Finite Group Databasebeta

← C2×C3×#65699 #14320226

Subgroups — C2×C3×#65699 #14320226

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×AGL(1,𝔽5)C211yesmaximal, characteristic
2C22×C3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C22×C3×C4⋊AGL(1,𝔽5)C212yesmaximal, complemented
4C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
5C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal, complemented
6C3×#65699C218yesmaximal, direct product factor
7C2×#65699C311yesmaximal, characteristic, direct product factor, Hall
8C24×C3×D5C2211yescharacteristic
9C23×C3×AGL(1,𝔽5)—24no—
10C23×C3×AGL(1,𝔽5)—28no—
11C23×C3×AGL(1,𝔽5)C2214yes—
12C23×C3×AGL(1,𝔽5)C2211yescharacteristic
13C23×C3×AGL(1,𝔽5)C2211yescharacteristic
14C23×C3×AGL(1,𝔽5)C2212yes—
15C22×C3×C4×D5C2212yes—
16C2×C3×C22⋊AGL(1,𝔽5)—24no—
17C2×C3×C22⋊AGL(1,𝔽5)C2214yes—
18C2×C3×C4⋊AGL(1,𝔽5)—28no—
19C2×C3×C4⋊AGL(1,𝔽5)C2218yescomplemented
20C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
21C2×C3×C22⋊Dic5C411yescharacteristic, complemented
22C2×C3×#685C412yescomplemented
23C3×D5×C22⋊C4C414yescomplemented
24C3×D5×C22⋊C4C2214yes—
25C3×(C2×AGL(1,𝔽5))⋊C4C2218yescomplemented
26C2×C3×#385—51nomaximal, Hall
27C24×AGL(1,𝔽5)C2×C311yescharacteristic
28C22×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic
29C22×C4⋊AGL(1,𝔽5)C2×C312yescomplemented
30C2×D5×C22⋊C4C2×C311yescharacteristic
31C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yescomplemented
32#65699C2×C318yesdirect product factor
33C24×C3×C5C2×C411yescharacteristic
34C23×C3×D5—24no—
35C23×C3×D5—24no—
36C23×C3×D5C2×C412yes—
37C23×C3×D5C2×C411yescharacteristic
38C23×C3×D5D414yes—
39C23×C3×D5Q814yes—
40C23×C3×D5C2312yes—
41C23×C3×D5C2311yescharacteristic
42C22×C3×AGL(1,𝔽5)—232no—
43C22×C3×AGL(1,𝔽5)—28no—
44C22×C3×AGL(1,𝔽5)—24no—
45C22×C3×AGL(1,𝔽5)—24no—
46C22×C3×AGL(1,𝔽5)—216no—
47C22×C3×AGL(1,𝔽5)—24no—
48C22×C3×AGL(1,𝔽5)—22no—
49C22×C3×AGL(1,𝔽5)—22no—
50C22×C3×AGL(1,𝔽5)—24no—
51C22×C3×AGL(1,𝔽5)D418yes—
52C22×C3×AGL(1,𝔽5)C2312yes—
53C22×C3×AGL(1,𝔽5)C2312yes—
54C22×C3×AGL(1,𝔽5)C2314yes—
55C22×C3×C4×C5C2×C412yescomplemented
56C22×C3×Dic5C2×C412yescomplemented
57C2×C3×C4×D5—24no—
58C2×C3×C4×D5—24no—
59C2×C3×C4×D5C2×C414yescomplemented
60C2×C3×C4×D5C2314yes—
61C3×C22⋊AGL(1,𝔽5)—28no—
62C3×C4⋊AGL(1,𝔽5)—216no—
63C3×C5×C22⋊C4C2×C414yescomplemented
64C3×C22⋊Dic5C2×C414yescomplemented
65C3×#685C2×C418yescomplemented
66C24×C3×C4—51no—
67C22×C3×C4⋊C4—52no—
68C22×C3×C22⋊C4—51no—
69C22×C3×C22⋊C4—51no—
70C3×#385—58no—
71C2×C3×#95—52no—
72C24×D5C22×C311yescharacteristic
73C23×AGL(1,𝔽5)—24no—
74C23×AGL(1,𝔽5)—28no—
75C23×AGL(1,𝔽5)C22×C314yes—
76C23×AGL(1,𝔽5)C22×C311yescharacteristic
77C23×AGL(1,𝔽5)C22×C311yescharacteristic
78C23×AGL(1,𝔽5)C22×C312yes—
79C22×C4×D5C22×C312yes—
80C2×C22⋊AGL(1,𝔽5)—24no—
81C2×C22⋊AGL(1,𝔽5)C22×C314yes—
82C2×C4⋊AGL(1,𝔽5)—28no—
83C2×C4⋊AGL(1,𝔽5)C22×C318yescomplemented
84C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
85C2×C22⋊Dic5C3×C411yescharacteristic, complemented
86C2×#685C3×C412yescomplemented
87D5×C22⋊C4C3×C414yescomplemented
88D5×C22⋊C4C22×C314yes—
89(C2×AGL(1,𝔽5))⋊C4C22×C318yescomplemented
90C2×#385—51noSylow
91C23×C3×C5—24no—
92C23×C3×C5C4⋊C414yescomplemented
93C23×C3×C5C22×C412yes—
94C23×C3×C5C22×C411yescharacteristic
95C22×C3×D5—24no—
96C22×C3×D5—28no—
97C22×C3×D5—28no—
98C22×C3×D5—216no—
99C22×C3×D5—28no—
100C22×C3×D5—24no—
101C22×C3×D5—24no—
102C22×C3×D5C4⋊C418yescomplemented
103C22×C3×D5C4⋊C414yescomplemented
104C22×C3×D5C22×C412yes—
105C22×C3×D5C22×C411yescharacteristic
106C22×C3×D5C2×D414yes—
107C22×C3×D5C2×D412yes—
108C22×C3×D5C2×D414yes—
109C22×C3×D5C2×Q814yes—
110C22×C3×D5C2×Q812yes—
111C22×C3×D5#4114yes—
112C22×C3×D5C2411yescharacteristic
113C2×C3×AGL(1,𝔽5)—232no—
114C2×C3×AGL(1,𝔽5)—216no—
115C2×C3×AGL(1,𝔽5)—24no—
116C2×C3×AGL(1,𝔽5)—24no—
117C2×C3×AGL(1,𝔽5)—24no—
118C2×C3×AGL(1,𝔽5)—22no—
119C2×C3×AGL(1,𝔽5)—22no—
120C2×C3×AGL(1,𝔽5)—24no—
121C2×C3×AGL(1,𝔽5)—44no—
122C2×C3×AGL(1,𝔽5)—44no—
123C2×C3×AGL(1,𝔽5)C2×D418yes—
124C2×C3×C4×C5—24no—
125C2×C3×C4×C5C22×C414yescomplemented
126C2×C3×Dic5—24no—
127C2×C3×Dic5C22×C414yescomplemented
128C3×C4×D5—28no—
129C3×C4×D5—24no—
130C3×C4×D5—24no—
131C25×C3—51no—
132C23×C3×C4—52no—
133C23×C3×C4—52no—
134C23×C3×C4—54no—
135C23×C3×C4—51no—
136C23×C3×C4—51no—
137C23×C3×C4—108no—
138C23×C3×C4—104no—
139C2×C3×C4⋊C4—58no—
140C2×C3×C4⋊C4—108no—
141C2×C3×C22⋊C4—51no—
142C2×C3×C22⋊C4—52no—
143C2×C3×C22⋊C4—54no—
144C2×C3×C22⋊C4—54no—
145C2×C3×C22⋊C4—54no—
146C2×C3×C22⋊C4—104no—
147C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
148C3×#95—58no—
149C24×C5C2×C3×C411yescharacteristic
150C23×D5—24no—
151C23×D5—24no—
152C23×D5C2×C3×C412yes—
153C23×D5C2×C3×C411yescharacteristic
154C23×D5C3×D414yes—
155C23×D5C3×Q814yes—
156C23×D5C23×C312yes—
157C23×D5C23×C311yescharacteristic
158C22×AGL(1,𝔽5)—232no—
159C22×AGL(1,𝔽5)—28no—
160C22×AGL(1,𝔽5)—24no—
161C22×AGL(1,𝔽5)—24no—
162C22×AGL(1,𝔽5)—216no—
163C22×AGL(1,𝔽5)—24no—
164C22×AGL(1,𝔽5)—22no—
165C22×AGL(1,𝔽5)—22no—
166C22×AGL(1,𝔽5)—24no—
167C22×AGL(1,𝔽5)C3×D418yes—
168C22×AGL(1,𝔽5)C23×C312yes—
169C22×AGL(1,𝔽5)C23×C312yes—
170C22×AGL(1,𝔽5)C23×C314yes—
171C22×C4×C5C2×C3×C412yescomplemented
172C22×Dic5C2×C3×C412yescomplemented
173C2×C4×D5—24no—
174C2×C4×D5—24no—
175C2×C4×D5C2×C3×C414yescomplemented
176C2×C4×D5C23×C314yes—
177C22⋊AGL(1,𝔽5)—28no—
178C4⋊AGL(1,𝔽5)—216no—
179C5×C22⋊C4C2×C3×C414yescomplemented
180C22⋊Dic5C2×C3×C414yescomplemented
181#685C2×C3×C418yescomplemented
182C24×C4—51no—
183C22×C4⋊C4—52no—
184C22×C22⋊C4—51no—
185C22×C22⋊C4—51no—
186#385—58no—
187C2×#95—52no—
188C22×C3×C5—24no—
189C22×C3×C5—28no—
190C22×C3×C5C2×C4⋊C412yes—
191C22×C3×C5C2×C4⋊C414yescomplemented
192C22×C3×C5C4×D414yes—
193C22×C3×C5C23×C411yescharacteristic
194C2×C3×D5—24no—
195C2×C3×D5—28no—
196C2×C3×D5—24no—
197C2×C3×D5—28no—
198C2×C3×D5—24no—
199C2×C3×D5—216no—
200C2×C3×D5C2×C4⋊C412yes—
201C2×C3×D5C2×C4⋊C414yescomplemented
202C2×C3×D5C4×D414yes—
203C2×C3×D5#12014yes—
204C2×C3×D5C22⋊Q818yes—
205C2×C3×D5#12314yes—
206C2×C3×D5C22×D412yes—
207C2×C3×D5C22×D411yescharacteristic
208C2×C3×D5C22×Q811yescharacteristic
209C2×C3×D5C2×#4112yes—
210C3×AGL(1,𝔽5)—28no—
211C3×AGL(1,𝔽5)—42no—
212C3×AGL(1,𝔽5)—42no—
213C3×C4×C5—24no—
214C3×Dic5—24no—
215C24×C3—51no—
216C24×C3—54no—
217C24×C3—54no—
218C24×C3—52no—
219C24×C3—52no—
220C24×C3—51no—
221C24×C3—104no—
222C24×C3—104no—
223C24×C3C2×AGL(1,𝔽5)11yescharacteristic
224C22×C3×C4—54no—
225C22×C3×C4—58no—
226C22×C3×C4—52no—
227C22×C3×C4—54no—
228C22×C3×C4—54no—
229C22×C3×C4—52no—
230C22×C3×C4—52no—
231C22×C3×C4—104no—
232C22×C3×C4—104no—
233C22×C3×C4—1016no—
234C22×C3×C4—104no—
235C22×C3×C4—104no—
236C22×C3×C4—108no—
237C22×C3×C4—1032no—
238C22×C3×C4—102no—
239C22×C3×C4—102no—
240C22×C3×C4—104no—
241C22×C3×C4—104no—
242C22×C3×C4C2×AGL(1,𝔽5)12yescomplemented
243C3×C4⋊C4—1016no—
244C3×C22⋊C4—54no—
245C3×C22⋊C4—58no—
246C3×C22⋊C4—108no—
247C3×C22⋊C4C2×AGL(1,𝔽5)14yescomplemented
248C23×C5—24no—
249C23×C5C3×C4⋊C414yescomplemented
250C23×C5C22×C3×C412yes—
251C23×C5C22×C3×C411yescharacteristic
252C22×D5—24no—
253C22×D5—28no—
254C22×D5—28no—
255C22×D5—216no—
256C22×D5—28no—
257C22×D5—24no—
258C22×D5—24no—
259C22×D5C3×C4⋊C418yescomplemented
260C22×D5C3×C4⋊C414yescomplemented
261C22×D5C22×C3×C412yes—
262C22×D5C22×C3×C411yescharacteristic
263C22×D5C2×C3×D414yes—
264C22×D5C2×C3×D412yes—
265C22×D5C2×C3×D414yes—
266C22×D5C2×C3×Q814yes—
267C22×D5C2×C3×Q812yes—
268C22×D5C3×#4114yes—
269C22×D5C24×C311yescharacteristic
270C2×AGL(1,𝔽5)—232no—
271C2×AGL(1,𝔽5)—216no—
272C2×AGL(1,𝔽5)—24no—
273C2×AGL(1,𝔽5)—24no—
274C2×AGL(1,𝔽5)—24no—
275C2×AGL(1,𝔽5)—22no—
276C2×AGL(1,𝔽5)—22no—
277C2×AGL(1,𝔽5)—24no—
278C2×AGL(1,𝔽5)—44no—
279C2×AGL(1,𝔽5)—44no—
280C2×AGL(1,𝔽5)C2×C3×D418yes—
281C2×C4×C5—24no—
282C2×C4×C5C22×C3×C414yescomplemented
283C2×Dic5—24no—
284C2×Dic5C22×C3×C414yescomplemented
285C4×D5—28no—
286C4×D5—24no—
287C4×D5—24no—
288C25—51no—
289C23×C4—52no—
290C23×C4—52no—
291C23×C4—51no—
292C23×C4—51no—
293C23×C4—54no—
294C23×C4—108no—
295C23×C4—104no—
296C2×C4⋊C4—58no—
297C2×C4⋊C4—108no—
298C2×C22⋊C4—51no—
299C2×C22⋊C4—52no—
300C2×C22⋊C4—54no—
301C2×C22⋊C4—54no—
302C2×C22⋊C4—54no—
303C2×C22⋊C4—104no—
304C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
305#95—58no—
306C2×C3×C5—24no—
307C2×C3×C5#38514yescomplemented
308C2×C3×C5C22×C4⋊C411yescharacteristic
309C2×C3×C5C2×C4×D412yes—
310C3×D5—24no—
311C3×D5#38514yescomplemented
312C3×D5C2×#12011yescharacteristic
313C3×D5C2×C22⋊Q812yes—
314C3×D5C2×#12311yescharacteristic
315C23×C3—24no—
316C23×C3—52no—
317C23×C3—52no—
318C23×C3—54no—
319C23×C3—54no—
320C23×C3—51no—
321C23×C3—51no—
322C23×C3—54no—
323C23×C3—58no—
324C23×C3—54no—
325C23×C3—54no—
326C23×C3—52no—
327C23×C3—108no—
328C23×C3—104no—
329C23×C3—1016no—
330C23×C3—108no—
331C23×C3—108no—
332C23×C3—104no—
333C23×C3—104no—
334C23×C3C4⋊AGL(1,𝔽5)14yescomplemented
335C23×C3C22×AGL(1,𝔽5)12yes—
336C23×C3C22×AGL(1,𝔽5)11yescharacteristic
337C2×C3×C4—24no—
338C2×C3×C4—58no—
339C2×C3×C4—54no—
340C2×C3×C4—104no—
341C2×C3×C4—108no—
342C2×C3×C4—104no—
343C2×C3×C4—1016no—
344C2×C3×C4—104no—
345C2×C3×C4—104no—
346C2×C3×C4—1032no—
347C2×C3×C4—104no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4—104no—
351C2×C3×C4—104no—
352C2×C3×C4—204no—
353C2×C3×C4—204no—
354C2×C3×C4C22×AGL(1,𝔽5)14yescomplemented
355C22×C5—28no—
356C22×C5—24no—
357C22×C5C2×C3×C4⋊C412yes—
358C22×C5C2×C3×C4⋊C414yescomplemented
359C22×C5C3×C4×D414yes—
360C22×C5C23×C3×C411yescharacteristic
361C2×D5—28no—
362C2×D5—24no—
363C2×D5—216no—
364C2×D5—24no—
365C2×D5—28no—
366C2×D5—24no—
367C2×D5C2×C3×C4⋊C412yes—
368C2×D5C2×C3×C4⋊C414yescomplemented
369C2×D5C3×C4×D414yes—
370C2×D5C3×#12014yes—
371C2×D5C3×C22⋊Q818yes—
372C2×D5C3×#12314yes—
373C2×D5C22×C3×D412yes—
374C2×D5C22×C3×D411yescharacteristic
375C2×D5C22×C3×Q811yescharacteristic
376C2×D5C2×C3×#4112yes—
377AGL(1,𝔽5)—28no—
378AGL(1,𝔽5)—42no—
379AGL(1,𝔽5)—42no—
380C4×C5—24no—
381Dic5—24no—
382C24—51no—
383C24—54no—
384C24—54no—
385C24—52no—
386C24—52no—
387C24—51no—
388C24—104no—
389C24—104no—
390C24C2×C3×AGL(1,𝔽5)11yescharacteristic
391C22×C4—54no—
392C22×C4—58no—
393C22×C4—52no—
394C22×C4—54no—
395C22×C4—54no—
396C22×C4—52no—
397C22×C4—52no—
398C22×C4—104no—
399C22×C4—104no—
400C22×C4—1016no—
401C22×C4—104no—
402C22×C4—104no—
403C22×C4—108no—
404C22×C4—1032no—
405C22×C4—102no—
406C22×C4—102no—
407C22×C4—104no—
408C22×C4—104no—
409C22×C4C2×C3×AGL(1,𝔽5)12yescomplemented
410C4⋊C4—1016no—
411C22⋊C4—54no—
412C22⋊C4—58no—
413C22⋊C4—108no—
414C22⋊C4C2×C3×AGL(1,𝔽5)14yescomplemented
415C3×C5C2×#38511yescharacteristic, complemented, Hall
416C22×C3—28no—
417C22×C3—24no—
418C22×C3—54no—
419C22×C3—58no—
420C22×C3—54no—
421C22×C3—52no—
422C22×C3—51no—
423C22×C3—51no—
424C22×C3—54no—
425C22×C3—52no—
426C22×C3—52no—
427C22×C3—54no—
428C22×C3—104no—
429C22×C3—104no—
430C22×C3—108no—
431C22×C3—1016no—
432C22×C3—108no—
433C22×C3—104no—
434C22×C3C2×C4⋊AGL(1,𝔽5)12yes—
435C22×C3C2×C4⋊AGL(1,𝔽5)14yescomplemented
436C22×C3D4×AGL(1,𝔽5)14yes—
437C22×C3C23×AGL(1,𝔽5)11yescharacteristic
438C3×C4—24no—
439C3×C4—108no—
440C3×C4—104no—
441C3×C4—202no—
442C3×C4—202no—
443C2×C5—24no—
444C2×C5C3×#38514yescomplemented
445C2×C5C22×C3×C4⋊C411yescharacteristic
446C2×C5C2×C3×C4×D412yes—
447D5—24no—
448D5C3×#38514yescomplemented
449D5C2×C3×#12011yescharacteristic
450D5C2×C3×C22⋊Q812yes—
451D5C2×C3×#12311yescharacteristic
452C23—24no—
453C23—52no—
454C23—52no—
455C23—54no—
456C23—54no—
457C23—51no—
458C23—51no—
459C23—54no—
460C23—54no—
461C23—58no—
462C23—54no—
463C23—52no—
464C23—108no—
465C23—104no—
466C23—108no—
467C23—1016no—
468C23—104no—
469C23—108no—
470C23—104no—
471C23C3×C4⋊AGL(1,𝔽5)14yescomplemented
472C23C22×C3×AGL(1,𝔽5)12yes—
473C23C22×C3×AGL(1,𝔽5)11yescharacteristic
474C2×C4—24no—
475C2×C4—58no—
476C2×C4—54no—
477C2×C4—104no—
478C2×C4—104no—
479C2×C4—108no—
480C2×C4—1016no—
481C2×C4—104no—
482C2×C4—104no—
483C2×C4—1032no—
484C2×C4—104no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—104no—
488C2×C4—104no—
489C2×C4—204no—
490C2×C4—204no—
491C2×C4C22×C3×AGL(1,𝔽5)14yescomplemented
492C2×C3—24no—
493C2×C3—51no—
494C2×C3—51no—
495C2×C3—52no—
496C2×C3—54no—
497C2×C3—104no—
498C2×C3#6569914yesdirect product factor
499C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
500C2×C3C2×D4×AGL(1,𝔽5)12yes—
501C5C2×C3×#38511yescharacteristic, complemented, Sylow
502C22—28no—
503C22—24no—
504C22—54no—
505C22—54no—
506C22—58no—
507C22—51no—
508C22—52no—
509C22—51no—
510C22—52no—
511C22—52no—
512C22—54no—
513C22—54no—
514C22—104no—
515C22—104no—
516C22—1016no—
517C22—108no—
518C22—108no—
519C22—104no—
520C22C2×C3×C4⋊AGL(1,𝔽5)12yes—
521C22C2×C3×C4⋊AGL(1,𝔽5)14yescomplemented
522C22C3×D4×AGL(1,𝔽5)14yes—
523C22C23×C3×AGL(1,𝔽5)11yescharacteristic
524C4—24no—
525C4—108no—
526C4—104no—
527C4—202no—
528C4—202no—
529C3C2×#6569911yescharacteristic, direct product factor, Sylow
530C2—24no—
531C2—51no—
532C2—51no—
533C2—54no—
534C2—52no—
535C2—104no—
536C2C3×#6569914yesdirect product factor
537C2C22×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
538C2C2×C3×D4×AGL(1,𝔽5)12yes—
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC22×D5C24×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C2×C3×#385
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C3×C4⋊AGL(1,𝔽5)C2semidirect
5. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
6. C3×#65699C2direct (N × H)
7. C2×#65699C3direct (N × H)
19. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
20. C2×C3×C5×C22⋊C4C4semidirect
21. C2×C3×C22⋊Dic5C4semidirect
22. C2×C3×#685C4semidirect
23. C3×D5×C22⋊C4C4semidirect
25. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
29. C22×C4⋊AGL(1,𝔽5)C2×C3semidirect
31. C2×(C2×AGL(1,𝔽5))⋊C4C2×C3semidirect
32. #65699C2×C3direct (N × H)
55. C22×C3×C4×C5C2×C4semidirect
56. C22×C3×Dic5C2×C4semidirect
59. C2×C3×C4×D5C2×C4semidirect
63. C3×C5×C22⋊C4C2×C4semidirect
64. C3×C22⋊Dic5C2×C4semidirect
65. C3×#685C2×C4semidirect
83. C2×C4⋊AGL(1,𝔽5)C22×C3semidirect
84. C2×C5×C22⋊C4C3×C4semidirect
85. C2×C22⋊Dic5C3×C4semidirect
86. C2×#685C3×C4semidirect
87. D5×C22⋊C4C3×C4semidirect
89. (C2×AGL(1,𝔽5))⋊C4C22×C3semidirect
92. C23×C3×C5C4⋊C4semidirect
102. C22×C3×D5C4⋊C4semidirect
103. C22×C3×D5C4⋊C4semidirect
125. C2×C3×C4×C5C22×C4semidirect
127. C2×C3×Dic5C22×C4semidirect
147. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
171. C22×C4×C5C2×C3×C4semidirect
172. C22×Dic5C2×C3×C4semidirect
175. C2×C4×D5C2×C3×C4semidirect
179. C5×C22⋊C4C2×C3×C4semidirect
180. C22⋊Dic5C2×C3×C4semidirect
181. #685C2×C3×C4semidirect
191. C22×C3×C5C2×C4⋊C4semidirect
201. C2×C3×D5C2×C4⋊C4semidirect
242. C22×C3×C4C2×AGL(1,𝔽5)semidirect
247. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
249. C23×C5C3×C4⋊C4semidirect
259. C22×D5C3×C4⋊C4semidirect
260. C22×D5C3×C4⋊C4semidirect
282. C2×C4×C5C22×C3×C4semidirect
284. C2×Dic5C22×C3×C4semidirect
304. C2×C22⋊C4C3×AGL(1,𝔽5)semidirect
307. C2×C3×C5#385semidirect
311. C3×D5#385semidirect
334. C23×C3C4⋊AGL(1,𝔽5)semidirect
354. C2×C3×C4C22×AGL(1,𝔽5)semidirect
358. C22×C5C2×C3×C4⋊C4semidirect
368. C2×D5C2×C3×C4⋊C4semidirect
409. C22×C4C2×C3×AGL(1,𝔽5)semidirect
414. C22⋊C4C2×C3×AGL(1,𝔽5)semidirect
415. C3×C5C2×#385semidirect
435. C22×C3C2×C4⋊AGL(1,𝔽5)semidirect
444. C2×C5C3×#385semidirect
448. D5C3×#385semidirect
471. C23C3×C4⋊AGL(1,𝔽5)semidirect
491. C2×C4C22×C3×AGL(1,𝔽5)semidirect
498. C2×C3#65699direct (N × H)
501. C5C2×C3×#385semidirect
521. C22C2×C3×C4⋊AGL(1,𝔽5)semidirect
529. C3C2×#65699direct (N × H)
536. C2C3×#65699direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×AGL(1,𝔽5)2
C22×C3×C22⋊AGL(1,𝔽5)2
C22×C3×C4⋊AGL(1,𝔽5)2
C2×C3×D5×C22⋊C42
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C3×#656992
C2×#656993
C2×C3×#3855