Finite Group Databasebeta

← #14289255

Subgroups — #14289255

Order 1920.

500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D12×Dic10C211yesmaximal, characteristic, complemented
2#11750795C211yesmaximal, characteristic, complemented
3#11747064C211yesmaximal, characteristic, complemented
4#11747037C211yesmaximal, characteristic
5C5×#4459C211yesmaximal, characteristic, complemented
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10598980—31nomaximal, Hall
9C2×D3×Dic10—21no—
10#91763C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91468—21no—
15#91417—22no—
16Dic5×D12—21no—
17#91365—21no—
18C2×#6658—21no—
19C2×#6654—21no—
20C3×C4×C5×C8C2211yescharacteristic
21#91105—22no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90969—21no—
25#90968—21no—
26#68266—51nomaximal, Hall
27D4×Dic10—31no—
28#65304—31no—
29#65137—31no—
30#64983—31no—
31C5×D4⋊C8—31no—
32#64702—31no—
33#64676D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30—21no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×#1204—22no—
42C2×D3×Dic5—22no—
43D3×Dic10—42no—
44D3×Dic10—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15—21no—
48C4⋊Dic15D412yes—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56#6668—22no—
57(C2×D3)⋊Dic5—22no—
58#6658—42no—
59#6654—42no—
60Q8×D12—51no—
61#5027—51no—
62#4843—51no—
63#4694—51no—
64C3×Q8⋊C8—51no—
65#4486—51no—
66#4459D511yescharacteristic, complemented
67C22×Dic10—61no—
68C4×C5×D4—31no—
69D4×Dic5—61no—
70C2×#686—61no—
71#4070—61no—
72C2×#677—61no—
73#4034—61no—
74#4024—62no—
75#4020—31no—
76#4015—31no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8C2×D311yescharacteristic
80#3953—62no—
81#3953—61no—
82#3941—61no—
83C4⋊#168C2×D311yescharacteristic
84#1627—151noSylow
85C22×D15—41no—
86C22×C5×D3—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—22no—
91D60—42no—
92D60—41no—
93D60—41no—
94D60—41no—
95D60—41no—
96Dic30—41no—
97Dic30—41no—
98C2×C5×Dic3—21no—
99C5×D12—21no—
100C5×D12SD1612yescomplemented
101C4×C5×D3—41no—
102C4×C5×D3—41no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C3×Dic10—21no—
106C3×Dic10D812yescomplemented
107#1204—44no—
108D3×Dic5—44no—
109C3×C5×C8—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C2×D3×Q8—101no—
113C3×C4×Q8—51no—
114C2×#215—101no—
115C2×D24—101no—
116#897—102no—
117#897—101no—
118#874—51no—
119C4×D12—101no—
120C4×D12C2×D511yescharacteristic
121#869—51no—
122#869—101no—
123C3×C4⋊C8—51no—
124C3×C4×C8C2×D511yescharacteristic
125#821—102no—
126#821—101no—
127#809—101no—
128C4⋊(C3⋊C8)C2×D511yescharacteristic
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C22×Dic5—62no—
132C2×D20—61no—
133C2×D20—61no—
134C2×D20—61no—
135C2×Dic10—62no—
136C2×Dic10—61no—
137C2×Dic10—122no—
138C2×Dic10—122no—
139C2×Dic10D1211yescharacteristic
140C2×C5×C8—21no—
141C2×C5×C8—61no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—61no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#686—122no—
147C4⋊Dic5—32no—
148C4⋊Dic5—61no—
149C4⋊Dic5D1211yescharacteristic
150#683—21no—
151#683—62no—
152C4×Dic5—21no—
153C2×#168—21no—
154#677—122no—
155D4×Q8—151no—
156#486—151no—
157#460—151no—
158#459—151no—
159#332—151no—
160Q8⋊C8—51no—
161D4⋊C8—31no—
162C22×C3×C5#12011yescharacteristic
163C2×D15—81no—
164C2×D15—81no—
165C2×D15—81no—
166C2×C5×D3—22no—
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C3×C4×C5—21no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—42no—
175C3×Dic5—22no—
176C3×Dic5—41no—
177C5×Dic3—41no—
178C2×C3×Q8—51no—
179D3×Q8—202no—
180D3×Q8—202no—
181C2×D12—101no—
182C2×D12—101no—
183C2×D12—101no—
184C2×D12D2011yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—102no—
187C2×Dic6—102no—
188C2×Dic6—101no—
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—21no—
197(C2×D3)⋊C4—102no—
198C4⋊Dic3—52no—
199C4⋊Dic3—102no—
200C4⋊Dic3—101no—
201C4⋊Dic3D2011yescharacteristic
202C2×C3⋊C8—21no—
203D24—202no—
204C23×C5—61no—
205C22×D5—121no—
206C5×D4—32no—
207C5×D4—61no—
208C2×C4×C5—61no—
209C2×C4×C5—121no—
210C2×C4×C5—121no—
211C2×C4×C5C2×D1211yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×Dic5—21no—
215C2×Dic5—21no—
216C2×Dic5—62no—
217C2×Dic5—124no—
218D20—122no—
219D20—121no—
220D20—121no—
221D20—121no—
222D20—121no—
223Dic10—21no—
224Dic10—124no—
225Dic10—121no—
226Dic10—121no—
227Dic10D2412yescomplemented
228C5×C8—41no—
229C5×C8—121no—
230#168—41no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—301no—
234C4⋊Q8—151no—
235C4⋊Q8—301no—
236#127—151no—
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8—51no—
240C4×D4—31no—
241C4×D4—301no—
242C4⋊C8—31no—
243C4⋊C8—51no—
244#102—301no—
245#102—301no—
246#102—302no—
247C4×C8D3×D511yescharacteristic
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251D15—161no—
252C5×D3—42no—
253C22×D3—21no—
254C22×D3—201no—
255C3×Q8—52no—
256C3×Q8—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4C2×D2011yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×Dic3—21no—
263C2×Dic3—102no—
264D12—21no—
265D12—202no—
266D12—201no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12#67712yescomplemented
271C4×D3—41no—
272C4×D3—41no—
273C4×D3—204no—
274Dic6—204no—
275Dic6—201no—
276Dic6—201no—
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—41no—
280C22×C5—62no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5#88211yescharacteristic
284C2×D5—241no—
285C2×D5—241no—
286C2×D5—241no—
287C4×C5—21no—
288C4×C5—121no—
289C4×C5C2×D2411yescharacteristic
290C4×C5#90811yescharacteristic
291C4×C5D3×SD1611yescharacteristic
292C4×C5#91811yescharacteristic
293Dic5—22no—
294Dic5—41no—
295Dic5—122no—
296C2×Q8—51no—
297C2×Q8—302no—
298C2×Q8—301no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—31no—
302C2×D4—301no—
303C2×D4—301no—
304C2×D4—301no—
305C22×C4—61no—
306C22×C4—302no—
307SD16—602no—
308D8—602no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—101no—
312C4⋊C4—31no—
313C4⋊C4—51no—
314C4⋊C4—101no—
315C4⋊C4—152no—
316C4⋊C4—302no—
317C4⋊C4—301no—
318C22⋊C4—61no—
319C22⋊C4—302no—
320C42—101no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3#402811yescharacteristic
324C2×D3—22no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—401no—
328C2×D3—401no—
329C2×D3—401no—
330C3×C4—21no—
331C3×C4—102no—
332C3×C4—201no—
333C3×C4C2×#67711yescharacteristic
334C3×C4#405511yescharacteristic
335C3×C4D5×D811yescharacteristic
336C3×C4#406011yescharacteristic
337Dic3—41no—
338Dic3—202no—
339C2×C5—122no—
340C2×C5#473211yescharacteristic
341C2×C5#480611yescharacteristic
342C2×C5#482711yescharacteristic
343D5—481no—
344C23—61no—
345C23—601no—
346Q8—52no—
347Q8—101no—
348Q8—604no—
349Q8—601no—
350Q8—601no—
351D4—32no—
352D4—61no—
353D4—602no—
354D4—601no—
355D4—601no—
356D4—601no—
357D4—601no—
358C2×C4—61no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4—302no—
364C2×C4—604no—
365C2×C4D5×D1211yescharacteristic
366C2×C4D3×D2011yescharacteristic
367C2×C4#679011yescharacteristic
368C8—41no—
369C8—121no—
370C8—201no—
371C2×C3#6502711yescharacteristic
372C2×C3#6506211yescharacteristic
373C2×C3#6511611yescharacteristic
374D3—42no—
375D3—801no—
376C5#6826611yescharacteristic, complemented, Sylow
377C22—62no—
378C22—121no—
379C22—121no—
380C22—1201no—
381C22—1201no—
382C22—1201no—
383C22#9147611yescharacteristic
384C4—21no—
385C4—102no—
386C4—121no—
387C4—201no—
388C4—602no—
389C4D5×D2411yescharacteristic
390C4#9124911yescharacteristic
391C4D3×#67711yescharacteristic
392C4#9126311yescharacteristic
393C3#1059898011yescharacteristic, complemented, Sylow
394C2—122no—
395C2—2401no—
396C2#1174712511yescharacteristic
397C2#1174811711yescharacteristic
398C2#1174813211yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11747037C2
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. D12×Dic10C2semidirect
2. #11750795C2semidirect
3. #11747064C2semidirect
5. C5×#4459C2semidirect
6. C3×#64676C2semidirect
7. #11745859C2semidirect
33. #64676D3semidirect
66. #4459D5semidirect
100. C5×D12SD16semidirect
106. C3×Dic10D8semidirect
227. Dic10D24semidirect
270. D12#677semidirect
322. C3×C5#1627semidirect
376. C5#68266semidirect
393. C3#10598980semidirect

Maximal subgroups

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

subgroupindex
D12×Dic102
#117507952
#117470642
#117470372
C5×#44592
C3×#646762
#117458592
#105989803
#682665