Finite Group Databasebeta

← #14280841

Subgroups — #14280841

Order 1920.

528 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 110 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×#91403C211yesmaximal, characteristic
2#11751986C212yesmaximal, complemented
3#11746785C211yesmaximal, characteristic, complemented
4C3×#64914C211yesmaximal, characteristic, complemented
5#11746567C212yesmaximal
6#10604159—31nomaximal, Hall
7C22×#1200C411yescharacteristic
8C2×#6714C411yescharacteristic
9C2×C4×C5×Dic3C411yescharacteristic
10C2×C3×#683C2211yescharacteristic
11C2×#6668C411yescharacteristic
12C2×#6667C2211yescharacteristic
13C2×Dic3×Dic5C2211yescharacteristic
14#91403—22no—
15#91403—22no—
16#91241C2212yes—
17C3×C22⋊#170C2212yes—
18Dic3⋊#170—22no—
19Dic3×#170—22no—
20#68124—51nomaximal, Hall
21C2×#4018—31no—
22#65748—32no—
23#64915—32no—
24#64914—31no—
25#64914D311yescharacteristic, complemented
26C23×D15C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C22×C5×Dic3C2×C411yescharacteristic
30C22×C5×Dic3C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2311yescharacteristic
33C2×#1200—21no—
34C2×#1200—21no—
35C2×#1200—22no—
36C2×#1200C814yescomplemented
37C2×C3⋊#170—22no—
38C2×C3×#170—22no—
39#6714—22no—
40C4×C5×Dic3—21no—
41C4×C5×Dic3—21no—
42C3×#683—22no—
43#6668—22no—
44#6667—22no—
45Dic3×Dic5D412yes—
46Dic3×Dic5D412yes—
47C2×#892—51no—
48#4718—52no—
49C3×#324—51no—
50#4528—51no—
51#4468—52no—
52C22×C4×D5—31no—
53C2×C42×C5—31no—
54C2×#685—31no—
55C2×#685—31no—
56C2×#683—31no—
57C2×#683C2×D311yescharacteristic
58C2×C4×Dic5—31no—
59#4018—62no—
60#4018—62no—
61C22⋊#170—32no—
62C22⋊#170C2×D312yes—
63C4⋊#170—62no—
64C4×#170—62no—
65#1458—151noSylow
66C23×C3×C5C22×C411yescharacteristic
67C22×D15—21no—
68C22×D15—21no—
69C22×D15—41no—
70C22×D15—41no—
71C22×D15C2×C812yes—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—41no—
74C2×Dic15—41no—
75C2×Dic15C22⋊C412yes—
76C2×C5×Dic3—21no—
77C2×C5×Dic3—41no—
78C2×C5×Dic3C22⋊C411yescharacteristic
79C2×C5×Dic3C22⋊C411yescharacteristic
80C2×C5×Dic3C2×C812yes—
81C2×C5×Dic3M1612yes—
82C2×C3×Dic5—21no—
83C2×C3×Dic5—21no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5C2×C812yes—
86C2×C3×Dic5C2×D412yes—
87#1200—24no—
88#1200—24no—
89C3⋊#170—42no—
90C3×#170—42no—
91C22×C4×D3—51no—
92C2×C3×C4⋊C4—51no—
93C2×(C2×D3)⋊C4—51no—
94C2×(C2×D3)⋊C4—51no—
95C2×C4⋊Dic3—51no—
96C2×C4×Dic3—51no—
97C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
98#892—102no—
99#892—102no—
100C3×C22⋊C8—52no—
101#830—52no—
102Dic3⋊C8—102no—
103C8×Dic3—102no—
104C23×D5—31no—
105C22×C4×C5—31no—
106C22×C4×C5—31no—
107C22×C4×C5C4×D311yescharacteristic
108C22×Dic5—31no—
109C22×Dic5C4×D311yescharacteristic
110C22×Dic5C22×D311yescharacteristic
111C2×C4×D5—34no—
112C2×C4×D5—62no—
113C2×C4×D5—61no—
114C2×C4×D5—61no—
115C2×#170—22no—
116C2×#170—62no—
117C42×C5—61no—
118C42×C5—61no—
119#685—62no—
120#685—62no—
121#683—22no—
122#683—62no—
123C4×Dic5—32no—
124C4×Dic5—32no—
125C2×#117—151no—
126#431—152no—
127#324—51no—
128#324—151no—
129#323—152no—
130C22×C3×C5—21no—
131C22×C3×C5—21no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5C22×C811yescharacteristic
134C22×C3×C5C2×M1611yescharacteristic
135C2×D15—22no—
136C2×D15—42no—
137C2×D15—41no—
138C2×D15—41no—
139C2×D15—42no—
140C3×C4×C5—41no—
141Dic15—22no—
142C3×Dic5—22no—
143C3×Dic5—22no—
144C5×Dic3—41no—
145C5×Dic3C22⋊C812yes—
146C5×Dic3C22⋊C812yes—
147C23×D3—51no—
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
151C22×Dic3—51no—
152C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
153C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
154C2×C4×D3—54no—
155C2×C4×D3—102no—
156C2×C4×D3—101no—
157C2×C4×D3—101no—
158C2×C3×C8—102no—
159C3×C4⋊C4—102no—
160(C2×D3)⋊C4—102no—
161(C2×D3)⋊C4—102no—
162C4⋊Dic3—102no—
163C4×Dic3—21no—
164C4×Dic3—21no—
165C4×Dic3—52no—
166C4×Dic3—52no—
167C2×C3⋊C8—102no—
168C23×C5C2×C4×D311yescharacteristic
169C22×D5—32no—
170C22×D5—61no—
171C22×D5—61no—
172C22×D5—121no—
173C22×D5—121no—
174C2×C4×C5—21no—
175C2×C4×C5—31no—
176C2×C4×C5—31no—
177C2×C4×C5—32no—
178C2×C4×C5—32no—
179C2×C4×C5—41no—
180C2×C4×C5—61no—
181C2×C4×C5—121no—
182C2×Dic5—21no—
183C2×Dic5—21no—
184C2×Dic5—32no—
185C2×Dic5—41no—
186C2×Dic5—121no—
187C2×Dic5D3×C812yes—
188C2×Dic5D3×D412yes—
189C4×D5—64no—
190C4×D5—64no—
191#170—42no—
192#170—122no—
193C23×C4—151no—
194#117—302no—
195#117—302no—
196C2×C4⋊C4—51no—
197C2×C4⋊C4—151no—
198C2×C22⋊C4—151no—
199C2×C22⋊C4—151no—
200C2×C42—31no—
201C2×C42—151no—
202C4⋊C8—302no—
203C22⋊C8—52no—
204C22⋊C8—152no—
205C4×C8—302no—
206C2×C3×C5—21no—
207C2×C3×C5—21no—
208C2×C3×C5C2×C22⋊C811yescharacteristic
209C2×C3×C5#41011yescharacteristic
210C2×C3×C5#41311yescharacteristic
211D15—42no—
212C23×C3C22×AGL(1,𝔽5)11yescharacteristic
213C22×D3—52no—
214C22×D3—101no—
215C22×D3—101no—
216C22×D3—201no—
217C22×D3—201no—
218C2×C3×C4—21no—
219C2×C3×C4—41no—
220C2×C3×C4—52no—
221C2×C3×C4—52no—
222C2×C3×C4—101no—
223C2×C3×C4—101no—
224C2×C3×C4—201no—
225C2×Dic3—21no—
226C2×Dic3—41no—
227C2×Dic3—52no—
228C2×Dic3—201no—
229C2×Dic3D5⋊C812yes—
230C2×Dic3#70012yes—
231C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
232C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
233C4×D3—104no—
234C4×D3—104no—
235C3×C8—202no—
236C3⋊C8—202no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5D3×C22⋊C411yescharacteristic
240C22×C5C2×D3×C811yescharacteristic
241C22×C5D3×M1611yescharacteristic
242C2×D5—62no—
243C2×D5—122no—
244C2×D5—121no—
245C2×D5—121no—
246C2×D5—122no—
247C4×C5—32no—
248C4×C5—32no—
249C4×C5—41no—
250C4×C5—121no—
251Dic5—22no—
252Dic5—22no—
253Dic5—62no—
254C24—151no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—154no—
260C22×C4—151no—
261C22×C4—301no—
262C22×C4—301no—
263C22×C4—302no—
264C22×C4D3×AGL(1,𝔽5)11yescharacteristic
265C2×C8—102no—
266C2×C8—302no—
267C4⋊C4—102no—
268C4⋊C4—302no—
269C22⋊C4—302no—
270C22⋊C4—302no—
271C42—61no—
272C42—61no—
273C42—152no—
274C42—152no—
275C3×C5#145811yescharacteristic, complemented, Hall
276C22×C3—21no—
277C22×C3—21no—
278C22×C3C2×D5⋊C811yescharacteristic
279C22×C3C2×#70011yescharacteristic
280C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
281C2×D3—102no—
282C2×D3—202no—
283C2×D3—201no—
284C2×D3—201no—
285C2×D3—202no—
286C3×C4—41no—
287C3×C4—102no—
288C3×C4—102no—
289Dic3—41no—
290Dic3—102no—
291Dic3#400312yes—
292Dic3#400312yes—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5D3×C22⋊C811yescharacteristic
296C2×C5#474011yescharacteristic
297C2×C5#475111yescharacteristic
298D5—122no—
299C23—152no—
300C23—301no—
301C23—301no—
302C23—601no—
303C23—601no—
304C23C2×D3×AGL(1,𝔽5)11yescharacteristic
305C2×C4—21no—
306C2×C4—32no—
307C2×C4—32no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—41no—
311C2×C4—52no—
312C2×C4—52no—
313C2×C4—61no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—121no—
317C2×C4—152no—
318C2×C4—201no—
319C2×C4—304no—
320C2×C4—304no—
321C2×C4—601no—
322C8—202no—
323C8—602no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3#6574511yescharacteristic
327C2×C3C2×#400311yescharacteristic
328C2×C3#6576111yescharacteristic
329D3—202no—
330C5#6812411yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—302no—
334C22—602no—
335C22—602no—
336C22—601no—
337C22—601no—
338C22D3×D5⋊C811yescharacteristic
339C22D3×#70011yescharacteristic
340C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
341C4—32no—
342C4—32no—
343C4—41no—
344C4—102no—
345C4—102no—
346C4—121no—
347C4—302no—
348C3#1060415911yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—602no—
352C2D3×#400311yescharacteristic
353C2#1175191711yescharacteristic
354C2#1175203011yescharacteristic
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×C5#1458
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
2. #11751986C2semidirect
3. #11746785C2semidirect
4. C3×#64914C2semidirect
25. #64914D3semidirect
36. C2×#1200C8semidirect
275. C3×C5#1458semidirect
330. C5#68124semidirect
348. C3#10604159semidirect

Maximal subgroups

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

subgroupindex
C2×#914032
#117519862
#117467852
C3×#649142
#117465672
#106041593
#681245