Finite Group Databasebeta

← #14327657

Subgroups — #14327657

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D5×Dic3C211yesmaximal, characteristic
2#11752438C211yesmaximal, characteristic
3C3×#65779C211yesmaximal, characteristic
4#11752028C211yesmaximal, characteristic, complemented
5#11752021C211yesmaximal, characteristic, complemented
6Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
7#11752018C211yesmaximal, characteristic, complemented
8#11752017C211yesmaximal, characteristic, complemented
9AGL(1,𝔽5)×#217C211yesmaximal, characteristic, complemented
10#11751984C211yesmaximal, characteristic, complemented
11C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic, complemented
12#11751840C211yesmaximal, characteristic, complemented
13#11751839C211yesmaximal, characteristic, complemented
14#11751832C211yesmaximal, characteristic, complemented
15#11751750C211yesmaximal, characteristic, complemented
16#10617180—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C23×C3×AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×#6763C2211yescharacteristic
23C2×#6763C2211yescharacteristic
24C2×#6763C2211yescharacteristic
25C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×C3×C22⋊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
33C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
34D4×Dic15C411yescharacteristic, complemented
35C5×D4×Dic3C411yescharacteristic, complemented
36#91559C411yescharacteristic, complemented
37#91559C411yescharacteristic, complemented
38Dic3×C22⋊D5C411yescharacteristic, complemented
39Dic3×C22⋊D5C411yescharacteristic, complemented
40D5×#217C2211yescharacteristic
41D5×#217C2211yescharacteristic
42#91434C411yescharacteristic, complemented
43Dic3×D20C411yescharacteristic, complemented
44D5×C4⋊Dic3C2211yescharacteristic
45C4×D5×Dic3C2211yescharacteristic
46#91235C2211yescharacteristic
47#91235C2211yescharacteristic
48C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
49C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
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#74674—51nomaximal, Hall
61C4×D4×D5—31no—
62#65779—31no—
63#65779D311yescharacteristic
64#65765—31no—
65#65764—31no—
66C4×C22⋊AGL(1,𝔽5)—31no—
67C2×(C2×AGL(1,𝔽5))⋊C4—31no—
68#65711—31no—
69#65711—31no—
70#65700—31no—
71#65700—31no—
72C22⋊C4×AGL(1,𝔽5)—31no—
73C22⋊C4×AGL(1,𝔽5)—31no—
74#65690—31no—
75#65686—31no—
76C23×C3×D5C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×ΓL(1,𝔽16)—22no—
79C22×ΓL(1,𝔽16)—22no—
80C22×ΓL(1,𝔽16)—41no—
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×ΓL(1,𝔽16)C2311yescharacteristic
85C22×C3×AGL(1,𝔽5)—22no—
86C22×C3×AGL(1,𝔽5)—22no—
87C22×C3×AGL(1,𝔽5)—41no—
88C22×C3×AGL(1,𝔽5)C2311yescharacteristic
89C22×C3×AGL(1,𝔽5)C2311yescharacteristic
90C22×C3×AGL(1,𝔽5)C2311yescharacteristic
91C22×C3×AGL(1,𝔽5)C2311yescharacteristic
92C2×C3×C5×D4C2×C411yescharacteristic
93C22×Dic15C2×C411yescharacteristic
94C22×Dic15C2×C411yescharacteristic, complemented
95C22×C5×Dic3C2×C411yescharacteristic
96C22×C5×Dic3C2×C411yescharacteristic, complemented
97C2×C3×C22⋊D5C2×C411yescharacteristic
98C2×C3×C22⋊D5C2×C411yescharacteristic
99C3×D4×D5—22no—
100C3×D4×D5—22no—
101C2×C3×D20C2×C411yescharacteristic
102C2×C3×C4×D5C2311yescharacteristic
103C2×D5×Dic3—41no—
104C2×D5×Dic3—41no—
105C2×D5×Dic3—41no—
106C2×D5×Dic3—41no—
107C2×D5×Dic3C2×C411yescharacteristic
108C2×D5×Dic3C2×C411yescharacteristic
109C2×D5×Dic3C2×C411yescharacteristic, complemented
110C2×D5×Dic3C2×C411yescharacteristic, complemented
111C2×D5×Dic3C2311yescharacteristic
112C2×D5×Dic3C2311yescharacteristic
113C2×D5×Dic3C2311yescharacteristic
114C2×D5×Dic3C2311yescharacteristic
115#6763—22no—
116#6763—22no—
117#6763—41no—
118C3×C22⋊AGL(1,𝔽5)—22no—
119C3×C22⋊AGL(1,𝔽5)—22no—
120C3×C22⋊AGL(1,𝔽5)—41no—
121Dic3⋊AGL(1,𝔽5)—41no—
122Dic3⋊AGL(1,𝔽5)—41no—
123Dic3×AGL(1,𝔽5)—22no—
124Dic3×AGL(1,𝔽5)—22no—
125Dic3×AGL(1,𝔽5)—41no—
126Dic3×AGL(1,𝔽5)—41no—
127#6719C2×C411yescharacteristic
128#6719C2×C411yescharacteristic, complemented
129C4⋊Dic15C2×C411yescharacteristic, complemented
130C4×Dic15C2×C411yescharacteristic, complemented
131C5×#217C2×C411yescharacteristic
132C5×#217C2×C411yescharacteristic, complemented
133C5×C4⋊Dic3C2×C411yescharacteristic, complemented
134C4×C5×Dic3C2×C411yescharacteristic, complemented
135#6668C2×C411yescharacteristic, complemented
136#6668C2×C411yescharacteristic, complemented
137#6665C2×C411yescharacteristic
138#6665C2×C411yescharacteristic
139#6665C2×C411yescharacteristic, complemented
140#6665C2×C411yescharacteristic, complemented
141Dic3×Dic5C2×C411yescharacteristic, complemented
142Dic3×Dic5C2×C411yescharacteristic, complemented
143C2×D4×Dic3—51no—
144C3×#386—51no—
145#5220—51no—
146C4×#217—51no—
147C2×C3⋊#95—51no—
148#4945—51no—
149#4944—51no—
150#4943—51no—
151#4942—51no—
152Dic3×C22⋊C4—51no—
153Dic3×C22⋊C4—51no—
154#4654—51no—
155#4653—51no—
156#4651—51no—
157#4648—51no—
158C23×AGL(1,𝔽5)—31no—
159C23×AGL(1,𝔽5)C2×D311yescharacteristic
160C2×D4×D5C2×D311yescharacteristic
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C2×C22⋊AGL(1,𝔽5)—31no—
164C2×C22⋊AGL(1,𝔽5)—31no—
165C2×C22⋊AGL(1,𝔽5)—31no—
166C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
167C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
168C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
169C2×C4⋊AGL(1,𝔽5)—31no—
170C2×C4⋊AGL(1,𝔽5)—31no—
171C2×C4×AGL(1,𝔽5)—31no—
172C2×C4×AGL(1,𝔽5)—31no—
173C2×C4×AGL(1,𝔽5)—31no—
174C2×C4×AGL(1,𝔽5)—31no—
175C4×C5×D4—31no—
176D4×Dic5—31no—
177C4×C22⋊D5—31no—
178C4×C22⋊D5—31no—
179#4039—31no—
180D5×C4⋊C4—31no—
181#4027—31no—
182#4027—31no—
183D5×C22⋊C4—31no—
184D5×C22⋊C4—31no—
185C4×D20—31no—
186C42×D5—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))⋊C4—31no—
194(C2×AGL(1,𝔽5))⋊C4—31no—
195(C2×AGL(1,𝔽5))⋊C4—31no—
196(C2×AGL(1,𝔽5))⋊C4—31no—
197(C2×AGL(1,𝔽5))⋊C4—31no—
198(C2×AGL(1,𝔽5))⋊C4—31no—
199(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
200(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
201#2353—151noSylow
202C23×C3×C5C22×C411yescharacteristic
203C23×C3×C5C22×C411yescharacteristic
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5C22×C411yescharacteristic
215C22×C3×D5C22×C411yescharacteristic
216C22×C3×D5#4112yes—
217C22×C3×D5#4112yes—
218C22×C3×D5C2411yescharacteristic
219C2×ΓL(1,𝔽16)—21no—
220C2×ΓL(1,𝔽16)—21no—
221C2×ΓL(1,𝔽16)—21no—
222C2×ΓL(1,𝔽16)—21no—
223C2×ΓL(1,𝔽16)—21no—
224C2×ΓL(1,𝔽16)—21no—
225C2×ΓL(1,𝔽16)—21no—
226C2×ΓL(1,𝔽16)—21no—
227C2×ΓL(1,𝔽16)—21no—
228C2×ΓL(1,𝔽16)—21no—
229C2×ΓL(1,𝔽16)—21no—
230C2×ΓL(1,𝔽16)—44no—
231C2×ΓL(1,𝔽16)#4112yes—
232C2×C3×AGL(1,𝔽5)—21no—
233C2×C3×AGL(1,𝔽5)—21no—
234C2×C3×AGL(1,𝔽5)—21no—
235C2×C3×AGL(1,𝔽5)—21no—
236C2×C3×AGL(1,𝔽5)—21no—
237C2×C3×AGL(1,𝔽5)—21no—
238C2×C3×AGL(1,𝔽5)—21no—
239C2×C3×AGL(1,𝔽5)—21no—
240C2×C3×AGL(1,𝔽5)—21no—
241C2×C3×AGL(1,𝔽5)—21no—
242C2×C3×AGL(1,𝔽5)—21no—
243C2×C3×AGL(1,𝔽5)—44no—
244C2×C3×AGL(1,𝔽5)#4112yes—
245C3×C5×D4—22no—
246C2×C3×C4×C5C22×C411yescharacteristic
247C2×Dic15—41no—
248C2×Dic15—41no—
249C2×Dic15C22×C411yescharacteristic
250C2×Dic15C22×C411yescharacteristic
251C2×Dic15C22×C411yescharacteristic
252C2×Dic15C22×C411yescharacteristic
253C2×C5×Dic3—41no—
254C2×C5×Dic3—41no—
255C2×C5×Dic3C22×C411yescharacteristic
256C2×C5×Dic3C22×C411yescharacteristic
257C2×C5×Dic3C22×C411yescharacteristic
258C2×C5×Dic3C22×C411yescharacteristic
259C3×C22⋊D5—22no—
260C3×C22⋊D5—22no—
261C2×C3×Dic5C22×C411yescharacteristic
262C3×D20—22no—
263C3×C4×D5—21no—
264C3×C4×D5—21no—
265D5×Dic3—21no—
266D5×Dic3—21no—
267D5×Dic3—21no—
268D5×Dic3—21no—
269D5×Dic3—21no—
270D5×Dic3—21no—
271D5×Dic3—21no—
272D5×Dic3—21no—
273D5×Dic3—41no—
274D5×Dic3—41no—
275D5×Dic3—41no—
276D5×Dic3—41no—
277C22×C3×D4—51no—
278C23×C3×C4—51no—
279C23×Dic3—51no—
280C23×Dic3—51no—
281C23×Dic3—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×#217—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290D4×Dic3—51no—
291D4×Dic3—51no—
292D4×Dic3—51no—
293D4×Dic3—51no—
294D4×Dic3—51no—
295D4×Dic3—51no—
296D4×Dic3—51no—
297D4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
298C2×C4⋊Dic3—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305C2×C4×Dic3—51no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C3⋊#95—51no—
313C3⋊#95—51no—
314C3⋊#95—51no—
315C3⋊#95—51no—
316C3⋊#95—51no—
317C3⋊#95—51no—
318C3⋊#95—51no—
319C3⋊#95—51no—
320C23×D5C22×D311yescharacteristic
321C23×D5C22×D311yescharacteristic
322C22×AGL(1,𝔽5)—22no—
323C22×AGL(1,𝔽5)—22no—
324C22×AGL(1,𝔽5)—31no—
325C22×AGL(1,𝔽5)—31no—
326C22×AGL(1,𝔽5)—31no—
327C22×AGL(1,𝔽5)—31no—
328C22×AGL(1,𝔽5)—41no—
329C22×AGL(1,𝔽5)—62no—
330C22×AGL(1,𝔽5)—62no—
331C22×AGL(1,𝔽5)—121no—
332C22×AGL(1,𝔽5)C22×D311yescharacteristic
333C22×AGL(1,𝔽5)C22×D311yescharacteristic
334C22×AGL(1,𝔽5)C22×D311yescharacteristic
335C22×AGL(1,𝔽5)C22×D311yescharacteristic
336C2×C5×D4C4×D311yescharacteristic
337C22×C4×C5—31no—
338C22×C4×C5—31no—
339C2×C22⋊D5C4×D311yescharacteristic
340C2×C22⋊D5C4×D311yescharacteristic
341C22×Dic5—31no—
342C22×Dic5—31no—
343D4×D5—22no—
344D4×D5—22no—
345C2×D20C4×D311yescharacteristic
346C2×C4×D5—31no—
347C2×C4×D5—31no—
348C2×C4×D5—31no—
349C2×C4×D5—31no—
350C2×C4×D5—31no—
351C2×C4×D5—31no—
352C2×C4×D5—31no—
353C2×C4×D5—31no—
354C2×C4×D5—121no—
355C2×C4×D5—121no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C2×C4×D5C22×D311yescharacteristic
359C22⋊AGL(1,𝔽5)—22no—
360C22⋊AGL(1,𝔽5)—22no—
361C22⋊AGL(1,𝔽5)—41no—
362C22⋊AGL(1,𝔽5)—62no—
363C22⋊AGL(1,𝔽5)—62no—
364C22⋊AGL(1,𝔽5)—121no—
365C4⋊AGL(1,𝔽5)—121no—
366C4⋊AGL(1,𝔽5)—121no—
367C4×AGL(1,𝔽5)—62no—
368C4×AGL(1,𝔽5)—62no—
369C4×AGL(1,𝔽5)—121no—
370C4×AGL(1,𝔽5)—121no—
371C5×C4⋊C4—31no—
372C5×C22⋊C4—31no—
373C5×C22⋊C4—31no—
374C42×C5—31no—
375C22⋊Dic5—31no—
376C22⋊Dic5—31no—
377#685—31no—
378#685—31no—
379#685—31no—
380#685—31no—
381C4⋊Dic5—31no—
382#683—31no—
383#683—31no—
384C4×Dic5—31no—
385C4×Dic5—31no—
386C4×Dic5—31no—
387C2×C4×D4—151no—
388#388—151no—
389#388—151no—
390#387—151no—
391#387—151no—
392#386—51no—
393#386—151no—
394#383—151no—
395#381—151no—
396#380—151no—
397C4×C22⋊C4—151no—
398C4×C22⋊C4—151no—
399C4×C22⋊C4—151no—
400#376—151no—
401C2×#95—151no—
402C22×C3×C5—21no—
403C22×C3×C5—21no—
404C22×C3×C5—21no—
405C22×C3×C5—21no—
406C22×C3×C5—21no—
407C22×C3×C5#11712yes—
408C22×C3×C5C23×C411yescharacteristic
409C2×C3×D5—21no—
410C2×C3×D5—21no—
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—22no—
414C2×C3×D5—22no—
415C2×C3×D5—21no—
416C2×C3×D5—21no—
417C2×C3×D5—21no—
418C2×C3×D5—41no—
419C2×C3×D5—41no—
420C2×C3×D5—41no—
421C2×C3×D5—41no—
422C2×C3×D5#11712yes—
423C2×C3×D5C2×#4111yescharacteristic
424C2×C3×D5C2×#4111yescharacteristic
425C2×C3×D5C2×#4111yescharacteristic
426C2×C3×D5C2×#4111yescharacteristic
427C2×C3×D5H(5,𝔽2)11yescharacteristic
428C2×C3×D5H(5,𝔽2)11yescharacteristic
429ΓL(1,𝔽16)—22no—
430ΓL(1,𝔽16)—41no—
431ΓL(1,𝔽16)—41no—
432ΓL(1,𝔽16)—41no—
433C3×AGL(1,𝔽5)—22no—
434C3×AGL(1,𝔽5)—41no—
435C3×AGL(1,𝔽5)—41no—
436C3×AGL(1,𝔽5)—41no—
437C3×C4×C5—21no—
438Dic15—21no—
439Dic15—21no—
440Dic15—21no—
441Dic15—21no—
442C3×Dic5—21no—
443C5×Dic3—21no—
444C5×Dic3—21no—
445C5×Dic3—21no—
446C5×Dic3—21no—
447C24×C3—51no—
448C24×C3—51no—
449C2×C3×D4—51no—
450C2×C3×D4—51no—
451C2×C3×D4—51no—
452C2×C3×D4—102no—
453C2×C3×D4—102no—
454C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4—51no—
459C22×C3×C4—51no—
460C22×C3×C4—102no—
461C22×C3×C4—102no—
462C22×C3×C4—201no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—102no—
478C22×Dic3—102no—
479C22×Dic3—201no—
480C22×Dic3—201no—
481C22×Dic3—201no—
482C22×Dic3—201no—
483C22×Dic3—201no—
484C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
485C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
486C3×C22⋊C4—102no—
487C3×C22⋊C4—102no—
488C3×C22⋊C4—201no—
489#217—51no—
490#217—51no—
491#217—51no—
492#217—51no—
493#217—51no—
494#217—51no—
495#217—102no—
496#217—102no—
497#217—201no—
498#217C2×AGL(1,𝔽5)11yescharacteristic
499#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
500C4⋊Dic3—51no—
501C4⋊Dic3—51no—
502C4⋊Dic3—51no—
503C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
504Dic3⋊C4—201no—
505Dic3⋊C4—201no—
506C4×Dic3—51no—
507C4×Dic3—51no—
508C4×Dic3—51no—
509C4×Dic3—102no—
510C4×Dic3—102no—
511C4×Dic3—201no—
512C4×Dic3—201no—
513C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
514C23×C5C2×C4×D311yescharacteristic
515C23×C5C2×C4×D311yescharacteristic
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—21no—
519C22×D5—21no—
520C22×D5—21no—
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—21no—
526C22×D5C2×C4×D311yescharacteristic
527C22×D5C2×C4×D311yescharacteristic
528C22×D5#23712yes—
529C22×D5#23712yes—
530C22×D5C23×D311yescharacteristic
531C2×AGL(1,𝔽5)—21no—
532C2×AGL(1,𝔽5)—21no—
533C2×AGL(1,𝔽5)—21no—
534C2×AGL(1,𝔽5)—21no—
535C2×AGL(1,𝔽5)—21no—
536C2×AGL(1,𝔽5)—21no—
537C2×AGL(1,𝔽5)—21no—
538C2×AGL(1,𝔽5)—21no—
539C2×AGL(1,𝔽5)—21no—
540C2×AGL(1,𝔽5)—21no—
541C2×AGL(1,𝔽5)—21no—
542C2×AGL(1,𝔽5)—32no—
543C2×AGL(1,𝔽5)—44no—
544C2×AGL(1,𝔽5)—61no—
545C2×AGL(1,𝔽5)—61no—
546C2×AGL(1,𝔽5)—61no—
547C2×AGL(1,𝔽5)—61no—
548C2×AGL(1,𝔽5)—61no—
549C2×AGL(1,𝔽5)—61no—
550C2×AGL(1,𝔽5)—61no—
551C2×AGL(1,𝔽5)—61no—
552C2×AGL(1,𝔽5)—61no—
553C2×AGL(1,𝔽5)—61no—
554C2×AGL(1,𝔽5)—61no—
555C2×AGL(1,𝔽5)—124no—
556C2×AGL(1,𝔽5)#23712yes—
557C5×D4—22no—
558C2×C4×C5—31no—
559C2×C4×C5—31no—
560C2×C4×C5—31no—
561C2×C4×C5—31no—
562C2×C4×C5—121no—
563C2×C4×C5—121no—
564C2×C4×C5C2×C4×D311yescharacteristic
565C22⋊D5—22no—
566C22⋊D5—22no—
567C2×Dic5—31no—
568C2×Dic5—31no—
569C2×Dic5—31no—
570C2×Dic5—31no—
571C2×Dic5—121no—
572C2×Dic5—121no—
573C2×Dic5C2×C4×D311yescharacteristic
574D20—22no—
575C4×D5—21no—
576C4×D5—21no—
577C4×D5—61no—
578C4×D5—61no—
579C4×D5—61no—
580C4×D5—61no—
581C4×D5—61no—
582C4×D5—61no—
583C4×D5—61no—
584C4×D5—61no—
585C4×D5—121no—
586C4×D5—121no—
587C4×D5—121no—
588C4×D5—121no—
589C22×D4—51no—
590C23×C4—51no—
591C23×C4—151no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—31no—
595C4×D4—151no—
596C4×D4—151no—
597C4×D4—151no—
598C4×D4—151no—
599C4×D4—151no—
600C4×D4—151no—
601C4×D4—151no—
602C2×C4⋊C4—151no—
603C2×C4⋊C4—151no—
604C2×C4⋊C4—151no—
605C2×C22⋊C4—51no—
606C2×C22⋊C4—51no—
607C2×C22⋊C4—51no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C22⋊C4—151no—
611C2×C22⋊C4—151no—
612C2×C22⋊C4—151no—
613C2×C42—151no—
614C2×C42—151no—
615C2×C42—151no—
616C2×C42—151no—
617C2×C42—151no—
618#95—51no—
619#95—51no—
620#95—151no—
621#95—151no—
622#95—151no—
623#95—151no—
624#95—151no—
625#95—151no—
626#95—151no—
627#95—151no—
628#95—151no—
629#95—151no—
630#95—151no—
631#95—151no—
632C2×C3×C5—22no—
633C2×C3×C5—41no—
634C2×C3×C5C2×#11711yescharacteristic
635C2×C3×C5C4×#4111yescharacteristic
636C2×C3×C5#51811yescharacteristic
637C3×D5—22no—
638C3×D5—41no—
639C3×D5#55111yescharacteristic
640C3×D5#55111yescharacteristic
641C3×D5#55311yescharacteristic
642C3×D5#55311yescharacteristic
643C23×C3—51no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—51no—
647C23×C3—51no—
648C23×C3—101no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3—101no—
653C23×C3—101no—
654C23×C3—101no—
655C23×C3—101no—
656C23×C3—101no—
657C23×C3—101no—
658C23×C3C22×AGL(1,𝔽5)11yescharacteristic
659C23×C3C22×AGL(1,𝔽5)11yescharacteristic
660C3×D4—22no—
661C3×D4—102no—
662C3×D4—102no—
663C3×D4—102no—
664C2×C3×C4—52no—
665C2×C3×C4—51no—
666C2×C3×C4—101no—
667C2×C3×C4—101no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—204no—
680C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—52no—
684C2×Dic3—51no—
685C2×Dic3—51no—
686C2×Dic3—51no—
687C2×Dic3—51no—
688C2×Dic3—101no—
689C2×Dic3—101no—
690C2×Dic3—101no—
691C2×Dic3—101no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—201no—
708C2×Dic3—201no—
709C2×Dic3—201no—
710C2×Dic3—201no—
711C2×Dic3—201no—
712C2×Dic3—201no—
713C2×Dic3—204no—
714C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
715C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
716C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
717C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
718C22×C5—21no—
719C22×C5—21no—
720C22×C5—21no—
721C22×C5—21no—
722C22×C5—21no—
723C22×C5#87712yes—
724C22×C5C22×C4×D311yescharacteristic
725C2×D5—21no—
726C2×D5—21no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—21no—
732C2×D5—21no—
733C2×D5—21no—
734C2×D5—41no—
735C2×D5—41no—
736C2×D5—41no—
737C2×D5—41no—
738C2×D5#87712yes—
739C2×D5C2×#23711yescharacteristic
740C2×D5C2×#23711yescharacteristic
741C2×D5C2×#23711yescharacteristic
742C2×D5#100411yescharacteristic
743C2×D5D3×#4111yescharacteristic
744C2×D5#100911yescharacteristic
745AGL(1,𝔽5)—22no—
746AGL(1,𝔽5)—41no—
747AGL(1,𝔽5)—41no—
748AGL(1,𝔽5)—41no—
749AGL(1,𝔽5)—62no—
750AGL(1,𝔽5)—121no—
751AGL(1,𝔽5)—121no—
752AGL(1,𝔽5)—121no—
753C4×C5—21no—
754C4×C5—61no—
755C4×C5—61no—
756C4×C5—61no—
757C4×C5—61no—
758Dic5—21no—
759Dic5—61no—
760Dic5—61no—
761Dic5—61no—
762Dic5—61no—
763C24—51no—
764C24—51no—
765C2×D4—51no—
766C2×D4—51no—
767C2×D4—51no—
768C2×D4—102no—
769C2×D4—102no—
770C2×D4D3×AGL(1,𝔽5)11yescharacteristic
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—51no—
774C22×C4—51no—
775C22×C4—51no—
776C22×C4—51no—
777C22×C4—51no—
778C22×C4—102no—
779C22×C4—102no—
780C22×C4—151no—
781C22×C4—151no—
782C22×C4—151no—
783C22×C4—151no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—201no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—601no—
798C22×C4—601no—
799C22×C4—601no—
800C22×C4—601no—
801C22×C4—601no—
802C4⋊C4—31no—
803C4⋊C4—151no—
804C4⋊C4—151no—
805C4⋊C4—151no—
806C4⋊C4—601no—
807C4⋊C4—601no—
808C22⋊C4—31no—
809C22⋊C4—31no—
810C22⋊C4—102no—
811C22⋊C4—102no—
812C22⋊C4—151no—
813C22⋊C4—151no—
814C22⋊C4—151no—
815C22⋊C4—151no—
816C22⋊C4—151no—
817C22⋊C4—151no—
818C22⋊C4—201no—
819C22⋊C4—302no—
820C22⋊C4—302no—
821C22⋊C4—601no—
822C42—31no—
823C42—151no—
824C42—151no—
825C42—151no—
826C42—302no—
827C42—302no—
828C42—601no—
829C42—601no—
830C3×C5#235311yescharacteristic, complemented, Hall
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—51no—
837C22×C3—51no—
838C22×C3—51no—
839C22×C3—51no—
840C22×C3—51no—
841C22×C3—51no—
842C22×C3—52no—
843C22×C3—102no—
844C22×C3—102no—
845C22×C3—102no—
846C22×C3—102no—
847C22×C3—101no—
848C22×C3—101no—
849C22×C3—101no—
850C22×C3—101no—
851C22×C3—101no—
852C22×C3—201no—
853C22×C3—201no—
854C22×C3—201no—
855C22×C3—201no—
856C22×C3#413012yes—
857C22×C3C23×AGL(1,𝔽5)11yescharacteristic
858C3×C4—21no—
859C3×C4—102no—
860C3×C4—101no—
861C3×C4—201no—
862C3×C4—201no—
863C3×C4—201no—
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—102no—
869Dic3—101no—
870Dic3—101no—
871Dic3—101no—
872Dic3—101no—
873Dic3—201no—
874Dic3—201no—
875Dic3—201no—
876C2×C5—22no—
877C2×C5—41no—
878C2×C5C2×#87711yescharacteristic
879C2×C5C4×#23711yescharacteristic
880C2×C5#554511yescharacteristic
881D5—22no—
882D5—41no—
883D5#558711yescharacteristic
884D5#560111yescharacteristic
885D5#561811yescharacteristic
886D5#565811yescharacteristic
887C23—51no—
888C23—52no—
889C23—52no—
890C23—51no—
891C23—51no—
892C23—101no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—101no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23C2×D3×AGL(1,𝔽5)11yescharacteristic
903C23C2×D3×AGL(1,𝔽5)11yescharacteristic
904D4—22no—
905D4—102no—
906D4—102no—
907D4—102no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—52no—
913C2×C4—51no—
914C2×C4—101no—
915C2×C4—101no—
916C2×C4—101no—
917C2×C4—101no—
918C2×C4—101no—
919C2×C4—101no—
920C2×C4—101no—
921C2×C4—101no—
922C2×C4—101no—
923C2×C4—101no—
924C2×C4—101no—
925C2×C4—101no—
926C2×C4—101no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—152no—
930C2×C4—151no—
931C2×C4—151no—
932C2×C4—151no—
933C2×C4—151no—
934C2×C4—204no—
935C2×C4—301no—
936C2×C4—301no—
937C2×C4—301no—
938C2×C4—301no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—601no—
955C2×C4—601no—
956C2×C4—601no—
957C2×C4—601no—
958C2×C4—601no—
959C2×C4—601no—
960C2×C4—604no—
961C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
962C2×C3—22no—
963C2×C3—41no—
964C2×C3—51no—
965C2×C3—51no—
966C2×C3—51no—
967C2×C3—51no—
968C2×C3—102no—
969C2×C3—201no—
970C2×C3C2×#413011yescharacteristic
971C2×C3#6625811yescharacteristic
972C2×C3#41×AGL(1,𝔽5)11yescharacteristic
973C5#7467411yescharacteristic, complemented, Sylow
974C22—21no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—51no—
980C22—51no—
981C22—51no—
982C22—51no—
983C22—51no—
984C22—51no—
985C22—52no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—101no—
991C22—101no—
992C22—101no—
993C22—101no—
994C22—101no—
995C22—201no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22#9192312yes—
1000C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1001C4—21no—
1002C4—61no—
1003C4—61no—
1004C4—61no—
1005C4—61no—
1006C4—102no—
1007C4—101no—
1008C4—201no—
1009C4—201no—
1010C4—201no—
1011C4—302no—
1012C4—301no—
1013C4—301no—
1014C4—301no—
1015C4—301no—
1016C4—601no—
1017C4—601no—
1018C4—601no—
1019C3#1061718011yescharacteristic, complemented, Sylow
1020C2—22no—
1021C2—41no—
1022C2—51no—
1023C2—51no—
1024C2—51no—
1025C2—51no—
1026C2—102no—
1027C2—201no—
1028C2AGL(1,𝔽5)×#23711yescharacteristic
1029C2#1175684511yescharacteristic
1030C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
4. #11752028C2semidirect
5. #11752021C2semidirect
6. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
7. #11752018C2semidirect
8. #11752017C2semidirect
9. AGL(1,𝔽5)×#217C2semidirect
10. #11751984C2semidirect
11. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
12. #11751840C2semidirect
13. #11751839C2semidirect
14. #11751832C2semidirect
15. #11751750C2semidirect
34. D4×Dic15C4semidirect
35. C5×D4×Dic3C4semidirect
36. #91559C4semidirect
37. #91559C4semidirect
38. Dic3×C22⋊D5C4semidirect
39. Dic3×C22⋊D5C4semidirect
42. #91434C4semidirect
43. Dic3×D20C4semidirect
94. C22×Dic15C2×C4semidirect
96. C22×C5×Dic3C2×C4semidirect
109. C2×D5×Dic3C2×C4semidirect
110. C2×D5×Dic3C2×C4semidirect
128. #6719C2×C4semidirect
129. C4⋊Dic15C2×C4semidirect
130. C4×Dic15C2×C4semidirect
132. C5×#217C2×C4semidirect
133. C5×C4⋊Dic3C2×C4semidirect
134. C4×C5×Dic3C2×C4semidirect
135. #6668C2×C4semidirect
136. #6668C2×C4semidirect
139. #6665C2×C4semidirect
140. #6665C2×C4semidirect
141. Dic3×Dic5C2×C4semidirect
142. Dic3×Dic5C2×C4semidirect
297. D4×Dic3AGL(1,𝔽5)semidirect
485. C22×Dic3C2×AGL(1,𝔽5)semidirect
499. #217C2×AGL(1,𝔽5)semidirect
503. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
513. C4×Dic3C2×AGL(1,𝔽5)semidirect
830. C3×C5#2353semidirect
973. C5#74674semidirect
1019. C3#10617180semidirect

Maximal subgroups

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

subgroupindex
D4×D5×Dic32
#117524382
C3×#657792
#117520282
#117520212
Dic3×C22⋊AGL(1,𝔽5)2
#117520182
#117520172
AGL(1,𝔽5)×#2172
#117519842
C2×(C2×AGL(1,𝔽5))⋊Dic32
#117518402
#117518392
#117518322
#117517502
#106171803
#746745