Finite Group Databasebeta

← #14283906

Subgroups — #14283906

Order 1920.

464 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 86 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#11753620C211yesmaximal, characteristic
2#11751873C211yesmaximal, characteristic
3#11751873C211yesmaximal, characteristic
4#11746741C211yesmaximal, characteristic, complemented
5C3×#64870C211yesmaximal, characteristic, complemented
6#11746507C211yesmaximal, characteristic, complemented
7#11746506C211yesmaximal, characteristic, complemented
8D5⋊#330—31nomaximal, Hall
9C2×#6738—21no—
10C2×#6738—21no—
11C4⋊C4×D15C411yescharacteristic
12C5×#890C411yescharacteristic
13C3×#4036C2211yescharacteristic
14#91437—21no—
15#91437C411yescharacteristic
16#91404—21no—
17C4×#1200C2211yescharacteristic
18#91388C2211yescharacteristic
19#91381C411yescharacteristic
20#91339—21no—
21#91336—21no—
22#91231C2211yescharacteristic
23#91231C2211yescharacteristic
24C3×#4002C2211yescharacteristic
25C3×#4002C2211yescharacteristic
26#91169—21no—
27#91169—21no—
28D3×#330—51nomaximal, Hall
29D5×#125—31no—
30#65676—31no—
31#65676—31no—
32#64870—31no—
33#64870—31no—
34#64870—31no—
35#64870D311yescharacteristic, complemented
36C2×C4×D15—21no—
37C2×C4×D15C2×C411yescharacteristic
38C2×#1200—21no—
39C2×#1200D411yescharacteristic
40C2×#1200D411yescharacteristic
41C2×C3⋊#170—21no—
42C2×C3⋊#170—21no—
43C2×C3×#170—21no—
44C2×C3×#170—21no—
45#6738—24no—
46#6738—24no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C4⋊Dic15C2×C411yescharacteristic
49#6712—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3C2×C411yescharacteristic
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3C2×C411yescharacteristic
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—21no—
57C3×C4×Dic5C2311yescharacteristic
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6669—21no—
61#6669—21no—
62#6668—21no—
63Dic3×Dic5D411yescharacteristic
64Dic3×Dic5D411yescharacteristic
65D3×#125—51no—
66D3×#97—51no—
67D3×#97—51no—
68C3×#330—51no—
69#4543—51no—
70#4465—51no—
71#4465—51no—
72C2×D5⋊C8—61no—
73C2×D5⋊C8—61no—
74C5×#125—31no—
75D5×C4⋊C4—31no—
76D5×C4⋊C4—31no—
77D5×C4⋊C4—61no—
78D5×C4⋊C4—61no—
79#4036—31no—
80#4036C2×D311yescharacteristic
81#4035—61no—
82#4035—61no—
83C42×D5—31no—
84#4016—31no—
85#4002—31no—
86#4002—31no—
87#4002—61no—
88#4002—61no—
89#4002C2×D311yescharacteristic
90#4002C2×D311yescharacteristic
91C2×#330—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15C22⋊C411yescharacteristic
97C4×D15—22no—
98C4×D15—42no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C3×Dic5—21no—
103C2×C3×Dic5C2×D411yescharacteristic
104C2×C3×Dic5C2×D411yescharacteristic
105#1200—22no—
106#1200—22no—
107#1200—42no—
108C3⋊#170—22no—
109C3⋊#170—22no—
110C3×#170—22no—
111C3×#170—22no—
112C3×#125—51no—
113C2×D3×C8—101no—
114C2×D3×C8—101no—
115D3×C4⋊C4—51no—
116D3×C4⋊C4—51no—
117D3×C4⋊C4—101no—
118D3×C4⋊C4—101no—
119#890—51no—
120#890AGL(1,𝔽5)11yescharacteristic
121#889—101no—
122#889—101no—
123C42×D3—51no—
124#870—51no—
125C3×#97—51no—
126C3×#97—51no—
127#815—101no—
128#815—101no—
129#803—51no—
130#803—51no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—61no—
135C2×C4×D5—61no—
136C2×#170—21no—
137C2×#170—21no—
138C2×#170—61no—
139C2×#170—61no—
140D5⋊C8—64no—
141D5⋊C8—64no—
142C5×C4⋊C4—31no—
143C5×C4⋊C4—61no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4C4×D311yescharacteristic
146C42×C5—31no—
147C4⋊Dic5—21no—
148C4⋊Dic5—31no—
149C4⋊Dic5—61no—
150C4⋊Dic5C4×D311yescharacteristic
151#683—21no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156#683—61no—
157C4×Dic5—31no—
158C4×Dic5—31no—
159C4×Dic5C22×D311yescharacteristic
160C2×#125—151no—
161C2×#97—151no—
162C2×#97—151no—
163#330—51no—
164#330—151no—
165#330—151no—
166#330—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×D15#10112yes—
169C2×D15#10412yes—
170C2×D15#10412yes—
171C3×C4×C5—21no—
172C3×C4×C5—41no—
173Dic15—21no—
174Dic15—41no—
175C3×Dic5—21no—
176C3×Dic5—21no—
177C3×Dic5—41no—
178C5×Dic3—21no—
179C5×Dic3—21no—
180C5×Dic3—41no—
181C2×C4×D3—51no—
182C2×C4×D3—51no—
183C2×C4×D3—51no—
184C2×C4×D3—101no—
185C2×C4×D3—101no—
186C2×C3×C8—101no—
187C2×C3×C8—101no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
192C3×C42—51no—
193C4⋊Dic3—21no—
194C4⋊Dic3—51no—
195C4⋊Dic3—101no—
196C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—101no—
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203C4×Dic3—51no—
204C4×Dic3—51no—
205C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208D3×C8—104no—
209D3×C8—104no—
210C22×D5—31no—
211C2×C4×C5—21no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5—61no—
215C2×C4×C5C2×C4×D311yescharacteristic
216C2×Dic5—21no—
217C2×Dic5—31no—
218C2×Dic5—61no—
219C2×Dic5D3×D411yescharacteristic
220C2×Dic5D3×D411yescharacteristic
221C4×D5—62no—
222C4×D5—62no—
223C4×D5—62no—
224C4×D5—122no—
225C4×D5—122no—
226#170—22no—
227#170—22no—
228#170—62no—
229#170—62no—
230C22×C8—301no—
231C22×C8—301no—
232#125—31no—
233#125—51no—
234#125—151no—
235#125—151no—
236#125—301no—
237#125—301no—
238C2×C4⋊C4—151no—
239C2×C4⋊C4—151no—
240C2×C4⋊C4—301no—
241C2×C4⋊C4—301no—
242C2×C42—151no—
243#97—51no—
244#97—51no—
245#97—151no—
246#97—151no—
247#97—301no—
248#97—301no—
249C2×C3×C5C2×#10111yescharacteristic
250C2×C3×C5C2×#10411yescharacteristic
251C2×C3×C5C2×#10411yescharacteristic
252D15#33014yescomplemented
253C22×D3—51no—
254C2×C3×C4—21no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—101no—
258C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—51no—
261C2×Dic3—101no—
262C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
263C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
264C4×D3—102no—
265C4×D3—102no—
266C4×D3—102no—
267C4×D3—202no—
268C4×D3—202no—
269C3×C8—102no—
270C3×C8—102no—
271C3⋊C8—102no—
272C3⋊C8—102no—
273C22×C5D3×C22⋊C411yescharacteristic
274C2×D5—32no—
275C2×D5—32no—
276C2×D5—32no—
277C4×C5—21no—
278C4×C5—41no—
279C4×C5—61no—
280C4×C5—61no—
281C4×C5—121no—
282Dic5—21no—
283Dic5—21no—
284Dic5—41no—
285Dic5—61no—
286Dic5—121no—
287C22×C4—151no—
288C22×C4—151no—
289C22×C4—151no—
290C22×C4—301no—
291C22×C4—301no—
292C2×C8—101no—
293C2×C8—101no—
294C2×C8—304no—
295C2×C8—304no—
296C2×C8—301no—
297C2×C8—301no—
298C4⋊C4—31no—
299C4⋊C4—51no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—101no—
303C4⋊C4—101no—
304C4⋊C4—151no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C4⋊C4—301no—
309C4⋊C4—301no—
310C4⋊C4—301no—
311C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
312C42—31no—
313C42—51no—
314C42—151no—
315C42—151no—
316C3×C5C2×#33011yescharacteristic, complemented, Hall
317C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
318C2×D3—52no—
319C2×D3—52no—
320C2×D3—52no—
321C3×C4—21no—
322C3×C4—41no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—201no—
326Dic3—21no—
327Dic3—21no—
328Dic3—41no—
329Dic3—101no—
330Dic3—201no—
331C2×C5D3×#10111yescharacteristic
332C2×C5D3×#10411yescharacteristic
333C2×C5D3×#10411yescharacteristic
334D5—34no—
335C23—151no—
336C2×C4—21no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—61no—
342C2×C4—101no—
343C2×C4—151no—
344C2×C4—302no—
345C2×C4—302no—
346C2×C4—302no—
347C2×C4—301no—
348C2×C4—602no—
349C2×C4—602no—
350C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
351C8—102no—
352C8—102no—
353C8—302no—
354C8—302no—
355C2×C3D5⋊#10111yescharacteristic
356C2×C3D5⋊#10411yescharacteristic
357C2×C3D5⋊#10411yescharacteristic
358D3—54no—
359C5D3×#33011yescharacteristic, complemented, Sylow
360C22—152no—
361C22—152no—
362C22—152no—
363C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
364C4—21no—
365C4—41no—
366C4—61no—
367C4—61no—
368C4—101no—
369C4—101no—
370C4—121no—
371C4—201no—
372C4—301no—
373C4—601no—
374C3D5⋊#33011yescharacteristic, complemented, Sylow
375C2—154no—
376C2#1175191811yescharacteristic
377C2#1175193511yescharacteristic
378C2#1175195911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#330
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746741C2semidirect
5. C3×#64870C2semidirect
6. #11746507C2semidirect
7. #11746506C2semidirect
35. #64870D3semidirect
252. D15#330semidirect
316. C3×C5C2×#330semidirect
359. C5D3×#330semidirect
374. C3D5⋊#330semidirect

Maximal subgroups

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

subgroupindex
#117536202
#117518732
#117467412
C3×#648702
#117465072
#117465062
D5⋊#3303
D3×#3305