Finite Group Databasebeta

← #14326554

Subgroups — #14326554

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#877C211yesmaximal, characteristic
2C22⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
3C3×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic
4#11752029C211yesmaximal, characteristic
5#11752027C211yesmaximal, characteristic
6#11751984C211yesmaximal, characteristic
7C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic
8C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9#11751750C211yesmaximal, characteristic, complemented
10#11751748C211yesmaximal, characteristic, complemented
11#11751747C211yesmaximal, characteristic, complemented
12#11751747C211yesmaximal, characteristic, complemented
13#11751746C211yesmaximal, characteristic, complemented
14#11751745C211yesmaximal, characteristic, complemented
15#11751745C211yesmaximal, characteristic, complemented
16#10617132—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C23×C3×AGL(1,𝔽5)C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×#6763C2211yescharacteristic
21C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
22C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
23C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
25C2×C3×C4×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
30#91766C411yescharacteristic, complemented
31C5×#877C411yescharacteristic, complemented
32C3×D5×C22⋊C4C2211yescharacteristic
33D5×#217C2211yescharacteristic
34#91532C411yescharacteristic, complemented
35#91529C411yescharacteristic, complemented
36#91394C411yescharacteristic, complemented
37#91394C411yescharacteristic, complemented
38#91393C411yescharacteristic, complemented
39#91393C411yescharacteristic, complemented
40D5×Dic3⋊C4C2211yescharacteristic
41D5×Dic3⋊C4C2211yescharacteristic
42C4×D5×Dic3C2211yescharacteristic
43C4×D5×Dic3C2211yescharacteristic
44#91235C2211yescharacteristic
45#91235C2211yescharacteristic
46C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
47C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
48(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
49(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
50(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
51(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
52(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
53(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
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#73455—51nomaximal, Hall
61D5×#117—31no—
62#65764—31no—
63C2×(C2×AGL(1,𝔽5))⋊C4—31no—
64#65711—31no—
65#65711—31no—
66#65711—31no—
67#65711—31no—
68#65699—31no—
69#65699—31no—
70C22⋊C4×AGL(1,𝔽5)—31no—
71C22⋊C4×AGL(1,𝔽5)D311yescharacteristic
72#65690—31no—
73#65689—31no—
74C4×C4⋊AGL(1,𝔽5)—31no—
75#65686—31no—
76C23×C3×D5C2311yescharacteristic
77C22×ΓL(1,𝔽16)—22no—
78C22×ΓL(1,𝔽16)—22no—
79C22×ΓL(1,𝔽16)—41no—
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)—22no—
85C22×C3×AGL(1,𝔽5)—22no—
86C22×C3×AGL(1,𝔽5)—41no—
87C22×C3×AGL(1,𝔽5)C2311yescharacteristic
88C22×C3×AGL(1,𝔽5)C2311yescharacteristic
89C22×C3×AGL(1,𝔽5)C2311yescharacteristic
90C22×C3×AGL(1,𝔽5)C2311yescharacteristic
91C22×Dic15C2×C411yescharacteristic
92C22×C5×Dic3C2×C411yescharacteristic
93C2×C3×C4×D5C2311yescharacteristic
94C2×C3×C4×D5C2311yescharacteristic
95C2×D5×Dic3—22no—
96C2×D5×Dic3—22no—
97C2×D5×Dic3C2×C411yescharacteristic
98C2×D5×Dic3C2×C411yescharacteristic
99C2×D5×Dic3C2311yescharacteristic
100C2×D5×Dic3C2311yescharacteristic
101C2×D5×Dic3C2311yescharacteristic
102C2×D5×Dic3C2311yescharacteristic
103#6763—22no—
104C4×ΓL(1,𝔽16)—22no—
105C4×ΓL(1,𝔽16)—41no—
106C3×C22⋊AGL(1,𝔽5)—22no—
107C3×C4×AGL(1,𝔽5)—22no—
108C3×C4×AGL(1,𝔽5)—41no—
109Dic3⋊AGL(1,𝔽5)—22no—
110Dic3⋊AGL(1,𝔽5)—22no—
111Dic3⋊AGL(1,𝔽5)—41no—
112Dic3⋊AGL(1,𝔽5)—41no—
113C3×C5×C22⋊C4C2×C411yescharacteristic
114#6719C2×C411yescharacteristic
115#6712C2×C411yescharacteristic, complemented
116#6712C2×C411yescharacteristic, complemented
117C4×Dic15C2×C411yescharacteristic, complemented
118C4×Dic15C2×C411yescharacteristic, complemented
119C5×#217C2×C411yescharacteristic
120C5×Dic3⋊C4C2×C411yescharacteristic, complemented
121C5×Dic3⋊C4C2×C411yescharacteristic, complemented
122C4×C5×Dic3C2×C411yescharacteristic, complemented
123C4×C5×Dic3C2×C411yescharacteristic, complemented
124C3×C22⋊Dic5C2×C411yescharacteristic
125C3×#685C2×C411yescharacteristic
126C3×#685C2×C411yescharacteristic
127Dic3⋊Dic5C2×C411yescharacteristic, complemented
128Dic3⋊Dic5C2×C411yescharacteristic, complemented
129#6669C2×C411yescharacteristic, complemented
130#6669C2×C411yescharacteristic, complemented
131#6665C2×C411yescharacteristic
132#6665C2×C411yescharacteristic
133Dic3×Dic5C2×C411yescharacteristic, complemented
134Dic3×Dic5C2×C411yescharacteristic, complemented
135Dic3×Dic5C2×C411yescharacteristic, complemented
136Dic3×Dic5C2×C411yescharacteristic, complemented
137C2×#877—51no—
138C3×C4×C22⋊C4—51no—
139#5210—51no—
140C2×C3⋊#95—51no—
141#4946—51no—
142#4943—51no—
143Dic3×C22⋊C4—51no—
144#4933—51no—
145#4933—51no—
146#4932—51no—
147C4×Dic3⋊C4—51no—
148#4652—51no—
149#4652—51no—
150#4651—51no—
151#4650—51no—
152C23×AGL(1,𝔽5)—31no—
153C23×AGL(1,𝔽5)C2×D311yescharacteristic
154C22×C4×D5—31no—
155C2×C22⋊AGL(1,𝔽5)—31no—
156C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
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)C2×D311yescharacteristic
164C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
165C5×#117—31no—
166#4072—31no—
167#4038—31no—
168#4038—31no—
169D5×C4⋊C4—31no—
170D5×C4⋊C4—31no—
171D5×C22⋊C4—31no—
172D5×C22⋊C4C2×D311yescharacteristic
173#4023—31no—
174#4023—31no—
175#4018—31no—
176#4018—31no—
177C42×D5—31no—
178C42×D5—31no—
179(C2×AGL(1,𝔽5))⋊C4—31no—
180(C2×AGL(1,𝔽5))⋊C4—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))⋊C4—31no—
190(C2×AGL(1,𝔽5))⋊C4—31no—
191(C2×AGL(1,𝔽5))⋊C4—31no—
192(C2×AGL(1,𝔽5))⋊C4—31no—
193(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
194(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
195#2343—151noSylow
196C23×C3×C5C22×C411yescharacteristic
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5C22×C411yescharacteristic
202C22×C3×D5#4112yes—
203C22×C3×D5#4112yes—
204C22×C3×D5C2411yescharacteristic
205C2×ΓL(1,𝔽16)—21no—
206C2×ΓL(1,𝔽16)—21no—
207C2×ΓL(1,𝔽16)—21no—
208C2×ΓL(1,𝔽16)—21no—
209C2×ΓL(1,𝔽16)—21no—
210C2×ΓL(1,𝔽16)—21no—
211C2×ΓL(1,𝔽16)—21no—
212C2×ΓL(1,𝔽16)—21no—
213C2×ΓL(1,𝔽16)—21no—
214C2×ΓL(1,𝔽16)—21no—
215C2×ΓL(1,𝔽16)—21no—
216C2×ΓL(1,𝔽16)—44no—
217C2×ΓL(1,𝔽16)#4112yes—
218C2×C3×AGL(1,𝔽5)—21no—
219C2×C3×AGL(1,𝔽5)—21no—
220C2×C3×AGL(1,𝔽5)—21no—
221C2×C3×AGL(1,𝔽5)—21no—
222C2×C3×AGL(1,𝔽5)—21no—
223C2×C3×AGL(1,𝔽5)—21no—
224C2×C3×AGL(1,𝔽5)—21no—
225C2×C3×AGL(1,𝔽5)—21no—
226C2×C3×AGL(1,𝔽5)—21no—
227C2×C3×AGL(1,𝔽5)—21no—
228C2×C3×AGL(1,𝔽5)—21no—
229C2×C3×AGL(1,𝔽5)—44no—
230C2×C3×AGL(1,𝔽5)#4112yes—
231C2×C3×C4×C5C22×C411yescharacteristic
232C2×C3×C4×C5C22×C411yescharacteristic
233C2×Dic15—22no—
234C2×Dic15C22×C411yescharacteristic
235C2×Dic15C22×C411yescharacteristic
236C2×Dic15C22×C411yescharacteristic
237C2×Dic15C22×C411yescharacteristic
238C2×C5×Dic3—22no—
239C2×C5×Dic3C22×C411yescharacteristic
240C2×C5×Dic3C22×C411yescharacteristic
241C2×C5×Dic3C22×C411yescharacteristic
242C2×C5×Dic3C22×C411yescharacteristic
243C2×C3×Dic5C22×C411yescharacteristic
244C2×C3×Dic5C22×C411yescharacteristic
245C3×C4×D5—21no—
246C3×C4×D5—21no—
247C3×C4×D5—21no—
248C3×C4×D5—21no—
249D5×Dic3—22no—
250D5×Dic3—22no—
251D5×Dic3—21no—
252D5×Dic3—21no—
253D5×Dic3—21no—
254D5×Dic3—21no—
255D5×Dic3—21no—
256D5×Dic3—21no—
257D5×Dic3—21no—
258D5×Dic3—21no—
259C23×C3×C4—51no—
260C23×Dic3—51no—
261C23×Dic3—51no—
262C2×C3×C22⋊C4—51no—
263C2×C3×C22⋊C4—51no—
264C2×C3×C42—51no—
265C2×C3×C42—51no—
266C2×#217—51no—
267C2×#217—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278#877—51no—
279#877—51no—
280#877—51no—
281#877—51no—
282#877—51no—
283#877—51no—
284#877—51no—
285#877AGL(1,𝔽5)11yescharacteristic, complemented
286C3×#95—51no—
287C3×#95—51no—
288C3⋊#95—51no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C3⋊#95—51no—
300C3⋊#95—51no—
301C3⋊#95—51no—
302C23×D5C22×D311yescharacteristic
303C22×AGL(1,𝔽5)—22no—
304C22×AGL(1,𝔽5)—22no—
305C22×AGL(1,𝔽5)—31no—
306C22×AGL(1,𝔽5)—31no—
307C22×AGL(1,𝔽5)—31no—
308C22×AGL(1,𝔽5)—31no—
309C22×AGL(1,𝔽5)—41no—
310C22×AGL(1,𝔽5)—62no—
311C22×AGL(1,𝔽5)—62no—
312C22×AGL(1,𝔽5)—121no—
313C22×AGL(1,𝔽5)C22×D311yescharacteristic
314C22×AGL(1,𝔽5)C22×D311yescharacteristic
315C22×AGL(1,𝔽5)C22×D311yescharacteristic
316C22×AGL(1,𝔽5)C22×D311yescharacteristic
317C22×C4×C5—31no—
318C22×Dic5—31no—
319C2×C4×D5—31no—
320C2×C4×D5—31no—
321C2×C4×D5—31no—
322C2×C4×D5—31no—
323C2×C4×D5—31no—
324C2×C4×D5—31no—
325C2×C4×D5—62no—
326C2×C4×D5—62no—
327C2×C4×D5C22×D311yescharacteristic
328C2×C4×D5C22×D311yescharacteristic
329C22⋊AGL(1,𝔽5)—22no—
330C22⋊AGL(1,𝔽5)—62no—
331C4⋊AGL(1,𝔽5)—62no—
332C4⋊AGL(1,𝔽5)—62no—
333C4⋊AGL(1,𝔽5)—121no—
334C4⋊AGL(1,𝔽5)—121no—
335C4×AGL(1,𝔽5)—22no—
336C4×AGL(1,𝔽5)—41no—
337C4×AGL(1,𝔽5)—62no—
338C4×AGL(1,𝔽5)—121no—
339C5×C4⋊C4—31no—
340C5×C4⋊C4—31no—
341C5×C22⋊C4—31no—
342C5×C22⋊C4C4×D311yescharacteristic
343C42×C5—31no—
344C42×C5—31no—
345C22⋊Dic5—31no—
346C22⋊Dic5C4×D311yescharacteristic
347#685—31no—
348#685—31no—
349#685C4×D311yescharacteristic
350#685C4×D311yescharacteristic
351C4⋊Dic5—31no—
352C4⋊Dic5—31no—
353#683—31no—
354#683—31no—
355#683—31no—
356#683—31no—
357C4×Dic5—31no—
358C4×Dic5—31no—
359C4×Dic5—31no—
360C4×Dic5—31no—
361C4×Dic5—31no—
362C4×Dic5—31no—
363C2×#117—151no—
364#387—151no—
365#387—151no—
366#387—151no—
367#387—151no—
368#385—151no—
369#385—151no—
370#383—151no—
371#382—151no—
372#381—151no—
373C4×C4⋊C4—151no—
374C4×C22⋊C4—51no—
375C4×C22⋊C4—151no—
376#376—151no—
377C2×#95—151no—
378C22×C3×C5—21no—
379C22×C3×C5—21no—
380C22×C3×C5#11712yes—
381C22×C3×C5C23×C411yescharacteristic
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5—22no—
387C2×C3×D5—22no—
388C2×C3×D5#11712yes—
389C2×C3×D5C2×#4111yescharacteristic
390C2×C3×D5C2×#4111yescharacteristic
391C2×C3×D5C2×#4111yescharacteristic
392C2×C3×D5C2×#4111yescharacteristic
393C2×C3×D5H(5,𝔽2)11yescharacteristic
394C2×C3×D52−1+411yescharacteristic
395ΓL(1,𝔽16)—22no—
396ΓL(1,𝔽16)—41no—
397ΓL(1,𝔽16)—41no—
398ΓL(1,𝔽16)—41no—
399C3×AGL(1,𝔽5)—22no—
400C3×AGL(1,𝔽5)—41no—
401C3×AGL(1,𝔽5)—41no—
402C3×AGL(1,𝔽5)—41no—
403C3×C4×C5—21no—
404C3×C4×C5—21no—
405Dic15—21no—
406Dic15—21no—
407Dic15—21no—
408Dic15—21no—
409C3×Dic5—21no—
410C3×Dic5—21no—
411C5×Dic3—21no—
412C5×Dic3—21no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C24×C3—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—201no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3—51no—
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3—102no—
437C22×Dic3—102no—
438C22×Dic3—102no—
439C22×Dic3—102no—
440C22×Dic3—201no—
441C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
442C3×C22⋊C4—51no—
443C3×C22⋊C4—51no—
444C3×C22⋊C4—51no—
445C3×C22⋊C4—102no—
446C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
447C3×C42—102no—
448C3×C42—201no—
449#217—51no—
450#217—51no—
451#217—51no—
452#217—102no—
453#217C2×AGL(1,𝔽5)11yescharacteristic
454Dic3⋊C4—51no—
455Dic3⋊C4—51no—
456Dic3⋊C4—51no—
457Dic3⋊C4—51no—
458Dic3⋊C4—51no—
459Dic3⋊C4—51no—
460Dic3⋊C4—102no—
461Dic3⋊C4—102no—
462Dic3⋊C4—201no—
463Dic3⋊C4—201no—
464Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
465Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
466C4×Dic3—51no—
467C4×Dic3—51no—
468C4×Dic3—51no—
469C4×Dic3—51no—
470C4×Dic3—51no—
471C4×Dic3—51no—
472C4×Dic3—102no—
473C4×Dic3—201no—
474C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
475C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
476C23×C5C2×C4×D311yescharacteristic
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5C2×C4×D311yescharacteristic
482C22×D5#23512yes—
483C22×D5#23512yes—
484C22×D5C23×D311yescharacteristic
485C2×AGL(1,𝔽5)—21no—
486C2×AGL(1,𝔽5)—21no—
487C2×AGL(1,𝔽5)—21no—
488C2×AGL(1,𝔽5)—21no—
489C2×AGL(1,𝔽5)—21no—
490C2×AGL(1,𝔽5)—21no—
491C2×AGL(1,𝔽5)—21no—
492C2×AGL(1,𝔽5)—21no—
493C2×AGL(1,𝔽5)—21no—
494C2×AGL(1,𝔽5)—21no—
495C2×AGL(1,𝔽5)—21no—
496C2×AGL(1,𝔽5)—32no—
497C2×AGL(1,𝔽5)—44no—
498C2×AGL(1,𝔽5)—61no—
499C2×AGL(1,𝔽5)—61no—
500C2×AGL(1,𝔽5)—61no—
501C2×AGL(1,𝔽5)—61no—
502C2×AGL(1,𝔽5)—61no—
503C2×AGL(1,𝔽5)—61no—
504C2×AGL(1,𝔽5)—61no—
505C2×AGL(1,𝔽5)—61no—
506C2×AGL(1,𝔽5)—61no—
507C2×AGL(1,𝔽5)—61no—
508C2×AGL(1,𝔽5)—61no—
509C2×AGL(1,𝔽5)—124no—
510C2×AGL(1,𝔽5)#23712yes—
511C2×C4×C5—31no—
512C2×C4×C5—31no—
513C2×C4×C5—31no—
514C2×C4×C5—31no—
515C2×C4×C5—62no—
516C2×C4×C5C2×C4×D311yescharacteristic
517C2×C4×C5C2×C4×D311yescharacteristic
518C2×Dic5—31no—
519C2×Dic5—31no—
520C2×Dic5—31no—
521C2×Dic5—31no—
522C2×Dic5—62no—
523C2×Dic5C2×C4×D311yescharacteristic
524C2×Dic5C2×C4×D311yescharacteristic
525C4×D5—21no—
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—21no—
529C4×D5—62no—
530C4×D5—62no—
531C4×D5—61no—
532C4×D5—61no—
533C4×D5—61no—
534C4×D5—61no—
535C4×D5—61no—
536C4×D5—61no—
537C4×D5—61no—
538C4×D5—61no—
539C23×C4—51no—
540C23×C4—151no—
541C23×C4—151no—
542#117—31no—
543#117—151no—
544#117—151no—
545#117—151no—
546#117—151no—
547#117—151no—
548#117—151no—
549#117—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C4⋊C4—151no—
554C2×C4⋊C4—151no—
555C2×C4⋊C4—151no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C42—51no—
561C2×C42—51no—
562C2×C42—151no—
563C2×C42—151no—
564C2×C42—151no—
565C2×C42—151no—
566#95—51no—
567#95—51no—
568#95—151no—
569#95—151no—
570#95—151no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95—151no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95—151no—
581#95—151no—
582C2×C3×C5—22no—
583C2×C3×C5C2×#11711yescharacteristic
584C2×C3×C5C4×#4111yescharacteristic
585C2×C3×C5#52011yescharacteristic
586C3×D5—22no—
587C3×D5#55111yescharacteristic
588C3×D5#55111yescharacteristic
589C3×D5#55211yescharacteristic
590C3×D5#55211yescharacteristic
591C23×C3—51no—
592C23×C3—52no—
593C23×C3—52no—
594C23×C3—51no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3C22×AGL(1,𝔽5)11yescharacteristic
600C2×C3×C4—52no—
601C2×C3×C4—51no—
602C2×C3×C4—51no—
603C2×C3×C4—101no—
604C2×C3×C4—101no—
605C2×C3×C4—101no—
606C2×C3×C4—101no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—204no—
619C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
620C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
621C2×Dic3—22no—
622C2×Dic3—52no—
623C2×Dic3—51no—
624C2×Dic3—51no—
625C2×Dic3—51no—
626C2×Dic3—51no—
627C2×Dic3—101no—
628C2×Dic3—101no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—101no—
638C2×Dic3—101no—
639C2×Dic3—102no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—204no—
650C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
651C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
652C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
653C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
654C22×C5—21no—
655C22×C5—21no—
656C22×C5#87212yes—
657C22×C5C22×C4×D311yescharacteristic
658C2×D5—21no—
659C2×D5—21no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5#87212yes—
665C2×D5C2×#23511yescharacteristic
666C2×D5C2×#23511yescharacteristic
667C2×D5C2×#23711yescharacteristic
668C2×D5#100411yescharacteristic
669C2×D5D3×#4111yescharacteristic
670C2×D5#101011yescharacteristic
671AGL(1,𝔽5)—22no—
672AGL(1,𝔽5)—41no—
673AGL(1,𝔽5)—41no—
674AGL(1,𝔽5)—41no—
675AGL(1,𝔽5)—62no—
676AGL(1,𝔽5)—121no—
677AGL(1,𝔽5)—121no—
678AGL(1,𝔽5)—121no—
679C4×C5—21no—
680C4×C5—21no—
681C4×C5—61no—
682C4×C5—61no—
683C4×C5—61no—
684C4×C5—61no—
685Dic5—21no—
686Dic5—21no—
687Dic5—61no—
688Dic5—61no—
689Dic5—61no—
690Dic5—61no—
691C24—51no—
692C22×C4—31no—
693C22×C4—51no—
694C22×C4—51no—
695C22×C4—51no—
696C22×C4—51no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—102no—
700C22×C4—102no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—201no—
713C22×C4—302no—
714C22×C4—302no—
715C22×C4—302no—
716C22×C4—302no—
717C22×C4—601no—
718C4⋊C4—31no—
719C4⋊C4—31no—
720C4⋊C4—151no—
721C4⋊C4—151no—
722C4⋊C4—151no—
723C4⋊C4—151no—
724C4⋊C4—151no—
725C4⋊C4—151no—
726C4⋊C4—302no—
727C4⋊C4—302no—
728C4⋊C4—601no—
729C4⋊C4—601no—
730C22⋊C4—31no—
731C22⋊C4—51no—
732C22⋊C4—51no—
733C22⋊C4—51no—
734C22⋊C4—102no—
735C22⋊C4—151no—
736C22⋊C4—151no—
737C22⋊C4—151no—
738C22⋊C4—302no—
739C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
740C42—31no—
741C42—31no—
742C42—102no—
743C42—151no—
744C42—151no—
745C42—151no—
746C42—151no—
747C42—151no—
748C42—151no—
749C42—201no—
750C42—302no—
751C42—601no—
752C3×C5#234311yescharacteristic, complemented, Hall
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—51no—
756C22×C3—51no—
757C22×C3—51no—
758C22×C3—51no—
759C22×C3—51no—
760C22×C3—51no—
761C22×C3—52no—
762C22×C3—102no—
763C22×C3—102no—
764C22×C3—102no—
765C22×C3—102no—
766C22×C3—101no—
767C22×C3—101no—
768C22×C3#413012yes—
769C22×C3C23×AGL(1,𝔽5)11yescharacteristic
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—102no—
773C3×C4—101no—
774C3×C4—101no—
775C3×C4—201no—
776C3×C4—201no—
777C3×C4—201no—
778Dic3—21no—
779Dic3—21no—
780Dic3—21no—
781Dic3—21no—
782Dic3—102no—
783Dic3—101no—
784Dic3—101no—
785Dic3—101no—
786Dic3—101no—
787Dic3—201no—
788Dic3—201no—
789Dic3—201no—
790C2×C5—22no—
791C2×C5C2×#87211yescharacteristic
792C2×C5C4×#23711yescharacteristic
793C2×C5#554611yescharacteristic
794D5—22no—
795D5#549511yescharacteristic
796D5#553111yescharacteristic
797D5#554111yescharacteristic
798D5#555611yescharacteristic
799C23—51no—
800C23—52no—
801C23—52no—
802C23—51no—
803C23—101no—
804C23—101no—
805C23—101no—
806C23—101no—
807C23C2×D3×AGL(1,𝔽5)11yescharacteristic
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—52no—
813C2×C4—51no—
814C2×C4—51no—
815C2×C4—62no—
816C2×C4—101no—
817C2×C4—101no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—101no—
826C2×C4—101no—
827C2×C4—101no—
828C2×C4—101no—
829C2×C4—101no—
830C2×C4—101no—
831C2×C4—152no—
832C2×C4—151no—
833C2×C4—151no—
834C2×C4—151no—
835C2×C4—151no—
836C2×C4—204no—
837C2×C4—301no—
838C2×C4—301no—
839C2×C4—301no—
840C2×C4—301no—
841C2×C4—301no—
842C2×C4—301no—
843C2×C4—301no—
844C2×C4—302no—
845C2×C4—302no—
846C2×C4—301no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—302no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—301no—
857C2×C4—301no—
858C2×C4—301no—
859C2×C4—604no—
860C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
861C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
862C2×C3—22no—
863C2×C3—51no—
864C2×C3—51no—
865C2×C3—51no—
866C2×C3—51no—
867C2×C3—102no—
868C2×C3C2×#413011yescharacteristic
869C2×C3#41×AGL(1,𝔽5)11yescharacteristic
870C2×C3#6626611yescharacteristic
871C5#7345511yescharacteristic, complemented, Sylow
872C22—21no—
873C22—21no—
874C22—51no—
875C22—51no—
876C22—51no—
877C22—51no—
878C22—51no—
879C22—51no—
880C22—52no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—101no—
886C22—101no—
887C22#9190912yes—
888C22C22×D3×AGL(1,𝔽5)11yescharacteristic
889C4—21no—
890C4—21no—
891C4—61no—
892C4—61no—
893C4—61no—
894C4—61no—
895C4—102no—
896C4—101no—
897C4—101no—
898C4—201no—
899C4—201no—
900C4—201no—
901C4—302no—
902C4—301no—
903C4—301no—
904C4—301no—
905C4—301no—
906C4—601no—
907C4—601no—
908C4—601no—
909C3#1061713211yescharacteristic, complemented, Sylow
910C2—22no—
911C2—51no—
912C2—51no—
913C2—51no—
914C2—51no—
915C2—102no—
916C2C2×#9190911yescharacteristic
917C2AGL(1,𝔽5)×#23711yescharacteristic
918C2#1175684611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
9. #11751750C2semidirect
10. #11751748C2semidirect
11. #11751747C2semidirect
12. #11751747C2semidirect
13. #11751746C2semidirect
14. #11751745C2semidirect
15. #11751745C2semidirect
30. #91766C4semidirect
31. C5×#877C4semidirect
34. #91532C4semidirect
35. #91529C4semidirect
36. #91394C4semidirect
37. #91394C4semidirect
38. #91393C4semidirect
39. #91393C4semidirect
115. #6712C2×C4semidirect
116. #6712C2×C4semidirect
117. C4×Dic15C2×C4semidirect
118. C4×Dic15C2×C4semidirect
120. C5×Dic3⋊C4C2×C4semidirect
121. C5×Dic3⋊C4C2×C4semidirect
122. C4×C5×Dic3C2×C4semidirect
123. C4×C5×Dic3C2×C4semidirect
127. Dic3⋊Dic5C2×C4semidirect
128. Dic3⋊Dic5C2×C4semidirect
129. #6669C2×C4semidirect
130. #6669C2×C4semidirect
133. Dic3×Dic5C2×C4semidirect
134. Dic3×Dic5C2×C4semidirect
135. Dic3×Dic5C2×C4semidirect
136. Dic3×Dic5C2×C4semidirect
285. #877AGL(1,𝔽5)semidirect
464. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
465. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
474. C4×Dic3C2×AGL(1,𝔽5)semidirect
475. C4×Dic3C2×AGL(1,𝔽5)semidirect
752. C3×C5#2343semidirect
871. C5#73455semidirect
909. C3#10617132semidirect

Maximal subgroups

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

subgroupindex
D5×#8772
C22⋊C4×ΓL(1,𝔽16)2
C3×C22⋊C4×AGL(1,𝔽5)2
#117520292
#117520272
#117519842
C2×(C2×AGL(1,𝔽5))⋊Dic32
C4×Dic3⋊AGL(1,𝔽5)2
#117517502
#117517482
#117517472
#117517462
#117517452
#106171323
#734555