Finite Group Databasebeta

← #14308988

Subgroups — #14308988

Order 1920.

932 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 120 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×#65817C211yesmaximal, characteristic, complemented
2C5×#4955C211yesmaximal, characteristic
3#11749496C212yesmaximal
4#11746347C211yesmaximal, characteristic, complemented
5#11746019C212yesmaximal, complemented
6#10600290—31nomaximal, Hall
7C24×C5×D3C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C2212yes—
10C2×C5×#217C2211yescharacteristic
11C2×C5×(C2×D3)⋊C4—22no—
12C2×C3×C22⋊Dic5C2212yes—
13C3×#4070—22no—
14C3×#4024—24no—
15C2×(C2×D3)⋊Dic5—24no—
16#71897—51nomaximal, Hall
17#65817D311yescharacteristic, complemented
18C5×#379—31no—
19#65536—32no—
20#64747—32no—
21#64746—31no—
22C24×C3×C5C2311yescharacteristic
23C23×C5×D3—21no—
24C23×C5×D3—22no—
25C23×C5×D3—21no—
26C23×C5×D3—22no—
27C23×C5×D3—44no—
28C23×C5×D3Q812yescomplemented
29C22×C3×C4×C5D412yes—
30C22×Dic15—22no—
31C22×C5×Dic3—21no—
32C22×C3×Dic5D414yes—
33C2×C3×Dic10—22no—
34C3×C5×C22⋊C4—22no—
35#6719—22no—
36#6719—22no—
37C5×#217—22no—
38C5×(C2×D3)⋊C4—44no—
39C3×C22⋊Dic5—22no—
40C3×C22⋊Dic5—22no—
41C3×C4⋊Dic5—22no—
42C3×#683—24no—
43(C2×D3)⋊Dic5—48no—
44C3×#543—51no—
45#4955—52no—
46#4955D511yescharacteristic
47#4526—51no—
48#4526—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—22no—
57#4024—24no—
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—44no—
80C2×Dic15—42no—
81C2×C5×Dic3—42no—
82C2×C5×Dic3—41no—
83C2×C3×Dic5—24no—
84C2×C3×Dic5—44no—
85C3×Dic10—82no—
86C24×D3C2×D511yescharacteristic
87C3×C22⋊Q8—104no—
88C3×C22⋊Q8—102no—
89C2×C3×C22⋊C4—52no—
90C2×C3×C22⋊C4C2×D511yescharacteristic
91C2×#217—52no—
92C2×#217C2×D511yescharacteristic
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—104no—
95C24×C5—32no—
96C24×C5—62no—
97C24×C5—61no—
98C24×C5—62no—
99C24×C5—61no—
100C24×C5—124no—
101C24×C5C22×D311yescharacteristic
102C22×C4×C5—61no—
103C22×C4×C5#6712yes—
104C22×Dic5—62no—
105C22×Dic5#6714yes—
106C2×Dic10—22no—
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—22no—
116#683—24no—
117#543—51no—
118#379—31no—
119#379—152no—
120#342—152no—
121#342—151no—
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—82no—
142C3×Dic5—44no—
143C5×Dic3—81no—
144C24×C3C22×D511yescharacteristic
145C23×D3—22no—
146C23×D3—21no—
147C23×D3—21no—
148C23×D3—22no—
149C23×D3—44no—
150C23×D3Dic1012yescomplemented
151C2×C3×Q8—102no—
152C22×C3×C4—54no—
153C22×C3×C4C22⋊D512yes—
154C22×Dic3—21no—
155C22×Dic3—102no—
156C3×C4⋊C4—104no—
157C3×C4⋊C4—102no—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—102no—
160C3×C22⋊C4—102no—
161#217—22no—
162#217—102no—
163#217—102no—
164(C2×D3)⋊C4—44no—
165(C2×D3)⋊C4—208no—
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—122no—
177C23×C5—121no—
178C23×C5—121no—
179C23×C5D3×Q811yescharacteristic
180C23×C5#23912yes—
181C23×C5#23911yescharacteristic
182C23×C5C2×#6711yescharacteristic
183C23×C5C2×#6712yes—
184C2×C4×C5—22no—
185C2×C4×C5—42no—
186C2×C4×C5—122no—
187C2×C4×C5—121no—
188C2×Dic5—24no—
189C2×Dic5—44no—
190C2×Dic5—124no—
191C2×Dic5—122no—
192Dic10—82no—
193C25—31no—
194C22⋊Q8—104no—
195C22⋊Q8—102no—
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—
227C3×Q8—402no—
228C2×C3×C4—22no—
229C2×C3×C4—42no—
230C2×C3×C4—104no—
231C2×C3×C4—204no—
232C2×Dic3—42no—
233C2×Dic3—41no—
234C2×Dic3—204no—
235C2×Dic3—202no—
236C22×C5—24no—
237C22×C5—22no—
238C22×C5—41no—
239C22×C5—42no—
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#94612yes—
250C22×C5#94611yescharacteristic
251C22×C5#94712yes—
252C22×C5#94711yescharacteristic
253C22×C5#95311yescharacteristic
254C4×C5—42no—
255C4×C5—241no—
256Dic5—44no—
257Dic5—242no—
258C24—32no—
259C24—61no—
260C24—62no—
261C24—62no—
262C24—61no—
263C24—124no—
264C24C2×D3×D511yescharacteristic
265C2×Q8—102no—
266C22×C4—54no—
267C22×C4—61no—
268C22×C4—302no—
269C22×C4#120112yes—
270C4⋊C4—104no—
271C4⋊C4—102no—
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—204no—
301Dic3—81no—
302Dic3—402no—
303C2×C5—22no—
304C2×C5—21no—
305C2×C5—22no—
306C2×C5—21no—
307C2×C5—124no—
308C2×C5#523111yescharacteristic
309C2×C5#524412yes—
310C23—42no—
311C23—64no—
312C23—68no—
313C23—64no—
314C23—62no—
315C23—122no—
316C23—124no—
317C23—124no—
318C23—128no—
319C23—124no—
320C23—121no—
321C23—122no—
322C23—121no—
323C23D3×Dic1011yescharacteristic
324C23#676812yes—
325C23#676911yescharacteristic
326C23C2×#120111yescharacteristic
327C23D5×#6712yes—
328Q8—402no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—104no—
332C2×C4—122no—
333C2×C4—121no—
334C2×C4—204no—
335C2×C4—604no—
336C2×C4—602no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3#6523611yescharacteristic
342C2×C3#6532112yes—
343D3—44no—
344C5#7189711yescharacteristic, complemented, Sylow
345C22—22no—
346C22—24no—
347C22—41no—
348C22—42no—
349C22—41no—
350C22—68no—
351C22—64no—
352C22—124no—
353C22—128no—
354C22—124no—
355C22—122no—
356C22—124no—
357C22—122no—
358C22#9132612yes—
359C22#9136911yescharacteristic
360C22#9137011yescharacteristic
361C22#9141012yes—
362C22#9156311yescharacteristic
363C4—42no—
364C4—204no—
365C4—241no—
366C4—1202no—
367C3#1060029011yescharacteristic, complemented, Sylow
368C2—21no—
369C2—22no—
370C2—22no—
371C2—21no—
372C2—124no—
373C2#1174874611yescharacteristic
374C2#1174917512yes—
subgroupG/H
centerC22#91563
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. C3×#65817C2semidirect
4. #11746347C2semidirect
5. #11746019C2semidirect
17. #65817D3semidirect
28. C23×C5×D3Q8semidirect
150. C23×D3Dic10semidirect
280. C3×C5#2029semidirect
344. C5#71897semidirect
367. C3#10600290semidirect

Maximal subgroups

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

subgroupindex
C3×#658172
C5×#49552
#117494962
#117463472
#117460192
#106002903
#718975