Finite Group Databasebeta

← C2×#11751836 #14320527

Subgroups — C2×#11751836 #14320527

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C22×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3C22×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4C22×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
6C2×#91235C211yesmaximal, characteristic, complemented
7C2×(C2×AGL(1,𝔽5))⋊Dic3C211yesmaximal, characteristic, complemented
8#11751836C218yesmaximal, direct product factor
9C2×#65700—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×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)—24no—
18C2×C3×C4⋊AGL(1,𝔽5)C2214yescomplemented
19C2×(C2×D3)⋊AGL(1,𝔽5)—24no—
20C2×(C2×D3)⋊AGL(1,𝔽5)—24no—
21C2×(C2×D3)⋊AGL(1,𝔽5)C2214yes—
22C2×(C2×D3)⋊AGL(1,𝔽5)C2214yes—
23C2×Dic3×AGL(1,𝔽5)—24no—
24C2×Dic3×AGL(1,𝔽5)C2214yescomplemented
25C2×#6714C411yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
27C2×#6667C411yescharacteristic, complemented
28C2×(C2×D3)⋊Dic5C411yescharacteristic, complemented
29D5×(C2×D3)⋊C4C414yescomplemented
30D5×(C2×D3)⋊C4C2214yes—
31#91235C2214yescomplemented
32(C2×AGL(1,𝔽5))⋊Dic3C2214yescomplemented
33C2×#4990—51nomaximal, Hall
34C22×C22⋊AGL(1,𝔽5)—31no—
35C22×C22⋊AGL(1,𝔽5)—31no—
36C22×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
37C22×C4×AGL(1,𝔽5)—31no—
38C2×D5×C22⋊C4—31no—
39C2×(C2×AGL(1,𝔽5))⋊C4—31no—
40C2×(C2×AGL(1,𝔽5))⋊C4—31no—
41#65700—38no—
42C23×D15C2×C411yescharacteristic
43C23×C5×D3C2×C411yescharacteristic
44C23×C3×D5C2311yescharacteristic
45C22×D3×D5—22no—
46C22×D3×D5—22no—
47C22×D3×D5—22no—
48C22×D3×D5—22no—
49C22×D3×D5—22no—
50C22×D3×D5—22no—
51C22×D3×D5C2×C412yes—
52C22×D3×D5C2312yes—
53C22×ΓL(1,𝔽16)—22no—
54C22×ΓL(1,𝔽16)—22no—
55C22×ΓL(1,𝔽16)—22no—
56C22×ΓL(1,𝔽16)—22no—
57C22×ΓL(1,𝔽16)—22no—
58C22×ΓL(1,𝔽16)D414yes—
59C22×ΓL(1,𝔽16)C2312yes—
60C22×ΓL(1,𝔽16)C2312yes—
61C22×C3×AGL(1,𝔽5)—22no—
62C22×C3×AGL(1,𝔽5)—22no—
63C22×C3×AGL(1,𝔽5)—22no—
64C22×C3×AGL(1,𝔽5)—22no—
65C22×C3×AGL(1,𝔽5)—22no—
66C22×C3×AGL(1,𝔽5)D414yes—
67C22×C3×AGL(1,𝔽5)C2312yes—
68C22×C3×AGL(1,𝔽5)C2312yes—
69C22×C3×C4×C5C2×C411yescharacteristic
70C22×Dic15C2×C411yescharacteristic
71C22×C5×Dic3C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2×C412yes—
76C2×C3×C4×D5C2312yes—
77C2×D5×Dic3—22no—
78C2×D5×Dic3—22no—
79C2×D5×Dic3C2×C412yes—
80C2×D5×Dic3C2312yes—
81C3×C4⋊AGL(1,𝔽5)—28no—
82(C2×D3)⋊AGL(1,𝔽5)—28no—
83(C2×D3)⋊AGL(1,𝔽5)—28no—
84Dic3×AGL(1,𝔽5)—28no—
85#6714C2×C414yescomplemented
86C5×(C2×D3)⋊C4C2×C414yescomplemented
87#6667C2×C414yescomplemented
88(C2×D3)⋊Dic5C2×C414yescomplemented
89C22×C3×C4⋊C4—51no—
90C22×(C2×D3)⋊C4—51no—
91C22×(C2×D3)⋊C4—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×C4×Dic3—51no—
94C2×C3⋊#95—51no—
95C2×C3⋊#95—51no—
96#4990—58no—
97C24×D5—31no—
98C23×AGL(1,𝔽5)—31no—
99C23×AGL(1,𝔽5)—31no—
100C23×AGL(1,𝔽5)C2×D311yescharacteristic
101C23×AGL(1,𝔽5)C2×D311yescharacteristic
102C22×C4×D5—31no—
103C22×C4×D5C2×D311yescharacteristic
104C2×C22⋊AGL(1,𝔽5)—34no—
105C2×C22⋊AGL(1,𝔽5)—34no—
106C2×C22⋊AGL(1,𝔽5)—64no—
107C2×C22⋊AGL(1,𝔽5)—64no—
108C2×C4⋊AGL(1,𝔽5)—24no—
109C2×C4⋊AGL(1,𝔽5)C2×D314yescomplemented
110C2×C4×AGL(1,𝔽5)—34no—
111C2×C4×AGL(1,𝔽5)—64no—
112C2×C5×C22⋊C4—31no—
113C2×C22⋊Dic5—31no—
114C2×#685—31no—
115C2×#685—31no—
116D5×C22⋊C4—34no—
117D5×C22⋊C4—34no—
118(C2×AGL(1,𝔽5))⋊C4—34no—
119(C2×AGL(1,𝔽5))⋊C4—34no—
120C2×#388—151noSylow
121C23×C3×C5C22×C411yescharacteristic
122C22×D15—22no—
123C22×D15—22no—
124C22×D15—22no—
125C22×D15C22×C412yes—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3—22no—
129C22×C5×D3C22×C412yes—
130C22×C3×D5C22×C411yescharacteristic
131C22×C3×D5C2×D412yes—
132C22×C3×D5C2×D412yes—
133C22×C3×D5#4112yes—
134C22×C3×D5#4112yes—
135C22×C3×D5#4112yes—
136C22×C3×D5#4112yes—
137C22×C3×D5C2411yescharacteristic
138C2×D3×D5—24no—
139C2×D3×D5—24no—
140C2×D3×D5—24no—
141C2×D3×D5—22no—
142C2×D3×D5—22no—
143C2×D3×D5—22no—
144C2×D3×D5—22no—
145C2×D3×D5—22no—
146C2×D3×D5—22no—
147C2×D3×D5—44no—
148C2×D3×D5—44no—
149C2×D3×D5—44no—
150C2×D3×D5—44no—
151C2×ΓL(1,𝔽16)—28no—
152C2×ΓL(1,𝔽16)—22no—
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—22no—
157C2×ΓL(1,𝔽16)—44no—
158C2×ΓL(1,𝔽16)C2×D414yes—
159C2×C3×AGL(1,𝔽5)—28no—
160C2×C3×AGL(1,𝔽5)—22no—
161C2×C3×AGL(1,𝔽5)—22no—
162C2×C3×AGL(1,𝔽5)—22no—
163C2×C3×AGL(1,𝔽5)—22no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—44no—
166C2×C3×AGL(1,𝔽5)C2×D414yes—
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5C22×C412yes—
169C2×Dic15—22no—
170C2×Dic15C22×C412yes—
171C2×C5×Dic3—22no—
172C2×C5×Dic3C22×C412yes—
173C2×C3×Dic5—22no—
174C2×C3×Dic5C22×C412yes—
175C3×C4×D5—24no—
176C3×C4×D5—22no—
177C3×C4×D5—22no—
178D5×Dic3—24no—
179D5×Dic3—22no—
180D5×Dic3—22no—
181C24×D3—51no—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4—51no—
185C23×Dic3—51no—
186C23×Dic3—51no—
187C23×Dic3—51no—
188C2×C3×C4⋊C4—54no—
189C2×C3×C4⋊C4—104no—
190C2×(C2×D3)⋊C4—51no—
191C2×(C2×D3)⋊C4—51no—
192C2×(C2×D3)⋊C4—51no—
193C2×(C2×D3)⋊C4—54no—
194C2×(C2×D3)⋊C4—54no—
195C2×(C2×D3)⋊C4—54no—
196C2×(C2×D3)⋊C4—54no—
197C2×(C2×D3)⋊C4—104no—
198C2×(C2×D3)⋊C4—104no—
199C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
200C2×C4×Dic3—54no—
201C2×C4×Dic3—104no—
202C3⋊#95—54no—
203C3⋊#95—54no—
204C24×C5—31no—
205C23×D5—31no—
206C23×D5—32no—
207C23×D5—32no—
208C23×D5—62no—
209C23×D5—62no—
210C23×D5—62no—
211C23×D5—62no—
212C23×D5—62no—
213C23×D5—62no—
214C23×D5C22×D311yescharacteristic
215C22×AGL(1,𝔽5)—22no—
216C22×AGL(1,𝔽5)—22no—
217C22×AGL(1,𝔽5)—22no—
218C22×AGL(1,𝔽5)—22no—
219C22×AGL(1,𝔽5)—22no—
220C22×AGL(1,𝔽5)—34no—
221C22×AGL(1,𝔽5)—32no—
222C22×AGL(1,𝔽5)—32no—
223C22×AGL(1,𝔽5)—62no—
224C22×AGL(1,𝔽5)—62no—
225C22×AGL(1,𝔽5)—62no—
226C22×AGL(1,𝔽5)—62no—
227C22×AGL(1,𝔽5)—62no—
228C22×AGL(1,𝔽5)#6714yes—
229C22×AGL(1,𝔽5)C22×D312yes—
230C22×AGL(1,𝔽5)C22×D312yes—
231C22×C4×C5—31no—
232C22×C4×C5C4×D311yescharacteristic
233C22×Dic5—31no—
234C22×Dic5C4×D311yescharacteristic
235C2×C4×D5—22no—
236C2×C4×D5—22no—
237C2×C4×D5—32no—
238C2×C4×D5—32no—
239C2×C4×D5—62no—
240C2×C4×D5—62no—
241C2×C4×D5C4×D312yes—
242C2×C4×D5C22×D312yes—
243C22⋊AGL(1,𝔽5)—68no—
244C22⋊AGL(1,𝔽5)—68no—
245C4⋊AGL(1,𝔽5)—28no—
246C4×AGL(1,𝔽5)—68no—
247C5×C22⋊C4—34no—
248C22⋊Dic5—34no—
249#685—34no—
250#685—34no—
251C22×C4⋊C4—51no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4—151no—
254C22×C22⋊C4—151no—
255C22×C42—151no—
256#388—158no—
257C2×#95—151no—
258C2×#95—151no—
259C22×C3×C5#11712yes—
260C22×C3×C5C4×D412yes—
261C22×C3×C5C4×D412yes—
262C22×C3×C5C23×C411yescharacteristic
263C2×D15—22no—
264C2×D15—22no—
265C2×D15—22no—
266C2×D15—44no—
267C2×C5×D3—22no—
268C2×C5×D3—22no—
269C2×C5×D3—22no—
270C2×C5×D3—44no—
271C2×C3×D5#11712yes—
272C2×C3×D5C4×D412yes—
273C2×C3×D5C4×D412yes—
274C2×C3×D5#12114yes—
275C2×C3×D5#12314yes—
276C2×C3×D5#12414yes—
277C2×C3×D5#12614yes—
278C2×C3×D5C22×D411yescharacteristic
279C2×C3×D5C22×D411yescharacteristic
280C2×C3×D5C2×#4111yescharacteristic
281C2×C3×D5C2×#4111yescharacteristic
282C2×C3×D5C2×#4111yescharacteristic
283C2×C3×D5C2×#4111yescharacteristic
284D3×D5—42no—
285D3×D5—42no—
286D3×D5—42no—
287D3×D5—42no—
288D3×D5—48no—
289ΓL(1,𝔽16)—24no—
290ΓL(1,𝔽16)—42no—
291C3×AGL(1,𝔽5)—24no—
292C3×AGL(1,𝔽5)—42no—
293C3×C4×C5—22no—
294Dic15—22no—
295C3×Dic5—22no—
296C5×Dic3—22no—
297C24×C3—51no—
298C23×D3—51no—
299C23×D3—52no—
300C23×D3—52no—
301C23×D3—102no—
302C23×D3—102no—
303C23×D3—102no—
304C23×D3—102no—
305C23×D3—102no—
306C23×D3—102no—
307C23×D3C2×AGL(1,𝔽5)11yescharacteristic
308C22×C3×C4—52no—
309C22×C3×C4—54no—
310C22×C3×C4—51no—
311C22×C3×C4—52no—
312C22×C3×C4—52no—
313C22×C3×C4—52no—
314C22×C3×C4—102no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4—102no—
319C22×C3×C4—102no—
320C22×C3×C4—102no—
321C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
322C22×Dic3—52no—
323C22×Dic3—54no—
324C22×Dic3—51no—
325C22×Dic3—52no—
326C22×Dic3—52no—
327C22×Dic3—52no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3—102no—
331C22×Dic3—102no—
332C22×Dic3—102no—
333C22×Dic3—102no—
334C22×Dic3—102no—
335C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
336C3×C4⋊C4—108no—
337(C2×D3)⋊C4—54no—
338(C2×D3)⋊C4—54no—
339(C2×D3)⋊C4—54no—
340(C2×D3)⋊C4—108no—
341(C2×D3)⋊C4—108no—
342(C2×D3)⋊C4C2×AGL(1,𝔽5)14yescomplemented
343C4×Dic3—108no—
344C23×C5—32no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5C2×C4×D311yescharacteristic
349C22×D5—32no—
350C22×D5—62no—
351C22×D5—62no—
352C22×D5—62no—
353C22×D5—64no—
354C22×D5—64no—
355C22×D5—64no—
356C22×D5—62no—
357C22×D5—62no—
358C22×D5—62no—
359C22×D5—62no—
360C22×D5—62no—
361C22×D5—62no—
362C22×D5—124no—
363C22×D5—124no—
364C22×D5—124no—
365C22×D5—124no—
366C22×D5C2×C4×D311yescharacteristic
367C22×D5#23512yes—
368C22×D5D3×D412yes—
369C22×D5#23712yes—
370C22×D5#23912yes—
371C22×D5#23912yes—
372C22×D5C2×#6712yes—
373C22×D5C23×D311yescharacteristic
374C2×AGL(1,𝔽5)—28no—
375C2×AGL(1,𝔽5)—22no—
376C2×AGL(1,𝔽5)—22no—
377C2×AGL(1,𝔽5)—22no—
378C2×AGL(1,𝔽5)—22no—
379C2×AGL(1,𝔽5)—22no—
380C2×AGL(1,𝔽5)—34no—
381C2×AGL(1,𝔽5)—44no—
382C2×AGL(1,𝔽5)—68no—
383C2×AGL(1,𝔽5)—62no—
384C2×AGL(1,𝔽5)—62no—
385C2×AGL(1,𝔽5)—62no—
386C2×AGL(1,𝔽5)—62no—
387C2×AGL(1,𝔽5)—62no—
388C2×AGL(1,𝔽5)—124no—
389C2×AGL(1,𝔽5)C2×#6714yes—
390C2×C4×C5—22no—
391C2×C4×C5—32no—
392C2×C4×C5—62no—
393C2×C4×C5C2×C4×D312yes—
394C2×Dic5—22no—
395C2×Dic5—32no—
396C2×Dic5—62no—
397C2×Dic5C2×C4×D312yes—
398C4×D5—24no—
399C4×D5—22no—
400C4×D5—22no—
401C4×D5—64no—
402C4×D5—62no—
403C4×D5—62no—
404C25—151no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—151no—
409C23×C4—151no—
410C23×C4—151no—
411C2×C4⋊C4—54no—
412C2×C4⋊C4—104no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—154no—
415C2×C22⋊C4—154no—
416C2×C22⋊C4—151no—
417C2×C22⋊C4—151no—
418C2×C22⋊C4—151no—
419C2×C22⋊C4—154no—
420C2×C22⋊C4—154no—
421C2×C22⋊C4—304no—
422C2×C22⋊C4—304no—
423C2×C42—154no—
424C2×C42—304no—
425#95—154no—
426#95—154no—
427C2×C3×C5#38814yescomplemented
428C2×C3×C5C2×#11711yescharacteristic
429C2×C3×C5C2×C4×D411yescharacteristic
430C2×C3×C5C2×C4×D411yescharacteristic
431D15—42no—
432C3×D5#38814yescomplemented
433C3×D5C2×#12111yescharacteristic
434C3×D5C2×#12311yescharacteristic
435C3×D5C2×#12411yescharacteristic
436C3×D5C2×#12611yescharacteristic
437C5×D3—42no—
438C23×C3—52no—
439C23×C3—52no—
440C23×C3—52no—
441C23×C3—52no—
442C23×C3—52no—
443C23×C3—52no—
444C23×C3—51no—
445C23×C3—51no—
446C23×C3C22×AGL(1,𝔽5)11yescharacteristic
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—52no—
451C22×D3—102no—
452C22×D3—102no—
453C22×D3—104no—
454C22×D3—102no—
455C22×D3—102no—
456C22×D3—104no—
457C22×D3—104no—
458C22×D3—102no—
459C22×D3—102no—
460C22×D3—102no—
461C22×D3—102no—
462C22×D3—102no—
463C22×D3—204no—
464C22×D3—204no—
465C22×D3—204no—
466C22×D3—204no—
467C22×D3C22×AGL(1,𝔽5)12yes—
468C2×C3×C4—22no—
469C2×C3×C4—54no—
470C2×C3×C4—52no—
471C2×C3×C4—102no—
472C2×C3×C4—104no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—108no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—102no—
480C2×C3×C4—102no—
481C2×C3×C4—204no—
482C2×C3×C4C22×AGL(1,𝔽5)12yes—
483C2×Dic3—22no—
484C2×Dic3—54no—
485C2×Dic3—52no—
486C2×Dic3—102no—
487C2×Dic3—104no—
488C2×Dic3—102no—
489C2×Dic3—108no—
490C2×Dic3—102no—
491C2×Dic3—102no—
492C2×Dic3—102no—
493C2×Dic3—102no—
494C2×Dic3—102no—
495C2×Dic3—102no—
496C2×Dic3—204no—
497C2×Dic3C22×AGL(1,𝔽5)12yes—
498C22×C5—62no—
499C22×C5—62no—
500C22×C5—62no—
501C22×C5—124no—
502C22×C5#89212yes—
503C22×C5#89312yes—
504C22×C5C4×#6712yes—
505C22×C5C22×C4×D311yescharacteristic
506C2×D5—62no—
507C2×D5—62no—
508C2×D5—62no—
509C2×D5—124no—
510C2×D5—128no—
511C2×D5—122no—
512C2×D5—122no—
513C2×D5—122no—
514C2×D5—122no—
515C2×D5#89212yes—
516C2×D5#89312yes—
517C2×D5#89414yes—
518C2×D5#89814yes—
519C2×D5C4×#6712yes—
520C2×D5#93914yes—
521C2×D5#94714yes—
522C2×D5C2×#23511yescharacteristic
523C2×D5C2×D3×D411yescharacteristic
524C2×D5C2×#23711yescharacteristic
525C2×D5C2×#23911yescharacteristic
526C2×D5C2×#23911yescharacteristic
527C2×D5C22×#6711yescharacteristic
528AGL(1,𝔽5)—24no—
529AGL(1,𝔽5)—42no—
530AGL(1,𝔽5)—64no—
531AGL(1,𝔽5)—122no—
532C4×C5—22no—
533C4×C5—62no—
534Dic5—22no—
535Dic5—62no—
536C24—31no—
537C24—51no—
538C24—152no—
539C24—152no—
540C24—151no—
541C24—302no—
542C24—302no—
543C24—302no—
544C24—302no—
545C24—302no—
546C24—302no—
547C22×C4—31no—
548C22×C4—52no—
549C22×C4—54no—
550C22×C4—51no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—52no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—152no—
562C22×C4—152no—
563C22×C4—152no—
564C22×C4—154no—
565C22×C4—151no—
566C22×C4—152no—
567C22×C4—302no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—302no—
571C22×C4—302no—
572C22×C4—302no—
573C22×C4—302no—
574C22×C4D3×AGL(1,𝔽5)11yescharacteristic
575C4⋊C4—108no—
576C22⋊C4—34no—
577C22⋊C4—154no—
578C22⋊C4—154no—
579C22⋊C4—154no—
580C22⋊C4—308no—
581C22⋊C4—308no—
582C42—308no—
583C3×C5C2×#38811yescharacteristic, complemented, Hall
584C22×C3—54no—
585C22×C3—54no—
586C22×C3—54no—
587C22×C3—54no—
588C22×C3—52no—
589C22×C3—51no—
590C22×C3—51no—
591C22×C3—52no—
592C22×C3—52no—
593C22×C3—51no—
594C22×C3—51no—
595C22×C3—51no—
596C22×C3—51no—
597C22×C3#413012yes—
598C22×C3D4×AGL(1,𝔽5)12yes—
599C22×C3D4×AGL(1,𝔽5)12yes—
600C22×C3C23×AGL(1,𝔽5)11yescharacteristic
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—44no—
605C2×D3—102no—
606C2×D3—102no—
607C2×D3—102no—
608C2×D3—202no—
609C2×D3—202no—
610C2×D3—202no—
611C2×D3—202no—
612C2×D3—208no—
613C2×D3—204no—
614C3×C4—22no—
615C3×C4—104no—
616C3×C4—102no—
617C3×C4—202no—
618Dic3—22no—
619Dic3—104no—
620Dic3—102no—
621Dic3—202no—
622C2×C5—122no—
623C2×C5#499014yescomplemented
624C2×C5C2×#89211yescharacteristic
625C2×C5C2×#89311yescharacteristic
626C2×C5C2×C4×#6711yescharacteristic
627D5—122no—
628D5#499014yescomplemented
629D5C2×#89411yescharacteristic
630D5C2×#89811yescharacteristic
631D5C2×#93911yescharacteristic
632D5C2×#94711yescharacteristic
633C23—32no—
634C23—52no—
635C23—52no—
636C23—52no—
637C23—52no—
638C23—52no—
639C23—52no—
640C23—51no—
641C23—51no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—152no—
646C23—302no—
647C23—302no—
648C23—302no—
649C23—302no—
650C23—304no—
651C23—302no—
652C23—304no—
653C23—302no—
654C23—304no—
655C23—302no—
656C23—302no—
657C23—302no—
658C23—604no—
659C23—604no—
660C23—604no—
661C23—604no—
662C23C2×D3×AGL(1,𝔽5)11yescharacteristic
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—54no—
666C2×C4—52no—
667C2×C4—62no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—104no—
671C2×C4—102no—
672C2×C4—102no—
673C2×C4—108no—
674C2×C4—102no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—154no—
679C2×C4—152no—
680C2×C4—204no—
681C2×C4—302no—
682C2×C4—302no—
683C2×C4—304no—
684C2×C4—302no—
685C2×C4—302no—
686C2×C4—308no—
687C2×C4—302no—
688C2×C4—302no—
689C2×C4—302no—
690C2×C4—302no—
691C2×C4—604no—
692C2×C4C2×D3×AGL(1,𝔽5)12yes—
693C2×C3—51no—
694C2×C3—51no—
695C2×C3—51no—
696C2×C3—51no—
697C2×C3—54no—
698C2×C3#6570014yescomplemented
699C2×C3C2×#413011yescharacteristic
700C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
701C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
702D3—42no—
703D3—202no—
704C5C2×#499011yescharacteristic, complemented, Sylow
705C22—51no—
706C22—51no—
707C22—52no—
708C22—51no—
709C22—51no—
710C22—52no—
711C22—51no—
712C22—51no—
713C22—52no—
714C22—54no—
715C22—54no—
716C22—54no—
717C22—54no—
718C22—62no—
719C22—62no—
720C22—62no—
721C22—124no—
722C22—302no—
723C22—302no—
724C22—302no—
725C22—602no—
726C22—602no—
727C22—602no—
728C22—608no—
729C22—602no—
730C22—604no—
731C22#9190712yes—
732C22#9192112yes—
733C22AGL(1,𝔽5)×#6712yes—
734C22C22×D3×AGL(1,𝔽5)11yescharacteristic
735C4—22no—
736C4—62no—
737C4—104no—
738C4—102no—
739C4—202no—
740C4—304no—
741C4—302no—
742C4—602no—
743C3C2×#6570011yescharacteristic, complemented, Sylow
744C2—51no—
745C2—51no—
746C2—51no—
747C2—54no—
748C2—51no—
749C2—122no—
750C2—602no—
751C2#1175183614yesdirect product factor
752C2C2×#9190711yescharacteristic
753C2C2×#9192111yescharacteristic
754C2C2×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×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊AGL(1,𝔽5)C2semidirect
4. C22×Dic3×AGL(1,𝔽5)C2semidirect
6. C2×#91235C2semidirect
7. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
8. #11751836C2direct (N × H)
18. C2×C3×C4⋊AGL(1,𝔽5)C22semidirect
24. C2×Dic3×AGL(1,𝔽5)C22semidirect
25. C2×#6714C4semidirect
26. C2×C5×(C2×D3)⋊C4C4semidirect
27. C2×#6667C4semidirect
28. C2×(C2×D3)⋊Dic5C4semidirect
29. D5×(C2×D3)⋊C4C4semidirect
31. #91235C22semidirect
32. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
36. C22×C4⋊AGL(1,𝔽5)D3semidirect
85. #6714C2×C4semidirect
86. C5×(C2×D3)⋊C4C2×C4semidirect
87. #6667C2×C4semidirect
88. (C2×D3)⋊Dic5C2×C4semidirect
109. C2×C4⋊AGL(1,𝔽5)C2×D3semidirect
199. C2×(C2×D3)⋊C4AGL(1,𝔽5)semidirect
342. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
427. C2×C3×C5#388semidirect
432. C3×D5#388semidirect
583. C3×C5C2×#388semidirect
623. C2×C5#4990semidirect
628. D5#4990semidirect
698. C2×C3#65700semidirect
704. C5C2×#4990semidirect
743. C3C2×#65700semidirect
751. C2#11751836direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊AGL(1,𝔽5)2
C22×(C2×D3)⋊AGL(1,𝔽5)2
C22×Dic3×AGL(1,𝔽5)2
C2×D5×(C2×D3)⋊C42
C2×#912352
C2×(C2×AGL(1,𝔽5))⋊Dic32
#117518362
C2×#657003
C2×#49905