Finite Group Databasebeta

← #14287397

Subgroups — #14287397

Order 1920.

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

normal subgroups only

This group has 332 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#11752364C211yesmaximal, characteristic
2#11751792C211yesmaximal, characteristic, complemented
3#11747261C211yesmaximal, characteristic
4C3×#64871C211yesmaximal, characteristic
5#11746513C211yesmaximal, characteristic, complemented
6#11746493C211yesmaximal, characteristic, complemented
7C3⋊C8×#170C211yesmaximal, characteristic, complemented
8#10603979—31nomaximal, Hall
9C2×#6758—21no—
10C3×#4039C2211yescharacteristic
11Dic5×Dic6C2211yescharacteristic
12C2×#6655C411yescharacteristic
13#91232—21no—
14C4⋊(C3⋊#170)C2211yescharacteristic
15C4×C3⋊#170C2211yescharacteristic
16C3×C4⋊#170C2211yescharacteristic
17C3×C4×#170C2211yescharacteristic
18#91177—21no—
19#91169—21no—
20#91092C411yescharacteristic
21C5×#810C411yescharacteristic
22#90965C411yescharacteristic
23Dic5×C3⋊C8C2211yescharacteristic
24#68161—51nomaximal, Hall
25#65788—31no—
26#65705—31no—
27#65077—31no—
28Q8⋊#170—31no—
29#64883—31no—
30C8×#170—31no—
31#64871D311yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3⋊#170—21no—
36C2×C3⋊#170D411yescharacteristic
37C2×C3⋊#170D411yescharacteristic
38#6758—42no—
39C2×C3×#170—21no—
40C2×C3×#170—21no—
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C4⋊Dic15C2×C411yescharacteristic
43C2×C3⋊#168C2×C411yescharacteristic
44C2×C5×C3⋊C8C2×C411yescharacteristic
45C3×#685—21no—
46C3×C4×Dic5C2311yescharacteristic
47Dic3⋊Dic5—21no—
48Dic3×Dic5—21no—
49#6655—22no—
50C4×#214—51no—
51#5012—51no—
52#4831—51no—
53C3×D4⋊C8—51no—
54#4480—51no—
55#4456—51no—
56C8×C3⋊C8—51no—
57C2×#700—61no—
58Q8×Dic5—31no—
59C2×#688—31no—
60#4039C2×D311yescharacteristic
61#4004—61no—
62#4003—61no—
63#4002—61no—
64C4⋊#170—31no—
65C4⋊#170C2×D311yescharacteristic
66C4×#170—31no—
67C4×#170C2×D311yescharacteristic
68C5×#103—31no—
69#3953—31no—
70C8×Dic5—31no—
71#3940—31no—
72#1590—151noSylow
73C22×C3×D5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5C22×C411yescharacteristic
76C2×Dic15—21no—
77C2×C5×Dic3—21no—
78C5×Dic6—21no—
79C5×Dic6—21no—
80C2×C3×Dic5C2×D411yescharacteristic
81C2×C3×Dic5#4111yescharacteristic
82C3×D20—21no—
83C3×D20—21no—
84C3×C4×D5—41no—
85C3×C4×D5—41no—
86C3⋊#170—21no—
87C3⋊#170—41no—
88C3⋊#170SD1612yescomplemented
89C3×#170—22no—
90C3×#170—41no—
91C3⋊#168M1612yescomplemented
92C5×C3⋊C8—21no—
93C3×C4×D4—51no—
94C2×#214—51no—
95C2×#208—101no—
96C4×Dic6—51no—
97C3×C4⋊C8—51no—
98C3×C4×C8—51no—
99#832—51no—
100#830—101no—
101#815—101no—
102Dic3⋊C8—101no—
103#810AGL(1,𝔽5)11yescharacteristic
104#808—51no—
105C4⋊(C3⋊C8)—51no—
106C4×C3⋊C8—51no—
107C4×C3⋊C8—51no—
108C2×C5×Q8—31no—
109C2×D20C4×D311yescharacteristic
110C2×C4×D5—21no—
111C2×#170—21no—
112C2×#170—21no—
113C2×#170—31no—
114C2×#170—31no—
115C2×#170—61no—
116#700—122no—
117C2×C5×C8—31no—
118C5×C4⋊C4C4×D311yescharacteristic
119#688—62no—
120#685—21no—
121C4⋊Dic5—31no—
122C4⋊Dic5—61no—
123C4×Dic5—61no—
124C4×Dic5C22×D311yescharacteristic
125C2×#168—31no—
126#446—151no—
127C4×SD16—151no—
128#436—151no—
129#334—151no—
130Q8⋊C8—151no—
131D4⋊C8—51no—
132C82—151no—
133C22×C3×C5C4×D411yescharacteristic
134C2×C3×D5—41no—
135C2×C3×D5—41no—
136C2×C3×D5—41no—
137C3×C4×C5—41no—
138C3×C4×C5C2×M1611yescharacteristic
139C3×C4×C5#13111yescharacteristic
140Dic15—41no—
141C3×Dic5—21no—
142C3×Dic5C2×SD1611yescharacteristic
143C3×Dic5#13511yescharacteristic
144C5×Dic3—41no—
145C2×C3×D4—51no—
146C22×C3×C4—101no—
147C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
148C2×C3×C8—101no—
149C2×C3×C8—101no—
150C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
151C3×C22⋊C4—101no—
152C3×C42—51no—
153#214—102no—
154C4⋊Dic3—51no—
155Dic3⋊C4—101no—
156C4×Dic3—101no—
157#208—202no—
158C2×C3⋊C8—51no—
159C2×C3⋊C8—51no—
160C2×C3⋊C8—51no—
161C2×C3⋊C8—101no—
162C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
163C22×D5—21no—
164C5×Q8—61no—
165C5×Q8—61no—
166C2×C4×C5—21no—
167C2×C4×C5—61no—
168C2×C4×C5C2×C4×D311yescharacteristic
169C2×Dic5—61no—
170C2×Dic5D3×D411yescharacteristic
171C2×Dic5#23711yescharacteristic
172D20—21no—
173D20—21no—
174C4×D5—41no—
175C4×D5—41no—
176#170—22no—
177#170—32no—
178#170—41no—
179#170—61no—
180#170—121no—
181C5×C8—61no—
182#168—32no—
183C2×SD16—151no—
184C2×M16—301no—
185C4×Q8—151no—
186C4×D4—51no—
187#106—151no—
188C4⋊C8—51no—
189C4⋊C8—151no—
190C4⋊C8—301no—
191#103—31no—
192#102—151no—
193C22⋊C8—301no—
194#97—301no—
195C4×C8—51no—
196C4×C8—151no—
197C4×C8—151no—
198C2×C3×C5#43611yescharacteristic
199C2×C3×C5C4×SD1611yescharacteristic
200C2×C3×C5#44311yescharacteristic
201C3×D5—81no—
202C23×C3—101no—
203C3×D4—101no—
204C3×D4—101no—
205C2×C3×C4—21no—
206C2×C3×C4—51no—
207C2×C3×C4—51no—
208C2×C3×C4—201no—
209C2×C3×C4—201no—
210C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—101no—
213Dic6—21no—
214Dic6—21no—
215C3×C8—102no—
216C3×C8—201no—
217C3⋊C8—21no—
218C3⋊C8—52no—
219C3⋊C8—52no—
220C3⋊C8—101no—
221C3⋊C8—201no—
222C22×C5#67⋊C411yescharacteristic
223C2×D5—41no—
224C2×D5—41no—
225C2×D5—41no—
226C4×C5—41no—
227C4×C5—121no—
228C4×C5#90111yescharacteristic
229C4×C5D3×M1611yescharacteristic
230Dic5—21no—
231Dic5—121no—
232Dic5#91211yescharacteristic
233Dic5D3×SD1611yescharacteristic
234C2×Q8—31no—
235C2×D4—51no—
236C22×C4—101no—
237SD16—302no—
238M16—602no—
239C2×C8—31no—
240C2×C8—101no—
241C2×C8—101no—
242C2×C8—151no—
243C2×C8—151no—
244C2×C8—151no—
245C2×C8—301no—
246C4⋊C4—151no—
247C4⋊C4—301no—
248C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
249C22⋊C4—101no—
250C42—51no—
251C42—301no—
252C3×C5#159011yescharacteristic, complemented, Hall
253C22×C3—201no—
254C22×C3—201no—
255C22×C3—201no—
256C22×C3D4×AGL(1,𝔽5)11yescharacteristic
257C3×C4—41no—
258C3×C4—51no—
259C3×C4—51no—
260C3×C4—101no—
261C3×C4D5⋊M1611yescharacteristic
262C3×C4#413111yescharacteristic
263Dic3—41no—
264Dic3—201no—
265C2×C5#472911yescharacteristic
266C2×C5#475811yescharacteristic
267C2×C5#482411yescharacteristic
268D5—81no—
269C23—101no—
270Q8—61no—
271Q8—61no—
272D4—101no—
273D4—101no—
274C2×C4—21no—
275C2×C4—51no—
276C2×C4—51no—
277C2×C4—61no—
278C2×C4—201no—
279C2×C4—201no—
280C2×C4—301no—
281C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
282C8—61no—
283C8—102no—
284C8—152no—
285C8—152no—
286C8—201no—
287C8—301no—
288C8—601no—
289C2×C3—401no—
290C2×C3#6569511yescharacteristic
291C2×C3SD16×AGL(1,𝔽5)11yescharacteristic
292C2×C3#6574011yescharacteristic
293C5#6816111yescharacteristic, complemented, Sylow
294C22—201no—
295C22—201no—
296C22—201no—
297C22#67⋊AGL(1,𝔽5)11yescharacteristic
298C4—41no—
299C4—51no—
300C4—51no—
301C4—101no—
302C4—121no—
303C4—601no—
304C4#9191111yescharacteristic
305C4#9191511yescharacteristic
306C3#1060397911yescharacteristic, complemented, Sylow
307C2—401no—
308C2#1175177311yescharacteristic
309C2#1175194511yescharacteristic
310C2#1175198111yescharacteristic
subgroupG/H
centerC22#67⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D20C2×C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1590
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751792C2semidirect
5. #11746513C2semidirect
6. #11746493C2semidirect
7. C3⋊C8×#170C2semidirect
88. C3⋊#170SD16semidirect
91. C3⋊#168M16semidirect
252. C3×C5#1590semidirect
293. C5#68161semidirect
306. C3#10603979semidirect

Maximal subgroups

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

subgroupindex
#117523642
#117517922
#117472612
C3×#648712
#117465132
#117464932
C3⋊C8×#1702
#106039793
#681615