Finite Group Databasebeta

← #14284091

Subgroups — #14284091

Order 1920.

424 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C3×D5×#125C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic
3C4×#6758C211yesmaximal, characteristic
4#11746741C212yesmaximal, complemented
5#11746741C212yesmaximal, complemented
6#10604578—31nomaximal, Hall
7C2×#6758—21no—
8C3×C5×#125C411yescharacteristic
9C3×D5×C4⋊C4—21no—
10C3×D5×C4⋊C4—21no—
11C3×D5×C4⋊C4C411yescharacteristic
12C3×D5×C4⋊C4C411yescharacteristic
13C3×#4036C2211yescharacteristic
14C3×#4036C2211yescharacteristic
15C3×#4035—21no—
16C3×#4035—21no—
17C3×C42×D5C2211yescharacteristic
18C3×#4016C411yescharacteristic
19#91233—21no—
20#91232—21no—
21#91231C2212yes—
22#91231C2212yes—
23C4×C3⋊#170—21no—
24#71735—51nomaximal, Hall
25D5×#125D311yescharacteristic
26#65684—31no—
27C4×#700—31no—
28#64870—32no—
29#64870—32no—
30C2×C3×C4×D5—21no—
31C2×C3×C4×D5—21no—
32C2×C3×C4×D5C2×C411yescharacteristic
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3⋊#170—22no—
36C2×C3⋊#170—22no—
37#6758—24no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4C2×C411yescharacteristic
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C42×C5C2×C411yescharacteristic
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5C2×C411yescharacteristic
46C3×C4⋊Dic5C2×C411yescharacteristic
47C3×#683—21no—
48C3×#683—21no—
49C3×#683—21no—
50C3×#683—21no—
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5C2311yescharacteristic
56C2×C3×#125—51no—
57#4926—51no—
58C4×#208—51no—
59#4543—52no—
60#4543—52no—
61C2×#700—61no—
62C5×#125Dic311yescharacteristic
63D5×C4⋊C4—21no—
64D5×C4⋊C4—21no—
65D5×C4⋊C4Dic311yescharacteristic
66D5×C4⋊C4Dic311yescharacteristic
67#4036C2×D311yescharacteristic
68#4036C2×D311yescharacteristic
69#4035—21no—
70#4035—21no—
71C42×D5C2×D311yescharacteristic
72#4016Dic311yescharacteristic
73#4004—61no—
74#4003—61no—
75#4002—32no—
76#4002—32no—
77C4×#170—61no—
78#1528—151noSylow
79C22×C3×D5C22⋊C411yescharacteristic
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×Dic5—21no—
86C2×C3×Dic5—21no—
87C2×C3×Dic5C22⋊C411yescharacteristic
88C2×C3×Dic5C2×D411yescharacteristic
89C2×C3×Dic5C2×D411yescharacteristic
90C3×C4×D5—22no—
91C3×C4×D5—22no—
92C3×C4×D5—41no—
93C3×C4×D5—42no—
94C3×C4×D5—42no—
95C3⋊#170—24no—
96C3⋊#170—42no—
97C3×#125—51no—
98C3×#125—51no—
99C3×#125—51no—
100C3×#125—101no—
101C3×#125—101no—
102C3×#125AGL(1,𝔽5)11yescharacteristic
103C2×C3×C4⋊C4—51no—
104C2×C3×C4⋊C4—51no—
105C2×C3×C4⋊C4—101no—
106C2×C3×C4⋊C4—101no—
107C2×C3×C42—51no—
108C2×#208—101no—
109#830—101no—
110C4⋊(C3⋊C8)—101no—
111#803—52no—
112#803—52no—
113C4×C3⋊C8—101no—
114C2×C4×D5—21no—
115C2×C4×D5—21no—
116C2×C4×D5C2×Dic311yescharacteristic
117C2×C4×D5#6711yescharacteristic
118C2×C4×D5#6711yescharacteristic
119C2×#170—62no—
120C2×#170—62no—
121#700—64no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4C2×Dic311yescharacteristic
125C5×C4⋊C4C2×Dic311yescharacteristic
126C42×C5C2×Dic311yescharacteristic
127C4⋊Dic5—21no—
128C4⋊Dic5—21no—
129C4⋊Dic5C2×Dic311yescharacteristic
130C4⋊Dic5C2×Dic311yescharacteristic
131#683—21no—
132#683—21no—
133#683—21no—
134#683—21no—
135#683—21no—
136#683—21no—
137C4×Dic5#6711yescharacteristic
138C4×Dic5#6711yescharacteristic
139C4×Dic5C22×D311yescharacteristic
140C2×#125—51no—
141#432—151no—
142C4×M16—151no—
143#330—152no—
144#330—152no—
145C22×C3×C5C2×C22⋊C411yescharacteristic
146C2×C3×D5—21no—
147C2×C3×D5—21no—
148C2×C3×D5#10412yes—
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151C3×C4×C5—21no—
152C3×C4×C5—41no—
153C3×C4×C5—41no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C3×Dic5—41no—
157C3×Dic5—41no—
158C3×Dic5#10112yes—
159C22×C3×C4—51no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4—101no—
163C22×C3×C4—101no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4—101no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
177C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
178C3×C42—51no—
179C3×C42—51no—
180C3×C42—51no—
181C3×C42C2×AGL(1,𝔽5)11yescharacteristic
182#208—104no—
183C2×C3⋊C8—102no—
184C2×C3⋊C8—102no—
185C22×D5#21711yescharacteristic
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5#21711yescharacteristic
189C2×C4×C5#21711yescharacteristic
190C2×C4×C5C22×Dic311yescharacteristic
191C2×Dic5—21no—
192C2×Dic5—21no—
193C2×Dic5#21711yescharacteristic
194C2×Dic5C2×#6711yescharacteristic
195C2×Dic5C2×#6711yescharacteristic
196C4×D5—22no—
197C4×D5—22no—
198C4×D5—41no—
199C4×D5—42no—
200C4×D5—42no—
201#170—64no—
202#170—122no—
203C2×M16—301no—
204#125—51no—
205#125—51no—
206#125—51no—
207#125—101no—
208#125—101no—
209#125ΓL(1,𝔽16)11yescharacteristic
210C2×C4⋊C4—51no—
211C2×C4⋊C4—51no—
212C2×C4⋊C4—101no—
213C2×C4⋊C4—101no—
214C2×C42—51no—
215C4⋊C8—301no—
216C22⋊C8—301no—
217#97—152no—
218#97—152no—
219C4×C8—301no—
220C2×C3×C5C2×#10111yescharacteristic
221C2×C3×C5C2×#10411yescharacteristic
222C2×C3×C5#42111yescharacteristic
223C3×D5—22no—
224C23×C3—51no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—51no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—102no—
231C2×C3×C4—102no—
232C2×C3×C4—101no—
233C2×C3×C4—101no—
234C2×C3×C4—201no—
235C2×C3×C4—202no—
236C2×C3×C4—202no—
237C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
238C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
239C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
240C3⋊C8—104no—
241C3⋊C8—202no—
242C22×C5C2×#21711yescharacteristic
243C2×D5—21no—
244C2×D5—21no—
245C2×D5#83712yes—
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—41no—
250C4×C5—41no—
251Dic5—21no—
252Dic5—21no—
253Dic5—41no—
254Dic5—41no—
255Dic5#83612yes—
256C22×C4—51no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—101no—
260C22×C4—101no—
261M16—304no—
262C2×C8—302no—
263C2×C8—302no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—51no—
267C4⋊C4—51no—
268C4⋊C4—101no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
277C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
278C42—51no—
279C42—51no—
280C42—51no—
281C42C2×ΓL(1,𝔽16)11yescharacteristic
282C3×C5#152811yescharacteristic, complemented, Hall
283C22×C3—52no—
284C22×C3—101no—
285C22×C3—101no—
286C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—52no—
293C3×C4—101no—
294C3×C4—101no—
295C3×C4—201no—
296C3×C4—201no—
297C2×C5C2×#83611yescharacteristic
298C2×C5C2×#83711yescharacteristic
299C2×C5#523611yescharacteristic
300D5—22no—
301C23—51no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—51no—
307C2×C4—102no—
308C2×C4—102no—
309C2×C4—101no—
310C2×C4—101no—
311C2×C4—201no—
312C2×C4—202no—
313C2×C4—202no—
314C2×C4#676311yescharacteristic
315C2×C4#676311yescharacteristic
316C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
317C8—304no—
318C8—602no—
319C2×C3—102no—
320C2×C3D5⋊#10111yescharacteristic
321C2×C3D5⋊#10411yescharacteristic
322C2×C3#6579511yescharacteristic
323C5#7173511yescharacteristic, complemented, Sylow
324C22—52no—
325C22—101no—
326C22—101no—
327C22C2×#676311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—52no—
334C4—101no—
335C4—101no—
336C4—201no—
337C4—201no—
338C3#1060457811yescharacteristic, complemented, Sylow
339C2—102no—
340C2D5⋊#83611yescharacteristic
341C2D5⋊#83711yescharacteristic
342C2#1175245411yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#125C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenter#125ΓL(1,𝔽16)
hypocenterC3×C5#1528
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
4. #11746741C2semidirect
5. #11746741C2semidirect
282. C3×C5#1528semidirect
323. C5#71735semidirect
338. C3#10604578semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1252
#117523432
C4×#67582
#117467412
#106045783
#717355