Finite Group Databasebeta

← #14289840

Subgroups — #14289840

Order 1920.

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

normal subgroups only

This group has 388 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×#66066C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11746916C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745840C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10599228—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4093—21no—
12C3×Q8×Dic5—21no—
13C3×#4044—22no—
14C3×#4043—21no—
15C3×#4038—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18#91094—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90990—21no—
23#90987—21no—
24#90971—21no—
25#90965—21no—
26#71932—51nomaximal, Hall
27#66066D311yescharacteristic
28#65382—31no—
29#65139—31no—
30#65131—31no—
31C5×#332—31no—
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10D411yescharacteristic
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D412yes—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C2×C5×C3⋊C8—21no—
46C2×C5×C3⋊C8—21no—
47C3×#685—22no—
48C3×#685—22no—
49C3×#685—21no—
50C3×C4⋊Dic5—22no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5—21no—
56C3×#556—51no—
57#5093—51no—
58#5021—51no—
59#5008—51no—
60#4547D511yescharacteristic, complemented
61#4535—51no—
62D4⋊(C3⋊C8)—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64#4093—21no—
65Q8×Dic5—21no—
66#4044—22no—
67#4043—21no—
68#4038—21no—
69C4×D20C2×D311yescharacteristic
70#4015—31no—
71C4×Dic10C2×D311yescharacteristic
72C5×C4⋊C8—31no—
73C5×C4⋊C8—31no—
74#3953—61no—
75#3950—61no—
76#3949—61no—
77#3948—61no—
78#3942—62no—
79C4×#168—31no—
80#1638—151noSylow
81C22×C3×D5—21no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—41no—
89Dic30—42no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×D20—21no—
94C3×D20—21no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3⋊#168—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×#126—102no—
104C3×#124—101no—
105C3×C22⋊Q8—101no—
106C3×C4×Q8—51no—
107C3×C4×Q8—101no—
108C3×C4×D4—51no—
109C3×#117—101no—
110#869—51no—
111#835—101no—
112#832—101no—
113#810—102no—
114#808—101no—
115#807—101no—
116C4⋊(C3⋊C8)C2×D511yescharacteristic
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—51no—
119C2×C5×Q8—21no—
120C2×D20#6711yescharacteristic
121C2×C4×D5—21no—
122C2×Dic10—61no—
123C2×Dic10#6711yescharacteristic
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4#6712yes—
128C42×C5C22×D311yescharacteristic
129#685—22no—
130#685—22no—
131#685—21no—
132C4⋊Dic5—22no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135C4⋊Dic5#6711yescharacteristic
136C4⋊Dic5#6711yescharacteristic
137#683—21no—
138C4×Dic5—22no—
139C4×Dic5—21no—
140C2×#168—61no—
141#556—51no—
142#487—151no—
143#477—151no—
144#476—151no—
145#332—31no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—81no—
159C3×Dic5—41no—
160C3×Dic5—41no—
161C3×Dic5—41no—
162C2×C3×Q8—21no—
163C2×C3×Q8—51no—
164C2×C3×D4—51no—
165C22×C3×C4—101no—
166C2×Dic6—101no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—102no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4D2012yes—
173C3×C22⋊C4—102no—
174C3×C22⋊C4—102no—
175C3×C22⋊C4—101no—
176C3×C42—102no—
177C3×C42—101no—
178C3×C42C22×D511yescharacteristic
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C22×D5—21no—
185C5×Q8—41no—
186C5×Q8—41no—
187C2×C4×C5—22no—
188C2×C4×C5C2×#6711yescharacteristic
189C2×C4×C5C2×#6711yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×Dic5—21no—
192C2×Dic5—21no—
193C2×Dic5—21no—
194C2×Dic5—121no—
195D20—21no—
196D20—21no—
197C4×D5—41no—
198C4×D5—41no—
199Dic10—21no—
200Dic10—21no—
201Dic10—122no—
202C5×C8—121no—
203C5×C8—121no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8D3×D511yescharacteristic
207#126—102no—
208#124—101no—
209C22⋊Q8—101no—
210C4×Q8—51no—
211C4×Q8—101no—
212C4×D4—51no—
213#117—101no—
214#107—301no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8—31no—
218#103—301no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C3×D5—81no—
226C23×C3—101no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—101no—
230C3×Q8—101no—
231C3×D4—101no—
232C3×D4—101no—
233C2×C3×C4—22no—
234C2×C3×C4—101no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4—201no—
238C2×C3×C4—201no—
239C2×C3×C4C2×D2011yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×Dic3—201no—
243Dic6—202no—
244C3⋊C8—41no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5#95311yescharacteristic
248C2×D5—41no—
249C2×D5—41no—
250C2×D5—41no—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5#95011yescharacteristic
254C4×C5#95011yescharacteristic
255C4×C5#95111yescharacteristic
256C4×C5#95111yescharacteristic
257Dic5—41no—
258Dic5—41no—
259Dic5—41no—
260Dic5—241no—
261C2×Q8—21no—
262C2×Q8—51no—
263C2×Q8—301no—
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—61no—
267C2×C8—61no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—102no—
273C4⋊C4—101no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4#120212yes—
277C22⋊C4—102no—
278C22⋊C4—102no—
279C22⋊C4—101no—
280C42—102no—
281C42—101no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—201no—
285C22×C3—201no—
286C22×C3—201no—
287C22×C3#402811yescharacteristic
288C3×C4—21no—
289C3×C4—42no—
290C3×C4—201no—
291C3×C4—201no—
292C3×C4—201no—
293C3×C4#405811yescharacteristic
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4#406411yescharacteristic
297Dic3—401no—
298C2×C5#523911yescharacteristic
299C2×C5#523911yescharacteristic
300C2×C5#524511yescharacteristic
301D5—81no—
302C23—101no—
303Q8—41no—
304Q8—41no—
305Q8—101no—
306Q8—101no—
307Q8—602no—
308D4—101no—
309D4—101no—
310C2×C4—22no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—201no—
315C2×C4—201no—
316C2×C4—601no—
317C2×C4C2×#120211yescharacteristic
318C2×C4D5×#6711yescharacteristic
319C2×C4D5×#6711yescharacteristic
320C8—121no—
321C8—121no—
322C8—601no—
323C2×C3—401no—
324C2×C3#6504211yescharacteristic
325C2×C3#6507211yescharacteristic
326C2×C3#6509911yescharacteristic
327C5#7193211yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22#9156411yescharacteristic
332C4—21no—
333C4—42no—
334C4—201no—
335C4—201no—
336C4—201no—
337C4—1201no—
338C4#9148411yescharacteristic
339C4#9149011yescharacteristic
340C4#9150811yescharacteristic
341C4#9151411yescharacteristic
342C3#1059922811yescharacteristic, complemented, Sylow
343C2—401no—
344C2#1174904911yescharacteristic
345C2#1174929511yescharacteristic
346C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1638
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. #11751194C2semidirect
3. #11746916C2semidirect
5. C5×#4547C2semidirect
6. #11745840C2semidirect
60. #4547D5semidirect
283. C3×C5#1638semidirect
327. C5#71932semidirect
342. C3#10599228semidirect

Maximal subgroups

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

subgroupindex
C3×#660662
#117511942
#117469162
#117468812
C5×#45472
#117458402
#117458342
#105992283
#719325