Finite Group Databasebeta

← #14288994

Subgroups — #14288994

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#11752657C211yesmaximal, characteristic, complemented
2C3×#65132C211yesmaximal, characteristic
3#11747071C211yesmaximal, characteristic, complemented
4#11747068C211yesmaximal, characteristic, complemented
5#11746302C211yesmaximal, characteristic, complemented
6C5×#4484C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10599037—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C2×C3×D40—21no—
12C3×#4020C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91431—22no—
15Dic3×D20—21no—
16D5×C4⋊Dic3—21no—
17#91381—21no—
18#91359—21no—
19C2×#6657—22no—
20C2×#6655—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3953—21no—
25#90964—21no—
26#71016—51nomaximal, Hall
27#65913—31no—
28#65316—31no—
29#65132D311yescharacteristic
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×Dic30D412yes—
35C2×C5×Dic6D411yescharacteristic
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×D5×Dic3—22no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C4×C5×Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×D40—42no—
54#6669—22no—
55#6668—22no—
56#6665—22no—
57#6657—44no—
58#6655—42no—
59#5543—51no—
60C3×#459—51no—
61#5076—51no—
62#5075—51no—
63D4⋊(C3⋊C8)—51no—
64#4484D511yescharacteristic, complemented
65#4481—51no—
66C4×C5×Q8—31no—
67#4092—61no—
68C2×#688—61no—
69C2×D40—21no—
70C2×#677—62no—
71#4042—62no—
72D5×C4⋊C4—61no—
73#4020C2×D311yescharacteristic
74C4×D20—61no—
75C4×D20C2×D311yescharacteristic
76#4016—61no—
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C4×C5×C8—31no—
80#3953—21no—
81#3941—61no—
82C4⋊#168—31no—
83#1622—151noSylow
84C22×C3×D5—21no—
85C22×C3×D5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90Dic30—42no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×Dic6—21no—
94C5×Dic6—21no—
95C2×C3×Dic5—21no—
96C3×D20—21no—
97C3×D20—42no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20SD1612yescomplemented
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105D5×Dic3—82no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C5×C3⋊C8—22no—
109C2×C3×D8—101no—
110C3×#127—51no—
111C3×C4×D4—51no—
112D4×Dic3—101no—
113C2×#214—102no—
114C2×#214—101no—
115C2×C4⋊Dic3—101no—
116#924—101no—
117#890—101no—
118#878—102no—
119#869—51no—
120C4×Dic6C2×D511yescharacteristic
121C3×C4⋊C8C2×D511yescharacteristic
122C3×#102—101no—
123#832—101no—
124C4⋊(C3⋊C8)—51no—
125C4×C3⋊C8C2×D511yescharacteristic
126C2×C5×Q8—31no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20—21no—
130C2×D20#6711yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5—62no—
133C2×Dic10—32no—
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—31no—
137C5×C4⋊C4—61no—
138C42×C5—61no—
139C42×C5C22×D311yescharacteristic
140#688—122no—
141#685—21no—
142#685—62no—
143C4⋊Dic5—61no—
144C4⋊Dic5—61no—
145C4⋊Dic5#6711yescharacteristic
146#683—62no—
147#683—62no—
148C2×#168—61no—
149D40—42no—
150#677—124no—
151#554—151no—
152#492—151no—
153#460—151no—
154#459—51no—
155#333—151no—
156Q8⋊C8—31no—
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×C3×D5—22no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—81no—
163C2×C3×D5—81no—
164C2×C3×D5—81no—
165C3×C4×C5—21no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—42no—
171C3×Dic5—41no—
172C5×Dic3—41no—
173C5×Dic3—41no—
174C2×C3×D4—51no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×C3×D4—101no—
178C22×C3×C4—101no—
179C22×Dic3—102no—
180C2×Dic6—52no—
181C2×Dic6D2011yescharacteristic
182C3×D8—202no—
183C2×C3×C8—21no—
184C3×C4⋊C4—51no—
185C3×C22⋊C4—101no—
186C3×C42C22×D511yescharacteristic
187#217—102no—
188#214—204no—
189#214—202no—
190C4⋊Dic3—102no—
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C4⋊Dic3D2011yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—102no—
196C4×Dic3—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199C22×D5—21no—
200C22×D5—41no—
201C5×Q8—61no—
202C5×Q8—61no—
203C2×C4×C5—61no—
204C2×C4×C5—61no—
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—21no—
209C2×Dic5—62no—
210D20—21no—
211D20—42no—
212D20—41no—
213D20—41no—
214D20—41no—
215D20—41no—
216D20#21412yescomplemented
217C4×D5—41no—
218C4×D5—41no—
219C4×D5—242no—
220Dic10—122no—
221C5×C8—41no—
222C5×C8—62no—
223#168—121no—
224C2×SD16—302no—
225C2×SD16—301no—
226C2×D8—101no—
227C4⋊Q8—151no—
228#127—51no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8—31no—
233C4×D4—51no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—151no—
237C4⋊C8D3×D511yescharacteristic
238#102—101no—
239#102—301no—
240C4×C8—31no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244C3×D5—42no—
245C3×D5—161no—
246C23×C3—101no—
247C23×C3—201no—
248C3×D4—52no—
249C3×D4—101no—
250C3×D4—202no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4—201no—
255C2×C3×C4—101no—
256C2×C3×C4—201no—
257C2×C3×C4—201no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—102no—
264C2×Dic3—402no—
265Dic6—21no—
266Dic6—21no—
267Dic6—202no—
268C3×C8—41no—
269C3⋊C8—22no—
270C3⋊C8—201no—
271C22×C5#93711yescharacteristic
272C2×D5—22no—
273C2×D5—41no—
274C2×D5—41no—
275C2×D5—81no—
276C2×D5—81no—
277C2×D5—81no—
278C4×C5—21no—
279C4×C5—121no—
280C4×C5—121no—
281C4×C5#91111yescharacteristic
282C4×C5#91211yescharacteristic
283C4×C5C2×#21411yescharacteristic
284C4×C5#95111yescharacteristic
285Dic5—41no—
286Dic5—122no—
287C2×Q8—31no—
288C2×Q8—152no—
289C2×D4—51no—
290C2×D4—101no—
291C2×D4—101no—
292C2×D4—101no—
293C22×C4—101no—
294C22×C4—302no—
295SD16—604no—
296SD16—602no—
297D8—202no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—301no—
301C4⋊C4—31no—
302C4⋊C4—51no—
303C4⋊C4—61no—
304C4⋊C4—302no—
305C4⋊C4—302no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C22⋊C4—101no—
309C22⋊C4—302no—
310C42—61no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—102no—
314C22×C3—201no—
315C22×C3—201no—
316C22×C3—401no—
317C22×C3—401no—
318C22×C3—401no—
319C22×C3#402811yescharacteristic
320C3×C4—21no—
321C3×C4—201no—
322C3×C4#405011yescharacteristic
323C3×C4#405411yescharacteristic
324C3×C4D5×SD1611yescharacteristic
325C3×C4#406411yescharacteristic
326Dic3—41no—
327Dic3—41no—
328Dic3—202no—
329C2×C5#504011yescharacteristic
330C2×C5#515811yescharacteristic
331C2×C5#519811yescharacteristic
332D5—42no—
333D5—161no—
334C23—101no—
335C23—201no—
336Q8—61no—
337Q8—61no—
338Q8—602no—
339D4—52no—
340D4—101no—
341D4—202no—
342D4—201no—
343D4—201no—
344D4—201no—
345D4—201no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—101no—
349C2×C4—201no—
350C2×C4—201no—
351C2×C4—302no—
352C2×C4—1202no—
353C2×C4D3×D2011yescharacteristic
354C2×C4#677711yescharacteristic
355C2×C4D5×#6711yescharacteristic
356C8—41no—
357C8—62no—
358C8—601no—
359C2×C3—202no—
360C2×C3—801no—
361C2×C3#6502311yescharacteristic
362C2×C3#6509511yescharacteristic
363C2×C3#6511111yescharacteristic
364C5#7101611yescharacteristic, complemented, Sylow
365C22—102no—
366C22—201no—
367C22—201no—
368C22—401no—
369C22—401no—
370C22—401no—
371C22#9147411yescharacteristic
372C4—21no—
373C4—121no—
374C4—121no—
375C4—201no—
376C4—602no—
377C4#9125411yescharacteristic
378C4#9127311yescharacteristic
379C4D5×#21411yescharacteristic
380C4#9150811yescharacteristic
381C3#1059903711yescharacteristic, complemented, Sylow
382C2—202no—
383C2—801no—
384C2#1174749311yescharacteristic
385C2#1174814911yescharacteristic
386C2#1174824211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC3×#65132C2
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. #11752657C2semidirect
3. #11747071C2semidirect
4. #11747068C2semidirect
5. #11746302C2semidirect
6. C5×#4484C2semidirect
7. #11745835C2semidirect
64. #4484D5semidirect
102. C3×D20SD16semidirect
216. D20#214semidirect
312. C3×C5#1622semidirect
364. C5#71016semidirect
381. C3#10599037semidirect

Maximal subgroups

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

subgroupindex
#117526572
C3×#651322
#117470712
#117470682
#117463022
C5×#44842
#117458352
#105990373
#710165