Finite Group Databasebeta

← #14289992

Subgroups — #14289992

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#11752651C211yesmaximal, characteristic
2C3×#65140C211yesmaximal, characteristic, complemented
3#11747104C211yesmaximal, characteristic, complemented
4#11746901C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic
7#11745840C211yesmaximal, characteristic, complemented
8#10599199—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#874C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91435—21no—
14#91423—22no—
15Dic5×D12—21no—
16#91373—21no—
17#91370—21no—
18C2×#6662—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3949—21no—
23C3×#3948—21no—
24#90971—21no—
25#90966—22no—
26#71128—51nomaximal, Hall
27#66047—31no—
28#65359—31no—
29#65140D311yescharacteristic, complemented
30#65138—31no—
31C5×#331—31no—
32#64704—31no—
33#64704—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C3×Dic10—21no—
39C2×C3×Dic10D411yescharacteristic
40C2×D3×Dic5—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53(C2×D3)⋊Dic5—22no—
54(C2×D3)⋊Dic5—22no—
55(C2×D3)⋊Dic5—22no—
56#6662—42no—
57#5585—51no—
58C3×#475—51no—
59#5090—51no—
60#5088—51no—
61#4535—51no—
62#4485D511yescharacteristic
63#4484—51no—
64C5×#127—31no—
65#4082—61no—
66#4082—61no—
67#4081—62no—
68D4×Dic5—61no—
69D4×Dic5—61no—
70C2×Dic20—61no—
71#4015C2×D311yescharacteristic
72C4×Dic10—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3964—62no—
77#3949—21no—
78#3948—21no—
79#3948—61no—
80C4×#168—31no—
81#1640—151noSylow
82C22×C5×D3—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C5×D12—42no—
91C5×D12—41no—
92C5×D12—41no—
93C5×D12—41no—
94C5×D12—41no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—41no—
98C3×Dic10—21no—
99C3×Dic10—21no—
100C3×Dic10—41no—
101C3×Dic10—41no—
102D3×Dic5—82no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107C3×C4×Q8—51no—
108#947—101no—
109C2×#216—101no—
110#894—102no—
111#893—101no—
112#875—101no—
113#874C2×D511yescharacteristic
114C4×D12—101no—
115C4×Dic6—51no—
116C3×#106—101no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×#103—101no—
119#835—101no—
120#809—102no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×D4—32no—
124C2×C5×D4—61no—
125C2×C5×D4—61no—
126C22×Dic5—62no—
127C2×Dic10—21no—
128C2×Dic10—31no—
129C2×Dic10#6711yescharacteristic
130C2×C5×C8—21no—
131C2×C5×C8—61no—
132C42×C5C22×D311yescharacteristic
133C22⋊Dic5—62no—
134C22⋊Dic5—62no—
135C22⋊Dic5—62no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—31no—
139C4⋊Dic5#6711yescharacteristic
140#683—21no—
141#683—61no—
142C4×Dic5—21no—
143C4×Dic5—61no—
144C2×#168—61no—
145Dic20—122no—
146#559—151no—
147#486—151no—
148#475—51no—
149#462—151no—
150#331—31no—
151Q8⋊C8—151no—
152Q8⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C2×C5×D3—42no—
157C3×C4×C5—21no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—41no—
163Dic15—41no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C3×Dic5—81no—
167C2×C3×Q8—51no—
168C2×C3×Q8—101no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12D2012yes—
172C2×C4×D3—102no—
173C2×Dic6—51no—
174C2×C3×C8—21no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C42—101no—
180C3×C42C22×D511yescharacteristic
181#216—202no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—102no—
185C4⋊Dic3—51no—
186Dic3⋊C4—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—101no—
190C23×C5—62no—
191C5×D4—122no—
192C5×D4—121no—
193C5×D4—121no—
194C5×D4—121no—
195C5×D4—121no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—41no—
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—242no—
205Dic10—21no—
206Dic10—21no—
207Dic10—41no—
208Dic10—41no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—41no—
212C5×C8—121no—
213#168—121no—
214C2×Q16—301no—
215C4⋊Q8—51no—
216#127—31no—
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—51no—
221C4×Q8—151no—
222C4×D4—301no—
223C4×D4—301no—
224#106—101no—
225C4⋊C8—31no—
226C4⋊C8D3×D511yescharacteristic
227#103—101no—
228#103—301no—
229#102—302no—
230C4×C8—151no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234C5×D3—82no—
235C22×D3—22no—
236C3×Q8—101no—
237C3×Q8—101no—
238C3×Q8—201no—
239C3×Q8—201no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—201no—
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×Dic3—101no—
247C2×Dic3—101no—
248D12—42no—
249D12—41no—
250D12—41no—
251D12—41no—
252D12—41no—
253C4×D3—402no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—41no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5—122no—
260C22×C5—122no—
261C22×C5—122no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5#91411yescharacteristic
265C4×C5#91611yescharacteristic
266C4×C5#94211yescharacteristic
267C4×C5#95011yescharacteristic
268Dic5—41no—
269Dic5—41no—
270Dic5—81no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—51no—
274C2×Q8—101no—
275C2×Q8—151no—
276C2×D4—32no—
277C2×D4—61no—
278C2×D4—61no—
279C22×C4—302no—
280Q16—602no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—301no—
284C4⋊C4—51no—
285C4⋊C4—101no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—151no—
289C4⋊C4—301no—
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—101no—
294C42—301no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3#402811yescharacteristic
298C2×D3—42no—
299C2×D3—42no—
300C2×D3—42no—
301C3×C4—21no—
302C3×C4—201no—
303C3×C4—201no—
304C3×C4—401no—
305C3×C4#405711yescharacteristic
306C3×C4#405811yescharacteristic
307C3×C4#406111yescharacteristic
308C3×C4#406211yescharacteristic
309Dic3—201no—
310Dic3—201no—
311C2×C5—242no—
312C2×C5#504711yescharacteristic
313C2×C5#517211yescharacteristic
314C2×C5#520211yescharacteristic
315C23—62no—
316Q8—101no—
317Q8—101no—
318Q8—201no—
319Q8—201no—
320Q8—301no—
321Q8—301no—
322D4—122no—
323D4—121no—
324D4—121no—
325D4—121no—
326D4—121no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—201no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4D3×D2011yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—41no—
337C8—121no—
338C8—601no—
339C2×C3#6503511yescharacteristic
340C2×C3#6507011yescharacteristic
341C2×C3#6507211yescharacteristic
342D3—82no—
343C5#7112811yescharacteristic, complemented, Sylow
344C22—122no—
345C22—122no—
346C22—122no—
347C22#9147411yescharacteristic
348C4—21no—
349C4—201no—
350C4—201no—
351C4—401no—
352C4—601no—
353C4—601no—
354C4#9125711yescharacteristic
355C4#9127611yescharacteristic
356C4#9149011yescharacteristic
357C4#9151311yescharacteristic
358C3#1059919911yescharacteristic, complemented, Sylow
359C2—242no—
360C2#1174751111yescharacteristic
361C2#1174788911yescharacteristic
362C2#1174824111yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
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. C3×#65140C2semidirect
3. #11747104C2semidirect
5. #11746305C2semidirect
7. #11745840C2semidirect
29. #65140D3semidirect
296. C3×C5#1640semidirect
343. C5#71128semidirect
358. C3#10599199semidirect

Maximal subgroups

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

subgroupindex
#117526512
C3×#651402
#117471042
#117469012
#117463052
C5×#44852
#117458402
#105991993
#711285