Finite Group Databasebeta

← #14280883

Subgroups — #14280883

Order 1920.

664 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 112 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×#91406C211yesmaximal, characteristic
2D3×C22⋊#170C212yesmaximal, complemented
3#11746785C211yesmaximal, characteristic, complemented
4C3×#64914C211yesmaximal, characteristic, complemented
5#11746567C212yesmaximal, complemented
6#10604201—31nomaximal, Hall
7C22×C4×D15C411yescharacteristic
8C22×#1203C411yescharacteristic
9C22×D3×Dic5C2211yescharacteristic
10C2×D3×#170—22no—
11C2×C5×(C2×D3)⋊C4C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×#6667C2211yescharacteristic
14C2×Dic3×Dic5C411yescharacteristic
15#91406—22no—
16#91406—22no—
17#91241C2212yes—
18C3×C22⋊#170C2212yes—
19(C2×D3)⋊#170—22no—
20#68143—51nomaximal, Hall
21C2×#4027—31no—
22C2×C22⋊#170—32no—
23#64915—32no—
24#64914—31no—
25#64914D311yescharacteristic, complemented
26C23×D15C2×C411yescharacteristic
27C23×C5×D3C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C2×C4×D15—21no—
31C2×C4×D15—21no—
32C2×C4×D15—42no—
33C22×C5×Dic3C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×#1203—22no—
37C2×#1203—22no—
38C2×#1203C814yescomplemented
39C2×D3×Dic5—42no—
40C2×D3×Dic5D412yes—
41C2×D3×Dic5D412yes—
42C2×C3⋊#170—22no—
43C2×C3×#170—22no—
44D3×#170—44no—
45C5×(C2×D3)⋊C4—22no—
46C3×#683—22no—
47#6667—22no—
48Dic3×Dic5—21no—
49Dic3×Dic5—21no—
50C2×#893—51no—
51D3×C22⋊C8—52no—
52C3×#324—51no—
53#4528—51no—
54#4468—52no—
55C22×C22⋊D5—31no—
56C23×Dic5—31no—
57C22×C4×D5—31no—
58C22×#170—62no—
59C2×C5×C22⋊C4—31no—
60C2×#685—31no—
61C2×#683C2×D311yescharacteristic
62C2×C4×Dic5—31no—
63#4027—62no—
64#4027—62no—
65C22⋊#170—32no—
66C22⋊#170—62no—
67C22⋊#170C2×D312yes—
68#1459—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×D15—21no—
71C22×D15—21no—
72C22×D15—41no—
73C22×D15—41no—
74C22×D15C2×C812yescomplemented
75C22×C5×D3—41no—
76C22×C5×D3—41no—
77C22×C5×D3C22⋊C412yes—
78C22×C5×D3C2×C812yes—
79C22×C5×D3M1612yes—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—41no—
82C2×Dic15—22no—
83C2×Dic15C22⋊C411yescharacteristic
84C2×Dic15C22⋊C411yescharacteristic
85C4×D15—42no—
86C4×D15—42no—
87C2×C5×Dic3—21no—
88C2×C5×Dic3—41no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C2×C812yescomplemented
93C2×C3×Dic5C2×D412yes—
94#1203—28no—
95D3×Dic5—24no—
96D3×Dic5—42no—
97C3⋊#170—42no—
98C3×#170—42no—
99C22×D12—51no—
100C22×C4×D3—51no—
101C22×C4×D3—51no—
102C2×C3×C4⋊C4—51no—
103C2×(C2×D3)⋊C4—51no—
104C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic
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×C5C4×D311yescharacteristic
116C2×C22⋊D5—34no—
117C2×C22⋊D5—62no—
118C2×C22⋊D5—62no—
119C22×Dic5—31no—
120C22×Dic5—32no—
121C22×Dic5—32no—
122C22×Dic5—122no—
123C22×Dic5C4×D311yescharacteristic
124C22×Dic5C22×D311yescharacteristic
125C2×C4×D5—61no—
126C2×C4×D5—61no—
127C2×C4×D5—122no—
128C2×#170—22no—
129C2×#170—62no—
130C2×#170—124no—
131C5×C22⋊C4—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—42no—
148C2×D15—41no—
149C2×D15—41no—
150C2×D15—42no—
151C2×C5×D3—22no—
152C2×C5×D3—22no—
153C2×C5×D3—42no—
154C2×C5×D3—42no—
155C2×C5×D3C22⋊C814yes—
156C3×C4×C5—41no—
157Dic15—21no—
158Dic15#9912yes—
159C3×Dic5—22no—
160C3×Dic5—22no—
161C5×Dic3—41no—
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—52no—
173C2×C4×D3—52no—
174C2×C4×D3—101no—
175C2×C4×D3—101no—
176C2×C4×D3—202no—
177C2×C4×D3—202no—
178C2×C3×C8—102no—
179C3×C4⋊C4—102no—
180(C2×D3)⋊C4—22no—
181(C2×D3)⋊C4—102no—
182C4×Dic3—101no—
183C4×Dic3—101no—
184C2×C3⋊C8—102no—
185D3×C8—204no—
186C23×C5—32no—
187C23×C5—32no—
188C23×C5—32no—
189C23×C5—121no—
190C23×C5—121no—
191C23×C5C2×C4×D311yescharacteristic
192C22×D5—32no—
193C22×D5—61no—
194C22×D5—61no—
195C22×D5—121no—
196C22×D5—121no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—61no—
200C2×C4×C5—121no—
201C22⋊D5—68no—
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—31no—
205C2×Dic5—31no—
206C2×Dic5—41no—
207C2×Dic5—64no—
208C2×Dic5—62no—
209C2×Dic5—122no—
210C2×Dic5D3×C812yescomplemented
211C2×Dic5D3×D412yes—
212C4×D5—122no—
213C4×D5—122no—
214#170—42no—
215#170—122no—
216C22×D4—151no—
217C23×C4—151no—
218C23×C4—151no—
219C22×C8—302no—
220C4×D4—302no—
221C4×D4—302no—
222C2×C4⋊C4—51no—
223C2×C22⋊C4—31no—
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—42no—
235C5×D3—24no—
236C23×C3C22×AGL(1,𝔽5)11yescharacteristic
237C22×D3—41no—
238C22×D3—41no—
239C22×D3—52no—
240C22×D3—101no—
241C22×D3—101no—
242C22×D3—201no—
243C22×D3—201no—
244C22×D3D5⋊C812yes—
245C22×D3#70012yes—
246C22×D3C22⋊AGL(1,𝔽5)12yes—
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—21no—
255C2×Dic3—41no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—102no—
259D12—108no—
260C4×D3—104no—
261C4×D3—202no—
262C4×D3—202no—
263C4×D3—202no—
264C3×C8—202no—
265C3⋊C8—202no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—34no—
269C22×C5—62no—
270C22×C5—62no—
271C22×C5—122no—
272C22×C5—122no—
273C22×C5D3×C22⋊C411yescharacteristic
274C22×C5C2×D3×C811yescharacteristic
275C22×C5D3×M1611yescharacteristic
276C2×D5—62no—
277C2×D5—122no—
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—122no—
281C4×C5—41no—
282C4×C5—121no—
283Dic5—22no—
284Dic5—22no—
285Dic5—32no—
286Dic5—61no—
287C24—31no—
288C24—151no—
289C2×D4—154no—
290C2×D4—302no—
291C2×D4—302no—
292C22×C4—31no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—152no—
296C22×C4—152no—
297C22×C4—151no—
298C22×C4—301no—
299C22×C4—301no—
300C22×C4—602no—
301C22×C4—602no—
302C22×C4D3×AGL(1,𝔽5)11yescharacteristic
303C2×C8—102no—
304C2×C8—302no—
305C2×C8—604no—
306C4⋊C4—102no—
307C22⋊C4—62no—
308C22⋊C4—302no—
309C42—301no—
310C42—301no—
311C3×C5#145911yescharacteristic, complemented, Hall
312C22×C3—21no—
313C22×C3—21no—
314C22×C3C2×D5⋊C811yescharacteristic
315C22×C3C2×#70011yescharacteristic
316C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
317C2×D3—22no—
318C2×D3—22no—
319C2×D3—42no—
320C2×D3—42no—
321C2×D3—102no—
322C2×D3—202no—
323C2×D3—201no—
324C2×D3—201no—
325C2×D3—202no—
326C2×D3#400314yes—
327C3×C4—41no—
328C3×C4—102no—
329C3×C4—102no—
330Dic3—41no—
331Dic3—52no—
332Dic3—101no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5—64no—
336C2×C5D3×C22⋊C811yescharacteristic
337C2×C5D3×#9911yescharacteristic
338C2×C5#475111yescharacteristic
339D5—122no—
340C23—32no—
341C23—32no—
342C23—32no—
343C23—121no—
344C23—121no—
345C23—152no—
346C23—301no—
347C23—301no—
348C23—601no—
349C23—601no—
350C23C2×D3×AGL(1,𝔽5)11yescharacteristic
351D4—308no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—52no—
355C2×C4—52no—
356C2×C4—61no—
357C2×C4—101no—
358C2×C4—101no—
359C2×C4—121no—
360C2×C4—151no—
361C2×C4—151no—
362C2×C4—201no—
363C2×C4—304no—
364C2×C4—302no—
365C2×C4—602no—
366C2×C4—602no—
367C2×C4—602no—
368C8—202no—
369C8—602no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3C2×#400311yescharacteristic
373C2×C3D5⋊#9911yescharacteristic
374C2×C3#6577711yescharacteristic
375D3—24no—
376D3—202no—
377C5#6814311yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—34no—
381C22—62no—
382C22—62no—
383C22—122no—
384C22—122no—
385C22—302no—
386C22—602no—
387C22—602no—
388C22—601no—
389C22—601no—
390C22D3×D5⋊C811yescharacteristic
391C22D3×#70011yescharacteristic
392C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
393C4—41no—
394C4—102no—
395C4—102no—
396C4—121no—
397C4—152no—
398C4—301no—
399C3#1060420111yescharacteristic, complemented, Sylow
400C2—21no—
401C2—21no—
402C2—64no—
403C2—602no—
404C2D3×#400311yescharacteristic
405C2#1175191611yescharacteristic
406C2#1175202411yescharacteristic
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. D3×C22⋊#170C2semidirect
3. #11746785C2semidirect
4. C3×#64914C2semidirect
5. #11746567C2semidirect
25. #64914D3semidirect
38. C2×#1203C8semidirect
74. C22×D15C2×C8semidirect
92. C2×C3×Dic5C2×C8semidirect
210. C2×Dic5D3×C8semidirect
311. C3×C5#1459semidirect
377. C5#68143semidirect
399. C3#10604201semidirect

Maximal subgroups

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

subgroupindex
C2×#914062
D3×C22⋊#1702
#117467852
C3×#649142
#117465672
#106042013
#681435