Finite Group Databasebeta

← #14317300

Subgroups — #14317300

Order 1920.

316 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 74 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#11750974C211yesmaximal, characteristic, complemented
2#11747980C211yesmaximal, characteristic
3C2×#90948C211yesmaximal, characteristic, complemented
4C2×#90942C211yesmaximal, characteristic
5C5×#4492C211yesmaximal, characteristic, complemented
6C3×#64711C211yesmaximal, characteristic
7#11745928C211yesmaximal, characteristic, complemented
8#10600030—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10#91776—21no—
11C2×C5×Dic12C2211yescharacteristic
12C2×C3×D40C2211yescharacteristic
13#91368—21no—
14C2×#6655—21no—
15C3×C5×#107C2211yescharacteristic
16C8×Dic15C2211yescharacteristic
17#91094—21no—
18C2×C5×C3⋊C16C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20#90948—22no—
21#90942—22no—
22#69205—51nomaximal, Hall
23#65480—31no—
24C2×#3961—31no—
25C2×#3932—31no—
26#65162—31no—
27C5×#358—31no—
28#64721—31no—
29#64711D311yescharacteristic
30C2×Dic30—21no—
31C2×C5×Dic6—21no—
32C2×C3×D20—21no—
33C2×C3×C5×C8C2311yescharacteristic
34C3×C5×C4⋊C4—21no—
35#6712—41no—
36C4×Dic15—41no—
37C4×Dic15D411yescharacteristic
38C2×C3⋊#168D411yescharacteristic
39Dic60—21no—
40Dic60D412yes—
41C5×Dic12—21no—
42C5×Dic12—21no—
43C3×D40—21no—
44C3×D40—21no—
45#6665—41no—
46#6665—41no—
47#6655—42no—
48C3×#672—21no—
49C5×C3⋊C16—21no—
50#5155—51no—
51C2×#827—51no—
52C2×Dic24—51no—
53#4873—51no—
54C3×#357—51no—
55Dic3⋊C16—51no—
56#4492D511yescharacteristic, complemented
57C2×C5×Q16—31no—
58#4093—61no—
59C2×#688—61no—
60C2×Dic20—31no—
61C2×D40C2×D311yescharacteristic
62#4033—61no—
63C2×C5×C16—31no—
64C5×#107C2×D311yescharacteristic
65#3961—62no—
66C8×Dic5—31no—
67C2×#672C2×D311yescharacteristic
68#3942—61no—
69#3932—62no—
70#2211—151noSylow
71C22×C3×D5—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—41no—
75C2×Dic15D811yescharacteristic
76C2×Dic15D811yescharacteristic
77Dic30—22no—
78Dic30—41no—
79C2×C5×Dic3—41no—
80C5×Dic6—41no—
81C5×Dic6—41no—
82C3×D20—41no—
83C3×D20—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3⋊#168—21no—
87C2×C3×D8—51no—
88#936—101no—
89C2×#214—101no—
90C2×Dic12—51no—
91C2×Dic12C2×D511yescharacteristic
92#887—101no—
93C2×C3×C16—51no—
94C3×#107C2×D511yescharacteristic
95#827—102no—
96C8×Dic3—51no—
97C2×C3⋊C16C2×D511yescharacteristic
98#810—101no—
99Dic24—102no—
100C2×C5×Q8—61no—
101C2×D20—21no—
102C2×Dic10—61no—
103C5×Q16—61no—
104C5×Q16—61no—
105C2×C5×C8C22×D311yescharacteristic
106C5×C4⋊C4—21no—
107#688—122no—
108#685—121no—
109#685—121no—
110#683—121no—
111C4×Dic5—31no—
112C4×Dic5—121no—
113C2×#168—31no—
114Dic20—32no—
115Dic20—61no—
116D40—21no—
117D40—21no—
118C5×C16—61no—
119#672—21no—
120C2×Q32—151no—
121C2×SD32—151no—
122#495—151no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358—31no—
126#357—51no—
127C22×C3×C5C2×D811yescharacteristic
128C2×C3×D5—81no—
129C2×C3×D5—81no—
130C2×C3×D5—81no—
131C3×C4×C5—81no—
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134Dic15—21no—
135Dic15—21no—
136Dic15—42no—
137C5×Dic3—81no—
138C2×C3×D4—101no—
139C2×Dic6—21no—
140C2×Dic6—101no—
141C3×D8—101no—
142C3×D8—101no—
143C2×C3×C8C22×D511yescharacteristic
144C3×C4⋊C4—21no—
145#217—201no—
146#217—201no—
147#214—202no—
148Dic3⋊C4—201no—
149C4×Dic3—51no—
150C4×Dic3—201no—
151C2×C3⋊C8—51no—
152Dic12—21no—
153Dic12—21no—
154Dic12—52no—
155Dic12—101no—
156C3×C16—101no—
157C3⋊C16—21no—
158C22×D5—41no—
159C5×Q8—121no—
160C5×Q8—121no—
161C2×C4×C5—41no—
162C2×C4×C5—121no—
163C2×C4×C5D3×D411yescharacteristic
164C2×Dic5—31no—
165C2×Dic5—31no—
166C2×Dic5—121no—
167D20—41no—
168D20—41no—
169Dic10—62no—
170Dic10—121no—
171C5×C8#23511yescharacteristic
172C5×C8D3×D411yescharacteristic
173#168—61no—
174C2×Q16—31no—
175C2×Q16—151no—
176C2×SD16—301no—
177C2×D8—51no—
178#124—301no—
179C4×Q8—301no—
180Q32—302no—
181SD32—302no—
182C2×C16—31no—
183C2×C16—51no—
184#107D3×D511yescharacteristic
185#103—301no—
186C4×C8—151no—
187C2×C3×C5#45911yescharacteristic
188C2×C3×C5#50811yescharacteristic
189C2×C3×C5#51011yescharacteristic
190C3×D5—161no—
191C23×C3—201no—
192C3×D4—201no—
193C3×D4—201no—
194C2×C3×C4—41no—
195C2×C3×C4D4×D511yescharacteristic
196C2×Dic3—41no—
197C2×Dic3—51no—
198C2×Dic3—51no—
199C2×Dic3—201no—
200Dic6—41no—
201Dic6—41no—
202Dic6—102no—
203Dic6—201no—
204C3×C8#70911yescharacteristic
205C3×C8D4×D511yescharacteristic
206C3⋊C8—101no—
207C22×C5D3×D811yescharacteristic
208C2×D5—81no—
209C2×D5—81no—
210C2×D5—81no—
211C4×C5—81no—
212C4×C5—241no—
213C4×C5#88411yescharacteristic
214C4×C5#91411yescharacteristic
215Dic5—61no—
216Dic5—61no—
217Dic5—122no—
218C2×Q8—61no—
219C2×Q8—301no—
220C2×D4—101no—
221Q16—61no—
222Q16—61no—
223Q16—152no—
224Q16—301no—
225SD16—602no—
226D8—101no—
227D8—101no—
228C2×C8—151no—
229C2×C8C2×D3×D511yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—601no—
232C22⋊C4—601no—
233C22⋊C4—601no—
234C42—151no—
235C42—601no—
236C16—61no—
237C16—101no—
238C3×C5#221111yescharacteristic, complemented, Hall
239C22×C3—401no—
240C22×C3—401no—
241C22×C3—401no—
242C22×C3D5×D811yescharacteristic
243C3×C4—81no—
244C3×C4#403011yescharacteristic
245C3×C4#406011yescharacteristic
246Dic3—81no—
247Dic3—101no—
248Dic3—101no—
249Dic3—202no—
250C2×C5#478611yescharacteristic
251C2×C5#491211yescharacteristic
252C2×C5#491511yescharacteristic
253D5—161no—
254C23—201no—
255Q8—121no—
256Q8—121no—
257Q8—302no—
258Q8—601no—
259D4—201no—
260D4—201no—
261C2×C4—41no—
262C2×C4—121no—
263C2×C4—151no—
264C2×C4—151no—
265C2×C4—601no—
266C2×C4#679011yescharacteristic
267C8—301no—
268C8#677111yescharacteristic
269C8#677711yescharacteristic
270C2×C3—801no—
271C2×C3#6507511yescharacteristic
272C2×C3#6520511yescharacteristic
273C2×C3#6520711yescharacteristic
274C5#6920511yescharacteristic, complemented, Sylow
275C22—401no—
276C22—401no—
277C22—401no—
278C22#9148111yescharacteristic
279C4—81no—
280C4—241no—
281C4—301no—
282C4—301no—
283C4—602no—
284C4#9146111yescharacteristic
285C4#9150611yescharacteristic
286C3#1060003011yescharacteristic, complemented, Sylow
287C2—801no—
288C2#1174740611yescharacteristic
289C2#1174828411yescharacteristic
290C2#1174830911yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
hypercenter#107D3×D5
hypocenterC3×C5#2211
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #11750974C2semidirect
3. C2×#90948C2semidirect
5. C5×#4492C2semidirect
7. #11745928C2semidirect
56. #4492D5semidirect
238. C3×C5#2211semidirect
274. C5#69205semidirect
286. C3#10600030semidirect

Maximal subgroups

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

subgroupindex
#117509742
#117479802
C2×#909482
C2×#909422
C5×#44922
C3×#647112
#117459282
#106000303
#692055