Finite Group Databasebeta

← #14303057

Subgroups — #14303057

Order 1920.

680 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 148 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#11756589C211yesmaximal, characteristic
2C3×#66153C211yesmaximal, characteristic, complemented
3C5×#5237C211yesmaximal, characteristic, complemented
4C2×#90960C212yesmaximal, complemented
5#11745990C212yesmaximal, complemented
6#10600930—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×D60C2211yescharacteristic
9#91836—21no—
10#91829—21no—
11#91826C414yes—
12#91819—22no—
13#91815C2211yescharacteristic
14C2×C5×#208C2212yes—
15C3×#4094—24no—
16C2×C3×#681—22no—
17C2×C3×#681C2212yes—
18C5×#836—21no—
19C5×#833—21no—
20#90960—24no—
21#72030—51nomaximal, Hall
22#66164—31no—
23#66153D311yescharacteristic, complemented
24C5×#413—31no—
25C2×#3955—32no—
26#64776—32no—
27C23×D15C2×C412yes—
28C3×C5×#41—22no—
29C3×C5×#41—22no—
30C2×C3×C5×Q8D411yescharacteristic
31C2×C3×C5×D4C2×C412yes—
32C2×C3×C5×D4D411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—24no—
36C2×D60—22no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—22no—
40#6719C2×C412yes—
41#6714—24no—
42C4⋊Dic15—21no—
43C4×Dic15—21no—
44C5×#208—22no—
45C5×#208—22no—
46C2×C5×C3⋊C8—22no—
47C3×#681—24no—
48C3×#681—22no—
49C3×#681D414yescomplemented
50C2×C3×#168—24no—
51C2×C3×#168—22no—
52C3×#568—51no—
53#5830—51no—
54#5237D511yescharacteristic, complemented
55C2×#823—52no—
56#4559—52no—
57C2×C5×#41C2×D311yescharacteristic
58C22×D20—31no—
59C2×C5×M16—32no—
60#4094—24no—
61#4093—61no—
62#4086—61no—
63#4083—34no—
64#4076—62no—
65#4072—31no—
66C2×#681—22no—
67C2×#681C2×D312yes—
68C5×#101—61no—
69C5×#100—61no—
70#3955—64no—
71#1914—151noSylow
72C23×C3×C5C22⋊C412yes—
73C23×C3×C5C22×C411yescharacteristic
74C22×D15—22no—
75C22×D15—24no—
76C22×D15—82no—
77C3×C5×Q8—22no—
78C3×C5×D4—24no—
79C3×C5×D4—22no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22⋊C412yes—
83C2×C3×C4×C5C2×D412yes—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4112yes—
87#1220—84no—
88C2×Dic15—22no—
89D60—41no—
90D60—42no—
91D60—41no—
92C3×#168—24no—
93C5×C3⋊C8—42no—
94C2×C3×#41C2×D511yescharacteristic
95C22×D12—51no—
96C3×#131—104no—
97C2×C3×M16—52no—
98C2×C3×M16—102no—
99#947—101no—
100#940—101no—
101#937—54no—
102#930—102no—
103#926—51no—
104C2×#208C2×D512yes—
105#836—21no—
106#833—21no—
107#823—104no—
108C23×D5—32no—
109C5×#41—22no—
110C5×#41—22no—
111C2×C5×Q8D1211yescharacteristic
112C2×C5×D4C4×D312yes—
113C2×C5×D4D1211yescharacteristic
114C22×C4×C5#6712yes—
115C22×C4×C5C22×D311yescharacteristic
116C2×C22⋊D5—64no—
117C2×D20—61no—
118C2×D20—62no—
119C2×D20—62no—
120C2×D20—61no—
121C5×M16—62no—
122C5×M16—62no—
123C2×C5×C8—62no—
124C22⋊Dic5—32no—
125#685—64no—
126C4⋊Dic5—61no—
127C4×Dic5—61no—
128#681—24no—
129#681—22no—
130#681#6714yescomplemented
131C2×#168—24no—
132C2×#168—22no—
133#568—51no—
134#535—151no—
135#413—31no—
136C2×#100—152no—
137#344—152no—
138C22×C3×C5—22no—
139C22×C3×C5—41no—
140C22×C3×C5—42no—
141C22×C3×C5C2×C22⋊C411yescharacteristic
142C22×C3×C5C4×D412yes—
143C2×D15—44no—
144C2×D15—42no—
145C2×D15—84no—
146C3×C4×C5—22no—
147C3×C4×C5#12011yescharacteristic
148C3×C4×C5#12112yes—
149C3×C4×C5#12311yescharacteristic
150Dic15—42no—
151C23×D3—52no—
152C3×#41—22no—
153C3×#41—22no—
154C2×C3×Q8C22⋊D511yescharacteristic
155C2×C3×D4C4×D512yes—
156C2×C3×D4C22⋊D511yescharacteristic
157C22×C3×C4D2012yes—
158C22×C3×C4C22×D511yescharacteristic
159C2×#67—104no—
160C2×D12—101no—
161C2×D12—102no—
162C2×D12—102no—
163C2×D12—101no—
164C3×M16—54no—
165C3×M16—104no—
166C3×M16—102no—
167C2×C3×C8—104no—
168C2×C3×C8—102no—
169#217—52no—
170(C2×D3)⋊C4—104no—
171C4⋊Dic3—101no—
172C4×Dic3—101no—
173#208—22no—
174#208—22no—
175C2×C3⋊C8—22no—
176C23×C5(C2×D3)⋊C412yes—
177C23×C5C2×C4×D311yescharacteristic
178C22×D5—62no—
179C22×D5—64no—
180C22×D5—242no—
181C5×Q8—22no—
182C5×D4—24no—
183C5×D4—22no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5(C2×D3)⋊C412yes—
187C2×C4×C5C2×D1211yescharacteristic
188C2×C4×C5#23512yes—
189C2×C4×C5C2×#6711yescharacteristic
190C2×C4×C5C2×#6712yes—
191C22⋊D5—244no—
192C2×Dic5—62no—
193D20—121no—
194D20—122no—
195D20—121no—
196C5×C8—122no—
197#168—24no—
198C2×#41D3×D511yescharacteristic
199C22×D4—151no—
200#131—104no—
201C2×M16—32no—
202C2×M16—52no—
203C2×M16—102no—
204#127—301no—
205#124—301no—
206#121—302no—
207#120—154no—
208#117—151no—
209#101—61no—
210#100—61no—
211#100—304no—
212C2×C3×C5—21no—
213C2×C3×C5—22no—
214C2×C3×C5—42no—
215C2×C3×C5#38611yescharacteristic
216D15—82no—
217C23×C3#68512yes—
218C23×C3C2×C4×D511yescharacteristic
219C22×D3—102no—
220C22×D3—104no—
221C22×D3—402no—
222C3×Q8—22no—
223C3×D4—24no—
224C3×D4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4#68512yes—
228C2×C3×C4C2×D2011yescharacteristic
229C2×C3×C4D4×D512yes—
230C2×C3×C4#71112yes—
231C2×C3×C4C2×C22⋊D511yescharacteristic
232#67—404no—
233C2×Dic3—102no—
234D12—201no—
235D12—201no—
236D12—202no—
237C3×C8—104no—
238C3⋊C8—42no—
239C22×C5—22no—
240C22×C5—41no—
241C22×C5—42no—
242C22×C5C2×(C2×D3)⋊C411yescharacteristic
243C22×C5C4×#6712yes—
244C2×D5—124no—
245C2×D5—122no—
246C2×D5—244no—
247C4×C5—22no—
248C4×C5#92911yescharacteristic
249C4×C5#93012yes—
250C4×C5#95311yescharacteristic
251Dic5—122no—
252C24—152no—
253#41—22no—
254#41—22no—
255C2×Q8#120311yescharacteristic
256C2×D4—304no—
257C2×D4—302no—
258C2×D4—301no—
259C2×D4—301no—
260C2×D4—302no—
261C2×D4#120012yes—
262C2×D4#120311yescharacteristic
263C22×C4#120212yes—
264C22×C4C2×D3×D511yescharacteristic
265M16—54no—
266M16—62no—
267M16—62no—
268M16—104no—
269M16—102no—
270C2×C8—62no—
271C2×C8—104no—
272C2×C8—102no—
273C4⋊C4—301no—
274C22⋊C4—152no—
275C22⋊C4—304no—
276C42—301no—
277C3×C5#191411yescharacteristic, complemented, Hall
278C22×C3—22no—
279C22×C3—41no—
280C22×C3—42no—
281C22×C3#402712yes—
282C22×C3C2×#68511yescharacteristic
283C2×D3—204no—
284C2×D3—202no—
285C2×D3—404no—
286C3×C4—22no—
287C3×C4#402811yescharacteristic
288C3×C4#403211yescharacteristic
289C3×C4#408512yes—
290Dic3—202no—
291C2×C5—21no—
292C2×C5—22no—
293C2×C5—42no—
294C2×C5#521311yescharacteristic
295D5—242no—
296C23—302no—
297C23—304no—
298C23—1202no—
299C23#666712yes—
300C23C2×#120011yescharacteristic
301Q8—22no—
302D4—24no—
303D4—22no—
304D4—601no—
305D4—601no—
306D4—602no—
307D4—1204no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—302no—
311C2×C4#666712yes—
312C2×C4#678212yes—
313C2×C4C2×#120211yescharacteristic
314C2×C4C2×#120311yescharacteristic
315C2×C4D5×#6712yes—
316C8—104no—
317C8—122no—
318C2×C3—21no—
319C2×C3—22no—
320C2×C3—42no—
321C2×C3#6524711yescharacteristic
322D3—402no—
323C5#7203011yescharacteristic, complemented, Sylow
324C22—22no—
325C22—41no—
326C22—42no—
327C22—604no—
328C22—602no—
329C22—1204no—
330C22C2×#666711yescharacteristic
331C22#9155212yes—
332C4—22no—
333C4—602no—
334C4#9154611yescharacteristic
335C4#9156411yescharacteristic
336C4#9156612yes—
337C3#1060093011yescharacteristic, complemented, Sylow
338C2—21no—
339C2—22no—
340C2—42no—
341C2—1202no—
342C2#1174949411yescharacteristic
subgroupG/H
centerC2#11749494
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radical#11756589C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1914
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#66153C2semidirect
3. C5×#5237C2semidirect
4. C2×#90960C2semidirect
5. #11745990C2semidirect
23. #66153D3semidirect
49. C3×#681D4semidirect
54. #5237D5semidirect
130. #681#67semidirect
277. C3×C5#1914semidirect
323. C5#72030semidirect
337. C3#10600930semidirect

Maximal subgroups

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

subgroupindex
#117565892
C3×#661532
C5×#52372
C2×#909602
#117459902
#106009303
#720305