Finite Group Databasebeta

← #14289182

Subgroups — #14289182

Order 1920.

420 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 90 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#11756326C211yesmaximal, characteristic, complemented
2C5×#5027C211yesmaximal, characteristic
3#11747086C211yesmaximal, characteristic
4#11746906C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745845C211yesmaximal, characteristic, complemented
8#10601827—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91833—21no—
11#91778—22no—
12#91776—21no—
13#91759—21no—
14#91758C2211yescharacteristic
15C4×Dic30—21no—
16C4×Dic30C2211yescharacteristic
17C2×C5×#215—21no—
18C5×#874C2211yescharacteristic
19C2×#6659—21no—
20C5×#809—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90967—21no—
25#90967—22no—
26#68265—51nomaximal, Hall
27#65901—31no—
28C5×#460—31no—
29#65364—31no—
30#65359—31no—
31Q8⋊#168D311yescharacteristic, complemented
32#64704—31no—
33#64702—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×Dic30D411yescharacteristic
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—21no—
45C4⋊Dic15D411yescharacteristic
46C4⋊Dic15D412yes—
47#6712—22no—
48#6712—22no—
49#6712—22no—
50#6712—21no—
51C4×Dic15—22no—
52C4×Dic15—21no—
53C5×#215—42no—
54C2×C5×C3⋊C8—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57#6659—42no—
58#5567—51no—
59#5027D511yescharacteristic
60#4848—51no—
61#4694—51no—
62C3×Q8⋊C8—51no—
63#4486—51no—
64#4456—51no—
65C2×C5×SD16—61no—
66C5×#127—31no—
67C4×C5×Q8C2×D311yescharacteristic
68#4090—61no—
69C2×#687—61no—
70#4035—62no—
71#4033—61no—
72#4016—61no—
73#4015—31no—
74C4×Dic10—31no—
75C4×Dic10—61no—
76C5×C4⋊C8—31no—
77C5×#102—61no—
78#3964—62no—
79#3964—61no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168C2×D311yescharacteristic
82#1626—151noSylow
83C22×C5×D3—41no—
84C3×C5×Q8—21no—
85C3×C5×Q8—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—22no—
94Dic30—21no—
95Dic30—41no—
96Dic30—41no—
97Dic30SD1612yescomplemented
98C5×D12—42no—
99C5×D12—41no—
100C5×D12—41no—
101C5×D12—41no—
102C5×D12—41no—
103C3×#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×C4×Q8C2×D511yescharacteristic
107#944—101no—
108C2×#215—21no—
109C2×#204—101no—
110#889—102no—
111#887—101no—
112#874C2×D511yescharacteristic
113#870—101no—
114#869—51no—
115C4×Dic6—51no—
116C4×Dic6—101no—
117C3×C4⋊C8—51no—
118C3×C4×C8—51no—
119#821—102no—
120#821—101no—
121#809—21no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8D1211yescharacteristic
124C2×C5×D4—61no—
125C2×C5×D4—61no—
126C2×C5×D4—61no—
127C2×Dic10—31no—
128C2×Dic10—61no—
129C5×SD16—122no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4D1211yescharacteristic
133C42×C5—21no—
134C42×C5C22×D311yescharacteristic
135#687—122no—
136C4⋊Dic5—31no—
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141#683—62no—
142#683—61no—
143C4×Dic5—62no—
144C4×Dic5—61no—
145C2×#168—21no—
146C2×#168—21no—
147#557—151no—
148#486—151no—
149#460—31no—
150#460—151no—
151#332—151no—
152Q8⋊C8—51no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C5×D3—81no—
156C2×C5×D3—81no—
157C2×C5×D3—81no—
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—22no—
166Dic15—42no—
167Dic15—41no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×Dic6—51no—
173C2×Dic6—101no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180#215—42no—
181C4⋊Dic3—51no—
182C4⋊Dic3—52no—
183C4⋊Dic3—101no—
184Dic3⋊C4—102no—
185Dic3⋊C4—102no—
186Dic3⋊C4—102no—
187Dic3⋊C4—101no—
188C4×Dic3—102no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191#204—202no—
192C23×C5—121no—
193C5×Q8—21no—
194C5×Q8—21no—
195C5×D4—122no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—121no—
199C5×D4—121no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×Dic5—61no—
206C2×Dic5—61no—
207C2×Dic5—62no—
208Dic10—32no—
209Dic10—61no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—121no—
213#168—41no—
214#168—41no—
215C2×SD16—61no—
216C2×SD16—301no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219#127—31no—
220#125—301no—
221#125—302no—
222C4×Q8—151no—
223C4×Q8—301no—
224C4×Q8—301no—
225C4×Q8D3×D511yescharacteristic
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—61no—
229#102—301no—
230#102—302no—
231C4×C8—51no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—161no—
236C22×D3—41no—
237C3×Q8—21no—
238C3×Q8—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C2×Dic3—101no—
245C2×Dic3—101no—
246C2×Dic3—102no—
247D12—42no—
248D12—41no—
249D12—41no—
250D12—41no—
251D12—41no—
252Dic6—52no—
253Dic6—101no—
254Dic6—201no—
255Dic6—201no—
256C3×C8—201no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5—241no—
260C22×C5—241no—
261C22×C5—241no—
262C22×C5#88211yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5#90411yescharacteristic
267C4×C5#90811yescharacteristic
268C4×C5D3×SD1611yescharacteristic
269C4×C5#91811yescharacteristic
270Dic5—62no—
271Dic5—122no—
272Dic5—121no—
273C2×Q8—151no—
274C2×Q8—301no—
275C2×Q8#120311yescharacteristic
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279SD16—122no—
280SD16—602no—
281C2×C8—61no—
282C2×C8—101no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—151no—
286C4⋊C4—152no—
287C4⋊C4—302no—
288C4⋊C4—302no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4#120311yescharacteristic
293C42—21no—
294C42—302no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3#408311yescharacteristic
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—81no—
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—41no—
305C3×C4D5×SD1611yescharacteristic
306C3×C4#406111yescharacteristic
307C3×C4#407811yescharacteristic
308C3×C4#409611yescharacteristic
309Dic3—102no—
310Dic3—202no—
311Dic3—201no—
312C2×C5—481no—
313C2×C5#473411yescharacteristic
314C2×C5#480611yescharacteristic
315C2×C5#482711yescharacteristic
316C23—121no—
317Q8—21no—
318Q8—21no—
319Q8—152no—
320Q8—301no—
321Q8—601no—
322Q8—601no—
323D4—122no—
324D4—121no—
325D4—121no—
326D4—121no—
327D4—121no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—302no—
333C2×C4C2×#120311yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—201no—
339C2×C3#6532611yescharacteristic
340C2×C3#6545911yescharacteristic
341C2×C3#6549011yescharacteristic
342D3—161no—
343C5#6826511yescharacteristic, complemented, Sylow
344C22—241no—
345C22—241no—
346C22—241no—
347C22#9157311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—302no—
352C4—601no—
353C4—602no—
354C4#9130311yescharacteristic
355C4#9130411yescharacteristic
356C4#9150511yescharacteristic
357C4#9152411yescharacteristic
358C3#1060182711yescharacteristic, complemented, Sylow
359C2—481no—
360C2#1174852611yescharacteristic
361C2#1174928711yescharacteristic
362C2#1174946111yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1626
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
1. #11756326C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #11745859C2semidirect
7. #11745845C2semidirect
31. Q8⋊#168D3semidirect
97. Dic30SD16semidirect
297. C3×C5#1626semidirect
343. C5#68265semidirect
358. C3#10601827semidirect

Maximal subgroups

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

subgroupindex
#117563262
C5×#50272
#117470862
#117469062
C3×Q8⋊#1682
#117458592
#117458452
#106018273
#682655