Finite Group Databasebeta

← #14289001

Subgroups — #14289001

Order 1920.

472 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752648C211yesmaximal, characteristic, complemented
2#11750949C211yesmaximal, characteristic, complemented
3#11747067C211yesmaximal, characteristic, complemented
4#11747028C211yesmaximal, characteristic
5C5×#4481C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745845C211yesmaximal, characteristic, complemented
8#10599283—31nomaximal, Hall
9C2×#6706—21no—
10#91763C2211yescharacteristic
11C4×Dic30C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91434—21no—
15#91421—22no—
16D5×C4⋊Dic3—21no—
17#91384—21no—
18#91360—21no—
19C2×#6660—22no—
20C2×#6653—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22#91105—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×#168C2211yescharacteristic
25#90968—21no—
26#68198—51nomaximal, Hall
27#66064—31no—
28#65374—31no—
29#65137—31no—
30#65132—31no—
31C5×#333—31no—
32#64704—31no—
33#64703D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×Dic6D412yes—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×D5×Dic3—22no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15D411yescharacteristic
45#6712—21no—
46C4×Dic15—21no—
47#6706—42no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6668—22no—
56#6665—22no—
57#6660—44no—
58#6653—42no—
59#5543—51no—
60#5015—51no—
61#4848—51no—
62#4693—51no—
63C3×D4⋊C8—51no—
64#4481D511yescharacteristic, complemented
65#4456—51no—
66C5×C4⋊Q8—31no—
67#4092—62no—
68C2×#688—62no—
69C2×D40—61no—
70C2×#677—61no—
71#4043—61no—
72#4039—61no—
73D5×C4⋊C4—61no—
74#4036—61no—
75#4020—31no—
76C4×D20C2×D311yescharacteristic
77C4×Dic10—31no—
78C5×C4⋊C8—31no—
79C5×C4⋊C8C2×D311yescharacteristic
80#3953—61no—
81#3953—61no—
82C4×#168C2×D311yescharacteristic
83#1622—151noSylow
84C22×D15—41no—
85C22×C3×D5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91D60—42no—
92D60—41no—
93D60—41no—
94D60—41no—
95D60—41no—
96Dic30—21no—
97Dic30—21no—
98C2×C5×Dic3—22no—
99C5×Dic6—42no—
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20SD1612yescomplemented
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105D5×Dic3—82no—
106C3×C5×C8—41no—
107C3×#168—22no—
108C5×C3⋊C8—41no—
109C3×C4×D4—51no—
110D4×Dic3—101no—
111C2×#213—101no—
112C2×C4⋊Dic3—101no—
113#924—101no—
114C2×#204—101no—
115C2×#204—102no—
116#890—101no—
117#878—102no—
118#874—51no—
119#869C2×D511yescharacteristic
120C4×Dic6—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C4×C8—51no—
123#821—101no—
124#809—101no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×Q8—32no—
127C2×D20—61no—
128C2×D20—61no—
129C2×D20—61no—
130C2×D20D1211yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5—62no—
133C2×Dic10—31no—
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C42×C5C22×D311yescharacteristic
139#688—124no—
140#685—21no—
141#685—62no—
142C4⋊Dic5—31no—
143C4⋊Dic5—62no—
144C4⋊Dic5D1211yescharacteristic
145#683—62no—
146#683—61no—
147C4×Dic5—61no—
148C2×#168—21no—
149D40—122no—
150#677—122no—
151#554—151no—
152#492—151no—
153#460—151no—
154#459—151no—
155#333—31no—
156Q8⋊C8—151no—
157D4⋊C8—51no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—81no—
160C2×D15—81no—
161C2×D15—81no—
162C2×C3×D5—22no—
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C3×C4×C5—21no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—41no—
171Dic15—41no—
172C3×Dic5—41no—
173C5×Dic3—42no—
174C2×C3×D4—51no—
175C22×C3×C4—101no—
176C22×Dic3—102no—
177C2×D12—101no—
178C2×D12—101no—
179C2×D12—101no—
180C2×Dic6—51no—
181C2×Dic6D2012yes—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C3×C4⋊C4—51no—
185C3×C22⋊C4—101no—
186C3×C42C22×D511yescharacteristic
187#217—102no—
188#213—202no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—51no—
192C4⋊Dic3—102no—
193Dic3⋊C4—102no—
194Dic3⋊C4—101no—
195C4×Dic3—101no—
196C2×C3⋊C8—21no—
197#204—202no—
198#204—204no—
199C22×D5—21no—
200C22×D5—121no—
201C5×Q8—122no—
202C2×C4×C5—62no—
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—61no—
208C2×Dic5—61no—
209D20—21no—
210D20—122no—
211D20—121no—
212D20—121no—
213D20—121no—
214D20—121no—
215D20#20412yescomplemented
216C4×D5—41no—
217C4×D5—41no—
218C4×D5—242no—
219Dic10—61no—
220Dic10—61no—
221C5×C8—41no—
222C5×C8—121no—
223#168—22no—
224C2×SD16—301no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8—31no—
228#127—151no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8—151no—
233C4×D4—51no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—31no—
237C4⋊C8D3×D511yescharacteristic
238#102—301no—
239#102—301no—
240C4×C8—51no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—161no—
245C3×D5—42no—
246C23×C3—101no—
247C22×D3—201no—
248C3×D4—52no—
249C3×D4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×Dic3—22no—
257C2×Dic3—101no—
258C2×Dic3—101no—
259C2×Dic3—402no—
260D12—202no—
261D12—201no—
262D12—201no—
263D12—201no—
264D12—201no—
265Dic6—42no—
266Dic6—101no—
267Dic6—101no—
268C3×C8—41no—
269C3×C8—102no—
270C3⋊C8—41no—
271C22×C5#88211yescharacteristic
272C2×D5—22no—
273C2×D5—41no—
274C2×D5—41no—
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—122no—
280C4×C5C2×#20411yescharacteristic
281C4×C5#90911yescharacteristic
282C4×C5#91111yescharacteristic
283C4×C5#91611yescharacteristic
284Dic5—41no—
285Dic5—121no—
286Dic5—121no—
287C2×Q8—32no—
288C2×Q8—151no—
289C2×D4—51no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4—301no—
293C22×C4—101no—
294C22×C4—302no—
295SD16—602no—
296SD16—604no—
297D8—602no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—101no—
301C4⋊C4—51no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—151no—
305C4⋊C4—302no—
306C4⋊C4—302no—
307C4⋊C4—301no—
308C22⋊C4—101no—
309C22⋊C4—302no—
310C42—301no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—102no—
314C22×C3—201no—
315C22×C3—201no—
316C22×C3#402811yescharacteristic
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—201no—
322C3×C4D5×SD1611yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406411yescharacteristic
325C3×C4#406511yescharacteristic
326Dic3—42no—
327Dic3—201no—
328Dic3—201no—
329C2×C5#473811yescharacteristic
330C2×C5#478111yescharacteristic
331C2×C5#482211yescharacteristic
332D5—42no—
333D5—481no—
334C23—101no—
335C23—601no—
336Q8—122no—
337Q8—301no—
338Q8—301no—
339D4—52no—
340D4—101no—
341D4—602no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—62no—
347C2×C4—101no—
348C2×C4—201no—
349C2×C4—201no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—1202no—
353C2×C4D5×D1211yescharacteristic
354C2×C4D3×D2011yescharacteristic
355C2×C4#679011yescharacteristic
356C8—41no—
357C8—102no—
358C8—121no—
359C2×C3—202no—
360C2×C3#6503611yescharacteristic
361C2×C3#6509511yescharacteristic
362C2×C3#6510011yescharacteristic
363D3—801no—
364C5#6819811yescharacteristic, complemented, Sylow
365C22—102no—
366C22—201no—
367C22—201no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9147611yescharacteristic
372C4—21no—
373C4—122no—
374C4—201no—
375C4—601no—
376C4—601no—
377C4D5×#20411yescharacteristic
378C4#9126111yescharacteristic
379C4#9149811yescharacteristic
380C4#9152111yescharacteristic
381C3#1059928311yescharacteristic, complemented, Sylow
382C2—202no—
383C2—2401no—
384C2#1174751811yescharacteristic
385C2#1174812811yescharacteristic
386C2#1174824911yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11747028C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752648C2semidirect
2. #11750949C2semidirect
3. #11747067C2semidirect
5. C5×#4481C2semidirect
6. C3×#64703C2semidirect
7. #11745845C2semidirect
33. #64703D3semidirect
64. #4481D5semidirect
102. C3×D20SD16semidirect
215. D20#204semidirect
312. C3×C5#1622semidirect
364. C5#68198semidirect
381. C3#10599283semidirect

Maximal subgroups

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

subgroupindex
#117526482
#117509492
#117470672
#117470282
C5×#44812
C3×#647032
#117458452
#105992833
#681985