Finite Group Databasebeta

← #14283146

Subgroups — #14283146

Order 1920.

692 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 106 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×#91449C211yesmaximal, characteristic
2#11752415C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4#11746496C214yesmaximal, complemented
5#10604911—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic, complemented
7C22×C3×C4×D5C2211yescharacteristic
8C22×#1201—21no—
9C2×#6758—21no—
10C2×C3×C22⋊AGL(1,𝔽5)—21no—
11C2×C3×C4×AGL(1,𝔽5)—21no—
12C2×C4⋊Dic15C411yescharacteristic, complemented
13C2×(C2×D3)⋊Dic5—21no—
14#91449—21no—
15#91449—21no—
16#91449C412yescomplemented
17#91449C2212yes—
18#91241—21no—
19#91232C2212yescomplemented
20C3×(C2×AGL(1,𝔽5))⋊C4C2212yescomplemented
21#69444—51nomaximal, Hall
22C2×#4084—31no—
23C4×C22⋊AGL(1,𝔽5)D311yescharacteristic, complemented
24#65756—31no—
25#64920—34no—
26C23×C5×D3—21no—
27C23×C3×D5D411yescharacteristic
28C22×C3×AGL(1,𝔽5)—22no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×Dic15—21no—
31C2×C5×D12—21no—
32C2×C5×D12—42no—
33C2×C5×D12C2×C412yes—
34C22×C3×Dic5D411yescharacteristic
35C2×C3×C4×D5—42no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5C2311yescharacteristic
40C2×#1201—22no—
41C2×#1201—22no—
42C2×#1201—44no—
43C2×C3⋊#170—22no—
44#6758—42no—
45C3×C22⋊AGL(1,𝔽5)—24no—
46C3×C4×AGL(1,𝔽5)—42no—
47C4⋊Dic15—21no—
48C4⋊Dic15C2×C412yes—
49(C2×D3)⋊Dic5—22no—
50(C2×D3)⋊Dic5—22no—
51C2×#930—51no—
52C3×C4×C22⋊C4—51no—
53#5207—51no—
54#4451—54no—
55C22×C5×D4—31no—
56C22×C22⋊D5—61no—
57C22×C4×D5C2×D311yescharacteristic
58C2×C22⋊AGL(1,𝔽5)—21no—
59C2×C4×AGL(1,𝔽5)—21no—
60C2×#700—61no—
61C2×C22⋊Dic5—61no—
62#4084—32no—
63#4084—32no—
64#4084—61no—
65#4084—61no—
66C2×C4⋊Dic5—31no—
67C22⋊#170—61no—
68(C2×AGL(1,𝔽5))⋊C4C2×D312yescomplemented
69#4003—32no—
70#1507—151noSylow
71C23×C3×C5C22⋊C411yescharacteristic
72C22×C5×D3—22no—
73C22×C5×D3—42no—
74C22×C5×D3—42no—
75C22×C5×D3—42no—
76C22×C3×D5—22no—
77C22×C3×D5—22no—
78C22×C3×D5—41no—
79C22×C3×D5C22⋊C411yescharacteristic
80C22×C3×D5C2×D411yescharacteristic
81C2×C3×AGL(1,𝔽5)—24no—
82C2×C3×AGL(1,𝔽5)—42no—
83C2×C3×AGL(1,𝔽5)—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×Dic15—22no—
88C2×Dic15—42no—
89C5×D12—42no—
90C5×D12—42no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C3×C4×D5—22no—
95C3×C4×D5—22no—
96C3×C4×D5—41no—
97C3×C4×D5—41no—
98#1201—44no—
99#1201—44no—
100C3⋊#170—42no—
101C23×C3×C4—51no—
102C22×#67—101no—
103C22×D12AGL(1,𝔽5)11yescharacteristic, complemented
104C2×C3×C22⋊C4—101no—
105C2×C3×C42—101no—
106#930—52no—
107#930—52no—
108#930—101no—
109#930—101no—
110C2×(C2×D3)⋊C4—101no—
111C2×C4⋊Dic3—51no—
112C2×#208—101no—
113C3×#95—52no—
114#830—52no—
115#830—101no—
116C24×C5—61no—
117C23×D5#6711yescharacteristic
118C22×AGL(1,𝔽5)—22no—
119C2×C5×D4—32no—
120C2×C5×D4—61no—
121C2×C5×D4—122no—
122C22×C4×C5C4×D311yescharacteristic
123C2×C22⋊D5—62no—
124C2×C22⋊D5—62no—
125C2×C22⋊D5—124no—
126C22×Dic5—61no—
127C22×Dic5D1211yescharacteristic
128C2×C4×D5—42no—
129C2×C4×D5C4×D311yescharacteristic
130C2×C4×D5D1211yescharacteristic
131C2×C4×D5#6711yescharacteristic
132C2×C4×D5C22×D311yescharacteristic
133C22⋊AGL(1,𝔽5)—24no—
134C2×#170—62no—
135C4×AGL(1,𝔽5)—42no—
136#700—122no—
137C22⋊Dic5—62no—
138C22⋊Dic5—62no—
139C4⋊Dic5—32no—
140C4⋊Dic5—61no—
141C2×#121—151no—
142#407—151no—
143C4×C22⋊C4—51no—
144#327—154no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5#10412yes—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C5×D3—42no—
150C2×C5×D3—42no—
151C2×C5×D3—42no—
152C2×C5×D3—84no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—44no—
159C2×C3×D5AGL(1,ℤ/8)12yes—
160C3×AGL(1,𝔽5)—44no—
161C3×C4×C5—21no—
162C3×C4×C5#9912yes—
163Dic15—42no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C24×C3—51no—
167C23×D3—21no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—102no—
174C22×C3×C4—202no—
175C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
176C2×#67—102no—
177C2×#67—102no—
178C2×#67—204no—
179C22×Dic3—101no—
180C2×D12—21no—
181C2×D12—42no—
182C2×D12C2×AGL(1,𝔽5)12yes—
183C3×C22⋊C4—104no—
184C3×C42—202no—
185(C2×D3)⋊C4—102no—
186(C2×D3)⋊C4—102no—
187C4⋊Dic3—52no—
188C4⋊Dic3—101no—
189#208—202no—
190C2×C3⋊C8—102no—
191C23×C5—62no—
192C23×C5—122no—
193C23×C5—122no—
194C23×C5—122no—
195C23×C5(C2×D3)⋊C411yescharacteristic
196C22×D5—22no—
197C22×D5—22no—
198C22×D5—41no—
199C22×D5(C2×D3)⋊C411yescharacteristic
200C22×D5C2×#6711yescharacteristic
201C2×AGL(1,𝔽5)—24no—
202C2×AGL(1,𝔽5)—42no—
203C2×AGL(1,𝔽5)—42no—
204C5×D4—122no—
205C5×D4—122no—
206C2×C4×C5—22no—
207C2×C4×C5(C2×D3)⋊C411yescharacteristic
208C2×C4×C5C2×C4×D311yescharacteristic
209C22⋊D5—124no—
210C22⋊D5—124no—
211C2×Dic5—41no—
212C2×Dic5—62no—
213C2×Dic5—122no—
214C2×Dic5(C2×D3)⋊C411yescharacteristic
215C2×Dic5C2×D1211yescharacteristic
216C4×D5—22no—
217C4×D5—22no—
218C4×D5—41no—
219C4×D5—41no—
220#170—122no—
221C22×D4—31no—
222C22×D4—301no—
223C23×C4—51no—
224C2×M16—301no—
225#121—152no—
226#121—152no—
227#121—301no—
228#121—301no—
229C2×C4⋊C4—151no—
230C2×C22⋊C4—101no—
231C2×C22⋊C4—301no—
232C2×C42—101no—
233C22⋊C8—152no—
234C22⋊C8—301no—
235#95—52no—
236C2×C3×C5—22no—
237C2×C3×C5C2×#9911yescharacteristic
238C2×C3×C5#41811yescharacteristic
239C2×C3×C5C2×#10411yescharacteristic
240C3×D5—22no—
241C3×D5—41no—
242C5×D3—82no—
243C23×C3—51no—
244C23×C3—51no—
245C23×C3—102no—
246C23×C3—102no—
247C23×C3—201no—
248C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
249C22×D3—22no—
250C22×D3—42no—
251C22×D3—42no—
252C22×D3—42no—
253C2×C3×C4—22no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—102no—
257C2×C3×C4—102no—
258C2×C3×C4—104no—
259C2×C3×C4—201no—
260C2×C3×C4—201no—
261C2×C3×C4—201no—
262C2×C3×C4—202no—
263C2×C3×C4—202no—
264C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
265C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
266#67—204no—
267#67—204no—
268C2×Dic3—102no—
269C2×Dic3—202no—
270D12—42no—
271D12—42no—
272C3⋊C8—202no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—122no—
276C22×C5—122no—
277C22×C5—122no—
278C22×C5—244no—
279C22×C5#80512yes—
280C22×C5C2×(C2×D3)⋊C411yescharacteristic
281C2×D5—21no—
282C2×D5—21no—
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—21no—
286C2×D5—44no—
287C2×D5#94912yes—
288AGL(1,𝔽5)—44no—
289C4×C5—21no—
290C4×C5#80612yes—
291Dic5—21no—
292Dic5—21no—
293Dic5—122no—
294C24—51no—
295C24—61no—
296C2×D4—32no—
297C2×D4—61no—
298C2×D4—122no—
299C2×D4—302no—
300C2×D4—302no—
301C2×D4—604no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—51no—
305C22×C4—51no—
306C22×C4—51no—
307C22×C4—102no—
308C22×C4—202no—
309C22×C4—301no—
310C22×C4D3×AGL(1,𝔽5)11yescharacteristic
311M16—602no—
312C2×C8—302no—
313C4⋊C4—152no—
314C4⋊C4—301no—
315C22⋊C4—104no—
316C22⋊C4—302no—
317C22⋊C4—302no—
318C42—202no—
319C3×C5#150711yescharacteristic, complemented, Hall
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—52no—
323C22×C3—101no—
324C22×C3—101no—
325C22×C3—101no—
326C22×C3—101no—
327C22×C3—101no—
328C22×C3—204no—
329C22×C3#400812yes—
330C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
331C2×D3—42no—
332C2×D3—42no—
333C2×D3—42no—
334C2×D3—84no—
335C3×C4—21no—
336C3×C4—101no—
337C3×C4—101no—
338C3×C4—204no—
339C3×C4#401112yes—
340Dic3—202no—
341C2×C5—22no—
342C2×C5—242no—
343C2×C5C2×#80511yescharacteristic
344C2×C5C2×#80611yescharacteristic
345C2×C5#500111yescharacteristic
346D5—22no—
347D5—41no—
348C23—51no—
349C23—51no—
350C23—62no—
351C23—102no—
352C23—102no—
353C23—122no—
354C23—122no—
355C23—122no—
356C23—201no—
357C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
358D4—122no—
359D4—122no—
360D4—604no—
361D4—604no—
362C2×C4—22no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—102no—
366C2×C4—102no—
367C2×C4—104no—
368C2×C4—201no—
369C2×C4—201no—
370C2×C4—201no—
371C2×C4—202no—
372C2×C4—202no—
373C2×C4—302no—
374C2×C4—602no—
375C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
376C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
377C8—602no—
378C2×C3—22no—
379C2×C3—102no—
380C2×C3—201no—
381C2×C3#6576711yescharacteristic
382C2×C3C2×#400811yescharacteristic
383C2×C3C2×#401111yescharacteristic
384D3—82no—
385C5#6944411yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—52no—
389C22—101no—
390C22—101no—
391C22—101no—
392C22—101no—
393C22—101no—
394C22—122no—
395C22—122no—
396C22—122no—
397C22—204no—
398C22—244no—
399C22#9115612yes—
400C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
401C4—21no—
402C4—101no—
403C4—101no—
404C4—204no—
405C4—602no—
406C4#9117212yes—
407C3#1060491111yescharacteristic, complemented, Sylow
408C2—22no—
409C2—102no—
410C2—201no—
411C2—242no—
412C2#1175170611yescharacteristic
413C2C2×#9115611yescharacteristic
414C2C2×#9117211yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91449C2
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1507
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752415C2semidirect
3. C3×C4×C22⋊AGL(1,𝔽5)C2semidirect
4. #11746496C2semidirect
6. C22×C5×D12C4semidirect
12. C2×C4⋊Dic15C4semidirect
16. #91449C4semidirect
19. #91232C22semidirect
20. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
23. C4×C22⋊AGL(1,𝔽5)D3semidirect
68. (C2×AGL(1,𝔽5))⋊C4C2×D3semidirect
103. C22×D12AGL(1,𝔽5)semidirect
319. C3×C5#1507semidirect
385. C5#69444semidirect
407. C3#10604911semidirect

Maximal subgroups

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

subgroupindex
C2×#914492
#117524152
C3×C4×C22⋊AGL(1,𝔽5)2
#117464962
#106049113
#694445