Finite Group Databasebeta

← #14289972

Subgroups — #14289972

Order 1920.

424 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#65919C211yesmaximal, characteristic
2#11751132C211yesmaximal, characteristic, complemented
3#11746943C211yesmaximal, characteristic, complemented
4#11746890C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic
7#11745841C211yesmaximal, characteristic, complemented
8#10599055—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C2×#6718—21no—
11#91758C2211yescharacteristic
12C3×#4093—21no—
13C3×#4040—22no—
14C3×#4039—21no—
15C3×#4021—21no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20—21no—
18C3×C4×Dic10C2211yescharacteristic
19#91094—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23#90987—21no—
24#90971—21no—
25#90965—22no—
26#71945—51nomaximal, Hall
27#65919D311yescharacteristic
28#65320—31no—
29#65140—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D412yes—
39C2×C3×C4×D5—22no—
40C2×C3×Dic10D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45#6718—42no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—22no—
52C3×#685—22no—
53C3×#685—22no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×#559—51no—
58#5070—51no—
59#5031—51no—
60#5020—51no—
61#4544—51no—
62#4535—51no—
63#4535D511yescharacteristic, complemented
64C4×C5×Q8C2×D311yescharacteristic
65#4093—21no—
66C2×#689—61no—
67#4040—22no—
68#4039—21no—
69#4021—21no—
70#4020C2×D311yescharacteristic
71C4×D20—21no—
72#4015—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3953—62no—
77#3949—61no—
78#3948—61no—
79#3942—61no—
80C4⋊#168—31no—
81#1640—151noSylow
82C22×C3×D5—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—41no—
91Dic30—41no—
92Dic30—41no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—42no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×C4×D5—82no—
101C3×Dic10—21no—
102C3×Dic10—21no—
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C3×#127—51no—
107C3×#124—101no—
108C3×#124—101no—
109C3×#123—102no—
110C3×C4×Q8—51no—
111C3×C4×Q8C2×D511yescharacteristic
112C3×C4×D4—101no—
113C3×C4×D4—101no—
114C2×#216—101no—
115#869—51no—
116#835—101no—
117#832—102no—
118#810—101no—
119#808—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8#6711yescharacteristic
124C2×D20—21no—
125C2×D20—21no—
126C2×D20#6712yes—
127C2×C4×D5—22no—
128C2×Dic10—61no—
129C2×Dic10#6711yescharacteristic
130C2×C5×C8—61no—
131C2×C5×C8—61no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4#6711yescharacteristic
134C42×C5—21no—
135C42×C5C22×D311yescharacteristic
136#689—122no—
137#685—22no—
138#685—22no—
139#685—22no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5#6711yescharacteristic
143#683—21no—
144C4×Dic5—21no—
145C2×#168—61no—
146#559—51no—
147#486—151no—
148#475—151no—
149#462—151no—
150#331—151no—
151Q8⋊C8—31no—
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—41no—
159C3×C4×C5—41no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—81no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C2×C3×Q8—51no—
168C2×C3×Q8D2011yescharacteristic
169C2×C3×D4—52no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C22×C3×C4—102no—
173C2×Dic6—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4D2011yescharacteristic
178C3×C22⋊C4—102no—
179C3×C22⋊C4—102no—
180C3×C22⋊C4—102no—
181C3×C42—21no—
182C3×C42—101no—
183C3×C42C22×D511yescharacteristic
184#216—202no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—101no—
190C22×D5—22no—
191C5×Q8—21no—
192C5×Q8—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—121no—
201D20—42no—
202D20—41no—
203D20—41no—
204D20—41no—
205D20—41no—
206C4×D5—82no—
207Dic10—21no—
208Dic10—21no—
209Dic10—121no—
210Dic10—121no—
211C5×C8—121no—
212C5×C8—121no—
213#168—121no—
214C2×Q16—301no—
215C4⋊Q8—151no—
216#127—51no—
217#124—101no—
218#124—101no—
219#123—102no—
220C4×Q8—51no—
221C4×Q8D3×D511yescharacteristic
222C4×D4—101no—
223C4×D4—101no—
224#106—301no—
225C4⋊C8—31no—
226C4⋊C8—151no—
227#103—301no—
228#103—301no—
229#102—302no—
230C4×C8—31no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234C3×D5—82no—
235C23×C3—102no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—101no—
239C3×Q8—101no—
240C3×D4—202no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—201no—
244C3×D4—201no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—402no—
250C2×C3×C4C2×D2011yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×Dic3—201no—
254Dic6—201no—
255Dic6—201no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#95311yescharacteristic
260C2×D5—42no—
261C2×D5—42no—
262C2×D5—42no—
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5#94911yescharacteristic
267C4×C5#95011yescharacteristic
268C4×C5#95011yescharacteristic
269C4×C5#95111yescharacteristic
270Dic5—41no—
271Dic5—41no—
272Dic5—241no—
273C2×Q8—51no—
274C2×Q8—301no—
275C2×Q8#120211yescharacteristic
276C2×D4—52no—
277C2×D4—101no—
278C2×D4—101no—
279C22×C4—102no—
280Q16—602no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—101no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4#120211yescharacteristic
290C22⋊C4—102no—
291C22⋊C4—102no—
292C22⋊C4—102no—
293C42—21no—
294C42—101no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—202no—
298C22×C3—202no—
299C22×C3—202no—
300C22×C3#402811yescharacteristic
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—201no—
305C3×C4—201no—
306C3×C4#405011yescharacteristic
307C3×C4#405411yescharacteristic
308C3×C4#406211yescharacteristic
309C3×C4#406411yescharacteristic
310Dic3—401no—
311C2×C5#523811yescharacteristic
312C2×C5#523911yescharacteristic
313C2×C5#524211yescharacteristic
314D5—82no—
315C23—102no—
316Q8—21no—
317Q8—21no—
318Q8—101no—
319Q8—101no—
320Q8—601no—
321Q8—601no—
322D4—202no—
323D4—201no—
324D4—201no—
325D4—201no—
326D4—201no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—402no—
332C2×C4—601no—
333C2×C4C2×#120211yescharacteristic
334C2×C4D5×#6711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—121no—
337C8—121no—
338C8—601no—
339C2×C3—402no—
340C2×C3#6502311yescharacteristic
341C2×C3#6509911yescharacteristic
342C2×C3#6511411yescharacteristic
343C5#7194511yescharacteristic, complemented, Sylow
344C22—202no—
345C22—202no—
346C22—202no—
347C22#9156411yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—201no—
352C4—201no—
353C4—1201no—
354C4#9130111yescharacteristic
355C4#9131111yescharacteristic
356C4#9150811yescharacteristic
357C4#9151411yescharacteristic
358C3#1059905511yescharacteristic, complemented, Sylow
359C2—402no—
360C2#1174851311yescharacteristic
361C2#1174929511yescharacteristic
362C2#1174946311yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×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. #11751132C2semidirect
3. #11746943C2semidirect
5. C5×#4535C2semidirect
7. #11745841C2semidirect
63. #4535D5semidirect
296. C3×C5#1640semidirect
343. C5#71945semidirect
358. C3#10599055semidirect

Maximal subgroups

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

subgroupindex
C3×#659192
#117511322
#117469432
#117468902
C5×#45352
#117458522
#117458412
#105990553
#719455