Finite Group Databasebeta

← C3×C5×#3524 #14276558

Subgroups — C3×C5×#3524 #14276558

Order 1920.

2060 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#559C213yesmaximal, complemented
2C3×C5×#557C211yesmaximal, characteristic, complemented
3C3×C5×#555C213yesmaximal, complemented
4C3×C5×#553C213yesmaximal, complemented
5C3×C5×#552C213yesmaximal, complemented
6C3×C5×#550C211yesmaximal, characteristic, complemented
7C3×C5×#548C211yesmaximal, characteristic, complemented
8C3×C5×#548C211yesmaximal, characteristic, complemented
9C3×C5×#542C213yesmaximal, complemented
10C3×C5×#540C213yesmaximal, complemented
11C3×C5×#529C213yesmaximal, complemented
12C3×C5×#529C213yesmaximal, complemented
13C3×C5×#520C211yesmaximal, characteristic, complemented
14C3×C5×#519C211yesmaximal, characteristic, complemented
15C3×C4×C5×#41C211yesmaximal, characteristic, complemented
16C5×#3524C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×#41C2211yescharacteristic
19C22×C3×C5×Q8C2211yescharacteristic
20C3×C5×C4⋊Q8C2213yes—
21C3×C5×#127C2213yes—
22C3×C5×#126C2211yescharacteristic
23C3×C5×#126C2213yes—
24C3×C5×#126C2216yes—
25C3×C5×#125C2213yes—
26C3×C5×#125C2213yes—
27C3×C5×#125C2213yes—
28C3×C5×#124C2213yes—
29C3×C5×#124C2213yes—
30C3×C5×#124C2213yes—
31C3×C5×#124C2216yes—
32C3×C5×#123C2216yes—
33C3×C5×#123C2213yes—
34C3×C5×#123C2213yes—
35C3×C5×#123C2216yes—
36C3×C5×C22⋊Q8C2213yes—
37C3×C5×C22⋊Q8C2213yes—
38C3×C5×C22⋊Q8C2213yes—
39C3×C5×#121C2213yes—
40C3×C5×#121C2213yes—
41C3×C5×#121C2213yes—
42C3×C5×#121C2213yes—
43C3×C5×#121C2216yes—
44C3×C5×#121C2213yes—
45C3×C4×C5×Q8C2211yescharacteristic
46C3×C4×C5×Q8C2211yescharacteristic
47C3×C4×C5×Q8C2213yes—
48C3×C4×C5×Q8C2211yescharacteristic
49C3×C4×C5×Q8C2213yes—
50C3×C4×C5×Q8C2211yescharacteristic
51C3×C4×C5×Q8C2213yes—
52C3×C4×C5×D4C2213yes—
53C3×C4×C5×D4C2213yes—
54C3×C4×C5×D4C2213yes—
55C3×C4×C5×D4C2213yes—
56C3×C4×C5×D4C2213yes—
57C3×C4×C5×D4C2213yes—
58C3×C4×C5×D4C2213yes—
59C3×C4×C5×D4C2216yes—
60C3×C5×#117C2213yes—
61C3×C5×#117C2213yes—
62C3×C5×#117C2213yes—
63C3×C5×#117C2213yes—
64C3×C5×#117C2216yes—
65C2×C3×C5×C4⋊C4C2213yes—
66C2×C3×C42×C5C2213yes—
67C3×#3524C511yesmaximal, characteristic, direct product factor, Hall
68C5×#559C2×C313yescomplemented
69C5×#557C2×C311yescharacteristic, complemented
70C5×#555C2×C313yescomplemented
71C5×#553C2×C313yescomplemented
72C5×#552C2×C313yescomplemented
73C5×#550C2×C311yescharacteristic, complemented
74C5×#548C2×C311yescharacteristic, complemented
75C5×#548C2×C311yescharacteristic, complemented
76C5×#542C2×C313yescomplemented
77C5×#540C2×C313yescomplemented
78C5×#529C2×C313yescomplemented
79C5×#529C2×C313yescomplemented
80C5×#520C2×C311yescharacteristic, complemented
81C5×#519C2×C311yescharacteristic, complemented
82C4×C5×#41C2×C311yescharacteristic, complemented
83C3×C5×#41—24no—
84C3×C5×#41—24no—
85C2×C3×C5×Q8—24no—
86C2×C3×C5×Q8C2313yes—
87C2×C3×C5×Q8C2313yes—
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C2×C3×C5×D4C2313yes—
91C2×C3×C5×D4C2313yes—
92C2×C3×C5×D4C2313yes—
93C2×C3×C5×D4C2316yes—
94C2×C3×C5×D4C2313yes—
95C22×C3×C4×C5C2313yes—
96C22×C3×C4×C5C2313yes—
97C22×C3×C4×C5C2313yes—
98C22×C3×C4×C5C2313yes—
99C22×C3×C4×C5C2313yes—
100C22×C3×C4×C5C2316yes—
101C3×C5×C4⋊C4C2313yes—
102C3×C5×C4⋊C4C2313yes—
103C3×C5×C4⋊C4C2313yes—
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C4⋊C4C2313yes—
106C3×C5×C4⋊C4C2313yes—
107C3×C5×C4⋊C4C2313yes—
108C3×C5×C4⋊C4C2313yes—
109C3×C5×C4⋊C4C2313yes—
110C3×C5×C4⋊C4C2316yes—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C4⋊C4C2313yes—
113C3×C5×C4⋊C4C2313yes—
114C3×C5×C4⋊C4C2311yescharacteristic
115C3×C5×C4⋊C4C2313yes—
116C3×C5×C22⋊C4C2311yescharacteristic
117C3×C5×C22⋊C4C2313yes—
118C3×C5×C22⋊C4C2313yes—
119C3×C5×C22⋊C4C2313yes—
120C3×C5×C22⋊C4C2316yes—
121C3×C5×C22⋊C4C2313yes—
122C3×C5×C22⋊C4C2316yes—
123C3×C5×C22⋊C4C2311yescharacteristic
124C3×C5×C22⋊C4C2313yes—
125C3×C5×C22⋊C4C2311yescharacteristic
126C3×C5×C22⋊C4C2313yes—
127C3×C5×C22⋊C4C2316yes—
128C3×C5×C22⋊C4C2313yes—
129C3×C42×C5C2311yescharacteristic
130C3×C42×C5C2313yes—
131C3×C42×C5C2313yes—
132C3×C42×C5C2313yes—
133C3×C42×C5C2316yes—
134C3×C42×C5C2313yes—
135C3×C42×C5C2313yes—
136C3×#559C2×C513yescomplemented
137C3×#557C2×C511yescharacteristic, complemented
138C3×#555C2×C513yescomplemented
139C3×#553C2×C513yescomplemented
140C3×#552C2×C513yescomplemented
141C3×#550C2×C511yescharacteristic, complemented
142C3×#548C2×C511yescharacteristic, complemented
143C3×#548C2×C511yescharacteristic, complemented
144C3×#542C2×C513yescomplemented
145C3×#540C2×C513yescomplemented
146C3×#529C2×C513yescomplemented
147C3×#529C2×C513yescomplemented
148C3×#520C2×C511yescharacteristic, complemented
149C3×#519C2×C511yescharacteristic, complemented
150C3×C4×#41C2×C511yescharacteristic, complemented
151C2×C5×#41C22×C311yescharacteristic
152C2×C5×#41C22×C311yescharacteristic
153C22×C5×Q8C22×C311yescharacteristic
154C5×C4⋊Q8C22×C313yes—
155C5×#127C22×C313yes—
156C5×#126C22×C311yescharacteristic
157C5×#126C22×C313yes—
158C5×#126C22×C316yes—
159C5×#125C22×C313yes—
160C5×#125C22×C313yes—
161C5×#125C22×C313yes—
162C5×#124C22×C313yes—
163C5×#124C22×C313yes—
164C5×#124C22×C313yes—
165C5×#124C22×C316yes—
166C5×#123C22×C316yes—
167C5×#123C22×C313yes—
168C5×#123C22×C313yes—
169C5×#123C22×C316yes—
170C5×C22⋊Q8C22×C313yes—
171C5×C22⋊Q8C22×C313yes—
172C5×C22⋊Q8C22×C313yes—
173C5×#121C22×C313yes—
174C5×#121C22×C313yes—
175C5×#121C22×C313yes—
176C5×#121C22×C313yes—
177C5×#121C22×C316yes—
178C5×#121C22×C313yes—
179C4×C5×Q8C22×C311yescharacteristic
180C4×C5×Q8C22×C311yescharacteristic
181C4×C5×Q8C22×C313yes—
182C4×C5×Q8C22×C311yescharacteristic
183C4×C5×Q8C22×C313yes—
184C4×C5×Q8C22×C311yescharacteristic
185C4×C5×Q8C22×C313yes—
186C4×C5×D4C22×C313yes—
187C4×C5×D4C22×C313yes—
188C4×C5×D4C22×C313yes—
189C4×C5×D4C22×C313yes—
190C4×C5×D4C22×C313yes—
191C4×C5×D4C22×C313yes—
192C4×C5×D4C22×C313yes—
193C4×C5×D4C22×C316yes—
194C5×#117C22×C313yes—
195C5×#117C22×C313yes—
196C5×#117C22×C313yes—
197C5×#117C22×C313yes—
198C5×#117C22×C316yes—
199C2×C5×C4⋊C4C22×C313yes—
200C2×C42×C5C22×C313yes—
201#3524C3×C511yescharacteristic, direct product factor, Sylow
202C23×C3×C5C2411yescharacteristic
203C23×C3×C5C2413yes—
204C23×C3×C5C2413yes—
205C3×C5×Q8—26no—
206C3×C5×Q8—43no—
207C3×C5×Q8#4114yes—
208C3×C5×D4—26no—
209C3×C5×D4—26no—
210C3×C5×D4—43no—
211C3×C5×D4—43no—
212C3×C5×D4—43no—
213C3×C5×D4—46no—
214C2×C3×C4×C5—26no—
215C2×C3×C4×C5—26no—
216C2×C3×C4×C5—26no—
217C2×C3×C4×C5—43no—
218C2×C3×C4×C5—46no—
219C2×C3×C4×C5—43no—
220C2×C3×C4×C5C2411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222C2×C3×C4×C5C2411yescharacteristic
223C2×C3×C4×C5C2413yes—
224C2×C3×C4×C5C2411yescharacteristic
225C2×C3×C4×C5C2413yes—
226C2×C3×C4×C5C2411yescharacteristic
227C2×C3×C4×C5C2413yes—
228C2×C3×C4×C5C2413yes—
229C2×C3×C4×C5C2413yes—
230C2×C3×C4×C5C2411yescharacteristic
231C2×C3×C4×C5C2413yes—
232C2×C3×#41C22×C511yescharacteristic
233C2×C3×#41C22×C511yescharacteristic
234C22×C3×Q8C22×C511yescharacteristic
235C3×C4⋊Q8C22×C513yes—
236C3×#127C22×C513yes—
237C3×#126C22×C511yescharacteristic
238C3×#126C22×C513yes—
239C3×#126C22×C516yes—
240C3×#125C22×C513yes—
241C3×#125C22×C513yes—
242C3×#125C22×C513yes—
243C3×#124C22×C513yes—
244C3×#124C22×C513yes—
245C3×#124C22×C516yes—
246C3×#124C22×C513yes—
247C3×#123C22×C513yes—
248C3×#123C22×C516yes—
249C3×#123C22×C516yes—
250C3×#123C22×C513yes—
251C3×C22⋊Q8C22×C513yes—
252C3×C22⋊Q8C22×C513yes—
253C3×C22⋊Q8C22×C513yes—
254C3×#121C22×C513yes—
255C3×#121C22×C513yes—
256C3×#121C22×C513yes—
257C3×#121C22×C513yes—
258C3×#121C22×C516yes—
259C3×#121C22×C513yes—
260C3×C4×Q8C22×C513yes—
261C3×C4×Q8C22×C513yes—
262C3×C4×Q8C22×C511yescharacteristic
263C3×C4×Q8C22×C511yescharacteristic
264C3×C4×Q8C22×C513yes—
265C3×C4×Q8C22×C511yescharacteristic
266C3×C4×Q8C22×C511yescharacteristic
267C3×C4×D4C22×C513yes—
268C3×C4×D4C22×C513yes—
269C3×C4×D4C22×C516yes—
270C3×C4×D4C22×C513yes—
271C3×C4×D4C22×C513yes—
272C3×C4×D4C22×C513yes—
273C3×C4×D4C22×C513yes—
274C3×C4×D4C22×C513yes—
275C3×#117C22×C513yes—
276C3×#117C22×C513yes—
277C3×#117C22×C513yes—
278C3×#117C22×C513yes—
279C3×#117C22×C516yes—
280C2×C3×C4⋊C4C22×C513yes—
281C2×C3×C42C22×C513yes—
282C5×#41—24no—
283C5×#41—24no—
284C2×C5×Q8—24no—
285C2×C5×Q8C23×C313yes—
286C2×C5×Q8C23×C313yes—
287C2×C5×Q8C23×C311yescharacteristic
288C2×C5×D4C23×C313yes—
289C2×C5×D4C23×C313yes—
290C2×C5×D4C23×C313yes—
291C2×C5×D4C23×C313yes—
292C2×C5×D4C23×C316yes—
293C2×C5×D4C23×C313yes—
294C22×C4×C5C23×C313yes—
295C22×C4×C5C23×C313yes—
296C22×C4×C5C23×C313yes—
297C22×C4×C5C23×C313yes—
298C22×C4×C5C23×C313yes—
299C22×C4×C5C23×C316yes—
300C5×C4⋊C4C23×C313yes—
301C5×C4⋊C4C23×C313yes—
302C5×C4⋊C4C23×C313yes—
303C5×C4⋊C4C23×C311yescharacteristic
304C5×C4⋊C4C23×C313yes—
305C5×C4⋊C4C23×C313yes—
306C5×C4⋊C4C23×C313yes—
307C5×C4⋊C4C23×C313yes—
308C5×C4⋊C4C23×C313yes—
309C5×C4⋊C4C23×C316yes—
310C5×C4⋊C4C23×C311yescharacteristic
311C5×C4⋊C4C23×C313yes—
312C5×C4⋊C4C23×C313yes—
313C5×C4⋊C4C23×C311yescharacteristic
314C5×C4⋊C4C23×C313yes—
315C5×C22⋊C4C23×C311yescharacteristic
316C5×C22⋊C4C23×C313yes—
317C5×C22⋊C4C23×C313yes—
318C5×C22⋊C4C23×C313yes—
319C5×C22⋊C4C23×C316yes—
320C5×C22⋊C4C23×C313yes—
321C5×C22⋊C4C23×C316yes—
322C5×C22⋊C4C23×C311yescharacteristic
323C5×C22⋊C4C23×C313yes—
324C5×C22⋊C4C23×C311yescharacteristic
325C5×C22⋊C4C23×C313yes—
326C5×C22⋊C4C23×C316yes—
327C5×C22⋊C4C23×C313yes—
328C42×C5C23×C311yescharacteristic
329C42×C5C23×C313yes—
330C42×C5C23×C313yes—
331C42×C5C23×C313yes—
332C42×C5C23×C316yes—
333C42×C5C23×C313yes—
334C42×C5C23×C313yes—
335#559C2×C3×C513yescomplemented
336#557C2×C3×C511yescharacteristic, complemented
337#555C2×C3×C513yescomplemented
338#553C2×C3×C513yescomplemented
339#552C2×C3×C513yescomplemented
340#550C2×C3×C511yescharacteristic, complemented
341#548C2×C3×C511yescharacteristic, complemented
342#548C2×C3×C511yescharacteristic, complemented
343#542C2×C3×C513yescomplemented
344#540C2×C3×C513yescomplemented
345#529C2×C3×C513yescomplemented
346#529C2×C3×C513yescomplemented
347#520C2×C3×C511yescharacteristic, complemented
348#519C2×C3×C511yescharacteristic, complemented
349C4×#41C2×C3×C511yescharacteristic, complemented
350C22×C3×C5—21no—
351C22×C3×C5—23no—
352C22×C3×C5—23no—
353C22×C3×C5—23no—
354C22×C3×C5—23no—
355C22×C3×C5—23no—
356C22×C3×C5—21no—
357C22×C3×C5—21no—
358C22×C3×C5—23no—
359C22×C3×C5C2511yescharacteristic
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5—23no—
363C3×C4×C5—21no—
364C3×C4×C5—23no—
365C3×C4×C5—21no—
366C3×C4×C5—23no—
367C3×C4×C5—23no—
368C3×C4×C5—21no—
369C3×C4×C5—23no—
370C3×C4×C5—21no—
371C3×C4×C5C2×#4116yes—
372C3×#41—24no—
373C3×#41—24no—
374C2×C3×Q8—24no—
375C2×C3×Q8C23×C513yes—
376C2×C3×Q8C23×C513yes—
377C2×C3×Q8C23×C511yescharacteristic
378C2×C3×D4C23×C513yes—
379C2×C3×D4C23×C513yes—
380C2×C3×D4C23×C513yes—
381C2×C3×D4C23×C513yes—
382C2×C3×D4C23×C516yes—
383C2×C3×D4C23×C513yes—
384C22×C3×C4C23×C513yes—
385C22×C3×C4C23×C513yes—
386C22×C3×C4C23×C513yes—
387C22×C3×C4C23×C513yes—
388C22×C3×C4C23×C513yes—
389C22×C3×C4C23×C516yes—
390C3×C4⋊C4C23×C513yes—
391C3×C4⋊C4C23×C513yes—
392C3×C4⋊C4C23×C513yes—
393C3×C4⋊C4C23×C511yescharacteristic
394C3×C4⋊C4C23×C513yes—
395C3×C4⋊C4C23×C513yes—
396C3×C4⋊C4C23×C513yes—
397C3×C4⋊C4C23×C513yes—
398C3×C4⋊C4C23×C513yes—
399C3×C4⋊C4C23×C516yes—
400C3×C4⋊C4C23×C511yescharacteristic
401C3×C4⋊C4C23×C513yes—
402C3×C4⋊C4C23×C513yes—
403C3×C4⋊C4C23×C511yescharacteristic
404C3×C4⋊C4C23×C513yes—
405C3×C22⋊C4C23×C511yescharacteristic
406C3×C22⋊C4C23×C513yes—
407C3×C22⋊C4C23×C513yes—
408C3×C22⋊C4C23×C513yes—
409C3×C22⋊C4C23×C516yes—
410C3×C22⋊C4C23×C513yes—
411C3×C22⋊C4C23×C516yes—
412C3×C22⋊C4C23×C511yescharacteristic
413C3×C22⋊C4C23×C513yes—
414C3×C22⋊C4C23×C511yescharacteristic
415C3×C22⋊C4C23×C513yes—
416C3×C22⋊C4C23×C516yes—
417C3×C22⋊C4C23×C513yes—
418C3×C42C23×C511yescharacteristic
419C3×C42C23×C513yes—
420C3×C42C23×C513yes—
421C3×C42C23×C513yes—
422C3×C42C23×C516yes—
423C3×C42C23×C513yes—
424C3×C42C23×C513yes—
425C23×C5C24×C311yescharacteristic
426C23×C5C24×C313yes—
427C23×C5C24×C313yes—
428C5×Q8—26no—
429C5×Q8—43no—
430C5×Q8C3×#4114yes—
431C5×D4—26no—
432C5×D4—26no—
433C5×D4—43no—
434C5×D4—43no—
435C5×D4—43no—
436C5×D4—46no—
437C2×C4×C5—26no—
438C2×C4×C5—26no—
439C2×C4×C5—26no—
440C2×C4×C5—43no—
441C2×C4×C5—46no—
442C2×C4×C5—43no—
443C2×C4×C5C24×C311yescharacteristic
444C2×C4×C5C24×C311yescharacteristic
445C2×C4×C5C24×C311yescharacteristic
446C2×C4×C5C24×C313yes—
447C2×C4×C5C24×C311yescharacteristic
448C2×C4×C5C24×C313yes—
449C2×C4×C5C24×C311yescharacteristic
450C2×C4×C5C24×C313yes—
451C2×C4×C5C24×C313yes—
452C2×C4×C5C24×C313yes—
453C2×C4×C5C24×C311yescharacteristic
454C2×C4×C5C24×C313yes—
455C2×#41C22×C3×C511yescharacteristic
456C2×#41C22×C3×C511yescharacteristic
457C22×Q8C22×C3×C511yescharacteristic
458C4⋊Q8C22×C3×C513yes—
459#127C22×C3×C513yes—
460#126C22×C3×C511yescharacteristic
461#126C22×C3×C513yes—
462#126C22×C3×C516yes—
463#125C22×C3×C513yes—
464#125C22×C3×C513yes—
465#125C22×C3×C513yes—
466#124C22×C3×C513yes—
467#124C22×C3×C513yes—
468#124C22×C3×C513yes—
469#124C22×C3×C516yes—
470#123C22×C3×C516yes—
471#123C22×C3×C513yes—
472#123C22×C3×C513yes—
473#123C22×C3×C516yes—
474C22⋊Q8C22×C3×C513yes—
475C22⋊Q8C22×C3×C513yes—
476C22⋊Q8C22×C3×C513yes—
477#121C22×C3×C513yes—
478#121C22×C3×C513yes—
479#121C22×C3×C513yes—
480#121C22×C3×C513yes—
481#121C22×C3×C516yes—
482#121C22×C3×C513yes—
483C4×Q8C22×C3×C511yescharacteristic
484C4×Q8C22×C3×C511yescharacteristic
485C4×Q8C22×C3×C513yes—
486C4×Q8C22×C3×C511yescharacteristic
487C4×Q8C22×C3×C513yes—
488C4×Q8C22×C3×C511yescharacteristic
489C4×Q8C22×C3×C513yes—
490C4×D4C22×C3×C513yes—
491C4×D4C22×C3×C513yes—
492C4×D4C22×C3×C513yes—
493C4×D4C22×C3×C513yes—
494C4×D4C22×C3×C513yes—
495C4×D4C22×C3×C513yes—
496C4×D4C22×C3×C513yes—
497C4×D4C22×C3×C516yes—
498#117C22×C3×C513yes—
499#117C22×C3×C513yes—
500#117C22×C3×C513yes—
501#117C22×C3×C513yes—
502#117C22×C3×C516yes—
503C2×C4⋊C4C22×C3×C513yes—
504C2×C42C22×C3×C513yes—
505C2×C3×C5—41no—
506C2×C3×C5—43no—
507C2×C3×C5—43no—
508C2×C3×C5C22×#4111yescharacteristic
509C2×C3×C5#58511yescharacteristic
510C2×C3×C5#58511yescharacteristic
511C23×C3C24×C511yescharacteristic
512C23×C3C24×C513yes—
513C23×C3C24×C513yes—
514C3×Q8—26no—
515C3×Q8—43no—
516C3×Q8C5×#4114yes—
517C3×D4—26no—
518C3×D4—26no—
519C3×D4—43no—
520C3×D4—43no—
521C3×D4—43no—
522C3×D4—46no—
523C2×C3×C4—26no—
524C2×C3×C4—26no—
525C2×C3×C4—26no—
526C2×C3×C4—43no—
527C2×C3×C4—46no—
528C2×C3×C4—43no—
529C2×C3×C4C24×C511yescharacteristic
530C2×C3×C4C24×C511yescharacteristic
531C2×C3×C4C24×C511yescharacteristic
532C2×C3×C4C24×C513yes—
533C2×C3×C4C24×C511yescharacteristic
534C2×C3×C4C24×C513yes—
535C2×C3×C4C24×C511yescharacteristic
536C2×C3×C4C24×C513yes—
537C2×C3×C4C24×C513yes—
538C2×C3×C4C24×C513yes—
539C2×C3×C4C24×C511yescharacteristic
540C2×C3×C4C24×C513yes—
541C22×C5—21no—
542C22×C5—23no—
543C22×C5—23no—
544C22×C5—23no—
545C22×C5—23no—
546C22×C5—23no—
547C22×C5—21no—
548C22×C5—21no—
549C22×C5—23no—
550C22×C5C25×C311yescharacteristic
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—23no—
554C4×C5—21no—
555C4×C5—23no—
556C4×C5—21no—
557C4×C5—23no—
558C4×C5—23no—
559C4×C5—21no—
560C4×C5—23no—
561C4×C5—21no—
562C4×C5C2×C3×#4116yes—
563#41—24no—
564#41—24no—
565C2×Q8—24no—
566C2×Q8C23×C3×C513yes—
567C2×Q8C23×C3×C513yes—
568C2×Q8C23×C3×C511yescharacteristic
569C2×D4C23×C3×C513yes—
570C2×D4C23×C3×C513yes—
571C2×D4C23×C3×C513yes—
572C2×D4C23×C3×C513yes—
573C2×D4C23×C3×C516yes—
574C2×D4C23×C3×C513yes—
575C22×C4C23×C3×C513yes—
576C22×C4C23×C3×C513yes—
577C22×C4C23×C3×C513yes—
578C22×C4C23×C3×C513yes—
579C22×C4C23×C3×C513yes—
580C22×C4C23×C3×C516yes—
581C4⋊C4C23×C3×C513yes—
582C4⋊C4C23×C3×C513yes—
583C4⋊C4C23×C3×C513yes—
584C4⋊C4C23×C3×C511yescharacteristic
585C4⋊C4C23×C3×C513yes—
586C4⋊C4C23×C3×C513yes—
587C4⋊C4C23×C3×C513yes—
588C4⋊C4C23×C3×C513yes—
589C4⋊C4C23×C3×C513yes—
590C4⋊C4C23×C3×C516yes—
591C4⋊C4C23×C3×C511yescharacteristic
592C4⋊C4C23×C3×C513yes—
593C4⋊C4C23×C3×C513yes—
594C4⋊C4C23×C3×C511yescharacteristic
595C4⋊C4C23×C3×C513yes—
596C22⋊C4C23×C3×C511yescharacteristic
597C22⋊C4C23×C3×C513yes—
598C22⋊C4C23×C3×C513yes—
599C22⋊C4C23×C3×C513yes—
600C22⋊C4C23×C3×C516yes—
601C22⋊C4C23×C3×C513yes—
602C22⋊C4C23×C3×C516yes—
603C22⋊C4C23×C3×C511yescharacteristic
604C22⋊C4C23×C3×C513yes—
605C22⋊C4C23×C3×C511yescharacteristic
606C22⋊C4C23×C3×C513yes—
607C22⋊C4C23×C3×C516yes—
608C22⋊C4C23×C3×C513yes—
609C42C23×C3×C511yescharacteristic
610C42C23×C3×C513yes—
611C42C23×C3×C513yes—
612C42C23×C3×C513yes—
613C42C23×C3×C516yes—
614C42C23×C3×C513yes—
615C42C23×C3×C513yes—
616C3×C5#352411yescharacteristic, direct product factor, Hall
617C22×C3—21no—
618C22×C3—23no—
619C22×C3—23no—
620C22×C3—23no—
621C22×C3—23no—
622C22×C3—23no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—23no—
626C22×C3C25×C511yescharacteristic
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—23no—
630C3×C4—21no—
631C3×C4—23no—
632C3×C4—21no—
633C3×C4—23no—
634C3×C4—23no—
635C3×C4—21no—
636C3×C4—23no—
637C3×C4—21no—
638C3×C4C2×C5×#4116yes—
639C2×C5—41no—
640C2×C5—43no—
641C2×C5—43no—
642C2×C5C22×C3×#4111yescharacteristic
643C2×C5C3×#58511yescharacteristic
644C2×C5C3×#58511yescharacteristic
645C23C24×C3×C511yescharacteristic
646C23C24×C3×C513yes—
647C23C24×C3×C513yes—
648Q8—26no—
649Q8—43no—
650Q8C3×C5×#4114yes—
651D4—26no—
652D4—26no—
653D4—43no—
654D4—43no—
655D4—43no—
656D4—46no—
657C2×C4—26no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—43no—
661C2×C4—46no—
662C2×C4—43no—
663C2×C4C24×C3×C511yescharacteristic
664C2×C4C24×C3×C511yescharacteristic
665C2×C4C24×C3×C511yescharacteristic
666C2×C4C24×C3×C513yes—
667C2×C4C24×C3×C511yescharacteristic
668C2×C4C24×C3×C513yes—
669C2×C4C24×C3×C511yescharacteristic
670C2×C4C24×C3×C513yes—
671C2×C4C24×C3×C513yes—
672C2×C4C24×C3×C513yes—
673C2×C4C24×C3×C511yescharacteristic
674C2×C4C24×C3×C513yes—
675C2×C3—41no—
676C2×C3—43no—
677C2×C3—43no—
678C2×C3C22×C5×#4111yescharacteristic
679C2×C3C5×#58511yescharacteristic
680C2×C3C5×#58511yescharacteristic
681C5C3×#352411yescharacteristic, direct product factor, Sylow
682C22—21no—
683C22—23no—
684C22—23no—
685C22—23no—
686C22—23no—
687C22—23no—
688C22—21no—
689C22—21no—
690C22—23no—
691C22C25×C3×C511yescharacteristic
692C4—21no—
693C4—21no—
694C4—23no—
695C4—21no—
696C4—23no—
697C4—21no—
698C4—23no—
699C4—23no—
700C4—21no—
701C4—23no—
702C4—21no—
703C4C2×C3×C5×#4116yes—
704C3C5×#352411yescharacteristic, direct product factor, Sylow
705C2—41no—
706C2—43no—
707C2—43no—
708C2C22×C3×C5×#4111yescharacteristic
709C2C3×C5×#58511yescharacteristic
710C2C3×C5×#58511yescharacteristic
subgroupG/H
center, socleC22×C3×C5C25
commutator, Frattini, cosocleC22C25×C3×C5
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×#559C2semidirect
2. C3×C5×#557C2semidirect
3. C3×C5×#555C2semidirect
4. C3×C5×#553C2semidirect
5. C3×C5×#552C2semidirect
6. C3×C5×#550C2semidirect
7. C3×C5×#548C2semidirect
8. C3×C5×#548C2semidirect
9. C3×C5×#542C2semidirect
10. C3×C5×#540C2semidirect
11. C3×C5×#529C2semidirect
12. C3×C5×#529C2semidirect
13. C3×C5×#520C2semidirect
14. C3×C5×#519C2semidirect
15. C3×C4×C5×#41C2semidirect
16. C5×#3524C3direct (N × H)
67. C3×#3524C5direct (N × H)
68. C5×#559C2×C3semidirect
69. C5×#557C2×C3semidirect
70. C5×#555C2×C3semidirect
71. C5×#553C2×C3semidirect
72. C5×#552C2×C3semidirect
73. C5×#550C2×C3semidirect
74. C5×#548C2×C3semidirect
75. C5×#548C2×C3semidirect
76. C5×#542C2×C3semidirect
77. C5×#540C2×C3semidirect
78. C5×#529C2×C3semidirect
79. C5×#529C2×C3semidirect
80. C5×#520C2×C3semidirect
81. C5×#519C2×C3semidirect
82. C4×C5×#41C2×C3semidirect
136. C3×#559C2×C5semidirect
137. C3×#557C2×C5semidirect
138. C3×#555C2×C5semidirect
139. C3×#553C2×C5semidirect
140. C3×#552C2×C5semidirect
141. C3×#550C2×C5semidirect
142. C3×#548C2×C5semidirect
143. C3×#548C2×C5semidirect
144. C3×#542C2×C5semidirect
145. C3×#540C2×C5semidirect
146. C3×#529C2×C5semidirect
147. C3×#529C2×C5semidirect
148. C3×#520C2×C5semidirect
149. C3×#519C2×C5semidirect
150. C3×C4×#41C2×C5semidirect
201. #3524C3×C5direct (N × H)
335. #559C2×C3×C5semidirect
336. #557C2×C3×C5semidirect
337. #555C2×C3×C5semidirect
338. #553C2×C3×C5semidirect
339. #552C2×C3×C5semidirect
340. #550C2×C3×C5semidirect
341. #548C2×C3×C5semidirect
342. #548C2×C3×C5semidirect
343. #542C2×C3×C5semidirect
344. #540C2×C3×C5semidirect
345. #529C2×C3×C5semidirect
346. #529C2×C3×C5semidirect
347. #520C2×C3×C5semidirect
348. #519C2×C3×C5semidirect
349. C4×#41C2×C3×C5semidirect
616. C3×C5#3524direct (N × H)
681. C5C3×#3524direct (N × H)
704. C3C5×#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5592
C3×C5×#5572
C3×C5×#5552
C3×C5×#5532
C3×C5×#5522
C3×C5×#5502
C3×C5×#5482
C3×C5×#5422
C3×C5×#5402
C3×C5×#5292
C3×C5×#5202
C3×C5×#5192
C3×C4×C5×#412
C5×#35243
C3×#35245