Finite Group Databasebeta

← #14285011

Subgroups — #14285011

Order 1920.

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

normal subgroups only

This group has 432 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#11753466C211yesmaximal, characteristic
2#11751923C211yesmaximal, characteristic
3#11751884C211yesmaximal, characteristic
4#11746744C211yesmaximal, characteristic, complemented
5C3×#64873C211yesmaximal, characteristic, complemented
6#11746511C211yesmaximal, characteristic, complemented
7#11746511C211yesmaximal, characteristic, complemented
8#10604444—31nomaximal, Hall
9C2×#6740—21no—
10C2×#6738—21no—
11#91786C411yescharacteristic
12C5×#887C411yescharacteristic
13C3×#4034C2211yescharacteristic
14#91411—21no—
15#91403—21no—
16C4×#1200C2211yescharacteristic
17#91383C411yescharacteristic
18#91376C2211yescharacteristic
19#91340C411yescharacteristic
20#91334—21no—
21Dic3×Dic10—21no—
22#91233C2211yescharacteristic
23#91233C2211yescharacteristic
24C3×#4004C2211yescharacteristic
25C3×#4004C2211yescharacteristic
26#91177—21no—
27Dic3⋊#170—21no—
28#68423—51nomaximal, Hall
29#65912—31no—
30#65682—31no—
31D5⋊(C4⋊C8)—31no—
32#64931—31no—
33#64931—31no—
34#64873—31no—
35#64873D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×Dic30C2×C411yescharacteristic
38C2×C5×Dic6C2×C411yescharacteristic
39C2×C3×Dic10—21no—
40C2×#1200D411yescharacteristic
41C2×#1200D411yescharacteristic
42C2×C3⋊#170—21no—
43C2×C3⋊#170—21no—
44C2×C3×#170—21no—
45C2×C3×#170—21no—
46#6740—42no—
47#6738—42no—
48C3×C5×C4⋊C4C2×C411yescharacteristic
49#6714—21no—
50C4⋊Dic15—21no—
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C4×C5×Dic3C2×C411yescharacteristic
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5C2311yescharacteristic
57#6669—21no—
58#6668—21no—
59#6668—21no—
60#6668—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5D411yescharacteristic
64Dic3×Dic5D411yescharacteristic
65#5728—51no—
66#4837—51no—
67D3×C4⋊C8—51no—
68C3×#332—51no—
69#4547—51no—
70#4481—51no—
71#4481—51no—
72C2×#700—61no—
73C2×D5⋊C8—61no—
74C4×C5×Q8—31no—
75#4092—31no—
76#4090—31no—
77#4043—31no—
78#4042—61no—
79#4035—61no—
80#4034C2×D311yescharacteristic
81#4018—61no—
82C42×D5—31no—
83C4×Dic10—31no—
84C4×Dic10—61no—
85#4004—31no—
86#4004—31no—
87#4004—61no—
88#4004C2×D311yescharacteristic
89#4004C2×D311yescharacteristic
90C4⋊#170—61no—
91#1550—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15C22⋊C411yescharacteristic
97C4×D15—41no—
98Dic30—41no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C5×Dic6—41no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5C2×D411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×Dic10—41no—
107C3×Dic10—41no—
108#1200—21no—
109#1200—21no—
110#1200SD1612yes—
111#1200Q1612yes—
112C3⋊#170—41no—
113C3⋊#170—41no—
114C3×#170—41no—
115C3×#170—41no—
116C3×C4⋊Q8—51no—
117#946—101no—
118Q8×Dic3—101no—
119C2×ΓL(1,𝔽25)—101no—
120C2×D3×C8—101no—
121#897—51no—
122#897—51no—
123#892—101no—
124#890—101no—
125#887—51no—
126#887AGL(1,𝔽5)11yescharacteristic
127C42×D3—51no—
128#869—51no—
129C3×C4⋊C8—51no—
130C3×C4⋊C8—51no—
131Dic3⋊C8—101no—
132Dic3⋊C8—101no—
133C4⋊(C3⋊C8)—51no—
134C4⋊(C3⋊C8)—51no—
135C2×C5×Q8—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×Dic10—21no—
140C2×Dic10—31no—
141C2×#170—21no—
142C2×#170—21no—
143C2×#170—61no—
144C2×#170—61no—
145#700—122no—
146D5⋊C8—122no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4C4×D311yescharacteristic
149C42×C5—31no—
150C42×C5—61no—
151#685—61no—
152#685—61no—
153C4⋊Dic5—61no—
154C4⋊Dic5C4×D311yescharacteristic
155#683—21no—
156#683—61no—
157#683—61no—
158#683—61no—
159#683—61no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—61no—
163C4×Dic5C22×D311yescharacteristic
164#533—151no—
165#423—151no—
166C2×C4⋊C8—151no—
167#333—151no—
168#333—151no—
169#332—51no—
170#332—151no—
171C22×C3×C5C2×C22⋊C411yescharacteristic
172C2×D15—21no—
173C2×D15—21no—
174C2×D15#10312yes—
175C3×C4×C5—21no—
176C3×C4×C5—41no—
177Dic15—21no—
178Dic15—41no—
179C3×Dic5—41no—
180C3×Dic5C2×SD1611yescharacteristic
181C3×Dic5C2×Q1611yescharacteristic
182C3×Dic5AGL(1,ℤ/8)11yescharacteristic
183C3×Dic5#13711yescharacteristic
184C5×Dic3—21no—
185C5×Dic3—41no—
186C5×Dic3#10312yes—
187C2×C3×Q8—101no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×C4×D3—51no—
191C2×Dic6—51no—
192C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
193C2×C3×C8—101no—
194C2×C3×C8—101no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
198C3×C42—51no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201C4⋊Dic3—101no—
202C4⋊Dic3—101no—
203C4⋊Dic3—101no—
204C4⋊Dic3—101no—
205Dic3⋊C4—21no—
206Dic3⋊C4—101no—
207C4×Dic3—21no—
208C4×Dic3—51no—
209C4×Dic3—51no—
210C4×Dic3—101no—
211C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214ΓL(1,𝔽25)—202no—
215D3×C8—202no—
216C22×D5—31no—
217C5×Q8—121no—
218C2×C4×C5—21no—
219C2×C4×C5—31no—
220C2×C4×C5—31no—
221C2×C4×C5—61no—
222C2×C4×C5C2×C4×D311yescharacteristic
223C2×Dic5—21no—
224C2×Dic5—31no—
225C2×Dic5—61no—
226C2×Dic5D3×D411yescharacteristic
227C2×Dic5D3×D411yescharacteristic
228C4×D5—32no—
229C4×D5—32no—
230C4×D5—61no—
231C4×D5—61no—
232C4×D5—121no—
233Dic10—41no—
234Dic10—41no—
235Dic10—121no—
236#170—41no—
237#170—41no—
238#170—121no—
239#170—121no—
240C2×M16—301no—
241C22×C8—301no—
242C4⋊Q8—51no—
243C4⋊Q8—151no—
244#125—301no—
245C22⋊Q8—151no—
246C22⋊Q8—151no—
247C22⋊Q8—301no—
248C4×Q8—31no—
249C4×Q8—151no—
250C4×Q8—301no—
251#117—301no—
252C2×C42—151no—
253C4⋊C8—51no—
254C4⋊C8—51no—
255C4⋊C8—151no—
256C4⋊C8—151no—
257C4⋊C8—301no—
258C4⋊C8—301no—
259C2×C3×C5#41311yescharacteristic
260C2×C3×C5C2×#10311yescharacteristic
261C2×C3×C5#41711yescharacteristic
262D15—22no—
263C22×D3—51no—
264C3×Q8—201no—
265C3×Q8—201no—
266C2×C3×C4—21no—
267C2×C3×C4—51no—
268C2×C3×C4—51no—
269C2×C3×C4—101no—
270C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—51no—
273C2×Dic3—101no—
274C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
275C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
276C4×D3—52no—
277C4×D3—52no—
278C4×D3—101no—
279C4×D3—101no—
280C4×D3—201no—
281Dic6—41no—
282Dic6—201no—
283C3×C8—201no—
284C3×C8—201no—
285C3⋊C8—201no—
286C3⋊C8—201no—
287C22×C5D3×C22⋊C411yescharacteristic
288C2×D5—32no—
289C2×D5—61no—
290C2×D5—61no—
291C4×C5—21no—
292C4×C5—32no—
293C4×C5—41no—
294C4×C5—61no—
295C4×C5—121no—
296Dic5—41no—
297Dic5—61no—
298Dic5—121no—
299Dic5#91111yescharacteristic
300Dic5D3×SD1611yescharacteristic
301Dic5#91511yescharacteristic
302Dic5D3×Q1611yescharacteristic
303C2×Q8—31no—
304C2×Q8—101no—
305C2×Q8—151no—
306C22×C4—151no—
307C22×C4—151no—
308C22×C4—151no—
309M16—602no—
310C2×C8—101no—
311C2×C8—101no—
312C2×C8—301no—
313C2×C8—301no—
314C2×C8—602no—
315C4⋊C4—51no—
316C4⋊C4—61no—
317C4⋊C4—101no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
324C22⋊C4—301no—
325C22⋊C4—301no—
326C42—31no—
327C42—51no—
328C42—61no—
329C42—151no—
330C42—151no—
331C42—301no—
332C3×C5#155011yescharacteristic, complemented, Hall
333C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
334C2×D3—52no—
335C2×D3—101no—
336C2×D3—101no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—51no—
340C3×C4—51no—
341C3×C4—51no—
342C3×C4—51no—
343C3×C4—201no—
344Dic3—21no—
345Dic3—41no—
346Dic3—101no—
347Dic3—201no—
348Dic3#400912yes—
349C2×C5#475111yescharacteristic
350C2×C5#477111yescharacteristic
351C2×C5D3×#10311yescharacteristic
352D5—62no—
353C23—151no—
354Q8—121no—
355Q8—201no—
356Q8—201no—
357Q8—601no—
358C2×C4—21no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—61no—
364C2×C4—101no—
365C2×C4—152no—
366C2×C4—152no—
367C2×C4—151no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4—301no—
371C2×C4—601no—
372C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
373C8—201no—
374C8—201no—
375C8—601no—
376C8—601no—
377C2×C3#6576111yescharacteristic
378C2×C3C2×#400911yescharacteristic
379C2×C3#6579311yescharacteristic
380D3—102no—
381C5#6842311yescharacteristic, complemented, Sylow
382C22—152no—
383C22—301no—
384C22—301no—
385C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
386C4—21no—
387C4—32no—
388C4—41no—
389C4—51no—
390C4—51no—
391C4—51no—
392C4—51no—
393C4—61no—
394C4—121no—
395C4—201no—
396C4—301no—
397C4—601no—
398C3#1060444411yescharacteristic, complemented, Sylow
399C2—302no—
400C2#1175191711yescharacteristic
401C2#1175193711yescharacteristic
402C2D3×#400911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1550
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746744C2semidirect
5. C3×#64873C2semidirect
6. #11746511C2semidirect
7. #11746511C2semidirect
35. #64873D3semidirect
332. C3×C5#1550semidirect
381. C5#68423semidirect
398. C3#10604444semidirect

Maximal subgroups

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

subgroupindex
#117534662
#117519232
#117518842
#117467442
C3×#648732
#117465112
#106044443
#684235