Finite Group Databasebeta

← #14326667

Subgroups — #14326667

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91909C211yesmaximal, characteristic
2C2×#91907C211yesmaximal, characteristic
3D3×D5×C4⋊C4C211yesmaximal, characteristic
4#11752370C211yesmaximal, characteristic, complemented
5C3×#65711C211yesmaximal, characteristic, complemented
6#11751854C211yesmaximal, characteristic
7#11751853C211yesmaximal, characteristic
8#11751853C211yesmaximal, characteristic
9#11751848C211yesmaximal, characteristic
10#11751844C211yesmaximal, characteristic, complemented
11#11751840C211yesmaximal, characteristic, complemented
12#11751839C211yesmaximal, characteristic, complemented
13#11751837C211yesmaximal, characteristic, complemented
14#11751833C211yesmaximal, characteristic, complemented
15AGL(1,𝔽5)×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10617103—31nomaximal, Hall
17C2×C4×D3×D5C2211yescharacteristic
18C2×C4×D3×D5C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
21C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
22C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
29C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
30C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
31C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
32C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
34C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
35C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
36#91909—24no—
37#91907—24no—
38C4⋊C4×D15C411yescharacteristic, complemented
39C5×D3×C4⋊C4C411yescharacteristic, complemented
40C3×D5×C4⋊C4C2211yescharacteristic
41#91437C411yescharacteristic, complemented
42D3×C4⋊Dic5C411yescharacteristic, complemented
43D5×C4⋊Dic3C2211yescharacteristic
44#91404C411yescharacteristic, complemented
45#91404C411yescharacteristic, complemented
46D3×#683C411yescharacteristic, complemented
47D3×#683C411yescharacteristic, complemented
48D5×Dic3⋊C4C2211yescharacteristic
49D5×Dic3⋊C4C2211yescharacteristic
50#91235C2211yescharacteristic
51#91235C2211yescharacteristic
52#91235C2211yescharacteristic
53#91235C2211yescharacteristic
54C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
55C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
56C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
57C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
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#74961—51nomaximal, Hall
63C2×#4130—31no—
64C2×#4130—31no—
65C2×D5×C4⋊C4—31no—
66#65765—31no—
67#65764—31no—
68#65764—31no—
69C4×C22⋊AGL(1,𝔽5)—31no—
70#65712—31no—
71#65712—31no—
72#65711—31no—
73#65711—31no—
74#65711—31no—
75#65711D311yescharacteristic, complemented
76C4⋊C4×AGL(1,𝔽5)—31no—
77C4⋊C4×AGL(1,𝔽5)—31no—
78C22×D3×D5C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)C2311yescharacteristic
85C22×C3×AGL(1,𝔽5)C2311yescharacteristic
86C22×C3×AGL(1,𝔽5)C2311yescharacteristic
87C2×C4×D15C2×C411yescharacteristic
88C2×C4×D15C2×C411yescharacteristic
89C2×C4×D15C2×C411yescharacteristic
90C2×C4×C5×D3C2×C411yescharacteristic
91C2×C4×C5×D3C2×C411yescharacteristic
92C2×C4×C5×D3C2×C411yescharacteristic
93C2×C3×C4×D5C2311yescharacteristic
94C2×C3×C4×D5C2311yescharacteristic
95C2×C3×C4×D5C2311yescharacteristic
96C2×#1200C2×C411yescharacteristic
97C2×#1200C2×C411yescharacteristic
98C2×#1200C2×C411yescharacteristic
99C2×D3×Dic5C2×C411yescharacteristic
100C2×D3×Dic5C2×C411yescharacteristic
101C2×D3×Dic5C2×C411yescharacteristic
102C2×D5×Dic3C2311yescharacteristic
103C2×D5×Dic3C2311yescharacteristic
104C2×D5×Dic3C2311yescharacteristic
105C4×D3×D5—22no—
106C4×D3×D5—22no—
107C4×D3×D5—22no—
108C4×D3×D5—22no—
109C4×D3×D5—22no—
110C4×D3×D5—22no—
111C4⋊ΓL(1,𝔽16)—22no—
112C4×ΓL(1,𝔽16)—22no—
113C3×C4⋊AGL(1,𝔽5)—22no—
114C3×C4×AGL(1,𝔽5)—22no—
115Dic3⋊AGL(1,𝔽5)—22no—
116Dic3⋊AGL(1,𝔽5)—22no—
117Dic3⋊AGL(1,𝔽5)—22no—
118Dic3⋊AGL(1,𝔽5)—22no—
119(C2×D3)⋊AGL(1,𝔽5)—22no—
120(C2×D3)⋊AGL(1,𝔽5)—22no—
121(C2×D3)⋊AGL(1,𝔽5)—22no—
122(C2×D3)⋊AGL(1,𝔽5)D414yes—
123Dic3×AGL(1,𝔽5)—22no—
124Dic3×AGL(1,𝔽5)—22no—
125Dic3×AGL(1,𝔽5)—22no—
126Dic3×AGL(1,𝔽5)—22no—
127C3×C5×C4⋊C4C2×C411yescharacteristic
128C4⋊Dic15C2×C411yescharacteristic
129#6712C2×C411yescharacteristic
130#6712C2×C411yescharacteristic
131C5×C4⋊Dic3C2×C411yescharacteristic
132C5×Dic3⋊C4C2×C411yescharacteristic
133C5×Dic3⋊C4C2×C411yescharacteristic
134C3×C4⋊Dic5C2×C411yescharacteristic
135C3×#683C2×C411yescharacteristic
136C3×#683C2×C411yescharacteristic
137Dic3⋊Dic5C2×C411yescharacteristic
138Dic3⋊Dic5C2×C411yescharacteristic
139#6669C2×C411yescharacteristic
140#6669C2×C411yescharacteristic
141#6668C2×C411yescharacteristic
142#6668C2×C411yescharacteristic
143C2×#892—51no—
144C2×D3×C4⋊C4—51no—
145C2×#872—51no—
146C3×#387—51no—
147#4980—51no—
148#4976—51no—
149C4×Dic3⋊C4—51no—
150#4667—51no—
151#4666—51no—
152#4664—51no—
153#4664—51no—
154#4654—51no—
155#4653—51no—
156#4649—51no—
157#4647—51no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C2×C22⋊AGL(1,𝔽5)—31no—
162C2×C22⋊AGL(1,𝔽5)—31no—
163C2×C22⋊AGL(1,𝔽5)—31no—
164C2×C22⋊AGL(1,𝔽5)—31no—
165#4130—64no—
166#4130—64no—
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)—31no—
172C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
173C2×C4×AGL(1,𝔽5)—31no—
174C2×C4×AGL(1,𝔽5)—31no—
175C2×C4×AGL(1,𝔽5)—31no—
176C2×C4×AGL(1,𝔽5)—31no—
177C2×C4×AGL(1,𝔽5)—31no—
178C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
179C2×C5×C4⋊C4—31no—
180C2×C4⋊Dic5—31no—
181C2×#683—31no—
182C2×#683—31no—
183D5×C4⋊C4—31no—
184D5×C4⋊C4—31no—
185D5×C4⋊C4—31no—
186D5×C4⋊C4—31no—
187D5×C4⋊C4—31no—
188D5×C4⋊C4—31no—
189D5×C4⋊C4—31no—
190D5×C4⋊C4C2×D311yescharacteristic
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(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
202(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
203#2344—151noSylow
204C22×D15C22×C411yescharacteristic
205C22×C5×D3C22×C411yescharacteristic
206C22×C3×D5C2411yescharacteristic
207C2×D3×D5—21no—
208C2×D3×D5—21no—
209C2×D3×D5—21no—
210C2×D3×D5—21no—
211C2×D3×D5C2×D412yes—
212C2×D3×D5#4112yes—
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)—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)C2×D412yes—
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)—21no—
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)C2×D412yes—
237C2×C3×C4×C5C22×C411yescharacteristic
238C2×C3×C4×C5C22×C411yescharacteristic
239C2×C3×C4×C5C22×C411yescharacteristic
240C2×Dic15C22×C411yescharacteristic
241C2×Dic15C22×C411yescharacteristic
242C2×Dic15C22×C411yescharacteristic
243C4×D15—22no—
244C4×D15—22no—
245C4×D15—22no—
246C2×C5×Dic3C22×C411yescharacteristic
247C2×C5×Dic3C22×C411yescharacteristic
248C2×C5×Dic3C22×C411yescharacteristic
249C4×C5×D3—22no—
250C4×C5×D3—22no—
251C4×C5×D3—22no—
252C2×C3×Dic5C22×C411yescharacteristic
253C2×C3×Dic5C22×C411yescharacteristic
254C2×C3×Dic5C22×C411yescharacteristic
255C3×C4×D5—21no—
256C3×C4×D5—21no—
257C3×C4×D5—21no—
258C3×C4×D5—21no—
259C3×C4×D5—21no—
260C3×C4×D5—21no—
261#1200—22no—
262#1200—22no—
263#1200—22no—
264D3×Dic5—22no—
265D3×Dic5—22no—
266D3×Dic5—22no—
267D5×Dic3—21no—
268D5×Dic3—21no—
269D5×Dic3—21no—
270D5×Dic3—21no—
271D5×Dic3#4112yes—
272D5×Dic3#4112yes—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3—51no—
276C2×C3×C4⋊C4—51no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C42—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×C4⋊Dic3—51no—
284C2×C4⋊Dic3—51no—
285C2×Dic3⋊C4—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×C4×Dic3—51no—
292C2×C4×Dic3—51no—
293C2×C4×Dic3—51no—
294C2×C4×Dic3—51no—
295C2×C4×Dic3—51no—
296#892—104no—
297D3×C4⋊C4—51no—
298D3×C4⋊C4—51no—
299D3×C4⋊C4—51no—
300D3×C4⋊C4—51no—
301D3×C4⋊C4—51no—
302D3×C4⋊C4—51no—
303D3×C4⋊C4—51no—
304D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
305#872—104no—
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—
318C23×D5—31no—
319C22×AGL(1,𝔽5)—31no—
320C22×AGL(1,𝔽5)—31no—
321C22×AGL(1,𝔽5)—31no—
322C22×AGL(1,𝔽5)—31no—
323C22×AGL(1,𝔽5)C22×D311yescharacteristic
324C22×AGL(1,𝔽5)C22×D311yescharacteristic
325C22×AGL(1,𝔽5)C22×D311yescharacteristic
326C22×AGL(1,𝔽5)C22×D311yescharacteristic
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×Dic5—31no—
331C22×Dic5—31no—
332C22×Dic5—31no—
333C2×C4×D5—31no—
334C2×C4×D5—31no—
335C2×C4×D5—31no—
336C2×C4×D5—31no—
337C2×C4×D5—31no—
338C2×C4×D5—31no—
339C2×C4×D5—31no—
340C2×C4×D5—31no—
341C2×C4×D5—31no—
342C2×C4×D5—62no—
343C2×C4×D5—62no—
344C2×C4×D5—62no—
345C2×C4×D5—62no—
346C2×C4×D5—62no—
347C2×C4×D5—62no—
348C2×C4×D5C22×D311yescharacteristic
349C2×C4×D5C22×D311yescharacteristic
350C2×C4×D5C22×D311yescharacteristic
351C22⋊AGL(1,𝔽5)—34no—
352C22⋊AGL(1,𝔽5)—62no—
353C22⋊AGL(1,𝔽5)—62no—
354C22⋊AGL(1,𝔽5)—62no—
355C4⋊AGL(1,𝔽5)—22no—
356C4⋊AGL(1,𝔽5)—62no—
357C4⋊AGL(1,𝔽5)—62no—
358C4⋊AGL(1,𝔽5)—62no—
359C4⋊AGL(1,𝔽5)—62no—
360C4⋊AGL(1,𝔽5)—62no—
361C4×AGL(1,𝔽5)—22no—
362C4×AGL(1,𝔽5)—62no—
363C4×AGL(1,𝔽5)—62no—
364C4×AGL(1,𝔽5)—62no—
365C4×AGL(1,𝔽5)—62no—
366C4×AGL(1,𝔽5)—62no—
367C5×C4⋊C4—31no—
368C5×C4⋊C4—31no—
369C5×C4⋊C4—31no—
370C5×C4⋊C4C4×D311yescharacteristic
371C4⋊Dic5—31no—
372C4⋊Dic5—31no—
373C4⋊Dic5—31no—
374C4⋊Dic5C4×D311yescharacteristic
375#683—31no—
376#683—31no—
377#683—31no—
378#683—31no—
379#683—31no—
380#683—31no—
381#683C4×D311yescharacteristic
382#683C4×D311yescharacteristic
383C2×#117—151no—
384C2×#117—151no—
385C22×C4⋊C4—151no—
386#389—151no—
387#389—151no—
388#387—51no—
389#387—151no—
390#387—151no—
391#387—151no—
392#381—151no—
393#381—151no—
394#380—151no—
395C4×C4⋊C4—151no—
396C4×C4⋊C4—151no—
397C4×C22⋊C4—151no—
398C22×C3×C5C23×C411yescharacteristic
399C2×D15—21no—
400C2×D15—21no—
401C2×D15C4×D412yes—
402C2×C5×D3—21no—
403C2×C5×D3—21no—
404C2×C5×D3C4×D412yes—
405C2×C3×D5C22×D411yescharacteristic
406C2×C3×D5C2×#4111yescharacteristic
407C2×C3×D5C2×#4111yescharacteristic
408C2×C3×D5C2×#4111yescharacteristic
409C2×C3×D52−1+411yescharacteristic
410C2×C3×D52−1+411yescharacteristic
411D3×D5—22no—
412D3×D5—22no—
413D3×D5—22no—
414D3×D5—22no—
415ΓL(1,𝔽16)—22no—
416ΓL(1,𝔽16)—41no—
417ΓL(1,𝔽16)—41no—
418ΓL(1,𝔽16)—41no—
419C3×AGL(1,𝔽5)—22no—
420C3×AGL(1,𝔽5)—41no—
421C3×AGL(1,𝔽5)—41no—
422C3×AGL(1,𝔽5)—41no—
423C3×C4×C5—21no—
424C3×C4×C5—21no—
425C3×C4×C5—21no—
426Dic15—21no—
427Dic15—21no—
428Dic15#11712yescomplemented
429C3×Dic5—21no—
430C3×Dic5—21no—
431C3×Dic5—21no—
432C5×Dic3—21no—
433C5×Dic3—21no—
434C5×Dic3#11712yescomplemented
435C23×D3—51no—
436C22×C3×C4—51no—
437C22×C3×C4—51no—
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—51no—
441C22×C3×C4—51no—
442C22×C3×C4—51no—
443C22×Dic3—51no—
444C22×Dic3—51no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C2×C4×D3—51no—
451C2×C4×D3—51no—
452C2×C4×D3—51no—
453C2×C4×D3—51no—
454C2×C4×D3—51no—
455C2×C4×D3—51no—
456C2×C4×D3—51no—
457C2×C4×D3—51no—
458C2×C4×D3—51no—
459C2×C4×D3—102no—
460C2×C4×D3—102no—
461C2×C4×D3—102no—
462C2×C4×D3—102no—
463C2×C4×D3—102no—
464C2×C4×D3—102no—
465C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
466C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
467C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
468C3×C4⋊C4—51no—
469C3×C4⋊C4—51no—
470C3×C4⋊C4—51no—
471C3×C4⋊C4—102no—
472C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
473C3×C42—102no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478C4⋊Dic3—51no—
479C4⋊Dic3—51no—
480C4⋊Dic3—51no—
481C4⋊Dic3—102no—
482C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
483Dic3⋊C4—51no—
484Dic3⋊C4—51no—
485Dic3⋊C4—51no—
486Dic3⋊C4—51no—
487Dic3⋊C4—51no—
488Dic3⋊C4—51no—
489Dic3⋊C4—102no—
490Dic3⋊C4—102no—
491Dic3⋊C4—102no—
492Dic3⋊C4—102no—
493Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
494Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
495C4×Dic3—102no—
496C4×Dic3—102no—
497C4×Dic3—102no—
498C4×Dic3—102no—
499C4×Dic3—102no—
500C23×C5—31no—
501C22×D5—31no—
502C22×D5—32no—
503C22×D5—32no—
504C22×D5—61no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5C23×D311yescharacteristic
509C2×AGL(1,𝔽5)—21no—
510C2×AGL(1,𝔽5)—21no—
511C2×AGL(1,𝔽5)—21no—
512C2×AGL(1,𝔽5)—21no—
513C2×AGL(1,𝔽5)—21no—
514C2×AGL(1,𝔽5)—21no—
515C2×AGL(1,𝔽5)—21no—
516C2×AGL(1,𝔽5)—21no—
517C2×AGL(1,𝔽5)—21no—
518C2×AGL(1,𝔽5)—21no—
519C2×AGL(1,𝔽5)—21no—
520C2×AGL(1,𝔽5)—32no—
521C2×AGL(1,𝔽5)—61no—
522C2×AGL(1,𝔽5)—61no—
523C2×AGL(1,𝔽5)—61no—
524C2×AGL(1,𝔽5)—61no—
525C2×AGL(1,𝔽5)—61no—
526C2×AGL(1,𝔽5)—61no—
527C2×AGL(1,𝔽5)—61no—
528C2×AGL(1,𝔽5)—61no—
529C2×AGL(1,𝔽5)—61no—
530C2×AGL(1,𝔽5)—61no—
531C2×AGL(1,𝔽5)—61no—
532C2×AGL(1,𝔽5)D3×D412yes—
533C2×C4×C5—31no—
534C2×C4×C5—31no—
535C2×C4×C5—31no—
536C2×C4×C5—62no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5C2×C4×D311yescharacteristic
540C2×C4×C5C2×C4×D311yescharacteristic
541C2×C4×C5C2×C4×D311yescharacteristic
542C2×Dic5—31no—
543C2×Dic5—31no—
544C2×Dic5—31no—
545C2×Dic5—62no—
546C2×Dic5—62no—
547C2×Dic5—62no—
548C2×Dic5C2×C4×D311yescharacteristic
549C2×Dic5C2×C4×D311yescharacteristic
550C2×Dic5C2×C4×D311yescharacteristic
551C4×D5—21no—
552C4×D5—21no—
553C4×D5—21no—
554C4×D5—21no—
555C4×D5—21no—
556C4×D5—21no—
557C4×D5—32no—
558C4×D5—32no—
559C4×D5—62no—
560C4×D5—62no—
561C4×D5—62no—
562C4×D5—62no—
563C4×D5—62no—
564C4×D5—62no—
565C4×D5—61no—
566C4×D5—61no—
567C4×D5—61no—
568C4×D5—61no—
569C23×C4—151no—
570C23×C4—151no—
571C23×C4—151no—
572#117—304no—
573#117—304no—
574C2×C4⋊C4—31no—
575C2×C4⋊C4—51no—
576C2×C4⋊C4—51no—
577C2×C4⋊C4—151no—
578C2×C4⋊C4—151no—
579C2×C4⋊C4—151no—
580C2×C4⋊C4—151no—
581C2×C4⋊C4—151no—
582C2×C4⋊C4—151no—
583C2×C4⋊C4—151no—
584C2×C4⋊C4—151no—
585C2×C4⋊C4—151no—
586C2×C4⋊C4—151no—
587C2×C4⋊C4—151no—
588C2×C4⋊C4—151no—
589C2×C4⋊C4—151no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C22⋊C4—151no—
593C2×C22⋊C4—151no—
594C2×C22⋊C4—151no—
595C2×C22⋊C4—151no—
596C2×C42—51no—
597C2×C42—151no—
598C2×C42—151no—
599C2×C42—151no—
600C2×C42—151no—
601C2×C42—151no—
602#95—51no—
603#95—51no—
604#95—51no—
605#95—51no—
606#95—151no—
607#95—151no—
608#95—151no—
609#95—151no—
610#95—151no—
611#95—151no—
612#95—151no—
613#95—151no—
614C2×C3×C5C2×#11711yescharacteristic
615C2×C3×C5C2×C4×D411yescharacteristic
616C2×C3×C5#51911yescharacteristic
617D15—22no—
618C3×D5#54711yescharacteristic
619C3×D5#54711yescharacteristic
620C3×D5#55211yescharacteristic
621C3×D5#55211yescharacteristic
622C5×D3—22no—
623C23×C3—51no—
624C22×D3—51no—
625C22×D3—52no—
626C22×D3—52no—
627C22×D3—101no—
628C22×D3—101no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3C22×AGL(1,𝔽5)11yescharacteristic
632C2×C3×C4—52no—
633C2×C3×C4—51no—
634C2×C3×C4—51no—
635C2×C3×C4—51no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648C2×C3×C4—101no—
649C2×C3×C4—101no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4—101no—
653C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
654C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
655C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
656C2×Dic3—51no—
657C2×Dic3—52no—
658C2×Dic3—52no—
659C2×Dic3—52no—
660C2×Dic3—51no—
661C2×Dic3—51no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—101no—
671C2×Dic3—101no—
672C2×Dic3—101no—
673C2×Dic3—101no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
678C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
679C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
680C4×D3—22no—
681C4×D3—22no—
682C4×D3—22no—
683C4×D3—102no—
684C4×D3—102no—
685C4×D3—102no—
686C4×D3—102no—
687C4×D3—102no—
688C4×D3—102no—
689C4×D3—102no—
690C4×D3—102no—
691C4×D3—102no—
692C22×C5—32no—
693C22×C5—61no—
694C22×C5—61no—
695C22×C5C22×C4×D311yescharacteristic
696C2×D5—32no—
697C2×D5—61no—
698C2×D5—61no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5C2×D3×D411yescharacteristic
704C2×D5#100711yescharacteristic
705C2×D5D3×#4111yescharacteristic
706C2×D5D3×#4111yescharacteristic
707C2×D5D3×#4111yescharacteristic
708C2×D5#101011yescharacteristic
709AGL(1,𝔽5)—22no—
710AGL(1,𝔽5)—41no—
711AGL(1,𝔽5)—41no—
712AGL(1,𝔽5)—41no—
713AGL(1,𝔽5)—62no—
714AGL(1,𝔽5)—121no—
715AGL(1,𝔽5)—121no—
716AGL(1,𝔽5)—121no—
717C4×C5—21no—
718C4×C5—21no—
719C4×C5—21no—
720C4×C5—32no—
721C4×C5—61no—
722C4×C5—61no—
723Dic5—21no—
724Dic5—21no—
725Dic5—21no—
726Dic5—32no—
727Dic5—61no—
728Dic5—61no—
729C24—151no—
730C22×C4—31no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—51no—
734C22×C4—51no—
735C22×C4—51no—
736C22×C4—51no—
737C22×C4—51no—
738C22×C4—51no—
739C22×C4—51no—
740C22×C4—151no—
741C22×C4—151no—
742C22×C4—151no—
743C22×C4—151no—
744C22×C4—151no—
745C22×C4—151no—
746C22×C4—151no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—151no—
750C22×C4—151no—
751C22×C4—151no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—151no—
756C22×C4—302no—
757C22×C4—302no—
758C22×C4—302no—
759C22×C4—302no—
760C22×C4—302no—
761C22×C4—302no—
762C4⋊C4—31no—
763C4⋊C4—31no—
764C4⋊C4—31no—
765C4⋊C4—51no—
766C4⋊C4—51no—
767C4⋊C4—51no—
768C4⋊C4—102no—
769C4⋊C4—151no—
770C4⋊C4—151no—
771C4⋊C4—151no—
772C4⋊C4—151no—
773C4⋊C4—151no—
774C4⋊C4—151no—
775C4⋊C4—151no—
776C4⋊C4—151no—
777C4⋊C4—151no—
778C4⋊C4—302no—
779C4⋊C4—302no—
780C4⋊C4—302no—
781C4⋊C4—302no—
782C4⋊C4—302no—
783C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
784C22⋊C4—154no—
785C22⋊C4—302no—
786C22⋊C4—302no—
787C22⋊C4—302no—
788C42—102no—
789C42—302no—
790C42—302no—
791C42—302no—
792C42—302no—
793C42—302no—
794C3×C5#234411yescharacteristic, complemented, Hall
795C22×C3—51no—
796C22×C3—51no—
797C22×C3—51no—
798C22×C3—51no—
799C22×C3—51no—
800C22×C3—51no—
801C22×C3C23×AGL(1,𝔽5)11yescharacteristic
802C2×D3—21no—
803C2×D3—21no—
804C2×D3—52no—
805C2×D3—102no—
806C2×D3—102no—
807C2×D3—102no—
808C2×D3—102no—
809C2×D3—101no—
810C2×D3—101no—
811C2×D3D4×AGL(1,𝔽5)12yes—
812C3×C4—21no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—102no—
816C3×C4—101no—
817C3×C4—101no—
818C3×C4—101no—
819C3×C4—201no—
820C3×C4—201no—
821C3×C4—201no—
822Dic3—21no—
823Dic3—21no—
824Dic3—52no—
825Dic3—102no—
826Dic3—101no—
827Dic3—101no—
828Dic3—201no—
829Dic3—201no—
830Dic3—201no—
831Dic3#413012yescomplemented
832C2×C5—62no—
833C2×C5D3×#11711yescharacteristic
834C2×C5C4×D3×D411yescharacteristic
835C2×C5#557211yescharacteristic
836D5—62no—
837D5#563111yescharacteristic
838D5#565511yescharacteristic
839D5#569311yescharacteristic
840D5#570811yescharacteristic
841C23—31no—
842C23—51no—
843C23—152no—
844C23—152no—
845C23—151no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—52no—
854C2×C4—51no—
855C2×C4—51no—
856C2×C4—51no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—101no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—152no—
878C2×C4—152no—
879C2×C4—151no—
880C2×C4—152no—
881C2×C4—151no—
882C2×C4—151no—
883C2×C4—302no—
884C2×C4—302no—
885C2×C4—302no—
886C2×C4—302no—
887C2×C4—302no—
888C2×C4—302no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—302no—
894C2×C4—302no—
895C2×C4—302no—
896C2×C4—301no—
897C2×C4—301no—
898C2×C4—301no—
899C2×C4—301no—
900C2×C4—301no—
901C2×C4—301no—
902C2×C4—301no—
903C2×C4—301no—
904C2×C4—301no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
908C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
909C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
910C2×C3—51no—
911C2×C3—51no—
912C2×C3—51no—
913C2×C3—51no—
914C2×C3C2×#413011yescharacteristic
915C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
916C2×C3#6626211yescharacteristic
917D3—22no—
918D3—102no—
919C5#7496111yescharacteristic, complemented, Sylow
920C22—32no—
921C22—51no—
922C22—51no—
923C22—51no—
924C22—51no—
925C22—51no—
926C22—51no—
927C22—61no—
928C22—61no—
929C22—152no—
930C22—302no—
931C22—302no—
932C22—302no—
933C22—302no—
934C22—301no—
935C22—301no—
936C22C22×D3×AGL(1,𝔽5)11yescharacteristic
937C4—21no—
938C4—21no—
939C4—21no—
940C4—32no—
941C4—61no—
942C4—61no—
943C4—102no—
944C4—101no—
945C4—101no—
946C4—101no—
947C4—152no—
948C4—201no—
949C4—201no—
950C4—201no—
951C4—302no—
952C4—301no—
953C4—301no—
954C4—601no—
955C4—601no—
956C4—601no—
957C3#1061710311yescharacteristic, complemented, Sylow
958C2—51no—
959C2—51no—
960C2—51no—
961C2—51no—
962C2—62no—
963C2—302no—
964C2D3×#413011yescharacteristic
965C2D3×D4×AGL(1,𝔽5)11yescharacteristic
966C2#1175684711yescharacteristic
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#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11752370C2semidirect
5. C3×#65711C2semidirect
10. #11751844C2semidirect
11. #11751840C2semidirect
12. #11751839C2semidirect
13. #11751837C2semidirect
14. #11751833C2semidirect
15. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
38. C4⋊C4×D15C4semidirect
39. C5×D3×C4⋊C4C4semidirect
41. #91437C4semidirect
42. D3×C4⋊Dic5C4semidirect
44. #91404C4semidirect
45. #91404C4semidirect
46. D3×#683C4semidirect
47. D3×#683C4semidirect
75. #65711D3semidirect
304. D3×C4⋊C4AGL(1,𝔽5)semidirect
428. Dic15#117semidirect
434. C5×Dic3#117semidirect
794. C3×C5#2344semidirect
831. Dic3#4130semidirect
919. C5#74961semidirect
957. C3#10617103semidirect

Maximal subgroups

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

subgroupindex
C2×#919092
C2×#919072
D3×D5×C4⋊C42
#117523702
C3×#657112
#117518542
#117518532
#117518482
#117518442
#117518402
#117518392
#117518372
#117518332
AGL(1,𝔽5)×Dic3⋊C42
#106171033
#749615