Finite Group Databasebeta

← #14329014

Subgroups — #14329014

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4130C211yesmaximal, characteristic
2C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
3D5×#924C211yesmaximal, characteristic
4C4×#6763C211yesmaximal, characteristic
5#11752018C212yesmaximal
6#11752017C212yesmaximal
7#11751861C211yesmaximal, characteristic, complemented
8#11751846C211yesmaximal, characteristic, complemented
9AGL(1,𝔽5)×Dic3⋊C4C212yesmaximal, complemented
10#11751752C211yesmaximal, characteristic, complemented
11#11751745C212yesmaximal, complemented
12#10617286—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×D5×Dic6C2211yescharacteristic
15C2×#6763C2211yescharacteristic
16C2×#6763C2211yescharacteristic
17C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
19C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
20C3×#4130—24no—
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×C4×AGL(1,𝔽5)C2212yes—
24C2×Dic3⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3⋊AGL(1,𝔽5)C2212yes—
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27C2×Dic3×AGL(1,𝔽5)C2212yes—
28ΓL(1,𝔽16)⋊Q8—24no—
29#91813C411yescharacteristic, complemented
30C5×#924C411yescharacteristic, complemented
31#91574C412yescomplemented
32D5×#217C2212yes—
33D5×C4⋊Dic3C2211yescharacteristic
34D5×Dic3⋊C4C2212yes—
35#91360C411yescharacteristic, complemented
36#91359C411yescharacteristic, complemented
37#91349C412yescomplemented
38#91235C2211yescharacteristic
39#91235C2211yescharacteristic
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#82243—51nomaximal, Hall
45C2×Q8×AGL(1,𝔽5)—31no—
46C2×#4130D311yescharacteristic
47D5×C22⋊Q8—31no—
48(C2×AGL(1,𝔽5))⋊Q8—31no—
49C4×C22⋊AGL(1,𝔽5)—31no—
50#65712—31no—
51#65711—32no—
52C4⋊C4×AGL(1,𝔽5)—31no—
53C4⋊C4×AGL(1,𝔽5)—32no—
54#65700—32no—
55#65700—32no—
56C23×C3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2312yes—
62C22×C3×AGL(1,𝔽5)C2312yes—
63C22×C3×C4×C5C2×C411yescharacteristic
64C2×Dic30C2×C411yescharacteristic
65C2×C5×Dic6C2×C411yescharacteristic
66C22×C3×Dic5C2×C411yescharacteristic
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5C2×C411yescharacteristic
70C2×C3×C4×D5C2×C411yescharacteristic
71C2×C3×C4×D5C2311yescharacteristic
72C2×C3×C4×D5C2311yescharacteristic
73C2×#1204C2×C412yes—
74C2×D5×Dic3C2312yes—
75C2×D5×Dic3C2312yes—
76D5×Dic6—22no—
77D5×Dic6—22no—
78#6763—22no—
79#6763—22no—
80C4×ΓL(1,𝔽16)—22no—
81C4×ΓL(1,𝔽16)—22no—
82C3×C22⋊AGL(1,𝔽5)—24no—
83C3×C4⋊AGL(1,𝔽5)—22no—
84C3×C4⋊AGL(1,𝔽5)D414yes—
85C3×C4×AGL(1,𝔽5)—24no—
86Dic3⋊AGL(1,𝔽5)—24no—
87Dic3⋊AGL(1,𝔽5)—24no—
88Dic3×AGL(1,𝔽5)—24no—
89Dic3×AGL(1,𝔽5)—24no—
90#6719C2×C412yes—
91C4⋊Dic15C2×C411yescharacteristic
92#6712C2×C412yes—
93C5×#217C2×C412yes—
94C5×C4⋊Dic3C2×C411yescharacteristic
95C5×Dic3⋊C4C2×C412yes—
96Dic3⋊Dic5C2×C412yes—
97#6669C2×C412yes—
98#6668C2×C412yes—
99#6665C2×C412yes—
100#6665C2×C412yes—
101C2×C3×#117—51no—
102C2×#924—51no—
103C2×#887—51no—
104C4×#217—51no—
105Dic3×C4⋊C4—51no—
106#4973—51no—
107#4972—51no—
108#4945—52no—
109#4944—52no—
110#4933—52no—
111C4×Dic3⋊C4—52no—
112C2×Q8×D5—31no—
113C22×C4×D5C2×D311yescharacteristic
114C2×C22⋊AGL(1,𝔽5)—31no—
115C2×C22⋊AGL(1,𝔽5)—31no—
116C2×C22⋊AGL(1,𝔽5)C2×D312yes—
117Q8×AGL(1,𝔽5)—64no—
118#4130—24no—
119C2×C4⋊AGL(1,𝔽5)—32no—
120C2×C4⋊AGL(1,𝔽5)—32no—
121C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
122C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
123C2×C4×AGL(1,𝔽5)—32no—
124C2×C4×AGL(1,𝔽5)—32no—
125C2×C4×AGL(1,𝔽5)—31no—
126C2×C4×AGL(1,𝔽5)—31no—
127C2×C4×AGL(1,𝔽5)C2×D312yes—
128C5×C22⋊Q8—31no—
129#4092—31no—
130#4070—31no—
131#4043—31no—
132#4042—32no—
133D5×C4⋊C4—32no—
134D5×C4⋊C4—31no—
135D5×C22⋊C4—32no—
136#4024—32no—
137(C2×AGL(1,𝔽5))⋊C4—32no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139(C2×AGL(1,𝔽5))⋊C4—32no—
140(C2×AGL(1,𝔽5))⋊C4—32no—
141(C2×AGL(1,𝔽5))⋊C4—31no—
142(C2×AGL(1,𝔽5))⋊C4—31no—
143#2362—151noSylow
144C23×C3×C5C22×C411yescharacteristic
145C22×C3×D5—21no—
146C22×C3×D5—21no—
147C22×C3×D5—21no—
148C22×C3×D5—21no—
149C22×C3×D5—21no—
150C22×C3×D5—21no—
151C22×C3×D5C22×C411yescharacteristic
152C22×C3×D5C2411yescharacteristic
153C2×ΓL(1,𝔽16)—21no—
154C2×ΓL(1,𝔽16)—21no—
155C2×ΓL(1,𝔽16)—21no—
156C2×ΓL(1,𝔽16)—21no—
157C2×ΓL(1,𝔽16)—21no—
158C2×ΓL(1,𝔽16)—21no—
159C2×ΓL(1,𝔽16)—21no—
160C2×ΓL(1,𝔽16)—21no—
161C2×ΓL(1,𝔽16)—21no—
162C2×ΓL(1,𝔽16)—21no—
163C2×ΓL(1,𝔽16)#4112yes—
164C2×ΓL(1,𝔽16)#4112yes—
165C2×C3×AGL(1,𝔽5)—22no—
166C2×C3×AGL(1,𝔽5)—22no—
167C2×C3×AGL(1,𝔽5)—22no—
168C2×C3×AGL(1,𝔽5)—22no—
169C2×C3×AGL(1,𝔽5)—22no—
170C2×C3×AGL(1,𝔽5)C2×D414yes—
171C2×C3×C4×C5—22no—
172C2×C3×C4×C5C22×C411yescharacteristic
173C2×C3×C4×C5C22×C411yescharacteristic
174C2×Dic15C22×C412yes—
175C2×Dic15C22×C412yes—
176Dic30—22no—
177C2×C5×Dic3C22×C412yes—
178C2×C5×Dic3C22×C412yes—
179C5×Dic6—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5C22×C411yescharacteristic
182C2×C3×Dic5C22×C411yescharacteristic
183C3×C4×D5—21no—
184C3×C4×D5—21no—
185C3×C4×D5—22no—
186C3×C4×D5—22no—
187C3×C4×D5C2×D412yes—
188C3×C4×D5#4112yes—
189#1204—24no—
190D5×Dic3—22no—
191D5×Dic3—22no—
192D5×Dic3—22no—
193D5×Dic3—22no—
194C23×C3×C4—51no—
195C22×Dic6—51no—
196C3×#117—104no—
197C2×C3×C4⋊C4—51no—
198C2×C3×C4⋊C4—51no—
199C2×C3×C22⋊C4—52no—
200C2×C3×C42—52no—
201C2×#217—52no—
202C2×#217—51no—
203C2×#217—51no—
204C2×C4⋊Dic3—51no—
205#924—51no—
206#924—51no—
207#924—52no—
208#924—51no—
209#924—52no—
210#924AGL(1,𝔽5)11yescharacteristic, complemented
211C2×Dic3⋊C4—52no—
212C2×Dic3⋊C4—52no—
213C2×Dic3⋊C4—52no—
214C2×C4×Dic3—52no—
215C2×C4×Dic3—52no—
216C2×C4×Dic3—51no—
217C2×C4×Dic3—51no—
218#887—104no—
219C3⋊#95—52no—
220C3⋊#95—52no—
221C3⋊#95—52no—
222C3⋊#95—52no—
223C3⋊#95—51no—
224C3⋊#95—51no—
225C23×D5C22×D311yescharacteristic
226C22×AGL(1,𝔽5)—31no—
227C22×AGL(1,𝔽5)—31no—
228C22×AGL(1,𝔽5)—31no—
229C22×AGL(1,𝔽5)—31no—
230C22×AGL(1,𝔽5)C22×D312yes—
231C22×AGL(1,𝔽5)C22×D312yes—
232C2×C5×Q8—31no—
233C22×C4×C5C4×D311yescharacteristic
234C22×Dic5C4×D311yescharacteristic
235Q8×D5—62no—
236Q8×D5—62no—
237C2×C4×D5—22no—
238C2×C4×D5—22no—
239C2×C4×D5—32no—
240C2×C4×D5—32no—
241C2×C4×D5C4×D311yescharacteristic
242C2×C4×D5C4×D311yescharacteristic
243C2×C4×D5C22×D311yescharacteristic
244C2×C4×D5C22×D311yescharacteristic
245C2×Dic10—31no—
246C2×Dic10—32no—
247C22⋊AGL(1,𝔽5)—24no—
248C22⋊AGL(1,𝔽5)—62no—
249C22⋊AGL(1,𝔽5)—62no—
250C4⋊AGL(1,𝔽5)—22no—
251C4⋊AGL(1,𝔽5)—64no—
252C4⋊AGL(1,𝔽5)—64no—
253C4⋊AGL(1,𝔽5)#6714yes—
254C4×AGL(1,𝔽5)—24no—
255C4×AGL(1,𝔽5)—64no—
256C4×AGL(1,𝔽5)—64no—
257C4×AGL(1,𝔽5)—62no—
258C4×AGL(1,𝔽5)—62no—
259C5×C4⋊C4—32no—
260C5×C4⋊C4—31no—
261C5×C22⋊C4—32no—
262C22⋊Dic5—32no—
263#685—32no—
264#685—32no—
265C4⋊Dic5—31no—
266C4⋊Dic5—32no—
267#683—32no—
268#683—32no—
269#683—32no—
270C2×C22⋊Q8—151no—
271C2×C4×Q8—151no—
272C2×#117—51no—
273#391—151no—
274#389—151no—
275#388—152no—
276#388—152no—
277#387—152no—
278C4×C4⋊C4—152no—
279C4×C4⋊C4—151no—
280C4×C22⋊C4—151no—
281C22×C3×C5—21no—
282C22×C3×C5—21no—
283C22×C3×C5—21no—
284C22×C3×C5C23×C411yescharacteristic
285C2×C3×D5—21no—
286C2×C3×D5—21no—
287C2×C3×D5—21no—
288C2×C3×D5—41no—
289C2×C3×D5—41no—
290C2×C3×D5—41no—
291C2×C3×D5—41no—
292C2×C3×D5C22×D411yescharacteristic
293C2×C3×D5C2×#4111yescharacteristic
294C2×C3×D5C2×#4111yescharacteristic
295C2×C3×D5C2×#4111yescharacteristic
296C2×C3×D52−1+411yescharacteristic
297C2×C3×D52−1+411yescharacteristic
298ΓL(1,𝔽16)—22no—
299ΓL(1,𝔽16)—22no—
300ΓL(1,𝔽16)—41no—
301ΓL(1,𝔽16)—41no—
302C3×AGL(1,𝔽5)—24no—
303C3×AGL(1,𝔽5)—42no—
304C3×C4×C5—21no—
305C3×C4×C5C4×D412yes—
306Dic15—22no—
307Dic15—22no—
308C3×Dic5—21no—
309C3×Dic5C4×D412yes—
310C5×Dic3—22no—
311C5×Dic3—22no—
312C24×C3—51no—
313C22×C3×C4—51no—
314C22×C3×C4—52no—
315C22×C3×C4—51no—
316C22×C3×C4—51no—
317C22×C3×C4—51no—
318C22×C3×C4—51no—
319C22×C3×C4—52no—
320C22×C3×C4—102no—
321C22×C3×C4—102no—
322C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
323C22×Dic3—51no—
324C22×Dic3—51no—
325C22×Dic3—52no—
326C22×Dic3—52no—
327C22×Dic3—51no—
328C22×Dic3—51no—
329C2×Dic6—51no—
330C2×Dic6—52no—
331C2×Dic6—102no—
332C2×Dic6—102no—
333C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
334C3×C4⋊C4—54no—
335C3×C4⋊C4—102no—
336C3×C22⋊C4—104no—
337C3×C42—104no—
338#217—52no—
339#217—52no—
340#217—52no—
341#217—102no—
342#217—102no—
343#217C2×AGL(1,𝔽5)12yes—
344C4⋊Dic3—51no—
345C4⋊Dic3—52no—
346C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
347Dic3⋊C4—52no—
348Dic3⋊C4—52no—
349Dic3⋊C4—52no—
350Dic3⋊C4—104no—
351Dic3⋊C4—104no—
352Dic3⋊C4C2×AGL(1,𝔽5)12yes—
353C4×Dic3—104no—
354C4×Dic3—104no—
355C4×Dic3—102no—
356C4×Dic3—102no—
357C23×C5C2×C4×D311yescharacteristic
358C22×D5—21no—
359C22×D5—21no—
360C22×D5—21no—
361C22×D5—21no—
362C22×D5—21no—
363C22×D5—21no—
364C22×D5C2×C4×D311yescharacteristic
365C22×D5C23×D311yescharacteristic
366C2×AGL(1,𝔽5)—22no—
367C2×AGL(1,𝔽5)—22no—
368C2×AGL(1,𝔽5)—22no—
369C2×AGL(1,𝔽5)—22no—
370C2×AGL(1,𝔽5)—22no—
371C2×AGL(1,𝔽5)—32no—
372C2×AGL(1,𝔽5)—32no—
373C2×AGL(1,𝔽5)—61no—
374C2×AGL(1,𝔽5)—61no—
375C2×AGL(1,𝔽5)—61no—
376C2×AGL(1,𝔽5)—61no—
377C2×AGL(1,𝔽5)—61no—
378C2×AGL(1,𝔽5)—61no—
379C2×AGL(1,𝔽5)—61no—
380C2×AGL(1,𝔽5)—61no—
381C2×AGL(1,𝔽5)—61no—
382C2×AGL(1,𝔽5)—61no—
383C2×AGL(1,𝔽5)C2×#6714yes—
384C5×Q8—62no—
385C2×C4×C5—22no—
386C2×C4×C5—32no—
387C2×C4×C5—32no—
388C2×C4×C5C2×C4×D311yescharacteristic
389C2×C4×C5C2×C4×D311yescharacteristic
390C2×Dic5—22no—
391C2×Dic5—32no—
392C2×Dic5—32no—
393C2×Dic5C2×C4×D311yescharacteristic
394C2×Dic5C2×C4×D311yescharacteristic
395C4×D5—21no—
396C4×D5—21no—
397C4×D5—22no—
398C4×D5—22no—
399C4×D5—62no—
400C4×D5—62no—
401C4×D5—62no—
402C4×D5—62no—
403C4×D5#23512yes—
404C4×D5C2×#6712yes—
405Dic10—62no—
406Dic10—64no—
407C22×Q8—151no—
408C23×C4—51no—
409C22⋊Q8—31no—
410C22⋊Q8—152no—
411C22⋊Q8—152no—
412C22⋊Q8—151no—
413C22⋊Q8—151no—
414C22⋊Q8—151no—
415C4×Q8—304no—
416#117—104no—
417C2×C4⋊C4—51no—
418C2×C4⋊C4—51no—
419C2×C4⋊C4—152no—
420C2×C4⋊C4—151no—
421C2×C4⋊C4—152no—
422C2×C4⋊C4—152no—
423C2×C22⋊C4—52no—
424C2×C22⋊C4—152no—
425C2×C22⋊C4—151no—
426C2×C22⋊C4—151no—
427C2×C42—52no—
428C2×C42—151no—
429C2×C42—152no—
430C2×C42—151no—
431C2×C42—152no—
432#95—151no—
433#95—151no—
434#95—152no—
435#95—152no—
436#95—152no—
437#95—152no—
438C2×C3×C5—41no—
439C2×C3×C5C2×C4×D411yescharacteristic
440C2×C3×C5C4×#4111yescharacteristic
441C2×C3×C5#51911yescharacteristic
442C3×D5—41no—
443C3×D5#54711yescharacteristic
444C3×D5#54811yescharacteristic
445C3×D5#55211yescharacteristic
446C3×D5#55611yescharacteristic
447C23×C3—51no—
448C23×C3—51no—
449C23×C3—101no—
450C23×C3—101no—
451C23×C3—101no—
452C23×C3—101no—
453C23×C3—101no—
454C23×C3—101no—
455C23×C3C22×AGL(1,𝔽5)11yescharacteristic
456C2×C3×C4—22no—
457C2×C3×C4—51no—
458C2×C3×C4—52no—
459C2×C3×C4—52no—
460C2×C3×C4—54no—
461C2×C3×C4—51no—
462C2×C3×C4—102no—
463C2×C3×C4—101no—
464C2×C3×C4—101no—
465C2×C3×C4—102no—
466C2×C3×C4—102no—
467C2×C3×C4—102no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4—102no—
472C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
473C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
474C2×Dic3—52no—
475C2×Dic3—52no—
476C2×Dic3—52no—
477C2×Dic3—52no—
478C2×Dic3—102no—
479C2×Dic3—102no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—101no—
483C2×Dic3—101no—
484C2×Dic3—101no—
485C2×Dic3—101no—
486C2×Dic3—101no—
487C2×Dic3—101no—
488C2×Dic3—101no—
489C2×Dic3—101no—
490C2×Dic3—101no—
491C2×Dic3—101no—
492C2×Dic3C22×AGL(1,𝔽5)12yes—
493C2×Dic3C22×AGL(1,𝔽5)12yes—
494Dic6—22no—
495Dic6—104no—
496Dic6—102no—
497C22×C5—21no—
498C22×C5—21no—
499C22×C5—21no—
500C22×C5C22×C4×D311yescharacteristic
501C2×D5—21no—
502C2×D5—21no—
503C2×D5—21no—
504C2×D5—41no—
505C2×D5—41no—
506C2×D5—41no—
507C2×D5—41no—
508C2×D5C2×#23511yescharacteristic
509C2×D5D3×#4111yescharacteristic
510C2×D5D3×#4111yescharacteristic
511C2×D5#101011yescharacteristic
512C2×D5#101011yescharacteristic
513C2×D5C22×#6711yescharacteristic
514AGL(1,𝔽5)—24no—
515AGL(1,𝔽5)—42no—
516AGL(1,𝔽5)—62no—
517AGL(1,𝔽5)—62no—
518AGL(1,𝔽5)—121no—
519AGL(1,𝔽5)—121no—
520C4×C5—21no—
521C4×C5—62no—
522C4×C5—62no—
523C4×C5C4×#6712yes—
524Dic5—21no—
525Dic5—62no—
526Dic5—62no—
527Dic5C4×#6712yes—
528C24—51no—
529C2×Q8—31no—
530C2×Q8—152no—
531C2×Q8—151no—
532C2×Q8—302no—
533C2×Q8—302no—
534C22×C4—51no—
535C22×C4—52no—
536C22×C4—51no—
537C22×C4—51no—
538C22×C4—51no—
539C22×C4—51no—
540C22×C4—52no—
541C22×C4—102no—
542C22×C4—102no—
543C22×C4—152no—
544C22×C4—152no—
545C22×C4—151no—
546C22×C4—151no—
547C22×C4—151no—
548C22×C4—151no—
549C22×C4D3×AGL(1,𝔽5)11yescharacteristic
550C4⋊C4—32no—
551C4⋊C4—31no—
552C4⋊C4—54no—
553C4⋊C4—102no—
554C4⋊C4—152no—
555C4⋊C4—152no—
556C4⋊C4—152no—
557C4⋊C4—152no—
558C4⋊C4—151no—
559C4⋊C4—304no—
560C4⋊C4—304no—
561C22⋊C4—32no—
562C22⋊C4—104no—
563C22⋊C4—152no—
564C22⋊C4—152no—
565C22⋊C4—152no—
566C22⋊C4—302no—
567C22⋊C4—302no—
568C42—104no—
569C42—302no—
570C42—304no—
571C42—302no—
572C42—304no—
573C3×C5#236211yescharacteristic, complemented, Hall
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—51no—
578C22×C3—51no—
579C22×C3—51no—
580C22×C3—51no—
581C22×C3—51no—
582C22×C3—51no—
583C22×C3—101no—
584C22×C3—101no—
585C22×C3—101no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3—201no—
589C22×C3—201no—
590C22×C3C23×AGL(1,𝔽5)11yescharacteristic
591C3×C4—21no—
592C3×C4—52no—
593C3×C4—104no—
594C3×C4—101no—
595C3×C4—202no—
596C3×C4D4×AGL(1,𝔽5)12yes—
597Dic3—22no—
598Dic3—22no—
599Dic3—102no—
600Dic3—102no—
601Dic3—102no—
602Dic3—102no—
603Dic3—201no—
604Dic3—201no—
605C2×C5—41no—
606C2×C5#551611yescharacteristic
607C2×C5#552211yescharacteristic
608C2×C5C2×C4×#6711yescharacteristic
609D5—41no—
610D5#552911yescharacteristic
611D5#553311yescharacteristic
612D5#582411yescharacteristic
613D5#583111yescharacteristic
614C23—51no—
615C23—51no—
616C23—101no—
617C23—101no—
618C23—101no—
619C23—101no—
620C23—101no—
621C23—101no—
622C23C2×D3×AGL(1,𝔽5)11yescharacteristic
623Q8—62no—
624Q8—304no—
625Q8—302no—
626C2×C4—22no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—51no—
630C2×C4—52no—
631C2×C4—52no—
632C2×C4—54no—
633C2×C4—51no—
634C2×C4—102no—
635C2×C4—101no—
636C2×C4—101no—
637C2×C4—102no—
638C2×C4—102no—
639C2×C4—102no—
640C2×C4—102no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4—102no—
644C2×C4—152no—
645C2×C4—152no—
646C2×C4—152no—
647C2×C4—152no—
648C2×C4—302no—
649C2×C4—302no—
650C2×C4—302no—
651C2×C4—302no—
652C2×C4—301no—
653C2×C4—301no—
654C2×C4—301no—
655C2×C4—301no—
656C2×C4—301no—
657C2×C4—301no—
658C2×C4—301no—
659C2×C4—301no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
663C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
664C2×C3—41no—
665C2×C3—51no—
666C2×C3—51no—
667C2×C3—51no—
668C2×C3—51no—
669C2×C3—201no—
670C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
671C2×C3#6626211yescharacteristic
672C2×C3#41×AGL(1,𝔽5)11yescharacteristic
673C5#8224311yescharacteristic, complemented, Sylow
674C22—21no—
675C22—21no—
676C22—21no—
677C22—51no—
678C22—51no—
679C22—51no—
680C22—51no—
681C22—51no—
682C22—51no—
683C22—101no—
684C22—101no—
685C22—101no—
686C22—201no—
687C22—201no—
688C22—201no—
689C22—201no—
690C22C22×D3×AGL(1,𝔽5)11yescharacteristic
691C4—21no—
692C4—52no—
693C4—62no—
694C4—62no—
695C4—104no—
696C4—101no—
697C4—202no—
698C4—302no—
699C4—302no—
700C4—302no—
701C4—302no—
702C4—601no—
703C4—601no—
704C4AGL(1,𝔽5)×#6712yes—
705C3#1061728611yescharacteristic, complemented, Sylow
706C2—41no—
707C2—51no—
708C2—51no—
709C2—51no—
710C2—51no—
711C2—201no—
712C2#1175681211yescharacteristic
713C2#1175683511yescharacteristic
714C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2362
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×ΓL(1,𝔽16)⋊Q8C2semidirect
7. #11751861C2semidirect
8. #11751846C2semidirect
9. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
10. #11751752C2semidirect
11. #11751745C2semidirect
29. #91813C4semidirect
30. C5×#924C4semidirect
31. #91574C4semidirect
35. #91360C4semidirect
36. #91359C4semidirect
37. #91349C4semidirect
210. #924AGL(1,𝔽5)semidirect
573. C3×C5#2362semidirect
673. C5#82243semidirect
705. C3#10617286semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41302
C2×ΓL(1,𝔽16)⋊Q82
D5×#9242
C4×#67632
#117520182
#117520172
#117518612
#117518462
AGL(1,𝔽5)×Dic3⋊C42
#117517522
#117517452
#106172863
#822435