Finite Group Databasebeta

← #14282269

Subgroups — #14282269

Order 1920.

532 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 100 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#11753400C211yesmaximal, characteristic
2#11751922C211yesmaximal, characteristic, complemented
3C4×#6740C211yesmaximal, characteristic, complemented
4#11746742C211yesmaximal, characteristic, complemented
5C3×#64871C211yesmaximal, characteristic, complemented
6#11746493C211yesmaximal, characteristic, complemented
7#11746492C211yesmaximal, characteristic, complemented
8#10604441—31nomaximal, Hall
9C2×#6766C411yescharacteristic
10C2×#6740—21no—
11C2×#6740—21no—
12#91781C411yescharacteristic
13C5×#887C411yescharacteristic
14C3×#4039C2211yescharacteristic
15#91444—21no—
16Dic3×D20C411yescharacteristic
17C4×#1200C2211yescharacteristic
18#91395—21no—
19#91394—21no—
20C4×D5×Dic3—21no—
21Dic5×Dic6C2211yescharacteristic
22C4⋊(C3⋊#170)C2211yescharacteristic
23C4×C3⋊#170C2211yescharacteristic
24C3×C4⋊#170C2211yescharacteristic
25C3×C4×#170C2211yescharacteristic
26Dic3⋊#170—21no—
27#91169—21no—
28#68174—51nomaximal, Hall
29C4×#713—31no—
30#65681—31no—
31C4×#700—31no—
32Q8⋊#170—31no—
33Q8⋊#170—31no—
34#64871—31no—
35#64871D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×C5×Dic6C2×C411yescharacteristic
38C2×C3×D20C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1202—21no—
41C2×#1200D411yescharacteristic
42C2×#1200D411yescharacteristic
43C2×D5×Dic3—21no—
44C2×D5×Dic3—21no—
45#6766—22no—
46#6766—22no—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170—21no—
51#6740—24no—
52#6740—42no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54#6714—21no—
55C4⋊Dic15C2×C411yescharacteristic
56C4×Dic15—21no—
57C5×Dic3⋊C4—21no—
58C4×C5×Dic3—21no—
59C4×C5×Dic3C2×C411yescharacteristic
60C3×#685—21no—
61C3×C4×Dic5C2311yescharacteristic
62Dic3⋊Dic5—21no—
63#6665—21no—
64Dic3×Dic5—21no—
65Dic3×Dic5D411yescharacteristic
66Dic3×Dic5D411yescharacteristic
67C4×#237—51no—
68#4837—51no—
69C4×ΓL(1,𝔽25)—51no—
70C3×D4⋊C8—51no—
71D4⋊(C3⋊C8)—51no—
72#4484—51no—
73#4456—51no—
74C2×#713—31no—
75C2×#700—61no—
76C2×#700—61no—
77C4×C5×Q8—31no—
78Q8×Dic5—31no—
79#4039—61no—
80#4039C2×D311yescharacteristic
81#4038—31no—
82#4038—61no—
83C4×D20—31no—
84C4×D20—61no—
85C42×D5—31no—
86C42×D5—61no—
87#4002—61no—
88C4⋊#170—31no—
89C4⋊#170—61no—
90C4⋊#170C2×D311yescharacteristic
91C4×#170—31no—
92C4×#170C2×D311yescharacteristic
93#1489—151noSylow
94C22×D15C22⋊C411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15C22⋊C411yescharacteristic
100C4×D15—21no—
101C4×D15—21no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3C22⋊C411yescharacteristic
104C2×C5×Dic3C22⋊C411yescharacteristic
105C5×Dic6—21no—
106C5×Dic6M1612yescomplemented
107C2×C3×Dic5C2×D411yescharacteristic
108C2×C3×Dic5C2×D411yescharacteristic
109C3×D20—21no—
110C3×D20M1612yescomplemented
111C3×C4×D5—41no—
112C3×C4×D5—41no—
113#1202—24no—
114#1200—21no—
115#1200—21no—
116#1200—22no—
117D5×Dic3—24no—
118D5×Dic3—42no—
119C3⋊#170—22no—
120C3⋊#170—41no—
121C3×#170—22no—
122C3×#170—41no—
123C2×#237—51no—
124C3×C4×D4—51no—
125D4×Dic3—51no—
126C4×#67—101no—
127C2×C4×Dic3—101no—
128C2×ΓL(1,𝔽25)—101no—
129C2×ΓL(1,𝔽25)—101no—
130#892—51no—
131#887AGL(1,𝔽5)11yescharacteristic
132#67⋊C4—101no—
133#877—101no—
134C42×D3—51no—
135C4×Dic6—51no—
136C3×C4⋊C8—51no—
137C3×C4×C8—51no—
138#815—101no—
139Dic3⋊C8—101no—
140C4⋊(C3⋊C8)—51no—
141C4×C3⋊C8—51no—
142C2×C5×Q8—31no—
143#713—62no—
144#713—62no—
145C2×D20—61no—
146C2×D20C4×D311yescharacteristic
147C2×C4×D5—21no—
148C2×C4×D5—31no—
149C2×C4×D5—31no—
150C2×C4×D5—31no—
151C2×C4×D5—61no—
152C2×C4×D5—61no—
153C2×#170—21no—
154C2×#170—21no—
155C2×#170—61no—
156C2×#170—61no—
157#700—64no—
158#700—122no—
159C5×C4⋊C4—61no—
160C5×C4⋊C4C4×D311yescharacteristic
161C42×C5—31no—
162C42×C5—61no—
163#685—21no—
164#685—61no—
165#685—61no—
166C4⋊Dic5—31no—
167C4⋊Dic5—61no—
168C4×Dic5—31no—
169C4×Dic5—31no—
170C4×Dic5—61no—
171C4×Dic5—61no—
172C4×Dic5C22×D311yescharacteristic
173C4×#41—151no—
174#423—151no—
175C4×M16—151no—
176Q8⋊C8—151no—
177Q8⋊C8—151no—
178D4⋊C8—51no—
179D4⋊C8—151no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C2×D15—21no—
182C2×D15—21no—
183C2×D15—21no—
184C2×C3×D5—22no—
185C2×C3×D5—41no—
186C2×C3×D5—41no—
187C3×C4×C5—41no—
188C3×C4×C5C2×M1611yescharacteristic
189C3×C4×C5C2×M1611yescharacteristic
190Dic15—21no—
191Dic15—41no—
192C3×Dic5—21no—
193C3×Dic5AGL(1,ℤ/8)11yescharacteristic
194C3×Dic5#13711yescharacteristic
195C5×Dic3—22no—
196C5×Dic3—21no—
197C5×Dic3#10412yes—
198C2×C3×D4—51no—
199C22×C3×C4—101no—
200C2×#67—101no—
201C22×Dic3—101no—
202C22×Dic3—101no—
203#237—102no—
204#237—102no—
205C2×C4×D3—51no—
206C2×C4×D3—51no—
207C2×C4×D3—51no—
208C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
209C2×C3×C8—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
212C3×C22⋊C4—101no—
213C3×C42—51no—
214#217—101no—
215(C2×D3)⋊C4—101no—
216C4⋊Dic3—51no—
217Dic3⋊C4—21no—
218Dic3⋊C4—101no—
219C4×Dic3—21no—
220C4×Dic3—51no—
221C4×Dic3—51no—
222C4×Dic3—101no—
223C4×Dic3—101no—
224C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227ΓL(1,𝔽25)—104no—
228ΓL(1,𝔽25)—202no—
229C22×D5—21no—
230C22×D5—31no—
231C5×Q8—32no—
232C5×Q8—61no—
233C2×C4×C5—21no—
234C2×C4×C5—31no—
235C2×C4×C5—31no—
236C2×C4×C5—61no—
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×Dic5—31no—
239C2×Dic5—61no—
240C2×Dic5D3×D411yescharacteristic
241C2×Dic5D3×D411yescharacteristic
242D20—21no—
243D20—64no—
244D20ΓL(1,𝔽25)12yescomplemented
245C4×D5—41no—
246C4×D5—41no—
247C4×D5—62no—
248C4×D5—64no—
249C4×D5—61no—
250C4×D5—61no—
251C4×D5—61no—
252C4×D5—61no—
253C4×D5—122no—
254#170—22no—
255#170—41no—
256#170—62no—
257#170—121no—
258C2×#41—151no—
259C2×M16—301no—
260C2×M16—301no—
261C4×Q8—31no—
262C4×Q8—151no—
263C4×D4—51no—
264C4×D4—151no—
265C4×D4—301no—
266C4×D4—301no—
267#117—151no—
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—41no—
281C3×D5—42no—
282C23×C3—101no—
283C22×D3—51no—
284C3×D4—52no—
285C3×D4—101no—
286C2×C3×C4—21no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—201no—
290C2×C3×C4—201no—
291C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
292#67—104no—
293C2×Dic3—21no—
294C2×Dic3—51no—
295C2×Dic3—104no—
296C2×Dic3—101no—
297C2×Dic3—202no—
298C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
299C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
300C4×D3—101no—
301C4×D3—101no—
302C4×D3—101no—
303C4×D3—101no—
304C4×D3—102no—
305Dic6—21no—
306Dic6#70012yescomplemented
307C3×C8—102no—
308C3×C8—201no—
309C3⋊C8—102no—
310C3⋊C8—201no—
311C22×C5D3×C22⋊C411yescharacteristic
312C2×D5—22no—
313C2×D5—41no—
314C2×D5—41no—
315C2×D5—61no—
316C2×D5—61no—
317C2×D5—61no—
318C4×C5—32no—
319C4×C5—41no—
320C4×C5—62no—
321C4×C5—61no—
322C4×C5C2×ΓL(1,𝔽25)11yescharacteristic
323C4×C5D3×M1611yescharacteristic
324Dic5—21no—
325Dic5—61no—
326Dic5—121no—
327Dic5#91111yescharacteristic
328Dic5#91511yescharacteristic
329#41—302no—
330#41—302no—
331C2×Q8—31no—
332C2×D4—51no—
333C2×D4—301no—
334C22×C4—101no—
335C22×C4—151no—
336C22×C4—151no—
337C22×C4—151no—
338C22×C4—301no—
339C22×C4—301no—
340M16—304no—
341M16—602no—
342C2×C8—101no—
343C2×C8—101no—
344C2×C8—301no—
345C2×C8—301no—
346C4⋊C4—61no—
347C4⋊C4—151no—
348C4⋊C4—301no—
349C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
350C22⋊C4—101no—
351C22⋊C4—301no—
352C22⋊C4—301no—
353C42—31no—
354C42—51no—
355C42—61no—
356C42—151no—
357C42—151no—
358C42—301no—
359C42—301no—
360C3×C5#148911yescharacteristic, complemented, Hall
361C22×C3—102no—
362C22×C3—201no—
363C22×C3—201no—
364C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
365C2×D3—101no—
366C2×D3—101no—
367C2×D3—101no—
368C3×C4—41no—
369C3×C4—51no—
370C3×C4—51no—
371C3×C4—101no—
372C3×C4C2×#70011yescharacteristic
373C3×C4D5⋊M1611yescharacteristic
374Dic3—21no—
375Dic3—22no—
376Dic3—101no—
377Dic3—201no—
378Dic3#401012yes—
379C2×C5#472611yescharacteristic
380C2×C5#477111yescharacteristic
381C2×C5D3×#10411yescharacteristic
382D5—42no—
383D5—121no—
384C23—101no—
385C23—151no—
386Q8—32no—
387Q8—61no—
388D4—52no—
389D4—101no—
390D4—304no—
391C2×C4—21no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—61no—
397C2×C4—151no—
398C2×C4—201no—
399C2×C4—201no—
400C2×C4—302no—
401C2×C4—301no—
402C2×C4—301no—
403C2×C4—304no—
404C2×C4—301no—
405C2×C4—301no—
406C2×C4—301no—
407C2×C4—602no—
408C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
409C8—102no—
410C8—201no—
411C8—302no—
412C8—601no—
413C2×C3—202no—
414C2×C3#6575611yescharacteristic
415C2×C3C2×#401011yescharacteristic
416C2×C3#6579311yescharacteristic
417D3—201no—
418C5#6817411yescharacteristic, complemented, Sylow
419C22—102no—
420C22—201no—
421C22—201no—
422C22—301no—
423C22—301no—
424C22—301no—
425C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
426C4—32no—
427C4—41no—
428C4—51no—
429C4—51no—
430C4—61no—
431C4—62no—
432C4—101no—
433C4—301no—
434C4—601no—
435C4D3×#70011yescharacteristic
436C4D5⋊ΓL(1,𝔽25)11yescharacteristic
437C3#1060444111yescharacteristic, complemented, Sylow
438C2—202no—
439C2—601no—
440C2#1175180211yescharacteristic
441C2#1175193711yescharacteristic
442C2D3×#401011yescharacteristic
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×#6766C4
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. #11751922C2semidirect
3. C4×#6740C2semidirect
4. #11746742C2semidirect
5. C3×#64871C2semidirect
6. #11746493C2semidirect
7. #11746492C2semidirect
35. #64871D3semidirect
106. C5×Dic6M16semidirect
110. C3×D20M16semidirect
244. D20ΓL(1,𝔽25)semidirect
306. Dic6#700semidirect
360. C3×C5#1489semidirect
418. C5#68174semidirect
437. C3#10604441semidirect

Maximal subgroups

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

subgroupindex
#117534002
#117519222
C4×#67402
#117467422
C3×#648712
#117464932
#117464922
#106044413
#681745