Finite Group Databasebeta

← #14291677

Subgroups — #14291677

Order 1920.

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

normal subgroups only

This group has 300 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#11750931C211yesmaximal, characteristic
2#11747104C211yesmaximal, characteristic
3#11746963C211yesmaximal, characteristic
4#11746947C211yesmaximal, characteristic
5C5×#4481C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic
7#11745865C211yesmaximal, characteristic
8#10599301—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6662—21no—
13C3×C5×C4⋊C8C2211yescharacteristic
14#91098—21no—
15C8×Dic15—21no—
16C4×C3⋊#168C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊#168C2211yescharacteristic
19#90988—21no—
20#90986—21no—
21#90986—21no—
22#90975—21no—
23#90971—21no—
24#68466—51nomaximal, Hall
25#65380—31no—
26#65368—31no—
27#65138—31no—
28#65119—31no—
29C5×#333—31no—
30#64706D311yescharacteristic
31#64700—31no—
32C2×Dic30D411yescharacteristic
33C2×C5×Dic6—21no—
34C2×C3×Dic10—21no—
35C2×C3×C5×C8—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15D411yescharacteristic
38#6712—21no—
39C4×Dic15—21no—
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3—21no—
44C2×C5×C3⋊C8—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168—21no—
48#6662—42no—
49#5090—51no—
50#5080—51no—
51#4850—51no—
52#4830—51no—
53C3×#332—51no—
54#4481D511yescharacteristic
55#4480—51no—
56C5×C4⋊Q8—31no—
57C2×Dic20—61no—
58#4015C2×D311yescharacteristic
59C4×Dic10—31no—
60C5×C4⋊C8—31no—
61C5×C4⋊C8C2×D311yescharacteristic
62#3948—61no—
63#3946—61no—
64C8×Dic5—61no—
65#3942—61no—
66#3940—61no—
67#3940—61no—
68#3939—61no—
69C4⋊#168C2×D311yescharacteristic
70C4×#168—31no—
71#1672—151noSylow
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5#4111yescharacteristic
75C2×Dic15—21no—
76C2×Dic15—21no—
77Dic30—21no—
78Dic30SD1612yes—
79C2×C5×Dic3—41no—
80C5×Dic6—81no—
81C2×C3×Dic5—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8—41no—
85C3⋊#168—21no—
86C3⋊#168Q1612yescomplemented
87C3×#168—41no—
88C5×C3⋊C8—41no—
89C3×C4⋊Q8—51no—
90C2×#216—101no—
91#869C2×D511yescharacteristic
92C4×Dic6—51no—
93C3×C4⋊C8—51no—
94C3×C4⋊C8C2×D511yescharacteristic
95#835—101no—
96#818—101no—
97#816—101no—
98Dic3⋊C8—101no—
99C8×Dic3—101no—
100#808—101no—
101#808—101no—
102C4⋊(C3⋊C8)C2×D511yescharacteristic
103C4×C3⋊C8—51no—
104C2×C5×Q8—61no—
105C2×Dic10—21no—
106C2×Dic10—31no—
107C2×C5×C8—21no—
108C2×C5×C8—61no—
109C5×C4⋊C4—61no—
110C5×C4⋊C4—61no—
111C42×C5C22×D311yescharacteristic
112C4⋊Dic5—21no—
113C4⋊Dic5—21no—
114C4⋊Dic5—31no—
115#683—61no—
116C4×Dic5—61no—
117C2×#168—21no—
118C2×#168—31no—
119C2×#168—31no—
120Dic20—122no—
121#498—151no—
122#477—151no—
123#462—151no—
124C8×Q8—151no—
125#334—151no—
126#333—31no—
127#332—51no—
128C22×C3×C5#12111yescharacteristic
129C3×C4×C5—21no—
130C3×C4×C5C2×SD1611yescharacteristic
131C3×C4×C5C2×Q1611yescharacteristic
132C3×C4×C5#13511yescharacteristic
133C3×C4×C5#13711yescharacteristic
134Dic15—22no—
135Dic15—41no—
136C3×Dic5—81no—
137C5×Dic3—81no—
138C2×C3×Q8—101no—
139C2×Dic6—21no—
140C2×Dic6—51no—
141C2×C3×C8—21no—
142C2×C3×C8—101no—
143C3×C4⋊C4—101no—
144C3×C4⋊C4—101no—
145C3×C42C22×D511yescharacteristic
146#216—202no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3—51no—
150Dic3⋊C4—101no—
151C4×Dic3—101no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—51no—
154C2×C3⋊C8—51no—
155C5×Q8—241no—
156C2×C4×C5—121no—
157C2×C4×C5#23511yescharacteristic
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5D3×D411yescharacteristic
160C2×Dic5—41no—
161C2×Dic5—61no—
162C2×Dic5—61no—
163Dic10—32no—
164Dic10—41no—
165Dic10—41no—
166Dic10—61no—
167C5×C8—41no—
168C5×C8—121no—
169#168—32no—
170#168—41no—
171#168—61no—
172C2×Q16—301no—
173C4⋊Q8—31no—
174C4⋊Q8—51no—
175C4×Q8—151no—
176#107—301no—
177#106—301no—
178#106—301no—
179C4⋊C8—31no—
180C4⋊C8—51no—
181C4⋊C8—301no—
182C4⋊C8D3×D511yescharacteristic
183#103—301no—
184#103—301no—
185C4×C8—151no—
186C4×C8—301no—
187C2×C3×C5#46211yescharacteristic
188C2×C3×C5#46511yescharacteristic
189C2×C3×C5#47111yescharacteristic
190C3×Q8—201no—
191C3×Q8—201no—
192C2×C3×C4—201no—
193C2×C3×C4#70911yescharacteristic
194C2×C3×C4D4×D511yescharacteristic
195C2×C3×C4D4×D511yescharacteristic
196C2×Dic3—41no—
197C2×Dic3—101no—
198C2×Dic3—101no—
199Dic6—52no—
200Dic6—81no—
201Dic6—101no—
202C3×C8—41no—
203C3×C8—201no—
204C3⋊C8—41no—
205C3⋊C8—52no—
206C3⋊C8—101no—
207C22×C5#88411yescharacteristic
208C4×C5—21no—
209C4×C5—241no—
210C4×C5#91211yescharacteristic
211C4×C5D3×SD1611yescharacteristic
212C4×C5#91511yescharacteristic
213C4×C5D3×Q1611yescharacteristic
214Dic5—62no—
215Dic5—81no—
216Dic5—121no—
217C2×Q8—61no—
218C2×Q8—101no—
219C2×Q8—151no—
220Q16—602no—
221C2×C8—21no—
222C2×C8—61no—
223C2×C8—101no—
224C2×C8—151no—
225C2×C8—151no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—101no—
229C4⋊C4—101no—
230C4⋊C4—151no—
231C4⋊C4—301no—
232C42—301no—
233C42C2×D3×D511yescharacteristic
234C3×C5#167211yescharacteristic, complemented, Hall
235C22×C3#403011yescharacteristic
236C3×C4—21no—
237C3×C4—401no—
238C3×C4D5×SD1611yescharacteristic
239C3×C4#406111yescharacteristic
240C3×C4D5×Q1611yescharacteristic
241C3×C4#406511yescharacteristic
242Dic3—81no—
243Dic3—102no—
244Dic3—201no—
245C2×C5#475411yescharacteristic
246C2×C5#477811yescharacteristic
247C2×C5#479511yescharacteristic
248Q8—152no—
249Q8—201no—
250Q8—201no—
251Q8—241no—
252Q8—301no—
253C2×C4—121no—
254C2×C4—201no—
255C2×C4—301no—
256C2×C4—301no—
257C2×C4#677111yescharacteristic
258C2×C4#677711yescharacteristic
259C2×C4#679011yescharacteristic
260C8—41no—
261C8—121no—
262C8—152no—
263C8—201no—
264C8—301no—
265C2×C3#6503711yescharacteristic
266C2×C3#6508211yescharacteristic
267C2×C3#6509611yescharacteristic
268C5#6846611yescharacteristic, complemented, Sylow
269C22#9146111yescharacteristic
270C4—21no—
271C4—241no—
272C4—302no—
273C4—401no—
274C4—601no—
275C4#9125511yescharacteristic
276C4#9127711yescharacteristic
277C4#9148811yescharacteristic
278C4#9151111yescharacteristic
279C3#1059930111yescharacteristic, complemented, Sylow
280C2#1174742711yescharacteristic
281C2#1174792611yescharacteristic
282C2#1174819911yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1672
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
86. C3⋊#168Q16semidirect
234. C3×C5#1672semidirect
268. C5#68466semidirect
279. C3#10599301semidirect

Maximal subgroups

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

subgroupindex
#117509312
#117471042
#117469632
#117469472
C5×#44812
C3×#647062
#117458652
#105993013
#684665