Finite Group Databasebeta

← C2×C3×#66046 #14495372

Subgroups — C2×C3×#66046 #14495372

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#126C211yesmaximal, characteristic, complemented
2C3×#66046C2116yesmaximal, direct product factor
3C2×C3×#4044C211yesmaximal, characteristic, complemented
4C2×C3×#4043C211yesmaximal, characteristic, complemented
5C2×C3×#4042C211yesmaximal, characteristic, complemented
6C2×C3×#4036C211yesmaximal, characteristic, complemented
7C2×C3×#4035C211yesmaximal, characteristic, complemented
8C2×C3×#4034C211yesmaximal, characteristic, complemented
9C2×C3×#4032C211yesmaximal, characteristic
10C2×C3×#4031C211yesmaximal, characteristic
11C2×C3×#4029C211yesmaximal, characteristic
12C2×C3×#4025C211yesmaximal, characteristic, complemented
13C2×C3×#4024C211yesmaximal, characteristic, complemented
14C2×C3×#4024C211yesmaximal, characteristic, complemented
15C2×C3×#4022C211yesmaximal, characteristic, complemented
16C2×C3×#4015C211yesmaximal, characteristic, complemented
17C2×#66046C311yesmaximal, characteristic, direct product factor, Hall
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×Dic10C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic
23C22×C3×Dic10C2211yescharacteristic
24C3×C5×#126C2218yescomplemented
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C42×C5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×C4⋊Dic5C2211yescharacteristic
40C2×C3×C4⋊Dic5C2211yescharacteristic
41C2×C3×C4⋊Dic5C2211yescharacteristic
42C2×C3×C4⋊Dic5C2211yescharacteristic
43C2×C3×C4⋊Dic5C2211yescharacteristic
44C2×C3×C4⋊Dic5C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C2×C3×#683C2211yescharacteristic
48C2×C3×#683C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic
50C2×C3×#683C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic
52C2×C3×C4×Dic5C2211yescharacteristic
53C2×C3×C4×Dic5C2211yescharacteristic
54C3×#4044C2218yescomplemented
55C3×#4043C2218yescomplemented
56C3×#4042C2218yescomplemented
57C3×#4036C2218yescomplemented
58C3×#4035C2218yescomplemented
59C3×#4034C2218yescomplemented
60C3×#4032C2218yes—
61C3×#4031C2218yes—
62C3×#4029C2218yes—
63C3×#4025C2218yescomplemented
64C3×#4024C2218yescomplemented
65C3×#4024C2218yescomplemented
66C3×#4022C2218yescomplemented
67C3×#4015C2218yescomplemented
68C2×C3×#563—51nomaximal, Hall
69C2×C5×#126C2×C311yescharacteristic, complemented
70#66046C2×C3116yesdirect product factor
71C2×#4044C2×C311yescharacteristic, complemented
72C2×#4043C2×C311yescharacteristic, complemented
73C2×#4042C2×C311yescharacteristic, complemented
74C2×#4036C2×C311yescharacteristic, complemented
75C2×#4035C2×C311yescharacteristic, complemented
76C2×#4034C2×C311yescharacteristic, complemented
77C2×#4032C2×C311yescharacteristic
78C2×#4031C2×C311yescharacteristic
79C2×#4029C2×C311yescharacteristic
80C2×#4025C2×C311yescharacteristic, complemented
81C2×#4024C2×C311yescharacteristic, complemented
82C2×#4024C2×C311yescharacteristic, complemented
83C2×#4022C2×C311yescharacteristic, complemented
84C2×#4015C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×C3×C22⋊D5—42no—
94C2×C3×C22⋊D5C2314yes—
95C22×C3×Dic5—42no—
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2314yes—
104C2×C3×C4×D5—42no—
105C2×C3×C4×D5C2314yes—
106C2×C3×Dic10—42no—
107C2×C3×Dic10—42no—
108C2×C3×Dic10—42no—
109C2×C3×Dic10C2314yes—
110C2×C3×Dic10C2314yes—
111C2×C3×Dic10C2314yes—
112C3×C5×C4⋊C4C2314yes—
113C3×C5×C4⋊C4C2314yes—
114C3×C5×C4⋊C4C2314yes—
115C3×C5×C22⋊C4C2314yes—
116C3×C5×C22⋊C4C2314yes—
117C3×C5×C22⋊C4C2314yes—
118C3×C42×C5C2314yes—
119C3×C22⋊Dic5C2314yes—
120C3×C22⋊Dic5C2314yes—
121C3×#685C2314yes—
122C3×#685C2314yes—
123C3×#685C2314yes—
124C3×#685C2314yes—
125C3×#685C2314yes—
126C3×C4⋊Dic5C2314yes—
127C3×C4⋊Dic5C2314yes—
128C3×C4⋊Dic5C2314yes—
129C3×C4⋊Dic5C2314yes—
130C3×C4⋊Dic5C2314yes—
131C3×C4⋊Dic5C2314yes—
132C3×#683C2314yes—
133C3×#683C2314yes—
134C3×#683C2314yes—
135C3×#683C2314yes—
136C3×#683C2314yes—
137C3×#683C2314yes—
138C3×#683C2314yes—
139C3×C4×Dic5C2314yes—
140C3×C4×Dic5C2314yes—
141C3×#563—516no—
142C2×C3×C4⋊Q8—51no—
143C2×C3×C4⋊Q8—51no—
144C2×C3×#126—51no—
145C2×C3×#126—51no—
146C2×C3×#126—51no—
147C2×C3×#126D511yescharacteristic, complemented
148C2×C3×#125—51no—
149C2×C3×#125—51no—
150C2×C3×#124—51no—
151C2×C3×#123—51no—
152C2×C3×#123—51no—
153C2×C3×C22⋊Q8—51no—
154C2×C3×C22⋊Q8—51no—
155C2×C3×C22⋊Q8—51no—
156C2×C3×C22⋊Q8—51no—
157C22×C22⋊D5C22×C311yescharacteristic
158C23×Dic5C22×C311yescharacteristic
159C22×C4×D5C22×C311yescharacteristic
160C22×Dic10C22×C311yescharacteristic
161C22×Dic10C22×C311yescharacteristic
162C22×Dic10C22×C311yescharacteristic
163C5×#126C22×C318yescomplemented
164C2×C5×C4⋊C4C22×C311yescharacteristic
165C2×C5×C4⋊C4C22×C311yescharacteristic
166C2×C5×C4⋊C4C22×C311yescharacteristic
167C2×C5×C22⋊C4C22×C311yescharacteristic
168C2×C5×C22⋊C4C22×C311yescharacteristic
169C2×C5×C22⋊C4C22×C311yescharacteristic
170C2×C42×C5C22×C311yescharacteristic
171C2×C22⋊Dic5C22×C311yescharacteristic
172C2×C22⋊Dic5C22×C311yescharacteristic
173C2×#685C22×C311yescharacteristic
174C2×#685C22×C311yescharacteristic
175C2×#685C22×C311yescharacteristic
176C2×#685C22×C311yescharacteristic
177C2×#685C22×C311yescharacteristic
178C2×C4⋊Dic5C22×C311yescharacteristic
179C2×C4⋊Dic5C22×C311yescharacteristic
180C2×C4⋊Dic5C22×C311yescharacteristic
181C2×C4⋊Dic5C22×C311yescharacteristic
182C2×C4⋊Dic5C22×C311yescharacteristic
183C2×C4⋊Dic5C22×C311yescharacteristic
184C2×#683C22×C311yescharacteristic
185C2×#683C22×C311yescharacteristic
186C2×#683C22×C311yescharacteristic
187C2×#683C22×C311yescharacteristic
188C2×#683C22×C311yescharacteristic
189C2×#683C22×C311yescharacteristic
190C2×#683C22×C311yescharacteristic
191C2×C4×Dic5C22×C311yescharacteristic
192C2×C4×Dic5C22×C311yescharacteristic
193#4044C22×C318yescomplemented
194#4043C22×C318yescomplemented
195#4042C22×C318yescomplemented
196#4036C22×C318yescomplemented
197#4035C22×C318yescomplemented
198#4034C22×C318yescomplemented
199#4032C22×C318yes—
200#4031C22×C318yes—
201#4029C22×C318yes—
202#4025C22×C318yescomplemented
203#4024C22×C318yescomplemented
204#4024C22×C318yescomplemented
205#4022C22×C318yescomplemented
206#4015C22×C318yescomplemented
207C2×#563—51noSylow
208C23×C3×C5—22no—
209C23×C3×C5—22no—
210C23×C3×C5—22no—
211C23×C3×C5C2412yes—
212C23×C3×C5C2411yescharacteristic
213C22×C3×D5—22no—
214C22×C3×D5—22no—
215C22×C3×D5—22no—
216C22×C3×D5C2412yes—
217C2×C3×C4×C5—22no—
218C2×C3×C4×C5—22no—
219C2×C3×C4×C5—22no—
220C2×C3×C4×C5—22no—
221C2×C3×C4×C5—22no—
222C2×C3×C4×C5—22no—
223C2×C3×C4×C5C2412yes—
224C2×C3×C4×C5C2412yes—
225C2×C3×C4×C5C2412yes—
226C2×C3×C4×C5C2412yes—
227C2×C3×C4×C5C2412yes—
228C2×C3×C4×C5C2412yes—
229C3×C22⋊D5—44no—
230C2×C3×Dic5—22no—
231C2×C3×Dic5—22no—
232C2×C3×Dic5—22no—
233C2×C3×Dic5—22no—
234C2×C3×Dic5—22no—
235C2×C3×Dic5—22no—
236C2×C3×Dic5—22no—
237C2×C3×Dic5—44no—
238C2×C3×Dic5C2412yes—
239C2×C3×Dic5C2412yes—
240C2×C3×Dic5C2412yes—
241C2×C3×Dic5C2412yes—
242C2×C3×Dic5C2412yes—
243C2×C3×Dic5C2412yes—
244C2×C3×Dic5C2412yes—
245C3×C4×D5—44no—
246C3×Dic10—44no—
247C3×Dic10—44no—
248C3×Dic10—44no—
249C22×C3×Q8—51no—
250C22×C3×Q8—51no—
251C22×C3×Q8—51no—
252C22×C3×D4—51no—
253C23×C3×C4—51no—
254C23×C3×C4—51no—
255C3×C4⋊Q8—58no—
256C3×C4⋊Q8—58no—
257C3×#126—58no—
258C3×#126—58no—
259C3×#126—58no—
260C3×#126C2×D518yescomplemented
261C3×#125—58no—
262C3×#125—58no—
263C3×#124—58no—
264C3×#123—58no—
265C3×#123—58no—
266C3×C22⋊Q8—58no—
267C3×C22⋊Q8—58no—
268C3×C22⋊Q8—58no—
269C3×C22⋊Q8—58no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C4⋊C4—51no—
274C2×C3×C4⋊C4—51no—
275C2×C3×C4⋊C4—51no—
276C2×C3×C4⋊C4—51no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C4⋊C4—51no—
281C2×C3×C4⋊C4—51no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C4⋊C4C2×D511yescharacteristic
284C2×C3×C4⋊C4C2×D511yescharacteristic
285C2×C3×C4⋊C4C2×D511yescharacteristic
286C2×C3×C22⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4C2×D511yescharacteristic
294C2×C3×C22⋊C4C2×D511yescharacteristic
295C2×C3×C22⋊C4C2×D511yescharacteristic
296C2×C3×C42—51no—
297C2×C3×C42—51no—
298C2×C3×C42C2×D511yescharacteristic
299C24×C5C23×C311yescharacteristic
300C23×D5C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C22×C4×C5C23×C311yescharacteristic
304C22×C4×C5C23×C311yescharacteristic
305C22×C4×C5C23×C311yescharacteristic
306C22×C4×C5C23×C311yescharacteristic
307C2×C22⋊D5—42no—
308C2×C22⋊D5C23×C314yes—
309C22×Dic5—42no—
310C22×Dic5C23×C311yescharacteristic
311C22×Dic5C23×C311yescharacteristic
312C22×Dic5C23×C311yescharacteristic
313C22×Dic5C23×C311yescharacteristic
314C22×Dic5C23×C311yescharacteristic
315C22×Dic5C23×C311yescharacteristic
316C22×Dic5C23×C311yescharacteristic
317C22×Dic5C23×C314yes—
318C2×C4×D5—42no—
319C2×C4×D5C23×C314yes—
320C2×Dic10—42no—
321C2×Dic10—42no—
322C2×Dic10—42no—
323C2×Dic10C23×C314yes—
324C2×Dic10C23×C314yes—
325C2×Dic10C23×C314yes—
326C5×C4⋊C4C23×C314yes—
327C5×C4⋊C4C23×C314yes—
328C5×C4⋊C4C23×C314yes—
329C5×C22⋊C4C23×C314yes—
330C5×C22⋊C4C23×C314yes—
331C5×C22⋊C4C23×C314yes—
332C42×C5C23×C314yes—
333C22⋊Dic5C23×C314yes—
334C22⋊Dic5C23×C314yes—
335#685C23×C314yes—
336#685C23×C314yes—
337#685C23×C314yes—
338#685C23×C314yes—
339#685C23×C314yes—
340C4⋊Dic5C23×C314yes—
341C4⋊Dic5C23×C314yes—
342C4⋊Dic5C23×C314yes—
343C4⋊Dic5C23×C314yes—
344C4⋊Dic5C23×C314yes—
345C4⋊Dic5C23×C314yes—
346#683C23×C314yes—
347#683C23×C314yes—
348#683C23×C314yes—
349#683C23×C314yes—
350#683C23×C314yes—
351#683C23×C314yes—
352#683C23×C314yes—
353C4×Dic5C23×C314yes—
354C4×Dic5C23×C314yes—
355#563—516no—
356C2×C4⋊Q8—51no—
357C2×C4⋊Q8—51no—
358C2×#126—51no—
359C2×#126—51no—
360C2×#126—51no—
361C2×#126C3×D511yescharacteristic, complemented
362C2×#125—51no—
363C2×#125—51no—
364C2×#124—51no—
365C2×#123—51no—
366C2×#123—51no—
367C2×C22⋊Q8—51no—
368C2×C22⋊Q8—51no—
369C2×C22⋊Q8—51no—
370C2×C22⋊Q8—51no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—44no—
375C22×C3×C5H(5,𝔽2)12yes—
376C22×C3×C52−1+412yes—
377C22×C3×C52−1+412yes—
378C22×C3×C5C2511yescharacteristic
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—44no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385C3×C4×C5—22no—
386C3×C4×C5—22no—
387C3×C4×C5—22no—
388C3×C4×C5—22no—
389C3×Dic5—22no—
390C3×Dic5—22no—
391C3×Dic5—22no—
392C3×Dic5—22no—
393C3×Dic5—22no—
394C3×Dic5—22no—
395C3×Dic5—22no—
396C24×C3—51no—
397C24×C3C22×D511yescharacteristic
398C2×C3×Q8—54no—
399C2×C3×Q8—54no—
400C2×C3×Q8—54no—
401C2×C3×Q8—202no—
402C2×C3×Q8—202no—
403C2×C3×Q8—202no—
404C2×C3×D4—54no—
405C2×C3×D4—202no—
406C22×C3×C4—51no—
407C22×C3×C4—51no—
408C22×C3×C4—51no—
409C22×C3×C4—51no—
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—54no—
414C22×C3×C4—54no—
415C22×C3×C4—202no—
416C22×C3×C4—202no—
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
422C22×C3×C4C22×D511yescharacteristic
423C3×C4⋊C4—54no—
424C3×C4⋊C4—54no—
425C3×C4⋊C4—54no—
426C3×C4⋊C4—54no—
427C3×C4⋊C4—54no—
428C3×C4⋊C4—54no—
429C3×C4⋊C4—54no—
430C3×C4⋊C4—54no—
431C3×C4⋊C4—54no—
432C3×C4⋊C4—54no—
433C3×C4⋊C4—54no—
434C3×C4⋊C4—54no—
435C3×C4⋊C4—54no—
436C3×C4⋊C4C22×D514yes—
437C3×C4⋊C4C22×D514yes—
438C3×C4⋊C4C22×D514yes—
439C3×C22⋊C4—54no—
440C3×C22⋊C4—54no—
441C3×C22⋊C4—54no—
442C3×C22⋊C4—54no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—54no—
445C3×C22⋊C4—54no—
446C3×C22⋊C4C22×D514yes—
447C3×C22⋊C4C22×D514yes—
448C3×C22⋊C4C22×D514yes—
449C3×C42—54no—
450C3×C42—54no—
451C3×C42C22×D514yes—
452C23×C5—22no—
453C23×C5—22no—
454C23×C5—22no—
455C23×C5C24×C312yes—
456C23×C5C24×C311yescharacteristic
457C22×D5—22no—
458C22×D5—22no—
459C22×D5—22no—
460C22×D5C24×C312yes—
461C2×C4×C5—22no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
467C2×C4×C5C24×C312yes—
468C2×C4×C5C24×C312yes—
469C2×C4×C5C24×C312yes—
470C2×C4×C5C24×C312yes—
471C2×C4×C5C24×C312yes—
472C2×C4×C5C24×C312yes—
473C22⋊D5—44no—
474C2×Dic5—22no—
475C2×Dic5—22no—
476C2×Dic5—22no—
477C2×Dic5—22no—
478C2×Dic5—22no—
479C2×Dic5—22no—
480C2×Dic5—22no—
481C2×Dic5—44no—
482C2×Dic5C24×C312yes—
483C2×Dic5C24×C312yes—
484C2×Dic5C24×C312yes—
485C2×Dic5C24×C312yes—
486C2×Dic5C24×C312yes—
487C2×Dic5C24×C312yes—
488C2×Dic5C24×C312yes—
489C4×D5—44no—
490Dic10—44no—
491Dic10—44no—
492Dic10—44no—
493C22×Q8—51no—
494C22×Q8—51no—
495C22×Q8—51no—
496C22×D4—51no—
497C23×C4—51no—
498C23×C4—51no—
499C4⋊Q8—58no—
500C4⋊Q8—58no—
501#126—58no—
502#126—58no—
503#126—58no—
504#126C2×C3×D518yescomplemented
505#125—58no—
506#125—58no—
507#124—58no—
508#123—58no—
509#123—58no—
510C22⋊Q8—58no—
511C22⋊Q8—58no—
512C22⋊Q8—58no—
513C22⋊Q8—58no—
514C2×C4⋊C4—51no—
515C2×C4⋊C4—51no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—51no—
522C2×C4⋊C4—51no—
523C2×C4⋊C4—51no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—51no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4C2×C3×D511yescharacteristic
528C2×C4⋊C4C2×C3×D511yescharacteristic
529C2×C4⋊C4C2×C3×D511yescharacteristic
530C2×C22⋊C4—51no—
531C2×C22⋊C4—51no—
532C2×C22⋊C4—51no—
533C2×C22⋊C4—51no—
534C2×C22⋊C4—51no—
535C2×C22⋊C4—51no—
536C2×C22⋊C4—51no—
537C2×C22⋊C4C2×C3×D511yescharacteristic
538C2×C22⋊C4C2×C3×D511yescharacteristic
539C2×C22⋊C4C2×C3×D511yescharacteristic
540C2×C42—51no—
541C2×C42—51no—
542C2×C42C2×C3×D511yescharacteristic
543C2×C3×C5—42no—
544C2×C3×C5#56314yescomplemented
545C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
546C2×C3×C5C2×2−1+411yescharacteristic
547C2×C3×C5C2×2−1+411yescharacteristic
548C3×D5—42no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—52no—
553C23×C3—102no—
554C23×C3—102no—
555C23×C3—102no—
556C23×C3C23×D512yes—
557C23×C3C23×D511yescharacteristic
558C3×Q8—204no—
559C3×Q8—204no—
560C3×Q8—204no—
561C3×D4—204no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—52no—
569C2×C3×C4—52no—
570C2×C3×C4—52no—
571C2×C3×C4—52no—
572C2×C3×C4—52no—
573C2×C3×C4—52no—
574C2×C3×C4—52no—
575C2×C3×C4—102no—
576C2×C3×C4—102no—
577C2×C3×C4—102no—
578C2×C3×C4—102no—
579C2×C3×C4—102no—
580C2×C3×C4—102no—
581C2×C3×C4—102no—
582C2×C3×C4—204no—
583C2×C3×C4—204no—
584C2×C3×C4C23×D512yes—
585C2×C3×C4C23×D512yes—
586C2×C3×C4C23×D512yes—
587C2×C3×C4C23×D512yes—
588C2×C3×C4C23×D512yes—
589C2×C3×C4C23×D512yes—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—22no—
593C22×C5—44no—
594C22×C5C3×H(5,𝔽2)12yes—
595C22×C5C3×2−1+412yes—
596C22×C5C3×2−1+412yes—
597C22×C5C25×C311yescharacteristic
598C2×D5—22no—
599C2×D5—22no—
600C2×D5—22no—
601C2×D5—44no—
602C4×C5—22no—
603C4×C5—22no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—22no—
607C4×C5—22no—
608Dic5—22no—
609Dic5—22no—
610Dic5—22no—
611Dic5—22no—
612Dic5—22no—
613Dic5—22no—
614Dic5—22no—
615C24—51no—
616C24C22×C3×D511yescharacteristic
617C2×Q8—54no—
618C2×Q8—54no—
619C2×Q8—54no—
620C2×Q8—202no—
621C2×Q8—202no—
622C2×Q8—202no—
623C2×D4—54no—
624C2×D4—202no—
625C22×C4—51no—
626C22×C4—51no—
627C22×C4—51no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—54no—
633C22×C4—54no—
634C22×C4—202no—
635C22×C4—202no—
636C22×C4C22×C3×D511yescharacteristic
637C22×C4C22×C3×D511yescharacteristic
638C22×C4C22×C3×D511yescharacteristic
639C22×C4C22×C3×D511yescharacteristic
640C22×C4C22×C3×D511yescharacteristic
641C22×C4C22×C3×D511yescharacteristic
642C4⋊C4—54no—
643C4⋊C4—54no—
644C4⋊C4—54no—
645C4⋊C4—54no—
646C4⋊C4—54no—
647C4⋊C4—54no—
648C4⋊C4—54no—
649C4⋊C4—54no—
650C4⋊C4—54no—
651C4⋊C4—54no—
652C4⋊C4—54no—
653C4⋊C4—54no—
654C4⋊C4—54no—
655C4⋊C4C22×C3×D514yes—
656C4⋊C4C22×C3×D514yes—
657C4⋊C4C22×C3×D514yes—
658C22⋊C4—54no—
659C22⋊C4—54no—
660C22⋊C4—54no—
661C22⋊C4—54no—
662C22⋊C4—54no—
663C22⋊C4—54no—
664C22⋊C4—54no—
665C22⋊C4C22×C3×D514yes—
666C22⋊C4C22×C3×D514yes—
667C22⋊C4C22×C3×D514yes—
668C42—54no—
669C42—54no—
670C42C22×C3×D514yes—
671C3×C5C2×#56311yescharacteristic, complemented, Hall
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—44no—
676C22×C3—102no—
677C22×C3—102no—
678C22×C3—102no—
679C22×C3—204no—
680C22×C3#414912yes—
681C22×C3#415012yes—
682C22×C3#415012yes—
683C22×C3C24×D511yescharacteristic
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—22no—
690C3×C4—102no—
691C3×C4—102no—
692C3×C4—102no—
693C3×C4—102no—
694C3×C4—102no—
695C3×C4—102no—
696C3×C4—102no—
697C2×C5—42no—
698C2×C5C3×#56314yescomplemented
699C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
700C2×C5C2×C3×2−1+411yescharacteristic
701C2×C5C2×C3×2−1+411yescharacteristic
702D5—42no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—52no—
707C23—102no—
708C23—102no—
709C23—102no—
710C23C23×C3×D512yes—
711C23C23×C3×D511yescharacteristic
712Q8—204no—
713Q8—204no—
714Q8—204no—
715D4—204no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—52no—
726C2×C4—52no—
727C2×C4—52no—
728C2×C4—52no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—204no—
737C2×C4—204no—
738C2×C4C23×C3×D512yes—
739C2×C4C23×C3×D512yes—
740C2×C4C23×C3×D512yes—
741C2×C4C23×C3×D512yes—
742C2×C4C23×C3×D512yes—
743C2×C4C23×C3×D512yes—
744C2×C3—42no—
745C2×C3—202no—
746C2×C3#6604614yesdirect product factor
747C2×C3C2×#414911yescharacteristic
748C2×C3C2×#415011yescharacteristic
749C2×C3C2×#415011yescharacteristic
750C5C2×C3×#56311yescharacteristic, complemented, Sylow
751C22—22no—
752C22—22no—
753C22—22no—
754C22—44no—
755C22—102no—
756C22—102no—
757C22—102no—
758C22—204no—
759C22C3×#414912yes—
760C22C3×#415012yes—
761C22C3×#415012yes—
762C22C24×C3×D511yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—102no—
770C4—102no—
771C4—102no—
772C4—102no—
773C4—102no—
774C4—102no—
775C4—102no—
776C3C2×#6604611yescharacteristic, direct product factor, Sylow
777C2—42no—
778C2—202no—
779C2C3×#6604614yesdirect product factor
780C2C2×C3×#414911yescharacteristic
781C2C2×C3×#415011yescharacteristic
782C2C2×C3×#415011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#126C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC2×C3×#126D5
hypocenterC5C2×C3×#563
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#126

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#126C2semidirect
2. C3×#66046C2direct (N × H)
3. C2×C3×#4044C2semidirect
4. C2×C3×#4043C2semidirect
5. C2×C3×#4042C2semidirect
6. C2×C3×#4036C2semidirect
7. C2×C3×#4035C2semidirect
8. C2×C3×#4034C2semidirect
12. C2×C3×#4025C2semidirect
13. C2×C3×#4024C2semidirect
14. C2×C3×#4024C2semidirect
15. C2×C3×#4022C2semidirect
16. C2×C3×#4015C2semidirect
17. C2×#66046C3direct (N × H)
24. C3×C5×#126C22semidirect
54. C3×#4044C22semidirect
55. C3×#4043C22semidirect
56. C3×#4042C22semidirect
57. C3×#4036C22semidirect
58. C3×#4035C22semidirect
59. C3×#4034C22semidirect
63. C3×#4025C22semidirect
64. C3×#4024C22semidirect
65. C3×#4024C22semidirect
66. C3×#4022C22semidirect
67. C3×#4015C22semidirect
69. C2×C5×#126C2×C3semidirect
70. #66046C2×C3direct (N × H)
71. C2×#4044C2×C3semidirect
72. C2×#4043C2×C3semidirect
73. C2×#4042C2×C3semidirect
74. C2×#4036C2×C3semidirect
75. C2×#4035C2×C3semidirect
76. C2×#4034C2×C3semidirect
80. C2×#4025C2×C3semidirect
81. C2×#4024C2×C3semidirect
82. C2×#4024C2×C3semidirect
83. C2×#4022C2×C3semidirect
84. C2×#4015C2×C3semidirect
147. C2×C3×#126D5semidirect
163. C5×#126C22×C3semidirect
193. #4044C22×C3semidirect
194. #4043C22×C3semidirect
195. #4042C22×C3semidirect
196. #4036C22×C3semidirect
197. #4035C22×C3semidirect
198. #4034C22×C3semidirect
202. #4025C22×C3semidirect
203. #4024C22×C3semidirect
204. #4024C22×C3semidirect
205. #4022C22×C3semidirect
206. #4015C22×C3semidirect
260. C3×#126C2×D5semidirect
361. C2×#126C3×D5semidirect
504. #126C2×C3×D5semidirect
544. C2×C3×C5#563semidirect
671. C3×C5C2×#563semidirect
698. C2×C5C3×#563semidirect
746. C2×C3#66046direct (N × H)
750. C5C2×C3×#563semidirect
776. C3C2×#66046direct (N × H)
779. C2C3×#66046direct (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×#1262
C3×#660462
C2×C3×#40442
C2×C3×#40432
C2×C3×#40422
C2×C3×#40362
C2×C3×#40352
C2×C3×#40342
C2×C3×#40322
C2×C3×#40312
C2×C3×#40292
C2×C3×#40252
C2×C3×#40242
C2×C3×#40222
C2×C3×#40152
C2×#660463
C2×C3×#5635