Finite Group Databasebeta

← #14322237

Subgroups — #14322237

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#889C211yesmaximal, characteristic
2C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
3C3×#65711C211yesmaximal, characteristic
4#11751846C211yesmaximal, characteristic
5#11751845C211yesmaximal, characteristic
6#11751844C211yesmaximal, characteristic
7#11751840C211yesmaximal, characteristic
8#11751837C211yesmaximal, characteristic
9#11751833C211yesmaximal, characteristic
10#11751833C211yesmaximal, characteristic
11#11751833C211yesmaximal, characteristic
12#11751833C211yesmaximal, characteristic
13C4×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic
14#11751746C211yesmaximal, characteristic
15#11751745C211yesmaximal, characteristic
16AGL(1,𝔽5)×#125—31nomaximal, Hall
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
28C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
29C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
30C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
31C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
32C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
33#91778C411yescharacteristic, complemented
34C5×#889C411yescharacteristic, complemented
35C3×D5×C4⋊C4C2211yescharacteristic
36D5×C4⋊Dic3C2211yescharacteristic
37D5×Dic3⋊C4C2211yescharacteristic
38D5×Dic3⋊C4C2211yescharacteristic
39D5×Dic3⋊C4C2211yescharacteristic
40D5×Dic3⋊C4C2211yescharacteristic
41C4×D5×Dic3C2211yescharacteristic
42#91382C411yescharacteristic, complemented
43#91379C411yescharacteristic, complemented
44#91346C411yescharacteristic, complemented
45#91343C411yescharacteristic, complemented
46#91339C411yescharacteristic, complemented
47#91336C411yescharacteristic, complemented
48#91235C2211yescharacteristic
49#91235C2211yescharacteristic
50C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
51C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
52C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
53C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
54(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
55(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
56(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
57(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
58(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
59(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
60#74943—51nomaximal, Hall
61D5×#125—31no—
62#65712—31no—
63#65712—31no—
64#65711—31no—
65#65711—31no—
66#65711—31no—
67#65711D311yescharacteristic
68C4⋊C4×AGL(1,𝔽5)—31no—
69C4⋊C4×AGL(1,𝔽5)—31no—
70C4⋊C4×AGL(1,𝔽5)—31no—
71C4⋊C4×AGL(1,𝔽5)—31no—
72C4⋊C4×AGL(1,𝔽5)—31no—
73C4⋊C4×AGL(1,𝔽5)—31no—
74#65689—31no—
75C42×AGL(1,𝔽5)—31no—
76C22×ΓL(1,𝔽16)C2311yescharacteristic
77C22×ΓL(1,𝔽16)C2311yescharacteristic
78C22×ΓL(1,𝔽16)C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×C3×AGL(1,𝔽5)C2311yescharacteristic
81C22×C3×AGL(1,𝔽5)C2311yescharacteristic
82C22×C3×AGL(1,𝔽5)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C2×C3×C4×D5C2311yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×D5×Dic3C2311yescharacteristic
88C2×D5×Dic3C2311yescharacteristic
89C2×D5×Dic3C2311yescharacteristic
90C2×D5×Dic3C2311yescharacteristic
91C4⋊ΓL(1,𝔽16)—22no—
92C4×ΓL(1,𝔽16)—22no—
93C4×ΓL(1,𝔽16)—22no—
94C4×ΓL(1,𝔽16)—22no—
95C3×C4⋊AGL(1,𝔽5)—22no—
96C3×C4×AGL(1,𝔽5)—22no—
97Dic3⋊AGL(1,𝔽5)—22no—
98Dic3⋊AGL(1,𝔽5)—22no—
99Dic3⋊AGL(1,𝔽5)—22no—
100Dic3⋊AGL(1,𝔽5)—22no—
101Dic3×AGL(1,𝔽5)—22no—
102Dic3×AGL(1,𝔽5)—22no—
103Dic3×AGL(1,𝔽5)—22no—
104Dic3×AGL(1,𝔽5)—22no—
105Dic3×AGL(1,𝔽5)—22no—
106Dic3×AGL(1,𝔽5)Q814yes—
107C3×C5×C4⋊C4C2×C411yescharacteristic
108C4⋊Dic15C2×C411yescharacteristic
109#6712C2×C411yescharacteristic
110#6712C2×C411yescharacteristic
111#6712C2×C411yescharacteristic
112#6712C2×C411yescharacteristic
113C4×Dic15C2×C411yescharacteristic
114C5×C4⋊Dic3C2×C411yescharacteristic
115C5×Dic3⋊C4C2×C411yescharacteristic
116C5×Dic3⋊C4C2×C411yescharacteristic
117C5×Dic3⋊C4C2×C411yescharacteristic
118C5×Dic3⋊C4C2×C411yescharacteristic
119C4×C5×Dic3C2×C411yescharacteristic
120C3×C4⋊Dic5C2×C411yescharacteristic
121C3×#683C2×C411yescharacteristic
122C3×#683C2×C411yescharacteristic
123Dic3⋊Dic5C2×C411yescharacteristic
124Dic3⋊Dic5C2×C411yescharacteristic
125Dic3⋊Dic5C2×C411yescharacteristic
126Dic3⋊Dic5C2×C411yescharacteristic
127#6669C2×C411yescharacteristic
128#6669C2×C411yescharacteristic
129#6669C2×C411yescharacteristic
130#6669C2×C411yescharacteristic
131#6668C2×C411yescharacteristic
132#6668C2×C411yescharacteristic
133Dic3×Dic5C2×C411yescharacteristic
134Dic3×Dic5C2×C411yescharacteristic
135C2×#889—51no—
136C3×#387—51no—
137#4976—51no—
138Dic3×C4⋊C4—51no—
139Dic3×C4⋊C4—51no—
140#4933—51no—
141C42×Dic3—51no—
142#4655—51no—
143#4654—51no—
144#4650—51no—
145#4649—51no—
146#4649—51no—
147#4649—51no—
148#4649—51no—
149#4647—51no—
150C2×C4⋊AGL(1,𝔽5)—31no—
151C2×C4⋊AGL(1,𝔽5)—31no—
152C2×C4⋊AGL(1,𝔽5)—31no—
153C2×C4⋊AGL(1,𝔽5)—31no—
154C2×C4⋊AGL(1,𝔽5)—31no—
155C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
156C2×C4×AGL(1,𝔽5)—31no—
157C2×C4×AGL(1,𝔽5)—31no—
158C2×C4×AGL(1,𝔽5)—31no—
159C2×C4×AGL(1,𝔽5)—31no—
160C2×C4×AGL(1,𝔽5)—31no—
161C2×C4×AGL(1,𝔽5)—31no—
162C2×C4×AGL(1,𝔽5)—31no—
163C2×C4×AGL(1,𝔽5)—31no—
164C2×C4×AGL(1,𝔽5)—31no—
165C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
166C5×#125—31no—
167D5×C4⋊C4—31no—
168D5×C4⋊C4—31no—
169D5×C4⋊C4—31no—
170D5×C4⋊C4—31no—
171D5×C4⋊C4—31no—
172D5×C4⋊C4C2×D311yescharacteristic
173#4036—31no—
174#4036—31no—
175#4035—31no—
176#4035—31no—
177#4035—31no—
178#4035—31no—
179C42×D5—31no—
180#4016—31no—
181(C2×AGL(1,𝔽5))⋊C4—31no—
182(C2×AGL(1,𝔽5))⋊C4—31no—
183(C2×AGL(1,𝔽5))⋊C4—31no—
184(C2×AGL(1,𝔽5))⋊C4—31no—
185(C2×AGL(1,𝔽5))⋊C4—31no—
186(C2×AGL(1,𝔽5))⋊C4—31no—
187(C2×AGL(1,𝔽5))⋊C4—31no—
188(C2×AGL(1,𝔽5))⋊C4—31no—
189(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
190(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
191(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
192(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
193C4×#125—151noSylow
194C22×C3×D5C2411yescharacteristic
195C2×ΓL(1,𝔽16)—21no—
196C2×ΓL(1,𝔽16)—21no—
197C2×ΓL(1,𝔽16)—21no—
198C2×ΓL(1,𝔽16)—21no—
199C2×ΓL(1,𝔽16)—21no—
200C2×ΓL(1,𝔽16)—21no—
201C2×ΓL(1,𝔽16)—21no—
202C2×ΓL(1,𝔽16)—21no—
203C2×ΓL(1,𝔽16)C2×Q812yes—
204C2×ΓL(1,𝔽16)#4112yes—
205C2×ΓL(1,𝔽16)#4112yes—
206C2×ΓL(1,𝔽16)#4112yes—
207C2×C3×AGL(1,𝔽5)—21no—
208C2×C3×AGL(1,𝔽5)—21no—
209C2×C3×AGL(1,𝔽5)—21no—
210C2×C3×AGL(1,𝔽5)—21no—
211C2×C3×AGL(1,𝔽5)—21no—
212C2×C3×AGL(1,𝔽5)—21no—
213C2×C3×AGL(1,𝔽5)—21no—
214C2×C3×AGL(1,𝔽5)—21no—
215C2×C3×AGL(1,𝔽5)—21no—
216C2×C3×AGL(1,𝔽5)—21no—
217C2×C3×AGL(1,𝔽5)C2×Q812yes—
218C2×C3×AGL(1,𝔽5)#4112yes—
219C2×C3×C4×C5C22×C411yescharacteristic
220C2×C3×C4×C5C22×C411yescharacteristic
221C2×C3×C4×C5C22×C411yescharacteristic
222C2×Dic15C22×C411yescharacteristic
223C2×Dic15C22×C411yescharacteristic
224C2×Dic15C22×C411yescharacteristic
225C2×Dic15C22×C411yescharacteristic
226C2×C5×Dic3C22×C411yescharacteristic
227C2×C5×Dic3C22×C411yescharacteristic
228C2×C5×Dic3C22×C411yescharacteristic
229C2×C5×Dic3C22×C411yescharacteristic
230C2×C3×Dic5C22×C411yescharacteristic
231C2×C3×Dic5C22×C411yescharacteristic
232C2×C3×Dic5C22×C411yescharacteristic
233C3×C4×D5—21no—
234C3×C4×D5—21no—
235C3×C4×D5—21no—
236C3×C4×D5—21no—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239D5×Dic3—21no—
240D5×Dic3—21no—
241D5×Dic3—21no—
242D5×Dic3—21no—
243D5×Dic3—21no—
244D5×Dic3—21no—
245D5×Dic3C2×Q812yes—
246D5×Dic3#4112yes—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—51no—
249C2×C3×C42—51no—
250C2×C4⋊Dic3—51no—
251C2×C4⋊Dic3—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×Dic3⋊C4—51no—
255C2×Dic3⋊C4—51no—
256C2×Dic3⋊C4—51no—
257C2×Dic3⋊C4—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×C4×Dic3—51no—
261C2×C4×Dic3—51no—
262C2×C4×Dic3—51no—
263C2×C4×Dic3—51no—
264C2×C4×Dic3—51no—
265C2×C4×Dic3—51no—
266C2×C4×Dic3—51no—
267C2×C4×Dic3—51no—
268C2×C4×Dic3—51no—
269C2×C4×Dic3—51no—
270#889—51no—
271#889—51no—
272#889—51no—
273#889—51no—
274#889—51no—
275#889—51no—
276#889—51no—
277#889AGL(1,𝔽5)11yescharacteristic, complemented
278C3×#95—51no—
279C3×#95—51no—
280C3×#95—51no—
281C3×#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C3⋊#95—51no—
289C3⋊#95—51no—
290C22×AGL(1,𝔽5)—31no—
291C22×AGL(1,𝔽5)—31no—
292C22×AGL(1,𝔽5)—31no—
293C22×AGL(1,𝔽5)—31no—
294C22×AGL(1,𝔽5)C22×D311yescharacteristic
295C22×AGL(1,𝔽5)C22×D311yescharacteristic
296C22×AGL(1,𝔽5)C22×D311yescharacteristic
297C22×AGL(1,𝔽5)C22×D311yescharacteristic
298C2×C4×D5—31no—
299C2×C4×D5—31no—
300C2×C4×D5—31no—
301C2×C4×D5—31no—
302C2×C4×D5C22×D311yescharacteristic
303C2×C4×D5C22×D311yescharacteristic
304C2×C4×D5C22×D311yescharacteristic
305C4⋊AGL(1,𝔽5)—22no—
306C4⋊AGL(1,𝔽5)—62no—
307C4⋊AGL(1,𝔽5)—62no—
308C4⋊AGL(1,𝔽5)—62no—
309C4⋊AGL(1,𝔽5)—62no—
310C4⋊AGL(1,𝔽5)—62no—
311C4×AGL(1,𝔽5)—22no—
312C4×AGL(1,𝔽5)—34no—
313C4×AGL(1,𝔽5)—62no—
314C4×AGL(1,𝔽5)—62no—
315C4×AGL(1,𝔽5)—62no—
316C4×AGL(1,𝔽5)—62no—
317C4×AGL(1,𝔽5)—62no—
318C4×AGL(1,𝔽5)—62no—
319C4×AGL(1,𝔽5)—62no—
320C4×AGL(1,𝔽5)—62no—
321C5×C4⋊C4—31no—
322C5×C4⋊C4—31no—
323C5×C4⋊C4—31no—
324C5×C4⋊C4—31no—
325C5×C4⋊C4—31no—
326C5×C4⋊C4C4×D311yescharacteristic
327C42×C5—31no—
328C4⋊Dic5—31no—
329C4⋊Dic5—31no—
330C4⋊Dic5—31no—
331C4⋊Dic5—31no—
332C4⋊Dic5—31no—
333C4⋊Dic5C4×D311yescharacteristic
334#683—31no—
335#683—31no—
336#683—31no—
337#683—31no—
338#683—31no—
339#683—31no—
340#683—31no—
341#683—31no—
342#683—31no—
343#683—31no—
344#683C4×D311yescharacteristic
345#683C4×D311yescharacteristic
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5—31no—
349C2×#125—151no—
350#389—151no—
351#389—151no—
352#387—51no—
353#387—151no—
354#387—151no—
355#387—151no—
356#382—151no—
357C4×C4⋊C4—151no—
358C4×C4⋊C4—151no—
359C4×C4⋊C4—151no—
360C4×C4⋊C4—151no—
361C4×C4⋊C4—151no—
362C4×C4⋊C4—151no—
363C43—151no—
364C22×C3×C5C23×C411yescharacteristic
365C2×C3×D5C22×Q811yescharacteristic
366C2×C3×D5C2×#4111yescharacteristic
367C2×C3×D5C2×#4111yescharacteristic
368C2×C3×D5C2×#4111yescharacteristic
369C2×C3×D5C2×#4111yescharacteristic
370C2×C3×D5C2×#4111yescharacteristic
371ΓL(1,𝔽16)—22no—
372ΓL(1,𝔽16)—41no—
373ΓL(1,𝔽16)—41no—
374ΓL(1,𝔽16)#12514yescomplemented
375C3×AGL(1,𝔽5)—22no—
376C3×AGL(1,𝔽5)—22no—
377C3×AGL(1,𝔽5)—41no—
378C3×AGL(1,𝔽5)—41no—
379C3×C4×C5—21no—
380C3×C4×C5—21no—
381C3×C4×C5—21no—
382Dic15—21no—
383Dic15—21no—
384Dic15—21no—
385Dic15C4×Q812yes—
386C3×Dic5—21no—
387C3×Dic5—21no—
388C3×Dic5—21no—
389C5×Dic3—21no—
390C5×Dic3—21no—
391C5×Dic3—21no—
392C5×Dic3C4×Q812yes—
393C22×C3×C4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×Dic3—51no—
401C22×Dic3—51no—
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3—51no—
407C22×Dic3—51no—
408C3×C4⋊C4—51no—
409C3×C4⋊C4—51no—
410C3×C4⋊C4—51no—
411C3×C4⋊C4—102no—
412C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
413C3×C42—102no—
414C4⋊Dic3—51no—
415C4⋊Dic3—51no—
416C4⋊Dic3—51no—
417C4⋊Dic3—102no—
418C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
419Dic3⋊C4—51no—
420Dic3⋊C4—51no—
421Dic3⋊C4—51no—
422Dic3⋊C4—51no—
423Dic3⋊C4—51no—
424Dic3⋊C4—51no—
425Dic3⋊C4—51no—
426Dic3⋊C4—51no—
427Dic3⋊C4—51no—
428Dic3⋊C4—51no—
429Dic3⋊C4—51no—
430Dic3⋊C4—51no—
431Dic3⋊C4—102no—
432Dic3⋊C4—102no—
433Dic3⋊C4—102no—
434Dic3⋊C4—102no—
435Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
436Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
437Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
438Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
439C4×Dic3—54no—
440C4×Dic3—51no—
441C4×Dic3—51no—
442C4×Dic3—51no—
443C4×Dic3—102no—
444C4×Dic3—102no—
445C4×Dic3—102no—
446C4×Dic3—102no—
447C4×Dic3—102no—
448C4×Dic3—102no—
449C4×Dic3—102no—
450C4×Dic3—102no—
451C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
452C22×D5C23×D311yescharacteristic
453C2×AGL(1,𝔽5)—21no—
454C2×AGL(1,𝔽5)—21no—
455C2×AGL(1,𝔽5)—21no—
456C2×AGL(1,𝔽5)—21no—
457C2×AGL(1,𝔽5)—21no—
458C2×AGL(1,𝔽5)—21no—
459C2×AGL(1,𝔽5)—21no—
460C2×AGL(1,𝔽5)—21no—
461C2×AGL(1,𝔽5)—21no—
462C2×AGL(1,𝔽5)—21no—
463C2×AGL(1,𝔽5)—32no—
464C2×AGL(1,𝔽5)—32no—
465C2×AGL(1,𝔽5)—32no—
466C2×AGL(1,𝔽5)—32no—
467C2×AGL(1,𝔽5)—61no—
468C2×AGL(1,𝔽5)—61no—
469C2×AGL(1,𝔽5)—61no—
470C2×AGL(1,𝔽5)—61no—
471C2×AGL(1,𝔽5)—61no—
472C2×AGL(1,𝔽5)—61no—
473C2×AGL(1,𝔽5)—61no—
474C2×AGL(1,𝔽5)—61no—
475C2×AGL(1,𝔽5)#23712yes—
476C2×AGL(1,𝔽5)D3×Q812yes—
477C2×C4×C5—31no—
478C2×C4×C5—31no—
479C2×C4×C5—31no—
480C2×C4×C5—31no—
481C2×C4×C5C2×C4×D311yescharacteristic
482C2×C4×C5C2×C4×D311yescharacteristic
483C2×C4×C5C2×C4×D311yescharacteristic
484C2×Dic5—31no—
485C2×Dic5—31no—
486C2×Dic5—31no—
487C2×Dic5—31no—
488C2×Dic5C2×C4×D311yescharacteristic
489C2×Dic5C2×C4×D311yescharacteristic
490C2×Dic5C2×C4×D311yescharacteristic
491C4×D5—21no—
492C4×D5—21no—
493C4×D5—21no—
494C4×D5—21no—
495C4×D5—21no—
496C4×D5—21no—
497C4×D5—32no—
498C4×D5—32no—
499C4×D5—61no—
500C4×D5—61no—
501C4×D5—61no—
502C4×D5—61no—
503C4×D5—61no—
504C4×D5—61no—
505#125—31no—
506#125—151no—
507#125—151no—
508#125—151no—
509#125—151no—
510#125—151no—
511#125—151no—
512#125—151no—
513C2×C4⋊C4—51no—
514C2×C4⋊C4—51no—
515C2×C4⋊C4—151no—
516C2×C4⋊C4—151no—
517C2×C4⋊C4—151no—
518C2×C4⋊C4—151no—
519C2×C4⋊C4—151no—
520C2×C4⋊C4—151no—
521C2×C4⋊C4—151no—
522C2×C4⋊C4—151no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C42—51no—
526C2×C42—151no—
527C2×C42—151no—
528C2×C42—151no—
529C2×C42—151no—
530C2×C42—151no—
531C2×C42—151no—
532C2×C42—151no—
533C2×C42—151no—
534C2×C42—151no—
535C2×C42—151no—
536#95—51no—
537#95—51no—
538#95—51no—
539#95—51no—
540#95—151no—
541#95—151no—
542#95—151no—
543#95—151no—
544#95—151no—
545#95—151no—
546#95—151no—
547#95—151no—
548C2×C3×C5C2×C4×Q811yescharacteristic
549C2×C3×C5C4×#4111yescharacteristic
550C2×C3×C5C4×#4111yescharacteristic
551C3×D5C2×#12511yescharacteristic
552C3×D5#52911yescharacteristic
553C3×D5#52911yescharacteristic
554C3×D5#53311yescharacteristic
555C23×C3—51no—
556C2×C3×C4—52no—
557C2×C3×C4—52no—
558C2×C3×C4—51no—
559C2×C3×C4—51no—
560C2×C3×C4—51no—
561C2×C3×C4—101no—
562C2×C3×C4—101no—
563C2×C3×C4—101no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
578C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
579C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
580C2×Dic3—52no—
581C2×Dic3—52no—
582C2×Dic3—52no—
583C2×Dic3—51no—
584C2×Dic3—52no—
585C2×Dic3—52no—
586C2×Dic3—52no—
587C2×Dic3—51no—
588C2×Dic3—51no—
589C2×Dic3—51no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—101no—
598C2×Dic3—101no—
599C2×Dic3—101no—
600C2×Dic3—101no—
601C2×Dic3—101no—
602C2×Dic3—101no—
603C2×Dic3—101no—
604C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
605C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
606C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
607C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
608C22×C5C22×C4×D311yescharacteristic
609C2×D5C2×#23711yescharacteristic
610C2×D5C2×D3×Q811yescharacteristic
611C2×D5D3×#4111yescharacteristic
612C2×D5D3×#4111yescharacteristic
613C2×D5D3×#4111yescharacteristic
614C2×D5D3×#4111yescharacteristic
615AGL(1,𝔽5)—22no—
616AGL(1,𝔽5)—22no—
617AGL(1,𝔽5)—34no—
618AGL(1,𝔽5)—41no—
619AGL(1,𝔽5)—41no—
620AGL(1,𝔽5)—62no—
621AGL(1,𝔽5)—121no—
622AGL(1,𝔽5)—121no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—21no—
626C4×C5—32no—
627C4×C5—61no—
628C4×C5—61no—
629C4×C5—61no—
630Dic5—21no—
631Dic5—21no—
632Dic5—21no—
633Dic5—32no—
634Dic5—61no—
635Dic5—61no—
636Dic5—61no—
637C22×C4—51no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—51no—
641C22×C4—51no—
642C22×C4—51no—
643C22×C4—51no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—151no—
647C22×C4—151no—
648C22×C4—151no—
649C22×C4—151no—
650C22×C4—151no—
651C22×C4—151no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—51no—
658C4⋊C4—51no—
659C4⋊C4—51no—
660C4⋊C4—102no—
661C4⋊C4—151no—
662C4⋊C4—151no—
663C4⋊C4—151no—
664C4⋊C4—151no—
665C4⋊C4—151no—
666C4⋊C4—151no—
667C4⋊C4—151no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4—151no—
673C4⋊C4—151no—
674C4⋊C4—151no—
675C4⋊C4—151no—
676C4⋊C4—302no—
677C4⋊C4—302no—
678C4⋊C4—302no—
679C4⋊C4—302no—
680C4⋊C4—302no—
681C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
682C42—31no—
683C42—102no—
684C42—151no—
685C42—151no—
686C42—154no—
687C42—151no—
688C42—302no—
689C42—302no—
690C42—302no—
691C42—302no—
692C42—302no—
693C42—302no—
694C42—302no—
695C42—302no—
696C3×C5C4×#12511yescharacteristic, complemented, Hall
697C22×C3—51no—
698C22×C3—51no—
699C22×C3—51no—
700C22×C3—51no—
701C22×C3—51no—
702C22×C3—51no—
703C22×C3C23×AGL(1,𝔽5)11yescharacteristic
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—102no—
708C3×C4—102no—
709C3×C4—101no—
710C3×C4—101no—
711C3×C4—101no—
712C3×C4—201no—
713C3×C4—201no—
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—54no—
718Dic3—52no—
719Dic3—102no—
720Dic3—101no—
721Dic3—101no—
722Dic3—101no—
723Dic3—201no—
724Dic3—201no—
725Dic3Q8×AGL(1,𝔽5)12yes—
726C2×C5#552211yescharacteristic
727C2×C5C4×#23711yescharacteristic
728C2×C5C4×D3×Q811yescharacteristic
729D5#562211yescharacteristic
730D5#564911yescharacteristic
731D5D3×#12511yescharacteristic
732D5#570611yescharacteristic
733C23—51no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—52no—
739C2×C4—52no—
740C2×C4—51no—
741C2×C4—51no—
742C2×C4—51no—
743C2×C4—101no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—152no—
760C2×C4—152no—
761C2×C4—152no—
762C2×C4—152no—
763C2×C4—152no—
764C2×C4—151no—
765C2×C4—152no—
766C2×C4—151no—
767C2×C4—151no—
768C2×C4—151no—
769C2×C4—301no—
770C2×C4—301no—
771C2×C4—301no—
772C2×C4—301no—
773C2×C4—301no—
774C2×C4—301no—
775C2×C4—301no—
776C2×C4—301no—
777C2×C4—301no—
778C2×C4—301no—
779C2×C4—301no—
780C2×C4—301no—
781C2×C4—301no—
782C2×C4—301no—
783C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
784C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
785C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
786C2×C3—51no—
787C2×C3—51no—
788C2×C3—51no—
789C2×C3—51no—
790C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
791C2×C3#41×AGL(1,𝔽5)11yescharacteristic
792C2×C3#41×AGL(1,𝔽5)11yescharacteristic
793C5#7494311yescharacteristic, complemented, Sylow
794C22—51no—
795C22—51no—
796C22—51no—
797C22—51no—
798C22—51no—
799C22—51no—
800C22C22×D3×AGL(1,𝔽5)11yescharacteristic
801C4—21no—
802C4—21no—
803C4—21no—
804C4—32no—
805C4—61no—
806C4—61no—
807C4—61no—
808C4—102no—
809C4—102no—
810C4—101no—
811C4—101no—
812C4—101no—
813C4—154no—
814C4—152no—
815C4—201no—
816C4—201no—
817C4—302no—
818C4—301no—
819C4—301no—
820C4—301no—
821C4—601no—
822C4—601no—
823C3AGL(1,𝔽5)×#12511yescharacteristic, complemented, Sylow
824C2—51no—
825C2—51no—
826C2—51no—
827C2—51no—
828C2#1175683511yescharacteristic
829C2AGL(1,𝔽5)×#23711yescharacteristic
830C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#125
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
33. #91778C4semidirect
34. C5×#889C4semidirect
42. #91382C4semidirect
43. #91379C4semidirect
44. #91346C4semidirect
45. #91343C4semidirect
46. #91339C4semidirect
47. #91336C4semidirect
277. #889AGL(1,𝔽5)semidirect
374. ΓL(1,𝔽16)#125semidirect
696. C3×C5C4×#125semidirect
793. C5#74943semidirect
823. C3AGL(1,𝔽5)×#125semidirect

Maximal subgroups

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

subgroupindex
D5×#8892
C4⋊C4×ΓL(1,𝔽16)2
C3×#657112
#117518462
#117518452
#117518442
#117518402
#117518372
#117518332
C4×Dic3×AGL(1,𝔽5)2
#117517462
#117517452
AGL(1,𝔽5)×#1253
#749435