Finite Group Databasebeta

← #14316525

Subgroups — #14316525

Order 1920.

432 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 74 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#11753973C211yesmaximal, characteristic
2C2×#91112C211yesmaximal, characteristic, complemented
3C5×#5192C211yesmaximal, characteristic, complemented
4C3×#65468C211yesmaximal, characteristic, complemented
5#11745920C211yesmaximal, characteristic, complemented
6#11745903C211yesmaximal, characteristic, complemented
7#11745887C211yesmaximal, characteristic, complemented
8#10601891—31nomaximal, Hall
9#92019—21no—
10C2×C3×C5×Q16C2211yescharacteristic, complemented
11C2×D120C2211yescharacteristic
12C5×#942—21no—
13C5×#901C2211yescharacteristic
14C3×#4050C2211yescharacteristic
15#91301—21no—
16#91275—21no—
17#91253—22no—
18D3×D40—21no—
19#91112—22no—
20C2×C3⋊#672C2211yescharacteristic, complemented
21C5×#836—21no—
22C5×#819C2211yescharacteristic, complemented
23C3×#3961—21no—
24C3×#3960—21no—
25C3×#3944C2211yescharacteristic, complemented
26#71523—51nomaximal, Hall
27#66086—31no—
28C5×#473—31no—
29#65468D311yescharacteristic, complemented
30C2×#3960—31no—
31#64781—31no—
32#64717—31no—
33#64715—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C5×#235D411yescharacteristic
37C3×#709—21no—
38#6790—42no—
39D3×D20—22no—
40D5×D12—41no—
41#6773—41no—
42#6769—22no—
43C3×C5×Q16—21no—
44C3×C5×Q16—21no—
45C2×C3×C5×C8C2311yescharacteristic
46D120—21no—
47D120D412yes—
48C5×#216—41no—
49C5×#215—41no—
50C5×#208—21no—
51C5×#208D411yescharacteristic
52C5×ΓL(1,𝔽25)—21no—
53C5×D3×C8—21no—
54C3×Dic20D411yescharacteristic
55C3×D40D411yescharacteristic
56C3×#677—21no—
57#6658—22no—
58#6653—22no—
59C3⋊#672—21no—
60C3×#672—21no—
61#5769—51no—
62C3×#510—51no—
63#5192D511yescharacteristic, complemented
64C2×#828—51no—
65#4567—51no—
66#4516—51no—
67#4515—51no—
68#4149—61no—
69C5×#137—61no—
70C2×C5×Q16C2×D311yescharacteristic, complemented
71C5×#131—31no—
72#4054—62no—
73#4054—61no—
74#4050—61no—
75#4050C2×D311yescharacteristic
76C2×D40—31no—
77C2×D40—61no—
78C5×#108—31no—
79C5×#101—61no—
80#3961—21no—
81#3960—21no—
82#3960—62no—
83#3944C2×D311yescharacteristic, complemented
84C2×#672—31no—
85#2194—151noSylow
86C22×D15—41no—
87C2×D3×D5—42no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92D60—22no—
93D60—41no—
94C5×#67—21no—
95C5×D12D811yescharacteristic
96C4×C5×D3—21no—
97C5×Dic6D811yescharacteristic
98C3×C22⋊D5—41no—
99C3×D20—21no—
100C3×C4×D5—41no—
101C3×Dic10—21no—
102#1203—42no—
103#1202—42no—
104#1200—42no—
105C3×C5×C8C2×D411yescharacteristic
106C3×C5×C8C2×D411yescharacteristic
107C5×C3⋊C8—21no—
108C5×C3⋊C8—41no—
109#1009—101no—
110C3×#135—51no—
111C2×C3×Q16C2×D511yescharacteristic, complemented
112#949—101no—
113#942—21no—
114#919—101no—
115#914—102no—
116D3×D8—101no—
117C2×D24—51no—
118#901C2×D511yescharacteristic
119C3×Q32—101no—
120C3×SD32—101no—
121C3×M32—51no—
122#836—21no—
123#828—102no—
124#819C2×D511yescharacteristic, complemented
125C2×C3⋊C16—51no—
126C5×#41—31no—
127C2×C5×Q8—21no—
128#713—121no—
129D4×D5—121no—
130D4×D5—122no—
131#709—21no—
132#709—62no—
133C2×D20—62no—
134C2×D20—61no—
135C5×Q16—21no—
136C5×Q16—21no—
137C5×Q16—121no—
138C5×SD16—121no—
139C5×M16—31no—
140C5×M16—61no—
141C5×M16—61no—
142C2×C5×C8—61no—
143C2×C5×C8C22×D311yescharacteristic
144Dic20#6711yescharacteristic
145D40—32no—
146D40—62no—
147D40—61no—
148D40#6711yescharacteristic
149#677—21no—
150#677—62no—
151#672—21no—
152#672—61no—
153#576—151no—
154#510—51no—
155C2×SD32—151no—
156#473—31no—
157#361—151no—
158#359—151no—
159#350—151no—
160C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
161C2×D15—42no—
162C2×D15—161no—
163C2×C5×D3—21no—
164C2×C3×D5—41no—
165D3×D5—162no—
166C3×C4×C5—81no—
167C3×C4×C5#12011yescharacteristic
168C3×C4×C5C2×D811yescharacteristic
169C3×Dic5—41no—
170C5×Dic3—21no—
171C3×#41—101no—
172C2×C3×Q8—21no—
173#239—102no—
174D3×D4—102no—
175D3×D4—202no—
176#235—201no—
177#235C22⋊D511yescharacteristic
178C2×D12—101no—
179C2×D12—201no—
180C3×Q16—21no—
181C3×Q16—21no—
182C3×Q16—51no—
183C3×SD16—101no—
184C3×D8—51no—
185C2×C3×C8C22×D511yescharacteristic
186#216—41no—
187#215—41no—
188#215—102no—
189#213—102no—
190#208—21no—
191#208C22⋊D511yescharacteristic
192D24—52no—
193D24—101no—
194ΓL(1,𝔽25)—21no—
195D3×C8—21no—
196C3×C16—101no—
197C3⋊C16—101no—
198C22×D5—122no—
199C22×D5—121no—
200C5×Q8—31no—
201C5×Q8—41no—
202C5×Q8—41no—
203C5×D4—31no—
204C5×D4—61no—
205C2×C4×C5—41no—
206C2×C4×C5—61no—
207C2×C4×C5D3×D411yescharacteristic
208C22⋊D5—41no—
209C22⋊D5—122no—
210D20—21no—
211D20—62no—
212D20—122no—
213D20—121no—
214C4×D5—41no—
215C4×D5—122no—
216Dic10—21no—
217C5×C8—61no—
218C5×C8—121no—
219C5×C8D3×D411yescharacteristic
220C5×C8C2×#6711yescharacteristic
221H(5,𝔽2)—301no—
222#137—61no—
223AGL(1,ℤ/8)—301no—
224AGL(1,ℤ/8)—302no—
225#135—51no—
226#135—301no—
227C2×Q16D3×D511yescharacteristic, complemented
228C2×D8—151no—
229C2×D8—301no—
230#131—31no—
231Q32—101no—
232SD32—101no—
233SD32—302no—
234M32—51no—
235C2×C16—151no—
236#108—31no—
237#101—61no—
238C2×C3×C5—21no—
239C2×C3×C5#44711yescharacteristic
240D15—82no—
241C3×D5—81no—
242C5×D3—41no—
243C22×D3—202no—
244C22×D3—201no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—101no—
248C3×D4—101no—
249C3×D4—201no—
250C2×C3×C4—41no—
251C2×C3×C4—201no—
252C2×C3×C4C2×C22⋊D511yescharacteristic
253#67—21no—
254#67—202no—
255D12—102no—
256D12—202no—
257D12—201no—
258D12#68611yescharacteristic
259C4×D3—21no—
260C4×D3—202no—
261Dic6#68611yescharacteristic
262C3×C8D4×D511yescharacteristic
263C3×C8D4×D511yescharacteristic
264C3⋊C8—21no—
265C3⋊C8—41no—
266C22×C5—61no—
267C22×C5#91111yescharacteristic
268C2×D5—41no—
269C2×D5—122no—
270C2×D5—482no—
271C2×D5—481no—
272C4×C5—61no—
273C4×C5—81no—
274C4×C5D3×D811yescharacteristic
275C4×C5#93711yescharacteristic
276Dic5—41no—
277#41—31no—
278#41—101no—
279#41—302no—
280#41—601no—
281C2×Q8—21no—
282C2×D4—302no—
283C2×D4—301no—
284C2×D4—601no—
285C2×D4—602no—
286Q16—21no—
287Q16—21no—
288Q16—51no—
289Q16—121no—
290SD16—101no—
291SD16—121no—
292SD16—302no—
293D8—51no—
294D8—152no—
295D8—302no—
296D8—301no—
297M16—31no—
298M16—61no—
299M16—61no—
300C2×C8—61no—
301C2×C8C2×D3×D511yescharacteristic
302C16—101no—
303C16—301no—
304C3×C5#219411yescharacteristic, complemented, Hall
305C22×C3—201no—
306C22×C3#409511yescharacteristic
307C2×D3—21no—
308C2×D3—202no—
309C2×D3—802no—
310C2×D3—801no—
311C3×C4—81no—
312C3×C4—201no—
313C3×C4C2×#68611yescharacteristic
314C3×C4#408311yescharacteristic
315Dic3—21no—
316C2×C5—21no—
317C2×C5—121no—
318C2×C5#515611yescharacteristic
319D5—81no—
320D5—242no—
321C23—602no—
322C23—601no—
323Q8—31no—
324Q8—41no—
325Q8—41no—
326Q8—101no—
327D4—31no—
328D4—61no—
329D4—101no—
330D4—201no—
331D4—302no—
332D4—602no—
333D4—602no—
334D4—601no—
335C2×C4—41no—
336C2×C4—61no—
337C2×C4—201no—
338C2×C4—602no—
339C2×C4D3×C22⋊D511yescharacteristic
340C8—61no—
341C8—121no—
342C8D5×#6711yescharacteristic
343C8#679011yescharacteristic
344C2×C3—21no—
345C2×C3—401no—
346C2×C3#6532511yescharacteristic
347D3—41no—
348D3—402no—
349C5#7152311yescharacteristic, complemented, Sylow
350C22—61no—
351C22—201no—
352C22—602no—
353C22—2401no—
354C22—2402no—
355C22#9148011yescharacteristic
356C4—61no—
357C4—81no—
358C4—201no—
359C4D3×#68611yescharacteristic
360C4#9157711yescharacteristic
361C3#1060189111yescharacteristic, complemented, Sylow
362C2—21no—
363C2—121no—
364C2—401no—
365C2—1202no—
366C2#1174915211yescharacteristic
subgroupG/H
centerC2#11749152
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC2×C3×C5#447
prime radical#11753973C2
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2194
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#91112C2semidirect
3. C5×#5192C2semidirect
4. C3×#65468C2semidirect
5. #11745920C2semidirect
6. #11745903C2semidirect
7. #11745887C2semidirect
10. C2×C3×C5×Q16C22semidirect
20. C2×C3⋊#672C22semidirect
22. C5×#819C22semidirect
25. C3×#3944C22semidirect
29. #65468D3semidirect
63. #5192D5semidirect
70. C2×C5×Q16C2×D3semidirect
83. #3944C2×D3semidirect
111. C2×C3×Q16C2×D5semidirect
124. #819C2×D5semidirect
227. C2×Q16D3×D5semidirect
304. C3×C5#2194semidirect
349. C5#71523semidirect
361. C3#10601891semidirect

Maximal subgroups

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

subgroupindex
#117539732
C2×#911122
C5×#51922
C3×#654682
#117459202
#117459032
#117458872
#106018913
#715235