Finite Group Databasebeta

← #14281911

Subgroups — #14281911

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#11752683C211yesmaximal, characteristic
2#11752339C211yesmaximal, characteristic, complemented
3C3×#65680C211yesmaximal, characteristic, complemented
4#11746493C212yesmaximal, complemented
5#11746489C212yesmaximal, complemented
6#10604552—31nomaximal, Hall
7#91759C411yescharacteristic
8C5×#875C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91449C411yescharacteristic
11#91447—21no—
12#91440—21no—
13Dic5×D12C2211yescharacteristic
14#91398—21no—
15#91372—21no—
16#91359C411yescharacteristic
17Dic5×Dic6C2211yescharacteristic
18#91232—21no—
19C4⋊(C3⋊#170)C2212yes—
20C4×C3⋊#170—21no—
21C3×#4003—21no—
22C3×C4⋊#170—21no—
23C3×C4×#170C2212yes—
24#70760—51nomaximal, Hall
25#66014—31no—
26#65680—31no—
27#65680D311yescharacteristic, complemented
28Q8⋊#170—32no—
29D4⋊#170—32no—
30C2×C5×D12C2×C411yescharacteristic
31C2×C5×Dic6C2×C411yescharacteristic
32C2×C3×C4×D5C2×C411yescharacteristic
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×#1201—21no—
36C2×D3×Dic5—21no—
37C2×C3⋊#170—22no—
38C2×C3×#170—22no—
39C3×C42×C5C2×C411yescharacteristic
40C4⋊Dic15C2×C411yescharacteristic
41C4⋊Dic15C2×C411yescharacteristic
42#6712—21no—
43#6712—21no—
44C5×(C2×D3)⋊C4—21no—
45C5×(C2×D3)⋊C4—21no—
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49Dic3⋊Dic5—21no—
50#6669—21no—
51(C2×D3)⋊Dic5—21no—
52(C2×D3)⋊Dic5—21no—
53#6665—21no—
54Dic3×Dic5—21no—
55#5479—51no—
56C3×#431—51no—
57#4925—51no—
58#4459—52no—
59#4456—52no—
60C5×#124—31no—
61#4092—31no—
62Q8×Dic5—31no—
63#4084—31no—
64D4×Dic5—31no—
65#4029—61no—
66#4027—61no—
67#4025—61no—
68#4023—61no—
69C42×D5C2×D311yescharacteristic
70#4016—31no—
71#4003—21no—
72#4003—61no—
73C4⋊#170—21no—
74C4⋊#170—32no—
75C4×#170—61no—
76C4×#170C2×D312yes—
77#1482—151noSylow
78C22×C5×D3—21no—
79C22×C3×D5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85C2×C5×Dic3—21no—
86C5×D12—22no—
87C5×Dic6—22no—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C2×C3×Dic5C2×D411yescharacteristic
90C2×C3×Dic5C2×D411yescharacteristic
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5—41no—
94#1201—42no—
95D3×Dic5—42no—
96C3⋊#170—42no—
97C3×#170—42no—
98C2×C3×C42—51no—
99#930—51no—
100#929—101no—
101C4×#67—101no—
102#924—51no—
103#876—101no—
104#875AGL(1,𝔽5)11yescharacteristic
105C4×D12—51no—
106#872—101no—
107#870—51no—
108C4×Dic6—51no—
109C3×C4⋊C8—101no—
110C3×C22⋊C8—101no—
111C3×C4×C8—52no—
112#830—101no—
113C4⋊(C3⋊C8)—52no—
114C4×C3⋊C8—101no—
115C2×C5×Q8—31no—
116C2×C5×D4—31no—
117C2×C22⋊D5—61no—
118C22×Dic5—61no—
119C2×C4×D5C4×D311yescharacteristic
120C2×C4×D5D1211yescharacteristic
121C2×C4×D5#6711yescharacteristic
122C2×#170—22no—
123C2×#170—62no—
124C5×C22⋊C4—61no—
125C5×C22⋊C4—61no—
126C42×C5C4×D311yescharacteristic
127C22⋊Dic5—61no—
128C22⋊Dic5—61no—
129#685—61no—
130C4⋊Dic5—31no—
131C4⋊Dic5—31no—
132C4⋊Dic5—61no—
133#683—61no—
134#683—61no—
135#683—61no—
136C4×Dic5—61no—
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×C5C2×C22⋊C411yescharacteristic
146C2×C5×D3—41no—
147C2×C5×D3—41no—
148C2×C5×D3—41no—
149C2×C3×D5—21no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5#13112yes—
155Dic15—41no—
156Dic15—41no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5#13512yes—
160C5×Dic3—41no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4—51no—
164C2×#67—101no—
165C2×D12C2×AGL(1,𝔽5)11yescharacteristic
166C2×C4×D3—101no—
167C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C8—102no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172C3×C42C2×AGL(1,𝔽5)11yescharacteristic
173#217—101no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—101no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—102no—
186C23×C5—61no—
187C22×D5(C2×D3)⋊C411yescharacteristic
188C5×Q8—62no—
189C5×D4—62no—
190C2×C4×C5—61no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C22⋊D5—122no—
195C2×Dic5—61no—
196C2×Dic5—61no—
197C2×Dic5—122no—
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5C2×D1211yescharacteristic
200C2×Dic5C2×#6711yescharacteristic
201C4×D5—22no—
202C4×D5—22no—
203C4×D5—41no—
204#170—42no—
205#170—122no—
206#126—301no—
207#125—151no—
208#124—31no—
209#123—301no—
210C22⋊Q8—151no—
211#121—151no—
212C4×Q8—151no—
213C4×D4—151no—
214C4×D4—301no—
215#117—301no—
216C2×C42—51no—
217C4⋊C8—101no—
218C4⋊C8—152no—
219C22⋊C8—101no—
220C22⋊C8—301no—
221C4×C8—52no—
222C4×C8—301no—
223C2×C3×C5#40811yescharacteristic
224C2×C3×C5#41611yescharacteristic
225C2×C3×C5#42111yescharacteristic
226C3×D5—41no—
227C5×D3—81no—
228C23×C3—51no—
229C22×D3—21no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—102no—
234C2×C3×C4—102no—
235C2×C3×C4—201no—
236C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
237C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
238C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
239#67—202no—
240C2×Dic3—21no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243D12—22no—
244C4×D3—202no—
245Dic6—22no—
246C3×C8—202no—
247C3⋊C8—202no—
248C22×C5—121no—
249C22×C5—121no—
250C22×C5—121no—
251C22×C5C2×(C2×D3)⋊C411yescharacteristic
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—21no—
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—121no—
258C4×C5#90712yes—
259Dic5—21no—
260Dic5—21no—
261Dic5—121no—
262Dic5—121no—
263Dic5#90412yes—
264C2×Q8—31no—
265C2×D4—31no—
266C2×D4—301no—
267C22×C4—51no—
268C22×C4—51no—
269C22×C4—51no—
270C22×C4—301no—
271C2×C8—102no—
272C2×C8—302no—
273C4⋊C4—151no—
274C4⋊C4—151no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C22⋊C4—61no—
280C22⋊C4—61no—
281C22⋊C4—301no—
282C22⋊C4—301no—
283C22⋊C4—301no—
284C42—51no—
285C42—51no—
286C42—51no—
287C42—301no—
288C42D3×AGL(1,𝔽5)11yescharacteristic
289C3×C5#148211yescharacteristic, complemented, Hall
290C22×C3—101no—
291C22×C3—101no—
292C22×C3—101no—
293C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—52no—
300C3×C4—101no—
301C3×C4—101no—
302C3×C4#413112yes—
303Dic3—41no—
304Dic3—201no—
305Dic3—201no—
306C2×C5—241no—
307C2×C5#500511yescharacteristic
308C2×C5#511311yescharacteristic
309C2×C5#512911yescharacteristic
310D5—41no—
311C23—51no—
312C23—61no—
313Q8—62no—
314D4—62no—
315D4—602no—
316C2×C4—51no—
317C2×C4—51no—
318C2×C4—51no—
319C2×C4—61no—
320C2×C4—102no—
321C2×C4—102no—
322C2×C4—201no—
323C2×C4—301no—
324C2×C4—301no—
325C2×C4—602no—
326C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
327C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
328C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
329C8—202no—
330C8—602no—
331C2×C3—201no—
332C2×C3#6577611yescharacteristic
333C2×C3#6579411yescharacteristic
334C2×C3#6579511yescharacteristic
335D3—81no—
336C5#7076011yescharacteristic, complemented, Sylow
337C22—101no—
338C22—101no—
339C22—101no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
344C4—21no—
345C4—21no—
346C4—52no—
347C4—101no—
348C4—101no—
349C4—121no—
350C4—601no—
351C4—601no—
352C4#9191312yes—
353C3#1060455211yescharacteristic, complemented, Sylow
354C2—201no—
355C2—241no—
356C2#1175170411yescharacteristic
357C2#1175172011yescharacteristic
358C2#1175181111yescharacteristic
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 radical#91449C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752339C2semidirect
3. C3×#65680C2semidirect
4. #11746493C2semidirect
5. #11746489C2semidirect
27. #65680D3semidirect
289. C3×C5#1482semidirect
336. C5#70760semidirect
353. C3#10604552semidirect

Maximal subgroups

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

subgroupindex
#117526832
#117523392
C3×#656802
#117464932
#117464892
#106045523
#707605