Finite Group Databasebeta

← #14316384

Subgroups — #14316384

Order 1920.

440 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 77 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#11756516C211yesmaximal, characteristic, complemented
2C2×C3×C5×D16C211yesmaximal, characteristic, complemented
3#11751261C211yesmaximal, characteristic, complemented
4#11751248C211yesmaximal, characteristic, complemented
5#11746384C211yesmaximal, characteristic, complemented
6#11746331C211yesmaximal, characteristic, complemented
7#11746329C211yesmaximal, characteristic, complemented
8#10602264—31nomaximal, Hall
9#92095—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×C3×C5×D8C2211yescharacteristic, complemented
12#91821—21no—
13#91821—21no—
14#91801—21no—
15#91800—22no—
16D8×D15—21no—
17#91793C2211yescharacteristic
18#91790C2211yescharacteristic
19C3×C5×D16—22no—
20C2×C3×C5×C16C2211yescharacteristic, complemented
21#91117—21no—
22#91111—21no—
23#91110—21no—
24#91103C2211yescharacteristic, complemented
25#91096C2211yescharacteristic, complemented
26#71471—51nomaximal, Hall
27#66091—31no—
28C2×C5×D16D311yescharacteristic, complemented
29#65449—31no—
30#65436—31no—
31#64783—31no—
32#64730—31no—
33#64728—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×#1220—42no—
37#6819—22no—
38#6819—41no—
39D4×D15—22no—
40D4×D15—41no—
41#6817—21no—
42#6817D411yescharacteristic
43C3×C5×D8—21no—
44C3×C5×D8—21no—
45C3×C5×D8—21no—
46C3×C5×D8D412yes—
47C2×C3×C5×C8C2311yescharacteristic
48#6716—22no—
49#6716—41no—
50#6715—22no—
51#6715—41no—
52#6710—21no—
53#6710D411yescharacteristic
54Dic60D411yescharacteristic
55D120D411yescharacteristic
56#6706—21no—
57#6705—21no—
58C8×D15—21no—
59C3×C5×C16—21no—
60C3⋊#672—21no—
61#5757—51no—
62C2×C3×D16D511yescharacteristic, complemented
63#5160—51no—
64#5147—51no—
65#4563—51no—
66#4510—51no—
67#4508—51no—
68#4144—61no—
69C2×C5×D8C2×D311yescharacteristic
70C2×C5×D8C2×D311yescharacteristic, complemented
71#4078—61no—
72#4078—61no—
73#4058—61no—
74#4057—62no—
75D5×D8—61no—
76#4050—31no—
77#4047—31no—
78C5×D16—22no—
79C2×C5×C16C2×D311yescharacteristic, complemented
80#3965—61no—
81#3959—61no—
82#3958—61no—
83#3951—31no—
84#3944—31no—
85#2192—151noSylow
86C23×C3×C5—41no—
87C23×C3×C5—41no—
88C22×D15—42no—
89C3×C5×D4—22no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—21no—
95#1220—42no—
96#1220—42no—
97#1220—41no—
98C2×Dic15—42no—
99D60—21no—
100D60D811yescharacteristic
101C4×D15—21no—
102C4×D15—41no—
103Dic30—21no—
104Dic30D811yescharacteristic
105C3×C5×C8C2×D411yescharacteristic
106C3×C5×C8C2×D411yescharacteristic
107C3⋊#168—21no—
108C3⋊#168—41no—
109#1004—101no—
110C2×C3×D8C2×D511yescharacteristic
111C2×C3×D8C2×D511yescharacteristic, complemented
112#932—101no—
113#932—101no—
114#912—101no—
115#911—102no—
116D3×D8—101no—
117#904—51no—
118#901—51no—
119C3×D16—22no—
120C2×C3×C16C2×D511yescharacteristic, complemented
121#833—101no—
122#827—101no—
123#826—101no—
124#819—51no—
125#812—51no—
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×C22⋊D5—122no—
129#711—62no—
130#711—121no—
131D4×D5—62no—
132D4×D5—121no—
133#709—31no—
134#709—61no—
135C5×D8—21no—
136C5×D8—21no—
137C5×D8—21no—
138C5×D8#6712yes—
139C2×C5×C8C22×D311yescharacteristic
140#687—62no—
141#687—121no—
142#686—62no—
143#686—121no—
144#681—31no—
145#681—61no—
146Dic20—31no—
147D40—31no—
148#677—61no—
149#676—61no—
150C8×D5—61no—
151C5×C16—21no—
152#672—61no—
153#576—151no—
154#509—151no—
155C2×D16D1511yescharacteristic, complemented
156#472—151no—
157#361—151no—
158#359—151no—
159#350—151no—
160C22×C3×C5—42no—
161C22×C3×C5—81no—
162C22×C3×C5—161no—
163C22×C3×C5—161no—
164C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
165C2×D15—21no—
166C2×D15—41no—
167C2×D15—162no—
168C3×C4×C5#12011yescharacteristic
169C3×C4×C5C2×D811yescharacteristic
170Dic15—21no—
171Dic15—41no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×#67—202no—
175#237—102no—
176#237—201no—
177D3×D4—102no—
178D3×D4—201no—
179#235—51no—
180#235—101no—
181C3×D8—21no—
182C3×D8—21no—
183C3×D8—21no—
184C3×D8C22⋊D512yes—
185C2×C3×C8C22×D511yescharacteristic
186#214—102no—
187#214—201no—
188#213—102no—
189#213—201no—
190#208—51no—
191#208—101no—
192Dic12—51no—
193D24—51no—
194#204—101no—
195ΓL(1,𝔽25)—101no—
196D3×C8—101no—
197C3×C16—21no—
198C3⋊C16—101no—
199C23×C5—41no—
200C23×C5—41no—
201C22×D5—122no—
202C5×D4—22no—
203C5×D4—41no—
204C5×D4—41no—
205C5×D4—41no—
206C2×C4×C5D3×D411yescharacteristic
207C22⋊D5—61no—
208C22⋊D5—122no—
209C22⋊D5—122no—
210C22⋊D5—121no—
211C2×Dic5—122no—
212D20—31no—
213D20—61no—
214C4×D5—61no—
215C4×D5—121no—
216Dic10—31no—
217Dic10—61no—
218C5×C8D3×D411yescharacteristic
219C5×C8C2×#6711yescharacteristic
220#168—61no—
221#168—121no—
222H(5,𝔽2)—301no—
223AGL(1,ℤ/8)—301no—
224AGL(1,ℤ/8)—302no—
225AGL(1,ℤ/8)—301no—
226#135—151no—
227#135—301no—
228C2×D8—301no—
229C2×D8C2×D1511yescharacteristic
230C2×D8C2×D1511yescharacteristic, complemented
231#131—151no—
232SD32—301no—
233D16—22no—
234D16—301no—
235M32—151no—
236C2×C16C2×D1511yescharacteristic, complemented
237#108—151no—
238#100—301no—
239C2×C3×C5—21no—
240C2×C3×C5—82no—
241C2×C3×C5—161no—
242C2×C3×C5#44711yescharacteristic
243D15—41no—
244D15—81no—
245C23×C3—41no—
246C23×C3—41no—
247C22×D3—202no—
248C3×D4—22no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C2×C3×C4D4×D511yescharacteristic
253#67—101no—
254#67—202no—
255#67—202no—
256#67—201no—
257C2×Dic3—202no—
258D12—51no—
259D12—101no—
260C4×D3—101no—
261C4×D3—201no—
262Dic6—51no—
263Dic6—101no—
264C3×C8D4×D511yescharacteristic
265C3×C8C2×C22⋊D511yescharacteristic
266C3⋊C8—101no—
267C3⋊C8—201no—
268C22×C5—42no—
269C22×C5—81no—
270C22×C5—161no—
271C22×C5—161no—
272C22×C5#91111yescharacteristic
273C2×D5—61no—
274C2×D5—121no—
275C2×D5—482no—
276C4×C5D3×D811yescharacteristic
277C4×C5#93711yescharacteristic
278Dic5—61no—
279Dic5—121no—
280#41—151no—
281#41—302no—
282#41—301no—
283#41—601no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—302no—
287C2×D4—601no—
288C2×D4—602no—
289Q16—151no—
290SD16—302no—
291SD16—301no—
292SD16—601no—
293D8—21no—
294D8—21no—
295D8—21no—
296D8—151no—
297D8—302no—
298D8—601no—
299D8#122012yes—
300M16—151no—
301M16—301no—
302M16—301no—
303C2×C8—301no—
304C2×C8C22×D1511yescharacteristic
305C16—21no—
306C16—301no—
307C3×C5#219211yescharacteristic, complemented, Hall
308C22×C3—42no—
309C22×C3—81no—
310C22×C3—161no—
311C22×C3—161no—
312C22×C3#405711yescharacteristic
313C2×D3—101no—
314C2×D3—201no—
315C2×D3—802no—
316C3×C4D5×D811yescharacteristic
317C3×C4#408311yescharacteristic
318Dic3—101no—
319Dic3—201no—
320C2×C5—21no—
321C2×C5—82no—
322C2×C5—161no—
323C2×C5#515611yescharacteristic
324D5—121no—
325D5—241no—
326C23—41no—
327C23—41no—
328C23—602no—
329Q8—151no—
330Q8—301no—
331D4—22no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—151no—
336D4—301no—
337D4—301no—
338D4—602no—
339D4—602no—
340D4—601no—
341C2×C4—301no—
342C2×C4—602no—
343C2×C4—601no—
344C2×C4D4×D1511yescharacteristic
345C8—301no—
346C8—601no—
347C8D4×D1511yescharacteristic
348C8C2×#122011yescharacteristic
349C2×C3—21no—
350C2×C3—82no—
351C2×C3—161no—
352C2×C3#6544511yescharacteristic
353D3—201no—
354D3—401no—
355C5#7147111yescharacteristic, complemented, Sylow
356C22—42no—
357C22—81no—
358C22—161no—
359C22—161no—
360C22—301no—
361C22—601no—
362C22—2402no—
363C22#9180011yescharacteristic
364C4—301no—
365C4—601no—
366C4D8×D1511yescharacteristic
367C4#9182611yescharacteristic
368C3#1060226411yescharacteristic, complemented, Sylow
369C2—21no—
370C2—82no—
371C2—161no—
372C2—601no—
373C2—1201no—
374C2#1175125711yescharacteristic
subgroupG/H
centerC2#11751257
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC2×C3×C5×D16C2
socleC2×C3×C5#447
hypercenterC2×D16D15
hypocenterC3×C5#2192
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #11756516C2semidirect
2. C2×C3×C5×D16C2semidirect
3. #11751261C2semidirect
4. #11751248C2semidirect
5. #11746384C2semidirect
6. #11746331C2semidirect
7. #11746329C2semidirect
11. C2×C3×C5×D8C22semidirect
20. C2×C3×C5×C16C22semidirect
24. #91103C22semidirect
25. #91096C22semidirect
28. C2×C5×D16D3semidirect
62. C2×C3×D16D5semidirect
70. C2×C5×D8C2×D3semidirect
79. C2×C5×C16C2×D3semidirect
111. C2×C3×D8C2×D5semidirect
120. C2×C3×C16C2×D5semidirect
155. C2×D16D15semidirect
230. C2×D8C2×D15semidirect
236. C2×C16C2×D15semidirect
307. C3×C5#2192semidirect
355. C5#71471semidirect
368. C3#10602264semidirect

Maximal subgroups

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

subgroupindex
#117565162
C2×C3×C5×D162
#117512612
#117512482
#117463842
#117463312
#117463292
#106022643
#714715