Finite Group Databasebeta

← #14313441

Subgroups — #14313441

Order 1920.

516 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 72 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#11755160C211yesmaximal, characteristic
2#11751862C212yesmaximal, complemented
3#11746799C211yesmaximal, characteristic, complemented
4C3×#64928C211yesmaximal, characteristic, complemented
5#11746554C212yesmaximal, complemented
6#10604996—31nomaximal, Hall
7C2×C5×#239C411yescharacteristic, complemented
8C2×#6765C2211yescharacteristic
9#91923—22no—
10#91833C411yescharacteristic, complemented
11C3×#4093C2211yescharacteristic
12#91463C2211yescharacteristic
13#91453—22no—
14#91441—22no—
15C4×D3×Dic5C411yescharacteristic, complemented
16#91373C411yescharacteristic, complemented
17#91228C2212yes—
18C3×#3999C2212yes—
19#91172—22no—
20#69158—51nomaximal, Hall
21#66166—31no—
22#65745—32no—
23#64928—31no—
24#64928D311yescharacteristic, complemented
25#64922—32no—
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C5×#239—41no—
29C5×#239—41no—
30C2×C5×D12—21no—
31C2×C5×D12C2×C411yescharacteristic
32C2×C4×C5×D3—21no—
33C2×C4×C5×D3C2×C411yescharacteristic
34C2×C3×D20C2311yescharacteristic
35C2×#1201—22no—
36C2×#1201D412yes—
37C2×D3×Dic5—21no—
38C2×D5×Dic3D412yes—
39#6765—41no—
40#6765—41no—
41#6763—22no—
42C3×C22⋊AGL(1,𝔽5)—22no—
43Dic3⋊AGL(1,𝔽5)—42no—
44Dic3×AGL(1,𝔽5)—42no—
45#6712—22no—
46C4×Dic15C2×C411yescharacteristic
47C3×#685—22no—
48C3×C4×Dic5C2×C411yescharacteristic
49(C2×D3)⋊Dic5—22no—
50Dic3×Dic5—21no—
51#5668—51no—
52#4740—52no—
53C3×#354—51no—
54#4541—51no—
55#4474—52no—
56C2×C5×#41—31no—
57C2×#709—31no—
58#4130—62no—
59#4093C2×D311yescharacteristic
60#4090—31no—
61#4086—31no—
62#4085—62no—
63#4082—31no—
64C4×C22⋊D5—62no—
65C2×C4×Dic5—31no—
66#4011—62no—
67#3999—32no—
68#3999C2×D312yes—
69#2126—151noSylow
70C22×C5×D3—21no—
71C22×C5×D3C22⋊C411yescharacteristic
72C22×C3×D5C2×D412yes—
73C2×ΓL(1,𝔽16)—42no—
74C2×C3×AGL(1,𝔽5)—42no—
75C3×C5×Q8—41no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×Dic15—21no—
79C2×Dic15C22⋊C412yes—
80Dic30—41no—
81C2×C5×Dic3C22⋊C411yescharacteristic
82C5×D12—41no—
83C5×D12—42no—
84C4×C5×D3—21no—
85C4×C5×D3—21no—
86C4×C5×D3—41no—
87C4×C5×D3—41no—
88C2×C3×Dic5—21no—
89C3×D20—41no—
90#1201—42no—
91#1201—44no—
92D3×Dic5—42no—
93D5×Dic3—22no—
94D5×Dic3—22no—
95C2×#239AGL(1,𝔽5)11yescharacteristic, complemented
96C2×#237—51no—
97C3×#124—51no—
98#944—51no—
99#940—51no—
100#884—102no—
101#67⋊C4—102no—
102#877—102no—
103#875—51no—
104C42×D3—51no—
105C3×#99—52no—
106#834—52no—
107#806—102no—
108C5×#41—121no—
109C5×#41—121no—
110C2×C5×Q8C4×D311yescharacteristic
111C2×C5×D4—31no—
112C2×C5×D4—61no—
113C22×C4×C5—31no—
114C22×C4×C5—61no—
115C2×C22⋊D5—32no—
116C2×C22⋊D5—62no—
117C22×Dic5—61no—
118#709—121no—
119#709—121no—
120C2×D20C22×D311yescharacteristic
121C2×C4×D5—32no—
122C2×Dic10—31no—
123C22⋊AGL(1,𝔽5)—22no—
124C22⋊AGL(1,𝔽5)—62no—
125C4⋊AGL(1,𝔽5)—122no—
126C4×AGL(1,𝔽5)—122no—
127C22⋊Dic5—62no—
128#685—22no—
129#683—62no—
130C4×Dic5—31no—
131C4×Dic5—61no—
132C4×Dic5C4×D311yescharacteristic
133#532—151no—
134#410—152no—
135#354—51no—
136#354—151no—
137#353—152no—
138C22×C3×C5C2×C22⋊C411yescharacteristic
139C2×C5×D3—21no—
140C2×C5×D3—41no—
141C2×C5×D3—42no—
142C2×C5×D3—41no—
143C2×C3×D5—22no—
144C2×C3×D5—42no—
145ΓL(1,𝔽16)—82no—
146C3×AGL(1,𝔽5)—82no—
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149Dic15—22no—
150Dic15—22no—
151C3×Dic5—41no—
152C5×Dic3#9911yescharacteristic
153C5×Dic3#9911yescharacteristic
154C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
155C2×C3×D4—51no—
156C2×#67—52no—
157C2×#67—102no—
158C22×Dic3—52no—
159#239—41no—
160#239—41no—
161#237—201no—
162#237—201no—
163C2×D12—21no—
164C2×D12C2×AGL(1,𝔽5)11yescharacteristic
165C2×C4×D3—21no—
166C2×C4×D3—101no—
167C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
168C2×Dic6—51no—
169C3×C22⋊C4—102no—
170C3×C22⋊C4—102no—
171C3×C42—51no—
172#217—102no—
173(C2×D3)⋊C4—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—202no—
176C4×Dic3—51no—
177C4×Dic3—101no—
178C4×Dic3—202no—
179C23×C5—31no—
180C23×C5—61no—
181C22×D5D3×D412yes—
182C2×AGL(1,𝔽5)—42no—
183C2×AGL(1,𝔽5)—122no—
184C5×Q8—41no—
185C5×D4—121no—
186C5×D4—122no—
187C2×C4×C5—21no—
188C2×C4×C5—31no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5—121no—
192C2×C4×C5—121no—
193C2×C4×C5C2×C4×D311yescharacteristic
194C22⋊D5—122no—
195C22⋊D5—124no—
196C2×Dic5—21no—
197C2×Dic5—32no—
198C2×Dic5—61no—
199C2×Dic5—122no—
200D20—41no—
201C4×D5—62no—
202C4×D5—62no—
203Dic10—121no—
204C2×#41—31no—
205C2×#41—151no—
206C4⋊Q8—151no—
207#127—151no—
208#124—51no—
209#124—151no—
210#121—302no—
211C4×D4—302no—
212#117—302no—
213C2×C42—151no—
214#99—52no—
215#99—152no—
216#99—302no—
217C2×C3×C5—21no—
218C2×C3×C5C2×#9911yescharacteristic
219C3×D5—42no—
220C5×D3—41no—
221C5×D3—81no—
222C23×C3—52no—
223C22×D3—21no—
224C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
225C3×Q8—41no—
226C3×D4—201no—
227C2×C3×C4—21no—
228C2×C3×C4—101no—
229C2×C3×C4—202no—
230C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
231#67—202no—
232#67—204no—
233C2×Dic3—52no—
234C2×Dic3—101no—
235C2×Dic3—102no—
236C2×Dic3—102no—
237C2×Dic3—202no—
238C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
239D12—41no—
240D12—42no—
241C4×D3—21no—
242C4×D3—21no—
243C4×D3—41no—
244C4×D3—41no—
245C4×D3—202no—
246Dic6—201no—
247C22×C5—61no—
248C22×C5—121no—
249C22×C5—122no—
250C22×C5—121no—
251C22×C5D3×C22⋊C411yescharacteristic
252C2×D5—22no—
253C2×D5—42no—
254AGL(1,𝔽5)—82no—
255AGL(1,𝔽5)—242no—
256C4×C5—21no—
257C4×C5—31no—
258C4×C5—31no—
259C4×C5—41no—
260Dic5—41no—
261Dic5—62no—
262Dic5—62no—
263#41—121no—
264#41—121no—
265#41—601no—
266#41—601no—
267C2×Q8—151no—
268C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
269C2×D4—31no—
270C2×D4—51no—
271C2×D4—61no—
272C2×D4—152no—
273C2×D4—302no—
274C22×C4—31no—
275C22×C4—61no—
276C22×C4—152no—
277C22×C4—301no—
278C4⋊C4—302no—
279C4⋊C4—602no—
280C22⋊C4—102no—
281C22⋊C4—102no—
282C22⋊C4—302no—
283C22⋊C4—302no—
284C42—51no—
285C42—151no—
286C42—301no—
287C42—602no—
288C3×C5#212611yescharacteristic, complemented, Hall
289C22×C3—102no—
290C22×C3—202no—
291C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
292C2×D3—21no—
293C2×D3—41no—
294C2×D3—42no—
295C2×D3—41no—
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—201no—
299C3×C4—402no—
300Dic3—102no—
301Dic3—102no—
302Dic3—402no—
303Dic3#401111yescharacteristic
304Dic3#401111yescharacteristic
305C2×C5—21no—
306C2×C5—121no—
307C2×C5—241no—
308C2×C5D3×#9911yescharacteristic
309D5—42no—
310C23—31no—
311C23—52no—
312C23—61no—
313Q8—41no—
314Q8—601no—
315D4—121no—
316D4—122no—
317D4—201no—
318D4—602no—
319D4—604no—
320C2×C4—21no—
321C2×C4—31no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—101no—
325C2×C4—121no—
326C2×C4—121no—
327C2×C4—152no—
328C2×C4—202no—
329C2×C4—302no—
330C2×C4—302no—
331C2×C4—301no—
332C2×C4—602no—
333C2×C4—602no—
334C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
335C2×C3—21no—
336C2×C3—202no—
337C2×C3C2×#401111yescharacteristic
338D3—41no—
339D3—81no—
340C5#6915811yescharacteristic, complemented, Sylow
341C22—61no—
342C22—102no—
343C22—121no—
344C22—122no—
345C22—121no—
346C22—202no—
347C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
348C4—21no—
349C4—31no—
350C4—31no—
351C4—41no—
352C4—201no—
353C4—302no—
354C4—302no—
355C4—402no—
356C4—1202no—
357C3#1060499611yescharacteristic, complemented, Sylow
358C2—21no—
359C2—121no—
360C2—202no—
361C2—241no—
362C2D3×#401111yescharacteristic
subgroupG/H
centerC2D3×#4011
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC2×C3×C5C2×#99
prime radical#11755160C2
cosocleC2×C3×D20C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2126
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11751862C2semidirect
3. #11746799C2semidirect
4. C3×#64928C2semidirect
5. #11746554C2semidirect
7. C2×C5×#239C4semidirect
10. #91833C4semidirect
15. C4×D3×Dic5C4semidirect
16. #91373C4semidirect
24. #64928D3semidirect
95. C2×#239AGL(1,𝔽5)semidirect
288. C3×C5#2126semidirect
340. C5#69158semidirect
357. C3#10604996semidirect

Maximal subgroups

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

subgroupindex
#117551602
#117518622
#117467992
C3×#649282
#117465542
#106049963
#691585