Finite Group Databasebeta

← #14298393

Subgroups — #14298393

Order 1920.

632 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C22×#6668C211yesmaximal, characteristic
2#11752457C211yesmaximal, characteristic
3C3×#65798C211yesmaximal, characteristic
4#11746574C214yesmaximal, complemented
5#10604908—31nomaximal, Hall
6C23×Dic15C411yescharacteristic
7C23×C5×Dic3C411yescharacteristic
8C23×C3×Dic5C2211yescharacteristic
9C2×#6762C2212yes—
10C2×C3×#704C2212yes—
11C2×#6668—21no—
12C2×#6668—21no—
13C2×#6668—21no—
14C2×#6668—21no—
15C2×#6668C412yes—
16C2×#6668C2212yes—
17#91241—21no—
18#91241—21no—
19C3×C22⋊#170—21no—
20C3×C22⋊#170—21no—
21#69973—51nomaximal, Hall
22C22×#683—31no—
23#65798—31no—
24#65798D311yescharacteristic
25#64919—34no—
26C24×C3×C5C2×C411yescharacteristic
27C22×Dic15—21no—
28C22×Dic15—21no—
29C22×Dic15—42no—
30C22×Dic15C2×C412yes—
31C22×C5×Dic3—21no—
32C22×C5×Dic3—21no—
33C22×C5×Dic3—42no—
34C22×C5×Dic3C2×C412yes—
35C22×C3×Dic5—24no—
36C22×C3×Dic5C2×C411yescharacteristic
37C22×C3×Dic5D411yescharacteristic
38C22×C3×Dic5D411yescharacteristic
39C22×C3×Dic5D411yescharacteristic
40C22×C3×Dic5D411yescharacteristic
41C22×C3×Dic5C2311yescharacteristic
42#6762—24no—
43C2×C3⋊#170—22no—
44C3×#704—24no—
45C2×C3×#170—22no—
46#6668—22no—
47#6668—22no—
48#6668—22no—
49#6668—22no—
50C22×C4⋊Dic3—51no—
51C3×#407—51no—
52#5207—51no—
53#4554—54no—
54C23×C4×C5—31no—
55C23×Dic5—31no—
56C23×Dic5C2×D311yescharacteristic
57C2×#704—32no—
58C2×#704C2×D312yes—
59C2×#683—32no—
60C2×#683—32no—
61C2×#683—61no—
62C2×#683—61no—
63C2×#683—61no—
64C2×#683—61no—
65C22⋊#170—21no—
66C22⋊#170—21no—
67C22⋊#170—61no—
68C22⋊#170—61no—
69#1821—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—22no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22×C411yescharacteristic
76C2×Dic15—22no—
77C2×Dic15—42no—
78C2×Dic15—42no—
79C2×Dic15—42no—
80C2×C5×Dic3—22no—
81C2×C5×Dic3—42no—
82C2×C5×Dic3—42no—
83C2×C5×Dic3—42no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—22no—
86C2×C3×Dic5—22no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C2×C3×Dic5#4114yes—
94C3⋊#170—42no—
95C3×#170—42no—
96C23×C3×C4—51no—
97C23×Dic3—51no—
98C23×Dic3AGL(1,𝔽5)11yescharacteristic
99C2×C3×M16—52no—
100C2×C4⋊Dic3—52no—
101C2×C4⋊Dic3—52no—
102C2×C4⋊Dic3—101no—
103C2×C4⋊Dic3—101no—
104C2×C4⋊Dic3—101no—
105C2×C4⋊Dic3—101no—
106C2×#208—52no—
107C3×C22⋊C8—101no—
108C3×C22⋊C8—101no—
109#830—101no—
110#830—101no—
111C24×C5C4×D311yescharacteristic
112C22×C4×C5—32no—
113C22×C4×C5—61no—
114C22×C4×C5—61no—
115C22×C4×C5—122no—
116C22×Dic5—24no—
117C22×Dic5—32no—
118C22×Dic5—61no—
119C22×Dic5—61no—
120C22×Dic5—122no—
121C22×Dic5C4×D311yescharacteristic
122C22×Dic5D1211yescharacteristic
123C22×Dic5D1211yescharacteristic
124C22×Dic5#6711yescharacteristic
125C22×Dic5#6711yescharacteristic
126C22×Dic5C22×D311yescharacteristic
127#704—24no—
128#704—64no—
129C2×#170—22no—
130C2×#170—62no—
131#683—62no—
132#683—62no—
133#683—62no—
134#683—62no—
135C22×C4⋊C4—151no—
136#407—51no—
137#407—151no—
138#343—154no—
139C22×C3×C5—28no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5#10012yes—
147C22×C3×C5#10112yes—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C22×C3×C5#11712yes—
150Dic15—42no—
151C3×Dic5—21no—
152C3×Dic5—21no—
153C3×Dic5#12312yes—
154C3×Dic5#12312yes—
155C5×Dic3—42no—
156C24×C3C2×AGL(1,𝔽5)11yescharacteristic
157C22×C3×C4—51no—
158C22×C3×C4—51no—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4—104no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—42no—
167C22×Dic3—52no—
168C22×Dic3—101no—
169C22×Dic3—101no—
170C22×Dic3—202no—
171C22×Dic3C2×AGL(1,𝔽5)12yes—
172C3×M16—104no—
173C2×C3×C8—102no—
174C4⋊Dic3—102no—
175C4⋊Dic3—102no—
176C4⋊Dic3—102no—
177C4⋊Dic3—102no—
178#208—104no—
179C2×C3⋊C8—102no—
180C23×C5—22no—
181C23×C5—22no—
182C23×C5—22no—
183C23×C5(C2×D3)⋊C411yescharacteristic
184C23×C5(C2×D3)⋊C411yescharacteristic
185C23×C5C2×C4×D311yescharacteristic
186C2×C4×C5—62no—
187C2×C4×C5—122no—
188C2×C4×C5—122no—
189C2×C4×C5—122no—
190C2×Dic5—22no—
191C2×Dic5—22no—
192C2×Dic5—22no—
193C2×Dic5—22no—
194C2×Dic5—22no—
195C2×Dic5—62no—
196C2×Dic5—122no—
197C2×Dic5—122no—
198C2×Dic5—122no—
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201C2×Dic5C2×D1211yescharacteristic
202C2×Dic5#23714yes—
203C2×Dic5C2×#6711yescharacteristic
204#170—42no—
205#170—122no—
206C23×C4—31no—
207C23×C4—51no—
208C23×C4—151no—
209C2×M16—52no—
210C2×M16—152no—
211C2×C4⋊C4—152no—
212C2×C4⋊C4—152no—
213C2×C4⋊C4—301no—
214C2×C4⋊C4—301no—
215C2×C4⋊C4—301no—
216C2×C4⋊C4—301no—
217C22⋊C8—101no—
218C22⋊C8—101no—
219C22⋊C8—301no—
220C22⋊C8—301no—
221C2×C3×C5—22no—
222C2×C3×C5—22no—
223C2×C3×C5—22no—
224C2×C3×C5#38111yescharacteristic
225C2×C3×C5C2×#10011yescharacteristic
226C2×C3×C5C2×#10111yescharacteristic
227C23×C3—22no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
231C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
232C23×C3C22×AGL(1,𝔽5)11yescharacteristic
233C2×C3×C4—54no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—51no—
238C2×C3×C4—102no—
239C2×C3×C4—102no—
240C2×C3×C4—102no—
241C2×C3×C4—102no—
242C2×C3×C4—102no—
243C2×Dic3—22no—
244C2×Dic3—42no—
245C2×Dic3—42no—
246C2×Dic3—42no—
247C2×Dic3—102no—
248C2×Dic3—202no—
249C2×Dic3—202no—
250C2×Dic3—202no—
251C3×C8—202no—
252C3⋊C8—202no—
253C22×C5—28no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5#82312yes—
261C22×C5#82412yes—
262C22×C5#87712yes—
263C22×C5C2×(C2×D3)⋊C411yescharacteristic
264C4×C5—122no—
265Dic5—21no—
266Dic5—21no—
267Dic5—122no—
268Dic5#88612yes—
269Dic5#93512yes—
270C24D3×AGL(1,𝔽5)11yescharacteristic
271C22×C4—32no—
272C22×C4—51no—
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—51no—
276C22×C4—51no—
277C22×C4—51no—
278C22×C4—61no—
279C22×C4—61no—
280C22×C4—104no—
281C22×C4—122no—
282C22×C4—152no—
283C22×C4—301no—
284C22×C4—301no—
285C22×C4—602no—
286M16—104no—
287M16—304no—
288C2×C8—102no—
289C2×C8—302no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C4⋊C4—302no—
293C4⋊C4—302no—
294C3×C5#182111yescharacteristic, complemented, Hall
295C22×C3—28no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3#400512yes—
303C22×C3#401312yes—
304C22×C3#413012yes—
305C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
306C3×C4—52no—
307C3×C4—52no—
308C3×C4—101no—
309C3×C4—101no—
310Dic3—42no—
311Dic3—202no—
312C2×C5—22no—
313C2×C5—22no—
314C2×C5—22no—
315C2×C5#494311yescharacteristic
316C2×C5C2×#82311yescharacteristic
317C2×C5C2×#82411yescharacteristic
318C23—22no—
319C23—22no—
320C23—22no—
321C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
322C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
323C23C2×D3×AGL(1,𝔽5)11yescharacteristic
324C2×C4—54no—
325C2×C4—51no—
326C2×C4—51no—
327C2×C4—51no—
328C2×C4—51no—
329C2×C4—62no—
330C2×C4—102no—
331C2×C4—102no—
332C2×C4—102no—
333C2×C4—102no—
334C2×C4—102no—
335C2×C4—122no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4—302no—
339C2×C4—602no—
340C2×C4—602no—
341C2×C4—602no—
342C8—202no—
343C8—602no—
344C2×C3—22no—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3C2×#400511yescharacteristic
348C2×C3#6576411yescharacteristic
349C2×C3C2×#401311yescharacteristic
350C5#6997311yescharacteristic, complemented, Sylow
351C22—28no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22#9117412yes—
359C22#9117512yes—
360C22#9192312yes—
361C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
362C4—52no—
363C4—52no—
364C4—101no—
365C4—101no—
366C4—122no—
367C4—602no—
368C3#1060490811yescharacteristic, complemented, Sylow
369C2—22no—
370C2—22no—
371C2—22no—
372C2#1175198411yescharacteristic
373C2C2×#9117411yescharacteristic
374C2C2×#9117511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
Fitting, prime radicalC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #11746574C2semidirect
294. C3×C5#1821semidirect
350. C5#69973semidirect
368. C3#10604908semidirect

Maximal subgroups

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

subgroupindex
C22×#66682
#117524572
C3×#657982
#117465742
#106049083
#699735