Finite Group Databasebeta

← #14298396

Subgroups — #14298396

Order 1920.

632 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 118 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×D5×C4⋊Dic3C211yesmaximal, characteristic
2#11752414C211yesmaximal, characteristic
3C3×#65755C211yesmaximal, characteristic
4#11746574C214yesmaximal, complemented
5#10604337—31nomaximal, Hall
6C22×C3×C4×D5C2211yescharacteristic
7C22×D5×Dic3C412yes—
8C2×#6762C2212yes—
9C2×C3×#704C2212yes—
10C2×C4⋊Dic15C411yescharacteristic
11C2×C5×C4⋊Dic3C411yescharacteristic
12C2×#6668C2212yes—
13D5×C4⋊Dic3—21no—
14D5×C4⋊Dic3—21no—
15D5×C4⋊Dic3—21no—
16D5×C4⋊Dic3—21no—
17#91232—21no—
18#91232—21no—
19C3×#4003—21no—
20C3×#4003—21no—
21#69973—51nomaximal, Hall
22C2×D5×C4⋊C4—31no—
23#65755—31no—
24#65755D311yescharacteristic
25#64919—34no—
26C23×C3×D5C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15C2×C412yes—
29C22×C5×Dic3C2×C412yes—
30C22×C3×Dic5C2311yescharacteristic
31C2×C3×C4×D5—24no—
32C2×C3×C4×D5D411yescharacteristic
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×D5×Dic3—22no—
37C2×D5×Dic3—22no—
38C2×D5×Dic3—44no—
39#6762—24no—
40C2×C3⋊#170—22no—
41C3×#704—24no—
42C2×C3×#170—22no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47#6668—22no—
48#6668—22no—
49C22×C4⋊Dic3—51no—
50C3×#407—51no—
51#5207—51no—
52#4554—54no—
53C22×C4×D5—32no—
54C22×C4×D5C2×D311yescharacteristic
55C2×#704—32no—
56C2×#704C2×D312yes—
57C2×C5×C4⋊C4—31no—
58C2×C4⋊Dic5—31no—
59C2×#683—32no—
60D5×C4⋊C4—61no—
61D5×C4⋊C4—61no—
62D5×C4⋊C4—61no—
63D5×C4⋊C4—61no—
64#4003—21no—
65#4003—21no—
66#4003—61no—
67#4003—61no—
68#1821—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×C3×D5—22no—
71C22×C3×D5—22no—
72C22×C3×D5—22no—
73C22×C3×D5C22⋊C411yescharacteristic
74C22×C3×D5C22⋊C411yescharacteristic
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22⋊C411yescharacteristic
78C2×Dic15—22no—
79C2×Dic15—42no—
80C2×C5×Dic3—22no—
81C2×C5×Dic3—42no—
82C2×C3×Dic5C2×D411yescharacteristic
83C2×C3×Dic5C2×D411yescharacteristic
84C2×C3×Dic5#4114yes—
85C3×C4×D5—22no—
86C3×C4×D5—22no—
87C3×C4×D5—22no—
88C3×C4×D5—22no—
89D5×Dic3—44no—
90D5×Dic3—44no—
91C3⋊#170—42no—
92C3×#170—42no—
93C23×C3×C4—51no—
94C23×Dic3—52no—
95C2×C3×M16—52no—
96C2×C4⋊Dic3—51no—
97C2×C4⋊Dic3—52no—
98C2×C4⋊Dic3—101no—
99C2×C4⋊Dic3—101no—
100C2×C4⋊Dic3—101no—
101C2×C4⋊Dic3—101no—
102C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
103C2×#208—52no—
104C3×C22⋊C8—101no—
105C3×C22⋊C8—101no—
106#830—101no—
107#830—101no—
108C23×D5C4×D311yescharacteristic
109C22×C4×C5—32no—
110C22×C4×C5C4×D311yescharacteristic
111C22×Dic5—32no—
112C22×Dic5C22×D311yescharacteristic
113C2×C4×D5—24no—
114C2×C4×D5—62no—
115C2×C4×D5—62no—
116C2×C4×D5—124no—
117C2×C4×D5D1211yescharacteristic
118C2×C4×D5D1211yescharacteristic
119C2×C4×D5#6711yescharacteristic
120C2×C4×D5#6711yescharacteristic
121#704—24no—
122#704—64no—
123C2×#170—22no—
124C2×#170—62no—
125C5×C4⋊C4—61no—
126C5×C4⋊C4—61no—
127C4⋊Dic5—61no—
128C4⋊Dic5—61no—
129#683—62no—
130#683—62no—
131C22×C4⋊C4—151no—
132#407—51no—
133#407—151no—
134#343—154no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C22×C3×C5#11712yes—
139C2×C3×D5—28no—
140C2×C3×D5—21no—
141C2×C3×D5—21no—
142C2×C3×D5—21no—
143C2×C3×D5—21no—
144C2×C3×D5#10012yes—
145C2×C3×D5#10112yes—
146C3×C4×C5—21no—
147C3×C4×C5—21no—
148Dic15—42no—
149C3×Dic5#12312yes—
150C3×Dic5#12312yes—
151C5×Dic3—42no—
152C24×C3—51no—
153C22×C3×C4—51no—
154C22×C3×C4—51no—
155C22×C3×C4—51no—
156C22×C3×C4—51no—
157C22×C3×C4—51no—
158C22×C3×C4—104no—
159C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
160C22×Dic3—52no—
161C22×Dic3—102no—
162C22×Dic3—102no—
163C22×Dic3—204no—
164C22×Dic3C2×AGL(1,𝔽5)12yes—
165C3×M16—104no—
166C2×C3×C8—102no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—102no—
170C4⋊Dic3—102no—
171C4⋊Dic3—101no—
172C4⋊Dic3—101no—
173#208—104no—
174C2×C3⋊C8—102no—
175C23×C5C2×C4×D311yescharacteristic
176C22×D5—22no—
177C22×D5—22no—
178C22×D5—22no—
179C22×D5(C2×D3)⋊C411yescharacteristic
180C22×D5(C2×D3)⋊C411yescharacteristic
181C2×C4×C5—22no—
182C2×C4×C5—62no—
183C2×C4×C5—122no—
184C2×C4×C5(C2×D3)⋊C411yescharacteristic
185C2×C4×C5(C2×D3)⋊C411yescharacteristic
186C2×Dic5—62no—
187C2×Dic5—122no—
188C2×Dic5C2×D1211yescharacteristic
189C2×Dic5#23714yes—
190C2×Dic5C2×#6711yescharacteristic
191C4×D5—22no—
192C4×D5—22no—
193C4×D5—22no—
194C4×D5—22no—
195C4×D5—124no—
196C4×D5—124no—
197#170—42no—
198#170—122no—
199C23×C4—51no—
200C23×C4—152no—
201C2×M16—52no—
202C2×M16—152no—
203C2×C4⋊C4—31no—
204C2×C4⋊C4—152no—
205C2×C4⋊C4—151no—
206C2×C4⋊C4—301no—
207C2×C4⋊C4—301no—
208C2×C4⋊C4—301no—
209C2×C4⋊C4—301no—
210C22⋊C8—101no—
211C22⋊C8—101no—
212C22⋊C8—301no—
213C22⋊C8—301no—
214C2×C3×C5—22no—
215C2×C3×C5#38111yescharacteristic
216C2×C3×C5C2×#10011yescharacteristic
217C2×C3×C5C2×#10111yescharacteristic
218C3×D5—22no—
219C3×D5—22no—
220C23×C3—51no—
221C23×C3—51no—
222C23×C3—102no—
223C23×C3—102no—
224C23×C3—102no—
225C23×C3C22×AGL(1,𝔽5)11yescharacteristic
226C2×C3×C4—22no—
227C2×C3×C4—54no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—102no—
231C2×C3×C4—102no—
232C2×C3×C4—102no—
233C2×C3×C4—102no—
234C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
235C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
236C2×Dic3—22no—
237C2×Dic3—42no—
238C2×Dic3—102no—
239C2×Dic3—204no—
240C2×Dic3—204no—
241C2×Dic3—202no—
242C3×C8—202no—
243C3⋊C8—202no—
244C22×C5—21no—
245C22×C5—21no—
246C22×C5#87712yes—
247C22×C5C2×(C2×D3)⋊C411yescharacteristic
248C2×D5—28no—
249C2×D5—21no—
250C2×D5—21no—
251C2×D5—21no—
252C2×D5—21no—
253C2×D5#82312yes—
254C2×D5#82412yes—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—122no—
258Dic5—122no—
259Dic5#88612yes—
260Dic5#93512yes—
261C24—51no—
262C22×C4—32no—
263C22×C4—51no—
264C22×C4—51no—
265C22×C4—51no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—104no—
269C22×C4—152no—
270C22×C4—302no—
271C22×C4—302no—
272C22×C4—604no—
273C22×C4D3×AGL(1,𝔽5)11yescharacteristic
274M16—104no—
275M16—304no—
276C2×C8—102no—
277C2×C8—302no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C4⋊C4—301no—
284C3×C5#182111yescharacteristic, complemented, Hall
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—52no—
288C22×C3—52no—
289C22×C3—108no—
290C22×C3—101no—
291C22×C3—101no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3#413012yes—
295C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—52no—
299C3×C4—52no—
300Dic3—42no—
301Dic3—202no—
302C2×C5—22no—
303C2×C5#494311yescharacteristic
304C2×C5C2×#82311yescharacteristic
305C2×C5C2×#82411yescharacteristic
306D5—22no—
307D5—22no—
308C23—51no—
309C23—51no—
310C23—102no—
311C23—102no—
312C23—102no—
313C23C2×D3×AGL(1,𝔽5)11yescharacteristic
314C2×C4—22no—
315C2×C4—54no—
316C2×C4—51no—
317C2×C4—51no—
318C2×C4—62no—
319C2×C4—102no—
320C2×C4—102no—
321C2×C4—102no—
322C2×C4—102no—
323C2×C4—122no—
324C2×C4—302no—
325C2×C4—604no—
326C2×C4—604no—
327C2×C4—602no—
328C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
329C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
330C8—202no—
331C8—602no—
332C2×C3—22no—
333C2×C3—102no—
334C2×C3—102no—
335C2×C3#6576411yescharacteristic
336C2×C3D5⋊#10011yescharacteristic
337C2×C3D5⋊#10111yescharacteristic
338C5#6997311yescharacteristic, complemented, Sylow
339C22—21no—
340C22—21no—
341C22—52no—
342C22—52no—
343C22—108no—
344C22—101no—
345C22—101no—
346C22—101no—
347C22—101no—
348C22#9192312yes—
349C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
350C4—21no—
351C4—21no—
352C4—52no—
353C4—52no—
354C4—122no—
355C4—602no—
356C3#1060433711yescharacteristic, complemented, Sylow
357C2—22no—
358C2—102no—
359C2—102no—
360C2D5⋊#82311yescharacteristic
361C2D5⋊#82411yescharacteristic
362C2#1175198411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746574C2semidirect
284. C3×C5#1821semidirect
338. C5#69973semidirect
356. C3#10604337semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Dic32
#117524142
C3×#657552
#117465742
#106043373
#699735