Finite Group Databasebeta

← #14284030

Subgroups — #14284030

Order 1920.

452 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 106 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#11752506C211yesmaximal, characteristic
2C4×#6758C211yesmaximal, characteristic
3C3×C4×#700C211yesmaximal, characteristic
4#11746506C214yesmaximal, complemented
5#10604634—31nomaximal, Hall
6C2×#6758—21no—
7C2×C3×#700—21no—
8#91758C411yescharacteristic
9C5×#869C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91388C2212yes—
12#91360—21no—
13#91359—21no—
14#91358C412yes—
15#91333—21no—
16Dic5×Dic6—21no—
17#91231C2212yes—
18C4×C3⋊#170—21no—
19C3×#4002C2212yes—
20C3×C4×#170—21no—
21#69862—51nomaximal, Hall
22#66062—31no—
23C4×#700—31no—
24C4×#700D311yescharacteristic
25#64870—34no—
26C2×Dic30—21no—
27C2×C5×Dic6—21no—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3⋊#170—22no—
32#6758—24no—
33C2×C3×#170—22no—
34C3×#700—24no—
35C3×C42×C5C2×C411yescharacteristic
36C4⋊Dic15—21no—
37C4⋊Dic15C2×C412yes—
38C5×C4⋊Dic3—21no—
39C5×C4⋊Dic3C2×C412yes—
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5D411yescharacteristic
42C3×C4×Dic5C2311yescharacteristic
43Dic3⋊Dic5—22no—
44#6669—22no—
45#6665—22no—
46Dic3×Dic5—22no—
47#5470—51no—
48C3×C4×M16—51no—
49C4×#208—51no—
50#4465—54no—
51C2×#700—21no—
52C2×#700—61no—
53C5×C4⋊Q8—31no—
54#4092—61no—
55Q8×Dic5—61no—
56#4043—61no—
57#4038—32no—
58#4036—32no—
59#4033—61no—
60C42×D5C2×D311yescharacteristic
61#4015—31no—
62#4002—32no—
63#4002C2×D312yes—
64C4×#170—21no—
65C4×#170—61no—
66#1526—151noSylow
67C22×C3×D5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22×C411yescharacteristic
71C2×Dic15—22no—
72Dic30—42no—
73C2×C5×Dic3—22no—
74C5×Dic6—42no—
75C2×C3×Dic5C22⋊C411yescharacteristic
76C2×C3×Dic5C2×D411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C3×C4×D5—22no—
79C3×C4×D5—22no—
80C3×C4×D5—22no—
81C3⋊#170—24no—
82C3×#170—24no—
83C2×C3×M16—101no—
84C2×C3×C42—51no—
85#926—52no—
86#924—101no—
87#924—101no—
88C2×#208—101no—
89#870—52no—
90#869—51no—
91#869AGL(1,𝔽5)11yescharacteristic
92C4×Dic6—101no—
93C4×Dic6—101no—
94C3×#97—52no—
95C3×C4×C8—101no—
96#803—52no—
97C4×C3⋊C8—101no—
98C2×C5×Q8—61no—
99C2×C4×D5C4×D311yescharacteristic
100C2×C4×D5D1211yescharacteristic
101C2×C4×D5#6711yescharacteristic
102C2×Dic10—61no—
103C2×#170—22no—
104C2×#170—62no—
105#700—24no—
106#700—64no—
107C5×C4⋊C4—32no—
108C5×C4⋊C4—61no—
109C42×C5C4×D311yescharacteristic
110#685—62no—
111C4⋊Dic5—32no—
112C4⋊Dic5—61no—
113C4⋊Dic5—62no—
114#683—62no—
115C4×Dic5—62no—
116C4×Dic5D1211yescharacteristic
117C4×Dic5#6711yescharacteristic
118C4×Dic5C22×D311yescharacteristic
119#533—151no—
120C4×M16—51no—
121C4×M16—151no—
122#330—154no—
123C22×C3×C5C2×C22⋊C411yescharacteristic
124C2×C3×D5—21no—
125C2×C3×D5—21no—
126C2×C3×D5—21no—
127C3×C4×C5—21no—
128C3×C4×C5#10412yes—
129C3×C4×C5#10412yes—
130Dic15—42no—
131C3×Dic5—21no—
132C3×Dic5—21no—
133C3×Dic5#10112yes—
134C5×Dic3—42no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C2×Dic6—21no—
139C2×Dic6—101no—
140C3×M16—104no—
141C2×C3×C8—102no—
142C3×C42—51no—
143C3×C42—51no—
144C3×C42—51no—
145C3×C42C2×AGL(1,𝔽5)11yescharacteristic
146#217—102no—
147C4⋊Dic3—21no—
148C4⋊Dic3—52no—
149C4⋊Dic3—101no—
150C4⋊Dic3C2×AGL(1,𝔽5)12yes—
151Dic3⋊C4—102no—
152Dic3⋊C4—102no—
153C4×Dic3—102no—
154#208—104no—
155C2×C3⋊C8—102no—
156C22×D5(C2×D3)⋊C411yescharacteristic
157C5×Q8—122no—
158C2×C4×C5—62no—
159C2×C4×C5(C2×D3)⋊C411yescharacteristic
160C2×C4×C5(C2×D3)⋊C411yescharacteristic
161C2×C4×C5C2×C4×D311yescharacteristic
162C2×Dic5—62no—
163C2×Dic5(C2×D3)⋊C411yescharacteristic
164C2×Dic5C2×D1211yescharacteristic
165C2×Dic5C2×#6711yescharacteristic
166C4×D5—22no—
167C4×D5—22no—
168C4×D5—22no—
169Dic10—122no—
170#170—24no—
171#170—64no—
172C2×M16—101no—
173C2×M16—301no—
174C4⋊Q8—31no—
175C4⋊Q8—151no—
176#125—152no—
177C22⋊Q8—301no—
178C22⋊Q8—301no—
179C4×Q8—301no—
180C4×Q8—301no—
181#117—152no—
182C2×C42—51no—
183#97—52no—
184#97—152no—
185C4×C8—101no—
186C4×C8—301no—
187C2×C3×C5C2×#10111yescharacteristic
188C2×C3×C5C2×#10411yescharacteristic
189C2×C3×C5C2×#10411yescharacteristic
190C3×D5—41no—
191C23×C3—51no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—102no—
196C2×C3×C4—102no—
197C2×C3×C4—102no—
198C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
199C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
200C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
201C2×Dic3—22no—
202C2×Dic3—102no—
203Dic6—42no—
204Dic6—202no—
205C3×C8—104no—
206C3⋊C8—104no—
207C22×C5C2×(C2×D3)⋊C411yescharacteristic
208C2×D5—21no—
209C2×D5—21no—
210C2×D5—21no—
211C4×C5—21no—
212C4×C5—122no—
213C4×C5#80512yes—
214C4×C5#82512yes—
215Dic5—21no—
216Dic5—21no—
217Dic5—122no—
218Dic5#82412yes—
219C2×Q8—61no—
220C2×Q8—301no—
221C22×C4—51no—
222C22×C4—51no—
223C22×C4—51no—
224M16—104no—
225M16—304no—
226C2×C8—102no—
227C2×C8—302no—
228C4⋊C4—32no—
229C4⋊C4—61no—
230C4⋊C4—152no—
231C4⋊C4—302no—
232C4⋊C4—302no—
233C4⋊C4—301no—
234C22⋊C4—302no—
235C42—51no—
236C42—51no—
237C42—51no—
238C42—302no—
239C42D3×AGL(1,𝔽5)11yescharacteristic
240C3×C5#152611yescharacteristic, complemented, Hall
241C22×C3—101no—
242C22×C3—101no—
243C22×C3—101no—
244C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
245C3×C4—21no—
246C3×C4—52no—
247C3×C4—101no—
248C3×C4—101no—
249C3×C4#400812yes—
250C3×C4#401012yes—
251Dic3—42no—
252Dic3—202no—
253C2×C5C2×#80511yescharacteristic
254C2×C5C2×#82411yescharacteristic
255C2×C5C2×#82511yescharacteristic
256D5—41no—
257C23—51no—
258Q8—122no—
259Q8—602no—
260C2×C4—51no—
261C2×C4—51no—
262C2×C4—51no—
263C2×C4—62no—
264C2×C4—102no—
265C2×C4—102no—
266C2×C4—102no—
267C2×C4—302no—
268C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
269C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
270C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
271C8—104no—
272C8—304no—
273C2×C3—201no—
274C2×C3C2×#400811yescharacteristic
275C2×C3C2×#401011yescharacteristic
276C2×C3D5⋊#10111yescharacteristic
277C5#6986211yescharacteristic, complemented, Sylow
278C22—101no—
279C22—101no—
280C22—101no—
281C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
282C4—21no—
283C4—52no—
284C4—101no—
285C4—101no—
286C4—122no—
287C4—602no—
288C4#9115512yes—
289C4#9115812yes—
290C3#1060463411yescharacteristic, complemented, Sylow
291C2—201no—
292C2C2×#9115511yescharacteristic
293C2C2×#9115811yescharacteristic
294C2D5⋊#82411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746506C2semidirect
240. C3×C5#1526semidirect
277. C5#69862semidirect
290. C3#10604634semidirect

Maximal subgroups

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

subgroupindex
#117525062
C4×#67582
C3×C4×#7002
#117465062
#106046343
#698625