—
197C4⋊C8—51no—
198C4⋊C8—301no—
199#103—101no—
200#102—301no—
201#97—301no—
202C4×C8—151no—
203C2×C3×C5#46011yescharacteristic
204C2×C3×C5#46811yescharacteristic
205C2×C3×C5#47111yescharacteristic
206D15—161no—
207C22×D3—201no—
208C3×Q8—41no—
209C3×Q8—41no—
210C3×Q8—101no—
211C3×Q8—101no—
212C2×C3×C4—41no—
213C2×C3×C4—101no—
214C2×C3×C4—101no—
215C2×C3×C4#70911yescharacteristic
216C2×C3×C4D4×D511yescharacteristic
217C2×C3×C4D4×D511yescharacteristic
218D12—201no—
219D12—201no—
220D12—201no—
221D12—201no—
222D12—401no—
223C3×C8—201no—
224C3⋊C8—41no—
225C3⋊C8—41no—
226C3⋊C8—52no—
227C3⋊C8—101no—
228C22×C5#93911yescharacteristic
229C2×D5—241no—
230C2×D5—241no—
231C2×D5—241no—
232C4×C5—21no—
233C4×C5—81no—
234C4×C5D3×SD1611yescharacteristic
235C4×C5#91411yescharacteristic
236C4×C5#94211yescharacteristic
237C4×C5#94911yescharacteristic
238Dic5—41no—
239Dic5—41no—
240C2×Q8—21no—
241C2×Q8—51no—
242C2×D4—301no—
243C2×D4—301no—
244C2×D4—301no—
245SD16—602no—
246SD16—602no—
247SD16—602no—
248C2×C8—61no—
249C2×C8—61no—
250C2×C8—101no—
251C2×C8—151no—
252C2×C8—151no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—51no—
256C4⋊C4—101no—
257C42—101no—
258C42C2×D3×D511yescharacteristic
259C3×C5#168611yescharacteristic, complemented, Hall
260C22×C3#403011yescharacteristic
261C2×D3—401no—
262C2×D3—401no—
263C2×D3—401no—
264C3×C4—21no—
265C3×C4—81no—
266C3×C4—201no—
267C3×C4—201no—
268C3×C4#405711yescharacteristic
269C3×C4D5×SD1611yescharacteristic
270C3×C4#406011yescharacteristic
271C3×C4#406411yescharacteristic
272C2×C5#504911yescharacteristic
273C2×C5#516311yescharacteristic
274C2×C5#520311yescharacteristic
275D5—481no—
276C23—601no—
277Q8—41no—
278Q8—41no—
279Q8—101no—
280Q8—101no—
281D4—601no—
282D4—601no—
283D4—601no—
284D4—601no—
285D4—1201no—
286C2×C4—41no—
287C2×C4—101no—
288C2×C4—101no—
289C2×C4#677911yescharacteristic
290C2×C4D5×#6711yescharacteristic
291C2×C4#679011yescharacteristic
292C8—121no—
293C8—121no—
294C8—152no—
295C8—201no—
296C8—301no—
297C2×C3#6504311yescharacteristic
298C2×C3#6505111yescharacteristic
299C2×C3#6510111yescharacteristic
300D3—801no—
301C5#7112011yescharacteristic, complemented, Sylow
302C22—1201no—
303C22—1201no—
304C22—1201no—
305C22#9155011yescharacteristic
306C4—21no—
307C4—81no—
308C4—201no—
309C4—201no—
310C4#9148711yescharacteristic
311C4#9150011yescharacteristic
312C4#9150211yescharacteristic
313C4#9151511yescharacteristic
314C3#1059926511yescharacteristic, complemented, Sylow
315C2—2401no—
316C2#1174900811yescharacteristic
317C2#1174927311yescharacteristic
318C2#1174937711yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#121
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1686
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
2. C3×#65383C2semidirect
4. #11746862C2semidirect
5. C5×#4547C2semidirect
6. #11745868C2semidirect
25. #65383D3semidirect
55. #4547D5semidirect
91. C3⋊#168SD16semidirect
259. C3×C5#1686semidirect
301. C5#71120semidirect
314. C3#10599265semidirect

Maximal subgroups

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

subgroupindex
#117511862
C3×#653832
#117470642
#117468622
C5×#45472
#117458682
#117458542
#105992653
#711205