Finite Group Databasebeta

← #14329820

Subgroups — #14329820

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#897C211yesmaximal, characteristic
2#11752370C211yesmaximal, characteristic, complemented
3C3×#65711C211yesmaximal, characteristic, complemented
4#11751934C211yesmaximal, characteristic
5#11751932C211yesmaximal, characteristic
6#11751931C211yesmaximal, characteristic
7D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
8AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic
9#11751848C211yesmaximal, characteristic
10#11751846C211yesmaximal, characteristic, complemented
11#11751842C211yesmaximal, characteristic, complemented
12#11751842C211yesmaximal, characteristic, complemented
13#11751840C211yesmaximal, characteristic, complemented
14#11751839C211yesmaximal, characteristic, complemented
15AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic, complemented
16#10617287—31nomaximal, Hall
17C22×D3×AGL(1,𝔽5)C2211yescharacteristic
18C22×D3×AGL(1,𝔽5)C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×D5×Dic6C2211yescharacteristic
21C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
22C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×(C2×D3)⋊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#91786C411yescharacteristic, complemented
34C5×#897C411yescharacteristic, complemented
35C3×D5×C4⋊C4C2211yescharacteristic
36D5×(C2×D3)⋊C4C2211yescharacteristic
37D5×(C2×D3)⋊C4C2211yescharacteristic
38#91419C411yescharacteristic, complemented
39#91419C411yescharacteristic, complemented
40#91417C411yescharacteristic, complemented
41#91417C411yescharacteristic, complemented
42D5×C4⋊Dic3C2211yescharacteristic
43D5×C4⋊Dic3C2211yescharacteristic
44#91383C411yescharacteristic, complemented
45#91365C411yescharacteristic, complemented
46#91235C2211yescharacteristic
47#91235C2211yescharacteristic
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#75311—51nomaximal, Hall
61D5×C22⋊Q8—31no—
62(C2×AGL(1,𝔽5))⋊Q8—31no—
63(C2×AGL(1,𝔽5))⋊Q8—31no—
64C4×C22⋊AGL(1,𝔽5)—31no—
65C2×(C2×AGL(1,𝔽5))⋊C4—31no—
66#65711—31no—
67#65711—31no—
68#65711—31no—
69#65711D311yescharacteristic, complemented
70C4⋊C4×AGL(1,𝔽5)—31no—
71C4⋊C4×AGL(1,𝔽5)—31no—
72#65699—31no—
73#65699—31no—
74C22⋊C4×AGL(1,𝔽5)—31no—
75C22⋊C4×AGL(1,𝔽5)—31no—
76C22×D3×D5C2311yescharacteristic
77C22×ΓL(1,𝔽16)C2311yescharacteristic
78C22×ΓL(1,𝔽16)C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×C3×AGL(1,𝔽5)C2311yescharacteristic
82C22×C3×AGL(1,𝔽5)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)C2311yescharacteristic
85C2×D3×AGL(1,𝔽5)—22no—
86C2×D3×AGL(1,𝔽5)—22no—
87C2×D3×AGL(1,𝔽5)—22no—
88C2×D3×AGL(1,𝔽5)—22no—
89C2×D3×AGL(1,𝔽5)—41no—
90C2×D3×AGL(1,𝔽5)—41no—
91C2×C4×D15C2×C411yescharacteristic
92C2×Dic30C2×C411yescharacteristic, complemented
93C2×C4×C5×D3C2×C411yescharacteristic
94C2×C5×Dic6C2×C411yescharacteristic, complemented
95C2×C3×C4×D5C2311yescharacteristic
96C2×C3×C4×D5C2311yescharacteristic
97C2×C3×C4×D5C2311yescharacteristic
98C2×#1204C2×C411yescharacteristic, complemented
99C2×#1204C2×C411yescharacteristic, complemented
100C2×#1200C2×C411yescharacteristic
101C2×D3×Dic5C2×C411yescharacteristic
102C2×D5×Dic3C2311yescharacteristic
103C2×D5×Dic3C2311yescharacteristic
104C2×D5×Dic3C2311yescharacteristic
105C4×D3×D5—41no—
106C4×D3×D5—41no—
107D5×Dic6—41no—
108D5×Dic6—41no—
109C4⋊ΓL(1,𝔽16)—22no—
110C4×ΓL(1,𝔽16)—22no—
111C3×C4⋊AGL(1,𝔽5)—22no—
112C3×C4×AGL(1,𝔽5)—22no—
113Dic3⋊AGL(1,𝔽5)—41no—
114Dic3⋊AGL(1,𝔽5)—41no—
115(C2×D3)⋊AGL(1,𝔽5)—22no—
116(C2×D3)⋊AGL(1,𝔽5)Q814yescomplemented
117Dic3×AGL(1,𝔽5)—41no—
118Dic3×AGL(1,𝔽5)—41no—
119Dic3×AGL(1,𝔽5)—41no—
120Dic3×AGL(1,𝔽5)—41no—
121C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
122#6714C2×C411yescharacteristic
123#6714C2×C411yescharacteristic
124C4⋊Dic15C2×C411yescharacteristic, complemented
125C4⋊Dic15C2×C411yescharacteristic, complemented
126C5×(C2×D3)⋊C4C2×C411yescharacteristic
127C5×(C2×D3)⋊C4C2×C411yescharacteristic
128C5×C4⋊Dic3C2×C411yescharacteristic, complemented
129C5×C4⋊Dic3C2×C411yescharacteristic, complemented
130C3×C4⋊Dic5C2×C411yescharacteristic, complemented
131C3×#683C2×C411yescharacteristic, complemented
132C3×#683C2×C411yescharacteristic, complemented
133#6668C2×C411yescharacteristic, complemented
134#6668C2×C411yescharacteristic, complemented
135#6668C2×C411yescharacteristic, complemented
136#6668C2×C411yescharacteristic, complemented
137#6667C2×C411yescharacteristic
138#6667C2×C411yescharacteristic
139(C2×D3)⋊Dic5C2×C411yescharacteristic
140(C2×D3)⋊Dic5C2×C411yescharacteristic
141C2×#897—51no—
142C3×#387—51no—
143#4989—51no—
144#4980—51no—
145Dic3×C4⋊C4—51no—
146C4×(C2×D3)⋊C4—51no—
147C4×C4⋊Dic3—51no—
148#4668—51no—
149#4666—51no—
150#4666—51no—
151D3×#95—51no—
152#4654—51no—
153#4653—51no—
154#4646—51no—
155#4646—51no—
156C23×AGL(1,𝔽5)—31no—
157C23×AGL(1,𝔽5)—31no—
158C2×Q8×D5—31no—
159C22×C4×D5—31no—
160C2×C22⋊AGL(1,𝔽5)—31no—
161C2×C22⋊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
166C2×C4×AGL(1,𝔽5)—31no—
167C2×C4×AGL(1,𝔽5)—31no—
168C2×C4×AGL(1,𝔽5)—31no—
169C2×C4×AGL(1,𝔽5)—31no—
170C2×C4×AGL(1,𝔽5)—31no—
171C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
172C5×C22⋊Q8—31no—
173#4092—31no—
174#4070—31no—
175#4043—31no—
176#4042—31no—
177#4042—31no—
178D5×C4⋊C4—31no—
179D5×C4⋊C4—31no—
180D5×C4⋊C4C2×D311yescharacteristic
181D5×C22⋊C4—31no—
182D5×C22⋊C4—31no—
183#4024—31no—
184#4024—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))⋊C4—31no—
194(C2×AGL(1,𝔽5))⋊C4—31no—
195(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
196(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
197(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
198(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
199#2368—151noSylow
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C2411yescharacteristic
203C2×D3×D5—21no—
204C2×D3×D5—21no—
205C2×D3×D5—21no—
206C2×D3×D5—21no—
207C2×D3×D5C2×Q812yes—
208C2×D3×D5#4112yes—
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)—21no—
217C2×ΓL(1,𝔽16)—21no—
218C2×ΓL(1,𝔽16)—21no—
219C2×ΓL(1,𝔽16)C2×Q812yes—
220C2×ΓL(1,𝔽16)#4112yes—
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)—21no—
230C2×C3×AGL(1,𝔽5)—21no—
231C2×C3×AGL(1,𝔽5)C2×Q812yes—
232C2×C3×AGL(1,𝔽5)#4112yes—
233D3×AGL(1,𝔽5)—44no—
234D3×AGL(1,𝔽5)—44no—
235C2×C3×C4×C5C22×C411yescharacteristic
236C2×C3×C4×C5C22×C411yescharacteristic
237C2×C3×C4×C5C22×C411yescharacteristic
238C2×Dic15C22×C411yescharacteristic
239C2×Dic15C22×C411yescharacteristic
240C2×Dic15C22×C411yescharacteristic
241C4×D15—41no—
242Dic30—41no—
243C2×C5×Dic3C22×C411yescharacteristic
244C2×C5×Dic3C22×C411yescharacteristic
245C2×C5×Dic3C22×C411yescharacteristic
246C4×C5×D3—41no—
247C5×Dic6—41no—
248C2×C3×Dic5C22×C411yescharacteristic
249C2×C3×Dic5C22×C411yescharacteristic
250C2×C3×Dic5C22×C411yescharacteristic
251C3×C4×D5—21no—
252C3×C4×D5—21no—
253C3×C4×D5—21no—
254C3×C4×D5—21no—
255C3×C4×D5—21no—
256C3×C4×D5—21no—
257#1204—41no—
258#1204—41no—
259#1200—41no—
260D3×Dic5—41no—
261D5×Dic3—21no—
262D5×Dic3—21no—
263D5×Dic3—21no—
264D5×Dic3—21no—
265D5×Dic3—21no—
266D5×Dic3—21no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C22×C4×D3—51no—
270C22×Dic6—51no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C42—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×C4⋊Dic3—51no—
279C2×C4⋊Dic3—51no—
280C2×C4⋊Dic3—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288#897—51no—
289#897—51no—
290#897—51no—
291#897—51no—
292#897—51no—
293#897—51no—
294#897—51no—
295#897AGL(1,𝔽5)11yescharacteristic, complemented
296C3×#95—51no—
297C3×#95—51no—
298C3×#95—51no—
299C3×#95—51no—
300C3⋊#95—51no—
301C3⋊#95—51no—
302C3⋊#95—51no—
303C3⋊#95—51no—
304C3⋊#95—51no—
305C3⋊#95—51no—
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C23×D5—31no—
311C22×AGL(1,𝔽5)—31no—
312C22×AGL(1,𝔽5)—31no—
313C22×AGL(1,𝔽5)—31no—
314C22×AGL(1,𝔽5)—31no—
315C22×AGL(1,𝔽5)—62no—
316C22×AGL(1,𝔽5)—62no—
317C22×AGL(1,𝔽5)—62no—
318C22×AGL(1,𝔽5)—62no—
319C22×AGL(1,𝔽5)—121no—
320C22×AGL(1,𝔽5)—121no—
321C22×AGL(1,𝔽5)C22×D311yescharacteristic
322C22×AGL(1,𝔽5)C22×D311yescharacteristic
323C22×AGL(1,𝔽5)C22×D311yescharacteristic
324C22×AGL(1,𝔽5)C22×D311yescharacteristic
325C2×C5×Q8—31no—
326C22×C4×C5—31no—
327C22×Dic5—31no—
328Q8×D5—121no—
329Q8×D5—121no—
330C2×C4×D5—31no—
331C2×C4×D5—31no—
332C2×C4×D5—31no—
333C2×C4×D5—31no—
334C2×C4×D5—31no—
335C2×C4×D5—121no—
336C2×C4×D5—121no—
337C2×C4×D5C22×D311yescharacteristic
338C2×C4×D5C22×D311yescharacteristic
339C2×C4×D5C22×D311yescharacteristic
340C2×Dic10—31no—
341C2×Dic10—31no—
342C2×Dic10—31no—
343C22⋊AGL(1,𝔽5)—34no—
344C22⋊AGL(1,𝔽5)—62no—
345C4⋊AGL(1,𝔽5)—22no—
346C4⋊AGL(1,𝔽5)—62no—
347C4⋊AGL(1,𝔽5)—121no—
348C4⋊AGL(1,𝔽5)—121no—
349C4×AGL(1,𝔽5)—22no—
350C4×AGL(1,𝔽5)—62no—
351C4×AGL(1,𝔽5)—121no—
352C4×AGL(1,𝔽5)—121no—
353C4×AGL(1,𝔽5)—121no—
354C4×AGL(1,𝔽5)—121no—
355C5×C4⋊C4—31no—
356C5×C4⋊C4—31no—
357C5×C4⋊C4C4×D311yescharacteristic, complemented
358C5×C22⋊C4—31no—
359C5×C22⋊C4—31no—
360C22⋊Dic5—31no—
361C22⋊Dic5—31no—
362#685—31no—
363#685—31no—
364#685—31no—
365#685—31no—
366C4⋊Dic5—31no—
367C4⋊Dic5—31no—
368C4⋊Dic5C4×D311yescharacteristic, complemented
369#683—31no—
370#683—31no—
371#683—31no—
372#683—31no—
373#683C4×D311yescharacteristic, complemented
374#683C4×D311yescharacteristic, complemented
375C2×C22⋊Q8—151no—
376#391—151no—
377#391—151no—
378#387—51no—
379#387—151no—
380#387—151no—
381#387—151no—
382#385—151no—
383#385—151no—
384C4×C4⋊C4—151no—
385C4×C4⋊C4—151no—
386C4×C22⋊C4—151no—
387C4×C22⋊C4—151no—
388C4×C22⋊C4—151no—
389C2×#95—151no—
390C22×C3×C5C23×C411yescharacteristic
391C2×D15—21no—
392C2×D15—21no—
393C2×D15C4×Q812yes—
394C2×C5×D3—21no—
395C2×C5×D3—21no—
396C2×C5×D3C4×Q812yes—
397C2×C3×D5C22×Q811yescharacteristic
398C2×C3×D5C2×#4111yescharacteristic
399C2×C3×D5C2×#4111yescharacteristic
400C2×C3×D5C2×#4111yescharacteristic
401C2×C3×D5H(5,𝔽2)11yescharacteristic
402C2×C3×D5H(5,𝔽2)11yescharacteristic
403D3×D5—22no—
404D3×D5—22no—
405D3×D5—22no—
406D3×D5—22no—
407ΓL(1,𝔽16)—22no—
408ΓL(1,𝔽16)—22no—
409ΓL(1,𝔽16)—41no—
410ΓL(1,𝔽16)—41no—
411C3×AGL(1,𝔽5)—22no—
412C3×AGL(1,𝔽5)—22no—
413C3×AGL(1,𝔽5)—41no—
414C3×AGL(1,𝔽5)—41no—
415C3×C4×C5—21no—
416C3×C4×C5—21no—
417C3×C4×C5—21no—
418Dic15—21no—
419Dic15—21no—
420Dic15—21no—
421C3×Dic5—21no—
422C3×Dic5—21no—
423C3×Dic5—21no—
424C5×Dic3—21no—
425C5×Dic3—21no—
426C5×Dic3—21no—
427C23×D3—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4—51no—
435C22×Dic3—51no—
436C22×Dic3—51no—
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3—51no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C2×C4×D3—51no—
443C2×C4×D3—51no—
444C2×C4×D3—51no—
445C2×C4×D3—102no—
446C2×C4×D3—102no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C2×C4×D3—201no—
450C2×C4×D3—201no—
451C2×C4×D3—201no—
452C2×C4×D3—201no—
453C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
454C2×Dic6—51no—
455C2×Dic6—51no—
456C2×Dic6—51no—
457C2×Dic6—201no—
458C2×Dic6—201no—
459C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
460C3×C4⋊C4—51no—
461C3×C4⋊C4—51no—
462C3×C4⋊C4—51no—
463C3×C4⋊C4—102no—
464C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
465C3×C42—102no—
466(C2×D3)⋊C4—54no—
467(C2×D3)⋊C4—51no—
468(C2×D3)⋊C4—51no—
469(C2×D3)⋊C4—51no—
470(C2×D3)⋊C4—51no—
471(C2×D3)⋊C4—51no—
472(C2×D3)⋊C4—51no—
473(C2×D3)⋊C4—102no—
474(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
475(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
476C4⋊Dic3—51no—
477C4⋊Dic3—51no—
478C4⋊Dic3—51no—
479C4⋊Dic3—51no—
480C4⋊Dic3—51no—
481C4⋊Dic3—51no—
482C4⋊Dic3—102no—
483C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
484C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
485Dic3⋊C4—201no—
486Dic3⋊C4—201no—
487C4×Dic3—102no—
488C4×Dic3—201no—
489C4×Dic3—201no—
490C4×Dic3—201no—
491C4×Dic3—201no—
492C23×C5—31no—
493C22×D5—31no—
494C22×D5—32no—
495C22×D5—32no—
496C22×D5—61no—
497C22×D5—61no—
498C22×D5—61no—
499C22×D5—61no—
500C22×D5C23×D311yescharacteristic
501C2×AGL(1,𝔽5)—21no—
502C2×AGL(1,𝔽5)—21no—
503C2×AGL(1,𝔽5)—21no—
504C2×AGL(1,𝔽5)—21no—
505C2×AGL(1,𝔽5)—21no—
506C2×AGL(1,𝔽5)—21no—
507C2×AGL(1,𝔽5)—21no—
508C2×AGL(1,𝔽5)—21no—
509C2×AGL(1,𝔽5)—21no—
510C2×AGL(1,𝔽5)—21no—
511C2×AGL(1,𝔽5)—32no—
512C2×AGL(1,𝔽5)—32no—
513C2×AGL(1,𝔽5)—61no—
514C2×AGL(1,𝔽5)—61no—
515C2×AGL(1,𝔽5)—61no—
516C2×AGL(1,𝔽5)—61no—
517C2×AGL(1,𝔽5)—61no—
518C2×AGL(1,𝔽5)—61no—
519C2×AGL(1,𝔽5)—61no—
520C2×AGL(1,𝔽5)—61no—
521C2×AGL(1,𝔽5)—61no—
522C2×AGL(1,𝔽5)—61no—
523C2×AGL(1,𝔽5)—124no—
524C2×AGL(1,𝔽5)—124no—
525C2×AGL(1,𝔽5)#23712yes—
526C2×AGL(1,𝔽5)D3×Q812yes—
527C5×Q8—121no—
528C2×C4×C5—31no—
529C2×C4×C5—31no—
530C2×C4×C5—31no—
531C2×C4×C5—121no—
532C2×C4×C5C2×C4×D311yescharacteristic
533C2×C4×C5C2×C4×D311yescharacteristic
534C2×C4×C5C2×C4×D311yescharacteristic
535C2×Dic5—31no—
536C2×Dic5—31no—
537C2×Dic5—31no—
538C2×Dic5—121no—
539C2×Dic5C2×C4×D311yescharacteristic
540C2×Dic5C2×C4×D311yescharacteristic
541C2×Dic5C2×C4×D311yescharacteristic
542C4×D5—21no—
543C4×D5—21no—
544C4×D5—21no—
545C4×D5—21no—
546C4×D5—21no—
547C4×D5—21no—
548C4×D5—61no—
549C4×D5—61no—
550C4×D5—61no—
551C4×D5—61no—
552C4×D5—61no—
553C4×D5—61no—
554C4×D5—121no—
555C4×D5—121no—
556Dic10—121no—
557Dic10—121no—
558Dic10—121no—
559C22×Q8—151no—
560C23×C4—151no—
561C23×C4—151no—
562C23×C4—151no—
563C22⋊Q8—31no—
564C22⋊Q8—151no—
565C22⋊Q8—151no—
566C22⋊Q8—151no—
567C22⋊Q8—151no—
568C22⋊Q8—151no—
569C22⋊Q8—151no—
570C22⋊Q8—151no—
571C2×C4⋊C4—51no—
572C2×C4⋊C4—51no—
573C2×C4⋊C4—151no—
574C2×C4⋊C4—151no—
575C2×C4⋊C4—151no—
576C2×C4⋊C4—151no—
577C2×C4⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C42—51no—
583C2×C42—151no—
584C2×C42—151no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C42—151no—
588#95—51no—
589#95—51no—
590#95—51no—
591#95—51no—
592#95—151no—
593#95—151no—
594#95—151no—
595#95—151no—
596#95—151no—
597#95—151no—
598#95—151no—
599#95—151no—
600#95—151no—
601#95—151no—
602C2×C3×C5C2×C4×Q811yescharacteristic
603C2×C3×C5C4×#4111yescharacteristic
604C2×C3×C5#51811yescharacteristic
605D15—22no—
606C3×D5#55111yescharacteristic
607C3×D5#55111yescharacteristic
608C3×D5#55411yescharacteristic
609C3×D5#55411yescharacteristic
610C5×D3—22no—
611C23×C3—51no—
612C22×D3—51no—
613C22×D3—52no—
614C22×D3—52no—
615C22×D3—101no—
616C22×D3—101no—
617C22×D3—101no—
618C22×D3—101no—
619C22×D3C22×AGL(1,𝔽5)11yescharacteristic
620C2×C3×C4—52no—
621C2×C3×C4—52no—
622C2×C3×C4—51no—
623C2×C3×C4—51no—
624C2×C3×C4—51no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
642C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
643C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
644C2×Dic3—52no—
645C2×Dic3—52no—
646C2×Dic3—51no—
647C2×Dic3—51no—
648C2×Dic3—51no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
666C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
667C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
668C4×D3—41no—
669C4×D3—201no—
670C4×D3—201no—
671C4×D3—201no—
672C4×D3—204no—
673C4×D3—204no—
674Dic6—41no—
675Dic6—201no—
676Dic6—201no—
677Dic6—201no—
678C22×C5—32no—
679C22×C5—61no—
680C22×C5—61no—
681C22×C5C22×C4×D311yescharacteristic
682C2×D5—32no—
683C2×D5—61no—
684C2×D5—61no—
685C2×D5—62no—
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5C2×#23711yescharacteristic
690C2×D5C2×D3×Q811yescharacteristic
691C2×D5D3×#4111yescharacteristic
692C2×D5D3×#4111yescharacteristic
693C2×D5#100911yescharacteristic
694C2×D5#100911yescharacteristic
695AGL(1,𝔽5)—22no—
696AGL(1,𝔽5)—22no—
697AGL(1,𝔽5)—41no—
698AGL(1,𝔽5)—41no—
699AGL(1,𝔽5)—62no—
700AGL(1,𝔽5)—62no—
701AGL(1,𝔽5)—121no—
702AGL(1,𝔽5)—121no—
703C4×C5—21no—
704C4×C5—21no—
705C4×C5—21no—
706C4×C5—61no—
707C4×C5—61no—
708C4×C5—61no—
709Dic5—21no—
710Dic5—21no—
711Dic5—21no—
712Dic5—61no—
713Dic5—61no—
714Dic5—61no—
715C24—151no—
716C2×Q8—31no—
717C2×Q8—151no—
718C2×Q8—151no—
719C2×Q8—151no—
720C2×Q8—601no—
721C2×Q8—601no—
722C22×C4—31no—
723C22×C4—51no—
724C22×C4—51no—
725C22×C4—51no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—51no—
730C22×C4—151no—
731C22×C4—151no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—601no—
745C22×C4—601no—
746C22×C4—601no—
747C22×C4—601no—
748C4⋊C4—31no—
749C4⋊C4—31no—
750C4⋊C4—51no—
751C4⋊C4—51no—
752C4⋊C4—51no—
753C4⋊C4—102no—
754C4⋊C4—151no—
755C4⋊C4—151no—
756C4⋊C4—151no—
757C4⋊C4—151no—
758C4⋊C4—151no—
759C4⋊C4—151no—
760C4⋊C4—302no—
761C4⋊C4—601no—
762C4⋊C4—601no—
763C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
764C22⋊C4—31no—
765C22⋊C4—31no—
766C22⋊C4—151no—
767C22⋊C4—151no—
768C22⋊C4—151no—
769C22⋊C4—151no—
770C22⋊C4—154no—
771C22⋊C4—151no—
772C22⋊C4—151no—
773C22⋊C4—302no—
774C42—102no—
775C42—302no—
776C42—601no—
777C42—601no—
778C42—601no—
779C42—601no—
780C3×C5#236811yescharacteristic, complemented, Hall
781C22×C3—51no—
782C22×C3—51no—
783C22×C3—51no—
784C22×C3—51no—
785C22×C3—51no—
786C22×C3—51no—
787C22×C3C23×AGL(1,𝔽5)11yescharacteristic
788C2×D3—21no—
789C2×D3—21no—
790C2×D3—52no—
791C2×D3—102no—
792C2×D3—102no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—101no—
796C2×D3—101no—
797C2×D3Q8×AGL(1,𝔽5)12yes—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—102no—
802C3×C4—102no—
803C3×C4—101no—
804C3×C4—101no—
805C3×C4—101no—
806C3×C4—201no—
807C3×C4—201no—
808Dic3—21no—
809Dic3—21no—
810Dic3—21no—
811Dic3—102no—
812Dic3—102no—
813Dic3—101no—
814Dic3—101no—
815Dic3—101no—
816Dic3—201no—
817Dic3—201no—
818C2×C5—62no—
819C2×C5#552111yescharacteristic
820C2×C5C4×#23711yescharacteristic
821C2×C5C4×D3×Q811yescharacteristic
822D5—62no—
823D5#563511yescharacteristic
824D5#565811yescharacteristic
825D5#569011yescharacteristic
826D5#570511yescharacteristic
827C23—31no—
828C23—51no—
829C23—152no—
830C23—152no—
831C23—151no—
832C23—301no—
833C23—301no—
834C23—301no—
835C23—301no—
836Q8—121no—
837Q8—601no—
838Q8—601no—
839Q8—601no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—52no—
844C2×C4—52no—
845C2×C4—51no—
846C2×C4—51no—
847C2×C4—51no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—121no—
865C2×C4—152no—
866C2×C4—152no—
867C2×C4—151no—
868C2×C4—151no—
869C2×C4—151no—
870C2×C4—301no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—301no—
881C2×C4—301no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—601no—
887C2×C4—601no—
888C2×C4—601no—
889C2×C4—604no—
890C2×C4—604no—
891C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
892C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
893C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
894C2×C3—51no—
895C2×C3—51no—
896C2×C3—51no—
897C2×C3—51no—
898C2×C3#6625811yescharacteristic
899C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
900C2×C3#41×AGL(1,𝔽5)11yescharacteristic
901D3—22no—
902D3—102no—
903C5#7531111yescharacteristic, complemented, Sylow
904C22—32no—
905C22—51no—
906C22—51no—
907C22—51no—
908C22—51no—
909C22—51no—
910C22—51no—
911C22—61no—
912C22—61no—
913C22—152no—
914C22—302no—
915C22—302no—
916C22—302no—
917C22—302no—
918C22—301no—
919C22—301no—
920C22C22×D3×AGL(1,𝔽5)11yescharacteristic
921C4—21no—
922C4—21no—
923C4—21no—
924C4—61no—
925C4—61no—
926C4—61no—
927C4—102no—
928C4—102no—
929C4—101no—
930C4—101no—
931C4—101no—
932C4—201no—
933C4—201no—
934C4—302no—
935C4—302no—
936C4—301no—
937C4—301no—
938C4—301no—
939C4—601no—
940C4—601no—
941C3#1061728711yescharacteristic, complemented, Sylow
942C2—51no—
943C2—51no—
944C2—51no—
945C2—51no—
946C2—62no—
947C2—302no—
948C2#1175683711yescharacteristic
949C2AGL(1,𝔽5)×#23711yescharacteristic
950C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2368
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752370C2semidirect
3. C3×#65711C2semidirect
10. #11751846C2semidirect
11. #11751842C2semidirect
12. #11751842C2semidirect
13. #11751840C2semidirect
14. #11751839C2semidirect
15. AGL(1,𝔽5)×C4⋊Dic3C2semidirect
33. #91786C4semidirect
34. C5×#897C4semidirect
38. #91419C4semidirect
39. #91419C4semidirect
40. #91417C4semidirect
41. #91417C4semidirect
44. #91383C4semidirect
45. #91365C4semidirect
69. #65711D3semidirect
92. C2×Dic30C2×C4semidirect
94. C2×C5×Dic6C2×C4semidirect
98. C2×#1204C2×C4semidirect
99. C2×#1204C2×C4semidirect
116. (C2×D3)⋊AGL(1,𝔽5)Q8semidirect
121. C3×C5×C4⋊C4C2×C4semidirect
124. C4⋊Dic15C2×C4semidirect
125. C4⋊Dic15C2×C4semidirect
128. C5×C4⋊Dic3C2×C4semidirect
129. C5×C4⋊Dic3C2×C4semidirect
130. C3×C4⋊Dic5C2×C4semidirect
131. C3×#683C2×C4semidirect
132. C3×#683C2×C4semidirect
133. #6668C2×C4semidirect
134. #6668C2×C4semidirect
135. #6668C2×C4semidirect
136. #6668C2×C4semidirect
295. #897AGL(1,𝔽5)semidirect
357. C5×C4⋊C4C4×D3semidirect
368. C4⋊Dic5C4×D3semidirect
373. #683C4×D3semidirect
374. #683C4×D3semidirect
459. C2×Dic6C2×AGL(1,𝔽5)semidirect
464. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
483. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
484. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
763. C4⋊C4D3×AGL(1,𝔽5)semidirect
780. C3×C5#2368semidirect
903. C5#75311semidirect
941. C3#10617287semidirect

Maximal subgroups

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

subgroupindex
D5×#8972
#117523702
C3×#657112
#117519342
#117519322
#117519312
D3×(C2×AGL(1,𝔽5))⋊C42
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518482
#117518462
#117518422
#117518402
#117518392
AGL(1,𝔽5)×C4⋊Dic32
#106172873
#753115