Finite Group Databasebeta

← #14289957

Subgroups — #14289957

Order 1920.

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

normal subgroups only

This group has 424 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#11752636C211yesmaximal, characteristic
2#11751195C211yesmaximal, characteristic, complemented
3C5×#5090C211yesmaximal, characteristic, complemented
4C3×#65377C211yesmaximal, characteristic
5#11745852C211yesmaximal, characteristic
6#11745845C211yesmaximal, characteristic, complemented
7#11745843C211yesmaximal, characteristic, complemented
8#10601853—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C2×C5×#216—21no—
12C4×C5×Dic6C2211yescharacteristic
13C3×#4020C2211yescharacteristic
14#91434—21no—
15Dic3×D20—21no—
16#91407—22no—
17#91368—21no—
18#91364—21no—
19#91094—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#835—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3941—22no—
25C3×C4×#168C2211yescharacteristic
26#71206—51nomaximal, Hall
27#65919—31no—
28C5×#462—31no—
29#65383—31no—
30#65377D311yescharacteristic
31Q8⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20D412yes—
40C2×D5×Dic3—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×#216—42no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C2×C3×#168—21no—
54#6665—22no—
55#6665—22no—
56#6665—22no—
57#5713—51no—
58C3×#486—51no—
59#5094—51no—
60#5090D511yescharacteristic, complemented
61#4544—51no—
62#4456—51no—
63#4456—51no—
64C2×C5×Q16—61no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C4×C5×Q8—31no—
67#4093—61no—
68#4040—62no—
69#4039—61no—
70#4021—61no—
71#4020C2×D311yescharacteristic
72C4×D20—61no—
73C4×Dic10—31no—
74C5×C4⋊C8—31no—
75C5×#103—61no—
76#3942—61no—
77#3941—22no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168C2×D311yescharacteristic
81#1640—151noSylow
82C22×C3×D5—22no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30—21no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×Dic6—21no—
96C5×Dic6—21no—
97C3×D20—42no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102D5×Dic3—82no—
103C3⋊#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8C2×D511yescharacteristic
107C3×#127—51no—
108C2×#216—21no—
109#936—101no—
110#936—101no—
111#935—102no—
112D4×Dic3—101no—
113D4×Dic3—101no—
114C4×Dic6—51no—
115C4×Dic6C2×D511yescharacteristic
116C3×#102—102no—
117C3×C4×C8—51no—
118#835—21no—
119#810—101no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×Q8—31no—
125C2×D20—21no—
126C2×D20—21no—
127C2×D20#6712yes—
128C2×C4×D5—62no—
129C2×Dic10—31no—
130C5×Q16—122no—
131C2×C5×C8—61no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—61no—
136C42×C5—61no—
137C42×C5C22×D311yescharacteristic
138#685—62no—
139#685—62no—
140#685—62no—
141C4⋊Dic5—31no—
142#683—61no—
143C4×Dic5—61no—
144C2×#168—21no—
145C2×#168—61no—
146#559—151no—
147#486—51no—
148#475—151no—
149#462—31no—
150#331—151no—
151Q8⋊C8—151no—
152Q8⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C3×C4×C5—21no—
158C3×C4×C5—81no—
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—41no—
164Dic15—41no—
165C5×Dic3—41no—
166C5×Dic3—41no—
167C2×C3×Q8—21no—
168C2×C3×D4—52no—
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C22×Dic3—102no—
172C2×Dic6—51no—
173C2×Dic6C22⋊D511yescharacteristic
174C2×C3×C8—101no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C42C22×D511yescharacteristic
178#217—102no—
179#217—102no—
180#217—102no—
181#216—42no—
182C4⋊Dic3—51no—
183C4⋊Dic3C22⋊D511yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—101no—
186C4×Dic3—21no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—101no—
190C22×D5—22no—
191C5×Q8—41no—
192C5×Q8—41no—
193C5×Q8—61no—
194C5×Q8—61no—
195C2×C4×C5—41no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—42no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—41no—
208C4×D5—242no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—121no—
212#168—41no—
213#168—121no—
214C2×Q16—61no—
215C4⋊Q8D3×D511yescharacteristic
216#127—51no—
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—31no—
221C4×Q8—151no—
222C4×D4—301no—
223C4×D4—301no—
224#106—301no—
225C4⋊C8—31no—
226C4⋊C8—151no—
227#103—61no—
228#103—301no—
229#102—102no—
230C4×C8—51no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234C3×D5—82no—
235C23×C3—102no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×D4—202no—
239C3×D4—201no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C2×C3×C4—41no—
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—101no—
250C2×Dic3—101no—
251C2×Dic3—402no—
252Dic6—21no—
253Dic6—21no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—42no—
261C2×D5—42no—
262C2×D5—42no—
263C4×C5—21no—
264C4×C5—81no—
265C4×C5—121no—
266C4×C5—121no—
267C4×C5#91111yescharacteristic
268C4×C5#91211yescharacteristic
269C4×C5#91511yescharacteristic
270C4×C5#91611yescharacteristic
271Dic5—121no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—31no—
275C2×Q8—151no—
276C2×D4—52no—
277C2×D4—101no—
278C2×D4—101no—
279C22×C4—302no—
280Q16—122no—
281C2×C8—61no—
282C2×C8—101no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—31no—
287C4⋊C4—61no—
288C4⋊C4—151no—
289C4⋊C4—301no—
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—61no—
294C42—301no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—202no—
298C22×C3—202no—
299C22×C3—202no—
300C22×C3#408311yescharacteristic
301C3×C4—21no—
302C3×C4—81no—
303C3×C4#406411yescharacteristic
304C3×C4#406511yescharacteristic
305C3×C4#407811yescharacteristic
306C3×C4#409611yescharacteristic
307Dic3—41no—
308Dic3—41no—
309Dic3—201no—
310Dic3—201no—
311C2×C5#506111yescharacteristic
312C2×C5#515811yescharacteristic
313C2×C5#517311yescharacteristic
314D5—82no—
315C23—102no—
316Q8—41no—
317Q8—41no—
318Q8—61no—
319Q8—61no—
320Q8—301no—
321Q8—301no—
322D4—202no—
323D4—201no—
324D4—201no—
325D4—201no—
326D4—201no—
327C2×C4—41no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4D5×#6711yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—601no—
339C2×C3—402no—
340C2×C3#6532611yescharacteristic
341C2×C3#6547611yescharacteristic
342C2×C3#6549111yescharacteristic
343C5#7120611yescharacteristic, complemented, Sylow
344C22—202no—
345C22—202no—
346C22—202no—
347C22#9157711yescharacteristic
348C4—21no—
349C4—81no—
350C4—121no—
351C4—121no—
352C4—601no—
353C4—601no—
354C4#9149311yescharacteristic
355C4#9149411yescharacteristic
356C4#9152111yescharacteristic
357C4#9152211yescharacteristic
358C3#1060185311yescharacteristic, complemented, Sylow
359C2—402no—
360C2#1174915711yescharacteristic
361C2#1174940411yescharacteristic
362C2#1174940911yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1640
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. #11751195C2semidirect
3. C5×#5090C2semidirect
6. #11745845C2semidirect
7. #11745843C2semidirect
60. #5090D5semidirect
296. C3×C5#1640semidirect
343. C5#71206semidirect
358. C3#10601853semidirect

Maximal subgroups

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

subgroupindex
#117526362
#117511952
C5×#50902
C3×#653772
#117458522
#117458452
#117458432
#106018533
#712065