Finite Group Databasebeta

← #14281901

Subgroups — #14281901

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#11754410C211yesmaximal, characteristic
2#11752413C211yesmaximal, characteristic, complemented
3C3×#65748C211yesmaximal, characteristic, complemented
4#11746494C212yesmaximal, complemented
5#11746488C212yesmaximal, complemented
6#10604478—31nomaximal, Hall
7#91813C411yescharacteristic
8C5×#930C411yescharacteristic
9C2×C3×C4×Dic5C2211yescharacteristic
10Dic5×#67—21no—
11#91539—21no—
12Dic5×D12C2211yescharacteristic
13#91398—21no—
14#91388C411yescharacteristic
15#91373C411yescharacteristic
16#91372—21no—
17#91333C2211yescharacteristic
18#91241—21no—
19#91233—21no—
20C4×C3⋊#170C2212yes—
21C3×C22⋊#170—21no—
22C3×C4⋊#170C2212yes—
23C3×C4×#170—21no—
24#70759—51nomaximal, Hall
25#65934—31no—
26#65754—31no—
27#65748D311yescharacteristic, complemented
28D4⋊#170—32no—
29#64872—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×#67—21no—
33C2×C5×D12C2×C411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C2×D3×Dic5—21no—
37C2×C3⋊#170—22no—
38C2×C3×#170—22no—
39#6719—21no—
40C4⋊Dic15C2×C411yescharacteristic
41#6712—21no—
42C5×(C2×D3)⋊C4—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C3×C4×Dic5C2×C411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5C2311yescharacteristic
48Dic3⋊Dic5—21no—
49#6669—21no—
50#6669—21no—
51(C2×D3)⋊Dic5—21no—
52(C2×D3)⋊Dic5—21no—
53(C2×D3)⋊Dic5—21no—
54Dic3×Dic5—21no—
55#5479—51no—
56C3×#431—51no—
57#4925—51no—
58#4484—52no—
59#4483—52no—
60C5×#121—31no—
61#4082—31no—
62#4081—61no—
63D4×Dic5—31no—
64D4×Dic5—61no—
65#4070—31no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4036—31no—
68#4033—31no—
69#4025—61no—
70#4023—61no—
71C22⋊#170—21no—
72C22⋊#170—61no—
73#4004—61no—
74C4⋊#170C2×D312yes—
75C4×#170—21no—
76C4×#170—32no—
77#1482—151noSylow
78C23×C3×C5C22⋊C411yescharacteristic
79C22×C5×D3—21no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85Dic30—22no—
86C5×#67—42no—
87C2×C5×Dic3—21no—
88C5×D12—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—41no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95D3×Dic5—42no—
96C3⋊#170—42no—
97C3×#170—42no—
98C2×C3×C42—51no—
99#930AGL(1,𝔽5)11yescharacteristic
100#929—101no—
101C4×#67—101no—
102#924—51no—
103#876—101no—
104#875—51no—
105C4×D12—51no—
106#872—101no—
107#870—51no—
108C4×Dic6—51no—
109C3×C4⋊C8—52no—
110C3×C22⋊C8—101no—
111C3×C4×C8—101no—
112#830—101no—
113C4⋊(C3⋊C8)—101no—
114C4×C3⋊C8—52no—
115C2×C5×D4—31no—
116C2×C5×D4—61no—
117C22×C4×C5C4×D311yescharacteristic
118C22×Dic5—61no—
119C22×Dic5D1211yescharacteristic
120C22×Dic5#6711yescharacteristic
121C2×Dic10—31no—
122C2×#170—22no—
123C2×#170—62no—
124C5×C4⋊C4—31no—
125C5×C22⋊C4—61no—
126C22⋊Dic5—61no—
127C22⋊Dic5—61no—
128C22⋊Dic5—61no—
129C22⋊Dic5—61no—
130C4⋊Dic5—31no—
131C4⋊Dic5—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#529—151no—
141#431—51no—
142#431—151no—
143Q8⋊C8—152no—
144D4⋊C8—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×C5×D3—41no—
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C3×C4×C5—21no—
153C3×C4×C5#13112yes—
154Dic15—41no—
155Dic15—41no—
156C3×Dic5—21no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5#13512yes—
160C5×Dic3—41no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
164C2×#67—21no—
165C2×D12C2×AGL(1,𝔽5)11yescharacteristic
166C2×C4×D3—101no—
167C2×Dic6—51no—
168C2×C3×C8—102no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42—51no—
173#217—101no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—101no—
176(C2×D3)⋊C4—101no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—102no—
186C23×C5—61no—
187C23×C5(C2×D3)⋊C411yescharacteristic
188C5×D4—62no—
189C5×D4—122no—
190C2×C4×C5—22no—
191C2×C4×C5—61no—
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×Dic5—22no—
195C2×Dic5—41no—
196C2×Dic5—61no—
197C2×Dic5—61no—
198C2×Dic5—122no—
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5(C2×D3)⋊C411yescharacteristic
201C2×Dic5C2×D1211yescharacteristic
202C2×Dic5C2×#6711yescharacteristic
203Dic10—62no—
204#170—42no—
205#170—122no—
206#126—301no—
207#125—151no—
208#124—151no—
209#123—301no—
210C22⋊Q8—151no—
211#121—31no—
212C4×Q8—151no—
213C4×D4—151no—
214C4×D4—301no—
215#117—301no—
216C2×C42—51no—
217C4⋊C8—52no—
218C4⋊C8—301no—
219C22⋊C8—101no—
220C22⋊C8—301no—
221C4×C8—101no—
222C4×C8—152no—
223C2×C3×C5—41no—
224C2×C3×C5#40811yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#42111yescharacteristic
227C5×D3—81no—
228C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
229C22×D3—21no—
230C2×C3×C4—22no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—51no—
234C2×C3×C4—51no—
235C2×C3×C4—102no—
236C2×C3×C4—201no—
237C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
238C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
239#67—42no—
240C2×Dic3—21no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243D12—22no—
244C4×D3—202no—
245Dic6—102no—
246C3×C8—202no—
247C3⋊C8—202no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5—121no—
254C22×C5C2×(C2×D3)⋊C411yescharacteristic
255C4×C5—21no—
256C4×C5—121no—
257C4×C5#90112yes—
258Dic5—21no—
259Dic5—21no—
260Dic5—21no—
261Dic5—121no—
262Dic5—121no—
263Dic5#95012yes—
264C2×Q8—151no—
265C2×D4—31no—
266C2×D4—61no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4—301no—
270C22×C4D3×AGL(1,𝔽5)11yescharacteristic
271C2×C8—102no—
272C2×C8—302no—
273C4⋊C4—31no—
274C4⋊C4—151no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C22⋊C4—61no—
280C22⋊C4—301no—
281C22⋊C4—301no—
282C22⋊C4—301no—
283C22⋊C4—301no—
284C42—51no—
285C42—51no—
286C42—51no—
287C42—51no—
288C42—301no—
289C3×C5#148211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C3×C4—21no—
298C3×C4—52no—
299C3×C4—101no—
300C3×C4—101no—
301C3×C4—101no—
302C3×C4#413112yes—
303Dic3—41no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—41no—
307C2×C5—241no—
308C2×C5#500211yescharacteristic
309C2×C5#511011yescharacteristic
310C2×C5#513911yescharacteristic
311C23—61no—
312C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
313Q8—302no—
314D4—62no—
315D4—122no—
316C2×C4—22no—
317C2×C4—51no—
318C2×C4—51no—
319C2×C4—51no—
320C2×C4—51no—
321C2×C4—61no—
322C2×C4—102no—
323C2×C4—201no—
324C2×C4—301no—
325C2×C4—301no—
326C2×C4—602no—
327C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
328C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
329C8—202no—
330C8—602no—
331C2×C3—41no—
332C2×C3#6576911yescharacteristic
333C2×C3#6577511yescharacteristic
334C2×C3#6579411yescharacteristic
335D3—81no—
336C5#7075911yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
344C4—21no—
345C4—52no—
346C4—101no—
347C4—101no—
348C4—101no—
349C4—121no—
350C4—601no—
351C4—601no—
352C4#9192712yes—
353C3#1060447811yescharacteristic, complemented, Sylow
354C2—41no—
355C2—241no—
356C2#1175170311yescharacteristic
357C2#1175171811yescharacteristic
358C2#1175199911yescharacteristic
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 radicalC5×#930C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752413C2semidirect
3. C3×#65748C2semidirect
4. #11746494C2semidirect
5. #11746488C2semidirect
27. #65748D3semidirect
289. C3×C5#1482semidirect
336. C5#70759semidirect
353. C3#10604478semidirect

Maximal subgroups

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

subgroupindex
#117544102
#117524132
C3×#657482
#117464942
#117464882
#106044783
#707595