Finite Group Databasebeta

← C3×#10613830 #14328102

Subgroups — C3×#10613830 #14328102

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
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#4099C211yesmaximal, characteristic
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×C3×#4027C211yesmaximal, characteristic, complemented
6C3×#65502C211yesmaximal, characteristic, complemented
7C3×#65499C211yesmaximal, characteristic, complemented
8C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
9C3×#65247C211yesmaximal, characteristic, complemented
10C3×#65246C211yesmaximal, characteristic, complemented
11C3×#65245C211yesmaximal, characteristic, complemented
12C3×#65235C211yesmaximal, characteristic, complemented
13C3×#65234C211yesmaximal, characteristic, complemented
14C3×#65233C211yesmaximal, characteristic, complemented
15C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
16#10613830C311yesmaximal, characteristic, direct product factor, Hall
17C25×C3×C5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic, complemented
26C2×C3×C5×C22⋊C4—24no—
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C3×#4099C418yescomplemented
32C2×C3×C22⋊Dic5—24no—
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C3×C4×C22⋊D5—24no—
41C2×C3×#685C2211yescharacteristic, complemented
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45C2×C3×#683C2211yescharacteristic, complemented
46C2×C3×#683C2211yescharacteristic, complemented
47C2×C3×C4×Dic5C2211yescharacteristic, complemented
48C2×C3×C4×Dic5C2211yescharacteristic, complemented
49C2×C3×C4×Dic5C2211yescharacteristic, complemented
50C3×#4027—24no—
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55C3×#3963C2211yescharacteristic, complemented
56C3×#3963C2211yescharacteristic, complemented
57C3×#2358—51nomaximal, Hall
58C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
59C2×#4099C2×C311yescharacteristic
60C22×C22⋊Dic5C2×C311yescharacteristic, complemented
61C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
62C2×#4027C2×C311yescharacteristic, complemented
63#65502C2×C311yescharacteristic, complemented
64#65499C2×C311yescharacteristic, complemented
65C4×C22⋊Dic5C2×C311yescharacteristic, complemented
66#65247C2×C311yescharacteristic, complemented
67#65246C2×C311yescharacteristic, complemented
68#65245C2×C311yescharacteristic, complemented
69#65235C2×C311yescharacteristic, complemented
70#65234C2×C311yescharacteristic, complemented
71#65233C2×C311yescharacteristic, complemented
72C22⋊C4×Dic5C2×C311yescharacteristic, complemented
73C24×C3×C5—22no—
74C24×C3×C5—22no—
75C24×C3×C5—22no—
76C24×C3×C5—22no—
77C24×C3×C5—41no—
78C24×C3×C5—41no—
79C24×C3×C5C2×C414yescomplemented
80C24×C3×C5C2311yescharacteristic
81C24×C3×C5C2311yescharacteristic
82C24×C3×C5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—22no—
87C22×C3×C4×C5—22no—
88C22×C3×C4×C5—41no—
89C22×C3×C4×C5—41no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5—22no—
97C2×C3×C22⋊D5—22no—
98C2×C3×C22⋊D5—41no—
99C2×C3×C22⋊D5—41no—
100C2×C3×C22⋊D5C2×C414yescomplemented
101C2×C3×C22⋊D5C2×C414yescomplemented
102C2×C3×C22⋊D5C2×C414yescomplemented
103C22×C3×Dic5—22no—
104C22×C3×Dic5—22no—
105C22×C3×Dic5—22no—
106C22×C3×Dic5—22no—
107C22×C3×Dic5—41no—
108C22×C3×Dic5—41no—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×C4×D5—22no—
117C2×C3×C4×D5—22no—
118C2×C3×C4×D5—41no—
119C3×C5×C22⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4—22no—
122C3×C5×C22⋊C4D414yescomplemented
123C3×C22⋊Dic5—22no—
124C3×C22⋊Dic5—22no—
125C3×C22⋊Dic5—22no—
126C3×C22⋊Dic5C2×C414yescomplemented
127C3×C22⋊Dic5C2×C414yescomplemented
128C3×C22⋊Dic5C2×C414yescomplemented
129C3×C22⋊Dic5D414yescomplemented
130C3×#685—22no—
131C3×#685—22no—
132C3×#685—41no—
133C3×#683—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⋊C4D511yescharacteristic, complemented
144C3×#390—51no—
145C3×#388—51no—
146C3×#388—51no—
147C3×#386—51no—
148C3×#386—51no—
149C3×#386—51no—
150C3×#385—51no—
151C3×#385—51no—
152C3×C4×C22⋊C4—51no—
153C3×C4×C22⋊C4—51no—
154C25×C5C22×C311yescharacteristic
155C23×C4×C5C22×C311yescharacteristic
156C23×C4×C5C22×C311yescharacteristic
157C22×C22⋊D5C22×C311yescharacteristic
158C22×C22⋊D5C22×C311yescharacteristic
159C22×C22⋊D5C22×C311yescharacteristic
160C23×Dic5C22×C311yescharacteristic
161C23×Dic5C22×C311yescharacteristic
162C22×C4×D5C22×C311yescharacteristic, complemented
163C2×C5×C22⋊C4—24no—
164C2×C5×C22⋊C4C22×C311yescharacteristic
165C2×C5×C22⋊C4C22×C311yescharacteristic
166C2×C5×C22⋊C4C22×C311yescharacteristic
167C2×C5×C22⋊C4C22×C311yescharacteristic
168#4099C3×C418yescomplemented
169C2×C22⋊Dic5—24no—
170C2×C22⋊Dic5C22×C311yescharacteristic
171C2×C22⋊Dic5C22×C311yescharacteristic
172C2×C22⋊Dic5C22×C311yescharacteristic
173C2×C22⋊Dic5C22×C311yescharacteristic
174C2×C22⋊Dic5C22×C311yescharacteristic
175C2×C22⋊Dic5C22×C311yescharacteristic
176C2×C22⋊Dic5C22×C311yescharacteristic
177C4×C22⋊D5—24no—
178C2×#685C22×C311yescharacteristic, complemented
179C2×#685C22×C311yescharacteristic, complemented
180C2×#685C22×C311yescharacteristic, complemented
181C2×#683C22×C311yescharacteristic, complemented
182C2×#683C22×C311yescharacteristic, complemented
183C2×#683C22×C311yescharacteristic, complemented
184C2×C4×Dic5C22×C311yescharacteristic, complemented
185C2×C4×Dic5C22×C311yescharacteristic, complemented
186C2×C4×Dic5C22×C311yescharacteristic, complemented
187#4027—24no—
188#3963C22×C311yescharacteristic, complemented
189#3963C22×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—28no—
204C23×C3×C5—28no—
205C23×C3×C5—21no—
206C23×C3×C5—21no—
207C23×C3×C5—21no—
208C23×C3×C5—21no—
209C23×C3×C5—21no—
210C23×C3×C5—21no—
211C23×C3×C5—44no—
212C23×C3×C5—44no—
213C23×C3×C5—44no—
214C23×C3×C5—44no—
215C23×C3×C5—44no—
216C23×C3×C5C22×C412yes—
217C23×C3×C5C22×C412yes—
218C23×C3×C5C22×C412yes—
219C23×C3×C5C2×D412yes—
220C23×C3×C5C2×D412yes—
221C23×C3×C5#4112yes—
222C23×C3×C5#4112yes—
223C23×C3×C5C2411yescharacteristic
224C22×C3×D5—21no—
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5—21no—
230C22×C3×D5C22×C412yes—
231C2×C3×C4×C5—21no—
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—44no—
242C2×C3×C4×C5—44no—
243C2×C3×C4×C5C2×D412yes—
244C2×C3×C4×C5C2×D412yes—
245C3×C22⋊D5—28no—
246C3×C22⋊D5—28no—
247C3×C22⋊D5—44no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
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—21no—
264C2×C3×Dic5—44no—
265C2×C3×Dic5—44no—
266C2×C3×Dic5C22×C412yes—
267C2×C3×Dic5C22×C412yes—
268C2×C3×Dic5C22×C412yes—
269C2×C3×Dic5C2×D412yes—
270C2×C3×Dic5C2×D412yes—
271C3×C4×D5—44no—
272C25×C3C2×D511yescharacteristic
273C22×C3×D4—51no—
274C22×C3×D4—51no—
275C22×C3×D4—51no—
276C23×C3×C4—51no—
277C23×C3×C4—51no—
278C23×C3×C4—51no—
279C23×C3×C4C2×D511yescharacteristic
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—24no—
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⋊C4C2×D511yescharacteristic
300C2×C3×C22⋊C4C2×D511yescharacteristic
301C2×C3×C22⋊C4C2×D511yescharacteristic
302C2×C3×C22⋊C4C2×D511yescharacteristic
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×#95—51no—
311C3×#95—51no—
312C24×C5—22no—
313C24×C5—22no—
314C24×C5—22no—
315C24×C5—22no—
316C24×C5—41no—
317C24×C5—41no—
318C24×C5C2×C3×C414yescomplemented
319C24×C5C23×C311yescharacteristic
320C24×C5C23×C311yescharacteristic
321C24×C5C23×C311yescharacteristic
322C23×D5C23×C311yescharacteristic
323C22×C4×C5—22no—
324C22×C4×C5—22no—
325C22×C4×C5—22no—
326C22×C4×C5—22no—
327C22×C4×C5—41no—
328C22×C4×C5—41no—
329C22×C4×C5C23×C311yescharacteristic
330C22×C4×C5C23×C311yescharacteristic
331C22×C4×C5C23×C311yescharacteristic
332C22×C4×C5C23×C311yescharacteristic
333C2×C22⋊D5—22no—
334C2×C22⋊D5—22no—
335C2×C22⋊D5—22no—
336C2×C22⋊D5—22no—
337C2×C22⋊D5—41no—
338C2×C22⋊D5—41no—
339C2×C22⋊D5C2×C3×C414yescomplemented
340C2×C22⋊D5C2×C3×C414yescomplemented
341C2×C22⋊D5C2×C3×C414yescomplemented
342C22×Dic5—22no—
343C22×Dic5—22no—
344C22×Dic5—22no—
345C22×Dic5—22no—
346C22×Dic5—41no—
347C22×Dic5—41no—
348C22×Dic5C23×C311yescharacteristic
349C22×Dic5C23×C311yescharacteristic
350C22×Dic5C23×C311yescharacteristic
351C22×Dic5C23×C311yescharacteristic
352C22×Dic5C23×C311yescharacteristic
353C22×Dic5C23×C311yescharacteristic
354C22×Dic5C23×C311yescharacteristic
355C2×C4×D5—22no—
356C2×C4×D5—22no—
357C2×C4×D5—41no—
358C5×C22⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4—22no—
361C5×C22⋊C4C3×D414yescomplemented
362C22⋊Dic5—22no—
363C22⋊Dic5—22no—
364C22⋊Dic5—22no—
365C22⋊Dic5C2×C3×C414yescomplemented
366C22⋊Dic5C2×C3×C414yescomplemented
367C22⋊Dic5C2×C3×C414yescomplemented
368C22⋊Dic5C3×D414yescomplemented
369#685—22no—
370#685—22no—
371#685—41no—
372#683—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⋊C4C3×D511yescharacteristic, complemented
383#390—51no—
384#388—51no—
385#388—51no—
386#386—51no—
387#386—51no—
388#386—51no—
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—22no—
403C22×C3×C5—22no—
404C22×C3×C5—22no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—416no—
409C22×C3×C5—41no—
410C22×C3×C5—41no—
411C22×C3×C5—41no—
412C22×C3×C5—41no—
413C22×C3×C5C4×D414yescomplemented
414C22×C3×C5C4×D414yescomplemented
415C22×C3×C5C23×C411yescharacteristic
416C22×C3×C5C22×D411yescharacteristic
417C22×C3×C5C22×D411yescharacteristic
418C22×C3×C5C2×#4111yescharacteristic
419C22×C3×C5C2×#4111yescharacteristic
420C22×C3×C5H(5,𝔽2)11yescharacteristic
421C22×C3×C5H(5,𝔽2)11yescharacteristic
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—41no—
432C3×C4×C5—41no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C3×Dic5—41no—
439C3×Dic5—41no—
440C24×C3—22no—
441C24×C3—22no—
442C24×C3—22no—
443C24×C3—22no—
444C24×C3—41no—
445C24×C3—41no—
446C24×C3—51no—
447C24×C3C4×D514yescomplemented
448C24×C3C22×D511yescharacteristic
449C24×C3C22×D511yescharacteristic
450C24×C3C22×D511yescharacteristic
451C2×C3×D4—54no—
452C2×C3×D4—54no—
453C2×C3×D4—54no—
454C2×C3×D4—102no—
455C2×C3×D4—102no—
456C2×C3×D4—102no—
457C2×C3×D4—102no—
458C2×C3×D4—201no—
459C2×C3×D4—201no—
460C22×C3×C4—22no—
461C22×C3×C4—22no—
462C22×C3×C4—22no—
463C22×C3×C4—22no—
464C22×C3×C4—41no—
465C22×C3×C4—41no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—102no—
474C22×C3×C4—102no—
475C22×C3×C4—102no—
476C22×C3×C4—102no—
477C22×C3×C4—102no—
478C22×C3×C4—102no—
479C22×C3×C4—201no—
480C22×C3×C4—201no—
481C22×C3×C4—201no—
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—22no—
492C3×C22⋊C4—54no—
493C3×C22⋊C4—54no—
494C3×C22⋊C4—54no—
495C3×C22⋊C4—54no—
496C3×C22⋊C4—102no—
497C3×C22⋊C4—102no—
498C3×C22⋊C4—102no—
499C3×C22⋊C4—102no—
500C3×C22⋊C4—102no—
501C3×C22⋊C4—201no—
502C3×C22⋊C4C22⋊D514yescomplemented
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—28no—
515C23×C5—28no—
516C23×C5—21no—
517C23×C5—21no—
518C23×C5—21no—
519C23×C5—21no—
520C23×C5—21no—
521C23×C5—21no—
522C23×C5—44no—
523C23×C5—44no—
524C23×C5—44no—
525C23×C5—44no—
526C23×C5—44no—
527C23×C5C22×C3×C412yes—
528C23×C5C22×C3×C412yes—
529C23×C5C22×C3×C412yes—
530C23×C5C2×C3×D412yes—
531C23×C5C2×C3×D412yes—
532C23×C5C3×#4112yes—
533C23×C5C3×#4112yes—
534C23×C5C24×C311yescharacteristic
535C22×D5—21no—
536C22×D5—21no—
537C22×D5—21no—
538C22×D5—21no—
539C22×D5—21no—
540C22×D5—21no—
541C22×D5C22×C3×C412yes—
542C2×C4×C5—21no—
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—44no—
553C2×C4×C5—44no—
554C2×C4×C5C2×C3×D412yes—
555C2×C4×C5C2×C3×D412yes—
556C22⋊D5—28no—
557C22⋊D5—28no—
558C22⋊D5—44no—
559C2×Dic5—21no—
560C2×Dic5—21no—
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—21no—
575C2×Dic5—44no—
576C2×Dic5—44no—
577C2×Dic5C22×C3×C412yes—
578C2×Dic5C22×C3×C412yes—
579C2×Dic5C22×C3×C412yes—
580C2×Dic5C2×C3×D412yes—
581C2×Dic5C2×C3×D412yes—
582C4×D5—44no—
583C25C2×C3×D511yescharacteristic
584C22×D4—51no—
585C22×D4—51no—
586C22×D4—51no—
587C23×C4—51no—
588C23×C4—51no—
589C23×C4—51no—
590C23×C4C2×C3×D511yescharacteristic
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—24no—
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⋊C4C2×C3×D511yescharacteristic
611C2×C22⋊C4C2×C3×D511yescharacteristic
612C2×C22⋊C4C2×C3×D511yescharacteristic
613C2×C22⋊C4C2×C3×D511yescharacteristic
614C2×C42—51no—
615C2×C42—51no—
616C2×C42—51no—
617#95—51no—
618#95—51no—
619#95—51no—
620#95—51no—
621#95—51no—
622#95—51no—
623C2×C3×C5—24no—
624C2×C3×C5—24no—
625C2×C3×C5—42no—
626C2×C3×C5C2×C4×D411yescharacteristic
627C2×C3×C5C2×C4×D411yescharacteristic
628C2×C3×C5#51811yescharacteristic
629C2×C3×C5D4211yescharacteristic
630C2×C3×C5#54611yescharacteristic
631C2×C3×C5#54611yescharacteristic
632C2×C3×C5#55111yescharacteristic
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—21no—
645C23×C3—21no—
646C23×C3—21no—
647C23×C3—21no—
648C23×C3—28no—
649C23×C3—28no—
650C23×C3—44no—
651C23×C3—44no—
652C23×C3—44no—
653C23×C3—44no—
654C23×C3—44no—
655C23×C3—52no—
656C23×C3—101no—
657C23×C3—101no—
658C23×C3—101no—
659C23×C3—101no—
660C23×C3—101no—
661C23×C3—101no—
662C23×C3C2×C4×D512yes—
663C23×C3C2×C4×D512yes—
664C23×C3C2×C4×D512yes—
665C23×C3#70912yes—
666C23×C3D4×D512yes—
667C23×C3#71112yes—
668C23×C3C2×C22⋊D512yes—
669C23×C3C23×D511yescharacteristic
670C3×D4—108no—
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—44no—
684C2×C3×C4—44no—
685C2×C3×C4—52no—
686C2×C3×C4—52no—
687C2×C3×C4—52no—
688C2×C3×C4—52no—
689C2×C3×C4—52no—
690C2×C3×C4—101no—
691C2×C3×C4—101no—
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—101no—
706C2×C3×C4—204no—
707C2×C3×C4—204no—
708C2×C3×C4—204no—
709C2×C3×C4C2×C22⋊D512yes—
710C2×C3×C4C2×C22⋊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—22no—
721C22×C5—22no—
722C22×C5—22no—
723C22×C5—22no—
724C22×C5—22no—
725C22×C5—22no—
726C22×C5—416no—
727C22×C5—41no—
728C22×C5—41no—
729C22×C5—41no—
730C22×C5—41no—
731C22×C5C3×C4×D414yescomplemented
732C22×C5C3×C4×D414yescomplemented
733C22×C5C23×C3×C411yescharacteristic
734C22×C5C22×C3×D411yescharacteristic
735C22×C5C22×C3×D411yescharacteristic
736C22×C5C2×C3×#4111yescharacteristic
737C22×C5C2×C3×#4111yescharacteristic
738C22×C5C3×H(5,𝔽2)11yescharacteristic
739C22×C5C3×H(5,𝔽2)11yescharacteristic
740C2×D5—22no—
741C2×D5—22no—
742C2×D5—22no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5—41no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—41no—
750C4×C5—41no—
751Dic5—22no—
752Dic5—22no—
753Dic5—22no—
754Dic5—22no—
755Dic5—22no—
756Dic5—41no—
757Dic5—41no—
758C24—22no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—41no—
763C24—41no—
764C24—51no—
765C24C3×C4×D514yescomplemented
766C24C22×C3×D511yescharacteristic
767C24C22×C3×D511yescharacteristic
768C24C22×C3×D511yescharacteristic
769C2×D4—54no—
770C2×D4—54no—
771C2×D4—54no—
772C2×D4—102no—
773C2×D4—102no—
774C2×D4—102no—
775C2×D4—102no—
776C2×D4—201no—
777C2×D4—201no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—51no—
789C22×C4—51no—
790C22×C4—51no—
791C22×C4—102no—
792C22×C4—102no—
793C22×C4—102no—
794C22×C4—102no—
795C22×C4—102no—
796C22×C4—102no—
797C22×C4—201no—
798C22×C4—201no—
799C22×C4—201no—
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—22no—
810C22⋊C4—54no—
811C22⋊C4—54no—
812C22⋊C4—54no—
813C22⋊C4—54no—
814C22⋊C4—102no—
815C22⋊C4—102no—
816C22⋊C4—102no—
817C22⋊C4—102no—
818C22⋊C4—102no—
819C22⋊C4—201no—
820C22⋊C4C3×C22⋊D514yescomplemented
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—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—416no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—102no—
846C22×C3—102no—
847C22×C3—102no—
848C22×C3—201no—
849C22×C3—201no—
850C22×C3—201no—
851C22×C3—201no—
852C22×C3#402714yescomplemented
853C22×C3C4×C22⋊D514yescomplemented
854C22×C3C22×C4×D511yescharacteristic
855C22×C3C2×#70911yescharacteristic
856C22×C3C2×D4×D511yescharacteristic
857C22×C3C2×#71111yescharacteristic
858C22×C3#414411yescharacteristic
859C22×C3#414411yescharacteristic
860C22×C3C22×C22⋊D511yescharacteristic
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—102no—
866C3×C4—102no—
867C3×C4—102no—
868C3×C4—102no—
869C3×C4—102no—
870C3×C4—201no—
871C3×C4—201no—
872C2×C5—24no—
873C2×C5—24no—
874C2×C5—42no—
875C2×C5C2×C3×C4×D411yescharacteristic
876C2×C5C2×C3×C4×D411yescharacteristic
877C2×C5C3×#51811yescharacteristic
878C2×C5C3×D4211yescharacteristic
879C2×C5C3×#54611yescharacteristic
880C2×C5C3×#54611yescharacteristic
881C2×C5C3×#55111yescharacteristic
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—28no—
898C23—28no—
899C23—44no—
900C23—44no—
901C23—44no—
902C23—44no—
903C23—44no—
904C23—52no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—101no—
911C23C2×C3×C4×D512yes—
912C23C2×C3×C4×D512yes—
913C23C2×C3×C4×D512yes—
914C23C3×#70912yes—
915C23C3×D4×D512yes—
916C23C3×#71112yes—
917C23C2×C3×C22⋊D512yes—
918C23C23×C3×D511yescharacteristic
919D4—108no—
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—44no—
933C2×C4—44no—
934C2×C4—52no—
935C2×C4—52no—
936C2×C4—52no—
937C2×C4—52no—
938C2×C4—52no—
939C2×C4—101no—
940C2×C4—101no—
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—101no—
955C2×C4—204no—
956C2×C4—204no—
957C2×C4—204no—
958C2×C4C2×C3×C22⋊D512yes—
959C2×C4C2×C3×C22⋊D512yes—
960C2×C3—24no—
961C2×C3—24no—
962C2×C3—42no—
963C2×C3—202no—
964C2×C3C2×#402711yescharacteristic
965C2×C3#6582011yescharacteristic
966C2×C3#6582411yescharacteristic
967C2×C3#6582911yescharacteristic
968C2×C3C2×C4×C22⋊D511yescharacteristic
969C2×C3D4×C22⋊D511yescharacteristic
970C2×C3#6614011yescharacteristic
971C5C3×#235811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—416no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—102no—
993C22—102no—
994C22—102no—
995C22—201no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22C3×#402714yescomplemented
1000C22C3×C4×C22⋊D514yescomplemented
1001C22C22×C3×C4×D511yescharacteristic
1002C22C2×C3×#70911yescharacteristic
1003C22C2×C3×D4×D511yescharacteristic
1004C22C2×C3×#71111yescharacteristic
1005C22C3×#414411yescharacteristic
1006C22C3×#414411yescharacteristic
1007C22C22×C3×C22⋊D511yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—41no—
1011C4—41no—
1012C4—102no—
1013C4—102no—
1014C4—102no—
1015C4—102no—
1016C4—102no—
1017C4—201no—
1018C4—201no—
1019C3#1061383011yescharacteristic, direct product factor, Sylow
1020C2—24no—
1021C2—24no—
1022C2—42no—
1023C2—202no—
1024C2C2×C3×#402711yescharacteristic
1025C2C3×#6582011yescharacteristic
1026C2C3×#6582411yescharacteristic
1027C2C3×#6582911yescharacteristic
1028C2C2×C3×C4×C22⋊D511yescharacteristic
1029C2C3×D4×C22⋊D511yescharacteristic
1030C2C3×#6614011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4099C2
cosocleC23×C5C24×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#2358
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C3×C22⋊Dic5C2semidirect
4. C2×C3×C4×C22⋊D5C2semidirect
5. C2×C3×#4027C2semidirect
6. C3×#65502C2semidirect
7. C3×#65499C2semidirect
8. C3×C4×C22⋊Dic5C2semidirect
9. C3×#65247C2semidirect
10. C3×#65246C2semidirect
11. C3×#65245C2semidirect
12. C3×#65235C2semidirect
13. C3×#65234C2semidirect
14. C3×#65233C2semidirect
15. C3×C22⋊C4×Dic5C2semidirect
16. #10613830C3direct (N × H)
25. C22×C3×C4×D5C22semidirect
31. C3×#4099C4semidirect
41. C2×C3×#685C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
44. C2×C3×#683C22semidirect
45. C2×C3×#683C22semidirect
46. C2×C3×#683C22semidirect
47. C2×C3×C4×Dic5C22semidirect
48. C2×C3×C4×Dic5C22semidirect
49. C2×C3×C4×Dic5C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. C3×#3963C22semidirect
56. C3×#3963C22semidirect
58. C22×C5×C22⋊C4C2×C3semidirect
60. C22×C22⋊Dic5C2×C3semidirect
61. C2×C4×C22⋊D5C2×C3semidirect
62. C2×#4027C2×C3semidirect
63. #65502C2×C3semidirect
64. #65499C2×C3semidirect
65. C4×C22⋊Dic5C2×C3semidirect
66. #65247C2×C3semidirect
67. #65246C2×C3semidirect
68. #65245C2×C3semidirect
69. #65235C2×C3semidirect
70. #65234C2×C3semidirect
71. #65233C2×C3semidirect
72. C22⋊C4×Dic5C2×C3semidirect
79. C24×C3×C5C2×C4semidirect
100. C2×C3×C22⋊D5C2×C4semidirect
101. C2×C3×C22⋊D5C2×C4semidirect
102. C2×C3×C22⋊D5C2×C4semidirect
122. C3×C5×C22⋊C4D4semidirect
126. C3×C22⋊Dic5C2×C4semidirect
127. C3×C22⋊Dic5C2×C4semidirect
128. C3×C22⋊Dic5C2×C4semidirect
129. C3×C22⋊Dic5D4semidirect
143. C22×C3×C22⋊C4D5semidirect
162. C22×C4×D5C22×C3semidirect
168. #4099C3×C4semidirect
178. C2×#685C22×C3semidirect
179. C2×#685C22×C3semidirect
180. C2×#685C22×C3semidirect
181. C2×#683C22×C3semidirect
182. C2×#683C22×C3semidirect
183. C2×#683C22×C3semidirect
184. C2×C4×Dic5C22×C3semidirect
185. C2×C4×Dic5C22×C3semidirect
186. C2×C4×Dic5C22×C3semidirect
188. #3963C22×C3semidirect
189. #3963C22×C3semidirect
190. #3963C22×C3semidirect
191. #3963C22×C3semidirect
192. #3963C22×C3semidirect
193. #3963C22×C3semidirect
318. C24×C5C2×C3×C4semidirect
339. C2×C22⋊D5C2×C3×C4semidirect
340. C2×C22⋊D5C2×C3×C4semidirect
341. C2×C22⋊D5C2×C3×C4semidirect
361. C5×C22⋊C4C3×D4semidirect
365. C22⋊Dic5C2×C3×C4semidirect
366. C22⋊Dic5C2×C3×C4semidirect
367. C22⋊Dic5C2×C3×C4semidirect
368. C22⋊Dic5C3×D4semidirect
382. C22×C22⋊C4C3×D5semidirect
413. C22×C3×C5C4×D4semidirect
414. C22×C3×C5C4×D4semidirect
447. C24×C3C4×D5semidirect
502. C3×C22⋊C4C22⋊D5semidirect
731. C22×C5C3×C4×D4semidirect
732. C22×C5C3×C4×D4semidirect
765. C24C3×C4×D5semidirect
820. C22⋊C4C3×C22⋊D5semidirect
824. C3×C5#2358semidirect
852. C22×C3#4027semidirect
853. C22×C3C4×C22⋊D5semidirect
971. C5C3×#2358semidirect
999. C22C3×#4027semidirect
1000. C22C3×C4×C22⋊D5semidirect
1019. C3#10613830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C2×C3×#40992
C22×C3×C22⋊Dic52
C2×C3×C4×C22⋊D52
C2×C3×#40272
C3×#655022
C3×#654992
C3×C4×C22⋊Dic52
C3×#652472
C3×#652462
C3×#652452
C3×#652352
C3×#652342
C3×#652332
C3×C22⋊C4×Dic52
#106138303
C3×#23585