Finite Group Databasebeta

← #14316399

Subgroups — #14316399

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#11753973C211yesmaximal, characteristic, complemented
2C2×#91110C211yesmaximal, characteristic, complemented
3C5×#5160C211yesmaximal, characteristic, complemented
4C3×#65436C211yesmaximal, characteristic, complemented
5#11745920C211yesmaximal, characteristic, complemented
6#11745903C211yesmaximal, characteristic, complemented
7#11745887C211yesmaximal, characteristic, complemented
8#10601887—31nomaximal, Hall
9#92019—21no—
10C2×C3×C5×D8C2211yescharacteristic, complemented
11C2×D120C2211yescharacteristic
12C5×#932—21no—
13C5×#901C2211yescharacteristic
14C3×#4050C2211yescharacteristic
15#91301—21no—
16#91275—21no—
17#91253—22no—
18D3×D40—21no—
19#91110—22no—
20C2×C3⋊#672C2211yescharacteristic, complemented
21C5×#833—21no—
22C5×#819C2211yescharacteristic, complemented
23C3×#3959—21no—
24C3×#3958—21no—
25C3×#3944C2211yescharacteristic, complemented
26#71517—51nomaximal, Hall
27#66086—31no—
28C5×#472—31no—
29#65436D311yescharacteristic, complemented
30C2×#3958—31no—
31#64781—31no—
32#64717—31no—
33#64715—31no—
34C2×C3×C5×D4—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×D8—21no—
44C3×C5×D8—21no—
45C2×C3×C5×C8C2311yescharacteristic
46D120—21no—
47D120D412yes—
48C5×#214—41no—
49C5×#213—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×#509—51no—
63#5160D511yescharacteristic, complemented
64C2×#826—51no—
65#4567—51no—
66#4516—51no—
67#4515—51no—
68#4149—61no—
69C5×AGL(1,ℤ/8)—61no—
70C2×C5×D8C2×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×#100—61no—
80#3959—21no—
81#3958—21no—
82#3958—62no—
83#3944C2×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—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×D8C2×D511yescharacteristic, complemented
112#949—101no—
113#932—21no—
114#919—101no—
115#914—102no—
116D3×D8—101no—
117C2×D24—51no—
118#901C2×D511yescharacteristic
119C3×SD32—101no—
120C3×D16—101no—
121C3×M32—51no—
122#833—21no—
123#826—102no—
124#819C2×D511yescharacteristic, complemented
125C2×C3⋊C16—51no—
126C5×#41—31no—
127C2×C5×D4—21no—
128#713—121no—
129D4×D5—121no—
130D4×D5—122no—
131#709—21no—
132#709—62no—
133C2×D20—62no—
134C2×D20—61no—
135C5×SD16—121no—
136C5×D8—21no—
137C5×D8—21no—
138C5×D8—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#509—51no—
155C2×D16—151no—
156#472—31no—
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—21no—
166C2×C3×D5—41no—
167D3×D5—162no—
168C3×C4×C5#12011yescharacteristic
169C3×C4×C5C2×D811yescharacteristic
170C3×Dic5—41no—
171C5×Dic3—21no—
172C3×#41—101no—
173C2×C3×D4—21no—
174#239—102no—
175D3×D4—102no—
176D3×D4—202no—
177#235—201no—
178#235C22⋊D511yescharacteristic
179C2×D12—101no—
180C2×D12—201no—
181C3×Q16—51no—
182C3×SD16—101no—
183C3×D8—21no—
184C3×D8—21no—
185C3×D8—51no—
186C2×C3×C8C22×D511yescharacteristic
187#215—102no—
188#214—41no—
189#213—41no—
190#213—102no—
191#208—21no—
192#208C22⋊D511yescharacteristic
193D24—52no—
194D24—101no—
195ΓL(1,𝔽25)—21no—
196D3×C8—21no—
197C3×C16—101no—
198C3⋊C16—101no—
199C23×C5—41no—
200C22×D5—122no—
201C22×D5—121no—
202C5×Q8—31no—
203C5×D4—31no—
204C5×D4—41no—
205C5×D4—41no—
206C5×D4—61no—
207C2×C4×C5—61no—
208C2×C4×C5D3×D411yescharacteristic
209C22⋊D5—41no—
210C22⋊D5—122no—
211D20—21no—
212D20—62no—
213D20—122no—
214D20—121no—
215C4×D5—41no—
216C4×D5—122no—
217Dic10—21no—
218C5×C8—61no—
219C5×C8—121no—
220C5×C8D3×D411yescharacteristic
221C5×C8C2×#6711yescharacteristic
222H(5,𝔽2)—301no—
223AGL(1,ℤ/8)—61no—
224AGL(1,ℤ/8)—301no—
225AGL(1,ℤ/8)—302no—
226#135—51no—
227#135—301no—
228C2×D8—151no—
229C2×D8—301no—
230C2×D8D3×D511yescharacteristic, complemented
231#131—31no—
232SD32—101no—
233D16—101no—
234D16—302no—
235M32—51no—
236C2×C16—151no—
237#108—31no—
238#100—61no—
239C2×C3×C5—21no—
240C2×C3×C5—161no—
241C2×C3×C5#44711yescharacteristic
242D15—82no—
243C3×D5—81no—
244C5×D3—41no—
245C23×C3—41no—
246C22×D3—202no—
247C22×D3—201no—
248C3×Q8—101no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—101no—
252C3×D4—201no—
253C2×C3×C4—201no—
254C2×C3×C4C2×C22⋊D511yescharacteristic
255#67—21no—
256#67—202no—
257D12—102no—
258D12—202no—
259D12—201no—
260D12#68611yescharacteristic
261C4×D3—21no—
262C4×D3—202no—
263Dic6#68611yescharacteristic
264C3×C8D4×D511yescharacteristic
265C3×C8D4×D511yescharacteristic
266C3⋊C8—21no—
267C3⋊C8—41no—
268C22×C5—61no—
269C22×C5—81no—
270C22×C5—161no—
271C22×C5#91111yescharacteristic
272C2×D5—41no—
273C2×D5—122no—
274C2×D5—482no—
275C2×D5—481no—
276C4×C5—61no—
277C4×C5D3×D811yescharacteristic
278C4×C5#93711yescharacteristic
279Dic5—41no—
280#41—31no—
281#41—101no—
282#41—302no—
283#41—601no—
284C2×D4—21no—
285C2×D4—302no—
286C2×D4—301no—
287C2×D4—601no—
288C2×D4—602no—
289Q16—51no—
290SD16—101no—
291SD16—121no—
292SD16—302no—
293D8—21no—
294D8—21no—
295D8—51no—
296D8—121no—
297D8—152no—
298D8—302no—
299D8—301no—
300M16—31no—
301M16—61no—
302M16—61no—
303C2×C8—61no—
304C2×C8C2×D3×D511yescharacteristic
305C16—101no—
306C16—301no—
307C3×C5#219211yescharacteristic, complemented, Hall
308C22×C3—81no—
309C22×C3—161no—
310C22×C3—201no—
311C22×C3#409511yescharacteristic
312C2×D3—21no—
313C2×D3—202no—
314C2×D3—802no—
315C2×D3—801no—
316C3×C4—201no—
317C3×C4C2×#68611yescharacteristic
318C3×C4#408311yescharacteristic
319Dic3—21no—
320C2×C5—21no—
321C2×C5—121no—
322C2×C5—161no—
323C2×C5#515611yescharacteristic
324D5—81no—
325D5—242no—
326C23—41no—
327C23—602no—
328C23—601no—
329Q8—31no—
330Q8—101no—
331D4—31no—
332D4—41no—
333D4—41no—
334D4—61no—
335D4—101no—
336D4—201no—
337D4—302no—
338D4—602no—
339D4—602no—
340D4—601no—
341C2×C4—61no—
342C2×C4—201no—
343C2×C4—602no—
344C2×C4D3×C22⋊D511yescharacteristic
345C8—61no—
346C8—121no—
347C8D5×#6711yescharacteristic
348C8#679011yescharacteristic
349C2×C3—21no—
350C2×C3—161no—
351C2×C3—401no—
352C2×C3#6532511yescharacteristic
353D3—41no—
354D3—402no—
355C5#7151711yescharacteristic, complemented, Sylow
356C22—61no—
357C22—81no—
358C22—161no—
359C22—201no—
360C22—602no—
361C22—2401no—
362C22—2402no—
363C22#9148011yescharacteristic
364C4—61no—
365C4—201no—
366C4D3×#68611yescharacteristic
367C4#9157711yescharacteristic
368C3#1060188711yescharacteristic, complemented, Sylow
369C2—21no—
370C2—121no—
371C2—161no—
372C2—401no—
373C2—1202no—
374C2#1174915211yescharacteristic
subgroupG/H
centerC2#11749152
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. #11753973C2semidirect
2. C2×#91110C2semidirect
3. C5×#5160C2semidirect
4. C3×#65436C2semidirect
5. #11745920C2semidirect
6. #11745903C2semidirect
7. #11745887C2semidirect
10. C2×C3×C5×D8C22semidirect
20. C2×C3⋊#672C22semidirect
22. C5×#819C22semidirect
25. C3×#3944C22semidirect
29. #65436D3semidirect
63. #5160D5semidirect
70. C2×C5×D8C2×D3semidirect
83. #3944C2×D3semidirect
111. C2×C3×D8C2×D5semidirect
124. #819C2×D5semidirect
230. C2×D8D3×D5semidirect
307. C3×C5#2192semidirect
355. C5#71517semidirect
368. C3#10601887semidirect

Maximal subgroups

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

subgroupindex
#117539732
C2×#911102
C5×#51602
C3×#654362
#117459202
#117459032
#117458872
#106018873
#715175