Finite Group Databasebeta

← #14319759

Subgroups — #14319759

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×#67C211yesmaximal, characteristic
3D5×#67⋊C4C211yesmaximal, characteristic
4C22⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
7C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic, complemented
8#11751931C211yesmaximal, characteristic, complemented
9D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic, complemented
10AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
12C4×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
13#11751833C211yesmaximal, characteristic, complemented
14#11751832C211yesmaximal, characteristic, complemented
15AGL(1,𝔽5)×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10617172—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C23×C3×AGL(1,𝔽5)C2211yescharacteristic
19C22×D3×AGL(1,𝔽5)C2211yescharacteristic
20C22×D3×AGL(1,𝔽5)C2211yescharacteristic
21C2×D5×#67C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C2×C4×D3×D5C2211yescharacteristic
24C2×#6763C2211yescharacteristic
25C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
26C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
27C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
29C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
30#67⋊AGL(1,𝔽5)C418yescomplemented
31AGL(1,𝔽5)×#67C418yescomplemented
32C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
34C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
35C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
36C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
37C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
38C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
39C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
40#91770C411yescharacteristic, complemented
41C5×#67⋊C4C411yescharacteristic, complemented
42C3×D5×C22⋊C4C2211yescharacteristic
43#67⋊Dic5C411yescharacteristic, complemented
44#91556C411yescharacteristic, complemented
45D5×(C2×D3)⋊C4C2211yescharacteristic
46#91442C411yescharacteristic, complemented
47#91441C411yescharacteristic, complemented
48#91396C411yescharacteristic, complemented
49#91395C411yescharacteristic, complemented
50D5×Dic3⋊C4C2211yescharacteristic
51C4×D5×Dic3C2211yescharacteristic
52#91235C2211yescharacteristic
53#91235C2211yescharacteristic
54C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
55C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
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(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
61(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
62#73436—51nomaximal, Hall
63C2×D4×AGL(1,𝔽5)—31no—
64C2×D4×AGL(1,𝔽5)—31no—
65C4×D4×D5—31no—
66C4×C22⋊AGL(1,𝔽5)—31no—
67C4×C22⋊AGL(1,𝔽5)—31no—
68C2×(C2×AGL(1,𝔽5))⋊C4—31no—
69C2×(C2×AGL(1,𝔽5))⋊C4—31no—
70C4⋊C4×AGL(1,𝔽5)—31no—
71C4⋊C4×AGL(1,𝔽5)—31no—
72C22⋊C4×AGL(1,𝔽5)—31no—
73C22⋊C4×AGL(1,𝔽5)—31no—
74C22⋊C4×AGL(1,𝔽5)—31no—
75C22⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
76C4×C4⋊AGL(1,𝔽5)—31no—
77#65686—31no—
78C23×C3×D5C2311yescharacteristic
79C22×D3×D5C2311yescharacteristic
80C22×ΓL(1,𝔽16)—41no—
81C22×ΓL(1,𝔽16)—41no—
82C22×ΓL(1,𝔽16)C2×C414yescomplemented
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×ΓL(1,𝔽16)C2311yescharacteristic
85C22×ΓL(1,𝔽16)C2311yescharacteristic
86C22×ΓL(1,𝔽16)C2311yescharacteristic
87C22×C3×AGL(1,𝔽5)—41no—
88C22×C3×AGL(1,𝔽5)—41no—
89C22×C3×AGL(1,𝔽5)C2×C414yescomplemented
90C22×C3×AGL(1,𝔽5)C2311yescharacteristic
91C22×C3×AGL(1,𝔽5)C2311yescharacteristic
92C22×C3×AGL(1,𝔽5)C2311yescharacteristic
93C22×C3×AGL(1,𝔽5)C2311yescharacteristic
94C2×D3×AGL(1,𝔽5)—41no—
95C2×D3×AGL(1,𝔽5)—41no—
96C2×D3×AGL(1,𝔽5)—41no—
97C2×D3×AGL(1,𝔽5)—41no—
98C2×D3×AGL(1,𝔽5)C2×C414yescomplemented
99C2×D3×AGL(1,𝔽5)C2×C414yescomplemented
100C2×#1220C2×C411yescharacteristic
101C22×Dic15C2×C411yescharacteristic, complemented
102C2×C4×D15C2×C411yescharacteristic, complemented
103C2×C5×#67C2×C411yescharacteristic
104C22×C5×Dic3C2×C411yescharacteristic, complemented
105C2×C4×C5×D3C2×C411yescharacteristic, complemented
106C2×C3×C4×D5C2311yescharacteristic
107C2×C3×C4×D5C2311yescharacteristic
108D5×#67C2×C414yes—
109D5×#67C2×C414yes—
110C2×#1202C2×C411yescharacteristic
111C2×#1201C2×C411yescharacteristic
112C2×#1200C2×C411yescharacteristic, complemented
113C2×D3×Dic5C2×C411yescharacteristic, complemented
114C2×D5×Dic3—41no—
115C2×D5×Dic3—41no—
116C2×D5×Dic3C2×C411yescharacteristic, complemented
117C2×D5×Dic3C2×C411yescharacteristic, complemented
118C2×D5×Dic3C2311yescharacteristic
119C2×D5×Dic3C2311yescharacteristic
120C2×D5×Dic3C2311yescharacteristic
121C4×D3×D5—41no—
122C4×D3×D5—41no—
123#6763C2×C414yescomplemented
124C4×ΓL(1,𝔽16)—41no—
125C4×ΓL(1,𝔽16)—41no—
126C3×C22⋊AGL(1,𝔽5)C2×C414yescomplemented
127C3×C4×AGL(1,𝔽5)—41no—
128C3×C4×AGL(1,𝔽5)—41no—
129Dic3⋊AGL(1,𝔽5)C2×C414yescomplemented
130Dic3⋊AGL(1,𝔽5)C2×C414yescomplemented
131(C2×D3)⋊AGL(1,𝔽5)C2×C414yescomplemented
132(C2×D3)⋊AGL(1,𝔽5)C2×C414yescomplemented
133Dic3×AGL(1,𝔽5)—41no—
134Dic3×AGL(1,𝔽5)—41no—
135Dic3×AGL(1,𝔽5)C2×C414yescomplemented
136Dic3×AGL(1,𝔽5)C2×C414yescomplemented
137C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
138#6714C2×C411yescharacteristic, complemented
139#6712C2×C411yescharacteristic, complemented
140C4×Dic15C2×C411yescharacteristic, complemented
141C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
142C5×Dic3⋊C4C2×C411yescharacteristic, complemented
143C4×C5×Dic3C2×C411yescharacteristic, complemented
144C3×C22⋊Dic5C2×C411yescharacteristic, complemented
145C3×#685C2×C411yescharacteristic, complemented
146C3×#685C2×C411yescharacteristic, complemented
147Dic3⋊Dic5C2×C411yescharacteristic, complemented
148#6669C2×C411yescharacteristic, complemented
149#6667C2×C411yescharacteristic, complemented
150(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
151Dic3×Dic5C2×C411yescharacteristic, complemented
152Dic3×Dic5C2×C411yescharacteristic, complemented
153C2×C4×#67—51no—
154C2×#67⋊C4—51no—
155C2×#67⋊C4—51no—
156C3×C4×C22⋊C4—51no—
157C2×C3⋊#95—51no—
158Dic3×C22⋊C4—51no—
159Dic3×C22⋊C4—51no—
160C4×(C2×D3)⋊C4—51no—
161C4×(C2×D3)⋊C4—51no—
162C4×Dic3⋊C4—51no—
163C4×Dic3⋊C4—51no—
164#4666—51no—
165D3×#95—51no—
166#4649—51no—
167#4648—51no—
168C23×AGL(1,𝔽5)—31no—
169C23×AGL(1,𝔽5)—31no—
170C23×AGL(1,𝔽5)—31no—
171C23×AGL(1,𝔽5)C2×D311yescharacteristic
172C2×D4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5—31no—
175C2×C22⋊AGL(1,𝔽5)—31no—
176C2×C22⋊AGL(1,𝔽5)—31no—
177C2×C22⋊AGL(1,𝔽5)—31no—
178C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
179D4×AGL(1,𝔽5)—38no—
180D4×AGL(1,𝔽5)—38no—
181C2×C4⋊AGL(1,𝔽5)—31no—
182C2×C4⋊AGL(1,𝔽5)—31no—
183C2×C4×AGL(1,𝔽5)—31no—
184C2×C4×AGL(1,𝔽5)—31no—
185C2×C4×AGL(1,𝔽5)—31no—
186C2×C4×AGL(1,𝔽5)—31no—
187C2×C4×AGL(1,𝔽5)—31no—
188C2×C4×AGL(1,𝔽5)—31no—
189C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
190C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
191C4×C5×D4—31no—
192D4×Dic5—31no—
193C4×C22⋊D5—31no—
194C4×C22⋊D5—31no—
195#4039—31no—
196D5×C4⋊C4—31no—
197#4027—31no—
198#4027—31no—
199D5×C22⋊C4—31no—
200D5×C22⋊C4C2×D311yescharacteristic
201C4×D20—31no—
202C42×D5—31no—
203(C2×AGL(1,𝔽5))⋊C4—31no—
204(C2×AGL(1,𝔽5))⋊C4—31no—
205(C2×AGL(1,𝔽5))⋊C4—31no—
206(C2×AGL(1,𝔽5))⋊C4—31no—
207(C2×AGL(1,𝔽5))⋊C4—31no—
208(C2×AGL(1,𝔽5))⋊C4—31no—
209(C2×AGL(1,𝔽5))⋊C4—31no—
210(C2×AGL(1,𝔽5))⋊C4—31no—
211(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
212(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
213#2275—151noSylow
214C23×C3×C5C22×C411yescharacteristic
215C22×D15C22×C411yescharacteristic
216C22×C5×D3C22×C411yescharacteristic
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5C22×C411yescharacteristic
222C22×C3×D5C22×C412yes—
223C22×C3×D5C22×C412yes—
224C22×C3×D5C2411yescharacteristic
225C2×D3×D5—21no—
226C2×D3×D5—21no—
227C2×D3×D5—21no—
228C2×D3×D5—21no—
229C2×D3×D5C22×C412yes—
230C2×D3×D5C22×C412yes—
231C2×ΓL(1,𝔽16)—21no—
232C2×ΓL(1,𝔽16)—21no—
233C2×ΓL(1,𝔽16)—21no—
234C2×ΓL(1,𝔽16)—21no—
235C2×ΓL(1,𝔽16)—21no—
236C2×ΓL(1,𝔽16)—21no—
237C2×ΓL(1,𝔽16)—21no—
238C2×ΓL(1,𝔽16)—21no—
239C2×ΓL(1,𝔽16)—44no—
240C2×ΓL(1,𝔽16)C22×C412yes—
241C2×ΓL(1,𝔽16)C22×C412yes—
242C2×ΓL(1,𝔽16)C22×C412yes—
243C2×ΓL(1,𝔽16)C22×C412yes—
244C2×C3×AGL(1,𝔽5)—21no—
245C2×C3×AGL(1,𝔽5)—21no—
246C2×C3×AGL(1,𝔽5)—21no—
247C2×C3×AGL(1,𝔽5)—21no—
248C2×C3×AGL(1,𝔽5)—21no—
249C2×C3×AGL(1,𝔽5)—21no—
250C2×C3×AGL(1,𝔽5)—21no—
251C2×C3×AGL(1,𝔽5)—21no—
252C2×C3×AGL(1,𝔽5)—44no—
253C2×C3×AGL(1,𝔽5)C22×C412yes—
254C2×C3×AGL(1,𝔽5)C22×C412yes—
255C2×C3×AGL(1,𝔽5)C22×C412yes—
256C2×C3×AGL(1,𝔽5)C22×C412yes—
257D3×AGL(1,𝔽5)—44no—
258D3×AGL(1,𝔽5)—44no—
259C2×C3×C4×C5C22×C411yescharacteristic
260C2×C3×C4×C5C22×C411yescharacteristic
261#1220C4214yescomplemented
262C2×Dic15—41no—
263C2×Dic15C22×C411yescharacteristic
264C2×Dic15C22×C411yescharacteristic
265C2×Dic15C22×C411yescharacteristic
266C4×D15—41no—
267C5×#67C4214yescomplemented
268C2×C5×Dic3—41no—
269C2×C5×Dic3C22×C411yescharacteristic
270C2×C5×Dic3C22×C411yescharacteristic
271C2×C5×Dic3C22×C411yescharacteristic
272C4×C5×D3—41no—
273C2×C3×Dic5C22×C411yescharacteristic
274C2×C3×Dic5C22×C411yescharacteristic
275C3×C4×D5—21no—
276C3×C4×D5—21no—
277C3×C4×D5—21no—
278C3×C4×D5—21no—
279#1202C4214yescomplemented
280#1201C4214yescomplemented
281#1200—41no—
282D3×Dic5—41no—
283D5×Dic3—21no—
284D5×Dic3—21no—
285D5×Dic3—21no—
286D5×Dic3—21no—
287D5×Dic3—41no—
288D5×Dic3—41no—
289D5×Dic3C22×C412yes—
290D5×Dic3C22×C412yes—
291C23×C3×C4—51no—
292C22×#67—51no—
293C23×Dic3—51no—
294C23×Dic3—51no—
295C22×C4×D3—51no—
296C22×C4×D3—51no—
297C22×C4×D3—51no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C42—51no—
301C2×C3×C42—51no—
302C2×#217—51no—
303C4×#67—58no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4—51no—
310C2×C4×Dic3—51no—
311C2×C4×Dic3—51no—
312C2×C4×Dic3—51no—
313C2×C4×Dic3—51no—
314C2×C4×Dic3—51no—
315C2×C4×Dic3—51no—
316C2×C4×Dic3—51no—
317#67⋊C4—58no—
318#67⋊C4—51no—
319#67⋊C4—51no—
320#67⋊C4—51no—
321#67⋊C4—51no—
322#67⋊C4—51no—
323#67⋊C4—51no—
324#67⋊C4—51no—
325#67⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
326C3×#95—51no—
327C3×#95—51no—
328C3⋊#95—51no—
329C3⋊#95—51no—
330C3⋊#95—51no—
331C3⋊#95—51no—
332C3⋊#95—51no—
333C3⋊#95—51no—
334C3⋊#95—51no—
335C3⋊#95—51no—
336C23×D5—31no—
337C23×D5C22×D311yescharacteristic
338C22×AGL(1,𝔽5)—31no—
339C22×AGL(1,𝔽5)—31no—
340C22×AGL(1,𝔽5)—31no—
341C22×AGL(1,𝔽5)—31no—
342C22×AGL(1,𝔽5)—34no—
343C22×AGL(1,𝔽5)—34no—
344C22×AGL(1,𝔽5)—34no—
345C22×AGL(1,𝔽5)—41no—
346C22×AGL(1,𝔽5)—41no—
347C22×AGL(1,𝔽5)—121no—
348C22×AGL(1,𝔽5)—121no—
349C22×AGL(1,𝔽5)—121no—
350C22×AGL(1,𝔽5)—121no—
351C22×AGL(1,𝔽5)—121no—
352C22×AGL(1,𝔽5)—121no—
353C22×AGL(1,𝔽5)C4×D314yescomplemented
354C22×AGL(1,𝔽5)C22×D311yescharacteristic
355C22×AGL(1,𝔽5)C22×D311yescharacteristic
356C22×AGL(1,𝔽5)C22×D311yescharacteristic
357C22×AGL(1,𝔽5)C22×D311yescharacteristic
358C2×C5×D4—31no—
359C22×C4×C5—31no—
360C22×C4×C5—31no—
361C2×C22⋊D5—31no—
362C2×C22⋊D5—31no—
363C22×Dic5—31no—
364C22×Dic5—31no—
365D4×D5—34no—
366D4×D5—34no—
367C2×D20—31no—
368C2×C4×D5—31no—
369C2×C4×D5—31no—
370C2×C4×D5—31no—
371C2×C4×D5—31no—
372C2×C4×D5—31no—
373C2×C4×D5—31no—
374C2×C4×D5—31no—
375C2×C4×D5—121no—
376C2×C4×D5—121no—
377C2×C4×D5—121no—
378C2×C4×D5—121no—
379C2×C4×D5C22×D311yescharacteristic
380C2×C4×D5C22×D311yescharacteristic
381C22⋊AGL(1,𝔽5)—34no—
382C22⋊AGL(1,𝔽5)—34no—
383C22⋊AGL(1,𝔽5)—34no—
384C22⋊AGL(1,𝔽5)C4×D314yescomplemented
385C4⋊AGL(1,𝔽5)—34no—
386C4⋊AGL(1,𝔽5)—34no—
387C4×AGL(1,𝔽5)—34no—
388C4×AGL(1,𝔽5)—34no—
389C4×AGL(1,𝔽5)—41no—
390C4×AGL(1,𝔽5)—41no—
391C4×AGL(1,𝔽5)—121no—
392C4×AGL(1,𝔽5)—121no—
393C4×AGL(1,𝔽5)—121no—
394C4×AGL(1,𝔽5)—121no—
395C5×C4⋊C4—31no—
396C5×C22⋊C4—31no—
397C5×C22⋊C4C4×D311yescharacteristic, complemented
398C42×C5—31no—
399C22⋊Dic5—31no—
400C22⋊Dic5C4×D311yescharacteristic, complemented
401#685—31no—
402#685—31no—
403#685C4×D311yescharacteristic, complemented
404#685C4×D311yescharacteristic, complemented
405C4⋊Dic5—31no—
406#683—31no—
407#683—31no—
408C4×Dic5—31no—
409C4×Dic5—31no—
410C4×Dic5—31no—
411C2×C4×D4—151no—
412C2×C4×D4—151no—
413C2×C4×D4—151no—
414C4×C4⋊C4—151no—
415C4×C4⋊C4—151no—
416C4×C4⋊C4—151no—
417C4×C22⋊C4—51no—
418C4×C22⋊C4—151no—
419C4×C22⋊C4—151no—
420C4×C22⋊C4—151no—
421C4×C22⋊C4—151no—
422C4×C22⋊C4—151no—
423#376—151no—
424C2×#95—151no—
425C2×#95—151no—
426C22×C3×C5—21no—
427C22×C3×C5—21no—
428C22×C3×C5C2×C4212yes—
429C22×C3×C5C23×C411yescharacteristic
430C2×D15—21no—
431C2×D15—21no—
432C2×D15C2×C4212yes—
433C2×C5×D3—21no—
434C2×C5×D3—21no—
435C2×C5×D3C2×C4212yes—
436C2×C3×D5—21no—
437C2×C3×D5—21no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5C2×C4212yes—
443C2×C3×D5C23×C411yescharacteristic
444C2×C3×D5C23×C411yescharacteristic
445C2×C3×D5H(5,𝔽2)11yescharacteristic
446C2×C3×D5H(5,𝔽2)11yescharacteristic
447C2×C3×D5H(5,𝔽2)11yescharacteristic
448C2×C3×D52−1+411yescharacteristic
449D3×D5—22no—
450D3×D5—22no—
451D3×D5—22no—
452D3×D5—22no—
453ΓL(1,𝔽16)—22no—
454ΓL(1,𝔽16)—22no—
455ΓL(1,𝔽16)—22no—
456ΓL(1,𝔽16)—22no—
457C3×AGL(1,𝔽5)—22no—
458C3×AGL(1,𝔽5)—22no—
459C3×AGL(1,𝔽5)—22no—
460C3×AGL(1,𝔽5)—22no—
461C3×C4×C5—21no—
462C3×C4×C5—21no—
463Dic15—21no—
464Dic15—21no—
465Dic15C2×C4212yes—
466C3×Dic5—21no—
467C3×Dic5—21no—
468C5×Dic3—21no—
469C5×Dic3—21no—
470C5×Dic3C2×C4212yes—
471C24×C3—51no—
472C23×D3—51no—
473C22×C3×C4—51no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—51no—
477C22×C3×C4—54no—
478C22×C3×C4—51no—
479C22×C3×C4—51no—
480C22×C3×C4—201no—
481C22×C3×C4—201no—
482C2×#67—51no—
483C2×#67—51no—
484C2×#67—54no—
485C2×#67—54no—
486C2×#67—51no—
487C2×#67C2×AGL(1,𝔽5)11yescharacteristic
488C22×Dic3—51no—
489C22×Dic3—51no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—54no—
494C22×Dic3—51no—
495C22×Dic3—51no—
496C22×Dic3—51no—
497C22×Dic3—51no—
498C22×Dic3—51no—
499C22×Dic3—201no—
500C22×Dic3—201no—
501C22×Dic3—201no—
502C22×Dic3—201no—
503C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
504C2×C4×D3—54no—
505C2×C4×D3—54no—
506C2×C4×D3—51no—
507C2×C4×D3—51no—
508C2×C4×D3—51no—
509C2×C4×D3—201no—
510C2×C4×D3—201no—
511C2×C4×D3—201no—
512C2×C4×D3—201no—
513C2×C4×D3—201no—
514C2×C4×D3—201no—
515C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
516C3×C22⋊C4—54no—
517C3×C22⋊C4—51no—
518C3×C22⋊C4—51no—
519C3×C22⋊C4—51no—
520C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
521C3×C42—201no—
522C3×C42—201no—
523#217—54no—
524(C2×D3)⋊C4—54no—
525(C2×D3)⋊C4—54no—
526(C2×D3)⋊C4—51no—
527(C2×D3)⋊C4—51no—
528(C2×D3)⋊C4—51no—
529(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
530Dic3⋊C4—54no—
531Dic3⋊C4—54no—
532Dic3⋊C4—51no—
533Dic3⋊C4—51no—
534Dic3⋊C4—51no—
535Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
536C4×Dic3—54no—
537C4×Dic3—54no—
538C4×Dic3—51no—
539C4×Dic3—51no—
540C4×Dic3—51no—
541C4×Dic3—201no—
542C4×Dic3—201no—
543C4×Dic3—201no—
544C4×Dic3—201no—
545C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
546C23×C5—31no—
547C23×C5C2×C4×D311yescharacteristic
548C22×D5—21no—
549C22×D5—21no—
550C22×D5—21no—
551C22×D5—21no—
552C22×D5—31no—
553C22×D5—32no—
554C22×D5—32no—
555C22×D5—61no—
556C22×D5—61no—
557C22×D5—61no—
558C22×D5—61no—
559C22×D5C2×C4×D311yescharacteristic
560C22×D5C2×C4×D312yes—
561C22×D5C2×C4×D312yes—
562C22×D5C23×D311yescharacteristic
563C2×AGL(1,𝔽5)—21no—
564C2×AGL(1,𝔽5)—21no—
565C2×AGL(1,𝔽5)—21no—
566C2×AGL(1,𝔽5)—21no—
567C2×AGL(1,𝔽5)—21no—
568C2×AGL(1,𝔽5)—21no—
569C2×AGL(1,𝔽5)—21no—
570C2×AGL(1,𝔽5)—21no—
571C2×AGL(1,𝔽5)—32no—
572C2×AGL(1,𝔽5)—32no—
573C2×AGL(1,𝔽5)—32no—
574C2×AGL(1,𝔽5)—32no—
575C2×AGL(1,𝔽5)—44no—
576C2×AGL(1,𝔽5)—61no—
577C2×AGL(1,𝔽5)—61no—
578C2×AGL(1,𝔽5)—61no—
579C2×AGL(1,𝔽5)—61no—
580C2×AGL(1,𝔽5)—61no—
581C2×AGL(1,𝔽5)—61no—
582C2×AGL(1,𝔽5)—61no—
583C2×AGL(1,𝔽5)—61no—
584C2×AGL(1,𝔽5)—124no—
585C2×AGL(1,𝔽5)—124no—
586C2×AGL(1,𝔽5)—124no—
587C2×AGL(1,𝔽5)C2×C4×D312yes—
588C2×AGL(1,𝔽5)C2×C4×D312yes—
589C2×AGL(1,𝔽5)C2×C4×D312yes—
590C2×AGL(1,𝔽5)C2×C4×D312yes—
591C5×D4—34no—
592C2×C4×C5—31no—
593C2×C4×C5—31no—
594C2×C4×C5—31no—
595C2×C4×C5—121no—
596C2×C4×C5—121no—
597C2×C4×C5C2×C4×D311yescharacteristic
598C2×C4×C5C2×C4×D311yescharacteristic
599C22⋊D5—34no—
600C22⋊D5—34no—
601C2×Dic5—31no—
602C2×Dic5—31no—
603C2×Dic5—31no—
604C2×Dic5—121no—
605C2×Dic5—121no—
606C2×Dic5C2×C4×D311yescharacteristic
607C2×Dic5C2×C4×D311yescharacteristic
608D20—34no—
609C4×D5—21no—
610C4×D5—21no—
611C4×D5—21no—
612C4×D5—21no—
613C4×D5—32no—
614C4×D5—32no—
615C4×D5—61no—
616C4×D5—61no—
617C4×D5—61no—
618C4×D5—61no—
619C4×D5—121no—
620C4×D5—121no—
621C4×D5—121no—
622C4×D5—121no—
623C22×D4—151no—
624C23×C4—51no—
625C23×C4—151no—
626C23×C4—151no—
627C23×C4—151no—
628C23×C4—151no—
629C23×C4—151no—
630C4×D4—31no—
631C4×D4—151no—
632C4×D4—151no—
633C4×D4—151no—
634C4×D4—151no—
635C4×D4—151no—
636C4×D4—151no—
637C4×D4—158no—
638C4×D4—158no—
639C4×D4—151no—
640C2×C4⋊C4—151no—
641C2×C4⋊C4—151no—
642C2×C4⋊C4—151no—
643C2×C22⋊C4—51no—
644C2×C22⋊C4—51no—
645C2×C22⋊C4—151no—
646C2×C22⋊C4—151no—
647C2×C22⋊C4—151no—
648C2×C22⋊C4—151no—
649C2×C42—51no—
650C2×C42—51no—
651C2×C42—151no—
652C2×C42—151no—
653C2×C42—151no—
654C2×C42—151no—
655C2×C42—151no—
656C2×C42—151no—
657C2×C42—151no—
658#95—51no—
659#95—51no—
660#95—151no—
661#95—151no—
662#95—151no—
663#95—151no—
664#95—151no—
665#95—151no—
666#95—151no—
667#95—151no—
668C2×C3×C5—22no—
669C2×C3×C5C22×C4211yescharacteristic
670C2×C3×C5#51811yescharacteristic
671C2×C3×C5#52011yescharacteristic
672D15—22no—
673C3×D5—22no—
674C3×D5#51811yescharacteristic
675C3×D5#51811yescharacteristic
676C3×D5#52011yescharacteristic
677C3×D5#52011yescharacteristic
678C5×D3—22no—
679C23×C3—51no—
680C23×C3—52no—
681C23×C3—52no—
682C23×C3—51no—
683C23×C3—101no—
684C23×C3—101no—
685C23×C3—101no—
686C23×C3—101no—
687C23×C3C22×AGL(1,𝔽5)11yescharacteristic
688C22×D3—51no—
689C22×D3—52no—
690C22×D3—52no—
691C22×D3—101no—
692C22×D3—101no—
693C22×D3—101no—
694C22×D3—101no—
695C22×D3C22×AGL(1,𝔽5)11yescharacteristic
696C2×C3×C4—52no—
697C2×C3×C4—52no—
698C2×C3×C4—52no—
699C2×C3×C4—52no—
700C2×C3×C4—51no—
701C2×C3×C4—51no—
702C2×C3×C4—101no—
703C2×C3×C4—101no—
704C2×C3×C4—101no—
705C2×C3×C4—101no—
706C2×C3×C4—101no—
707C2×C3×C4—101no—
708C2×C3×C4—101no—
709C2×C3×C4—101no—
710C2×C3×C4—101no—
711C2×C3×C4—101no—
712C2×C3×C4—101no—
713C2×C3×C4—101no—
714C2×C3×C4—204no—
715C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
716C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
717#67—54no—
718#67—54no—
719#67—54no—
720#67C4×AGL(1,𝔽5)14yescomplemented
721C2×Dic3—41no—
722C2×Dic3—51no—
723C2×Dic3—52no—
724C2×Dic3—52no—
725C2×Dic3—52no—
726C2×Dic3—52no—
727C2×Dic3—52no—
728C2×Dic3—52no—
729C2×Dic3—51no—
730C2×Dic3—51no—
731C2×Dic3—101no—
732C2×Dic3—101no—
733C2×Dic3—101no—
734C2×Dic3—101no—
735C2×Dic3—101no—
736C2×Dic3—101no—
737C2×Dic3—101no—
738C2×Dic3—101no—
739C2×Dic3—101no—
740C2×Dic3—101no—
741C2×Dic3—101no—
742C2×Dic3—101no—
743C2×Dic3—201no—
744C2×Dic3—201no—
745C2×Dic3—201no—
746C2×Dic3—204no—
747C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
748C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
749C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
750C4×D3—41no—
751C4×D3—201no—
752C4×D3—201no—
753C4×D3—201no—
754C4×D3—204no—
755C4×D3—204no—
756C22×C5—21no—
757C22×C5—21no—
758C22×C5—32no—
759C22×C5—61no—
760C22×C5—61no—
761C22×C5C42×D312yes—
762C22×C5C22×C4×D311yescharacteristic
763C2×D5—21no—
764C2×D5—21no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—22no—
769C2×D5—32no—
770C2×D5—61no—
771C2×D5—61no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—62no—
776C2×D5C42×D312yes—
777C2×D5C22×C4×D311yescharacteristic
778C2×D5C22×C4×D311yescharacteristic
779C2×D5#100411yescharacteristic
780C2×D5#100411yescharacteristic
781C2×D5#100911yescharacteristic
782C2×D5#101011yescharacteristic
783AGL(1,𝔽5)—22no—
784AGL(1,𝔽5)—22no—
785AGL(1,𝔽5)—22no—
786AGL(1,𝔽5)—22no—
787AGL(1,𝔽5)—62no—
788AGL(1,𝔽5)—62no—
789AGL(1,𝔽5)—62no—
790AGL(1,𝔽5)—62no—
791C4×C5—21no—
792C4×C5—21no—
793C4×C5—32no—
794C4×C5—61no—
795C4×C5—61no—
796Dic5—21no—
797Dic5—21no—
798Dic5—32no—
799Dic5—61no—
800Dic5—61no—
801C24—51no—
802C24—151no—
803C2×D4—31no—
804C2×D4—151no—
805C2×D4—154no—
806C2×D4—154no—
807C2×D4—151no—
808C2×D4—151no—
809C22×C4—31no—
810C22×C4—31no—
811C22×C4—51no—
812C22×C4—51no—
813C22×C4—51no—
814C22×C4—51no—
815C22×C4—54no—
816C22×C4—51no—
817C22×C4—51no—
818C22×C4—151no—
819C22×C4—151no—
820C22×C4—151no—
821C22×C4—151no—
822C22×C4—151no—
823C22×C4—151no—
824C22×C4—151no—
825C22×C4—154no—
826C22×C4—154no—
827C22×C4—151no—
828C22×C4—151no—
829C22×C4—151no—
830C22×C4—151no—
831C22×C4—154no—
832C22×C4—151no—
833C22×C4—151no—
834C22×C4—201no—
835C22×C4—201no—
836C22×C4—601no—
837C22×C4—601no—
838C22×C4—601no—
839C22×C4—601no—
840C22×C4—601no—
841C22×C4—601no—
842C22×C4—601no—
843C22×C4—601no—
844C22×C4—601no—
845C22×C4—601no—
846C4⋊C4—31no—
847C4⋊C4—151no—
848C4⋊C4—151no—
849C4⋊C4—154no—
850C4⋊C4—154no—
851C4⋊C4—151no—
852C22⋊C4—31no—
853C22⋊C4—54no—
854C22⋊C4—51no—
855C22⋊C4—51no—
856C22⋊C4—51no—
857C22⋊C4—151no—
858C22⋊C4—151no—
859C22⋊C4—154no—
860C22⋊C4—154no—
861C22⋊C4—154no—
862C22⋊C4—151no—
863C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
864C42—31no—
865C42—151no—
866C42—151no—
867C42—154no—
868C42—154no—
869C42—151no—
870C42—201no—
871C42—201no—
872C42—601no—
873C42—601no—
874C42—601no—
875C42—601no—
876C3×C5#227511yescharacteristic, complemented, Hall
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—51no—
880C22×C3—51no—
881C22×C3—51no—
882C22×C3—51no—
883C22×C3—51no—
884C22×C3—51no—
885C22×C3—52no—
886C22×C3—102no—
887C22×C3—102no—
888C22×C3—102no—
889C22×C3—102no—
890C22×C3—101no—
891C22×C3—101no—
892C22×C3C2×C4×AGL(1,𝔽5)12yes—
893C22×C3C23×AGL(1,𝔽5)11yescharacteristic
894C2×D3—21no—
895C2×D3—21no—
896C2×D3—52no—
897C2×D3—102no—
898C2×D3—102no—
899C2×D3—102no—
900C2×D3—102no—
901C2×D3—101no—
902C2×D3—101no—
903C2×D3C2×C4×AGL(1,𝔽5)12yes—
904C3×C4—21no—
905C3×C4—21no—
906C3×C4—102no—
907C3×C4—102no—
908C3×C4—102no—
909C3×C4—102no—
910C3×C4—101no—
911C3×C4—101no—
912Dic3—21no—
913Dic3—21no—
914Dic3—52no—
915Dic3—102no—
916Dic3—102no—
917Dic3—102no—
918Dic3—102no—
919Dic3—101no—
920Dic3—101no—
921Dic3C2×C4×AGL(1,𝔽5)12yes—
922C2×C5—22no—
923C2×C5—62no—
924C2×C5C2×C42×D311yescharacteristic
925C2×C5#554511yescharacteristic
926C2×C5#554611yescharacteristic
927D5—22no—
928D5—62no—
929D5#548611yescharacteristic
930D5#552311yescharacteristic
931D5#554511yescharacteristic
932D5#554611yescharacteristic
933C23—31no—
934C23—51no—
935C23—52no—
936C23—52no—
937C23—51no—
938C23—101no—
939C23—101no—
940C23—101no—
941C23—101no—
942C23—152no—
943C23—152no—
944C23—151no—
945C23—301no—
946C23—301no—
947C23—301no—
948C23—301no—
949C23C2×D3×AGL(1,𝔽5)11yescharacteristic
950D4—34no—
951D4—154no—
952D4—154no—
953D4—154no—
954C2×C4—31no—
955C2×C4—31no—
956C2×C4—31no—
957C2×C4—52no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—51no—
962C2×C4—51no—
963C2×C4—101no—
964C2×C4—101no—
965C2×C4—101no—
966C2×C4—101no—
967C2×C4—101no—
968C2×C4—101no—
969C2×C4—101no—
970C2×C4—101no—
971C2×C4—101no—
972C2×C4—101no—
973C2×C4—101no—
974C2×C4—101no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—152no—
978C2×C4—152no—
979C2×C4—151no—
980C2×C4—152no—
981C2×C4—152no—
982C2×C4—152no—
983C2×C4—152no—
984C2×C4—151no—
985C2×C4—151no—
986C2×C4—204no—
987C2×C4—301no—
988C2×C4—301no—
989C2×C4—301no—
990C2×C4—301no—
991C2×C4—301no—
992C2×C4—301no—
993C2×C4—301no—
994C2×C4—301no—
995C2×C4—301no—
996C2×C4—301no—
997C2×C4—301no—
998C2×C4—301no—
999C2×C4—601no—
1000C2×C4—601no—
1001C2×C4—601no—
1002C2×C4—601no—
1003C2×C4—601no—
1004C2×C4—604no—
1005C2×C4—604no—
1006C2×C4—601no—
1007C2×C4—604no—
1008C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
1009C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
1010C2×C3—22no—
1011C2×C3—51no—
1012C2×C3—51no—
1013C2×C3—51no—
1014C2×C3—51no—
1015C2×C3—102no—
1016C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
1017C2×C3#6625811yescharacteristic
1018C2×C3#6626611yescharacteristic
1019D3—22no—
1020D3—102no—
1021C5#7343611yescharacteristic, complemented, Sylow
1022C22—21no—
1023C22—21no—
1024C22—32no—
1025C22—51no—
1026C22—51no—
1027C22—51no—
1028C22—51no—
1029C22—51no—
1030C22—51no—
1031C22—52no—
1032C22—61no—
1033C22—61no—
1034C22—102no—
1035C22—102no—
1036C22—102no—
1037C22—102no—
1038C22—101no—
1039C22—101no—
1040C22—152no—
1041C22—302no—
1042C22—302no—
1043C22—302no—
1044C22—302no—
1045C22—301no—
1046C22—301no—
1047C22C4×D3×AGL(1,𝔽5)12yes—
1048C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1049C4—21no—
1050C4—21no—
1051C4—32no—
1052C4—61no—
1053C4—61no—
1054C4—102no—
1055C4—102no—
1056C4—102no—
1057C4—102no—
1058C4—101no—
1059C4—101no—
1060C4—152no—
1061C4—302no—
1062C4—302no—
1063C4—302no—
1064C4—302no—
1065C4—301no—
1066C4—301no—
1067C3#1061717211yescharacteristic, complemented, Sylow
1068C2—22no—
1069C2—51no—
1070C2—51no—
1071C2—51no—
1072C2—51no—
1073C2—62no—
1074C2—102no—
1075C2—302no—
1076C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
1077C2#1175684511yescharacteristic
1078C2#1175684611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C22⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2275
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22⋊C4×ΓL(1,𝔽16)C2semidirect
5. C3×C22⋊C4×AGL(1,𝔽5)C2semidirect
6. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
7. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
8. #11751931C2semidirect
9. D3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
10. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
11. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
12. C4×(C2×D3)⋊AGL(1,𝔽5)C2semidirect
13. #11751833C2semidirect
14. #11751832C2semidirect
15. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
30. #67⋊AGL(1,𝔽5)C4semidirect
31. AGL(1,𝔽5)×#67C4semidirect
40. #91770C4semidirect
41. C5×#67⋊C4C4semidirect
43. #67⋊Dic5C4semidirect
44. #91556C4semidirect
46. #91442C4semidirect
47. #91441C4semidirect
48. #91396C4semidirect
49. #91395C4semidirect
75. C22⋊C4×AGL(1,𝔽5)D3semidirect
82. C22×ΓL(1,𝔽16)C2×C4semidirect
89. C22×C3×AGL(1,𝔽5)C2×C4semidirect
98. C2×D3×AGL(1,𝔽5)C2×C4semidirect
99. C2×D3×AGL(1,𝔽5)C2×C4semidirect
101. C22×Dic15C2×C4semidirect
102. C2×C4×D15C2×C4semidirect
104. C22×C5×Dic3C2×C4semidirect
105. C2×C4×C5×D3C2×C4semidirect
112. C2×#1200C2×C4semidirect
113. C2×D3×Dic5C2×C4semidirect
116. C2×D5×Dic3C2×C4semidirect
117. C2×D5×Dic3C2×C4semidirect
123. #6763C2×C4semidirect
126. C3×C22⋊AGL(1,𝔽5)C2×C4semidirect
129. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
130. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
131. (C2×D3)⋊AGL(1,𝔽5)C2×C4semidirect
132. (C2×D3)⋊AGL(1,𝔽5)C2×C4semidirect
135. Dic3×AGL(1,𝔽5)C2×C4semidirect
136. Dic3×AGL(1,𝔽5)C2×C4semidirect
137. C3×C5×C22⋊C4C2×C4semidirect
138. #6714C2×C4semidirect
139. #6712C2×C4semidirect
140. C4×Dic15C2×C4semidirect
141. C5×(C2×D3)⋊C4C2×C4semidirect
142. C5×Dic3⋊C4C2×C4semidirect
143. C4×C5×Dic3C2×C4semidirect
144. C3×C22⋊Dic5C2×C4semidirect
145. C3×#685C2×C4semidirect
146. C3×#685C2×C4semidirect
147. Dic3⋊Dic5C2×C4semidirect
148. #6669C2×C4semidirect
149. #6667C2×C4semidirect
150. (C2×D3)⋊Dic5C2×C4semidirect
151. Dic3×Dic5C2×C4semidirect
152. Dic3×Dic5C2×C4semidirect
261. #1220C42semidirect
267. C5×#67C42semidirect
279. #1202C42semidirect
280. #1201C42semidirect
325. #67⋊C4AGL(1,𝔽5)semidirect
353. C22×AGL(1,𝔽5)C4×D3semidirect
384. C22⋊AGL(1,𝔽5)C4×D3semidirect
397. C5×C22⋊C4C4×D3semidirect
400. C22⋊Dic5C4×D3semidirect
403. #685C4×D3semidirect
404. #685C4×D3semidirect
503. C22×Dic3C2×AGL(1,𝔽5)semidirect
515. C2×C4×D3C2×AGL(1,𝔽5)semidirect
520. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
529. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
535. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
545. C4×Dic3C2×AGL(1,𝔽5)semidirect
720. #67C4×AGL(1,𝔽5)semidirect
863. C22⋊C4D3×AGL(1,𝔽5)semidirect
876. C3×C5#2275semidirect
1021. C5#73436semidirect
1067. C3#10617172semidirect

Maximal subgroups

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

subgroupindex
C2×#67⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
D5×#67⋊C42
C22⋊C4×ΓL(1,𝔽16)2
C3×C22⋊C4×AGL(1,𝔽5)2
Dic3×C22⋊AGL(1,𝔽5)2
C2×(C2×AGL(1,𝔽5))⋊Dic32
#117519312
D3×(C2×AGL(1,𝔽5))⋊C42
AGL(1,𝔽5)×(C2×D3)⋊C42
C4×Dic3⋊AGL(1,𝔽5)2
C4×(C2×D3)⋊AGL(1,𝔽5)2
#117518332
#117518322
AGL(1,𝔽5)×Dic3⋊C42
#106171723
#734365