Finite Group Databasebeta

← #14289391

Subgroups — #14289391

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
2#11751192C211yesmaximal, characteristic, complemented
3C5×#5085C211yesmaximal, characteristic
4C3×#65380C211yesmaximal, characteristic, complemented
5#11745853C211yesmaximal, characteristic
6#11745844C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10602063—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C2×C5×#215—22no—
12C5×#874C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91435—21no—
15#91423—22no—
16Dic5×D12—21no—
17#91373—21no—
18#91370—21no—
19#91094—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71159—51nomaximal, Hall
27#66047—31no—
28C5×#492—31no—
29#65380—31no—
30#65380D311yescharacteristic, complemented
31#64764—31no—
32#64676—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12D412yes—
39C2×C3×Dic10D411yescharacteristic
40C2×D3×Dic5—22no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15D411yescharacteristic
45#6712—21no—
46C4×Dic15—21no—
47C2×C3⋊#168—21no—
48C5×#215—44no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54(C2×D3)⋊Dic5—22no—
55(C2×D3)⋊Dic5—22no—
56(C2×D3)⋊Dic5—22no—
57#5585—51no—
58C3×#477—51no—
59#5091—51no—
60#5085D511yescharacteristic
61#4535—51no—
62#4485—51no—
63#4484—51no—
64C2×C5×SD16—62no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C5×#127—31no—
67#4082—61no—
68#4082—61no—
69#4081—62no—
70D4×Dic5—61no—
71D4×Dic5—61no—
72C4×Dic10—31no—
73C4×Dic10C2×D311yescharacteristic
74C4×C5×C8—31no—
75#3942—21no—
76#3942—61no—
77#3939—21no—
78#3939—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1630—151noSylow
82C22×C5×D3—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
88C2×Dic15—21no—
89C2×Dic15—21no—
90Dic30—21no—
91Dic30—21no—
92C5×D12—42no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101D3×Dic5—82no—
102C3⋊#168—41no—
103C3×#168—41no—
104C5×C3⋊C8—22no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4×Q8—51no—
107#947—101no—
108C2×#215—22no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874C2×D511yescharacteristic
113C4×D12—101no—
114C4×Dic6—51no—
115C3×#107—101no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#810—101no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4×C3⋊C8C2×D511yescharacteristic
122C2×C5×Q8—21no—
123C2×C5×D4—32no—
124C2×C5×D4—61no—
125C2×C5×D4—61no—
126C22×Dic5—62no—
127C2×Dic10—31no—
128C2×Dic10#6711yescharacteristic
129C5×SD16—124no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C42×C5C22×D311yescharacteristic
134C22⋊Dic5—62no—
135C22⋊Dic5—62no—
136C22⋊Dic5—62no—
137C4⋊Dic5—31no—
138C4⋊Dic5#6711yescharacteristic
139#683—21no—
140#683—61no—
141C4×Dic5—21no—
142C4×Dic5—61no—
143C2×#168—21no—
144C2×#168—61no—
145#559—151no—
146#492—31no—
147#477—51no—
148#477—151no—
149#331—151no—
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—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—41no—
163Dic15—41no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C2×C3×Q8—21no—
167C2×C3×Q8—51no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12C22⋊D512yes—
171C2×C4×D3—102no—
172C2×Dic6—51no—
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—44no—
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×Q8—42no—
191C5×D4—122no—
192C5×D4—121no—
193C5×D4—121no—
194C5×D4—121no—
195C5×D4—121no—
196C2×C4×C5—41no—
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—242no—
205Dic10—21no—
206Dic10—21no—
207Dic10—61no—
208Dic10—61no—
209C5×C8—62no—
210#168—41no—
211#168—121no—
212C2×SD16—62no—
213C4⋊Q8D3×D511yescharacteristic
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—51no—
225C4⋊C8—151no—
226#103—101no—
227#103—301no—
228C4×C8—31no—
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C5×D3—82no—
233C22×D3—22no—
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—101no—
244C2×Dic3—101no—
245D12—42no—
246D12—41no—
247D12—41no—
248D12—41no—
249D12—41no—
250C4×D3—402no—
251Dic6—101no—
252Dic6—101no—
253C3×C8—201no—
254C3⋊C8—22no—
255C3⋊C8—201no—
256C22×C5—122no—
257C22×C5—122no—
258C22×C5—122no—
259C22×C5#93711yescharacteristic
260C4×C5—21no—
261C4×C5—81no—
262C4×C5#91811yescharacteristic
263C4×C5#91911yescharacteristic
264C4×C5#94211yescharacteristic
265C4×C5#95011yescharacteristic
266Dic5—41no—
267Dic5—41no—
268Dic5—121no—
269Dic5—121no—
270C2×Q8—21no—
271C2×Q8—51no—
272C2×Q8—151no—
273C2×D4—32no—
274C2×D4—61no—
275C2×D4—61no—
276C22×C4—302no—
277SD16—124no—
278C2×C8—61no—
279C2×C8—101no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—51no—
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#408311yescharacteristic
295C2×D3—42no—
296C2×D3—42no—
297C2×D3—42no—
298C3×C4—21no—
299C3×C4—81no—
300C3×C4—201no—
301C3×C4—201no—
302C3×C4#406111yescharacteristic
303C3×C4#406111yescharacteristic
304C3×C4#406211yescharacteristic
305C3×C4#406211yescharacteristic
306Dic3—201no—
307Dic3—201no—
308C2×C5—242no—
309C2×C5#504711yescharacteristic
310C2×C5#518711yescharacteristic
311C2×C5#519811yescharacteristic
312C23—62no—
313Q8—42no—
314Q8—101no—
315Q8—101no—
316Q8—301no—
317Q8—301no—
318D4—122no—
319D4—121no—
320D4—121no—
321D4—121no—
322D4—121no—
323C2×C4—41no—
324C2×C4—101no—
325C2×C4—101no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—1202no—
329C2×C4D5×#6711yescharacteristic
330C2×C4D3×C22⋊D511yescharacteristic
331C2×C4#679011yescharacteristic
332C8—62no—
333C8—201no—
334C8—601no—
335C2×C3#6536611yescharacteristic
336C2×C3#6546211yescharacteristic
337C2×C3#6546211yescharacteristic
338D3—82no—
339C5#7115911yescharacteristic, complemented, Sylow
340C22—122no—
341C22—122no—
342C22—122no—
343C22#9157711yescharacteristic
344C4—21no—
345C4—81no—
346C4—201no—
347C4—201no—
348C4—601no—
349C4—601no—
350C4#9151311yescharacteristic
351C4#9151411yescharacteristic
352C4#9152311yescharacteristic
353C4#9152411yescharacteristic
354C3#1060206311yescharacteristic, complemented, Sylow
355C2—242no—
356C2#1174916511yescharacteristic
357C2#1174940511yescharacteristic
358C2#1174940711yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
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
2. #11751192C2semidirect
4. C3×#65380C2semidirect
6. #11745844C2semidirect
7. #11745841C2semidirect
30. #65380D3semidirect
293. C3×C5#1630semidirect
339. C5#71159semidirect
354. C3#10602063semidirect

Maximal subgroups

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

subgroupindex
#117526512
#117511922
C5×#50852
C3×#653802
#117458532
#117458442
#117458412
#106020633
#711595