Finite Group Databasebeta

← #14317299

Subgroups — #14317299

Order 1920.

316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C5×#4873C211yesmaximal, characteristic, complemented
2#11747974C211yesmaximal, characteristic
3C2×#90946C211yesmaximal, characteristic, complemented
4C2×#90945C211yesmaximal, characteristic
5#11746312C211yesmaximal, characteristic
6C3×#64712C211yesmaximal, characteristic, complemented
7Dic3⋊#672C211yesmaximal, characteristic, complemented
8#10601708—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C5×#887—21no—
12C2×C3×Dic20C2211yescharacteristic
13#91374—21no—
14C2×#6658—21no—
15C3×C5×#107C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C5×C8×Dic3C2211yescharacteristic
18C5×#810—21no—
19C2×C3×#672C2211yescharacteristic
20#90946—22no—
21#90945—22no—
22#69237—51nomaximal, Hall
23C4×C5×Q16—31no—
24C2×#3961—31no—
25C2×#3960—31no—
26#64985—31no—
27#64712D311yescharacteristic, complemented
28#64711—31no—
29C4⋊#672—31no—
30C2×D60—21no—
31C2×C5×Dic6—21no—
32C2×C3×Dic10—21no—
33C2×C3×C5×C8C2311yescharacteristic
34C3×C5×C4⋊C4—21no—
35D120—21no—
36D120—21no—
37C5×Dic3⋊C4—41no—
38C4×C5×Dic3—41no—
39C4×C5×Dic3D411yescharacteristic
40C2×C5×C3⋊C8D411yescharacteristic
41C5×Dic12—21no—
42C5×Dic12D412yes—
43C3×Dic20—21no—
44C3×Dic20—21no—
45#6667—41no—
46#6667—41no—
47#6658—42no—
48C3⋊#672—21no—
49C3×#672—21no—
50#5191—51no—
51C2×#829—51no—
52C2×#800—51no—
53#4873D511yescharacteristic, complemented
54C3×#358—51no—
55Dic3⋊C16—51no—
56#4491—51no—
57C2×C5×Q16—31no—
58C4×C5×Q8—61no—
59C2×Dic20C2×D311yescharacteristic
60C2×D40—31no—
61C2×#677—61no—
62#4021—61no—
63C5×#107C2×D311yescharacteristic
64C5×#103—61no—
65C4×C5×C8—31no—
66#3961—62no—
67#3960—62no—
68C2×#672—31no—
69C2×#672C2×D311yescharacteristic
70#2211—151noSylow
71C22×D15—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74D60—41no—
75D60—41no—
76C2×C5×Dic3—41no—
77C2×C5×Dic3D811yescharacteristic
78C2×C5×Dic3D811yescharacteristic
79C5×Dic6—22no—
80C5×Dic6—41no—
81C2×C3×Dic5—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C5×C3⋊C8—21no—
87C2×C3×Q16—51no—
88#947—101no—
89C2×#215—101no—
90C2×Dic12C2×D511yescharacteristic
91C2×D24—51no—
92#887—21no—
93C2×C3×C16—51no—
94C3×#107C2×D511yescharacteristic
95#829—102no—
96C8×Dic3C2×D511yescharacteristic
97C2×C3⋊C16—51no—
98#810—21no—
99#800—102no—
100C2×C5×Q8—61no—
101C2×D20—61no—
102C2×Dic10—21no—
103C5×Q16—32no—
104C5×Q16—61no—
105C2×C5×C8—31no—
106C2×C5×C8C22×D311yescharacteristic
107C5×C4⋊C4—21no—
108C5×C4⋊C4—121no—
109C42×C5—31no—
110C42×C5—121no—
111#685—121no—
112#685—121no—
113Dic20—21no—
114Dic20—21no—
115D40—61no—
116D40—61no—
117#677—122no—
118#672—21no—
119#672—61no—
120C2×Q32—151no—
121C2×SD32—151no—
122#495—151no—
123C4×Q16—31no—
124C4⋊C16—151no—
125#358—51no—
126#357—151no—
127C22×C3×C5C2×D811yescharacteristic
128C2×D15—81no—
129C2×D15—81no—
130C2×D15—81no—
131C3×C4×C5—81no—
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134C3×Dic5—81no—
135C5×Dic3—21no—
136C5×Dic3—21no—
137C5×Dic3—42no—
138C2×C3×Q8—101no—
139C2×D12—101no—
140C2×Dic6—21no—
141C3×Q16—101no—
142C3×Q16—101no—
143C2×C3×C8C22×D511yescharacteristic
144C3×C4⋊C4—21no—
145#215—202no—
146(C2×D3)⋊C4—201no—
147(C2×D3)⋊C4—201no—
148Dic3⋊C4—41no—
149C4×Dic3—41no—
150C4×Dic3C22⋊D511yescharacteristic
151C2×C3⋊C8C22⋊D511yescharacteristic
152Dic12—21no—
153Dic12D2012yes—
154D24—101no—
155D24—101no—
156C3×C16—101no—
157C3⋊C16—101no—
158C22×D5—121no—
159C5×Q8—62no—
160C5×Q8—121no—
161C2×C4×C5—31no—
162C2×C4×C5—31no—
163C2×C4×C5—41no—
164C2×C4×C5—121no—
165C2×C4×C5D3×D411yescharacteristic
166C2×Dic5—41no—
167D20—121no—
168D20—121no—
169Dic10—41no—
170Dic10—41no—
171C5×C8—61no—
172C5×C8#23511yescharacteristic
173C5×C8D3×D411yescharacteristic
174C2×Q16—31no—
175C2×Q16—51no—
176C2×SD16—301no—
177C2×D8—151no—
178#124—301no—
179C4×Q8—61no—
180Q32—302no—
181SD32—302no—
182C2×C16—51no—
183C2×C16—151no—
184#107D3×D511yescharacteristic
185#103—61no—
186C4×C8—31no—
187C2×C3×C5#45911yescharacteristic
188C2×C3×C5#50811yescharacteristic
189C2×C3×C5#51011yescharacteristic
190D15—161no—
191C22×D3—201no—
192C3×Q8—201no—
193C3×Q8—201no—
194C2×C3×C4—41no—
195C2×C3×C4—201no—
196C2×C3×C4C2×C22⋊D511yescharacteristic
197C2×Dic3—41no—
198C2×Dic3#68611yescharacteristic
199C2×Dic3#68611yescharacteristic
200D12—201no—
201D12—201no—
202Dic6—22no—
203Dic6—41no—
204C3×C8C2×D2011yescharacteristic
205C3×C8#70911yescharacteristic
206C3⋊C8—21no—
207C22×C5D3×D811yescharacteristic
208C2×D5—241no—
209C2×D5—241no—
210C2×D5—241no—
211C4×C5—61no—
212C4×C5—61no—
213C4×C5—81no—
214C4×C5—122no—
215C4×C5#88411yescharacteristic
216C4×C5#91411yescharacteristic
217Dic5—81no—
218C2×Q8—61no—
219C2×Q8—101no—
220C2×D4—301no—
221Q16—32no—
222Q16—61no—
223Q16—101no—
224Q16—101no—
225SD16—602no—
226D8—301no—
227D8—301no—
228C2×C8—31no—
229C2×C8C2×D3×D511yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—121no—
232C22⋊C4—601no—
233C22⋊C4—601no—
234C42—31no—
235C42—121no—
236C16—101no—
237C16—301no—
238C3×C5#221111yescharacteristic, complemented, Hall
239C22×C3C2×#68611yescharacteristic
240C2×D3—401no—
241C2×D3—401no—
242C2×D3—401no—
243C3×C4—81no—
244C3×C4—401no—
245C3×C4#407611yescharacteristic
246C3×C4#409511yescharacteristic
247Dic3—21no—
248Dic3—21no—
249Dic3—42no—
250C2×C5#478611yescharacteristic
251C2×C5#491611yescharacteristic
252C2×C5#491811yescharacteristic
253D5—481no—
254C23—601no—
255Q8—62no—
256Q8—121no—
257Q8—201no—
258Q8—201no—
259D4—601no—
260D4—601no—
261C2×C4—31no—
262C2×C4—31no—
263C2×C4—41no—
264C2×C4—121no—
265C2×C4—201no—
266C2×C4D3×C22⋊D511yescharacteristic
267C8—61no—
268C8#677111yescharacteristic
269C8D3×D2011yescharacteristic
270C2×C3#6530411yescharacteristic
271C2×C3#6546811yescharacteristic
272C2×C3#6548311yescharacteristic
273D3—801no—
274C5#6923711yescharacteristic, complemented, Sylow
275C22—1201no—
276C22—1201no—
277C22—1201no—
278C22D3×#68611yescharacteristic
279C4—61no—
280C4—61no—
281C4—81no—
282C4—122no—
283C4—401no—
284C4#9145411yescharacteristic
285C4#9150411yescharacteristic
286C3#1060170811yescharacteristic, complemented, Sylow
287C2—2401no—
288C2#1174740211yescharacteristic
289C2#1174828211yescharacteristic
290C2#1174830711yescharacteristic
subgroupG/H
centerC22D3×#686
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
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. C5×#4873C2semidirect
3. C2×#90946C2semidirect
6. C3×#64712C2semidirect
7. Dic3⋊#672C2semidirect
27. #64712D3semidirect
53. #4873D5semidirect
238. C3×C5#2211semidirect
274. C5#69237semidirect
286. C3#10601708semidirect

Maximal subgroups

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

subgroupindex
C5×#48732
#117479742
C2×#909462
C2×#909452
#117463122
C3×#647122
Dic3⋊#6722
#106017083
#692375