Finite Group Databasebeta

← C2×C3×#65970 #14483788

Subgroups — C2×C3×#65970 #14483788

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#4092C211yesmaximal, characteristic, complemented
3C2×C3×#4090C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
5C22×C3×#683C211yesmaximal, characteristic, complemented
6C3×#65970C2116yesmaximal, direct product factor
7C2×C3×#4042C211yesmaximal, characteristic, complemented
8C2×C3×#4042C211yesmaximal, characteristic, complemented
9C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#4035C211yesmaximal, characteristic, complemented
11C2×C3×#4035C211yesmaximal, characteristic, complemented
12C2×C3×#4033C211yesmaximal, characteristic, complemented
13C2×C3×#4027C211yesmaximal, characteristic
14C2×C3×#4027C211yesmaximal, characteristic
15C2×C3×#4024C211yesmaximal, characteristic, complemented
16C2×C3×#4024C211yesmaximal, characteristic, complemented
17C2×#65970C311yesmaximal, characteristic, direct product factor, Hall
18C22×C3×C5×Q8C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic
27C22×C3×Dic10C2211yescharacteristic
28C3×C5×C22⋊Q8C2218yescomplemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C3×C5×C4⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C3×#4092C2218yescomplemented
36C3×#4090C2218yescomplemented
37C3×C4×C22⋊D5C2218yes—
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×C4⋊Dic5C2211yescharacteristic
42C2×C3×C4⋊Dic5C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C2×C3×#683C2211yescharacteristic
48C2×C3×#683C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic
50C2×C3×#683C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic
52C2×C3×#683C2211yescharacteristic
53C2×C3×#683C2211yescharacteristic
54C2×C3×#683C2218yescomplemented
55C2×C3×C4×Dic5C2211yescharacteristic
56C2×C3×C4×Dic5C2211yescharacteristic
57C2×C3×C4×Dic5C2211yescharacteristic
58C3×#4042C2218yescomplemented
59C3×#4042C2218yescomplemented
60C3×D5×C4⋊C4C2218yescomplemented
61C3×#4035C2218yescomplemented
62C3×#4035C2218yescomplemented
63C3×#4033C2218yescomplemented
64C3×#4027C2218yes—
65C3×#4027C2218yes—
66C3×#4024C2218yescomplemented
67C3×#4024C2218yescomplemented
68C2×C3×#554—51nomaximal, Hall
69C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
70C2×#4092C2×C311yescharacteristic, complemented
71C2×#4090C2×C311yescharacteristic, complemented
72C2×C4×C22⋊D5C2×C311yescharacteristic
73C22×#683C2×C311yescharacteristic, complemented
74#65970C2×C3116yesdirect product factor
75C2×#4042C2×C311yescharacteristic, complemented
76C2×#4042C2×C311yescharacteristic, complemented
77C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
78C2×#4035C2×C311yescharacteristic, complemented
79C2×#4035C2×C311yescharacteristic, complemented
80C2×#4033C2×C311yescharacteristic, complemented
81C2×#4027C2×C311yescharacteristic
82C2×#4027C2×C311yescharacteristic
83C2×#4024C2×C311yescharacteristic, complemented
84C2×#4024C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C2×C3×C5×Q8—42no—
88C2×C3×C5×Q8C2314yes—
89C22×C3×C4×C5—42no—
90C22×C3×C4×C5C2311yescharacteristic
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⋊D5Q818yescomplemented
98C2×C3×C22⋊D5C2314yes—
99C22×C3×Dic5—24no—
100C22×C3×Dic5—42no—
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2314yes—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2314yes—
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
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—24no—
117C2×C3×Dic10—42no—
118C2×C3×Dic10C2314yes—
119C2×C3×Dic10C2314yes—
120C3×C5×C4⋊C4C2314yes—
121C3×C5×C4⋊C4C2314yes—
122C3×C5×C4⋊C4C2314yes—
123C3×C5×C22⋊C4C2314yes—
124C3×C5×C22⋊C4C2314yes—
125C3×C22⋊Dic5C2314yes—
126C3×#685C2314yes—
127C3×#685C2314yes—
128C3×#685C2314yes—
129C3×C4⋊Dic5C2314yes—
130C3×C4⋊Dic5C2314yes—
131C3×#683C2314yes—
132C3×#683C2314yes—
133C3×#683C2314yes—
134C3×#683C2314yes—
135C3×#683C2314yes—
136C3×#683C2314yes—
137C3×#683C2314yes—
138C3×#683C2314yes—
139C3×#683C2314yes—
140C3×#683C2314yes—
141C3×#683C2314yes—
142C3×C4×Dic5C2314yes—
143C3×C4×Dic5C2314yes—
144C3×C4×Dic5C2314yes—
145C3×#554—516no—
146C2×C3×C4⋊Q8—51no—
147C2×C3×#125—51no—
148C2×C3×#125—51no—
149C2×C3×C22⋊Q8—51no—
150C2×C3×C22⋊Q8—51no—
151C2×C3×C22⋊Q8—51no—
152C2×C3×C22⋊Q8—51no—
153C2×C3×C22⋊Q8—51no—
154C2×C3×C22⋊Q8D511yescharacteristic, complemented
155C2×C3×C4×Q8—51no—
156C2×C3×C4×D4—51no—
157C2×C3×C4×D4—51no—
158C2×C3×C4×D4—51no—
159C22×C3×C4⋊C4—51no—
160C22×C3×C4⋊C4—51no—
161C22×C5×Q8C22×C311yescharacteristic
162C23×C4×C5C22×C311yescharacteristic
163C22×C22⋊D5C22×C311yescharacteristic
164C23×Dic5C22×C311yescharacteristic
165C23×Dic5C22×C311yescharacteristic
166C22×C4×D5C22×C311yescharacteristic
167C22×C4×D5C22×C311yescharacteristic
168C22×C4×D5C22×C311yescharacteristic
169C22×Dic10C22×C311yescharacteristic
170C22×Dic10C22×C311yescharacteristic
171C5×C22⋊Q8C22×C318yescomplemented
172C2×C5×C4⋊C4C22×C311yescharacteristic
173C2×C5×C4⋊C4C22×C311yescharacteristic
174C2×C5×C4⋊C4C22×C311yescharacteristic
175C2×C5×C22⋊C4C22×C311yescharacteristic
176C2×C5×C22⋊C4C22×C311yescharacteristic
177C2×C22⋊Dic5C22×C311yescharacteristic
178#4092C22×C318yescomplemented
179#4090C22×C318yescomplemented
180C4×C22⋊D5C22×C318yes—
181C2×#685C22×C311yescharacteristic
182C2×#685C22×C311yescharacteristic
183C2×#685C22×C311yescharacteristic
184C2×C4⋊Dic5C22×C311yescharacteristic
185C2×C4⋊Dic5C22×C311yescharacteristic
186C2×#683C22×C311yescharacteristic
187C2×#683C22×C311yescharacteristic
188C2×#683C22×C311yescharacteristic
189C2×#683C22×C311yescharacteristic
190C2×#683C22×C311yescharacteristic
191C2×#683C22×C311yescharacteristic
192C2×#683C22×C311yescharacteristic
193C2×#683C22×C311yescharacteristic
194C2×#683C22×C311yescharacteristic
195C2×#683C22×C311yescharacteristic
196C2×#683C22×C311yescharacteristic
197C2×#683C22×C318yescomplemented
198C2×C4×Dic5C22×C311yescharacteristic
199C2×C4×Dic5C22×C311yescharacteristic
200C2×C4×Dic5C22×C311yescharacteristic
201#4042C22×C318yescomplemented
202#4042C22×C318yescomplemented
203D5×C4⋊C4C22×C318yescomplemented
204#4035C22×C318yescomplemented
205#4035C22×C318yescomplemented
206#4033C22×C318yescomplemented
207#4027C22×C318yes—
208#4027C22×C318yes—
209#4024C22×C318yescomplemented
210#4024C22×C318yescomplemented
211C2×#554—51noSylow
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2×Q814yes—
215C23×C3×C5C2412yes—
216C23×C3×C5C2411yescharacteristic
217C22×C3×D5—22no—
218C22×C3×D5—22no—
219C22×C3×D5C2×Q814yes—
220C22×C3×D5C2412yes—
221C3×C5×Q8—44no—
222C2×C3×C4×C5—22no—
223C2×C3×C4×C5—22no—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5—22no—
228C2×C3×C4×C5—44no—
229C2×C3×C4×C5C2412yes—
230C2×C3×C4×C5C2412yes—
231C2×C3×C4×C5C2412yes—
232C2×C3×C4×C5C2412yes—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235C3×C22⋊D5C2×Q8116yescomplemented
236C2×C3×Dic5—22no—
237C2×C3×Dic5—22no—
238C2×C3×Dic5—22no—
239C2×C3×Dic5—22no—
240C2×C3×Dic5—22no—
241C2×C3×Dic5—28no—
242C2×C3×Dic5—44no—
243C2×C3×Dic5C2×Q814yes—
244C2×C3×Dic5#4114yes—
245C2×C3×Dic5C2412yes—
246C2×C3×Dic5C2412yes—
247C2×C3×Dic5C2412yes—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C3×C4×D5—28no—
253C3×C4×D5—44no—
254C3×C4×D5—44no—
255C3×Dic10—28no—
256C3×Dic10—44no—
257C22×C3×Q8—51no—
258C22×C3×Q8—51no—
259C22×C3×Q8C2×D511yescharacteristic
260C22×C3×D4—51no—
261C23×C3×C4—51no—
262C23×C3×C4—51no—
263C23×C3×C4—51no—
264C23×C3×C4—51no—
265C23×C3×C4—51no—
266C23×C3×C4C2×D511yescharacteristic
267C3×C4⋊Q8—58no—
268C3×#125—58no—
269C3×#125—58no—
270C3×C22⋊Q8—58no—
271C3×C22⋊Q8—58no—
272C3×C22⋊Q8—58no—
273C3×C22⋊Q8—58no—
274C3×C22⋊Q8—58no—
275C3×C22⋊Q8C2×D518yescomplemented
276C3×C4×Q8—58no—
277C3×C4×D4—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—58no—
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—51no—
293C2×C3×C4⋊C4—51no—
294C2×C3×C4⋊C4—58no—
295C2×C3×C4⋊C4C2×D511yescharacteristic
296C2×C3×C4⋊C4C2×D511yescharacteristic
297C2×C3×C4⋊C4C2×D511yescharacteristic
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×C42—51no—
305C2×C3×C42—51no—
306C2×C3×C42—51no—
307C24×C5C23×C311yescharacteristic
308C23×D5C23×C311yescharacteristic
309C2×C5×Q8—42no—
310C2×C5×Q8C23×C314yes—
311C22×C4×C5—42no—
312C22×C4×C5C23×C311yescharacteristic
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⋊D5C3×Q818yescomplemented
320C2×C22⋊D5C23×C314yes—
321C22×Dic5—24no—
322C22×Dic5—42no—
323C22×Dic5C23×C311yescharacteristic
324C22×Dic5C23×C311yescharacteristic
325C22×Dic5C23×C311yescharacteristic
326C22×Dic5C23×C311yescharacteristic
327C22×Dic5C23×C314yes—
328C22×Dic5C23×C311yescharacteristic
329C22×Dic5C23×C314yes—
330C22×Dic5C23×C311yescharacteristic
331C22×Dic5C23×C311yescharacteristic
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—24no—
339C2×Dic10—42no—
340C2×Dic10C23×C314yes—
341C2×Dic10C23×C314yes—
342C5×C4⋊C4C23×C314yes—
343C5×C4⋊C4C23×C314yes—
344C5×C4⋊C4C23×C314yes—
345C5×C22⋊C4C23×C314yes—
346C5×C22⋊C4C23×C314yes—
347C22⋊Dic5C23×C314yes—
348#685C23×C314yes—
349#685C23×C314yes—
350#685C23×C314yes—
351C4⋊Dic5C23×C314yes—
352C4⋊Dic5C23×C314yes—
353#683C23×C314yes—
354#683C23×C314yes—
355#683C23×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—
366C4×Dic5C23×C314yes—
367#554—516no—
368C2×C4⋊Q8—51no—
369C2×#125—51no—
370C2×#125—51no—
371C2×C22⋊Q8—51no—
372C2×C22⋊Q8—51no—
373C2×C22⋊Q8—51no—
374C2×C22⋊Q8—51no—
375C2×C22⋊Q8—51no—
376C2×C22⋊Q8C3×D511yescharacteristic, complemented
377C2×C4×Q8—51no—
378C2×C4×D4—51no—
379C2×C4×D4—51no—
380C2×C4×D4—51no—
381C22×C4⋊C4—51no—
382C22×C4⋊C4—51no—
383C22×C3×C5—28no—
384C22×C3×C5—22no—
385C22×C3×C5—22no—
386C22×C3×C5C22×Q814yes—
387C22×C3×C5C22×Q812yes—
388C22×C3×C5C2×#4112yes—
389C22×C3×C5H(5,𝔽2)12yes—
390C22×C3×C5C2511yescharacteristic
391C2×C3×D5—28no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5C22×Q814yes—
395C3×C4×C5—22no—
396C3×C4×C5—22no—
397C3×C4×C5—22no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401C3×Dic5—22no—
402C3×Dic5—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5C22×Q814yes—
407C3×Dic5C2×#4114yes—
408C24×C3—51no—
409C24×C3C22×D511yescharacteristic
410C2×C3×Q8—42no—
411C2×C3×Q8—54no—
412C2×C3×Q8—54no—
413C2×C3×Q8—104no—
414C2×C3×Q8—202no—
415C2×C3×Q8C22×D514yes—
416C2×C3×D4—58no—
417C2×C3×D4—54no—
418C22×C3×C4—42no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—54no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4—54no—
428C22×C3×C4—54no—
429C22×C3×C4—54no—
430C22×C3×C4—54no—
431C22×C3×C4—104no—
432C22×C3×C4—104no—
433C22×C3×C4—202no—
434C22×C3×C4—202no—
435C22×C3×C4—202no—
436C22×C3×C4C22×D511yescharacteristic
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⋊C4—54no—
456C3×C4⋊C4C22×D514yes—
457C3×C4⋊C4C22×D514yes—
458C3×C4⋊C4C22×D514yes—
459C3×C22⋊C4—54no—
460C3×C22⋊C4—54no—
461C3×C22⋊C4—54no—
462C3×C22⋊C4—54no—
463C3×C22⋊C4C22×D514yes—
464C3×C22⋊C4C22×D514yes—
465C3×C42—54no—
466C3×C42—54no—
467C3×C42—54no—
468C23×C5—22no—
469C23×C5—22no—
470C23×C5C2×C3×Q814yes—
471C23×C5C24×C312yes—
472C23×C5C24×C311yescharacteristic
473C22×D5—22no—
474C22×D5—22no—
475C22×D5C2×C3×Q814yes—
476C22×D5C24×C312yes—
477C5×Q8—44no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—22no—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—44no—
485C2×C4×C5C24×C312yes—
486C2×C4×C5C24×C312yes—
487C2×C4×C5C24×C312yes—
488C2×C4×C5C24×C312yes—
489C2×C4×C5C24×C312yes—
490C2×C4×C5C24×C312yes—
491C22⋊D5C2×C3×Q8116yescomplemented
492C2×Dic5—22no—
493C2×Dic5—22no—
494C2×Dic5—22no—
495C2×Dic5—22no—
496C2×Dic5—22no—
497C2×Dic5—28no—
498C2×Dic5—44no—
499C2×Dic5C2×C3×Q814yes—
500C2×Dic5C3×#4114yes—
501C2×Dic5C24×C312yes—
502C2×Dic5C24×C312yes—
503C2×Dic5C24×C312yes—
504C2×Dic5C24×C312yes—
505C2×Dic5C24×C312yes—
506C2×Dic5C24×C312yes—
507C2×Dic5C24×C312yes—
508C4×D5—28no—
509C4×D5—44no—
510C4×D5—44no—
511Dic10—28no—
512Dic10—44no—
513C22×Q8—51no—
514C22×Q8—51no—
515C22×Q8C2×C3×D511yescharacteristic
516C22×D4—51no—
517C23×C4—51no—
518C23×C4—51no—
519C23×C4—51no—
520C23×C4—51no—
521C23×C4—51no—
522C23×C4C2×C3×D511yescharacteristic
523C4⋊Q8—58no—
524#125—58no—
525#125—58no—
526C22⋊Q8—58no—
527C22⋊Q8—58no—
528C22⋊Q8—58no—
529C22⋊Q8—58no—
530C22⋊Q8—58no—
531C22⋊Q8C2×C3×D518yescomplemented
532C4×Q8—58no—
533C4×D4—58no—
534C4×D4—58no—
535C4×D4—58no—
536C2×C4⋊C4—51no—
537C2×C4⋊C4—51no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—58no—
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×C4⋊C4C2×C3×D511yescharacteristic
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4C2×C3×D511yescharacteristic
559C2×C22⋊C4C2×C3×D511yescharacteristic
560C2×C42—51no—
561C2×C42—51no—
562C2×C42—51no—
563C2×C3×C5—24no—
564C2×C3×C5#55414yescomplemented
565C2×C3×C5C23×Q811yescharacteristic
566C2×C3×C5C22×#4111yescharacteristic
567C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
568C3×D5—24no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—54no—
572C23×C3—52no—
573C23×C3—102no—
574C23×C3—102no—
575C23×C3Q8×D514yes—
576C23×C3C23×D512yes—
577C23×C3C23×D511yescharacteristic
578C3×Q8—44no—
579C3×Q8—108no—
580C3×Q8—204no—
581C3×D4—516no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—44no—
589C2×C3×C4—54no—
590C2×C3×C4—54no—
591C2×C3×C4—52no—
592C2×C3×C4—52no—
593C2×C3×C4—52no—
594C2×C3×C4—52no—
595C2×C3×C4—52no—
596C2×C3×C4—52no—
597C2×C3×C4—52no—
598C2×C3×C4—108no—
599C2×C3×C4—108no—
600C2×C3×C4—102no—
601C2×C3×C4—102no—
602C2×C3×C4—102no—
603C2×C3×C4—102no—
604C2×C3×C4—102no—
605C2×C3×C4—204no—
606C2×C3×C4—204no—
607C2×C3×C4—204no—
608C2×C3×C4C23×D512yes—
609C2×C3×C4C23×D512yes—
610C2×C3×C4C23×D512yes—
611C2×C3×C4C23×D512yes—
612C2×C3×C4C23×D512yes—
613C2×C3×C4C23×D512yes—
614C22×C5—22no—
615C22×C5—22no—
616C22×C5—28no—
617C22×C5C22×C3×Q814yes—
618C22×C5C22×C3×Q812yes—
619C22×C5C2×C3×#4112yes—
620C22×C5C3×H(5,𝔽2)12yes—
621C22×C5C25×C311yescharacteristic
622C2×D5—22no—
623C2×D5—22no—
624C2×D5—28no—
625C2×D5C22×C3×Q814yes—
626C4×C5—22no—
627C4×C5—22no—
628C4×C5—22no—
629C4×C5—22no—
630C4×C5—22no—
631C4×C5—22no—
632Dic5—22no—
633Dic5—22no—
634Dic5—22no—
635Dic5—22no—
636Dic5—22no—
637Dic5C22×C3×Q814yes—
638Dic5C2×C3×#4114yes—
639C24—51no—
640C24C22×C3×D511yescharacteristic
641C2×Q8—42no—
642C2×Q8—54no—
643C2×Q8—54no—
644C2×Q8—104no—
645C2×Q8—202no—
646C2×Q8C22×C3×D514yes—
647C2×D4—58no—
648C2×D4—54no—
649C22×C4—42no—
650C22×C4—51no—
651C22×C4—51no—
652C22×C4—51no—
653C22×C4—51no—
654C22×C4—51no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—54no—
658C22×C4—54no—
659C22×C4—54no—
660C22×C4—54no—
661C22×C4—54no—
662C22×C4—104no—
663C22×C4—104no—
664C22×C4—202no—
665C22×C4—202no—
666C22×C4—202no—
667C22×C4C22×C3×D511yescharacteristic
668C22×C4C22×C3×D511yescharacteristic
669C22×C4C22×C3×D511yescharacteristic
670C22×C4C22×C3×D511yescharacteristic
671C22×C4C22×C3×D511yescharacteristic
672C22×C4C22×C3×D511yescharacteristic
673C22×C4C22×C3×D514yes—
674C4⋊C4—54no—
675C4⋊C4—54no—
676C4⋊C4—54no—
677C4⋊C4—54no—
678C4⋊C4—54no—
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⋊C4C22×C3×D514yes—
688C4⋊C4C22×C3×D514yes—
689C4⋊C4C22×C3×D514yes—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—54no—
693C22⋊C4—54no—
694C22⋊C4C22×C3×D514yes—
695C22⋊C4C22×C3×D514yes—
696C42—54no—
697C42—54no—
698C42—54no—
699C3×C5C2×#55411yescharacteristic, complemented, Hall
700C22×C3—28no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—54no—
704C22×C3—108no—
705C22×C3—102no—
706C22×C3—102no—
707C22×C3#414412yes—
708C22×C3C2×Q8×D514yes—
709C22×C3C2×Q8×D512yes—
710C22×C3D5×#4112yes—
711C22×C3C24×D511yescharacteristic
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—54no—
719C3×C4—54no—
720C3×C4—102no—
721C3×C4—102no—
722C3×C4—102no—
723C3×C4—102no—
724C3×C4—102no—
725C2×C5—24no—
726C2×C5C3×#55414yescomplemented
727C2×C5C23×C3×Q811yescharacteristic
728C2×C5C22×C3×#4111yescharacteristic
729C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
730D5—24no—
731C23—22no—
732C23—22no—
733C23—54no—
734C23—52no—
735C23—102no—
736C23—102no—
737C23C3×Q8×D514yes—
738C23C23×C3×D512yes—
739C23C23×C3×D511yescharacteristic
740Q8—44no—
741Q8—108no—
742Q8—204no—
743D4—516no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—44no—
751C2×C4—54no—
752C2×C4—54no—
753C2×C4—52no—
754C2×C4—52no—
755C2×C4—52no—
756C2×C4—52no—
757C2×C4—52no—
758C2×C4—52no—
759C2×C4—52no—
760C2×C4—108no—
761C2×C4—108no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4—204no—
770C2×C4C23×C3×D512yes—
771C2×C4C23×C3×D512yes—
772C2×C4C23×C3×D512yes—
773C2×C4C23×C3×D512yes—
774C2×C4C23×C3×D512yes—
775C2×C4C23×C3×D512yes—
776C2×C3—24no—
777C2×C3—104no—
778C2×C3#6597014yesdirect product factor
779C2×C3C2×#414411yescharacteristic
780C2×C3C22×Q8×D511yescharacteristic
781C2×C3C2×D5×#4111yescharacteristic
782C5C2×C3×#55411yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—28no—
786C22—54no—
787C22—102no—
788C22—102no—
789C22—108no—
790C22C3×#414412yes—
791C22C2×C3×Q8×D514yes—
792C22C2×C3×Q8×D512yes—
793C22C3×D5×#4112yes—
794C22C24×C3×D511yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—54no—
802C4—54no—
803C4—102no—
804C4—102no—
805C4—102no—
806C4—102no—
807C4—102no—
808C3C2×#6597011yescharacteristic, direct product factor, Sylow
809C2—24no—
810C2—104no—
811C2C3×#6597014yesdirect product factor
812C2C2×C3×#414411yescharacteristic
813C2C22×C3×Q8×D511yescharacteristic
814C2C2×C3×D5×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC2×C3×C22⋊Q8D5
hypocenterC5C2×C3×#554
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C22⋊Q8C2semidirect
2. C2×C3×#4092C2semidirect
3. C2×C3×#4090C2semidirect
5. C22×C3×#683C2semidirect
6. C3×#65970C2direct (N × H)
7. C2×C3×#4042C2semidirect
8. C2×C3×#4042C2semidirect
9. C2×C3×D5×C4⋊C4C2semidirect
10. C2×C3×#4035C2semidirect
11. C2×C3×#4035C2semidirect
12. C2×C3×#4033C2semidirect
15. C2×C3×#4024C2semidirect
16. C2×C3×#4024C2semidirect
17. C2×#65970C3direct (N × H)
28. C3×C5×C22⋊Q8C22semidirect
35. C3×#4092C22semidirect
36. C3×#4090C22semidirect
54. C2×C3×#683C22semidirect
58. C3×#4042C22semidirect
59. C3×#4042C22semidirect
60. C3×D5×C4⋊C4C22semidirect
61. C3×#4035C22semidirect
62. C3×#4035C22semidirect
63. C3×#4033C22semidirect
66. C3×#4024C22semidirect
67. C3×#4024C22semidirect
69. C2×C5×C22⋊Q8C2×C3semidirect
70. C2×#4092C2×C3semidirect
71. C2×#4090C2×C3semidirect
73. C22×#683C2×C3semidirect
74. #65970C2×C3direct (N × H)
75. C2×#4042C2×C3semidirect
76. C2×#4042C2×C3semidirect
77. C2×D5×C4⋊C4C2×C3semidirect
78. C2×#4035C2×C3semidirect
79. C2×#4035C2×C3semidirect
80. C2×#4033C2×C3semidirect
83. C2×#4024C2×C3semidirect
84. C2×#4024C2×C3semidirect
97. C2×C3×C22⋊D5Q8semidirect
154. C2×C3×C22⋊Q8D5semidirect
171. C5×C22⋊Q8C22×C3semidirect
178. #4092C22×C3semidirect
179. #4090C22×C3semidirect
197. C2×#683C22×C3semidirect
201. #4042C22×C3semidirect
202. #4042C22×C3semidirect
203. D5×C4⋊C4C22×C3semidirect
204. #4035C22×C3semidirect
205. #4035C22×C3semidirect
206. #4033C22×C3semidirect
209. #4024C22×C3semidirect
210. #4024C22×C3semidirect
235. C3×C22⋊D5C2×Q8semidirect
275. C3×C22⋊Q8C2×D5semidirect
319. C2×C22⋊D5C3×Q8semidirect
376. C2×C22⋊Q8C3×D5semidirect
491. C22⋊D5C2×C3×Q8semidirect
531. C22⋊Q8C2×C3×D5semidirect
564. C2×C3×C5#554semidirect
699. C3×C5C2×#554semidirect
726. C2×C5C3×#554semidirect
778. C2×C3#65970direct (N × H)
782. C5C2×C3×#554semidirect
808. C3C2×#65970direct (N × H)
811. C2C3×#65970direct (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×C22⋊Q82
C2×C3×#40922
C2×C3×#40902
C2×C3×C4×C22⋊D52
C22×C3×#6832
C3×#659702
C2×C3×#40422
C2×C3×D5×C4⋊C42
C2×C3×#40352
C2×C3×#40332
C2×C3×#40272
C2×C3×#40242
C2×#659703
C2×C3×#5545