Finite Group Databasebeta

← C5×A4×C22⋊C8 #14510951

Subgroups — C5×A4×C22⋊C8 #14510951

Order 1920.

524 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C22×C4×C5×A4C211yesmaximal, characteristic
2C2×C5×C8×A4C212yesmaximal, complemented
3C22×C5×C22⋊C8C311yesmaximal, characteristic, complemented, Hall
4C23×C5×A4C411yescharacteristic
5C2×C4×C5×A4—22no—
6C2×C4×C5×A4C411yescharacteristic
7C2×C4×C5×A4C2211yescharacteristic
8C5×C8×A4—22no—
9C3×C5×C22⋊C8—41nomaximal
10A4×C22⋊C8C511yesmaximal, characteristic, direct product factor, Hall
11C24×C4×C5C2×C311yescharacteristic
12C23×C5×C8C2×C312yescomplemented
13C2×C5×C22⋊C8—31no—
14C2×C5×C22⋊C8—32no—
15C2×C5×C22⋊C8—31no—
16C22×C5×A4—21no—
17C22×C5×A4—21no—
18C22×C5×A4C812yescomplemented
19C22×C5×A4C2×C411yescharacteristic
20C22×C3×C4×C5—41no—
21C4×C5×A4—21no—
22C4×C5×A4D412yes—
23C2×C3×C5×C8—42no—
24C22×C4×A4C2×C511yescharacteristic
25C2×C8×A4C2×C512yescomplemented
26C25×C5C3×C411yescharacteristic
27C23×C4×C5—22no—
28C23×C4×C5—31no—
29C23×C4×C5—31no—
30C23×C4×C5—31no—
31C23×C4×C5—31no—
32C23×C4×C5—62no—
33C23×C4×C5C3×C411yescharacteristic
34C23×C4×C5C22×C311yescharacteristic
35C22×C5×C8—22no—
36C22×C5×C8—32no—
37C22×C5×C8—32no—
38C22×C5×C8—62no—
39C5×C22⋊C8—32no—
40C5×C22⋊C8—31no—
41C5×C22⋊C8—32no—
42C5×C22⋊C8A411yescharacteristic, direct product factor
43C22×C22⋊C8C3×C511yescharacteristic, complemented, Sylow
44C23×C3×C5—41no—
45C2×C5×A4—22no—
46C2×C5×A4C22⋊C411yescharacteristic
47C2×C5×A4C2×C811yescharacteristic
48C2×C5×A4M1611yescharacteristic
49C2×C3×C4×C5—41no—
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5—82no—
52C3×C5×C8—82no—
53C23×A4C4×C511yescharacteristic
54C2×C4×A4—22no—
55C2×C4×A4C4×C511yescharacteristic
56C2×C4×A4C22×C511yescharacteristic
57C8×A4—22no—
58C3×C22⋊C8—41no—
59C24×C5—21no—
60C24×C5—21no—
61C24×C5—31no—
62C24×C5—32no—
63C24×C5—31no—
64C24×C5—61no—
65C24×C5—61no—
66C24×C5C3×C812yescomplemented
67C24×C5C2×C3×C411yescharacteristic
68C22×C4×C5—21no—
69C22×C4×C5—31no—
70C22×C4×C5—32no—
71C22×C4×C5—31no—
72C22×C4×C5—32no—
73C22×C4×C5—31no—
74C22×C4×C5—31no—
75C22×C4×C5—31no—
76C22×C4×C5—31no—
77C22×C4×C5—31no—
78C22×C4×C5—62no—
79C22×C4×C5—62no—
80C22×C4×C5—62no—
81C22×C4×C5—62no—
82C22×C4×C5—62no—
83C22×C4×C5—62no—
84C22×C4×C5—62no—
85C22×C4×C5—62no—
86C22×C4×C5—61no—
87C22×C4×C5C3×D412yes—
88C22×C4×C5C2×A411yescharacteristic
89C2×C5×C8—32no—
90C2×C5×C8—62no—
91C2×C5×C8—62no—
92C2×C5×C8—62no—
93C2×C5×C8—62no—
94C2×C5×C8C2×A412yescomplemented
95C24×C4C2×C3×C511yescharacteristic
96C23×C8C2×C3×C512yescomplemented
97C2×C22⋊C8—31no—
98C2×C22⋊C8—31no—
99C2×C22⋊C8—32no—
100C22×C3×C5—42no—
101C22×C3×C5—41no—
102C22×C3×C5—81no—
103C22×C3×C5—81no—
104C5×A4C22⋊C811yescharacteristic, direct product factor
105C3×C4×C5—42no—
106C3×C4×C5—81no—
107C22×A4—21no—
108C22×A4—21no—
109C22×A4C5×C812yescomplemented
110C22×A4C2×C4×C511yescharacteristic
111C22×C3×C4—41no—
112C4×A4—21no—
113C4×A4C5×D412yes—
114C2×C3×C8—42no—
115C23×C5—22no—
116C23×C5—31no—
117C23×C5—31no—
118C23×C5—31no—
119C23×C5—31no—
120C23×C5—32no—
121C23×C5—32no—
122C23×C5—32no—
123C23×C5—32no—
124C23×C5—31no—
125C23×C5—61no—
126C23×C5—61no—
127C23×C5—61no—
128C23×C5—61no—
129C23×C5—62no—
130C23×C5—61no—
131C23×C5—61no—
132C23×C5—62no—
133C23×C5—62no—
134C23×C5—61no—
135C23×C5—61no—
136C23×C5—64no—
137C23×C5C3×C22⋊C411yescharacteristic
138C23×C5C2×C3×C811yescharacteristic
139C23×C5C3×M1611yescharacteristic
140C23×C5C4×A411yescharacteristic
141C2×C4×C5—22no—
142C2×C4×C5—32no—
143C2×C4×C5—31no—
144C2×C4×C5—32no—
145C2×C4×C5—32no—
146C2×C4×C5—32no—
147C2×C4×C5—31no—
148C2×C4×C5—62no—
149C2×C4×C5—61no—
150C2×C4×C5—61no—
151C2×C4×C5—62no—
152C2×C4×C5—64no—
153C2×C4×C5—62no—
154C2×C4×C5—61no—
155C2×C4×C5—61no—
156C2×C4×C5C4×A411yescharacteristic
157C2×C4×C5C22×A411yescharacteristic
158C5×C8—22no—
159C5×C8—62no—
160C25C3×C4×C511yescharacteristic
161C23×C4—22no—
162C23×C4—31no—
163C23×C4—31no—
164C23×C4—31no—
165C23×C4—31no—
166C23×C4—62no—
167C23×C4C3×C4×C511yescharacteristic
168C23×C4C22×C3×C511yescharacteristic
169C22×C8—22no—
170C22×C8—32no—
171C22×C8—32no—
172C22×C8—62no—
173C22⋊C8—32no—
174C22⋊C8—31no—
175C22⋊C8—32no—
176C22⋊C8C5×A411yescharacteristic, direct product factor
177C2×C3×C5—41no—
178C2×C3×C5—41no—
179C2×C3×C5—41no—
180C2×C3×C5—82no—
181C23×C3—41no—
182C2×A4—22no—
183C2×A4C5×C22⋊C411yescharacteristic
184C2×A4C2×C5×C811yescharacteristic
185C2×A4C5×M1611yescharacteristic
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—82no—
189C3×C8—82no—
190C22×C5—21no—
191C22×C5—21no—
192C22×C5—31no—
193C22×C5—31no—
194C22×C5—31no—
195C22×C5—32no—
196C22×C5—31no—
197C22×C5—31no—
198C22×C5—31no—
199C22×C5—31no—
200C22×C5—31no—
201C22×C5—31no—
202C22×C5—32no—
203C22×C5—62no—
204C22×C5—62no—
205C22×C5—62no—
206C22×C5—62no—
207C22×C5—62no—
208C22×C5—62no—
209C22×C5—62no—
210C22×C5—62no—
211C22×C5—61no—
212C22×C5—61no—
213C22×C5C3×C22⋊C811yescharacteristic, complemented
214C22×C5C8×A412yescomplemented
215C22×C5C2×C4×A411yescharacteristic
216C4×C5—21no—
217C4×C5—32no—
218C4×C5—61no—
219C4×C5D4×A412yes—
220C24—21no—
221C24—21no—
222C24—31no—
223C24—32no—
224C24—31no—
225C24—61no—
226C24—61no—
227C24C3×C5×C812yescomplemented
228C24C2×C3×C4×C511yescharacteristic
229C22×C4—21no—
230C22×C4—31no—
231C22×C4—32no—
232C22×C4—31no—
233C22×C4—32no—
234C22×C4—31no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—31no—
238C22×C4—31no—
239C22×C4—62no—
240C22×C4—62no—
241C22×C4—62no—
242C22×C4—62no—
243C22×C4—62no—
244C22×C4—62no—
245C22×C4—62no—
246C22×C4—62no—
247C22×C4—61no—
248C22×C4C3×C5×D412yes—
249C22×C4C2×C5×A411yescharacteristic
250C2×C8—32no—
251C2×C8—62no—
252C2×C8—62no—
253C2×C8—62no—
254C2×C8—62no—
255C2×C8C2×C5×A412yescomplemented
256C3×C5—41noHall
257C22×C3—41no—
258C22×C3—42no—
259C22×C3—81no—
260C22×C3—81no—
261A4C5×C22⋊C811yescharacteristic, direct product factor
262C3×C4—42no—
263C3×C4—81no—
264C2×C5—22no—
265C2×C5—31no—
266C2×C5—31no—
267C2×C5—31no—
268C2×C5—31no—
269C2×C5—62no—
270C2×C5A4×C22⋊C411yescharacteristic
271C2×C5C2×C8×A411yescharacteristic
272C2×C5A4×M1611yescharacteristic
273C23—22no—
274C23—31no—
275C23—31no—
276C23—31no—
277C23—31no—
278C23—32no—
279C23—32no—
280C23—31no—
281C23—32no—
282C23—32no—
283C23—61no—
284C23—61no—
285C23—61no—
286C23—61no—
287C23—62no—
288C23—61no—
289C23—61no—
290C23—62no—
291C23—62no—
292C23—61no—
293C23—61no—
294C23—64no—
295C23C3×C5×C22⋊C411yescharacteristic
296C23C2×C3×C5×C811yescharacteristic
297C23C3×C5×M1611yescharacteristic
298C23C4×C5×A411yescharacteristic
299C2×C4—22no—
300C2×C4—32no—
301C2×C4—31no—
302C2×C4—32no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—31no—
306C2×C4—62no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—62no—
310C2×C4—64no—
311C2×C4—62no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4C4×C5×A411yescharacteristic
315C2×C4C22×C5×A411yescharacteristic
316C8—22no—
317C8—62no—
318C2×C3—41no—
319C2×C3—41no—
320C2×C3—41no—
321C2×C3—82no—
322C5A4×C22⋊C811yescharacteristic, direct product factor, Sylow
323C22—21no—
324C22—21no—
325C22—31no—
326C22—31no—
327C22—31no—
328C22—32no—
329C22—31no—
330C22—31no—
331C22—31no—
332C22—31no—
333C22—31no—
334C22—31no—
335C22—32no—
336C22—62no—
337C22—62no—
338C22—62no—
339C22—62no—
340C22—62no—
341C22—62no—
342C22—62no—
343C22—62no—
344C22—61no—
345C22—61no—
346C22C3×C5×C22⋊C811yescharacteristic, complemented
347C22C5×C8×A412yescomplemented
348C22C2×C4×C5×A411yescharacteristic
349C4—21no—
350C4—32no—
351C4—61no—
352C4C5×D4×A412yes—
353C3—41noSylow
354C2—22no—
355C2—31no—
356C2—31no—
357C2—31no—
358C2—31no—
359C2—62no—
360C2C5×A4×C22⋊C411yescharacteristic
361C2C2×C5×C8×A411yescharacteristic
362C2C5×A4×M1611yescharacteristic
subgroupG/H
centerC2×C4×C5C22×A4
commutatorC23C2×C3×C5×C8
FrattiniC2×C4C22×C5×A4
FittingC22×C5×C22⋊C8C3
socleC24×C5C2×C3×C4
prime radicalC23×C5×A4C4
cosocleC23×C4C22×C3×C5
hypercenterC5×C22⋊C8A4
hypocenterC22C3×C5×C22⋊C8
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C4×C5 ◁ C5×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C5×C8×A4C2semidirect
3. C22×C5×C22⋊C8C3semidirect
10. A4×C22⋊C8C5direct (N × H)
12. C23×C5×C8C2×C3semidirect
18. C22×C5×A4C8semidirect
25. C2×C8×A4C2×C5semidirect
42. C5×C22⋊C8A4direct (N × H)
43. C22×C22⋊C8C3×C5semidirect
66. C24×C5C3×C8semidirect
94. C2×C5×C8C2×A4semidirect
96. C23×C8C2×C3×C5semidirect
104. C5×A4C22⋊C8direct (N × H)
109. C22×A4C5×C8semidirect
176. C22⋊C8C5×A4direct (N × H)
213. C22×C5C3×C22⋊C8semidirect
214. C22×C5C8×A4semidirect
227. C24C3×C5×C8semidirect
255. C2×C8C2×C5×A4semidirect
261. A4C5×C22⋊C8direct (N × H)
322. C5A4×C22⋊C8direct (N × H)
346. C22C3×C5×C22⋊C8semidirect
347. C22C5×C8×A4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×A42
C2×C5×C8×A42
C22×C5×C22⋊C83
C3×C5×C22⋊C84
A4×C22⋊C85