Finite Group Databasebeta

← #14296878

Subgroups — #14296878

Order 1920.

1224 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C22×#6817C211yesmaximal, characteristic
2C5×#5211C211yesmaximal, characteristic, complemented
3C3×#65500C211yesmaximal, characteristic, complemented
4C2×#90997C214yesmaximal, complemented
5#10600330—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×#1220C2212yes—
8C2×#6817—22no—
9C2×#6817—22no—
10C2×#6817—28no—
11C22×D60C411yescharacteristic, complemented
12C22×C4×D15C412yescomplemented
13C22×Dic30C411yescharacteristic, complemented
14C2×C5×#217C2212yes—
15C2×C3×C22⋊Dic5C2212yes—
16C5×C3⋊#95—22no—
17C3×#3963—22no—
18#90997—28no—
19#69537—51nomaximal, Hall
20C22×#709—31no—
21C5×#381—31no—
22#65500D311yescharacteristic, complemented
23C2×#3938—34no—
24C24×C3×C5C2311yescharacteristic
25C23×D15C2×C412yes—
26C22×C3×C4×C5—24no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5D412yes—
30C22×C3×C4×C5D412yes—
31C2×#1220—22no—
32C2×#1220—24no—
33C2×#1220—22no—
34C2×#1220D418yes—
35C22×Dic15C2×C412yes—
36#6817—216no—
37#6817—216no—
38C2×D60—24no—
39C2×D60—22no—
40C2×C4×D15—24no—
41C2×C4×D15—24no—
42C2×C4×D15—24no—
43C2×Dic30—22no—
44C2×Dic30—24no—
45C22×C5×Dic3—22no—
46C22×C3×Dic5—22no—
47C5×#217—24no—
48C3×C22⋊Dic5—24no—
49C22×#235—51no—
50C3×#381—51no—
51#5211D511yescharacteristic, complemented
52C2×#806—54no—
53C23×C4×C5C2×D311yescharacteristic
54C22×C22⋊D5—32no—
55C2×#709—68no—
56C2×#709—62no—
57C2×#709—62no—
58C22×D20—31no—
59C22×C4×D5—32no—
60C22×Dic10—31no—
61C2×C5×C22⋊C4—32no—
62C2×C22⋊Dic5C2×D312yes—
63C5×#95—62no—
64#3963—22no—
65#3938—68no—
66#1782—151noSylow
67C23×C3×C5—42no—
68C23×C3×C5C22×C411yescharacteristic
69C23×C3×C5C2×D411yescharacteristic
70C23×C3×C5C2×D411yescharacteristic
71C23×C3×C5C2×D414yes—
72C22×D15—22no—
73C22×D15—22no—
74C22×D15—44no—
75C22×D15C22⋊C414yes—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—24no—
79C2×C3×C4×C5—24no—
80C2×C3×C4×C5C22⋊C412yes—
81C2×C3×C4×C5C22⋊C412yes—
82#1220—28no—
83#1220—28no—
84C2×Dic15—22no—
85C2×Dic15—22no—
86C2×Dic15C22⋊C414yes—
87D60—28no—
88C4×D15—216no—
89Dic30—28no—
90C2×C5×Dic3—44no—
91C2×C5×Dic3—42no—
92C2×C3×Dic5—44no—
93C2×C3×Dic5—42no—
94C23×C3×C4C2×D511yescharacteristic
95C22×#67—52no—
96C2×#235—108no—
97C2×#235—102no—
98C2×#235—102no—
99C22×D12—51no—
100C22×C4×D3—52no—
101C22×Dic6—51no—
102C2×C3×C22⋊C4—52no—
103C2×#217C2×D512yes—
104C3×#95—102no—
105C3⋊#95—22no—
106#806—108no—
107C24×C5C22×D311yescharacteristic
108C23×D5—32no—
109C22×C4×C5—24no—
110C22×C4×C5—62no—
111C22×C4×C5C4×D311yescharacteristic
112C22×C4×C5C4×D311yescharacteristic
113C22×C4×C5D1212yes—
114C22×C4×C5#6712yes—
115C2×C22⋊D5—38no—
116C2×C22⋊D5—62no—
117C2×C22⋊D5—64no—
118C2×C22⋊D5—62no—
119C22×Dic5—22no—
120C22×Dic5—32no—
121#709—616no—
122#709—616no—
123C2×D20—64no—
124C2×D20—62no—
125C2×C4×D5—64no—
126C2×C4×D5—64no—
127C2×C4×D5—64no—
128C2×Dic10—64no—
129C2×Dic10—62no—
130C5×C22⋊C4—64no—
131C22⋊Dic5—24no—
132C22×#41—151no—
133C2×#99—154no—
134#381—31no—
135#381—51no—
136C22×C3×C5—22no—
137C22×C3×C5—22no—
138C22×C3×C5—22no—
139C22×C3×C5—44no—
140C22×C3×C5C2×C22⋊C412yes—
141C22×C3×C5C2×C22⋊C411yescharacteristic
142C22×C3×C5#12012yes—
143C22×C3×C5#12012yes—
144C2×D15—24no—
145C2×D15—44no—
146C2×D15—44no—
147C2×D15—44no—
148C3×C4×C5—22no—
149C3×C4×C5—22no—
150Dic15—24no—
151C3×Dic5—82no—
152C5×Dic3—82no—
153C24×C3C22×D511yescharacteristic
154C23×D3—52no—
155C22×C3×C4—24no—
156C22×C3×C4—102no—
157C22×C3×C4C4×D511yescharacteristic
158C22×C3×C4C4×D511yescharacteristic
159C22×C3×C4D2012yes—
160C22×C3×C4C22⋊D512yes—
161C2×#67—58no—
162C2×#67—102no—
163C2×#67—104no—
164C2×#67—102no—
165C22×Dic3—22no—
166C22×Dic3—52no—
167#235—1016no—
168#235—1016no—
169C2×D12—104no—
170C2×D12—102no—
171C2×C4×D3—104no—
172C2×C4×D3—104no—
173C2×C4×D3—104no—
174C2×Dic6—104no—
175C2×Dic6—102no—
176C3×C22⋊C4—104no—
177#217—24no—
178C23×C5—42no—
179C23×C5C2×C4×D311yescharacteristic
180C23×C5C2×D1211yescharacteristic
181C23×C5D3×D414yes—
182C23×C5C2×#6711yescharacteristic
183C22×D5—34no—
184C22×D5—62no—
185C22×D5—62no—
186C22×D5—124no—
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—24no—
190C2×C4×C5—24no—
191C2×C4×C5—124no—
192C2×C4×C5—122no—
193C2×C4×C5(C2×D3)⋊C412yes—
194C2×C4×C5(C2×D3)⋊C412yes—
195C22⋊D5—68no—
196C22⋊D5—68no—
197C2×Dic5—34no—
198C2×Dic5—44no—
199C2×Dic5—42no—
200C2×Dic5—62no—
201C2×Dic5—62no—
202D20—68no—
203C4×D5—616no—
204Dic10—68no—
205C2×#41—308no—
206C2×#41—302no—
207C2×#41—302no—
208C22×Q8—151no—
209C22×D4—152no—
210C22×D4—151no—
211C23×C4—152no—
212C23×C4D3×D511yescharacteristic
213C2×C22⋊C4—32no—
214C2×C22⋊C4—52no—
215#99—308no—
216#95—62no—
217#95—102no—
218C2×C3×C5—22no—
219C2×C3×C5—22no—
220C2×C3×C5—22no—
221C2×C3×C5#37911yescharacteristic
222C2×C3×C5#41012yes—
223D15—44no—
224C23×C3—42no—
225C23×C3C2×C4×D511yescharacteristic
226C23×C3C2×D2011yescharacteristic
227C23×C3D4×D514yes—
228C23×C3C2×C22⋊D511yescharacteristic
229C22×D3—54no—
230C22×D3—102no—
231C22×D3—102no—
232C22×D3—204no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—204no—
238C2×C3×C4—202no—
239C2×C3×C4#68512yes—
240C2×C3×C4#68512yes—
241#67—108no—
242#67—108no—
243C2×Dic3—44no—
244C2×Dic3—42no—
245C2×Dic3—54no—
246C2×Dic3—102no—
247C2×Dic3—102no—
248D12—108no—
249C4×D3—1016no—
250Dic6—108no—
251C22×C5—22no—
252C22×C5—22no—
253C22×C5—22no—
254C22×C5—44no—
255C22×C5D3×C22⋊C412yes—
256C22×C5#88212yes—
257C22×C5C2×(C2×D3)⋊C411yescharacteristic
258C22×C5#93712yes—
259C2×D5—64no—
260C2×D5—124no—
261C2×D5—124no—
262C2×D5—124no—
263C4×C5—22no—
264C4×C5—22no—
265C4×C5—242no—
266Dic5—64no—
267Dic5—82no—
268C24—152no—
269C24C2×D3×D511yescharacteristic
270#41—3016no—
271#41—3016no—
272C2×Q8—304no—
273C2×Q8—302no—
274C2×D4—158no—
275C2×D4—304no—
276C2×D4—302no—
277C2×D4—302no—
278C2×D4—304no—
279C2×D4—302no—
280C22×C4—24no—
281C22×C4—62no—
282C22×C4—102no—
283C22×C4—152no—
284C22×C4—304no—
285C22×C4—304no—
286C22×C4—304no—
287C22×C4#120011yescharacteristic
288C22×C4#120011yescharacteristic
289C22×C4#120212yes—
290C22×C4#120312yes—
291C22⋊C4—64no—
292C22⋊C4—104no—
293C3×C5#178211yescharacteristic, complemented, Hall
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—44no—
298C22×C3D5×C22⋊C412yes—
299C22×C3#402812yes—
300C22×C3C2×#68511yescharacteristic
301C22×C3#408312yes—
302C2×D3—104no—
303C2×D3—204no—
304C2×D3—204no—
305C2×D3—204no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—402no—
309Dic3—82no—
310Dic3—104no—
311C2×C5—22no—
312C2×C5—22no—
313C2×C5—22no—
314C2×C5#495511yescharacteristic
315C2×C5#500612yes—
316D5—124no—
317C23—42no—
318C23—154no—
319C23—302no—
320C23—302no—
321C23—604no—
322C23C2×#120011yescharacteristic
323C23C2×#120211yescharacteristic
324C23C2×#120311yescharacteristic
325C23#679014yes—
326Q8—308no—
327D4—308no—
328D4—308no—
329D4—308no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—124no—
335C2×C4—122no—
336C2×C4—154no—
337C2×C4—204no—
338C2×C4—202no—
339C2×C4—3016no—
340C2×C4—302no—
341C2×C4—302no—
342C2×C4#666712yes—
343C2×C4#666712yes—
344C2×C3—22no—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3#6524411yescharacteristic
348C2×C3#6529512yes—
349D3—204no—
350C5#6953711yescharacteristic, complemented, Sylow
351C22—22no—
352C22—22no—
353C22—22no—
354C22—44no—
355C22—304no—
356C22—604no—
357C22—604no—
358C22—604no—
359C22C2×#666711yescharacteristic
360C22#9156112yes—
361C22#9157212yes—
362C22#9157312yes—
363C4—22no—
364C4—22no—
365C4—242no—
366C4—304no—
367C4—402no—
368C3#1060033011yescharacteristic, complemented, Sylow
369C2—22no—
370C2—22no—
371C2—22no—
372C2—604no—
373C2#1174862612yes—
374C2#1174950211yescharacteristic
subgroupG/H
centerC22C2×#6667
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6817C2
cosocleC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1782
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C5×#5211C2semidirect
3. C3×#65500C2semidirect
4. C2×#90997C2semidirect
11. C22×D60C4semidirect
12. C22×C4×D15C4semidirect
13. C22×Dic30C4semidirect
22. #65500D3semidirect
51. #5211D5semidirect
293. C3×C5#1782semidirect
350. C5#69537semidirect
368. C3#10600330semidirect

Maximal subgroups

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

subgroupindex
C22×#68172
C5×#52112
C3×#655002
C2×#909972
#106003303
#695375