Finite Group Databasebeta

← #14327766

Subgroups — #14327766

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91923C212yesmaximal, complemented
2D4×D5×Dic3C211yesmaximal, characteristic
3#11752439C211yesmaximal, characteristic
4C3×#65780C211yesmaximal, characteristic
5#11752028C212yesmaximal, complemented
6#11752018C212yesmaximal, complemented
7#11752017C212yesmaximal, complemented
8#11751860C211yesmaximal, characteristic, complemented
9C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10#11751846C211yesmaximal, characteristic, complemented
11AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#10617181—31nomaximal, Hall
13C2×C3×D4×D5C2211yescharacteristic
14C22×D5×Dic3C2212yes—
15C2×#6763C2212yes—
16C2×#6763C2212yes—
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
19C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
20C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
21C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2212yes—
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2212yes—
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27#91923—28no—
28C2×Dic3×AGL(1,𝔽5)C2212yes—
29C2×Dic3×AGL(1,𝔽5)C2212yes—
30D4×Dic15C411yescharacteristic, complemented
31C5×D4×Dic3C411yescharacteristic, complemented
32#91559C412yescomplemented
33Dic3×C22⋊D5C412yescomplemented
34D5×#217C2212yes—
35#91434C411yescharacteristic, complemented
36Dic3×D20C411yescharacteristic, complemented
37D5×C4⋊Dic3C2211yescharacteristic
38C4×D5×Dic3C2211yescharacteristic
39(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43#76302—51nomaximal, Hall
44C2×#4130—32no—
45C4×D4×D5—31no—
46#65780—31no—
47#65780D311yescharacteristic
48#65765—32no—
49C4⋊C4×AGL(1,𝔽5)—31no—
50C4⋊C4×AGL(1,𝔽5)—31no—
51#65700—32no—
52#65700—32no—
53#65688—31no—
54C4×C4⋊AGL(1,𝔽5)—31no—
55C23×C3×D5C2312yes—
56C22×ΓL(1,𝔽16)C2312yes—
57C22×ΓL(1,𝔽16)C2311yescharacteristic
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×D4C2×C411yescharacteristic
63C22×Dic15C2×C412yes—
64C22×C5×Dic3C2×C412yes—
65C2×C3×C22⋊D5C2×C412yes—
66C3×D4×D5—22no—
67C3×D4×D5—22no—
68C2×C3×D20C2×C411yescharacteristic
69C2×C3×C4×D5C2311yescharacteristic
70C2×D5×Dic3—24no—
71C2×D5×Dic3—24no—
72C2×D5×Dic3C2×C412yes—
73C2×D5×Dic3C2×C412yes—
74C2×D5×Dic3C2312yes—
75C2×D5×Dic3C2311yescharacteristic
76C2×D5×Dic3C2311yescharacteristic
77#6763—24no—
78#6763—42no—
79C4⋊ΓL(1,𝔽16)—22no—
80C4×ΓL(1,𝔽16)—22no—
81C3×C22⋊AGL(1,𝔽5)—24no—
82C3×C22⋊AGL(1,𝔽5)—42no—
83C3×C4⋊AGL(1,𝔽5)—22no—
84C3×C4×AGL(1,𝔽5)—22no—
85Dic3⋊AGL(1,𝔽5)—24no—
86Dic3⋊AGL(1,𝔽5)—22no—
87Dic3⋊AGL(1,𝔽5)—42no—
88Dic3⋊AGL(1,𝔽5)D414yescomplemented
89Dic3×AGL(1,𝔽5)—24no—
90Dic3×AGL(1,𝔽5)—24no—
91#6719C2×C412yes—
92C4⋊Dic15C2×C411yescharacteristic
93C4×Dic15C2×C411yescharacteristic
94C5×#217C2×C412yes—
95C5×C4⋊Dic3C2×C411yescharacteristic
96C4×C5×Dic3C2×C411yescharacteristic
97#6668C2×C412yes—
98#6665C2×C412yes—
99#6665C2×C412yes—
100Dic3×Dic5C2×C411yescharacteristic
101Dic3×Dic5C2×C411yescharacteristic
102C2×D4×Dic3—51no—
103C2×#877—52no—
104C3×#390—51no—
105#5221—51no—
106#4975—51no—
107Dic3×C4⋊C4—51no—
108#4945—52no—
109#4944—52no—
110#4942—52no—
111C4×C4⋊Dic3—51no—
112C4×Dic3⋊C4—51no—
113C2×D4×D5C2×D311yescharacteristic
114C22×C4×D5—32no—
115C2×C22⋊AGL(1,𝔽5)—32no—
116C2×C22⋊AGL(1,𝔽5)—32no—
117C2×C22⋊AGL(1,𝔽5)C2×D312yes—
118C2×C22⋊AGL(1,𝔽5)C2×D312yes—
119#4130—68no—
120C2×C4⋊AGL(1,𝔽5)—31no—
121C2×C4⋊AGL(1,𝔽5)—31no—
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
126C2×C4×AGL(1,𝔽5)—32no—
127C2×C4×AGL(1,𝔽5)—32no—
128C2×C4×AGL(1,𝔽5)—31no—
129C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
130C4×C5×D4—31no—
131D4×Dic5—31no—
132C4×C22⋊D5—32no—
133#4039—31no—
134D5×C4⋊C4—31no—
135#4027—32no—
136D5×C22⋊C4—32no—
137C4×D20—31no—
138C42×D5—31no—
139(C2×AGL(1,𝔽5))⋊C4—31no—
140(C2×AGL(1,𝔽5))⋊C4—31no—
141(C2×AGL(1,𝔽5))⋊C4—32no—
142(C2×AGL(1,𝔽5))⋊C4—32no—
143#2354—151noSylow
144C23×C3×C5C22×C412yes—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5C22×C412yes—
152C22×C3×D5C2411yescharacteristic
153C2×ΓL(1,𝔽16)—21no—
154C2×ΓL(1,𝔽16)—21no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—21no—
157C2×ΓL(1,𝔽16)—21no—
158C2×ΓL(1,𝔽16)—22no—
159C2×ΓL(1,𝔽16)—22no—
160C2×ΓL(1,𝔽16)—21no—
161C2×ΓL(1,𝔽16)C2×D412yes—
162C2×C3×AGL(1,𝔽5)—21no—
163C2×C3×AGL(1,𝔽5)—21no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—21no—
166C2×C3×AGL(1,𝔽5)—21no—
167C2×C3×AGL(1,𝔽5)—22no—
168C2×C3×AGL(1,𝔽5)—22no—
169C2×C3×AGL(1,𝔽5)—21no—
170C2×C3×AGL(1,𝔽5)C2×D412yes—
171C3×C5×D4—22no—
172C2×C3×C4×C5C22×C411yescharacteristic
173C2×Dic15—24no—
174C2×Dic15C22×C411yescharacteristic
175C2×Dic15C22×C412yes—
176C2×Dic15C22×C411yescharacteristic
177C2×C5×Dic3—24no—
178C2×C5×Dic3C22×C411yescharacteristic
179C2×C5×Dic3C22×C412yes—
180C2×C5×Dic3C22×C411yescharacteristic
181C3×C22⋊D5—24no—
182C2×C3×Dic5C22×C411yescharacteristic
183C3×D20—22no—
184C3×C4×D5#4112yes—
185C3×C4×D5#4112yes—
186D5×Dic3—22no—
187D5×Dic3—22no—
188D5×Dic3—21no—
189D5×Dic3—21no—
190D5×Dic3—24no—
191D5×Dic3—24no—
192D5×Dic3C2×D412yes—
193D5×Dic3#4112yes—
194C22×C3×D4—51no—
195C23×Dic3—52no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C42—51no—
200C2×#217—52no—
201C2×#217—52no—
202C2×#217—52no—
203D4×Dic3—51no—
204D4×Dic3—52no—
205D4×Dic3—52no—
206D4×Dic3—51no—
207D4×Dic3—51no—
208D4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
209C2×C4⋊Dic3—51no—
210C2×C4⋊Dic3—51no—
211C2×Dic3⋊C4—51no—
212C2×Dic3⋊C4—51no—
213C2×Dic3⋊C4—52no—
214C2×Dic3⋊C4—52no—
215C2×C4×Dic3—51no—
216C2×C4×Dic3—52no—
217C2×C4×Dic3—52no—
218C2×C4×Dic3—51no—
219#877—108no—
220C3⋊#95—51no—
221C3⋊#95—51no—
222C3⋊#95—52no—
223C3⋊#95—52no—
224C23×D5C22×D312yes—
225C22×AGL(1,𝔽5)—31no—
226C22×AGL(1,𝔽5)—32no—
227C22×AGL(1,𝔽5)—31no—
228C22×AGL(1,𝔽5)C22×D312yes—
229C22×AGL(1,𝔽5)C22×D311yescharacteristic
230C22×AGL(1,𝔽5)C22×D311yescharacteristic
231C2×C5×D4C4×D311yescharacteristic
232C22×C4×C5—32no—
233C2×C22⋊D5C4×D312yes—
234C22×Dic5—32no—
235D4×D5—22no—
236D4×D5—22no—
237C2×D20C4×D311yescharacteristic
238C2×C4×D5—31no—
239C2×C4×D5—32no—
240C2×C4×D5—32no—
241C2×C4×D5—32no—
242C2×C4×D5—31no—
243C2×C4×D5—64no—
244C2×C4×D5—64no—
245C2×C4×D5C22×D311yescharacteristic
246C22⋊AGL(1,𝔽5)—24no—
247C22⋊AGL(1,𝔽5)—42no—
248C22⋊AGL(1,𝔽5)—64no—
249C22⋊AGL(1,𝔽5)—122no—
250C4⋊AGL(1,𝔽5)—22no—
251C4⋊AGL(1,𝔽5)—34no—
252C4⋊AGL(1,𝔽5)—64no—
253C4⋊AGL(1,𝔽5)—62no—
254C4⋊AGL(1,𝔽5)—62no—
255C4⋊AGL(1,𝔽5)—122no—
256C4×AGL(1,𝔽5)—22no—
257C4×AGL(1,𝔽5)—64no—
258C4×AGL(1,𝔽5)—64no—
259C4×AGL(1,𝔽5)—62no—
260C5×C4⋊C4—31no—
261C5×C22⋊C4—32no—
262C42×C5—31no—
263C22⋊Dic5—32no—
264#685—32no—
265#685—32no—
266C4⋊Dic5—31no—
267#683—32no—
268C4×Dic5—31no—
269C4×Dic5—31no—
270C4×Dic5—31no—
271C2×C4×D4—151no—
272C2×#117—152no—
273#390—51no—
274#390—151no—
275#388—152no—
276#388—152no—
277#384—151no—
278#380—152no—
279C4×C4⋊C4—151no—
280C4×C4⋊C4—151no—
281C4×C4⋊C4—151no—
282C22×C3×C5—22no—
283C22×C3×C5—22no—
284C22×C3×C5—22no—
285C22×C3×C5C23×C411yescharacteristic
286C2×C3×D5—22no—
287C2×C3×D5—22no—
288C2×C3×D5—22no—
289C2×C3×D5—42no—
290C2×C3×D5—42no—
291C2×C3×D5—42no—
292C2×C3×D5—42no—
293C2×C3×D5C22×D411yescharacteristic
294C2×C3×D5C2×#4111yescharacteristic
295C2×C3×D5C2×#4111yescharacteristic
296C2×C3×D5C2×#4111yescharacteristic
297C2×C3×D5H(5,𝔽2)11yescharacteristic
298C2×C3×D52−1+411yescharacteristic
299ΓL(1,𝔽16)—22no—
300ΓL(1,𝔽16)—42no—
301ΓL(1,𝔽16)—41no—
302C3×AGL(1,𝔽5)—22no—
303C3×AGL(1,𝔽5)—42no—
304C3×AGL(1,𝔽5)—41no—
305C3×C4×C5#11712yescomplemented
306Dic15—22no—
307Dic15—21no—
308Dic15C4×D412yes—
309C3×Dic5#11712yescomplemented
310C5×Dic3—22no—
311C5×Dic3—21no—
312C5×Dic3C4×D412yes—
313C24×C3—52no—
314C2×C3×D4—52no—
315C2×C3×D4—51no—
316C2×C3×D4—102no—
317C2×C3×D4—102no—
318C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
319C22×C3×C4—51no—
320C22×C3×C4—51no—
321C22×C3×C4—51no—
322C22×C3×C4—52no—
323C22×Dic3—51no—
324C22×Dic3—51no—
325C22×Dic3—52no—
326C22×Dic3—52no—
327C22×Dic3—51no—
328C22×Dic3—52no—
329C22×Dic3—52no—
330C22×Dic3—51no—
331C22×Dic3—52no—
332C22×Dic3—104no—
333C22×Dic3—104no—
334C22×Dic3C2×AGL(1,𝔽5)12yes—
335C3×C4⋊C4—102no—
336C3×C22⋊C4—104no—
337C3×C22⋊C4—202no—
338C3×C42—102no—
339#217—52no—
340#217—52no—
341#217—52no—
342#217—104no—
343#217—202no—
344#217C2×AGL(1,𝔽5)12yes—
345C4⋊Dic3—51no—
346C4⋊Dic3—52no—
347C4⋊Dic3—102no—
348C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
349Dic3⋊C4—54no—
350Dic3⋊C4—104no—
351Dic3⋊C4—102no—
352Dic3⋊C4—202no—
353C4×Dic3—51no—
354C4×Dic3—51no—
355C4×Dic3—51no—
356C4×Dic3—104no—
357C4×Dic3—104no—
358C4×Dic3—102no—
359C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
360C23×C5C2×C4×D312yes—
361C22×D5—22no—
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5C2×C4×D312yes—
368C22×D5C23×D311yescharacteristic
369C2×AGL(1,𝔽5)—21no—
370C2×AGL(1,𝔽5)—21no—
371C2×AGL(1,𝔽5)—22no—
372C2×AGL(1,𝔽5)—21no—
373C2×AGL(1,𝔽5)—22no—
374C2×AGL(1,𝔽5)—22no—
375C2×AGL(1,𝔽5)—21no—
376C2×AGL(1,𝔽5)—21no—
377C2×AGL(1,𝔽5)—32no—
378C2×AGL(1,𝔽5)—61no—
379C2×AGL(1,𝔽5)—61no—
380C2×AGL(1,𝔽5)—62no—
381C2×AGL(1,𝔽5)—61no—
382C2×AGL(1,𝔽5)—62no—
383C2×AGL(1,𝔽5)—62no—
384C2×AGL(1,𝔽5)—61no—
385C2×AGL(1,𝔽5)—61no—
386C2×AGL(1,𝔽5)D3×D412yes—
387C5×D4—22no—
388C2×C4×C5—31no—
389C2×C4×C5—31no—
390C2×C4×C5—32no—
391C2×C4×C5—64no—
392C2×C4×C5C2×C4×D311yescharacteristic
393C22⋊D5—24no—
394C2×Dic5—31no—
395C2×Dic5—31no—
396C2×Dic5—32no—
397C2×Dic5—64no—
398C2×Dic5C2×C4×D311yescharacteristic
399D20—22no—
400C4×D5—32no—
401C4×D5—32no—
402C4×D5—64no—
403C4×D5—64no—
404C4×D5—62no—
405C4×D5—61no—
406C4×D5—62no—
407C4×D5—61no—
408C4×D5#23712yes—
409C4×D5#23712yes—
410C22×D4—51no—
411C23×C4—152no—
412C4×D4—31no—
413C4×D4—151no—
414C4×D4—152no—
415C4×D4—151no—
416C4×D4—152no—
417C4×D4—151no—
418#117—308no—
419C2×C4⋊C4—51no—
420C2×C4⋊C4—151no—
421C2×C4⋊C4—151no—
422C2×C4⋊C4—152no—
423C2×C4⋊C4—151no—
424C2×C4⋊C4—151no—
425C2×C4⋊C4—152no—
426C2×C22⋊C4—52no—
427C2×C22⋊C4—52no—
428C2×C22⋊C4—152no—
429C2×C22⋊C4—152no—
430C2×C22⋊C4—152no—
431C2×C42—51no—
432C2×C42—151no—
433C2×C42—152no—
434C2×C42—152no—
435C2×C42—151no—
436#95—152no—
437#95—152no—
438#95—151no—
439#95—151no—
440C2×C3×C5—42no—
441C2×C3×C5C2×#11711yescharacteristic
442C2×C3×C5C2×C4×D411yescharacteristic
443C2×C3×C5#52011yescharacteristic
444C3×D5—42no—
445C3×D5#54711yescharacteristic
446C3×D5#55011yescharacteristic
447C3×D5#55511yescharacteristic
448C3×D5#55611yescharacteristic
449C23×C3—51no—
450C23×C3—52no—
451C23×C3—102no—
452C23×C3—102no—
453C23×C3—102no—
454C23×C3—102no—
455C23×C3—102no—
456C23×C3—102no—
457C23×C3C22×AGL(1,𝔽5)12yes—
458C3×D4—22no—
459C3×D4—104no—
460C3×D4—102no—
461C2×C3×C4—51no—
462C2×C3×C4—52no—
463C2×C3×C4—52no—
464C2×C3×C4—52no—
465C2×C3×C4—101no—
466C2×C3×C4—101no—
467C2×C3×C4—102no—
468C2×C3×C4—101no—
469C2×C3×C4—102no—
470C2×C3×C4—101no—
471C2×C3×C4—101no—
472C2×C3×C4—102no—
473C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
474C2×Dic3—24no—
475C2×Dic3—51no—
476C2×Dic3—52no—
477C2×Dic3—52no—
478C2×Dic3—52no—
479C2×Dic3—51no—
480C2×Dic3—52no—
481C2×Dic3—104no—
482C2×Dic3—102no—
483C2×Dic3—101no—
484C2×Dic3—101no—
485C2×Dic3—102no—
486C2×Dic3—104no—
487C2×Dic3—101no—
488C2×Dic3—101no—
489C2×Dic3—104no—
490C2×Dic3—102no—
491C2×Dic3—101no—
492C2×Dic3—101no—
493C2×Dic3—102no—
494C2×Dic3—102no—
495C2×Dic3—101no—
496C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
497C2×Dic3C22×AGL(1,𝔽5)12yes—
498C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
499C22×C5—22no—
500C22×C5—22no—
501C22×C5—22no—
502C22×C5C22×C4×D311yescharacteristic
503C2×D5—22no—
504C2×D5—22no—
505C2×D5—22no—
506C2×D5—42no—
507C2×D5—42no—
508C2×D5—42no—
509C2×D5—42no—
510C2×D5C2×D3×D411yescharacteristic
511C2×D5C2×#23711yescharacteristic
512C2×D5C2×#23711yescharacteristic
513C2×D5#100411yescharacteristic
514C2×D5D3×#4111yescharacteristic
515C2×D5#101011yescharacteristic
516AGL(1,𝔽5)—22no—
517AGL(1,𝔽5)—42no—
518AGL(1,𝔽5)—41no—
519AGL(1,𝔽5)—62no—
520AGL(1,𝔽5)—122no—
521AGL(1,𝔽5)—121no—
522C4×C5—32no—
523C4×C5—62no—
524C4×C5—61no—
525C4×C5#87712yescomplemented
526Dic5—32no—
527Dic5—62no—
528Dic5—61no—
529Dic5#87712yescomplemented
530C24—52no—
531C2×D4—52no—
532C2×D4—51no—
533C2×D4—102no—
534C2×D4—102no—
535C2×D4D3×AGL(1,𝔽5)11yescharacteristic
536C22×C4—32no—
537C22×C4—51no—
538C22×C4—51no—
539C22×C4—51no—
540C22×C4—52no—
541C22×C4—151no—
542C22×C4—152no—
543C22×C4—151no—
544C22×C4—152no—
545C22×C4—152no—
546C22×C4—151no—
547C22×C4—152no—
548C22×C4—151no—
549C22×C4—152no—
550C22×C4—304no—
551C22×C4—304no—
552C4⋊C4—31no—
553C4⋊C4—102no—
554C4⋊C4—152no—
555C4⋊C4—154no—
556C4⋊C4—151no—
557C4⋊C4—302no—
558C4⋊C4—304no—
559C4⋊C4—302no—
560C4⋊C4—602no—
561C22⋊C4—32no—
562C22⋊C4—104no—
563C22⋊C4—152no—
564C22⋊C4—152no—
565C22⋊C4—152no—
566C22⋊C4—202no—
567C22⋊C4—304no—
568C22⋊C4—602no—
569C42—31no—
570C42—102no—
571C42—151no—
572C42—151no—
573C42—151no—
574C42—304no—
575C42—302no—
576C42—304no—
577C3×C5#235411yescharacteristic, complemented, Hall
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—51no—
582C22×C3—51no—
583C22×C3—51no—
584C22×C3—51no—
585C22×C3—51no—
586C22×C3—51no—
587C22×C3—102no—
588C22×C3—102no—
589C22×C3—102no—
590C22×C3—202no—
591C22×C3—202no—
592C22×C3—202no—
593C22×C3—202no—
594C22×C3C23×AGL(1,𝔽5)11yescharacteristic
595C3×C4—52no—
596C3×C4—102no—
597C3×C4—202no—
598C3×C4—201no—
599C3×C4#413012yescomplemented
600Dic3—22no—
601Dic3—21no—
602Dic3—52no—
603Dic3—102no—
604Dic3—102no—
605Dic3—101no—
606Dic3—202no—
607Dic3—201no—
608Dic3D4×AGL(1,𝔽5)12yes—
609C2×C5—42no—
610C2×C5C2×#87711yescharacteristic
611C2×C5C4×D3×D411yescharacteristic
612C2×C5#554611yescharacteristic
613D5—42no—
614D5#561111yescharacteristic
615D5#561611yescharacteristic
616D5#567111yescharacteristic
617D5#571811yescharacteristic
618C23—51no—
619C23—52no—
620C23—102no—
621C23—102no—
622C23—102no—
623C23—102no—
624C23—102no—
625C23—102no—
626C23C2×D3×AGL(1,𝔽5)12yes—
627D4—22no—
628D4—104no—
629D4—102no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—32no—
633C2×C4—51no—
634C2×C4—52no—
635C2×C4—52no—
636C2×C4—52no—
637C2×C4—64no—
638C2×C4—101no—
639C2×C4—101no—
640C2×C4—101no—
641C2×C4—102no—
642C2×C4—101no—
643C2×C4—102no—
644C2×C4—102no—
645C2×C4—101no—
646C2×C4—152no—
647C2×C4—152no—
648C2×C4—151no—
649C2×C4—152no—
650C2×C4—151no—
651C2×C4—152no—
652C2×C4—304no—
653C2×C4—304no—
654C2×C4—302no—
655C2×C4—301no—
656C2×C4—302no—
657C2×C4—301no—
658C2×C4—304no—
659C2×C4—301no—
660C2×C4—301no—
661C2×C4—302no—
662C2×C4—301no—
663C2×C4—301no—
664C2×C4—302no—
665C2×C4—301no—
666C2×C4—302no—
667C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
668C2×C3—42no—
669C2×C3—51no—
670C2×C3—51no—
671C2×C3—51no—
672C2×C3—51no—
673C2×C3—202no—
674C2×C3C2×#413011yescharacteristic
675C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
676C2×C3#6626611yescharacteristic
677C5#7630211yescharacteristic, complemented, Sylow
678C22—22no—
679C22—22no—
680C22—22no—
681C22—51no—
682C22—51no—
683C22—51no—
684C22—51no—
685C22—51no—
686C22—51no—
687C22—102no—
688C22—102no—
689C22—102no—
690C22—202no—
691C22—202no—
692C22—202no—
693C22—202no—
694C22C22×D3×AGL(1,𝔽5)11yescharacteristic
695C4—32no—
696C4—52no—
697C4—62no—
698C4—61no—
699C4—102no—
700C4—152no—
701C4—202no—
702C4—201no—
703C4—302no—
704C4—302no—
705C4—301no—
706C4—602no—
707C4—601no—
708C4#9192312yescomplemented
709C3#1061718111yescharacteristic, complemented, Sylow
710C2—42no—
711C2—51no—
712C2—51no—
713C2—51no—
714C2—51no—
715C2—202no—
716C2D3×D4×AGL(1,𝔽5)11yescharacteristic
717C2#1175684611yescharacteristic
718C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91923C2semidirect
5. #11752028C2semidirect
6. #11752018C2semidirect
7. #11752017C2semidirect
8. #11751860C2semidirect
9. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
10. #11751846C2semidirect
11. AGL(1,𝔽5)×C4⋊Dic3C2semidirect
30. D4×Dic15C4semidirect
31. C5×D4×Dic3C4semidirect
32. #91559C4semidirect
33. Dic3×C22⋊D5C4semidirect
35. #91434C4semidirect
36. Dic3×D20C4semidirect
88. Dic3⋊AGL(1,𝔽5)D4semidirect
208. D4×Dic3AGL(1,𝔽5)semidirect
305. C3×C4×C5#117semidirect
309. C3×Dic5#117semidirect
525. C4×C5#877semidirect
529. Dic5#877semidirect
577. C3×C5#2354semidirect
599. C3×C4#4130semidirect
677. C5#76302semidirect
708. C4#91923semidirect
709. C3#10617181semidirect

Maximal subgroups

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

subgroupindex
C2×#919232
D4×D5×Dic32
#117524392
C3×#657802
#117520282
#117520182
#117520172
#117518602
C4×Dic3⋊AGL(1,𝔽5)2
#117518462
AGL(1,𝔽5)×C4⋊Dic32
#106171813
#763025