Finite Group Databasebeta

← #14279966

Subgroups — #14279966

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic
2C22×C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
3C2×#91235C211yesmaximal, characteristic
4C2×#91235C211yesmaximal, characteristic
5C2×#91235C211yesmaximal, characteristic
6C2×#91235C211yesmaximal, characteristic
7C3×D5×#95C211yesmaximal, characteristic
8#10603801—31nomaximal, Hall
9C23×ΓL(1,𝔽16)C2211yescharacteristic
10C23×ΓL(1,𝔽16)C2211yescharacteristic
11C23×ΓL(1,𝔽16)C2211yescharacteristic
12C23×ΓL(1,𝔽16)C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×C4⋊ΓL(1,𝔽16)—22no—
17C2×C4⋊ΓL(1,𝔽16)—22no—
18C2×C4⋊ΓL(1,𝔽16)C414yescomplemented
19C2×C4×ΓL(1,𝔽16)—22no—
20C2×C4×ΓL(1,𝔽16)—22no—
21C2×C4×ΓL(1,𝔽16)—22no—
22#91235—22no—
23#91235—22no—
24#91235—22no—
25#91235C414yescomplemented
26C3×C5×#95C411yescharacteristic, complemented
27C3×#3963C411yescharacteristic, complemented
28C3×#3963C411yescharacteristic, complemented
29C3×#3963C411yescharacteristic, complemented
30#69407—51nomaximal, Hall
31C22×C4⋊AGL(1,𝔽5)—31no—
32C22×C4×AGL(1,𝔽5)—31no—
33C2×(C2×AGL(1,𝔽5))⋊C4—31no—
34C2×(C2×AGL(1,𝔽5))⋊C4—31no—
35C2×(C2×AGL(1,𝔽5))⋊C4—31no—
36C2×(C2×AGL(1,𝔽5))⋊C4—31no—
37D5×#95D311yescharacteristic
38C23×C3×D5C2311yescharacteristic
39C22×ΓL(1,𝔽16)—21no—
40C22×ΓL(1,𝔽16)—21no—
41C22×ΓL(1,𝔽16)—21no—
42C22×ΓL(1,𝔽16)—21no—
43C22×ΓL(1,𝔽16)—21no—
44C22×ΓL(1,𝔽16)—21no—
45C22×ΓL(1,𝔽16)—21no—
46C22×ΓL(1,𝔽16)—21no—
47C22×ΓL(1,𝔽16)—21no—
48C22×ΓL(1,𝔽16)—21no—
49C22×ΓL(1,𝔽16)—21no—
50C22×ΓL(1,𝔽16)—21no—
51C22×ΓL(1,𝔽16)—21no—
52C22×ΓL(1,𝔽16)—21no—
53C22×ΓL(1,𝔽16)—21no—
54C22×ΓL(1,𝔽16)—21no—
55C22×ΓL(1,𝔽16)—21no—
56C22×ΓL(1,𝔽16)—21no—
57C22×ΓL(1,𝔽16)—21no—
58C22×ΓL(1,𝔽16)—21no—
59C22×ΓL(1,𝔽16)C2×C412yes—
60C22×ΓL(1,𝔽16)C2×C412yes—
61C22×ΓL(1,𝔽16)C2×C412yes—
62C22×ΓL(1,𝔽16)C2×C412yes—
63C22×ΓL(1,𝔽16)D412yes—
64C22×ΓL(1,𝔽16)D412yes—
65C22×ΓL(1,𝔽16)D412yes—
66C22×ΓL(1,𝔽16)Q812yes—
67C22×C3×C4×C5C2×C411yescharacteristic
68C22×C3×C4×C5C2×C411yescharacteristic
69C22×C3×C4×C5C2×C411yescharacteristic
70C22×C3×Dic5C2×C411yescharacteristic
71C22×C3×Dic5C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—21no—
76C2×C3×C4×D5—21no—
77C2×C3×C4×D5—21no—
78C2×C3×C4×D5—21no—
79C2×C3×C4×D5—21no—
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5C2×C412yes—
88C2×C3×C4×D5C2×C412yes—
89C2×C3×C4×D5D412yes—
90C2×C3×C4×D5Q812yes—
91C4⋊ΓL(1,𝔽16)—28no—
92C4×ΓL(1,𝔽16)—28no—
93C22×C4⋊Dic3—51no—
94C22×C4×Dic3—51no—
95C2×C3×#95—51no—
96C2×C3⋊#95—51no—
97C2×C3⋊#95—51no—
98C2×C3⋊#95—51no—
99C2×C3⋊#95—51no—
100C23×AGL(1,𝔽5)—31no—
101C23×AGL(1,𝔽5)—31no—
102C23×AGL(1,𝔽5)—31no—
103C23×AGL(1,𝔽5)—31no—
104C22×C4×D5C2×D311yescharacteristic
105C22×C4×D5C2×D311yescharacteristic
106C22×C4×D5C2×D311yescharacteristic
107C2×C4⋊AGL(1,𝔽5)—34no—
108C2×C4⋊AGL(1,𝔽5)—62no—
109C2×C4⋊AGL(1,𝔽5)—62no—
110C2×C4×AGL(1,𝔽5)—62no—
111C2×C4×AGL(1,𝔽5)—62no—
112C2×C4×AGL(1,𝔽5)—62no—
113(C2×AGL(1,𝔽5))⋊C4—34no—
114(C2×AGL(1,𝔽5))⋊C4—62no—
115(C2×AGL(1,𝔽5))⋊C4—62no—
116(C2×AGL(1,𝔽5))⋊C4—62no—
117C5×#95Dic311yescharacteristic, complemented
118#3963Dic311yescharacteristic, complemented
119#3963Dic311yescharacteristic, complemented
120#3963Dic311yescharacteristic, complemented
121#1436—151noSylow
122C23×C3×C5C22×C411yescharacteristic
123C22×C3×D5C22×C411yescharacteristic
124C22×C3×D5C22×C411yescharacteristic
125C22×C3×D5C2×D411yescharacteristic
126C22×C3×D5C2×D411yescharacteristic
127C22×C3×D5C2×D411yescharacteristic
128C22×C3×D5C2×D411yescharacteristic
129C22×C3×D5C2×Q811yescharacteristic
130C22×C3×D5C2×Q811yescharacteristic
131C22×C3×D5#4111yescharacteristic
132C22×C3×D5#4111yescharacteristic
133C22×C3×D5#4111yescharacteristic
134C22×C3×D5#4111yescharacteristic
135C22×C3×D5#4111yescharacteristic
136C22×C3×D5#4111yescharacteristic
137C2×ΓL(1,𝔽16)—22no—
138C2×ΓL(1,𝔽16)—22no—
139C2×ΓL(1,𝔽16)—22no—
140C2×ΓL(1,𝔽16)—22no—
141C2×ΓL(1,𝔽16)—22no—
142C2×ΓL(1,𝔽16)—22no—
143C2×ΓL(1,𝔽16)—22no—
144C2×ΓL(1,𝔽16)—22no—
145C2×ΓL(1,𝔽16)—22no—
146C2×ΓL(1,𝔽16)—22no—
147C2×ΓL(1,𝔽16)—22no—
148C2×ΓL(1,𝔽16)—22no—
149C2×ΓL(1,𝔽16)—22no—
150C2×ΓL(1,𝔽16)—22no—
151C2×ΓL(1,𝔽16)—22no—
152C2×ΓL(1,𝔽16)—22no—
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—41no—
156C2×ΓL(1,𝔽16)—41no—
157C2×ΓL(1,𝔽16)—41no—
158C2×ΓL(1,𝔽16)—41no—
159C2×ΓL(1,𝔽16)—41no—
160C2×ΓL(1,𝔽16)—41no—
161C2×ΓL(1,𝔽16)—41no—
162C2×ΓL(1,𝔽16)—41no—
163C2×ΓL(1,𝔽16)C22⋊C414yes—
164C2×ΓL(1,𝔽16)C4⋊C414yescomplemented
165C2×C3×C4×C5—21no—
166C2×C3×C4×C5—21no—
167C2×C3×C4×C5—21no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5C4212yescomplemented
173C2×C3×C4×C5C4⋊C412yescomplemented
174C2×C3×Dic5—21no—
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177C2×C3×Dic5—21no—
178C2×C3×Dic5—21no—
179C2×C3×Dic5—21no—
180C2×C3×Dic5—21no—
181C2×C3×Dic5C4212yescomplemented
182C2×C3×Dic5C4⋊C412yescomplemented
183C3×C4×D5—22no—
184C3×C4×D5—22no—
185C3×C4×D5—22no—
186C3×C4×D5—22no—
187C3×C4×D5—22no—
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190C3×C4×D5—22no—
191C3×C4×D5—41no—
192C3×C4×D5—41no—
193C3×C4×D5—41no—
194C3×C4×D5—41no—
195C23×C3×C4—51no—
196C23×C3×C4—51no—
197C23×C3×C4—51no—
198C23×Dic3—51no—
199C23×Dic3—51no—
200C23×Dic3—51no—
201C23×Dic3—51no—
202C2×C4⋊Dic3—54no—
203C2×C4⋊Dic3—102no—
204C2×C4⋊Dic3—102no—
205C2×C4×Dic3—102no—
206C2×C4×Dic3—102no—
207C2×C4×Dic3—102no—
208C3×#95—51no—
209C3×#95—51no—
210C3×#95—51no—
211C3×#95AGL(1,𝔽5)11yescharacteristic, complemented
212C3⋊#95—54no—
213C3⋊#95—102no—
214C3⋊#95—102no—
215C3⋊#95—102no—
216C23×D5C22×D311yescharacteristic
217C22×AGL(1,𝔽5)—32no—
218C22×AGL(1,𝔽5)—32no—
219C22×AGL(1,𝔽5)—32no—
220C22×AGL(1,𝔽5)—32no—
221C22×AGL(1,𝔽5)—32no—
222C22×AGL(1,𝔽5)—32no—
223C22×AGL(1,𝔽5)—32no—
224C22×AGL(1,𝔽5)—32no—
225C22×AGL(1,𝔽5)—61no—
226C22×AGL(1,𝔽5)—61no—
227C22×AGL(1,𝔽5)—61no—
228C22×AGL(1,𝔽5)—61no—
229C22×AGL(1,𝔽5)—61no—
230C22×AGL(1,𝔽5)—61no—
231C22×AGL(1,𝔽5)—61no—
232C22×AGL(1,𝔽5)—61no—
233C22×AGL(1,𝔽5)—61no—
234C22×AGL(1,𝔽5)—61no—
235C22×AGL(1,𝔽5)—61no—
236C22×AGL(1,𝔽5)—61no—
237C22×AGL(1,𝔽5)—61no—
238C22×AGL(1,𝔽5)—61no—
239C22×AGL(1,𝔽5)—61no—
240C22×AGL(1,𝔽5)—61no—
241C22×AGL(1,𝔽5)—61no—
242C22×AGL(1,𝔽5)—61no—
243C22×AGL(1,𝔽5)—61no—
244C22×AGL(1,𝔽5)—61no—
245C22×C4×C5C2×Dic311yescharacteristic
246C22×C4×C5C2×Dic311yescharacteristic
247C22×C4×C5C2×Dic311yescharacteristic
248C22×Dic5C2×Dic311yescharacteristic
249C22×Dic5C2×Dic311yescharacteristic
250C22×Dic5C2×Dic311yescharacteristic
251C2×C4×D5—21no—
252C2×C4×D5—21no—
253C2×C4×D5—21no—
254C2×C4×D5—21no—
255C2×C4×D5—21no—
256C2×C4×D5—21no—
257C2×C4×D5—21no—
258C2×C4×D5—21no—
259C2×C4×D5—21no—
260C2×C4×D5—21no—
261C2×C4×D5—21no—
262C2×C4×D5—21no—
263C2×C4×D5—21no—
264C2×C4×D5—21no—
265C2×C4×D5Dic612yes—
266C2×C4×D5C4×D312yes—
267C2×C4×D5C4×D312yes—
268C2×C4×D5D1212yes—
269C4⋊AGL(1,𝔽5)—68no—
270C4×AGL(1,𝔽5)—68no—
271C22×C4⋊C4—151no—
272C22×C42—151no—
273C2×#95—51no—
274C2×#95—151no—
275C2×#95—151no—
276C2×#95—151no—
277C2×#95—151no—
278C22×C3×C5C2×C4211yescharacteristic
279C22×C3×C5C2×C4⋊C411yescharacteristic
280C22×C3×C5#11711yescharacteristic
281C22×C3×C5C4×D411yescharacteristic
282C22×C3×C5C4×D411yescharacteristic
283C22×C3×C5C4×D411yescharacteristic
284C22×C3×C5C4×Q811yescharacteristic
285C2×C3×D5C2×C22⋊C411yescharacteristic
286C2×C3×D5C2×C4⋊C411yescharacteristic
287C2×C3×D5#11711yescharacteristic
288C2×C3×D5#11711yescharacteristic
289C2×C3×D5C4×D411yescharacteristic
290C2×C3×D5C4×D411yescharacteristic
291C2×C3×D5C4×D411yescharacteristic
292C2×C3×D5C4×D411yescharacteristic
293C2×C3×D5C4×D411yescharacteristic
294C2×C3×D5C4×Q811yescharacteristic
295C2×C3×D5C4×Q811yescharacteristic
296C2×C3×D5C4×Q811yescharacteristic
297C2×C3×D5#12011yescharacteristic
298C2×C3×D5#12111yescharacteristic
299C2×C3×D5#12111yescharacteristic
300C2×C3×D5C22⋊Q811yescharacteristic
301C2×C3×D5C22⋊Q811yescharacteristic
302C2×C3×D5C22⋊Q811yescharacteristic
303C2×C3×D5C22⋊Q811yescharacteristic
304C2×C3×D5#12311yescharacteristic
305C2×C3×D5#12311yescharacteristic
306C2×C3×D5#12311yescharacteristic
307C2×C3×D5#12411yescharacteristic
308C2×C3×D5#12511yescharacteristic
309C2×C3×D5#12511yescharacteristic
310C2×C3×D5#12611yescharacteristic
311C2×C3×D5#12611yescharacteristic
312C2×C3×D5C4⋊Q811yescharacteristic
313ΓL(1,𝔽16)—24no—
314ΓL(1,𝔽16)—24no—
315ΓL(1,𝔽16)—42no—
316ΓL(1,𝔽16)—42no—
317C3×C4×C5—22no—
318C3×C4×C5—22no—
319C3×C4×C5—41no—
320C3×Dic5—22no—
321C3×Dic5—22no—
322C3×Dic5—41no—
323C24×C3—51no—
324C22×C3×C4—51no—
325C22×C3×C4—51no—
326C22×C3×C4—52no—
327C22×C3×C4—52no—
328C22×C3×C4—52no—
329C22×C3×C4—52no—
330C22×C3×C4—51no—
331C22×C3×C4—101no—
332C22×C3×C4—101no—
333C22×C3×C4—101no—
334C22×C3×C4—101no—
335C22×C3×C4—101no—
336C22×C3×C4—101no—
337C22×C3×C4—101no—
338C22×C3×C4—101no—
339C22×C3×C4—101no—
340C22×C3×C4—101no—
341C22×C3×C4—101no—
342C22×C3×C4—101no—
343C22×C3×C4—101no—
344C22×C3×C4—101no—
345C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
346C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
347C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
348C22×Dic3—52no—
349C22×Dic3—52no—
350C22×Dic3—52no—
351C22×Dic3—52no—
352C22×Dic3—52no—
353C22×Dic3—52no—
354C22×Dic3—52no—
355C22×Dic3—52no—
356C22×Dic3—101no—
357C22×Dic3—101no—
358C22×Dic3—101no—
359C22×Dic3—101no—
360C22×Dic3—101no—
361C22×Dic3—101no—
362C22×Dic3—101no—
363C22×Dic3—101no—
364C22×Dic3—101no—
365C22×Dic3—101no—
366C22×Dic3—101no—
367C22×Dic3—101no—
368C22×Dic3—101no—
369C22×Dic3—101no—
370C22×Dic3—101no—
371C22×Dic3—101no—
372C22×Dic3—101no—
373C22×Dic3—101no—
374C22×Dic3—101no—
375C22×Dic3—101no—
376C4⋊Dic3—108no—
377C4×Dic3—108no—
378C23×C5C22×Dic311yescharacteristic
379C22×D5C2×Dic611yescharacteristic
380C22×D5C2×C4×D311yescharacteristic
381C22×D5C2×C4×D311yescharacteristic
382C22×D5C2×D1211yescharacteristic
383C22×D5#23511yescharacteristic
384C22×D5#23511yescharacteristic
385C22×D5D3×D411yescharacteristic
386C22×D5D3×D411yescharacteristic
387C22×D5D3×D411yescharacteristic
388C22×D5#23711yescharacteristic
389C22×D5#23711yescharacteristic
390C22×D5#23711yescharacteristic
391C22×D5D3×Q811yescharacteristic
392C22×D5#23911yescharacteristic
393C2×AGL(1,𝔽5)—34no—
394C2×AGL(1,𝔽5)—34no—
395C2×AGL(1,𝔽5)—62no—
396C2×AGL(1,𝔽5)—62no—
397C2×AGL(1,𝔽5)—62no—
398C2×AGL(1,𝔽5)—62no—
399C2×AGL(1,𝔽5)—62no—
400C2×AGL(1,𝔽5)—62no—
401C2×AGL(1,𝔽5)—62no—
402C2×AGL(1,𝔽5)—62no—
403C2×AGL(1,𝔽5)—62no—
404C2×AGL(1,𝔽5)—62no—
405C2×AGL(1,𝔽5)—62no—
406C2×AGL(1,𝔽5)—62no—
407C2×AGL(1,𝔽5)—62no—
408C2×AGL(1,𝔽5)—62no—
409C2×AGL(1,𝔽5)—62no—
410C2×AGL(1,𝔽5)—62no—
411C2×AGL(1,𝔽5)—62no—
412C2×AGL(1,𝔽5)—62no—
413C2×AGL(1,𝔽5)—121no—
414C2×AGL(1,𝔽5)—121no—
415C2×AGL(1,𝔽5)—121no—
416C2×AGL(1,𝔽5)—121no—
417C2×AGL(1,𝔽5)—121no—
418C2×AGL(1,𝔽5)—121no—
419C2×AGL(1,𝔽5)—121no—
420C2×AGL(1,𝔽5)—121no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5C4×Dic312yescomplemented
429C2×C4×C5C4⋊Dic312yescomplemented
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5C4×Dic312yescomplemented
438C2×Dic5C4⋊Dic312yescomplemented
439C4×D5—22no—
440C4×D5—22no—
441C4×D5—22no—
442C4×D5—22no—
443C4×D5—22no—
444C4×D5—22no—
445C4×D5—22no—
446C4×D5—22no—
447C4×D5—41no—
448C4×D5—41no—
449C4×D5—41no—
450C4×D5—41no—
451C23×C4—51no—
452C23×C4—51no—
453C23×C4—51no—
454C23×C4—151no—
455C23×C4—151no—
456C23×C4—151no—
457C23×C4—151no—
458C2×C4⋊C4—154no—
459C2×C4⋊C4—302no—
460C2×C4⋊C4—302no—
461C2×C42—302no—
462C2×C42—302no—
463C2×C42—302no—
464#95—51no—
465#95—51no—
466#95—51no—
467#95—154no—
468#95—302no—
469#95—302no—
470#95—302no—
471#95ΓL(1,𝔽16)11yescharacteristic, complemented
472C2×C3×C5C4×C22⋊C411yescharacteristic
473C2×C3×C5C4×C4⋊C411yescharacteristic
474C2×C3×C5C4×C4⋊C411yescharacteristic
475C2×C3×C5#38511yescharacteristic
476C2×C3×C5#38711yescharacteristic
477C2×C3×C5#38811yescharacteristic
478C2×C3×C5#38911yescharacteristic
479C3×D5#38511yescharacteristic
480C3×D5#38611yescharacteristic
481C3×D5#38711yescharacteristic
482C3×D5#38711yescharacteristic
483C3×D5#38711yescharacteristic
484C3×D5#38811yescharacteristic
485C3×D5#38911yescharacteristic
486C3×D5#39111yescharacteristic
487C23×C3—51no—
488C23×C3—51no—
489C23×C3—51no—
490C23×C3—51no—
491C23×C3—51no—
492C23×C3—51no—
493C23×C3—51no—
494C23×C3—51no—
495C23×C3—51no—
496C23×C3—51no—
497C23×C3—51no—
498C23×C3—51no—
499C23×C3—51no—
500C23×C3—51no—
501C23×C3C22×AGL(1,𝔽5)11yescharacteristic
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—52no—
510C2×C3×C4—52no—
511C2×C3×C4—102no—
512C2×C3×C4—102no—
513C2×C3×C4—102no—
514C2×C3×C4—102no—
515C2×C3×C4—102no—
516C2×C3×C4—102no—
517C2×C3×C4—102no—
518C2×C3×C4—102no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—201no—
527C2×C3×C4—201no—
528C2×C3×C4—201no—
529C2×C3×C4—201no—
530C2×C3×C4C4×AGL(1,𝔽5)12yescomplemented
531C2×C3×C4C4⋊AGL(1,𝔽5)12yescomplemented
532C2×Dic3—54no—
533C2×Dic3—54no—
534C2×Dic3—102no—
535C2×Dic3—102no—
536C2×Dic3—102no—
537C2×Dic3—102no—
538C2×Dic3—102no—
539C2×Dic3—102no—
540C2×Dic3—102no—
541C2×Dic3—102no—
542C2×Dic3—102no—
543C2×Dic3—102no—
544C2×Dic3—102no—
545C2×Dic3—102no—
546C2×Dic3—102no—
547C2×Dic3—102no—
548C2×Dic3—102no—
549C2×Dic3—102no—
550C2×Dic3—102no—
551C2×Dic3—102no—
552C2×Dic3—201no—
553C2×Dic3—201no—
554C2×Dic3—201no—
555C2×Dic3—201no—
556C2×Dic3—201no—
557C2×Dic3—201no—
558C2×Dic3—201no—
559C2×Dic3—201no—
560C22×C5C2×C4×Dic311yescharacteristic
561C22×C5C2×C4⋊Dic311yescharacteristic
562C22×C5#92611yescharacteristic
563C22×C5D4×Dic311yescharacteristic
564C22×C5D4×Dic311yescharacteristic
565C22×C5D4×Dic311yescharacteristic
566C22×C5Q8×Dic311yescharacteristic
567C2×D5C4×Dic611yescharacteristic
568C2×D5C4×Dic611yescharacteristic
569C2×D5C4×D1211yescharacteristic
570C2×D5C4×D1211yescharacteristic
571C2×D5#87711yescharacteristic
572C2×D5#87811yescharacteristic
573C2×D5#87811yescharacteristic
574C2×D5#87911yescharacteristic
575C2×D5D3×C22⋊C411yescharacteristic
576C2×D5#67⋊C411yescharacteristic
577C2×D5#67⋊C411yescharacteristic
578C2×D5#88211yescharacteristic
579C2×D5#88311yescharacteristic
580C2×D5#88411yescharacteristic
581C2×D5#88511yescharacteristic
582C2×D5#88611yescharacteristic
583C2×D5#88711yescharacteristic
584C2×D5#88811yescharacteristic
585C2×D5#88911yescharacteristic
586C2×D5#89011yescharacteristic
587C2×D5D3×C4⋊C411yescharacteristic
588C2×D5#89211yescharacteristic
589C2×D5#89311yescharacteristic
590C2×D5#89411yescharacteristic
591C2×D5#89511yescharacteristic
592C2×D5#89611yescharacteristic
593C2×D5#89711yescharacteristic
594C2×D5#89811yescharacteristic
595AGL(1,𝔽5)—64no—
596AGL(1,𝔽5)—64no—
597AGL(1,𝔽5)—122no—
598AGL(1,𝔽5)—122no—
599C4×C5—22no—
600C4×C5—22no—
601C4×C5—41no—
602Dic5—22no—
603Dic5—22no—
604Dic5—41no—
605C24—51no—
606C22×C4—51no—
607C22×C4—51no—
608C22×C4—52no—
609C22×C4—52no—
610C22×C4—52no—
611C22×C4—52no—
612C22×C4—51no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—152no—
628C22×C4—152no—
629C22×C4—152no—
630C22×C4—152no—
631C22×C4—152no—
632C22×C4—152no—
633C22×C4—152no—
634C22×C4—152no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4—301no—
638C22×C4—301no—
639C22×C4—301no—
640C22×C4—301no—
641C22×C4—301no—
642C22×C4—301no—
643C22×C4—301no—
644C22×C4—301no—
645C22×C4—301no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4—301no—
650C22×C4—301no—
651C22×C4—301no—
652C22×C4—301no—
653C22×C4—301no—
654C22×C4—301no—
655C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
656C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
657C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
658C4⋊C4—308no—
659C42—308no—
660C3×C5#143611yescharacteristic, complemented, Hall
661C22×C3—51no—
662C22×C3—51no—
663C22×C3—51no—
664C22×C3—51no—
665C22×C3—51no—
666C22×C3—51no—
667C22×C3—51no—
668C22×C3—51no—
669C22×C3—51no—
670C22×C3—51no—
671C22×C3—51no—
672C22×C3—51no—
673C22×C3—51no—
674C22×C3—51no—
675C22×C3—51no—
676C22×C3—51no—
677C22×C3—51no—
678C22×C3—51no—
679C22×C3—51no—
680C22×C3—51no—
681C22×C3—51no—
682C22×C3—51no—
683C22×C3—51no—
684C22×C3—51no—
685C22×C3—51no—
686C22×C3—51no—
687C22×C3—51no—
688C22×C3—51no—
689C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
690C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
691C22×C3#413011yescharacteristic
692C22×C3D4×AGL(1,𝔽5)11yescharacteristic
693C22×C3D4×AGL(1,𝔽5)11yescharacteristic
694C22×C3D4×AGL(1,𝔽5)11yescharacteristic
695C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—41no—
699C3×C4—102no—
700C3×C4—102no—
701C3×C4—201no—
702Dic3—104no—
703Dic3—104no—
704Dic3—202no—
705Dic3—202no—
706C2×C5C4×C4⋊Dic311yescharacteristic
707C2×C5Dic3×C22⋊C411yescharacteristic
708C2×C5#495011yescharacteristic
709C2×C5#495111yescharacteristic
710C2×C5Dic3×C4⋊C411yescharacteristic
711C2×C5#498011yescharacteristic
712C2×C5#498411yescharacteristic
713D5#464611yescharacteristic
714D5#464711yescharacteristic
715D5#465311yescharacteristic
716D5#465411yescharacteristic
717D5#465511yescharacteristic
718D5#466511yescharacteristic
719D5#466811yescharacteristic
720D5#467011yescharacteristic
721C23—51no—
722C23—51no—
723C23—51no—
724C23—51no—
725C23—51no—
726C23—51no—
727C23—51no—
728C23—51no—
729C23—51no—
730C23—51no—
731C23—51no—
732C23—51no—
733C23—51no—
734C23—51no—
735C23C22×ΓL(1,𝔽16)11yescharacteristic
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—52no—
744C2×C4—52no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—154no—
761C2×C4—154no—
762C2×C4—201no—
763C2×C4—201no—
764C2×C4—201no—
765C2×C4—201no—
766C2×C4—302no—
767C2×C4—302no—
768C2×C4—302no—
769C2×C4—302no—
770C2×C4—302no—
771C2×C4—302no—
772C2×C4—302no—
773C2×C4—302no—
774C2×C4—302no—
775C2×C4—302no—
776C2×C4—302no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—302no—
784C2×C4—601no—
785C2×C4—601no—
786C2×C4—601no—
787C2×C4—601no—
788C2×C4—601no—
789C2×C4—601no—
790C2×C4—601no—
791C2×C4—601no—
792C2×C4C4×ΓL(1,𝔽16)12yescomplemented
793C2×C4C4⋊ΓL(1,𝔽16)12yescomplemented
794C2×C3—51no—
795C2×C3—51no—
796C2×C3—51no—
797C2×C3—51no—
798C2×C3—51no—
799C2×C3—51no—
800C2×C3—51no—
801C2×C3—51no—
802C2×C3C4×C4⋊AGL(1,𝔽5)11yescharacteristic
803C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
804C2×C3#6569911yescharacteristic
805C2×C3#6570011yescharacteristic
806C2×C3C4⋊C4×AGL(1,𝔽5)11yescharacteristic
807C2×C3#6571111yescharacteristic
808C2×C3#6571211yescharacteristic
809C5#6940711yescharacteristic, complemented, Sylow
810C22—51no—
811C22—51no—
812C22—51no—
813C22—51no—
814C22—51no—
815C22—51no—
816C22—51no—
817C22—51no—
818C22—51no—
819C22—51no—
820C22—51no—
821C22—51no—
822C22—51no—
823C22—51no—
824C22—51no—
825C22—51no—
826C22—51no—
827C22—51no—
828C22—51no—
829C22—51no—
830C22—51no—
831C22—51no—
832C22—51no—
833C22—51no—
834C22—51no—
835C22—51no—
836C22—51no—
837C22—51no—
838C22C2×C4×ΓL(1,𝔽16)11yescharacteristic
839C22C2×C4⋊ΓL(1,𝔽16)11yescharacteristic
840C22#9198911yescharacteristic
841C22D4×ΓL(1,𝔽16)11yescharacteristic
842C22D4×ΓL(1,𝔽16)11yescharacteristic
843C22D4×ΓL(1,𝔽16)11yescharacteristic
844C22Q8×ΓL(1,𝔽16)11yescharacteristic
845C4—22no—
846C4—22no—
847C4—41no—
848C4—102no—
849C4—102no—
850C4—201no—
851C4—304no—
852C4—304no—
853C4—602no—
854C4—602no—
855C3#1060380111yescharacteristic, complemented, Sylow
856C2—51no—
857C2—51no—
858C2—51no—
859C2—51no—
860C2—51no—
861C2—51no—
862C2—51no—
863C2—51no—
864C2C4×C4⋊ΓL(1,𝔽16)11yescharacteristic
865C2C22⋊C4×ΓL(1,𝔽16)11yescharacteristic
866C2#1175235811yescharacteristic
867C2#1175235911yescharacteristic
868C2C4⋊C4×ΓL(1,𝔽16)11yescharacteristic
869C2#1175237011yescharacteristic
870C2#1175237111yescharacteristic
subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C2×C42
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radical, cosocleC23×C3×D5C23
hypercenter#95ΓL(1,𝔽16)
hypocenterC3×C5#1436
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
18. C2×C4⋊ΓL(1,𝔽16)C4semidirect
25. #91235C4semidirect
26. C3×C5×#95C4semidirect
27. C3×#3963C4semidirect
28. C3×#3963C4semidirect
29. C3×#3963C4semidirect
117. C5×#95Dic3semidirect
118. #3963Dic3semidirect
119. #3963Dic3semidirect
120. #3963Dic3semidirect
164. C2×ΓL(1,𝔽16)C4⋊C4semidirect
172. C2×C3×C4×C5C42semidirect
173. C2×C3×C4×C5C4⋊C4semidirect
181. C2×C3×Dic5C42semidirect
182. C2×C3×Dic5C4⋊C4semidirect
211. C3×#95AGL(1,𝔽5)semidirect
428. C2×C4×C5C4×Dic3semidirect
429. C2×C4×C5C4⋊Dic3semidirect
437. C2×Dic5C4×Dic3semidirect
438. C2×Dic5C4⋊Dic3semidirect
471. #95ΓL(1,𝔽16)semidirect
530. C2×C3×C4C4×AGL(1,𝔽5)semidirect
531. C2×C3×C4C4⋊AGL(1,𝔽5)semidirect
660. C3×C5#1436semidirect
792. C2×C4C4×ΓL(1,𝔽16)semidirect
793. C2×C4C4⋊ΓL(1,𝔽16)semidirect
809. C5#69407semidirect
855. C3#10603801semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊ΓL(1,𝔽16)2
C22×C4×ΓL(1,𝔽16)2
C2×#912352
C3×D5×#952
#106038013
#694075