Finite Group Databasebeta

← #14283192

Subgroups — #14283192

Order 1920.

588 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×#91359C211yesmaximal, characteristic
2C4×#6763C211yesmaximal, characteristic
3C3×#65756C211yesmaximal, characteristic
4#11746500C214yesmaximal, complemented
5#10604956—31nomaximal, Hall
6C22×C5×Dic6C411yescharacteristic, complemented
7C22×C3×C4×D5C2211yescharacteristic
8C2×#6763—21no—
9C2×C4×ΓL(1,𝔽16)—21no—
10C2×C3×#700—21no—
11C2×C4⋊Dic15C411yescharacteristic, complemented
12C2×#6669—21no—
13C2×#6665—21no—
14#91359—21no—
15#91359—21no—
16#91359C412yescomplemented
17#91359C2212yes—
18#91235C2212yes—
19C3×C22⋊#170—21no—
20C3×#4003C2212yes—
21#69980—51nomaximal, Hall
22C2×#4092—31no—
23C4×C22⋊AGL(1,𝔽5)—31no—
24#65756D311yescharacteristic
25#64926—34no—
26C23×C3×D5D411yescharacteristic
27C22×ΓL(1,𝔽16)—22no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×Dic15—21no—
30C22×C5×Dic3—21no—
31C2×C5×Dic6—21no—
32C2×C5×Dic6—42no—
33C2×C5×Dic6C2×C412yes—
34C22×C3×Dic5D411yescharacteristic
35C2×C3×C4×D5—42no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5C2311yescharacteristic
40#6763—24no—
41C4×ΓL(1,𝔽16)—42no—
42C2×C3×#170—22no—
43C3×#700—42no—
44C4⋊Dic15—21no—
45C4⋊Dic15C2×C412yes—
46#6669—22no—
47#6669—22no—
48#6665—22no—
49#6665—22no—
50C2×#924—51no—
51C3×#407—51no—
52C4×#217—51no—
53#4467—54no—
54C22×C5×Q8—31no—
55C22×C4×D5C2×D311yescharacteristic
56C2×C22⋊AGL(1,𝔽5)—61no—
57C2×C4×AGL(1,𝔽5)—61no—
58C2×#700—21no—
59#4092—32no—
60#4092—32no—
61#4092—61no—
62#4092—61no—
63C2×#685—61no—
64C2×C4⋊Dic5—31no—
65C2×#683—61no—
66C22⋊#170—21no—
67(C2×AGL(1,𝔽5))⋊C4—32no—
68#4003C2×D312yes—
69#1508—151noSylow
70C23×C3×C5C22⋊C411yescharacteristic
71C22×C3×D5—22no—
72C22×C3×D5—22no—
73C22×C3×D5—41no—
74C22×C3×D5C22⋊C411yescharacteristic
75C22×C3×D5C2×D411yescharacteristic
76C2×ΓL(1,𝔽16)—24no—
77C2×ΓL(1,𝔽16)—42no—
78C2×ΓL(1,𝔽16)—42no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×Dic15—22no—
83C2×Dic15—42no—
84C2×C5×Dic3—22no—
85C2×C5×Dic3—42no—
86C5×Dic6—42no—
87C5×Dic6—42no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5—41no—
94C3×C4×D5—41no—
95C3×#170—42no—
96C23×C3×C4—51no—
97C22×Dic6AGL(1,𝔽5)11yescharacteristic, complemented
98C2×C3×M16—101no—
99C2×#217—101no—
100C2×#217—101no—
101C2×C4⋊Dic3—51no—
102#924—52no—
103#924—52no—
104#924—101no—
105#924—101no—
106C2×Dic3⋊C4—101no—
107C2×C4×Dic3—101no—
108C3×C22⋊C8—52no—
109C3×C22⋊C8—101no—
110C3⋊#95—52no—
111C23×D5D1211yescharacteristic
112C22×AGL(1,𝔽5)—62no—
113C2×C5×Q8—32no—
114C2×C5×Q8—61no—
115C2×C5×Q8—122no—
116C22×C4×C5—61no—
117C22×C4×C5C4×D311yescharacteristic
118C22×Dic5—61no—
119C22×Dic5#6711yescharacteristic
120C2×C4×D5—42no—
121C2×C4×D5C4×D311yescharacteristic
122C2×C4×D5D1211yescharacteristic
123C2×C4×D5#6711yescharacteristic
124C2×C4×D5C22×D311yescharacteristic
125C22⋊AGL(1,𝔽5)—64no—
126C2×#170—22no—
127C4×AGL(1,𝔽5)—122no—
128#700—42no—
129#685—62no—
130#685—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—61no—
133#683—62no—
134#683—62no—
135C2×C22⋊Q8—151no—
136#407—51no—
137C4×C22⋊C4—151no—
138#328—154no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5#10412yes—
142C22×C3×C5C2×C22⋊C411yescharacteristic
143C2×C3×D5—21no—
144C2×C3×D5—21no—
145C2×C3×D5—21no—
146C2×C3×D5—21no—
147C2×C3×D5—21no—
148C2×C3×D5—44no—
149C2×C3×D5#13712yes—
150ΓL(1,𝔽16)—44no—
151C3×C4×C5—21no—
152C3×C4×C5#9912yes—
153Dic15—42no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C5×Dic3—42no—
157C24×C3—51no—
158C22×C3×C4—51no—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4—202no—
164C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
165C22×Dic3—21no—
166C22×Dic3—102no—
167C22×Dic3—101no—
168C2×Dic6—21no—
169C2×Dic6—42no—
170C2×Dic6C2×AGL(1,𝔽5)12yes—
171C3×M16—202no—
172C2×C3×C8—102no—
173#217—102no—
174#217—102no—
175#217—104no—
176C4⋊Dic3—52no—
177C4⋊Dic3—101no—
178Dic3⋊C4—102no—
179Dic3⋊C4—102no—
180C4×Dic3—202no—
181C23×C5(C2×D3)⋊C411yescharacteristic
182C22×D5—22no—
183C22×D5—22no—
184C22×D5—41no—
185C22×D5(C2×D3)⋊C411yescharacteristic
186C22×D5C2×D1211yescharacteristic
187C2×AGL(1,𝔽5)—64no—
188C2×AGL(1,𝔽5)—122no—
189C2×AGL(1,𝔽5)—122no—
190C5×Q8—122no—
191C5×Q8—122no—
192C2×C4×C5—22no—
193C2×C4×C5—62no—
194C2×C4×C5—122no—
195C2×C4×C5(C2×D3)⋊C411yescharacteristic
196C2×C4×C5C2×C4×D311yescharacteristic
197C2×Dic5—41no—
198C2×Dic5—62no—
199C2×Dic5—122no—
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201C2×Dic5C2×#6711yescharacteristic
202C4×D5—22no—
203C4×D5—22no—
204C4×D5—41no—
205C4×D5—41no—
206#170—42no—
207C22×Q8—31no—
208C23×C4—51no—
209C2×M16—101no—
210C22⋊Q8—152no—
211C22⋊Q8—152no—
212C22⋊Q8—301no—
213C22⋊Q8—301no—
214C2×C4⋊C4—151no—
215C2×C4⋊C4—301no—
216C2×C22⋊C4—301no—
217C2×C22⋊C4—301no—
218C2×C42—301no—
219C22⋊C8—52no—
220C22⋊C8—101no—
221#95—152no—
222C2×C3×C5—22no—
223C2×C3×C5C2×#9911yescharacteristic
224C2×C3×C5#41911yescharacteristic
225C2×C3×C5C2×#10411yescharacteristic
226C3×D5—22no—
227C3×D5—41no—
228C23×C3—51no—
229C23×C3—51no—
230C23×C3—102no—
231C23×C3—102no—
232C23×C3—201no—
233C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
234C2×C3×C4—22no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—102no—
238C2×C3×C4—102no—
239C2×C3×C4—201no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
243C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
244C2×Dic3—22no—
245C2×Dic3—42no—
246C2×Dic3—104no—
247C2×Dic3—102no—
248C2×Dic3—202no—
249C2×Dic3—202no—
250C2×Dic3—202no—
251Dic6—42no—
252Dic6—42no—
253C3×C8—202no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5#82512yes—
257C22×C5C2×(C2×D3)⋊C411yescharacteristic
258C2×D5—21no—
259C2×D5—21no—
260C2×D5—21no—
261C2×D5—21no—
262C2×D5—21no—
263C2×D5—44no—
264C2×D5#90912yes—
265AGL(1,𝔽5)—124no—
266C4×C5—21no—
267C4×C5—122no—
268C4×C5#80612yes—
269Dic5—21no—
270Dic5—21no—
271Dic5—122no—
272C24—51no—
273C2×Q8—32no—
274C2×Q8—61no—
275C2×Q8—122no—
276C22×C4—51no—
277C22×C4—51no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—61no—
282C22×C4—202no—
283C22×C4—302no—
284C22×C4—301no—
285C22×C4D3×AGL(1,𝔽5)11yescharacteristic
286M16—202no—
287C2×C8—102no—
288C4⋊C4—152no—
289C4⋊C4—302no—
290C4⋊C4—302no—
291C4⋊C4—301no—
292C22⋊C4—302no—
293C22⋊C4—302no—
294C22⋊C4—304no—
295C42—602no—
296C3×C5#150811yescharacteristic, complemented, Hall
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—52no—
300C22×C3—101no—
301C22×C3—101no—
302C22×C3—101no—
303C22×C3—101no—
304C22×C3—101no—
305C22×C3—204no—
306C22×C3#401012yes—
307C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
308C3×C4—21no—
309C3×C4—101no—
310C3×C4—101no—
311C3×C4#401112yes—
312Dic3—42no—
313Dic3—204no—
314Dic3—202no—
315C2×C5—22no—
316C2×C5C2×#80611yescharacteristic
317C2×C5#512011yescharacteristic
318C2×C5C2×#82511yescharacteristic
319D5—22no—
320D5—41no—
321C23—51no—
322C23—51no—
323C23—102no—
324C23—102no—
325C23—201no—
326C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
327Q8—122no—
328Q8—122no—
329C2×C4—22no—
330C2×C4—51no—
331C2×C4—51no—
332C2×C4—62no—
333C2×C4—102no—
334C2×C4—102no—
335C2×C4—122no—
336C2×C4—201no—
337C2×C4—201no—
338C2×C4—201no—
339C2×C4—304no—
340C2×C4—302no—
341C2×C4—602no—
342C2×C4—602no—
343C2×C4—602no—
344C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
345C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
346C8—202no—
347C2×C3—22no—
348C2×C3—102no—
349C2×C3—201no—
350C2×C3#6578211yescharacteristic
351C2×C3C2×#401011yescharacteristic
352C2×C3C2×#401111yescharacteristic
353C5#6998011yescharacteristic, complemented, Sylow
354C22—21no—
355C22—21no—
356C22—52no—
357C22—101no—
358C22—101no—
359C22—101no—
360C22—101no—
361C22—101no—
362C22—204no—
363C22#9115712yes—
364C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
365C4—21no—
366C4—101no—
367C4—101no—
368C4—122no—
369C4—604no—
370C4—602no—
371C4#9117212yes—
372C3#1060495611yescharacteristic, complemented, Sylow
373C2—22no—
374C2—102no—
375C2—201no—
376C2#1175171211yescharacteristic
377C2C2×#9115711yescharacteristic
378C2C2×#9117211yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746500C2semidirect
6. C22×C5×Dic6C4semidirect
11. C2×C4⋊Dic15C4semidirect
16. #91359C4semidirect
97. C22×Dic6AGL(1,𝔽5)semidirect
296. C3×C5#1508semidirect
353. C5#69980semidirect
372. C3#10604956semidirect

Maximal subgroups

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

subgroupindex
C2×#913592
C4×#67632
C3×#657562
#117465002
#106049563
#699805