Finite Group Databasebeta

← #14290614

Subgroups — #14290614

Order 1920.

400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752507C211yesmaximal, characteristic
2C3×#65130C211yesmaximal, characteristic
3#11746960C211yesmaximal, characteristic, complemented
4#11746927C211yesmaximal, characteristic, complemented
5#11746303C211yesmaximal, characteristic, complemented
6C5×#4484C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic
8#10599043—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C2×C3×#677—21no—
12C3×C4×D20C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91364—21no—
15#91362—22no—
16#91359—21no—
17#91358—21no—
18#91340—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×#3948—21no—
23#90990—22no—
24#90986—21no—
25#90972—21no—
26#71049—51nomaximal, Hall
27#65918—31no—
28#65309—31no—
29#65130D311yescharacteristic
30#64971—31no—
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×Dic30—21no—
35C2×C5×Dic6D411yescharacteristic
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15D412yes—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3D411yescharacteristic
45C5×Dic3⋊C4—21no—
46C4×C5×Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×#685—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×#677—42no—
53#6669—22no—
54#6665—22no—
55#6665—22no—
56Dic3×Dic5—22no—
57#5542—51no—
58C3×#461—51no—
59#5094—51no—
60#5078—51no—
61D4⋊(C3⋊C8)—51no—
62#4484D511yescharacteristic, complemented
63#4482—51no—
64C4×C5×Q8—31no—
65#4092—61no—
66C2×#677—21no—
67#4044—62no—
68#4038—61no—
69#4021—61no—
70C4×D20C2×D311yescharacteristic
71#4015—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10—61no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3967—61no—
77#3950—62no—
78#3948—21no—
79#3940—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C22×C3×D5—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87Dic30—41no—
88Dic30—41no—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—21no—
91C5×Dic6—21no—
92C5×Dic6—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—41no—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C5×C3⋊C8—22no—
104C2×C3×SD16—101no—
105C3×C4⋊Q8—51no—
106C3×C4×D4—51no—
107#936—101no—
108#926—101no—
109#924—101no—
110#887—101no—
111#879—102no—
112#869—51no—
113C4×Dic6C2×D511yescharacteristic
114C3×C4⋊C8C2×D511yescharacteristic
115C3×#103—101no—
116#810—101no—
117#808—101no—
118#807—102no—
119C4⋊(C3⋊C8)—51no—
120C4×C3⋊C8C2×D511yescharacteristic
121C2×C5×Q8—31no—
122C2×D20#6711yescharacteristic
123C2×C4×D5—21no—
124C2×Dic10—21no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C42×C5—61no—
131C42×C5C22×D311yescharacteristic
132#685—21no—
133#685—62no—
134#685—62no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139C4⋊Dic5#6711yescharacteristic
140#683—62no—
141C4×Dic5—62no—
142C2×#168—61no—
143#677—42no—
144#556—151no—
145#500—151no—
146#475—151no—
147#461—51no—
148#332—151no—
149Q8⋊C8—31no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C3×C4×C5—21no—
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—42no—
161C3×Dic5—41no—
162C3×Dic5—81no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C2×C3×Q8—101no—
166C2×C3×D4—51no—
167C22×C3×C4—101no—
168C2×Dic6—101no—
169C2×Dic6D2011yescharacteristic
170C3×SD16—202no—
171C2×C3×C8—21no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C22⋊C4—101no—
176C3×C42C22×D511yescharacteristic
177#217—102no—
178#217—102no—
179C4⋊Dic3—52no—
180C4⋊Dic3—101no—
181C4⋊Dic3D2011yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—102no—
184C4×Dic3—21no—
185C4×Dic3—102no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C22×D5—21no—
189C5×Q8—61no—
190C5×Q8—61no—
191C2×C4×C5—61no—
192C2×C4×C5—61no—
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—41no—
198C2×Dic5—62no—
199D20—21no—
200D20—21no—
201C4×D5—41no—
202C4×D5—41no—
203Dic10—41no—
204Dic10—41no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—41no—
208C5×C8—62no—
209#168—121no—
210C2×SD16—101no—
211C4⋊Q8—51no—
212C4⋊Q8—151no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—31no—
217C4×Q8—301no—
218C4×D4—51no—
219#117—301no—
220#107—302no—
221#106—301no—
222C4⋊C8—151no—
223C4⋊C8D3×D511yescharacteristic
224#103—101no—
225#103—301no—
226C4×C8—31no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C3×D5—81no—
231C23×C3—101no—
232C3×Q8—201no—
233C3×Q8—201no—
234C3×D4—101no—
235C3×D4—101no—
236C2×C3×C4—101no—
237C2×C3×C4—201no—
238C2×C3×C4—201no—
239C2×C3×C4—201no—
240C2×C3×C4C2×D2011yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—102no—
246Dic6—21no—
247Dic6—21no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—41no—
251C3⋊C8—22no—
252C3⋊C8—201no—
253C22×C5#93711yescharacteristic
254C2×D5—41no—
255C2×D5—41no—
256C2×D5—41no—
257C4×C5—21no—
258C4×C5—121no—
259C4×C5—121no—
260C4×C5#91511yescharacteristic
261C4×C5#91611yescharacteristic
262C4×C5#93211yescharacteristic
263C4×C5#95011yescharacteristic
264Dic5—41no—
265Dic5—81no—
266Dic5—122no—
267C2×Q8—31no—
268C2×Q8—101no—
269C2×Q8—301no—
270C2×D4—51no—
271C22×C4—101no—
272SD16—202no—
273C2×C8—21no—
274C2×C8—61no—
275C2×C8—301no—
276C4⋊C4—31no—
277C4⋊C4—51no—
278C4⋊C4—61no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—152no—
282C4⋊C4—302no—
283C4⋊C4—301no—
284C22⋊C4—101no—
285C22⋊C4—302no—
286C22⋊C4—302no—
287C42—61no—
288C42—302no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—201no—
292C22×C3—201no—
293C22×C3—201no—
294C22×C3#402811yescharacteristic
295C3×C4—21no—
296C3×C4—201no—
297C3×C4—401no—
298C3×C4#405011yescharacteristic
299C3×C4#405511yescharacteristic
300C3×C4#406011yescharacteristic
301C3×C4#406511yescharacteristic
302Dic3—41no—
303Dic3—41no—
304Dic3—202no—
305C2×C5#503711yescharacteristic
306C2×C5#517311yescharacteristic
307C2×C5#520511yescharacteristic
308D5—81no—
309C23—101no—
310Q8—61no—
311Q8—61no—
312Q8—201no—
313Q8—201no—
314Q8—601no—
315Q8—601no—
316D4—101no—
317D4—101no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—101no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—302no—
325C2×C4D3×D2011yescharacteristic
326C2×C4#677711yescharacteristic
327C2×C4D5×#6711yescharacteristic
328C8—41no—
329C8—62no—
330C8—601no—
331C2×C3—401no—
332C2×C3#6502211yescharacteristic
333C2×C3#6510011yescharacteristic
334C2×C3#6511511yescharacteristic
335C5#7104911yescharacteristic, complemented, Sylow
336C22—201no—
337C22—201no—
338C22—201no—
339C22#9147411yescharacteristic
340C4—21no—
341C4—121no—
342C4—121no—
343C4—201no—
344C4—401no—
345C4—602no—
346C4#9127211yescharacteristic
347C4#9127411yescharacteristic
348C4#9149111yescharacteristic
349C4#9151611yescharacteristic
350C3#1059904311yescharacteristic, complemented, Sylow
351C2—401no—
352C2#1174751211yescharacteristic
353C2#1174814711yescharacteristic
354C2#1174825211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1650
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
3. #11746960C2semidirect
4. #11746927C2semidirect
5. #11746303C2semidirect
6. C5×#4484C2semidirect
62. #4484D5semidirect
290. C3×C5#1650semidirect
335. C5#71049semidirect
350. C3#10599043semidirect

Maximal subgroups

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

subgroupindex
#117525072
C3×#651302
#117469602
#117469272
#117463032
C5×#44842
#117458352
#105990433
#710495