Finite Group Databasebeta

← #14282208

Subgroups — #14282208

Order 1920.

492 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C4×#6773C211yesmaximal, characteristic
2#11752339C211yesmaximal, characteristic, complemented
3C3×#65683C211yesmaximal, characteristic, complemented
4#11746492C212yesmaximal, complemented
5#11746490C212yesmaximal, complemented
6#10604440—31nomaximal, Hall
7C2×#6773C411yescharacteristic
8C4×D60C411yescharacteristic
9C4×C5×Dic6C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91444—21no—
12C4×#1202—21no—
13#91418C2211yescharacteristic
14#91402—21no—
15C4×#1200—21no—
16#91358C411yescharacteristic
17Dic5×Dic6C2211yescharacteristic
18#91232—21no—
19C4⋊(C3⋊#170)—21no—
20C4×C3⋊#170C2212yes—
21C3×#4003—21no—
22C3×#4002—21no—
23C3×C4⋊#170C2212yes—
24#70798—51nomaximal, Hall
25C4×#713—31no—
26#65683D311yescharacteristic, complemented
27#65680—31no—
28Q8⋊#170—32no—
29#64871—32no—
30C2×D60C2×C411yescharacteristic
31C2×C4×D15—21no—
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×C4×D5C2×C411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×#1202—21no—
37C2×#1200—21no—
38C2×#1200—21no—
39#6773—22no—
40#6773—22no—
41C2×C3⋊#170—22no—
42C2×C3×#170—22no—
43C3×C42×C5C2×C411yescharacteristic
44#6714—21no—
45C4⋊Dic15C2×C411yescharacteristic
46C5×C4⋊Dic3C2×C411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51C3×C4×Dic5C2311yescharacteristic
52Dic3⋊Dic5—21no—
53#6667—21no—
54#6665—21no—
55Dic3×Dic5—21no—
56Dic3×Dic5—21no—
57C4×#235—51no—
58C3×#432—51no—
59#4925—51no—
60#4484—52no—
61#4483—52no—
62C2×#713—31no—
63C4×C5×Q8—31no—
64Q8×Dic5—31no—
65#4039—31no—
66#4039—61no—
67#4038—31no—
68#4038—61no—
69C4×D20—31no—
70C4×D20—61no—
71C42×D5—61no—
72C42×D5C2×D311yescharacteristic
73#4003—21no—
74#4003—61no—
75#4002—21no—
76C4⋊#170—61no—
77C4⋊#170C2×D312yes—
78C4×#170—32no—
79#1488—151noSylow
80C22×D15—21no—
81C22×C3×D5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×Dic15—21no—
86D60—21no—
87D60M1612yes—
88C4×D15—42no—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—21no—
91C5×Dic6—21no—
92C5×Dic6M1612yes—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—22no—
99C3×C4×D5—41no—
100#1202—24no—
101#1200—24no—
102#1200—42no—
103C3⋊#170—42no—
104C3×#170—42no—
105C2×#235—51no—
106C2×C3×C42—51no—
107C4×#67—101no—
108C4×#67—101no—
109#926—51no—
110C4×D12—51no—
111C4×D12—51no—
112#872—101no—
113C42×D3—101no—
114C4×Dic6—51no—
115C4×Dic6AGL(1,𝔽5)11yescharacteristic
116C3×C4⋊C8—52no—
117C3×C22⋊C8—101no—
118C3×#97—101no—
119#830—101no—
120C4⋊(C3⋊C8)—101no—
121C4×C3⋊C8—52no—
122C2×C5×Q8—31no—
123#713—62no—
124#713—62no—
125C2×D20—31no—
126C2×D20—61no—
127C2×C4×D5—61no—
128C2×C4×D5—61no—
129C2×C4×D5—61no—
130C2×C4×D5C4×D311yescharacteristic
131C2×C4×D5D1211yescharacteristic
132C2×C4×D5#6711yescharacteristic
133C2×#170—22no—
134C2×#170—62no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—61no—
137C42×C5—61no—
138C42×C5C4×D311yescharacteristic
139#685—61no—
140#685—61no—
141#685—61no—
142C4⋊Dic5—31no—
143C4⋊Dic5—61no—
144C4×Dic5—61no—
145C4×Dic5—61no—
146C4×Dic5D1211yescharacteristic
147C4×Dic5#6711yescharacteristic
148C4×Dic5C22×D311yescharacteristic
149C4×#41—151no—
150#432—51no—
151#431—151no—
152Q8⋊C8—152no—
153D4⋊C8—152no—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—41no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5C2×M1611yescharacteristic
164C3×C4×C5C2×M1611yescharacteristic
165Dic15—41no—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C3×Dic5#13512yes—
169C5×Dic3—22no—
170C5×Dic3—41no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C2×#67—101no—
175#235—102no—
176#235—102no—
177C2×D12—51no—
178C2×C4×D3—101no—
179C2×C4×D3—101no—
180C2×C4×D3—101no—
181C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
182C2×C3×C8—102no—
183C3×C42—51no—
184C3×C42—51no—
185C3×C42—51no—
186C3×C42C2×AGL(1,𝔽5)11yescharacteristic
187#217—101no—
188(C2×D3)⋊C4—101no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3—51no—
191C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
192Dic3⋊C4—21no—
193Dic3⋊C4—101no—
194C4×Dic3—21no—
195C4×Dic3—101no—
196C4×Dic3—101no—
197C2×C3⋊C8—102no—
198C22×D5—61no—
199C22×D5(C2×D3)⋊C411yescharacteristic
200C5×Q8—32no—
201C5×Q8—61no—
202C2×C4×C5—61no—
203C2×C4×C5—61no—
204C2×C4×C5(C2×D3)⋊C411yescharacteristic
205C2×C4×C5(C2×D3)⋊C411yescharacteristic
206C2×C4×C5C2×C4×D311yescharacteristic
207C2×Dic5—61no—
208C2×Dic5(C2×D3)⋊C411yescharacteristic
209C2×Dic5C2×D1211yescharacteristic
210C2×Dic5C2×#6711yescharacteristic
211D20—32no—
212D20—64no—
213D20—61no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—22no—
217C4×D5—41no—
218C4×D5—64no—
219C4×D5—122no—
220C4×D5—122no—
221#170—42no—
222#170—122no—
223C2×#41—151no—
224C4×Q8—31no—
225C4×Q8—151no—
226C4×D4—151no—
227C4×D4—151no—
228C4×D4—301no—
229C4×D4—301no—
230#117—151no—
231#117—301no—
232C2×C42—51no—
233C2×C42—301no—
234C4⋊C8—52no—
235C4⋊C8—301no—
236C22⋊C8—101no—
237C22⋊C8—301no—
238#97—101no—
239C4×C8—152no—
240C2×C3×C5#40711yescharacteristic
241C2×C3×C5#41611yescharacteristic
242C2×C3×C5#42111yescharacteristic
243D15—42no—
244C3×D5—41no—
245C23×C3—51no—
246C22×D3—101no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—102no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—201no—
254C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
255C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
256C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
257#67—104no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—101no—
261D12—52no—
262D12—101no—
263C4×D3—104no—
264C4×D3—202no—
265C4×D3—202no—
266Dic6—21no—
267Dic6#70012yes—
268C3×C8—202no—
269C3⋊C8—202no—
270C22×C5C2×(C2×D3)⋊C411yescharacteristic
271C2×D5—21no—
272C2×D5—21no—
273C2×D5—21no—
274C2×D5—62no—
275C2×D5—121no—
276C2×D5—121no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—62no—
280C4×C5—121no—
281C4×C5D3×M1611yescharacteristic
282C4×C5D3×M1611yescharacteristic
283Dic5—21no—
284Dic5—21no—
285Dic5—121no—
286Dic5#95012yes—
287#41—302no—
288#41—302no—
289C2×Q8—31no—
290C2×D4—151no—
291C2×D4—301no—
292C22×C4—51no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—301no—
296C22×C4—301no—
297C22×C4—301no—
298C2×C8—102no—
299C2×C8—302no—
300C4⋊C4—31no—
301C4⋊C4—61no—
302C4⋊C4—151no—
303C4⋊C4—301no—
304C22⋊C4—301no—
305C22⋊C4—301no—
306C22⋊C4—301no—
307C42—51no—
308C42—51no—
309C42—51no—
310C42—61no—
311C42—301no—
312C42—301no—
313C42D3×AGL(1,𝔽5)11yescharacteristic
314C3×C5#148811yescharacteristic, complemented, Hall
315C22×C3—101no—
316C22×C3—101no—
317C22×C3—101no—
318C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
319C2×D3—102no—
320C2×D3—201no—
321C2×D3—201no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—52no—
325C3×C4—101no—
326C3×C4—101no—
327C3×C4C2×#70011yescharacteristic
328C3×C4D5⋊M1611yescharacteristic
329Dic3—22no—
330Dic3—41no—
331Dic3—201no—
332C2×C5#500211yescharacteristic
333C2×C5#512611yescharacteristic
334C2×C5#513911yescharacteristic
335D5—41no—
336D5—122no—
337C23—51no—
338C23—301no—
339Q8—32no—
340Q8—61no—
341D4—152no—
342D4—304no—
343D4—301no—
344C2×C4—51no—
345C2×C4—51no—
346C2×C4—51no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—102no—
350C2×C4—101no—
351C2×C4—101no—
352C2×C4—201no—
353C2×C4—304no—
354C2×C4—301no—
355C2×C4—602no—
356C2×C4—602no—
357C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
358C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
359C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
360C8—202no—
361C8—602no—
362C2×C3—201no—
363C2×C3#6575611yescharacteristic
364C2×C3#6578411yescharacteristic
365C2×C3#6579411yescharacteristic
366D3—202no—
367C5#7079811yescharacteristic, complemented, Sylow
368C22—101no—
369C22—101no—
370C22—101no—
371C22—302no—
372C22—601no—
373C22—601no—
374C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
375C4—21no—
376C4—21no—
377C4—52no—
378C4—62no—
379C4—101no—
380C4—101no—
381C4—121no—
382C4—601no—
383C4D3×#70011yescharacteristic
384C4#9191511yescharacteristic
385C3#1060444011yescharacteristic, complemented, Sylow
386C2—201no—
387C2—602no—
388C2#1175170311yescharacteristic
389C2#1175172311yescharacteristic
390C2#1175180611yescharacteristic
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 radicalC2×#6773C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1488
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×#65683C2semidirect
4. #11746492C2semidirect
5. #11746490C2semidirect
26. #65683D3semidirect
314. C3×C5#1488semidirect
367. C5#70798semidirect
385. C3#10604440semidirect

Maximal subgroups

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

subgroupindex
C4×#67732
#117523392
C3×#656832
#117464922
#117464902
#106044403
#707985