Finite Group Databasebeta

← #14301516

Subgroups — #14301516

Order 1920.

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

normal subgroups only

This group has 648 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
1C3×#66262C211yesmaximal, characteristic
2D5×#944C211yesmaximal, characteristic
3D5⋊#836C211yesmaximal, characteristic
4#11751711C212yesmaximal
5#11746523C212yesmaximal
6#10604670—31nomaximal, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×D5×Dic6C2211yescharacteristic
9D5⋊#208C2212yes—
10C3×Q8×AGL(1,𝔽5)—24no—
11C3×#4130—22no—
12C3×#4130C2212yes—
13#91833C411yescharacteristic, complemented
14C5×#944C411yescharacteristic, complemented
15D5×Dic3⋊C4—22no—
16C4×D5×Dic3C2211yescharacteristic
17#91389C411yescharacteristic, complemented
18#91385C411yescharacteristic, complemented
19#91327—22no—
20#91234—22no—
21#91153—24no—
22#71660—51nomaximal, Hall
23#66262D311yescharacteristic
24D5×C4⋊Q8—31no—
25D5⋊#101—31no—
26#65782—32no—
27#64862—32no—
28C2×C3×C5×Q8C2×C411yescharacteristic
29C2×Dic30C2×C411yescharacteristic
30C2×C5×Dic6C2×C411yescharacteristic
31C3×Q8×D5—22no—
32C3×Q8×D5—22no—
33C2×C3×C4×D5D412yes—
34C2×C3×C4×D5C2311yescharacteristic
35C2×C3×Dic10C2×C411yescharacteristic
36C2×C3×Dic10D412yes—
37C2×#1204—21no—
38C2×D5×Dic3—21no—
39C2×D5×Dic3—21no—
40D5×Dic6—22no—
41D5×Dic6—22no—
42#6762—22no—
43#6758—22no—
44D5⋊(C3⋊C8)—22no—
45C3×C22⋊AGL(1,𝔽5)—22no—
46C3×C4⋊AGL(1,𝔽5)—24no—
47C3×C4⋊AGL(1,𝔽5)D414yes—
48C3×C4×AGL(1,𝔽5)—24no—
49C3×C4×AGL(1,𝔽5)—22no—
50#6712—22no—
51C4×Dic15C2×C411yescharacteristic
52C5×Dic3⋊C4—22no—
53C4×C5×Dic3C2×C411yescharacteristic
54Dic3⋊Dic5—22no—
55#6669—22no—
56Dic3×Dic5—21no—
57C3×#519—51no—
58C2×#944—51no—
59C2×#836—51no—
60#5004—52no—
61#4532—52no—
62C2×Q8×D5—31no—
63C2×Q8×D5C2×D311yescharacteristic
64Q8×AGL(1,𝔽5)—24no—
65#4130—22no—
66#4130C2×D312yes—
67D5⋊M16—32no—
68C5×C4⋊Q8—31no—
69#4090—31no—
70#4090—31no—
71D5×C4⋊C4—62no—
72#4034—62no—
73C42×D5—31no—
74#4015—31no—
75#4009—64no—
76#4005—62no—
77#1886—151noSylow
78C22×C3×D5C2×D411yescharacteristic
79C2×C3×AGL(1,𝔽5)—24no—
80C3×C5×Q8—22no—
81C2×C3×C4×C5C22⋊C412yes—
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85Dic30—22no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C5×Dic6—22no—
89C2×C3×Dic5C22⋊C412yes—
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5C2×D412yes—
94C3×C4×D5#4112yes—
95C3×Dic10—22no—
96C3×Dic10—24no—
97#1204—42no—
98D5×Dic3—24no—
99D5×Dic3—41no—
100D5×Dic3—41no—
101C3⋊#170—42no—
102C22×C3×Q8—51no—
103C22×Dic6—51no—
104C3×C4×Q8—104no—
105C3×#117—52no—
106C3×#117—102no—
107#944—51no—
108#944—51no—
109#944—51no—
110#944—102no—
111#944AGL(1,𝔽5)11yescharacteristic, complemented
112C2×Dic3⋊C4—102no—
113C2×C4×Dic3—51no—
114C2×#208—52no—
115#836—102no—
116#810—104no—
117C2×C5×Q8—31no—
118C2×C5×Q8C4×D311yescharacteristic
119Q8×D5—22no—
120Q8×D5—22no—
121Q8×D5—62no—
122Q8×D5—62no—
123C2×C4×D5—61no—
124C2×C4×D5—61no—
125C2×C4×D5#6712yes—
126C2×C4×D5C22×D311yescharacteristic
127C2×Dic10—31no—
128C2×Dic10—61no—
129C2×Dic10C4×D311yescharacteristic
130C2×Dic10D1212yes—
131C22⋊AGL(1,𝔽5)—22no—
132#704—62no—
133C4⋊AGL(1,𝔽5)—24no—
134C4⋊AGL(1,𝔽5)#6714yes—
135C4×AGL(1,𝔽5)—24no—
136C4×AGL(1,𝔽5)—22no—
137#700—62no—
138D5⋊C8—62no—
139C5×C4⋊C4—62no—
140C42×C5—31no—
141C4⋊Dic5—62no—
142#683—62no—
143#683—62no—
144C4×Dic5—31no—
145C4×Dic5—61no—
146C2×C4⋊Q8—151no—
147#519—51no—
148#419—152no—
149C2×#101—151no—
150#339—152no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×C3×D5—22no—
153C2×C3×D5#12011yescharacteristic
154C2×C3×D5#12311yescharacteristic
155C3×AGL(1,𝔽5)—44no—
156C3×C4×C5—22no—
157C3×C4×C5C4×D412yes—
158Dic15—22no—
159Dic15—41no—
160C3×Dic5—22no—
161C3×Dic5#12112yes—
162C5×Dic3—22no—
163C5×Dic3—41no—
164C2×C3×Q8—52no—
165C2×C3×Q8—51no—
166C2×C3×Q8—102no—
167C2×C3×Q8—102no—
168C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—52no—
171C22×Dic3—101no—
172C22×Dic3—101no—
173C2×Dic6—51no—
174C2×Dic6—102no—
175C2×Dic6—102no—
176C2×Dic6—101no—
177C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
178C3×C4⋊C4—54no—
179C3×C4⋊C4—104no—
180C3×C22⋊C4—102no—
181C3×C42—102no—
182C3×C42—104no—
183Dic3⋊C4—22no—
184Dic3⋊C4—102no—
185Dic3⋊C4—102no—
186Dic3⋊C4—102no—
187C4×Dic3—51no—
188C4×Dic3—101no—
189C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
190#208—102no—
191#208—102no—
192C2×C3⋊C8—102no—
193C22×D5C2×#6711yescharacteristic
194C2×AGL(1,𝔽5)—24no—
195C5×Q8—22no—
196C5×Q8—62no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5(C2×D3)⋊C412yes—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×Dic5—61no—
202C2×Dic5—61no—
203C2×Dic5(C2×D3)⋊C412yes—
204C2×Dic5C2×D1211yescharacteristic
205C4×D5—22no—
206C4×D5—22no—
207C4×D5—64no—
208C4×D5—121no—
209C4×D5—121no—
210C4×D5#23512yes—
211C4×D5C2×#6712yes—
212Dic10—22no—
213Dic10—24no—
214Dic10—62no—
215Dic10—122no—
216#170—122no—
217C22×Q8—51no—
218C22×Q8—151no—
219C2×M16—152no—
220C4⋊Q8—31no—
221C4⋊Q8—151no—
222C4⋊Q8—151no—
223C4⋊Q8—151no—
224C4⋊Q8—302no—
225C4×Q8—104no—
226#117—52no—
227#117—102no—
228C2×C4⋊C4—302no—
229C2×C42—151no—
230#103—304no—
231#101—302no—
232C2×C3×C5—21no—
233C2×C3×C5#38611yescharacteristic
234C3×D5—21no—
235C3×D5#45612yes—
236C23×C3—51no—
237C3×Q8—22no—
238C3×Q8—104no—
239C3×Q8—102no—
240C2×C3×C4—51no—
241C2×C3×C4—52no—
242C2×C3×C4—52no—
243C2×C3×C4—52no—
244C2×C3×C4—102no—
245C2×C3×C4—102no—
246C2×C3×C4—104no—
247C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
248C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—104no—
252C2×Dic3—101no—
253C2×Dic3—101no—
254C2×Dic3—201no—
255C2×Dic3—201no—
256Dic6—22no—
257Dic6—102no—
258Dic6—202no—
259C3⋊C8—202no—
260C22×C5C2×(C2×D3)⋊C411yescharacteristic
261C2×D5—22no—
262C2×D5#92911yescharacteristic
263C2×D5#95311yescharacteristic
264AGL(1,𝔽5)—44no—
265C4×C5—22no—
266C4×C5—62no—
267C4×C5—121no—
268C4×C5C4×#6712yes—
269Dic5—22no—
270Dic5—62no—
271Dic5—121no—
272Dic5#93012yes—
273C2×Q8—31no—
274C2×Q8—52no—
275C2×Q8—51no—
276C2×Q8—102no—
277C2×Q8—102no—
278C2×Q8—151no—
279C2×Q8—301no—
280C2×Q8—302no—
281C2×Q8—302no—
282C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
283C22×C4—51no—
284C22×C4—52no—
285C22×C4—301no—
286C22×C4—301no—
287M16—302no—
288M16—302no—
289C2×C8—302no—
290C4⋊C4—54no—
291C4⋊C4—62no—
292C4⋊C4—104no—
293C4⋊C4—302no—
294C4⋊C4—302no—
295C4⋊C4—302no—
296C22⋊C4—102no—
297C42—31no—
298C42—102no—
299C42—104no—
300C42—151no—
301C42—301no—
302C3×C5#188611yescharacteristic, complemented, Hall
303C22×C3—51no—
304C22×C3—51no—
305C22×C3—102no—
306C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307C3×C4—22no—
308C3×C4—52no—
309C3×C4—102no—
310C3×C4—204no—
311C3×C4D4×AGL(1,𝔽5)12yes—
312Dic3—22no—
313Dic3—41no—
314Dic3—102no—
315Dic3—201no—
316C2×C5—21no—
317C2×C5#521311yescharacteristic
318D5—21no—
319D5#524612yes—
320C23—51no—
321Q8—22no—
322Q8—62no—
323Q8—104no—
324Q8—102no—
325Q8—302no—
326Q8—602no—
327C2×C4—51no—
328C2×C4—52no—
329C2×C4—52no—
330C2×C4—52no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—102no—
334C2×C4—102no—
335C2×C4—104no—
336C2×C4—304no—
337C2×C4—301no—
338C2×C4—301no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
342C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
343C8—602no—
344C2×C3—21no—
345C2×C3—52no—
346C2×C3—101no—
347C2×C3#6577911yescharacteristic
348C5#7166011yescharacteristic, complemented, Sylow
349C22—51no—
350C22—51no—
351C22—102no—
352C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
353C4—22no—
354C4—52no—
355C4—62no—
356C4—102no—
357C4—121no—
358C4—204no—
359C4—302no—
360C4—601no—
361C4AGL(1,𝔽5)×#6712yes—
362C3#1060467011yescharacteristic, complemented, Sylow
363C2—21no—
364C2—52no—
365C2—101no—
366C2#1175202211yescharacteristic
subgroupG/H
centerC2#11752022
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC2×C3×C5#386
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#1886
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
13. #91833C4semidirect
14. C5×#944C4semidirect
17. #91389C4semidirect
18. #91385C4semidirect
111. #944AGL(1,𝔽5)semidirect
302. C3×C5#1886semidirect
348. C5#71660semidirect
362. C3#10604670semidirect

Maximal subgroups

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

subgroupindex
C3×#662622
D5×#9442
D5⋊#8362
#117517112
#117465232
#106046703
#716605