Finite Group Databasebeta

← #14282144

Subgroups — #14282144

Order 1920.

496 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 126 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×Dic5×Dic6C211yesmaximal, characteristic
2#11752417C211yesmaximal, characteristic
3C3×#65754C211yesmaximal, characteristic
4#11746493C214yesmaximal, complemented
5#10604968—31nomaximal, Hall
6C22×C5×Dic6C411yescharacteristic
7C2×#6762—21no—
8C2×C4⋊Dic15C411yescharacteristic
9C2×C3×C4×Dic5C2211yescharacteristic
10C2×Dic3⋊Dic5—21no—
11C2×Dic3×Dic5—21no—
12Dic5×Dic6—21no—
13Dic5×Dic6—21no—
14Dic5×Dic6C412yes—
15Dic5×Dic6C2212yes—
16#91233—21no—
17C4⋊(C3⋊#170)C2212yes—
18C3×C22⋊#170—21no—
19C3×#4004—21no—
20C3×C4×#170C2212yes—
21#70770—51nomaximal, Hall
22C2×Q8×Dic5—31no—
23#65758—31no—
24#65754D311yescharacteristic
25Q8⋊#170—34no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15—21no—
28C22×C5×Dic3—21no—
29C2×C5×Dic6—21no—
30C2×C5×Dic6—24no—
31C2×C5×Dic6C2×C412yes—
32C22×C3×Dic5D411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34#6762—42no—
35C2×C3⋊#170—22no—
36C2×C3×#170—22no—
37C4⋊Dic15—21no—
38C4⋊Dic15C2×C412yes—
39C3×C4×Dic5C2×C411yescharacteristic
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5D411yescharacteristic
42C3×C4×Dic5C2311yescharacteristic
43Dic3⋊Dic5—22no—
44Dic3⋊Dic5—22no—
45Dic3×Dic5—22no—
46Dic3×Dic5—22no—
47C2×C4×Dic6—51no—
48C3×#431—51no—
49#4924—51no—
50#4456—54no—
51C22×C5×Q8—31no—
52C2×#704—61no—
53Q8×Dic5—32no—
54Q8×Dic5—32no—
55Q8×Dic5—61no—
56Q8×Dic5—61no—
57C2×C4⋊Dic5—31no—
58C2×C4⋊Dic5—61no—
59C2×C4×Dic5—61no—
60C2×C4×Dic5C2×D311yescharacteristic
61C22⋊#170—21no—
62#4004—21no—
63#4004—61no—
64C4⋊#170—32no—
65C4×#170C2×D312yes—
66#1487—151noSylow
67C23×C3×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22×C411yescharacteristic
71C2×Dic15—22no—
72C2×Dic15—42no—
73C2×C5×Dic3—24no—
74C2×C5×Dic3—22no—
75C5×Dic6—24no—
76C5×Dic6—22no—
77C5×Dic6M1614yescomplemented
78C2×C3×Dic5—41no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C22⋊C411yescharacteristic
81C2×C3×Dic5SD1612yes—
82C2×C3×Dic5Q1612yes—
83C2×C3×Dic5C2×D411yescharacteristic
84C2×C3×Dic5C2×D411yescharacteristic
85C3⋊#170—42no—
86C3×#170—42no—
87C22×Dic6AGL(1,𝔽5)11yescharacteristic
88C2×C3×C42—51no—
89C2×C4⋊Dic3—51no—
90C2×Dic3⋊C4—101no—
91C2×C4×Dic3—101no—
92C2×#208—101no—
93C4×Dic6—52no—
94C4×Dic6—52no—
95C4×Dic6—101no—
96C4×Dic6—101no—
97C3×C4⋊C8—101no—
98C3×C22⋊C8—101no—
99C3×C4×C8—52no—
100C4⋊(C3⋊C8)—52no—
101C4⋊(C3⋊C8)—101no—
102C2×C5×Q8—32no—
103C2×C5×Q8—64no—
104C2×C5×Q8—61no—
105C22×C4×C5—61no—
106C22×C4×C5C4×D311yescharacteristic
107C22×Dic5—61no—
108C22×Dic5D1211yescharacteristic
109C22×Dic5#6711yescharacteristic
110#704—122no—
111C2×#170—22no—
112C2×#170—62no—
113C4⋊Dic5—32no—
114C4⋊Dic5—61no—
115C4⋊Dic5—62no—
116C4⋊Dic5—62no—
117C4×Dic5—62no—
118C4×Dic5—62no—
119C4×Dic5C4×D311yescharacteristic
120C4×Dic5D1211yescharacteristic
121C4×Dic5#6711yescharacteristic
122C4×Dic5C22×D311yescharacteristic
123C2×C4×Q8—151no—
124#431—51no—
125#423—151no—
126Q8⋊C8—154no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5#10312yes—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C3×C4×C5—21no—
132C3×C4×C5C2×M1612yes—
133Dic15—42no—
134C3×Dic5—21no—
135C3×Dic5—21no—
136C3×Dic5#10312yes—
137C3×Dic5C2×SD1611yescharacteristic
138C3×Dic5C2×Q1611yescharacteristic
139C5×Dic3—24no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
143C22×Dic3—21no—
144C22×Dic3—101no—
145C2×Dic6—21no—
146C2×Dic6—24no—
147C2×Dic6C2×AGL(1,𝔽5)12yes—
148C2×C3×C8—102no—
149C3×C42—51no—
150C3×C42—51no—
151C3×C42—51no—
152C3×C42—51no—
153C4⋊Dic3—52no—
154C4⋊Dic3—101no—
155Dic3⋊C4—102no—
156Dic3⋊C4—102no—
157C4×Dic3—102no—
158C4×Dic3—102no—
159#208—202no—
160C2×C3⋊C8—102no—
161C23×C5(C2×D3)⋊C411yescharacteristic
162C5×Q8—34no—
163C5×Q8—64no—
164C5×Q8—62no—
165C2×C4×C5—22no—
166C2×C4×C5—64no—
167C2×C4×C5—62no—
168C2×C4×C5(C2×D3)⋊C411yescharacteristic
169C2×C4×C5C2×C4×D311yescharacteristic
170C2×Dic5—41no—
171C2×Dic5—62no—
172C2×Dic5—122no—
173C2×Dic5#20412yes—
174C2×Dic5Dic1212yes—
175C2×Dic5(C2×D3)⋊C411yescharacteristic
176C2×Dic5(C2×D3)⋊C411yescharacteristic
177C2×Dic5C2×D1211yescharacteristic
178C2×Dic5C2×#6711yescharacteristic
179#170—42no—
180#170—122no—
181C22×Q8—31no—
182C2×M16—301no—
183C4×Q8—152no—
184C4×Q8—152no—
185C4×Q8—301no—
186C4×Q8—301no—
187C2×C4⋊C4—151no—
188C2×C4⋊C4—301no—
189C2×C42—51no—
190C2×C42—301no—
191C4⋊C8—101no—
192C4⋊C8—152no—
193C4⋊C8—301no—
194C22⋊C8—101no—
195C4×C8—52no—
196C2×C3×C5—22no—
197C2×C3×C5#40711yescharacteristic
198C2×C3×C5C2×#10311yescharacteristic
199C2×C3×C5#42111yescharacteristic
200C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
201C2×C3×C4—22no—
202C2×C3×C4—51no—
203C2×C3×C4—51no—
204C2×C3×C4—52no—
205C2×C3×C4—52no—
206C2×C3×C4—51no—
207C2×C3×C4—51no—
208C2×C3×C4—201no—
209C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
210C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
211C2×Dic3—24no—
212C2×Dic3—22no—
213C2×Dic3—102no—
214C2×Dic3—202no—
215Dic6—24no—
216Dic6—22no—
217Dic6#70414yescomplemented
218C3×C8—202no—
219C3⋊C8—202no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5#81612yes—
223C22×C5C2×(C2×D3)⋊C411yescharacteristic
224C4×C5—21no—
225C4×C5—64no—
226C4×C5D3×M1612yes—
227Dic5—21no—
228Dic5—21no—
229Dic5—122no—
230Dic5#81612yes—
231Dic5C2×#20411yescharacteristic
232Dic5C2×Dic1211yescharacteristic
233C2×Q8—32no—
234C2×Q8—64no—
235C2×Q8—61no—
236C22×C4—51no—
237C22×C4—51no—
238C22×C4—61no—
239C22×C4—301no—
240C22×C4D3×AGL(1,𝔽5)11yescharacteristic
241M16—602no—
242C2×C8—102no—
243C2×C8—302no—
244C4⋊C4—152no—
245C4⋊C4—302no—
246C4⋊C4—302no—
247C4⋊C4—301no—
248C42—51no—
249C42—51no—
250C42—51no—
251C42—51no—
252C42—302no—
253C42—302no—
254C3×C5#148711yescharacteristic, complemented, Hall
255C22×C3—21no—
256C22×C3—21no—
257C22×C3#400912yes—
258C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
259C3×C4—21no—
260C3×C4—52no—
261C3×C4—51no—
262C3×C4—51no—
263C3×C4—101no—
264C3×C4—101no—
265C3×C4C2×#70412yes—
266Dic3—24no—
267Dic3—202no—
268C2×C5—22no—
269C2×C5#500511yescharacteristic
270C2×C5C2×#81611yescharacteristic
271C2×C5#512611yescharacteristic
272C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
273Q8—34no—
274Q8—64no—
275Q8—62no—
276C2×C4—22no—
277C2×C4—52no—
278C2×C4—52no—
279C2×C4—51no—
280C2×C4—51no—
281C2×C4—51no—
282C2×C4—51no—
283C2×C4—64no—
284C2×C4—62no—
285C2×C4—201no—
286C2×C4—302no—
287C2×C4—602no—
288C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
289C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
290C8—202no—
291C8—602no—
292C2×C3—22no—
293C2×C3C2×#400911yescharacteristic
294C2×C3#6578411yescharacteristic
295C2×C3#6579811yescharacteristic
296C5#7077011yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22#9115412yes—
300C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
301C4—21no—
302C4—51no—
303C4—52no—
304C4—51no—
305C4—64no—
306C4—101no—
307C4—101no—
308C4—602no—
309C4D3×#70412yes—
310C3#1060496811yescharacteristic, complemented, Sylow
311C2—22no—
312C2C2×#9115411yescharacteristic
313C2#1175172411yescharacteristic
314C2#1175200011yescharacteristic
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#1487
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746493C2semidirect
77. C5×Dic6M16semidirect
217. Dic6#704semidirect
254. C3×C5#1487semidirect
296. C5#70770semidirect
310. C3#10604968semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×Dic62
#117524172
C3×#657542
#117464932
#106049683
#707705