Finite Group Databasebeta

← C3×#10607567 #14328099

Subgroups — C3×#10607567 #14328099

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×#4039C211yesmaximal, characteristic, complemented
2C2×C3×#4028C211yesmaximal, characteristic
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×C4×D20C211yesmaximal, characteristic, complemented
6C3×C5×#388C211yesmaximal, characteristic, complemented
7C3×#65278C211yesmaximal, characteristic, complemented
8C3×#65246C211yesmaximal, characteristic, complemented
9C3×#65245C211yesmaximal, characteristic, complemented
10C3×#65240C211yesmaximal, characteristic, complemented
11C3×C4×#685C211yesmaximal, characteristic, complemented
12C3×#64957C211yesmaximal, characteristic, complemented
13C3×#64955C211yesmaximal, characteristic, complemented
14C3×#64954C211yesmaximal, characteristic, complemented
15C3×#64954C211yesmaximal, characteristic, complemented
16#10607567C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic, complemented
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C42×C5C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
43C2×C3×#683C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C2×C3×C4×Dic5C2211yescharacteristic, complemented
46C3×#4039—24no—
47C3×#4028C418yescomplemented
48C3×D5×C22⋊C4—24no—
49C3×D5×C22⋊C4—24no—
50C3×C4×D20—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×#4039C2×C311yescharacteristic, complemented
59C2×#4028C2×C311yescharacteristic
60C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
61C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
62C2×C4×D20C2×C311yescharacteristic, complemented
63C5×#388C2×C311yescharacteristic, complemented
64#65278C2×C311yescharacteristic, complemented
65#65246C2×C311yescharacteristic, complemented
66#65245C2×C311yescharacteristic, complemented
67#65240C2×C311yescharacteristic, complemented
68C4×#685C2×C311yescharacteristic, complemented
69#64957C2×C311yescharacteristic, complemented
70#64955C2×C311yescharacteristic, complemented
71#64954C2×C311yescharacteristic, complemented
72#64954C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—41no—
79C23×C3×D5—41no—
80C23×C3×D5C2×C414yescomplemented
81C23×C3×D5C2311yescharacteristic
82C23×C3×D5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×C3×C22⋊D5—41no—
91C2×C3×C22⋊D5—41no—
92C2×C3×C22⋊D5C2×C414yescomplemented
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×C3×D20—22no—
99C2×C3×D20—22no—
100C2×C3×D20—22no—
101C2×C3×D20—22no—
102C2×C3×D20C2×C414yescomplemented
103C2×C3×D20C2×C414yescomplemented
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—22no—
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C2×C3×C4×D5—22no—
113C2×C3×C4×D5—22no—
114C2×C3×C4×D5—41no—
115C2×C3×C4×D5—41no—
116C2×C3×C4×D5—41no—
117C2×C3×C4×D5—41no—
118C2×C3×C4×D5—41no—
119C3×C5×C4⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4—22no—
122C3×C5×C22⋊C4C2×C414yescomplemented
123C3×C42×C5—22no—
124C3×C22⋊Dic5—22no—
125C3×C22⋊Dic5—22no—
126C3×#685—22no—
127C3×#685—22no—
128C3×#685—22no—
129C3×#685—22no—
130C3×#685—41no—
131C3×#685C2×C414yescomplemented
132C3×#685C2×C414yescomplemented
133C3×#685D414yescomplemented
134C3×#685D414yescomplemented
135C3×C4⋊Dic5—22no—
136C3×#683—41no—
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×#388D511yescharacteristic, complemented
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—
154C24×D5C22×C311yescharacteristic
155C22×C22⋊D5C22×C311yescharacteristic
156C22×D20C22×C311yescharacteristic
157C22×D20C22×C311yescharacteristic
158C22×C4×D5C22×C311yescharacteristic
159C22×C4×D5C22×C311yescharacteristic
160C22×C4×D5C22×C311yescharacteristic
161C22×C4×D5C22×C311yescharacteristic
162C22×C4×D5C22×C311yescharacteristic, complemented
163C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
164C2×C5×C22⋊C4C22×C311yescharacteristic
165C2×C5×C22⋊C4C22×C311yescharacteristic
166C2×C5×C22⋊C4C22×C311yescharacteristic
167C2×C42×C5C22×C311yescharacteristic, complemented
168C2×C22⋊Dic5C22×C311yescharacteristic
169C2×C22⋊Dic5C22×C311yescharacteristic
170C2×#685C22×C311yescharacteristic
171C2×#685C22×C311yescharacteristic
172C2×#685C22×C311yescharacteristic
173C2×#685C22×C311yescharacteristic
174C2×#685C22×C311yescharacteristic
175C2×#685C22×C311yescharacteristic
176C2×#685C22×C311yescharacteristic, complemented
177C2×#685C22×C311yescharacteristic, complemented
178C2×#685C22×C311yescharacteristic, complemented
179C2×C4⋊Dic5C22×C311yescharacteristic, complemented
180C2×#683C22×C311yescharacteristic, complemented
181C2×C4×Dic5C22×C311yescharacteristic, complemented
182C2×C4×Dic5C22×C311yescharacteristic, complemented
183#4039—24no—
184#4028C3×C418yescomplemented
185D5×C22⋊C4—24no—
186D5×C22⋊C4—24no—
187C4×D20—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×C5C22×C412yes—
202C23×C3×C5C2411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—28no—
218C22×C3×D5—28no—
219C22×C3×D5—44no—
220C22×C3×D5—44no—
221C22×C3×D5—44no—
222C22×C3×D5—44no—
223C22×C3×D5—44no—
224C22×C3×D5C22×C412yes—
225C22×C3×D5C22×C412yes—
226C22×C3×D5C22×C412yes—
227C22×C3×D5C2×D412yes—
228C22×C3×D5C2×D412yes—
229C22×C3×D5#4112yes—
230C22×C3×D5#4112yes—
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—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—21no—
244C2×C3×C4×C5—21no—
245C2×C3×C4×C5C22×C412yes—
246C2×C3×C4×C5C22×C412yes—
247C2×C3×C4×C5C2×D412yes—
248C2×C3×C4×C5C2×D412yes—
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×Dic5C22×C412yes—
263C2×C3×Dic5C2×D412yes—
264C2×C3×Dic5C2×D412yes—
265C3×D20—28no—
266C3×D20—28no—
267C3×C4×D5—44no—
268C3×C4×D5—44no—
269C3×C4×D5—44no—
270C3×C4×D5—44no—
271C3×C4×D5—44no—
272C25×C3—51no—
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×C4—51no—
280C23×C3×C4—51no—
281C3×#120—58no—
282C3×C4×D4—104no—
283C3×C4×D4—104no—
284C2×C3×C4⋊C4—51no—
285C2×C3×C4⋊C4—51no—
286C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
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
302C2×C3×C22⋊C4C2×D511yescharacteristic
303C2×C3×C42—51no—
304C2×C3×C42—51no—
305C2×C3×C42C2×D511yescharacteristic, complemented
306C3×#95—51no—
307C3×#95—51no—
308C3×#95—51no—
309C3×#95—51no—
310C3×#95C2×D511yescharacteristic, complemented
311C3×#95C2×D511yescharacteristic, complemented
312C24×C5C23×C311yescharacteristic
313C23×D5—22no—
314C23×D5—22no—
315C23×D5—22no—
316C23×D5—22no—
317C23×D5—41no—
318C23×D5—41no—
319C23×D5C2×C3×C414yescomplemented
320C23×D5C23×C311yescharacteristic
321C23×D5C23×C311yescharacteristic
322C23×D5C23×C311yescharacteristic
323C22×C4×C5C23×C311yescharacteristic
324C22×C4×C5C23×C311yescharacteristic
325C22×C4×C5C23×C311yescharacteristic
326C22×C4×C5C23×C311yescharacteristic
327C22×C4×C5C23×C311yescharacteristic
328C22×C4×C5C23×C311yescharacteristic
329C2×C22⋊D5—41no—
330C2×C22⋊D5—41no—
331C2×C22⋊D5C2×C3×C414yescomplemented
332C22×Dic5C23×C311yescharacteristic
333C22×Dic5C23×C311yescharacteristic
334C22×Dic5C23×C311yescharacteristic
335C22×Dic5C23×C311yescharacteristic
336C22×Dic5C23×C311yescharacteristic
337C2×D20—22no—
338C2×D20—22no—
339C2×D20—22no—
340C2×D20—22no—
341C2×D20C2×C3×C414yescomplemented
342C2×D20C2×C3×C414yescomplemented
343C2×C4×D5—22no—
344C2×C4×D5—22no—
345C2×C4×D5—22no—
346C2×C4×D5—22no—
347C2×C4×D5—22no—
348C2×C4×D5—22no—
349C2×C4×D5—22no—
350C2×C4×D5—22no—
351C2×C4×D5—22no—
352C2×C4×D5—22no—
353C2×C4×D5—41no—
354C2×C4×D5—41no—
355C2×C4×D5—41no—
356C2×C4×D5—41no—
357C2×C4×D5—41no—
358C5×C4⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4—22no—
361C5×C22⋊C4C2×C3×C414yescomplemented
362C42×C5—22no—
363C22⋊Dic5—22no—
364C22⋊Dic5—22no—
365#685—22no—
366#685—22no—
367#685—22no—
368#685—22no—
369#685—41no—
370#685C2×C3×C414yescomplemented
371#685C2×C3×C414yescomplemented
372#685C3×D414yescomplemented
373#685C3×D414yescomplemented
374C4⋊Dic5—22no—
375#683—41no—
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#388C3×D511yescharacteristic, complemented
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—41no—
397C22×C3×C5—41no—
398C22×C3×C5—41no—
399C22×C3×C5—41no—
400C22×C3×C5C23×C411yescharacteristic
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C2×#4111yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5H(5,𝔽2)11yescharacteristic
406C22×C3×C5H(5,𝔽2)11yescharacteristic
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—22no—
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—416no—
423C2×C3×D5—41no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5C4×D414yescomplemented
428C2×C3×D5C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433C3×C4×C5—41no—
434C3×C4×C5—41no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C3×Dic5—41no—
439C3×Dic5—41no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—51no—
443C24×C3—54no—
444C24×C3—102no—
445C24×C3—102no—
446C24×C3—102no—
447C24×C3—102no—
448C24×C3—201no—
449C24×C3—201no—
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—51no—
461C22×C3×C4—51no—
462C22×C3×C4—51no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—102no—
466C22×C3×C4—102no—
467C22×C3×C4—102no—
468C22×C3×C4—102no—
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—201no—
476C22×C3×C4—201no—
477C22×C3×C4—201no—
478C22×C3×C4—201no—
479C22×C3×C4—201no—
480C22×C3×C4C22×D511yescharacteristic
481C22×C3×C4C22×D511yescharacteristic
482C22×C3×C4C22×D511yescharacteristic
483C22×C3×C4C22×D511yescharacteristic
484C22×C3×C4C22×D511yescharacteristic
485C22×C3×C4C22×D511yescharacteristic
486C3×C4⋊C4—22no—
487C3×C4⋊C4—102no—
488C3×C4⋊C4—201no—
489C3×C22⋊C4—22no—
490C3×C22⋊C4—22no—
491C3×C22⋊C4—54no—
492C3×C22⋊C4—54no—
493C3×C22⋊C4—54no—
494C3×C22⋊C4—54no—
495C3×C22⋊C4—102no—
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⋊C4C4×D514yescomplemented
503C3×C42—22no—
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×C5C22×C3×C412yes—
513C23×C5C24×C311yescharacteristic
514C22×D5—21no—
515C22×D5—21no—
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—21no—
519C22×D5—21no—
520C22×D5—21no—
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—21no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—28no—
529C22×D5—28no—
530C22×D5—44no—
531C22×D5—44no—
532C22×D5—44no—
533C22×D5—44no—
534C22×D5—44no—
535C22×D5C22×C3×C412yes—
536C22×D5C22×C3×C412yes—
537C22×D5C22×C3×C412yes—
538C22×D5C2×C3×D412yes—
539C22×D5C2×C3×D412yes—
540C22×D5C3×#4112yes—
541C22×D5C3×#4112yes—
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—21no—
553C2×C4×C5—21no—
554C2×C4×C5—21no—
555C2×C4×C5—21no—
556C2×C4×C5C22×C3×C412yes—
557C2×C4×C5C22×C3×C412yes—
558C2×C4×C5C2×C3×D412yes—
559C2×C4×C5C2×C3×D412yes—
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×Dic5C22×C3×C412yes—
574C2×Dic5C2×C3×D412yes—
575C2×Dic5C2×C3×D412yes—
576D20—28no—
577D20—28no—
578C4×D5—44no—
579C4×D5—44no—
580C4×D5—44no—
581C4×D5—44no—
582C4×D5—44no—
583C25—51no—
584C22×D4—51no—
585C22×D4—51no—
586C22×D4—51no—
587C23×C4—51no—
588C23×C4—51no—
589C23×C4—51no—
590C23×C4—51no—
591C23×C4—51no—
592#120—58no—
593C4×D4—104no—
594C4×D4—104no—
595C2×C4⋊C4—51no—
596C2×C4⋊C4—51no—
597C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
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
613C2×C22⋊C4C2×C3×D511yescharacteristic
614C2×C42—51no—
615C2×C42—51no—
616C2×C42C2×C3×D511yescharacteristic, complemented
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—42no—
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5#51811yescharacteristic
627C2×C3×C5D4211yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#55111yescharacteristic
631C3×D5—24no—
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—52no—
641C23×C3—52no—
642C23×C3—52no—
643C23×C3—52no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—52no—
647C23×C3—108no—
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—101no—
660C23×C3—101no—
661C23×C3—101no—
662C23×C3—101no—
663C23×C3—204no—
664C23×C3—204no—
665C23×C3—204no—
666C23×C3—204no—
667C23×C3—204no—
668C23×C3C2×C4×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—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
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—204no—
703C2×C3×C4—204no—
704C2×C3×C4—204no—
705C2×C3×C4—204no—
706C2×C3×C4—204no—
707C2×C3×C4C2×C4×D512yes—
708C2×C3×C4C2×C4×D512yes—
709C2×C3×C4D4×D512yes—
710C2×C3×C4D4×D512yes—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—41no—
715C22×C5—41no—
716C22×C5—41no—
717C22×C5—41no—
718C22×C5C23×C3×C411yescharacteristic
719C22×C5C22×C3×D411yescharacteristic
720C22×C5C22×C3×D411yescharacteristic
721C22×C5C2×C3×#4111yescharacteristic
722C22×C5C2×C3×#4111yescharacteristic
723C22×C5C3×H(5,𝔽2)11yescharacteristic
724C22×C5C3×H(5,𝔽2)11yescharacteristic
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—22no—
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—416no—
741C2×D5—41no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5C3×C4×D414yescomplemented
746C2×D5C3×C4×D414yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—22no—
750C4×C5—22no—
751C4×C5—41no—
752C4×C5—41no—
753Dic5—22no—
754Dic5—22no—
755Dic5—22no—
756Dic5—41no—
757Dic5—41no—
758C24—51no—
759C24—51no—
760C24—51no—
761C24—54no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—102no—
766C24—201no—
767C24—201no—
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—51no—
779C22×C4—51no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—102no—
784C22×C4—102no—
785C22×C4—102no—
786C22×C4—102no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—102no—
792C22×C4—102no—
793C22×C4—201no—
794C22×C4—201no—
795C22×C4—201no—
796C22×C4—201no—
797C22×C4—201no—
798C22×C4C22×C3×D511yescharacteristic
799C22×C4C22×C3×D511yescharacteristic
800C22×C4C22×C3×D511yescharacteristic
801C22×C4C22×C3×D511yescharacteristic
802C22×C4C22×C3×D511yescharacteristic
803C22×C4C22×C3×D511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—102no—
806C4⋊C4—201no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—54no—
810C22⋊C4—54no—
811C22⋊C4—54no—
812C22⋊C4—54no—
813C22⋊C4—102no—
814C22⋊C4—102no—
815C22⋊C4—102no—
816C22⋊C4—102no—
817C22⋊C4—102no—
818C22⋊C4—102no—
819C22⋊C4—201no—
820C22⋊C4C3×C4×D514yescomplemented
821C42—22no—
822C42—102no—
823C42—201no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—54no—
833C22×C3—54no—
834C22×C3—102no—
835C22×C3—102no—
836C22×C3—102no—
837C22×C3—102no—
838C22×C3—102no—
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—102no—
849C22×C3—2016no—
850C22×C3—201no—
851C22×C3—201no—
852C22×C3—201no—
853C22×C3—201no—
854C22×C3C22×C4×D511yescharacteristic
855C22×C3C2×D4×D511yescharacteristic
856C22×C3C2×D4×D511yescharacteristic
857C22×C3D5×#4111yescharacteristic
858C22×C3D5×#4111yescharacteristic
859C22×C3#414911yescharacteristic
860C22×C3#414911yescharacteristic
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—102no—
868C3×C4—102no—
869C3×C4—102no—
870C3×C4—201no—
871C3×C4—201no—
872C2×C5—42no—
873C2×C5C2×C3×C4×D411yescharacteristic
874C2×C5C2×C3×C4×D411yescharacteristic
875C2×C5C3×#51811yescharacteristic
876C2×C5C3×D4211yescharacteristic
877C2×C5C3×#54611yescharacteristic
878C2×C5C3×#54611yescharacteristic
879C2×C5C3×#55111yescharacteristic
880D5—24no—
881D5—24no—
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—52no—
890C23—52no—
891C23—52no—
892C23—52no—
893C23—52no—
894C23—52no—
895C23—52no—
896C23—108no—
897C23—108no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—101no—
911C23—101no—
912C23—204no—
913C23—204no—
914C23—204no—
915C23—204no—
916C23—204no—
917C23C2×C3×C4×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—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
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—204no—
952C2×C4—204no—
953C2×C4—204no—
954C2×C4—204no—
955C2×C4—204no—
956C2×C4C2×C3×C4×D512yes—
957C2×C4C2×C3×C4×D512yes—
958C2×C4C3×D4×D512yes—
959C2×C4C3×D4×D512yes—
960C2×C3—42no—
961C2×C3—104no—
962C2×C3—104no—
963C2×C3—202no—
964C2×C3#6585511yescharacteristic
965C2×C3C4×D4×D511yescharacteristic
966C2×C3C4×D4×D511yescharacteristic
967C2×C3#6594311yescharacteristic
968C2×C3#6598811yescharacteristic
969C2×C3#6601011yescharacteristic
970C2×C3#6603911yescharacteristic
971C5C3×#235811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—41no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—54no—
980C22—54no—
981C22—102no—
982C22—102no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—102no—
992C22—102no—
993C22—102no—
994C22—102no—
995C22—102no—
996C22—2016no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22—201no—
1001C22C22×C3×C4×D511yescharacteristic
1002C22C2×C3×D4×D511yescharacteristic
1003C22C2×C3×D4×D511yescharacteristic
1004C22C3×D5×#4111yescharacteristic
1005C22C3×D5×#4111yescharacteristic
1006C22C3×#414911yescharacteristic
1007C22C3×#414911yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—41no—
1014C4—102no—
1015C4—102no—
1016C4—102no—
1017C4—201no—
1018C4—201no—
1019C3#1060756711yescharacteristic, direct product factor, Sylow
1020C2—42no—
1021C2—104no—
1022C2—104no—
1023C2—202no—
1024C2C3×#6585511yescharacteristic
1025C2C3×C4×D4×D511yescharacteristic
1026C2C3×C4×D4×D511yescharacteristic
1027C2C3×#6594311yescharacteristic
1028C2C3×#6598811yescharacteristic
1029C2C3×#6601011yescharacteristic
1030C2C3×#6603911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC2×C3×#4028C2
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2358
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4039C2semidirect
3. C2×C3×D5×C22⋊C4C2semidirect
4. C2×C3×D5×C22⋊C4C2semidirect
5. C2×C3×C4×D20C2semidirect
6. C3×C5×#388C2semidirect
7. C3×#65278C2semidirect
8. C3×#65246C2semidirect
9. C3×#65245C2semidirect
10. C3×#65240C2semidirect
11. C3×C4×#685C2semidirect
12. C3×#64957C2semidirect
13. C3×#64955C2semidirect
14. C3×#64954C2semidirect
15. C3×#64954C2semidirect
16. #10607567C3direct (N × H)
25. C22×C3×C4×D5C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
30. C2×C3×C42×C5C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×#685C22semidirect
41. C2×C3×#685C22semidirect
42. C2×C3×C4⋊Dic5C22semidirect
43. C2×C3×#683C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C2×C3×C4×Dic5C22semidirect
47. C3×#4028C4semidirect
51. C3×C5×#95C22semidirect
52. C3×C5×#95C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. C3×#3963C22semidirect
56. C3×#3963C22semidirect
58. C2×#4039C2×C3semidirect
60. C2×D5×C22⋊C4C2×C3semidirect
61. C2×D5×C22⋊C4C2×C3semidirect
62. C2×C4×D20C2×C3semidirect
63. C5×#388C2×C3semidirect
64. #65278C2×C3semidirect
65. #65246C2×C3semidirect
66. #65245C2×C3semidirect
67. #65240C2×C3semidirect
68. C4×#685C2×C3semidirect
69. #64957C2×C3semidirect
70. #64955C2×C3semidirect
71. #64954C2×C3semidirect
72. #64954C2×C3semidirect
80. C23×C3×D5C2×C4semidirect
92. C2×C3×C22⋊D5C2×C4semidirect
102. C2×C3×D20C2×C4semidirect
103. C2×C3×D20C2×C4semidirect
122. C3×C5×C22⋊C4C2×C4semidirect
131. C3×#685C2×C4semidirect
132. C3×#685C2×C4semidirect
133. C3×#685D4semidirect
134. C3×#685D4semidirect
146. C3×#388D5semidirect
162. C22×C4×D5C22×C3semidirect
163. C2×C5×C4⋊C4C22×C3semidirect
167. C2×C42×C5C22×C3semidirect
176. C2×#685C22×C3semidirect
177. C2×#685C22×C3semidirect
178. C2×#685C22×C3semidirect
179. C2×C4⋊Dic5C22×C3semidirect
180. C2×#683C22×C3semidirect
181. C2×C4×Dic5C22×C3semidirect
182. C2×C4×Dic5C22×C3semidirect
184. #4028C3×C4semidirect
188. C5×#95C22×C3semidirect
189. C5×#95C22×C3semidirect
190. #3963C22×C3semidirect
191. #3963C22×C3semidirect
192. #3963C22×C3semidirect
193. #3963C22×C3semidirect
286. C2×C3×C4⋊C4C2×D5semidirect
305. C2×C3×C42C2×D5semidirect
310. C3×#95C2×D5semidirect
311. C3×#95C2×D5semidirect
319. C23×D5C2×C3×C4semidirect
331. C2×C22⋊D5C2×C3×C4semidirect
341. C2×D20C2×C3×C4semidirect
342. C2×D20C2×C3×C4semidirect
361. C5×C22⋊C4C2×C3×C4semidirect
370. #685C2×C3×C4semidirect
371. #685C2×C3×C4semidirect
372. #685C3×D4semidirect
373. #685C3×D4semidirect
385. #388C3×D5semidirect
427. C2×C3×D5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
502. C3×C22⋊C4C4×D5semidirect
597. C2×C4⋊C4C2×C3×D5semidirect
616. C2×C42C2×C3×D5semidirect
621. #95C2×C3×D5semidirect
622. #95C2×C3×D5semidirect
745. C2×D5C3×C4×D4semidirect
746. C2×D5C3×C4×D4semidirect
820. C22⋊C4C3×C4×D5semidirect
824. C3×C5#2358semidirect
971. C5C3×#2358semidirect
1019. C3#10607567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×C3×#40282
C2×C3×D5×C22⋊C42
C2×C3×C4×D202
C3×C5×#3882
C3×#652782
C3×#652462
C3×#652452
C3×#652402
C3×C4×#6852
C3×#649572
C3×#649552
C3×#649542
#106075673
C3×#23585