Finite Group Databasebeta

← #14283291

Subgroups — #14283291

Order 1920.

652 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 98 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#11752414C211yesmaximal, characteristic, complemented
3C3×#65764C211yesmaximal, characteristic, complemented
4#11746496C214yesmaximal, complemented
5#10604912—31nomaximal, Hall
6C22×C5×D12C411yescharacteristic, complemented
7C22×C3×C4×D5C2211yescharacteristic
8C22×#1201—21no—
9C2×#6762—21no—
10C2×C3×C22⋊AGL(1,𝔽5)—21no—
11C2×C4⋊Dic15C411yescharacteristic, complemented
12C2×(C2×D3)⋊Dic5—21no—
13#91449—21no—
14#91449—21no—
15#91449C412yescomplemented
16#91449C2212yes—
17#91232—21no—
18#91232C2212yescomplemented
19C3×(C2×AGL(1,𝔽5))⋊C4—21no—
20C3×(C2×AGL(1,𝔽5))⋊C4C2212yescomplemented
21#69531—51nomaximal, Hall
22C2×#4084—31no—
23#65764D311yescharacteristic, complemented
24#65755—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—
43#6762—42no—
44C2×C3⋊#170—22no—
45C3×C22⋊AGL(1,𝔽5)—42no—
46C4⋊Dic15—21no—
47C4⋊Dic15C2×C412yes—
48(C2×D3)⋊Dic5—22no—
49(C2×D3)⋊Dic5—22no—
50C2×#930—51no—
51C3×#381—51no—
52#5207—51no—
53#4451—54no—
54C22×C5×D4—31no—
55C22×C22⋊D5—61no—
56C22×C4×D5C2×D311yescharacteristic
57C2×C22⋊AGL(1,𝔽5)—21no—
58C2×#704—61no—
59C2×C22⋊Dic5—61no—
60#4084—32no—
61#4084—32no—
62#4084—61no—
63#4084—61no—
64C2×C4⋊Dic5—31no—
65(C2×AGL(1,𝔽5))⋊C4—21no—
66(C2×AGL(1,𝔽5))⋊C4C2×D312yescomplemented
67#4003—32no—
68#4003—61no—
69#1510—151noSylow
70C23×C3×C5C22⋊C411yescharacteristic
71C22×C5×D3—22no—
72C22×C5×D3—42no—
73C22×C5×D3—42no—
74C22×C5×D3—42no—
75C22×C3×D5—22no—
76C22×C3×D5—22no—
77C22×C3×D5—41no—
78C22×C3×D5C22⋊C411yescharacteristic
79C22×C3×D5C2×D411yescharacteristic
80C2×C3×AGL(1,𝔽5)—42no—
81C2×C3×AGL(1,𝔽5)—42no—
82C2×C3×AGL(1,𝔽5)—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×Dic15—22no—
87C2×Dic15—42no—
88C5×D12—42no—
89C5×D12—42no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C3×C4×D5—41no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97#1201—44no—
98#1201—44no—
99C3⋊#170—42no—
100C23×C3×C4—51no—
101C22×#67—101no—
102C22×D12AGL(1,𝔽5)11yescharacteristic, complemented
103C2×C3×C22⋊C4—101no—
104#930—52no—
105#930—52no—
106#930—101no—
107#930—101no—
108C2×(C2×D3)⋊C4—101no—
109C2×C4⋊Dic3—51no—
110C2×#208—101no—
111C3×#95—52no—
112C3×#95—101no—
113#830—52no—
114#830—101no—
115C24×C5—61no—
116C23×D5#6711yescharacteristic
117C22×AGL(1,𝔽5)—22no—
118C2×C5×D4—32no—
119C2×C5×D4—61no—
120C2×C5×D4—122no—
121C22×C4×C5C4×D311yescharacteristic
122C2×C22⋊D5—62no—
123C2×C22⋊D5—62no—
124C2×C22⋊D5—124no—
125C22×Dic5—61no—
126C22×Dic5D1211yescharacteristic
127C2×C4×D5—42no—
128C2×C4×D5C4×D311yescharacteristic
129C2×C4×D5D1211yescharacteristic
130C2×C4×D5#6711yescharacteristic
131C2×C4×D5C22×D311yescharacteristic
132C22⋊AGL(1,𝔽5)—42no—
133#704—122no—
134C2×#170—62no—
135C22⋊Dic5—62no—
136C22⋊Dic5—62no—
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139C2×#121—151no—
140#407—151no—
141#381—51no—
142#327—154no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5#9912yes—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C2×C5×D3—42no—
148C2×C5×D3—42no—
149C2×C5×D3—42no—
150C2×C5×D3—84no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—44no—
157C2×C3×D5AGL(1,ℤ/8)12yes—
158C3×AGL(1,𝔽5)—82no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161Dic15—42no—
162C3×Dic5—21no—
163C3×Dic5—21no—
164C24×C3—51no—
165C23×D3—21no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—102no—
172C22×C3×C4—202no—
173C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
174C2×#67—102no—
175C2×#67—102no—
176C2×#67—204no—
177C22×Dic3—101no—
178C2×D12—21no—
179C2×D12—42no—
180C2×D12C2×AGL(1,𝔽5)12yes—
181C3×C22⋊C4—202no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184C4⋊Dic3—52no—
185C4⋊Dic3—101no—
186#208—202no—
187C2×C3⋊C8—102no—
188C23×C5—62no—
189C23×C5—122no—
190C23×C5—122no—
191C23×C5—122no—
192C23×C5(C2×D3)⋊C411yescharacteristic
193C22×D5—22no—
194C22×D5—22no—
195C22×D5—41no—
196C22×D5(C2×D3)⋊C411yescharacteristic
197C22×D5C2×#6711yescharacteristic
198C2×AGL(1,𝔽5)—42no—
199C2×AGL(1,𝔽5)—42no—
200C2×AGL(1,𝔽5)—42no—
201C5×D4—122no—
202C5×D4—122no—
203C2×C4×C5—22no—
204C2×C4×C5(C2×D3)⋊C411yescharacteristic
205C2×C4×C5C2×C4×D311yescharacteristic
206C22⋊D5—124no—
207C22⋊D5—124no—
208C2×Dic5—22no—
209C2×Dic5—62no—
210C2×Dic5—122no—
211C2×Dic5(C2×D3)⋊C411yescharacteristic
212C2×Dic5C2×D1211yescharacteristic
213C4×D5—41no—
214C4×D5—41no—
215C4×D5—41no—
216C4×D5—41no—
217#170—122no—
218C22×D4—31no—
219C22×D4—301no—
220C23×C4—51no—
221C2×M16—301no—
222#121—152no—
223#121—152no—
224#121—301no—
225#121—301no—
226C2×C4⋊C4—151no—
227C2×C22⋊C4—101no—
228C2×C22⋊C4—301no—
229C22⋊C8—152no—
230C22⋊C8—301no—
231#95—52no—
232#95—101no—
233C2×C3×C5—22no—
234C2×C3×C5C2×#9911yescharacteristic
235C2×C3×C5#41811yescharacteristic
236C2×C3×C5#42111yescharacteristic
237C3×D5—22no—
238C3×D5—41no—
239C5×D3—82no—
240C23×C3—51no—
241C23×C3—51no—
242C23×C3—102no—
243C23×C3—102no—
244C23×C3—201no—
245C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
246C22×D3—22no—
247C22×D3—42no—
248C22×D3—42no—
249C22×D3—42no—
250C2×C3×C4—22no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—102no—
254C2×C3×C4—201no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4—201no—
258C2×C3×C4—202no—
259C2×C3×C4—202no—
260C2×C3×C4—202no—
261C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
262C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
263#67—204no—
264#67—204no—
265C2×Dic3—102no—
266C2×Dic3—202no—
267D12—42no—
268D12—42no—
269C3⋊C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—122no—
273C22×C5—122no—
274C22×C5—122no—
275C22×C5—244no—
276C22×C5#80612yes—
277C22×C5C2×(C2×D3)⋊C411yescharacteristic
278C2×D5—21no—
279C2×D5—21no—
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—21no—
283C2×D5—44no—
284C2×D5#94912yes—
285AGL(1,𝔽5)—82no—
286C4×C5—21no—
287C4×C5—21no—
288Dic5—21no—
289Dic5—21no—
290Dic5—122no—
291C24—51no—
292C24—61no—
293C2×D4—32no—
294C2×D4—61no—
295C2×D4—122no—
296C2×D4—302no—
297C2×D4—302no—
298C2×D4—604no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—102no—
305C22×C4—202no—
306C22×C4—301no—
307C22×C4D3×AGL(1,𝔽5)11yescharacteristic
308M16—602no—
309C2×C8—302no—
310C4⋊C4—152no—
311C4⋊C4—301no—
312C22⋊C4—202no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—52no—
319C22×C3—101no—
320C22×C3—101no—
321C22×C3—101no—
322C22×C3—101no—
323C22×C3—101no—
324C22×C3—204no—
325C22×C3#401112yes—
326C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
327C2×D3—42no—
328C2×D3—42no—
329C2×D3—42no—
330C2×D3—84no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—101no—
334C3×C4—101no—
335C3×C4—402no—
336Dic3—202no—
337C2×C5—22no—
338C2×C5—242no—
339C2×C5C2×#80611yescharacteristic
340C2×C5#500111yescharacteristic
341C2×C5#500511yescharacteristic
342D5—22no—
343D5—41no—
344C23—51no—
345C23—51no—
346C23—62no—
347C23—102no—
348C23—102no—
349C23—122no—
350C23—122no—
351C23—122no—
352C23—201no—
353C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
354D4—122no—
355D4—122no—
356D4—604no—
357D4—604no—
358C2×C4—22no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—102no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4—201no—
365C2×C4—201no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4—202no—
369C2×C4—302no—
370C2×C4—602no—
371C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
372C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
373C8—602no—
374C2×C3—22no—
375C2×C3—102no—
376C2×C3—201no—
377C2×C3#6576711yescharacteristic
378C2×C3#6576911yescharacteristic
379C2×C3C2×#401111yescharacteristic
380D3—82no—
381C5#6953111yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—52no—
385C22—101no—
386C22—101no—
387C22—101no—
388C22—101no—
389C22—101no—
390C22—122no—
391C22—122no—
392C22—122no—
393C22—204no—
394C22—244no—
395C22#9117212yes—
396C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
397C4—21no—
398C4—21no—
399C4—101no—
400C4—101no—
401C4—402no—
402C4—602no—
403C3#1060491211yescharacteristic, complemented, Sylow
404C2—22no—
405C2—102no—
406C2—201no—
407C2—242no—
408C2#1175170611yescharacteristic
409C2#1175171911yescharacteristic
410C2C2×#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#1510
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. #11752414C2semidirect
3. C3×#65764C2semidirect
4. #11746496C2semidirect
6. C22×C5×D12C4semidirect
11. C2×C4⋊Dic15C4semidirect
15. #91449C4semidirect
18. #91232C22semidirect
20. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
23. #65764D3semidirect
66. (C2×AGL(1,𝔽5))⋊C4C2×D3semidirect
102. C22×D12AGL(1,𝔽5)semidirect
315. C3×C5#1510semidirect
381. C5#69531semidirect
403. C3#10604912semidirect

Maximal subgroups

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

subgroupindex
C2×#914492
#117524142
C3×#657642
#117464962
#106049123
#695315