Finite Group Databasebeta

← #14308989

Subgroups — #14308989

Order 1920.

932 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 116 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#11756242C211yesmaximal, characteristic, complemented
2C5×#4955C211yesmaximal, characteristic
3#11749496C212yesmaximal
4C3×#64746C211yesmaximal, characteristic, complemented
5#11746020C212yesmaximal, complemented
6#10600290—31nomaximal, Hall
7C24×C5×D3C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C2212yes—
10#91813—22no—
11#91767—24no—
12C2×C5×#217C2211yescharacteristic
13C2×C5×(C2×D3)⋊C4—22no—
14C2×C3×C22⋊Dic5C2212yes—
15C2×(C2×D3)⋊Dic5—24no—
16#68971—51nomaximal, Hall
17#65817—31no—
18C5×#379—31no—
19#65536—32no—
20#64747—32no—
21#64746D311yescharacteristic, complemented
22C24×C3×C5C2311yescharacteristic
23C23×C5×D3—21no—
24C23×C5×D3—22no—
25C23×C5×D3—22no—
26C23×C5×D3—21no—
27C23×C5×D3—44no—
28C23×C5×D3Q812yescomplemented
29C22×C3×C4×C5D412yes—
30C22×Dic15D414yes—
31C2×Dic30—22no—
32C22×C5×Dic3—21no—
33C22×C3×Dic5—22no—
34C3×C5×C22⋊C4—22no—
35#6719—22no—
36#6719—22no—
37C4⋊Dic15—22no—
38#6712—24no—
39C5×#217—22no—
40C5×(C2×D3)⋊C4—44no—
41C3×C22⋊Dic5—22no—
42C3×C22⋊Dic5—22no—
43(C2×D3)⋊Dic5—48no—
44#5483—51no—
45#4955—52no—
46#4955D511yescharacteristic
47C3×#342—51no—
48#4527—52no—
49C25×C5—31no—
50C2×C5×C22⋊C4—31no—
51C2×C5×C22⋊C4—62no—
52C2×C5×C22⋊C4C2×D311yescharacteristic
53C2×C22⋊Dic5—32no—
54C2×C22⋊Dic5—64no—
55C2×C22⋊Dic5C2×D312yes—
56#4070—62no—
57#4024—64no—
58#2029—151noSylow
59C23×C3×C5—42no—
60C23×C3×C5C2×D412yes—
61C23×C3×C5C2×D411yescharacteristic
62C23×C3×C5C2×Q811yescharacteristic
63C23×C3×C5#4111yescharacteristic
64C23×C3×C5#4112yes—
65C22×C5×D3—28no—
66C22×C5×D3—24no—
67C22×C5×D3—24no—
68C22×C5×D3—22no—
69C22×C5×D3—44no—
70C22×C5×D3—48no—
71C22×C5×D3—44no—
72C22×C5×D3—44no—
73C22×C5×D3—42no—
74C22×C5×D3—41no—
75C22×C5×D3—42no—
76C22×C5×D3—41no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×Dic15—24no—
80C2×Dic15—44no—
81Dic30—82no—
82C2×C5×Dic3—42no—
83C2×C5×Dic3—41no—
84C2×C3×Dic5—44no—
85C2×C3×Dic5—42no—
86C24×D3C2×D511yescharacteristic
87C2×C3×C22⋊C4—52no—
88C2×C3×C22⋊C4C2×D511yescharacteristic
89C2×#217—52no—
90C2×#217C2×D511yescharacteristic
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—104no—
93#924—102no—
94#878—104no—
95C24×C5—32no—
96C24×C5—61no—
97C24×C5—62no—
98C24×C5—62no—
99C24×C5—61no—
100C24×C5—124no—
101C24×C5C22×D311yescharacteristic
102C22×C4×C5—61no—
103C22×C4×C5D1212yes—
104C22×Dic5—22no—
105C22×Dic5—34no—
106C2×Dic10—62no—
107C5×C22⋊C4—22no—
108C5×C22⋊C4—62no—
109C5×C22⋊C4—124no—
110C22⋊Dic5—22no—
111C22⋊Dic5—22no—
112C22⋊Dic5—62no—
113C22⋊Dic5—62no—
114C22⋊Dic5—128no—
115C4⋊Dic5—62no—
116#683—64no—
117#543—151no—
118#379—31no—
119#379—152no—
120#342—51no—
121#342—152no—
122C22×C3×C5—24no—
123C22×C3×C5—22no—
124C22×C3×C5—41no—
125C22×C3×C5—41no—
126C22×C3×C5—42no—
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5C22⋊Q812yes—
129C22×C3×C5C22⋊Q811yescharacteristic
130C22×C3×C5#12412yes—
131C22×C3×C5#12411yescharacteristic
132C2×C5×D3—28no—
133C2×C5×D3—24no—
134C2×C5×D3—44no—
135C2×C5×D3—48no—
136C2×C5×D3—44no—
137C2×C5×D3—42no—
138C2×C5×D3—42no—
139C2×C5×D3—44no—
140C3×C4×C5—42no—
141Dic15—44no—
142C3×Dic5—82no—
143C5×Dic3—81no—
144C24×C3C22×D511yescharacteristic
145C23×D3—22no—
146C23×D3—21no—
147C23×D3—21no—
148C23×D3—22no—
149C23×D3—44no—
150C23×D3Dic1012yescomplemented
151C22×C3×C4—102no—
152C22×C3×C4C22⋊D512yes—
153C22×Dic3—21no—
154C22×Dic3—54no—
155C2×Dic6—102no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—102no—
158C3×C22⋊C4—102no—
159#217—22no—
160#217—102no—
161#217—102no—
162(C2×D3)⋊C4—44no—
163(C2×D3)⋊C4—208no—
164C4⋊Dic3—102no—
165Dic3⋊C4—104no—
166C23×C5—42no—
167C23×C5—68no—
168C23×C5—64no—
169C23×C5—64no—
170C23×C5—62no—
171C23×C5—124no—
172C23×C5—122no—
173C23×C5—124no—
174C23×C5—128no—
175C23×C5—124no—
176C23×C5—121no—
177C23×C5—121no—
178C23×C5—122no—
179C23×C5C2×D1211yescharacteristic
180C23×C5#23512yes—
181C23×C5D3×D412yes—
182C23×C5#23711yescharacteristic
183C23×C5D3×Q811yescharacteristic
184C2×C4×C5—22no—
185C2×C4×C5—42no—
186C2×C4×C5—122no—
187C2×C4×C5—121no—
188C2×Dic5—44no—
189C2×Dic5—42no—
190C2×Dic5—64no—
191C2×Dic5—124no—
192Dic10—242no—
193C25—31no—
194C22⋊Q8—304no—
195C22⋊Q8—302no—
196C2×C22⋊C4—31no—
197C2×C22⋊C4—52no—
198C2×C22⋊C4—62no—
199C2×C22⋊C4—152no—
200C2×C22⋊C4—304no—
201C2×C22⋊C4D3×D511yescharacteristic
202C2×C3×C5—21no—
203C2×C3×C5—22no—
204C2×C3×C5—22no—
205C2×C3×C5—21no—
206C2×C3×C5#39311yescharacteristic
207C2×C3×C5B(4,𝔽2)12yes—
208C5×D3—44no—
209C23×C3—42no—
210C23×C3C2×Dic1011yescharacteristic
211C23×C3#70911yescharacteristic
212C23×C3D4×D512yes—
213C23×C3#71112yes—
214C23×C3C2×C22⋊D511yescharacteristic
215C22×D3—24no—
216C22×D3—28no—
217C22×D3—24no—
218C22×D3—22no—
219C22×D3—44no—
220C22×D3—44no—
221C22×D3—48no—
222C22×D3—42no—
223C22×D3—44no—
224C22×D3—42no—
225C22×D3—41no—
226C22×D3—41no—
227C2×C3×C4—22no—
228C2×C3×C4—42no—
229C2×C3×C4—204no—
230C2×C3×C4—202no—
231C2×Dic3—42no—
232C2×Dic3—41no—
233C2×Dic3—104no—
234C2×Dic3—204no—
235Dic6—402no—
236C22×C5—24no—
237C22×C5—22no—
238C22×C5—42no—
239C22×C5—41no—
240C22×C5—41no—
241C22×C5—68no—
242C22×C5—64no—
243C22×C5—128no—
244C22×C5—124no—
245C22×C5—124no—
246C22×C5—122no—
247C22×C5—122no—
248C22×C5—124no—
249C22×C5#87511yescharacteristic
250C22×C5#88211yescharacteristic
251C22×C5#88512yes—
252C22×C5#89612yes—
253C22×C5#89711yescharacteristic
254C4×C5—42no—
255C4×C5—241no—
256Dic5—82no—
257Dic5—124no—
258C24—32no—
259C24—61no—
260C24—62no—
261C24—61no—
262C24—62no—
263C24—124no—
264C24C2×D3×D511yescharacteristic
265C2×Q8—302no—
266C22×C4—61no—
267C22×C4—102no—
268C22×C4—154no—
269C22×C4#120312yes—
270C4⋊C4—304no—
271C4⋊C4—302no—
272C22⋊C4—22no—
273C22⋊C4—62no—
274C22⋊C4—102no—
275C22⋊C4—102no—
276C22⋊C4—124no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—608no—
280C3×C5#202911yescharacteristic, complemented, Hall
281C22×C3—22no—
282C22×C3—24no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—42no—
286C22×C3#402412yes—
287C22×C3#403112yes—
288C22×C3#407011yescharacteristic
289C22×C3#408211yescharacteristic
290C22×C3#408311yescharacteristic
291C2×D3—28no—
292C2×D3—24no—
293C2×D3—44no—
294C2×D3—48no—
295C2×D3—44no—
296C2×D3—42no—
297C2×D3—44no—
298C2×D3—42no—
299C3×C4—42no—
300C3×C4—402no—
301Dic3—81no—
302Dic3—204no—
303C2×C5—22no—
304C2×C5—21no—
305C2×C5—22no—
306C2×C5—21no—
307C2×C5—124no—
308C2×C5#467311yescharacteristic
309C2×C5#474112yes—
310C23—42no—
311C23—64no—
312C23—68no—
313C23—64no—
314C23—62no—
315C23—122no—
316C23—124no—
317C23—124no—
318C23—124no—
319C23—128no—
320C23—122no—
321C23—121no—
322C23—121no—
323C23#676511yescharacteristic
324C23D3×Dic1011yescharacteristic
325C23#677212yes—
326C23C2×#120311yescharacteristic
327C23#679012yes—
328Q8—1202no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—122no—
332C2×C4—121no—
333C2×C4—204no—
334C2×C4—202no—
335C2×C4—304no—
336C2×C4—604no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3#6523611yescharacteristic
342C2×C3#6532112yes—
343D3—44no—
344C5#6897111yescharacteristic, complemented, Sylow
345C22—22no—
346C22—24no—
347C22—41no—
348C22—41no—
349C22—42no—
350C22—68no—
351C22—64no—
352C22—124no—
353C22—128no—
354C22—124no—
355C22—122no—
356C22—124no—
357C22—122no—
358C22#9136511yescharacteristic
359C22#9137311yescharacteristic
360C22#9143212yes—
361C22#9146212yes—
362C22#9157311yescharacteristic
363C4—42no—
364C4—241no—
365C4—402no—
366C4—604no—
367C3#1060029011yescharacteristic, complemented, Sylow
368C2—21no—
369C2—22no—
370C2—22no—
371C2—21no—
372C2—124no—
373C2#1174879511yescharacteristic
374C2#1174918012yes—
subgroupG/H
centerC22#91573
commutator, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC24×C5×D3C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2029
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11756242C2semidirect
4. C3×#64746C2semidirect
5. #11746020C2semidirect
21. #64746D3semidirect
28. C23×C5×D3Q8semidirect
150. C23×D3Dic10semidirect
280. C3×C5#2029semidirect
344. C5#68971semidirect
367. C3#10600290semidirect

Maximal subgroups

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

subgroupindex
#117562422
C5×#49552
#117494962
C3×#647462
#117460202
#106002903
#689715