Finite Group Databasebeta

← #14330255

Subgroups — #14330255

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#126C211yesmaximal, characteristic
2#11752371C211yesmaximal, characteristic, complemented
3#11752370C211yesmaximal, characteristic, complemented
4#11752370C211yesmaximal, characteristic, complemented
5#11752370C211yesmaximal, characteristic, complemented
6C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
7C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
8#11752359C211yesmaximal, characteristic
9#11752359C211yesmaximal, characteristic
10#11752359C211yesmaximal, characteristic
11#11752358C211yesmaximal, characteristic
12C22⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
13C22⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
14C4×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
15#11752345C211yesmaximal, characteristic, complemented
16#10617359—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C2×#6763C2211yescharacteristic
19C2×#6763C2211yescharacteristic
20C2×#6763C2211yescharacteristic
21C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
22C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
23C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
24C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
25C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
26C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
27C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
28C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
29C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
30C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
31C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
32C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
33C3×C5×#126C411yescharacteristic, complemented
34C3×#4044C411yescharacteristic, complemented
35C3×#4044C411yescharacteristic, complemented
36C3×#4044C411yescharacteristic, complemented
37C3×D5×C4⋊C4C2211yescharacteristic
38C3×D5×C4⋊C4C2211yescharacteristic
39C3×D5×C4⋊C4C2211yescharacteristic
40C3×D5×C22⋊C4C2211yescharacteristic
41C3×D5×C22⋊C4C2211yescharacteristic
42C3×D5×C22⋊C4C2211yescharacteristic
43C3×#4025C411yescharacteristic, complemented
44C3×#4025C411yescharacteristic, complemented
45C3×#4025C411yescharacteristic, complemented
46C3×#4022C411yescharacteristic, complemented
47C3×C42×D5C2211yescharacteristic
48#91235C2211yescharacteristic
49#91235C2211yescharacteristic
50#91235C2211yescharacteristic
51#91235C2211yescharacteristic
52#91235C2211yescharacteristic
53#91235C2211yescharacteristic
54#91235C2211yescharacteristic
55#91235C2211yescharacteristic
56#91235C2211yescharacteristic
57#91235C2211yescharacteristic
58#91235C2211yescharacteristic
59#91235C2211yescharacteristic
60#83075—51nomaximal, Hall
61D5×#126D311yescharacteristic
62#65712—31no—
63#65711—31no—
64#65711—31no—
65#65711—31no—
66C4⋊C4×AGL(1,𝔽5)—31no—
67C4⋊C4×AGL(1,𝔽5)—31no—
68#65700—31no—
69#65700—31no—
70#65700—31no—
71#65699—31no—
72C22⋊C4×AGL(1,𝔽5)—31no—
73C22⋊C4×AGL(1,𝔽5)—31no—
74C4×C4⋊AGL(1,𝔽5)—31no—
75#65686—31no—
76C23×C3×D5C2311yescharacteristic
77C22×ΓL(1,𝔽16)—22no—
78C22×ΓL(1,𝔽16)—22no—
79C22×ΓL(1,𝔽16)—41no—
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×ΓL(1,𝔽16)C2311yescharacteristic
85C22×ΓL(1,𝔽16)C2311yescharacteristic
86C22×ΓL(1,𝔽16)C2311yescharacteristic
87C22×ΓL(1,𝔽16)C2311yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×C4×D5C2311yescharacteristic
94#6763—22no—
95#6763—22no—
96#6763—41no—
97C4⋊ΓL(1,𝔽16)—22no—
98C4⋊ΓL(1,𝔽16)—22no—
99C4⋊ΓL(1,𝔽16)—22no—
100C4⋊ΓL(1,𝔽16)—22no—
101C4⋊ΓL(1,𝔽16)—41no—
102C4×ΓL(1,𝔽16)—22no—
103C4×ΓL(1,𝔽16)—22no—
104C4×ΓL(1,𝔽16)—22no—
105C4×ΓL(1,𝔽16)—22no—
106C4×ΓL(1,𝔽16)—41no—
107C4×ΓL(1,𝔽16)—41no—
108C4×ΓL(1,𝔽16)—41no—
109C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
110C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
111C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
112C3×C5×C22⋊C4C2×C411yescharacteristic
113C3×C5×C22⋊C4C2×C411yescharacteristic
114C3×C5×C22⋊C4C2×C411yescharacteristic
115C3×C42×C5C2×C411yescharacteristic, complemented
116C3×C22⋊Dic5C2×C411yescharacteristic
117C3×C22⋊Dic5C2×C411yescharacteristic
118C3×C22⋊Dic5C2×C411yescharacteristic
119C3×#685C2×C411yescharacteristic
120C3×#685C2×C411yescharacteristic
121C3×#685C2×C411yescharacteristic
122C3×#685C2×C411yescharacteristic
123C3×#685C2×C411yescharacteristic
124C3×#685C2×C411yescharacteristic
125C3×C4⋊Dic5C2×C411yescharacteristic, complemented
126C3×C4⋊Dic5C2×C411yescharacteristic, complemented
127C3×C4⋊Dic5C2×C411yescharacteristic, complemented
128C3×#683C2×C411yescharacteristic, complemented
129C3×#683C2×C411yescharacteristic, complemented
130C3×#683C2×C411yescharacteristic, complemented
131C3×#683C2×C411yescharacteristic, complemented
132C3×#683C2×C411yescharacteristic, complemented
133C3×#683C2×C411yescharacteristic, complemented
134C3×C4×Dic5C2×C411yescharacteristic, complemented
135C3×C4×Dic5C2×C411yescharacteristic, complemented
136C3×C4×Dic5C2×C411yescharacteristic, complemented
137C2×C3×#126—51no—
138#4984—51no—
139#4980—51no—
140#4980—51no—
141#4980—51no—
142Dic3×C4⋊C4—51no—
143Dic3×C4⋊C4—51no—
144#4951—51no—
145#4951—51no—
146#4951—51no—
147#4950—51no—
148Dic3×C22⋊C4—51no—
149Dic3×C22⋊C4—51no—
150C4×C4⋊Dic3—51no—
151#4932—51no—
152C23×AGL(1,𝔽5)—31no—
153C2×C22⋊AGL(1,𝔽5)—31no—
154C2×C22⋊AGL(1,𝔽5)—31no—
155C2×C22⋊AGL(1,𝔽5)—31no—
156C2×C4⋊AGL(1,𝔽5)—31no—
157C2×C4⋊AGL(1,𝔽5)—31no—
158C2×C4⋊AGL(1,𝔽5)—31no—
159C2×C4⋊AGL(1,𝔽5)—31no—
160C2×C4⋊AGL(1,𝔽5)—31no—
161C2×C4×AGL(1,𝔽5)—31no—
162C2×C4×AGL(1,𝔽5)—31no—
163C2×C4×AGL(1,𝔽5)—31no—
164C2×C4×AGL(1,𝔽5)—31no—
165C2×C4×AGL(1,𝔽5)—31no—
166C2×C4×AGL(1,𝔽5)—31no—
167C2×C4×AGL(1,𝔽5)—31no—
168C5×#126Dic311yescharacteristic, complemented
169#4044Dic311yescharacteristic, complemented
170#4044Dic311yescharacteristic, complemented
171#4044Dic311yescharacteristic, complemented
172D5×C4⋊C4C2×D311yescharacteristic
173D5×C4⋊C4C2×D311yescharacteristic
174D5×C4⋊C4C2×D311yescharacteristic
175D5×C22⋊C4C2×D311yescharacteristic
176D5×C22⋊C4C2×D311yescharacteristic
177D5×C22⋊C4C2×D311yescharacteristic
178#4025Dic311yescharacteristic, complemented
179#4025Dic311yescharacteristic, complemented
180#4025Dic311yescharacteristic, complemented
181#4022Dic311yescharacteristic, complemented
182C42×D5C2×D311yescharacteristic
183(C2×AGL(1,𝔽5))⋊C4—31no—
184(C2×AGL(1,𝔽5))⋊C4—31no—
185(C2×AGL(1,𝔽5))⋊C4—31no—
186(C2×AGL(1,𝔽5))⋊C4—31no—
187(C2×AGL(1,𝔽5))⋊C4—31no—
188(C2×AGL(1,𝔽5))⋊C4—31no—
189(C2×AGL(1,𝔽5))⋊C4—31no—
190(C2×AGL(1,𝔽5))⋊C4—31no—
191(C2×AGL(1,𝔽5))⋊C4—31no—
192(C2×AGL(1,𝔽5))⋊C4—31no—
193(C2×AGL(1,𝔽5))⋊C4—31no—
194(C2×AGL(1,𝔽5))⋊C4—31no—
195#2373—151noSylow
196C23×C3×C5C22×C411yescharacteristic
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5C22×C411yescharacteristic
204C22×C3×D5C2411yescharacteristic
205C2×ΓL(1,𝔽16)—21no—
206C2×ΓL(1,𝔽16)—21no—
207C2×ΓL(1,𝔽16)—21no—
208C2×ΓL(1,𝔽16)—21no—
209C2×ΓL(1,𝔽16)—21no—
210C2×ΓL(1,𝔽16)—21no—
211C2×ΓL(1,𝔽16)—21no—
212C2×ΓL(1,𝔽16)—21no—
213C2×ΓL(1,𝔽16)—21no—
214C2×ΓL(1,𝔽16)—21no—
215C2×ΓL(1,𝔽16)—21no—
216C2×ΓL(1,𝔽16)—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)—21no—
225C2×ΓL(1,𝔽16)—44no—
226C2×ΓL(1,𝔽16)#4112yes—
227C2×ΓL(1,𝔽16)#4112yes—
228C2×ΓL(1,𝔽16)#4112yes—
229C2×ΓL(1,𝔽16)#4112yes—
230C2×C3×C4×C5C22×C411yescharacteristic
231C2×C3×C4×C5C22×C411yescharacteristic
232C2×C3×C4×C5C22×C411yescharacteristic
233C2×C3×C4×C5C22×C411yescharacteristic
234C2×C3×C4×C5C22×C411yescharacteristic
235C2×C3×C4×C5C22×C411yescharacteristic
236C2×C3×Dic5C22×C411yescharacteristic
237C2×C3×Dic5C22×C411yescharacteristic
238C2×C3×Dic5C22×C411yescharacteristic
239C2×C3×Dic5C22×C411yescharacteristic
240C2×C3×Dic5C22×C411yescharacteristic
241C2×C3×Dic5C22×C411yescharacteristic
242C3×C4×D5—21no—
243C3×C4×D5—21no—
244C3×C4×D5—21no—
245C3×C4×D5—21no—
246C3×C4×D5—21no—
247C3×C4×D5—21no—
248C3×C4×D5—21no—
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251C3×C4×D5—21no—
252C3×C4×D5—21no—
253C3×C4×D5—21no—
254C23×Dic3—51no—
255C3×#126—51no—
256C3×#126—51no—
257C3×#126—51no—
258C3×#126—51no—
259C3×#126—51no—
260C3×#126—51no—
261C3×#126—51no—
262C3×#126AGL(1,𝔽5)11yescharacteristic, complemented
263C2×C3×C4⋊C4—51no—
264C2×C3×C4⋊C4—51no—
265C2×C3×C4⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C42—51no—
270C2×#217—51no—
271C2×#217—51no—
272C2×#217—51no—
273C2×C4⋊Dic3—51no—
274C2×C4⋊Dic3—51no—
275C2×C4⋊Dic3—51no—
276C2×C4⋊Dic3—51no—
277C2×C4⋊Dic3—51no—
278C2×C4×Dic3—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C3⋊#95—51no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C23×D5C22×D311yescharacteristic
298C22×AGL(1,𝔽5)—31no—
299C22×AGL(1,𝔽5)—31no—
300C22×AGL(1,𝔽5)—31no—
301C22×AGL(1,𝔽5)—31no—
302C22×AGL(1,𝔽5)—31no—
303C22×AGL(1,𝔽5)—31no—
304C22×AGL(1,𝔽5)—31no—
305C22×AGL(1,𝔽5)—31no—
306C22×AGL(1,𝔽5)—62no—
307C22×AGL(1,𝔽5)—62no—
308C22×AGL(1,𝔽5)—121no—
309C2×C4×D5C22×D311yescharacteristic
310C2×C4×D5C22×D311yescharacteristic
311C2×C4×D5C22×D311yescharacteristic
312C2×C4×D5C22×D311yescharacteristic
313C2×C4×D5C22×D311yescharacteristic
314C2×C4×D5C22×D311yescharacteristic
315C22⋊AGL(1,𝔽5)—62no—
316C22⋊AGL(1,𝔽5)—62no—
317C22⋊AGL(1,𝔽5)—121no—
318C4⋊AGL(1,𝔽5)—62no—
319C4⋊AGL(1,𝔽5)—62no—
320C4⋊AGL(1,𝔽5)—62no—
321C4⋊AGL(1,𝔽5)—62no—
322C4⋊AGL(1,𝔽5)—121no—
323C4×AGL(1,𝔽5)—62no—
324C4×AGL(1,𝔽5)—62no—
325C4×AGL(1,𝔽5)—62no—
326C4×AGL(1,𝔽5)—62no—
327C4×AGL(1,𝔽5)—121no—
328C4×AGL(1,𝔽5)—121no—
329C4×AGL(1,𝔽5)—121no—
330C5×C4⋊C4C2×Dic311yescharacteristic, complemented
331C5×C4⋊C4C2×Dic311yescharacteristic, complemented
332C5×C4⋊C4C2×Dic311yescharacteristic, complemented
333C5×C22⋊C4C2×Dic311yescharacteristic
334C5×C22⋊C4C2×Dic311yescharacteristic
335C5×C22⋊C4C2×Dic311yescharacteristic
336C42×C5C2×Dic311yescharacteristic, complemented
337C22⋊Dic5C2×Dic311yescharacteristic
338C22⋊Dic5C2×Dic311yescharacteristic
339C22⋊Dic5C2×Dic311yescharacteristic
340#685C2×Dic311yescharacteristic
341#685C2×Dic311yescharacteristic
342#685C2×Dic311yescharacteristic
343#685C2×Dic311yescharacteristic
344#685C2×Dic311yescharacteristic
345#685C2×Dic311yescharacteristic
346C4⋊Dic5C2×Dic311yescharacteristic, complemented
347C4⋊Dic5C2×Dic311yescharacteristic, complemented
348C4⋊Dic5C2×Dic311yescharacteristic, complemented
349#683C2×Dic311yescharacteristic, complemented
350#683C2×Dic311yescharacteristic, complemented
351#683C2×Dic311yescharacteristic, complemented
352#683C2×Dic311yescharacteristic, complemented
353#683C2×Dic311yescharacteristic, complemented
354#683C2×Dic311yescharacteristic, complemented
355C4×Dic5C2×Dic311yescharacteristic, complemented
356C4×Dic5C2×Dic311yescharacteristic, complemented
357C4×Dic5C2×Dic311yescharacteristic, complemented
358C2×#126—51no—
359#389—151no—
360#388—151no—
361#388—151no—
362#388—151no—
363#387—151no—
364#387—151no—
365#387—151no—
366#385—151no—
367C4×C4⋊C4—151no—
368C4×C4⋊C4—151no—
369C4×C4⋊C4—151no—
370C4×C22⋊C4—151no—
371C4×C22⋊C4—151no—
372#376—151no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5C23×C411yescharacteristic
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5C2×#4111yescharacteristic
385C2×C3×D5C2×#4111yescharacteristic
386C2×C3×D5C2×#4111yescharacteristic
387C2×C3×D5C2×#4111yescharacteristic
388C2×C3×D5H(5,𝔽2)11yescharacteristic
389C2×C3×D52−1+411yescharacteristic
390ΓL(1,𝔽16)—22no—
391ΓL(1,𝔽16)—22no—
392ΓL(1,𝔽16)—22no—
393ΓL(1,𝔽16)—22no—
394ΓL(1,𝔽16)—41no—
395ΓL(1,𝔽16)—41no—
396ΓL(1,𝔽16)—41no—
397ΓL(1,𝔽16)—41no—
398C3×C4×C5—21no—
399C3×C4×C5—21no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—21no—
404C3×Dic5—21no—
405C3×Dic5—21no—
406C3×Dic5—21no—
407C3×Dic5—21no—
408C3×Dic5—21no—
409C3×Dic5—21no—
410C24×C3—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3—51no—
421C22×Dic3—51no—
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3—102no—
426C22×Dic3—102no—
427C22×Dic3—201no—
428C3×C4⋊C4—51no—
429C3×C4⋊C4—51no—
430C3×C4⋊C4—51no—
431C3×C4⋊C4—51no—
432C3×C4⋊C4—51no—
433C3×C4⋊C4—51no—
434C3×C4⋊C4—51no—
435C3×C4⋊C4—51no—
436C3×C4⋊C4—51no—
437C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
438C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
439C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
440C3×C22⋊C4—51no—
441C3×C22⋊C4—51no—
442C3×C22⋊C4—51no—
443C3×C22⋊C4—51no—
444C3×C22⋊C4—51no—
445C3×C22⋊C4—51no—
446C3×C22⋊C4—51no—
447C3×C22⋊C4—51no—
448C3×C22⋊C4—51no—
449C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
450C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
451C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
452C3×C42—51no—
453C3×C42—51no—
454C3×C42—51no—
455C3×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
456#217—102no—
457#217—102no—
458#217—201no—
459C4⋊Dic3—102no—
460C4⋊Dic3—102no—
461C4⋊Dic3—102no—
462C4⋊Dic3—102no—
463C4⋊Dic3—201no—
464C4×Dic3—102no—
465C4×Dic3—102no—
466C4×Dic3—102no—
467C4×Dic3—102no—
468C4×Dic3—201no—
469C4×Dic3—201no—
470C4×Dic3—201no—
471C23×C5C22×Dic311yescharacteristic
472C22×D5—21no—
473C22×D5—21no—
474C22×D5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5C22×Dic311yescharacteristic
479C22×D5C23×D311yescharacteristic
480C2×AGL(1,𝔽5)—32no—
481C2×AGL(1,𝔽5)—32no—
482C2×AGL(1,𝔽5)—32no—
483C2×AGL(1,𝔽5)—32no—
484C2×AGL(1,𝔽5)—61no—
485C2×AGL(1,𝔽5)—61no—
486C2×AGL(1,𝔽5)—61no—
487C2×AGL(1,𝔽5)—61no—
488C2×AGL(1,𝔽5)—61no—
489C2×AGL(1,𝔽5)—61no—
490C2×AGL(1,𝔽5)—61no—
491C2×AGL(1,𝔽5)—61no—
492C2×AGL(1,𝔽5)—61no—
493C2×AGL(1,𝔽5)—61no—
494C2×AGL(1,𝔽5)—61no—
495C2×AGL(1,𝔽5)—61no—
496C2×AGL(1,𝔽5)—61no—
497C2×AGL(1,𝔽5)—61no—
498C2×AGL(1,𝔽5)—61no—
499C2×AGL(1,𝔽5)—61no—
500C2×AGL(1,𝔽5)—61no—
501C2×AGL(1,𝔽5)—61no—
502C2×AGL(1,𝔽5)—61no—
503C2×AGL(1,𝔽5)—61no—
504C2×AGL(1,𝔽5)—124no—
505C2×C4×C5C22×Dic311yescharacteristic
506C2×C4×C5C22×Dic311yescharacteristic
507C2×C4×C5C22×Dic311yescharacteristic
508C2×C4×C5C22×Dic311yescharacteristic
509C2×C4×C5C22×Dic311yescharacteristic
510C2×C4×C5C22×Dic311yescharacteristic
511C2×Dic5C22×Dic311yescharacteristic
512C2×Dic5C22×Dic311yescharacteristic
513C2×Dic5C22×Dic311yescharacteristic
514C2×Dic5C22×Dic311yescharacteristic
515C2×Dic5C22×Dic311yescharacteristic
516C2×Dic5C22×Dic311yescharacteristic
517C4×D5—21no—
518C4×D5—21no—
519C4×D5—21no—
520C4×D5—21no—
521C4×D5—21no—
522C4×D5—21no—
523C4×D5—21no—
524C4×D5—21no—
525C4×D5—21no—
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—21no—
529C23×C4—151no—
530#126—51no—
531#126—51no—
532#126—51no—
533#126—51no—
534#126—51no—
535#126—51no—
536#126—51no—
537#126ΓL(1,𝔽16)11yescharacteristic, complemented
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—151no—
542C2×C4⋊C4—151no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C22⋊C4—51no—
547C2×C22⋊C4—51no—
548C2×C22⋊C4—51no—
549C2×C22⋊C4—151no—
550C2×C22⋊C4—151no—
551C2×C22⋊C4—151no—
552C2×C42—51no—
553C2×C42—151no—
554C2×C42—151no—
555C2×C42—151no—
556C2×C42—151no—
557C2×C42—151no—
558C2×C42—151no—
559C2×C42—151no—
560#95—151no—
561#95—151no—
562#95—151no—
563#95—151no—
564#95—151no—
565#95—151no—
566#95—151no—
567#95—151no—
568#95—151no—
569#95—151no—
570#95—151no—
571#95—151no—
572C2×C3×C5—41no—
573C2×C3×C5C4×#4111yescharacteristic
574C2×C3×C5C4×#4111yescharacteristic
575C2×C3×C5#52011yescharacteristic
576C3×D5—41no—
577C3×D5#55111yescharacteristic
578C3×D5#55211yescharacteristic
579C3×D5#55311yescharacteristic
580C3×D5#55611yescharacteristic
581C23×C3—51no—
582C23×C3—51no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3—101no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3C22×AGL(1,𝔽5)11yescharacteristic
590C2×C3×C4—51no—
591C2×C3×C4—51no—
592C2×C3×C4—51no—
593C2×C3×C4—51no—
594C2×C3×C4—51no—
595C2×C3×C4—51no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—101no—
603C2×C3×C4—101no—
604C2×C3×C4—101no—
605C2×C3×C4—101no—
606C2×C3×C4—101no—
607C2×C3×C4—101no—
608C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
609C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
610C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
611C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
612C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
613C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
614C2×Dic3—52no—
615C2×Dic3—52no—
616C2×Dic3—52no—
617C2×Dic3—52no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3—101no—
624C2×Dic3—101no—
625C2×Dic3—101no—
626C2×Dic3—101no—
627C2×Dic3—101no—
628C2×Dic3—101no—
629C2×Dic3—101no—
630C2×Dic3—101no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—101no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—101no—
637C2×Dic3—101no—
638C2×Dic3—204no—
639C22×C5—21no—
640C22×C5—21no—
641C22×C5—21no—
642C22×C5C23×Dic311yescharacteristic
643C2×D5—21no—
644C2×D5—21no—
645C2×D5—21no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5D3×#4111yescharacteristic
651C2×D5D3×#4111yescharacteristic
652C2×D5D3×#4111yescharacteristic
653C2×D5D3×#4111yescharacteristic
654C2×D5#100911yescharacteristic
655C2×D5#101011yescharacteristic
656AGL(1,𝔽5)—62no—
657AGL(1,𝔽5)—62no—
658AGL(1,𝔽5)—62no—
659AGL(1,𝔽5)—62no—
660AGL(1,𝔽5)—121no—
661AGL(1,𝔽5)—121no—
662AGL(1,𝔽5)—121no—
663AGL(1,𝔽5)—121no—
664C4×C5—21no—
665C4×C5—21no—
666C4×C5—21no—
667C4×C5—21no—
668C4×C5—21no—
669C4×C5—21no—
670Dic5—21no—
671Dic5—21no—
672Dic5—21no—
673Dic5—21no—
674Dic5—21no—
675Dic5—21no—
676C24—51no—
677C22×C4—51no—
678C22×C4—51no—
679C22×C4—51no—
680C22×C4—51no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—151no—
684C22×C4—151no—
685C22×C4—151no—
686C22×C4—151no—
687C22×C4—151no—
688C22×C4—151no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—302no—
692C22×C4—302no—
693C22×C4—601no—
694C4⋊C4—51no—
695C4⋊C4—51no—
696C4⋊C4—51no—
697C4⋊C4—51no—
698C4⋊C4—51no—
699C4⋊C4—51no—
700C4⋊C4—51no—
701C4⋊C4—51no—
702C4⋊C4—51no—
703C4⋊C4—302no—
704C4⋊C4—302no—
705C4⋊C4—302no—
706C4⋊C4—302no—
707C4⋊C4—601no—
708C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
709C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
710C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
711C22⋊C4—51no—
712C22⋊C4—51no—
713C22⋊C4—51no—
714C22⋊C4—51no—
715C22⋊C4—51no—
716C22⋊C4—51no—
717C22⋊C4—51no—
718C22⋊C4—51no—
719C22⋊C4—51no—
720C22⋊C4—302no—
721C22⋊C4—302no—
722C22⋊C4—601no—
723C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
724C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
725C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
726C42—51no—
727C42—51no—
728C42—51no—
729C42—302no—
730C42—302no—
731C42—302no—
732C42—302no—
733C42—601no—
734C42—601no—
735C42—601no—
736C42C2×ΓL(1,𝔽16)11yescharacteristic, complemented
737C3×C5#237311yescharacteristic, complemented, Hall
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—51no—
742C22×C3—51no—
743C22×C3—51no—
744C22×C3—51no—
745C22×C3—51no—
746C22×C3—51no—
747C22×C3—101no—
748C22×C3—101no—
749C22×C3—101no—
750C22×C3—201no—
751C22×C3—201no—
752C22×C3—201no—
753C22×C3—201no—
754C22×C3C23×AGL(1,𝔽5)11yescharacteristic
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—101no—
762C3×C4—101no—
763C3×C4—101no—
764C3×C4—101no—
765C3×C4—101no—
766C3×C4—101no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771Dic3—201no—
772Dic3—201no—
773Dic3—201no—
774Dic3—201no—
775C2×C5—41no—
776C2×C5Dic3×#4111yescharacteristic
777C2×C5Dic3×#4111yescharacteristic
778C2×C5#582711yescharacteristic
779D5—41no—
780D5#570211yescharacteristic
781D5#570511yescharacteristic
782D5#570811yescharacteristic
783D5#570911yescharacteristic
784C23—51no—
785C23—51no—
786C23—101no—
787C23—101no—
788C23—101no—
789C23—101no—
790C23—101no—
791C23—101no—
792C23C22×ΓL(1,𝔽16)11yescharacteristic
793C2×C4—51no—
794C2×C4—51no—
795C2×C4—51no—
796C2×C4—51no—
797C2×C4—51no—
798C2×C4—51no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—101no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—101no—
805C2×C4—101no—
806C2×C4—101no—
807C2×C4—101no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—152no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—301no—
816C2×C4—301no—
817C2×C4—301no—
818C2×C4—301no—
819C2×C4—301no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—604no—
836C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
837C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
838C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
839C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
840C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
841C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
842C2×C3—41no—
843C2×C3—51no—
844C2×C3—51no—
845C2×C3—51no—
846C2×C3—51no—
847C2×C3—201no—
848C2×C3#41×AGL(1,𝔽5)11yescharacteristic
849C2×C3#41×AGL(1,𝔽5)11yescharacteristic
850C2×C3#6626611yescharacteristic
851C5#8307511yescharacteristic, complemented, Sylow
852C22—21no—
853C22—21no—
854C22—21no—
855C22—51no—
856C22—51no—
857C22—51no—
858C22—51no—
859C22—51no—
860C22—51no—
861C22—101no—
862C22—101no—
863C22—101no—
864C22—201no—
865C22—201no—
866C22—201no—
867C22—201no—
868C22C23×ΓL(1,𝔽16)11yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—101no—
876C4—101no—
877C4—101no—
878C4—101no—
879C4—101no—
880C4—101no—
881C4—302no—
882C4—302no—
883C4—302no—
884C4—302no—
885C4—601no—
886C4—601no—
887C4—601no—
888C4—601no—
889C3#1061735911yescharacteristic, complemented, Sylow
890C2—41no—
891C2—51no—
892C2—51no—
893C2—51no—
894C2—51no—
895C2—201no—
896C2#41×ΓL(1,𝔽16)11yescharacteristic
897C2#41×ΓL(1,𝔽16)11yescharacteristic
898C2#1175699511yescharacteristic
subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#126C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenter#126ΓL(1,𝔽16)
hypocenterC3×C5#2373
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
2. #11752371C2semidirect
3. #11752370C2semidirect
4. #11752370C2semidirect
5. #11752370C2semidirect
6. C4⋊C4×ΓL(1,𝔽16)C2semidirect
7. C4⋊C4×ΓL(1,𝔽16)C2semidirect
14. C4×C4⋊ΓL(1,𝔽16)C2semidirect
15. #11752345C2semidirect
33. C3×C5×#126C4semidirect
34. C3×#4044C4semidirect
35. C3×#4044C4semidirect
36. C3×#4044C4semidirect
43. C3×#4025C4semidirect
44. C3×#4025C4semidirect
45. C3×#4025C4semidirect
46. C3×#4022C4semidirect
109. C3×C5×C4⋊C4C2×C4semidirect
110. C3×C5×C4⋊C4C2×C4semidirect
111. C3×C5×C4⋊C4C2×C4semidirect
115. C3×C42×C5C2×C4semidirect
125. C3×C4⋊Dic5C2×C4semidirect
126. C3×C4⋊Dic5C2×C4semidirect
127. C3×C4⋊Dic5C2×C4semidirect
128. C3×#683C2×C4semidirect
129. C3×#683C2×C4semidirect
130. C3×#683C2×C4semidirect
131. C3×#683C2×C4semidirect
132. C3×#683C2×C4semidirect
133. C3×#683C2×C4semidirect
134. C3×C4×Dic5C2×C4semidirect
135. C3×C4×Dic5C2×C4semidirect
136. C3×C4×Dic5C2×C4semidirect
168. C5×#126Dic3semidirect
169. #4044Dic3semidirect
170. #4044Dic3semidirect
171. #4044Dic3semidirect
178. #4025Dic3semidirect
179. #4025Dic3semidirect
180. #4025Dic3semidirect
181. #4022Dic3semidirect
262. C3×#126AGL(1,𝔽5)semidirect
330. C5×C4⋊C4C2×Dic3semidirect
331. C5×C4⋊C4C2×Dic3semidirect
332. C5×C4⋊C4C2×Dic3semidirect
336. C42×C5C2×Dic3semidirect
346. C4⋊Dic5C2×Dic3semidirect
347. C4⋊Dic5C2×Dic3semidirect
348. C4⋊Dic5C2×Dic3semidirect
349. #683C2×Dic3semidirect
350. #683C2×Dic3semidirect
351. #683C2×Dic3semidirect
352. #683C2×Dic3semidirect
353. #683C2×Dic3semidirect
354. #683C2×Dic3semidirect
355. C4×Dic5C2×Dic3semidirect
356. C4×Dic5C2×Dic3semidirect
357. C4×Dic5C2×Dic3semidirect
437. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
438. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
439. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
455. C3×C42C2×AGL(1,𝔽5)semidirect
537. #126ΓL(1,𝔽16)semidirect
708. C4⋊C4C2×ΓL(1,𝔽16)semidirect
709. C4⋊C4C2×ΓL(1,𝔽16)semidirect
710. C4⋊C4C2×ΓL(1,𝔽16)semidirect
736. C42C2×ΓL(1,𝔽16)semidirect
737. C3×C5#2373semidirect
851. C5#83075semidirect
889. C3#10617359semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1262
#117523712
#117523702
C4⋊C4×ΓL(1,𝔽16)2
#117523592
#117523582
C22⋊C4×ΓL(1,𝔽16)2
C4×C4⋊ΓL(1,𝔽16)2
#117523452
#106173593
#830755