Finite Group Databasebeta

← #14289250

Subgroups — #14289250

Order 1920.

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

normal subgroups only

This group has 500 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
1#11752539C211yesmaximal, characteristic, complemented
2C5×#4694C211yesmaximal, characteristic, complemented
3#11747060C211yesmaximal, characteristic, complemented
4#11747045C211yesmaximal, characteristic
5#11746280C211yesmaximal, characteristic, complemented
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745857C211yesmaximal, characteristic, complemented
8#10601998—31nomaximal, Hall
9C2×D15⋊Q8—21no—
10C4×D60C2211yescharacteristic
11C5×#874C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91468—21no—
15#91419—22no—
16#91418—21no—
17#91383—21no—
18C2×#6656—21no—
19C2×#6654—21no—
20C3×C4×C5×C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#821—22no—
23C3×C4⋊#168C2211yescharacteristic
24#90967—21no—
25#90966—21no—
26#68266—51nomaximal, Hall
27#66061—31no—
28C5×#486—31no—
29#65364—31no—
30#65361—31no—
31#64767—31no—
32#64679—31no—
33#64676D311yescharacteristic, complemented
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×Dic6—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×#1204—22no—
42C2×#1200—22no—
43D15⋊Q8—42no—
44D15⋊Q8—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—21no—
48C4⋊Dic15D411yescharacteristic
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D412yes—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56#6668—22no—
57#6667—22no—
58#6656—42no—
59#6654—42no—
60Q8×D12—51no—
61#5027—51no—
62#4843—51no—
63#4694D511yescharacteristic, complemented
64C3×Q8⋊C8—51no—
65#4486—51no—
66#4459—51no—
67C2×Q8×D5—61no—
68C5×C4⋊Q8—31no—
69C5×#127—31no—
70#4092—61no—
71C2×#687—61no—
72C2×#686—61no—
73#4042—62no—
74#4039—61no—
75#4034—61no—
76C4×D20—31no—
77C4×Dic10C2×D311yescharacteristic
78C5×#102—62no—
79C4×C5×C8C2×D311yescharacteristic
80#3964—61no—
81#3964—61no—
82C4⋊#168—31no—
83C4⋊#168C2×D311yescharacteristic
84#1627—151noSylow
85C22×D15—21no—
86C22×C5×D3—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91D60—21no—
92D60SD1612yescomplemented
93C4×D15—41no—
94C4×D15—41no—
95C2×C5×Dic3—22no—
96C5×D12—42no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C5×D12—41no—
101C5×Dic6—41no—
102C5×Dic6—41no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C3×Dic10—21no—
106C3×Dic10D812yescomplemented
107#1204—44no—
108#1200—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3×#168—41no—
112C2×D3×Q8—101no—
113C3×C4×Q8—51no—
114C2×#215—101no—
115C2×D24—101no—
116#897—101no—
117#897—102no—
118#874C2×D511yescharacteristic
119C4×D12—51no—
120C4×D12—101no—
121#869—101no—
122#869C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×C4×C8C2×D511yescharacteristic
125#821—22no—
126#821—101no—
127#809—101no—
128C4⋊(C3⋊C8)—51no—
129C2×C5×Q8—61no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133Q8×D5—122no—
134Q8×D5—122no—
135C2×D20—31no—
136C2×C4×D5—62no—
137C2×C4×D5—61no—
138C2×Dic10—62no—
139C2×Dic10D1211yescharacteristic
140C2×C5×C8—21no—
141C5×C4⋊C4—32no—
142C5×C4⋊C4—61no—
143C42×C5C22×D311yescharacteristic
144#687—122no—
145#686—122no—
146#685—62no—
147#685—61no—
148C4⋊Dic5—31no—
149C4⋊Dic5D1211yescharacteristic
150#683—21no—
151#683—62no—
152C4×Dic5—21no—
153C2×#168—21no—
154C2×#168—61no—
155D4×Q8—151no—
156#486—31no—
157#460—151no—
158#459—151no—
159#332—151no—
160Q8⋊C8—51no—
161D4⋊C8—151no—
162C22×C3×C5#12011yescharacteristic
163C2×D15—22no—
164C2×D15—41no—
165C2×D15—41no—
166C2×C5×D3—81no—
167C2×C5×D3—81no—
168C2×C5×D3—81no—
169C3×C4×C5—21no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—41no—
175C3×Dic5—22no—
176C3×Dic5—41no—
177C5×Dic3—42no—
178C2×C3×Q8—51no—
179D3×Q8—202no—
180D3×Q8—202no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—51no—
185C2×C4×D3—102no—
186C2×C4×D3—101no—
187C2×Dic6—21no—
188C2×Dic6—102no—
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—101no—
193C3×C42—101no—
194C3×C42C22×D511yescharacteristic
195#215—202no—
196(C2×D3)⋊C4—102no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—21no—
199C4⋊Dic3—51no—
200C4⋊Dic3—102no—
201C4⋊Dic3C22⋊D512yes—
202C2×C3⋊C8—101no—
203D24—202no—
204C23×C5—121no—
205C22×D5—61no—
206C5×Q8—121no—
207C5×Q8—121no—
208C5×D4—122no—
209C5×D4—121no—
210C5×D4—121no—
211C5×D4—121no—
212C5×D4—121no—
213C2×C4×C5—62no—
214C2×C4×C5C2×D1211yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5D3×D411yescharacteristic
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—61no—
220D20—32no—
221D20—61no—
222C4×D5—124no—
223C4×D5—121no—
224C4×D5—121no—
225Dic10—21no—
226Dic10—124no—
227Dic10D2412yescomplemented
228C5×C8—41no—
229#168—41no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—301no—
234C4⋊Q8—31no—
235C4⋊Q8—301no—
236#127—31no—
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8—51no—
240C4×D4—151no—
241C4×D4—301no—
242C4⋊C8—51no—
243C4⋊C8—151no—
244#102—62no—
245#102—301no—
246#102—301no—
247C4×C8D3×D511yescharacteristic
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251D15—42no—
252C5×D3—161no—
253C22×D3—41no—
254C22×D3—101no—
255C3×Q8—52no—
256C3×Q8—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C2×Dic3—22no—
263C2×Dic3—101no—
264D12—42no—
265D12—41no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—52no—
270D12—101no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—41no—
275Dic6—41no—
276Dic6—204no—
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—201no—
280C22×C5—241no—
281C22×C5—241no—
282C22×C5—241no—
283C22×C5#88211yescharacteristic
284C2×D5—62no—
285C2×D5—121no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5—122no—
289C4×C5C2×D2411yescharacteristic
290C4×C5#90811yescharacteristic
291C4×C5D3×SD1611yescharacteristic
292C4×C5#91811yescharacteristic
293Dic5—22no—
294Dic5—41no—
295Dic5—121no—
296C2×Q8—51no—
297C2×Q8—61no—
298C2×Q8—302no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—151no—
305C22×C4—302no—
306C22×C4—301no—
307SD16—602no—
308D8—602no—
309C2×C8—21no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—32no—
313C4⋊C4—51no—
314C4⋊C4—61no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C4⋊C4—302no—
318C22⋊C4—302no—
319C22⋊C4—301no—
320C42—101no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3#408311yescharacteristic
324C2×D3—81no—
325C2×D3—81no—
326C2×D3—81no—
327C2×D3—102no—
328C2×D3—201no—
329C2×D3—201no—
330C3×C4—21no—
331C3×C4—102no—
332C3×C4—201no—
333C3×C4D5×D811yescharacteristic
334C3×C4#405711yescharacteristic
335C3×C4D5×SD1611yescharacteristic
336C3×C4#406111yescharacteristic
337Dic3—42no—
338Dic3—201no—
339C2×C5—481no—
340C2×C5#473211yescharacteristic
341C2×C5#480611yescharacteristic
342C2×C5#482711yescharacteristic
343D5—122no—
344C23—121no—
345C23—301no—
346Q8—52no—
347Q8—101no—
348Q8—121no—
349Q8—121no—
350Q8—604no—
351D4—122no—
352D4—121no—
353D4—121no—
354D4—121no—
355D4—121no—
356D4—152no—
357D4—301no—
358C2×C4—62no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4D5×D1211yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D3×C22⋊D511yescharacteristic
368C8—41no—
369C8—201no—
370C8—601no—
371C2×C3#6535111yescharacteristic
372C2×C3#6544511yescharacteristic
373C2×C3#6545911yescharacteristic
374D3—161no—
375D3—202no—
376C5#6826611yescharacteristic, complemented, Sylow
377C22—241no—
378C22—241no—
379C22—241no—
380C22—302no—
381C22—601no—
382C22—601no—
383C22#9147511yescharacteristic
384C4—21no—
385C4—102no—
386C4—122no—
387C4—201no—
388C4—601no—
389C4D5×D2411yescharacteristic
390C4#9125011yescharacteristic
391C4#9125511yescharacteristic
392C4#9128011yescharacteristic
393C3#1060199811yescharacteristic, complemented, Sylow
394C2—481no—
395C2—602no—
396C2#1174712311yescharacteristic
397C2#1174790111yescharacteristic
398C2#1174811611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11747045C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1627
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
1. #11752539C2semidirect
2. C5×#4694C2semidirect
3. #11747060C2semidirect
5. #11746280C2semidirect
6. C3×#64676C2semidirect
7. #11745857C2semidirect
33. #64676D3semidirect
63. #4694D5semidirect
92. D60SD16semidirect
106. C3×Dic10D8semidirect
227. Dic10D24semidirect
322. C3×C5#1627semidirect
376. C5#68266semidirect
393. C3#10601998semidirect

Maximal subgroups

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

subgroupindex
#117525392
C5×#46942
#117470602
#117470452
#117462802
C3×#646762
#117458572
#106019983
#682665