Finite Group Databasebeta

← #14316400

Subgroups — #14316400

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#11753971C211yesmaximal, characteristic, complemented
2#11751248C211yesmaximal, characteristic, complemented
3C5×#5160C211yesmaximal, characteristic, complemented
4C2×C3×#3958C211yesmaximal, characteristic, complemented
5#11745915C211yesmaximal, characteristic, complemented
6#11745908C211yesmaximal, characteristic, complemented
7#11745888C211yesmaximal, characteristic, complemented
8#10601887—31nomaximal, Hall
9#92017—21no—
10C2×C3×C5×D8C2211yescharacteristic, complemented
11#91793C2211yescharacteristic
12C5×#932—21no—
13C5×#901C2211yescharacteristic
14C2×C3×D40C2211yescharacteristic
15#91312—21no—
16#91273—21no—
17#91254—22no—
18D3×D40—21no—
19#91111—21no—
20#91110—21no—
21#91096C2211yescharacteristic, complemented
22C5×#833—21no—
23C5×#819C2211yescharacteristic, complemented
24C3×#3958—22no—
25C2×C3×#672C2211yescharacteristic, complemented
26#71471—51nomaximal, Hall
27#66086—31no—
28C5×#472—31no—
29#65436—31no—
30C2×#3958D311yescharacteristic, complemented
31#64781—31no—
32#64717—31no—
33#64715—31no—
34C2×C3×C5×D4—21no—
35#6817—21no—
36C5×#235D411yescharacteristic
37C2×C3×D20—21no—
38D5×#67—42no—
39#6777—41no—
40D3×D20—22no—
41#6766—41no—
42#6765—22no—
43C3×C5×D8—21no—
44C3×C5×D8—21no—
45C2×C3×C5×C8C2311yescharacteristic
46Dic60D411yescharacteristic
47D120D411yescharacteristic
48#6706—21no—
49C5×#214—41no—
50C5×#213—41no—
51C5×#208—21no—
52C5×#208D411yescharacteristic
53C5×ΓL(1,𝔽25)—21no—
54C5×D3×C8—21no—
55C3×D40—21no—
56C3×D40D412yes—
57#6657—22no—
58#6653—22no—
59C3⋊#672—21no—
60C3×#672—21no—
61#5757—51no—
62C2×C3×D16—51no—
63#5160D511yescharacteristic, complemented
64#5147—51no—
65#4563—51no—
66#4510—51no—
67#4508—51no—
68#4149—61no—
69C5×AGL(1,ℤ/8)—61no—
70C2×C5×D8C2×D311yescharacteristic, complemented
71C5×#131—31no—
72#4054—61no—
73#4054—62no—
74#4050—31no—
75#4050—61no—
76C2×D40—61no—
77C2×D40C2×D311yescharacteristic
78C5×#108—31no—
79C5×#100—61no—
80#3959—61no—
81#3958—22no—
82#3958—61no—
83#3944—31no—
84C2×#672C2×D311yescharacteristic, complemented
85#2192—151noSylow
86C23×C3×C5—41no—
87C22×C3×D5—41no—
88C2×D3×D5—42no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92#1220—41no—
93D60—21no—
94C4×D15—41no—
95Dic30—21no—
96C5×#67—21no—
97C5×D12D811yescharacteristic
98C4×C5×D3—21no—
99C5×Dic6D811yescharacteristic
100C3×D20—22no—
101C3×D20—41no—
102#1202—42no—
103#1201—42no—
104D5×Dic3—42no—
105C3×C5×C8C2×D411yescharacteristic
106C3×C5×C8C2×D411yescharacteristic
107C5×C3⋊C8—21no—
108C5×C3⋊C8—41no—
109#1004—101no—
110C2×C3×D8—51no—
111C2×C3×D8C2×D511yescharacteristic, complemented
112#932—21no—
113#932—101no—
114#912—101no—
115#911—102no—
116D3×D8—101no—
117#904—51no—
118#901C2×D511yescharacteristic
119C3×D16—102no—
120C2×C3×C16—51no—
121#833—21no—
122#827—101no—
123#826—101no—
124#819C2×D511yescharacteristic, complemented
125#812—51no—
126C5×#41—31no—
127C2×C5×D4—21no—
128#713—121no—
129D4×D5—121no—
130D4×D5—122no—
131#709—62no—
132#709—61no—
133C2×D20—21no—
134C2×D20—62no—
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—31no—
145D40—21no—
146D40—31no—
147D40—62no—
148D40#6712yes—
149#677—62no—
150#677—61no—
151#672—21no—
152#672—61no—
153#576—151no—
154#509—151no—
155C2×D16—51no—
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—41no—
164C2×C5×D3—21no—
165C2×C3×D5—42no—
166C2×C3×D5—161no—
167D3×D5—162no—
168C3×C4×C5#12011yescharacteristic
169C3×C4×C5C2×D811yescharacteristic
170Dic15—41no—
171C5×Dic3—21no—
172C2×C3×D4—21no—
173C2×C3×D4—101no—
174C2×#67—202no—
175#237—102no—
176#237—201no—
177D3×D4—102no—
178D3×D4—201no—
179#235—101no—
180#235C22⋊D511yescharacteristic
181C3×D8—21no—
182C3×D8—21no—
183C3×D8—52no—
184C3×D8—101no—
185C2×C3×C8C22×D511yescharacteristic
186#214—41no—
187#214—102no—
188#213—41no—
189#213—102no—
190#208—21no—
191#208C22⋊D511yescharacteristic
192Dic12—51no—
193D24—51no—
194#204—101no—
195ΓL(1,𝔽25)—21no—
196D3×C8—21no—
197C3×C16—101no—
198C3⋊C16—101no—
199C23×C5—41no—
200C22×D5—41no—
201C22×D5—122no—
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—122no—
210C22⋊D5—121no—
211D20—22no—
212D20—41no—
213D20—61no—
214D20—122no—
215C4×D5—122no—
216C4×D5—121no—
217Dic10—61no—
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—151no—
227#135—301no—
228C2×D8—51no—
229C2×D8—301no—
230C2×D8D3×D511yescharacteristic, complemented
231#131—31no—
232SD32—301no—
233D16—102no—
234D16—301no—
235M32—151no—
236C2×C16—51no—
237#108—31no—
238#100—61no—
239C2×C3×C5—21no—
240C2×C3×C5—161no—
241C2×C3×C5#44711yescharacteristic
242D15—81no—
243C3×D5—82no—
244C5×D3—41no—
245C23×C3—41no—
246C23×C3—201no—
247C22×D3—202no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—102no—
251C3×D4—201no—
252C2×C3×C4C2×C22⋊D511yescharacteristic
253#67—21no—
254#67—202no—
255#67—202no—
256#67—201no—
257C2×Dic3—202no—
258D12—101no—
259D12#68611yescharacteristic
260C4×D3—21no—
261C4×D3—201no—
262Dic6—101no—
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—42no—
273C2×D5—121no—
274C2×D5—161no—
275C2×D5—482no—
276C4×C5—61no—
277C4×C5D3×D811yescharacteristic
278C4×C5#93711yescharacteristic
279Dic5—121no—
280#41—31no—
281#41—302no—
282#41—301no—
283#41—601no—
284C2×D4—21no—
285C2×D4—101no—
286C2×D4—302no—
287C2×D4—601no—
288C2×D4—602no—
289Q16—151no—
290SD16—121no—
291SD16—302no—
292SD16—301no—
293D8—21no—
294D8—21no—
295D8—52no—
296D8—101no—
297D8—121no—
298D8—151no—
299D8—302no—
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—202no—
311C22×C3—801no—
312C22×C3#409511yescharacteristic
313C2×D3—21no—
314C2×D3—201no—
315C2×D3—802no—
316C3×C4C2×#68611yescharacteristic
317C3×C4#408311yescharacteristic
318Dic3—21no—
319Dic3—201no—
320C2×C5—21no—
321C2×C5—121no—
322C2×C5—161no—
323C2×C5#515611yescharacteristic
324D5—82no—
325D5—241no—
326C23—41no—
327C23—201no—
328C23—602no—
329Q8—31no—
330Q8—301no—
331D4—31no—
332D4—41no—
333D4—41no—
334D4—61no—
335D4—102no—
336D4—201no—
337D4—301no—
338D4—602no—
339D4—602no—
340D4—601no—
341C2×C4—61no—
342C2×C4—602no—
343C2×C4—601no—
344C2×C4D3×C22⋊D511yescharacteristic
345C8—61no—
346C8—121no—
347C8D5×#6711yescharacteristic
348C8#679011yescharacteristic
349C2×C3—21no—
350C2×C3—161no—
351C2×C3—402no—
352C2×C3#6532511yescharacteristic
353D3—41no—
354D3—401no—
355C5#7147111yescharacteristic, complemented, Sylow
356C22—61no—
357C22—81no—
358C22—161no—
359C22—202no—
360C22—601no—
361C22—801no—
362C22—2402no—
363C22#9148011yescharacteristic
364C4—61no—
365C4—601no—
366C4D3×#68611yescharacteristic
367C4#9157711yescharacteristic
368C3#1060188711yescharacteristic, complemented, Sylow
369C2—21no—
370C2—121no—
371C2—161no—
372C2—402no—
373C2—1201no—
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. #11753971C2semidirect
2. #11751248C2semidirect
3. C5×#5160C2semidirect
4. C2×C3×#3958C2semidirect
5. #11745915C2semidirect
6. #11745908C2semidirect
7. #11745888C2semidirect
10. C2×C3×C5×D8C22semidirect
21. #91096C22semidirect
23. C5×#819C22semidirect
25. C2×C3×#672C22semidirect
30. C2×#3958D3semidirect
63. #5160D5semidirect
70. C2×C5×D8C2×D3semidirect
84. C2×#672C2×D3semidirect
111. C2×C3×D8C2×D5semidirect
124. #819C2×D5semidirect
230. C2×D8D3×D5semidirect
307. C3×C5#2192semidirect
355. C5#71471semidirect
368. C3#10601887semidirect

Maximal subgroups

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

subgroupindex
#117539712
#117512482
C5×#51602
C2×C3×#39582
#117459152
#117459082
#117458882
#106018873
#714715