Finite Group Databasebeta

← #14316523

Subgroups — #14316523

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#11753963C211yesmaximal, characteristic
2C2×#91112C211yesmaximal, characteristic, complemented
3C5×#5179C211yesmaximal, characteristic, complemented
4C3×#65481C211yesmaximal, characteristic, complemented
5#11745919C211yesmaximal, characteristic, complemented
6#11745905C211yesmaximal, characteristic, complemented
7#11745885C211yesmaximal, characteristic, complemented
8#10602316—31nomaximal, Hall
9#92019—21no—
10C2×C3×C5×Q16C2211yescharacteristic, complemented
11C2×D120C2211yescharacteristic
12C5×#904C2211yescharacteristic
13C3×#4088—21no—
14C3×#4047C2211yescharacteristic
15#91305—21no—
16#91271—21no—
17#91249—22no—
18D5×D24—21no—
19#91112—22no—
20C2×C3⋊#672C2211yescharacteristic, complemented
21C5×#829—21no—
22C5×#828—21no—
23C5×#812C2211yescharacteristic, complemented
24C3×#3968—21no—
25C3×#3951C2211yescharacteristic, complemented
26#71098—51nomaximal, Hall
27#66103—31no—
28C5×#510—31no—
29#65481D311yescharacteristic, complemented
30C2×#3960—31no—
31#64787—31no—
32#64736—31no—
33#64735—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C5×#235—21no—
37C3×#709D411yescharacteristic
38#6790—42no—
39D3×D20—41no—
40D5×D12—22no—
41#6773—22no—
42#6769—41no—
43C3×C5×Q16—21no—
44C3×C5×Q16—21no—
45C2×C3×C5×C8C2311yescharacteristic
46D120—21no—
47D120D412yes—
48C5×Dic12D411yescharacteristic
49C5×D24D411yescharacteristic
50C5×#204—21no—
51C3×#689—41no—
52C3×#688—41no—
53C3×#681—21no—
54C3×#681D411yescharacteristic
55C3×#676—21no—
56C3×C8×D5—21no—
57#6660—22no—
58#6654—22no—
59C3⋊#672—21no—
60C5×C3⋊C16—21no—
61#5752—51no—
62C3×#473—51no—
63#5179D511yescharacteristic, complemented
64C2×#828—51no—
65#4561—51no—
66#4497—51no—
67#4495—51no—
68#4149—61no—
69C5×#135—31no—
70C2×C5×Q16C2×D311yescharacteristic, complemented
71#4095—61no—
72#4088—21no—
73#4065—61no—
74#4060—62no—
75D5×D8—61no—
76C2×D40—31no—
77#4047C2×D311yescharacteristic
78C5×Q32—61no—
79C5×SD32—61no—
80C5×M32—31no—
81#3968—21no—
82#3960—62no—
83#3951C2×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—41no—
95C5×D12—21no—
96C4×C5×D3—41no—
97C5×Dic6—21no—
98C3×C22⋊D5—21no—
99C3×D20D811yescharacteristic
100C3×C4×D5—21no—
101C3×Dic10D811yescharacteristic
102#1203—42no—
103#1202—42no—
104#1200—42no—
105C3×C5×C8C2×D411yescharacteristic
106C3×C5×C8C2×D411yescharacteristic
107C3×#168—21no—
108C3×#168—41no—
109#1009—101no—
110C3×#137—101no—
111C2×C3×Q16C2×D511yescharacteristic, complemented
112C3×#131—51no—
113#908—102no—
114#908—101no—
115#904—101no—
116#904C2×D511yescharacteristic
117C2×D24—51no—
118C2×D24—101no—
119C3×#108—51no—
120C3×#101—101no—
121#829—21no—
122#828—21no—
123#828—102no—
124#812C2×D511yescharacteristic, complemented
125C2×C3⋊C16—51no—
126C5×#41—61no—
127C2×C5×Q8—21no—
128#713—62no—
129D4×D5—62no—
130D4×D5—122no—
131#709—121no—
132#709#6711yescharacteristic
133C2×D20—61no—
134C2×D20—121no—
135C5×Q16—21no—
136C5×Q16—21no—
137C5×Q16—31no—
138C5×SD16—61no—
139C5×D8—31no—
140C2×C5×C8C22×D311yescharacteristic
141#689—41no—
142#688—41no—
143#688—62no—
144#686—62no—
145#681—21no—
146#681#6711yescharacteristic
147D40—32no—
148D40—61no—
149#676—21no—
150C8×D5—21no—
151C5×C16—61no—
152#672—61no—
153#576—151no—
154#510—31no—
155C2×SD32—151no—
156#473—51no—
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—41no—
164C2×C3×D5—21no—
165D3×D5—162no—
166C3×C4×C5—81no—
167C3×C4×C5#12011yescharacteristic
168C3×C4×C5C2×D811yescharacteristic
169C3×Dic5—21no—
170C5×Dic3—41no—
171C3×#41—51no—
172C2×C3×Q8—21no—
173#239—201no—
174D3×D4—201no—
175D3×D4—202no—
176#235—21no—
177#235—102no—
178C2×D12—102no—
179C2×D12—101no—
180C3×Q16—21no—
181C3×Q16—21no—
182C3×Q16—201no—
183C3×SD16—201no—
184C3×M16—51no—
185C3×M16—101no—
186C3×M16—101no—
187C2×C3×C8—101no—
188C2×C3×C8C22×D511yescharacteristic
189Dic12C22⋊D511yescharacteristic
190D24—52no—
191D24—102no—
192D24—101no—
193D24C22⋊D511yescharacteristic
194#204—21no—
195#204—102no—
196C3⋊C16—21no—
197C3⋊C16—101no—
198C22×D5—122no—
199C22×D5—121no—
200C5×Q8—41no—
201C5×Q8—41no—
202C5×Q8—61no—
203C5×D4—61no—
204C5×D4—121no—
205C2×C4×C5—41no—
206C2×C4×C5—121no—
207C2×C4×C5C2×#6711yescharacteristic
208C22⋊D5—21no—
209C22⋊D5—122no—
210D20—62no—
211D20—122no—
212D20—121no—
213D20#21311yescharacteristic
214C4×D5—21no—
215C4×D5—122no—
216Dic10#21311yescharacteristic
217C5×C8D3×D411yescharacteristic
218C5×C8D3×D411yescharacteristic
219#168—21no—
220#168—41no—
221H(5,𝔽2)—301no—
222#137—101no—
223AGL(1,ℤ/8)—301no—
224AGL(1,ℤ/8)—302no—
225#135—31no—
226#135—301no—
227C2×Q16D3×D511yescharacteristic, complemented
228C2×D8—151no—
229C2×D8—301no—
230#131—51no—
231Q32—61no—
232SD32—61no—
233SD32—302no—
234M32—31no—
235C2×C16—151no—
236#108—51no—
237#101—101no—
238C2×C3×C5—21no—
239C2×C3×C5#44711yescharacteristic
240D15—82no—
241C3×D5—41no—
242C5×D3—81no—
243C22×D3—202no—
244C22×D3—201no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—51no—
248C3×D4—51no—
249C3×D4—101no—
250C2×C3×C4—41no—
251C2×C3×C4—101no—
252C2×C3×C4D4×D511yescharacteristic
253#67—41no—
254#67—202no—
255D12—21no—
256D12—102no—
257D12—202no—
258D12—201no—
259C4×D3—41no—
260C4×D3—202no—
261Dic6—21no—
262C3×C8—101no—
263C3×C8—201no—
264C3×C8D4×D511yescharacteristic
265C3×C8C2×C22⋊D511yescharacteristic
266C22×C5—121no—
267C22×C5#94911yescharacteristic
268C2×D5—21no—
269C2×D5—122no—
270C2×D5—482no—
271C2×D5—481no—
272C4×C5—81no—
273C4×C5—121no—
274C4×C5C2×#21311yescharacteristic
275C4×C5#93711yescharacteristic
276Dic5—21no—
277#41—51no—
278#41—61no—
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—31no—
289Q16—201no—
290SD16—61no—
291SD16—201no—
292SD16—302no—
293D8—31no—
294D8—152no—
295D8—302no—
296D8—301no—
297M16—51no—
298M16—101no—
299M16—101no—
300C2×C8—101no—
301C2×C8C2×D3×D511yescharacteristic
302C16—61no—
303C16—301no—
304C3×C5#219411yescharacteristic, complemented, Hall
305C22×C3—101no—
306C22×C3#405711yescharacteristic
307C2×D3—41no—
308C2×D3—202no—
309C2×D3—802no—
310C2×D3—801no—
311C3×C4—81no—
312C3×C4—101no—
313C3×C4D5×D811yescharacteristic
314C3×C4#408311yescharacteristic
315Dic3—41no—
316C2×C5—21no—
317C2×C5—241no—
318C2×C5#503611yescharacteristic
319D5—41no—
320D5—242no—
321C23—602no—
322C23—601no—
323Q8—41no—
324Q8—41no—
325Q8—51no—
326Q8—61no—
327D4—51no—
328D4—61no—
329D4—101no—
330D4—121no—
331D4—302no—
332D4—602no—
333D4—602no—
334D4—601no—
335C2×C4—41no—
336C2×C4—101no—
337C2×C4—121no—
338C2×C4—602no—
339C2×C4D5×#6711yescharacteristic
340C8—101no—
341C8—201no—
342C8D3×C22⋊D511yescharacteristic
343C8#679011yescharacteristic
344C2×C3—21no—
345C2×C3—201no—
346C2×C3#6544511yescharacteristic
347D3—81no—
348D3—402no—
349C5#7109811yescharacteristic, complemented, Sylow
350C22—101no—
351C22—121no—
352C22—602no—
353C22—2401no—
354C22—2402no—
355C22#9147811yescharacteristic
356C4—81no—
357C4—101no—
358C4—121no—
359C4D5×#21311yescharacteristic
360C4#9157711yescharacteristic
361C3#1060231611yescharacteristic, complemented, Sylow
362C2—21no—
363C2—201no—
364C2—241no—
365C2—1202no—
366C2#1174915111yescharacteristic
subgroupG/H
centerC2#11749151
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC2×C3×C5#447
prime radical#11753963C2
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×#5179C2semidirect
4. C3×#65481C2semidirect
5. #11745919C2semidirect
6. #11745905C2semidirect
7. #11745885C2semidirect
10. C2×C3×C5×Q16C22semidirect
20. C2×C3⋊#672C22semidirect
23. C5×#812C22semidirect
25. C3×#3951C22semidirect
29. #65481D3semidirect
63. #5179D5semidirect
70. C2×C5×Q16C2×D3semidirect
83. #3951C2×D3semidirect
111. C2×C3×Q16C2×D5semidirect
124. #812C2×D5semidirect
227. C2×Q16D3×D5semidirect
304. C3×C5#2194semidirect
349. C5#71098semidirect
361. C3#10602316semidirect

Maximal subgroups

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

subgroupindex
#117539632
C2×#911122
C5×#51792
C3×#654812
#117459192
#117459052
#117458852
#106023163
#710985