Finite Group Databasebeta

← C2×C3×#65955 #14495279

Subgroups — C2×C3×#65955 #14495279

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic, complemented
2C2×C3×#4085C211yesmaximal, characteristic, complemented
3C2×C3×#4085C211yesmaximal, characteristic, complemented
4C2×C3×#4084C211yesmaximal, characteristic, complemented
5C2×C3×#4082C211yesmaximal, characteristic, complemented
6C2×C3×#4081C211yesmaximal, characteristic, complemented
7C2×C3×#4081C211yesmaximal, characteristic, complemented
8C2×C3×#4075C211yesmaximal, characteristic, complemented
9C2×C3×#4070C211yesmaximal, characteristic, complemented
10C3×#65955C2116yesmaximal, direct product factor
11C2×C3×#4042C211yesmaximal, characteristic, complemented
12C2×C3×#4035C211yesmaximal, characteristic, complemented
13C2×C3×#4031C211yesmaximal, characteristic, complemented
14C2×C3×#4029C211yesmaximal, characteristic, complemented
15C2×C3×#4024C211yesmaximal, characteristic, complemented
16C2×C3×#4024C211yesmaximal, characteristic, complemented
17C2×#65955C311yesmaximal, characteristic, direct product factor, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic
27C22×C3×C4×D5C2211yescharacteristic
28C22×C3×Dic10C2211yescharacteristic
29C22×C3×Dic10C2211yescharacteristic
30C3×C5×#121C2218yescomplemented
31C2×C3×C5×C4⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C3×#4085C2218yescomplemented
42C3×#4085C2218yescomplemented
43C3×#4084C2218yescomplemented
44C3×#4082C2218yescomplemented
45C3×#4081C2218yescomplemented
46C3×#4081C2218yescomplemented
47C3×#4075C2218yescomplemented
48C2×C3×#685C2211yescharacteristic
49C2×C3×#685C2211yescharacteristic
50C2×C3×#685C2211yescharacteristic
51C2×C3×C4⋊Dic5C2211yescharacteristic
52C2×C3×C4⋊Dic5C2211yescharacteristic
53C3×#4070C2218yescomplemented
54C2×C3×#683C2211yescharacteristic
55C2×C3×#683C2211yescharacteristic
56C2×C3×#683C2211yescharacteristic
57C2×C3×#683C2211yescharacteristic
58C2×C3×#683C2211yescharacteristic
59C2×C3×#683C2211yescharacteristic
60C2×C3×#683C2211yescharacteristic
61C2×C3×C4×Dic5C2211yescharacteristic
62C3×#4042C2218yescomplemented
63C3×#4035C2218yescomplemented
64C3×#4031C2218yescomplemented
65C3×#4029C2218yescomplemented
66C3×#4024C2218yescomplemented
67C3×#4024C2218yescomplemented
68C2×C3×#562—51nomaximal, Hall
69C2×C5×#121C2×C311yescharacteristic, complemented
70C2×#4085C2×C311yescharacteristic, complemented
71C2×#4085C2×C311yescharacteristic, complemented
72C2×#4084C2×C311yescharacteristic, complemented
73C2×#4082C2×C311yescharacteristic, complemented
74C2×#4081C2×C311yescharacteristic, complemented
75C2×#4081C2×C311yescharacteristic, complemented
76C2×#4075C2×C311yescharacteristic, complemented
77C2×#4070C2×C311yescharacteristic, complemented
78#65955C2×C3116yesdirect product factor
79C2×#4042C2×C311yescharacteristic, complemented
80C2×#4035C2×C311yescharacteristic, complemented
81C2×#4031C2×C311yescharacteristic, complemented
82C2×#4029C2×C311yescharacteristic, complemented
83C2×#4024C2×C311yescharacteristic, complemented
84C2×#4024C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C24×C3×C5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C2×C3×C5×D4—42no—
90C2×C3×C5×D4—42no—
91C2×C3×C5×D4—42no—
92C2×C3×C5×D4C2314yes—
93C2×C3×C5×D4C2314yes—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2314yes—
101C2×C3×C22⋊D5—42no—
102C2×C3×C22⋊D5—42no—
103C2×C3×C22⋊D5—42no—
104C2×C3×C22⋊D5C2314yes—
105C2×C3×C22⋊D5C2314yes—
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5—42no—
108C22×C3×Dic5—42no—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2314yes—
117C22×C3×Dic5C2314yes—
118C2×C3×C4×D5—42no—
119C2×C3×C4×D5C2314yes—
120C2×C3×Dic10—42no—
121C2×C3×Dic10—42no—
122C2×C3×Dic10C2314yes—
123C2×C3×Dic10C2314yes—
124C3×C5×C4⋊C4C2314yes—
125C3×C5×C22⋊C4C2314yes—
126C3×C5×C22⋊C4C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×C22⋊Dic5C2314yes—
129C3×C22⋊Dic5C2314yes—
130C3×C22⋊Dic5C2314yes—
131C3×C22⋊Dic5C2314yes—
132C3×C22⋊Dic5C2314yes—
133C3×C22⋊Dic5C2314yes—
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×C4⋊Dic5C2314yes—
138C3×C4⋊Dic5C2314yes—
139C3×#683C2314yes—
140C3×#683C2314yes—
141C3×#683C2314yes—
142C3×#683C2314yes—
143C3×#683C2314yes—
144C3×#683C2314yes—
145C3×#683C2314yes—
146C3×C4×Dic5C2314yes—
147C3×#562—516no—
148C2×C3×#125—51no—
149C2×C3×#124—51no—
150C2×C3×#124—51no—
151C2×C3×#123—51no—
152C2×C3×#123—51no—
153C2×C3×#123—51no—
154C2×C3×#123—51no—
155C2×C3×C22⋊Q8—51no—
156C2×C3×C22⋊Q8—51no—
157C2×C3×C22⋊Q8—51no—
158C2×C3×C22⋊Q8—51no—
159C2×C3×#121—51no—
160C2×C3×#121—51no—
161C2×C3×#121—51no—
162C2×C3×#121D511yescharacteristic, complemented
163C22×C5×D4C22×C311yescharacteristic
164C22×C5×D4C22×C311yescharacteristic
165C22×C5×D4C22×C311yescharacteristic
166C23×C4×C5C22×C311yescharacteristic
167C22×C22⋊D5C22×C311yescharacteristic
168C22×C22⋊D5C22×C311yescharacteristic
169C22×C22⋊D5C22×C311yescharacteristic
170C23×Dic5C22×C311yescharacteristic
171C23×Dic5C22×C311yescharacteristic
172C22×C4×D5C22×C311yescharacteristic
173C22×Dic10C22×C311yescharacteristic
174C22×Dic10C22×C311yescharacteristic
175C5×#121C22×C318yescomplemented
176C2×C5×C4⋊C4C22×C311yescharacteristic
177C2×C5×C22⋊C4C22×C311yescharacteristic
178C2×C5×C22⋊C4C22×C311yescharacteristic
179C2×C22⋊Dic5C22×C311yescharacteristic
180C2×C22⋊Dic5C22×C311yescharacteristic
181C2×C22⋊Dic5C22×C311yescharacteristic
182C2×C22⋊Dic5C22×C311yescharacteristic
183C2×C22⋊Dic5C22×C311yescharacteristic
184C2×C22⋊Dic5C22×C311yescharacteristic
185C2×C22⋊Dic5C22×C311yescharacteristic
186#4085C22×C318yescomplemented
187#4085C22×C318yescomplemented
188#4084C22×C318yescomplemented
189#4082C22×C318yescomplemented
190#4081C22×C318yescomplemented
191#4081C22×C318yescomplemented
192#4075C22×C318yescomplemented
193C2×#685C22×C311yescharacteristic
194C2×#685C22×C311yescharacteristic
195C2×#685C22×C311yescharacteristic
196C2×C4⋊Dic5C22×C311yescharacteristic
197C2×C4⋊Dic5C22×C311yescharacteristic
198#4070C22×C318yescomplemented
199C2×#683C22×C311yescharacteristic
200C2×#683C22×C311yescharacteristic
201C2×#683C22×C311yescharacteristic
202C2×#683C22×C311yescharacteristic
203C2×#683C22×C311yescharacteristic
204C2×#683C22×C311yescharacteristic
205C2×#683C22×C311yescharacteristic
206C2×C4×Dic5C22×C311yescharacteristic
207#4042C22×C318yescomplemented
208#4035C22×C318yescomplemented
209#4031C22×C318yescomplemented
210#4029C22×C318yescomplemented
211#4024C22×C318yescomplemented
212#4024C22×C318yescomplemented
213C2×#562—51noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2412yes—
225C23×C3×C5C2412yes—
226C23×C3×C5C2411yescharacteristic
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5C2412yes—
231C3×C5×D4—44no—
232C3×C5×D4—44no—
233C3×C5×D4—44no—
234C2×C3×C4×C5—22no—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5—44no—
239C2×C3×C4×C5C2412yes—
240C2×C3×C4×C5C2412yes—
241C2×C3×C4×C5C2412yes—
242C2×C3×C4×C5C2412yes—
243C3×C22⋊D5—44no—
244C3×C22⋊D5—44no—
245C3×C22⋊D5—44no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5—22no—
249C2×C3×Dic5—22no—
250C2×C3×Dic5—22no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—44no—
254C2×C3×Dic5—44no—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C3×C4×D5—44no—
263C3×Dic10—44no—
264C3×Dic10—44no—
265C22×C3×Q8—51no—
266C22×C3×Q8—51no—
267C22×C3×D4—51no—
268C22×C3×D4—51no—
269C22×C3×D4—51no—
270C22×C3×D4C2×D511yescharacteristic
271C22×C3×D4C2×D511yescharacteristic
272C22×C3×D4C2×D511yescharacteristic
273C23×C3×C4—51no—
274C23×C3×C4—51no—
275C23×C3×C4—51no—
276C23×C3×C4C2×D511yescharacteristic
277C3×#125—58no—
278C3×#124—58no—
279C3×#124—58no—
280C3×#123—58no—
281C3×#123—58no—
282C3×#123—58no—
283C3×#123—58no—
284C3×C22⋊Q8—58no—
285C3×C22⋊Q8—58no—
286C3×C22⋊Q8—58no—
287C3×C22⋊Q8—58no—
288C3×#121—58no—
289C3×#121—58no—
290C3×#121—58no—
291C3×#121C2×D518yescomplemented
292C2×C3×C4⋊C4—51no—
293C2×C3×C4⋊C4—51no—
294C2×C3×C4⋊C4—51no—
295C2×C3×C4⋊C4—51no—
296C2×C3×C4⋊C4—51no—
297C2×C3×C4⋊C4—51no—
298C2×C3×C4⋊C4—51no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4C2×D511yescharacteristic
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—51no—
305C2×C3×C22⋊C4—51no—
306C2×C3×C22⋊C4—51no—
307C2×C3×C22⋊C4—51no—
308C2×C3×C22⋊C4—51no—
309C2×C3×C22⋊C4—51no—
310C2×C3×C22⋊C4—51no—
311C2×C3×C22⋊C4—51no—
312C2×C3×C22⋊C4C2×D511yescharacteristic
313C2×C3×C22⋊C4C2×D511yescharacteristic
314C2×C3×C42—51no—
315C24×C5C23×C311yescharacteristic
316C24×C5C23×C311yescharacteristic
317C24×C5C23×C311yescharacteristic
318C23×D5C23×C311yescharacteristic
319C2×C5×D4—42no—
320C2×C5×D4—42no—
321C2×C5×D4—42no—
322C2×C5×D4C23×C314yes—
323C2×C5×D4C23×C314yes—
324C2×C5×D4C23×C314yes—
325C22×C4×C5—42no—
326C22×C4×C5C23×C311yescharacteristic
327C22×C4×C5C23×C311yescharacteristic
328C22×C4×C5C23×C311yescharacteristic
329C22×C4×C5C23×C311yescharacteristic
330C22×C4×C5C23×C314yes—
331C2×C22⋊D5—42no—
332C2×C22⋊D5—42no—
333C2×C22⋊D5—42no—
334C2×C22⋊D5C23×C314yes—
335C2×C22⋊D5C23×C314yes—
336C2×C22⋊D5C23×C314yes—
337C22×Dic5—42no—
338C22×Dic5—42no—
339C22×Dic5C23×C311yescharacteristic
340C22×Dic5C23×C311yescharacteristic
341C22×Dic5C23×C311yescharacteristic
342C22×Dic5C23×C311yescharacteristic
343C22×Dic5C23×C311yescharacteristic
344C22×Dic5C23×C311yescharacteristic
345C22×Dic5C23×C311yescharacteristic
346C22×Dic5C23×C314yes—
347C22×Dic5C23×C314yes—
348C2×C4×D5—42no—
349C2×C4×D5C23×C314yes—
350C2×Dic10—42no—
351C2×Dic10—42no—
352C2×Dic10C23×C314yes—
353C2×Dic10C23×C314yes—
354C5×C4⋊C4C23×C314yes—
355C5×C22⋊C4C23×C314yes—
356C5×C22⋊C4C23×C314yes—
357C22⋊Dic5C23×C314yes—
358C22⋊Dic5C23×C314yes—
359C22⋊Dic5C23×C314yes—
360C22⋊Dic5C23×C314yes—
361C22⋊Dic5C23×C314yes—
362C22⋊Dic5C23×C314yes—
363C22⋊Dic5C23×C314yes—
364#685C23×C314yes—
365#685C23×C314yes—
366#685C23×C314yes—
367C4⋊Dic5C23×C314yes—
368C4⋊Dic5C23×C314yes—
369#683C23×C314yes—
370#683C23×C314yes—
371#683C23×C314yes—
372#683C23×C314yes—
373#683C23×C314yes—
374#683C23×C314yes—
375#683C23×C314yes—
376C4×Dic5C23×C314yes—
377#562—516no—
378C2×#125—51no—
379C2×#124—51no—
380C2×#124—51no—
381C2×#123—51no—
382C2×#123—51no—
383C2×#123—51no—
384C2×#123—51no—
385C2×C22⋊Q8—51no—
386C2×C22⋊Q8—51no—
387C2×C22⋊Q8—51no—
388C2×C22⋊Q8—51no—
389C2×#121—51no—
390C2×#121—51no—
391C2×#121—51no—
392C2×#121C3×D511yescharacteristic, complemented
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—44no—
403C22×C3×C5—44no—
404C22×C3×C5—44no—
405C22×C3×C5H(5,𝔽2)12yes—
406C22×C3×C5H(5,𝔽2)12yes—
407C22×C3×C52−1+412yes—
408C22×C3×C5C2511yescharacteristic
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×Dic5—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C3×Dic5—22no—
424C24×C3—51no—
425C24×C3C22×D511yescharacteristic
426C24×C3C22×D511yescharacteristic
427C24×C3C22×D511yescharacteristic
428C2×C3×Q8—54no—
429C2×C3×Q8—54no—
430C2×C3×Q8—202no—
431C2×C3×Q8—202no—
432C2×C3×D4—42no—
433C2×C3×D4—42no—
434C2×C3×D4—42no—
435C2×C3×D4—54no—
436C2×C3×D4—54no—
437C2×C3×D4—54no—
438C2×C3×D4—202no—
439C2×C3×D4—202no—
440C2×C3×D4—202no—
441C2×C3×D4C22×D514yes—
442C2×C3×D4C22×D514yes—
443C2×C3×D4C22×D514yes—
444C22×C3×C4—42no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4—54no—
453C22×C3×C4—54no—
454C22×C3×C4—54no—
455C22×C3×C4—202no—
456C22×C3×C4—202no—
457C22×C3×C4—202no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D514yes—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C4⋊C4—54no—
467C3×C4⋊C4—54no—
468C3×C4⋊C4—54no—
469C3×C4⋊C4—54no—
470C3×C4⋊C4—54no—
471C3×C4⋊C4—54no—
472C3×C4⋊C4C22×D514yes—
473C3×C22⋊C4—54no—
474C3×C22⋊C4—54no—
475C3×C22⋊C4—54no—
476C3×C22⋊C4—54no—
477C3×C22⋊C4—54no—
478C3×C22⋊C4—54no—
479C3×C22⋊C4—54no—
480C3×C22⋊C4—54no—
481C3×C22⋊C4—54no—
482C3×C22⋊C4—54no—
483C3×C22⋊C4C22×D514yes—
484C3×C22⋊C4C22×D514yes—
485C3×C42—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5—22no—
494C23×C5—22no—
495C23×C5C24×C312yes—
496C23×C5C24×C312yes—
497C23×C5C24×C312yes—
498C23×C5C24×C311yescharacteristic
499C22×D5—22no—
500C22×D5—22no—
501C22×D5—22no—
502C22×D5C24×C312yes—
503C5×D4—44no—
504C5×D4—44no—
505C5×D4—44no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—22no—
509C2×C4×C5—22no—
510C2×C4×C5—44no—
511C2×C4×C5C24×C312yes—
512C2×C4×C5C24×C312yes—
513C2×C4×C5C24×C312yes—
514C2×C4×C5C24×C312yes—
515C22⋊D5—44no—
516C22⋊D5—44no—
517C22⋊D5—44no—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—22no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—44no—
526C2×Dic5—44no—
527C2×Dic5C24×C312yes—
528C2×Dic5C24×C312yes—
529C2×Dic5C24×C312yes—
530C2×Dic5C24×C312yes—
531C2×Dic5C24×C312yes—
532C2×Dic5C24×C312yes—
533C2×Dic5C24×C312yes—
534C4×D5—44no—
535Dic10—44no—
536Dic10—44no—
537C22×Q8—51no—
538C22×Q8—51no—
539C22×D4—51no—
540C22×D4—51no—
541C22×D4—51no—
542C22×D4C2×C3×D511yescharacteristic
543C22×D4C2×C3×D511yescharacteristic
544C22×D4C2×C3×D511yescharacteristic
545C23×C4—51no—
546C23×C4—51no—
547C23×C4—51no—
548C23×C4C2×C3×D511yescharacteristic
549#125—58no—
550#124—58no—
551#124—58no—
552#123—58no—
553#123—58no—
554#123—58no—
555#123—58no—
556C22⋊Q8—58no—
557C22⋊Q8—58no—
558C22⋊Q8—58no—
559C22⋊Q8—58no—
560#121—58no—
561#121—58no—
562#121—58no—
563#121C2×C3×D518yescomplemented
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—51no—
569C2×C4⋊C4—51no—
570C2×C4⋊C4—51no—
571C2×C4⋊C4—51no—
572C2×C4⋊C4—51no—
573C2×C4⋊C4C2×C3×D511yescharacteristic
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—51no—
580C2×C22⋊C4—51no—
581C2×C22⋊C4—51no—
582C2×C22⋊C4—51no—
583C2×C22⋊C4—51no—
584C2×C22⋊C4C2×C3×D511yescharacteristic
585C2×C22⋊C4C2×C3×D511yescharacteristic
586C2×C42—51no—
587C2×C3×C5—42no—
588C2×C3×C5—42no—
589C2×C3×C5—42no—
590C2×C3×C5#56214yescomplemented
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
593C2×C3×C5C2×2−1+411yescharacteristic
594C3×D5—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—52no—
605C23×C3—102no—
606C23×C3—102no—
607C23×C3—102no—
608C23×C3C23×D512yes—
609C23×C3C23×D512yes—
610C23×C3C23×D512yes—
611C23×C3C23×D511yescharacteristic
612C3×Q8—204no—
613C3×Q8—204no—
614C3×D4—44no—
615C3×D4—44no—
616C3×D4—44no—
617C3×D4—204no—
618C3×D4—204no—
619C3×D4—204no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—44no—
625C2×C3×C4—52no—
626C2×C3×C4—52no—
627C2×C3×C4—52no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—52no—
631C2×C3×C4—52no—
632C2×C3×C4—102no—
633C2×C3×C4—102no—
634C2×C3×C4—102no—
635C2×C3×C4—102no—
636C2×C3×C4—102no—
637C2×C3×C4—102no—
638C2×C3×C4—102no—
639C2×C3×C4—204no—
640C2×C3×C4—204no—
641C2×C3×C4—204no—
642C2×C3×C4C23×D512yes—
643C2×C3×C4C23×D512yes—
644C2×C3×C4C23×D512yes—
645C2×C3×C4C23×D512yes—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—22no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—44no—
656C22×C5—44no—
657C22×C5—44no—
658C22×C5C3×H(5,𝔽2)12yes—
659C22×C5C3×H(5,𝔽2)12yes—
660C22×C5C3×2−1+412yes—
661C22×C5C25×C311yescharacteristic
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—44no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—22no—
670Dic5—22no—
671Dic5—22no—
672Dic5—22no—
673Dic5—22no—
674Dic5—22no—
675Dic5—22no—
676Dic5—22no—
677C24—51no—
678C24C22×C3×D511yescharacteristic
679C24C22×C3×D511yescharacteristic
680C24C22×C3×D511yescharacteristic
681C2×Q8—54no—
682C2×Q8—54no—
683C2×Q8—202no—
684C2×Q8—202no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—54no—
689C2×D4—54no—
690C2×D4—54no—
691C2×D4—202no—
692C2×D4—202no—
693C2×D4—202no—
694C2×D4C22×C3×D514yes—
695C2×D4C22×C3×D514yes—
696C2×D4C22×C3×D514yes—
697C22×C4—42no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—54no—
706C22×C4—54no—
707C22×C4—54no—
708C22×C4—202no—
709C22×C4—202no—
710C22×C4—202no—
711C22×C4C22×C3×D511yescharacteristic
712C22×C4C22×C3×D511yescharacteristic
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715C22×C4C22×C3×D514yes—
716C4⋊C4—54no—
717C4⋊C4—54no—
718C4⋊C4—54no—
719C4⋊C4—54no—
720C4⋊C4—54no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—54no—
724C4⋊C4—54no—
725C4⋊C4C22×C3×D514yes—
726C22⋊C4—54no—
727C22⋊C4—54no—
728C22⋊C4—54no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—54no—
733C22⋊C4—54no—
734C22⋊C4—54no—
735C22⋊C4—54no—
736C22⋊C4C22×C3×D514yes—
737C22⋊C4C22×C3×D514yes—
738C42—54no—
739C3×C5C2×#56211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—44no—
750C22×C3—44no—
751C22×C3—44no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—204no—
756C22×C3#414412yes—
757C22×C3#414412yes—
758C22×C3#415012yes—
759C22×C3C24×D511yescharacteristic
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—102no—
765C3×C4—102no—
766C3×C4—102no—
767C3×C4—102no—
768C3×C4—102no—
769C3×C4—102no—
770C3×C4—102no—
771C2×C5—42no—
772C2×C5—42no—
773C2×C5—42no—
774C2×C5C3×#56214yescomplemented
775C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
776C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
777C2×C5C2×C3×2−1+411yescharacteristic
778D5—42no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—52no—
789C23—102no—
790C23—102no—
791C23—102no—
792C23C23×C3×D512yes—
793C23C23×C3×D512yes—
794C23C23×C3×D512yes—
795C23C23×C3×D511yescharacteristic
796Q8—204no—
797Q8—204no—
798D4—44no—
799D4—44no—
800D4—44no—
801D4—204no—
802D4—204no—
803D4—204no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—44no—
809C2×C4—52no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—52no—
813C2×C4—52no—
814C2×C4—52no—
815C2×C4—52no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—204no—
824C2×C4—204no—
825C2×C4—204no—
826C2×C4C23×C3×D512yes—
827C2×C4C23×C3×D512yes—
828C2×C4C23×C3×D512yes—
829C2×C4C23×C3×D512yes—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—42no—
833C2×C3—202no—
834C2×C3#6595514yesdirect product factor
835C2×C3C2×#414411yescharacteristic
836C2×C3C2×#414411yescharacteristic
837C2×C3C2×#415011yescharacteristic
838C5C2×C3×#56211yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—102no—
852C22—102no—
853C22—102no—
854C22—204no—
855C22C3×#414412yes—
856C22C3×#414412yes—
857C22C3×#415012yes—
858C22C24×C3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—102no—
864C4—102no—
865C4—102no—
866C4—102no—
867C4—102no—
868C4—102no—
869C4—102no—
870C3C2×#6595511yescharacteristic, direct product factor, Sylow
871C2—42no—
872C2—42no—
873C2—42no—
874C2—202no—
875C2C3×#6595514yesdirect product factor
876C2C2×C3×#414411yescharacteristic
877C2C2×C3×#414411yescharacteristic
878C2C2×C3×#415011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×C3×#121D5
hypocenterC5C2×C3×#562
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#121C2semidirect
2. C2×C3×#4085C2semidirect
3. C2×C3×#4085C2semidirect
4. C2×C3×#4084C2semidirect
5. C2×C3×#4082C2semidirect
6. C2×C3×#4081C2semidirect
7. C2×C3×#4081C2semidirect
8. C2×C3×#4075C2semidirect
9. C2×C3×#4070C2semidirect
10. C3×#65955C2direct (N × H)
11. C2×C3×#4042C2semidirect
12. C2×C3×#4035C2semidirect
13. C2×C3×#4031C2semidirect
14. C2×C3×#4029C2semidirect
15. C2×C3×#4024C2semidirect
16. C2×C3×#4024C2semidirect
17. C2×#65955C3direct (N × H)
30. C3×C5×#121C22semidirect
41. C3×#4085C22semidirect
42. C3×#4085C22semidirect
43. C3×#4084C22semidirect
44. C3×#4082C22semidirect
45. C3×#4081C22semidirect
46. C3×#4081C22semidirect
47. C3×#4075C22semidirect
53. C3×#4070C22semidirect
62. C3×#4042C22semidirect
63. C3×#4035C22semidirect
64. C3×#4031C22semidirect
65. C3×#4029C22semidirect
66. C3×#4024C22semidirect
67. C3×#4024C22semidirect
69. C2×C5×#121C2×C3semidirect
70. C2×#4085C2×C3semidirect
71. C2×#4085C2×C3semidirect
72. C2×#4084C2×C3semidirect
73. C2×#4082C2×C3semidirect
74. C2×#4081C2×C3semidirect
75. C2×#4081C2×C3semidirect
76. C2×#4075C2×C3semidirect
77. C2×#4070C2×C3semidirect
78. #65955C2×C3direct (N × H)
79. C2×#4042C2×C3semidirect
80. C2×#4035C2×C3semidirect
81. C2×#4031C2×C3semidirect
82. C2×#4029C2×C3semidirect
83. C2×#4024C2×C3semidirect
84. C2×#4024C2×C3semidirect
162. C2×C3×#121D5semidirect
175. C5×#121C22×C3semidirect
186. #4085C22×C3semidirect
187. #4085C22×C3semidirect
188. #4084C22×C3semidirect
189. #4082C22×C3semidirect
190. #4081C22×C3semidirect
191. #4081C22×C3semidirect
192. #4075C22×C3semidirect
198. #4070C22×C3semidirect
207. #4042C22×C3semidirect
208. #4035C22×C3semidirect
209. #4031C22×C3semidirect
210. #4029C22×C3semidirect
211. #4024C22×C3semidirect
212. #4024C22×C3semidirect
291. C3×#121C2×D5semidirect
392. C2×#121C3×D5semidirect
563. #121C2×C3×D5semidirect
590. C2×C3×C5#562semidirect
739. C3×C5C2×#562semidirect
774. C2×C5C3×#562semidirect
834. C2×C3#65955direct (N × H)
838. C5C2×C3×#562semidirect
870. C3C2×#65955direct (N × H)
875. C2C3×#65955direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C2×C3×#40852
C2×C3×#40842
C2×C3×#40822
C2×C3×#40812
C2×C3×#40752
C2×C3×#40702
C3×#659552
C2×C3×#40422
C2×C3×#40352
C2×C3×#40312
C2×C3×#40292
C2×C3×#40242
C2×#659553
C2×C3×#5625