Finite Group Databasebeta

← #14289393

Subgroups — #14289393

Order 1920.

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

normal subgroups only

This group has 436 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#11752662C211yesmaximal, characteristic
2#11751186C211yesmaximal, characteristic
3C5×#5091C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5#11745854C211yesmaximal, characteristic
6#11745842C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601952—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6717—22no—
11#91763C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91433—22no—
15#91428—21no—
16#91418—21no—
17#91375—21no—
18#91374—21no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#810—21no—
21C5×#807—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71159—51nomaximal, Hall
27#65919—31no—
28C5×#477—31no—
29#65380D311yescharacteristic, complemented
30#65374—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×#1200—22no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6717—44no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54#6667—22no—
55#6667—22no—
56#6667—22no—
57#5585—51no—
58C3×#477—51no—
59#5091D511yescharacteristic, complemented
60#5085—51no—
61#4535—51no—
62#4485—51no—
63#4484—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×Q8—31no—
66#4093—61no—
67C2×#688—62no—
68#4040—62no—
69#4039—61no—
70#4021—61no—
71#4020—31no—
72C4×D20—61no—
73C4×Dic10C2×D311yescharacteristic
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3942—21no—
78#3939—21no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1630—151noSylow
82C22×D15—22no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88D60—42no—
89D60—41no—
90D60—41no—
91D60—41no—
92D60—41no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×Dic6—21no—
96C5×Dic6—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101#1200—82no—
102C3⋊#168—22no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4×Q8—51no—
107#947—101no—
108C2×#215—102no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874—51no—
113C4×D12—101no—
114C4×Dic6C2×D511yescharacteristic
115C3×#107—101no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#810—21no—
119#807—21no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4×C3⋊C8—51no—
122C2×C5×Q8—21no—
123C2×C5×Q8—31no—
124C2×D20—32no—
125C2×D20—61no—
126C2×D20—61no—
127C2×C4×D5—62no—
128C2×Dic10#6711yescharacteristic
129C2×C5×C8—61no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—61no—
134C42×C5—61no—
135C42×C5C22×D311yescharacteristic
136#688—124no—
137#685—62no—
138#685—62no—
139#685—62no—
140C4⋊Dic5#6711yescharacteristic
141#683—21no—
142C4×Dic5—21no—
143C2×#168—21no—
144C2×#168—61no—
145#559—151no—
146#492—151no—
147#477—31no—
148#477—51no—
149#331—151no—
150Q8⋊C8—151no—
151Q8⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×D15—42no—
154C2×D15—42no—
155C2×D15—42no—
156C3×C4×C5—21no—
157C3×C4×C5—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×Dic5—41no—
163C3×Dic5—41no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C2×C3×Q8—21no—
167C2×C3×Q8—51no—
168C2×D12—52no—
169C2×D12—101no—
170C2×D12—101no—
171C2×C4×D3—102no—
172C2×Dic6C22⋊D511yescharacteristic
173C2×C3×C8—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C42—101no—
179C3×C42C22×D511yescharacteristic
180#215—204no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184C4⋊Dic3C22⋊D511yescharacteristic
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—101no—
189C22×D5—62no—
190C5×Q8—42no—
191C5×Q8—61no—
192C5×Q8—61no—
193C2×C4×C5—41no—
194C2×C4×C5—61no—
195C2×C4×C5—61no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201D20—122no—
202D20—121no—
203D20—121no—
204D20—121no—
205D20—121no—
206C4×D5—242no—
207Dic10—21no—
208Dic10—21no—
209C5×C8—121no—
210#168—41no—
211#168—62no—
212C2×SD16—302no—
213C4⋊Q8D3×D511yescharacteristic
214#127—151no—
215#124—301no—
216#124—301no—
217#123—302no—
218C4×Q8—31no—
219C4×Q8—51no—
220C4×D4—301no—
221C4×D4—301no—
222#107—61no—
223#107—101no—
224C4⋊C8—31no—
225C4⋊C8—51no—
226#103—61no—
227#103—101no—
228C4×C8—151no—
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232D15—82no—
233C22×D3—102no—
234C3×Q8—42no—
235C3×Q8—101no—
236C3×Q8—101no—
237C2×C3×C4—41no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245D12—202no—
246D12—201no—
247D12—201no—
248D12—201no—
249D12—201no—
250C4×D3—402no—
251Dic6—21no—
252Dic6—21no—
253C3×C8—201no—
254C3⋊C8—41no—
255C3⋊C8—102no—
256C22×C5#93711yescharacteristic
257C2×D5—122no—
258C2×D5—122no—
259C2×D5—122no—
260C4×C5—21no—
261C4×C5—81no—
262C4×C5—121no—
263C4×C5—121no—
264C4×C5#91811yescharacteristic
265C4×C5#91911yescharacteristic
266C4×C5#94211yescharacteristic
267C4×C5#95011yescharacteristic
268Dic5—41no—
269Dic5—41no—
270C2×Q8—21no—
271C2×Q8—31no—
272C2×Q8—51no—
273C2×D4—152no—
274C2×D4—301no—
275C2×D4—301no—
276C22×C4—302no—
277SD16—604no—
278C2×C8—61no—
279C2×C8—101no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—31no—
284C4⋊C4—51no—
285C4⋊C4—61no—
286C4⋊C4—101no—
287C22⋊C4—302no—
288C22⋊C4—302no—
289C22⋊C4—302no—
290C42—61no—
291C42—101no—
292C42C2×D3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3#408311yescharacteristic
295C2×D3—202no—
296C2×D3—202no—
297C2×D3—202no—
298C3×C4—21no—
299C3×C4—81no—
300C3×C4—201no—
301C3×C4—201no—
302C3×C4#406411yescharacteristic
303C3×C4#406511yescharacteristic
304C3×C4#408811yescharacteristic
305C3×C4#409611yescharacteristic
306Dic3—41no—
307Dic3—41no—
308C2×C5#504711yescharacteristic
309C2×C5#518711yescharacteristic
310C2×C5#519811yescharacteristic
311D5—242no—
312C23—302no—
313Q8—42no—
314Q8—61no—
315Q8—61no—
316Q8—101no—
317Q8—101no—
318D4—602no—
319D4—601no—
320D4—601no—
321D4—601no—
322D4—601no—
323C2×C4—41no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—1202no—
329C2×C4D5×#6711yescharacteristic
330C2×C4D3×C22⋊D511yescharacteristic
331C2×C4#679011yescharacteristic
332C8—121no—
333C8—201no—
334C8—302no—
335C2×C3#6533611yescharacteristic
336C2×C3#6547611yescharacteristic
337C2×C3#6548711yescharacteristic
338D3—402no—
339C5#7115911yescharacteristic, complemented, Sylow
340C22—602no—
341C22—602no—
342C22—602no—
343C22#9157711yescharacteristic
344C4—21no—
345C4—81no—
346C4—121no—
347C4—121no—
348C4—201no—
349C4—201no—
350C4#9151511yescharacteristic
351C4#9151611yescharacteristic
352C4#9151911yescharacteristic
353C4#9152011yescharacteristic
354C3#1060195211yescharacteristic, complemented, Sylow
355C2—1202no—
356C2#1174916411yescharacteristic
357C2#1174940611yescharacteristic
358C2#1174940811yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C5×#5091C2semidirect
4. C3×#65380C2semidirect
6. #11745842C2semidirect
7. #11745840C2semidirect
29. #65380D3semidirect
59. #5091D5semidirect
293. C3×C5#1630semidirect
339. C5#71159semidirect
354. C3#10601952semidirect

Maximal subgroups

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

subgroupindex
#117526622
#117511862
C5×#50912
C3×#653802
#117458542
#117458422
#117458402
#106019523
#711595