Finite Group Databasebeta

← #14290563

Subgroups — #14290563

Order 1920.

468 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D12×Dic10C211yesmaximal, characteristic
2C5×#4846C211yesmaximal, characteristic
3#11747094C211yesmaximal, characteristic, complemented
4#11746955C211yesmaximal, characteristic, complemented
5#11746307C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic
8#10601907—31nomaximal, Hall
9C2×D3×Dic10—21no—
10#91758C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91468—21no—
15#91417—22no—
16Dic5×D12—21no—
17#91365—21no—
18C2×#6661—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#821—21no—
22C5×#818—21no—
23C3×C4×#168C2211yescharacteristic
24#90988—22no—
25#90972—21no—
26#68273—51nomaximal, Hall
27D4×Dic10—31no—
28C5×#474—31no—
29#65379—31no—
30#65367—31no—
31D4⋊#168—31no—
32#64706—31no—
33#64704D311yescharacteristic, complemented
34C2×Dic30—21no—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×#1204—22no—
40C2×D3×Dic5—22no—
41D3×Dic10—42no—
42D3×Dic10—42no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15D412yes—
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56#6668—22no—
57(C2×D3)⋊Dic5—22no—
58#6661—42no—
59Q8×D12—51no—
60#5031—51no—
61#4846D511yescharacteristic
62#4682—51no—
63C3×Q8⋊C8—51no—
64#4486—51no—
65#4459—51no—
66C22×Dic10—61no—
67C5×C4⋊Q8—31no—
68C4×C5×D4—31no—
69C2×#689—61no—
70D4×Dic5—61no—
71#4070—61no—
72#4034—61no—
73#4024—62no—
74#4015—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×#107—61no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#102—61no—
79#3967—61no—
80#3939—62no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1649—151noSylow
84C22×C5×D3—21no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—22no—
89Dic30—41no—
90Dic30—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—41no—
93C5×D12—21no—
94C5×D12Q1612yescomplemented
95C4×C5×D3—41no—
96C4×C5×D3—41no—
97C5×Dic6—41no—
98C5×Dic6—41no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×Dic10—21no—
102C3×Dic10D812yes—
103#1204—44no—
104D3×Dic5—44no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3×#168—22no—
108C2×D3×Q8—101no—
109C3×C4×Q8—51no—
110C2×#216—101no—
111#897—102no—
112#897—101no—
113C4×D12—101no—
114C4×D12C2×D511yescharacteristic
115#869—51no—
116#869—101no—
117#869C2×D511yescharacteristic
118C3×C4⋊C8C2×D511yescharacteristic
119C3×C4×C8—51no—
120#821—21no—
121#818—21no—
122#818—102no—
123#810—101no—
124C4⋊(C3⋊C8)—51no—
125C2×C5×Q8—61no—
126C2×C5×D4—31no—
127C22×C4×C5—61no—
128C22×Dic5—62no—
129C2×Dic10—62no—
130C2×Dic10—61no—
131C2×Dic10—122no—
132C2×Dic10—122no—
133C2×Dic10D1211yescharacteristic
134C2×C5×C8—21no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C22⋊C4—61no—
139C42×C5C22×D311yescharacteristic
140C22⋊Dic5—62no—
141#689—122no—
142C4⋊Dic5—32no—
143C4⋊Dic5—61no—
144C4⋊Dic5D1211yescharacteristic
145#683—21no—
146#683—62no—
147C4×Dic5—21no—
148C2×#168—21no—
149C2×#168—61no—
150D4×Q8—151no—
151#500—151no—
152#474—31no—
153#462—151no—
154#332—151no—
155Q8⋊C8—51no—
156D4⋊C8—151no—
157C22×C3×C5#12011yescharacteristic
158C2×C5×D3—22no—
159C2×C5×D3—41no—
160C2×C5×D3—41no—
161C3×C4×C5—21no—
162C3×C4×C5C2×D811yescharacteristic
163C3×C4×C5C2×Q1611yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166Dic15—42no—
167C3×Dic5—22no—
168C3×Dic5—41no—
169C5×Dic3—41no—
170C5×Dic3—81no—
171C2×C3×Q8—51no—
172D3×Q8—202no—
173D3×Q8—202no—
174C2×D12C22⋊D511yescharacteristic
175C2×C4×D3—21no—
176C2×C4×D3—102no—
177C2×Dic6—21no—
178C2×Dic6—102no—
179C2×Dic6—101no—
180C2×C3×C8—21no—
181C2×C3×C8—101no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—101no—
184C3×C42—101no—
185C3×C42C22×D511yescharacteristic
186#216—202no—
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—102no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—52no—
192C4⋊Dic3—102no—
193C4⋊Dic3—101no—
194C4⋊Dic3C22⋊D511yescharacteristic
195C2×C3⋊C8—101no—
196C23×C5—61no—
197C5×Q8—121no—
198C5×Q8—121no—
199C5×D4—32no—
200C5×D4—61no—
201C2×C4×C5—61no—
202C2×C4×C5—121no—
203C2×C4×C5—121no—
204C2×C4×C5—121no—
205C2×C4×C5C2×D1211yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×Dic5—21no—
209C2×Dic5—21no—
210C2×Dic5—62no—
211C2×Dic5—124no—
212Dic10—21no—
213Dic10—124no—
214Dic10—121no—
215Dic10—121no—
216Dic10D2412yes—
217C5×C8—41no—
218#168—22no—
219#168—121no—
220C22×Q8—301no—
221C2×Q16—301no—
222C4⋊Q8—31no—
223C4⋊Q8—151no—
224C4⋊Q8—301no—
225C22⋊Q8—302no—
226C22⋊Q8—301no—
227C4×Q8—51no—
228C4×D4—31no—
229C4×D4—301no—
230#107—61no—
231#107—302no—
232C4⋊C8—151no—
233C4⋊C8D3×D511yescharacteristic
234#103—301no—
235#102—61no—
236C4×C8—51no—
237C2×C3×C5#44711yescharacteristic
238C2×C3×C5#45111yescharacteristic
239C2×C3×C5#45611yescharacteristic
240C5×D3—42no—
241C22×D3—21no—
242C3×Q8—52no—
243C3×Q8—101no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—41no—
251C2×Dic3—102no—
252D12—21no—
253D12#68912yescomplemented
254C4×D3—41no—
255C4×D3—41no—
256C4×D3—204no—
257Dic6—41no—
258Dic6—41no—
259Dic6—204no—
260Dic6—201no—
261Dic6—201no—
262C3×C8—41no—
263C3×C8—102no—
264C3⋊C8—201no—
265C22×C5—62no—
266C22×C5—121no—
267C22×C5—121no—
268C22×C5#88211yescharacteristic
269C4×C5—21no—
270C4×C5—121no—
271C4×C5—241no—
272C4×C5C2×D2411yescharacteristic
273C4×C5#90811yescharacteristic
274C4×C5#91511yescharacteristic
275C4×C5D3×Q1611yescharacteristic
276Dic5—22no—
277Dic5—41no—
278Dic5—122no—
279C2×Q8—51no—
280C2×Q8—61no—
281C2×Q8—302no—
282C2×Q8—301no—
283C2×Q8—602no—
284C2×Q8—602no—
285C2×D4—31no—
286C22×C4—61no—
287C22×C4—302no—
288Q16—602no—
289C2×C8—21no—
290C2×C8—101no—
291C2×C8—301no—
292C4⋊C4—31no—
293C4⋊C4—51no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—101no—
297C4⋊C4—152no—
298C4⋊C4—302no—
299C4⋊C4—301no—
300C22⋊C4—61no—
301C22⋊C4—302no—
302C42—101no—
303C42C2×D3×D511yescharacteristic
304C3×C5#164911yescharacteristic, complemented, Hall
305C22×C3#408311yescharacteristic
306C2×D3—22no—
307C2×D3—41no—
308C2×D3—41no—
309C3×C4—21no—
310C3×C4—102no—
311C3×C4—201no—
312C3×C4D5×D811yescharacteristic
313C3×C4#405711yescharacteristic
314C3×C4C2×#68911yescharacteristic
315C3×C4#409711yescharacteristic
316Dic3—41no—
317Dic3—81no—
318Dic3—202no—
319C2×C5—122no—
320C2×C5#473211yescharacteristic
321C2×C5#480911yescharacteristic
322C2×C5#482611yescharacteristic
323C23—61no—
324Q8—52no—
325Q8—101no—
326Q8—121no—
327Q8—121no—
328Q8—604no—
329Q8—601no—
330Q8—601no—
331D4—32no—
332D4—61no—
333C2×C4—61no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—121no—
337C2×C4—121no—
338C2×C4—121no—
339C2×C4—302no—
340C2×C4—604no—
341C2×C4D5×D1211yescharacteristic
342C2×C4#677711yescharacteristic
343C2×C4D3×C22⋊D511yescharacteristic
344C8—41no—
345C8—102no—
346C8—601no—
347C2×C3#6533911yescharacteristic
348C2×C3#6544511yescharacteristic
349C2×C3#6549411yescharacteristic
350D3—42no—
351C5#6827311yescharacteristic, complemented, Sylow
352C22—62no—
353C22—121no—
354C22—121no—
355C22#9147511yescharacteristic
356C4—21no—
357C4—102no—
358C4—121no—
359C4—201no—
360C4—241no—
361C4—602no—
362C4D5×D2411yescharacteristic
363C4#9125011yescharacteristic
364C4#9148611yescharacteristic
365C4D3×#68911yescharacteristic
366C3#1060190711yescharacteristic, complemented, Sylow
367C2—122no—
368C2#1174749511yescharacteristic
369C2#1174811611yescharacteristic
370C2#1174825711yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1649
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11747094C2semidirect
4. #11746955C2semidirect
5. #11746307C2semidirect
6. C3×#64704C2semidirect
33. #64704D3semidirect
94. C5×D12Q16semidirect
253. D12#689semidirect
304. C3×C5#1649semidirect
351. C5#68273semidirect
366. C3#10601907semidirect

Maximal subgroups

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

subgroupindex
D12×Dic102
C5×#48462
#117470942
#117469552
#117463072
C3×#647042
#117458372
#106019073
#682735