Finite Group Databasebeta

← #14285331

Subgroups — #14285331

Order 1920.

492 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 94 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#11754330C211yesmaximal, characteristic
2#11752416C211yesmaximal, characteristic, complemented
3C3×#65758C211yesmaximal, characteristic, complemented
4#11746510C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10604488—31nomaximal, Hall
7C2×#6782—21no—
8C2×C3×#704—21no—
9#91819C411yescharacteristic
10C5×#930C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91566—21no—
13#91468C2211yescharacteristic
14#91451C2211yescharacteristic
15#91418C411yescharacteristic
16Dic5×D12C411yescharacteristic
17#91405—21no—
18#91350—21no—
19#91241—21no—
20#91233C2212yes—
21#91231—21no—
22C3×#4004C2212yes—
23C3×C4⋊#170—21no—
24#70504—51nomaximal, Hall
25#65930—31no—
26#65758D311yescharacteristic, complemented
27#65757—31no—
28#64925—32no—
29#64873—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32C2×D60C2×C411yescharacteristic
33C2×C5×#67—21no—
34C2×C5×D12C2×C411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C22×C3×Dic5D411yescharacteristic
37C2×#1204—21no—
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1200—21no—
41#6782—44no—
42C2×D3×Dic5—21no—
43C2×C3⋊#170—22no—
44C3×#704—42no—
45C2×C3×#170—22no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C3×C4×Dic5C2×C411yescharacteristic
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5C2311yescharacteristic
54#6668—21no—
55#6667—21no—
56(C2×D3)⋊Dic5—21no—
57#5477—51no—
58C3×#423—51no—
59#4926—51no—
60#4486—52no—
61#4485—52no—
62C2×#711—61no—
63C2×#704—21no—
64C5×#121—31no—
65#4086—31no—
66#4085—61no—
67D4×Dic5—31no—
68#4076—31no—
69C2×C4×Dic5C2×D311yescharacteristic
70#4039—31no—
71#4034—31no—
72#4031—61no—
73#4027—61no—
74C22⋊#170—61no—
75#4004—32no—
76#4004C2×D312yes—
77#4002—61no—
78C4⋊#170—21no—
79#1557—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C22×C5×D3—21no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86#1220—42no—
87C2×Dic15—21no—
88D60—41no—
89C5×#67—42no—
90C2×C5×Dic3—21no—
91C5×D12—41no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C2×C3×Dic5C2×D411yescharacteristic
99#1204—42no—
100#1203—42no—
101#1203—41no—
102#1203—41no—
103#1200—42no—
104D3×Dic5—42no—
105C3⋊#170—42no—
106C3×#170—42no—
107C2×#235—101no—
108C2×C3×M16—101no—
109C2×C3×C42—51no—
110#930—51no—
111#930—101no—
112#930AGL(1,𝔽5)11yescharacteristic
113#875—101no—
114#874—51no—
115C4×D12—51no—
116C4×D12—51no—
117C4×D12—101no—
118#869—51no—
119C3×C4⋊C8—52no—
120C3×C4⋊C8—101no—
121#830—101no—
122C4⋊(C3⋊C8)—52no—
123#803—101no—
124C2×C5×D4—31no—
125C2×C5×D4—61no—
126C22×C4×C5C4×D311yescharacteristic
127C2×C22⋊D5—61no—
128C2×C22⋊D5—61no—
129C2×C22⋊D5—61no—
130C22×Dic5—61no—
131C22×Dic5D1211yescharacteristic
132C22×Dic5#6711yescharacteristic
133#711—124no—
134C2×D20—31no—
135C2×C4×D5—61no—
136C2×Dic10—61no—
137#704—42no—
138C2×#170—22no—
139C2×#170—62no—
140C5×C4⋊C4—31no—
141C5×C22⋊C4—61no—
142C22⋊Dic5—61no—
143#685—61no—
144#685—61no—
145C4⋊Dic5—31no—
146#683—61no—
147C4×Dic5C4×D311yescharacteristic
148C4×Dic5D1211yescharacteristic
149C4×Dic5#6711yescharacteristic
150C4×Dic5C22×D311yescharacteristic
151#532—151no—
152#432—151no—
153#423—51no—
154#332—152no—
155#331—152no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5C2×C22⋊C411yescharacteristic
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—41no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×Dic5AGL(1,ℤ/8)12yes—
172C3×Dic5AGL(1,ℤ/8)11yescharacteristic
173C3×Dic5#13711yescharacteristic
174C5×Dic3—41no—
175C22×C3×C4—51no—
176C22×C3×C4—51no—
177C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
178C2×#67—21no—
179C2×#67—101no—
180#235—204no—
181C2×D12—51no—
182C2×D12—101no—
183C2×D12—101no—
184C2×D12C2×AGL(1,𝔽5)11yescharacteristic
185C2×C4×D3—101no—
186C2×C4×D3—101no—
187C2×Dic6—101no—
188C3×M16—202no—
189C2×C3×C8—102no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42—51no—
193C3×C42—51no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—101no—
196(C2×D3)⋊C4—101no—
197(C2×D3)⋊C4—101no—
198C4⋊Dic3—51no—
199C4⋊Dic3—101no—
200C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
201C2×C3⋊C8—102no—
202C23×C5—61no—
203C23×C5(C2×D3)⋊C411yescharacteristic
204C22×D5—61no—
205C5×D4—121no—
206C5×D4—122no—
207C2×C4×C5—41no—
208C2×C4×C5—61no—
209C2×C4×C5(C2×D3)⋊C411yescharacteristic
210C2×C4×C5C2×C4×D311yescharacteristic
211C22⋊D5—122no—
212C22⋊D5—122no—
213C22⋊D5—121no—
214C22⋊D5—121no—
215C2×Dic5—22no—
216C2×Dic5—21no—
217C2×Dic5—21no—
218C2×Dic5—61no—
219C2×Dic5—122no—
220C2×Dic5(C2×D3)⋊C411yescharacteristic
221C2×Dic5(C2×D3)⋊C411yescharacteristic
222C2×Dic5C2×D1211yescharacteristic
223C2×Dic5C2×#6711yescharacteristic
224D20—121no—
225C4×D5—122no—
226Dic10—122no—
227#170—42no—
228#170—122no—
229C2×#41—301no—
230C2×M16—101no—
231C4⋊Q8—151no—
232#127—151no—
233#124—301no—
234#121—31no—
235#121—151no—
236#121—301no—
237C4×D4—151no—
238C4×D4—151no—
239C4×D4—301no—
240C2×C42—51no—
241C4⋊C8—52no—
242C4⋊C8—101no—
243C4⋊C8—152no—
244C22⋊C8—301no—
245#97—301no—
246C2×C3×C5—41no—
247C2×C3×C5#41311yescharacteristic
248C2×C3×C5#41711yescharacteristic
249C2×C3×C5#41811yescharacteristic
250D15—81no—
251C5×D3—81no—
252C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
253C22×D3—21no—
254C22×D3—101no—
255C2×C3×C4—41no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—101no—
261C2×C3×C4—102no—
262C2×C3×C4—101no—
263C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
264C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
265#67—42no—
266#67—202no—
267C2×Dic3—21no—
268C2×Dic3—101no—
269D12—41no—
270D12—201no—
271D12—201no—
272D12—201no—
273D12—202no—
274C4×D3—202no—
275C4×D3—202no—
276Dic6—202no—
277C3×C8—202no—
278C3⋊C8—202no—
279C22×C5—21no—
280C22×C5—21no—
281C22×C5—21no—
282C22×C5—121no—
283C22×C5—121no—
284C22×C5—121no—
285C22×C5C2×(C2×D3)⋊C411yescharacteristic
286C2×D5—121no—
287C2×D5—121no—
288C2×D5—121no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—121no—
292Dic5—21no—
293Dic5—21no—
294Dic5—121no—
295Dic5#90812yes—
296Dic5#93211yescharacteristic
297Dic5#94211yescharacteristic
298#41—604no—
299C2×Q8—301no—
300C2×D4—31no—
301C2×D4—61no—
302C2×D4—151no—
303C2×D4—301no—
304C2×D4—301no—
305C2×D4—301no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—301no—
309C22×C4—301no—
310C22×C4D3×AGL(1,𝔽5)11yescharacteristic
311M16—202no—
312C2×C8—102no—
313C2×C8—302no—
314C4⋊C4—31no—
315C4⋊C4—151no—
316C4⋊C4—301no—
317C22⋊C4—61no—
318C22⋊C4—301no—
319C22⋊C4—301no—
320C22⋊C4—301no—
321C42—51no—
322C42—51no—
323C42—51no—
324C42—51no—
325C3×C5#155711yescharacteristic, complemented, Hall
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—201no—
334C2×D3—201no—
335C2×D3—201no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—51no—
339C3×C4—51no—
340C3×C4—52no—
341C3×C4—101no—
342C3×C4—101no—
343Dic3—41no—
344Dic3—201no—
345C2×C5—41no—
346C2×C5—241no—
347C2×C5#496611yescharacteristic
348C2×C5#513111yescharacteristic
349C2×C5#513211yescharacteristic
350D5—241no—
351C23—61no—
352C23—301no—
353C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
354Q8—602no—
355D4—121no—
356D4—122no—
357D4—601no—
358D4—602no—
359D4—601no—
360D4—601no—
361D4—602no—
362C2×C4—41no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—61no—
368C2×C4—101no—
369C2×C4—102no—
370C2×C4—101no—
371C2×C4—301no—
372C2×C4—602no—
373C2×C4—602no—
374C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
375C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
376C8—202no—
377C8—602no—
378C2×C3—41no—
379C2×C3#6576711yescharacteristic
380C2×C3#6577711yescharacteristic
381C2×C3#6579311yescharacteristic
382D3—81no—
383D3—401no—
384C5#7050411yescharacteristic, complemented, Sylow
385C22—21no—
386C22—21no—
387C22—21no—
388C22—121no—
389C22—121no—
390C22—121no—
391C22—601no—
392C22—601no—
393C22—601no—
394C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
395C4—21no—
396C4—21no—
397C4—51no—
398C4—51no—
399C4—52no—
400C4—101no—
401C4—101no—
402C4—121no—
403C4—601no—
404C3#1060448811yescharacteristic, complemented, Sylow
405C2—41no—
406C2—241no—
407C2—1201no—
408C2#1175170511yescharacteristic
409C2#1175170711yescharacteristic
410C2#1175200811yescharacteristic
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 radical#11754330C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1557
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752416C2semidirect
3. C3×#65758C2semidirect
4. #11746510C2semidirect
5. #11746508C2semidirect
26. #65758D3semidirect
325. C3×C5#1557semidirect
384. C5#70504semidirect
404. C3#10604488semidirect

Maximal subgroups

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

subgroupindex
#117543302
#117524162
C3×#657582
#117465102
#117465082
#106044883
#705045