Finite Group Databasebeta

← C2×C3×#65861 #14483236

Subgroups — C2×C3×#65861 #14483236

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×C3×#4075C211yesmaximal, characteristic, complemented
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C3×#65861C2116yesmaximal, direct product factor
5C2×C3×#4044C211yesmaximal, characteristic, complemented
6C2×C3×#4042C211yesmaximal, characteristic, complemented
7C2×C3×#4040C211yesmaximal, characteristic, complemented
8C2×C3×#4040C211yesmaximal, characteristic, complemented
9C2×C3×#4028C211yesmaximal, characteristic
10C2×C3×#4027C211yesmaximal, characteristic, complemented
11C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
12C2×C3×#4024C211yesmaximal, characteristic, complemented
13C2×C3×#4022C211yesmaximal, characteristic, complemented
14C2×C3×#4021C211yesmaximal, characteristic, complemented
15C2×C3×C4×D20C211yesmaximal, characteristic, complemented
16C2×C3×#4018C211yesmaximal, characteristic, complemented
17C2×#65861C311yesmaximal, characteristic, direct product factor, Hall
18C24×C3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×D20C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×C3×Dic10C2211yescharacteristic, complemented
28C3×C5×#117C2218yescomplemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
30C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C42×C5C2211yescharacteristic, complemented
34C2×C3×C42×C5C2211yescharacteristic, complemented
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C3×#4075C2218yescomplemented
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2218yescomplemented
46C2×C3×#685C2211yescharacteristic, complemented
47C2×C3×#685C2211yescharacteristic, complemented
48C2×C3×#685C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#683C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C2×C3×#683C2211yescharacteristic, complemented
55C2×C3×C4×Dic5C2211yescharacteristic, complemented
56C3×#4044C2218yescomplemented
57C3×#4042C2218yescomplemented
58C3×#4040C2218yescomplemented
59C3×#4040C2218yescomplemented
60C3×#4028C2218yes—
61C3×#4027C2218yescomplemented
62C3×D5×C22⋊C4C2218yescomplemented
63C3×#4024C2218yescomplemented
64C3×#4022C2218yescomplemented
65C3×#4021C2218yescomplemented
66C3×C4×D20C2218yescomplemented
67C3×#4018C2218yescomplemented
68C2×C3×#551—51nomaximal, Hall
69C2×C5×#117C2×C311yescharacteristic, complemented
70C2×#4075C2×C311yescharacteristic, complemented
71C22×#685C2×C311yescharacteristic, complemented
72#65861C2×C3116yesdirect product factor
73C2×#4044C2×C311yescharacteristic, complemented
74C2×#4042C2×C311yescharacteristic, complemented
75C2×#4040C2×C311yescharacteristic, complemented
76C2×#4040C2×C311yescharacteristic, complemented
77C2×#4028C2×C311yescharacteristic
78C2×#4027C2×C311yescharacteristic, complemented
79C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
80C2×#4024C2×C311yescharacteristic, complemented
81C2×#4022C2×C311yescharacteristic, complemented
82C2×#4021C2×C311yescharacteristic, complemented
83C2×C4×D20C2×C311yescharacteristic, complemented
84C2×#4018C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5—24no—
87C23×C3×D5—24no—
88C23×C3×D5—42no—
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2314yes—
92C23×C3×D5C2311yescharacteristic
93C22×C3×C4×C5—24no—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2314yes—
101C2×C3×C22⋊D5—24no—
102C2×C3×C22⋊D5C2314yes—
103C22×C3×Dic5—42no—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2314yes—
110C2×C3×D20—24no—
111C2×C3×D20—42no—
112C2×C3×D20C2314yes—
113C2×C3×D20C2314yes—
114C2×C3×C4×D5—24no—
115C2×C3×C4×D5—42no—
116C2×C3×C4×D5—42no—
117C2×C3×C4×D5C2314yes—
118C2×C3×C4×D5C2314yes—
119C2×C3×C4×D5C2314yescomplemented
120C2×C3×Dic10—42no—
121C2×C3×Dic10C2314yescomplemented
122C3×C5×C4⋊C4C2314yescomplemented
123C3×C5×C4⋊C4C2314yescomplemented
124C3×C5×C22⋊C4C2314yes—
125C3×C5×C22⋊C4C2314yes—
126C3×C42×C5C2314yescomplemented
127C3×C42×C5C2314yescomplemented
128C3×C22⋊Dic5C2314yes—
129C3×#685C2314yes—
130C3×#685C2314yes—
131C3×#685C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#685C2314yescomplemented
138C3×#685C2314yescomplemented
139C3×#685C2314yescomplemented
140C3×C4⋊Dic5C2314yescomplemented
141C3×#683C2314yescomplemented
142C3×#683C2314yescomplemented
143C3×#683C2314yescomplemented
144C3×#683C2314yescomplemented
145C3×#683C2314yescomplemented
146C3×C4×Dic5C2314yescomplemented
147C3×#551—516no—
148C2×C3×#126—51no—
149C2×C3×#126—51no—
150C2×C3×#124—51no—
151C2×C3×#123—51no—
152C2×C3×#123—51no—
153C2×C3×#123—51no—
154C2×C3×C22⋊Q8—51no—
155C2×C3×C22⋊Q8—51no—
156C2×C3×#120—51no—
157C2×C3×C4×D4—51no—
158C2×C3×C4×D4—51no—
159C2×C3×#117—51no—
160C2×C3×#117D511yescharacteristic, complemented
161C22×C3×C22⋊C4—51no—
162C22×C3×C22⋊C4—51no—
163C24×D5C22×C311yescharacteristic
164C23×C4×C5C22×C311yescharacteristic
165C22×C22⋊D5C22×C311yescharacteristic
166C23×Dic5C22×C311yescharacteristic
167C22×D20C22×C311yescharacteristic
168C22×D20C22×C311yescharacteristic
169C22×C4×D5C22×C311yescharacteristic
170C22×C4×D5C22×C311yescharacteristic
171C22×C4×D5C22×C311yescharacteristic, complemented
172C22×Dic10C22×C311yescharacteristic, complemented
173C5×#117C22×C318yescomplemented
174C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
175C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
176C2×C5×C22⋊C4C22×C311yescharacteristic
177C2×C5×C22⋊C4C22×C311yescharacteristic
178C2×C42×C5C22×C311yescharacteristic, complemented
179C2×C42×C5C22×C311yescharacteristic, complemented
180C2×C22⋊Dic5C22×C311yescharacteristic
181#4075C22×C318yescomplemented
182C2×#685C22×C311yescharacteristic
183C2×#685C22×C311yescharacteristic
184C2×#685C22×C311yescharacteristic
185C2×#685C22×C311yescharacteristic
186C2×#685C22×C311yescharacteristic
187C2×#685C22×C311yescharacteristic
188C2×#685C22×C311yescharacteristic
189C2×#685C22×C311yescharacteristic
190C2×#685C22×C318yescomplemented
191C2×#685C22×C311yescharacteristic, complemented
192C2×#685C22×C311yescharacteristic, complemented
193C2×#685C22×C311yescharacteristic, complemented
194C2×C4⋊Dic5C22×C311yescharacteristic, complemented
195C2×#683C22×C311yescharacteristic, complemented
196C2×#683C22×C311yescharacteristic, complemented
197C2×#683C22×C311yescharacteristic, complemented
198C2×#683C22×C311yescharacteristic, complemented
199C2×#683C22×C311yescharacteristic, complemented
200C2×C4×Dic5C22×C311yescharacteristic, complemented
201#4044C22×C318yescomplemented
202#4042C22×C318yescomplemented
203#4040C22×C318yescomplemented
204#4040C22×C318yescomplemented
205#4028C22×C318yes—
206#4027C22×C318yescomplemented
207D5×C22⋊C4C22×C318yescomplemented
208#4024C22×C318yescomplemented
209#4022C22×C318yescomplemented
210#4021C22×C318yescomplemented
211C4×D20C22×C318yescomplemented
212#4018C22×C318yescomplemented
213C2×#551—51noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5#4114yes—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×C3×D5—22no—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5—22no—
223C22×C3×D5—28no—
224C22×C3×D5—22no—
225C22×C3×D5—22no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—28no—
229C22×C3×D5—44no—
230C22×C3×D5—416no—
231C22×C3×D5#4114yes—
232C22×C3×D5C2412yes—
233C22×C3×D5C2412yes—
234C22×C3×D5C2412yes—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—28no—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5—22no—
241C2×C3×C4×C5—22no—
242C2×C3×C4×C5C2412yes—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×C3×C4×C5C2412yes—
248C3×C22⋊D5—28no—
249C2×C3×Dic5—22no—
250C2×C3×Dic5—22no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—44no—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C3×D20—28no—
261C3×D20—44no—
262C3×C4×D5—28no—
263C3×C4×D5—44no—
264C3×C4×D5—44no—
265C3×Dic10—44no—
266C25×C3—51no—
267C22×C3×Q8—51no—
268C22×C3×D4—51no—
269C22×C3×D4—51no—
270C22×C3×D4—51no—
271C23×C3×C4—51no—
272C23×C3×C4—51no—
273C23×C3×C4—51no—
274C23×C3×C4—51no—
275C23×C3×C4C2×D511yescharacteristic
276C3×#126—58no—
277C3×#126—58no—
278C3×#124—58no—
279C3×#123—58no—
280C3×#123—58no—
281C3×#123—58no—
282C3×C22⋊Q8—58no—
283C3×C22⋊Q8—58no—
284C3×#120—58no—
285C3×C4×D4—58no—
286C3×C4×D4—58no—
287C3×#117—58no—
288C3×#117C2×D518yescomplemented
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C4⋊C4—51no—
292C2×C3×C4⋊C4—51no—
293C2×C3×C4⋊C4—51no—
294C2×C3×C4⋊C4—51no—
295C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
296C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
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⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—58no—
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—58no—
311C2×C3×C22⋊C4C2×D511yescharacteristic
312C2×C3×C22⋊C4C2×D511yescharacteristic
313C2×C3×C42—51no—
314C2×C3×C42C2×D511yescharacteristic, complemented
315C2×C3×C42C2×D511yescharacteristic, complemented
316C24×C5C23×C311yescharacteristic
317C23×D5—24no—
318C23×D5—24no—
319C23×D5—42no—
320C23×D5C23×C311yescharacteristic
321C23×D5C23×C311yescharacteristic
322C23×D5C23×C314yes—
323C23×D5C23×C311yescharacteristic
324C22×C4×C5—24no—
325C22×C4×C5C23×C311yescharacteristic
326C22×C4×C5C23×C311yescharacteristic
327C22×C4×C5C23×C311yescharacteristic
328C22×C4×C5C23×C311yescharacteristic
329C22×C4×C5C23×C311yescharacteristic
330C22×C4×C5C23×C311yescharacteristic
331C22×C4×C5C23×C314yes—
332C2×C22⋊D5—24no—
333C2×C22⋊D5C23×C314yes—
334C22×Dic5—42no—
335C22×Dic5C23×C311yescharacteristic
336C22×Dic5C23×C311yescharacteristic
337C22×Dic5C23×C311yescharacteristic
338C22×Dic5C23×C311yescharacteristic
339C22×Dic5C23×C311yescharacteristic
340C22×Dic5C23×C314yes—
341C2×D20—24no—
342C2×D20—42no—
343C2×D20C23×C314yes—
344C2×D20C23×C314yes—
345C2×C4×D5—24no—
346C2×C4×D5—42no—
347C2×C4×D5—42no—
348C2×C4×D5C23×C314yes—
349C2×C4×D5C23×C314yes—
350C2×C4×D5C23×C314yescomplemented
351C2×Dic10—42no—
352C2×Dic10C23×C314yescomplemented
353C5×C4⋊C4C23×C314yescomplemented
354C5×C4⋊C4C23×C314yescomplemented
355C5×C22⋊C4C23×C314yes—
356C5×C22⋊C4C23×C314yes—
357C42×C5C23×C314yescomplemented
358C42×C5C23×C314yescomplemented
359C22⋊Dic5C23×C314yes—
360#685C23×C314yes—
361#685C23×C314yes—
362#685C23×C314yes—
363#685C23×C314yes—
364#685C23×C314yes—
365#685C23×C314yes—
366#685C23×C314yes—
367#685C23×C314yes—
368#685C23×C314yescomplemented
369#685C23×C314yescomplemented
370#685C23×C314yescomplemented
371C4⋊Dic5C23×C314yescomplemented
372#683C23×C314yescomplemented
373#683C23×C314yescomplemented
374#683C23×C314yescomplemented
375#683C23×C314yescomplemented
376#683C23×C314yescomplemented
377C4×Dic5C23×C314yescomplemented
378#551—516no—
379C2×#126—51no—
380C2×#126—51no—
381C2×#124—51no—
382C2×#123—51no—
383C2×#123—51no—
384C2×#123—51no—
385C2×C22⋊Q8—51no—
386C2×C22⋊Q8—51no—
387C2×#120—51no—
388C2×C4×D4—51no—
389C2×C4×D4—51no—
390C2×#117—51no—
391C2×#117C3×D511yescharacteristic, complemented
392C22×C22⋊C4—51no—
393C22×C22⋊C4—51no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5C2×#4114yes—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5C2×#4112yes—
400C22×C3×C5H(5,𝔽2)12yes—
401C22×C3×C5C2511yescharacteristic
402C2×C3×D5—28no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—416no—
412C2×C3×D5—44no—
413C2×C3×D5—44no—
414C2×C3×D5C2×#4114yes—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419C3×C4×C5—22no—
420C3×C4×C5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C3×Dic5—22no—
424C3×Dic5—22no—
425C3×Dic5—22no—
426C24×C3—51no—
427C24×C3—51no—
428C24×C3—51no—
429C24×C3—54no—
430C24×C3—104no—
431C24×C3—104no—
432C24×C3—202no—
433C24×C3C22×D511yescharacteristic
434C2×C3×Q8—54no—
435C2×C3×Q8—202no—
436C2×C3×D4—54no—
437C2×C3×D4—54no—
438C2×C3×D4—54no—
439C2×C3×D4—104no—
440C2×C3×D4—104no—
441C2×C3×D4—202no—
442C22×C3×C4—24no—
443C22×C3×C4—51no—
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—54no—
449C22×C3×C4—54no—
450C22×C3×C4—54no—
451C22×C3×C4—54no—
452C22×C3×C4—104no—
453C22×C3×C4—202no—
454C22×C3×C4—202no—
455C22×C3×C4—202no—
456C22×C3×C4C22×D514yes—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
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⋊C4C22×D514yescomplemented
470C3×C4⋊C4C22×D514yescomplemented
471C3×C22⋊C4—54no—
472C3×C22⋊C4—54no—
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—
486C3×C42C22×D514yescomplemented
487C3×C42C22×D514yescomplemented
488C23×C5—22no—
489C23×C5—22no—
490C23×C5C3×#4114yes—
491C23×C5C24×C312yes—
492C23×C5C24×C311yescharacteristic
493C22×D5—22no—
494C22×D5—22no—
495C22×D5—22no—
496C22×D5—22no—
497C22×D5—28no—
498C22×D5—22no—
499C22×D5—22no—
500C22×D5—22no—
501C22×D5—22no—
502C22×D5—28no—
503C22×D5—44no—
504C22×D5—416no—
505C22×D5C3×#4114yes—
506C22×D5C24×C312yes—
507C22×D5C24×C312yes—
508C22×D5C24×C312yes—
509C2×C4×C5—22no—
510C2×C4×C5—22no—
511C2×C4×C5—28no—
512C2×C4×C5—22no—
513C2×C4×C5—22no—
514C2×C4×C5—22no—
515C2×C4×C5—22no—
516C2×C4×C5C24×C312yes—
517C2×C4×C5C24×C312yes—
518C2×C4×C5C24×C312yes—
519C2×C4×C5C24×C312yes—
520C2×C4×C5C24×C312yes—
521C2×C4×C5C24×C312yes—
522C22⋊D5—28no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—22no—
526C2×Dic5—22no—
527C2×Dic5—22no—
528C2×Dic5—44no—
529C2×Dic5C24×C312yes—
530C2×Dic5C24×C312yes—
531C2×Dic5C24×C312yes—
532C2×Dic5C24×C312yes—
533C2×Dic5C24×C312yes—
534D20—28no—
535D20—44no—
536C4×D5—28no—
537C4×D5—44no—
538C4×D5—44no—
539Dic10—44no—
540C25—51no—
541C22×Q8—51no—
542C22×D4—51no—
543C22×D4—51no—
544C22×D4—51no—
545C23×C4—51no—
546C23×C4—51no—
547C23×C4—51no—
548C23×C4—51no—
549C23×C4C2×C3×D511yescharacteristic
550#126—58no—
551#126—58no—
552#124—58no—
553#123—58no—
554#123—58no—
555#123—58no—
556C22⋊Q8—58no—
557C22⋊Q8—58no—
558#120—58no—
559C4×D4—58no—
560C4×D4—58no—
561#117—58no—
562#117C2×C3×D518yescomplemented
563C2×C4⋊C4—51no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—51no—
569C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
570C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
571C2×C22⋊C4—51no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—58no—
579C2×C22⋊C4—51no—
580C2×C22⋊C4—51no—
581C2×C22⋊C4—51no—
582C2×C22⋊C4—51no—
583C2×C22⋊C4—51no—
584C2×C22⋊C4—58no—
585C2×C22⋊C4C2×C3×D511yescharacteristic
586C2×C22⋊C4C2×C3×D511yescharacteristic
587C2×C42—51no—
588C2×C42C2×C3×D511yescharacteristic, complemented
589C2×C42C2×C3×D511yescharacteristic, complemented
590C2×C3×C5—24no—
591C2×C3×C5#55114yescomplemented
592C2×C3×C5C22×#4111yescharacteristic
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
595C3×D5—24no—
596C3×D5—42no—
597C3×D5—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—54no—
601C23×C3—52no—
602C23×C3—52no—
603C23×C3—52no—
604C23×C3—108no—
605C23×C3—102no—
606C23×C3—102no—
607C23×C3—102no—
608C23×C3—108no—
609C23×C3—102no—
610C23×C3—102no—
611C23×C3—102no—
612C23×C3—102no—
613C23×C3—102no—
614C23×C3—204no—
615C23×C3—2016no—
616C23×C3#70914yes—
617C23×C3C23×D512yes—
618C23×C3C23×D511yescharacteristic
619C3×Q8—204no—
620C3×D4—108no—
621C3×D4—108no—
622C3×D4—204no—
623C2×C3×C4—28no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—52no—
631C2×C3×C4—52no—
632C2×C3×C4—52no—
633C2×C3×C4—52no—
634C2×C3×C4—52no—
635C2×C3×C4—108no—
636C2×C3×C4—102no—
637C2×C3×C4—102no—
638C2×C3×C4—102no—
639C2×C3×C4—102no—
640C2×C3×C4—102no—
641C2×C3×C4—204no—
642C2×C3×C4—204no—
643C2×C3×C4—204no—
644C2×C3×C4C23×D512yes—
645C2×C3×C4C23×D512yes—
646C2×C3×C4C23×D512yes—
647C2×C3×C4C23×D512yes—
648C2×C3×C4C23×D512yes—
649C2×C3×C4C23×D512yes—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—28no—
653C22×C5C2×C3×#4114yes—
654C22×C5C2×C3×#4112yes—
655C22×C5C2×C3×#4112yes—
656C22×C5C3×H(5,𝔽2)12yes—
657C22×C5C25×C311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—28no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—416no—
668C2×D5—44no—
669C2×D5—44no—
670C2×D5C2×C3×#4114yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—22no—
674C4×C5—22no—
675C4×C5—22no—
676C4×C5—22no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—22no—
681Dic5—22no—
682C24—51no—
683C24—51no—
684C24—51no—
685C24—54no—
686C24—104no—
687C24—104no—
688C24—202no—
689C24C22×C3×D511yescharacteristic
690C2×Q8—54no—
691C2×Q8—202no—
692C2×D4—54no—
693C2×D4—54no—
694C2×D4—54no—
695C2×D4—104no—
696C2×D4—104no—
697C2×D4—202no—
698C22×C4—24no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—54no—
705C22×C4—54no—
706C22×C4—54no—
707C22×C4—54no—
708C22×C4—104no—
709C22×C4—202no—
710C22×C4—202no—
711C22×C4—202no—
712C22×C4C22×C3×D511yescharacteristic
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715C22×C4C22×C3×D511yescharacteristic
716C22×C4C22×C3×D511yescharacteristic
717C22×C4C22×C3×D511yescharacteristic
718C22×C4C22×C3×D514yes—
719C4⋊C4—54no—
720C4⋊C4—54no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—54no—
724C4⋊C4—54no—
725C4⋊C4C22×C3×D514yescomplemented
726C4⋊C4C22×C3×D514yescomplemented
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⋊C4—54no—
737C22⋊C4—54no—
738C22⋊C4—54no—
739C22⋊C4C22×C3×D514yes—
740C22⋊C4C22×C3×D514yes—
741C42—54no—
742C42C22×C3×D514yescomplemented
743C42C22×C3×D514yescomplemented
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—54no—
749C22×C3—108no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—2016no—
759C22×C3—204no—
760C22×C3—204no—
761C22×C3C2×#70914yes—
762C22×C3C2×#70912yes—
763C22×C3D5×#4112yes—
764C22×C3#414912yes—
765C22×C3C24×D511yescharacteristic
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—102no—
773C3×C4—102no—
774C3×C4—102no—
775C3×C4—102no—
776C3×C4—102no—
777C2×C5—24no—
778C2×C5C3×#55114yescomplemented
779C2×C5C22×C3×#4111yescharacteristic
780C2×C5C22×C3×#4111yescharacteristic
781C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
782D5—24no—
783D5—42no—
784D5—42no—
785C23—22no—
786C23—22no—
787C23—54no—
788C23—52no—
789C23—52no—
790C23—52no—
791C23—108no—
792C23—102no—
793C23—102no—
794C23—102no—
795C23—108no—
796C23—102no—
797C23—102no—
798C23—102no—
799C23—102no—
800C23—102no—
801C23—204no—
802C23—2016no—
803C23C3×#70914yes—
804C23C23×C3×D512yes—
805C23C23×C3×D511yescharacteristic
806Q8—204no—
807D4—108no—
808D4—108no—
809D4—204no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—52no—
820C2×C4—52no—
821C2×C4—52no—
822C2×C4—108no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—204no—
829C2×C4—204no—
830C2×C4—204no—
831C2×C4C23×C3×D512yes—
832C2×C4C23×C3×D512yes—
833C2×C4C23×C3×D512yes—
834C2×C4C23×C3×D512yes—
835C2×C4C23×C3×D512yes—
836C2×C4C23×C3×D512yes—
837C2×C3—24no—
838C2×C3—104no—
839C2×C3—202no—
840C2×C3—202no—
841C2×C3#6586114yesdirect product factor
842C2×C3C22×#70911yescharacteristic
843C2×C3C2×D5×#4111yescharacteristic
844C2×C3C2×#414911yescharacteristic
845C5C2×C3×#55111yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—54no—
850C22—108no—
851C22—102no—
852C22—102no—
853C22—102no—
854C22—102no—
855C22—102no—
856C22—102no—
857C22—102no—
858C22—102no—
859C22—2016no—
860C22—204no—
861C22—204no—
862C22C2×C3×#70914yes—
863C22C2×C3×#70912yes—
864C22C3×D5×#4112yes—
865C22C3×#414912yes—
866C22C24×C3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—102no—
874C4—102no—
875C4—102no—
876C4—102no—
877C4—102no—
878C3C2×#6586111yescharacteristic, direct product factor, Sylow
879C2—24no—
880C2—104no—
881C2—202no—
882C2—202no—
883C2C3×#6586114yesdirect product factor
884C2C22×C3×#70911yescharacteristic
885C2C2×C3×D5×#4111yescharacteristic
886C2C2×C3×#414911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC2×C3×#4028C2
hypercenterC2×C3×#117D5
hypocenterC5C2×C3×#551
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
2. C2×C3×#4075C2semidirect
3. C22×C3×#685C2semidirect
4. C3×#65861C2direct (N × H)
5. C2×C3×#4044C2semidirect
6. C2×C3×#4042C2semidirect
7. C2×C3×#4040C2semidirect
8. C2×C3×#4040C2semidirect
10. C2×C3×#4027C2semidirect
11. C2×C3×D5×C22⋊C4C2semidirect
12. C2×C3×#4024C2semidirect
13. C2×C3×#4022C2semidirect
14. C2×C3×#4021C2semidirect
15. C2×C3×C4×D20C2semidirect
16. C2×C3×#4018C2semidirect
17. C2×#65861C3direct (N × H)
26. C22×C3×C4×D5C22semidirect
27. C22×C3×Dic10C22semidirect
28. C3×C5×#117C22semidirect
29. C2×C3×C5×C4⋊C4C22semidirect
30. C2×C3×C5×C4⋊C4C22semidirect
33. C2×C3×C42×C5C22semidirect
34. C2×C3×C42×C5C22semidirect
36. C3×#4075C22semidirect
45. C2×C3×#685C22semidirect
46. C2×C3×#685C22semidirect
47. C2×C3×#685C22semidirect
48. C2×C3×#685C22semidirect
49. C2×C3×C4⋊Dic5C22semidirect
50. C2×C3×#683C22semidirect
51. C2×C3×#683C22semidirect
52. C2×C3×#683C22semidirect
53. C2×C3×#683C22semidirect
54. C2×C3×#683C22semidirect
55. C2×C3×C4×Dic5C22semidirect
56. C3×#4044C22semidirect
57. C3×#4042C22semidirect
58. C3×#4040C22semidirect
59. C3×#4040C22semidirect
61. C3×#4027C22semidirect
62. C3×D5×C22⋊C4C22semidirect
63. C3×#4024C22semidirect
64. C3×#4022C22semidirect
65. C3×#4021C22semidirect
66. C3×C4×D20C22semidirect
67. C3×#4018C22semidirect
69. C2×C5×#117C2×C3semidirect
70. C2×#4075C2×C3semidirect
71. C22×#685C2×C3semidirect
72. #65861C2×C3direct (N × H)
73. C2×#4044C2×C3semidirect
74. C2×#4042C2×C3semidirect
75. C2×#4040C2×C3semidirect
76. C2×#4040C2×C3semidirect
78. C2×#4027C2×C3semidirect
79. C2×D5×C22⋊C4C2×C3semidirect
80. C2×#4024C2×C3semidirect
81. C2×#4022C2×C3semidirect
82. C2×#4021C2×C3semidirect
83. C2×C4×D20C2×C3semidirect
84. C2×#4018C2×C3semidirect
119. C2×C3×C4×D5C23semidirect
121. C2×C3×Dic10C23semidirect
122. C3×C5×C4⋊C4C23semidirect
123. C3×C5×C4⋊C4C23semidirect
126. C3×C42×C5C23semidirect
127. C3×C42×C5C23semidirect
137. C3×#685C23semidirect
138. C3×#685C23semidirect
139. C3×#685C23semidirect
140. C3×C4⋊Dic5C23semidirect
141. C3×#683C23semidirect
142. C3×#683C23semidirect
143. C3×#683C23semidirect
144. C3×#683C23semidirect
145. C3×#683C23semidirect
146. C3×C4×Dic5C23semidirect
160. C2×C3×#117D5semidirect
171. C22×C4×D5C22×C3semidirect
172. C22×Dic10C22×C3semidirect
173. C5×#117C22×C3semidirect
174. C2×C5×C4⋊C4C22×C3semidirect
175. C2×C5×C4⋊C4C22×C3semidirect
178. C2×C42×C5C22×C3semidirect
179. C2×C42×C5C22×C3semidirect
181. #4075C22×C3semidirect
190. C2×#685C22×C3semidirect
191. C2×#685C22×C3semidirect
192. C2×#685C22×C3semidirect
193. C2×#685C22×C3semidirect
194. C2×C4⋊Dic5C22×C3semidirect
195. C2×#683C22×C3semidirect
196. C2×#683C22×C3semidirect
197. C2×#683C22×C3semidirect
198. C2×#683C22×C3semidirect
199. C2×#683C22×C3semidirect
200. C2×C4×Dic5C22×C3semidirect
201. #4044C22×C3semidirect
202. #4042C22×C3semidirect
203. #4040C22×C3semidirect
204. #4040C22×C3semidirect
206. #4027C22×C3semidirect
207. D5×C22⋊C4C22×C3semidirect
208. #4024C22×C3semidirect
209. #4022C22×C3semidirect
210. #4021C22×C3semidirect
211. C4×D20C22×C3semidirect
212. #4018C22×C3semidirect
288. C3×#117C2×D5semidirect
295. C2×C3×C4⋊C4C2×D5semidirect
296. C2×C3×C4⋊C4C2×D5semidirect
314. C2×C3×C42C2×D5semidirect
315. C2×C3×C42C2×D5semidirect
350. C2×C4×D5C23×C3semidirect
352. C2×Dic10C23×C3semidirect
353. C5×C4⋊C4C23×C3semidirect
354. C5×C4⋊C4C23×C3semidirect
357. C42×C5C23×C3semidirect
358. C42×C5C23×C3semidirect
368. #685C23×C3semidirect
369. #685C23×C3semidirect
370. #685C23×C3semidirect
371. C4⋊Dic5C23×C3semidirect
372. #683C23×C3semidirect
373. #683C23×C3semidirect
374. #683C23×C3semidirect
375. #683C23×C3semidirect
376. #683C23×C3semidirect
377. C4×Dic5C23×C3semidirect
391. C2×#117C3×D5semidirect
469. C3×C4⋊C4C22×D5semidirect
470. C3×C4⋊C4C22×D5semidirect
486. C3×C42C22×D5semidirect
487. C3×C42C22×D5semidirect
562. #117C2×C3×D5semidirect
569. C2×C4⋊C4C2×C3×D5semidirect
570. C2×C4⋊C4C2×C3×D5semidirect
588. C2×C42C2×C3×D5semidirect
589. C2×C42C2×C3×D5semidirect
591. C2×C3×C5#551semidirect
725. C4⋊C4C22×C3×D5semidirect
726. C4⋊C4C22×C3×D5semidirect
742. C42C22×C3×D5semidirect
743. C42C22×C3×D5semidirect
744. C3×C5C2×#551semidirect
778. C2×C5C3×#551semidirect
841. C2×C3#65861direct (N × H)
845. C5C2×C3×#551semidirect
878. C3C2×#65861direct (N × H)
883. C2C3×#65861direct (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×#1172
C2×C3×#40752
C22×C3×#6852
C3×#658612
C2×C3×#40442
C2×C3×#40422
C2×C3×#40402
C2×C3×#40282
C2×C3×#40272
C2×C3×D5×C22⋊C42
C2×C3×#40242
C2×C3×#40222
C2×C3×#40212
C2×C3×C4×D202
C2×C3×#40182
C2×#658613
C2×C3×#5515