Finite Group Databasebeta

← #14289983

Subgroups — #14289983

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#11750950C211yesmaximal, characteristic, complemented
3#11746945C211yesmaximal, characteristic, complemented
4#11746890C211yesmaximal, characteristic
5C5×#4484C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic
7#11745844C211yesmaximal, characteristic, complemented
8#10599047—31nomaximal, Hall
9C2×Dic60—21no—
10#91758C2211yescharacteristic
11C4×Dic30C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×#4020C2211yescharacteristic
14#91434—21no—
15Dic3×D20—21no—
16#91407—22no—
17#91368—21no—
18#91364—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91100—21no—
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90985—21no—
24#90973—21no—
25#90965—22no—
26#68406—51nomaximal, Hall
27#65919—31no—
28#65309—31no—
29#65138—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64705D311yescharacteristic
33#64676—31no—
34C2×Dic30—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20D412yes—
40C2×D5×Dic3—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48Dic60—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—
58#5070—51no—
59#4851—51no—
60#4849—51no—
61C3×#331—51no—
62#4484—51no—
63#4484D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4093—61no—
66C2×Dic20—61no—
67#4040—62no—
68#4039—61no—
69#4021—61no—
70#4020C2×D311yescharacteristic
71C4×D20—61no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3967—61no—
77#3953—62no—
78#3948—61no—
79#3940—61no—
80C4⋊#168C2×D311yescharacteristic
81#1640—151noSylow
82C22×C3×D5—22no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88C2×Dic15—41no—
89Dic30—21no—
90Dic30—21no—
91Dic30—41no—
92Dic30—41no—
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×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×#127—51no—
107#936—101no—
108#936—101no—
109#935—102no—
110D4×Dic3—101no—
111D4×Dic3—101no—
112C2×Dic12—101no—
113#869—51no—
114C4×Dic6—51no—
115C4×Dic6C2×D511yescharacteristic
116C3×C4⋊C8—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118#832—102no—
119#817—101no—
120#816—101no—
121#816—101no—
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8—31no—
124C2×D20—21no—
125C2×D20—21no—
126C2×D20D1212yes—
127C2×C4×D5—62no—
128C2×Dic10—31no—
129C2×Dic10—61no—
130C2×C5×C8—21no—
131C2×C5×C8—61no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—61no—
134C42×C5—61no—
135C42×C5C22×D311yescharacteristic
136#685—62no—
137#685—62no—
138#685—62no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142#683—61no—
143C4×Dic5—61no—
144C2×#168—21no—
145Dic20—122no—
146#559—151no—
147#486—151no—
148#475—151no—
149#462—151no—
150#331—51no—
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#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—41no—
163Dic15—41no—
164Dic15—81no—
165C5×Dic3—41no—
166C5×Dic3—41no—
167C2×C3×D4—52no—
168C2×C3×D4—101no—
169C2×C3×D4—101no—
170C22×Dic3—102no—
171C2×Dic6—51no—
172C2×Dic6—101no—
173C2×Dic6D2011yescharacteristic
174C2×C3×C8—21no—
175C2×C3×C8—101no—
176C3×C42C22×D511yescharacteristic
177#217—102no—
178#217—102no—
179#217—102no—
180C4⋊Dic3—51no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183C4⋊Dic3D2011yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—101no—
186C4×Dic3—21no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189Dic12—202no—
190C22×D5—22no—
191C5×Q8—61no—
192C5×Q8—61no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—61no—
199C2×Dic5—61no—
200C2×Dic5—121no—
201D20—42no—
202D20—41no—
203D20—41no—
204D20—41no—
205D20—41no—
206C4×D5—242no—
207Dic10—61no—
208Dic10—61no—
209Dic10—121no—
210Dic10—121no—
211C5×C8—41no—
212C5×C8—121no—
213#168—41no—
214C2×Q16—301no—
215C4⋊Q8—151no—
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—51no—
226C4⋊C8D3×D511yescharacteristic
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×D4—202no—
237C3×D4—201no—
238C3×D4—201no—
239C3×D4—201no—
240C3×D4—201no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—101no—
247C2×Dic3—101no—
248C2×Dic3—201no—
249C2×Dic3—402no—
250Dic6—21no—
251Dic6—21no—
252Dic6—101no—
253Dic6—101no—
254Dic6—201no—
255Dic6—201no—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—42no—
261C2×D5—42no—
262C2×D5—42no—
263C4×C5—21no—
264C4×C5—121no—
265C4×C5—121no—
266C4×C5#91111yescharacteristic
267C4×C5#91211yescharacteristic
268C4×C5#91511yescharacteristic
269C4×C5#91611yescharacteristic
270Dic5—121no—
271Dic5—121no—
272Dic5—241no—
273C2×Q8—31no—
274C2×Q8—151no—
275C2×Q8—301no—
276C2×D4—52no—
277C2×D4—101no—
278C2×D4—101no—
279C22×C4—302no—
280Q16—602no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—101no—
284C4⋊C4—31no—
285C4⋊C4—61no—
286C4⋊C4—151no—
287C4⋊C4—301no—
288C4⋊C4—301no—
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#402811yescharacteristic
301C3×C4—21no—
302C3×C4#405011yescharacteristic
303C3×C4#405511yescharacteristic
304C3×C4#406011yescharacteristic
305C3×C4#406511yescharacteristic
306Dic3—41no—
307Dic3—41no—
308Dic3—201no—
309Dic3—201no—
310Dic3—401no—
311C2×C5#474611yescharacteristic
312C2×C5#478111yescharacteristic
313C2×C5#478311yescharacteristic
314D5—82no—
315C23—102no—
316Q8—61no—
317Q8—61no—
318Q8—301no—
319Q8—301no—
320Q8—601no—
321Q8—601no—
322D4—202no—
323D4—201no—
324D4—201no—
325D4—201no—
326D4—201no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—301no—
330C2×C4—301no—
331C2×C4—601no—
332C2×C4—1202no—
333C2×C4D5×D1211yescharacteristic
334C2×C4D3×D2011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—41no—
337C8—121no—
338C8—201no—
339C2×C3—402no—
340C2×C3#6502211yescharacteristic
341C2×C3#6510011yescharacteristic
342C2×C3#6511411yescharacteristic
343C5#6840611yescharacteristic, complemented, Sylow
344C22—202no—
345C22—202no—
346C22—202no—
347C22#9147611yescharacteristic
348C4—21no—
349C4—121no—
350C4—121no—
351C4—601no—
352C4—601no—
353C4—1201no—
354C4#9127311yescharacteristic
355C4#9127411yescharacteristic
356C4#9149811yescharacteristic
357C4#9152111yescharacteristic
358C3#1059904711yescharacteristic, complemented, Sylow
359C2—402no—
360C2#1174751811yescharacteristic
361C2#1174816211yescharacteristic
362C2#1174825011yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1640
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. #11750950C2semidirect
3. #11746945C2semidirect
5. C5×#4484C2semidirect
7. #11745844C2semidirect
63. #4484D5semidirect
296. C3×C5#1640semidirect
343. C5#68406semidirect
358. C3#10599047semidirect

Maximal subgroups

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

subgroupindex
#117526362
#117509502
#117469452
#117468902
C5×#44842
C3×#647052
#117458442
#105990473
#684065