Finite Group Databasebeta

← #14284837

Subgroups — #14284837

Order 1920.

480 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 118 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
1D5×#869C211yesmaximal, characteristic
2#11752341C211yesmaximal, characteristic
3C3×#65678C211yesmaximal, characteristic
4#11746510C214yesmaximal, complemented
5#10604658—31nomaximal, Hall
6C2×D5×Dic6—21no—
7C2×#6758—21no—
8#91758C411yescharacteristic
9C5×#869C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91468—21no—
12#91468C2212yes—
13D5×C4⋊Dic3—21no—
14D5×C4⋊Dic3C412yes—
15#91376—21no—
16#91233—21no—
17#91233C2212yes—
18C3×#4004C2212yes—
19C3×#4003—21no—
20C3×C4×#170—21no—
21#70778—51nomaximal, Hall
22D5×C4⋊Q8—31no—
23#65682—31no—
24#65678D311yescharacteristic
25#64873—34no—
26C2×Dic30—21no—
27C2×C5×Dic6—21no—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×#1204—22no—
32C2×D5×Dic3—22no—
33D5×Dic6—42no—
34D5×Dic6—42no—
35C2×C3⋊#170—22no—
36#6758—42no—
37C2×C3×#170—22no—
38C3×C42×C5C2×C411yescharacteristic
39C4⋊Dic15—21no—
40C4⋊Dic15C2×C412yes—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3C2×C412yes—
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46#6668—22no—
47#6668—22no—
48C2×#869—51no—
49C3×#431—51no—
50#4924—51no—
51#4486—54no—
52C2×Q8×D5—61no—
53C2×#700—61no—
54C5×C4⋊Q8—31no—
55#4090—61no—
56D5×C4⋊C4—32no—
57D5×C4⋊C4—61no—
58#4034—32no—
59#4034—61no—
60C42×D5C2×D311yescharacteristic
61#4015—31no—
62#4004—32no—
63#4004—61no—
64#4004C2×D312yes—
65#4003—21no—
66C4×#170—21no—
67#1546—151noSylow
68C22×C3×D5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×Dic15—22no—
73Dic30—42no—
74C2×C5×Dic3—22no—
75C5×Dic6—42no—
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C3×C4×D5—22no—
80C3×C4×D5—22no—
81C3×C4×D5D812yes—
82C3×C4×D5SD1612yes—
83#1204—42no—
84#1204—42no—
85D5×Dic3—44no—
86C3⋊#170—42no—
87C3×#170—42no—
88C22×Dic6—101no—
89C2×C3×C42—51no—
90C2×C4⋊Dic3—52no—
91C2×C4⋊Dic3—101no—
92C2×#208—101no—
93#869—51no—
94#869—52no—
95#869—101no—
96#869—101no—
97#869AGL(1,𝔽5)11yescharacteristic
98C3×C4⋊C8—52no—
99C3×C22⋊C8—101no—
100C3×C4×C8—101no—
101C4⋊(C3⋊C8)—52no—
102C4⋊(C3⋊C8)—101no—
103C2×C5×Q8—61no—
104Q8×D5—122no—
105Q8×D5—122no—
106C2×C4×D5—62no—
107C2×C4×D5C4×D311yescharacteristic
108C2×C4×D5D1211yescharacteristic
109C2×C4×D5#6711yescharacteristic
110C2×Dic10—61no—
111C2×Dic10—62no—
112C2×#170—22no—
113C2×#170—62no—
114#700—122no—
115C5×C4⋊C4—32no—
116C5×C4⋊C4—61no—
117C42×C5C4×D311yescharacteristic
118C4⋊Dic5—32no—
119C4⋊Dic5—61no—
120#683—62no—
121#683—62no—
122C4×Dic5D1211yescharacteristic
123C4×Dic5#6711yescharacteristic
124C4×Dic5C22×D311yescharacteristic
125C2×C4⋊Q8—151no—
126#431—51no—
127#423—151no—
128#332—154no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×C3×D5—21no—
131C2×C3×D5—21no—
132C2×C3×D5#10212yes—
133C3×C4×C5—21no—
134C3×C4×C5—21no—
135C3×C4×C5#10212yes—
136Dic15—42no—
137C3×Dic5#10112yes—
138C3×Dic5C2×D811yescharacteristic
139C3×Dic5C2×SD1611yescharacteristic
140C3×Dic5#13712yes—
141C5×Dic3—42no—
142C22×C3×C4—51no—
143C22×C3×C4—51no—
144C22×C3×C4—51no—
145C22×Dic3—102no—
146C2×Dic6—21no—
147C2×Dic6—102no—
148C2×Dic6—101no—
149C2×Dic6—202no—
150C2×Dic6—202no—
151C2×C3×C8—102no—
152C3×C42—51no—
153C3×C42—51no—
154C3×C42—51no—
155C3×C42C2×AGL(1,𝔽5)11yescharacteristic
156C4⋊Dic3—21no—
157C4⋊Dic3—52no—
158C4⋊Dic3—102no—
159C4⋊Dic3—102no—
160C4⋊Dic3—101no—
161C4⋊Dic3C2×AGL(1,𝔽5)12yes—
162#208—202no—
163C2×C3⋊C8—102no—
164C22×D5(C2×D3)⋊C411yescharacteristic
165C5×Q8—122no—
166C2×C4×C5—62no—
167C2×C4×C5(C2×D3)⋊C411yescharacteristic
168C2×C4×C5(C2×D3)⋊C411yescharacteristic
169C2×C4×C5C2×C4×D311yescharacteristic
170C2×Dic5—62no—
171C2×Dic5(C2×D3)⋊C411yescharacteristic
172C2×Dic5C2×D1211yescharacteristic
173C2×Dic5C2×#6711yescharacteristic
174C4×D5—22no—
175C4×D5—22no—
176C4×D5—124no—
177C4×D5#20412yes—
178C4×D5D2412yes—
179Dic10—122no—
180Dic10—122no—
181Dic10—122no—
182#170—42no—
183#170—122no—
184C22×Q8—301no—
185C2×M16—301no—
186C4⋊Q8—31no—
187C4⋊Q8—152no—
188C4⋊Q8—151no—
189C4⋊Q8—301no—
190C4⋊Q8—301no—
191C2×C4⋊C4—152no—
192C2×C4⋊C4—301no—
193C2×C42—51no—
194C4⋊C8—52no—
195C4⋊C8—152no—
196C4⋊C8—301no—
197C22⋊C8—101no—
198C4×C8—101no—
199C2×C3×C5C2×#10111yescharacteristic
200C2×C3×C5C2×#10211yescharacteristic
201C2×C3×C5#41911yescharacteristic
202C3×D5—22no—
203C23×C3—51no—
204C2×C3×C4—51no—
205C2×C3×C4—51no—
206C2×C3×C4—51no—
207C2×C3×C4—52no—
208C2×C3×C4—52no—
209C2×C3×C4—102no—
210C2×C3×C4—102no—
211C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
212C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
213C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
214C2×Dic3—22no—
215C2×Dic3—102no—
216C2×Dic3—204no—
217Dic6—42no—
218Dic6—202no—
219Dic6—202no—
220Dic6—202no—
221C3×C8—202no—
222C3⋊C8—202no—
223C22×C5C2×(C2×D3)⋊C411yescharacteristic
224C2×D5—21no—
225C2×D5—21no—
226C2×D5#82112yes—
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—122no—
230C4×C5#82112yes—
231Dic5—122no—
232Dic5#82412yes—
233Dic5C2×#20411yescharacteristic
234Dic5C2×D2411yescharacteristic
235Dic5#95112yes—
236C2×Q8—61no—
237C2×Q8—302no—
238C2×Q8—301no—
239C2×Q8—602no—
240C2×Q8—602no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—302no—
245M16—602no—
246C2×C8—102no—
247C2×C8—302no—
248C4⋊C4—32no—
249C4⋊C4—61no—
250C4⋊C4—152no—
251C4⋊C4—302no—
252C4⋊C4—302no—
253C4⋊C4—301no—
254C42—51no—
255C42—51no—
256C42—51no—
257C42D3×AGL(1,𝔽5)11yescharacteristic
258C3×C5#154611yescharacteristic, complemented, Hall
259C22×C3—52no—
260C22×C3—101no—
261C22×C3—101no—
262C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—51no—
266C3×C4—51no—
267C3×C4—52no—
268C3×C4—52no—
269C3×C4#400712yes—
270Dic3—42no—
271Dic3—202no—
272C2×C5#500411yescharacteristic
273C2×C5C2×#82111yescharacteristic
274C2×C5C2×#82411yescharacteristic
275D5—22no—
276C23—51no—
277Q8—122no—
278Q8—602no—
279Q8—602no—
280Q8—602no—
281C2×C4—51no—
282C2×C4—51no—
283C2×C4—51no—
284C2×C4—52no—
285C2×C4—52no—
286C2×C4—62no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—302no—
290C2×C4—604no—
291C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
292C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
293C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
294C8—202no—
295C8—602no—
296C2×C3—102no—
297C2×C3C2×#400711yescharacteristic
298C2×C3#6578211yescharacteristic
299C2×C3D5⋊#10111yescharacteristic
300C5#7077811yescharacteristic, complemented, Sylow
301C22—52no—
302C22—101no—
303C22—101no—
304C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
305C4—21no—
306C4—21no—
307C4—51no—
308C4—51no—
309C4—52no—
310C4—52no—
311C4—122no—
312C4—602no—
313C4#9115212yes—
314C3#1060465811yescharacteristic, complemented, Sylow
315C2—102no—
316C2C2×#9115211yescharacteristic
317C2#1175171111yescharacteristic
318C2D5⋊#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#1546
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. #11746510C2semidirect
258. C3×C5#1546semidirect
300. C5#70778semidirect
314. C3#10604658semidirect

Maximal subgroups

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

subgroupindex
D5×#8692
#117523412
C3×#656782
#117465102
#106046583
#707785