Finite Group Databasebeta

← C2×C3×#65829 #14483242

Subgroups — C2×C3×#65829 #14483242

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
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#4099C211yesmaximal, characteristic
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×C3×#4075C211yesmaximal, characteristic, complemented
5C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
6C2×C3×#4072C211yesmaximal, characteristic, complemented
7C2×C3×#4070C211yesmaximal, characteristic, complemented
8C3×#65829C2116yesmaximal, direct product factor
9C2×C3×#4032C211yesmaximal, characteristic, complemented
10C2×C3×#4031C211yesmaximal, characteristic, complemented
11C2×C3×#4029C211yesmaximal, characteristic, complemented
12C2×C3×#4027C211yesmaximal, characteristic, complemented
13C2×C3×#4025C211yesmaximal, characteristic, complemented
14C2×C3×#4025C211yesmaximal, characteristic, complemented
15C2×C3×#4024C211yesmaximal, characteristic, complemented
16C2×C3×#4023C211yesmaximal, characteristic, complemented
17C2×#65829C311yesmaximal, characteristic, direct product factor, Hall
18C25×C3×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×C3×Dic10C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2218yescomplemented
33C3×#4099C2218yes—
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
41C2×C3×C22⋊Dic5C2218yescomplemented
42C3×#4075C2218yescomplemented
43C3×C4×C22⋊D5C2218yescomplemented
44C2×C3×#685C2211yescharacteristic, complemented
45C2×C3×#685C2211yescharacteristic, complemented
46C2×C3×#685C2211yescharacteristic, complemented
47C3×#4072C2218yescomplemented
48C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
51C3×#4070C2218yescomplemented
52C2×C3×#683C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C2×C3×#683C2211yescharacteristic, complemented
55C2×C3×#683C2211yescharacteristic, complemented
56C2×C3×#683C2211yescharacteristic, complemented
57C2×C3×C4×Dic5C2211yescharacteristic, complemented
58C2×C3×C4×Dic5C2211yescharacteristic, complemented
59C2×C3×C4×Dic5C2211yescharacteristic, complemented
60C3×#4032C2218yescomplemented
61C3×#4031C2218yescomplemented
62C3×#4029C2218yescomplemented
63C3×#4027C2218yescomplemented
64C3×#4025C2218yescomplemented
65C3×#4025C2218yescomplemented
66C3×#4024C2218yescomplemented
67C3×#4023C2218yescomplemented
68C2×C3×#551—51nomaximal, Hall
69C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
70C2×#4099C2×C311yescharacteristic
71C22×C22⋊Dic5C2×C311yescharacteristic, complemented
72C2×#4075C2×C311yescharacteristic, complemented
73C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
74C2×#4072C2×C311yescharacteristic, complemented
75C2×#4070C2×C311yescharacteristic, complemented
76#65829C2×C3116yesdirect product factor
77C2×#4032C2×C311yescharacteristic, complemented
78C2×#4031C2×C311yescharacteristic, complemented
79C2×#4029C2×C311yescharacteristic, complemented
80C2×#4027C2×C311yescharacteristic, complemented
81C2×#4025C2×C311yescharacteristic, complemented
82C2×#4025C2×C311yescharacteristic, complemented
83C2×#4024C2×C311yescharacteristic, complemented
84C2×#4023C2×C311yescharacteristic, complemented
85C24×C3×C5—24no—
86C24×C3×C5—24no—
87C24×C3×C5—42no—
88C24×C3×C5C2311yescharacteristic
89C24×C3×C5C2314yes—
90C24×C3×C5C2311yescharacteristic
91C24×C3×C5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×C3×C4×C5—24no—
94C22×C3×C4×C5—42no—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2314yes—
100C22×C3×C4×C5C2314yes—
101C2×C3×C22⋊D5—24no—
102C2×C3×C22⋊D5—24no—
103C2×C3×C22⋊D5—42no—
104C2×C3×C22⋊D5C2314yes—
105C2×C3×C22⋊D5C2314yes—
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5—24no—
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×D5C2314yescomplemented
120C2×C3×Dic10—42no—
121C2×C3×Dic10C2314yescomplemented
122C3×C5×C22⋊C4C2314yes—
123C3×C5×C22⋊C4C2314yes—
124C3×C5×C22⋊C4C2314yes—
125C3×C5×C22⋊C4C2314yes—
126C3×C22⋊Dic5C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×C22⋊Dic5C2314yes—
129C3×C22⋊Dic5C2314yes—
130C3×C22⋊Dic5C2314yes—
131C3×C22⋊Dic5C2314yes—
132C3×C22⋊Dic5C2314yes—
133C3×#685C2314yescomplemented
134C3×#685C2314yescomplemented
135C3×#685C2314yescomplemented
136C3×C4⋊Dic5C2314yescomplemented
137C3×C4⋊Dic5C2314yescomplemented
138C3×C4⋊Dic5C2314yescomplemented
139C3×#683C2314yescomplemented
140C3×#683C2314yescomplemented
141C3×#683C2314yescomplemented
142C3×#683C2314yescomplemented
143C3×#683C2314yescomplemented
144C3×C4×Dic5C2314yescomplemented
145C3×C4×Dic5C2314yescomplemented
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×#117—51no—
161C22×C3×C22⋊C4—51no—
162C22×C3×C22⋊C4D511yescharacteristic, complemented
163C25×C5C22×C311yescharacteristic
164C23×C4×C5C22×C311yescharacteristic
165C23×C4×C5C22×C311yescharacteristic
166C22×C22⋊D5C22×C311yescharacteristic
167C22×C22⋊D5C22×C311yescharacteristic
168C22×C22⋊D5C22×C311yescharacteristic
169C23×Dic5C22×C311yescharacteristic
170C23×Dic5C22×C311yescharacteristic
171C22×C4×D5C22×C311yescharacteristic, complemented
172C22×Dic10C22×C311yescharacteristic, complemented
173C2×C5×C22⋊C4C22×C311yescharacteristic
174C2×C5×C22⋊C4C22×C311yescharacteristic
175C2×C5×C22⋊C4C22×C311yescharacteristic
176C2×C5×C22⋊C4C22×C311yescharacteristic
177C2×C5×C22⋊C4C22×C318yescomplemented
178#4099C22×C318yes—
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
186C2×C22⋊Dic5C22×C318yescomplemented
187#4075C22×C318yescomplemented
188C4×C22⋊D5C22×C318yescomplemented
189C2×#685C22×C311yescharacteristic, complemented
190C2×#685C22×C311yescharacteristic, complemented
191C2×#685C22×C311yescharacteristic, complemented
192#4072C22×C318yescomplemented
193C2×C4⋊Dic5C22×C311yescharacteristic, complemented
194C2×C4⋊Dic5C22×C311yescharacteristic, complemented
195C2×C4⋊Dic5C22×C311yescharacteristic, complemented
196#4070C22×C318yescomplemented
197C2×#683C22×C311yescharacteristic, complemented
198C2×#683C22×C311yescharacteristic, complemented
199C2×#683C22×C311yescharacteristic, complemented
200C2×#683C22×C311yescharacteristic, complemented
201C2×#683C22×C311yescharacteristic, complemented
202C2×C4×Dic5C22×C311yescharacteristic, complemented
203C2×C4×Dic5C22×C311yescharacteristic, complemented
204C2×C4×Dic5C22×C311yescharacteristic, complemented
205#4032C22×C318yescomplemented
206#4031C22×C318yescomplemented
207#4029C22×C318yescomplemented
208#4027C22×C318yescomplemented
209#4025C22×C318yescomplemented
210#4025C22×C318yescomplemented
211#4024C22×C318yescomplemented
212#4023C22×C318yescomplemented
213C2×#551—51noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—28no—
219C23×C3×C5—28no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—44no—
224C23×C3×C5—416no—
225C23×C3×C5#4114yes—
226C23×C3×C5#4114yes—
227C23×C3×C5C2412yes—
228C23×C3×C5C2412yes—
229C23×C3×C5C2412yes—
230C23×C3×C5C2411yescharacteristic
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5C2412yes—
235C2×C3×C4×C5—28no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5—44no—
241C2×C3×C4×C5C2412yes—
242C2×C3×C4×C5C2412yes—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245C3×C22⋊D5—28no—
246C3×C22⋊D5—28no—
247C3×C22⋊D5—44no—
248C2×C3×Dic5—28no—
249C2×C3×Dic5—22no—
250C2×C3×Dic5—22no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—44no—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263C2×C3×Dic5C2412yes—
264C3×C4×D5—44no—
265C3×Dic10—44no—
266C25×C3C2×D511yescharacteristic
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×C4C2×D511yescharacteristic
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×#117—58no—
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⋊C4—51no—
296C2×C3×C4⋊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⋊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⋊C4C2×D511yescharacteristic
309C2×C3×C22⋊C4C2×D511yescharacteristic
310C2×C3×C22⋊C4C2×D511yescharacteristic
311C2×C3×C22⋊C4C2×D511yescharacteristic
312C2×C3×C22⋊C4C2×D518yescomplemented
313C2×C3×C42—51no—
314C2×C3×C42—51no—
315C2×C3×C42—51no—
316C24×C5—24no—
317C24×C5—24no—
318C24×C5—42no—
319C24×C5C23×C311yescharacteristic
320C24×C5C23×C314yes—
321C24×C5C23×C311yescharacteristic
322C24×C5C23×C311yescharacteristic
323C23×D5C23×C311yescharacteristic
324C22×C4×C5—24no—
325C22×C4×C5—42no—
326C22×C4×C5C23×C311yescharacteristic
327C22×C4×C5C23×C311yescharacteristic
328C22×C4×C5C23×C311yescharacteristic
329C22×C4×C5C23×C311yescharacteristic
330C22×C4×C5C23×C314yes—
331C22×C4×C5C23×C314yes—
332C2×C22⋊D5—24no—
333C2×C22⋊D5—24no—
334C2×C22⋊D5—42no—
335C2×C22⋊D5C23×C314yes—
336C2×C22⋊D5C23×C314yes—
337C2×C22⋊D5C23×C314yes—
338C22×Dic5—24no—
339C22×Dic5—42no—
340C22×Dic5C23×C311yescharacteristic
341C22×Dic5C23×C311yescharacteristic
342C22×Dic5C23×C311yescharacteristic
343C22×Dic5C23×C311yescharacteristic
344C22×Dic5C23×C311yescharacteristic
345C22×Dic5C23×C311yescharacteristic
346C22×Dic5C23×C311yescharacteristic
347C22×Dic5C23×C314yes—
348C22×Dic5C23×C314yes—
349C2×C4×D5—42no—
350C2×C4×D5C23×C314yescomplemented
351C2×Dic10—42no—
352C2×Dic10C23×C314yescomplemented
353C5×C22⋊C4C23×C314yes—
354C5×C22⋊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×C314yescomplemented
365#685C23×C314yescomplemented
366#685C23×C314yescomplemented
367C4⋊Dic5C23×C314yescomplemented
368C4⋊Dic5C23×C314yescomplemented
369C4⋊Dic5C23×C314yescomplemented
370#683C23×C314yescomplemented
371#683C23×C314yescomplemented
372#683C23×C314yescomplemented
373#683C23×C314yescomplemented
374#683C23×C314yescomplemented
375C4×Dic5C23×C314yescomplemented
376C4×Dic5C23×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×#117—51no—
392C22×C22⋊C4—51no—
393C22×C22⋊C4C3×D511yescharacteristic, complemented
394C22×C3×C5—28no—
395C22×C3×C5—28no—
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—22no—
403C22×C3×C5—416no—
404C22×C3×C5—44no—
405C22×C3×C5C2×#4114yes—
406C22×C3×C5C2×#4112yes—
407C22×C3×C5C2×#4114yes—
408C22×C3×C5C2×#4112yes—
409C22×C3×C5H(5,𝔽2)12yes—
410C22×C3×C5C2511yescharacteristic
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—22no—
414C2×C3×D5—44no—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C3×Dic5—22no—
424C3×Dic5—22no—
425C3×Dic5—22no—
426C24×C3—24no—
427C24×C3—24no—
428C24×C3—42no—
429C24×C3—51no—
430C24×C3C22×D511yescharacteristic
431C24×C3C22×D514yes—
432C24×C3C22×D511yescharacteristic
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—42no—
444C22×C3×C4—54no—
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—104no—
455C22×C3×C4—202no—
456C22×C3×C4—202no—
457C22×C3×C4C22×D514yes—
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×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⋊C4C22×D514yes—
482C3×C22⋊C4C22×D514yes—
483C3×C22⋊C4C22×D514yes—
484C3×C22⋊C4C22×D514yes—
485C3×C42—54no—
486C3×C42—54no—
487C3×C42—54no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—28no—
493C23×C5—22no—
494C23×C5—28no—
495C23×C5—22no—
496C23×C5—22no—
497C23×C5—44no—
498C23×C5—416no—
499C23×C5C3×#4114yes—
500C23×C5C3×#4114yes—
501C23×C5C24×C312yes—
502C23×C5C24×C312yes—
503C23×C5C24×C312yes—
504C23×C5C24×C311yescharacteristic
505C22×D5—22no—
506C22×D5—22no—
507C22×D5—22no—
508C22×D5C24×C312yes—
509C2×C4×C5—28no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—22no—
513C2×C4×C5—22no—
514C2×C4×C5—44no—
515C2×C4×C5C24×C312yes—
516C2×C4×C5C24×C312yes—
517C2×C4×C5C24×C312yes—
518C2×C4×C5C24×C312yes—
519C22⋊D5—28no—
520C22⋊D5—28no—
521C22⋊D5—44no—
522C2×Dic5—28no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—22no—
526C2×Dic5—22no—
527C2×Dic5—22no—
528C2×Dic5—22no—
529C2×Dic5—22no—
530C2×Dic5—44no—
531C2×Dic5C24×C312yes—
532C2×Dic5C24×C312yes—
533C2×Dic5C24×C312yes—
534C2×Dic5C24×C312yes—
535C2×Dic5C24×C312yes—
536C2×Dic5C24×C312yes—
537C2×Dic5C24×C312yes—
538C4×D5—44no—
539Dic10—44no—
540C25C2×C3×D511yescharacteristic
541C22×Q8—51no—
542C22×D4—51no—
543C22×D4—51no—
544C22×D4—51no—
545C23×C4—51no—
546C23×C4—51no—
547C23×C4—51no—
548C23×C4C2×C3×D511yescharacteristic
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#117—58no—
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⋊C4—51no—
570C2×C4⋊C4—51no—
571C2×C22⋊C4—51no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—58no—
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⋊C4C2×C3×D511yescharacteristic
583C2×C22⋊C4C2×C3×D511yescharacteristic
584C2×C22⋊C4C2×C3×D511yescharacteristic
585C2×C22⋊C4C2×C3×D511yescharacteristic
586C2×C22⋊C4C2×C3×D518yescomplemented
587C2×C42—51no—
588C2×C42—51no—
589C2×C42—51no—
590C2×C3×C5—24no—
591C2×C3×C5—24no—
592C2×C3×C5—42no—
593C2×C3×C5#55114yescomplemented
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C22×#4111yescharacteristic
596C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
597C3×D5—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—28no—
603C23×C3—22no—
604C23×C3—28no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—44no—
608C23×C3—416no—
609C23×C3—52no—
610C23×C3—102no—
611C23×C3—102no—
612C23×C3—102no—
613C23×C3#70914yes—
614C23×C3#71114yes—
615C23×C3C23×D512yes—
616C23×C3C23×D512yes—
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—44no—
629C2×C3×C4—52no—
630C2×C3×C4—52no—
631C2×C3×C4—52no—
632C2×C3×C4—52no—
633C2×C3×C4—52no—
634C2×C3×C4—52no—
635C2×C3×C4—52no—
636C2×C3×C4—108no—
637C2×C3×C4—102no—
638C2×C3×C4—102no—
639C2×C3×C4—102no—
640C2×C3×C4—102no—
641C2×C3×C4—102no—
642C2×C3×C4—102no—
643C2×C3×C4—102no—
644C2×C3×C4—204no—
645C2×C3×C4—204no—
646C2×C3×C4C23×D512yes—
647C2×C3×C4C23×D512yes—
648C2×C3×C4C23×D512yes—
649C2×C3×C4C23×D512yes—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—28no—
655C22×C5—28no—
656C22×C5—22no—
657C22×C5—22no—
658C22×C5—22no—
659C22×C5—416no—
660C22×C5—44no—
661C22×C5C2×C3×#4114yes—
662C22×C5C2×C3×#4112yes—
663C22×C5C2×C3×#4114yes—
664C22×C5C2×C3×#4112yes—
665C22×C5C3×H(5,𝔽2)12yes—
666C22×C5C25×C311yescharacteristic
667C2×D5—22no—
668C2×D5—22no—
669C2×D5—22no—
670C2×D5—44no—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—22no—
674C4×C5—22no—
675Dic5—22no—
676Dic5—22no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—22no—
681Dic5—22no—
682C24—24no—
683C24—24no—
684C24—42no—
685C24—51no—
686C24C22×C3×D511yescharacteristic
687C24C22×C3×D514yes—
688C24C22×C3×D511yescharacteristic
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—42no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—51no—
706C22×C4—51no—
707C22×C4—54no—
708C22×C4—54no—
709C22×C4—54no—
710C22×C4—104no—
711C22×C4—202no—
712C22×C4—202no—
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715C22×C4C22×C3×D511yescharacteristic
716C22×C4C22×C3×D511yescharacteristic
717C22×C4C22×C3×D514yes—
718C22×C4C22×C3×D514yes—
719C4⋊C4—54no—
720C4⋊C4—54no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—54no—
724C4⋊C4—54no—
725C4⋊C4—54no—
726C4⋊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⋊C4—54no—
737C22⋊C4C22×C3×D514yes—
738C22⋊C4C22×C3×D514yes—
739C22⋊C4C22×C3×D514yes—
740C22⋊C4C22×C3×D514yes—
741C42—54no—
742C42—54no—
743C42—54no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—28no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—416no—
755C22×C3—44no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—102no—
759C22×C3—204no—
760C22×C3C2×#70914yes—
761C22×C3C2×#70912yes—
762C22×C3C2×#71114yes—
763C22×C3C2×#71112yes—
764C22×C3#414412yes—
765C22×C3C24×D511yescharacteristic
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—102no—
771C3×C4—102no—
772C3×C4—102no—
773C3×C4—102no—
774C3×C4—102no—
775C3×C4—102no—
776C3×C4—102no—
777C2×C5—24no—
778C2×C5—24no—
779C2×C5—42no—
780C2×C5C3×#55114yescomplemented
781C2×C5C22×C3×#4111yescharacteristic
782C2×C5C22×C3×#4111yescharacteristic
783C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
784D5—42no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—28no—
790C23—22no—
791C23—28no—
792C23—22no—
793C23—22no—
794C23—44no—
795C23—416no—
796C23—52no—
797C23—102no—
798C23—102no—
799C23—102no—
800C23C3×#70914yes—
801C23C3×#71114yes—
802C23C23×C3×D512yes—
803C23C23×C3×D512yes—
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—44no—
816C2×C4—52no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—52no—
820C2×C4—52no—
821C2×C4—52no—
822C2×C4—52no—
823C2×C4—108no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—204no—
832C2×C4—204no—
833C2×C4C23×C3×D512yes—
834C2×C4C23×C3×D512yes—
835C2×C4C23×C3×D512yes—
836C2×C4C23×C3×D512yes—
837C2×C3—24no—
838C2×C3—24no—
839C2×C3—42no—
840C2×C3—202no—
841C2×C3#6582914yesdirect product factor
842C2×C3C22×#70911yescharacteristic
843C2×C3C22×#71111yescharacteristic
844C2×C3C2×#414411yescharacteristic
845C5C2×C3×#55111yescharacteristic, complemented, Sylow
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—28no—
851C22—28no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—416no—
856C22—44no—
857C22—102no—
858C22—102no—
859C22—102no—
860C22—204no—
861C22C2×C3×#70914yes—
862C22C2×C3×#70912yes—
863C22C2×C3×#71114yes—
864C22C2×C3×#71112yes—
865C22C3×#414412yes—
866C22C24×C3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—102no—
872C4—102no—
873C4—102no—
874C4—102no—
875C4—102no—
876C4—102no—
877C4—102no—
878C3C2×#6582911yescharacteristic, direct product factor, Sylow
879C2—24no—
880C2—24no—
881C2—42no—
882C2—202no—
883C2C3×#6582914yesdirect product factor
884C2C22×C3×#70911yescharacteristic
885C2C22×C3×#71111yescharacteristic
886C2C2×C3×#414411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4099C2
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C2×C3×#551
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C3×C22⋊Dic5C2semidirect
4. C2×C3×#4075C2semidirect
5. C2×C3×C4×C22⋊D5C2semidirect
6. C2×C3×#4072C2semidirect
7. C2×C3×#4070C2semidirect
8. C3×#65829C2direct (N × H)
9. C2×C3×#4032C2semidirect
10. C2×C3×#4031C2semidirect
11. C2×C3×#4029C2semidirect
12. C2×C3×#4027C2semidirect
13. C2×C3×#4025C2semidirect
14. C2×C3×#4025C2semidirect
15. C2×C3×#4024C2semidirect
16. C2×C3×#4023C2semidirect
17. C2×#65829C3direct (N × H)
26. C22×C3×C4×D5C22semidirect
27. C22×C3×Dic10C22semidirect
32. C2×C3×C5×C22⋊C4C22semidirect
41. C2×C3×C22⋊Dic5C22semidirect
42. C3×#4075C22semidirect
43. C3×C4×C22⋊D5C22semidirect
44. C2×C3×#685C22semidirect
45. C2×C3×#685C22semidirect
46. C2×C3×#685C22semidirect
47. C3×#4072C22semidirect
48. C2×C3×C4⋊Dic5C22semidirect
49. C2×C3×C4⋊Dic5C22semidirect
50. C2×C3×C4⋊Dic5C22semidirect
51. C3×#4070C22semidirect
52. C2×C3×#683C22semidirect
53. C2×C3×#683C22semidirect
54. C2×C3×#683C22semidirect
55. C2×C3×#683C22semidirect
56. C2×C3×#683C22semidirect
57. C2×C3×C4×Dic5C22semidirect
58. C2×C3×C4×Dic5C22semidirect
59. C2×C3×C4×Dic5C22semidirect
60. C3×#4032C22semidirect
61. C3×#4031C22semidirect
62. C3×#4029C22semidirect
63. C3×#4027C22semidirect
64. C3×#4025C22semidirect
65. C3×#4025C22semidirect
66. C3×#4024C22semidirect
67. C3×#4023C22semidirect
69. C22×C5×C22⋊C4C2×C3semidirect
71. C22×C22⋊Dic5C2×C3semidirect
72. C2×#4075C2×C3semidirect
73. C2×C4×C22⋊D5C2×C3semidirect
74. C2×#4072C2×C3semidirect
75. C2×#4070C2×C3semidirect
76. #65829C2×C3direct (N × H)
77. C2×#4032C2×C3semidirect
78. C2×#4031C2×C3semidirect
79. C2×#4029C2×C3semidirect
80. C2×#4027C2×C3semidirect
81. C2×#4025C2×C3semidirect
82. C2×#4025C2×C3semidirect
83. C2×#4024C2×C3semidirect
84. C2×#4023C2×C3semidirect
119. C2×C3×C4×D5C23semidirect
121. C2×C3×Dic10C23semidirect
133. C3×#685C23semidirect
134. C3×#685C23semidirect
135. C3×#685C23semidirect
136. C3×C4⋊Dic5C23semidirect
137. C3×C4⋊Dic5C23semidirect
138. C3×C4⋊Dic5C23semidirect
139. C3×#683C23semidirect
140. C3×#683C23semidirect
141. C3×#683C23semidirect
142. C3×#683C23semidirect
143. C3×#683C23semidirect
144. C3×C4×Dic5C23semidirect
145. C3×C4×Dic5C23semidirect
146. C3×C4×Dic5C23semidirect
162. C22×C3×C22⋊C4D5semidirect
171. C22×C4×D5C22×C3semidirect
172. C22×Dic10C22×C3semidirect
177. C2×C5×C22⋊C4C22×C3semidirect
186. C2×C22⋊Dic5C22×C3semidirect
187. #4075C22×C3semidirect
188. C4×C22⋊D5C22×C3semidirect
189. C2×#685C22×C3semidirect
190. C2×#685C22×C3semidirect
191. C2×#685C22×C3semidirect
192. #4072C22×C3semidirect
193. C2×C4⋊Dic5C22×C3semidirect
194. C2×C4⋊Dic5C22×C3semidirect
195. C2×C4⋊Dic5C22×C3semidirect
196. #4070C22×C3semidirect
197. C2×#683C22×C3semidirect
198. C2×#683C22×C3semidirect
199. C2×#683C22×C3semidirect
200. C2×#683C22×C3semidirect
201. C2×#683C22×C3semidirect
202. C2×C4×Dic5C22×C3semidirect
203. C2×C4×Dic5C22×C3semidirect
204. C2×C4×Dic5C22×C3semidirect
205. #4032C22×C3semidirect
206. #4031C22×C3semidirect
207. #4029C22×C3semidirect
208. #4027C22×C3semidirect
209. #4025C22×C3semidirect
210. #4025C22×C3semidirect
211. #4024C22×C3semidirect
212. #4023C22×C3semidirect
312. C2×C3×C22⋊C4C2×D5semidirect
350. C2×C4×D5C23×C3semidirect
352. C2×Dic10C23×C3semidirect
364. #685C23×C3semidirect
365. #685C23×C3semidirect
366. #685C23×C3semidirect
367. C4⋊Dic5C23×C3semidirect
368. C4⋊Dic5C23×C3semidirect
369. C4⋊Dic5C23×C3semidirect
370. #683C23×C3semidirect
371. #683C23×C3semidirect
372. #683C23×C3semidirect
373. #683C23×C3semidirect
374. #683C23×C3semidirect
375. C4×Dic5C23×C3semidirect
376. C4×Dic5C23×C3semidirect
377. C4×Dic5C23×C3semidirect
393. C22×C22⋊C4C3×D5semidirect
586. C2×C22⋊C4C2×C3×D5semidirect
593. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
780. C2×C5C3×#551semidirect
841. C2×C3#65829direct (N × H)
845. C5C2×C3×#551semidirect
878. C3C2×#65829direct (N × H)
883. C2C3×#65829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C2×C3×#40992
C22×C3×C22⋊Dic52
C2×C3×#40752
C2×C3×C4×C22⋊D52
C2×C3×#40722
C2×C3×#40702
C3×#658292
C2×C3×#40322
C2×C3×#40312
C2×C3×#40292
C2×C3×#40272
C2×C3×#40252
C2×C3×#40242
C2×C3×#40232
C2×#658293
C2×C3×#5515