Finite Group Databasebeta

← C3×#10611735 #14424193

Subgroups — C3×#10611735 #14424193

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4144C211yesmaximal, characteristic, complemented
2C2×C3×#4057C211yesmaximal, characteristic, complemented
3C2×C3×D5×D8C211yesmaximal, characteristic, complemented
4C3×#65941C211yesmaximal, characteristic, complemented
5C3×C5×#447C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7C3×#65447C211yesmaximal, characteristic, complemented
8C3×#65445C211yesmaximal, characteristic, complemented
9C3×#65326C211yesmaximal, characteristic, complemented
10C3×#65070C211yesmaximal, characteristic, complemented
11C3×#65062C211yesmaximal, characteristic, complemented
12C3×#65061C211yesmaximal, characteristic, complemented
13C3×#65059C211yesmaximal, characteristic, complemented
14C3×#65023C211yesmaximal, characteristic, complemented
15C3×#65016C211yesmaximal, characteristic, complemented
16#10611735C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic, complemented
18C22×C3×C22⋊D5—21no—
19C22×C3×C22⋊D5—21no—
20C3×#4144—24no—
21C3×#4144—24no—
22C2×C3×#711—21no—
23C2×C3×#711C2211yescharacteristic
24C2×C3×#711C2211yescharacteristic, complemented
25C2×C3×D4×D5—21no—
26C2×C3×D4×D5C2211yescharacteristic
27C2×C3×D4×D5C2211yescharacteristic, complemented
28C2×C3×D4×D5C2211yescharacteristic, complemented
29C2×C3×#709C2211yescharacteristic
30C2×C3×#709C2211yescharacteristic, complemented
31C2×C3×C5×D8C2211yescharacteristic, complemented
32C2×C3×C5×D8C2211yescharacteristic, complemented
33C3×C5×#121C2211yescharacteristic, complemented
34C3×#4086—21no—
35C3×#4084C2211yescharacteristic, complemented
36C3×#4083—21no—
37C2×C3×#687C2211yescharacteristic, complemented
38C2×C3×#686C2211yescharacteristic, complemented
39C2×C3×#686C2211yescharacteristic, complemented
40C2×C3×#686C2211yescharacteristic, complemented
41C3×#4076C2211yescharacteristic, complemented
42C3×#4057—24no—
43C3×D5×D8—24no—
44C2×C3×D40C2211yescharacteristic, complemented
45C2×C3×#677C2211yescharacteristic, complemented
46C2×C3×#676C2211yescharacteristic, complemented
47C2×C3×C8×D5C2211yescharacteristic, complemented
48C3×#4041C2211yescharacteristic, complemented
49C3×#4038C2211yescharacteristic, complemented
50C3×#4031—21no—
51C3×#4028—21no—
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C5×C22⋊C8C2211yescharacteristic, complemented
55C3×#3964C2211yescharacteristic, complemented
56C3×#3964C2211yescharacteristic, complemented
57C3×C22⋊#168C2211yescharacteristic, complemented
58C3×#3953C2211yescharacteristic, complemented
59C3×#3952C2211yescharacteristic, complemented
60C3×#3952C2211yescharacteristic, complemented
61C3×#3948C2211yescharacteristic, complemented
62C3×#3942C2211yescharacteristic, complemented
63C3×#3941C2211yescharacteristic, complemented
64C3×#3008—51nomaximal, Hall
65C2×#4144C2×C311yescharacteristic, complemented
66C2×#4057C2×C311yescharacteristic, complemented
67C2×D5×D8C2×C311yescharacteristic, complemented
68#65941C2×C311yescharacteristic, complemented
69C5×#447C2×C311yescharacteristic, complemented
70#65506C2×C311yescharacteristic, complemented
71#65447C2×C311yescharacteristic, complemented
72#65445C2×C311yescharacteristic, complemented
73#65326C2×C311yescharacteristic, complemented
74#65070C2×C311yescharacteristic, complemented
75#65062C2×C311yescharacteristic, complemented
76#65061C2×C311yescharacteristic, complemented
77#65059C2×C311yescharacteristic, complemented
78#65023C2×C311yescharacteristic, complemented
79#65016C2×C311yescharacteristic, complemented
80C24×C3×C5—21no—
81C23×C3×D5—21no—
82C23×C3×D5—21no—
83C23×C3×D5—21no—
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—22no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C2×C3×C22⋊D5—28no—
93C2×C3×C22⋊D5—28no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5—21no—
98C2×C3×C22⋊D5—21no—
99C2×C3×C22⋊D5—21no—
100C2×C3×C22⋊D5—21no—
101C2×C3×C22⋊D5—21no—
102C2×C3×C22⋊D5D411yescharacteristic
103C2×C3×C22⋊D5D411yescharacteristic
104C22×C3×Dic5—21no—
105C22×C3×Dic5—21no—
106C3×#711—28no—
107C3×#711—22no—
108C3×#711—22no—
109C3×#711—22no—
110C3×#711D414yescomplemented
111C3×D4×D5—28no—
112C3×D4×D5—22no—
113C3×D4×D5—22no—
114C3×D4×D5—22no—
115C3×D4×D5—22no—
116C3×D4×D5—22no—
117C3×D4×D5D414yescomplemented
118C3×#709—22no—
119C3×#709—22no—
120C3×#709—22no—
121C3×#709—22no—
122C2×C3×D20—21no—
123C2×C3×D20D411yescharacteristic
124C2×C3×D20C2311yescharacteristic
125C2×C3×D20C2311yescharacteristic
126C2×C3×C4×D5—21no—
127C2×C3×C4×D5C2311yescharacteristic
128C2×C3×C4×D5C2311yescharacteristic
129C2×C3×Dic10D411yescharacteristic
130C2×C3×Dic10C2311yescharacteristic
131C3×C5×D8—22no—
132C3×C5×D8—22no—
133C2×C3×C5×C8C2311yescharacteristic
134C2×C3×C5×C8C2311yescharacteristic
135C3×C5×C4⋊C4C2311yescharacteristic
136C3×C5×C22⋊C4—21no—
137C3×C22⋊Dic5—21no—
138C3×#687—22no—
139C3×#686—22no—
140C3×#686—22no—
141C3×#686—22no—
142C3×#685—21no—
143C3×#685—21no—
144C3×#685—21no—
145C3×C4⋊Dic5C2311yescharacteristic
146C3×C4×Dic5—21no—
147C2×C3×#168C2311yescharacteristic
148C2×C3×#168C2311yescharacteristic
149C3×D40—22no—
150C3×#677—22no—
151C3×#676—22no—
152C3×C8×D5—22no—
153C2×C3×H(5,𝔽2)—51no—
154C2×C3×AGL(1,ℤ/8)—51no—
155C22×C3×D8—51no—
156C3×#535—51no—
157C3×#449—51no—
158C3×#449—51no—
159C3×#449—51no—
160C3×#449—51no—
161C3×#447—51no—
162C3×#447—51no—
163C3×#447—51no—
164C3×#447D511yescharacteristic, complemented
165C3×#418—51no—
166C3×#416—51no—
167C3×#408—51no—
168C22×C5×D4C22×C311yescharacteristic, complemented
169C22×C22⋊D5—21no—
170C22×C22⋊D5—21no—
171#4144—24no—
172#4144—24no—
173C2×#711—21no—
174C2×#711C22×C311yescharacteristic
175C2×#711C22×C311yescharacteristic, complemented
176C2×D4×D5—21no—
177C2×D4×D5C22×C311yescharacteristic
178C2×D4×D5C22×C311yescharacteristic, complemented
179C2×D4×D5C22×C311yescharacteristic, complemented
180C2×#709C22×C311yescharacteristic
181C2×#709C22×C311yescharacteristic, complemented
182C2×C5×D8C22×C311yescharacteristic, complemented
183C2×C5×D8C22×C311yescharacteristic, complemented
184C5×#121C22×C311yescharacteristic, complemented
185#4086—21no—
186#4084C22×C311yescharacteristic, complemented
187#4083—21no—
188C2×#687C22×C311yescharacteristic, complemented
189C2×#686C22×C311yescharacteristic, complemented
190C2×#686C22×C311yescharacteristic, complemented
191C2×#686C22×C311yescharacteristic, complemented
192#4076C22×C311yescharacteristic, complemented
193#4057—24no—
194D5×D8—24no—
195C2×D40C22×C311yescharacteristic, complemented
196C2×#677C22×C311yescharacteristic, complemented
197C2×#676C22×C311yescharacteristic, complemented
198C2×C8×D5C22×C311yescharacteristic, complemented
199#4041C22×C311yescharacteristic, complemented
200#4038C22×C311yescharacteristic, complemented
201#4031—21no—
202#4028—21no—
203C5×#102C22×C311yescharacteristic, complemented
204C5×#102C22×C311yescharacteristic, complemented
205C5×C22⋊C8C22×C311yescharacteristic, complemented
206#3964C22×C311yescharacteristic, complemented
207#3964C22×C311yescharacteristic, complemented
208C22⋊#168C22×C311yescharacteristic, complemented
209#3953C22×C311yescharacteristic, complemented
210#3952C22×C311yescharacteristic, complemented
211#3952C22×C311yescharacteristic, complemented
212#3948C22×C311yescharacteristic, complemented
213#3942C22×C311yescharacteristic, complemented
214#3941C22×C311yescharacteristic, complemented
215#3008—51noSylow
216C23×C3×C5—24no—
217C23×C3×C5—21no—
218C23×C3×C5—21no—
219C23×C3×C5—21no—
220C23×C3×C5—81no—
221C23×C3×C5—81no—
222C23×C3×C5C2×D411yescharacteristic
223C22×C3×D5—21no—
224C22×C3×D5—24no—
225C22×C3×D5—24no—
226C22×C3×D5—21no—
227C22×C3×D5—42no—
228C22×C3×D5—81no—
229C22×C3×D5—81no—
230C22×C3×D5—81no—
231C22×C3×D5—81no—
232C22×C3×D5—81no—
233C22×C3×D5—81no—
234C22×C3×D5C2×D411yescharacteristic
235C22×C3×D5C2×D411yescharacteristic
236C3×C5×D4—24no—
237C3×C5×D4—21no—
238C3×C5×D4—21no—
239C3×C5×D4—21no—
240C3×C5×D4—21no—
241C3×C5×D4—81no—
242C3×C5×D4C2×D412yes—
243C3×C5×D4C2×D412yes—
244C2×C3×C4×C5—21no—
245C2×C3×C4×C5—21no—
246C2×C3×C4×C5—21no—
247C2×C3×C4×C5C2×D411yescharacteristic
248C2×C3×C4×C5C2411yescharacteristic
249C3×C22⋊D5—24no—
250C3×C22⋊D5—24no—
251C3×C22⋊D5—24no—
252C3×C22⋊D5—22no—
253C3×C22⋊D5—24no—
254C3×C22⋊D5—22no—
255C3×C22⋊D5—24no—
256C3×C22⋊D5—42no—
257C3×C22⋊D5—81no—
258C3×C22⋊D5—81no—
259C2×C3×Dic5—24no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—24no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5C2×D411yescharacteristic
264C2×C3×Dic5C2×D411yescharacteristic
265C3×D20—22no—
266C3×D20—21no—
267C3×D20—21no—
268C3×D20—21no—
269C3×D20—81no—
270C3×D20C2×D412yes—
271C3×C4×D5—24no—
272C3×C4×D5—21no—
273C3×C4×D5—21no—
274C3×C4×D5C2×D412yes—
275C3×C4×D5C2×D412yes—
276C3×Dic10—21no—
277C3×Dic10—22no—
278C3×Dic10C2×D412yes—
279C3×C5×C8—21no—
280C3×C5×C8—21no—
281C3×#168—21no—
282C3×#168—21no—
283C3×H(5,𝔽2)—104no—
284C3×H(5,𝔽2)—104no—
285C2×C3×#41—51no—
286C2×C3×#41—51no—
287C2×C3×#41—51no—
288C2×C3×#41—51no—
289C2×C3×#41—101no—
290C22×C3×D4—51no—
291C22×C3×D4—51no—
292C22×C3×D4—51no—
293C22×C3×D4—101no—
294C22×C3×D4—101no—
295C22×C3×D4—101no—
296C22×C3×D4C2×D511yescharacteristic, complemented
297C3×AGL(1,ℤ/8)—104no—
298C2×C3×SD16—51no—
299C2×C3×SD16—51no—
300C2×C3×D8—51no—
301C2×C3×D8—51no—
302C2×C3×D8—51no—
303C2×C3×D8—51no—
304C2×C3×D8—104no—
305C2×C3×D8C2×D511yescharacteristic, complemented
306C2×C3×D8C2×D511yescharacteristic, complemented
307C2×C3×M16—51no—
308C22×C3×C8—51no—
309C3×#127—101no—
310C3×#124—101no—
311C3×#121—51no—
312C3×#121—51no—
313C3×#121—51no—
314C3×#121C2×D511yescharacteristic, complemented
315C3×#120—101no—
316C3×#120—101no—
317C3×#117—51no—
318C3×#103—51no—
319C3×#103—51no—
320C3×#102—51no—
321C3×#102—51no—
322C3×#102—51no—
323C3×#102—51no—
324C3×#102C2×D511yescharacteristic, complemented
325C3×#102C2×D511yescharacteristic, complemented
326C3×C22⋊C8—51no—
327C3×C22⋊C8—51no—
328C3×C22⋊C8—51no—
329C3×C22⋊C8C2×D511yescharacteristic, complemented
330C24×C5—21no—
331C23×D5—21no—
332C23×D5—21no—
333C23×D5—21no—
334C2×C5×D4—22no—
335C2×C5×D4—22no—
336C2×C5×D4—21no—
337C2×C5×D4—21no—
338C2×C5×D4C23×C311yescharacteristic
339C2×C5×D4C23×C311yescharacteristic
340C2×C5×D4C23×C311yescharacteristic
341C22×C4×C5C23×C311yescharacteristic
342C2×C22⋊D5—28no—
343C2×C22⋊D5—28no—
344C2×C22⋊D5—21no—
345C2×C22⋊D5—21no—
346C2×C22⋊D5—21no—
347C2×C22⋊D5—21no—
348C2×C22⋊D5—21no—
349C2×C22⋊D5—21no—
350C2×C22⋊D5—21no—
351C2×C22⋊D5—21no—
352C2×C22⋊D5C3×D411yescharacteristic
353C2×C22⋊D5C3×D411yescharacteristic
354C22×Dic5—21no—
355C22×Dic5—21no—
356#711—28no—
357#711—22no—
358#711—22no—
359#711—22no—
360#711C3×D414yescomplemented
361D4×D5—28no—
362D4×D5—22no—
363D4×D5—22no—
364D4×D5—22no—
365D4×D5—22no—
366D4×D5—22no—
367D4×D5C3×D414yescomplemented
368#709—22no—
369#709—22no—
370#709—22no—
371#709—22no—
372C2×D20—21no—
373C2×D20C3×D411yescharacteristic
374C2×D20C23×C311yescharacteristic
375C2×D20C23×C311yescharacteristic
376C2×C4×D5—21no—
377C2×C4×D5C23×C311yescharacteristic
378C2×C4×D5C23×C311yescharacteristic
379C2×Dic10C3×D411yescharacteristic
380C2×Dic10C23×C311yescharacteristic
381C5×D8—22no—
382C5×D8—22no—
383C2×C5×C8C23×C311yescharacteristic
384C2×C5×C8C23×C311yescharacteristic
385C5×C4⋊C4C23×C311yescharacteristic
386C5×C22⋊C4—21no—
387C22⋊Dic5—21no—
388#687—22no—
389#686—22no—
390#686—22no—
391#686—22no—
392#685—21no—
393#685—21no—
394#685—21no—
395C4⋊Dic5C23×C311yescharacteristic
396C4×Dic5—21no—
397C2×#168C23×C311yescharacteristic
398C2×#168C23×C311yescharacteristic
399D40—22no—
400#677—22no—
401#676—22no—
402C8×D5—22no—
403C2×H(5,𝔽2)—51no—
404C2×AGL(1,ℤ/8)—51no—
405C22×D8—51no—
406#535—51no—
407#449—51no—
408#449—51no—
409#449—51no—
410#449—51no—
411#447—51no—
412#447—51no—
413#447—51no—
414#447C3×D511yescharacteristic, complemented
415#418—51no—
416#416—51no—
417#408—51no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—21no—
421C22×C3×C5—21no—
422C22×C3×C5—21no—
423C22×C3×C5—41no—
424C22×C3×C5—41no—
425C22×C3×C5—41no—
426C22×C3×C5—41no—
427C22×C3×C5—41no—
428C22×C3×C5—41no—
429C22×C3×C5—41no—
430C22×C3×C5—84no—
431C22×C3×C5C22×D411yescharacteristic
432C2×C3×D5—21no—
433C2×C3×D5—21no—
434C2×C3×D5—21no—
435C2×C3×D5—22no—
436C2×C3×D5—21no—
437C2×C3×D5—21no—
438C2×C3×D5—41no—
439C2×C3×D5—41no—
440C2×C3×D5—41no—
441C2×C3×D5—41no—
442C2×C3×D5—41no—
443C2×C3×D5—84no—
444C2×C3×D5—84no—
445C2×C3×D5—84no—
446C2×C3×D5#12012yes—
447C3×C4×C5—21no—
448C3×C4×C5—41no—
449C3×C4×C5C22×D411yescharacteristic
450C3×C4×C5C22×D411yescharacteristic
451C3×Dic5—21no—
452C3×Dic5—22no—
453C3×Dic5—41no—
454C3×Dic5#12012yes—
455C24×C3—21no—
456C24×C3—101no—
457C24×C3—101no—
458C24×C3—101no—
459C3×#41—54no—
460C3×#41—102no—
461C3×#41—102no—
462C3×#41—102no—
463C3×#41—102no—
464C3×#41—102no—
465C3×#41—102no—
466C3×#41—108no—
467C3×#41—102no—
468C2×C3×Q8—51no—
469C2×C3×Q8—51no—
470C2×C3×D4—22no—
471C2×C3×D4—22no—
472C2×C3×D4—21no—
473C2×C3×D4—21no—
474C2×C3×D4—54no—
475C2×C3×D4—51no—
476C2×C3×D4—51no—
477C2×C3×D4—51no—
478C2×C3×D4—51no—
479C2×C3×D4—51no—
480C2×C3×D4—101no—
481C2×C3×D4—102no—
482C2×C3×D4—102no—
483C2×C3×D4—102no—
484C2×C3×D4—101no—
485C2×C3×D4—101no—
486C2×C3×D4—101no—
487C2×C3×D4—102no—
488C2×C3×D4—108no—
489C2×C3×D4—101no—
490C2×C3×D4—101no—
491C2×C3×D4—108no—
492C2×C3×D4—108no—
493C2×C3×D4—101no—
494C2×C3×D4—102no—
495C2×C3×D4—101no—
496C2×C3×D4—101no—
497C2×C3×D4C22×D511yescharacteristic
498C2×C3×D4C22×D511yescharacteristic
499C2×C3×D4C22×D511yescharacteristic
500C22×C3×C4—51no—
501C22×C3×C4—51no—
502C22×C3×C4—101no—
503C22×C3×C4—101no—
504C22×C3×C4—101no—
505C22×C3×C4C22×D511yescharacteristic
506C3×SD16—102no—
507C3×SD16—102no—
508C3×D8—22no—
509C3×D8—22no—
510C3×D8—102no—
511C3×D8—102no—
512C3×D8—102no—
513C3×D8—102no—
514C3×M16—102no—
515C2×C3×C8—51no—
516C2×C3×C8—51no—
517C2×C3×C8—102no—
518C2×C3×C8C22×D511yescharacteristic
519C2×C3×C8C22×D511yescharacteristic
520C3×C4⋊C4—51no—
521C3×C4⋊C4C22×D511yescharacteristic
522C3×C22⋊C4—21no—
523C3×C22⋊C4—101no—
524C3×C22⋊C4—101no—
525C3×C22⋊C4—101no—
526C3×C22⋊C4—101no—
527C3×C42—101no—
528C23×C5—24no—
529C23×C5—21no—
530C23×C5—21no—
531C23×C5—21no—
532C23×C5—81no—
533C23×C5—81no—
534C23×C5C2×C3×D411yescharacteristic
535C22×D5—21no—
536C22×D5—24no—
537C22×D5—24no—
538C22×D5—21no—
539C22×D5—42no—
540C22×D5—81no—
541C22×D5—81no—
542C22×D5—81no—
543C22×D5—81no—
544C22×D5—81no—
545C22×D5—81no—
546C22×D5C2×C3×D411yescharacteristic
547C22×D5C2×C3×D411yescharacteristic
548C5×D4—24no—
549C5×D4—21no—
550C5×D4—21no—
551C5×D4—21no—
552C5×D4—21no—
553C5×D4—81no—
554C5×D4C2×C3×D412yes—
555C5×D4C2×C3×D412yes—
556C2×C4×C5—21no—
557C2×C4×C5—21no—
558C2×C4×C5—21no—
559C2×C4×C5C2×C3×D411yescharacteristic
560C2×C4×C5C24×C311yescharacteristic
561C22⋊D5—24no—
562C22⋊D5—24no—
563C22⋊D5—24no—
564C22⋊D5—22no—
565C22⋊D5—24no—
566C22⋊D5—22no—
567C22⋊D5—24no—
568C22⋊D5—42no—
569C22⋊D5—81no—
570C22⋊D5—81no—
571C2×Dic5—24no—
572C2×Dic5—21no—
573C2×Dic5—24no—
574C2×Dic5—21no—
575C2×Dic5C2×C3×D411yescharacteristic
576C2×Dic5C2×C3×D411yescharacteristic
577D20—22no—
578D20—21no—
579D20—21no—
580D20—21no—
581D20—81no—
582D20C2×C3×D412yes—
583C4×D5—24no—
584C4×D5—21no—
585C4×D5—21no—
586C4×D5C2×C3×D412yes—
587C4×D5C2×C3×D412yes—
588Dic10—21no—
589Dic10—22no—
590Dic10C2×C3×D412yes—
591C5×C8—21no—
592C5×C8—21no—
593#168—21no—
594#168—21no—
595H(5,𝔽2)—104no—
596H(5,𝔽2)—104no—
597C2×#41—51no—
598C2×#41—51no—
599C2×#41—51no—
600C2×#41—51no—
601C2×#41—101no—
602C22×D4—51no—
603C22×D4—51no—
604C22×D4—51no—
605C22×D4—101no—
606C22×D4—101no—
607C22×D4—101no—
608C22×D4C2×C3×D511yescharacteristic, complemented
609AGL(1,ℤ/8)—104no—
610C2×SD16—51no—
611C2×SD16—51no—
612C2×D8—51no—
613C2×D8—51no—
614C2×D8—51no—
615C2×D8—51no—
616C2×D8—104no—
617C2×D8C2×C3×D511yescharacteristic, complemented
618C2×D8C2×C3×D511yescharacteristic, complemented
619C2×M16—51no—
620C22×C8—51no—
621#127—101no—
622#124—101no—
623#121—51no—
624#121—51no—
625#121—51no—
626#121C2×C3×D511yescharacteristic, complemented
627#120—101no—
628#120—101no—
629#117—51no—
630#103—51no—
631#103—51no—
632#102—51no—
633#102—51no—
634#102—51no—
635#102—51no—
636#102C2×C3×D511yescharacteristic, complemented
637#102C2×C3×D511yescharacteristic, complemented
638C22⋊C8—51no—
639C22⋊C8—51no—
640C22⋊C8—51no—
641C22⋊C8C2×C3×D511yescharacteristic, complemented
642C2×C3×C5—42no—
643C2×C3×C5—42no—
644C2×C3×C5—41no—
645C2×C3×C5—81no—
646C2×C3×C5C2×#12011yescharacteristic
647C2×C3×C5#57611yescharacteristic
648C2×C3×C5#57611yescharacteristic
649C3×D5—22no—
650C3×D5—41no—
651C3×D5—42no—
652C3×D5—81no—
653C23×C3—24no—
654C23×C3—21no—
655C23×C3—21no—
656C23×C3—21no—
657C23×C3—51no—
658C23×C3—51no—
659C23×C3—81no—
660C23×C3—81no—
661C23×C3—104no—
662C23×C3—104no—
663C23×C3—101no—
664C23×C3—101no—
665C23×C3—202no—
666C23×C3—401no—
667C23×C3—401no—
668C23×C3—401no—
669C23×C3—401no—
670C23×C3—401no—
671C23×C3—401no—
672C23×C3D4×D511yescharacteristic
673C3×Q8—52no—
674C3×Q8—102no—
675C3×Q8—101no—
676C3×D4—24no—
677C3×D4—21no—
678C3×D4—21no—
679C3×D4—21no—
680C3×D4—21no—
681C3×D4—52no—
682C3×D4—81no—
683C3×D4—102no—
684C3×D4—102no—
685C3×D4—104no—
686C3×D4—102no—
687C3×D4—104no—
688C3×D4—104no—
689C3×D4—104no—
690C3×D4—104no—
691C3×D4—101no—
692C3×D4—101no—
693C3×D4—101no—
694C3×D4—202no—
695C3×D4—401no—
696C3×D4—401no—
697C3×D4—401no—
698C3×D4D4×D512yes—
699C3×D4D4×D512yes—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—51no—
704C2×C3×C4—52no—
705C2×C3×C4—52no—
706C2×C3×C4—51no—
707C2×C3×C4—104no—
708C2×C3×C4—104no—
709C2×C3×C4—104no—
710C2×C3×C4—101no—
711C2×C3×C4—101no—
712C2×C3×C4—101no—
713C2×C3×C4—101no—
714C2×C3×C4D4×D511yescharacteristic
715C2×C3×C4C23×D511yescharacteristic
716C3×C8—21no—
717C3×C8—21no—
718C3×C8—101no—
719C3×C8—101no—
720C22×C5—21no—
721C22×C5—21no—
722C22×C5—22no—
723C22×C5—22no—
724C22×C5—21no—
725C22×C5—41no—
726C22×C5—41no—
727C22×C5—41no—
728C22×C5—41no—
729C22×C5—41no—
730C22×C5—41no—
731C22×C5—41no—
732C22×C5—84no—
733C22×C5C22×C3×D411yescharacteristic
734C2×D5—21no—
735C2×D5—21no—
736C2×D5—21no—
737C2×D5—21no—
738C2×D5—21no—
739C2×D5—22no—
740C2×D5—41no—
741C2×D5—41no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—84no—
746C2×D5—84no—
747C2×D5—84no—
748C2×D5C3×#12012yes—
749C4×C5—21no—
750C4×C5—41no—
751C4×C5C22×C3×D411yescharacteristic
752C4×C5C22×C3×D411yescharacteristic
753Dic5—21no—
754Dic5—22no—
755Dic5—41no—
756Dic5C3×#12012yes—
757C24—21no—
758C24—101no—
759C24—101no—
760C24—101no—
761#41—54no—
762#41—102no—
763#41—102no—
764#41—102no—
765#41—102no—
766#41—102no—
767#41—102no—
768#41—108no—
769#41—102no—
770C2×Q8—51no—
771C2×Q8—51no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—54no—
777C2×D4—51no—
778C2×D4—51no—
779C2×D4—51no—
780C2×D4—51no—
781C2×D4—51no—
782C2×D4—101no—
783C2×D4—102no—
784C2×D4—102no—
785C2×D4—102no—
786C2×D4—101no—
787C2×D4—101no—
788C2×D4—101no—
789C2×D4—102no—
790C2×D4—108no—
791C2×D4—101no—
792C2×D4—101no—
793C2×D4—108no—
794C2×D4—108no—
795C2×D4—101no—
796C2×D4—102no—
797C2×D4—101no—
798C2×D4—101no—
799C2×D4C22×C3×D511yescharacteristic
800C2×D4C22×C3×D511yescharacteristic
801C2×D4C22×C3×D511yescharacteristic
802C22×C4—51no—
803C22×C4—51no—
804C22×C4—101no—
805C22×C4—101no—
806C22×C4—101no—
807C22×C4C22×C3×D511yescharacteristic
808SD16—102no—
809SD16—102no—
810D8—22no—
811D8—22no—
812D8—102no—
813D8—102no—
814D8—102no—
815D8—102no—
816M16—102no—
817C2×C8—51no—
818C2×C8—51no—
819C2×C8—102no—
820C2×C8C22×C3×D511yescharacteristic
821C2×C8C22×C3×D511yescharacteristic
822C4⋊C4—51no—
823C4⋊C4C22×C3×D511yescharacteristic
824C22⋊C4—21no—
825C22⋊C4—101no—
826C22⋊C4—101no—
827C22⋊C4—101no—
828C22⋊C4—101no—
829C42—101no—
830C3×C5#300811yescharacteristic, complemented, Hall
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—52no—
844C22×C3—84no—
845C22×C3—101no—
846C22×C3—101no—
847C22×C3—101no—
848C22×C3—101no—
849C22×C3—102no—
850C22×C3—101no—
851C22×C3—201no—
852C22×C3—201no—
853C22×C3—201no—
854C22×C3—201no—
855C22×C3—201no—
856C22×C3—404no—
857C22×C3—404no—
858C22×C3—404no—
859C22×C3C2×D4×D511yescharacteristic
860C3×C4—21no—
861C3×C4—41no—
862C3×C4—52no—
863C3×C4—101no—
864C3×C4—102no—
865C3×C4—201no—
866C3×C4C2×D4×D511yescharacteristic
867C3×C4C2×D4×D511yescharacteristic
868C2×C5—42no—
869C2×C5—42no—
870C2×C5—41no—
871C2×C5—81no—
872C2×C5C2×C3×#12011yescharacteristic
873C2×C5C3×#57611yescharacteristic
874C2×C5C3×#57611yescharacteristic
875D5—22no—
876D5—41no—
877D5—42no—
878D5—81no—
879C23—24no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—51no—
884C23—51no—
885C23—81no—
886C23—81no—
887C23—104no—
888C23—104no—
889C23—101no—
890C23—101no—
891C23—202no—
892C23—401no—
893C23—401no—
894C23—401no—
895C23—401no—
896C23—401no—
897C23—401no—
898C23C3×D4×D511yescharacteristic
899Q8—52no—
900Q8—102no—
901Q8—101no—
902D4—24no—
903D4—21no—
904D4—21no—
905D4—21no—
906D4—21no—
907D4—52no—
908D4—81no—
909D4—102no—
910D4—102no—
911D4—104no—
912D4—102no—
913D4—104no—
914D4—104no—
915D4—104no—
916D4—104no—
917D4—101no—
918D4—101no—
919D4—101no—
920D4—202no—
921D4—401no—
922D4—401no—
923D4—401no—
924D4C3×D4×D512yes—
925D4C3×D4×D512yes—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—51no—
930C2×C4—52no—
931C2×C4—52no—
932C2×C4—51no—
933C2×C4—104no—
934C2×C4—104no—
935C2×C4—104no—
936C2×C4—101no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4C3×D4×D511yescharacteristic
941C2×C4C23×C3×D511yescharacteristic
942C8—21no—
943C8—21no—
944C8—101no—
945C8—101no—
946C2×C3—41no—
947C2×C3—42no—
948C2×C3—42no—
949C2×C3—81no—
950C2×C3—102no—
951C2×C3—201no—
952C2×C3—202no—
953C2×C3—401no—
954C2×C3D5×#12011yescharacteristic
955C2×C3#6609111yescharacteristic
956C2×C3#6610811yescharacteristic
957C5C3×#300811yescharacteristic, complemented, Sylow
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—21no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—52no—
971C22—84no—
972C22—101no—
973C22—101no—
974C22—101no—
975C22—102no—
976C22—101no—
977C22—101no—
978C22—201no—
979C22—201no—
980C22—201no—
981C22—201no—
982C22—201no—
983C22—404no—
984C22—404no—
985C22—404no—
986C22C2×C3×D4×D511yescharacteristic
987C4—21no—
988C4—41no—
989C4—52no—
990C4—101no—
991C4—102no—
992C4—201no—
993C4C2×C3×D4×D511yescharacteristic
994C4C2×C3×D4×D511yescharacteristic
995C3#1061173511yescharacteristic, direct product factor, Sylow
996C2—41no—
997C2—42no—
998C2—42no—
999C2—81no—
1000C2—102no—
1001C2—201no—
1002C2—202no—
1003C2—401no—
1004C2C3×D5×#12011yescharacteristic
1005C2C3×#6609111yescharacteristic
1006C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#447C2
socleC22×C3×C5C22×D4
hypercenterC3×#447D5
hypocenterC5C3×#3008
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#447

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4144C2semidirect
2. C2×C3×#4057C2semidirect
3. C2×C3×D5×D8C2semidirect
4. C3×#65941C2semidirect
5. C3×C5×#447C2semidirect
6. C3×#65506C2semidirect
7. C3×#65447C2semidirect
8. C3×#65445C2semidirect
9. C3×#65326C2semidirect
10. C3×#65070C2semidirect
11. C3×#65062C2semidirect
12. C3×#65061C2semidirect
13. C3×#65059C2semidirect
14. C3×#65023C2semidirect
15. C3×#65016C2semidirect
16. #10611735C3direct (N × H)
17. C22×C3×C5×D4C22semidirect
24. C2×C3×#711C22semidirect
27. C2×C3×D4×D5C22semidirect
28. C2×C3×D4×D5C22semidirect
30. C2×C3×#709C22semidirect
31. C2×C3×C5×D8C22semidirect
32. C2×C3×C5×D8C22semidirect
33. C3×C5×#121C22semidirect
35. C3×#4084C22semidirect
37. C2×C3×#687C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#686C22semidirect
40. C2×C3×#686C22semidirect
41. C3×#4076C22semidirect
44. C2×C3×D40C22semidirect
45. C2×C3×#677C22semidirect
46. C2×C3×#676C22semidirect
47. C2×C3×C8×D5C22semidirect
48. C3×#4041C22semidirect
49. C3×#4038C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C5×C22⋊C8C22semidirect
55. C3×#3964C22semidirect
56. C3×#3964C22semidirect
57. C3×C22⋊#168C22semidirect
58. C3×#3953C22semidirect
59. C3×#3952C22semidirect
60. C3×#3952C22semidirect
61. C3×#3948C22semidirect
62. C3×#3942C22semidirect
63. C3×#3941C22semidirect
65. C2×#4144C2×C3semidirect
66. C2×#4057C2×C3semidirect
67. C2×D5×D8C2×C3semidirect
68. #65941C2×C3semidirect
69. C5×#447C2×C3semidirect
70. #65506C2×C3semidirect
71. #65447C2×C3semidirect
72. #65445C2×C3semidirect
73. #65326C2×C3semidirect
74. #65070C2×C3semidirect
75. #65062C2×C3semidirect
76. #65061C2×C3semidirect
77. #65059C2×C3semidirect
78. #65023C2×C3semidirect
79. #65016C2×C3semidirect
110. C3×#711D4semidirect
117. C3×D4×D5D4semidirect
164. C3×#447D5semidirect
168. C22×C5×D4C22×C3semidirect
175. C2×#711C22×C3semidirect
178. C2×D4×D5C22×C3semidirect
179. C2×D4×D5C22×C3semidirect
181. C2×#709C22×C3semidirect
182. C2×C5×D8C22×C3semidirect
183. C2×C5×D8C22×C3semidirect
184. C5×#121C22×C3semidirect
186. #4084C22×C3semidirect
188. C2×#687C22×C3semidirect
189. C2×#686C22×C3semidirect
190. C2×#686C22×C3semidirect
191. C2×#686C22×C3semidirect
192. #4076C22×C3semidirect
195. C2×D40C22×C3semidirect
196. C2×#677C22×C3semidirect
197. C2×#676C22×C3semidirect
198. C2×C8×D5C22×C3semidirect
199. #4041C22×C3semidirect
200. #4038C22×C3semidirect
203. C5×#102C22×C3semidirect
204. C5×#102C22×C3semidirect
205. C5×C22⋊C8C22×C3semidirect
206. #3964C22×C3semidirect
207. #3964C22×C3semidirect
208. C22⋊#168C22×C3semidirect
209. #3953C22×C3semidirect
210. #3952C22×C3semidirect
211. #3952C22×C3semidirect
212. #3948C22×C3semidirect
213. #3942C22×C3semidirect
214. #3941C22×C3semidirect
296. C22×C3×D4C2×D5semidirect
305. C2×C3×D8C2×D5semidirect
306. C2×C3×D8C2×D5semidirect
314. C3×#121C2×D5semidirect
324. C3×#102C2×D5semidirect
325. C3×#102C2×D5semidirect
329. C3×C22⋊C8C2×D5semidirect
360. #711C3×D4semidirect
367. D4×D5C3×D4semidirect
414. #447C3×D5semidirect
608. C22×D4C2×C3×D5semidirect
617. C2×D8C2×C3×D5semidirect
618. C2×D8C2×C3×D5semidirect
626. #121C2×C3×D5semidirect
636. #102C2×C3×D5semidirect
637. #102C2×C3×D5semidirect
641. C22⋊C8C2×C3×D5semidirect
830. C3×C5#3008semidirect
957. C5C3×#3008semidirect
995. C3#10611735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41442
C2×C3×#40572
C2×C3×D5×D82
C3×#659412
C3×C5×#4472
C3×#655062
C3×#654472
C3×#654452
C3×#653262
C3×#650702
C3×#650622
C3×#650612
C3×#650592
C3×#650232
C3×#650162
#106117353
C3×#30085