Finite Group Databasebeta

← D3×#64855 #14313617

Subgroups — D3×#64855 #14313617

Order 1920.

480 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 76 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
1D3×#4015C211yesmaximal, characteristic
2D3×#4005C212yesmaximal
3#11746726C211yesmaximal, characteristic, complemented
4C3×#64855C211yesmaximal, characteristic, complemented
5#11746561C212yesmaximal, complemented
6C2×#64855—31nomaximal, Hall
7C2×D3×Dic10C411yescharacteristic
8C2×D3×Dic10C2211yescharacteristic
9D3×#704—22no—
10#91758C411yescharacteristic
11C42×C5×D3C411yescharacteristic
12C3×#4015C2211yescharacteristic
13#91469—22no—
14D3×C4⋊Dic5—22no—
15#91389C411yescharacteristic
16#91389C2211yescharacteristic
17#91234C2212yes—
18C3×#4005C2212yes—
19#91175—22no—
20D3×#356—51nomaximal, Hall
21C2×#4015—31no—
22C2×#4005—32no—
23#64855—31no—
24#64855—32no—
25#64855D311yescharacteristic, direct product factor
26C2×Dic30C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C2×C4×C5×D3—21no—
29C2×C4×C5×D3C2×C411yescharacteristic
30C2×C3×Dic10C2×C411yescharacteristic
31C2×C3×Dic10C2311yescharacteristic
32C2×#1204—21no—
33C2×#1204D412yes—
34C2×D3×Dic5—21no—
35C2×D3×Dic5D412yes—
36D3×Dic10—41no—
37D3×Dic10—41no—
38D3×Dic10—41no—
39D3×Dic10—41no—
40#6762—22no—
41C3×#704—22no—
42#6739—42no—
43D3×#170—42no—
44C3×C42×C5C2×C411yescharacteristic
45C4⋊Dic15—22no—
46C4×C5×Dic3—21no—
47C4×C5×Dic3C2×C411yescharacteristic
48C3×C4⋊Dic5—22no—
49Dic3⋊Dic5—22no—
50Dic3⋊Dic5—22no—
51D3×C4⋊Q8—51no—
52D3×#101—52no—
53C3×#356—51no—
54#4548—51no—
55#4478—52no—
56C22×Dic10—31no—
57C22×Dic10—31no—
58C2×#704—62no—
59C2×C42×C5—31no—
60C2×C4⋊Dic5—62no—
61#4015—31no—
62#4015—31no—
63#4015—31no—
64#4015—62no—
65#4015C2×D311yescharacteristic
66#4005—32no—
67#4005—62no—
68#4005C2×D312yes—
69C2×#356—151noSylow
70C22×C5×D3C22⋊C411yescharacteristic
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×Dic15—21no—
74C2×Dic15C22⋊C412yes—
75Dic30—41no—
76Dic30—41no—
77C2×C5×Dic3—21no—
78C2×C5×Dic3C22⋊C411yescharacteristic
79C4×C5×D3—24no—
80C4×C5×D3—21no—
81C4×C5×D3—21no—
82C2×C3×Dic5—21no—
83C2×C3×Dic5C2×D412yes—
84C3×Dic10—41no—
85C3×Dic10—41no—
86#1204—42no—
87#1204—42no—
88D3×Dic5—22no—
89D3×Dic5—22no—
90D3×Dic5—41no—
91D3×Dic5—41no—
92C3⋊#170—42no—
93C3×#170—42no—
94C2×D3×Q8—51no—
95C2×D3×Q8—51no—
96C3×C4⋊Q8—51no—
97#944—51no—
98#944—51no—
99D3×M16—102no—
100D3×C4⋊C4—102no—
101#888—102no—
102C42×D3AGL(1,𝔽5)11yescharacteristic
103#869—51no—
104C3×#101—52no—
105#836—52no—
106#824—102no—
107C22×C4×C5—31no—
108C22×C4×C5—61no—
109C22×Dic5—32no—
110C22×Dic5—61no—
111C2×Dic10—31no—
112C2×Dic10—32no—
113C2×Dic10—31no—
114C2×Dic10—61no—
115C2×Dic10—121no—
116C2×Dic10—121no—
117C2×Dic10—121no—
118C2×Dic10—121no—
119C2×Dic10C4×D311yescharacteristic
120C2×Dic10C22×D311yescharacteristic
121#704—22no—
122#704—62no—
123#704—122no—
124C2×#170—122no—
125C42×C5—31no—
126C42×C5—61no—
127C42×C5C4×D311yescharacteristic
128C4⋊Dic5—22no—
129C4⋊Dic5—62no—
130C4⋊Dic5—62no—
131C4⋊Dic5—62no—
132C2×C4⋊Q8—151no—
133C2×#101—152no—
134#356—51no—
135#356—152no—
136#356—151no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C2×C5×D3—22no—
139C2×C5×D3#9911yescharacteristic
140C2×C5×D3#9911yescharacteristic
141C3×C4×C5—22no—
142C3×C4×C5—21no—
143Dic15—22no—
144Dic15—41no—
145C3×Dic5—22no—
146C3×Dic5—41no—
147C5×Dic3—22no—
148C5×Dic3—21no—
149C2×C3×Q8—51no—
150C2×C3×Q8—51no—
151D3×Q8—201no—
152D3×Q8—201no—
153D3×Q8—201no—
154D3×Q8—201no—
155C2×C4×D3—21no—
156C2×C4×D3—52no—
157C2×C4×D3—101no—
158C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
159C2×Dic6—51no—
160C2×Dic6—52no—
161C2×Dic6—51no—
162C2×Dic6—101no—
163C3×M16—102no—
164C3×C4⋊C4—102no—
165C3×C42C2×AGL(1,𝔽5)11yescharacteristic
166C4⋊Dic3—102no—
167Dic3⋊C4—102no—
168Dic3⋊C4—102no—
169C4×Dic3—21no—
170C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
171#208—102no—
172ΓL(1,𝔽25)—202no—
173D3×C8—202no—
174C23×C5—31no—
175C2×C4×C5—21no—
176C2×C4×C5—31no—
177C2×C4×C5—61no—
178C2×C4×C5—61no—
179C2×C4×C5—64no—
180C2×C4×C5—61no—
181C2×C4×C5C2×C4×D311yescharacteristic
182C2×Dic5—21no—
183C2×Dic5—32no—
184C2×Dic5—62no—
185C2×Dic5—62no—
186C2×Dic5—61no—
187C2×Dic5—121no—
188C2×Dic5—121no—
189C2×Dic5D3×D412yes—
190Dic10—41no—
191Dic10—41no—
192Dic10—122no—
193Dic10—122no—
194Dic10—121no—
195Dic10—121no—
196#170—42no—
197#170—122no—
198C22×Q8—151no—
199C22×Q8—151no—
200C2×M16—302no—
201C4⋊Q8—51no—
202C4⋊Q8—151no—
203C4⋊Q8—151no—
204C4⋊Q8—151no—
205C4⋊Q8—302no—
206C2×C4⋊C4—302no—
207C2×C42—31no—
208#101—52no—
209#101—152no—
210#101—302no—
211C2×C3×C5—21no—
212C2×C3×C5C2×#9911yescharacteristic
213C5×D3—21no—
214C5×D3#35612yescomplemented
215C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
216C3×Q8—201no—
217C3×Q8—201no—
218C2×C3×C4—21no—
219C2×C3×C4—52no—
220C2×C3×C4—101no—
221C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
222C2×Dic3—21no—
223C2×Dic3—52no—
224C2×Dic3—101no—
225C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
226C4×D3—24no—
227C4×D3—21no—
228C4×D3—21no—
229C4×D3—102no—
230C4×D3—102no—
231C4×D3—201no—
232C4×D3—201no—
233Dic6—202no—
234Dic6—202no—
235Dic6—201no—
236Dic6—201no—
237C3×C8—202no—
238C3⋊C8—202no—
239C22×C5—31no—
240C22×C5—31no—
241C22×C5—62no—
242C22×C5D3×C22⋊C411yescharacteristic
243C4×C5—22no—
244C4×C5—21no—
245C4×C5—62no—
246C4×C5—61no—
247Dic5—22no—
248Dic5—41no—
249Dic5—62no—
250Dic5—121no—
251C2×Q8—51no—
252C2×Q8—51no—
253C2×Q8—152no—
254C2×Q8—151no—
255C2×Q8—151no—
256C2×Q8—301no—
257C2×Q8—601no—
258C2×Q8—601no—
259C2×Q8—601no—
260C2×Q8—601no—
261C22×C4—31no—
262C22×C4—61no—
263C22×C4—152no—
264C22×C4—301no—
265M16—102no—
266M16—302no—
267M16—602no—
268C2×C8—602no—
269C4⋊C4—102no—
270C4⋊C4—302no—
271C4⋊C4—302no—
272C4⋊C4—302no—
273C42—31no—
274C42—61no—
275C42D3×AGL(1,𝔽5)11yescharacteristic
276C3×C5C2×#35611yescharacteristic, complemented, Hall
277C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
278C2×D3—22no—
279C2×D3#399911yescharacteristic
280C2×D3#399911yescharacteristic
281C3×C4—22no—
282C3×C4—21no—
283C3×C4—102no—
284C3×C4—201no—
285Dic3—22no—
286Dic3—21no—
287Dic3—102no—
288Dic3—201no—
289C2×C5—21no—
290C2×C5—32no—
291C2×C5—61no—
292C2×C5D3×#9911yescharacteristic
293C23—31no—
294Q8—201no—
295Q8—201no—
296Q8—601no—
297Q8—601no—
298Q8—602no—
299Q8—602no—
300C2×C4—21no—
301C2×C4—31no—
302C2×C4—52no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—64no—
306C2×C4—61no—
307C2×C4—101no—
308C2×C4—152no—
309C2×C4—302no—
310C2×C4—302no—
311C2×C4—301no—
312C2×C4—601no—
313C2×C4—601no—
314C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
315C8—202no—
316C8—602no—
317C2×C3—21no—
318C2×C3C2×#399911yescharacteristic
319D3—21no—
320D3#6485512yesdirect product factor
321C5D3×#35611yescharacteristic, complemented, Sylow
322C22—31no—
323C22—31no—
324C22—62no—
325C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
326C4—22no—
327C4—21no—
328C4—62no—
329C4—61no—
330C4—102no—
331C4—201no—
332C4—302no—
333C4—601no—
334C3C2×#6485511yescharacteristic, complemented, Sylow
335C2—21no—
336C2—32no—
337C2—61no—
338C2D3×#399911yescharacteristic
subgroupG/H
centerC2D3×#3999
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC2×C3×C5C2×#99
prime radicalC22×C5×D3C22⋊C4
cosocleC2×C3×Dic10C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#356
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11746726C2semidirect
4. C3×#64855C2semidirect
5. #11746561C2semidirect
25. #64855D3direct (N × H)
214. C5×D3#356semidirect
276. C3×C5C2×#356semidirect
320. D3#64855direct (N × H)
321. C5D3×#356semidirect
334. C3C2×#64855semidirect

Maximal subgroups

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

subgroupindex
D3×#40152
D3×#40052
#117467262
C3×#648552
#117465612
C2×#648553
D3×#3565