Finite Group Databasebeta

← C3×#10606610 #14328105

Subgroups — C3×#10606610 #14328105

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4083C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C2×C3×#4027C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×C5×#386C211yesmaximal, characteristic, complemented
7C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C3×#65247C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic, complemented
10C3×#65245C211yesmaximal, characteristic, complemented
11C3×#65235C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64958C211yesmaximal, characteristic, complemented
14C3×#64957C211yesmaximal, characteristic, complemented
15C3×#64955C211yesmaximal, characteristic, complemented
16#10606610C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic, complemented
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
32C3×#4083C418yescomplemented
33C3×D4×Dic5—24no—
34C2×C3×#685—24no—
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45C2×C3×#683C2211yescharacteristic, complemented
46C2×C3×C4×Dic5C2211yescharacteristic, complemented
47C2×C3×C4×Dic5C2211yescharacteristic, complemented
48C2×C3×C4×Dic5C2211yescharacteristic, complemented
49C3×#4027—24no—
50C3×D5×C22⋊C4—24no—
51C3×C5×#95C2211yescharacteristic, complemented
52C3×C5×#95C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55C3×#3963C2211yescharacteristic, complemented
56C3×#3963C2211yescharacteristic, complemented
57C3×#2358—51nomaximal, Hall
58C2×#4083C2×C311yescharacteristic
59C2×D4×Dic5C2×C311yescharacteristic, complemented
60C22×#685C2×C311yescharacteristic, complemented
61C2×#4027C2×C311yescharacteristic, complemented
62C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
63C5×#386C2×C311yescharacteristic, complemented
64C4×C22⋊Dic5C2×C311yescharacteristic, complemented
65#65247C2×C311yescharacteristic, complemented
66#65246C2×C311yescharacteristic, complemented
67#65245C2×C311yescharacteristic, complemented
68#65235C2×C311yescharacteristic, complemented
69#64959C2×C311yescharacteristic, complemented
70#64958C2×C311yescharacteristic, complemented
71#64957C2×C311yescharacteristic, complemented
72#64955C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—41no—
80C23×C3×D5—41no—
81C23×C3×D5C2×C414yescomplemented
82C23×C3×D5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—22no—
86C2×C3×C5×D4C2×C414yescomplemented
87C22×C3×C4×C5—22no—
88C22×C3×C4×C5—22no—
89C22×C3×C4×C5—41no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5—22no—
97C2×C3×C22⋊D5—41no—
98C2×C3×C22⋊D5—41no—
99C2×C3×C22⋊D5C2×C414yescomplemented
100C2×C3×C22⋊D5C2×C414yescomplemented
101C22×C3×Dic5—22no—
102C22×C3×Dic5—22no—
103C22×C3×Dic5—22no—
104C22×C3×Dic5—22no—
105C22×C3×Dic5—41no—
106C22×C3×Dic5—41no—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C2×C3×C4×D5—22no—
114C2×C3×C4×D5—22no—
115C2×C3×C4×D5—22no—
116C2×C3×C4×D5—22no—
117C2×C3×C4×D5—41no—
118C2×C3×C4×D5—41no—
119C3×C5×C22⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4—41no—
122C3×C22⋊Dic5—22no—
123C3×C22⋊Dic5C2×C414yescomplemented
124C3×C22⋊Dic5D414yescomplemented
125C3×#685—22no—
126C3×#685—22no—
127C3×#685—22no—
128C3×#685—22no—
129C3×#685—22no—
130C3×#685C2×C414yescomplemented
131C3×#685C2×C414yescomplemented
132C3×#685D414yescomplemented
133C3×C4⋊Dic5—22no—
134C3×#683—22no—
135C3×#683—41no—
136C3×C4×Dic5—22no—
137C3×C4×Dic5—22no—
138C3×C4×Dic5—41no—
139C2×C3×#120—51no—
140C2×C3×C4×D4—51no—
141C2×C3×C4×D4—51no—
142C22×C3×C22⋊C4—51no—
143C22×C3×C22⋊C4—51no—
144C3×#390—51no—
145C3×#388—51no—
146C3×#388—51no—
147C3×#386—51no—
148C3×#386—51no—
149C3×#386D511yescharacteristic, complemented
150C3×#385—51no—
151C3×#385—51no—
152C3×C4×C22⋊C4—51no—
153C3×C4×C22⋊C4—51no—
154C24×D5C22×C311yescharacteristic
155C22×C5×D4C22×C311yescharacteristic
156C23×C4×C5C22×C311yescharacteristic
157C22×C22⋊D5C22×C311yescharacteristic
158C22×C22⋊D5C22×C311yescharacteristic
159C23×Dic5C22×C311yescharacteristic
160C23×Dic5C22×C311yescharacteristic, complemented
161C22×C4×D5C22×C311yescharacteristic
162C22×C4×D5C22×C311yescharacteristic
163C2×C5×C22⋊C4C22×C311yescharacteristic
164C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
165C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
166C2×C22⋊Dic5C22×C311yescharacteristic
167C2×C22⋊Dic5C22×C311yescharacteristic
168C2×C22⋊Dic5C22×C311yescharacteristic, complemented
169#4083C3×C418yescomplemented
170D4×Dic5—24no—
171C2×#685—24no—
172C2×#685C22×C311yescharacteristic
173C2×#685C22×C311yescharacteristic
174C2×#685C22×C311yescharacteristic
175C2×#685C22×C311yescharacteristic
176C2×#685C22×C311yescharacteristic
177C2×#685C22×C311yescharacteristic
178C2×#685C22×C311yescharacteristic
179C2×#685C22×C311yescharacteristic
180C2×C4⋊Dic5C22×C311yescharacteristic, complemented
181C2×#683C22×C311yescharacteristic, complemented
182C2×#683C22×C311yescharacteristic, complemented
183C2×C4×Dic5C22×C311yescharacteristic, complemented
184C2×C4×Dic5C22×C311yescharacteristic, complemented
185C2×C4×Dic5C22×C311yescharacteristic, complemented
186#4027—24no—
187D5×C22⋊C4—24no—
188C5×#95C22×C311yescharacteristic, complemented
189C5×#95C22×C311yescharacteristic, complemented
190#3963C22×C311yescharacteristic, complemented
191#3963C22×C311yescharacteristic, complemented
192#3963C22×C311yescharacteristic, complemented
193#3963C22×C311yescharacteristic, complemented
194#2358—51noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5C22×C412yes—
206C23×C3×C5C22×C412yes—
207C23×C3×C5C2×D412yes—
208C23×C3×C5#4112yes—
209C23×C3×C5C2411yescharacteristic
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—28no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—28no—
222C22×C3×D5—44no—
223C22×C3×D5—44no—
224C22×C3×D5—44no—
225C22×C3×D5—44no—
226C22×C3×D5—44no—
227C22×C3×D5C22×C412yes—
228C22×C3×D5C22×C412yes—
229C22×C3×D5C2×D412yes—
230C22×C3×D5#4112yes—
231C3×C5×D4—28no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—21no—
244C2×C3×C4×C5—21no—
245C2×C3×C4×C5—44no—
246C2×C3×C4×C5C22×C412yes—
247C2×C3×C4×C5C2×D412yes—
248C3×C22⋊D5—28no—
249C3×C22⋊D5—44no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—44no—
264C2×C3×Dic5—44no—
265C2×C3×Dic5C22×C412yes—
266C2×C3×Dic5C22×C412yes—
267C2×C3×Dic5C2×D412yes—
268C2×C3×Dic5C2×D412yes—
269C2×C3×Dic5C2×D412yes—
270C3×C4×D5—44no—
271C3×C4×D5—44no—
272C25×C3—51no—
273C22×C3×D4—51no—
274C22×C3×D4—51no—
275C22×C3×D4C2×D511yescharacteristic
276C23×C3×C4—51no—
277C23×C3×C4—51no—
278C23×C3×C4—51no—
279C23×C3×C4—51no—
280C23×C3×C4C2×D511yescharacteristic
281C3×#120—58no—
282C3×C4×D4—104no—
283C3×C4×D4—104no—
284C2×C3×C4⋊C4—51no—
285C2×C3×C4⋊C4—51no—
286C2×C3×C4⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4—51no—
294C2×C3×C22⋊C4—51no—
295C2×C3×C22⋊C4—51no—
296C2×C3×C22⋊C4—51no—
297C2×C3×C22⋊C4—51no—
298C2×C3×C22⋊C4—104no—
299C2×C3×C22⋊C4—104no—
300C2×C3×C22⋊C4C2×D511yescharacteristic
301C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
302C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
303C2×C3×C42—51no—
304C2×C3×C42—51no—
305C2×C3×C42—51no—
306C3×#95—51no—
307C3×#95—51no—
308C3×#95—51no—
309C3×#95—51no—
310C3×#95C2×D511yescharacteristic, complemented
311C3×#95C2×D511yescharacteristic, complemented
312C24×C5C23×C311yescharacteristic
313C24×C5C23×C311yescharacteristic
314C23×D5—22no—
315C23×D5—22no—
316C23×D5—22no—
317C23×D5—22no—
318C23×D5—41no—
319C23×D5—41no—
320C23×D5C2×C3×C414yescomplemented
321C23×D5C23×C311yescharacteristic
322C23×D5C23×C311yescharacteristic
323C2×C5×D4—22no—
324C2×C5×D4—22no—
325C2×C5×D4C2×C3×C414yescomplemented
326C22×C4×C5—22no—
327C22×C4×C5—22no—
328C22×C4×C5—41no—
329C22×C4×C5C23×C311yescharacteristic
330C22×C4×C5C23×C311yescharacteristic
331C22×C4×C5C23×C311yescharacteristic
332C22×C4×C5C23×C311yescharacteristic
333C22×C4×C5C23×C311yescharacteristic
334C2×C22⋊D5—22no—
335C2×C22⋊D5—22no—
336C2×C22⋊D5—41no—
337C2×C22⋊D5—41no—
338C2×C22⋊D5C2×C3×C414yescomplemented
339C2×C22⋊D5C2×C3×C414yescomplemented
340C22×Dic5—22no—
341C22×Dic5—22no—
342C22×Dic5—22no—
343C22×Dic5—22no—
344C22×Dic5—41no—
345C22×Dic5—41no—
346C22×Dic5C23×C311yescharacteristic
347C22×Dic5C23×C311yescharacteristic
348C22×Dic5C23×C311yescharacteristic
349C22×Dic5C23×C311yescharacteristic
350C22×Dic5C23×C311yescharacteristic
351C22×Dic5C23×C311yescharacteristic
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—22no—
355C2×C4×D5—22no—
356C2×C4×D5—41no—
357C2×C4×D5—41no—
358C5×C22⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4—41no—
361C22⋊Dic5—22no—
362C22⋊Dic5C2×C3×C414yescomplemented
363C22⋊Dic5C3×D414yescomplemented
364#685—22no—
365#685—22no—
366#685—22no—
367#685—22no—
368#685—22no—
369#685C2×C3×C414yescomplemented
370#685C2×C3×C414yescomplemented
371#685C3×D414yescomplemented
372C4⋊Dic5—22no—
373#683—22no—
374#683—41no—
375C4×Dic5—22no—
376C4×Dic5—22no—
377C4×Dic5—41no—
378C2×#120—51no—
379C2×C4×D4—51no—
380C2×C4×D4—51no—
381C22×C22⋊C4—51no—
382C22×C22⋊C4—51no—
383#390—51no—
384#388—51no—
385#388—51no—
386#386—51no—
387#386—51no—
388#386C3×D511yescharacteristic, complemented
389#385—51no—
390#385—51no—
391C4×C22⋊C4—51no—
392C4×C22⋊C4—51no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5—41no—
403C22×C3×C5—41no—
404C22×C3×C5—41no—
405C22×C3×C5—41no—
406C22×C3×C5C4×D414yescomplemented
407C22×C3×C5C23×C411yescharacteristic
408C22×C3×C5C22×D411yescharacteristic
409C22×C3×C5C22×D411yescharacteristic
410C22×C3×C5C2×#4111yescharacteristic
411C22×C3×C5C2×#4111yescharacteristic
412C22×C3×C5H(5,𝔽2)11yescharacteristic
413C22×C3×C5H(5,𝔽2)11yescharacteristic
414C2×C3×D5—22no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—416no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—41no—
432C3×C4×C5—41no—
433C3×C4×C5—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C3×Dic5—22no—
439C3×Dic5—41no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—54no—
443C24×C3—102no—
444C24×C3—102no—
445C24×C3—102no—
446C24×C3—102no—
447C24×C3—201no—
448C24×C3—201no—
449C24×C3C22×D511yescharacteristic
450C24×C3C22×D511yescharacteristic
451C2×C3×D4—22no—
452C2×C3×D4—22no—
453C2×C3×D4—54no—
454C2×C3×D4—54no—
455C2×C3×D4—102no—
456C2×C3×D4—102no—
457C2×C3×D4—201no—
458C2×C3×D4—201no—
459C2×C3×D4C4×D514yescomplemented
460C22×C3×C4—22no—
461C22×C3×C4—22no—
462C22×C3×C4—41no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—102no—
470C22×C3×C4—102no—
471C22×C3×C4—102no—
472C22×C3×C4—102no—
473C22×C3×C4—102no—
474C22×C3×C4—102no—
475C22×C3×C4—102no—
476C22×C3×C4—102no—
477C22×C3×C4—201no—
478C22×C3×C4—201no—
479C22×C3×C4—201no—
480C22×C3×C4—201no—
481C22×C3×C4C22×D511yescharacteristic
482C22×C3×C4C22×D511yescharacteristic
483C22×C3×C4C22×D511yescharacteristic
484C22×C3×C4C22×D511yescharacteristic
485C22×C3×C4C22×D511yescharacteristic
486C3×C4⋊C4—102no—
487C3×C4⋊C4—102no—
488C3×C4⋊C4—201no—
489C3×C22⋊C4—22no—
490C3×C22⋊C4—22no—
491C3×C22⋊C4—41no—
492C3×C22⋊C4—54no—
493C3×C22⋊C4—54no—
494C3×C22⋊C4—54no—
495C3×C22⋊C4—54no—
496C3×C22⋊C4—54no—
497C3×C22⋊C4—102no—
498C3×C22⋊C4—102no—
499C3×C22⋊C4—102no—
500C3×C22⋊C4—102no—
501C3×C22⋊C4—102no—
502C3×C22⋊C4—102no—
503C3×C42—102no—
504C3×C42—102no—
505C3×C42—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—21no—
514C23×C5—21no—
515C23×C5—21no—
516C23×C5C22×C3×C412yes—
517C23×C5C22×C3×C412yes—
518C23×C5C2×C3×D412yes—
519C23×C5C3×#4112yes—
520C23×C5C24×C311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—28no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—21no—
530C22×D5—21no—
531C22×D5—21no—
532C22×D5—28no—
533C22×D5—44no—
534C22×D5—44no—
535C22×D5—44no—
536C22×D5—44no—
537C22×D5—44no—
538C22×D5C22×C3×C412yes—
539C22×D5C22×C3×C412yes—
540C22×D5C2×C3×D412yes—
541C22×D5C3×#4112yes—
542C5×D4—28no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—21no—
555C2×C4×C5—21no—
556C2×C4×C5—44no—
557C2×C4×C5C22×C3×C412yes—
558C2×C4×C5C2×C3×D412yes—
559C22⋊D5—28no—
560C22⋊D5—44no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—21no—
571C2×Dic5—21no—
572C2×Dic5—21no—
573C2×Dic5—21no—
574C2×Dic5—44no—
575C2×Dic5—44no—
576C2×Dic5C22×C3×C412yes—
577C2×Dic5C22×C3×C412yes—
578C2×Dic5C2×C3×D412yes—
579C2×Dic5C2×C3×D412yes—
580C2×Dic5C2×C3×D412yes—
581C4×D5—44no—
582C4×D5—44no—
583C25—51no—
584C22×D4—51no—
585C22×D4—51no—
586C22×D4C2×C3×D511yescharacteristic
587C23×C4—51no—
588C23×C4—51no—
589C23×C4—51no—
590C23×C4—51no—
591C23×C4C2×C3×D511yescharacteristic
592#120—58no—
593C4×D4—104no—
594C4×D4—104no—
595C2×C4⋊C4—51no—
596C2×C4⋊C4—51no—
597C2×C4⋊C4—51no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—51no—
605C2×C22⋊C4—51no—
606C2×C22⋊C4—51no—
607C2×C22⋊C4—51no—
608C2×C22⋊C4—51no—
609C2×C22⋊C4—104no—
610C2×C22⋊C4—104no—
611C2×C22⋊C4C2×C3×D511yescharacteristic
612C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
613C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
614C2×C42—51no—
615C2×C42—51no—
616C2×C42—51no—
617#95—51no—
618#95—51no—
619#95—51no—
620#95—51no—
621#95C2×C3×D511yescharacteristic, complemented
622#95C2×C3×D511yescharacteristic, complemented
623C2×C3×C5—24no—
624C2×C3×C5—42no—
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5C2×C4×D411yescharacteristic
627C2×C3×C5#51811yescharacteristic
628C2×C3×C5D4211yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#54611yescharacteristic
631C2×C3×C5#55111yescharacteristic
632C3×D5—24no—
633C3×D5—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—52no—
647C23×C3—52no—
648C23×C3—108no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3—101no—
653C23×C3—101no—
654C23×C3—101no—
655C23×C3—101no—
656C23×C3—101no—
657C23×C3—101no—
658C23×C3—101no—
659C23×C3—108no—
660C23×C3—204no—
661C23×C3—204no—
662C23×C3—204no—
663C23×C3—204no—
664C23×C3—204no—
665C23×C3C2×C4×D512yes—
666C23×C3C2×C4×D512yes—
667C23×C3D4×D512yes—
668C23×C3#71112yes—
669C23×C3C23×D511yescharacteristic
670C3×D4—28no—
671C3×D4—108no—
672C3×D4—204no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—44no—
687C2×C3×C4—52no—
688C2×C3×C4—52no—
689C2×C3×C4—52no—
690C2×C3×C4—52no—
691C2×C3×C4—52no—
692C2×C3×C4—101no—
693C2×C3×C4—101no—
694C2×C3×C4—101no—
695C2×C3×C4—101no—
696C2×C3×C4—101no—
697C2×C3×C4—101no—
698C2×C3×C4—101no—
699C2×C3×C4—101no—
700C2×C3×C4—101no—
701C2×C3×C4—101no—
702C2×C3×C4—101no—
703C2×C3×C4—101no—
704C2×C3×C4—101no—
705C2×C3×C4—204no—
706C2×C3×C4—204no—
707C2×C3×C4—204no—
708C2×C3×C4—204no—
709C2×C3×C4C2×C4×D512yes—
710C2×C3×C4D4×D512yes—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—22no—
719C22×C5—22no—
720C22×C5—41no—
721C22×C5—41no—
722C22×C5—41no—
723C22×C5—41no—
724C22×C5C3×C4×D414yescomplemented
725C22×C5C23×C3×C411yescharacteristic
726C22×C5C22×C3×D411yescharacteristic
727C22×C5C22×C3×D411yescharacteristic
728C22×C5C2×C3×#4111yescharacteristic
729C22×C5C2×C3×#4111yescharacteristic
730C22×C5C3×H(5,𝔽2)11yescharacteristic
731C22×C5C3×H(5,𝔽2)11yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—22no—
739C2×D5—22no—
740C2×D5—22no—
741C2×D5—416no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5C3×C4×D414yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—41no—
751C4×C5—41no—
752Dic5—22no—
753Dic5—22no—
754Dic5—22no—
755Dic5—22no—
756Dic5—22no—
757Dic5—41no—
758C24—51no—
759C24—51no—
760C24—54no—
761C24—102no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—201no—
766C24—201no—
767C24C22×C3×D511yescharacteristic
768C24C22×C3×D511yescharacteristic
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—54no—
772C2×D4—54no—
773C2×D4—102no—
774C2×D4—102no—
775C2×D4—201no—
776C2×D4—201no—
777C2×D4C3×C4×D514yescomplemented
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—41no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—102no—
792C22×C4—102no—
793C22×C4—102no—
794C22×C4—102no—
795C22×C4—201no—
796C22×C4—201no—
797C22×C4—201no—
798C22×C4—201no—
799C22×C4C22×C3×D511yescharacteristic
800C22×C4C22×C3×D511yescharacteristic
801C22×C4C22×C3×D511yescharacteristic
802C22×C4C22×C3×D511yescharacteristic
803C22×C4C22×C3×D511yescharacteristic
804C4⋊C4—102no—
805C4⋊C4—102no—
806C4⋊C4—201no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—41no—
810C22⋊C4—54no—
811C22⋊C4—54no—
812C22⋊C4—54no—
813C22⋊C4—54no—
814C22⋊C4—54no—
815C22⋊C4—102no—
816C22⋊C4—102no—
817C22⋊C4—102no—
818C22⋊C4—102no—
819C22⋊C4—102no—
820C22⋊C4—102no—
821C42—102no—
822C42—102no—
823C42—201no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—54no—
839C22×C3—102no—
840C22×C3—102no—
841C22×C3—102no—
842C22×C3—102no—
843C22×C3—102no—
844C22×C3—102no—
845C22×C3—102no—
846C22×C3—102no—
847C22×C3—102no—
848C22×C3—2016no—
849C22×C3—201no—
850C22×C3—201no—
851C22×C3—201no—
852C22×C3—201no—
853C22×C3#402714yescomplemented
854C22×C3C22×C4×D511yescharacteristic
855C22×C3C2×D4×D511yescharacteristic
856C22×C3C2×D4×D511yescharacteristic
857C22×C3C2×#71111yescharacteristic
858C22×C3#414411yescharacteristic
859C22×C3D5×#4111yescharacteristic
860C22×C3#414911yescharacteristic
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—102no—
867C3×C4—102no—
868C3×C4—102no—
869C3×C4—102no—
870C3×C4—102no—
871C3×C4—201no—
872C2×C5—24no—
873C2×C5—42no—
874C2×C5C2×C3×C4×D411yescharacteristic
875C2×C5C2×C3×C4×D411yescharacteristic
876C2×C5C3×#51811yescharacteristic
877C2×C5C3×D4211yescharacteristic
878C2×C5C3×#54611yescharacteristic
879C2×C5C3×#54611yescharacteristic
880C2×C5C3×#55111yescharacteristic
881D5—24no—
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—52no—
894C23—52no—
895C23—52no—
896C23—52no—
897C23—108no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—108no—
909C23—204no—
910C23—204no—
911C23—204no—
912C23—204no—
913C23—204no—
914C23C2×C3×C4×D512yes—
915C23C2×C3×C4×D512yes—
916C23C3×D4×D512yes—
917C23C3×#71112yes—
918C23C23×C3×D511yescharacteristic
919D4—28no—
920D4—108no—
921D4—204no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—44no—
936C2×C4—52no—
937C2×C4—52no—
938C2×C4—52no—
939C2×C4—52no—
940C2×C4—52no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—101no—
948C2×C4—101no—
949C2×C4—101no—
950C2×C4—101no—
951C2×C4—101no—
952C2×C4—101no—
953C2×C4—101no—
954C2×C4—204no—
955C2×C4—204no—
956C2×C4—204no—
957C2×C4—204no—
958C2×C4C2×C3×C4×D512yes—
959C2×C4C3×D4×D512yes—
960C2×C3—24no—
961C2×C3—42no—
962C2×C3—104no—
963C2×C3—202no—
964C2×C3C2×#402711yescharacteristic
965C2×C3C4×D4×D511yescharacteristic
966C2×C3#6587911yescharacteristic
967C2×C3#6592511yescharacteristic
968C2×C3#6594311yescharacteristic
969C2×C3#6594411yescharacteristic
970C2×C3#6599211yescharacteristic
971C5C3×#235811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—54no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—102no—
992C22—102no—
993C22—102no—
994C22—102no—
995C22—2016no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22C3×#402714yescomplemented
1001C22C22×C3×C4×D511yescharacteristic
1002C22C2×C3×D4×D511yescharacteristic
1003C22C2×C3×D4×D511yescharacteristic
1004C22C2×C3×#71111yescharacteristic
1005C22C3×#414411yescharacteristic
1006C22C3×D5×#4111yescharacteristic
1007C22C3×#414911yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—41no—
1012C4—41no—
1013C4—102no—
1014C4—102no—
1015C4—102no—
1016C4—102no—
1017C4—102no—
1018C4—201no—
1019C3#1060661011yescharacteristic, direct product factor, Sylow
1020C2—24no—
1021C2—42no—
1022C2—104no—
1023C2—202no—
1024C2C2×C3×#402711yescharacteristic
1025C2C3×C4×D4×D511yescharacteristic
1026C2C3×#6587911yescharacteristic
1027C2C3×#6592511yescharacteristic
1028C2C3×#6594311yescharacteristic
1029C2C3×#6594411yescharacteristic
1030C2C3×#6599211yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC2×C3×#4083C2
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2358
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. C22×C3×#685C2semidirect
4. C2×C3×#4027C2semidirect
5. C2×C3×D5×C22⋊C4C2semidirect
6. C3×C5×#386C2semidirect
7. C3×C4×C22⋊Dic5C2semidirect
8. C3×#65247C2semidirect
9. C3×#65246C2semidirect
10. C3×#65245C2semidirect
11. C3×#65235C2semidirect
12. C3×#64959C2semidirect
13. C3×#64958C2semidirect
14. C3×#64957C2semidirect
15. C3×#64955C2semidirect
16. #10606610C3direct (N × H)
23. C23×C3×Dic5C22semidirect
27. C2×C3×C5×C22⋊C4C22semidirect
28. C2×C3×C5×C22⋊C4C22semidirect
31. C2×C3×C22⋊Dic5C22semidirect
32. C3×#4083C4semidirect
43. C2×C3×C4⋊Dic5C22semidirect
44. C2×C3×#683C22semidirect
45. C2×C3×#683C22semidirect
46. C2×C3×C4×Dic5C22semidirect
47. C2×C3×C4×Dic5C22semidirect
48. C2×C3×C4×Dic5C22semidirect
51. C3×C5×#95C22semidirect
52. C3×C5×#95C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. C3×#3963C22semidirect
56. C3×#3963C22semidirect
59. C2×D4×Dic5C2×C3semidirect
60. C22×#685C2×C3semidirect
61. C2×#4027C2×C3semidirect
62. C2×D5×C22⋊C4C2×C3semidirect
63. C5×#386C2×C3semidirect
64. C4×C22⋊Dic5C2×C3semidirect
65. #65247C2×C3semidirect
66. #65246C2×C3semidirect
67. #65245C2×C3semidirect
68. #65235C2×C3semidirect
69. #64959C2×C3semidirect
70. #64958C2×C3semidirect
71. #64957C2×C3semidirect
72. #64955C2×C3semidirect
81. C23×C3×D5C2×C4semidirect
86. C2×C3×C5×D4C2×C4semidirect
99. C2×C3×C22⋊D5C2×C4semidirect
100. C2×C3×C22⋊D5C2×C4semidirect
123. C3×C22⋊Dic5C2×C4semidirect
124. C3×C22⋊Dic5D4semidirect
130. C3×#685C2×C4semidirect
131. C3×#685C2×C4semidirect
132. C3×#685D4semidirect
149. C3×#386D5semidirect
160. C23×Dic5C22×C3semidirect
164. C2×C5×C22⋊C4C22×C3semidirect
165. C2×C5×C22⋊C4C22×C3semidirect
168. C2×C22⋊Dic5C22×C3semidirect
169. #4083C3×C4semidirect
180. C2×C4⋊Dic5C22×C3semidirect
181. C2×#683C22×C3semidirect
182. C2×#683C22×C3semidirect
183. C2×C4×Dic5C22×C3semidirect
184. C2×C4×Dic5C22×C3semidirect
185. C2×C4×Dic5C22×C3semidirect
188. C5×#95C22×C3semidirect
189. C5×#95C22×C3semidirect
190. #3963C22×C3semidirect
191. #3963C22×C3semidirect
192. #3963C22×C3semidirect
193. #3963C22×C3semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
302. C2×C3×C22⋊C4C2×D5semidirect
310. C3×#95C2×D5semidirect
311. C3×#95C2×D5semidirect
320. C23×D5C2×C3×C4semidirect
325. C2×C5×D4C2×C3×C4semidirect
338. C2×C22⋊D5C2×C3×C4semidirect
339. C2×C22⋊D5C2×C3×C4semidirect
362. C22⋊Dic5C2×C3×C4semidirect
363. C22⋊Dic5C3×D4semidirect
369. #685C2×C3×C4semidirect
370. #685C2×C3×C4semidirect
371. #685C3×D4semidirect
388. #386C3×D5semidirect
406. C22×C3×C5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
459. C2×C3×D4C4×D5semidirect
612. C2×C22⋊C4C2×C3×D5semidirect
613. C2×C22⋊C4C2×C3×D5semidirect
621. #95C2×C3×D5semidirect
622. #95C2×C3×D5semidirect
724. C22×C5C3×C4×D4semidirect
746. C2×D5C3×C4×D4semidirect
777. C2×D4C3×C4×D5semidirect
824. C3×C5#2358semidirect
853. C22×C3#4027semidirect
971. C5C3×#2358semidirect
1000. C22C3×#4027semidirect
1019. C3#10606610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40832
C2×C3×D4×Dic52
C22×C3×#6852
C2×C3×#40272
C2×C3×D5×C22⋊C42
C3×C5×#3862
C3×C4×C22⋊Dic52
C3×#652472
C3×#652462
C3×#652452
C3×#652352
C3×#649592
C3×#649582
C3×#649572
C3×#649552
#106066103
C3×#23585