Finite Group Databasebeta

← C2×#11752359 #14320457

Subgroups — C2×#11752359 #14320457

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6763C211yesmaximal, characteristic
2C22×#6763C211yesmaximal, characteristic
3C22×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C22×C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
6C2×#91235C211yesmaximal, characteristic, complemented
7C2×#91235C211yesmaximal, characteristic, complemented
8#11752359C218yesmaximal, direct product factor
9C2×#65700—31nomaximal, Hall
10C24×C3×D5C2211yescharacteristic
11C23×ΓL(1,𝔽16)C2211yescharacteristic
12C23×ΓL(1,𝔽16)C2211yescharacteristic
13C23×ΓL(1,𝔽16)C2211yescharacteristic
14C23×ΓL(1,𝔽16)C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×#6763—24no—
18C2×#6763—24no—
19C2×#6763C2214yes—
20C2×#6763C2214yes—
21C2×C4⋊ΓL(1,𝔽16)—24no—
22C2×C4⋊ΓL(1,𝔽16)C2214yescomplemented
23C2×C4×ΓL(1,𝔽16)—24no—
24C2×C4×ΓL(1,𝔽16)C2214yescomplemented
25C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
26C2×C3×C22⋊Dic5C411yescharacteristic, complemented
27C2×C3×#685C411yescharacteristic, complemented
28C2×C3×#685C411yescharacteristic, complemented
29C3×D5×C22⋊C4C414yescomplemented
30C3×D5×C22⋊C4C2214yes—
31#91235C2214yescomplemented
32#91235C2214yescomplemented
33C2×#4951—51nomaximal, Hall
34C22×C22⋊AGL(1,𝔽5)—31no—
35C22×C22⋊AGL(1,𝔽5)—31no—
36C22×C4⋊AGL(1,𝔽5)—31no—
37C22×C4×AGL(1,𝔽5)—31no—
38C2×D5×C22⋊C4D311yescharacteristic
39C2×(C2×AGL(1,𝔽5))⋊C4—31no—
40C2×(C2×AGL(1,𝔽5))⋊C4—31no—
41#65700—38no—
42C24×C3×C5C2×C411yescharacteristic
43C23×C3×D5—22no—
44C23×C3×D5—22no—
45C23×C3×D5—22no—
46C23×C3×D5—22no—
47C23×C3×D5—22no—
48C23×C3×D5—22no—
49C23×C3×D5C2×C412yes—
50C23×C3×D5C2×C411yescharacteristic
51C23×C3×D5C2312yes—
52C23×C3×D5C2311yescharacteristic
53C22×ΓL(1,𝔽16)—22no—
54C22×ΓL(1,𝔽16)—22no—
55C22×ΓL(1,𝔽16)—22no—
56C22×ΓL(1,𝔽16)—22no—
57C22×ΓL(1,𝔽16)—22no—
58C22×ΓL(1,𝔽16)—22no—
59C22×ΓL(1,𝔽16)—22no—
60C22×ΓL(1,𝔽16)—22no—
61C22×ΓL(1,𝔽16)—22no—
62C22×ΓL(1,𝔽16)—22no—
63C22×ΓL(1,𝔽16)D414yes—
64C22×ΓL(1,𝔽16)D414yes—
65C22×ΓL(1,𝔽16)C2312yes—
66C22×ΓL(1,𝔽16)C2312yes—
67C22×ΓL(1,𝔽16)C2312yes—
68C22×ΓL(1,𝔽16)C2312yes—
69C22×C3×C4×C5C2×C411yescharacteristic
70C22×C3×C4×C5C2×C411yescharacteristic
71C22×C3×Dic5C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—22no—
77C2×C3×C4×D5C2×C412yes—
78C2×C3×C4×D5C2×C412yes—
79C2×C3×C4×D5C2312yes—
80C2×C3×C4×D5C2312yes—
81#6763—28no—
82#6763—28no—
83C4⋊ΓL(1,𝔽16)—28no—
84C4×ΓL(1,𝔽16)—28no—
85C3×C5×C22⋊C4C2×C414yescomplemented
86C3×C22⋊Dic5C2×C414yescomplemented
87C3×#685C2×C414yescomplemented
88C3×#685C2×C414yescomplemented
89C22×C3×C22⋊C4—51no—
90C22×#217—51no—
91C22×#217—51no—
92C22×C4⋊Dic3—51no—
93C22×C4×Dic3—51no—
94C2×C3⋊#95—51no—
95C2×C3⋊#95—51no—
96#4951—58no—
97C24×D5C2×D311yescharacteristic
98C23×AGL(1,𝔽5)—31no—
99C23×AGL(1,𝔽5)—31no—
100C23×AGL(1,𝔽5)—31no—
101C23×AGL(1,𝔽5)—31no—
102C22×C4×D5C2×D311yescharacteristic
103C22×C4×D5C2×D311yescharacteristic
104C2×C22⋊AGL(1,𝔽5)—34no—
105C2×C22⋊AGL(1,𝔽5)—34no—
106C2×C22⋊AGL(1,𝔽5)—64no—
107C2×C22⋊AGL(1,𝔽5)—64no—
108C2×C4⋊AGL(1,𝔽5)—34no—
109C2×C4⋊AGL(1,𝔽5)—64no—
110C2×C4×AGL(1,𝔽5)—34no—
111C2×C4×AGL(1,𝔽5)—64no—
112C2×C5×C22⋊C4Dic311yescharacteristic, complemented
113C2×C22⋊Dic5Dic311yescharacteristic, complemented
114C2×#685Dic311yescharacteristic, complemented
115C2×#685Dic311yescharacteristic, complemented
116D5×C22⋊C4Dic314yescomplemented
117D5×C22⋊C4C2×D314yes—
118(C2×AGL(1,𝔽5))⋊C4—34no—
119(C2×AGL(1,𝔽5))⋊C4—34no—
120C2×#388—151noSylow
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C22×C411yescharacteristic
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5—22no—
129C22×C3×D5—24no—
130C22×C3×D5—24no—
131C22×C3×D5—24no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5—22no—
136C22×C3×D5—22no—
137C22×C3×D5—22no—
138C22×C3×D5—44no—
139C22×C3×D5—44no—
140C22×C3×D5—44no—
141C22×C3×D5—44no—
142C22×C3×D5C22×C412yes—
143C22×C3×D5C22×C411yescharacteristic
144C22×C3×D5C2×D412yes—
145C22×C3×D5C2×D412yes—
146C22×C3×D5#4112yes—
147C22×C3×D5#4112yes—
148C22×C3×D5#4112yes—
149C22×C3×D5#4112yes—
150C22×C3×D5C2411yescharacteristic
151C2×ΓL(1,𝔽16)—28no—
152C2×ΓL(1,𝔽16)—28no—
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—22no—
157C2×ΓL(1,𝔽16)—22no—
158C2×ΓL(1,𝔽16)—22no—
159C2×ΓL(1,𝔽16)—22no—
160C2×ΓL(1,𝔽16)—22no—
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)—44no—
164C2×ΓL(1,𝔽16)—44no—
165C2×ΓL(1,𝔽16)C2×D414yes—
166C2×ΓL(1,𝔽16)C2×D414yes—
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5—22no—
169C2×C3×C4×C5C22×C412yes—
170C2×C3×C4×C5C22×C412yes—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5C22×C412yes—
174C2×C3×Dic5C22×C412yes—
175C3×C4×D5—24no—
176C3×C4×D5—24no—
177C3×C4×D5—22no—
178C3×C4×D5—22no—
179C3×C4×D5—22no—
180C3×C4×D5—22no—
181C25×C3—51no—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×Dic3—51no—
185C23×Dic3—51no—
186C23×Dic3—51no—
187C23×Dic3—51no—
188C2×C3×C22⋊C4—51no—
189C2×C3×C22⋊C4—51no—
190C2×C3×C22⋊C4—51no—
191C2×C3×C22⋊C4—54no—
192C2×C3×C22⋊C4—54no—
193C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
194C2×#217—54no—
195C2×#217—54no—
196C2×#217—104no—
197C2×#217—104no—
198C2×C4⋊Dic3—54no—
199C2×C4⋊Dic3—104no—
200C2×C4×Dic3—54no—
201C2×C4×Dic3—104no—
202C3⋊#95—54no—
203C3⋊#95—54no—
204C24×C5C2×Dic311yescharacteristic
205C23×D5—22no—
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—22no—
209C23×D5—22no—
210C23×D5—22no—
211C23×D5C2×Dic312yes—
212C23×D5C2×Dic311yescharacteristic
213C23×D5C22×D312yes—
214C23×D5C22×D311yescharacteristic
215C22×AGL(1,𝔽5)—34no—
216C22×AGL(1,𝔽5)—34no—
217C22×AGL(1,𝔽5)—32no—
218C22×AGL(1,𝔽5)—32no—
219C22×AGL(1,𝔽5)—32no—
220C22×AGL(1,𝔽5)—32no—
221C22×AGL(1,𝔽5)—62no—
222C22×AGL(1,𝔽5)—62no—
223C22×AGL(1,𝔽5)—62no—
224C22×AGL(1,𝔽5)—62no—
225C22×AGL(1,𝔽5)—62no—
226C22×AGL(1,𝔽5)—62no—
227C22×AGL(1,𝔽5)—62no—
228C22×AGL(1,𝔽5)—62no—
229C22×AGL(1,𝔽5)—62no—
230C22×AGL(1,𝔽5)—62no—
231C22×C4×C5C2×Dic311yescharacteristic
232C22×C4×C5C2×Dic311yescharacteristic
233C22×Dic5C2×Dic311yescharacteristic
234C22×Dic5C2×Dic311yescharacteristic
235C2×C4×D5—22no—
236C2×C4×D5—22no—
237C2×C4×D5—22no—
238C2×C4×D5—22no—
239C2×C4×D5C2×Dic312yes—
240C2×C4×D5C2×Dic312yes—
241C2×C4×D5C22×D312yes—
242C2×C4×D5C22×D312yes—
243C22⋊AGL(1,𝔽5)—68no—
244C22⋊AGL(1,𝔽5)—68no—
245C4⋊AGL(1,𝔽5)—68no—
246C4×AGL(1,𝔽5)—68no—
247C5×C22⋊C4C2×Dic314yescomplemented
248C22⋊Dic5C2×Dic314yescomplemented
249#685C2×Dic314yescomplemented
250#685C2×Dic314yescomplemented
251C22×C4⋊C4—151no—
252C22×C22⋊C4—51no—
253C22×C22⋊C4—151no—
254C22×C22⋊C4—151no—
255C22×C42—151no—
256#388—158no—
257C2×#95—151no—
258C2×#95—151no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—22no—
262C22×C3×C5—44no—
263C22×C3×C5#11712yes—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C4×D412yes—
266C22×C3×C5C23×C411yescharacteristic
267C2×C3×D5—22no—
268C2×C3×D5—22no—
269C2×C3×D5—22no—
270C2×C3×D5—44no—
271C2×C3×D5—42no—
272C2×C3×D5—42no—
273C2×C3×D5—42no—
274C2×C3×D5—42no—
275C2×C3×D5—48no—
276C2×C3×D5#11712yes—
277C2×C3×D5C4×D412yes—
278C2×C3×D5C4×D412yes—
279C2×C3×D5#12114yes—
280C2×C3×D5#12314yes—
281C2×C3×D5#12414yes—
282C2×C3×D5#12614yes—
283C2×C3×D5C22×D411yescharacteristic
284C2×C3×D5C22×D411yescharacteristic
285C2×C3×D5C2×#4111yescharacteristic
286C2×C3×D5C2×#4111yescharacteristic
287C2×C3×D5C2×#4111yescharacteristic
288C2×C3×D5C2×#4111yescharacteristic
289ΓL(1,𝔽16)—24no—
290ΓL(1,𝔽16)—24no—
291ΓL(1,𝔽16)—42no—
292ΓL(1,𝔽16)—42no—
293C3×C4×C5—22no—
294C3×C4×C5—22no—
295C3×Dic5—22no—
296C3×Dic5—22no—
297C24×C3—51no—
298C24×C3—52no—
299C24×C3—52no—
300C24×C3—51no—
301C24×C3—102no—
302C24×C3—102no—
303C24×C3—102no—
304C24×C3—102no—
305C24×C3—102no—
306C24×C3—102no—
307C24×C3C2×AGL(1,𝔽5)11yescharacteristic
308C22×C3×C4—51no—
309C22×C3×C4—51no—
310C22×C3×C4—52no—
311C22×C3×C4—52no—
312C22×C3×C4—52no—
313C22×C3×C4—52no—
314C22×C3×C4—102no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
319C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
320C22×Dic3—52no—
321C22×Dic3—52no—
322C22×Dic3—54no—
323C22×Dic3—54no—
324C22×Dic3—52no—
325C22×Dic3—52no—
326C22×Dic3—102no—
327C22×Dic3—102no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3—102no—
331C22×Dic3—102no—
332C22×Dic3—102no—
333C22×Dic3—102no—
334C22×Dic3—102no—
335C22×Dic3—102no—
336C3×C22⋊C4—54no—
337C3×C22⋊C4—54no—
338C3×C22⋊C4—54no—
339C3×C22⋊C4C2×AGL(1,𝔽5)14yescomplemented
340#217—108no—
341#217—108no—
342C4⋊Dic3—108no—
343C4×Dic3—108no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5C22×Dic312yes—
348C23×C5C22×Dic311yescharacteristic
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—24no—
353C22×D5—24no—
354C22×D5—24no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—44no—
362C22×D5—44no—
363C22×D5—44no—
364C22×D5—44no—
365C22×D5#23512yes—
366C22×D5#23512yes—
367C22×D5D3×D412yes—
368C22×D5D3×D412yes—
369C22×D5#23712yes—
370C22×D5#23712yes—
371C22×D5C22×Dic312yes—
372C22×D5C22×Dic311yescharacteristic
373C22×D5C23×D311yescharacteristic
374C2×AGL(1,𝔽5)—34no—
375C2×AGL(1,𝔽5)—34no—
376C2×AGL(1,𝔽5)—68no—
377C2×AGL(1,𝔽5)—68no—
378C2×AGL(1,𝔽5)—62no—
379C2×AGL(1,𝔽5)—62no—
380C2×AGL(1,𝔽5)—62no—
381C2×AGL(1,𝔽5)—62no—
382C2×AGL(1,𝔽5)—62no—
383C2×AGL(1,𝔽5)—62no—
384C2×AGL(1,𝔽5)—62no—
385C2×AGL(1,𝔽5)—62no—
386C2×AGL(1,𝔽5)—62no—
387C2×AGL(1,𝔽5)—62no—
388C2×AGL(1,𝔽5)—124no—
389C2×AGL(1,𝔽5)—124no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5C22×Dic312yes—
393C2×C4×C5C22×Dic312yes—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5C22×Dic312yes—
397C2×Dic5C22×Dic312yes—
398C4×D5—24no—
399C4×D5—24no—
400C4×D5—22no—
401C4×D5—22no—
402C4×D5—22no—
403C4×D5—22no—
404C25—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—151no—
408C23×C4—151no—
409C23×C4—151no—
410C23×C4—151no—
411C2×C4⋊C4—154no—
412C2×C4⋊C4—304no—
413C2×C22⋊C4—51no—
414C2×C22⋊C4—51no—
415C2×C22⋊C4—51no—
416C2×C22⋊C4—54no—
417C2×C22⋊C4—54no—
418C2×C22⋊C4—154no—
419C2×C22⋊C4—154no—
420C2×C22⋊C4—304no—
421C2×C22⋊C4—304no—
422C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic, complemented
423C2×C42—154no—
424C2×C42—304no—
425#95—154no—
426#95—154no—
427C2×C3×C5—42no—
428C2×C3×C5#38814yescomplemented
429C2×C3×C5C2×#11711yescharacteristic
430C2×C3×C5C2×C4×D411yescharacteristic
431C2×C3×C5C2×C4×D411yescharacteristic
432C3×D5—42no—
433C3×D5#38814yescomplemented
434C3×D5C2×#12111yescharacteristic
435C3×D5C2×#12311yescharacteristic
436C3×D5C2×#12411yescharacteristic
437C3×D5C2×#12611yescharacteristic
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—52no—
442C23×C3—52no—
443C23×C3—52no—
444C23×C3—52no—
445C23×C3—52no—
446C23×C3—52no—
447C23×C3—51no—
448C23×C3—51no—
449C23×C3—52no—
450C23×C3—102no—
451C23×C3—102no—
452C23×C3—104no—
453C23×C3—102no—
454C23×C3—102no—
455C23×C3—104no—
456C23×C3—104no—
457C23×C3—102no—
458C23×C3—102no—
459C23×C3—102no—
460C23×C3—102no—
461C23×C3—102no—
462C23×C3—204no—
463C23×C3—204no—
464C23×C3—204no—
465C23×C3—204no—
466C23×C3C22×AGL(1,𝔽5)12yes—
467C23×C3C22×AGL(1,𝔽5)11yescharacteristic
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—52no—
471C2×C3×C4—52no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—104no—
475C2×C3×C4—104no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—102no—
480C2×C3×C4C22×AGL(1,𝔽5)12yes—
481C2×C3×C4C22×AGL(1,𝔽5)12yes—
482C2×Dic3—54no—
483C2×Dic3—54no—
484C2×Dic3—102no—
485C2×Dic3—108no—
486C2×Dic3—108no—
487C2×Dic3—102no—
488C2×Dic3—102no—
489C2×Dic3—102no—
490C2×Dic3—102no—
491C2×Dic3—102no—
492C2×Dic3—102no—
493C2×Dic3—102no—
494C2×Dic3—102no—
495C2×Dic3—102no—
496C2×Dic3—204no—
497C2×Dic3—204no—
498C22×C5—22no—
499C22×C5—22no—
500C22×C5—22no—
501C22×C5—44no—
502C22×C5#92612yes—
503C22×C5D4×Dic312yes—
504C22×C5D4×Dic312yes—
505C22×C5C23×Dic311yescharacteristic
506C2×D5—22no—
507C2×D5—22no—
508C2×D5—22no—
509C2×D5—44no—
510C2×D5—48no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—42no—
515C2×D5#87914yes—
516C2×D5#88314yes—
517C2×D5#88414yes—
518C2×D5#88514yes—
519C2×D5#92612yes—
520C2×D5D4×Dic312yes—
521C2×D5D4×Dic312yes—
522C2×D5C2×#23511yescharacteristic
523C2×D5C2×#23511yescharacteristic
524C2×D5C2×D3×D411yescharacteristic
525C2×D5C2×D3×D411yescharacteristic
526C2×D5C2×#23711yescharacteristic
527C2×D5C2×#23711yescharacteristic
528AGL(1,𝔽5)—64no—
529AGL(1,𝔽5)—64no—
530AGL(1,𝔽5)—122no—
531AGL(1,𝔽5)—122no—
532C4×C5—22no—
533C4×C5—22no—
534Dic5—22no—
535Dic5—22no—
536C24—51no—
537C24—52no—
538C24—52no—
539C24—51no—
540C24—102no—
541C24—102no—
542C24—102no—
543C24—102no—
544C24—102no—
545C24—102no—
546C24C2×ΓL(1,𝔽16)11yescharacteristic
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—152no—
558C22×C4—152no—
559C22×C4—154no—
560C22×C4—154no—
561C22×C4—152no—
562C22×C4—152no—
563C22×C4—302no—
564C22×C4—302no—
565C22×C4—302no—
566C22×C4—302no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—302no—
571C22×C4—302no—
572C22×C4—302no—
573C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
574C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
575C4⋊C4—308no—
576C22⋊C4—54no—
577C22⋊C4—54no—
578C22⋊C4—54no—
579C22⋊C4—308no—
580C22⋊C4—308no—
581C22⋊C4C2×ΓL(1,𝔽16)14yescomplemented
582C42—308no—
583C3×C5C2×#38811yescharacteristic, complemented, Hall
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—44no—
588C22×C3—54no—
589C22×C3—54no—
590C22×C3—54no—
591C22×C3—54no—
592C22×C3—52no—
593C22×C3—51no—
594C22×C3—51no—
595C22×C3—52no—
596C22×C3—52no—
597C22×C3—51no—
598C22×C3—51no—
599C22×C3—51no—
600C22×C3—51no—
601C22×C3—102no—
602C22×C3—102no—
603C22×C3—102no—
604C22×C3—202no—
605C22×C3—202no—
606C22×C3—202no—
607C22×C3—202no—
608C22×C3—208no—
609C22×C3—204no—
610C22×C3#413012yes—
611C22×C3D4×AGL(1,𝔽5)12yes—
612C22×C3D4×AGL(1,𝔽5)12yes—
613C22×C3C23×AGL(1,𝔽5)11yescharacteristic
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—102no—
617C3×C4—102no—
618Dic3—104no—
619Dic3—104no—
620Dic3—202no—
621Dic3—202no—
622C2×C5—42no—
623C2×C5#495114yescomplemented
624C2×C5C2×#92611yescharacteristic
625C2×C5C2×D4×Dic311yescharacteristic
626C2×C5C2×D4×Dic311yescharacteristic
627D5—42no—
628D5#495114yescomplemented
629D5C2×#87911yescharacteristic
630D5C2×#88311yescharacteristic
631D5C2×#88411yescharacteristic
632D5C2×#88511yescharacteristic
633C23—22no—
634C23—22no—
635C23—22no—
636C23—52no—
637C23—52no—
638C23—52no—
639C23—52no—
640C23—52no—
641C23—52no—
642C23—51no—
643C23—51no—
644C23—52no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—104no—
650C23—102no—
651C23—102no—
652C23—104no—
653C23—104no—
654C23—102no—
655C23—102no—
656C23—102no—
657C23—204no—
658C23—204no—
659C23—204no—
660C23—204no—
661C23C22×ΓL(1,𝔽16)12yes—
662C23C22×ΓL(1,𝔽16)11yescharacteristic
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—52no—
666C2×C4—52no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—104no—
672C2×C4—104no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—154no—
676C2×C4—154no—
677C2×C4—302no—
678C2×C4—308no—
679C2×C4—308no—
680C2×C4—302no—
681C2×C4—302no—
682C2×C4—302no—
683C2×C4—302no—
684C2×C4—302no—
685C2×C4—302no—
686C2×C4—302no—
687C2×C4—302no—
688C2×C4—302no—
689C2×C4—604no—
690C2×C4—604no—
691C2×C4C22×ΓL(1,𝔽16)12yes—
692C2×C4C22×ΓL(1,𝔽16)12yes—
693C2×C3—42no—
694C2×C3—51no—
695C2×C3—51no—
696C2×C3—51no—
697C2×C3—51no—
698C2×C3—54no—
699C2×C3—202no—
700C2×C3#6570014yescomplemented
701C2×C3C2×#413011yescharacteristic
702C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
703C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
704C5C2×#495111yescharacteristic, complemented, Sylow
705C22—22no—
706C22—22no—
707C22—22no—
708C22—44no—
709C22—54no—
710C22—54no—
711C22—54no—
712C22—54no—
713C22—51no—
714C22—51no—
715C22—52no—
716C22—51no—
717C22—51no—
718C22—51no—
719C22—51no—
720C22—52no—
721C22—52no—
722C22—102no—
723C22—102no—
724C22—102no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—208no—
729C22—202no—
730C22—204no—
731C22#9198912yes—
732C22D4×ΓL(1,𝔽16)12yes—
733C22D4×ΓL(1,𝔽16)12yes—
734C22C23×ΓL(1,𝔽16)11yescharacteristic
735C4—22no—
736C4—22no—
737C4—102no—
738C4—102no—
739C4—304no—
740C4—304no—
741C4—602no—
742C4—602no—
743C3C2×#6570011yescharacteristic, complemented, Sylow
744C2—42no—
745C2—51no—
746C2—51no—
747C2—51no—
748C2—54no—
749C2—51no—
750C2—202no—
751C2#1175235914yesdirect product factor
752C2C2×#9198911yescharacteristic
753C2C2×D4×ΓL(1,𝔽16)11yescharacteristic
754C2C2×D4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC22×C3×D5C24
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5C2×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊ΓL(1,𝔽16)C2semidirect
4. C22×C4×ΓL(1,𝔽16)C2semidirect
6. C2×#91235C2semidirect
7. C2×#91235C2semidirect
8. #11752359C2direct (N × H)
22. C2×C4⋊ΓL(1,𝔽16)C22semidirect
24. C2×C4×ΓL(1,𝔽16)C22semidirect
25. C2×C3×C5×C22⋊C4C4semidirect
26. C2×C3×C22⋊Dic5C4semidirect
27. C2×C3×#685C4semidirect
28. C2×C3×#685C4semidirect
29. C3×D5×C22⋊C4C4semidirect
31. #91235C22semidirect
32. #91235C22semidirect
85. C3×C5×C22⋊C4C2×C4semidirect
86. C3×C22⋊Dic5C2×C4semidirect
87. C3×#685C2×C4semidirect
88. C3×#685C2×C4semidirect
112. C2×C5×C22⋊C4Dic3semidirect
113. C2×C22⋊Dic5Dic3semidirect
114. C2×#685Dic3semidirect
115. C2×#685Dic3semidirect
116. D5×C22⋊C4Dic3semidirect
193. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
247. C5×C22⋊C4C2×Dic3semidirect
248. C22⋊Dic5C2×Dic3semidirect
249. #685C2×Dic3semidirect
250. #685C2×Dic3semidirect
339. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
422. C2×C22⋊C4ΓL(1,𝔽16)semidirect
428. C2×C3×C5#388semidirect
433. C3×D5#388semidirect
581. C22⋊C4C2×ΓL(1,𝔽16)semidirect
583. C3×C5C2×#388semidirect
623. C2×C5#4951semidirect
628. D5#4951semidirect
700. C2×C3#65700semidirect
704. C5C2×#4951semidirect
743. C3C2×#65700semidirect
751. C2#11752359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67632
C22×C4⋊ΓL(1,𝔽16)2
C22×C4×ΓL(1,𝔽16)2
C2×C3×D5×C22⋊C42
C2×#912352
#117523592
C2×#657003
C2×#49515