Finite Group Databasebeta

← #14280882

Subgroups — #14280882

Order 1920.

664 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 108 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×#91446C211yesmaximal, characteristic
2#11752042C212yesmaximal, complemented
3#11746785C211yesmaximal, characteristic, complemented
4C3×#64914C211yesmaximal, characteristic, complemented
5#11746566C212yesmaximal, complemented
6#10604878—31nomaximal, Hall
7C22×C4×C5×D3C411yescharacteristic
8C22×#1203C411yescharacteristic
9C22×#1200C2211yescharacteristic
10C2×#6738—22no—
11C2×#6714C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×(C2×D3)⋊Dic5C2211yescharacteristic
14C2×Dic3×Dic5C411yescharacteristic
15#91446—22no—
16#91446—22no—
17#91241C2212yes—
18C3×C22⋊#170C2212yes—
19#91171—22no—
20#68143—51nomaximal, Hall
21C2×C4×C22⋊D5—31no—
22D5⋊(C22⋊C8)—32no—
23#64933—32no—
24#64914—31no—
25#64914D311yescharacteristic, complemented
26C23×D15C2×C411yescharacteristic
27C23×C5×D3C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C22×C5×Dic3C2×C411yescharacteristic
31C2×C4×C5×D3—21no—
32C2×C4×C5×D3—21no—
33C2×C4×C5×D3—42no—
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×#1203—22no—
37C2×#1203—22no—
38C2×#1203C814yescomplemented
39C2×#1200—42no—
40C2×#1200D412yes—
41C2×#1200D412yes—
42C2×C3⋊#170—22no—
43C2×C3×#170—22no—
44#6738—44no—
45#6714—22no—
46C3×#683—22no—
47(C2×D3)⋊Dic5—22no—
48Dic3×Dic5—21no—
49Dic3×Dic5—21no—
50C2×#893—51no—
51D3×C22⋊C8—52no—
52C3×#324—51no—
53#4528—51no—
54#4468—52no—
55C23×C4×C5—31no—
56C22×C22⋊D5—31no—
57C22×C4×D5—31no—
58C2×D5⋊C8—62no—
59C2×C22⋊Dic5—31no—
60C4×C22⋊D5—62no—
61C4×C22⋊D5—62no—
62C2×#685—31no—
63C2×#683C2×D311yescharacteristic
64C2×C4×Dic5—31no—
65C22⋊#170—32no—
66C22⋊#170C2×D312yes—
67#4003—62no—
68#1459—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×D15—41no—
71C22×D15—41no—
72C22×D15C22⋊C412yes—
73C22×D15C2×C812yes—
74C22×D15M1612yes—
75C22×C5×D3—21no—
76C22×C5×D3—21no—
77C22×C5×D3—41no—
78C22×C5×D3—41no—
79C22×C5×D3C2×C812yescomplemented
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—41no—
82C2×Dic15—21no—
83C2×Dic15—41no—
84C2×C5×Dic3—22no—
85C2×C5×Dic3C22⋊C411yescharacteristic
86C2×C5×Dic3C22⋊C411yescharacteristic
87C4×C5×D3—42no—
88C4×C5×D3—42no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C2×C812yescomplemented
93C2×C3×Dic5C2×D412yes—
94#1203—28no—
95#1200—24no—
96#1200—42no—
97C3⋊#170—42no—
98C3×#170—42no—
99C22×D12—51no—
100C22×C4×D3—51no—
101C22×C4×D3AGL(1,𝔽5)11yescharacteristic
102C2×C3×C4⋊C4—51no—
103C2×(C2×D3)⋊C4—51no—
104C2×(C2×D3)⋊C4—51no—
105C2×C4×Dic3—51no—
106C2×D3×C8—102no—
107#893—102no—
108#893—102no—
109C3×C22⋊C8—52no—
110#830—52no—
111(C2×D3)⋊C8—102no—
112C24×C5—31no—
113C23×D5—31no—
114C22×C4×C5—31no—
115C22×C4×C5—61no—
116C22×C4×C5—61no—
117C22×C4×C5—122no—
118C22×C4×C5C4×D311yescharacteristic
119C2×C22⋊D5—34no—
120C2×C22⋊D5—62no—
121C2×C22⋊D5—62no—
122C22×Dic5—31no—
123C22×Dic5C4×D311yescharacteristic
124C22×Dic5C22×D311yescharacteristic
125C2×C4×D5—32no—
126C2×C4×D5—32no—
127C2×C4×D5—122no—
128C2×#170—22no—
129C2×#170—62no—
130D5⋊C8—124no—
131C22⋊Dic5—62no—
132#685—62no—
133#683—22no—
134C4×Dic5—61no—
135C4×Dic5—61no—
136C2×C4×D4—151no—
137C2×C22⋊C8—152no—
138#324—51no—
139#324—151no—
140#323—152no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5C2×C22⋊C411yescharacteristic
144C22×C3×C5C22×C811yescharacteristic
145C22×C3×C5C2×M1611yescharacteristic
146C2×D15—22no—
147C2×D15—22no—
148C2×D15—42no—
149C2×D15—42no—
150C2×D15C22⋊C814yes—
151C2×C5×D3—22no—
152C2×C5×D3—42no—
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C2×C5×D3—42no—
156C3×C4×C5—41no—
157Dic15—41no—
158C3×Dic5—22no—
159C3×Dic5—22no—
160C5×Dic3—21no—
161C5×Dic3#9912yes—
162C23×D3—51no—
163C23×D3C2×AGL(1,𝔽5)11yescharacteristic
164C22×C3×C4—51no—
165C22×C3×C4—51no—
166C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
167C22×Dic3—51no—
168C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
169C2×D12—54no—
170C2×D12—102no—
171C2×D12—102no—
172C2×C4×D3—21no—
173C2×C4×D3—21no—
174C2×C4×D3—42no—
175C2×C4×D3—52no—
176C2×C4×D3—52no—
177C2×C4×D3—202no—
178C2×C3×C8—102no—
179C3×C4⋊C4—102no—
180(C2×D3)⋊C4—102no—
181(C2×D3)⋊C4—102no—
182C4×Dic3—101no—
183C4×Dic3—101no—
184C2×C3⋊C8—102no—
185D3×C8—204no—
186C23×C5—32no—
187C23×C5—61no—
188C23×C5—61no—
189C23×C5—121no—
190C23×C5—121no—
191C23×C5C2×C4×D311yescharacteristic
192C22×D5—32no—
193C22×D5—32no—
194C22×D5—32no—
195C22×D5—121no—
196C22×D5—121no—
197C2×C4×C5—21no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—41no—
201C2×C4×C5—62no—
202C2×C4×C5—122no—
203C2×C4×C5—122no—
204C22⋊D5—68no—
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—41no—
208C2×Dic5—61no—
209C2×Dic5—121no—
210C2×Dic5D3×C812yescomplemented
211C2×Dic5D3×D412yes—
212C4×D5—64no—
213C4×D5—122no—
214#170—42no—
215#170—122no—
216C22×D4—151no—
217C23×C4—31no—
218C23×C4—151no—
219C22×C8—302no—
220C4×D4—302no—
221C4×D4—302no—
222C2×C4⋊C4—51no—
223C2×C22⋊C4—151no—
224C2×C22⋊C4—151no—
225C2×C42—151no—
226C22⋊C8—52no—
227C22⋊C8—152no—
228C22⋊C8—302no—
229C2×C3×C5—21no—
230C2×C3×C5—21no—
231C2×C3×C5C2×C22⋊C811yescharacteristic
232C2×C3×C5C2×#9911yescharacteristic
233C2×C3×C5#41311yescharacteristic
234D15—24no—
235C5×D3—42no—
236C23×C3C22×AGL(1,𝔽5)11yescharacteristic
237C22×D3—21no—
238C22×D3—21no—
239C22×D3—41no—
240C22×D3—41no—
241C22×D3—52no—
242C22×D3—52no—
243C22×D3—52no—
244C22×D3—201no—
245C22×D3—201no—
246C22×D3D5⋊C812yescomplemented
247C2×C3×C4—21no—
248C2×C3×C4—41no—
249C2×C3×C4—52no—
250C2×C3×C4—52no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—201no—
254C2×Dic3—22no—
255C2×Dic3—101no—
256C2×Dic3—201no—
257C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
258C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
259D12—108no—
260C4×D3—42no—
261C4×D3—42no—
262C4×D3—104no—
263C4×D3—202no—
264C3×C8—202no—
265C3⋊C8—202no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—62no—
269C22×C5—122no—
270C22×C5—122no—
271C22×C5—121no—
272C22×C5—121no—
273C22×C5D3×C22⋊C411yescharacteristic
274C22×C5C2×D3×C811yescharacteristic
275C22×C5D3×M1611yescharacteristic
276C2×D5—34no—
277C2×D5—62no—
278C2×D5—62no—
279C2×D5—122no—
280C2×D5—122no—
281C4×C5—32no—
282C4×C5—41no—
283C4×C5—61no—
284Dic5—22no—
285Dic5—22no—
286Dic5—121no—
287C24—31no—
288C24—151no—
289C2×D4—154no—
290C2×D4—302no—
291C2×D4—302no—
292C22×C4—31no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—61no—
296C22×C4—61no—
297C22×C4—122no—
298C22×C4—152no—
299C22×C4—152no—
300C22×C4—151no—
301C22×C4—602no—
302C22×C4D3×AGL(1,𝔽5)11yescharacteristic
303C2×C8—102no—
304C2×C8—302no—
305C2×C8—604no—
306C4⋊C4—102no—
307C22⋊C4—302no—
308C22⋊C4—302no—
309C42—301no—
310C42—301no—
311C3×C5#145911yescharacteristic, complemented, Hall
312C22×C3—21no—
313C22×C3—21no—
314C22×C3C2×D5⋊C811yescharacteristic
315C22×C3D5⋊M1611yescharacteristic
316C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
317C2×D3—22no—
318C2×D3—42no—
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—42no—
322C2×D3—54no—
323C2×D3—102no—
324C2×D3—102no—
325C2×D3—202no—
326C2×D3—202no—
327C3×C4—41no—
328C3×C4—102no—
329C3×C4—102no—
330Dic3—21no—
331Dic3—201no—
332Dic3#401112yes—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5—122no—
336C2×C5D3×C22⋊C811yescharacteristic
337C2×C5D3×#9911yescharacteristic
338C2×C5#475111yescharacteristic
339D5—64no—
340C23—32no—
341C23—61no—
342C23—61no—
343C23—121no—
344C23—121no—
345C23—152no—
346C23—152no—
347C23—152no—
348C23—601no—
349C23—601no—
350C23C2×D3×AGL(1,𝔽5)11yescharacteristic
351D4—308no—
352C2×C4—21no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—41no—
356C2×C4—52no—
357C2×C4—52no—
358C2×C4—62no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—122no—
362C2×C4—122no—
363C2×C4—201no—
364C2×C4—304no—
365C2×C4—301no—
366C2×C4—602no—
367C2×C4—601no—
368C8—202no—
369C8—602no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3D5⋊(C22⋊C8)11yescharacteristic
373C2×C3#6576111yescharacteristic
374C2×C3C2×#401111yescharacteristic
375D3—42no—
376D3—104no—
377C5#6814311yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—62no—
381C22—122no—
382C22—122no—
383C22—121no—
384C22—121no—
385C22—154no—
386C22—302no—
387C22—302no—
388C22—602no—
389C22—602no—
390C22D3×D5⋊C811yescharacteristic
391C22#9191511yescharacteristic
392C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
393C4—32no—
394C4—41no—
395C4—61no—
396C4—102no—
397C4—102no—
398C4—601no—
399C3#1060487811yescharacteristic, complemented, Sylow
400C2—21no—
401C2—21no—
402C2—122no—
403C2—304no—
404C2#1175188311yescharacteristic
405C2#1175191711yescharacteristic
406C2D3×#401111yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C22×C8
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1203C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1459
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752042C2semidirect
3. #11746785C2semidirect
4. C3×#64914C2semidirect
5. #11746566C2semidirect
25. #64914D3semidirect
38. C2×#1203C8semidirect
79. C22×C5×D3C2×C8semidirect
92. C2×C3×Dic5C2×C8semidirect
210. C2×Dic5D3×C8semidirect
246. C22×D3D5⋊C8semidirect
311. C3×C5#1459semidirect
377. C5#68143semidirect
399. C3#10604878semidirect

Maximal subgroups

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

subgroupindex
C2×#914462
#117520422
#117467852
C3×#649142
#117465662
#106048783
#681435