Finite Group Databasebeta

← #14284259

Subgroups — #14284259

Order 1920.

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

normal subgroups only

This group has 424 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#11754615C211yesmaximal, characteristic
2C2×#91231C211yesmaximal, characteristic
3C3×#65757C211yesmaximal, characteristic
4#11746507C212yesmaximal, complemented
5#11746506C212yesmaximal, complemented
6#10604351—31nomaximal, Hall
7C22×C3⋊#170—21no—
8#91815C411yescharacteristic
9C5×#926C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11#91574—21no—
12#91574—21no—
13#91468C411yescharacteristic
14#91468C411yescharacteristic
15C4×#1204—21no—
16C4×#1204—21no—
17#91388C2211yescharacteristic
18#91388C2211yescharacteristic
19#91231—21no—
20#91231C2212yes—
21C3×C22⋊#170—21no—
22C3×#4004—21no—
23C3×#4002C2212yes—
24#70813—51nomaximal, Hall
25#65851—31no—
26#65757D311yescharacteristic
27C2×#4002—31no—
28#64870—32no—
29#64870—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×Dic5D411yescharacteristic
32C22×C3×Dic5D411yescharacteristic
33C2×#1204—21no—
34C2×#1204—21no—
35C2×C3⋊#170—24no—
36C2×C3⋊#170—22no—
37C2×C3×#170—22no—
38#6719—21no—
39C4⋊Dic15C2×C411yescharacteristic
40C4⋊Dic15C2×C411yescharacteristic
41C4×Dic15—21no—
42C5×#217—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×C4⋊Dic3C2×C411yescharacteristic
45C4×C5×Dic3—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5C2311yescharacteristic
50Dic3⋊Dic5—21no—
51Dic3⋊Dic5—21no—
52#6669—21no—
53#6669—21no—
54#6668—21no—
55#6668—21no—
56#5470—51no—
57C3×#432—51no—
58C2×#803—51no—
59#4465—52no—
60#4465—52no—
61C22×#170—61no—
62C5×#117—31no—
63#4072—31no—
64C2×C4×Dic5C2×D311yescharacteristic
65#4036—31no—
66#4036—31no—
67#4034—31no—
68#4034—31no—
69#4024—61no—
70#4024—61no—
71C4×Dic10—61no—
72C4×Dic10—61no—
73C22⋊#170—21no—
74#4004—21no—
75#4002—32no—
76#4002—61no—
77#4002C2×D312yes—
78#1531—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85C2×C5×Dic3—21no—
86C2×C5×Dic3—21no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93#1204—42no—
94#1204—42no—
95C3⋊#170—24no—
96C3×#170—42no—
97C2×C3×C42—51no—
98#926—51no—
99#926AGL(1,𝔽5)11yescharacteristic
100#924—101no—
101#924—101no—
102C22×C3⋊C8—101no—
103#870—51no—
104#870—51no—
105#869—51no—
106#869—51no—
107C4×Dic6—101no—
108C4×Dic6—101no—
109C3×C4⋊C8—101no—
110C3×C22⋊C8—101no—
111C3×#97—52no—
112#803—52no—
113#803—101no—
114C22×C4×C5C4×D311yescharacteristic
115C22×Dic5D1211yescharacteristic
116C22×Dic5#6711yescharacteristic
117C2×Dic10—61no—
118C2×Dic10—61no—
119C2×#170—22no—
120C2×#170—64no—
121C2×#170—62no—
122C5×C4⋊C4—31no—
123C5×C4⋊C4—31no—
124C5×C22⋊C4—61no—
125C42×C5—61no—
126C22⋊Dic5—61no—
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
129C4⋊Dic5—61no—
130C4⋊Dic5—61no—
131#683—61no—
132#683—61no—
133#683—61no—
134#683—61no—
135C4×Dic5—61no—
136C4×Dic5C4×D311yescharacteristic
137C4×Dic5D1211yescharacteristic
138C4×Dic5#6711yescharacteristic
139C4×Dic5C22×D311yescharacteristic
140#533—151no—
141#432—51no—
142C2×#97—151no—
143#330—152no—
144#330—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5#10112yes—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151Dic15—41no—
152Dic15—41no—
153C3×Dic5—21no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C3×Dic5#10412yes—
157C5×Dic3—41no—
158C5×Dic3—41no—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
162C2×Dic6—101no—
163C2×Dic6—101no—
164C2×C3×C8—102no—
165C3×C42—51no—
166C3×C42—51no—
167C3×C42—51no—
168C3×C42—51no—
169#217—21no—
170#217—101no—
171C4⋊Dic3—51no—
172C4⋊Dic3—51no—
173C4⋊Dic3—101no—
174C4⋊Dic3—101no—
175C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
176C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
177Dic3⋊C4—101no—
178Dic3⋊C4—101no—
179Dic3⋊C4—101no—
180Dic3⋊C4—101no—
181C4×Dic3—21no—
182C4×Dic3—101no—
183C2×C3⋊C8—102no—
184C2×C3⋊C8—104no—
185C23×C5(C2×D3)⋊C411yescharacteristic
186C2×C4×C5—22no—
187C2×C4×C5—61no—
188C2×C4×C5—61no—
189C2×C4×C5(C2×D3)⋊C411yescharacteristic
190C2×C4×C5C2×C4×D311yescharacteristic
191C2×Dic5—22no—
192C2×Dic5—41no—
193C2×Dic5—61no—
194C2×Dic5—61no—
195C2×Dic5(C2×D3)⋊C411yescharacteristic
196C2×Dic5(C2×D3)⋊C411yescharacteristic
197C2×Dic5C2×D1211yescharacteristic
198C2×Dic5C2×#6711yescharacteristic
199Dic10—122no—
200Dic10—122no—
201#170—42no—
202#170—64no—
203C22×C8—301no—
204C4⋊Q8—151no—
205C4⋊Q8—151no—
206#125—151no—
207#125—151no—
208C22⋊Q8—301no—
209C22⋊Q8—301no—
210C4×Q8—301no—
211C4×Q8—301no—
212#117—31no—
213#117—151no—
214C2×C42—51no—
215C4⋊C8—101no—
216C22⋊C8—101no—
217#97—52no—
218#97—152no—
219#97—301no—
220C2×C3×C5—22no—
221C2×C3×C5C2×#10111yescharacteristic
222C2×C3×C5C2×#10411yescharacteristic
223C2×C3×C5#42111yescharacteristic
224C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
225C2×C3×C4—22no—
226C2×C3×C4—51no—
227C2×C3×C4—51no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—102no—
231C2×C3×C4—201no—
232C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
233C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—101no—
237C2×Dic3—101no—
238Dic6—202no—
239Dic6—202no—
240C3×C8—202no—
241C3⋊C8—104no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5#82412yes—
245C22×C5C2×(C2×D3)⋊C411yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—121no—
249C4×C5—121no—
250Dic5—21no—
251Dic5—21no—
252Dic5—21no—
253Dic5—121no—
254Dic5—121no—
255Dic5#82512yes—
256C2×Q8—301no—
257C2×Q8—301no—
258C22×C4—51no—
259C22×C4—51no—
260C22×C4D3×AGL(1,𝔽5)11yescharacteristic
261C2×C8—102no—
262C2×C8—302no—
263C2×C8—304no—
264C4⋊C4—31no—
265C4⋊C4—31no—
266C4⋊C4—151no—
267C4⋊C4—151no—
268C4⋊C4—301no—
269C4⋊C4—301no—
270C4⋊C4—301no—
271C4⋊C4—301no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C22⋊C4—61no—
275C22⋊C4—301no—
276C42—51no—
277C42—51no—
278C42—51no—
279C42—51no—
280C42—61no—
281C42—301no—
282C3×C5#153111yescharacteristic, complemented, Hall
283C22×C3—21no—
284C22×C3—21no—
285C22×C3#400512yes—
286C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—52no—
290C3×C4—101no—
291C3×C4—101no—
292C3×C4—101no—
293Dic3—41no—
294Dic3—41no—
295Dic3—201no—
296Dic3—201no—
297C2×C5—22no—
298C2×C5#500511yescharacteristic
299C2×C5C2×#82411yescharacteristic
300C2×C5C2×#82511yescharacteristic
301C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
302Q8—602no—
303Q8—602no—
304C2×C4—22no—
305C2×C4—51no—
306C2×C4—51no—
307C2×C4—51no—
308C2×C4—51no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—102no—
312C2×C4—201no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
316C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
317C8—202no—
318C8—304no—
319C2×C3—22no—
320C2×C3C2×#400511yescharacteristic
321C2×C3D5⋊#10411yescharacteristic
322C2×C3#6579511yescharacteristic
323C5#7081311yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22#9117512yes—
327C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
328C4—21no—
329C4—21no—
330C4—52no—
331C4—101no—
332C4—101no—
333C4—101no—
334C4—121no—
335C4—121no—
336C4—601no—
337C4—601no—
338C3#1060435111yescharacteristic, complemented, Sylow
339C2—22no—
340C2D5⋊#82511yescharacteristic
341C2#1175172011yescharacteristic
342C2C2×#9117511yescharacteristic
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 radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1531
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
4. #11746507C2semidirect
5. #11746506C2semidirect
282. C3×C5#1531semidirect
323. C5#70813semidirect
338. C3#10604351semidirect

Maximal subgroups

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

subgroupindex
#117546152
C2×#912312
C3×#657572
#117465072
#117465062
#106043513
#708135