Finite Group Databasebeta

← C3×#10604220 #14302047

Subgroups — C3×#10604220 #14302047

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×#4028C211yesmaximal, characteristic
3C3×#65800C211yesmaximal, characteristic, complemented
4C2×C3×#3999C212yesmaximal, complemented
5C3×#64917C212yesmaximal, complemented
6#10604220C311yesmaximal, characteristic, direct product factor, Hall
7C24×C3×D5C2211yescharacteristic
8C23×C3×AGL(1,𝔽5)—21no—
9C22×C3×C22⋊D5C411yescharacteristic, complemented
10C22×C3×D20C411yescharacteristic, complemented
11C22×C3×D20C2211yescharacteristic
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×C5×C22⋊C4C411yescharacteristic, complemented
19C2×C3×#685C411yescharacteristic, complemented
20C2×C3×#685C2211yescharacteristic
21C3×#4028—21no—
22C3×#4028—21no—
23C3×#4028—21no—
24C3×#4028—21no—
25C3×#3999—24no—
26C3×#1898—51nomaximal, Hall
27C22×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
28C2×#4028C2×C311yescharacteristic
29#65800C2×C311yescharacteristic, complemented
30C2×#3999C2×C312yescomplemented
31#64917C2×C312yescomplemented
32C24×C3×C5C2×C411yescharacteristic
33C23×C3×D5—22no—
34C23×C3×D5—22no—
35C23×C3×D5—42no—
36C23×C3×D5—42no—
37C23×C3×D5C2×C411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic, complemented
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—
49C22×C3×C4×C5C2×C411yescharacteristic, complemented
50C22×C3×C4×C5C2×C411yescharacteristic, complemented
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5—42no—
54C22×C3×Dic5C2×C411yescharacteristic, complemented
55C2×C3×D20—21no—
56C2×C3×D20—21no—
57C2×C3×D20—22no—
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20—22no—
61C2×C3×D20—42no—
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×C5×C22⋊C4—21no—
70C3×C5×C22⋊C4—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×C22⋊D5C3×C411yescharacteristic, complemented
83C22×D20C3×C411yescharacteristic, complemented
84C22×D20C22×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×C5×C22⋊C4C3×C411yescharacteristic, complemented
92C2×#685C3×C411yescharacteristic, complemented
93C2×#685C22×C311yescharacteristic
94#4028—21no—
95#4028—21no—
96#4028—21no—
97#4028—21no—
98#3999—24no—
99#1898—51noSylow
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5—41no—
103C23×C3×C5C22⋊C411yescharacteristic
104C23×C3×C5C22⋊C411yescharacteristic
105C23×C3×C5C22×C411yescharacteristic
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5—21no—
109C22×C3×D5—21no—
110C22×C3×D5—22no—
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—21no—
115C22×C3×D5—22no—
116C22×C3×D5—22no—
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—22no—
120C22×C3×D5—41no—
121C22×C3×D5—41no—
122C22×C3×D5—41no—
123C22×C3×D5—41no—
124C22×C3×D5—41no—
125C22×C3×D5—41no—
126C22×C3×D5—41no—
127C22×C3×D5—48no—
128C22×C3×D5—48no—
129C22×C3×D5—41no—
130C22×C3×D5—41no—
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—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—41no—
148C3×C22⋊D5—42no—
149C3×C22⋊D5—42no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—41no—
152C3×D20—42no—
153C3×D20—42no—
154C3×D20—41no—
155C3×D20—42no—
156C3×D20—41no—
157C25×C3—51no—
158C22×C3×D4—51no—
159C22×C3×D4—51no—
160C22×C3×D4—51no—
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—52no—
170C2×C3×C22⋊C4—104no—
171C2×C3×C22⋊C4—101no—
172C2×C3×C22⋊C4—101no—
173C2×C3×C22⋊C4—101no—
174C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
175C3×#99—104no—
176C24×C5C2×C3×C411yescharacteristic
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—42no—
180C23×D5—42no—
181C23×D5C2×C3×C411yescharacteristic
182C23×D5C2×C3×C411yescharacteristic, complemented
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—
193C22×C4×C5C2×C3×C411yescharacteristic, complemented
194C22×C4×C5C2×C3×C411yescharacteristic, complemented
195C2×C22⋊D5—21no—
196C2×C22⋊D5—21no—
197C2×C22⋊D5—42no—
198C22×Dic5C2×C3×C411yescharacteristic, complemented
199C2×D20—21no—
200C2×D20—21no—
201C2×D20—22no—
202C2×D20—21no—
203C2×D20—21no—
204C2×D20—22no—
205C2×D20—42no—
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
213C5×C22⋊C4—21no—
214C5×C22⋊C4—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#9912yescomplemented
233C22×C3×C5C2×C22⋊C411yescharacteristic
234C22×C3×C5C4×D412yes—
235C2×C3×D5—24no—
236C2×C3×D5—24no—
237C2×C3×D5—21no—
238C2×C3×D5—21no—
239C2×C3×D5—21no—
240C2×C3×D5—21no—
241C2×C3×D5—21no—
242C2×C3×D5—21no—
243C2×C3×D5—21no—
244C2×C3×D5—21no—
245C2×C3×D5—21no—
246C2×C3×D5—42no—
247C2×C3×D5—42no—
248C2×C3×D5—44no—
249C2×C3×D5—44no—
250C2×C3×D5—44no—
251C2×C3×D5—42no—
252C2×C3×D5—42no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C2×C3×D5—41no—
256C2×C3×D5—82no—
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×C4×C5—41no—
265C3×Dic5—41no—
266C24×C3—51no—
267C24×C3—51no—
268C24×C3—51no—
269C24×C3—51no—
270C24×C3—51no—
271C24×C3—51no—
272C24×C3—51no—
273C24×C3—102no—
274C24×C3—102no—
275C24×C3—202no—
276C24×C3—202no—
277C24×C3C2×AGL(1,𝔽5)11yescharacteristic
278C2×C3×D4—102no—
279C2×C3×D4—101no—
280C2×C3×D4—101no—
281C2×C3×D4—101no—
282C2×C3×D4—101no—
283C2×C3×D4—102no—
284C2×C3×D4—101no—
285C2×C3×D4—101no—
286C2×C3×D4—202no—
287C2×C3×D4—202no—
288C22×C3×C4—51no—
289C22×C3×C4—102no—
290C22×C3×C4—104no—
291C22×C3×C4—102no—
292C22×C3×C4—202no—
293C22×C3×C4—202no—
294C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
295C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
296C3×C22⋊C4—21no—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—54no—
299C3×C22⋊C4—101no—
300C3×C22⋊C4—101no—
301C3×C22⋊C4—101no—
302C3×C22⋊C4—101no—
303C3×C22⋊C4—102no—
304C3×C22⋊C4—104no—
305C3×C22⋊C4—102no—
306C3×C22⋊C4—102no—
307C3×C22⋊C4—202no—
308C3×C22⋊C4—202no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—41no—
312C23×C5C3×C22⋊C411yescharacteristic
313C23×C5C3×C22⋊C411yescharacteristic
314C23×C5C22×C3×C411yescharacteristic
315C22×D5—22no—
316C22×D5—22no—
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—21no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—21no—
327C22×D5—21no—
328C22×D5—22no—
329C22×D5—41no—
330C22×D5—41no—
331C22×D5—41no—
332C22×D5—41no—
333C22×D5—41no—
334C22×D5—41no—
335C22×D5—41no—
336C22×D5—48no—
337C22×D5—48no—
338C22×D5—41no—
339C22×D5—41no—
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—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—22no—
356C2×C4×C5—41no—
357C22⋊D5—42no—
358C22⋊D5—42no—
359C2×Dic5—21no—
360C2×Dic5—41no—
361D20—42no—
362D20—42no—
363D20—41no—
364D20—42no—
365D20—41no—
366C25—51no—
367C22×D4—51no—
368C22×D4—51no—
369C22×D4—51no—
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—52no—
379C2×C22⋊C4—104no—
380C2×C22⋊C4—101no—
381C2×C22⋊C4—101no—
382C2×C22⋊C4—101no—
383C2×C22⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
384#99—104no—
385C2×C3×C5—22no—
386C2×C3×C5—22no—
387C2×C3×C5—41no—
388C2×C3×C5#38611yescharacteristic
389C2×C3×C5C2×#9911yescharacteristic
390C2×C3×C5C2×#9911yescharacteristic
391C3×D5—21no—
392C3×D5—22no—
393C3×D5—22no—
394C3×D5—21no—
395C3×D5—41no—
396C3×D5—81no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—41no—
400C23×C3—51no—
401C23×C3—51no—
402C23×C3—51no—
403C23×C3—52no—
404C23×C3—52no—
405C23×C3—51no—
406C23×C3—101no—
407C23×C3—102no—
408C23×C3—101no—
409C23×C3—101no—
410C23×C3—102no—
411C23×C3—102no—
412C23×C3—102no—
413C23×C3—102no—
414C23×C3—101no—
415C23×C3—102no—
416C23×C3—102no—
417C23×C3—102no—
418C23×C3—101no—
419C23×C3—102no—
420C23×C3—201no—
421C23×C3—201no—
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—201no—
435C3×D4—202no—
436C3×D4—201no—
437C3×D4—202no—
438C3×D4—202no—
439C3×D4—202no—
440C3×D4—202no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—41no—
445C2×C3×C4—104no—
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×C5C3×#9912yescomplemented
463C22×C5C2×C3×C22⋊C411yescharacteristic
464C22×C5C3×C4×D412yes—
465C2×D5—24no—
466C2×D5—24no—
467C2×D5—21no—
468C2×D5—21no—
469C2×D5—21no—
470C2×D5—21no—
471C2×D5—21no—
472C2×D5—21no—
473C2×D5—21no—
474C2×D5—21no—
475C2×D5—21no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—44no—
479C2×D5—44no—
480C2×D5—44no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—41no—
484C2×D5—41no—
485C2×D5—41no—
486C2×D5—82no—
487C2×D5C3×#9912yescomplemented
488C2×D5C3×#12011yescharacteristic
489C2×D5C3×#12112yes—
490C2×D5C3×#12311yescharacteristic
491AGL(1,𝔽5)—44no—
492AGL(1,𝔽5)—82no—
493C4×C5—41no—
494C4×C5—41no—
495Dic5—41no—
496C24—51no—
497C24—51no—
498C24—51no—
499C24—51no—
500C24—51no—
501C24—51no—
502C24—51no—
503C24—102no—
504C24—102no—
505C24—202no—
506C24—202no—
507C24C2×C3×AGL(1,𝔽5)11yescharacteristic
508C2×D4—102no—
509C2×D4—101no—
510C2×D4—101no—
511C2×D4—101no—
512C2×D4—101no—
513C2×D4—102no—
514C2×D4—101no—
515C2×D4—101no—
516C2×D4—202no—
517C2×D4—202no—
518C22×C4—51no—
519C22×C4—102no—
520C22×C4—104no—
521C22×C4—102no—
522C22×C4—202no—
523C22×C4—202no—
524C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
525C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—54no—
529C22⋊C4—101no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C22⋊C4—101no—
533C22⋊C4—102no—
534C22⋊C4—104no—
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—52no—
549C22×C3—51no—
550C22×C3—52no—
551C22×C3—51no—
552C22×C3—104no—
553C22×C3—104no—
554C22×C3—101no—
555C22×C3—101no—
556C22×C3—101no—
557C22×C3—101no—
558C22×C3—101no—
559C22×C3—101no—
560C22×C3—101no—
561C22×C3—101no—
562C22×C3—101no—
563C22×C3—202no—
564C22×C3—202no—
565C22×C3—204no—
566C22×C3—204no—
567C22×C3—204no—
568C22×C3—202no—
569C22×C3—202no—
570C22×C3—201no—
571C22×C3—201no—
572C22×C3—201no—
573C22×C3—402no—
574C22×C3#399912yescomplemented
575C22×C3D4×AGL(1,𝔽5)12yes—
576C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—204no—
580C3×C4—201no—
581C3×C4—402no—
582C2×C5—22no—
583C2×C5—22no—
584C2×C5—41no—
585C2×C5C3×#38611yescharacteristic
586C2×C5C2×C3×#9911yescharacteristic
587C2×C5C2×C3×#9911yescharacteristic
588D5—21no—
589D5—22no—
590D5—22no—
591D5—21no—
592D5—41no—
593D5—81no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—51no—
598C23—51no—
599C23—51no—
600C23—52no—
601C23—52no—
602C23—51no—
603C23—101no—
604C23—102no—
605C23—101no—
606C23—101no—
607C23—102no—
608C23—102no—
609C23—102no—
610C23—102no—
611C23—101no—
612C23—102no—
613C23—102no—
614C23—102no—
615C23—101no—
616C23—102no—
617C23—201no—
618C23—201no—
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—201no—
632D4—202no—
633D4—201no—
634D4—202no—
635D4—202no—
636D4—202no—
637D4—202no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—41no—
642C2×C4—104no—
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—101no—
655C2×C3—102no—
656C2×C3—102no—
657C2×C3—101no—
658C2×C3—201no—
659C2×C3—401no—
660C2×C3C2×#399911yescharacteristic
661C2×C3D5⋊#9911yescharacteristic
662C2×C3#6577911yescharacteristic
663C5C3×#189811yescharacteristic, complemented, Sylow
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—44no—
672C22—52no—
673C22—51no—
674C22—52no—
675C22—51no—
676C22—104no—
677C22—104no—
678C22—101no—
679C22—101no—
680C22—101no—
681C22—101no—
682C22—101no—
683C22—101no—
684C22—101no—
685C22—101no—
686C22—101no—
687C22—202no—
688C22—202no—
689C22—204no—
690C22—204no—
691C22—204no—
692C22—202no—
693C22—202no—
694C22—201no—
695C22—201no—
696C22—201no—
697C22—402no—
698C22C3×#399912yescomplemented
699C22C3×D4×AGL(1,𝔽5)12yes—
700C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
701C4—41no—
702C4—41no—
703C4—204no—
704C4—201no—
705C4—402no—
706C3#1060422011yescharacteristic, direct product factor, Sylow
707C2—22no—
708C2—22no—
709C2—41no—
710C2—101no—
711C2—102no—
712C2—102no—
713C2—101no—
714C2—201no—
715C2—401no—
716C2C2×C3×#399911yescharacteristic
717C2C3×D5⋊#9911yescharacteristic
718C2C3×#6577911yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4028C2
cosocleC23×D5C23×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1898
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×C22⋊C4

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×#3999C2semidirect
5. C3×#64917C2semidirect
6. #10604220C3direct (N × H)
9. C22×C3×C22⋊D5C4semidirect
10. C22×C3×D20C4semidirect
18. C2×C3×C5×C22⋊C4C4semidirect
19. C2×C3×#685C4semidirect
27. C22×C22⋊AGL(1,𝔽5)C2×C3semidirect
29. #65800C2×C3semidirect
30. C2×#3999C2×C3semidirect
31. #64917C2×C3semidirect
38. C23×C3×D5C2×C4semidirect
49. C22×C3×C4×C5C2×C4semidirect
50. C22×C3×C4×C5C2×C4semidirect
54. C22×C3×Dic5C2×C4semidirect
68. C3×C22⋊AGL(1,𝔽5)D4semidirect
82. C22×C22⋊D5C3×C4semidirect
83. C22×D20C3×C4semidirect
91. C2×C5×C22⋊C4C3×C4semidirect
92. C2×#685C3×C4semidirect
174. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
182. C23×D5C2×C3×C4semidirect
193. C22×C4×C5C2×C3×C4semidirect
194. C22×C4×C5C2×C3×C4semidirect
198. C22×Dic5C2×C3×C4semidirect
212. C22⋊AGL(1,𝔽5)C3×D4semidirect
232. C22×C3×C5#99semidirect
257. C2×C3×D5#99semidirect
294. C22×C3×C4C2×AGL(1,𝔽5)semidirect
295. C22×C3×C4C2×AGL(1,𝔽5)semidirect
383. C2×C22⋊C4C3×AGL(1,𝔽5)semidirect
462. C22×C5C3×#99semidirect
487. C2×D5C3×#99semidirect
524. C22×C4C2×C3×AGL(1,𝔽5)semidirect
525. C22×C4C2×C3×AGL(1,𝔽5)semidirect
539. C3×C5#1898semidirect
574. C22×C3#3999semidirect
663. C5C3×#1898semidirect
698. C22C3×#3999semidirect
706. C3#10604220direct (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×#40282
C3×#658002
C2×C3×#39992
C3×#649172
#106042203
C3×#18985