Finite Group Databasebeta

← #14281165

Subgroups — #14281165

Order 1920.

472 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4×#1204C211yesmaximal, characteristic
2#11752418C211yesmaximal, characteristic
3C3×#65759C211yesmaximal, characteristic
4#11746569C212yesmaximal
5#11746568C212yesmaximal
6#10604164—31nomaximal, Hall
7C22×#1204C411yescharacteristic
8C2×C4×Dic15C411yescharacteristic
9C2×C4×C5×Dic3C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×Dic3⋊Dic5C2211yescharacteristic
12C2×#6669C2211yescharacteristic
13C2×#6668C411yescharacteristic
14C4×#1204—21no—
15C4×#1204—21no—
16C4×#1204—21no—
17C4×#1204—21no—
18#91241C2212yes—
19#91231—21no—
20C4⋊(C3⋊#170)—21no—
21C3×C22⋊#170C2212yes—
22C3×#4002—21no—
23C3×C4⋊#170—21no—
24#70830—51nomaximal, Hall
25C2×C4×Dic10—31no—
26#65759—31no—
27#65759D311yescharacteristic
28#64914—32no—
29#64913—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×Dic15C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C22×C5×Dic3C2×C411yescharacteristic
34C22×C5×Dic3C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2311yescharacteristic
37C2×#1204—22no—
38C2×#1204—22no—
39C2×#1204—21no—
40C2×#1204—21no—
41C2×C3⋊#170—22no—
42C2×C3×#170—22no—
43C4×Dic15—21no—
44C4×Dic15—21no—
45C4×C5×Dic3—21no—
46C4×C5×Dic3—21no—
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51Dic3⋊Dic5—21no—
52Dic3⋊Dic5—21no—
53#6669—21no—
54#6669—21no—
55#6668—21no—
56#6668—21no—
57C2×C4×Dic6—51no—
58C3×#432—51no—
59#4926—51no—
60#4469—52no—
61#4469—52no—
62C22×Dic10—31no—
63C2×C42×C5—31no—
64C2×C4⋊Dic5—31no—
65C2×#683—31no—
66C2×#683—31no—
67C2×C4×Dic5—31no—
68C2×C4×Dic5C2×D311yescharacteristic
69C4×Dic10—61no—
70C4×Dic10—61no—
71C4×Dic10—61no—
72C4×Dic10—61no—
73C22⋊#170—32no—
74C22⋊#170C2×D312yes—
75#4002—21no—
76#4002—61no—
77C4⋊#170—21no—
78C4⋊#170—61no—
79#1467—151noSylow
80C23×C3×C5C22×C411yescharacteristic
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×Dic15—21no—
85C2×Dic15—21no—
86C2×Dic15—21no—
87C2×Dic15—41no—
88C2×Dic15M1612yes—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—41no—
93C2×C5×Dic3M1612yes—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—41no—
97C2×C3×Dic5C22⋊C411yescharacteristic
98C2×C3×Dic5C22⋊C411yescharacteristic
99C2×C3×Dic5C2×D411yescharacteristic
100C2×C3×Dic5C2×D411yescharacteristic
101#1204—24no—
102#1204—24no—
103C3⋊#170—42no—
104C3×#170—42no—
105C22×Dic6—51no—
106C2×C3×C42—51no—
107C2×C4⋊Dic3—51no—
108C2×Dic3⋊C4—51no—
109C2×Dic3⋊C4—51no—
110C2×C4×Dic3—51no—
111C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
112C4×Dic6—101no—
113C4×Dic6—101no—
114C4×Dic6—101no—
115C4×Dic6—101no—
116C3×C4⋊C8—101no—
117C3×C22⋊C8—52no—
118C3×#97—101no—
119#830—52no—
120C4⋊(C3⋊C8)—101no—
121#803—101no—
122C22×C4×C5—31no—
123C22×C4×C5—31no—
124C22×C4×C5C4×D311yescharacteristic
125C22×Dic5—31no—
126C22×Dic5—31no—
127C22×Dic5C4×D311yescharacteristic
128C22×Dic5C22×D311yescharacteristic
129C2×Dic10—62no—
130C2×Dic10—62no—
131C2×Dic10—61no—
132C2×Dic10—61no—
133C2×#170—22no—
134C2×#170—62no—
135C42×C5—61no—
136C42×C5—61no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—61no—
140#683—61no—
141#683—61no—
142#683—61no—
143C4×Dic5—61no—
144C4×Dic5—61no—
145C4×Dic5D1211yescharacteristic
146C4×Dic5D1211yescharacteristic
147C4×Dic5#6711yescharacteristic
148C4×Dic5#6711yescharacteristic
149C2×C4×Q8—151no—
150#432—51no—
151#432—151no—
152#324—152no—
153#324—152no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C2×M1611yescharacteristic
158C22×C3×C5C2×M1611yescharacteristic
159C3×C4×C5—21no—
160C3×C4×C5#10112yes—
161Dic15—22no—
162Dic15—41no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C5×Dic3—22no—
168C5×Dic3—41no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
172C22×Dic3—51no—
173C22×Dic3—51no—
174C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
175C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
176C2×Dic6—102no—
177C2×Dic6—101no—
178C2×Dic6—101no—
179C2×Dic6—102no—
180C2×C3×C8—102no—
181C3×C42—51no—
182C3×C42—51no—
183C3×C42—51no—
184C3×C42—51no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189Dic3⋊C4—101no—
190Dic3⋊C4—101no—
191C4×Dic3—21no—
192C4×Dic3—21no—
193C4×Dic3—101no—
194C4×Dic3—101no—
195C2×C3⋊C8—102no—
196C23×C5C2×C4×D311yescharacteristic
197C2×C4×C5—22no—
198C2×C4×C5—32no—
199C2×C4×C5—61no—
200C2×C4×C5—61no—
201C2×C4×C5—61no—
202C2×C4×C5—121no—
203C2×C4×C5(C2×D3)⋊C411yescharacteristic
204C2×C4×C5(C2×D3)⋊C411yescharacteristic
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—32no—
208C2×Dic5—41no—
209C2×Dic5—61no—
210C2×Dic5—61no—
211C2×Dic5—61no—
212C2×Dic5—121no—
213C2×Dic5(C2×D3)⋊C411yescharacteristic
214C2×Dic5(C2×D3)⋊C411yescharacteristic
215C2×Dic5C2×D1211yescharacteristic
216C2×Dic5C2×#6711yescharacteristic
217Dic10—64no—
218Dic10—64no—
219#170—42no—
220#170—122no—
221C22×Q8—151no—
222C4×Q8—301no—
223C4×Q8—301no—
224C4×Q8—301no—
225C4×Q8—301no—
226C2×C4⋊C4—151no—
227C2×C4⋊C4—151no—
228C2×C4⋊C4—151no—
229C2×C42—31no—
230C2×C42—51no—
231C2×C42—151no—
232C4⋊C8—101no—
233C4⋊C8—301no—
234C22⋊C8—52no—
235C22⋊C8—152no—
236#97—101no—
237#97—301no—
238C2×C3×C5—21no—
239C2×C3×C5—21no—
240C2×C3×C5#40711yescharacteristic
241C2×C3×C5#41011yescharacteristic
242C2×C3×C5C2×#10111yescharacteristic
243C23×C3C22×AGL(1,𝔽5)11yescharacteristic
244C2×C3×C4—22no—
245C2×C3×C4—51no—
246C2×C3×C4—51no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—201no—
252C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
253C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—41no—
258C2×Dic3—52no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261C2×Dic3—101no—
262C2×Dic3—201no—
263C2×Dic3#70012yes—
264Dic6—104no—
265Dic6—104no—
266C3×C8—202no—
267C3⋊C8—202no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5D3×M1611yescharacteristic
271C22×C5D3×M1611yescharacteristic
272C22×C5C2×(C2×D3)⋊C411yescharacteristic
273C4×C5—21no—
274C4×C5—62no—
275C4×C5—121no—
276C4×C5#82412yes—
277Dic5—21no—
278Dic5—21no—
279Dic5—21no—
280Dic5—21no—
281Dic5—62no—
282Dic5—121no—
283C2×Q8—302no—
284C2×Q8—301no—
285C2×Q8—301no—
286C2×Q8—302no—
287C22×C4—31no—
288C22×C4—31no—
289C22×C4—51no—
290C22×C4—51no—
291C22×C4—151no—
292C22×C4—151no—
293C22×C4D3×AGL(1,𝔽5)11yescharacteristic
294C2×C8—102no—
295C2×C8—302no—
296C4⋊C4—301no—
297C4⋊C4—301no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C42—51no—
303C42—51no—
304C42—51no—
305C42—51no—
306C42—61no—
307C42—61no—
308C42—301no—
309C42—301no—
310C3×C5#146711yescharacteristic, complemented, Hall
311C22×C3—21no—
312C22×C3—21no—
313C22×C3C2×#70011yescharacteristic
314C22×C3D5⋊M1611yescharacteristic
315C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
316C3×C4—21no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4—101no—
320C3×C4—101no—
321C3×C4#400512yes—
322Dic3—22no—
323Dic3—41no—
324Dic3—102no—
325Dic3—201no—
326C2×C5—21no—
327C2×C5—21no—
328C2×C5#500611yescharacteristic
329C2×C5#512611yescharacteristic
330C2×C5C2×#82411yescharacteristic
331C23C2×D3×AGL(1,𝔽5)11yescharacteristic
332Q8—304no—
333Q8—304no—
334C2×C4—22no—
335C2×C4—32no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—51no—
339C2×C4—51no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—121no—
346C2×C4—152no—
347C2×C4—201no—
348C2×C4—301no—
349C2×C4—301no—
350C2×C4—301no—
351C2×C4—601no—
352C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
353C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
354C8—202no—
355C8—602no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3#6574511yescharacteristic
359C2×C3#6575611yescharacteristic
360C2×C3C2×#400511yescharacteristic
361C5#7083011yescharacteristic, complemented, Sylow
362C22—21no—
363C22—21no—
364C22D3×#70011yescharacteristic
365C22#9191511yescharacteristic
366C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
367C4—21no—
368C4—62no—
369C4—101no—
370C4—101no—
371C4—101no—
372C4—101no—
373C4—121no—
374C4—302no—
375C4—601no—
376C4#9117512yes—
377C3#1060416411yescharacteristic, complemented, Sylow
378C2—21no—
379C2—21no—
380C2#1175180611yescharacteristic
381C2#1175181511yescharacteristic
382C2C2×#9117511yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1467
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
310. C3×C5#1467semidirect
361. C5#70830semidirect
377. C3#10604164semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12042
#117524182
C3×#657592
#117465692
#117465682
#106041643
#708305