Finite Group Databasebeta

← C2×C3×#65994 #14480921

Subgroups — C2×C3×#65994 #14480921

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic, complemented
2C2×C3×#4084C211yesmaximal, characteristic
3C2×C3×#4081C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×C3×#4070C211yesmaximal, characteristic, complemented
6C3×#65994C2116yesmaximal, direct product factor
7C2×C3×#4042C211yesmaximal, characteristic, complemented
8C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
9C2×C3×#4036C211yesmaximal, characteristic, complemented
10C2×C3×#4035C211yesmaximal, characteristic, complemented
11C2×C3×#4029C211yesmaximal, characteristic, complemented
12C2×C3×#4029C211yesmaximal, characteristic, complemented
13C2×C3×#4027C211yesmaximal, characteristic, complemented
14C2×C3×#4025C211yesmaximal, characteristic, complemented
15C2×C3×#4025C211yesmaximal, characteristic, complemented
16C2×C3×#4024C211yesmaximal, characteristic, complemented
17C2×#65994C311yesmaximal, characteristic, direct product factor, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic
27C3×C5×#123C2218yescomplemented
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C3×#4084C2218yes—
39C3×#4081C2218yescomplemented
40C3×C4×C22⋊D5C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×C4⋊Dic5C2211yescharacteristic
44C2×C3×C4⋊Dic5C2211yescharacteristic
45C2×C3×C4⋊Dic5C2211yescharacteristic
46C2×C3×C4⋊Dic5C2211yescharacteristic
47C3×#4070C2218yescomplemented
48C2×C3×#683C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic
50C2×C3×#683C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic
52C2×C3×#683C2211yescharacteristic
53C2×C3×#683C2211yescharacteristic
54C2×C3×#683C2211yescharacteristic
55C2×C3×#683C2211yescharacteristic
56C2×C3×C4×Dic5C2211yescharacteristic
57C2×C3×C4×Dic5C2211yescharacteristic
58C3×#4042C2218yescomplemented
59C3×D5×C4⋊C4C2218yescomplemented
60C3×#4036C2218yescomplemented
61C3×#4035C2218yescomplemented
62C3×#4029C2218yescomplemented
63C3×#4029C2218yescomplemented
64C3×#4027C2218yescomplemented
65C3×#4025C2218yescomplemented
66C3×#4025C2218yescomplemented
67C3×#4024C2218yescomplemented
68C2×C3×#539—51nomaximal, Hall
69C2×C5×#123C2×C311yescharacteristic, complemented
70C2×#4084C2×C311yescharacteristic
71C2×#4081C2×C311yescharacteristic, complemented
72C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
73C2×#4070C2×C311yescharacteristic, complemented
74#65994C2×C3116yesdirect product factor
75C2×#4042C2×C311yescharacteristic, complemented
76C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
77C2×#4036C2×C311yescharacteristic, complemented
78C2×#4035C2×C311yescharacteristic, complemented
79C2×#4029C2×C311yescharacteristic, complemented
80C2×#4029C2×C311yescharacteristic, complemented
81C2×#4027C2×C311yescharacteristic, complemented
82C2×#4025C2×C311yescharacteristic, complemented
83C2×#4025C2×C311yescharacteristic, complemented
84C2×#4024C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C2×C3×C5×D4—42no—
89C2×C3×C5×D4C2314yes—
90C22×C3×C4×C5—42no—
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2314yes—
97C2×C3×C22⋊D5—24no—
98C2×C3×C22⋊D5—24no—
99C2×C3×C22⋊D5C2314yes—
100C2×C3×C22⋊D5C2314yes—
101C22×C3×Dic5—42no—
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2314yes—
110C2×C3×C4×D5—24no—
111C2×C3×C4×D5—42no—
112C2×C3×C4×D5—42no—
113C2×C3×C4×D5C2314yes—
114C2×C3×C4×D5C2314yes—
115C2×C3×C4×D5C2314yes—
116C2×C3×Dic10—42no—
117C2×C3×Dic10C2314yes—
118C3×C5×C4⋊C4C2314yes—
119C3×C5×C4⋊C4C2314yes—
120C3×C5×C22⋊C4C2314yes—
121C3×C5×C22⋊C4C2314yes—
122C3×C5×C22⋊C4C2314yes—
123C3×C22⋊Dic5C2314yes—
124C3×C22⋊Dic5C2314yes—
125C3×C22⋊Dic5C2314yes—
126C3×C22⋊Dic5C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×#685C2314yes—
129C3×#685C2314yes—
130C3×C4⋊Dic5C2314yes—
131C3×C4⋊Dic5C2314yes—
132C3×C4⋊Dic5C2314yes—
133C3×C4⋊Dic5C2314yes—
134C3×#683C2314yes—
135C3×#683C2314yes—
136C3×#683C2314yes—
137C3×#683C2314yes—
138C3×#683C2314yes—
139C3×#683C2314yes—
140C3×#683C2314yes—
141C3×#683C2314yes—
142C3×C4×Dic5C2314yes—
143C3×C4×Dic5C2314yes—
144C3×#539—516no—
145C2×C3×#126—51no—
146C2×C3×#126—51no—
147C2×C3×#125—51no—
148C2×C3×#125—51no—
149C2×C3×#123—51no—
150C2×C3×#123—51no—
151C2×C3×#123—51no—
152C2×C3×#123D511yescharacteristic, complemented
153C2×C3×C22⋊Q8—51no—
154C2×C3×C22⋊Q8—51no—
155C2×C3×C22⋊Q8—51no—
156C2×C3×#121—51no—
157C2×C3×C4×D4—51no—
158C2×C3×C4×D4—51no—
159C22×C3×C4⋊C4—51no—
160C22×C5×D4C22×C311yescharacteristic
161C23×C4×C5C22×C311yescharacteristic
162C22×C22⋊D5C22×C311yescharacteristic
163C22×C22⋊D5C22×C311yescharacteristic
164C23×Dic5C22×C311yescharacteristic
165C22×C4×D5C22×C311yescharacteristic
166C22×C4×D5C22×C311yescharacteristic
167C22×C4×D5C22×C311yescharacteristic
168C22×Dic10C22×C311yescharacteristic
169C5×#123C22×C318yescomplemented
170C2×C5×C4⋊C4C22×C311yescharacteristic
171C2×C5×C4⋊C4C22×C311yescharacteristic
172C2×C5×C22⋊C4C22×C311yescharacteristic
173C2×C5×C22⋊C4C22×C311yescharacteristic
174C2×C5×C22⋊C4C22×C311yescharacteristic
175C2×C22⋊Dic5C22×C311yescharacteristic
176C2×C22⋊Dic5C22×C311yescharacteristic
177C2×C22⋊Dic5C22×C311yescharacteristic
178C2×C22⋊Dic5C22×C311yescharacteristic
179C2×C22⋊Dic5C22×C311yescharacteristic
180#4084C22×C318yes—
181#4081C22×C318yescomplemented
182C4×C22⋊D5C22×C318yescomplemented
183C2×#685C22×C311yescharacteristic
184C2×#685C22×C311yescharacteristic
185C2×C4⋊Dic5C22×C311yescharacteristic
186C2×C4⋊Dic5C22×C311yescharacteristic
187C2×C4⋊Dic5C22×C311yescharacteristic
188C2×C4⋊Dic5C22×C311yescharacteristic
189#4070C22×C318yescomplemented
190C2×#683C22×C311yescharacteristic
191C2×#683C22×C311yescharacteristic
192C2×#683C22×C311yescharacteristic
193C2×#683C22×C311yescharacteristic
194C2×#683C22×C311yescharacteristic
195C2×#683C22×C311yescharacteristic
196C2×#683C22×C311yescharacteristic
197C2×#683C22×C311yescharacteristic
198C2×C4×Dic5C22×C311yescharacteristic
199C2×C4×Dic5C22×C311yescharacteristic
200#4042C22×C318yescomplemented
201D5×C4⋊C4C22×C318yescomplemented
202#4036C22×C318yescomplemented
203#4035C22×C318yescomplemented
204#4029C22×C318yescomplemented
205#4029C22×C318yescomplemented
206#4027C22×C318yescomplemented
207#4025C22×C318yescomplemented
208#4025C22×C318yescomplemented
209#4024C22×C318yescomplemented
210C2×#539—51noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2412yes—
219C23×C3×C5C2411yescharacteristic
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5#4114yes—
223C22×C3×D5C2412yes—
224C3×C5×D4—44no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5—22no—
228C2×C3×C4×C5—22no—
229C2×C3×C4×C5—22no—
230C2×C3×C4×C5—44no—
231C2×C3×C4×C5C2412yes—
232C2×C3×C4×C5C2412yes—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C3×C22⋊D5—28no—
237C3×C22⋊D5—28no—
238C2×C3×Dic5—22no—
239C2×C3×Dic5—22no—
240C2×C3×Dic5—22no—
241C2×C3×Dic5—22no—
242C2×C3×Dic5—22no—
243C2×C3×Dic5—22no—
244C2×C3×Dic5—22no—
245C2×C3×Dic5—44no—
246C2×C3×Dic5C2412yes—
247C2×C3×Dic5C2412yes—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C2×C3×Dic5C2412yes—
253C3×C4×D5—28no—
254C3×C4×D5—44no—
255C3×C4×D5—44no—
256C3×Dic10—44no—
257C22×C3×Q8—51no—
258C22×C3×D4—51no—
259C22×C3×D4—51no—
260C22×C3×D4C2×D511yescharacteristic
261C23×C3×C4—51no—
262C23×C3×C4—51no—
263C23×C3×C4—51no—
264C23×C3×C4—51no—
265C23×C3×C4C2×D511yescharacteristic
266C3×#126—58no—
267C3×#126—58no—
268C3×#125—58no—
269C3×#125—58no—
270C3×#123—58no—
271C3×#123—58no—
272C3×#123—58no—
273C3×#123C2×D518yescomplemented
274C3×C22⋊Q8—58no—
275C3×C22⋊Q8—58no—
276C3×C22⋊Q8—58no—
277C3×#121—58no—
278C3×C4×D4—58no—
279C3×C4×D4—58no—
280C2×C3×C4⋊C4—51no—
281C2×C3×C4⋊C4—51no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C4⋊C4—51no—
284C2×C3×C4⋊C4—51no—
285C2×C3×C4⋊C4—51no—
286C2×C3×C4⋊C4—51no—
287C2×C3×C4⋊C4—51no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C4⋊C4—51no—
292C2×C3×C4⋊C4—58no—
293C2×C3×C4⋊C4C2×D511yescharacteristic
294C2×C3×C4⋊C4C2×D511yescharacteristic
295C2×C3×C22⋊C4—51no—
296C2×C3×C22⋊C4—51no—
297C2×C3×C22⋊C4—51no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4C2×D511yescharacteristic
303C2×C3×C22⋊C4C2×D511yescharacteristic
304C2×C3×C22⋊C4C2×D511yescharacteristic
305C2×C3×C42—51no—
306C2×C3×C42—51no—
307C24×C5C23×C311yescharacteristic
308C24×C5C23×C311yescharacteristic
309C23×D5C23×C311yescharacteristic
310C2×C5×D4—42no—
311C2×C5×D4C23×C314yes—
312C22×C4×C5—42no—
313C22×C4×C5C23×C311yescharacteristic
314C22×C4×C5C23×C311yescharacteristic
315C22×C4×C5C23×C311yescharacteristic
316C22×C4×C5C23×C311yescharacteristic
317C22×C4×C5C23×C311yescharacteristic
318C22×C4×C5C23×C314yes—
319C2×C22⋊D5—24no—
320C2×C22⋊D5—24no—
321C2×C22⋊D5C23×C314yes—
322C2×C22⋊D5C23×C314yes—
323C22×Dic5—42no—
324C22×Dic5C23×C311yescharacteristic
325C22×Dic5C23×C311yescharacteristic
326C22×Dic5C23×C311yescharacteristic
327C22×Dic5C23×C311yescharacteristic
328C22×Dic5C23×C311yescharacteristic
329C22×Dic5C23×C311yescharacteristic
330C22×Dic5C23×C311yescharacteristic
331C22×Dic5C23×C314yes—
332C2×C4×D5—24no—
333C2×C4×D5—42no—
334C2×C4×D5—42no—
335C2×C4×D5C23×C314yes—
336C2×C4×D5C23×C314yes—
337C2×C4×D5C23×C314yes—
338C2×Dic10—42no—
339C2×Dic10C23×C314yes—
340C5×C4⋊C4C23×C314yes—
341C5×C4⋊C4C23×C314yes—
342C5×C22⋊C4C23×C314yes—
343C5×C22⋊C4C23×C314yes—
344C5×C22⋊C4C23×C314yes—
345C22⋊Dic5C23×C314yes—
346C22⋊Dic5C23×C314yes—
347C22⋊Dic5C23×C314yes—
348C22⋊Dic5C23×C314yes—
349C22⋊Dic5C23×C314yes—
350#685C23×C314yes—
351#685C23×C314yes—
352C4⋊Dic5C23×C314yes—
353C4⋊Dic5C23×C314yes—
354C4⋊Dic5C23×C314yes—
355C4⋊Dic5C23×C314yes—
356#683C23×C314yes—
357#683C23×C314yes—
358#683C23×C314yes—
359#683C23×C314yes—
360#683C23×C314yes—
361#683C23×C314yes—
362#683C23×C314yes—
363#683C23×C314yes—
364C4×Dic5C23×C314yes—
365C4×Dic5C23×C314yes—
366#539—516no—
367C2×#126—51no—
368C2×#126—51no—
369C2×#125—51no—
370C2×#125—51no—
371C2×#123—51no—
372C2×#123—51no—
373C2×#123—51no—
374C2×#123C3×D511yescharacteristic, complemented
375C2×C22⋊Q8—51no—
376C2×C22⋊Q8—51no—
377C2×C22⋊Q8—51no—
378C2×#121—51no—
379C2×C4×D4—51no—
380C2×C4×D4—51no—
381C22×C4⋊C4—51no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—22no—
385C22×C3×C5—22no—
386C22×C3×C5—22no—
387C22×C3×C5—22no—
388C22×C3×C5—44no—
389C22×C3×C5—44no—
390C22×C3×C5C2×#4112yes—
391C22×C3×C5H(5,𝔽2)12yes—
392C22×C3×C52−1+412yes—
393C22×C3×C5C2511yescharacteristic
394C2×C3×D5—28no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5C2×#4114yes—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401C3×C4×C5—22no—
402C3×C4×C5—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5—22no—
408C3×Dic5—22no—
409C3×Dic5—22no—
410C24×C3—51no—
411C24×C3C22×D511yescharacteristic
412C24×C3C22×D511yescharacteristic
413C2×C3×Q8—54no—
414C2×C3×Q8—202no—
415C2×C3×D4—42no—
416C2×C3×D4—54no—
417C2×C3×D4—54no—
418C2×C3×D4—104no—
419C2×C3×D4—104no—
420C2×C3×D4C22×D514yes—
421C22×C3×C4—42no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—54no—
430C22×C3×C4—54no—
431C22×C3×C4—54no—
432C22×C3×C4—54no—
433C22×C3×C4—104no—
434C22×C3×C4—202no—
435C22×C3×C4—202no—
436C22×C3×C4—202no—
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C22×C3×C4C22×D514yes—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4—54no—
446C3×C4⋊C4—54no—
447C3×C4⋊C4—54no—
448C3×C4⋊C4—54no—
449C3×C4⋊C4—54no—
450C3×C4⋊C4—54no—
451C3×C4⋊C4—54no—
452C3×C4⋊C4—54no—
453C3×C4⋊C4—54no—
454C3×C4⋊C4—54no—
455C3×C4⋊C4C22×D514yes—
456C3×C4⋊C4C22×D514yes—
457C3×C22⋊C4—54no—
458C3×C22⋊C4—54no—
459C3×C22⋊C4—54no—
460C3×C22⋊C4—54no—
461C3×C22⋊C4—54no—
462C3×C22⋊C4—54no—
463C3×C22⋊C4—54no—
464C3×C22⋊C4C22×D514yes—
465C3×C22⋊C4C22×D514yes—
466C3×C22⋊C4C22×D514yes—
467C3×C42—54no—
468C3×C42—54no—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5—22no—
473C23×C5—22no—
474C23×C5—22no—
475C23×C5C24×C312yes—
476C23×C5C24×C312yes—
477C23×C5C24×C311yescharacteristic
478C22×D5—22no—
479C22×D5—22no—
480C22×D5C3×#4114yes—
481C22×D5C24×C312yes—
482C5×D4—44no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—44no—
489C2×C4×C5C24×C312yes—
490C2×C4×C5C24×C312yes—
491C2×C4×C5C24×C312yes—
492C2×C4×C5C24×C312yes—
493C2×C4×C5C24×C312yes—
494C22⋊D5—28no—
495C22⋊D5—28no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—22no—
500C2×Dic5—22no—
501C2×Dic5—22no—
502C2×Dic5—22no—
503C2×Dic5—44no—
504C2×Dic5C24×C312yes—
505C2×Dic5C24×C312yes—
506C2×Dic5C24×C312yes—
507C2×Dic5C24×C312yes—
508C2×Dic5C24×C312yes—
509C2×Dic5C24×C312yes—
510C2×Dic5C24×C312yes—
511C4×D5—28no—
512C4×D5—44no—
513C4×D5—44no—
514Dic10—44no—
515C22×Q8—51no—
516C22×D4—51no—
517C22×D4—51no—
518C22×D4C2×C3×D511yescharacteristic
519C23×C4—51no—
520C23×C4—51no—
521C23×C4—51no—
522C23×C4—51no—
523C23×C4C2×C3×D511yescharacteristic
524#126—58no—
525#126—58no—
526#125—58no—
527#125—58no—
528#123—58no—
529#123—58no—
530#123—58no—
531#123C2×C3×D518yescomplemented
532C22⋊Q8—58no—
533C22⋊Q8—58no—
534C22⋊Q8—58no—
535#121—58no—
536C4×D4—58no—
537C4×D4—58no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—51no—
543C2×C4⋊C4—51no—
544C2×C4⋊C4—51no—
545C2×C4⋊C4—51no—
546C2×C4⋊C4—51no—
547C2×C4⋊C4—51no—
548C2×C4⋊C4—51no—
549C2×C4⋊C4—51no—
550C2×C4⋊C4—58no—
551C2×C4⋊C4C2×C3×D511yescharacteristic
552C2×C4⋊C4C2×C3×D511yescharacteristic
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4C2×C3×D511yescharacteristic
561C2×C22⋊C4C2×C3×D511yescharacteristic
562C2×C22⋊C4C2×C3×D511yescharacteristic
563C2×C42—51no—
564C2×C42—51no—
565C2×C3×C5—42no—
566C2×C3×C5—42no—
567C2×C3×C5#53914yescomplemented
568C2×C3×C5C22×#4111yescharacteristic
569C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
570C2×C3×C5C2×2−1+411yescharacteristic
571C3×D5—24no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—54no—
579C23×C3—52no—
580C23×C3—102no—
581C23×C3—102no—
582C23×C3C23×D512yes—
583C23×C3C23×D512yes—
584C23×C3C23×D511yescharacteristic
585C3×Q8—204no—
586C3×D4—44no—
587C3×D4—108no—
588C3×D4—108no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—44no—
595C2×C3×C4—52no—
596C2×C3×C4—52no—
597C2×C3×C4—52no—
598C2×C3×C4—52no—
599C2×C3×C4—52no—
600C2×C3×C4—52no—
601C2×C3×C4—52no—
602C2×C3×C4—108no—
603C2×C3×C4—102no—
604C2×C3×C4—102no—
605C2×C3×C4—102no—
606C2×C3×C4—102no—
607C2×C3×C4—102no—
608C2×C3×C4—102no—
609C2×C3×C4—102no—
610C2×C3×C4—204no—
611C2×C3×C4—204no—
612C2×C3×C4—204no—
613C2×C3×C4C23×D512yes—
614C2×C3×C4C23×D512yes—
615C2×C3×C4C23×D512yes—
616C2×C3×C4C23×D512yes—
617C2×C3×C4C23×D512yes—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—22no—
622C22×C5—22no—
623C22×C5—22no—
624C22×C5—44no—
625C22×C5—44no—
626C22×C5C2×C3×#4112yes—
627C22×C5C3×H(5,𝔽2)12yes—
628C22×C5C3×2−1+412yes—
629C22×C5C25×C311yescharacteristic
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—28no—
633C2×D5C2×C3×#4114yes—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—22no—
638C4×C5—22no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—22no—
643Dic5—22no—
644Dic5—22no—
645Dic5—22no—
646C24—51no—
647C24C22×C3×D511yescharacteristic
648C24C22×C3×D511yescharacteristic
649C2×Q8—54no—
650C2×Q8—202no—
651C2×D4—42no—
652C2×D4—54no—
653C2×D4—54no—
654C2×D4—104no—
655C2×D4—104no—
656C2×D4C22×C3×D514yes—
657C22×C4—42no—
658C22×C4—51no—
659C22×C4—51no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—54no—
666C22×C4—54no—
667C22×C4—54no—
668C22×C4—54no—
669C22×C4—104no—
670C22×C4—202no—
671C22×C4—202no—
672C22×C4—202no—
673C22×C4C22×C3×D511yescharacteristic
674C22×C4C22×C3×D511yescharacteristic
675C22×C4C22×C3×D511yescharacteristic
676C22×C4C22×C3×D511yescharacteristic
677C22×C4C22×C3×D511yescharacteristic
678C22×C4C22×C3×D514yes—
679C4⋊C4—54no—
680C4⋊C4—54no—
681C4⋊C4—54no—
682C4⋊C4—54no—
683C4⋊C4—54no—
684C4⋊C4—54no—
685C4⋊C4—54no—
686C4⋊C4—54no—
687C4⋊C4—54no—
688C4⋊C4—54no—
689C4⋊C4—54no—
690C4⋊C4—54no—
691C4⋊C4C22×C3×D514yes—
692C4⋊C4C22×C3×D514yes—
693C22⋊C4—54no—
694C22⋊C4—54no—
695C22⋊C4—54no—
696C22⋊C4—54no—
697C22⋊C4—54no—
698C22⋊C4—54no—
699C22⋊C4—54no—
700C22⋊C4C22×C3×D514yes—
701C22⋊C4C22×C3×D514yes—
702C22⋊C4C22×C3×D514yes—
703C42—54no—
704C42—54no—
705C3×C5C2×#53911yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—44no—
713C22×C3—44no—
714C22×C3—54no—
715C22×C3—108no—
716C22×C3—102no—
717C22×C3—102no—
718C22×C3#414412yes—
719C22×C3D5×#4112yes—
720C22×C3#415012yes—
721C22×C3C24×D511yescharacteristic
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—102no—
728C3×C4—102no—
729C3×C4—102no—
730C3×C4—102no—
731C3×C4—102no—
732C3×C4—102no—
733C3×C4—102no—
734C2×C5—42no—
735C2×C5—42no—
736C2×C5C3×#53914yescomplemented
737C2×C5C22×C3×#4111yescharacteristic
738C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
739C2×C5C2×C3×2−1+411yescharacteristic
740D5—24no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—54no—
748C23—52no—
749C23—102no—
750C23—102no—
751C23C23×C3×D512yes—
752C23C23×C3×D512yes—
753C23C23×C3×D511yescharacteristic
754Q8—204no—
755D4—44no—
756D4—108no—
757D4—108no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—52no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—52no—
771C2×C4—108no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—204no—
780C2×C4—204no—
781C2×C4—204no—
782C2×C4C23×C3×D512yes—
783C2×C4C23×C3×D512yes—
784C2×C4C23×C3×D512yes—
785C2×C4C23×C3×D512yes—
786C2×C4C23×C3×D512yes—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—104no—
790C2×C3#6599414yesdirect product factor
791C2×C3C2×#414411yescharacteristic
792C2×C3C2×D5×#4111yescharacteristic
793C2×C3C2×#415011yescharacteristic
794C5C2×C3×#53911yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—44no—
803C22—54no—
804C22—102no—
805C22—102no—
806C22—108no—
807C22C3×#414412yes—
808C22C3×D5×#4112yes—
809C22C3×#415012yes—
810C22C24×C3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—102no—
817C4—102no—
818C4—102no—
819C4—102no—
820C4—102no—
821C4—102no—
822C4—102no—
823C3C2×#6599411yescharacteristic, direct product factor, Sylow
824C2—42no—
825C2—42no—
826C2—104no—
827C2C3×#6599414yesdirect product factor
828C2C2×C3×#414411yescharacteristic
829C2C2×C3×D5×#4111yescharacteristic
830C2C2×C3×#415011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
prime radicalC2×C3×#4084C2
hypercenterC2×C3×#123D5
hypocenterC5C2×C3×#539
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#123C2semidirect
3. C2×C3×#4081C2semidirect
4. C2×C3×C4×C22⋊D5C2semidirect
5. C2×C3×#4070C2semidirect
6. C3×#65994C2direct (N × H)
7. C2×C3×#4042C2semidirect
8. C2×C3×D5×C4⋊C4C2semidirect
9. C2×C3×#4036C2semidirect
10. C2×C3×#4035C2semidirect
11. C2×C3×#4029C2semidirect
12. C2×C3×#4029C2semidirect
13. C2×C3×#4027C2semidirect
14. C2×C3×#4025C2semidirect
15. C2×C3×#4025C2semidirect
16. C2×C3×#4024C2semidirect
17. C2×#65994C3direct (N × H)
27. C3×C5×#123C22semidirect
39. C3×#4081C22semidirect
40. C3×C4×C22⋊D5C22semidirect
47. C3×#4070C22semidirect
58. C3×#4042C22semidirect
59. C3×D5×C4⋊C4C22semidirect
60. C3×#4036C22semidirect
61. C3×#4035C22semidirect
62. C3×#4029C22semidirect
63. C3×#4029C22semidirect
64. C3×#4027C22semidirect
65. C3×#4025C22semidirect
66. C3×#4025C22semidirect
67. C3×#4024C22semidirect
69. C2×C5×#123C2×C3semidirect
71. C2×#4081C2×C3semidirect
72. C2×C4×C22⋊D5C2×C3semidirect
73. C2×#4070C2×C3semidirect
74. #65994C2×C3direct (N × H)
75. C2×#4042C2×C3semidirect
76. C2×D5×C4⋊C4C2×C3semidirect
77. C2×#4036C2×C3semidirect
78. C2×#4035C2×C3semidirect
79. C2×#4029C2×C3semidirect
80. C2×#4029C2×C3semidirect
81. C2×#4027C2×C3semidirect
82. C2×#4025C2×C3semidirect
83. C2×#4025C2×C3semidirect
84. C2×#4024C2×C3semidirect
152. C2×C3×#123D5semidirect
169. C5×#123C22×C3semidirect
181. #4081C22×C3semidirect
182. C4×C22⋊D5C22×C3semidirect
189. #4070C22×C3semidirect
200. #4042C22×C3semidirect
201. D5×C4⋊C4C22×C3semidirect
202. #4036C22×C3semidirect
203. #4035C22×C3semidirect
204. #4029C22×C3semidirect
205. #4029C22×C3semidirect
206. #4027C22×C3semidirect
207. #4025C22×C3semidirect
208. #4025C22×C3semidirect
209. #4024C22×C3semidirect
273. C3×#123C2×D5semidirect
374. C2×#123C3×D5semidirect
531. #123C2×C3×D5semidirect
567. C2×C3×C5#539semidirect
705. C3×C5C2×#539semidirect
736. C2×C5C3×#539semidirect
790. C2×C3#65994direct (N × H)
794. C5C2×C3×#539semidirect
823. C3C2×#65994direct (N × H)
827. C2C3×#65994direct (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×#1232
C2×C3×#40842
C2×C3×#40812
C2×C3×C4×C22⋊D52
C2×C3×#40702
C3×#659942
C2×C3×#40422
C2×C3×D5×C4⋊C42
C2×C3×#40362
C2×C3×#40352
C2×C3×#40292
C2×C3×#40272
C2×C3×#40252
C2×C3×#40242
C2×#659943
C2×C3×#5395