Finite Group Databasebeta

← #14276858

Subgroups — #14276858

Order 1920.

456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C4×#6763C211yesmaximal, characteristic
2D5⋊#830C211yesmaximal, characteristic
3C2×C3×#3952C211yesmaximal, characteristic
4#10598766—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6763C412yes—
7C2×C4×ΓL(1,𝔽16)—21no—
8C2×D5⋊(C3⋊C8)—21no—
9C22×C3×C5×C8C411yescharacteristic, complemented
10C22×C3×#168C411yescharacteristic, complemented
11#91241C412yescomplemented
12#91235—21no—
13#91232—21no—
14C3×#3952—21no—
15C3×#3952—21no—
16#67677—51nomaximal, Hall
17C4×C22⋊AGL(1,𝔽5)—31no—
18D5⋊(C22⋊C8)—31no—
19C2×#3952D311yescharacteristic
20C23×C3×D5C2×C411yescharacteristic
21C22×ΓL(1,𝔽16)—22no—
22C22×C3×C4×C5C2×C411yescharacteristic
23C22×C3×Dic5C2×C411yescharacteristic
24C2×C3×C4×D5—41no—
25C2×C3×C4×D5—41no—
26C2×C3×C4×D5D411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×C4×D5Q811yescharacteristic
30#6763—22no—
31#6763C814yescomplemented
32C2×C3⋊#170—22no—
33C4×ΓL(1,𝔽16)—41no—
34C4×ΓL(1,𝔽16)—41no—
35D5⋊(C3⋊C8)—41no—
36D5⋊(C3⋊C8)—41no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—41no—
39C2×C3×#168—21no—
40C2×C3×#168—41no—
41C2×C3×C22⋊C8—51no—
42C4×#217—51no—
43C2×#830—51no—
44C22×C4×D5C2×D311yescharacteristic
45C2×C22⋊AGL(1,𝔽5)—32no—
46C2×C4×AGL(1,𝔽5)—61no—
47C2×D5⋊C8—61no—
48C22×C5×C8Dic311yescharacteristic, complemented
49C22×#168Dic311yescharacteristic, complemented
50C22⋊#170—32no—
51(C2×AGL(1,𝔽5))⋊C4—61no—
52#4003—61no—
53#3952—21no—
54#3952—21no—
55#1282—151noSylow
56C23×C3×C5C4211yescharacteristic
57C22×C3×D5—41no—
58C22×C3×D5—41no—
59C22×C3×D5C22⋊C411yescharacteristic
60C22×C3×D5C4⋊C411yescharacteristic
61C22×C3×D5C2×C812yes—
62C22×C3×D5M1612yes—
63C2×ΓL(1,𝔽16)—24no—
64C2×ΓL(1,𝔽16)—42no—
65C2×ΓL(1,𝔽16)—42no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C4⋊C411yescharacteristic
70C2×C3×Dic5—41no—
71C2×C3×Dic5C22⋊C411yescharacteristic
72C2×C3×Dic5C4⋊C411yescharacteristic
73C3×C4×D5—21no—
74C3×C4×D5—21no—
75C3×C4×D5—21no—
76C3×C4×D5—21no—
77C3×C4×D5—41no—
78C3×C4×D5—41no—
79C3⋊#170—42no—
80C3×C5×C8—41no—
81C3×#168—41no—
82C23×C3×C4—51no—
83C22×C3×C8—51no—
84C22×C3×C8AGL(1,𝔽5)11yescharacteristic, complemented
85C2×#217—52no—
86C2×C4×Dic3—101no—
87C22×C3⋊C8—101no—
88C3×C22⋊C8—101no—
89C3×C22⋊C8—101no—
90C3⋊#95—101no—
91#830—52no—
92#830—101no—
93C23×D5C4×D311yescharacteristic
94C22×AGL(1,𝔽5)—62no—
95C22×C4×C5C2×Dic311yescharacteristic
96C22×Dic5C4×D311yescharacteristic
97C2×C4×D5—41no—
98C2×C4×D5—41no—
99C2×C4×D5Dic611yescharacteristic
100C2×C4×D5D1211yescharacteristic
101C2×C4×D5#6711yescharacteristic
102C2×C4×D5#6711yescharacteristic
103C22⋊AGL(1,𝔽5)—34no—
104C22⋊AGL(1,𝔽5)—62no—
105C2×#170—62no—
106C4×AGL(1,𝔽5)—121no—
107C4×AGL(1,𝔽5)—121no—
108D5⋊C8—121no—
109D5⋊C8—121no—
110C2×C5×C8—21no—
111C2×C5×C8—41no—
112C2×#168—21no—
113C2×#168—41no—
114C2×C22⋊C8—51no—
115C2×C22⋊C8—151no—
116C4×C22⋊C4—151no—
117C22×C3×C5—21no—
118C22×C3×C5—21no—
119C22×C3×C5#9511yescharacteristic
120C22×C3×C5C4×C811yescharacteristic
121C22×C3×C5#9711yescharacteristic
122C2×C3×D5—21no—
123C2×C3×D5—21no—
124C2×C3×D5—21no—
125C2×C3×D5—21no—
126C2×C3×D5—42no—
127C2×C3×D5—42no—
128C2×C3×D5C22⋊C812yes—
129C2×C3×D5C4⋊C812yes—
130ΓL(1,𝔽16)—44no—
131C3×C4×C5—21no—
132C3×C4×C5#9911yescharacteristic
133C3×C4×C5#9911yescharacteristic
134C3×Dic5—21no—
135C3×Dic5—21no—
136C24×C3—51no—
137C22×C3×C4—51no—
138C22×C3×C4—51no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4—201no—
143C22×C3×C4—201no—
144C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
145C22×Dic3—102no—
146C2×C3×C8—21no—
147C2×C3×C8—41no—
148C2×C3×C8—101no—
149C2×C3×C8—201no—
150#217—54no—
151#217—102no—
152C4×Dic3—201no—
153C4×Dic3—201no—
154C2×C3⋊C8—102no—
155C2×C3⋊C8—201no—
156C2×C3⋊C8—201no—
157C23×C5C4×Dic311yescharacteristic
158C22×D5—41no—
159C22×D5—41no—
160C22×D5D3×C812yes—
161C22×D5ΓL(1,𝔽25)12yes—
162C22×D5Dic3⋊C411yescharacteristic
163C22×D5(C2×D3)⋊C411yescharacteristic
164C2×AGL(1,𝔽5)—64no—
165C2×AGL(1,𝔽5)—122no—
166C2×AGL(1,𝔽5)—122no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5C4⋊Dic311yescharacteristic
170C2×C4×C5#21711yescharacteristic
171C2×Dic5—41no—
172C2×Dic5Dic3⋊C411yescharacteristic
173C2×Dic5(C2×D3)⋊C411yescharacteristic
174C4×D5—21no—
175C4×D5—21no—
176C4×D5—21no—
177C4×D5—21no—
178C4×D5—41no—
179C4×D5—41no—
180#170—122no—
181C5×C8—41no—
182#168—41no—
183C23×C4—51no—
184C22×C8—51no—
185C22×C8—301no—
186C22×C8ΓL(1,𝔽16)11yescharacteristic, complemented
187C2×C22⋊C4—152no—
188C2×C42—301no—
189C22⋊C8—101no—
190C22⋊C8—101no—
191C22⋊C8—152no—
192C22⋊C8—301no—
193#95—301no—
194C2×C3×C5—21no—
195C2×C3×C5—21no—
196C2×C3×C5#33611yescharacteristic
197C2×C3×C5#34211yescharacteristic
198C2×C3×C5#34411yescharacteristic
199C3×D5—22no—
200C3×D5—22no—
201C23×C3—51no—
202C23×C3—51no—
203C23×C3—52no—
204C23×C3—52no—
205C23×C3—201no—
206C23×C3—201no—
207C23×C3C4×AGL(1,𝔽5)11yescharacteristic
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—51no—
211C2×C3×C4—51no—
212C2×C3×C4—101no—
213C2×C3×C4—101no—
214C2×C3×C4—101no—
215C2×C3×C4—101no—
216C2×C3×C4—201no—
217C2×C3×C4—201no—
218C2×C3×C4—201no—
219C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
220C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
221C2×Dic3—104no—
222C2×Dic3—202no—
223C2×Dic3—202no—
224C3×C8—41no—
225C3×C8—201no—
226C3⋊C8—202no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5C8×Dic311yescharacteristic
230C22×C5#81511yescharacteristic
231C22×C5C3⋊#9511yescharacteristic
232C2×D5—21no—
233C2×D5—21no—
234C2×D5—21no—
235C2×D5—21no—
236C2×D5—42no—
237C2×D5—42no—
238C2×D5Dic3⋊C812yes—
239C2×D5(C2×D3)⋊C812yes—
240AGL(1,𝔽5)—124no—
241C4×C5—21no—
242C4×C5#83411yescharacteristic
243C4×C5#83411yescharacteristic
244Dic5—21no—
245Dic5—21no—
246C24—51no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—51no—
250C22×C4—51no—
251C22×C4—51no—
252C22×C4—201no—
253C22×C4—201no—
254C22×C4—302no—
255C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—101no—
259C2×C8—201no—
260C2×C8—302no—
261C2×C8—601no—
262C2×C8—601no—
263C22⋊C4—154no—
264C22⋊C4—302no—
265C42—601no—
266C42—601no—
267C3×C5#128211yescharacteristic, complemented, Hall
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—52no—
271C22×C3—52no—
272C22×C3—101no—
273C22×C3—101no—
274C22×C3—101no—
275C22×C3—101no—
276C22×C3—202no—
277C22×C3—202no—
278C22×C3C8×AGL(1,𝔽5)11yescharacteristic
279C22×C3#399211yescharacteristic
280C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
281C3×C4—21no—
282C3×C4—101no—
283C3×C4—101no—
284C3×C4#399911yescharacteristic
285C3×C4#401111yescharacteristic
286Dic3—204no—
287C2×C5—21no—
288C2×C5—21no—
289C2×C5#452611yescharacteristic
290C2×C5#455011yescharacteristic
291C2×C5#455611yescharacteristic
292D5—22no—
293D5—22no—
294C23—51no—
295C23—51no—
296C23—52no—
297C23—52no—
298C23—201no—
299C23—201no—
300C23C4×ΓL(1,𝔽16)11yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—101no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—201no—
310C2×C4—201no—
311C2×C4—201no—
312C2×C4—304no—
313C2×C4—602no—
314C2×C4—602no—
315C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
316C2×C4#676311yescharacteristic
317C8—41no—
318C8—201no—
319C8—602no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—102no—
323C2×C3—102no—
324C2×C3(C2×AGL(1,𝔽5))⋊C811yescharacteristic
325C2×C3#6489411yescharacteristic
326C2×C3#6491711yescharacteristic
327C5#6767711yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—52no—
331C22—52no—
332C22—101no—
333C22—101no—
334C22—101no—
335C22—101no—
336C22—202no—
337C22—202no—
338C22C8×ΓL(1,𝔽16)11yescharacteristic
339C22#9122111yescharacteristic
340C22#9123511yescharacteristic
341C4—21no—
342C4—101no—
343C4—101no—
344C4—604no—
345C4#9122811yescharacteristic
346C4#9124011yescharacteristic
347C3#1059876611yescharacteristic, complemented, Sylow
348C2—21no—
349C2—21no—
350C2—102no—
351C2—102no—
352C2#1174676311yescharacteristic
353C2#1174676511yescharacteristic
354C2#1174678811yescharacteristic
subgroupG/H
centerC2×C4#6763
commutatorC22×C3×C5C4×C8
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC22×C3×C5#95
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×D5C22
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5#1282
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
9. C22×C3×C5×C8C4semidirect
10. C22×C3×#168C4semidirect
11. #91241C4semidirect
31. #6763C8semidirect
48. C22×C5×C8Dic3semidirect
49. C22×#168Dic3semidirect
84. C22×C3×C8AGL(1,𝔽5)semidirect
186. C22×C8ΓL(1,𝔽16)semidirect
267. C3×C5#1282semidirect
327. C5#67677semidirect
347. C3#10598766semidirect

Maximal subgroups

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

subgroupindex
C4×#67632
D5⋊#8302
C2×C3×#39522
#105987663
#676775