Finite Group Databasebeta

← #14313520

Subgroups — #14313520

Order 1920.

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

normal subgroups only

This group has 540 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#11754941C211yesmaximal, characteristic
2#11751862C212yesmaximal, complemented
3#11746793C211yesmaximal, characteristic, complemented
4C3×#64922C211yesmaximal, characteristic, complemented
5#11746554C212yesmaximal, complemented
6#10604918—31nomaximal, Hall
7C2×C5×D3×D4C411yescharacteristic, complemented
8C2×#6765C2211yescharacteristic
9#91923—22no—
10#91825C411yescharacteristic, complemented
11C3×#4086C2211yescharacteristic
12#91568—22no—
13#91549—22no—
14#91463C2211yescharacteristic
15#91373C411yescharacteristic, complemented
16#91371C411yescharacteristic, complemented
17#91228C2212yescomplemented
18C3×#3999C2212yescomplemented
19#91172—22no—
20#69152—51nomaximal, Hall
21#66139—31no—
22#65745—32no—
23#64922—31no—
24#64922—32no—
25#64922D311yescharacteristic, complemented
26C23×C5×D3—21no—
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×Dic30C2×C411yescharacteristic
29C2×C5×#67—21no—
30C5×D3×D4—42no—
31C2×C5×D12C2×C411yescharacteristic
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C3×C22⋊D5—22no—
34C2×C3×D20C2311yescharacteristic
35C2×#1201—22no—
36C2×#1201D412yes—
37C2×D5×Dic3D412yes—
38#6765—42no—
39#6763—22no—
40C3×C22⋊AGL(1,𝔽5)—22no—
41Dic3⋊AGL(1,𝔽5)—42no—
42Dic3×AGL(1,𝔽5)—42no—
43#6719—22no—
44C4×Dic15C2×C411yescharacteristic
45C3×C4×Dic5C2×C411yescharacteristic
46Dic3⋊Dic5—21no—
47(C2×D3)⋊Dic5—21no—
48(C2×D3)⋊Dic5—22no—
49#5715—51no—
50#4740—52no—
51C3×#353—51no—
52#4545—51no—
53#4474—52no—
54C22×C5×D4—31no—
55C2×#709—31no—
56#4130—62no—
57#4099—62no—
58#4086—31no—
59#4086C2×D311yescharacteristic
60#4084—62no—
61#4082—31no—
62#4082—31no—
63#4072—31no—
64#4011—62no—
65#3999—32no—
66#3999C2×D312yescomplemented
67#2128—151noSylow
68C23×C3×C5—21no—
69C22×C5×D3—21no—
70C22×C5×D3—42no—
71C22×C5×D3—82no—
72C22×C5×D3C22⋊C411yescharacteristic
73C22×C3×D5C2×D412yes—
74C2×ΓL(1,𝔽16)—42no—
75C2×C3×AGL(1,𝔽5)—42no—
76C3×C5×D4—41no—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×Dic15—21no—
79C2×Dic15C22⋊C412yes—
80Dic30—41no—
81C5×#67—42no—
82C2×C5×Dic3C22⋊C411yescharacteristic
83C5×D12—41no—
84C4×C5×D3—22no—
85C3×C22⋊D5—82no—
86C2×C3×Dic5—21no—
87C3×D20—41no—
88#1201—42no—
89#1201—82no—
90D5×Dic3—22no—
91D5×Dic3—22no—
92C2×#237—51no—
93C2×D3×D4AGL(1,𝔽5)11yescharacteristic, complemented
94C3×#127—51no—
95#940—51no—
96#939—102no—
97#937—102no—
98#936—51no—
99#877—102no—
100#875—51no—
101#872—51no—
102C3×#99—52no—
103#834—52no—
104#806—102no—
105C24×C5—61no—
106C2×C5×D4—31no—
107C2×C5×D4—61no—
108C2×C5×D4—122no—
109C2×C5×D4C4×D311yescharacteristic
110C22×C4×C5—31no—
111C2×C22⋊D5—22no—
112C2×C22⋊D5—32no—
113C2×C22⋊D5—62no—
114#709—122no—
115C2×D20C22×D311yescharacteristic
116C2×C4×D5—32no—
117C2×Dic10—31no—
118C22⋊AGL(1,𝔽5)—22no—
119C22⋊AGL(1,𝔽5)—62no—
120C4⋊AGL(1,𝔽5)—122no—
121C4×AGL(1,𝔽5)—122no—
122C22⋊Dic5—62no—
123C22⋊Dic5—61no—
124C22⋊Dic5—62no—
125C4⋊Dic5—61no—
126C4×Dic5—31no—
127C4×Dic5C4×D311yescharacteristic
128#535—151no—
129#410—152no—
130#353—51no—
131#353—152no—
132#353—151no—
133C22×C3×C5—42no—
134C22×C3×C5—41no—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C2×C5×D3—21no—
137C2×C5×D3—41no—
138C2×C5×D3—42no—
139C2×C5×D3—41no—
140C2×C5×D3—84no—
141C2×C3×D5—22no—
142C2×C3×D5—42no—
143ΓL(1,𝔽16)—82no—
144C3×AGL(1,𝔽5)—82no—
145C3×C4×C5—21no—
146Dic15—22no—
147Dic15—41no—
148C3×Dic5—41no—
149C5×Dic3#9912yes—
150C23×D3—21no—
151C2×C3×D4—51no—
152C2×C3×D4—102no—
153C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
154C2×#67—21no—
155C2×#67—52no—
156C2×#67—102no—
157C22×Dic3—52no—
158#237—202no—
159D3×D4—42no—
160C2×D12C2×AGL(1,𝔽5)11yescharacteristic
161C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
162C2×Dic6—51no—
163C3×C22⋊C4—102no—
164C3×C42—51no—
165#217—102no—
166#217—102no—
167(C2×D3)⋊C4—102no—
168(C2×D3)⋊C4—101no—
169Dic3⋊C4—101no—
170Dic3⋊C4—202no—
171C4×Dic3—51no—
172C4×Dic3—202no—
173C23×C5—21no—
174C23×C5—31no—
175C23×C5—61no—
176C23×C5—122no—
177C23×C5—242no—
178C22×D5D3×D412yes—
179C2×AGL(1,𝔽5)—42no—
180C2×AGL(1,𝔽5)—122no—
181C5×D4—41no—
182C5×D4—121no—
183C5×D4—122no—
184C2×C4×C5—31no—
185C2×C4×C5—62no—
186C2×C4×C5C2×C4×D311yescharacteristic
187C22⋊D5—82no—
188C22⋊D5—122no—
189C22⋊D5—242no—
190C2×Dic5—21no—
191C2×Dic5—32no—
192C2×Dic5—61no—
193D20—41no—
194C4×D5—62no—
195C4×D5—62no—
196Dic10—121no—
197C2×#41—151no—
198C22×D4—31no—
199#127—51no—
200#127—151no—
201#124—151no—
202#124—151no—
203#121—302no—
204#120—302no—
205#117—151no—
206#117—302no—
207#99—52no—
208#99—152no—
209#99—302no—
210C2×C3×C5—21no—
211C2×C3×C5—81no—
212C2×C3×C5C2×#9911yescharacteristic
213C3×D5—42no—
214C5×D3—41no—
215C5×D3—81no—
216C23×C3—21no—
217C23×C3—52no—
218C22×D3—21no—
219C22×D3—42no—
220C22×D3—82no—
221C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
222C3×D4—41no—
223C3×D4—201no—
224C3×D4—402no—
225C2×C3×C4—101no—
226C2×C3×C4—202no—
227C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
228#67—42no—
229#67—202no—
230#67—402no—
231C2×Dic3—52no—
232C2×Dic3—102no—
233C2×Dic3—102no—
234C2×Dic3—101no—
235C2×Dic3—202no—
236C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
237D12—41no—
238C4×D3—22no—
239Dic6—201no—
240C22×C5—42no—
241C22×C5—41no—
242C22×C5—61no—
243C22×C5—121no—
244C22×C5—122no—
245C22×C5—121no—
246C22×C5—244no—
247C22×C5D3×C22⋊C411yescharacteristic
248C2×D5—22no—
249C2×D5—42no—
250AGL(1,𝔽5)—82no—
251AGL(1,𝔽5)—242no—
252C4×C5—21no—
253C4×C5—32no—
254Dic5—41no—
255Dic5—62no—
256Dic5—121no—
257C24—61no—
258#41—602no—
259C2×Q8—151no—
260C2×D4—31no—
261C2×D4—51no—
262C2×D4—61no—
263C2×D4—102no—
264C2×D4—122no—
265C2×D4—152no—
266C2×D4—302no—
267C2×D4D3×AGL(1,𝔽5)11yescharacteristic
268C22×C4—31no—
269C22×C4—152no—
270C4⋊C4—301no—
271C4⋊C4—602no—
272C22⋊C4—102no—
273C22⋊C4—302no—
274C22⋊C4—301no—
275C22⋊C4—302no—
276C22⋊C4—302no—
277C42—51no—
278C42—151no—
279C42—602no—
280C3×C5#212811yescharacteristic, complemented, Hall
281C22×C3—42no—
282C22×C3—41no—
283C22×C3—102no—
284C22×C3—202no—
285C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
286C2×D3—21no—
287C2×D3—41no—
288C2×D3—42no—
289C2×D3—41no—
290C2×D3—84no—
291C3×C4—21no—
292C3×C4—201no—
293C3×C4—402no—
294Dic3—102no—
295Dic3—201no—
296Dic3—402no—
297Dic3#401112yes—
298C2×C5—21no—
299C2×C5—81no—
300C2×C5—121no—
301C2×C5—241no—
302C2×C5D3×#9911yescharacteristic
303D5—42no—
304C23—21no—
305C23—31no—
306C23—52no—
307C23—61no—
308C23—122no—
309C23—242no—
310Q8—601no—
311D4—41no—
312D4—121no—
313D4—122no—
314D4—201no—
315D4—402no—
316D4—602no—
317D4—1202no—
318C2×C4—31no—
319C2×C4—62no—
320C2×C4—101no—
321C2×C4—152no—
322C2×C4—202no—
323C2×C4—302no—
324C2×C4—302no—
325C2×C4—301no—
326C2×C4—602no—
327C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
328C2×C3—21no—
329C2×C3—81no—
330C2×C3—202no—
331C2×C3C2×#401111yescharacteristic
332D3—41no—
333D3—81no—
334C5#6915211yescharacteristic, complemented, Sylow
335C22—42no—
336C22—41no—
337C22—61no—
338C22—102no—
339C22—121no—
340C22—122no—
341C22—121no—
342C22—202no—
343C22—244no—
344C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
345C4—21no—
346C4—32no—
347C4—201no—
348C4—302no—
349C4—402no—
350C4—601no—
351C4—1202no—
352C3#1060491811yescharacteristic, complemented, Sylow
353C2—21no—
354C2—81no—
355C2—121no—
356C2—202no—
357C2—241no—
358C2D3×#401111yescharacteristic
subgroupG/H
centerC2D3×#4011
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5C2×#99
prime radical#11754941C2
cosocleC2×C3×D20C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2128
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751862C2semidirect
3. #11746793C2semidirect
4. C3×#64922C2semidirect
5. #11746554C2semidirect
7. C2×C5×D3×D4C4semidirect
10. #91825C4semidirect
15. #91373C4semidirect
16. #91371C4semidirect
17. #91228C22semidirect
18. C3×#3999C22semidirect
25. #64922D3semidirect
66. #3999C2×D3semidirect
93. C2×D3×D4AGL(1,𝔽5)semidirect
280. C3×C5#2128semidirect
334. C5#69152semidirect
352. C3#10604918semidirect

Maximal subgroups

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

subgroupindex
#117549412
#117518622
#117467932
C3×#649222
#117465542
#106049183
#691525