Finite Group Databasebeta

← #14316397

Subgroups — #14316397

Order 1920.

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

normal subgroups only

This group has 440 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, complemented
2C2×#91110C211yesmaximal, characteristic, complemented
3C5×#5147C211yesmaximal, characteristic, complemented
4C3×#65449C211yesmaximal, characteristic, complemented
5#11745919C211yesmaximal, characteristic, complemented
6#11745905C211yesmaximal, characteristic, complemented
7#11745885C211yesmaximal, characteristic, complemented
8#10602310—31nomaximal, Hall
9#92019—21no—
10C2×C3×C5×D8C2211yescharacteristic, complemented
11C2×D120C2211yescharacteristic
12C5×#904C2211yescharacteristic
13C3×#4078—21no—
14C3×#4047C2211yescharacteristic
15#91305—21no—
16#91271—21no—
17#91249—22no—
18D5×D24—21no—
19#91110—22no—
20C2×C3⋊#672C2211yescharacteristic, complemented
21C5×#827—21no—
22C5×#826—21no—
23C5×#812C2211yescharacteristic, complemented
24C3×#3965—21no—
25C3×#3951C2211yescharacteristic, complemented
26#71094—51nomaximal, Hall
27#66103—31no—
28C5×#509—31no—
29#65449D311yescharacteristic, complemented
30C2×#3958—31no—
31#64787—31no—
32#64736—31no—
33#64735—31no—
34C2×C3×C5×D4—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×D8—21no—
44C3×C5×D8—21no—
45C2×C3×C5×C8C2311yescharacteristic
46D120—21no—
47D120D412yes—
48C5×Dic12D411yescharacteristic
49C5×D24D411yescharacteristic
50C5×#204—21no—
51C3×#687—41no—
52C3×#686—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×#472—51no—
63#5147D511yescharacteristic, complemented
64C2×#826—51no—
65#4561—51no—
66#4497—51no—
67#4495—51no—
68#4149—61no—
69C5×#135—31no—
70C2×C5×D8C2×D311yescharacteristic, complemented
71#4095—61no—
72#4078—21no—
73#4065—61no—
74#4060—62no—
75D5×D8—61no—
76C2×D40—31no—
77#4047C2×D311yescharacteristic
78C5×SD32—61no—
79C5×D16—61no—
80C5×M32—31no—
81#3965—21no—
82#3958—62no—
83#3951C2×D311yescharacteristic, complemented
84C2×#672—31no—
85#2192—151noSylow
86C23×C3×C5—41no—
87C22×D15—41no—
88C2×D3×D5—42no—
89C3×C5×D4—41no—
90C3×C5×D4—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×AGL(1,ℤ/8)—101no—
111C2×C3×D8C2×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×#100—101no—
121#827—21no—
122#826—21no—
123#826—102no—
124#812C2×D511yescharacteristic, complemented
125C2×C3⋊C16—51no—
126C5×#41—61no—
127C2×C5×D4—21no—
128#713—62no—
129D4×D5—62no—
130D4×D5—122no—
131#709—121no—
132#709#6711yescharacteristic
133C2×D20—61no—
134C2×D20—121no—
135C5×Q16—31no—
136C5×SD16—61no—
137C5×D8—21no—
138C5×D8—21no—
139C5×D8—31no—
140C2×C5×C8C22×D311yescharacteristic
141#688—62no—
142#687—41no—
143#686—41no—
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#509—31no—
155C2×D16—151no—
156#472—51no—
157#361—151no—
158#359—151no—
159#350—151no—
160C22×C3×C5—81no—
161C22×C3×C5—161no—
162C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
163C2×D15—42no—
164C2×D15—161no—
165C2×C5×D3—41no—
166C2×C3×D5—21no—
167D3×D5—162no—
168C3×C4×C5#12011yescharacteristic
169C3×C4×C5C2×D811yescharacteristic
170C3×Dic5—21no—
171C5×Dic3—41no—
172C3×#41—51no—
173C2×C3×D4—21no—
174#239—201no—
175D3×D4—201no—
176D3×D4—202no—
177#235—21no—
178#235—102no—
179C2×D12—102no—
180C2×D12—101no—
181C3×SD16—201no—
182C3×D8—21no—
183C3×D8—21no—
184C3×D8—201no—
185C3×M16—51no—
186C3×M16—101no—
187C3×M16—101no—
188C2×C3×C8—101no—
189C2×C3×C8C22×D511yescharacteristic
190Dic12C22⋊D511yescharacteristic
191D24—52no—
192D24—102no—
193D24—101no—
194D24C22⋊D511yescharacteristic
195#204—21no—
196#204—102no—
197C3⋊C16—21no—
198C3⋊C16—101no—
199C23×C5—41no—
200C22×D5—122no—
201C22×D5—121no—
202C5×Q8—61no—
203C5×D4—41no—
204C5×D4—41no—
205C5×D4—61no—
206C5×D4—121no—
207C2×C4×C5—121no—
208C2×C4×C5C2×#6711yescharacteristic
209C22⋊D5—21no—
210C22⋊D5—122no—
211D20—62no—
212D20—122no—
213D20—121no—
214D20#21311yescharacteristic
215C4×D5—21no—
216C4×D5—122no—
217Dic10#21311yescharacteristic
218C5×C8D3×D411yescharacteristic
219C5×C8D3×D411yescharacteristic
220#168—21no—
221#168—41no—
222H(5,𝔽2)—301no—
223AGL(1,ℤ/8)—101no—
224AGL(1,ℤ/8)—301no—
225AGL(1,ℤ/8)—302no—
226#135—31no—
227#135—301no—
228C2×D8—151no—
229C2×D8—301no—
230C2×D8D3×D511yescharacteristic, complemented
231#131—51no—
232SD32—61no—
233D16—61no—
234D16—302no—
235M32—31no—
236C2×C16—151no—
237#108—51no—
238#100—101no—
239C2×C3×C5—21no—
240C2×C3×C5—161no—
241C2×C3×C5#44711yescharacteristic
242D15—82no—
243C3×D5—41no—
244C5×D3—81no—
245C23×C3—41no—
246C22×D3—202no—
247C22×D3—201no—
248C3×Q8—51no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—51no—
252C3×D4—101no—
253C2×C3×C4—101no—
254C2×C3×C4D4×D511yescharacteristic
255#67—41no—
256#67—202no—
257D12—21no—
258D12—102no—
259D12—202no—
260D12—201no—
261C4×D3—41no—
262C4×D3—202no—
263Dic6—21no—
264C3×C8—101no—
265C3×C8—201no—
266C3×C8D4×D511yescharacteristic
267C3×C8C2×C22⋊D511yescharacteristic
268C22×C5—81no—
269C22×C5—121no—
270C22×C5—161no—
271C22×C5#94911yescharacteristic
272C2×D5—21no—
273C2×D5—122no—
274C2×D5—482no—
275C2×D5—481no—
276C4×C5—121no—
277C4×C5C2×#21311yescharacteristic
278C4×C5#93711yescharacteristic
279Dic5—21no—
280#41—51no—
281#41—61no—
282#41—302no—
283#41—601no—
284C2×D4—21no—
285C2×D4—302no—
286C2×D4—301no—
287C2×D4—601no—
288C2×D4—602no—
289Q16—31no—
290SD16—61no—
291SD16—201no—
292SD16—302no—
293D8—21no—
294D8—21no—
295D8—31no—
296D8—152no—
297D8—201no—
298D8—302no—
299D8—301no—
300M16—51no—
301M16—101no—
302M16—101no—
303C2×C8—101no—
304C2×C8C2×D3×D511yescharacteristic
305C16—61no—
306C16—301no—
307C3×C5#219211yescharacteristic, complemented, Hall
308C22×C3—81no—
309C22×C3—101no—
310C22×C3—161no—
311C22×C3#405711yescharacteristic
312C2×D3—41no—
313C2×D3—202no—
314C2×D3—802no—
315C2×D3—801no—
316C3×C4—101no—
317C3×C4D5×D811yescharacteristic
318C3×C4#408311yescharacteristic
319Dic3—41no—
320C2×C5—21no—
321C2×C5—161no—
322C2×C5—241no—
323C2×C5#503611yescharacteristic
324D5—41no—
325D5—242no—
326C23—41no—
327C23—602no—
328C23—601no—
329Q8—51no—
330Q8—61no—
331D4—41no—
332D4—41no—
333D4—51no—
334D4—61no—
335D4—101no—
336D4—121no—
337D4—302no—
338D4—602no—
339D4—602no—
340D4—601no—
341C2×C4—101no—
342C2×C4—121no—
343C2×C4—602no—
344C2×C4D5×#6711yescharacteristic
345C8—101no—
346C8—201no—
347C8D3×C22⋊D511yescharacteristic
348C8#679011yescharacteristic
349C2×C3—21no—
350C2×C3—161no—
351C2×C3—201no—
352C2×C3#6544511yescharacteristic
353D3—81no—
354D3—402no—
355C5#7109411yescharacteristic, complemented, Sylow
356C22—81no—
357C22—101no—
358C22—121no—
359C22—161no—
360C22—602no—
361C22—2401no—
362C22—2402no—
363C22#9147811yescharacteristic
364C4—101no—
365C4—121no—
366C4D5×#21311yescharacteristic
367C4#9157711yescharacteristic
368C3#1060231011yescharacteristic, complemented, Sylow
369C2—21no—
370C2—161no—
371C2—201no—
372C2—241no—
373C2—1202no—
374C2#1174915111yescharacteristic
subgroupG/H
centerC2#11749151
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC2×C3×C5#447
hypercenterC2×D8D3×D5
hypocenterC3×C5#2192
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #11753963C2semidirect
2. C2×#91110C2semidirect
3. C5×#5147C2semidirect
4. C3×#65449C2semidirect
5. #11745919C2semidirect
6. #11745905C2semidirect
7. #11745885C2semidirect
10. C2×C3×C5×D8C22semidirect
20. C2×C3⋊#672C22semidirect
23. C5×#812C22semidirect
25. C3×#3951C22semidirect
29. #65449D3semidirect
63. #5147D5semidirect
70. C2×C5×D8C2×D3semidirect
83. #3951C2×D3semidirect
111. C2×C3×D8C2×D5semidirect
124. #812C2×D5semidirect
230. C2×D8D3×D5semidirect
307. C3×C5#2192semidirect
355. C5#71094semidirect
368. C3#10602310semidirect

Maximal subgroups

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

subgroupindex
#117539632
C2×#911102
C5×#51472
C3×#654492
#117459192
#117459052
#117458852
#106023103
#710945