Finite Group Databasebeta

← #14281248

Subgroups — #14281248

Order 1920.

512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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×C3×#4082C211yesmaximal, characteristic
2#11752418C211yesmaximal, characteristic, complemented
3#11752413C211yesmaximal, characteristic, complemented
4#11746804C214yesmaximal, complemented
5#10604936—31nomaximal, Hall
6C22×C3×C5×D4C411yescharacteristic
7C22×C3×Dic10C411yescharacteristic
8C2×C3×C22⋊Dic5C412yes—
9C2×C3×C22⋊Dic5C2212yes—
10C3×#4082—21no—
11C3×#4082—21no—
12C3×#4082—21no—
13C3×#4082—21no—
14C2×C3×C4×Dic5C2211yescharacteristic
15#91241C2212yes—
16#91241C2212yes—
17#91233—21no—
18#91231—21no—
19C4⋊(C3⋊#170)—21no—
20C4×C3⋊#170—21no—
21#71720—51nomaximal, Hall
22C2×#4082D311yescharacteristic
23#65759—31no—
24#65754—31no—
25#64933—34no—
26C24×C3×C5C2×C412yes—
27C2×C3×C5×D4—21no—
28C2×C3×C5×D4—21no—
29C2×C3×C5×D4—42no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2×C412yes—
33C22×C3×Dic5C2311yescharacteristic
34C2×C3×Dic10—21no—
35C2×C3×Dic10—21no—
36C2×C3×Dic10—42no—
37C2×C3⋊#170—22no—
38C2×C3⋊#170—22no—
39C3×C22⋊Dic5—22no—
40C3×C22⋊Dic5—22no—
41C3×C22⋊Dic5—22no—
42C3×C22⋊Dic5—22no—
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C2×C3×#124—51no—
48#4926—51no—
49#4925—51no—
50#4525—54no—
51C22×C5×D4Dic311yescharacteristic
52C22×Dic10Dic311yescharacteristic
53C2×C22⋊Dic5Dic312yes—
54C2×C22⋊Dic5C2×D312yes—
55#4082—21no—
56#4082—21no—
57#4082—21no—
58#4082—21no—
59C2×C4×Dic5C2×D311yescharacteristic
60C22⋊#170—32no—
61C22⋊#170—32no—
62#4004—61no—
63#4002—61no—
64C4⋊#170—61no—
65C4×#170—61no—
66#1469—151noSylow
67C23×C3×C5—22no—
68C23×C3×C5—24no—
69C23×C3×C5—42no—
70C23×C3×C5—42no—
71C23×C3×C5C22×C411yescharacteristic
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×Dic5—22no—
78C2×C3×Dic5—22no—
79C2×C3×Dic5—41no—
80C2×C3×Dic5—42no—
81C2×C3×Dic5C22⋊C411yescharacteristic
82C2×C3×Dic5C22⋊C411yescharacteristic
83C2×C3×Dic5C2×D411yescharacteristic
84C2×C3×Dic5C2×D411yescharacteristic
85C3×Dic10—42no—
86C3×Dic10—42no—
87C3⋊#170—42no—
88C3⋊#170—42no—
89C22×C3×Q8—51no—
90C22×C3×D4AGL(1,𝔽5)11yescharacteristic
91C3×#124—101no—
92C3×#124—101no—
93C3×#124—101no—
94C3×#124—101no—
95C2×C3×C22⋊C4—52no—
96C2×C3×C22⋊C4—52no—
97C2×C3×C42—51no—
98#830—52no—
99#830—52no—
100C4⋊(C3⋊C8)—101no—
101C4⋊(C3⋊C8)—101no—
102#803—101no—
103C4×C3⋊C8—101no—
104C24×C5C2×Dic312yes—
105C2×C5×D4—21no—
106C2×C5×D4—21no—
107C2×C5×D4—42no—
108C22×C4×C5C2×Dic311yescharacteristic
109C22×Dic5C2×Dic311yescharacteristic
110C22×Dic5C2×Dic312yes—
111C22×Dic5C22×D311yescharacteristic
112C2×Dic10—21no—
113C2×Dic10—21no—
114C2×Dic10—42no—
115C2×#170—62no—
116C2×#170—62no—
117C22⋊Dic5—22no—
118C22⋊Dic5—22no—
119C22⋊Dic5—22no—
120C22⋊Dic5—22no—
121C4×Dic5#6711yescharacteristic
122C4×Dic5#6711yescharacteristic
123C4×Dic5#6711yescharacteristic
124C4×Dic5#6711yescharacteristic
125C2×#124—51no—
126#432—151no—
127#431—151no—
128#323—154no—
129C22×C3×C5—21no—
130C22×C3×C5—21no—
131C22×C3×C5—42no—
132C22×C3×C5—42no—
133C22×C3×C5—42no—
134C22×C3×C5—84no—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C22×C3×C5#13112yes—
137C3×C4×C5—21no—
138C3×C4×C5#10012yes—
139C3×Dic5—21no—
140C3×Dic5—21no—
141C3×Dic5—21no—
142C3×Dic5—21no—
143C3×Dic5—42no—
144C24×C3C2×AGL(1,𝔽5)12yes—
145C2×C3×Q8—101no—
146C2×C3×Q8—101no—
147C2×C3×Q8—202no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—42no—
151C22×C3×C4—51no—
152C22×C3×C4—51no—
153C22×C3×C4—52no—
154C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
155C3×C22⋊C4—102no—
156C3×C22⋊C4—102no—
157C3×C22⋊C4—102no—
158C3×C22⋊C4—102no—
159C3×C42—51no—
160C3×C42—51no—
161C3×C42—51no—
162C3×C42—51no—
163C2×C3⋊C8—102no—
164C2×C3⋊C8—102no—
165C23×C5—22no—
166C23×C5—24no—
167C23×C5—42no—
168C23×C5—42no—
169C23×C5C22×Dic311yescharacteristic
170C5×D4—42no—
171C5×D4—42no—
172C2×C4×C5—22no—
173C2×C4×C5#21711yescharacteristic
174C2×C4×C5#21711yescharacteristic
175C2×Dic5—22no—
176C2×Dic5—22no—
177C2×Dic5—41no—
178C2×Dic5—42no—
179C2×Dic5#21711yescharacteristic
180C2×Dic5#21711yescharacteristic
181C2×Dic5C2×#6711yescharacteristic
182C2×Dic5C2×#6711yescharacteristic
183Dic10—42no—
184Dic10—42no—
185#170—122no—
186#170—122no—
187C22×Q8—51no—
188C22×D4ΓL(1,𝔽16)11yescharacteristic
189#124—101no—
190#124—101no—
191#124—101no—
192#124—101no—
193C2×C22⋊C4—52no—
194C2×C22⋊C4—52no—
195C2×C42—51no—
196C4⋊C8—301no—
197C4⋊C8—301no—
198C22⋊C8—152no—
199C22⋊C8—152no—
200#97—301no—
201C4×C8—301no—
202C2×C3×C5—22no—
203C2×C3×C5—82no—
204C2×C3×C5#40811yescharacteristic
205C2×C3×C5#41011yescharacteristic
206C2×C3×C5C2×#10011yescharacteristic
207C23×C3—22no—
208C23×C3—24no—
209C23×C3—42no—
210C23×C3—42no—
211C23×C3C22×AGL(1,𝔽5)11yescharacteristic
212C3×Q8—202no—
213C3×Q8—202no—
214C3×D4—42no—
215C3×D4—42no—
216C2×C3×C4—22no—
217C2×C3×C4—51no—
218C2×C3×C4—51no—
219C2×C3×C4—51no—
220C2×C3×C4—51no—
221C2×C3×C4—102no—
222C2×C3×C4—102no—
223C2×C3×C4—201no—
224C2×C3×C4—202no—
225C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
226C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
227C3⋊C8—202no—
228C3⋊C8—202no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—42no—
232C22×C5—42no—
233C22×C5—42no—
234C22×C5—84no—
235C22×C5#94812yes—
236C22×C5C2×#21711yescharacteristic
237C4×C5—21no—
238C4×C5#83312yes—
239Dic5—21no—
240Dic5—21no—
241Dic5—21no—
242Dic5—21no—
243Dic5—42no—
244C24C2×ΓL(1,𝔽16)12yes—
245C2×Q8—101no—
246C2×Q8—101no—
247C2×Q8—202no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—42no—
251C22×C4—51no—
252C22×C4—51no—
253C22×C4—52no—
254C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
255C2×C8—302no—
256C2×C8—302no—
257C22⋊C4—102no—
258C22⋊C4—102no—
259C22⋊C4—102no—
260C22⋊C4—102no—
261C42—51no—
262C42—51no—
263C42—51no—
264C42—51no—
265C3×C5#146911yescharacteristic, complemented, Hall
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—42no—
271C22×C3—84no—
272C22×C3#413112yes—
273C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
274C3×C4—21no—
275C3×C4—101no—
276C3×C4—101no—
277C3×C4—101no—
278C3×C4—101no—
279C3×C4—202no—
280C3×C4#401312yes—
281C2×C5—22no—
282C2×C5—82no—
283C2×C5C2×#83311yescharacteristic
284C2×C5#523411yescharacteristic
285C2×C5#524011yescharacteristic
286C23—22no—
287C23—24no—
288C23—42no—
289C23—42no—
290C23C22×ΓL(1,𝔽16)11yescharacteristic
291Q8—202no—
292Q8—202no—
293D4—42no—
294D4—42no—
295C2×C4—22no—
296C2×C4—51no—
297C2×C4—51no—
298C2×C4—51no—
299C2×C4—51no—
300C2×C4—102no—
301C2×C4—102no—
302C2×C4—201no—
303C2×C4—202no—
304C2×C4#676311yescharacteristic
305C2×C4#676311yescharacteristic
306C8—602no—
307C8—602no—
308C2×C3—22no—
309C2×C3—82no—
310C2×C3#6577111yescharacteristic
311C2×C3#6577611yescharacteristic
312C2×C3C2×#401311yescharacteristic
313C5#7172011yescharacteristic, complemented, Sylow
314C22—21no—
315C22—21no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—84no—
320C22#9199012yes—
321C22C2×#676311yescharacteristic
322C4—21no—
323C4—101no—
324C4—101no—
325C4—101no—
326C4—101no—
327C4—202no—
328C4#9124212yes—
329C3#1060493611yescharacteristic, complemented, Sylow
330C2—22no—
331C2—82no—
332C2#1175243011yescharacteristic
333C2#1175243511yescharacteristic
334C2C2×#9124211yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
Fitting, prime radicalC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5#1469
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11752418C2semidirect
3. #11752413C2semidirect
4. #11746804C2semidirect
265. C3×C5#1469semidirect
313. C5#71720semidirect
329. C3#10604936semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40822
#117524182
#117524132
#117468042
#106049363
#717205