Finite Group Databasebeta

← #14289409

Subgroups — #14289409

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#11752651C211yesmaximal, characteristic
2C3×#65139C211yesmaximal, characteristic, complemented
3#11747081C211yesmaximal, characteristic
4#11746917C211yesmaximal, characteristic, complemented
5#11746305C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic
7#11745840C211yesmaximal, characteristic, complemented
8#10599197—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#874C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91435—21no—
14#91423—22no—
15Dic5×D12—21no—
16#91373—21no—
17#91370—21no—
18C2×#6656—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3950—21no—
23C3×#3948—21no—
24#90990—21no—
25#90974—21no—
26#71159—51nomaximal, Hall
27#66047—31no—
28#65365—31no—
29#65139—31no—
30#65139D311yescharacteristic, complemented
31C5×#331—31no—
32#64704—31no—
33#64704—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C3×Dic10—21no—
39C2×C3×Dic10D411yescharacteristic
40C2×D3×Dic5—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53(C2×D3)⋊Dic5—22no—
54(C2×D3)⋊Dic5—22no—
55(C2×D3)⋊Dic5—22no—
56#6656—44no—
57#5585—51no—
58C3×#477—51no—
59#5091—51no—
60#5085—51no—
61#4535—51no—
62#4485D511yescharacteristic
63#4484—51no—
64C5×#127—31no—
65#4082—61no—
66#4082—61no—
67#4081—62no—
68D4×Dic5—61no—
69D4×Dic5—61no—
70C2×#687—62no—
71#4015C2×D311yescharacteristic
72C4×Dic10—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3950—21no—
77#3950—61no—
78#3948—21no—
79#3948—61no—
80C4×#168—31no—
81#1630—151noSylow
82C22×C5×D3—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C5×D12—42no—
91C5×D12—41no—
92C5×D12—41no—
93C5×D12—41no—
94C5×D12—41no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—41no—
98C3×Dic10—21no—
99C3×Dic10—21no—
100C3×Dic10—42no—
101D3×Dic5—82no—
102C3×C5×C8—41no—
103C3⋊#168—22no—
104C5×C3⋊C8—41no—
105C3×C4⋊Q8—51no—
106C3×C4×Q8—51no—
107#947—101no—
108C2×#215—102no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874C2×D511yescharacteristic
113C4×D12—101no—
114C4×Dic6—51no—
115C3×#107—101no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#103—101no—
118#810—101no—
119#807—101no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4×C3⋊C8—51no—
122C2×C5×D4—32no—
123C2×C5×D4—61no—
124C2×C5×D4—61no—
125C22×Dic5—62no—
126C2×Dic10—21no—
127C2×Dic10—31no—
128C2×Dic10#6711yescharacteristic
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C42×C5C22×D311yescharacteristic
132C22⋊Dic5—62no—
133C22⋊Dic5—62no—
134C22⋊Dic5—62no—
135#687—124no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—31no—
139C4⋊Dic5#6711yescharacteristic
140#683—21no—
141#683—61no—
142C4×Dic5—21no—
143C4×Dic5—61no—
144C2×#168—61no—
145#559—151no—
146#492—151no—
147#477—51no—
148#477—151no—
149#331—31no—
150Q8⋊C8—151no—
151Q8⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×C5×D3—42no—
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C3×C4×C5—21no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—41no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C3×Dic5—81no—
166C2×C3×Q8—51no—
167C2×C3×Q8—101no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12D2012yes—
171C2×C4×D3—102no—
172C2×Dic6—51no—
173C2×C3×C8—21no—
174C3×C4⋊C4—51no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
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⋊Dic3—51no—
185Dic3⋊C4—101no—
186C4×Dic3—101no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—101no—
189C23×C5—62no—
190C5×D4—122no—
191C5×D4—121no—
192C5×D4—121no—
193C5×D4—121no—
194C5×D4—121no—
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—41no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203C2×Dic5—242no—
204Dic10—21no—
205Dic10—21no—
206Dic10—42no—
207Dic10—61no—
208Dic10—61no—
209C5×C8—41no—
210C5×C8—121no—
211#168—62no—
212C2×SD16—302no—
213C4⋊Q8—51no—
214#127—31no—
215#124—301no—
216#124—301no—
217#123—302no—
218C4×Q8—51no—
219C4×Q8—151no—
220C4×D4—301no—
221C4×D4—301no—
222#107—101no—
223#107—301no—
224C4⋊C8—31no—
225C4⋊C8D3×D511yescharacteristic
226#103—101no—
227#103—301no—
228C4×C8—151no—
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C5×D3—82no—
233C22×D3—22no—
234C3×Q8—101no—
235C3×Q8—101no—
236C3×Q8—202no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—201no—
240C2×C3×C4C2×D2011yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×Dic3—101no—
244C2×Dic3—101no—
245D12—42no—
246D12—41no—
247D12—41no—
248D12—41no—
249D12—41no—
250C4×D3—402no—
251Dic6—101no—
252Dic6—101no—
253C3×C8—41no—
254C3⋊C8—41no—
255C3⋊C8—102no—
256C22×C5—122no—
257C22×C5—122no—
258C22×C5—122no—
259C22×C5#93711yescharacteristic
260C4×C5—21no—
261C4×C5#91811yescharacteristic
262C4×C5#91911yescharacteristic
263C4×C5#94211yescharacteristic
264C4×C5#95011yescharacteristic
265Dic5—41no—
266Dic5—41no—
267Dic5—81no—
268Dic5—121no—
269Dic5—121no—
270C2×Q8—51no—
271C2×Q8—101no—
272C2×Q8—151no—
273C2×D4—32no—
274C2×D4—61no—
275C2×D4—61no—
276C22×C4—302no—
277SD16—604no—
278C2×C8—21no—
279C2×C8—61no—
280C2×C8—301no—
281C4⋊C4—51no—
282C4⋊C4—101no—
283C4⋊C4—101no—
284C4⋊C4—101no—
285C4⋊C4—151no—
286C4⋊C4—301no—
287C22⋊C4—302no—
288C22⋊C4—302no—
289C22⋊C4—302no—
290C42—101no—
291C42—301no—
292C42C2×D3×D511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3#402811yescharacteristic
295C2×D3—42no—
296C2×D3—42no—
297C2×D3—42no—
298C3×C4—21no—
299C3×C4—201no—
300C3×C4—201no—
301C3×C4—401no—
302C3×C4#405811yescharacteristic
303C3×C4#405811yescharacteristic
304C3×C4#406111yescharacteristic
305C3×C4#406111yescharacteristic
306Dic3—201no—
307Dic3—201no—
308C2×C5—242no—
309C2×C5#504711yescharacteristic
310C2×C5#518711yescharacteristic
311C2×C5#519811yescharacteristic
312C23—62no—
313Q8—101no—
314Q8—101no—
315Q8—202no—
316Q8—301no—
317Q8—301no—
318D4—122no—
319D4—121no—
320D4—121no—
321D4—121no—
322D4—121no—
323C2×C4—101no—
324C2×C4—101no—
325C2×C4—201no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—1202no—
329C2×C4D3×D2011yescharacteristic
330C2×C4#677711yescharacteristic
331C2×C4D5×#6711yescharacteristic
332C8—41no—
333C8—121no—
334C8—302no—
335C2×C3#6503611yescharacteristic
336C2×C3#6507211yescharacteristic
337C2×C3#6507211yescharacteristic
338D3—82no—
339C5#7115911yescharacteristic, complemented, Sylow
340C22—122no—
341C22—122no—
342C22—122no—
343C22#9147411yescharacteristic
344C4—21no—
345C4—201no—
346C4—201no—
347C4—401no—
348C4—601no—
349C4—601no—
350C4#9127911yescharacteristic
351C4#9128011yescharacteristic
352C4#9149011yescharacteristic
353C4#9151311yescharacteristic
354C3#1059919711yescharacteristic, complemented, Sylow
355C2—242no—
356C2#1174751111yescharacteristic
357C2#1174815111yescharacteristic
358C2#1174824311yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1630
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
2. C3×#65139C2semidirect
4. #11746917C2semidirect
5. #11746305C2semidirect
7. #11745840C2semidirect
30. #65139D3semidirect
293. C3×C5#1630semidirect
339. C5#71159semidirect
354. C3#10599197semidirect

Maximal subgroups

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

subgroupindex
#117526512
C3×#651392
#117470812
#117469172
#117463052
C5×#44852
#117458402
#105991973
#711595