Finite Group Databasebeta

← #14313639

Subgroups — #14313639

Order 1920.

500 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 93 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×#66002C211yesmaximal, characteristic
2#11752436C212yesmaximal, complemented
3#11746800C212yesmaximal, complemented
4#11746727C212yesmaximal, complemented
5#10604549—31nomaximal, Hall
6C2×C3×#713C411yescharacteristic
7C2×C3×#711C2211yescharacteristic
8C2×#6762—22no—
9C3×C5×#124C411yescharacteristic
10C3×#4090C2211yescharacteristic
11C3×#4086C411yescharacteristic
12C3×#4030—22no—
13C3×#4027—22no—
14C3×#4021C2211yescharacteristic
15C3×C42×D5C411yescharacteristic
16#91242—22no—
17#91234C2214yes—
18#71820—51nomaximal, Hall
19#66002D311yescharacteristic
20#65777—32no—
21#64929—32no—
22#64856—32no—
23C2×C3×C5×Q8C2×C411yescharacteristic
24C2×C3×C5×D4C2×C411yescharacteristic
25C2×C3×C22⋊D5—22no—
26C2×C3×C22⋊D5D412yes—
27C22×C3×Dic5D412yes—
28C3×#713—41no—
29C3×#713—41no—
30C3×#711—41no—
31C3×#711—41no—
32C2×C3×D20—21no—
33C2×C3×D20C2×C411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×Dic10C2311yescharacteristic
38#6762—24no—
39#6762—42no—
40C2×C3⋊#170—42no—
41C3×C5×C22⋊C4—22no—
42C3×C42×C5C2×C411yescharacteristic
43C3×#685—22no—
44C3×#683—22no—
45C3×C4×Dic5—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47C3×#532—51no—
48#5237—52no—
49#4548—52no—
50#4542—52no—
51C2×#713Dic311yescharacteristic
52C2×#711C2×D311yescharacteristic
53C2×#704—62no—
54C5×#124Dic311yescharacteristic
55#4090C2×D311yescharacteristic
56#4086Dic311yescharacteristic
57#4030—22no—
58#4027—22no—
59#4021C2×D311yescharacteristic
60C42×D5Dic311yescharacteristic
61#4013—62no—
62#4005—34no—
63#2132—151noSylow
64C23×C3×C5C22⋊C412yes—
65C22×C3×D5—21no—
66C22×C3×D5C22⋊C411yescharacteristic
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5C22×C411yescharacteristic
72C3×C22⋊D5—42no—
73C3×C22⋊D5—44no—
74C2×C3×Dic5—21no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C2×D412yes—
79C3×D20—41no—
80C3×D20—42no—
81C3×C4×D5—21no—
82C3×C4×D5—21no—
83C3×C4×D5—42no—
84C3×C4×D5—41no—
85C3×C4×D5—41no—
86C3×Dic10—41no—
87C3⋊#170—44no—
88C2×C3×#41—51no—
89C2×C3×#41—51no—
90C3×C4⋊Q8—51no—
91C3×#127—51no—
92C3×#124—51no—
93C3×#124AGL(1,𝔽5)11yescharacteristic
94C3×#121—102no—
95C3×C4×D4—102no—
96C2×C3×C42—51no—
97C2×#208—102no—
98#836—54no—
99#833—102no—
100C2×C5×Q8C2×Dic311yescharacteristic
101C2×C5×D4C2×Dic311yescharacteristic
102C2×C22⋊D5—22no—
103C2×C22⋊D5#6712yes—
104C22×Dic5#6712yes—
105#713—41no—
106#713—41no—
107#711—41no—
108#711—41no—
109C2×D20—21no—
110C2×D20C2×Dic311yescharacteristic
111C2×C4×D5—21no—
112C2×C4×D5—21no—
113C2×C4×D5C2×Dic311yescharacteristic
114C2×Dic10C22×D311yescharacteristic
115#704—64no—
116#704—122no—
117C2×#170—122no—
118C5×C22⋊C4—22no—
119C42×C5C2×Dic311yescharacteristic
120#685—22no—
121#683—22no—
122C4×Dic5—21no—
123C4×Dic5C2×Dic311yescharacteristic
124#532—51no—
125#413—152no—
126#356—152no—
127#355—152no—
128C22×C3×C5—22no—
129C22×C3×C5—42no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×C3×D5—21no—
132C2×C3×D5—41no—
133C2×C3×D5—42no—
134C2×C3×D5—41no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138C3×Dic5—22no—
139C3×Dic5—22no—
140C3×Dic5#9911yescharacteristic
141C3×Dic5#9911yescharacteristic
142C3×#41—201no—
143C3×#41—201no—
144C3×#41—201no—
145C3×#41—201no—
146C2×C3×Q8—51no—
147C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
148C2×C3×D4—52no—
149C2×C3×D4—51no—
150C2×C3×D4—101no—
151C2×C3×D4—102no—
152C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
153C22×C3×C4—52no—
154C22×C3×C4—51no—
155C22×C3×C4—101no—
156C22×C3×C4—101no—
157C3×C4⋊C4—102no—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—102no—
160C3×C42—51no—
161C3×C42—101no—
162C3×C42C2×AGL(1,𝔽5)11yescharacteristic
163#208—104no—
164#208—202no—
165C2×C3⋊C8—202no—
166C23×C5#21712yes—
167C22×D5—21no—
168C22×D5#21711yescharacteristic
169C5×Q8—41no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5C22×Dic311yescharacteristic
174C22⋊D5—42no—
175C22⋊D5—44no—
176C2×Dic5—21no—
177C2×Dic5—22no—
178C2×Dic5—22no—
179C2×Dic5#21711yescharacteristic
180C2×Dic5C2×#6712yes—
181D20—41no—
182D20—42no—
183C4×D5—21no—
184C4×D5—21no—
185C4×D5—42no—
186C4×D5—41no—
187C4×D5—41no—
188Dic10—41no—
189#170—124no—
190C2×#41—51no—
191C2×#41—51no—
192C2×M16—302no—
193C4⋊Q8—51no—
194#127—51no—
195#124—51no—
196#124ΓL(1,𝔽16)11yescharacteristic
197#121—102no—
198C4×D4—102no—
199C2×C42—51no—
200#101—154no—
201#100—302no—
202C2×C3×C5—21no—
203C2×C3×C5—42no—
204C2×C3×C5C2×#9911yescharacteristic
205C3×D5—41no—
206C3×D5—81no—
207C23×C3—51no—
208C23×C3—101no—
209C23×C3C22⋊AGL(1,𝔽5)12yes—
210C3×Q8—41no—
211C3×Q8—201no—
212C3×D4—41no—
213C3×D4—201no—
214C3×D4—202no—
215C3×D4—202no—
216C3×D4—204no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—51no—
220C2×C3×C4—52no—
221C2×C3×C4—101no—
222C2×C3×C4—101no—
223C2×C3×C4—102no—
224C2×C3×C4—102no—
225C2×C3×C4—101no—
226C2×C3×C4—201no—
227C2×C3×C4—201no—
228C2×C3×C4—202no—
229C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
230C3⋊C8—204no—
231C22×C5—22no—
232C22×C5—42no—
233C22×C5C2×#21711yescharacteristic
234C2×D5—21no—
235C2×D5—41no—
236C2×D5—42no—
237C2×D5—41no—
238C4×C5—21no—
239C4×C5—41no—
240C4×C5—41no—
241Dic5—22no—
242Dic5—22no—
243Dic5#83411yescharacteristic
244Dic5#83411yescharacteristic
245#41—201no—
246#41—201no—
247#41—201no—
248#41—201no—
249C2×Q8—51no—
250C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
251C2×D4—52no—
252C2×D4—51no—
253C2×D4—101no—
254C2×D4—102no—
255C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
256C22×C4—52no—
257C22×C4—51no—
258C22×C4—101no—
259C22×C4—101no—
260M16—304no—
261M16—602no—
262C2×C8—602no—
263C4⋊C4—102no—
264C22⋊C4—22no—
265C22⋊C4—102no—
266C42—51no—
267C42—101no—
268C42C2×ΓL(1,𝔽16)11yescharacteristic
269C3×C5#213211yescharacteristic, complemented, Hall
270C22×C3—22no—
271C22×C3—42no—
272C22×C3—101no—
273C22×C3—201no—
274C22×C3—202no—
275C22×C3—201no—
276C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—51no—
281C3×C4—51no—
282C3×C4—102no—
283C3×C4—102no—
284C2×C5—21no—
285C2×C5—42no—
286C2×C5C2×#83411yescharacteristic
287D5—41no—
288D5—81no—
289C23—51no—
290C23—101no—
291C23#676312yes—
292Q8—41no—
293Q8—201no—
294D4—41no—
295D4—201no—
296D4—202no—
297D4—202no—
298D4—204no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—51no—
302C2×C4—52no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—102no—
306C2×C4—102no—
307C2×C4—101no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—202no—
311C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
312C8—604no—
313C2×C3—21no—
314C2×C3—42no—
315C2×C3—201no—
316C2×C3—401no—
317C2×C3D5⋊#9911yescharacteristic
318C5#7182011yescharacteristic, complemented, Sylow
319C22—22no—
320C22—42no—
321C22—101no—
322C22—201no—
323C22—202no—
324C22—201no—
325C22C2×#676311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—51no—
330C4—51no—
331C4—102no—
332C4—102no—
333C3#1060454911yescharacteristic, complemented, Sylow
334C2—21no—
335C2—42no—
336C2—201no—
337C2—401no—
338C2D5⋊#83411yescharacteristic
subgroupG/H
centerC2D5⋊#834
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#124C4
socleC2×C3×C5C2×#99
prime radicalC3×#66002C2
cosocleC2×C3×Dic10C23
hypercenter#124ΓL(1,𝔽16)
hypocenterC3×C5#2132
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752436C2semidirect
3. #11746800C2semidirect
4. #11746727C2semidirect
269. C3×C5#2132semidirect
318. C5#71820semidirect
333. C3#10604549semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
#117524362
#117468002
#117467272
#106045493
#718205