Finite Group Databasebeta

← C3×#10604943 #14302049

Subgroups — C3×#10604943 #14302049

Order 1920.

1196 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
1C22×C3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×C3×#4083C211yesmaximal, characteristic
3C3×#65800C211yesmaximal, characteristic, complemented
4C2×C3×#4011C212yesmaximal, complemented
5C3×#64917C212yesmaximal, complemented
6#10604943C311yesmaximal, characteristic, direct product factor, Hall
7C24×C3×D5C2211yescharacteristic
8C23×C3×AGL(1,𝔽5)—21no—
9C22×C3×C5×D4C411yescharacteristic, complemented
10C22×C3×C22⋊D5C411yescharacteristic, complemented
11C22×C3×C22⋊D5C2211yescharacteristic
12C2×C3×C22⋊AGL(1,𝔽5)—21no—
13C2×C3×C22⋊AGL(1,𝔽5)—24no—
14C2×C3×C22⋊AGL(1,𝔽5)—21no—
15C2×C3×C22⋊AGL(1,𝔽5)—21no—
16C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
17C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
18C2×C3×C22⋊Dic5C411yescharacteristic, complemented
19C3×#4083—21no—
20C3×#4083—21no—
21C3×#4083—21no—
22C3×#4083—21no—
23C2×C3×#685C411yescharacteristic, complemented
24C2×C3×#685C2211yescharacteristic
25C3×#4011—24no—
26C3×#1898—51nomaximal, Hall
27C22×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
28C2×#4083C2×C311yescharacteristic
29#65800C2×C311yescharacteristic, complemented
30C2×#4011C2×C312yescomplemented
31#64917C2×C312yescomplemented
32C24×C3×C5C2×C411yescharacteristic
33C24×C3×C5C2×C411yescharacteristic, complemented
34C23×C3×D5—22no—
35C23×C3×D5—22no—
36C23×C3×D5—42no—
37C23×C3×D5—42no—
38C23×C3×D5C2×C411yescharacteristic
39C23×C3×D5D411yescharacteristic
40C23×C3×D5D411yescharacteristic
41C23×C3×D5D411yescharacteristic
42C23×C3×D5D411yescharacteristic
43C23×C3×D5C2311yescharacteristic
44C22×C3×AGL(1,𝔽5)—24no—
45C22×C3×AGL(1,𝔽5)—22no—
46C22×C3×AGL(1,𝔽5)—22no—
47C22×C3×AGL(1,𝔽5)—42no—
48C22×C3×AGL(1,𝔽5)—42no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—42no—
52C22×C3×C4×C5C2×C411yescharacteristic, complemented
53C2×C3×C22⋊D5—21no—
54C2×C3×C22⋊D5—21no—
55C2×C3×C22⋊D5—21no—
56C2×C3×C22⋊D5—21no—
57C2×C3×C22⋊D5—22no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5—42no—
60C22×C3×Dic5C2×C411yescharacteristic, complemented
61C22×C3×Dic5C2×C411yescharacteristic, complemented
62C3×C22⋊AGL(1,𝔽5)—24no—
63C3×C22⋊AGL(1,𝔽5)—22no—
64C3×C22⋊AGL(1,𝔽5)—22no—
65C3×C22⋊AGL(1,𝔽5)—22no—
66C3×C22⋊AGL(1,𝔽5)—42no—
67C3×C22⋊AGL(1,𝔽5)—42no—
68C3×C22⋊AGL(1,𝔽5)D414yescomplemented
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×#685—21no—
72C3×#685—21no—
73C3×#685—21no—
74C3×#685—21no—
75C2×C3×#120—51no—
76C22×C3×C22⋊C4—51no—
77C2×C3×#99—52no—
78C3×#379—51no—
79C3×#342—52no—
80C24×D5C22×C311yescharacteristic
81C23×AGL(1,𝔽5)—21no—
82C22×C5×D4C3×C411yescharacteristic, complemented
83C22×C22⋊D5C3×C411yescharacteristic, complemented
84C22×C22⋊D5C22×C311yescharacteristic
85C2×C22⋊AGL(1,𝔽5)—21no—
86C2×C22⋊AGL(1,𝔽5)—24no—
87C2×C22⋊AGL(1,𝔽5)—21no—
88C2×C22⋊AGL(1,𝔽5)—21no—
89C2×C22⋊AGL(1,𝔽5)C22×C312yes—
90C2×C22⋊AGL(1,𝔽5)C22×C312yes—
91C2×C22⋊Dic5C3×C411yescharacteristic, complemented
92#4083—21no—
93#4083—21no—
94#4083—21no—
95#4083—21no—
96C2×#685C3×C411yescharacteristic, complemented
97C2×#685C22×C311yescharacteristic
98#4011—24no—
99#1898—51noSylow
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5—21no—
103C23×C3×C5—22no—
104C23×C3×C5—41no—
105C23×C3×C5—41no—
106C23×C3×C5—41no—
107C23×C3×C5C22⋊C411yescharacteristic
108C23×C3×C5C22⋊C411yescharacteristic
109C23×C3×C5C22×C411yescharacteristic
110C22×C3×D5—22no—
111C22×C3×D5—22no—
112C22×C3×D5—21no—
113C22×C3×D5—21no—
114C22×C3×D5—22no—
115C22×C3×D5—22no—
116C22×C3×D5—22no—
117C22×C3×D5—22no—
118C22×C3×D5—21no—
119C22×C3×D5—22no—
120C22×C3×D5—22no—
121C22×C3×D5—21no—
122C22×C3×D5—41no—
123C22×C3×D5—41no—
124C22×C3×D5—41no—
125C22×C3×D5—41no—
126C22×C3×D5—41no—
127C22×C3×D5—41no—
128C22×C3×D5—41no—
129C22×C3×D5—48no—
130C22×C3×D5—48no—
131C22×C3×D5C22⋊C411yescharacteristic
132C22×C3×D5C22⋊C411yescharacteristic
133C22×C3×D5C2×D411yescharacteristic
134C22×C3×D5C2×D411yescharacteristic
135C22×C3×D5C2×D412yes—
136C22×C3×D5#4112yes—
137C2×C3×AGL(1,𝔽5)—24no—
138C2×C3×AGL(1,𝔽5)—48no—
139C2×C3×AGL(1,𝔽5)—42no—
140C2×C3×AGL(1,𝔽5)—42no—
141C2×C3×AGL(1,𝔽5)—42no—
142C2×C3×AGL(1,𝔽5)—42no—
143C2×C3×AGL(1,𝔽5)—42no—
144C3×C5×D4—42no—
145C3×C5×D4—42no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—41no—
148C3×C22⋊D5—42no—
149C3×C22⋊D5—42no—
150C3×C22⋊D5—41no—
151C3×C22⋊D5—42no—
152C3×C22⋊D5—41no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—41no—
157C25×C3—51no—
158C22×C3×D4—51no—
159C22×C3×D4—51no—
160C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
161C23×C3×C4—101no—
162C3×#120—101no—
163C3×#120—101no—
164C3×#120—101no—
165C3×#120—101no—
166C2×C3×C22⋊C4—52no—
167C2×C3×C22⋊C4—51no—
168C2×C3×C22⋊C4—51no—
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—52no—
171C2×C3×C22⋊C4—104no—
172C2×C3×C22⋊C4—101no—
173C2×C3×C22⋊C4—101no—
174C2×C3×C22⋊C4—101no—
175C3×#99—104no—
176C24×C5C2×C3×C411yescharacteristic
177C24×C5C2×C3×C411yescharacteristic, complemented
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—42no—
181C23×D5—42no—
182C23×D5C2×C3×C411yescharacteristic
183C23×D5C3×D411yescharacteristic
184C23×D5C3×D411yescharacteristic
185C23×D5C3×D411yescharacteristic
186C23×D5C3×D411yescharacteristic
187C23×D5C23×C311yescharacteristic
188C22×AGL(1,𝔽5)—24no—
189C22×AGL(1,𝔽5)—22no—
190C22×AGL(1,𝔽5)—22no—
191C22×AGL(1,𝔽5)—42no—
192C22×AGL(1,𝔽5)—42no—
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—42no—
196C22×C4×C5C2×C3×C411yescharacteristic, complemented
197C2×C22⋊D5—21no—
198C2×C22⋊D5—21no—
199C2×C22⋊D5—22no—
200C2×C22⋊D5—21no—
201C2×C22⋊D5—21no—
202C2×C22⋊D5—22no—
203C2×C22⋊D5—42no—
204C22×Dic5C2×C3×C411yescharacteristic, complemented
205C22×Dic5C2×C3×C411yescharacteristic, complemented
206C22⋊AGL(1,𝔽5)—24no—
207C22⋊AGL(1,𝔽5)—22no—
208C22⋊AGL(1,𝔽5)—22no—
209C22⋊AGL(1,𝔽5)—22no—
210C22⋊AGL(1,𝔽5)—42no—
211C22⋊AGL(1,𝔽5)—42no—
212C22⋊AGL(1,𝔽5)C3×D414yescomplemented
213C22⋊Dic5—21no—
214C22⋊Dic5—21no—
215#685—21no—
216#685—21no—
217#685—21no—
218#685—21no—
219C2×#120—51no—
220C22×C22⋊C4—51no—
221C2×#99—52no—
222#379—51no—
223#342—52no—
224C22×C3×C5—21no—
225C22×C3×C5—21no—
226C22×C3×C5—21no—
227C22×C3×C5—21no—
228C22×C3×C5—21no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5—44no—
232C22×C3×C5—41no—
233C22×C3×C5—41no—
234C22×C3×C5—41no—
235C22×C3×C5—82no—
236C22×C3×C5#9912yescomplemented
237C22×C3×C5C2×C22⋊C411yescharacteristic
238C22×C3×C5C4×D412yes—
239C2×C3×D5—24no—
240C2×C3×D5—24no—
241C2×C3×D5—21no—
242C2×C3×D5—21no—
243C2×C3×D5—21no—
244C2×C3×D5—21no—
245C2×C3×D5—21no—
246C2×C3×D5—21no—
247C2×C3×D5—21no—
248C2×C3×D5—21no—
249C2×C3×D5—21no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C2×C3×D5—44no—
253C2×C3×D5—44no—
254C2×C3×D5—44no—
255C2×C3×D5—42no—
256C2×C3×D5—42no—
257C2×C3×D5#9912yescomplemented
258C2×C3×D5#12011yescharacteristic
259C2×C3×D5#12112yes—
260C2×C3×D5#12311yescharacteristic
261C3×AGL(1,𝔽5)—44no—
262C3×AGL(1,𝔽5)—82no—
263C3×C4×C5—41no—
264C3×Dic5—41no—
265C3×Dic5—41no—
266C24×C3—51no—
267C24×C3—51no—
268C24×C3—51no—
269C24×C3—51no—
270C24×C3—51no—
271C24×C3—51no—
272C24×C3—102no—
273C24×C3—102no—
274C24×C3—202no—
275C24×C3—202no—
276C24×C3C2×AGL(1,𝔽5)11yescharacteristic
277C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—42no—
281C2×C3×D4—102no—
282C2×C3×D4—101no—
283C2×C3×D4—101no—
284C2×C3×D4—101no—
285C2×C3×D4—101no—
286C2×C3×D4—102no—
287C2×C3×D4—202no—
288C22×C3×C4—51no—
289C22×C3×C4—51no—
290C22×C3×C4—102no—
291C22×C3×C4—104no—
292C22×C3×C4—102no—
293C22×C3×C4—202no—
294C22×C3×C4—202no—
295C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
296C3×C22⋊C4—54no—
297C3×C22⋊C4—101no—
298C3×C22⋊C4—101no—
299C3×C22⋊C4—101no—
300C3×C22⋊C4—101no—
301C3×C22⋊C4—102no—
302C3×C22⋊C4—104no—
303C3×C22⋊C4—101no—
304C3×C22⋊C4—101no—
305C3×C22⋊C4—102no—
306C3×C22⋊C4—102no—
307C3×C22⋊C4—202no—
308C3×C22⋊C4—202no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—21no—
312C23×C5—22no—
313C23×C5—41no—
314C23×C5—41no—
315C23×C5—41no—
316C23×C5C3×C22⋊C411yescharacteristic
317C23×C5C3×C22⋊C411yescharacteristic
318C23×C5C22×C3×C411yescharacteristic
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—22no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—21no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—21no—
331C22×D5—41no—
332C22×D5—41no—
333C22×D5—41no—
334C22×D5—41no—
335C22×D5—41no—
336C22×D5—41no—
337C22×D5—41no—
338C22×D5—48no—
339C22×D5—48no—
340C22×D5C3×C22⋊C411yescharacteristic
341C22×D5C3×C22⋊C411yescharacteristic
342C22×D5C2×C3×D411yescharacteristic
343C22×D5C2×C3×D411yescharacteristic
344C22×D5C2×C3×D412yes—
345C22×D5C3×#4112yes—
346C2×AGL(1,𝔽5)—24no—
347C2×AGL(1,𝔽5)—48no—
348C2×AGL(1,𝔽5)—42no—
349C2×AGL(1,𝔽5)—42no—
350C2×AGL(1,𝔽5)—42no—
351C2×AGL(1,𝔽5)—42no—
352C2×AGL(1,𝔽5)—42no—
353C5×D4—42no—
354C5×D4—42no—
355C2×C4×C5—21no—
356C2×C4×C5—41no—
357C22⋊D5—42no—
358C22⋊D5—42no—
359C22⋊D5—41no—
360C22⋊D5—42no—
361C22⋊D5—41no—
362C2×Dic5—21no—
363C2×Dic5—21no—
364C2×Dic5—22no—
365C2×Dic5—41no—
366C25—51no—
367C22×D4—51no—
368C22×D4—51no—
369C22×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
370C23×C4—101no—
371#120—101no—
372#120—101no—
373#120—101no—
374#120—101no—
375C2×C22⋊C4—52no—
376C2×C22⋊C4—51no—
377C2×C22⋊C4—51no—
378C2×C22⋊C4—51no—
379C2×C22⋊C4—52no—
380C2×C22⋊C4—104no—
381C2×C22⋊C4—101no—
382C2×C22⋊C4—101no—
383C2×C22⋊C4—101no—
384#99—104no—
385C2×C3×C5—22no—
386C2×C3×C5—22no—
387C2×C3×C5—41no—
388C2×C3×C5—81no—
389C2×C3×C5#38611yescharacteristic
390C2×C3×C5C2×#9911yescharacteristic
391C2×C3×C5C2×#9911yescharacteristic
392C3×D5—21no—
393C3×D5—22no—
394C3×D5—22no—
395C3×D5—21no—
396C3×D5—41no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—51no—
405C23×C3—51no—
406C23×C3—51no—
407C23×C3—52no—
408C23×C3—52no—
409C23×C3—51no—
410C23×C3—101no—
411C23×C3—102no—
412C23×C3—101no—
413C23×C3—101no—
414C23×C3—102no—
415C23×C3—102no—
416C23×C3—102no—
417C23×C3—102no—
418C23×C3—101no—
419C23×C3—102no—
420C23×C3—102no—
421C23×C3—102no—
422C23×C3—201no—
423C23×C3—201no—
424C23×C3—201no—
425C23×C3—201no—
426C23×C3—201no—
427C23×C3—201no—
428C23×C3—201no—
429C23×C3—208no—
430C23×C3—208no—
431C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
432C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
433C23×C3C22×AGL(1,𝔽5)11yescharacteristic
434C3×D4—42no—
435C3×D4—42no—
436C3×D4—201no—
437C3×D4—202no—
438C3×D4—201no—
439C3×D4—202no—
440C3×D4—202no—
441C2×C3×C4—21no—
442C2×C3×C4—41no—
443C2×C3×C4—104no—
444C2×C3×C4—102no—
445C2×C3×C4—101no—
446C2×C3×C4—101no—
447C2×C3×C4—208no—
448C2×C3×C4—202no—
449C2×C3×C4—202no—
450C2×C3×C4—201no—
451C2×C3×C4—202no—
452C2×C3×C4—202no—
453C2×C3×C4—202no—
454C22×C5—21no—
455C22×C5—21no—
456C22×C5—21no—
457C22×C5—21no—
458C22×C5—21no—
459C22×C5—21no—
460C22×C5—21no—
461C22×C5—44no—
462C22×C5—41no—
463C22×C5—41no—
464C22×C5—41no—
465C22×C5—82no—
466C22×C5C3×#9912yescomplemented
467C22×C5C2×C3×C22⋊C411yescharacteristic
468C22×C5C3×C4×D412yes—
469C2×D5—24no—
470C2×D5—24no—
471C2×D5—21no—
472C2×D5—21no—
473C2×D5—21no—
474C2×D5—21no—
475C2×D5—21no—
476C2×D5—21no—
477C2×D5—21no—
478C2×D5—21no—
479C2×D5—21no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—44no—
483C2×D5—44no—
484C2×D5—44no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5C3×#9912yescomplemented
488C2×D5C3×#12011yescharacteristic
489C2×D5C3×#12112yes—
490C2×D5C3×#12311yescharacteristic
491AGL(1,𝔽5)—44no—
492AGL(1,𝔽5)—82no—
493C4×C5—41no—
494Dic5—41no—
495Dic5—41no—
496C24—51no—
497C24—51no—
498C24—51no—
499C24—51no—
500C24—51no—
501C24—51no—
502C24—102no—
503C24—102no—
504C24—202no—
505C24—202no—
506C24C2×C3×AGL(1,𝔽5)11yescharacteristic
507C24C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—102no—
512C2×D4—101no—
513C2×D4—101no—
514C2×D4—101no—
515C2×D4—101no—
516C2×D4—102no—
517C2×D4—202no—
518C22×C4—51no—
519C22×C4—51no—
520C22×C4—102no—
521C22×C4—104no—
522C22×C4—102no—
523C22×C4—202no—
524C22×C4—202no—
525C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
526C22⋊C4—54no—
527C22⋊C4—101no—
528C22⋊C4—101no—
529C22⋊C4—101no—
530C22⋊C4—101no—
531C22⋊C4—102no—
532C22⋊C4—104no—
533C22⋊C4—101no—
534C22⋊C4—101no—
535C22⋊C4—102no—
536C22⋊C4—102no—
537C22⋊C4—202no—
538C22⋊C4—202no—
539C3×C5#189811yescharacteristic, complemented, Hall
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—44no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—52no—
552C22×C3—51no—
553C22×C3—52no—
554C22×C3—51no—
555C22×C3—82no—
556C22×C3—104no—
557C22×C3—104no—
558C22×C3—101no—
559C22×C3—101no—
560C22×C3—101no—
561C22×C3—101no—
562C22×C3—101no—
563C22×C3—101no—
564C22×C3—101no—
565C22×C3—101no—
566C22×C3—101no—
567C22×C3—202no—
568C22×C3—202no—
569C22×C3—204no—
570C22×C3—204no—
571C22×C3—204no—
572C22×C3—202no—
573C22×C3—202no—
574C22×C3#401112yescomplemented
575C22×C3D4×AGL(1,𝔽5)12yes—
576C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
577C3×C4—41no—
578C3×C4—204no—
579C3×C4—201no—
580C3×C4—201no—
581C3×C4—402no—
582C2×C5—22no—
583C2×C5—22no—
584C2×C5—41no—
585C2×C5—81no—
586C2×C5C3×#38611yescharacteristic
587C2×C5C2×C3×#9911yescharacteristic
588C2×C5C2×C3×#9911yescharacteristic
589D5—21no—
590D5—22no—
591D5—22no—
592D5—21no—
593D5—41no—
594C23—22no—
595C23—22no—
596C23—21no—
597C23—22no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—51no—
602C23—51no—
603C23—51no—
604C23—52no—
605C23—52no—
606C23—51no—
607C23—101no—
608C23—102no—
609C23—101no—
610C23—101no—
611C23—102no—
612C23—102no—
613C23—102no—
614C23—102no—
615C23—101no—
616C23—102no—
617C23—102no—
618C23—102no—
619C23—201no—
620C23—201no—
621C23—201no—
622C23—201no—
623C23—201no—
624C23—201no—
625C23—201no—
626C23—208no—
627C23—208no—
628C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
629C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
630C23C22×C3×AGL(1,𝔽5)11yescharacteristic
631D4—42no—
632D4—42no—
633D4—201no—
634D4—202no—
635D4—201no—
636D4—202no—
637D4—202no—
638C2×C4—21no—
639C2×C4—41no—
640C2×C4—104no—
641C2×C4—102no—
642C2×C4—101no—
643C2×C4—101no—
644C2×C4—208no—
645C2×C4—202no—
646C2×C4—202no—
647C2×C4—201no—
648C2×C4—202no—
649C2×C4—202no—
650C2×C4—202no—
651C2×C3—22no—
652C2×C3—22no—
653C2×C3—41no—
654C2×C3—81no—
655C2×C3—101no—
656C2×C3—102no—
657C2×C3—102no—
658C2×C3—101no—
659C2×C3—201no—
660C2×C3D5⋊#9911yescharacteristic
661C2×C3#6577911yescharacteristic
662C2×C3C2×#401111yescharacteristic
663C5C3×#189811yescharacteristic, complemented, Sylow
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—44no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—52no—
676C22—51no—
677C22—52no—
678C22—51no—
679C22—82no—
680C22—104no—
681C22—104no—
682C22—101no—
683C22—101no—
684C22—101no—
685C22—101no—
686C22—101no—
687C22—101no—
688C22—101no—
689C22—101no—
690C22—101no—
691C22—202no—
692C22—202no—
693C22—204no—
694C22—204no—
695C22—204no—
696C22—202no—
697C22—202no—
698C22C3×#401112yescomplemented
699C22C3×D4×AGL(1,𝔽5)12yes—
700C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
701C4—41no—
702C4—204no—
703C4—201no—
704C4—201no—
705C4—402no—
706C3#1060494311yescharacteristic, direct product factor, Sylow
707C2—22no—
708C2—22no—
709C2—41no—
710C2—81no—
711C2—101no—
712C2—102no—
713C2—102no—
714C2—101no—
715C2—201no—
716C2C3×D5⋊#9911yescharacteristic
717C2C3×#6577911yescharacteristic
718C2C2×C3×#401111yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4083C2
cosocleC23×D5C23×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#1898
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊AGL(1,𝔽5)C2semidirect
3. C3×#65800C2semidirect
4. C2×C3×#4011C2semidirect
5. C3×#64917C2semidirect
6. #10604943C3direct (N × H)
9. C22×C3×C5×D4C4semidirect
10. C22×C3×C22⋊D5C4semidirect
18. C2×C3×C22⋊Dic5C4semidirect
23. C2×C3×#685C4semidirect
27. C22×C22⋊AGL(1,𝔽5)C2×C3semidirect
29. #65800C2×C3semidirect
30. C2×#4011C2×C3semidirect
31. #64917C2×C3semidirect
33. C24×C3×C5C2×C4semidirect
52. C22×C3×C4×C5C2×C4semidirect
60. C22×C3×Dic5C2×C4semidirect
61. C22×C3×Dic5C2×C4semidirect
68. C3×C22⋊AGL(1,𝔽5)D4semidirect
82. C22×C5×D4C3×C4semidirect
83. C22×C22⋊D5C3×C4semidirect
91. C2×C22⋊Dic5C3×C4semidirect
96. C2×#685C3×C4semidirect
160. C22×C3×D4AGL(1,𝔽5)semidirect
177. C24×C5C2×C3×C4semidirect
196. C22×C4×C5C2×C3×C4semidirect
204. C22×Dic5C2×C3×C4semidirect
205. C22×Dic5C2×C3×C4semidirect
212. C22⋊AGL(1,𝔽5)C3×D4semidirect
236. C22×C3×C5#99semidirect
257. C2×C3×D5#99semidirect
277. C24×C3C2×AGL(1,𝔽5)semidirect
295. C22×C3×C4C2×AGL(1,𝔽5)semidirect
369. C22×D4C3×AGL(1,𝔽5)semidirect
466. C22×C5C3×#99semidirect
487. C2×D5C3×#99semidirect
507. C24C2×C3×AGL(1,𝔽5)semidirect
525. C22×C4C2×C3×AGL(1,𝔽5)semidirect
539. C3×C5#1898semidirect
574. C22×C3#4011semidirect
663. C5C3×#1898semidirect
698. C22C3×#4011semidirect
706. C3#10604943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊AGL(1,𝔽5)2
C2×C3×#40832
C3×#658002
C2×C3×#40112
C3×#649172
#106049433
C3×#18985