Finite Group Databasebeta

← C3×#10606398 #14324366

Subgroups — C3×#10606398 #14324366

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4086C211yesmaximal, characteristic
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C3×#4027C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6C3×#65502C211yesmaximal, characteristic, complemented
7C3×#65247C211yesmaximal, characteristic, complemented
8C3×#65246C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic, complemented
10C3×#65245C211yesmaximal, characteristic, complemented
11C3×#65245C211yesmaximal, characteristic, complemented
12C3×#64954C211yesmaximal, characteristic, complemented
13C3×#64954C211yesmaximal, characteristic, complemented
14C3×#64939C211yesmaximal, characteristic, complemented
15C3×#64937C211yesmaximal, characteristic, complemented
16#10606398C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C3×#4086C418yescomplemented
34C3×C4×C22⋊D5—24no—
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C3×#4027—24no—
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2328—51nomaximal, Hall
56C2×#4086C2×C311yescharacteristic
57C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
58C2×#4027C2×C311yescharacteristic, complemented
59C5×#386C2×C311yescharacteristic, complemented
60#65509C2×C311yescharacteristic, complemented
61#65502C2×C311yescharacteristic, complemented
62#65247C2×C311yescharacteristic, complemented
63#65246C2×C311yescharacteristic, complemented
64#65246C2×C311yescharacteristic, complemented
65#65245C2×C311yescharacteristic, complemented
66#65245C2×C311yescharacteristic, complemented
67#64954C2×C311yescharacteristic, complemented
68#64954C2×C311yescharacteristic, complemented
69#64939C2×C311yescharacteristic, complemented
70#64937C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4—41no—
77C2×C3×C5×D4C2×C414yescomplemented
78C22×C3×C4×C5—22no—
79C22×C3×C4×C5—41no—
80C22×C3×C4×C5—41no—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×C3×C22⋊D5—22no—
87C2×C3×C22⋊D5—22no—
88C2×C3×C22⋊D5—22no—
89C2×C3×C22⋊D5—22no—
90C2×C3×C22⋊D5—41no—
91C2×C3×C22⋊D5—41no—
92C2×C3×C22⋊D5—41no—
93C2×C3×C22⋊D5—41no—
94C2×C3×C22⋊D5C2×C414yescomplemented
95C2×C3×C22⋊D5C2×C414yescomplemented
96C2×C3×C22⋊D5C2×C414yescomplemented
97C2×C3×C22⋊D5C2×C414yescomplemented
98C22×C3×Dic5—22no—
99C22×C3×Dic5—41no—
100C22×C3×Dic5—41no—
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×C3×D20—41no—
108C2×C3×D20—41no—
109C2×C3×D20C2×C414yescomplemented
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C2×C3×C4×D5—41no—
113C2×C3×C4×D5—41no—
114C2×C3×C4×D5—41no—
115C2×C3×C4×D5—41no—
116C3×C5×C22⋊C4—22no—
117C3×C5×C22⋊C4—41no—
118C3×C5×C22⋊C4—41no—
119C3×C22⋊Dic5—22no—
120C3×C22⋊Dic5—41no—
121C3×C22⋊Dic5—41no—
122C3×#685—22no—
123C3×#685—22no—
124C3×#685—41no—
125C3×#685—41no—
126C3×#685—41no—
127C3×#685—41no—
128C3×#683—22no—
129C3×#683—22no—
130C3×C4×Dic5—22no—
131C3×C4×Dic5C2×C414yescomplemented
132C3×C4×Dic5D414yescomplemented
133C2×C3×#127—51no—
134C2×C3×C4×D4—51no—
135C2×C3×C4×D4—51no—
136C3×#390—51no—
137C3×#390—51no—
138C3×#386—51no—
139C3×#386—51no—
140C3×#386—51no—
141C3×#386—51no—
142C3×#386—51no—
143C3×#386—51no—
144C3×#386—51no—
145C3×#386D511yescharacteristic, complemented
146C3×#382—51no—
147C3×#376—51no—
148C22×C5×D4C22×C311yescharacteristic
149C23×C4×C5C22×C311yescharacteristic
150C22×C22⋊D5C22×C311yescharacteristic
151C22×C22⋊D5C22×C311yescharacteristic
152C22×C22⋊D5C22×C311yescharacteristic
153C22×C22⋊D5C22×C311yescharacteristic
154C23×Dic5C22×C311yescharacteristic
155C22×D20C22×C311yescharacteristic
156C22×C4×D5C22×C311yescharacteristic
157C22×C4×D5C22×C311yescharacteristic
158C2×C5×C22⋊C4C22×C311yescharacteristic
159C2×C5×C22⋊C4C22×C311yescharacteristic
160C2×C5×C22⋊C4C22×C311yescharacteristic
161C2×C22⋊Dic5C22×C311yescharacteristic
162C2×C22⋊Dic5C22×C311yescharacteristic
163C2×C22⋊Dic5C22×C311yescharacteristic
164#4086C3×C418yescomplemented
165C4×C22⋊D5—24no—
166C2×#685C22×C311yescharacteristic
167C2×#685C22×C311yescharacteristic
168C2×#685C22×C311yescharacteristic
169C2×#685C22×C311yescharacteristic
170C2×#685C22×C311yescharacteristic
171C2×#685C22×C311yescharacteristic
172C2×#683C22×C311yescharacteristic
173C2×#683C22×C311yescharacteristic
174C2×C4×Dic5C22×C311yescharacteristic
175C2×C4×Dic5C22×C311yescharacteristic
176C2×C4×Dic5C22×C311yescharacteristic
177#4027—24no—
178C5×#95C22×C311yescharacteristic
179C5×#95C22×C311yescharacteristic
180#3963C22×C311yescharacteristic
181#3963C22×C311yescharacteristic
182#3963C22×C311yescharacteristic
183#3963C22×C311yescharacteristic
184#3963C22×C311yescharacteristic
185#3963C22×C311yescharacteristic
186#2328—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5C22×C412yes—
215C22×C3×D5C22×C412yes—
216C3×C5×D4—44no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—44no—
231C2×C3×C4×C5C22×C412yes—
232C2×C3×C4×C5C2×D412yes—
233C3×C22⋊D5—28no—
234C3×C22⋊D5—28no—
235C3×C22⋊D5—44no—
236C3×C22⋊D5—44no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—44no—
251C2×C3×Dic5C22×C412yes—
252C2×C3×Dic5C22×C412yes—
253C2×C3×Dic5C2×D412yes—
254C2×C3×Dic5C2×D412yes—
255C2×C3×Dic5#4112yes—
256C3×D20—44no—
257C3×C4×D5—44no—
258C3×C4×D5—44no—
259C22×C3×D4—51no—
260C22×C3×D4—51no—
261C22×C3×D4—51no—
262C22×C3×D4—51no—
263C22×C3×D4—51no—
264C22×C3×D4C2×D511yescharacteristic
265C23×C3×C4—51no—
266C23×C3×C4—51no—
267C23×C3×C4—51no—
268C23×C3×C4C2×D511yescharacteristic
269C3×#127—58no—
270C3×C4×D4—104no—
271C3×C4×D4—104no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C4⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4C2×D511yescharacteristic
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×C3×C22⋊C4C2×D511yescharacteristic
286C2×C3×C42—51no—
287C2×C3×C42—51no—
288C2×C3×C42—51no—
289C3×#95—51no—
290C3×#95—51no—
291C3×#95—51no—
292C3×#95—51no—
293C3×#95—51no—
294C3×#95—51no—
295C3×#95C2×D511yescharacteristic
296C3×#95C2×D511yescharacteristic
297C24×C5C23×C311yescharacteristic
298C24×C5C23×C311yescharacteristic
299C23×D5C23×C311yescharacteristic
300C23×D5C23×C311yescharacteristic
301C2×C5×D4—41no—
302C2×C5×D4—41no—
303C2×C5×D4C2×C3×C414yescomplemented
304C22×C4×C5—22no—
305C22×C4×C5—41no—
306C22×C4×C5—41no—
307C22×C4×C5C23×C311yescharacteristic
308C22×C4×C5C23×C311yescharacteristic
309C22×C4×C5C23×C311yescharacteristic
310C22×C4×C5C23×C311yescharacteristic
311C22×C4×C5C23×C311yescharacteristic
312C2×C22⋊D5—22no—
313C2×C22⋊D5—22no—
314C2×C22⋊D5—22no—
315C2×C22⋊D5—22no—
316C2×C22⋊D5—41no—
317C2×C22⋊D5—41no—
318C2×C22⋊D5—41no—
319C2×C22⋊D5—41no—
320C2×C22⋊D5C2×C3×C414yescomplemented
321C2×C22⋊D5C2×C3×C414yescomplemented
322C2×C22⋊D5C2×C3×C414yescomplemented
323C2×C22⋊D5C2×C3×C414yescomplemented
324C22×Dic5—22no—
325C22×Dic5—41no—
326C22×Dic5—41no—
327C22×Dic5C23×C311yescharacteristic
328C22×Dic5C23×C311yescharacteristic
329C22×Dic5C23×C311yescharacteristic
330C22×Dic5C23×C311yescharacteristic
331C22×Dic5C23×C311yescharacteristic
332C22×Dic5C23×C311yescharacteristic
333C2×D20—41no—
334C2×D20—41no—
335C2×D20C2×C3×C414yescomplemented
336C2×C4×D5—22no—
337C2×C4×D5—22no—
338C2×C4×D5—41no—
339C2×C4×D5—41no—
340C2×C4×D5—41no—
341C2×C4×D5—41no—
342C5×C22⋊C4—22no—
343C5×C22⋊C4—41no—
344C5×C22⋊C4—41no—
345C22⋊Dic5—22no—
346C22⋊Dic5—41no—
347C22⋊Dic5—41no—
348#685—22no—
349#685—22no—
350#685—41no—
351#685—41no—
352#685—41no—
353#685—41no—
354#683—22no—
355#683—22no—
356C4×Dic5—22no—
357C4×Dic5C2×C3×C414yescomplemented
358C4×Dic5C3×D414yescomplemented
359C2×#127—51no—
360C2×C4×D4—51no—
361C2×C4×D4—51no—
362#390—51no—
363#390—51no—
364#386—51no—
365#386—51no—
366#386—51no—
367#386—51no—
368#386—51no—
369#386—51no—
370#386—51no—
371#386C3×D511yescharacteristic, complemented
372#382—51no—
373#376—51no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C23×C411yescharacteristic
389C22×C3×C5C22×D411yescharacteristic
390C22×C3×C5C2×#4111yescharacteristic
391C22×C3×C5H(5,𝔽2)11yescharacteristic
392C22×C3×C5H(5,𝔽2)11yescharacteristic
393C22×C3×C5H(5,𝔽2)11yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—22no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—41no—
407C2×C3×D5—41no—
408C2×C3×D5—41no—
409C3×C4×C5—22no—
410C3×C4×C5—22no—
411C3×C4×C5—41no—
412C3×C4×C5—41no—
413C3×C4×C5—41no—
414C3×Dic5—22no—
415C3×Dic5—22no—
416C3×Dic5—41no—
417C3×Dic5—41no—
418C3×Dic5—41no—
419C3×Dic5C4×D414yes—
420C24×C3—51no—
421C24×C3—51no—
422C24×C3C22×D511yescharacteristic
423C24×C3C22×D511yescharacteristic
424C2×C3×D4—41no—
425C2×C3×D4—41no—
426C2×C3×D4—54no—
427C2×C3×D4—54no—
428C2×C3×D4—54no—
429C2×C3×D4—54no—
430C2×C3×D4—54no—
431C2×C3×D4—102no—
432C2×C3×D4—102no—
433C2×C3×D4—102no—
434C2×C3×D4—102no—
435C2×C3×D4—201no—
436C2×C3×D4—201no—
437C2×C3×D4—201no—
438C2×C3×D4—201no—
439C2×C3×D4—201no—
440C2×C3×D4—201no—
441C2×C3×D4C4×D514yescomplemented
442C22×C3×C4—22no—
443C22×C3×C4—41no—
444C22×C3×C4—41no—
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—102no—
452C22×C3×C4—102no—
453C22×C3×C4—102no—
454C22×C3×C4—201no—
455C22×C3×C4—201no—
456C22×C3×C4—201no—
457C22×C3×C4—201no—
458C22×C3×C4—201no—
459C22×C3×C4—201no—
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×C3×C4C22×D511yescharacteristic
464C22×C3×C4C22×D511yescharacteristic
465C3×C4⋊C4—102no—
466C3×C4⋊C4—102no—
467C3×C22⋊C4—22no—
468C3×C22⋊C4—41no—
469C3×C22⋊C4—41no—
470C3×C22⋊C4—102no—
471C3×C22⋊C4—102no—
472C3×C22⋊C4—102no—
473C3×C22⋊C4—201no—
474C3×C22⋊C4—201no—
475C3×C22⋊C4—201no—
476C3×C22⋊C4—201no—
477C3×C22⋊C4—201no—
478C3×C22⋊C4—201no—
479C3×C42—54no—
480C3×C42—54no—
481C3×C42—102no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5C22×C3×C412yes—
495C23×C5C22×C3×C412yes—
496C23×C5C24×C311yescharacteristic
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—21no—
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—21no—
504C22×D5—21no—
505C22×D5—21no—
506C22×D5—21no—
507C22×D5—21no—
508C22×D5—21no—
509C22×D5C22×C3×C412yes—
510C22×D5C22×C3×C412yes—
511C5×D4—44no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—21no—
520C2×C4×C5—21no—
521C2×C4×C5—21no—
522C2×C4×C5—21no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—44no—
526C2×C4×C5C22×C3×C412yes—
527C2×C4×C5C2×C3×D412yes—
528C22⋊D5—28no—
529C22⋊D5—28no—
530C22⋊D5—44no—
531C22⋊D5—44no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5—21no—
538C2×Dic5—21no—
539C2×Dic5—21no—
540C2×Dic5—21no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—44no—
546C2×Dic5C22×C3×C412yes—
547C2×Dic5C22×C3×C412yes—
548C2×Dic5C2×C3×D412yes—
549C2×Dic5C2×C3×D412yes—
550C2×Dic5C3×#4112yes—
551D20—44no—
552C4×D5—44no—
553C4×D5—44no—
554C22×D4—51no—
555C22×D4—51no—
556C22×D4—51no—
557C22×D4—51no—
558C22×D4—51no—
559C22×D4C2×C3×D511yescharacteristic
560C23×C4—51no—
561C23×C4—51no—
562C23×C4—51no—
563C23×C4C2×C3×D511yescharacteristic
564#127—58no—
565C4×D4—104no—
566C4×D4—104no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—51no—
569C2×C22⋊C4—51no—
570C2×C22⋊C4—51no—
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⋊C4C2×C3×D511yescharacteristic
579C2×C22⋊C4C2×C3×D511yescharacteristic
580C2×C22⋊C4C2×C3×D511yescharacteristic
581C2×C42—51no—
582C2×C42—51no—
583C2×C42—51no—
584#95—51no—
585#95—51no—
586#95—51no—
587#95—51no—
588#95—51no—
589#95—51no—
590#95C2×C3×D511yescharacteristic
591#95C2×C3×D511yescharacteristic
592C2×C3×C5—42no—
593C2×C3×C5—42no—
594C2×C3×C5C2×C4×D411yescharacteristic
595C2×C3×C5#51811yescharacteristic
596C2×C3×C5#51811yescharacteristic
597C2×C3×C5#53511yescharacteristic
598C2×C3×C5#53511yescharacteristic
599C2×C3×C5#54011yescharacteristic
600C2×C3×C5#54011yescharacteristic
601C3×D5—42no—
602C3×D5—42no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—21no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—52no—
616C23×C3—52no—
617C23×C3—101no—
618C23×C3—101no—
619C23×C3—101no—
620C23×C3—101no—
621C23×C3—101no—
622C23×C3—101no—
623C23×C3—101no—
624C23×C3—101no—
625C23×C3—101no—
626C23×C3—101no—
627C23×C3—101no—
628C23×C3—101no—
629C23×C3C2×C4×D512yes—
630C23×C3C2×C4×D512yes—
631C23×C3C23×D511yescharacteristic
632C3×D4—44no—
633C3×D4—108no—
634C3×D4—108no—
635C3×D4—204no—
636C3×D4—204no—
637C3×D4—204no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—44no—
652C2×C3×C4—52no—
653C2×C3×C4—52no—
654C2×C3×C4—52no—
655C2×C3×C4—52no—
656C2×C3×C4—52no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4—101no—
662C2×C3×C4—101no—
663C2×C3×C4—101no—
664C2×C3×C4—101no—
665C2×C3×C4—101no—
666C2×C3×C4—101no—
667C2×C3×C4—101no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—204no—
671C2×C3×C4—204no—
672C2×C3×C4—204no—
673C2×C3×C4C2×C4×D512yes—
674C2×C3×C4D4×D512yes—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—41no—
682C22×C5—41no—
683C22×C5—41no—
684C22×C5—41no—
685C22×C5—41no—
686C22×C5—41no—
687C22×C5—41no—
688C22×C5—41no—
689C22×C5C23×C3×C411yescharacteristic
690C22×C5C22×C3×D411yescharacteristic
691C22×C5C2×C3×#4111yescharacteristic
692C22×C5C3×H(5,𝔽2)11yescharacteristic
693C22×C5C3×H(5,𝔽2)11yescharacteristic
694C22×C5C3×H(5,𝔽2)11yescharacteristic
695C22×C5C3×H(5,𝔽2)11yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—41no—
703C2×D5—41no—
704C2×D5—41no—
705C2×D5—41no—
706C2×D5—41no—
707C2×D5—41no—
708C2×D5—41no—
709C2×D5—41no—
710C4×C5—22no—
711C4×C5—22no—
712C4×C5—41no—
713C4×C5—41no—
714C4×C5—41no—
715Dic5—22no—
716Dic5—22no—
717Dic5—41no—
718Dic5—41no—
719Dic5—41no—
720Dic5C3×C4×D414yes—
721C24—51no—
722C24—51no—
723C24C22×C3×D511yescharacteristic
724C24C22×C3×D511yescharacteristic
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—54no—
728C2×D4—54no—
729C2×D4—54no—
730C2×D4—54no—
731C2×D4—54no—
732C2×D4—102no—
733C2×D4—102no—
734C2×D4—102no—
735C2×D4—102no—
736C2×D4—201no—
737C2×D4—201no—
738C2×D4—201no—
739C2×D4—201no—
740C2×D4—201no—
741C2×D4—201no—
742C2×D4C3×C4×D514yescomplemented
743C22×C4—22no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—51no—
749C22×C4—51no—
750C22×C4—51no—
751C22×C4—51no—
752C22×C4—102no—
753C22×C4—102no—
754C22×C4—102no—
755C22×C4—201no—
756C22×C4—201no—
757C22×C4—201no—
758C22×C4—201no—
759C22×C4—201no—
760C22×C4—201no—
761C22×C4C22×C3×D511yescharacteristic
762C22×C4C22×C3×D511yescharacteristic
763C22×C4C22×C3×D511yescharacteristic
764C22×C4C22×C3×D511yescharacteristic
765C22×C4C22×C3×D511yescharacteristic
766C4⋊C4—102no—
767C4⋊C4—102no—
768C22⋊C4—22no—
769C22⋊C4—41no—
770C22⋊C4—41no—
771C22⋊C4—102no—
772C22⋊C4—102no—
773C22⋊C4—102no—
774C22⋊C4—201no—
775C22⋊C4—201no—
776C22⋊C4—201no—
777C22⋊C4—201no—
778C22⋊C4—201no—
779C22⋊C4—201no—
780C42—54no—
781C42—54no—
782C42—102no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—102no—
799C22×C3—102no—
800C22×C3—102no—
801C22×C3—102no—
802C22×C3—102no—
803C22×C3—102no—
804C22×C3—201no—
805C22×C3—201no—
806C22×C3—201no—
807C22×C3—201no—
808C22×C3—201no—
809C22×C3—201no—
810C22×C3—201no—
811C22×C3—201no—
812C22×C3C22×C4×D511yescharacteristic
813C22×C3C2×D4×D511yescharacteristic
814C22×C3#414411yescharacteristic
815C22×C3#414411yescharacteristic
816C22×C3#414411yescharacteristic
817C22×C3D5×#4111yescharacteristic
818C22×C3#414911yescharacteristic
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—54no—
825C3×C4—102no—
826C3×C4—102no—
827C3×C4—201no—
828C3×C4—201no—
829C3×C4—201no—
830C2×C5—42no—
831C2×C5—42no—
832C2×C5C2×C3×C4×D411yescharacteristic
833C2×C5C3×#51811yescharacteristic
834C2×C5C3×#51811yescharacteristic
835C2×C5C3×#53511yescharacteristic
836C2×C5C3×#53511yescharacteristic
837C2×C5C3×#54011yescharacteristic
838C2×C5C3×#54011yescharacteristic
839D5—42no—
840D5—42no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—52no—
854C23—52no—
855C23—101no—
856C23—101no—
857C23—101no—
858C23—101no—
859C23—101no—
860C23—101no—
861C23—101no—
862C23—101no—
863C23—101no—
864C23—101no—
865C23—101no—
866C23—101no—
867C23C2×C3×C4×D512yes—
868C23C2×C3×C4×D512yes—
869C23C23×C3×D511yescharacteristic
870D4—44no—
871D4—108no—
872D4—108no—
873D4—204no—
874D4—204no—
875D4—204no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—44no—
890C2×C4—52no—
891C2×C4—52no—
892C2×C4—52no—
893C2×C4—52no—
894C2×C4—52no—
895C2×C4—101no—
896C2×C4—101no—
897C2×C4—101no—
898C2×C4—101no—
899C2×C4—101no—
900C2×C4—101no—
901C2×C4—101no—
902C2×C4—101no—
903C2×C4—101no—
904C2×C4—101no—
905C2×C4—101no—
906C2×C4—101no—
907C2×C4—101no—
908C2×C4—204no—
909C2×C4—204no—
910C2×C4—204no—
911C2×C4C2×C3×C4×D512yes—
912C2×C4C3×D4×D512yes—
913C2×C3—42no—
914C2×C3—42no—
915C2×C3—202no—
916C2×C3—202no—
917C2×C3#6582011yescharacteristic
918C2×C3C4×D4×D511yescharacteristic
919C2×C3#6587911yescharacteristic
920C2×C3#6592611yescharacteristic
921C2×C3#6594111yescharacteristic
922C2×C3#6594911yescharacteristic
923C2×C3#6599711yescharacteristic
924C5C3×#232811yescharacteristic, complemented, Sylow
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—102no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—201no—
946C22—201no—
947C22—201no—
948C22—201no—
949C22—201no—
950C22—201no—
951C22—201no—
952C22—201no—
953C22C22×C3×C4×D511yescharacteristic
954C22C2×C3×D4×D511yescharacteristic
955C22C3×#414411yescharacteristic
956C22C3×#414411yescharacteristic
957C22C3×#414411yescharacteristic
958C22C3×D5×#4111yescharacteristic
959C22C3×#414911yescharacteristic
960C4—22no—
961C4—22no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—54no—
966C4—102no—
967C4—102no—
968C4—201no—
969C4—201no—
970C4—201no—
971C3#1060639811yescharacteristic, direct product factor, Sylow
972C2—42no—
973C2—42no—
974C2—202no—
975C2—202no—
976C2C3×#6582011yescharacteristic
977C2C3×C4×D4×D511yescharacteristic
978C2C3×#6587911yescharacteristic
979C2C3×#6592611yescharacteristic
980C2C3×#6594111yescharacteristic
981C2C3×#6594911yescharacteristic
982C2C3×#6599711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC2×C3×#4086C2
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2328
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C22⋊D5C2semidirect
3. C2×C3×#4027C2semidirect
4. C3×C5×#386C2semidirect
5. C3×#65509C2semidirect
6. C3×#65502C2semidirect
7. C3×#65247C2semidirect
8. C3×#65246C2semidirect
9. C3×#65246C2semidirect
10. C3×#65245C2semidirect
11. C3×#65245C2semidirect
12. C3×#64954C2semidirect
13. C3×#64954C2semidirect
14. C3×#64939C2semidirect
15. C3×#64937C2semidirect
16. #10606398C3direct (N × H)
33. C3×#4086C4semidirect
57. C2×C4×C22⋊D5C2×C3semidirect
58. C2×#4027C2×C3semidirect
59. C5×#386C2×C3semidirect
60. #65509C2×C3semidirect
61. #65502C2×C3semidirect
62. #65247C2×C3semidirect
63. #65246C2×C3semidirect
64. #65246C2×C3semidirect
65. #65245C2×C3semidirect
66. #65245C2×C3semidirect
67. #64954C2×C3semidirect
68. #64954C2×C3semidirect
69. #64939C2×C3semidirect
70. #64937C2×C3semidirect
77. C2×C3×C5×D4C2×C4semidirect
94. C2×C3×C22⋊D5C2×C4semidirect
95. C2×C3×C22⋊D5C2×C4semidirect
96. C2×C3×C22⋊D5C2×C4semidirect
97. C2×C3×C22⋊D5C2×C4semidirect
109. C2×C3×D20C2×C4semidirect
131. C3×C4×Dic5C2×C4semidirect
132. C3×C4×Dic5D4semidirect
145. C3×#386D5semidirect
164. #4086C3×C4semidirect
303. C2×C5×D4C2×C3×C4semidirect
320. C2×C22⋊D5C2×C3×C4semidirect
321. C2×C22⋊D5C2×C3×C4semidirect
322. C2×C22⋊D5C2×C3×C4semidirect
323. C2×C22⋊D5C2×C3×C4semidirect
335. C2×D20C2×C3×C4semidirect
357. C4×Dic5C2×C3×C4semidirect
358. C4×Dic5C3×D4semidirect
371. #386C3×D5semidirect
441. C2×C3×D4C4×D5semidirect
742. C2×D4C3×C4×D5semidirect
783. C3×C5#2328semidirect
924. C5C3×#2328semidirect
971. C3#10606398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40862
C2×C3×C4×C22⋊D52
C2×C3×#40272
C3×C5×#3862
C3×#655092
C3×#655022
C3×#652472
C3×#652462
C3×#652452
C3×#649542
C3×#649392
C3×#649372
#106063983
C3×#23285