Finite Group Databasebeta

← C2×#11751932 #14320270

Subgroups — C2×#11751932 #14320270

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×AGL(1,𝔽5)C211yesmaximal, characteristic
2C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
5C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
6C2×#91235C211yesmaximal, characteristic, complemented
7C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic, complemented
8#11751932C218yesmaximal, direct product factor
9C2×#65699—31nomaximal, Hall
10C23×D3×D5C2211yescharacteristic
11C23×ΓL(1,𝔽16)C2211yescharacteristic
12C23×ΓL(1,𝔽16)C2211yescharacteristic
13C23×C3×AGL(1,𝔽5)C2211yescharacteristic
14C23×C3×AGL(1,𝔽5)C2211yescharacteristic
15C22×D3×AGL(1,𝔽5)—24no—
16C22×D3×AGL(1,𝔽5)—24no—
17C22×D3×AGL(1,𝔽5)—24no—
18C22×D3×AGL(1,𝔽5)C2214yes—
19C22×C3×C4×D5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C2×C3×C4⋊AGL(1,𝔽5)—24no—
22C2×C3×C4⋊AGL(1,𝔽5)C2214yescomplemented
23C2×Dic3⋊AGL(1,𝔽5)—24no—
24C2×Dic3⋊AGL(1,𝔽5)C2214yescomplemented
25C2×(C2×D3)⋊AGL(1,𝔽5)—24no—
26C2×(C2×D3)⋊AGL(1,𝔽5)C2214yes—
27C2×#6714C411yescharacteristic, complemented
28C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
29C2×#6667C411yescharacteristic, complemented
30C2×(C2×D3)⋊Dic5C411yescharacteristic, complemented
31D5×(C2×D3)⋊C4C414yescomplemented
32D5×(C2×D3)⋊C4C2214yes—
33#91235C2214yescomplemented
34(C2×AGL(1,𝔽5))⋊Dic3C2214yescomplemented
35C2×#4989—51nomaximal, Hall
36C24×AGL(1,𝔽5)—31no—
37C22×C22⋊AGL(1,𝔽5)—31no—
38C22×C4⋊AGL(1,𝔽5)—31no—
39C22×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
40C2×D5×C22⋊C4—31no—
41C2×(C2×AGL(1,𝔽5))⋊C4—31no—
42C2×(C2×AGL(1,𝔽5))⋊C4—31no—
43#65699—38no—
44C23×D15C2×C411yescharacteristic
45C23×C5×D3C2×C411yescharacteristic
46C23×C3×D5C2311yescharacteristic
47C22×D3×D5—22no—
48C22×D3×D5—22no—
49C22×D3×D5—22no—
50C22×D3×D5—22no—
51C22×D3×D5C2×C412yes—
52C22×D3×D5D414yes—
53C22×D3×D5Q814yes—
54C22×D3×D5C2312yes—
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)D414yes—
61C22×ΓL(1,𝔽16)C2312yes—
62C22×ΓL(1,𝔽16)C2312yes—
63C22×C3×AGL(1,𝔽5)—22no—
64C22×C3×AGL(1,𝔽5)—22no—
65C22×C3×AGL(1,𝔽5)—22no—
66C22×C3×AGL(1,𝔽5)—22no—
67C22×C3×AGL(1,𝔽5)—22no—
68C22×C3×AGL(1,𝔽5)D414yes—
69C22×C3×AGL(1,𝔽5)C2312yes—
70C22×C3×AGL(1,𝔽5)C2312yes—
71C2×D3×AGL(1,𝔽5)—232no—
72C2×D3×AGL(1,𝔽5)—28no—
73C2×D3×AGL(1,𝔽5)—28no—
74C2×D3×AGL(1,𝔽5)—28no—
75C22×C3×C4×C5C2×C411yescharacteristic, complemented
76C22×Dic15C2×C411yescharacteristic, complemented
77C22×C5×Dic3C2×C411yescharacteristic, complemented
78C22×C3×Dic5C2×C411yescharacteristic, complemented
79C2×C3×C4×D5—22no—
80C2×C3×C4×D5—22no—
81C2×C3×C4×D5C2×C412yescomplemented
82C2×C3×C4×D5C2312yes—
83C2×D5×Dic3—22no—
84C2×D5×Dic3—22no—
85C2×D5×Dic3C2×C412yescomplemented
86C2×D5×Dic3C2312yes—
87C3×C4⋊AGL(1,𝔽5)—28no—
88Dic3⋊AGL(1,𝔽5)—28no—
89(C2×D3)⋊AGL(1,𝔽5)—28no—
90#6714C2×C414yescomplemented
91C5×(C2×D3)⋊C4C2×C414yescomplemented
92#6667C2×C414yescomplemented
93(C2×D3)⋊Dic5C2×C414yescomplemented
94C23×C4×D3—51no—
95C22×C3×C4⋊C4—51no—
96C22×(C2×D3)⋊C4—51no—
97C22×(C2×D3)⋊C4—51no—
98C22×Dic3⋊C4—51no—
99C2×C3⋊#95—51no—
100C2×C3⋊#95—51no—
101#4989—58no—
102C24×D5—31no—
103C23×AGL(1,𝔽5)—31no—
104C23×AGL(1,𝔽5)—31no—
105C23×AGL(1,𝔽5)—34no—
106C23×AGL(1,𝔽5)—64no—
107C23×AGL(1,𝔽5)—64no—
108C23×AGL(1,𝔽5)—64no—
109C23×AGL(1,𝔽5)C2×D311yescharacteristic
110C23×AGL(1,𝔽5)C2×D311yescharacteristic
111C22×C4×D5—31no—
112C22×C4×D5C2×D311yescharacteristic
113C2×C22⋊AGL(1,𝔽5)—34no—
114C2×C22⋊AGL(1,𝔽5)—64no—
115C2×C4⋊AGL(1,𝔽5)—24no—
116C2×C4⋊AGL(1,𝔽5)—34no—
117C2×C4⋊AGL(1,𝔽5)—64no—
118C2×C4⋊AGL(1,𝔽5)C2×D314yescomplemented
119C2×C5×C22⋊C4—31no—
120C2×C22⋊Dic5—31no—
121C2×#685—31no—
122C2×#685—31no—
123D5×C22⋊C4—34no—
124D5×C22⋊C4—34no—
125(C2×AGL(1,𝔽5))⋊C4—34no—
126(C2×AGL(1,𝔽5))⋊C4—34no—
127C2×#385—151noSylow
128C23×C3×C5C22×C411yescharacteristic
129C22×D15—22no—
130C22×D15—22no—
131C22×D15C4⋊C414yescomplemented
132C22×D15C22×C412yes—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3C4⋊C414yescomplemented
136C22×C5×D3C22×C412yes—
137C22×C3×D5C22×C411yescharacteristic
138C22×C3×D5C2×D412yes—
139C22×C3×D5C2×D412yes—
140C22×C3×D5C2×D412yes—
141C22×C3×D5C2×Q812yes—
142C22×C3×D5#4112yes—
143C22×C3×D5#4112yes—
144C22×C3×D5C2411yescharacteristic
145C2×D3×D5—24no—
146C2×D3×D5—24no—
147C2×D3×D5—28no—
148C2×D3×D5—28no—
149C2×D3×D5—28no—
150C2×D3×D5—28no—
151C2×D3×D5—22no—
152C2×D3×D5—22no—
153C2×D3×D5—22no—
154C2×D3×D5—22no—
155C2×D3×D5C4⋊C418yescomplemented
156C2×D3×D5C2×D414yes—
157C2×D3×D5C2×Q814yes—
158C2×ΓL(1,𝔽16)—28no—
159C2×ΓL(1,𝔽16)—22no—
160C2×ΓL(1,𝔽16)—22no—
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)—22no—
164C2×ΓL(1,𝔽16)—44no—
165C2×ΓL(1,𝔽16)C2×D414yes—
166C2×C3×AGL(1,𝔽5)—28no—
167C2×C3×AGL(1,𝔽5)—22no—
168C2×C3×AGL(1,𝔽5)—22no—
169C2×C3×AGL(1,𝔽5)—22no—
170C2×C3×AGL(1,𝔽5)—22no—
171C2×C3×AGL(1,𝔽5)—22no—
172C2×C3×AGL(1,𝔽5)—44no—
173C2×C3×AGL(1,𝔽5)C2×D414yes—
174D3×AGL(1,𝔽5)—232no—
175C2×C3×C4×C5—22no—
176C2×C3×C4×C5C22×C412yescomplemented
177C2×Dic15—22no—
178C2×Dic15C22×C412yescomplemented
179C2×C5×Dic3—22no—
180C2×C5×Dic3C22×C412yescomplemented
181C2×C3×Dic5—22no—
182C2×C3×Dic5C22×C412yescomplemented
183C3×C4×D5—24no—
184C3×C4×D5—22no—
185C3×C4×D5—22no—
186D5×Dic3—24no—
187D5×Dic3—22no—
188D5×Dic3—22no—
189C24×D3—51no—
190C23×C3×C4—51no—
191C23×C3×C4—51no—
192C23×C3×C4—51no—
193C23×Dic3—51no—
194C23×Dic3—51no—
195C23×Dic3—51no—
196C22×C4×D3—54no—
197C22×C4×D3—104no—
198C22×C4×D3—104no—
199C22×C4×D3—104no—
200C2×C3×C4⋊C4—54no—
201C2×C3×C4⋊C4—104no—
202C2×(C2×D3)⋊C4—51no—
203C2×(C2×D3)⋊C4—51no—
204C2×(C2×D3)⋊C4—51no—
205C2×(C2×D3)⋊C4—54no—
206C2×(C2×D3)⋊C4—54no—
207C2×(C2×D3)⋊C4—54no—
208C2×(C2×D3)⋊C4—104no—
209C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
210C2×Dic3⋊C4—54no—
211C2×Dic3⋊C4—104no—
212C3⋊#95—54no—
213C3⋊#95—54no—
214C24×C5—31no—
215C23×D5—31no—
216C23×D5—32no—
217C23×D5—34no—
218C23×D5—34no—
219C23×D5—32no—
220C23×D5—62no—
221C23×D5—62no—
222C23×D5—62no—
223C23×D5—62no—
224C23×D5C22×D311yescharacteristic
225C22×AGL(1,𝔽5)—22no—
226C22×AGL(1,𝔽5)—22no—
227C22×AGL(1,𝔽5)—22no—
228C22×AGL(1,𝔽5)—22no—
229C22×AGL(1,𝔽5)—22no—
230C22×AGL(1,𝔽5)—34no—
231C22×AGL(1,𝔽5)—32no—
232C22×AGL(1,𝔽5)—32no—
233C22×AGL(1,𝔽5)—68no—
234C22×AGL(1,𝔽5)—68no—
235C22×AGL(1,𝔽5)—632no—
236C22×AGL(1,𝔽5)—62no—
237C22×AGL(1,𝔽5)—62no—
238C22×AGL(1,𝔽5)—68no—
239C22×AGL(1,𝔽5)—62no—
240C22×AGL(1,𝔽5)—62no—
241C22×AGL(1,𝔽5)—62no—
242C22×AGL(1,𝔽5)#6714yes—
243C22×AGL(1,𝔽5)C22×D312yes—
244C22×AGL(1,𝔽5)C22×D312yes—
245C22×C4×C5—31no—
246C22×C4×C5C4×D311yescharacteristic, complemented
247C22×Dic5—31no—
248C22×Dic5C4×D311yescharacteristic, complemented
249C2×C4×D5—22no—
250C2×C4×D5—22no—
251C2×C4×D5—32no—
252C2×C4×D5—32no—
253C2×C4×D5—62no—
254C2×C4×D5—62no—
255C2×C4×D5C4×D312yescomplemented
256C2×C4×D5C22×D312yes—
257C22⋊AGL(1,𝔽5)—68no—
258C4⋊AGL(1,𝔽5)—28no—
259C4⋊AGL(1,𝔽5)—68no—
260C5×C22⋊C4—34no—
261C22⋊Dic5—34no—
262#685—34no—
263#685—34no—
264C24×C4—151no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—151no—
267C22×C22⋊C4—151no—
268C22×C22⋊C4—151no—
269#385—158no—
270C2×#95—151no—
271C2×#95—151no—
272C22×C3×C5C2×C4⋊C412yes—
273C22×C3×C5C4×D412yes—
274C22×C3×C5C4×D412yes—
275C22×C3×C5C23×C411yescharacteristic
276C2×D15—22no—
277C2×D15—22no—
278C2×D15—28no—
279C2×D15C2×C4⋊C414yescomplemented
280C2×C5×D3—22no—
281C2×C5×D3—22no—
282C2×C5×D3—28no—
283C2×C5×D3C2×C4⋊C414yescomplemented
284C2×C3×D5C2×C4⋊C412yes—
285C2×C3×D5C4×D412yes—
286C2×C3×D5C4×D412yes—
287C2×C3×D5#12014yes—
288C2×C3×D5C22⋊Q814yes—
289C2×C3×D5C22⋊Q814yes—
290C2×C3×D5#12314yes—
291C2×C3×D5C22×D411yescharacteristic
292C2×C3×D5C22×D411yescharacteristic
293C2×C3×D5C22×D411yescharacteristic
294C2×C3×D5C22×Q811yescharacteristic
295C2×C3×D5C2×#4111yescharacteristic
296C2×C3×D5C2×#4111yescharacteristic
297D3×D5—24no—
298D3×D5—24no—
299D3×D5—24no—
300D3×D5—24no—
301D3×D5—216no—
302ΓL(1,𝔽16)—24no—
303ΓL(1,𝔽16)—42no—
304C3×AGL(1,𝔽5)—24no—
305C3×AGL(1,𝔽5)—42no—
306C3×C4×C5—22no—
307Dic15—22no—
308C3×Dic5—22no—
309C5×Dic3—22no—
310C24×C3—51no—
311C23×D3—51no—
312C23×D3—54no—
313C23×D3—54no—
314C23×D3—52no—
315C23×D3—52no—
316C23×D3—102no—
317C23×D3—102no—
318C23×D3—102no—
319C23×D3—102no—
320C23×D3C2×AGL(1,𝔽5)11yescharacteristic
321C22×C3×C4—52no—
322C22×C3×C4—54no—
323C22×C3×C4—51no—
324C22×C3×C4—52no—
325C22×C3×C4—52no—
326C22×C3×C4—52no—
327C22×C3×C4—102no—
328C22×C3×C4—102no—
329C22×C3×C4—102no—
330C22×C3×C4—102no—
331C22×C3×C4—102no—
332C22×C3×C4—102no—
333C22×C3×C4—102no—
334C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
335C22×Dic3—52no—
336C22×Dic3—54no—
337C22×Dic3—51no—
338C22×Dic3—52no—
339C22×Dic3—52no—
340C22×Dic3—52no—
341C22×Dic3—102no—
342C22×Dic3—102no—
343C22×Dic3—102no—
344C22×Dic3—102no—
345C22×Dic3—102no—
346C22×Dic3—102no—
347C22×Dic3—102no—
348C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
349C2×C4×D3—108no—
350C2×C4×D3—108no—
351C2×C4×D3—108no—
352C2×C4×D3—1032no—
353C3×C4⋊C4—108no—
354(C2×D3)⋊C4—54no—
355(C2×D3)⋊C4—54no—
356(C2×D3)⋊C4—54no—
357(C2×D3)⋊C4—108no—
358(C2×D3)⋊C4C2×AGL(1,𝔽5)14yescomplemented
359Dic3⋊C4—108no—
360C23×C5—34no—
361C23×C5—32no—
362C23×C5—62no—
363C23×C5—62no—
364C23×C5C2×C4×D311yescharacteristic
365C22×D5—34no—
366C22×D5—32no—
367C22×D5—38no—
368C22×D5—34no—
369C22×D5—34no—
370C22×D5—62no—
371C22×D5—62no—
372C22×D5—64no—
373C22×D5—68no—
374C22×D5—68no—
375C22×D5—64no—
376C22×D5—68no—
377C22×D5—68no—
378C22×D5—62no—
379C22×D5—62no—
380C22×D5—62no—
381C22×D5—62no—
382C22×D5C2×C4×D311yescharacteristic
383C22×D5#23512yes—
384C22×D5D3×D412yes—
385C22×D5D3×D412yes—
386C22×D5D3×Q812yes—
387C22×D5#23912yes—
388C22×D5C2×#6712yes—
389C22×D5C23×D311yescharacteristic
390C2×AGL(1,𝔽5)—28no—
391C2×AGL(1,𝔽5)—22no—
392C2×AGL(1,𝔽5)—22no—
393C2×AGL(1,𝔽5)—22no—
394C2×AGL(1,𝔽5)—22no—
395C2×AGL(1,𝔽5)—22no—
396C2×AGL(1,𝔽5)—34no—
397C2×AGL(1,𝔽5)—44no—
398C2×AGL(1,𝔽5)—632no—
399C2×AGL(1,𝔽5)—68no—
400C2×AGL(1,𝔽5)—62no—
401C2×AGL(1,𝔽5)—62no—
402C2×AGL(1,𝔽5)—62no—
403C2×AGL(1,𝔽5)—62no—
404C2×AGL(1,𝔽5)—62no—
405C2×AGL(1,𝔽5)—124no—
406C2×AGL(1,𝔽5)C2×#6714yes—
407C2×C4×C5—22no—
408C2×C4×C5—32no—
409C2×C4×C5—62no—
410C2×C4×C5C2×C4×D312yescomplemented
411C2×Dic5—22no—
412C2×Dic5—32no—
413C2×Dic5—62no—
414C2×Dic5C2×C4×D312yescomplemented
415C4×D5—24no—
416C4×D5—22no—
417C4×D5—22no—
418C4×D5—64no—
419C4×D5—62no—
420C4×D5—62no—
421C25—151no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—151no—
426C23×C4—154no—
427C23×C4—151no—
428C23×C4—151no—
429C23×C4—304no—
430C23×C4—304no—
431C23×C4—304no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—154no—
435C2×C4⋊C4—304no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—154no—
438C2×C22⋊C4—154no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—151no—
441C2×C22⋊C4—151no—
442C2×C22⋊C4—154no—
443C2×C22⋊C4—304no—
444#95—154no—
445#95—154no—
446C2×C3×C5#38514yescomplemented
447C2×C3×C5C22×C4⋊C411yescharacteristic
448C2×C3×C5C2×C4×D411yescharacteristic
449C2×C3×C5C2×C4×D411yescharacteristic
450D15—24no—
451C3×D5#38514yescomplemented
452C3×D5C2×#12011yescharacteristic
453C3×D5C2×C22⋊Q811yescharacteristic
454C3×D5C2×C22⋊Q811yescharacteristic
455C3×D5C2×#12311yescharacteristic
456C5×D3—24no—
457C23×C3—52no—
458C23×C3—52no—
459C23×C3—52no—
460C23×C3—52no—
461C23×C3—52no—
462C23×C3—52no—
463C23×C3—51no—
464C23×C3—51no—
465C23×C3C22×AGL(1,𝔽5)11yescharacteristic
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—54no—
469C22×D3—52no—
470C22×D3—58no—
471C22×D3—54no—
472C22×D3—54no—
473C22×D3—108no—
474C22×D3—102no—
475C22×D3—102no—
476C22×D3—108no—
477C22×D3—108no—
478C22×D3—108no—
479C22×D3—104no—
480C22×D3—104no—
481C22×D3—102no—
482C22×D3—102no—
483C22×D3—102no—
484C22×D3—102no—
485C22×D3C4⋊AGL(1,𝔽5)14yescomplemented
486C22×D3C22×AGL(1,𝔽5)12yes—
487C2×C3×C4—22no—
488C2×C3×C4—54no—
489C2×C3×C4—52no—
490C2×C3×C4—102no—
491C2×C3×C4—104no—
492C2×C3×C4—102no—
493C2×C3×C4—108no—
494C2×C3×C4—102no—
495C2×C3×C4—102no—
496C2×C3×C4—102no—
497C2×C3×C4—102no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—204no—
501C2×C3×C4C22×AGL(1,𝔽5)12yescomplemented
502C2×Dic3—22no—
503C2×Dic3—54no—
504C2×Dic3—52no—
505C2×Dic3—102no—
506C2×Dic3—104no—
507C2×Dic3—102no—
508C2×Dic3—108no—
509C2×Dic3—102no—
510C2×Dic3—102no—
511C2×Dic3—102no—
512C2×Dic3—102no—
513C2×Dic3—102no—
514C2×Dic3—102no—
515C2×Dic3—204no—
516C2×Dic3C22×AGL(1,𝔽5)12yescomplemented
517C4×D3—1032no—
518C22×C5—34no—
519C22×C5—68no—
520C22×C5—62no—
521C22×C5—62no—
522C22×C5D3×C4⋊C412yes—
523C22×C5#89312yes—
524C22×C5C4×#6712yes—
525C22×C5C22×C4×D311yescharacteristic
526C2×D5—34no—
527C2×D5—68no—
528C2×D5—62no—
529C2×D5—62no—
530C2×D5—616no—
531C2×D5—64no—
532C2×D5—64no—
533C2×D5—64no—
534C2×D5—64no—
535C2×D5D3×C4⋊C412yes—
536C2×D5#89312yes—
537C2×D5#89414yes—
538C2×D5#89614yes—
539C2×D5C4×#6712yes—
540C2×D5#93714yes—
541C2×D5#94614yes—
542C2×D5C2×#23511yescharacteristic
543C2×D5C2×D3×D411yescharacteristic
544C2×D5C2×D3×D411yescharacteristic
545C2×D5C2×D3×Q811yescharacteristic
546C2×D5C2×#23911yescharacteristic
547C2×D5C22×#6711yescharacteristic
548AGL(1,𝔽5)—24no—
549AGL(1,𝔽5)—42no—
550AGL(1,𝔽5)—64no—
551AGL(1,𝔽5)—122no—
552C4×C5—22no—
553C4×C5—62no—
554Dic5—22no—
555Dic5—62no—
556C24—31no—
557C24—51no—
558C24—152no—
559C24—152no—
560C24—154no—
561C24—154no—
562C24—151no—
563C24—302no—
564C24—302no—
565C24—302no—
566C24—302no—
567C22×C4—31no—
568C22×C4—52no—
569C22×C4—54no—
570C22×C4—51no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—152no—
582C22×C4—152no—
583C22×C4—152no—
584C22×C4—154no—
585C22×C4—151no—
586C22×C4—152no—
587C22×C4—308no—
588C22×C4—302no—
589C22×C4—302no—
590C22×C4—308no—
591C22×C4—308no—
592C22×C4—3032no—
593C22×C4—302no—
594C22×C4—302no—
595C22×C4—302no—
596C22×C4—302no—
597C22×C4—302no—
598C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
599C4⋊C4—108no—
600C4⋊C4—308no—
601C22⋊C4—34no—
602C22⋊C4—154no—
603C22⋊C4—154no—
604C22⋊C4—154no—
605C22⋊C4—308no—
606C3×C5C2×#38511yescharacteristic, complemented, Hall
607C22×C3—54no—
608C22×C3—54no—
609C22×C3—54no—
610C22×C3—54no—
611C22×C3—52no—
612C22×C3—51no—
613C22×C3—51no—
614C22×C3—52no—
615C22×C3—52no—
616C22×C3—51no—
617C22×C3—51no—
618C22×C3—51no—
619C22×C3—51no—
620C22×C3C2×C4⋊AGL(1,𝔽5)12yes—
621C22×C3D4×AGL(1,𝔽5)12yes—
622C22×C3D4×AGL(1,𝔽5)12yes—
623C22×C3C23×AGL(1,𝔽5)11yescharacteristic
624C2×D3—28no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—54no—
628C2×D3—104no—
629C2×D3—104no—
630C2×D3—104no—
631C2×D3—104no—
632C2×D3—1016no—
633C2×D3—108no—
634C2×D3—102no—
635C2×D3—102no—
636C2×D3C2×C4⋊AGL(1,𝔽5)14yescomplemented
637C3×C4—22no—
638C3×C4—104no—
639C3×C4—102no—
640C3×C4—202no—
641Dic3—22no—
642Dic3—104no—
643Dic3—102no—
644Dic3—202no—
645C2×C5—64no—
646C2×C5#498914yescomplemented
647C2×C5C2×D3×C4⋊C411yescharacteristic
648C2×C5C2×#89311yescharacteristic
649C2×C5C2×C4×#6711yescharacteristic
650D5—64no—
651D5#498914yescomplemented
652D5C2×#89411yescharacteristic
653D5C2×#89611yescharacteristic
654D5C2×#93711yescharacteristic
655D5C2×#94611yescharacteristic
656C23—34no—
657C23—32no—
658C23—52no—
659C23—52no—
660C23—52no—
661C23—52no—
662C23—52no—
663C23—52no—
664C23—51no—
665C23—51no—
666C23—62no—
667C23—62no—
668C23—154no—
669C23—158no—
670C23—154no—
671C23—154no—
672C23—152no—
673C23—302no—
674C23—302no—
675C23—308no—
676C23—302no—
677C23—304no—
678C23—302no—
679C23—304no—
680C23—308no—
681C23—308no—
682C23—308no—
683C23—302no—
684C23—302no—
685C23C2×D3×AGL(1,𝔽5)11yescharacteristic
686C2×C4—22no—
687C2×C4—32no—
688C2×C4—54no—
689C2×C4—52no—
690C2×C4—62no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—104no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—108no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—154no—
702C2×C4—152no—
703C2×C4—204no—
704C2×C4—302no—
705C2×C4—302no—
706C2×C4—304no—
707C2×C4—3032no—
708C2×C4—302no—
709C2×C4—302no—
710C2×C4—308no—
711C2×C4—302no—
712C2×C4—302no—
713C2×C4—302no—
714C2×C4—302no—
715C2×C4—604no—
716C2×C4C2×D3×AGL(1,𝔽5)12yescomplemented
717C2×C3—51no—
718C2×C3—51no—
719C2×C3—51no—
720C2×C3—51no—
721C2×C3—54no—
722C2×C3#6569914yescomplemented
723C2×C3C22×C4⋊AGL(1,𝔽5)11yescharacteristic
724C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
725C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
726D3—24no—
727D3—104no—
728C5C2×#498911yescharacteristic, complemented, Sylow
729C22—34no—
730C22—51no—
731C22—52no—
732C22—51no—
733C22—51no—
734C22—51no—
735C22—52no—
736C22—51no—
737C22—51no—
738C22—52no—
739C22—54no—
740C22—54no—
741C22—54no—
742C22—54no—
743C22—62no—
744C22—62no—
745C22—68no—
746C22—154no—
747C22—304no—
748C22—304no—
749C22—3016no—
750C22—304no—
751C22—304no—
752C22—302no—
753C22—302no—
754C22—308no—
755C22D3×C4⋊AGL(1,𝔽5)12yes—
756C22#9192112yes—
757C22AGL(1,𝔽5)×#6712yes—
758C22C22×D3×AGL(1,𝔽5)11yescharacteristic
759C4—22no—
760C4—62no—
761C4—104no—
762C4—102no—
763C4—202no—
764C4—304no—
765C4—302no—
766C4—602no—
767C3C2×#6569911yescharacteristic, complemented, Sylow
768C2—51no—
769C2—51no—
770C2—54no—
771C2—51no—
772C2—51no—
773C2—64no—
774C2—304no—
775C2#1175193214yesdirect product factor
776C2C2×D3×C4⋊AGL(1,𝔽5)11yescharacteristic
777C2C2×#9192111yescharacteristic
778C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×D3×D5C22
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#385
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊AGL(1,𝔽5)C2semidirect
3. C22×Dic3⋊AGL(1,𝔽5)C2semidirect
6. C2×#91235C2semidirect
7. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
8. #11751932C2direct (N × H)
22. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
24. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
27. C2×#6714C4semidirect
28. C2×C5×(C2×D3)⋊C4C4semidirect
29. C2×#6667C4semidirect
30. C2×(C2×D3)⋊Dic5C4semidirect
31. D5×(C2×D3)⋊C4C4semidirect
33. #91235C22semidirect
34. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
39. C22×C4⋊AGL(1,𝔽5)D3semidirect
75. C22×C3×C4×C5C2×C4semidirect
76. C22×Dic15C2×C4semidirect
77. C22×C5×Dic3C2×C4semidirect
78. C22×C3×Dic5C2×C4semidirect
81. C2×C3×C4×D5C2×C4semidirect
85. C2×D5×Dic3C2×C4semidirect
90. #6714C2×C4semidirect
91. C5×(C2×D3)⋊C4C2×C4semidirect
92. #6667C2×C4semidirect
93. (C2×D3)⋊Dic5C2×C4semidirect
118. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
131. C22×D15C4⋊C4semidirect
135. C22×C5×D3C4⋊C4semidirect
155. C2×D3×D5C4⋊C4semidirect
176. C2×C3×C4×C5C22×C4semidirect
178. C2×Dic15C22×C4semidirect
180. C2×C5×Dic3C22×C4semidirect
182. C2×C3×Dic5C22×C4semidirect
209. C2×(C2×D3)⋊C4AGL(1,𝔽5)semidirect
246. C22×C4×C5C4×D3semidirect
248. C22×Dic5C4×D3semidirect
255. C2×C4×D5C4×D3semidirect
279. C2×D15C2×C4⋊C4semidirect
283. C2×C5×D3C2×C4⋊C4semidirect
334. C22×C3×C4C2×AGL(1,𝔽5)semidirect
348. C22×Dic3C2×AGL(1,𝔽5)semidirect
358. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
410. C2×C4×C5C2×C4×D3semidirect
414. C2×Dic5C2×C4×D3semidirect
446. C2×C3×C5#385semidirect
451. C3×D5#385semidirect
485. C22×D3C4⋊AGL(1,𝔽5)semidirect
501. C2×C3×C4C22×AGL(1,𝔽5)semidirect
516. C2×Dic3C22×AGL(1,𝔽5)semidirect
598. C22×C4D3×AGL(1,𝔽5)semidirect
606. C3×C5C2×#385semidirect
636. C2×D3C2×C4⋊AGL(1,𝔽5)semidirect
646. C2×C5#4989semidirect
651. D5#4989semidirect
716. C2×C4C2×D3×AGL(1,𝔽5)semidirect
722. C2×C3#65699semidirect
728. C5C2×#4989semidirect
767. C3C2×#65699semidirect
775. C2#11751932direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×AGL(1,𝔽5)2
C22×C3×C4⋊AGL(1,𝔽5)2
C22×Dic3⋊AGL(1,𝔽5)2
C22×(C2×D3)⋊AGL(1,𝔽5)2
C2×D5×(C2×D3)⋊C42
C2×#912352
C2×(C2×AGL(1,𝔽5))⋊Dic32
#117519322
C2×#656993
C2×#49895