Finite Group Databasebeta

← #14292006

Subgroups — #14292006

Order 1920.

332 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5093C211yesmaximal, characteristic, complemented
2C3×#65372C211yesmaximal, characteristic
3C3⋊C8×D20C211yesmaximal, characteristic
4#11746886C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11745866C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10602025—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C2×C3×#688—21no—
12C3×C4×D20C2211yescharacteristic
13C2×D5×C3⋊C8—21no—
14C4⋊(C3⋊#168)C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C5×#810—21no—
17C5×#810—21no—
18C4×C5×C3⋊C8C2211yescharacteristic
19C3×#3967—21no—
20C3×C4⋊#168C2211yescharacteristic
21#90989—21no—
22#90964—21no—
23#90955—21no—
24#71038—51nomaximal, Hall
25C5×#487—31no—
26#65376—31no—
27#65372D311yescharacteristic
28C8×D20—31no—
29#64767—31no—
30#64767—31no—
31#64677—31no—
32C2×C3×C5×Q8—21no—
33C2×C5×Dic6—21no—
34C2×C3×D20D411yescharacteristic
35C2×C3×C4×D5—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C42×C5C2311yescharacteristic
39C2×C3⋊#168—21no—
40C2×C3⋊#168—21no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C2×C5×C3⋊C8D411yescharacteristic
44C2×C5×C3⋊C8D411yescharacteristic
45C3×#688—42no—
46C3×#685—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C2×C3×#168—21no—
49D5×C3⋊C8—42no—
50C3×#461—51no—
51#5093D511yescharacteristic, complemented
52D4×C3⋊C8—51no—
53#5007—51no—
54#4547—51no—
55#4486—51no—
56#4480—51no—
57C5×C4⋊Q8—31no—
58C5×C4⋊Q8C2×D311yescharacteristic
59C2×#688—21no—
60C2×C8×D5—61no—
61C4×D20C2×D311yescharacteristic
62C5×#103—61no—
63C5×#103—61no—
64C4×C5×C8—31no—
65#3967—21no—
66#3952—61no—
67#3941—61no—
68#3939—61no—
69C4⋊#168—31no—
70C4⋊#168—31no—
71C4⋊#168C2×D311yescharacteristic
72#1679—151noSylow
73C22×C3×D5—21no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C2×C5×Dic3—41no—
81C5×Dic6—41no—
82C5×Dic6—41no—
83C2×C3×Dic5—21no—
84C3×D20—21no—
85C3×D20SD1612yes—
86C3×C4×D5—41no—
87C3×C4×D5—41no—
88C3⋊#168—41no—
89C3⋊#168—41no—
90C3×#168—41no—
91C5×C3⋊C8—21no—
92C5×C3⋊C8—21no—
93C2×C3×SD16—101no—
94C3×C4⋊Q8C2×D511yescharacteristic
95C3×C4×D4—51no—
96C22×C3⋊C8—101no—
97#869C2×D511yescharacteristic
98C3×C4⋊C8—51no—
99C3×#103—101no—
100#832—101no—
101#830—101no—
102#810—21no—
103#810—21no—
104#807—101no—
105C4⋊(C3⋊C8)—51no—
106C4⋊(C3⋊C8)—51no—
107C4×C3⋊C8C2×D511yescharacteristic
108C2×C5×Q8—21no—
109C2×C5×Q8—61no—
110C2×D20#6711yescharacteristic
111C2×C4×D5—21no—
112C2×C5×C8—31no—
113C2×C5×C8—31no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—61no—
117C5×C4⋊C4—61no—
118C42×C5C22×D311yescharacteristic
119#688—42no—
120#685—21no—
121C4⋊Dic5#6711yescharacteristic
122C2×#168—21no—
123C2×#168—61no—
124C2×#168—61no—
125C8×D5—122no—
126#487—31no—
127#474—151no—
128#461—51no—
129C8×D4—151no—
130#334—151no—
131#332—151no—
132#332—151no—
133C22×C3×C5#12111yescharacteristic
134C2×C3×D5—22no—
135C2×C3×D5—41no—
136C2×C3×D5—41no—
137C3×C4×C5—21no—
138C3×C4×C5—81no—
139C3×C4×C5C2×SD1611yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C3×Dic5—41no—
144C5×Dic3—81no—
145C2×C3×Q8—21no—
146C2×C3×D4—51no—
147C22×C3×C4—101no—
148C2×Dic6—21no—
149C3×SD16—202no—
150C2×C3×C8—101no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—51no—
154C3×C22⋊C4—101no—
155C3×C42C22×D511yescharacteristic
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C2×C3⋊C8—101no—
159C2×C3⋊C8—101no—
160C2×C3⋊C8—202no—
161C2×C3⋊C8C22⋊D511yescharacteristic
162C2×C3⋊C8C22⋊D511yescharacteristic
163C22×D5—21no—
164C5×Q8—41no—
165C5×Q8—41no—
166C5×Q8—121no—
167C5×Q8—121no—
168C2×C4×C5—41no—
169C2×C4×C5—121no—
170C2×C4×C5D3×D411yescharacteristic
171C2×C4×C5#23711yescharacteristic
172C2×C4×C5C2×#6711yescharacteristic
173C2×Dic5—21no—
174D20—21no—
175D20#21412yes—
176C4×D5—41no—
177C4×D5—41no—
178C5×C8—61no—
179C5×C8—61no—
180#168—41no—
181#168—121no—
182#168—121no—
183C2×SD16—101no—
184C22×C8—301no—
185C4⋊Q8—31no—
186C4⋊Q8D3×D511yescharacteristic
187C4×D4—51no—
188#107—301no—
189C4⋊C8—51no—
190C4⋊C8—151no—
191C4⋊C8—151no—
192#103—61no—
193#103—61no—
194#103—101no—
195#102—301no—
196C22⋊C8—301no—
197C4×C8—31no—
198C2×C3×C5#46311yescharacteristic
199C2×C3×C5#46511yescharacteristic
200C2×C3×C5#47311yescharacteristic
201C3×D5—42no—
202C23×C3—101no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×D4—52no—
206C3×D4—101no—
207C2×C3×C4—41no—
208C2×C3×C4—101no—
209C2×C3×C4—201no—
210C2×C3×C4—201no—
211C2×C3×C4D4×D511yescharacteristic
212C2×C3×C4#71111yescharacteristic
213C2×C3×C4C2×C22⋊D511yescharacteristic
214C2×Dic3—41no—
215Dic6—41no—
216Dic6—41no—
217C3×C8—201no—
218C3⋊C8—21no—
219C3⋊C8—21no—
220C3⋊C8—201no—
221C3⋊C8—201no—
222C22×C5#93911yescharacteristic
223C2×D5—22no—
224C2×D5—41no—
225C2×D5—41no—
226C4×C5—21no—
227C4×C5—81no—
228C4×C5—241no—
229C4×C5#91411yescharacteristic
230C4×C5#91611yescharacteristic
231C4×C5C2×#21411yescharacteristic
232C4×C5#95011yescharacteristic
233Dic5—41no—
234C2×Q8—21no—
235C2×Q8—61no—
236C2×D4—51no—
237C22×C4—101no—
238SD16—202no—
239C2×C8—31no—
240C2×C8—31no—
241C2×C8—101no—
242C2×C8—301no—
243C2×C8—301no—
244C2×C8—602no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—51no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C22⋊C4—101no—
251C42C2×D3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3—102no—
254C22×C3—201no—
255C22×C3—201no—
256C22×C3#408411yescharacteristic
257C3×C4—21no—
258C3×C4—81no—
259C3×C4—201no—
260C3×C4D5×SD1611yescharacteristic
261C3×C4#406211yescharacteristic
262C3×C4#409511yescharacteristic
263C3×C4#409611yescharacteristic
264Dic3—81no—
265C2×C5#504111yescharacteristic
266C2×C5#516511yescharacteristic
267C2×C5#520411yescharacteristic
268D5—42no—
269C23—101no—
270Q8—41no—
271Q8—41no—
272Q8—121no—
273Q8—121no—
274D4—52no—
275D4—101no—
276C2×C4—41no—
277C2×C4—101no—
278C2×C4—121no—
279C2×C4—201no—
280C2×C4—201no—
281C2×C4#678011yescharacteristic
282C2×C4D5×#6711yescharacteristic
283C2×C4D3×C22⋊D511yescharacteristic
284C8—61no—
285C8—61no—
286C8—201no—
287C8—601no—
288C8—601no—
289C2×C3—202no—
290C2×C3#6534611yescharacteristic
291C2×C3#6546011yescharacteristic
292C2×C3#6548111yescharacteristic
293C5#7103811yescharacteristic, complemented, Sylow
294C22—102no—
295C22—201no—
296C22—201no—
297C22#9154911yescharacteristic
298C4—21no—
299C4—81no—
300C4—201no—
301C4—241no—
302C4D5×#21411yescharacteristic
303C4#9149211yescharacteristic
304C4#9150411yescharacteristic
305C4#9151711yescharacteristic
306C3#1060202511yescharacteristic, complemented, Sylow
307C2—202no—
308C2#1174912011yescharacteristic
309C2#1174922811yescharacteristic
310C2#1174937511yescharacteristic
subgroupG/H
centerC22#91549
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1679
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
1. C5×#5093C2semidirect
5. #11746368C2semidirect
6. #11745866C2semidirect
7. #11745857C2semidirect
51. #5093D5semidirect
252. C3×C5#1679semidirect
293. C5#71038semidirect
306. C3#10602025semidirect

Maximal subgroups

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

subgroupindex
C5×#50932
C3×#653722
C3⋊C8×D202
#117468862
#117463682
#117458662
#117458572
#106020253
#710385