Finite Group Databasebeta

← #14317123

Subgroups — #14317123

Order 1920.

332 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C2×#91112C211yesmaximal, characteristic
2C3×#65470C211yesmaximal, characteristic, complemented
3#11747766C211yesmaximal, characteristic
4C2×#90943C211yesmaximal, characteristic
5C5×#4564C211yesmaximal, characteristic, complemented
6#11745927C211yesmaximal, characteristic, complemented
7#11745897C211yesmaximal, characteristic, complemented
8#10600027—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C2×D120C2211yescharacteristic
11C3×#4090—21no—
12C2×C3×#689—21no—
13C2×C3×Dic20C2211yescharacteristic
14#91418—21no—
15#91112—22no—
16C2×C3⋊#672C2211yescharacteristic
17C5×#818C2211yescharacteristic
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×C8×Dic5C2211yescharacteristic
20#90969—21no—
21#90943—22no—
22#71315—51nomaximal, Hall
23#65470D311yescharacteristic, complemented
24C2×#3960—31no—
25C2×#3932—31no—
26#65161—31no—
27C5×#358—31no—
28#64721—31no—
29#64712—31no—
30C2×C3×C5×Q8—21no—
31C2×D60—21no—
32C2×C3×Dic10—21no—
33C2×#1200—41no—
34C3×C5×Q16—21no—
35C3×C5×Q16—21no—
36C2×C3×C5×C8C2311yescharacteristic
37D120—21no—
38D120D412yes—
39C5×C4⋊Dic3—21no—
40C3×#689—42no—
41C3×#683—41no—
42C3×#683—41no—
43C3×C4×Dic5D411yescharacteristic
44C2×C3×#168D411yescharacteristic
45C3×Dic20—21no—
46C3×Dic20—21no—
47#6667—41no—
48C3⋊#672—21no—
49C5×C3⋊C16—21no—
50C3×#494—51no—
51C2×#828—51no—
52C2×#828—51no—
53C4×D24—51no—
54#4564—51no—
55#4564D511yescharacteristic, complemented
56C4⋊(C3⋊C16)—51no—
57C2×C5×Q16C2×D311yescharacteristic
58#4090—21no—
59C2×#689—21no—
60C2×Dic20C2×D311yescharacteristic
61C2×D40—31no—
62#4039—61no—
63C2×C5×C16—31no—
64C5×#107—31no—
65#3960—62no—
66C8×Dic5C2×D311yescharacteristic
67C2×#672—31no—
68#3941—61no—
69#3932—62no—
70#2208—151noSylow
71C22×D15—41no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76D60—22no—
77D60—41no—
78C2×C5×Dic3—41no—
79C2×C3×Dic5—41no—
80C2×C3×Dic5D811yescharacteristic
81C2×C3×Dic5D811yescharacteristic
82C3×Dic10—41no—
83C3×Dic10—41no—
84#1200—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3×#168—21no—
88C2×C3×Q16—51no—
89C2×C3×Q16—101no—
90C2×C3×Q16C2×D511yescharacteristic
91C3×C4⋊Q8—101no—
92C2×D24—51no—
93C4×D12—101no—
94C3×C4×C8—51no—
95#828—102no—
96#828—102no—
97#821—101no—
98#818C2×D511yescharacteristic
99C2×C3⋊C16—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×Q8—21no—
102C2×D20—61no—
103C2×C4×D5—121no—
104C2×Dic10—21no—
105C5×Q16—21no—
106C5×Q16—21no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—61no—
109#689—42no—
110#685—121no—
111#683—41no—
112#683—41no—
113C4×Dic5#6711yescharacteristic
114C2×#168#6711yescharacteristic
115Dic20—21no—
116Dic20—21no—
117D40—32no—
118D40—61no—
119C5×C16—61no—
120#672—61no—
121C2×SD32—151no—
122C2×SD32—151no—
123#494—51no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—31no—
127#358—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×D15—42no—
130C2×D15—81no—
131C2×D15—81no—
132C3×C4×C5—81no—
133C3×C4×C5#12111yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135C3×Dic5—21no—
136C3×Dic5—81no—
137C3×Dic5SD3212yescomplemented
138C5×Dic3—81no—
139C2×C3×Q8—21no—
140C2×C3×Q8—101no—
141C2×D12—101no—
142C2×C4×D3—201no—
143C3×Q16—21no—
144C3×Q16—21no—
145C3×Q16—101no—
146C3×Q16—101no—
147C3×Q16—202no—
148C2×C3×C8—51no—
149C2×C3×C8C22×D511yescharacteristic
150C3×C4⋊C4—201no—
151C3×C4⋊C4—201no—
152C3×C42—51no—
153(C2×D3)⋊C4—201no—
154C4⋊Dic3—21no—
155D24—52no—
156D24—101no—
157C3⋊C16—21no—
158C3⋊C16—101no—
159C22×D5—121no—
160C5×Q8—41no—
161C5×Q8—41no—
162C2×C4×C5—41no—
163C2×C4×C5—121no—
164C2×C4×C5C2×#6711yescharacteristic
165C2×Dic5—41no—
166C2×Dic5#21311yescharacteristic
167C2×Dic5#21311yescharacteristic
168D20—62no—
169D20—121no—
170C4×D5—242no—
171Dic10—41no—
172Dic10—41no—
173C5×C8D3×D411yescharacteristic
174C5×C8#23711yescharacteristic
175#168—21no—
176C2×Q16—51no—
177C2×Q16—101no—
178C2×Q16D3×D511yescharacteristic
179C2×D8—151no—
180C4⋊Q8—101no—
181C4×D4—301no—
182SD32—302no—
183SD32—302no—
184C2×C16—31no—
185C2×C16—151no—
186#107—31no—
187#102—301no—
188C4×C8—51no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192D15—82no—
193C22×D3—201no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—201no—
197C3×Q8—201no—
198C2×C3×C4—41no—
199C2×C3×C4—51no—
200C2×C3×C4—51no—
201C2×C3×C4—201no—
202C2×C3×C4D4×D511yescharacteristic
203C2×Dic3—41no—
204D12—102no—
205D12—201no—
206C4×D3—402no—
207C3×C8—101no—
208C3×C8#70911yescharacteristic
209C3×C8D4×D511yescharacteristic
210C22×C5C2×#21311yescharacteristic
211C2×D5—122no—
212C2×D5—241no—
213C2×D5—241no—
214C4×C5—81no—
215C4×C5—241no—
216C4×C5#93211yescharacteristic
217C4×C5#93811yescharacteristic
218Dic5—21no—
219Dic5—81no—
220Dic5#82812yescomplemented
221C2×Q8—21no—
222C2×Q8—101no—
223C2×D4—301no—
224C22×C4—601no—
225Q16—21no—
226Q16—21no—
227Q16—101no—
228Q16—101no—
229Q16—202no—
230D8—152no—
231D8—301no—
232C2×C8—51no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—61no—
235C4⋊C4—201no—
236C4⋊C4—201no—
237C22⋊C4—601no—
238C42—51no—
239C16—61no—
240C16—301no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3D5×D811yescharacteristic
243C2×D3—202no—
244C2×D3—401no—
245C2×D3—401no—
246C3×C4—52no—
247C3×C4—81no—
248C3×C4—101no—
249C3×C4—401no—
250C3×C4#403011yescharacteristic
251C3×C4#406011yescharacteristic
252Dic3—81no—
253C2×C5#507211yescharacteristic
254C2×C5C2×#82811yescharacteristic
255C2×C5#517911yescharacteristic
256D5—242no—
257C23—601no—
258Q8—41no—
259Q8—41no—
260Q8—201no—
261Q8—201no—
262D4—302no—
263D4—601no—
264C2×C4—41no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—121no—
268C2×C4—201no—
269C2×C4—1202no—
270C2×C4D5×#6711yescharacteristic
271C8—101no—
272C8#677911yescharacteristic
273C8#679011yescharacteristic
274C2×C3#6507511yescharacteristic
275C2×C3D5×SD3211yescharacteristic
276C2×C3#6520711yescharacteristic
277D3—402no—
278C5#7131511yescharacteristic, complemented, Sylow
279C22—602no—
280C22—1201no—
281C22—1201no—
282C22D5×#21311yescharacteristic
283C4—52no—
284C4—81no—
285C4—101no—
286C4—241no—
287C4—401no—
288C4#9149111yescharacteristic
289C4#9153311yescharacteristic
290C3#1060002711yescharacteristic, complemented, Sylow
291C2—1202no—
292C2D5×#82811yescharacteristic
293C2#1174830211yescharacteristic
294C2#1174897611yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2208
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C3×#65470C2semidirect
5. C5×#4564C2semidirect
6. #11745927C2semidirect
7. #11745897C2semidirect
23. #65470D3semidirect
55. #4564D5semidirect
137. C3×Dic5SD32semidirect
220. Dic5#828semidirect
241. C3×C5#2208semidirect
278. C5#71315semidirect
290. C3#10600027semidirect

Maximal subgroups

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

subgroupindex
C2×#911122
C3×#654702
#117477662
C2×#909432
C5×#45642
#117459272
#117458972
#106000273
#713155