Finite Group Databasebeta

← #14289775

Subgroups — #14289775

Order 1920.

456 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C5×#5727C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11746961C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602708—31nomaximal, Hall
9C2×C5×D3×Q8—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91758C2211yescharacteristic
12C5×#946—21no—
13C5×#896—22no—
14C5×#893—21no—
15C5×#888—21no—
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18#91094—22no—
19C4×C3⋊#168C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90985—21no—
24#90973—21no—
25#90967—21no—
26#68459—51nomaximal, Hall
27C5×D4×Q8—31no—
28#65382—31no—
29#65310—31no—
30#65297—31no—
31#64767D311yescharacteristic, complemented
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C5×D3×Q8—42no—
37C5×D3×Q8—42no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—22no—
40C2×C4×C5×D3—21no—
41C2×C5×Dic6—22no—
42C2×C5×Dic6D411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D412yes—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—22no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—22no—
54C5×Dic3⋊C4—21no—
55C4×C5×Dic3—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58#5727D511yescharacteristic
59#5093—51no—
60#4850—51no—
61#4842—51no—
62C3×#332—51no—
63#4484—51no—
64#4483—51no—
65C22×C5×Q8—61no—
66C5×C4⋊Q8—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×C22⋊Q8—61no—
69C5×C22⋊Q8—62no—
70C4×C5×Q8—31no—
71C4×C5×D4—31no—
72C4×C5×D4—61no—
73#4015—31no—
74#3967—61no—
75#3964—61no—
76#3942—62no—
77#3940—61no—
78#3939—61no—
79C4⋊#168C2×D311yescharacteristic
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1637—151noSylow
83C22×C5×D3—21no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—41no—
91Dic30—42no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—21no—
96C5×D12Q1612yes—
97C4×C5×D3—44no—
98C4×C5×D3—41no—
99C4×C5×D3—41no—
100C5×Dic6—21no—
101C5×Dic6—44no—
102C5×Dic6SD1612yes—
103C3⋊#168—41no—
104C3×#168—41no—
105C3×#168—41no—
106C2×D3×Q8—21no—
107C3×C4⋊Q8C2×D511yescharacteristic
108#946—21no—
109#896—22no—
110#893—21no—
111#888—21no—
112C4×D12C2×D511yescharacteristic
113#869—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4⋊C8—51no—
117#821—101no—
118#818—101no—
119#817—101no—
120#816—101no—
121#810—102no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—21no—
124C2×C5×Q8—31no—
125C2×C5×Q8—62no—
126C2×C5×Q8—122no—
127C2×C5×Q8—122no—
128C2×C5×D4—31no—
129C22×C4×C5—62no—
130C22×C4×C5—61no—
131C2×Dic10—61no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—62no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4D1212yes—
138C5×C22⋊C4—62no—
139C5×C22⋊C4—61no—
140C42×C5—61no—
141C42×C5C22×D311yescharacteristic
142C4⋊Dic5—61no—
143C4⋊Dic5—61no—
144C2×#168—21no—
145C2×#168—21no—
146C2×#168—61no—
147D4×Q8—31no—
148#487—151no—
149#477—151no—
150#476—151no—
151#332—51no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C5×D3—22no—
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C3×C4×C5—21no—
159C3×C4×C5—42no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—81no—
165C5×Dic3—22no—
166C5×Dic3—41no—
167C5×Dic3—41no—
168C2×C3×Q8—21no—
169D3×Q8—42no—
170D3×Q8—42no—
171C2×D12C22⋊D511yescharacteristic
172C2×C4×D3—22no—
173C2×C4×D3—21no—
174C2×Dic6—22no—
175C2×Dic6—101no—
176C2×Dic6C22⋊D511yescharacteristic
177C2×C3×C8—101no—
178C2×C3×C8—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4C22⋊D512yes—
181C3×C42C22×D511yescharacteristic
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3—101no—
185C4⋊Dic3—101no—
186C4⋊Dic3C22⋊D511yescharacteristic
187C4⋊Dic3C22⋊D511yescharacteristic
188Dic3⋊C4—22no—
189Dic3⋊C4—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—101no—
192C23×C5—61no—
193C5×Q8—32no—
194C5×Q8—41no—
195C5×Q8—41no—
196C5×Q8—61no—
197C5×Q8—124no—
198C5×D4—32no—
199C5×D4—61no—
200C2×C4×C5—22no—
201C2×C4×C5—61no—
202C2×C4×C5—61no—
203C2×C4×C5—61no—
204C2×C4×C5—124no—
205C2×C4×C5—121no—
206C2×C4×C5—121no—
207C2×C4×C5C2×D1211yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×Dic5—121no—
211Dic10—122no—
212#168—41no—
213#168—41no—
214#168—121no—
215C22×Q8—61no—
216C4⋊Q8—61no—
217C4⋊Q8—151no—
218C4⋊Q8D3×D511yescharacteristic
219C22⋊Q8—61no—
220C22⋊Q8—62no—
221C4×Q8—31no—
222C4×D4—31no—
223C4×D4—61no—
224#107—301no—
225#106—301no—
226C4⋊C8—51no—
227C4⋊C8—51no—
228#103—301no—
229#103—302no—
230#102—301no—
231C4×C8—151no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—42no—
236C22×D3—21no—
237C3×Q8—41no—
238C3×Q8—41no—
239C2×C3×C4—22no—
240C2×C3×C4C2×C22⋊D511yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—201no—
247D12—21no—
248D12#68912yes—
249C4×D3—44no—
250C4×D3—41no—
251C4×D3—41no—
252Dic6—21no—
253Dic6—44no—
254Dic6—202no—
255Dic6#68712yes—
256C3×C8—201no—
257C3×C8—201no—
258C3⋊C8—201no—
259C22×C5—62no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5#88211yescharacteristic
263C4×C5—21no—
264C4×C5—42no—
265C4×C5—62no—
266C4×C5—121no—
267C4×C5—121no—
268C4×C5#91111yescharacteristic
269C4×C5D3×SD1611yescharacteristic
270C4×C5#91511yescharacteristic
271C4×C5D3×Q1611yescharacteristic
272Dic5—241no—
273C2×Q8—21no—
274C2×Q8—31no—
275C2×Q8—62no—
276C2×Q8—122no—
277C2×Q8—122no—
278C2×Q8—301no—
279C2×D4—31no—
280C22×C4—62no—
281C22×C4—61no—
282C2×C8—101no—
283C2×C8—101no—
284C2×C8—301no—
285C4⋊C4—21no—
286C4⋊C4—31no—
287C4⋊C4—31no—
288C4⋊C4—62no—
289C4⋊C4—61no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4#120312yes—
293C22⋊C4—62no—
294C22⋊C4—61no—
295C42—61no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#409911yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—21no—
303C3×C4—42no—
304C3×C4#407811yescharacteristic
305C3×C4C2×#68711yescharacteristic
306C3×C4#408811yescharacteristic
307C3×C4C2×#68911yescharacteristic
308Dic3—22no—
309Dic3—41no—
310Dic3—41no—
311Dic3—401no—
312C2×C5—122no—
313C2×C5#475311yescharacteristic
314C2×C5#477611yescharacteristic
315C2×C5#480911yescharacteristic
316C23—61no—
317Q8—32no—
318Q8—41no—
319Q8—41no—
320Q8—61no—
321Q8—124no—
322Q8—602no—
323D4—32no—
324D4—61no—
325C2×C4—22no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—124no—
330C2×C4—121no—
331C2×C4—121no—
332C2×C4—601no—
333C2×C4C2×#120311yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—201no—
337C8—201no—
338C8—601no—
339C2×C3#6550711yescharacteristic
340C2×C3#6551711yescharacteristic
341C2×C3#6553411yescharacteristic
342D3—42no—
343C5#6845911yescharacteristic, complemented, Sylow
344C22—62no—
345C22—121no—
346C22—121no—
347C22#9157011yescharacteristic
348C4—21no—
349C4—42no—
350C4—62no—
351C4—121no—
352C4—121no—
353C4—1201no—
354C4D3×#68711yescharacteristic
355C4#9149411yescharacteristic
356C4D3×#68911yescharacteristic
357C4#9151811yescharacteristic
358C3#1060270811yescharacteristic, complemented, Sylow
359C2—122no—
360C2#1174905611yescharacteristic
361C2#1174930211yescharacteristic
362C2#1174938711yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11746961C2semidirect
5. C3×#64767C2semidirect
6. #11745842C2semidirect
31. #64767D3semidirect
297. C3×C5#1637semidirect
343. C5#68459semidirect
358. C3#10602708semidirect

Maximal subgroups

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

subgroupindex
C5×#57272
#117511942
#117469612
#117468832
C3×#647672
#117458422
#117458362
#106027083
#684595