Finite Group Databasebeta

← #14289042

Subgroups — #14289042

Order 1920.

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

normal subgroups only

This group has 456 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#11752472C211yesmaximal, characteristic, complemented
2C5×#4848C211yesmaximal, characteristic
3#11747086C211yesmaximal, characteristic
4#11747081C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10601826—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C2×C5×#204—21no—
11C5×#874C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91470—21no—
15#91469—21no—
16#91344—21no—
17#91340—21no—
18#91327—22no—
19C2×#6659—21no—
20C2×#6656—22no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×#821—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90967—21no—
26#68504—51nomaximal, Hall
27Q8×Dic10—31no—
28C5×#460—31no—
29#65365—31no—
30#65364—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64701D311yescharacteristic, complemented
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10D412yes—
40C2×#1204—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C4×C5×Dic3—21no—
50C5×#204—42no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6669—22no—
56Dic3×Dic5—22no—
57#6659—42no—
58#6656—44no—
59#5722—51no—
60#5085—51no—
61#4848—51no—
62#4848D511yescharacteristic
63C3×#333—51no—
64#4484—51no—
65#4484—51no—
66C2×C5×SD16—61no—
67C5×#127—31no—
68C4×C5×Q8—31no—
69Q8×Dic5—61no—
70C2×#687—61no—
71C2×#687—62no—
72#4034—61no—
73#4034—62no—
74#4015—61no—
75#4015C2×D311yescharacteristic
76C4×Dic10—31no—
77C4×Dic10—61no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—61no—
80#3964—61no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1623—151noSylow
84C22×C5×D3—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90Dic30—21no—
91Dic30SD1612yescomplemented
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C5×D12—42no—
95C5×D12—41no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×Dic6—21no—
100C5×Dic6SD1612yescomplemented
101C2×C3×Dic5—22no—
102C3×Dic10—42no—
103#1204—82no—
104C3×C5×C8—41no—
105C3⋊#168—22no—
106C3×#168—41no—
107C3×C4⋊Q8—51no—
108#944—102no—
109C2×#215—102no—
110C2×#204—21no—
111C2×#204—101no—
112#888—101no—
113#888—101no—
114#887—101no—
115#887—101no—
116#874C2×D511yescharacteristic
117C4×Dic6—51no—
118C4×Dic6C2×D511yescharacteristic
119C3×C4⋊C8—51no—
120C3×C4⋊C8C2×D511yescharacteristic
121#821—21no—
122#821—101no—
123C4×C3⋊C8—51no—
124C2×C5×Q8—31no—
125C2×C5×D4—61no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C2×Dic10—31no—
129C2×Dic10—62no—
130C2×Dic10D1212yes—
131C5×SD16—122no—
132C2×C5×C8—21no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—61no—
135C42×C5—61no—
136C42×C5C22×D311yescharacteristic
137#687—122no—
138#687—124no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4⋊Dic5—62no—
143#683—62no—
144#683—61no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—21no—
148C2×#168—61no—
149Q82—151no—
150#492—151no—
151#460—31no—
152#460—151no—
153#333—51no—
154Q8⋊C8—151no—
155Q8⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—81no—
158C2×C5×D3—81no—
159C2×C5×D3—81no—
160C3×C4×C5—21no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5C2×SD1611yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—22no—
166Dic15—41no—
167C3×Dic5—42no—
168C5×Dic3—22no—
169C5×Dic3—41no—
170C2×C3×Q8—52no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×Dic6—51no—
175C2×Dic6—102no—
176C2×Dic6C22⋊D511yescharacteristic
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C42C22×D511yescharacteristic
182#215—204no—
183C4⋊Dic3—51no—
184C4⋊Dic3C22⋊D511yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—102no—
187Dic3⋊C4—102no—
188Dic3⋊C4—101no—
189C4×Dic3—21no—
190C4×Dic3—102no—
191C4×Dic3—101no—
192C2×C3⋊C8—101no—
193#204—42no—
194#204—202no—
195C23×C5—121no—
196C5×Q8—32no—
197C5×Q8—61no—
198C5×D4—122no—
199C5×D4—121no—
200C5×D4—121no—
201C5×D4—121no—
202C5×D4—121no—
203C2×C4×C5—61no—
204C2×C4×C5—61no—
205C2×C4×C5C2×D1211yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×Dic5—22no—
209C2×Dic5—61no—
210C2×Dic5—61no—
211Dic10—32no—
212Dic10—42no—
213Dic10—61no—
214Dic10—242no—
215C5×C8—41no—
216#168—41no—
217#168—62no—
218C2×SD16—61no—
219C2×SD16—301no—
220C2×SD16—302no—
221C4⋊Q8—51no—
222C4⋊Q8—301no—
223C4⋊Q8—301no—
224C4⋊Q8—302no—
225#127—31no—
226C4×Q8—31no—
227C4×Q8—151no—
228C4×Q8—301no—
229C4×Q8—301no—
230C4⋊C8—51no—
231C4⋊C8D3×D511yescharacteristic
232#102—61no—
233#102—301no—
234C4×C8—151no—
235C2×C3×C5#44811yescharacteristic
236C2×C3×C5#44811yescharacteristic
237C2×C3×C5#45311yescharacteristic
238C5×D3—161no—
239C22×D3—41no—
240C3×Q8—202no—
241C2×C3×C4—102no—
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—101no—
248C2×Dic3—101no—
249D12—42no—
250D12—41no—
251D12—41no—
252D12—41no—
253D12—41no—
254Dic6—21no—
255Dic6—52no—
256Dic6—101no—
257Dic6—402no—
258Dic6#68712yescomplemented
259C3×C8—41no—
260C3×C8—201no—
261C3⋊C8—102no—
262C22×C5—241no—
263C22×C5—241no—
264C22×C5—241no—
265C22×C5#88211yescharacteristic
266C4×C5—21no—
267C4×C5—62no—
268C4×C5—121no—
269C4×C5D3×SD1611yescharacteristic
270C4×C5D3×SD1611yescharacteristic
271C4×C5#91811yescharacteristic
272C4×C5#91811yescharacteristic
273Dic5—42no—
274Dic5—62no—
275Dic5—121no—
276C2×Q8—31no—
277C2×Q8—52no—
278C2×Q8—151no—
279C2×Q8—302no—
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—61no—
283SD16—122no—
284SD16—602no—
285SD16—604no—
286C2×C8—21no—
287C2×C8—101no—
288C2×C8—301no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—101no—
292C4⋊C4—101no—
293C4⋊C4—151no—
294C4⋊C4—302no—
295C4⋊C4—302no—
296C4⋊C4—301no—
297C42—61no—
298C42—302no—
299C42—301no—
300C42C2×D3×D511yescharacteristic
301C3×C5#162311yescharacteristic, complemented, Hall
302C22×C3#408311yescharacteristic
303C2×D3—81no—
304C2×D3—81no—
305C2×D3—81no—
306C3×C4—21no—
307C3×C4—202no—
308C3×C4D5×SD1611yescharacteristic
309C3×C4#406111yescharacteristic
310C3×C4C2×#68711yescharacteristic
311C3×C4#409711yescharacteristic
312Dic3—22no—
313Dic3—41no—
314Dic3—102no—
315Dic3—201no—
316C2×C5—481no—
317C2×C5#474711yescharacteristic
318C2×C5#480611yescharacteristic
319C2×C5#480611yescharacteristic
320C23—121no—
321Q8—32no—
322Q8—61no—
323Q8—152no—
324Q8—202no—
325Q8—301no—
326Q8—1202no—
327D4—122no—
328D4—121no—
329D4—121no—
330D4—121no—
331D4—121no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—102no—
335C2×C4—301no—
336C2×C4—301no—
337C2×C4D5×D1211yescharacteristic
338C2×C4#677711yescharacteristic
339C2×C4D3×C22⋊D511yescharacteristic
340C8—41no—
341C8—201no—
342C8—302no—
343C2×C3#6532911yescharacteristic
344C2×C3#6545911yescharacteristic
345C2×C3#6548711yescharacteristic
346D3—161no—
347C5#6850411yescharacteristic, complemented, Sylow
348C22—241no—
349C22—241no—
350C22—241no—
351C22#9147511yescharacteristic
352C4—21no—
353C4—62no—
354C4—121no—
355C4—202no—
356C4—302no—
357C4—601no—
358C4#9125511yescharacteristic
359C4#9128011yescharacteristic
360C4D3×#68711yescharacteristic
361C4#9151011yescharacteristic
362C3#1060182611yescharacteristic, complemented, Sylow
363C2—481no—
364C2#1174749411yescharacteristic
365C2#1174790111yescharacteristic
366C2#1174824611yescharacteristic
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#1623
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. #11752472C2semidirect
5. #11746305C2semidirect
6. C3×#64701C2semidirect
7. #11745842C2semidirect
33. #64701D3semidirect
91. Dic30SD16semidirect
100. C5×Dic6SD16semidirect
258. Dic6#687semidirect
301. C3×C5#1623semidirect
347. C5#68504semidirect
362. C3#10601826semidirect

Maximal subgroups

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

subgroupindex
#117524722
C5×#48482
#117470862
#117470812
#117463052
C3×#647012
#117458422
#106018263
#685045