Finite Group Databasebeta

← #14316510

Subgroups — #14316510

Order 1920.

432 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 77 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#11756516C211yesmaximal, characteristic
2C2×C3×C5×SD32C211yesmaximal, characteristic, complemented
3#11751293C211yesmaximal, characteristic, complemented
4#11751280C211yesmaximal, characteristic, complemented
5#11746384C211yesmaximal, characteristic, complemented
6#11746331C211yesmaximal, characteristic, complemented
7#11746329C211yesmaximal, characteristic, complemented
8#10602283—31nomaximal, Hall
9#92095—21no—
10C2×C3×C5×Q16C2211yescharacteristic, complemented
11C2×C3×C5×D8C2211yescharacteristic
12#91831—21no—
13#91821—21no—
14#91801—21no—
15#91800—22no—
16D8×D15—21no—
17#91793C2211yescharacteristic
18#91790C2211yescharacteristic
19C3×C5×SD32—22no—
20C2×C3×C5×C16C2211yescharacteristic, complemented
21#91120—21no—
22#91113—21no—
23#91112—21no—
24#91103C2211yescharacteristic, complemented
25#91096C2211yescharacteristic, complemented
26#71490—51nomaximal, Hall
27#66091—31no—
28C2×C5×SD32D311yescharacteristic, complemented
29#65481—31no—
30#65468—31no—
31#64783—31no—
32#64730—31no—
33#64728—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×#1220—42no—
37#6819—22no—
38#6819—41no—
39D4×D15—22no—
40D4×D15—41no—
41#6817—21no—
42#6817D411yescharacteristic
43C3×C5×Q16—21no—
44C3×C5×Q16—21no—
45C3×C5×D8—21no—
46C3×C5×D8D412yes—
47C2×C3×C5×C8C2311yescharacteristic
48#6718—41no—
49#6717—41no—
50#6716—22no—
51#6715—22no—
52#6710—21no—
53#6710D411yescharacteristic
54Dic60D411yescharacteristic
55D120D411yescharacteristic
56#6706—21no—
57#6705—21no—
58C8×D15—21no—
59C3×C5×C16—21no—
60C3⋊#672—21no—
61#5757—51no—
62C2×C3×SD32D511yescharacteristic, complemented
63#5192—51no—
64#5179—51no—
65#4563—51no—
66#4510—51no—
67#4508—51no—
68#4144—61no—
69C2×C5×Q16C2×D311yescharacteristic, complemented
70C2×C5×D8C2×D311yescharacteristic
71#4088—61no—
72#4078—61no—
73#4058—61no—
74#4057—62no—
75D5×D8—61no—
76#4050—31no—
77#4047—31no—
78C5×SD32—22no—
79C2×C5×C16C2×D311yescharacteristic, complemented
80#3968—61no—
81#3961—61no—
82#3960—61no—
83#3951—31no—
84#3944—31no—
85#2194—151noSylow
86C23×C3×C5—41no—
87C22×D15—42no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×D4—22no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—21no—
95#1220—42no—
96#1220—42no—
97#1220—41no—
98C2×Dic15—42no—
99D60—21no—
100D60D811yescharacteristic
101C4×D15—21no—
102C4×D15—41no—
103Dic30—21no—
104Dic30D811yescharacteristic
105C3×C5×C8C2×D411yescharacteristic
106C3×C5×C8C2×D411yescharacteristic
107C3⋊#168—21no—
108C3⋊#168—41no—
109#1004—101no—
110C2×C3×Q16C2×D511yescharacteristic, complemented
111C2×C3×D8C2×D511yescharacteristic
112#942—101no—
113#932—101no—
114#912—101no—
115#911—102no—
116D3×D8—101no—
117#904—51no—
118#901—51no—
119C3×SD32—22no—
120C2×C3×C16C2×D511yescharacteristic, complemented
121#836—101no—
122#829—101no—
123#828—101no—
124#819—51no—
125#812—51no—
126C2×C5×Q8—21no—
127C2×C5×D4—21no—
128C2×C22⋊D5—122no—
129#711—62no—
130#711—121no—
131D4×D5—62no—
132D4×D5—121no—
133#709—31no—
134#709—61no—
135C5×Q16—21no—
136C5×Q16—21no—
137C5×D8—21no—
138C5×D8#6712yes—
139C2×C5×C8C22×D311yescharacteristic
140#689—121no—
141#688—121no—
142#687—62no—
143#686—62no—
144#681—31no—
145#681—61no—
146Dic20—31no—
147D40—31no—
148#677—61no—
149#676—61no—
150C8×D5—61no—
151C5×C16—21no—
152#672—61no—
153#576—151no—
154#510—151no—
155C2×SD32D1511yescharacteristic, complemented
156#473—151no—
157#361—151no—
158#359—151no—
159#350—151no—
160C22×C3×C5—42no—
161C22×C3×C5—161no—
162C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
163C2×D15—21no—
164C2×D15—41no—
165C2×D15—162no—
166C3×C4×C5—81no—
167C3×C4×C5#12011yescharacteristic
168C3×C4×C5C2×D811yescharacteristic
169Dic15—21no—
170Dic15—41no—
171C2×C3×Q8—21no—
172C2×C3×D4—21no—
173C2×#67—202no—
174#237—102no—
175#237—201no—
176D3×D4—102no—
177D3×D4—201no—
178#235—51no—
179#235—101no—
180C3×Q16—21no—
181C3×Q16—21no—
182C3×D8—21no—
183C3×D8C22⋊D512yes—
184C2×C3×C8C22×D511yescharacteristic
185#216—201no—
186#215—201no—
187#214—102no—
188#213—102no—
189#208—51no—
190#208—101no—
191Dic12—51no—
192D24—51no—
193#204—101no—
194ΓL(1,𝔽25)—101no—
195D3×C8—101no—
196C3×C16—21no—
197C3⋊C16—101no—
198C23×C5—41no—
199C22×D5—122no—
200C5×Q8—41no—
201C5×Q8—41no—
202C5×D4—22no—
203C5×D4—41no—
204C2×C4×C5—41no—
205C2×C4×C5D3×D411yescharacteristic
206C22⋊D5—61no—
207C22⋊D5—122no—
208C22⋊D5—122no—
209C22⋊D5—121no—
210C2×Dic5—122no—
211D20—31no—
212D20—61no—
213C4×D5—61no—
214C4×D5—121no—
215Dic10—31no—
216Dic10—61no—
217C5×C8D3×D411yescharacteristic
218C5×C8C2×#6711yescharacteristic
219#168—61no—
220#168—121no—
221H(5,𝔽2)—301no—
222#137—301no—
223AGL(1,ℤ/8)—301no—
224AGL(1,ℤ/8)—302no—
225#135—151no—
226#135—301no—
227C2×Q16C2×D1511yescharacteristic, complemented
228C2×D8—301no—
229C2×D8C2×D1511yescharacteristic
230#131—151no—
231Q32—301no—
232SD32—22no—
233SD32—301no—
234M32—151no—
235C2×C16C2×D1511yescharacteristic, complemented
236#108—151no—
237#101—301no—
238C2×C3×C5—21no—
239C2×C3×C5—82no—
240C2×C3×C5#44711yescharacteristic
241D15—41no—
242D15—81no—
243C23×C3—41no—
244C22×D3—202no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×D4—22no—
248C3×D4—41no—
249C2×C3×C4—41no—
250C2×C3×C4D4×D511yescharacteristic
251#67—101no—
252#67—202no—
253#67—202no—
254#67—201no—
255C2×Dic3—202no—
256D12—51no—
257D12—101no—
258C4×D3—101no—
259C4×D3—201no—
260Dic6—51no—
261Dic6—101no—
262C3×C8D4×D511yescharacteristic
263C3×C8C2×C22⋊D511yescharacteristic
264C3⋊C8—101no—
265C3⋊C8—201no—
266C22×C5—42no—
267C22×C5—161no—
268C22×C5#91111yescharacteristic
269C2×D5—61no—
270C2×D5—121no—
271C2×D5—482no—
272C4×C5—81no—
273C4×C5D3×D811yescharacteristic
274C4×C5#93711yescharacteristic
275Dic5—61no—
276Dic5—121no—
277#41—151no—
278#41—302no—
279#41—301no—
280#41—601no—
281C2×Q8—21no—
282C2×D4—21no—
283C2×D4—302no—
284C2×D4—601no—
285C2×D4—602no—
286Q16—21no—
287Q16—21no—
288Q16—151no—
289Q16—601no—
290SD16—302no—
291SD16—301no—
292SD16—601no—
293D8—21no—
294D8—151no—
295D8—302no—
296D8#122012yes—
297M16—151no—
298M16—301no—
299M16—301no—
300C2×C8—301no—
301C2×C8C22×D1511yescharacteristic
302C16—21no—
303C16—301no—
304C3×C5#219411yescharacteristic, complemented, Hall
305C22×C3—42no—
306C22×C3—161no—
307C22×C3#405711yescharacteristic
308C2×D3—101no—
309C2×D3—201no—
310C2×D3—802no—
311C3×C4—81no—
312C3×C4D5×D811yescharacteristic
313C3×C4#408311yescharacteristic
314Dic3—101no—
315Dic3—201no—
316C2×C5—21no—
317C2×C5—82no—
318C2×C5#515611yescharacteristic
319D5—121no—
320D5—241no—
321C23—41no—
322C23—602no—
323Q8—41no—
324Q8—41no—
325Q8—151no—
326Q8—301no—
327D4—22no—
328D4—41no—
329D4—151no—
330D4—301no—
331D4—301no—
332D4—602no—
333D4—602no—
334D4—601no—
335C2×C4—41no—
336C2×C4—301no—
337C2×C4—602no—
338C2×C4—601no—
339C2×C4D4×D1511yescharacteristic
340C8—301no—
341C8—601no—
342C8D4×D1511yescharacteristic
343C8C2×#122011yescharacteristic
344C2×C3—21no—
345C2×C3—82no—
346C2×C3#6544511yescharacteristic
347D3—201no—
348D3—401no—
349C5#7149011yescharacteristic, complemented, Sylow
350C22—42no—
351C22—161no—
352C22—301no—
353C22—601no—
354C22—2402no—
355C22#9180011yescharacteristic
356C4—81no—
357C4—301no—
358C4—601no—
359C4D8×D1511yescharacteristic
360C4#9182611yescharacteristic
361C3#1060228311yescharacteristic, complemented, Sylow
362C2—21no—
363C2—82no—
364C2—601no—
365C2—1201no—
366C2#1175125711yescharacteristic
subgroupG/H
centerC2#11751257
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC2×C3×C5×SD32C2
socleC2×C3×C5#447
prime radical#11756516C2
hypercenterC2×SD32D15
hypocenterC3×C5#2194
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×SD32C2semidirect
3. #11751293C2semidirect
4. #11751280C2semidirect
5. #11746384C2semidirect
6. #11746331C2semidirect
7. #11746329C2semidirect
10. C2×C3×C5×Q16C22semidirect
20. C2×C3×C5×C16C22semidirect
24. #91103C22semidirect
25. #91096C22semidirect
28. C2×C5×SD32D3semidirect
62. C2×C3×SD32D5semidirect
69. C2×C5×Q16C2×D3semidirect
79. C2×C5×C16C2×D3semidirect
110. C2×C3×Q16C2×D5semidirect
120. C2×C3×C16C2×D5semidirect
155. C2×SD32D15semidirect
227. C2×Q16C2×D15semidirect
235. C2×C16C2×D15semidirect
304. C3×C5#2194semidirect
349. C5#71490semidirect
361. C3#10602283semidirect

Maximal subgroups

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

subgroupindex
#117565162
C2×C3×C5×SD322
#117512932
#117512802
#117463842
#117463312
#117463292
#106022833
#714905