Finite Group Databasebeta

← #14288974

Subgroups — #14288974

Order 1920.

472 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#5730C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11747078C211yesmaximal, characteristic, complemented
4#11747037C211yesmaximal, characteristic
5C3×#64766C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602716—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6717—22no—
11#91763C2211yescharacteristic
12C5×#946—22no—
13C5×#897—21no—
14C5×#893—21no—
15C5×D3×C4⋊C4—21no—
16C5×#890—21no—
17C4×C5×D12C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C2×#6660—21no—
20C2×#6654—21no—
21C4×C3⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90969—21no—
25#90969—21no—
26#68490—51nomaximal, Hall
27C5×#554—31no—
28#65374—31no—
29#65316—31no—
30#65304—31no—
31#64766D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D412yes—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C4×C5×D3—22no—
41C2×C5×Dic6D411yescharacteristic
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6717—44no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3—22no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—22no—
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57#6660—42no—
58#6654—42no—
59#5730D511yescharacteristic, complemented
60#5085—51no—
61#4848—51no—
62#4843—51no—
63C3×#333—51no—
64#4484—51no—
65#4483—51no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#125—61no—
68C5×C22⋊Q8—61no—
69C5×C22⋊Q8—62no—
70C4×C5×Q8—31no—
71C4×C5×D4—31no—
72C4×C5×D4—61no—
73C2×C5×C4⋊C4—61no—
74C2×#688—61no—
75C2×#688—62no—
76C2×#686—61no—
77#4020—31no—
78#3941—61no—
79#3941—61no—
80C4⋊#168C2×D311yescharacteristic
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1622—151noSylow
84C22×D15—41no—
85C22×C5×D3—21no—
86C3×C5×Q8—42no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91D60—42no—
92D60—41no—
93D60—41no—
94D60—41no—
95D60—41no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C5×D12—21no—
100C5×D12SD1612yescomplemented
101C4×C5×D3—41no—
102C4×C5×D3—41no—
103C4×C5×D3—82no—
104C5×Dic6—21no—
105C5×Dic6—21no—
106C3⋊#168—22no—
107C3×#168—41no—
108C3×#168—41no—
109C3×C4⋊Q8C2×D511yescharacteristic
110#946—22no—
111C2×#215—102no—
112C2×D24—101no—
113C2×#204—101no—
114#897—21no—
115#893—21no—
116D3×C4⋊C4—21no—
117#890—21no—
118#874—51no—
119C4×D12C2×D511yescharacteristic
120C4×Dic6C2×D511yescharacteristic
121C3×C4⋊C8—51no—
122C3×C4⋊C8—51no—
123#821—101no—
124#821—101no—
125C4×C3⋊C8—51no—
126C2×C5×Q8—31no—
127C2×C5×Q8D1212yes—
128C2×C5×D4—31no—
129C22×C4×C5—62no—
130C22×C4×C5—61no—
131C2×D20—61no—
132C2×D20—61no—
133C2×D20—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—31no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—62no—
139C5×C4⋊C4—62no—
140C5×C4⋊C4—61no—
141C5×C22⋊C4—62no—
142C5×C22⋊C4—61no—
143C42×C5—61no—
144C42×C5C22×D311yescharacteristic
145#688—122no—
146#688—124no—
147#686—122no—
148C2×#168—21no—
149C2×#168—21no—
150C2×#168—61no—
151#554—31no—
152#492—151no—
153#460—151no—
154#459—151no—
155#333—51no—
156Q8⋊C8—151no—
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—81no—
160C2×D15—81no—
161C2×D15—81no—
162C2×C5×D3—22no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C3×C4×C5—21no—
166C3×C4×C5—42no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5#13711yescharacteristic
171C5×Dic3—41no—
172C5×Dic3—41no—
173C5×Dic3—41no—
174C2×C3×Q8C22⋊D512yes—
175C2×D12—101no—
176C2×D12—101no—
177C2×D12—101no—
178C2×D12C22⋊D511yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—22no—
181C2×Dic6C22⋊D511yescharacteristic
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187#215—204no—
188(C2×D3)⋊C4—22no—
189(C2×D3)⋊C4—21no—
190C4⋊Dic3—22no—
191C4⋊Dic3C22⋊D511yescharacteristic
192C4⋊Dic3C22⋊D511yescharacteristic
193Dic3⋊C4—22no—
194Dic3⋊C4—21no—
195C4×Dic3—21no—
196C2×C3⋊C8—101no—
197D24—202no—
198#204—202no—
199C23×C5—61no—
200C22×D5—121no—
201C5×Q8—42no—
202C5×Q8—61no—
203C5×Q8—61no—
204C5×D4—32no—
205C5×D4—61no—
206C2×C4×C5—22no—
207C2×C4×C5—61no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5—121no—
211C2×C4×C5—121no—
212C2×C4×C5—242no—
213C2×C4×C5C2×D1211yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216D20—122no—
217D20—121no—
218D20—121no—
219D20—121no—
220D20—121no—
221#168—41no—
222#168—41no—
223#168—62no—
224C2×SD16—301no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8D3×D511yescharacteristic
228#127—151no—
229#125—61no—
230C22⋊Q8—61no—
231C22⋊Q8—62no—
232C4×Q8—31no—
233C4×D4—31no—
234C4×D4—61no—
235C2×C4⋊C4—61no—
236C4⋊C8—51no—
237C4⋊C8—51no—
238#102—301no—
239#102—301no—
240C4×C8—151no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—161no—
245C5×D3—42no—
246C22×D3—21no—
247C22×D3—201no—
248C3×Q8—42no—
249C2×C3×C4—22no—
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×C3×C4C2×C22⋊D511yescharacteristic
252C2×C3×C4C2×C22⋊D511yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256D12—21no—
257D12—202no—
258D12—201no—
259D12—201no—
260D12—201no—
261D12—201no—
262D12#68812yescomplemented
263C4×D3—41no—
264C4×D3—41no—
265C4×D3—82no—
266Dic6—21no—
267Dic6—21no—
268C3×C8—201no—
269C3×C8—201no—
270C3⋊C8—102no—
271C22×C5—62no—
272C22×C5—121no—
273C22×C5—121no—
274C22×C5#88211yescharacteristic
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—42no—
280C4×C5—121no—
281C4×C5—121no—
282C4×C5—121no—
283C4×C5D3×SD1611yescharacteristic
284C4×C5#91411yescharacteristic
285C4×C5#91811yescharacteristic
286C4×C5#91911yescharacteristic
287C2×Q8—31no—
288C2×Q8#120312yes—
289C2×D4—31no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4—301no—
293C22×C4—62no—
294C22×C4—61no—
295SD16—602no—
296SD16—604no—
297D8—602no—
298C2×C8—101no—
299C2×C8—101no—
300C2×C8—301no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—62no—
306C4⋊C4—62no—
307C4⋊C4—61no—
308C22⋊C4—62no—
309C22⋊C4—61no—
310C42—61no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3#409911yescharacteristic
314C2×D3—22no—
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—42no—
322C3×C4C2×#68811yescharacteristic
323C3×C4#408811yescharacteristic
324C3×C4#409511yescharacteristic
325C3×C4#409611yescharacteristic
326Dic3—41no—
327Dic3—41no—
328Dic3—41no—
329C2×C5—122no—
330C2×C5#474711yescharacteristic
331C2×C5#480611yescharacteristic
332C2×C5#481011yescharacteristic
333D5—481no—
334C23—61no—
335C23—601no—
336Q8—42no—
337Q8—61no—
338Q8—61no—
339D4—32no—
340D4—61no—
341D4—602no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—22no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—242no—
353C2×C4C2×#120311yescharacteristic
354C2×C4D3×C22⋊D511yescharacteristic
355C2×C4D3×C22⋊D511yescharacteristic
356C8—201no—
357C8—201no—
358C8—302no—
359C2×C3#6551611yescharacteristic
360C2×C3#6552711yescharacteristic
361C2×C3#6553011yescharacteristic
362D3—42no—
363D3—801no—
364C5#6849011yescharacteristic, complemented, Sylow
365C22—62no—
366C22—121no—
367C22—121no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9157011yescharacteristic
372C4—21no—
373C4—42no—
374C4—121no—
375C4—121no—
376C4—121no—
377C4D3×#68811yescharacteristic
378C4#9150411yescharacteristic
379C4#9151911yescharacteristic
380C4#9152011yescharacteristic
381C3#1060271611yescharacteristic, complemented, Sylow
382C2—122no—
383C2—2401no—
384C2#1174914111yescharacteristic
385C2#1174927911yescharacteristic
386C2#1174928211yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11747037C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5730C2semidirect
2. #11751186C2semidirect
3. #11747078C2semidirect
5. C3×#64766C2semidirect
6. #11745842C2semidirect
7. #11745836C2semidirect
31. #64766D3semidirect
59. #5730D5semidirect
100. C5×D12SD16semidirect
262. D12#688semidirect
312. C3×C5#1622semidirect
364. C5#68490semidirect
381. C3#10602716semidirect

Maximal subgroups

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

subgroupindex
C5×#57302
#117511862
#117470782
#117470372
C3×#647662
#117458422
#117458362
#106027163
#684905