Finite Group Databasebeta

← #14302816

Subgroups — #14302816

Order 1920.

624 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 106 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#11756985C211yesmaximal, characteristic
2#11754788C211yesmaximal, characteristic
3C3×#65771C211yesmaximal, characteristic
4#11751711C212yesmaximal, complemented
5#11746518C212yesmaximal, complemented
6#10604570—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×D5×Dic6C2211yescharacteristic
9C2×#6762—22no—
10#91990—24no—
11D5⋊#208C2212yes—
12C3×#4130C2212yes—
13#91825C411yescharacteristic, complemented
14C5×#936C411yescharacteristic, complemented
15#91574—22no—
16#91548—22no—
17#91389C411yescharacteristic, complemented
18#91385C411yescharacteristic, complemented
19#91357C2211yescharacteristic
20C3×#4011—22no—
21#91153—24no—
22#70046—51nomaximal, Hall
23#66256—31no—
24#66009—31no—
25#65782—32no—
26#65771D311yescharacteristic
27#64863—32no—
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×Dic30C2×C411yescharacteristic
30C2×C5×Dic6C2×C411yescharacteristic
31C2×C3×C22⋊D5D412yes—
32C22×C3×Dic5D412yes—
33C3×#711—22no—
34C3×#711—22no—
35C2×C3×C4×D5C2311yescharacteristic
36C2×C3×Dic10C2×C411yescharacteristic
37C2×#1204—21no—
38C2×D5×Dic3—21no—
39D5×Dic6—22no—
40D5×Dic6—22no—
41#6762—24no—
42#6762—22no—
43C2×C3⋊#170—24no—
44#6758—22no—
45D5⋊(C3⋊C8)D414yes—
46C3×C22⋊AGL(1,𝔽5)—22no—
47C3×C4⋊AGL(1,𝔽5)—22no—
48C3×C4×AGL(1,𝔽5)—22no—
49#6719—22no—
50C4×Dic15C2×C411yescharacteristic
51C5×#217—22no—
52C4×C5×Dic3C2×C411yescharacteristic
53Dic3⋊Dic5—22no—
54#6669—22no—
55#6668—21no—
56#6665—21no—
57#5825—51no—
58#5819—51no—
59C3×#410—51no—
60#5004—52no—
61#4531—52no—
62C2×Q8×D5—31no—
63C2×#711C2×D311yescharacteristic
64C2×#704—62no—
65#4131—64no—
66#4130C2×D312yes—
67D5⋊M16—32no—
68C5×#124—31no—
69#4090—31no—
70#4082—31no—
71#4029—62no—
72#4024—62no—
73#4018—31no—
74#4015—31no—
75#4011—22no—
76#4009—64no—
77#1909—151noSylow
78C23×C3×C5C22⋊C412yes—
79C22×C3×D5C2×D411yescharacteristic
80C2×C3×AGL(1,𝔽5)—42no—
81C3×C5×D4—22no—
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85Dic30—22no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C5×Dic6—22no—
89C3×C22⋊D5—24no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5C22⋊C412yes—
93C2×C3×Dic5C2×D411yescharacteristic
94C3×C4×D5C2×D412yes—
95C3×C4×D5#4112yes—
96C3×Dic10—22no—
97#1204—41no—
98#1204—41no—
99D5×Dic3—42no—
100C3⋊#170—24no—
101C2×C3×#41—51no—
102C22×Dic6—51no—
103C3×#117—52no—
104#948—104no—
105#944—51no—
106#944—51no—
107#936—51no—
108#936AGL(1,𝔽5)11yescharacteristic, complemented
109#935—102no—
110#926—51no—
111#924—102no—
112C2×#208—52no—
113C2×#208—102no—
114C3×#99—102no—
115#810—104no—
116C2×C5×Q8—31no—
117C2×C5×D4C4×D311yescharacteristic
118C2×C22⋊D5#6712yes—
119C22×Dic5D1212yes—
120Q8×D5—62no—
121Q8×D5—62no—
122#711—22no—
123#711—22no—
124C2×C4×D5—61no—
125C2×C4×D5C22×D311yescharacteristic
126C2×Dic10—31no—
127C2×Dic10—61no—
128C2×Dic10C4×D311yescharacteristic
129C22⋊AGL(1,𝔽5)—22no—
130#704—64no—
131#704—62no—
132C2×#170—64no—
133C4⋊AGL(1,𝔽5)—22no—
134C4×AGL(1,𝔽5)—22no—
135#700—62no—
136D5⋊C8—34no—
137C5×C22⋊C4—62no—
138C42×C5—31no—
139C22⋊Dic5—62no—
140#685—61no—
141C4⋊Dic5—62no—
142#683—62no—
143#683—61no—
144C4×Dic5—31no—
145#568—151no—
146#536—151no—
147#419—152no—
148#410—51no—
149H(3,ℤ/4)—152no—
150C22×C3×C5—22no—
151C22×C3×C5—42no—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×C3×D5—41no—
154C2×C3×D5#12112yes—
155C3×AGL(1,𝔽5)—82no—
156C3×C4×C5C4×D412yes—
157Dic15—41no—
158Dic15—41no—
159C3×Dic5—22no—
160C3×Dic5#12011yescharacteristic
161C3×Dic5#12311yescharacteristic
162C5×Dic3—41no—
163C5×Dic3—41no—
164C3×#41—102no—
165C3×#41—102no—
166C2×C3×Q8—51no—
167C2×C3×D4—52no—
168C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—52no—
171C22×Dic3—101no—
172C2×Dic6—51no—
173C2×Dic6—102no—
174C2×Dic6—102no—
175C2×Dic6—101no—
176C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
177C3×C4⋊C4—102no—
178C3×C22⋊C4—102no—
179C3×C42—102no—
180#217—22no—
181#217—101no—
182#217—102no—
183C4⋊Dic3—101no—
184Dic3⋊C4—102no—
185Dic3⋊C4—102no—
186C4×Dic3—51no—
187C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
188#208—102no—
189#208—102no—
190#208—104no—
191C2×C3⋊C8—54no—
192C2×C3⋊C8—104no—
193C23×C5(C2×D3)⋊C412yes—
194C22×D5C2×#6711yescharacteristic
195C2×AGL(1,𝔽5)—42no—
196C5×Q8—62no—
197C5×D4—22no—
198C2×C4×C5—61no—
199C2×C4×C5—61no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C22⋊D5—24no—
202C2×Dic5—22no—
203C2×Dic5—22no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5(C2×D3)⋊C412yes—
207C2×Dic5C2×D1211yescharacteristic
208C4×D5—122no—
209C4×D5D3×D412yes—
210C4×D5#23712yes—
211Dic10—22no—
212Dic10—62no—
213Dic10—121no—
214Dic10—121no—
215#170—64no—
216C2×#41—51no—
217C22×Q8—151no—
218#131—304no—
219C2×M16—152no—
220C2×M16—302no—
221C4⋊Q8—151no—
222C4⋊Q8—151no—
223#124—31no—
224#124—151no—
225#123—302no—
226C22⋊Q8—302no—
227#117—52no—
228#117—151no—
229#103—304no—
230#99—102no—
231C2×C3×C5—21no—
232C2×C3×C5—42no—
233C2×C3×C5#38611yescharacteristic
234C3×D5—22no—
235C23×C3—51no—
236C23×C3C22⋊AGL(1,𝔽5)12yes—
237C3×Q8—102no—
238C3×D4—22no—
239C3×D4—104no—
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—202no—
247C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252C2×Dic3—202no—
253Dic6—22no—
254Dic6—102no—
255Dic6—201no—
256Dic6—201no—
257C3⋊C8—104no—
258C22×C5—22no—
259C22×C5—42no—
260C22×C5C2×(C2×D3)⋊C411yescharacteristic
261C2×D5—41no—
262C2×D5#93912yes—
263AGL(1,𝔽5)—82no—
264C4×C5—121no—
265C4×C5—121no—
266C4×C5#67⋊C412yes—
267Dic5—22no—
268Dic5—121no—
269Dic5—121no—
270Dic5#88211yescharacteristic
271Dic5#88611yescharacteristic
272#41—102no—
273#41—102no—
274C2×Q8—31no—
275C2×Q8—51no—
276C2×Q8—151no—
277C2×Q8—301no—
278C2×Q8—302no—
279C2×Q8—302no—
280C2×D4—52no—
281C2×D4D3×AGL(1,𝔽5)11yescharacteristic
282C22×C4—51no—
283C22×C4—52no—
284C22×C4—301no—
285M16—302no—
286M16—302no—
287M16—304no—
288C2×C8—154no—
289C2×C8—304no—
290C4⋊C4—102no—
291C4⋊C4—301no—
292C4⋊C4—302no—
293C4⋊C4—302no—
294C22⋊C4—62no—
295C22⋊C4—102no—
296C22⋊C4—301no—
297C22⋊C4—302no—
298C42—31no—
299C42—102no—
300C42—151no—
301C3×C5#190911yescharacteristic, complemented, Hall
302C22×C3—22no—
303C22×C3—42no—
304C22×C3—52no—
305C22×C3—201no—
306C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307C3×C4—51no—
308C3×C4—51no—
309C3×C4—102no—
310C3×C4—402no—
311C3×C4D4×AGL(1,𝔽5)12yes—
312Dic3—41no—
313Dic3—41no—
314Dic3—201no—
315Dic3—201no—
316C2×C5—21no—
317C2×C5—42no—
318C2×C5#495811yescharacteristic
319D5—22no—
320C23—51no—
321C23(C2×D3)⋊AGL(1,𝔽5)12yes—
322Q8—62no—
323Q8—102no—
324Q8—302no—
325Q8—601no—
326Q8—601no—
327D4—22no—
328D4—104no—
329C2×C4—51no—
330C2×C4—52no—
331C2×C4—52no—
332C2×C4—52no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—102no—
336C2×C4—102no—
337C2×C4—202no—
338C2×C4—301no—
339C2×C4—301no—
340C2×C4—602no—
341C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
342C8—304no—
343C2×C3—21no—
344C2×C3—42no—
345C2×C3—102no—
346C2×C3#6577911yescharacteristic
347C5#7004611yescharacteristic, complemented, Sylow
348C22—22no—
349C22—42no—
350C22—52no—
351C22—201no—
352C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
353C4—51no—
354C4—51no—
355C4—102no—
356C4—121no—
357C4—121no—
358C4—402no—
359C4—601no—
360C4—601no—
361C4#67⋊AGL(1,𝔽5)12yes—
362C3#1060457011yescharacteristic, complemented, Sylow
363C2—21no—
364C2—42no—
365C2—102no—
366C2#1175202611yescharacteristic
subgroupG/H
centerC2#11752026
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5#386
prime radicalC2×C3×#711C22
cosocleC2×C3×C4×D5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1909
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #11751711C2semidirect
5. #11746518C2semidirect
13. #91825C4semidirect
14. C5×#936C4semidirect
17. #91389C4semidirect
18. #91385C4semidirect
108. #936AGL(1,𝔽5)semidirect
301. C3×C5#1909semidirect
347. C5#70046semidirect
362. C3#10604570semidirect

Maximal subgroups

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

subgroupindex
#117569852
#117547882
C3×#657712
#117517112
#117465182
#106045703
#700465