Finite Group Databasebeta

← #14282274

Subgroups — #14282274

Order 1920.

532 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 96 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#11753408C211yesmaximal, characteristic
2#11751921C211yesmaximal, characteristic, complemented
3C4×#6739C211yesmaximal, characteristic, complemented
4#11746743C211yesmaximal, characteristic, complemented
5C3×#64872C211yesmaximal, characteristic, complemented
6#11746491C211yesmaximal, characteristic, complemented
7#11746490C211yesmaximal, characteristic, complemented
8#10604362—31nomaximal, Hall
9C2×#6769C411yescharacteristic
10C2×#6739—21no—
11C2×#6739—21no—
12#91782C411yescharacteristic
13C5×#892C411yescharacteristic
14C3×#4033C2211yescharacteristic
15#91418C2211yescharacteristic
16#91406—21no—
17#91405—21no—
18#91403—21no—
19C4×#1200—21no—
20C4×D3×Dic5C2211yescharacteristic
21#91331C411yescharacteristic
22C4⋊(C3⋊#170)C2211yescharacteristic
23C4×C3⋊#170C2211yescharacteristic
24C3×C4⋊#170C2211yescharacteristic
25C3×C4×#170C2211yescharacteristic
26#91177—21no—
27#91169—21no—
28#68238—51nomaximal, Hall
29#65856—31no—
30#65758—31no—
31C4×#704—31no—
32#64872—31no—
33#64872D311yescharacteristic, complemented
34#64871—31no—
35#64871—31no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15—21no—
38C2×C4×C5×D3C2×C411yescharacteristic
39C2×C3×Dic10C2×C411yescharacteristic
40C2×#1203—21no—
41C2×#1200—21no—
42C2×#1200—21no—
43C2×D3×Dic5D411yescharacteristic
44C2×D3×Dic5D411yescharacteristic
45#6769—22no—
46#6769—22no—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170—21no—
51#6739—24no—
52#6739—42no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54#6714—21no—
55C4×Dic15C2×C411yescharacteristic
56C5×(C2×D3)⋊C4—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic
58C4×C5×Dic3—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5C2311yescharacteristic
62#6668—21no—
63#6667—21no—
64Dic3×Dic5—21no—
65Dic3×Dic5D411yescharacteristic
66Dic3×Dic5D411yescharacteristic
67C4×#239—51no—
68#4837—51no—
69C4×ΓL(1,𝔽25)—51no—
70C3×Q8⋊C8—51no—
71#4535—51no—
72#4483—51no—
73#4459—51no—
74C2×#709—31no—
75C2×#704—61no—
76C2×#704—61no—
77C5×#117—31no—
78C2×C4×Dic5—31no—
79#4039—31no—
80#4039—31no—
81#4033—31no—
82#4033C2×D311yescharacteristic
83#4027—61no—
84#4027—61no—
85#4018—61no—
86C42×D5—61no—
87#4004—61no—
88#4002—61no—
89C4⋊#170—31no—
90C4⋊#170C2×D311yescharacteristic
91C4×#170—31no—
92C4×#170C2×D311yescharacteristic
93#1489—151noSylow
94C22×D15—21no—
95C22×C5×D3C22⋊C411yescharacteristic
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C2×Dic15C22⋊C411yescharacteristic
100D60—21no—
101D60M1612yescomplemented
102C4×D15—42no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3C22⋊C411yescharacteristic
105C4×C5×D3—21no—
106C4×C5×D3—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5C2×D411yescharacteristic
109C2×C3×Dic5C2×D411yescharacteristic
110C3×Dic10—21no—
111C3×Dic10M1612yescomplemented
112#1203—24no—
113#1200—24no—
114#1200—41no—
115#1200—41no—
116D3×Dic5—22no—
117D3×Dic5—21no—
118D3×Dic5—21no—
119C3⋊#170—22no—
120C3⋊#170—41no—
121C3×#170—22no—
122C3×#170—41no—
123C2×#239—51no—
124C3×C4×Q8—51no—
125Q8×Dic3—51no—
126C2×ΓL(1,𝔽25)—101no—
127C2×ΓL(1,𝔽25)—101no—
128#893—51no—
129#893—101no—
130#892—101no—
131#892AGL(1,𝔽5)11yescharacteristic
132C4×D12—51no—
133C4×D12—101no—
134C42×D3—51no—
135C42×D3—101no—
136C3×C4⋊C8—51no—
137C3×C4×C8—51no—
138#815—101no—
139Dic3⋊C8—101no—
140C4⋊(C3⋊C8)—51no—
141C4×C3⋊C8—51no—
142C22×C4×C5—31no—
143C2×C22⋊D5—61no—
144C22×Dic5—31no—
145C22×Dic5—31no—
146#709—62no—
147#709—62no—
148C2×D20—31no—
149C2×C4×D5—61no—
150C2×C4×D5—61no—
151C2×C4×D5—61no—
152C2×Dic10C4×D311yescharacteristic
153#704—64no—
154#704—122no—
155C2×#170—21no—
156C2×#170—21no—
157C2×#170—61no—
158C2×#170—61no—
159C5×C4⋊C4—31no—
160C5×C4⋊C4C4×D311yescharacteristic
161C5×C22⋊C4—61no—
162C42×C5—61no—
163#685—61no—
164#685—61no—
165#683—21no—
166#683—61no—
167C4×Dic5—21no—
168C4×Dic5—31no—
169C4×Dic5—31no—
170C4×Dic5—31no—
171C4×Dic5—61no—
172C4×Dic5C22×D311yescharacteristic
173C4×#41—151no—
174#423—151no—
175C4×M16—151no—
176Q8⋊C8—51no—
177Q8⋊C8—151no—
178D4⋊C8—151no—
179D4⋊C8—151no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C2×D15—22no—
182C2×D15—41no—
183C2×D15—41no—
184C2×C5×D3—21no—
185C2×C5×D3—21no—
186C2×C5×D3—21no—
187C3×C4×C5—41no—
188C3×C4×C5C2×M1611yescharacteristic
189C3×C4×C5C2×M1611yescharacteristic
190Dic15—21no—
191Dic15#10412yes—
192C3×Dic5—22no—
193C3×Dic5—21no—
194C3×Dic5AGL(1,ℤ/8)11yescharacteristic
195C3×Dic5#13711yescharacteristic
196C5×Dic3—21no—
197C5×Dic3—41no—
198C2×C3×Q8—51no—
199#239—102no—
200#239—102no—
201C2×D12—51no—
202C2×D12—101no—
203C2×C4×D3—51no—
204C2×C4×D3—51no—
205C2×C4×D3—101no—
206C2×C4×D3—101no—
207C2×C4×D3—101no—
208C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
209C2×C3×C8—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4—101no—
212C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
213C3×C42—51no—
214C3×C42—101no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—101no—
217(C2×D3)⋊C4—101no—
218C4⋊Dic3—101no—
219C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
220C4×Dic3—21no—
221C4×Dic3—51no—
222C4×Dic3—51no—
223C4×Dic3—51no—
224C4×Dic3—101no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227ΓL(1,𝔽25)—104no—
228ΓL(1,𝔽25)—202no—
229C23×C5—31no—
230C22×D5—61no—
231C2×C4×C5—21no—
232C2×C4×C5—31no—
233C2×C4×C5—61no—
234C2×C4×C5—61no—
235C2×C4×C5—61no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C22⋊D5—64no—
238C2×Dic5—21no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—62no—
242C2×Dic5—61no—
243C2×Dic5—61no—
244C2×Dic5D3×D411yescharacteristic
245C2×Dic5D3×D411yescharacteristic
246D20—32no—
247D20—61no—
248C4×D5—64no—
249C4×D5—122no—
250C4×D5—121no—
251C4×D5—121no—
252Dic10—21no—
253Dic10ΓL(1,𝔽25)12yescomplemented
254#170—22no—
255#170—41no—
256#170—62no—
257#170—121no—
258C2×#41—151no—
259C2×M16—301no—
260C2×M16—301no—
261C4×Q8—51no—
262C4×Q8—151no—
263C4×D4—151no—
264C4×D4—151no—
265C4×D4—301no—
266C4×D4—301no—
267#117—31no—
268#117—301no—
269C2×C42—151no—
270C2×C42—301no—
271C4⋊C8—51no—
272C4⋊C8—151no—
273C4⋊C8—301no—
274#97—301no—
275C4×C8—51no—
276C4×C8—151no—
277C2×C3×C5#40711yescharacteristic
278C2×C3×C5#41711yescharacteristic
279C2×C3×C5C2×#10411yescharacteristic
280D15—42no—
281C5×D3—41no—
282C22×D3—101no—
283C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
284C3×Q8—52no—
285C3×Q8—101no—
286C2×C3×C4—21no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—101no—
290C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—51no—
293C2×Dic3—51no—
294C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
295D12—52no—
296D12—104no—
297D12—101no—
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—104no—
301C4×D3—102no—
302C4×D3—101no—
303C4×D3—101no—
304C4×D3—201no—
305C4×D3—201no—
306C4×D3—202no—
307C3×C8—102no—
308C3×C8—201no—
309C3⋊C8—102no—
310C3⋊C8—201no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5—61no—
314C22×C5D3×C22⋊C411yescharacteristic
315C2×D5—62no—
316C2×D5—121no—
317C2×D5—121no—
318C4×C5—41no—
319C4×C5—61no—
320C4×C5—121no—
321C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
322C4×C5D3×M1611yescharacteristic
323Dic5—22no—
324Dic5—21no—
325Dic5—32no—
326Dic5—61no—
327Dic5#91411yescharacteristic
328Dic5#91811yescharacteristic
329#41—302no—
330#41—302no—
331C2×Q8—51no—
332C2×D4—151no—
333C2×D4—301no—
334C22×C4—31no—
335C22×C4—151no—
336C22×C4—151no—
337C22×C4—301no—
338C22×C4—301no—
339C22×C4—301no—
340M16—304no—
341M16—602no—
342C2×C8—101no—
343C2×C8—101no—
344C2×C8—301no—
345C2×C8—301no—
346C4⋊C4—31no—
347C4⋊C4—101no—
348C4⋊C4—301no—
349C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
350C22⋊C4—61no—
351C22⋊C4—301no—
352C22⋊C4—301no—
353C42—51no—
354C42—61no—
355C42—101no—
356C42—151no—
357C42—151no—
358C42—151no—
359C42—301no—
360C3×C5#148911yescharacteristic, complemented, Hall
361C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
362C2×D3—21no—
363C2×D3—21no—
364C2×D3—21no—
365C2×D3—102no—
366C2×D3—201no—
367C2×D3—201no—
368C3×C4—41no—
369C3×C4—51no—
370C3×C4—51no—
371C3×C4—101no—
372C3×C4—102no—
373C3×C4D5⋊M1611yescharacteristic
374C3×C4D5⋊M1611yescharacteristic
375Dic3—21no—
376Dic3—41no—
377Dic3—52no—
378Dic3—101no—
379C2×C5—121no—
380C2×C5#472611yescharacteristic
381C2×C5#480311yescharacteristic
382C2×C5D3×#10411yescharacteristic
383D5—122no—
384C23—31no—
385C23—301no—
386Q8—52no—
387Q8—101no—
388D4—152no—
389D4—304no—
390D4—301no—
391C2×C4—21no—
392C2×C4—31no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—101no—
399C2×C4—151no—
400C2×C4—151no—
401C2×C4—301no—
402C2×C4—301no—
403C2×C4—304no—
404C2×C4—302no—
405C2×C4—602no—
406C2×C4—601no—
407C2×C4—601no—
408C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
409C8—102no—
410C8—201no—
411C8—302no—
412C8—601no—
413C2×C3#6575511yescharacteristic
414C2×C3D5⋊#10411yescharacteristic
415C2×C3#6579311yescharacteristic
416D3—41no—
417D3—202no—
418C5#6823811yescharacteristic, complemented, Sylow
419C22—61no—
420C22—61no—
421C22—61no—
422C22—302no—
423C22—601no—
424C22—601no—
425C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
426C4—41no—
427C4—51no—
428C4—51no—
429C4—61no—
430C4—102no—
431C4—101no—
432C4—121no—
433C4—152no—
434C4—301no—
435C4#9191511yescharacteristic
436C4D5⋊ΓL(1,𝔽25)11yescharacteristic
437C3#1060436211yescharacteristic, complemented, Sylow
438C2—121no—
439C2—602no—
440C2#1175191911yescharacteristic
441C2#1175193511yescharacteristic
442C2#1175196111yescharacteristic
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 radicalC2×#6769C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1489
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751921C2semidirect
3. C4×#6739C2semidirect
4. #11746743C2semidirect
5. C3×#64872C2semidirect
6. #11746491C2semidirect
7. #11746490C2semidirect
33. #64872D3semidirect
101. D60M16semidirect
111. C3×Dic10M16semidirect
253. Dic10ΓL(1,𝔽25)semidirect
360. C3×C5#1489semidirect
418. C5#68238semidirect
437. C3#10604362semidirect

Maximal subgroups

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

subgroupindex
#117534082
#117519212
C4×#67392
#117467432
C3×#648722
#117464912
#117464902
#106043623
#682385