Finite Group Databasebeta

← #14284835

Subgroups — #14284835

Order 1920.

480 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#91468C211yesmaximal, characteristic
2#11752417C211yesmaximal, characteristic
3C3×#65754C211yesmaximal, characteristic
4#11746510C214yesmaximal, complemented
5#10604277—31nomaximal, Hall
6C22×#1204—21no—
7C2×#6762—21no—
8C2×C4⋊Dic15C411yescharacteristic
9C2×C5×C4⋊Dic3C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×#6668—21no—
12#91468—21no—
13#91468—21no—
14#91468C412yes—
15#91468C2212yes—
16#91233C2212yes—
17C4⋊(C3⋊#170)—21no—
18C3×C22⋊#170—21no—
19C3×#4004C2212yes—
20C3×C4×#170—21no—
21#70778—51nomaximal, Hall
22C2×#4034—31no—
23#65758—31no—
24#65754D311yescharacteristic
25#64873—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15—21no—
28C22×C5×Dic3—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31C2×#1204—22no—
32C2×#1204—22no—
33C2×#1204—42no—
34C2×#1204—42no—
35#6762—42no—
36C2×C3⋊#170—22no—
37C2×C3×#170—22no—
38C4⋊Dic15—21no—
39C4⋊Dic15C2×C412yes—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3C2×C412yes—
42C3×C4×Dic5C2×C411yescharacteristic
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—
52C22×Dic10—61no—
53C2×#704—61no—
54C2×C5×C4⋊C4—31no—
55C2×C4⋊Dic5—31no—
56C2×#683—61no—
57C2×C4×Dic5C2×D311yescharacteristic
58#4034—32no—
59#4034—32no—
60#4034—61no—
61#4034—61no—
62C22⋊#170—21no—
63#4004—32no—
64#4004C2×D312yes—
65C4⋊#170—61no—
66C4×#170—21no—
67#1546—151noSylow
68C23×C3×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×Dic15—22no—
73C2×Dic15—42no—
74C2×C5×Dic3—22no—
75C2×C5×Dic3—42no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C22⋊C411yescharacteristic
79C2×C3×Dic5D812yes—
80C2×C3×Dic5SD1612yes—
81C2×C3×Dic5C2×D411yescharacteristic
82C2×C3×Dic5C2×D411yescharacteristic
83#1204—44no—
84#1204—42no—
85#1204—42no—
86C3⋊#170—42no—
87C3×#170—42no—
88C22×Dic6—101no—
89C2×C3×C42—51no—
90C2×C4⋊Dic3—51no—
91C2×C4⋊Dic3—101no—
92C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
93C2×#208—101no—
94#869—52no—
95#869—52no—
96#869—101no—
97#869—101no—
98C3×C4⋊C8—52no—
99C3×C22⋊C8—101no—
100C3×C4×C8—101no—
101C4⋊(C3⋊C8)—52no—
102C4⋊(C3⋊C8)—101no—
103C22×C4×C5—61no—
104C22×C4×C5C4×D311yescharacteristic
105C22×Dic5—61no—
106C22×Dic5D1211yescharacteristic
107C22×Dic5#6711yescharacteristic
108C2×Dic10—62no—
109C2×Dic10—62no—
110C2×Dic10—122no—
111C2×Dic10—122no—
112#704—122no—
113C2×#170—22no—
114C2×#170—62no—
115C5×C4⋊C4—32no—
116C5×C4⋊C4—61no—
117C4⋊Dic5—32no—
118C4⋊Dic5—61no—
119#683—62no—
120#683—62no—
121C4×Dic5C4×D311yescharacteristic
122C4×Dic5D1211yescharacteristic
123C4×Dic5#6711yescharacteristic
124C4×Dic5C22×D311yescharacteristic
125C2×C4⋊Q8—151no—
126#431—51no—
127#423—151no—
128#332—154no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5#10212yes—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C3×C4×C5—21no—
134C3×C4×C5#10112yes—
135Dic15—42no—
136C3×Dic5—21no—
137C3×Dic5#10212yes—
138C3×Dic5C2×D811yescharacteristic
139C3×Dic5C2×SD1611yescharacteristic
140C3×Dic5#13712yes—
141C5×Dic3—42no—
142C22×C3×C4—51no—
143C22×C3×C4—51no—
144C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
145C22×Dic3—21no—
146C22×Dic3—101no—
147C2×Dic6—102no—
148C2×Dic6—102no—
149C2×Dic6—202no—
150C2×Dic6—202no—
151C2×C3×C8—102no—
152C3×C42—51no—
153C3×C42—51no—
154C3×C42—51no—
155C3×C42—51no—
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—
164C23×C5(C2×D3)⋊C411yescharacteristic
165C2×C4×C5—22no—
166C2×C4×C5—62no—
167C2×C4×C5—122no—
168C2×C4×C5(C2×D3)⋊C411yescharacteristic
169C2×C4×C5C2×C4×D311yescharacteristic
170C2×Dic5—22no—
171C2×Dic5—62no—
172C2×Dic5—122no—
173C2×Dic5#20412yes—
174C2×Dic5D2412yes—
175C2×Dic5(C2×D3)⋊C411yescharacteristic
176C2×Dic5(C2×D3)⋊C411yescharacteristic
177C2×Dic5C2×D1211yescharacteristic
178C2×Dic5C2×#6711yescharacteristic
179Dic10—124no—
180Dic10—122no—
181Dic10—122no—
182#170—42no—
183#170—122no—
184C22×Q8—301no—
185C2×M16—301no—
186C4⋊Q8—152no—
187C4⋊Q8—152no—
188C4⋊Q8—301no—
189C4⋊Q8—301no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—151no—
192C2×C4⋊C4—301no—
193C2×C42—51no—
194C4⋊C8—52no—
195C4⋊C8—152no—
196C4⋊C8—301no—
197C22⋊C8—101no—
198C4×C8—101no—
199C2×C3×C5—22no—
200C2×C3×C5C2×#10111yescharacteristic
201C2×C3×C5C2×#10211yescharacteristic
202C2×C3×C5#41911yescharacteristic
203C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
204C2×C3×C4—22no—
205C2×C3×C4—51no—
206C2×C3×C4—51no—
207C2×C3×C4—51no—
208C2×C3×C4—52no—
209C2×C3×C4—52no—
210C2×C3×C4—51no—
211C2×C3×C4—102no—
212C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
213C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
214C2×Dic3—22no—
215C2×Dic3—42no—
216C2×Dic3—102no—
217C2×Dic3—202no—
218Dic6—204no—
219Dic6—202no—
220Dic6—202no—
221C3×C8—202no—
222C3⋊C8—202no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5#82112yes—
226C22×C5C2×(C2×D3)⋊C411yescharacteristic
227C4×C5—21no—
228C4×C5—122no—
229C4×C5#82412yes—
230Dic5—21no—
231Dic5—122no—
232Dic5#82112yes—
233Dic5C2×#20411yescharacteristic
234Dic5C2×D2411yescharacteristic
235Dic5#95112yes—
236C2×Q8—302no—
237C2×Q8—302no—
238C2×Q8—602no—
239C2×Q8—602no—
240C22×C4—51no—
241C22×C4—51no—
242C22×C4—61no—
243C22×C4—301no—
244C22×C4D3×AGL(1,𝔽5)11yescharacteristic
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—
257C42—51no—
258C3×C5#154611yescharacteristic, complemented, Hall
259C22×C3—21no—
260C22×C3—21no—
261C22×C3#400712yes—
262C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C3×C4—21no—
264C3×C4—52no—
265C3×C4—51no—
266C3×C4—51no—
267C3×C4—52no—
268C3×C4—101no—
269C3×C4#400512yes—
270Dic3—42no—
271Dic3—202no—
272C2×C5—22no—
273C2×C5#500411yescharacteristic
274C2×C5C2×#82111yescharacteristic
275C2×C5C2×#82411yescharacteristic
276C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
277Q8—602no—
278Q8—604no—
279Q8—602no—
280C2×C4—22no—
281C2×C4—52no—
282C2×C4—52no—
283C2×C4—51no—
284C2×C4—51no—
285C2×C4—51no—
286C2×C4—51no—
287C2×C4—62no—
288C2×C4—102no—
289C2×C4—122no—
290C2×C4—302no—
291C2×C4—602no—
292C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
293C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
294C8—202no—
295C8—602no—
296C2×C3—22no—
297C2×C3C2×#400511yescharacteristic
298C2×C3C2×#400711yescharacteristic
299C2×C3#6578211yescharacteristic
300C5#7077811yescharacteristic, complemented, Sylow
301C22—21no—
302C22—21no—
303C22#9115212yes—
304C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
305C4—21no—
306C4—51no—
307C4—52no—
308C4—51no—
309C4—52no—
310C4—101no—
311C4—122no—
312C4—602no—
313C4#9117512yes—
314C3#1060427711yescharacteristic, complemented, Sylow
315C2—22no—
316C2C2×#9115211yescharacteristic
317C2#1175171111yescharacteristic
318C2C2×#9117511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1546
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

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#10604277semidirect

Maximal subgroups

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

subgroupindex
C2×#914682
#117524172
C3×#657542
#117465102
#106042773
#707785