Finite Group Databasebeta

← #14291313

Subgroups — #14291313

Order 1920.

376 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 100 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#11751116C211yesmaximal, characteristic
2C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
3C3×#65296C211yesmaximal, characteristic, complemented
4#11747075C211yesmaximal, characteristic, complemented
5#11745866C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10601639—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C2×#6715—21no—
11#91763C2211yescharacteristic
12C22×C5×C3⋊C8—21no—
13C3×#4015C2211yescharacteristic
14C2×#6658—21no—
15C2×#6658—21no—
16#91093—21no—
17C4⋊(C3⋊#168)C2211yescharacteristic
18C5×#830—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#71100—51nomaximal, Hall
25C5×C8×D4—31no—
26#65304—31no—
27#65296D311yescharacteristic, complemented
28#64982—31no—
29#64705—31no—
30#64702—31no—
31#64677—31no—
32C2×C3×C5×D4D411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×C3×Dic10—21no—
38C3×C5×C4⋊C4D411yescharacteristic
39C3×C5×C22⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41#6715—42no—
42C2×C3⋊#168—21no—
43C2×C5×C3⋊C8—21no—
44C2×C5×C3⋊C8—42no—
45C2×C5×C3⋊C8D411yescharacteristic
46C2×C5×C3⋊C8D411yescharacteristic
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C2×C3×#168—21no—
50#6658—42no—
51#6658—42no—
52C3×#474—51no—
53#5085—51no—
54#5015—51no—
55D4×C3⋊C8D511yescharacteristic, complemented
56#4547—51no—
57#4485—51no—
58#4480—51no—
59C22×C5×C8—61no—
60C4×C5×D4C2×D311yescharacteristic
61C2×#686—61no—
62C2×#677—61no—
63C2×#677—61no—
64#4020—31no—
65#4015C2×D311yescharacteristic
66C5×C4⋊C8—31no—
67C5×C22⋊C8—61no—
68C4×C5×C8—31no—
69#3964—21no—
70#3941—61no—
71#3939—21no—
72C4⋊#168—31no—
73C4⋊#168C2×D311yescharacteristic
74#1665—151noSylow
75C23×C3×C5—21no—
76C22×D15—41no—
77C3×C5×D4—21no—
78C3×C5×D4SD1612yescomplemented
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85D60—41no—
86D60—41no—
87D60—41no—
88D60—41no—
89D60—81no—
90C2×C3×Dic5—41no—
91C3×Dic10—41no—
92C3×Dic10—41no—
93C3⋊#168—41no—
94C3×#168—41no—
95C5×C3⋊C8—21no—
96C5×C3⋊C8—41no—
97C5×C3⋊C8D812yescomplemented
98C3×C4⋊Q8—51no—
99C3×C4×D4C2×D511yescharacteristic
100C2×#215—101no—
101C2×#215—101no—
102C2×#213—101no—
103C22×C3⋊C8—21no—
104#874—51no—
105C3×#107—101no—
106C3×C4⋊C8—51no—
107C3×#102—101no—
108#830—21no—
109#809—101no—
110C4⋊(C3⋊C8)—51no—
111C4⋊(C3⋊C8)C2×D511yescharacteristic
112C4×C3⋊C8C2×D511yescharacteristic
113C2×C5×D4#6711yescharacteristic
114C22×C4×C5—21no—
115C2×D20—61no—
116C2×D20—61no—
117C2×D20—61no—
118C2×Dic10—21no—
119C2×C5×C8—31no—
120C2×C5×C8—31no—
121C2×C5×C8—61no—
122C2×C5×C8—122no—
123C5×C4⋊C4#6711yescharacteristic
124C5×C22⋊C4—21no—
125C42×C5C22×D311yescharacteristic
126#686—122no—
127C4⋊Dic5—21no—
128C4⋊Dic5—21no—
129C2×#168—21no—
130C2×#168—61no—
131#677—122no—
132#677—122no—
133#492—151no—
134#474—51no—
135#459—151no—
136C8×D4—31no—
137#334—151no—
138#332—151no—
139#331—151no—
140C22×C3×C5—22no—
141C22×C3×C5—41no—
142C22×C3×C5—41no—
143C22×C3×C5#12111yescharacteristic
144C2×D15—81no—
145C2×D15—81no—
146C2×D15—81no—
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5C2×SD1611yescharacteristic
151C3×C4×C5#13511yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C3×Dic5—81no—
154C2×C3×Q8—101no—
155C2×C3×D4D2011yescharacteristic
156C22×C3×C4—21no—
157C2×D12—101no—
158C2×D12—101no—
159C2×D12—101no—
160C2×C3×C8—101no—
161C3×C4⋊C4—101no—
162C3×C4⋊C4—101no—
163C3×C4⋊C4D2011yescharacteristic
164C3×C22⋊C4—21no—
165C3×C42C22×D511yescharacteristic
166#215—202no—
167#215—202no—
168#213—202no—
169C2×C3⋊C8—21no—
170C2×C3⋊C8—42no—
171C2×C3⋊C8—101no—
172C2×C3⋊C8C22⋊D511yescharacteristic
173C2×C3⋊C8C22⋊D511yescharacteristic
174C23×C5—21no—
175C22×D5—121no—
176C5×D4—21no—
177C5×D4#21512yescomplemented
178C2×C4×C5—21no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5D3×D411yescharacteristic
182C2×C4×C5#23711yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C2×Dic5—41no—
185D20—121no—
186D20—121no—
187D20—121no—
188D20—121no—
189D20—241no—
190Dic10—41no—
191Dic10—41no—
192C5×C8—32no—
193C5×C8—61no—
194C5×C8—121no—
195#168—41no—
196#168—121no—
197C2×SD16—301no—
198C2×SD16—301no—
199C2×D8—301no—
200C22×C8—61no—
201C4⋊Q8—51no—
202#127—151no—
203C4×D4D3×D511yescharacteristic
204#107—101no—
205C4⋊C8—31no—
206C4⋊C8—51no—
207C4⋊C8—151no—
208#102—101no—
209#102—301no—
210C22⋊C8—61no—
211C4×C8—31no—
212C2×C3×C5—42no—
213C2×C3×C5#45911yescharacteristic
214C2×C3×C5#46511yescharacteristic
215C2×C3×C5#47111yescharacteristic
216D15—161no—
217C23×C3—21no—
218C22×D3—201no—
219C3×Q8—201no—
220C3×Q8—201no—
221C3×D4—21no—
222C3×D4#67712yescomplemented
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—201no—
227C2×C3×C4C2×D2011yescharacteristic
228C2×C3×C4#70911yescharacteristic
229C2×C3×C4C2×C22⋊D511yescharacteristic
230D12—201no—
231D12—201no—
232D12—201no—
233D12—201no—
234D12—401no—
235C3×C8—201no—
236C3⋊C8—21no—
237C3⋊C8—41no—
238C3⋊C8—201no—
239C3⋊C8#68612yescomplemented
240C22×C5—22no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5#93911yescharacteristic
244C2×D5—241no—
245C2×D5—241no—
246C2×D5—241no—
247C4×C5—21no—
248C4×C5—41no—
249C4×C5D3×D811yescharacteristic
250C4×C5#91111yescharacteristic
251C4×C5C2×#21511yescharacteristic
252C4×C5#95011yescharacteristic
253Dic5—81no—
254C2×Q8—101no—
255C2×D4—301no—
256C2×D4—301no—
257C2×D4—301no—
258C2×D4#120211yescharacteristic
259C22×C4—21no—
260SD16—602no—
261SD16—602no—
262D8—602no—
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—61no—
266C2×C8—101no—
267C2×C8—122no—
268C2×C8—301no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4#120211yescharacteristic
272C22⋊C4—21no—
273C42C2×D3×D511yescharacteristic
274C3×C5#166511yescharacteristic, complemented, Hall
275C22×C3—22no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3#407611yescharacteristic
279C2×D3—401no—
280C2×D3—401no—
281C2×D3—401no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—401no—
285C3×C4C2×#67711yescharacteristic
286C3×C4#405011yescharacteristic
287C3×C4C2×#68611yescharacteristic
288C3×C4#409511yescharacteristic
289C2×C5—42no—
290C2×C5#504811yescharacteristic
291C2×C5#515011yescharacteristic
292C2×C5#520311yescharacteristic
293D5—481no—
294C23—21no—
295C23—601no—
296Q8—201no—
297Q8—201no—
298D4—21no—
299D4—601no—
300D4—601no—
301D4—601no—
302D4—601no—
303D4—1201no—
304D4#665812yescomplemented
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—201no—
309C2×C4#677911yescharacteristic
310C2×C4C2×#120211yescharacteristic
311C2×C4D3×C22⋊D511yescharacteristic
312C8—32no—
313C8—61no—
314C8—121no—
315C8—201no—
316C8—601no—
317C2×C3—42no—
318C2×C3#6530411yescharacteristic
319C2×C3#6540311yescharacteristic
320C2×C3#6543011yescharacteristic
321D3—801no—
322C5#7110011yescharacteristic, complemented, Sylow
323C22—22no—
324C22—41no—
325C22—41no—
326C22—1201no—
327C22—1201no—
328C22—1201no—
329C22#9156911yescharacteristic
330C4—21no—
331C4—41no—
332C4—401no—
333C4#9131111yescharacteristic
334C4C2×#665811yescharacteristic
335C4D3×#68611yescharacteristic
336C4#9148011yescharacteristic
337C3#1060163911yescharacteristic, complemented, Sylow
338C2—42no—
339C2—2401no—
340C2#1174854111yescharacteristic
341C2#1174909911yescharacteristic
342C2#1174945011yescharacteristic
subgroupG/H
centerC22#91569
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#121
prime radical#11751116C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1665
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C5×D4×C3⋊C8C2semidirect
3. C3×#65296C2semidirect
4. #11747075C2semidirect
5. #11745866C2semidirect
6. #11745856C2semidirect
7. #11745854C2semidirect
27. #65296D3semidirect
55. D4×C3⋊C8D5semidirect
78. C3×C5×D4SD16semidirect
97. C5×C3⋊C8D8semidirect
177. C5×D4#215semidirect
222. C3×D4#677semidirect
239. C3⋊C8#686semidirect
274. C3×C5#1665semidirect
304. D4#6658semidirect
322. C5#71100semidirect
337. C3#10601639semidirect

Maximal subgroups

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

subgroupindex
#117511162
C5×D4×C3⋊C82
C3×#652962
#117470752
#117458662
#117458562
#117458542
#106016393
#711005