Finite Group Databasebeta

← #14329443

Subgroups — #14329443

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×ΓL(1,𝔽16)C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic
3D5×#944C211yesmaximal, characteristic
4C3×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic
5C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
6#11751845C212yesmaximal
7#11751844C212yesmaximal
8Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
9#11751833C212yesmaximal
10#11751752C211yesmaximal, characteristic
11#11751747C212yesmaximal
12#10617388—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×D5×Dic6C2211yescharacteristic
15Q8×ΓL(1,𝔽16)—24no—
16C2×C4⋊ΓL(1,𝔽16)C2212yes—
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)C2212yes—
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
22C2×Dic3⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C2×Dic3×AGL(1,𝔽5)C2212yes—
27AGL(1,𝔽5)×Dic6—24no—
28#91833C411yescharacteristic, complemented
29C5×#944C411yescharacteristic, complemented
30D5×Dic3⋊C4C2212yes—
31D5×Dic3⋊C4C2212yes—
32C4×D5×Dic3C2211yescharacteristic
33#91389C411yescharacteristic, complemented
34#91385C411yescharacteristic, complemented
35#91327C412yescomplemented
36#91327C412yescomplemented
37C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
38C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
44#76492—51nomaximal, Hall
45C2×Q8×AGL(1,𝔽5)—31no—
46C2×Q8×AGL(1,𝔽5)—31no—
47D5×C4⋊Q8—31no—
48(C2×AGL(1,𝔽5))⋊Q8—31no—
49(C2×AGL(1,𝔽5))⋊Q8D311yescharacteristic
50#65712—32no—
51#65711—32no—
52#65711—32no—
53C4⋊C4×AGL(1,𝔽5)—32no—
54C4×C4⋊AGL(1,𝔽5)—31no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2312yes—
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2311yescharacteristic
62C2×C3×C5×Q8C2×C411yescharacteristic
63C2×Dic30C2×C411yescharacteristic
64C2×C5×Dic6C2×C411yescharacteristic
65C3×Q8×D5—22no—
66C3×Q8×D5—22no—
67C2×C3×C4×D5C2312yes—
68C2×C3×C4×D5C2311yescharacteristic
69C2×C3×Dic10C2×C412yes—
70C2×C3×Dic10C2×C411yescharacteristic
71C2×#1204C2×C412yes—
72C2×D5×Dic3C2312yes—
73C2×D5×Dic3C2311yescharacteristic
74C2×D5×Dic3C2311yescharacteristic
75D5×Dic6—22no—
76D5×Dic6—22no—
77C4⋊ΓL(1,𝔽16)—24no—
78C4⋊ΓL(1,𝔽16)D414yes—
79C4×ΓL(1,𝔽16)—24no—
80C4×ΓL(1,𝔽16)—22no—
81C3×C4⋊AGL(1,𝔽5)—22no—
82C3×C4×AGL(1,𝔽5)—22no—
83Dic3⋊AGL(1,𝔽5)—24no—
84Dic3⋊AGL(1,𝔽5)—22no—
85Dic3⋊AGL(1,𝔽5)Q814yescomplemented
86Dic3×AGL(1,𝔽5)—24no—
87Dic3×AGL(1,𝔽5)—24no—
88#6712C2×C412yes—
89#6712C2×C412yes—
90C4×Dic15C2×C411yescharacteristic
91C5×Dic3⋊C4C2×C412yes—
92C5×Dic3⋊C4C2×C412yes—
93C4×C5×Dic3C2×C411yescharacteristic
94Dic3⋊Dic5C2×C412yes—
95Dic3⋊Dic5C2×C412yes—
96#6669C2×C412yes—
97#6669C2×C412yes—
98Dic3×Dic5C2×C411yescharacteristic
99Dic3×Dic5C2×C411yescharacteristic
100C2×Q8×Dic3—51no—
101C2×#944—51no—
102C2×C4×Dic6—51no—
103C3×#391—51no—
104Dic3×C4⋊C4—51no—
105#4973—51no—
106C4×Dic3⋊C4—51no—
107#4655—52no—
108#4652—52no—
109#4649—52no—
110#4647—52no—
111C2×Q8×D5—31no—
112C2×Q8×D5C2×D311yescharacteristic
113Q8×AGL(1,𝔽5)—64no—
114Q8×AGL(1,𝔽5)—64no—
115C2×C4⋊AGL(1,𝔽5)—31no—
116C2×C4⋊AGL(1,𝔽5)—31no—
117C2×C4⋊AGL(1,𝔽5)—31no—
118C2×C4⋊AGL(1,𝔽5)—32no—
119C2×C4⋊AGL(1,𝔽5)—32no—
120C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
121C2×C4×AGL(1,𝔽5)—32no—
122C2×C4×AGL(1,𝔽5)—32no—
123C2×C4×AGL(1,𝔽5)—31no—
124C2×C4×AGL(1,𝔽5)—32no—
125C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
126C5×C4⋊Q8—31no—
127#4090—31no—
128#4090—31no—
129D5×C4⋊C4—32no—
130D5×C4⋊C4—32no—
131#4034—32no—
132#4034—32no—
133C42×D5—31no—
134#4015—31no—
135(C2×AGL(1,𝔽5))⋊C4—32no—
136(C2×AGL(1,𝔽5))⋊C4—31no—
137(C2×AGL(1,𝔽5))⋊C4—31no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139(C2×AGL(1,𝔽5))⋊C4—32no—
140(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
141(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
142#2365—151noSylow
143C22×C3×D5C2411yescharacteristic
144C2×ΓL(1,𝔽16)—21no—
145C2×ΓL(1,𝔽16)—22no—
146C2×ΓL(1,𝔽16)—22no—
147C2×ΓL(1,𝔽16)—21no—
148C2×ΓL(1,𝔽16)—21no—
149C2×ΓL(1,𝔽16)—21no—
150C2×ΓL(1,𝔽16)—21no—
151C2×ΓL(1,𝔽16)C2×D414yes—
152C2×ΓL(1,𝔽16)C2×Q812yes—
153C2×C3×AGL(1,𝔽5)—21no—
154C2×C3×AGL(1,𝔽5)—21no—
155C2×C3×AGL(1,𝔽5)—21no—
156C2×C3×AGL(1,𝔽5)—22no—
157C2×C3×AGL(1,𝔽5)—21no—
158C2×C3×AGL(1,𝔽5)—22no—
159C2×C3×AGL(1,𝔽5)—21no—
160C2×C3×AGL(1,𝔽5)—22no—
161C2×C3×AGL(1,𝔽5)C2×Q812yes—
162C3×C5×Q8—22no—
163C2×C3×C4×C5C22×C412yes—
164C2×C3×C4×C5C22×C411yescharacteristic
165C2×Dic15C22×C411yescharacteristic
166C2×Dic15C22×C412yes—
167C2×Dic15C22×C411yescharacteristic
168Dic30—22no—
169C2×C5×Dic3C22×C411yescharacteristic
170C2×C5×Dic3C22×C412yes—
171C2×C5×Dic3C22×C411yescharacteristic
172C5×Dic6—22no—
173C2×C3×Dic5C22×C412yes—
174C2×C3×Dic5C22×C411yescharacteristic
175C3×C4×D5—22no—
176C3×C4×D5—22no—
177C3×C4×D5C2×D412yes—
178C3×C4×D5#4112yes—
179C3×Dic10—22no—
180C3×Dic10—24no—
181#1204—24no—
182D5×Dic3—22no—
183D5×Dic3—22no—
184D5×Dic3—21no—
185D5×Dic3—21no—
186D5×Dic3C2×Q812yes—
187D5×Dic3#4112yes—
188C22×C3×Q8—51no—
189C22×Dic6—51no—
190C2×C3×C4⋊C4—51no—
191C2×C3×C42—51no—
192Q8×Dic3—104no—
193#944—51no—
194#944—51no—
195#944—52no—
196#944—52no—
197#944—51no—
198#944AGL(1,𝔽5)11yescharacteristic, complemented
199C2×C4⋊Dic3—51no—
200C2×C4⋊Dic3—52no—
201C2×Dic3⋊C4—51no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4—51no—
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—51no—
207C2×C4×Dic3—52no—
208C2×C4×Dic3—52no—
209C2×C4×Dic3—52no—
210C2×C4×Dic3—51no—
211C4×Dic6—104no—
212C3×#95—52no—
213C3×#95—52no—
214C3⋊#95—52no—
215C3⋊#95—52no—
216C3⋊#95—51no—
217C3⋊#95—52no—
218C3⋊#95—51no—
219C22×AGL(1,𝔽5)—32no—
220C22×AGL(1,𝔽5)—31no—
221C22×AGL(1,𝔽5)—31no—
222C22×AGL(1,𝔽5)C22×D312yes—
223C22×AGL(1,𝔽5)C22×D311yescharacteristic
224C22×AGL(1,𝔽5)C22×D311yescharacteristic
225C2×C5×Q8—31no—
226C2×C5×Q8C4×D311yescharacteristic
227Q8×D5—22no—
228Q8×D5—22no—
229Q8×D5—62no—
230Q8×D5—62no—
231C2×C4×D5—31no—
232C2×C4×D5—32no—
233C2×C4×D5—31no—
234C2×C4×D5C22×D312yes—
235C2×C4×D5C22×D311yescharacteristic
236C2×Dic10—31no—
237C2×Dic10—32no—
238C2×Dic10C4×D311yescharacteristic
239C2×Dic10C4×D312yes—
240C4⋊AGL(1,𝔽5)—22no—
241C4⋊AGL(1,𝔽5)—34no—
242C4⋊AGL(1,𝔽5)—34no—
243C4⋊AGL(1,𝔽5)—64no—
244C4⋊AGL(1,𝔽5)—62no—
245C4⋊AGL(1,𝔽5)—64no—
246C4×AGL(1,𝔽5)—22no—
247C4×AGL(1,𝔽5)—64no—
248C4×AGL(1,𝔽5)—64no—
249C4×AGL(1,𝔽5)—64no—
250C4×AGL(1,𝔽5)—62no—
251C5×C4⋊C4—32no—
252C5×C4⋊C4—32no—
253C42×C5—31no—
254C4⋊Dic5—32no—
255C4⋊Dic5—32no—
256#683—32no—
257#683—32no—
258#683—32no—
259#683—32no—
260C4×Dic5—31no—
261C4×Dic5—31no—
262C4×Dic5—31no—
263C2×C4⋊Q8—151no—
264C2×C4×Q8—151no—
265C2×C4×Q8—151no—
266#391—51no—
267#391—151no—
268#389—152no—
269#387—152no—
270#387—152no—
271C4×C4⋊C4—152no—
272C4×C4⋊C4—151no—
273C4×C4⋊C4—151no—
274C22×C3×C5C23×C411yescharacteristic
275C2×C3×D5C22×D411yescharacteristic
276C2×C3×D5C22×Q811yescharacteristic
277C2×C3×D5C2×#4111yescharacteristic
278C2×C3×D5C2×#4111yescharacteristic
279C2×C3×D52−1+411yescharacteristic
280C2×C3×D52−1+411yescharacteristic
281ΓL(1,𝔽16)—24no—
282ΓL(1,𝔽16)—22no—
283ΓL(1,𝔽16)—41no—
284C3×AGL(1,𝔽5)—22no—
285C3×AGL(1,𝔽5)—41no—
286C3×AGL(1,𝔽5)—42no—
287C3×C4×C5—22no—
288C3×C4×C5C4×D412yes—
289Dic15—22no—
290Dic15—21no—
291Dic15C4×Q812yescomplemented
292C3×Dic5—22no—
293C3×Dic5C4×D412yes—
294C5×Dic3—22no—
295C5×Dic3—21no—
296C5×Dic3C4×Q812yescomplemented
297C2×C3×Q8—52no—
298C2×C3×Q8—51no—
299C2×C3×Q8—102no—
300C2×C3×Q8—102no—
301C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
302C22×C3×C4—51no—
303C22×C3×C4—51no—
304C22×C3×C4—52no—
305C22×C3×C4—52no—
306C22×C3×C4—51no—
307C22×Dic3—51no—
308C22×Dic3—51no—
309C22×Dic3—52no—
310C22×Dic3—51no—
311C22×Dic3—52no—
312C22×Dic3—51no—
313C2×Dic6—51no—
314C2×Dic6—52no—
315C2×Dic6—102no—
316C2×Dic6—102no—
317C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
318C3×C4⋊C4—102no—
319C3×C42—102no—
320C4⋊Dic3—54no—
321C4⋊Dic3—104no—
322Dic3⋊C4—54no—
323Dic3⋊C4—52no—
324Dic3⋊C4—52no—
325Dic3⋊C4—52no—
326Dic3⋊C4—52no—
327Dic3⋊C4—52no—
328Dic3⋊C4—52no—
329Dic3⋊C4—104no—
330Dic3⋊C4—102no—
331Dic3⋊C4C2×AGL(1,𝔽5)12yes—
332Dic3⋊C4C2×AGL(1,𝔽5)12yes—
333C4×Dic3—51no—
334C4×Dic3—51no—
335C4×Dic3—51no—
336C4×Dic3—104no—
337C4×Dic3—104no—
338C4×Dic3—104no—
339C4×Dic3—102no—
340C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
341C22×D5C23×D311yescharacteristic
342C2×AGL(1,𝔽5)—21no—
343C2×AGL(1,𝔽5)—21no—
344C2×AGL(1,𝔽5)—21no—
345C2×AGL(1,𝔽5)—22no—
346C2×AGL(1,𝔽5)—21no—
347C2×AGL(1,𝔽5)—22no—
348C2×AGL(1,𝔽5)—21no—
349C2×AGL(1,𝔽5)—22no—
350C2×AGL(1,𝔽5)—34no—
351C2×AGL(1,𝔽5)—32no—
352C2×AGL(1,𝔽5)—61no—
353C2×AGL(1,𝔽5)—62no—
354C2×AGL(1,𝔽5)—62no—
355C2×AGL(1,𝔽5)—61no—
356C2×AGL(1,𝔽5)—61no—
357C2×AGL(1,𝔽5)—61no—
358C2×AGL(1,𝔽5)—61no—
359C2×AGL(1,𝔽5)D3×Q812yes—
360C5×Q8—22no—
361C5×Q8—62no—
362C2×C4×C5—31no—
363C2×C4×C5—31no—
364C2×C4×C5—32no—
365C2×C4×C5C2×C4×D312yes—
366C2×C4×C5C2×C4×D311yescharacteristic
367C2×Dic5—31no—
368C2×Dic5—31no—
369C2×Dic5—32no—
370C2×Dic5C2×C4×D312yes—
371C2×Dic5C2×C4×D311yescharacteristic
372C4×D5—22no—
373C4×D5—22no—
374C4×D5—32no—
375C4×D5—32no—
376C4×D5—62no—
377C4×D5—62no—
378C4×D5—61no—
379C4×D5—61no—
380C4×D5D3×D412yes—
381C4×D5#23712yes—
382Dic10—22no—
383Dic10—24no—
384Dic10—62no—
385Dic10—64no—
386C22×Q8—51no—
387C22×Q8—151no—
388C4⋊Q8—31no—
389C4⋊Q8—151no—
390C4⋊Q8—152no—
391C4⋊Q8—152no—
392C4⋊Q8—151no—
393C4⋊Q8—151no—
394C4×Q8—304no—
395C4×Q8—304no—
396C2×C4⋊C4—51no—
397C2×C4⋊C4—152no—
398C2×C4⋊C4—152no—
399C2×C4⋊C4—151no—
400C2×C4⋊C4—151no—
401C2×C4⋊C4—152no—
402C2×C4⋊C4—152no—
403C2×C4⋊C4—151no—
404C2×C42—51no—
405C2×C42—151no—
406C2×C42—152no—
407C2×C42—152no—
408C2×C42—151no—
409C2×C42—152no—
410#95—52no—
411#95—52no—
412#95—151no—
413#95—152no—
414#95—151no—
415#95—152no—
416#95—152no—
417C2×C3×C5C2×C4×D411yescharacteristic
418C2×C3×C5C2×C4×Q811yescharacteristic
419C2×C3×C5#51911yescharacteristic
420C3×D5#54711yescharacteristic
421C3×D5D4×Q811yescharacteristic
422C3×D5#55611yescharacteristic
423C3×D5#55711yescharacteristic
424C23×C3—51no—
425C3×Q8—22no—
426C3×Q8—104no—
427C3×Q8—102no—
428C2×C3×C4—51no—
429C2×C3×C4—52no—
430C2×C3×C4—52no—
431C2×C3×C4—52no—
432C2×C3×C4—52no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—101no—
436C2×C3×C4—101no—
437C2×C3×C4—102no—
438C2×C3×C4—101no—
439C2×C3×C4—101no—
440C2×C3×C4—102no—
441C2×C3×C4—101no—
442C2×C3×C4—102no—
443C2×C3×C4C22×AGL(1,𝔽5)12yes—
444C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
445C2×Dic3—51no—
446C2×Dic3—52no—
447C2×Dic3—52no—
448C2×Dic3—54no—
449C2×Dic3—52no—
450C2×Dic3—51no—
451C2×Dic3—52no—
452C2×Dic3—102no—
453C2×Dic3—102no—
454C2×Dic3—101no—
455C2×Dic3—101no—
456C2×Dic3—101no—
457C2×Dic3—102no—
458C2×Dic3—102no—
459C2×Dic3—101no—
460C2×Dic3—101no—
461C2×Dic3—101no—
462C2×Dic3—101no—
463C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
464C2×Dic3C22×AGL(1,𝔽5)12yes—
465C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
466Dic6—22no—
467Dic6—104no—
468Dic6—102no—
469C22×C5C22×C4×D311yescharacteristic
470C2×D5C2×D3×D411yescharacteristic
471C2×D5C2×#23711yescharacteristic
472C2×D5C2×D3×Q811yescharacteristic
473C2×D5#100711yescharacteristic
474C2×D5D3×#4111yescharacteristic
475C2×D5#101011yescharacteristic
476AGL(1,𝔽5)—22no—
477AGL(1,𝔽5)—42no—
478AGL(1,𝔽5)—41no—
479AGL(1,𝔽5)—62no—
480AGL(1,𝔽5)—64no—
481AGL(1,𝔽5)—121no—
482C4×C5—22no—
483C4×C5—32no—
484C4×C5—62no—
485C4×C5—61no—
486C4×C5#67⋊C412yes—
487Dic5—22no—
488Dic5—32no—
489Dic5—62no—
490Dic5—61no—
491Dic5#67⋊C412yes—
492C2×Q8—31no—
493C2×Q8—52no—
494C2×Q8—51no—
495C2×Q8—102no—
496C2×Q8—102no—
497C2×Q8—152no—
498C2×Q8—151no—
499C2×Q8—302no—
500C2×Q8—302no—
501C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
502C22×C4—51no—
503C22×C4—51no—
504C22×C4—52no—
505C22×C4—52no—
506C22×C4—51no—
507C22×C4—151no—
508C22×C4—151no—
509C22×C4—152no—
510C22×C4—151no—
511C22×C4—152no—
512C22×C4—151no—
513C4⋊C4—32no—
514C4⋊C4—32no—
515C4⋊C4—102no—
516C4⋊C4—152no—
517C4⋊C4—152no—
518C4⋊C4—152no—
519C4⋊C4—152no—
520C4⋊C4—154no—
521C4⋊C4—154no—
522C4⋊C4—152no—
523C4⋊C4—152no—
524C4⋊C4—304no—
525C4⋊C4—304no—
526C4⋊C4—302no—
527C42—31no—
528C42—102no—
529C42—151no—
530C42—151no—
531C42—151no—
532C42—302no—
533C42—304no—
534C42—304no—
535C42—304no—
536C3×C5#236511yescharacteristic, complemented, Hall
537C22×C3—51no—
538C22×C3—51no—
539C22×C3—51no—
540C22×C3—51no—
541C22×C3—51no—
542C22×C3—51no—
543C22×C3C23×AGL(1,𝔽5)11yescharacteristic
544C3×C4—22no—
545C3×C4—52no—
546C3×C4—102no—
547C3×C4—102no—
548C3×C4—201no—
549C3×C4—202no—
550C3×C4D4×AGL(1,𝔽5)12yes—
551Dic3—22no—
552Dic3—21no—
553Dic3—52no—
554Dic3—104no—
555Dic3—102no—
556Dic3—102no—
557Dic3—101no—
558Dic3—201no—
559Dic3Q8×AGL(1,𝔽5)12yescomplemented
560C2×C5C2×#67⋊C411yescharacteristic
561C2×C5C4×D3×Q811yescharacteristic
562C2×C5#557211yescharacteristic
563D5#563111yescharacteristic
564D5#563211yescharacteristic
565D5#567111yescharacteristic
566D5#572111yescharacteristic
567C23—51no—
568Q8—22no—
569Q8—62no—
570Q8—104no—
571Q8—102no—
572Q8—304no—
573Q8—302no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—32no—
577C2×C4—51no—
578C2×C4—52no—
579C2×C4—52no—
580C2×C4—52no—
581C2×C4—52no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—101no—
585C2×C4—101no—
586C2×C4—101no—
587C2×C4—102no—
588C2×C4—102no—
589C2×C4—101no—
590C2×C4—102no—
591C2×C4—101no—
592C2×C4—152no—
593C2×C4—152no—
594C2×C4—151no—
595C2×C4—154no—
596C2×C4—152no—
597C2×C4—151no—
598C2×C4—152no—
599C2×C4—302no—
600C2×C4—302no—
601C2×C4—301no—
602C2×C4—301no—
603C2×C4—301no—
604C2×C4—302no—
605C2×C4—301no—
606C2×C4—302no—
607C2×C4—301no—
608C2×C4—301no—
609C2×C4—301no—
610C2×C4C2×D3×AGL(1,𝔽5)12yes—
611C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
612C2×C3—51no—
613C2×C3—51no—
614C2×C3—51no—
615C2×C3—51no—
616C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
617C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
618C2×C3#6626211yescharacteristic
619C5#7649211yescharacteristic, complemented, Sylow
620C22—51no—
621C22—51no—
622C22—51no—
623C22—51no—
624C22—51no—
625C22—51no—
626C22C22×D3×AGL(1,𝔽5)11yescharacteristic
627C4—22no—
628C4—32no—
629C4—52no—
630C4—61no—
631C4—62no—
632C4—102no—
633C4—102no—
634C4—152no—
635C4—202no—
636C4—201no—
637C4—302no—
638C4—304no—
639C4—301no—
640C4—302no—
641C4—601no—
642C4#67⋊AGL(1,𝔽5)12yes—
643C3#1061738811yescharacteristic, complemented, Sylow
644C2—51no—
645C2—51no—
646C2—51no—
647C2—51no—
648C2#1175684711yescharacteristic
649C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
650C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×Q8C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2365
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
28. #91833C4semidirect
29. C5×#944C4semidirect
33. #91389C4semidirect
34. #91385C4semidirect
35. #91327C4semidirect
36. #91327C4semidirect
85. Dic3⋊AGL(1,𝔽5)Q8semidirect
198. #944AGL(1,𝔽5)semidirect
291. Dic15C4×Q8semidirect
296. C5×Dic3C4×Q8semidirect
536. C3×C5#2365semidirect
559. Dic3Q8×AGL(1,𝔽5)semidirect
619. C5#76492semidirect
643. C3#10617388semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×ΓL(1,𝔽16)2
C2×AGL(1,𝔽5)×Dic62
D5×#9442
C3×(C2×AGL(1,𝔽5))⋊Q82
C4×Dic3⋊AGL(1,𝔽5)2
#117518452
#117518442
Dic3×C4⋊AGL(1,𝔽5)2
#117518332
#117517522
#117517472
#106173883
#764925