Finite Group Databasebeta

← #14289259

Subgroups — #14289259

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
1Dic6×D20C211yesmaximal, characteristic, complemented
2C5×#4848C211yesmaximal, characteristic, complemented
3#11747026C211yesmaximal, characteristic
4#11746906C211yesmaximal, characteristic, complemented
5#11746303C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745843C211yesmaximal, characteristic, complemented
8#10601828—31nomaximal, Hall
9C2×D5×Dic6—21no—
10#91758C2211yescharacteristic
11C2×C5×#204—21no—
12C5×#874C2211yescharacteristic
13C4×C5×Dic6C2211yescharacteristic
14C3×C4×D20C2211yescharacteristic
15#91469—21no—
16Dic3×D20—21no—
17#91422—22no—
18#91360—21no—
19C2×#6652—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#821—21no—
23C3×C4×#168C2211yescharacteristic
24#90967—22no—
25#90966—21no—
26#68187—51nomaximal, Hall
27Q8×D20—31no—
28C5×#460—31no—
29#65361—31no—
30#65359—31no—
31Q8⋊#168—31no—
32#64703D311yescharacteristic, complemented
33#64702—31no—
34C2×Dic30—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×#1204—22no—
42C2×D5×Dic3—22no—
43D5×Dic6—42no—
44D5×Dic6—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15—21no—
48C4⋊Dic15D412yes—
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C5×#204—42no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C2×C3×#168—21no—
57Dic3⋊Dic5—22no—
58#6665—22no—
59#6652—42no—
60D4×Dic6—51no—
61#5015—51no—
62#4848D511yescharacteristic, complemented
63#4694—51no—
64C3×D4⋊C8—51no—
65#4482—51no—
66#4456—51no—
67C2×Q8×D5—61no—
68C2×C5×SD16—61no—
69C5×#127—31no—
70C4×C5×Q8—31no—
71C2×#686—61no—
72#4043—62no—
73#4043—61no—
74C4×D20—61no—
75C4×D20C2×D311yescharacteristic
76#4015—31no—
77#4015—61no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—61no—
80#3964—62no—
81#3964—61no—
82C4⋊#168—31no—
83C4×#168C2×D311yescharacteristic
84#1627—151noSylow
85C22×C5×D3—41no—
86C22×C3×D5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—22no—
91Dic30—41no—
92Dic30—41no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—42no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C5×Dic6—21no—
101C5×Dic6D812yescomplemented
102C2×C3×Dic5—21no—
103C3×D20—21no—
104C3×D20SD1612yescomplemented
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107#1204—44no—
108D5×Dic3—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3×#168—41no—
112C22×Dic6—101no—
113C3×C4×D4—51no—
114D4×Dic3—101no—
115C2×#213—101no—
116#924—101no—
117C2×#204—21no—
118#888—101no—
119#878—102no—
120#874C2×D511yescharacteristic
121#869—51no—
122C4×Dic6C2×D511yescharacteristic
123C3×C4⋊C8C2×D511yescharacteristic
124C3×C4×C8—51no—
125#821—21no—
126#821—102no—
127#809—101no—
128C4⋊(C3⋊C8)—51no—
129C2×C5×Q8—31no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133Q8×D5—122no—
134Q8×D5—122no—
135C2×D20D1211yescharacteristic
136C2×C4×D5—21no—
137C2×C4×D5—62no—
138C2×Dic10—62no—
139C2×Dic10—61no—
140C5×SD16—122no—
141C2×C5×C8—21no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—61no—
144C42×C5—61no—
145C42×C5C22×D311yescharacteristic
146#686—122no—
147#685—21no—
148#685—62no—
149C4⋊Dic5—32no—
150C4⋊Dic5—62no—
151C4⋊Dic5—61no—
152C4⋊Dic5D1211yescharacteristic
153C2×#168—21no—
154C2×#168—61no—
155D4×Q8—151no—
156#486—151no—
157#460—31no—
158#459—151no—
159#332—151no—
160Q8⋊C8—151no—
161D4⋊C8—51no—
162C22×C3×C5#12011yescharacteristic
163C2×C5×D3—81no—
164C2×C5×D3—81no—
165C2×C5×D3—81no—
166C2×C3×D5—22no—
167C2×C3×D5—41no—
168C2×C3×D5—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—41no—
176C5×Dic3—22no—
177C5×Dic3—41no—
178C2×C3×D4—51no—
179C22×C3×C4—101no—
180C22×Dic3—102no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×Dic6—102no—
185C2×Dic6—101no—
186C2×Dic6—202no—
187C2×Dic6—202no—
188C2×Dic6C22⋊D511yescharacteristic
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C3×C4⋊C4—51no—
192C3×C22⋊C4—101no—
193C3×C42C22×D511yescharacteristic
194#217—102no—
195#213—202no—
196C4⋊Dic3—52no—
197C4⋊Dic3—101no—
198C4⋊Dic3C22⋊D511yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—102no—
201C4×Dic3—21no—
202C2×C3⋊C8—101no—
203#204—42no—
204C23×C5—121no—
205C22×D5—21no—
206C5×Q8—32no—
207C5×Q8—61no—
208C5×D4—122no—
209C5×D4—121no—
210C5×D4—121no—
211C5×D4—121no—
212C5×D4—121no—
213C2×C4×C5—61no—
214C2×C4×C5—61no—
215C2×C4×C5C2×D1211yescharacteristic
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×Dic5—21no—
219C2×Dic5—62no—
220D20—21no—
221D20#20412yescomplemented
222C4×D5—41no—
223C4×D5—41no—
224C4×D5—124no—
225Dic10—124no—
226Dic10—121no—
227Dic10—121no—
228C5×C8—41no—
229#168—41no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—61no—
233C2×D8—301no—
234C4⋊Q8—151no—
235C4⋊Q8—301no—
236#127—31no—
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8—31no—
240C4×D4—51no—
241C4×D4—301no—
242C4⋊C8—151no—
243C4⋊C8D3×D511yescharacteristic
244#102—61no—
245#102—301no—
246#102—302no—
247C4×C8—51no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251C3×D5—42no—
252C5×D3—161no—
253C23×C3—101no—
254C22×D3—41no—
255C3×D4—52no—
256C3×D4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—201no—
259C2×C3×C4—201no—
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—102no—
266C2×Dic3—204no—
267D12—42no—
268D12—41no—
269D12—41no—
270D12—41no—
271D12—41no—
272Dic6—21no—
273Dic6—204no—
274Dic6—201no—
275Dic6—201no—
276Dic6#68612yescomplemented
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—201no—
280C22×C5—241no—
281C22×C5—241no—
282C22×C5—241no—
283C22×C5#88211yescharacteristic
284C2×D5—22no—
285C2×D5—41no—
286C2×D5—41no—
287C4×C5—21no—
288C4×C5—62no—
289C4×C5—121no—
290C4×C5C2×#20411yescharacteristic
291C4×C5#90911yescharacteristic
292C4×C5D3×D811yescharacteristic
293C4×C5#91411yescharacteristic
294Dic5—41no—
295Dic5—122no—
296C2×Q8—31no—
297C2×Q8—302no—
298C2×Q8—301no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—51no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C22×C4—101no—
306C22×C4—302no—
307SD16—122no—
308D8—602no—
309C2×C8—21no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—51no—
314C4⋊C4—61no—
315C4⋊C4—152no—
316C4⋊C4—302no—
317C4⋊C4—301no—
318C22⋊C4—101no—
319C22⋊C4—302no—
320C42—61no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3—102no—
324C22×C3—201no—
325C22×C3—201no—
326C22×C3#408311yescharacteristic
327C2×D3—81no—
328C2×D3—81no—
329C2×D3—81no—
330C3×C4—21no—
331C3×C4—201no—
332C3×C4D5×SD1611yescharacteristic
333C3×C4#406111yescharacteristic
334C3×C4C2×#68611yescharacteristic
335C3×C4#409511yescharacteristic
336Dic3—22no—
337Dic3—41no—
338Dic3—202no—
339C2×C5—481no—
340C2×C5#473811yescharacteristic
341C2×C5#477311yescharacteristic
342C2×C5#482711yescharacteristic
343D5—42no—
344C23—101no—
345C23—121no—
346Q8—32no—
347Q8—61no—
348Q8—604no—
349Q8—601no—
350Q8—601no—
351D4—52no—
352D4—101no—
353D4—122no—
354D4—121no—
355D4—121no—
356D4—121no—
357D4—121no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—101no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—302no—
364C2×C4—604no—
365C2×C4D5×D1211yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D3×C22⋊D511yescharacteristic
368C8—41no—
369C8—201no—
370C8—601no—
371C2×C3—202no—
372C2×C3#6532511yescharacteristic
373C2×C3#6545911yescharacteristic
374C2×C3#6549011yescharacteristic
375D3—161no—
376C5#6818711yescharacteristic, complemented, Sylow
377C22—102no—
378C22—201no—
379C22—201no—
380C22—241no—
381C22—241no—
382C22—241no—
383C22#9147511yescharacteristic
384C4—21no—
385C4—62no—
386C4—121no—
387C4—201no—
388C4—602no—
389C4D5×#20411yescharacteristic
390C4#9126011yescharacteristic
391C4D3×#68611yescharacteristic
392C4#9150411yescharacteristic
393C3#1060182811yescharacteristic, complemented, Sylow
394C2—202no—
395C2—481no—
396C2#1174748211yescharacteristic
397C2#1174812711yescharacteristic
398C2#1174825611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11747026C2
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. Dic6×D20C2semidirect
2. C5×#4848C2semidirect
4. #11746906C2semidirect
5. #11746303C2semidirect
6. C3×#64703C2semidirect
7. #11745843C2semidirect
32. #64703D3semidirect
62. #4848D5semidirect
101. C5×Dic6D8semidirect
104. C3×D20SD16semidirect
221. D20#204semidirect
276. Dic6#686semidirect
322. C3×C5#1627semidirect
376. C5#68187semidirect
393. C3#10601828semidirect

Maximal subgroups

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

subgroupindex
Dic6×D202
C5×#48482
#117470262
#117469062
#117463032
C3×#647032
#117458432
#106018283
#681875