Finite Group Databasebeta

← #14289209

Subgroups — #14289209

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#11752482C211yesmaximal, characteristic, complemented
2C5×#4848C211yesmaximal, characteristic
3#11747086C211yesmaximal, characteristic
4#11746901C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10601823—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C2×C5×#204—21no—
11C5×#874C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91389—21no—
15#91384—21no—
16#91346—22no—
17#91344—21no—
18Dic3×Dic10—21no—
19C2×#6659—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×#821—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90967—21no—
25#90966—22no—
26#68456—51nomaximal, Hall
27#65904—31no—
28C5×#460—31no—
29#65364—31no—
30#65359—31no—
31Q8⋊#168—31no—
32#64706D311yescharacteristic, complemented
33#64704—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10—21no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C5×#204—42no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D412yes—
52C2×C3×#168—21no—
53Dic3⋊Dic5—22no—
54Dic3⋊Dic5—22no—
55#6668—22no—
56Dic3×Dic5—22no—
57#6659—42no—
58#5721—51no—
59#5088—51no—
60#4848—51no—
61#4848D511yescharacteristic
62C3×#332—51no—
63#4484—51no—
64#4484—51no—
65C2×C5×SD16—61no—
66C5×#127—31no—
67C4×C5×Q8—31no—
68Q8×Dic5—61no—
69C2×#687—61no—
70#4036—61no—
71#4036—62no—
72#4015—61no—
73#4015C2×D311yescharacteristic
74C4×Dic10—31no—
75C4×Dic10—61no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#102—61no—
78#3964—61no—
79#3964—62no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1626—151noSylow
83C22×C5×D3—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89Dic30—21no—
90Dic30—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×D12—42no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C5×D12—41no—
98C5×Dic6—21no—
99C5×Dic6SD1612yescomplemented
100C2×C3×Dic5—22no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C3×C4⋊Q8—51no—
107Q8×Dic3—101no—
108#944—101no—
109C2×#204—21no—
110C2×#204—101no—
111#890—101no—
112#889—102no—
113#887—101no—
114#874C2×D511yescharacteristic
115C4×Dic6—51no—
116C4×Dic6C2×D511yescharacteristic
117C3×C4⋊C8—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119#821—21no—
120#821—101no—
121#809—102no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—31no—
124C2×C5×D4—61no—
125C2×C5×D4—61no—
126C2×C5×D4—61no—
127C2×Dic10—21no—
128C2×Dic10—31no—
129C5×SD16—122no—
130C2×C5×C8—21no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#687—122no—
136C4⋊Dic5—21no—
137C4⋊Dic5—31no—
138C4⋊Dic5—62no—
139C4⋊Dic5—62no—
140C4⋊Dic5D1212yes—
141#683—62no—
142#683—61no—
143C4×Dic5—62no—
144C4×Dic5—61no—
145C2×#168—21no—
146C2×#168—61no—
147#557—151no—
148#486—151no—
149#460—31no—
150#460—151no—
151#332—51no—
152Q8⋊C8—151no—
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×C5C2×SD1611yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—41no—
164Dic15—41no—
165C3×Dic5—42no—
166C5×Dic3—22no—
167C5×Dic3—41no—
168C2×C3×Q8—101no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×Dic6—51no—
173C2×Dic6C22⋊D511yescharacteristic
174C2×C3×C8—21no—
175C2×C3×C8—101no—
176C3×C4⋊C4—52no—
177C3×C4⋊C4—101no—
178C3×C42C22×D511yescharacteristic
179C4⋊Dic3—51no—
180C4⋊Dic3—102no—
181C4⋊Dic3C22⋊D511yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185Dic3⋊C4—101no—
186C4×Dic3—21no—
187C4×Dic3—102no—
188C4×Dic3—101no—
189C2×C3⋊C8—101no—
190#204—42no—
191#204—202no—
192C23×C5—121no—
193C5×Q8—32no—
194C5×Q8—61no—
195C5×D4—122no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—121no—
199C5×D4—121no—
200C2×C4×C5—61no—
201C2×C4×C5—61no—
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×Dic5—22no—
206C2×Dic5—61no—
207C2×Dic5—61no—
208Dic10—41no—
209Dic10—41no—
210Dic10—61no—
211Dic10—61no—
212C5×C8—41no—
213#168—41no—
214#168—121no—
215C2×SD16—61no—
216C2×SD16—301no—
217C4⋊Q8—51no—
218C4⋊Q8—301no—
219#127—31no—
220#125—301no—
221#125—302no—
222C4×Q8—31no—
223C4×Q8—151no—
224C4×Q8—301no—
225C4×Q8—301no—
226C4⋊C8—51no—
227C4⋊C8D3×D511yescharacteristic
228#102—61no—
229#102—302no—
230#102—301no—
231C4×C8—151no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—161no—
236C22×D3—41no—
237C3×Q8—201no—
238C3×Q8—201no—
239C2×C3×C4—102no—
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—101no—
246C2×Dic3—101no—
247D12—42no—
248D12—41no—
249D12—41no—
250D12—41no—
251D12—41no—
252Dic6—21no—
253Dic6—101no—
254Dic6—101no—
255Dic6#68712yescomplemented
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—201no—
259C22×C5—241no—
260C22×C5—241no—
261C22×C5—241no—
262C22×C5#88211yescharacteristic
263C4×C5—21no—
264C4×C5—62no—
265C4×C5—121no—
266C4×C5#91111yescharacteristic
267C4×C5D3×SD1611yescharacteristic
268C4×C5#91611yescharacteristic
269C4×C5#91811yescharacteristic
270Dic5—42no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—31no—
274C2×Q8—101no—
275C2×Q8—151no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279SD16—122no—
280SD16—602no—
281C2×C8—21no—
282C2×C8—101no—
283C2×C8—301no—
284C4⋊C4—31no—
285C4⋊C4—52no—
286C4⋊C4—61no—
287C4⋊C4—101no—
288C4⋊C4—151no—
289C4⋊C4—302no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C42—61no—
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—202no—
304C3×C4#406011yescharacteristic
305C3×C4#406211yescharacteristic
306C3×C4C2×#68711yescharacteristic
307C3×C4#409711yescharacteristic
308Dic3—22no—
309Dic3—41no—
310Dic3—201no—
311Dic3—201no—
312C2×C5—481no—
313C2×C5#475311yescharacteristic
314C2×C5#478111yescharacteristic
315C2×C5#480611yescharacteristic
316C23—121no—
317Q8—32no—
318Q8—61no—
319Q8—201no—
320Q8—201no—
321Q8—301no—
322Q8—301no—
323D4—122no—
324D4—121no—
325D4—121no—
326D4—121no—
327D4—121no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—102no—
331C2×C4—301no—
332C2×C4—301no—
333C2×C4D5×D1211yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—41no—
337C8—201no—
338C8—601no—
339C2×C3#6532911yescharacteristic
340C2×C3#6546111yescharacteristic
341C2×C3#6549011yescharacteristic
342D3—161no—
343C5#6845611yescharacteristic, complemented, Sylow
344C22—241no—
345C22—241no—
346C22—241no—
347C22#9147511yescharacteristic
348C4—21no—
349C4—62no—
350C4—121no—
351C4—202no—
352C4—601no—
353C4—601no—
354C4#9125811yescharacteristic
355C4#9127611yescharacteristic
356C4D3×#68711yescharacteristic
357C4#9151011yescharacteristic
358C3#1060182311yescharacteristic, complemented, Sylow
359C2—481no—
360C2#1174749411yescharacteristic
361C2#1174815311yescharacteristic
362C2#1174825911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1626
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. #11752482C2semidirect
5. #11746305C2semidirect
6. C3×#64706C2semidirect
7. #11745842C2semidirect
32. #64706D3semidirect
99. C5×Dic6SD16semidirect
255. Dic6#687semidirect
297. C3×C5#1626semidirect
343. C5#68456semidirect
358. C3#10601823semidirect

Maximal subgroups

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

subgroupindex
#117524822
C5×#48482
#117470862
#117469012
#117463052
C3×#647062
#117458422
#106018233
#684565