Finite Group Databasebeta

← #14280794

Subgroups — #14280794

Order 1920.

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

normal subgroups only

This group has 656 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×#91404C211yesmaximal, characteristic
2#11752042C212yesmaximal
3#11746785C211yesmaximal, characteristic, complemented
4C3×#64914C211yesmaximal, characteristic, complemented
5#11746568C212yesmaximal, complemented
6D5⋊#324—31nomaximal, Hall
7C22×C4×D15C411yescharacteristic
8C22×#1200C411yescharacteristic
9C22×#1200C2211yescharacteristic
10C2×#6738—22no—
11C2×C5×Dic3⋊C4C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×Dic3⋊Dic5C2211yescharacteristic
14C2×#6668C411yescharacteristic
15#91404—22no—
16#91404—22no—
17#91241C2212yes—
18C3×C22⋊#170C2212yes—
19#91171—22no—
20D3×#324—51nomaximal, Hall
21C2×D5×C4⋊C4—31no—
22D5⋊(C22⋊C8)—32no—
23#64914—31no—
24#64914D311yescharacteristic, complemented
25#64913—32no—
26C23×D15C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C2×C4×D15—21no—
30C2×C4×D15—21no—
31C2×C4×D15—42no—
32C22×C5×Dic3C2×C411yescharacteristic
33C22×C5×Dic3C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×#1200—21no—
37C2×#1200—21no—
38C2×#1200—22no—
39C2×#1200—42no—
40C2×#1200C814yescomplemented
41C2×#1200D412yes—
42C2×#1200D412yes—
43C2×C3⋊#170—22no—
44C2×C3×#170—22no—
45#6738—44no—
46C5×Dic3⋊C4—22no—
47C3×#683—22no—
48Dic3⋊Dic5—22no—
49#6668—22no—
50C2×D3×C4⋊C4—51no—
51D3×C22⋊C8—52no—
52C3×#324—51no—
53#4528—51no—
54#4469—52no—
55C22×C4×D5—31no—
56C22×C4×D5—31no—
57C22×C4×D5—31no—
58C2×D5⋊C8—62no—
59C2×C5×C4⋊C4—31no—
60C2×C4⋊Dic5—31no—
61C2×#683—31no—
62C2×#683C2×D311yescharacteristic
63D5×C4⋊C4—62no—
64D5×C4⋊C4—62no—
65C22⋊#170—32no—
66C22⋊#170C2×D312yes—
67#4003—62no—
68C2×#324—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×D15—22no—
71C22×D15—22no—
72C22×D15C22⋊C411yescharacteristic
73C22×D15C22⋊C411yescharacteristic
74C22×D15C2×C812yes—
75C22×D15M1612yes—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—41no—
78C2×Dic15—21no—
79C2×Dic15—41no—
80C4×D15—42no—
81C4×D15—42no—
82C2×C5×Dic3—21no—
83C2×C5×Dic3—21no—
84C2×C5×Dic3—41no—
85C2×C5×Dic3C22⋊C412yes—
86C2×C5×Dic3C2×C812yescomplemented
87C2×C3×Dic5—21no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—41no—
90C2×C3×Dic5C2×C812yescomplemented
91C2×C3×Dic5C2×D412yes—
92#1200—24no—
93#1200—24no—
94#1200—24no—
95#1200—42no—
96C3⋊#170—42no—
97C3×#170—42no—
98C22×C4×D3—51no—
99C22×C4×D3—51no—
100C22×C4×D3—51no—
101C2×C3×C4⋊C4—51no—
102C2×C4⋊Dic3—51no—
103C2×Dic3⋊C4—51no—
104C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic
105C2×D3×C8—102no—
106D3×C4⋊C4—102no—
107D3×C4⋊C4—102no—
108C3×C22⋊C8—52no—
109#830—52no—
110(C2×D3)⋊C8—102no—
111C23×D5—31no—
112C22×C4×C5—31no—
113C22×C4×C5—31no—
114C22×C4×C5C4×D311yescharacteristic
115C22×Dic5—31no—
116C22×Dic5C4×D311yescharacteristic
117C22×Dic5C22×D311yescharacteristic
118C2×C4×D5—34no—
119C2×C4×D5—32no—
120C2×C4×D5—32no—
121C2×C4×D5—62no—
122C2×C4×D5—61no—
123C2×C4×D5—61no—
124C2×C4×D5—61no—
125C2×C4×D5—61no—
126C2×C4×D5—122no—
127C2×C4×D5—122no—
128C2×#170—22no—
129C2×#170—62no—
130D5⋊C8—124no—
131C5×C4⋊C4—62no—
132C4⋊Dic5—62no—
133#683—22no—
134#683—62no—
135C22×C4⋊C4—151no—
136C2×C22⋊C8—152no—
137#324—51no—
138#324—152no—
139#324—151no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5C2×C22⋊C411yescharacteristic
143C22×C3×C5C22×C811yescharacteristic
144C22×C3×C5C2×M1611yescharacteristic
145C2×D15—21no—
146C2×D15—21no—
147C2×D15—24no—
148C2×D15—24no—
149C2×D15C22⋊C812yes—
150C2×D15C22⋊C812yes—
151C2×D15#9912yes—
152C2×D15#10112yes—
153C3×C4×C5—41no—
154Dic15—41no—
155C3×Dic5—22no—
156C3×Dic5—22no—
157C5×Dic3—22no—
158C5×Dic3—22no—
159C23×D3—51no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
163C22×Dic3—51no—
164C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
165C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
166C2×C4×D3—54no—
167C2×C4×D3—52no—
168C2×C4×D3—52no—
169C2×C4×D3—101no—
170C2×C4×D3—101no—
171C2×C4×D3—102no—
172C2×C4×D3—101no—
173C2×C4×D3—101no—
174C2×C4×D3—202no—
175C2×C4×D3—202no—
176C2×C3×C8—102no—
177C3×C4⋊C4—102no—
178C4⋊Dic3—102no—
179Dic3⋊C4—22no—
180Dic3⋊C4—102no—
181C2×C3⋊C8—102no—
182D3×C8—204no—
183C23×C5C2×C4×D311yescharacteristic
184C22×D5—31no—
185C22×D5—31no—
186C22×D5—32no—
187C22×D5—32no—
188C22×D5—62no—
189C22×D5—62no—
190C2×C4×C5—21no—
191C2×C4×C5—32no—
192C2×C4×C5—32no—
193C2×C4×C5—41no—
194C2×C4×C5—61no—
195C2×C4×C5—61no—
196C2×C4×C5—121no—
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—41no—
200C2×Dic5—61no—
201C2×Dic5—121no—
202C2×Dic5D3×C812yescomplemented
203C2×Dic5D3×D412yes—
204C4×D5—64no—
205C4×D5—64no—
206C4×D5—64no—
207C4×D5—122no—
208C4×D5—122no—
209C4×D5—122no—
210#170—42no—
211#170—122no—
212C23×C4—151no—
213C23×C4—151no—
214C23×C4—151no—
215C22×C8—302no—
216C2×C4⋊C4—31no—
217C2×C4⋊C4—51no—
218C2×C4⋊C4—151no—
219C2×C4⋊C4—151no—
220C2×C4⋊C4—302no—
221C2×C4⋊C4—302no—
222C22⋊C8—52no—
223C22⋊C8—152no—
224C22⋊C8—302no—
225C2×C3×C5—21no—
226C2×C3×C5—21no—
227C2×C3×C5C2×C22⋊C811yescharacteristic
228C2×C3×C5C2×#9911yescharacteristic
229C2×C3×C5C2×#10111yescharacteristic
230D15—22no—
231D15#32414yescomplemented
232C23×C3C22×AGL(1,𝔽5)11yescharacteristic
233C22×D3—51no—
234C22×D3—52no—
235C22×D3—52no—
236C22×D3—51no—
237C22×D3—102no—
238C22×D3—102no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—52no—
242C2×C3×C4—52no—
243C2×C3×C4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—201no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—41no—
249C2×Dic3—101no—
250C2×Dic3—201no—
251C2×Dic3D5⋊C812yescomplemented
252C2×Dic3C22⋊AGL(1,𝔽5)12yes—
253C4×D3—104no—
254C4×D3—104no—
255C4×D3—104no—
256C4×D3—202no—
257C4×D3—202no—
258C4×D3—202no—
259C3×C8—202no—
260C3⋊C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5D3×C22⋊C411yescharacteristic
264C22×C5C2×D3×C811yescharacteristic
265C22×C5D3×M1611yescharacteristic
266C2×D5—32no—
267C2×D5—32no—
268C2×D5—32no—
269C2×D5—32no—
270C2×D5—64no—
271C2×D5—64no—
272C2×D5—61no—
273C2×D5—61no—
274C4×C5—41no—
275C4×C5—62no—
276C4×C5—62no—
277Dic5—22no—
278Dic5—22no—
279Dic5—121no—
280C24—151no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—51no—
284C22×C4—51no—
285C22×C4—152no—
286C22×C4—154no—
287C22×C4—152no—
288C22×C4—151no—
289C22×C4—301no—
290C22×C4—301no—
291C22×C4—301no—
292C22×C4—301no—
293C22×C4—302no—
294C22×C4—602no—
295C22×C4—602no—
296C22×C4D3×AGL(1,𝔽5)11yescharacteristic
297C2×C8—102no—
298C2×C8—302no—
299C2×C8—604no—
300C4⋊C4—62no—
301C4⋊C4—102no—
302C4⋊C4—302no—
303C4⋊C4—302no—
304C3×C5C2×#32411yescharacteristic, complemented, Hall
305C22×C3—21no—
306C22×C3—21no—
307C22×C3C2×D5⋊C811yescharacteristic
308C22×C3D5⋊M1611yescharacteristic
309C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C2×D3—52no—
311C2×D3—52no—
312C2×D3—52no—
313C2×D3—52no—
314C2×D3—104no—
315C2×D3—104no—
316C2×D3—101no—
317C2×D3—101no—
318C3×C4—41no—
319C3×C4—102no—
320C3×C4—102no—
321Dic3—22no—
322Dic3—22no—
323Dic3—201no—
324C2×C5—21no—
325C2×C5—21no—
326C2×C5D3×C22⋊C811yescharacteristic
327C2×C5D3×#9911yescharacteristic
328C2×C5D3×#10111yescharacteristic
329D5—34no—
330D5—62no—
331C23—151no—
332C23—152no—
333C23—152no—
334C23—151no—
335C23—302no—
336C23—302no—
337C23C2×D3×AGL(1,𝔽5)11yescharacteristic
338C2×C4—21no—
339C2×C4—32no—
340C2×C4—32no—
341C2×C4—41no—
342C2×C4—52no—
343C2×C4—52no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—101no—
347C2×C4—101no—
348C2×C4—121no—
349C2×C4—201no—
350C2×C4—304no—
351C2×C4—304no—
352C2×C4—304no—
353C2×C4—301no—
354C2×C4—602no—
355C2×C4—602no—
356C2×C4—602no—
357C2×C4—601no—
358C8—202no—
359C8—602no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3D5⋊(C22⋊C8)11yescharacteristic
363C2×C3D5⋊#9911yescharacteristic
364C2×C3D5⋊#10111yescharacteristic
365D3—54no—
366D3—102no—
367C5D3×#32411yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—152no—
371C22—152no—
372C22—152no—
373C22—152no—
374C22—304no—
375C22—304no—
376C22—301no—
377C22—301no—
378C22D3×D5⋊C811yescharacteristic
379C22#9191511yescharacteristic
380C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
381C4—41no—
382C4—62no—
383C4—62no—
384C4—102no—
385C4—102no—
386C4—601no—
387C3D5⋊#32411yescharacteristic, complemented, Sylow
388C2—21no—
389C2—21no—
390C2—154no—
391C2—302no—
392C2#1175188311yescharacteristic
393C2#1175191811yescharacteristic
394C2#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 radicalC23×D15C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#324
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
3. #11746785C2semidirect
4. C3×#64914C2semidirect
5. #11746568C2semidirect
24. #64914D3semidirect
40. C2×#1200C8semidirect
86. C2×C5×Dic3C2×C8semidirect
90. C2×C3×Dic5C2×C8semidirect
202. C2×Dic5D3×C8semidirect
231. D15#324semidirect
251. C2×Dic3D5⋊C8semidirect
304. C3×C5C2×#324semidirect
367. C5D3×#324semidirect
387. C3D5⋊#324semidirect

Maximal subgroups

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

subgroupindex
C2×#914042
#117520422
#117467852
C3×#649142
#117465682
D5⋊#3243
D3×#3245