Finite Group Databasebeta

← #14289996

Subgroups — #14289996

Order 1920.

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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
1#11752662C211yesmaximal, characteristic
2C5×#4851C211yesmaximal, characteristic, complemented
3#11747094C211yesmaximal, characteristic, complemented
4#11746912C211yesmaximal, characteristic
5#11746306C211yesmaximal, characteristic
6C3×#64704C211yesmaximal, characteristic, complemented
7#11745843C211yesmaximal, characteristic, complemented
8#10601921—31nomaximal, Hall
9#91763C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91433—22no—
14#91428—21no—
15#91418—21no—
16#91375—21no—
17#91374—21no—
18C2×#6661—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#817—21no—
22C5×#816—21no—
23C3×C4×#168C2211yescharacteristic
24#90972—21no—
25#90969—22no—
26#68262—51nomaximal, Hall
27#65919—31no—
28C5×#475—31no—
29#65379—31no—
30#65377—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64704D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60D412yes—
37C2×C5×Dic6—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×#1200—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52C2×C3×#168—21no—
53#6667—22no—
54#6667—22no—
55#6667—22no—
56#6661—42no—
57#5585—51no—
58#5031—51no—
59#4851D511yescharacteristic, complemented
60#4694—51no—
61C3×Q8⋊C8—51no—
62#4485—51no—
63#4456—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8—31no—
66#4093—61no—
67C2×#689—61no—
68#4040—62no—
69#4039—61no—
70#4021—61no—
71#4020—31no—
72C4×D20—61no—
73C4×Dic10C2×D311yescharacteristic
74C5×#106—61no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—61no—
77#3967—61no—
78#3941—62no—
79C4⋊#168—31no—
80C4×#168C2×D311yescharacteristic
81#1640—151noSylow
82C22×D15—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86D60—42no—
87D60—41no—
88D60—41no—
89D60—41no—
90D60—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—41no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C3×Dic10—21no—
101C3×Dic10—21no—
102#1200—82no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C3×C4×Q8—51no—
107#947—101no—
108C2×#216—101no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874—51no—
113C4×D12—101no—
114#869C2×D511yescharacteristic
115C4×Dic6C2×D511yescharacteristic
116C3×C4⋊C8C2×D511yescharacteristic
117C3×C4×C8—51no—
118#821—102no—
119#817—21no—
120#816—21no—
121#810—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—31no—
124C2×C5×Q8—61no—
125C2×D20—32no—
126C2×D20—61no—
127C2×D20—61no—
128C2×C4×D5—62no—
129C2×Dic10D1211yescharacteristic
130C2×C5×C8—21no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4—61no—
135C42×C5—61no—
136C42×C5C22×D311yescharacteristic
137#689—122no—
138#685—62no—
139#685—62no—
140#685—62no—
141C4⋊Dic5D1211yescharacteristic
142#683—21no—
143C4×Dic5—21no—
144C2×#168—21no—
145C2×#168—61no—
146#559—151no—
147#486—151no—
148#475—31no—
149#462—151no—
150#331—151no—
151Q8⋊C8—51no—
152Q8⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×D15—42no—
155C2×D15—42no—
156C2×D15—42no—
157C3×C4×C5—21no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×Dic5—41no—
163C3×Dic5—41no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C5×Dic3—81no—
167C2×C3×Q8—51no—
168C2×D12—52no—
169C2×D12—101no—
170C2×D12—101no—
171C2×C4×D3—102no—
172C2×Dic6—21no—
173C2×Dic6C22⋊D511yescharacteristic
174C2×C3×C8—21no—
175C2×C3×C8—101no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C42—101no—
179C3×C42C22×D511yescharacteristic
180#216—202no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3C22⋊D511yescharacteristic
187Dic3⋊C4—21no—
188C4×Dic3—21no—
189C2×C3⋊C8—101no—
190C22×D5—62no—
191C5×Q8—61no—
192C5×Q8—61no—
193C5×Q8—121no—
194C5×Q8—121no—
195C2×C4×C5—61no—
196C2×C4×C5—61no—
197C2×C4×C5—121no—
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203D20—122no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—121no—
208C4×D5—242no—
209Dic10—21no—
210Dic10—21no—
211C5×C8—41no—
212#168—41no—
213#168—121no—
214C2×Q16—301no—
215C4⋊Q8—31no—
216#127—151no—
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—31no—
221C4×Q8—51no—
222C4×D4—301no—
223C4×D4—301no—
224#106—61no—
225C4⋊C8—151no—
226C4⋊C8D3×D511yescharacteristic
227#103—61no—
228#103—301no—
229#102—302no—
230C4×C8—51no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234D15—82no—
235C22×D3—102no—
236C3×Q8—101no—
237C3×Q8—101no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—41no—
246D12—202no—
247D12—201no—
248D12—201no—
249D12—201no—
250D12—201no—
251C4×D3—402no—
252Dic6—21no—
253Dic6—21no—
254Dic6—41no—
255Dic6—41no—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—201no—
259C22×C5#88211yescharacteristic
260C2×D5—122no—
261C2×D5—122no—
262C2×D5—122no—
263C4×C5—21no—
264C4×C5—121no—
265C4×C5—121no—
266C4×C5—241no—
267C4×C5#90411yescharacteristic
268C4×C5#90811yescharacteristic
269C4×C5#91611yescharacteristic
270C4×C5#91811yescharacteristic
271Dic5—41no—
272Dic5—41no—
273C2×Q8—31no—
274C2×Q8—51no—
275C2×Q8—61no—
276C2×D4—152no—
277C2×D4—301no—
278C2×D4—301no—
279C22×C4—302no—
280Q16—602no—
281C2×C8—21no—
282C2×C8—101no—
283C2×C8—301no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—101no—
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—61no—
294C42—101no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3#408311yescharacteristic
298C2×D3—202no—
299C2×D3—202no—
300C2×D3—202no—
301C3×C4—21no—
302C3×C4—201no—
303C3×C4—201no—
304C3×C4#406011yescharacteristic
305C3×C4#406211yescharacteristic
306C3×C4#408811yescharacteristic
307C3×C4#409611yescharacteristic
308Dic3—41no—
309Dic3—41no—
310Dic3—81no—
311C2×C5#473411yescharacteristic
312C2×C5#480811yescharacteristic
313C2×C5#482511yescharacteristic
314D5—242no—
315C23—302no—
316Q8—61no—
317Q8—61no—
318Q8—101no—
319Q8—101no—
320Q8—121no—
321Q8—121no—
322D4—602no—
323D4—601no—
324D4—601no—
325D4—601no—
326D4—601no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—121no—
332C2×C4—1202no—
333C2×C4D5×D1211yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—41no—
337C8—201no—
338C8—601no—
339C2×C3#6533611yescharacteristic
340C2×C3#6546111yescharacteristic
341C2×C3#6549111yescharacteristic
342D3—402no—
343C5#6826211yescharacteristic, complemented, Sylow
344C22—602no—
345C22—602no—
346C22—602no—
347C22#9147511yescharacteristic
348C4—21no—
349C4—121no—
350C4—121no—
351C4—201no—
352C4—201no—
353C4—241no—
354C4#9124911yescharacteristic
355C4#9126911yescharacteristic
356C4#9149511yescharacteristic
357C4#9152011yescharacteristic
358C3#1060192111yescharacteristic, complemented, Sylow
359C2—1202no—
360C2#1174751611yescharacteristic
361C2#1174790011yescharacteristic
362C2#1174824511yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1640
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
2. C5×#4851C2semidirect
3. #11747094C2semidirect
6. C3×#64704C2semidirect
7. #11745843C2semidirect
33. #64704D3semidirect
59. #4851D5semidirect
296. C3×C5#1640semidirect
343. C5#68262semidirect
358. C3#10601921semidirect

Maximal subgroups

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

subgroupindex
#117526622
C5×#48512
#117470942
#117469122
#117463062
C3×#647042
#117458432
#106019213
#682625