Finite Group Databasebeta

← #14284764

Subgroups — #14284764

Order 1920.

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

normal subgroups only

This group has 404 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
1#11752498C211yesmaximal, characteristic
2#11752337C211yesmaximal, characteristic
3C3×#65678C211yesmaximal, characteristic
4#11746510C212yesmaximal, complemented
5#11746509C212yesmaximal, complemented
6#10604584—31nomaximal, Hall
7#91759C411yescharacteristic
8C5×#870C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91468C2211yescharacteristic
11#91468C2211yescharacteristic
12#91358C411yescharacteristic
13#91358C411yescharacteristic
14#91349—21no—
15#91349—21no—
16#91323—21no—
17#91323—21no—
18#91233C2212yes—
19#91232—21no—
20C4×C3⋊#170—21no—
21C3×#4004C2212yes—
22C3×#4003—21no—
23C3×C4×#170—21no—
24#70777—51nomaximal, Hall
25#66022—31no—
26#65678—31no—
27#65678D311yescharacteristic
28#64873—32no—
29#64873—32no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×#1204—21no—
34C2×#1204—21no—
35C2×C3⋊#170—22no—
36C2×C3×#170—22no—
37C3×C42×C5C2×C411yescharacteristic
38C4⋊Dic15C2×C411yescharacteristic
39C4⋊Dic15C2×C411yescharacteristic
40#6712—21no—
41#6712—21no—
42C5×C4⋊Dic3C2×C411yescharacteristic
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×Dic3⋊C4—21no—
45C5×Dic3⋊C4—21no—
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49#6668—21no—
50#6668—21no—
51#6665—21no—
52#6665—21no—
53Dic3×Dic5—21no—
54Dic3×Dic5—21no—
55#5470—51no—
56C3×#431—51no—
57#4925—51no—
58#4486—52no—
59#4482—52no—
60C5×#125—31no—
61#4042—61no—
62#4042—61no—
63#4038—31no—
64#4038—31no—
65#4034—31no—
66#4034—31no—
67#4033—61no—
68#4033—61no—
69C42×D5C2×D311yescharacteristic
70#4016—31no—
71#4004—32no—
72#4004C2×D312yes—
73#4003—21no—
74#4003—61no—
75C4×#170—21no—
76C4×#170—61no—
77#1544—151noSylow
78C22×C3×D5C22⋊C411yescharacteristic
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22×C411yescharacteristic
82C2×Dic15—21no—
83C2×Dic15—21no—
84C2×C5×Dic3—21no—
85C2×C5×Dic3—21no—
86C2×C3×Dic5C22⋊C411yescharacteristic
87C2×C3×Dic5C2×D411yescharacteristic
88C2×C3×Dic5C2×D411yescharacteristic
89C3×C4×D5—22no—
90C3×C4×D5—22no—
91C3×C4×D5—22no—
92#1204—42no—
93#1204—42no—
94C3⋊#170—42no—
95C3×#170—42no—
96C2×C3×C42—51no—
97#926—51no—
98#926—51no—
99#924—101no—
100#924—101no—
101#870—51no—
102#870AGL(1,𝔽5)11yescharacteristic
103#869—51no—
104#869—51no—
105C4×Dic6—101no—
106C4×Dic6—101no—
107C3×C4⋊C8—52no—
108C3×C22⋊C8—101no—
109C3×C4×C8—101no—
110#830—101no—
111C4⋊(C3⋊C8)—52no—
112C4×C3⋊C8—101no—
113C2×C4×D5C4×D311yescharacteristic
114C2×C4×D5D1211yescharacteristic
115C2×C4×D5#6711yescharacteristic
116C2×Dic10—61no—
117C2×Dic10—61no—
118C2×#170—22no—
119C2×#170—62no—
120C5×C4⋊C4—31no—
121C5×C4⋊C4—31no—
122C5×C4⋊C4—61no—
123C5×C4⋊C4—61no—
124C42×C5C4×D311yescharacteristic
125#685—61no—
126#685—61no—
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
129#683—61no—
130#683—61no—
131#683—61no—
132#683—61no—
133C4×Dic5—61no—
134C4×Dic5—61no—
135C4×Dic5D1211yescharacteristic
136C4×Dic5#6711yescharacteristic
137C4×Dic5C22×D311yescharacteristic
138#533—151no—
139#431—51no—
140#431—151no—
141#332—152no—
142#332—152no—
143C22×C3×C5C2×C22⋊C411yescharacteristic
144C2×C3×D5—21no—
145C2×C3×D5—21no—
146C2×C3×D5—21no—
147C3×C4×C5—21no—
148C3×C4×C5—21no—
149C3×C4×C5—21no—
150Dic15—41no—
151Dic15—41no—
152C3×Dic5#10112yes—
153C3×Dic5#13512yes—
154C3×Dic5#13512yes—
155C5×Dic3—41no—
156C5×Dic3—41no—
157C22×C3×C4—51no—
158C22×C3×C4—51no—
159C22×C3×C4—51no—
160C2×Dic6—101no—
161C2×Dic6—101no—
162C2×C3×C8—102no—
163C3×C42—51no—
164C3×C42—51no—
165C3×C42—51no—
166C3×C42C2×AGL(1,𝔽5)11yescharacteristic
167#217—101no—
168#217—101no—
169C4⋊Dic3—51no—
170C4⋊Dic3—51no—
171C4⋊Dic3—101no—
172C4⋊Dic3—101no—
173C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
174C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
175Dic3⋊C4—21no—
176Dic3⋊C4—21no—
177Dic3⋊C4—101no—
178Dic3⋊C4—101no—
179C4×Dic3—101no—
180C4×Dic3—101no—
181C2×C3⋊C8—102no—
182C22×D5(C2×D3)⋊C411yescharacteristic
183C2×C4×C5—61no—
184C2×C4×C5—61no—
185C2×C4×C5(C2×D3)⋊C411yescharacteristic
186C2×C4×C5(C2×D3)⋊C411yescharacteristic
187C2×C4×C5C2×C4×D311yescharacteristic
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5(C2×D3)⋊C411yescharacteristic
191C2×Dic5C2×D1211yescharacteristic
192C2×Dic5C2×#6711yescharacteristic
193C4×D5—22no—
194C4×D5—22no—
195C4×D5—22no—
196Dic10—122no—
197Dic10—122no—
198#170—42no—
199#170—122no—
200C4⋊Q8—151no—
201C4⋊Q8—151no—
202#125—31no—
203#125—151no—
204C22⋊Q8—301no—
205C22⋊Q8—301no—
206C4×Q8—301no—
207C4×Q8—301no—
208#117—151no—
209#117—151no—
210C2×C42—51no—
211C4⋊C8—52no—
212C4⋊C8—152no—
213C22⋊C8—101no—
214C22⋊C8—301no—
215C4×C8—101no—
216C4×C8—301no—
217C2×C3×C5C2×#10111yescharacteristic
218C2×C3×C5#41611yescharacteristic
219C2×C3×C5#41611yescharacteristic
220C3×D5—41no—
221C23×C3—51no—
222C2×C3×C4—51no—
223C2×C3×C4—51no—
224C2×C3×C4—51no—
225C2×C3×C4—102no—
226C2×C3×C4—102no—
227C2×C3×C4—102no—
228C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
229C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
230C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—101no—
234C2×Dic3—101no—
235Dic6—202no—
236Dic6—202no—
237C3×C8—202no—
238C3⋊C8—202no—
239C22×C5C2×(C2×D3)⋊C411yescharacteristic
240C2×D5—21no—
241C2×D5—21no—
242C2×D5—21no—
243C4×C5—21no—
244C4×C5—21no—
245C4×C5—21no—
246C4×C5—121no—
247C4×C5—121no—
248Dic5—121no—
249Dic5—121no—
250Dic5#82412yes—
251Dic5#90412yes—
252Dic5#95012yes—
253C2×Q8—301no—
254C2×Q8—301no—
255C22×C4—51no—
256C22×C4—51no—
257C22×C4—51no—
258C2×C8—102no—
259C2×C8—302no—
260C4⋊C4—31no—
261C4⋊C4—31no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4—151no—
265C4⋊C4—151no—
266C4⋊C4—301no—
267C4⋊C4—301no—
268C4⋊C4—301no—
269C4⋊C4—301no—
270C22⋊C4—301no—
271C22⋊C4—301no—
272C42—51no—
273C42—51no—
274C42—51no—
275C42—301no—
276C42—301no—
277C42D3×AGL(1,𝔽5)11yescharacteristic
278C3×C5#154411yescharacteristic, complemented, Hall
279C22×C3—101no—
280C22×C3—101no—
281C22×C3—101no—
282C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—52no—
287C3×C4—52no—
288C3×C4—52no—
289Dic3—41no—
290Dic3—41no—
291Dic3—201no—
292Dic3—201no—
293C2×C5#500211yescharacteristic
294C2×C5#511311yescharacteristic
295C2×C5C2×#82411yescharacteristic
296D5—41no—
297C23—51no—
298Q8—602no—
299Q8—602no—
300C2×C4—51no—
301C2×C4—51no—
302C2×C4—51no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—102no—
306C2×C4—102no—
307C2×C4—102no—
308C2×C4—301no—
309C2×C4—301no—
310C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
311C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
312C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
313C8—202no—
314C8—602no—
315C2×C3—201no—
316C2×C3D5⋊#10111yescharacteristic
317C2×C3#6579411yescharacteristic
318C2×C3#6579411yescharacteristic
319C5#7077711yescharacteristic, complemented, Sylow
320C22—101no—
321C22—101no—
322C22—101no—
323C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—52no—
328C4—52no—
329C4—52no—
330C4—121no—
331C4—121no—
332C4—601no—
333C4—601no—
334C3#1060458411yescharacteristic, complemented, Sylow
335C2—201no—
336C2#1175170311yescharacteristic
337C2#1175170411yescharacteristic
338C2D5⋊#82411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1544
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746510C2semidirect
5. #11746509C2semidirect
278. C3×C5#1544semidirect
319. C5#70777semidirect
334. C3#10604584semidirect

Maximal subgroups

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

subgroupindex
#117524982
#117523372
C3×#656782
#117465102
#117465092
#106045843
#707775