Finite Group Databasebeta

← #14285014

Subgroups — #14285014

Order 1920.

432 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 114 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#11754174C211yesmaximal, characteristic
2C2×#91233C211yesmaximal, characteristic
3C3×#65758C211yesmaximal, characteristic
4#11746511C212yesmaximal, complemented
5#11746510C212yesmaximal, complemented
6#10604518—31nomaximal, Hall
7C22×C3⋊#170—21no—
8C2×C3×#704—21no—
9#91813C411yescharacteristic
10C5×#924C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91574—21no—
13#91528—21no—
14#91468C2211yescharacteristic
15#91378—21no—
16#91376C2211yescharacteristic
17#91333C411yescharacteristic
18Dic5×Dic6C411yescharacteristic
19#91323—21no—
20#91233—21no—
21#91233C2212yes—
22C3×#4004C2212yes—
23C3×C4⋊#170—21no—
24#70509—51nomaximal, Hall
25#65956—31no—
26#65758D311yescharacteristic
27C2×#4004—31no—
28#64931—32no—
29#64873—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C2×#1204—21no—
36C2×C3⋊#170—22no—
37C2×C3⋊#170—42no—
38C3×#704—42no—
39C2×C3×#170—22no—
40#6719—21no—
41C4⋊Dic15C2×C411yescharacteristic
42#6712—21no—
43C5×#217—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×Dic3⋊C4—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51#6669—21no—
52#6668—21no—
53#6668—21no—
54#6668—21no—
55Dic3×Dic5—21no—
56Dic3×Dic5—21no—
57#5470—51no—
58C3×#423—51no—
59C2×C4⋊(C3⋊C8)—51no—
60#4486—52no—
61#4481—52no—
62C2×#704—21no—
63C22×#170—61no—
64C5×C22⋊Q8—31no—
65Q8×Dic5—31no—
66#4090—31no—
67#4070—31no—
68C2×C4×Dic5C2×D311yescharacteristic
69#4035—61no—
70#4034—31no—
71#4033—31no—
72#4033—61no—
73#4024—61no—
74#4023—61no—
75#4004—32no—
76#4004—61no—
77#4004C2×D312yes—
78C4⋊#170—21no—
79#1550—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×Dic15—21no—
85C2×Dic15—21no—
86Dic30—41no—
87C2×C5×Dic3—21no—
88C2×C5×Dic3—21no—
89C5×Dic6—41no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5SD1612yes—
95C2×C3×Dic5Q1612yes—
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98#1204—41no—
99#1204—41no—
100C3⋊#170—42no—
101C3×#170—42no—
102C2×C3×M16—101no—
103C2×C3×C42—51no—
104#926—101no—
105#924—51no—
106#924—101no—
107#924AGL(1,𝔽5)11yescharacteristic
108C22×C3⋊C8—101no—
109#870—101no—
110#869—51no—
111#869—51no—
112C4×Dic6—51no—
113C4×Dic6—51no—
114C4×Dic6—101no—
115C3×C4⋊C8—52no—
116C3×C4⋊C8—101no—
117C4⋊(C3⋊C8)—52no—
118C4⋊(C3⋊C8)—101no—
119C2×C5×Q8—31no—
120C22×C4×C5C4×D311yescharacteristic
121C22×Dic5D1211yescharacteristic
122C22×Dic5#6711yescharacteristic
123C2×Dic10—31no—
124C2×Dic10—61no—
125#704—42no—
126C2×#170—22no—
127C2×#170—62no—
128C2×#170—122no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—61no—
131C5×C22⋊C4—61no—
132C22⋊Dic5—61no—
133C4⋊Dic5—31no—
134C4⋊Dic5—61no—
135#683—61no—
136#683—61no—
137#683—61no—
138#683—61no—
139#683—61no—
140C4×Dic5—61no—
141C4×Dic5—61no—
142C4×Dic5C4×D311yescharacteristic
143C4×Dic5D1211yescharacteristic
144C4×Dic5#6711yescharacteristic
145C4×Dic5C22×D311yescharacteristic
146#533—151no—
147#423—51no—
148C2×C4⋊C8—151no—
149#333—152no—
150#332—152no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5#10312yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157Dic15—41no—
158Dic15—41no—
159C3×Dic5—21no—
160C3×Dic5#10312yes—
161C3×Dic5C2×SD1611yescharacteristic
162C3×Dic5C2×Q1611yescharacteristic
163C3×Dic5AGL(1,ℤ/8)11yescharacteristic
164C3×Dic5#13711yescharacteristic
165C5×Dic3—41no—
166C5×Dic3—41no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
170C2×Dic6—51no—
171C2×Dic6—101no—
172C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
173C3×M16—202no—
174C2×C3×C8—102no—
175C3×C42—51no—
176C3×C42—51no—
177C3×C42—51no—
178C3×C42—51no—
179#217—21no—
180#217—101no—
181C4⋊Dic3—51no—
182C4⋊Dic3—101no—
183C4⋊Dic3—101no—
184C4⋊Dic3—101no—
185C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
186Dic3⋊C4—21no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189Dic3⋊C4—101no—
190C4×Dic3—101no—
191C4×Dic3—101no—
192C2×C3⋊C8—102no—
193C2×C3⋊C8—202no—
194C23×C5(C2×D3)⋊C411yescharacteristic
195C5×Q8—121no—
196C2×C4×C5—41no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—61no—
204C2×Dic5—61no—
205C2×Dic5(C2×D3)⋊C411yescharacteristic
206C2×Dic5(C2×D3)⋊C411yescharacteristic
207C2×Dic5#21412yes—
208C2×Dic5#21612yes—
209C2×Dic5C2×D1211yescharacteristic
210C2×Dic5C2×#6711yescharacteristic
211Dic10—121no—
212Dic10—121no—
213Dic10—121no—
214#170—42no—
215#170—122no—
216C2×M16—101no—
217C22×C8—301no—
218C4⋊Q8—151no—
219C4⋊Q8—151no—
220#125—301no—
221C22⋊Q8—31no—
222C22⋊Q8—151no—
223C22⋊Q8—301no—
224C4×Q8—151no—
225C4×Q8—151no—
226C4×Q8—301no—
227#117—301no—
228C2×C42—51no—
229C4⋊C8—52no—
230C4⋊C8—101no—
231C4⋊C8—152no—
232C4⋊C8—301no—
233C2×C3×C5—22no—
234C2×C3×C5#41311yescharacteristic
235C2×C3×C5C2×#10311yescharacteristic
236C2×C3×C5#41711yescharacteristic
237C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
238C2×C3×C4—41no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—51no—
242C2×C3×C4—52no—
243C2×C3×C4—52no—
244C2×C3×C4—51no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
248C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—101no—
252C2×Dic3—101no—
253Dic6—41no—
254Dic6—201no—
255Dic6—201no—
256Dic6—201no—
257C3×C8—202no—
258C3⋊C8—202no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5#81012yes—
262C22×C5C2×(C2×D3)⋊C411yescharacteristic
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—121no—
266C4×C5—121no—
267Dic5—21no—
268Dic5—121no—
269Dic5—121no—
270Dic5#81012yes—
271Dic5#90811yescharacteristic
272Dic5#90911yescharacteristic
273Dic5C2×#21411yescharacteristic
274Dic5C2×#21611yescharacteristic
275C2×Q8—31no—
276C2×Q8—151no—
277C2×Q8—301no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4D3×AGL(1,𝔽5)11yescharacteristic
281M16—202no—
282C2×C8—102no—
283C2×C8—302no—
284C2×C8—602no—
285C4⋊C4—31no—
286C4⋊C4—61no—
287C4⋊C4—151no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C4⋊C4—301no—
294C22⋊C4—61no—
295C22⋊C4—301no—
296C42—51no—
297C42—51no—
298C42—51no—
299C42—51no—
300C42—301no—
301C42—301no—
302C3×C5#155011yescharacteristic, complemented, Hall
303C22×C3—21no—
304C22×C3—21no—
305C22×C3#400912yes—
306C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—51no—
310C3×C4—51no—
311C3×C4—52no—
312C3×C4—51no—
313C3×C4—51no—
314C3×C4—101no—
315Dic3—41no—
316Dic3—41no—
317Dic3—201no—
318Dic3—201no—
319C2×C5—22no—
320C2×C5C2×#81011yescharacteristic
321C2×C5#513211yescharacteristic
322C2×C5#513311yescharacteristic
323C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
324Q8—121no—
325Q8—601no—
326Q8—601no—
327Q8—601no—
328C2×C4—41no—
329C2×C4—52no—
330C2×C4—52no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—51no—
334C2×C4—51no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—301no—
340C2×C4—301no—
341C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
342C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
343C8—202no—
344C8—602no—
345C2×C3—22no—
346C2×C3#6577711yescharacteristic
347C2×C3C2×#400911yescharacteristic
348C2×C3#6579311yescharacteristic
349C5#7050911yescharacteristic, complemented, Sylow
350C22—21no—
351C22—21no—
352C22#9115312yes—
353C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
354C4—21no—
355C4—21no—
356C4—51no—
357C4—51no—
358C4—51no—
359C4—52no—
360C4—51no—
361C4—101no—
362C4—121no—
363C4—121no—
364C4—601no—
365C4—601no—
366C3#1060451811yescharacteristic, complemented, Sylow
367C2—22no—
368C2#1175170811yescharacteristic
369C2C2×#9115311yescharacteristic
370C2#1175200811yescharacteristic
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×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1550
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. #11746511C2semidirect
5. #11746510C2semidirect
302. C3×C5#1550semidirect
349. C5#70509semidirect
366. C3#10604518semidirect

Maximal subgroups

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

subgroupindex
#117541742
C2×#912332
C3×#657582
#117465112
#117465102
#106045183
#705095