Finite Group Databasebeta

← C3×C5×#3532 #14276566

Subgroups — C3×C5×#3532 #14276566

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×H(3,𝔽4)C211yesmaximal, characteristic, complemented
2C3×C5×#560C213yesmaximal, complemented
3C3×C5×#551C213yesmaximal, complemented
4C3×C5×#546C216yesmaximal, complemented
5C3×C5×D42C213yesmaximal, complemented
6C3×C5×#538C216yesmaximal, complemented
7C3×C5×#535C213yesmaximal, complemented
8C3×C5×#534C213yesmaximal, complemented
9C2×C3×C5×#120C213yesmaximal, complemented
10C5×#3532C311yesmaximal, characteristic, direct product factor, Hall
11C25×C3×C5C2211yescharacteristic, complemented
12C2×C3×C5×#41C2213yescomplemented
13C22×C3×C5×D4C2213yescomplemented
14C22×C3×C5×D4C2216yescomplemented
15C22×C3×C5×D4C2213yescomplemented
16C3×C5×#127C2211yescharacteristic, complemented
17C3×C5×#127C2213yescomplemented
18C3×C5×#126C2212yescomplemented
19C3×C5×#126C2216yescomplemented
20C3×C5×#124C2213yescomplemented
21C3×C5×#124C2213yescomplemented
22C3×C5×#124C2216yescomplemented
23C3×C5×#123C2213yescomplemented
24C3×C5×#123C2213yescomplemented
25C3×C5×#123C2216yescomplemented
26C3×C5×#123C2216yescomplemented
27C3×C5×C22⋊Q8C2216yescomplemented
28C3×C5×#121C2216yescomplemented
29C3×C5×#121C2216yescomplemented
30C3×C5×#121C2216yescomplemented
31C3×C5×#121C2216yescomplemented
32C3×C5×#121C2216yescomplemented
33C3×C5×#120C2213yes—
34C3×C5×#120C2216yescomplemented
35C3×C5×#120C2216yescomplemented
36C3×C5×#120C2213yescomplemented
37C3×C5×#120C2213yescomplemented
38C3×C5×#120C2213yescomplemented
39C3×C5×#120C2216yescomplemented
40C3×C5×#120C2211yescharacteristic, complemented
41C3×C5×#120C2213yescomplemented
42C3×C4×C5×D4C2216yescomplemented
43C3×C4×C5×D4C2216yescomplemented
44C3×C5×#117C2213yescomplemented
45C2×C3×C5×C22⋊C4C2213yescomplemented
46C2×C3×C5×C22⋊C4C2216yescomplemented
47C2×C3×C5×C22⋊C4C2213yescomplemented
48C3×#3532C511yesmaximal, characteristic, direct product factor, Hall
49C5×H(3,𝔽4)C2×C311yescharacteristic, complemented
50C5×#560C2×C313yescomplemented
51C5×#551C2×C313yescomplemented
52C5×#546C2×C316yescomplemented
53C5×D42C2×C313yescomplemented
54C5×#538C2×C316yescomplemented
55C5×#535C2×C313yescomplemented
56C5×#534C2×C313yescomplemented
57C2×C5×#120C2×C313yescomplemented
58C24×C3×C5—46no—
59C24×C3×C5C2313yes—
60C24×C3×C5C2313yes—
61C24×C3×C5C2313yes—
62C24×C3×C5C2311yescharacteristic
63C24×C3×C5C2311yescharacteristic, complemented
64C3×C5×#41—46no—
65C2×C3×C5×Q8C2313yescomplemented
66C2×C3×C5×D4—46no—
67C2×C3×C5×D4—412no—
68C2×C3×C5×D4—46no—
69C2×C3×C5×D4C2316yes—
70C2×C3×C5×D4C2316yes—
71C2×C3×C5×D4C2313yes—
72C2×C3×C5×D4C2313yes—
73C2×C3×C5×D4C2316yes—
74C2×C3×C5×D4C2313yes—
75C2×C3×C5×D4C2316yes—
76C2×C3×C5×D4C2313yes—
77C2×C3×C5×D4C2313yescomplemented
78C2×C3×C5×D4C2316yescomplemented
79C22×C3×C4×C5C2313yes—
80C22×C3×C4×C5C2316yes—
81C22×C3×C4×C5C2316yescomplemented
82C22×C3×C4×C5C2313yescomplemented
83C3×C5×C4⋊C4C2316yescomplemented
84C3×C5×C4⋊C4C2316yescomplemented
85C3×C5×C4⋊C4C2316yescomplemented
86C3×C5×C22⋊C4C2316yes—
87C3×C5×C22⋊C4C2316yes—
88C3×C5×C22⋊C4C2313yes—
89C3×C5×C22⋊C4C2316yes—
90C3×C5×C22⋊C4C2316yes—
91C3×C5×C22⋊C4C2316yes—
92C3×C5×C22⋊C4C2313yes—
93C3×C5×C22⋊C4C2313yescomplemented
94C3×C5×C22⋊C4C2313yescomplemented
95C3×C5×C22⋊C4C2316yescomplemented
96C3×C5×C22⋊C4C2316yescomplemented
97C3×C42×C5C2311yescharacteristic, complemented
98C3×C42×C5C2313yescomplemented
99C3×C42×C5C2312yescomplemented
100C3×H(3,𝔽4)C2×C511yescharacteristic, complemented
101C3×#560C2×C513yescomplemented
102C3×#551C2×C513yescomplemented
103C3×#546C2×C516yescomplemented
104C3×D42C2×C513yescomplemented
105C3×#538C2×C516yescomplemented
106C3×#535C2×C513yescomplemented
107C3×#534C2×C513yescomplemented
108C2×C3×#120C2×C513yescomplemented
109C25×C5C22×C311yescharacteristic, complemented
110C2×C5×#41C22×C313yescomplemented
111C22×C5×D4C22×C313yescomplemented
112C22×C5×D4C22×C316yescomplemented
113C22×C5×D4C22×C313yescomplemented
114C5×#127C22×C311yescharacteristic, complemented
115C5×#127C22×C313yescomplemented
116C5×#126C22×C312yescomplemented
117C5×#126C22×C316yescomplemented
118C5×#124C22×C313yescomplemented
119C5×#124C22×C313yescomplemented
120C5×#124C22×C316yescomplemented
121C5×#123C22×C313yescomplemented
122C5×#123C22×C313yescomplemented
123C5×#123C22×C316yescomplemented
124C5×#123C22×C316yescomplemented
125C5×C22⋊Q8C22×C316yescomplemented
126C5×#121C22×C316yescomplemented
127C5×#121C22×C316yescomplemented
128C5×#121C22×C316yescomplemented
129C5×#121C22×C316yescomplemented
130C5×#121C22×C316yescomplemented
131C5×#120C22×C313yes—
132C5×#120C22×C316yescomplemented
133C5×#120C22×C316yescomplemented
134C5×#120C22×C313yescomplemented
135C5×#120C22×C313yescomplemented
136C5×#120C22×C313yescomplemented
137C5×#120C22×C316yescomplemented
138C5×#120C22×C311yescharacteristic, complemented
139C5×#120C22×C313yescomplemented
140C4×C5×D4C22×C316yescomplemented
141C4×C5×D4C22×C316yescomplemented
142C5×#117C22×C313yescomplemented
143C2×C5×C22⋊C4C22×C313yescomplemented
144C2×C5×C22⋊C4C22×C316yescomplemented
145C2×C5×C22⋊C4C22×C313yescomplemented
146#3532C3×C511yescharacteristic, direct product factor, Sylow
147C23×C3×C5—212no—
148C23×C3×C5—26no—
149C23×C3×C5—26no—
150C23×C3×C5—43no—
151C23×C3×C5—46no—
152C23×C3×C5—43no—
153C23×C3×C5—46no—
154C23×C3×C5—43no—
155C23×C3×C5—416no—
156C23×C3×C5C2413yes—
157C23×C3×C5C2411yescharacteristic
158C23×C3×C5C2413yes—
159C23×C3×C5C2413yes—
160C23×C3×C5C2413yes—
161C3×C5×Q8—43no—
162C3×C5×D4—212no—
163C3×C5×D4—212no—
164C3×C5×D4—43no—
165C3×C5×D4—43no—
166C3×C5×D4—43no—
167C3×C5×D4—43no—
168C3×C5×D4—46no—
169C3×C5×D4—46no—
170C3×C5×D4—46no—
171C3×C5×D4—43no—
172C2×C3×C4×C5—26no—
173C2×C3×C4×C5—46no—
174C2×C3×C4×C5—43no—
175C2×C3×C4×C5—46no—
176C2×C3×C4×C5C2413yes—
177C2×C3×C4×C5C2416yes—
178C2×C3×C4×C5C2416yes—
179C2×C3×C4×C5C2413yes—
180C25×C3C22×C511yescharacteristic, complemented
181C2×C3×#41C22×C513yescomplemented
182C22×C3×D4C22×C513yescomplemented
183C22×C3×D4C22×C516yescomplemented
184C22×C3×D4C22×C513yescomplemented
185C3×#127C22×C513yescomplemented
186C3×#127C22×C511yescharacteristic, complemented
187C3×#126C22×C516yescomplemented
188C3×#126C22×C512yescomplemented
189C3×#124C22×C513yescomplemented
190C3×#124C22×C516yescomplemented
191C3×#124C22×C513yescomplemented
192C3×#123C22×C513yescomplemented
193C3×#123C22×C516yescomplemented
194C3×#123C22×C513yescomplemented
195C3×#123C22×C516yescomplemented
196C3×C22⋊Q8C22×C516yescomplemented
197C3×#121C22×C516yescomplemented
198C3×#121C22×C516yescomplemented
199C3×#121C22×C516yescomplemented
200C3×#121C22×C516yescomplemented
201C3×#121C22×C516yescomplemented
202C3×#120C22×C513yes—
203C3×#120C22×C513yescomplemented
204C3×#120C22×C513yescomplemented
205C3×#120C22×C516yescomplemented
206C3×#120C22×C516yescomplemented
207C3×#120C22×C513yescomplemented
208C3×#120C22×C516yescomplemented
209C3×#120C22×C513yescomplemented
210C3×#120C22×C511yescharacteristic, complemented
211C3×C4×D4C22×C516yescomplemented
212C3×C4×D4C22×C516yescomplemented
213C3×#117C22×C513yescomplemented
214C2×C3×C22⋊C4C22×C513yescomplemented
215C2×C3×C22⋊C4C22×C516yescomplemented
216C2×C3×C22⋊C4C22×C513yescomplemented
217C24×C5—46no—
218C24×C5C23×C313yes—
219C24×C5C23×C313yes—
220C24×C5C23×C313yes—
221C24×C5C23×C311yescharacteristic
222C24×C5C23×C311yescharacteristic, complemented
223C5×#41—46no—
224C2×C5×Q8C23×C313yescomplemented
225C2×C5×D4—46no—
226C2×C5×D4—412no—
227C2×C5×D4—46no—
228C2×C5×D4C23×C316yes—
229C2×C5×D4C23×C316yes—
230C2×C5×D4C23×C313yes—
231C2×C5×D4C23×C313yes—
232C2×C5×D4C23×C316yes—
233C2×C5×D4C23×C313yes—
234C2×C5×D4C23×C316yes—
235C2×C5×D4C23×C313yes—
236C2×C5×D4C23×C313yescomplemented
237C2×C5×D4C23×C316yescomplemented
238C22×C4×C5C23×C313yes—
239C22×C4×C5C23×C316yes—
240C22×C4×C5C23×C316yescomplemented
241C22×C4×C5C23×C313yescomplemented
242C5×C4⋊C4C23×C316yescomplemented
243C5×C4⋊C4C23×C316yescomplemented
244C5×C4⋊C4C23×C316yescomplemented
245C5×C22⋊C4C23×C316yes—
246C5×C22⋊C4C23×C316yes—
247C5×C22⋊C4C23×C313yes—
248C5×C22⋊C4C23×C316yes—
249C5×C22⋊C4C23×C316yes—
250C5×C22⋊C4C23×C316yes—
251C5×C22⋊C4C23×C313yes—
252C5×C22⋊C4C23×C313yescomplemented
253C5×C22⋊C4C23×C313yescomplemented
254C5×C22⋊C4C23×C316yescomplemented
255C5×C22⋊C4C23×C316yescomplemented
256C42×C5C23×C311yescharacteristic, complemented
257C42×C5C23×C313yescomplemented
258C42×C5C23×C312yescomplemented
259H(3,𝔽4)C2×C3×C511yescharacteristic, complemented
260#560C2×C3×C513yescomplemented
261#551C2×C3×C513yescomplemented
262#546C2×C3×C516yescomplemented
263D42C2×C3×C513yescomplemented
264#538C2×C3×C516yescomplemented
265#535C2×C3×C513yescomplemented
266#534C2×C3×C513yescomplemented
267C2×#120C2×C3×C513yescomplemented
268C22×C3×C5—26no—
269C22×C3×C5—26no—
270C22×C3×C5—23no—
271C22×C3×C5—26no—
272C22×C3×C5—23no—
273C22×C3×C5—23no—
274C22×C3×C5—26no—
275C22×C3×C5—23no—
276C22×C3×C5—412no—
277C22×C3×C5—412no—
278C22×C3×C5—44no—
279C22×C3×C5—86no—
280C22×C3×C5—82no—
281C22×C3×C5H(5,𝔽2)16yes—
282C22×C3×C5C2511yescharacteristic
283C3×C4×C5—23no—
284C3×C4×C5—23no—
285C3×C4×C5—26no—
286C3×C4×C5—26no—
287C24×C3—46no—
288C24×C3C23×C513yes—
289C24×C3C23×C513yes—
290C24×C3C23×C513yes—
291C24×C3C23×C511yescharacteristic
292C24×C3C23×C511yescharacteristic, complemented
293C3×#41—46no—
294C2×C3×Q8C23×C513yescomplemented
295C2×C3×D4—46no—
296C2×C3×D4—412no—
297C2×C3×D4—46no—
298C2×C3×D4C23×C516yes—
299C2×C3×D4C23×C516yes—
300C2×C3×D4C23×C513yes—
301C2×C3×D4C23×C513yes—
302C2×C3×D4C23×C516yes—
303C2×C3×D4C23×C513yes—
304C2×C3×D4C23×C516yes—
305C2×C3×D4C23×C513yes—
306C2×C3×D4C23×C513yescomplemented
307C2×C3×D4C23×C516yescomplemented
308C22×C3×C4C23×C513yes—
309C22×C3×C4C23×C516yes—
310C22×C3×C4C23×C516yescomplemented
311C22×C3×C4C23×C513yescomplemented
312C3×C4⋊C4C23×C516yescomplemented
313C3×C4⋊C4C23×C516yescomplemented
314C3×C4⋊C4C23×C516yescomplemented
315C3×C22⋊C4C23×C516yes—
316C3×C22⋊C4C23×C516yes—
317C3×C22⋊C4C23×C513yes—
318C3×C22⋊C4C23×C516yes—
319C3×C22⋊C4C23×C516yes—
320C3×C22⋊C4C23×C516yes—
321C3×C22⋊C4C23×C513yes—
322C3×C22⋊C4C23×C513yescomplemented
323C3×C22⋊C4C23×C513yescomplemented
324C3×C22⋊C4C23×C516yescomplemented
325C3×C22⋊C4C23×C516yescomplemented
326C3×C42C23×C511yescharacteristic, complemented
327C3×C42C23×C513yescomplemented
328C3×C42C23×C512yescomplemented
329C23×C5—212no—
330C23×C5—26no—
331C23×C5—26no—
332C23×C5—43no—
333C23×C5—46no—
334C23×C5—43no—
335C23×C5—46no—
336C23×C5—43no—
337C23×C5—416no—
338C23×C5C24×C313yes—
339C23×C5C24×C311yescharacteristic
340C23×C5C24×C313yes—
341C23×C5C24×C313yes—
342C23×C5C24×C313yes—
343C5×Q8—43no—
344C5×D4—212no—
345C5×D4—212no—
346C5×D4—43no—
347C5×D4—43no—
348C5×D4—43no—
349C5×D4—43no—
350C5×D4—46no—
351C5×D4—46no—
352C5×D4—46no—
353C5×D4—43no—
354C2×C4×C5—26no—
355C2×C4×C5—46no—
356C2×C4×C5—43no—
357C2×C4×C5—46no—
358C2×C4×C5C24×C313yes—
359C2×C4×C5C24×C316yes—
360C2×C4×C5C24×C316yes—
361C2×C4×C5C24×C313yes—
362C25C22×C3×C511yescharacteristic, complemented
363C2×#41C22×C3×C513yescomplemented
364C22×D4C22×C3×C513yescomplemented
365C22×D4C22×C3×C516yescomplemented
366C22×D4C22×C3×C513yescomplemented
367#127C22×C3×C511yescharacteristic, complemented
368#127C22×C3×C513yescomplemented
369#126C22×C3×C512yescomplemented
370#126C22×C3×C516yescomplemented
371#124C22×C3×C513yescomplemented
372#124C22×C3×C513yescomplemented
373#124C22×C3×C516yescomplemented
374#123C22×C3×C513yescomplemented
375#123C22×C3×C513yescomplemented
376#123C22×C3×C516yescomplemented
377#123C22×C3×C516yescomplemented
378C22⋊Q8C22×C3×C516yescomplemented
379#121C22×C3×C516yescomplemented
380#121C22×C3×C516yescomplemented
381#121C22×C3×C516yescomplemented
382#121C22×C3×C516yescomplemented
383#121C22×C3×C516yescomplemented
384#120C22×C3×C513yes—
385#120C22×C3×C516yescomplemented
386#120C22×C3×C516yescomplemented
387#120C22×C3×C513yescomplemented
388#120C22×C3×C513yescomplemented
389#120C22×C3×C513yescomplemented
390#120C22×C3×C516yescomplemented
391#120C22×C3×C511yescharacteristic, complemented
392#120C22×C3×C513yescomplemented
393C4×D4C22×C3×C516yescomplemented
394C4×D4C22×C3×C516yescomplemented
395#117C22×C3×C513yescomplemented
396C2×C22⋊C4C22×C3×C513yescomplemented
397C2×C22⋊C4C22×C3×C516yescomplemented
398C2×C22⋊C4C22×C3×C513yescomplemented
399C2×C3×C5—26no—
400C2×C3×C5—43no—
401C2×C3×C5—41no—
402C2×C3×C5—43no—
403C2×C3×C5—43no—
404C2×C3×C5C2×H(5,𝔽2)13yes—
405C23×C3—212no—
406C23×C3—26no—
407C23×C3—26no—
408C23×C3—43no—
409C23×C3—46no—
410C23×C3—43no—
411C23×C3—46no—
412C23×C3—43no—
413C23×C3—416no—
414C23×C3C24×C513yes—
415C23×C3C24×C511yescharacteristic
416C23×C3C24×C513yes—
417C23×C3C24×C513yes—
418C23×C3C24×C513yes—
419C3×Q8—43no—
420C3×D4—212no—
421C3×D4—212no—
422C3×D4—43no—
423C3×D4—43no—
424C3×D4—43no—
425C3×D4—43no—
426C3×D4—46no—
427C3×D4—46no—
428C3×D4—46no—
429C3×D4—43no—
430C2×C3×C4—26no—
431C2×C3×C4—46no—
432C2×C3×C4—43no—
433C2×C3×C4—46no—
434C2×C3×C4C24×C513yes—
435C2×C3×C4C24×C516yes—
436C2×C3×C4C24×C516yes—
437C2×C3×C4C24×C513yes—
438C22×C5—26no—
439C22×C5—26no—
440C22×C5—23no—
441C22×C5—26no—
442C22×C5—23no—
443C22×C5—23no—
444C22×C5—26no—
445C22×C5—23no—
446C22×C5—412no—
447C22×C5—412no—
448C22×C5—44no—
449C22×C5—86no—
450C22×C5—82no—
451C22×C5C3×H(5,𝔽2)16yes—
452C22×C5C25×C311yescharacteristic
453C4×C5—23no—
454C4×C5—23no—
455C4×C5—26no—
456C4×C5—26no—
457C24—46no—
458C24C23×C3×C513yes—
459C24C23×C3×C513yes—
460C24C23×C3×C513yes—
461C24C23×C3×C511yescharacteristic
462C24C23×C3×C511yescharacteristic, complemented
463#41—46no—
464C2×Q8C23×C3×C513yescomplemented
465C2×D4—46no—
466C2×D4—412no—
467C2×D4—46no—
468C2×D4C23×C3×C516yes—
469C2×D4C23×C3×C516yes—
470C2×D4C23×C3×C513yes—
471C2×D4C23×C3×C513yes—
472C2×D4C23×C3×C516yes—
473C2×D4C23×C3×C513yes—
474C2×D4C23×C3×C516yes—
475C2×D4C23×C3×C513yes—
476C2×D4C23×C3×C513yescomplemented
477C2×D4C23×C3×C516yescomplemented
478C22×C4C23×C3×C513yes—
479C22×C4C23×C3×C516yes—
480C22×C4C23×C3×C516yescomplemented
481C22×C4C23×C3×C513yescomplemented
482C4⋊C4C23×C3×C516yescomplemented
483C4⋊C4C23×C3×C516yescomplemented
484C4⋊C4C23×C3×C516yescomplemented
485C22⋊C4C23×C3×C516yes—
486C22⋊C4C23×C3×C516yes—
487C22⋊C4C23×C3×C513yes—
488C22⋊C4C23×C3×C516yes—
489C22⋊C4C23×C3×C516yes—
490C22⋊C4C23×C3×C516yes—
491C22⋊C4C23×C3×C513yes—
492C22⋊C4C23×C3×C513yescomplemented
493C22⋊C4C23×C3×C513yescomplemented
494C22⋊C4C23×C3×C516yescomplemented
495C22⋊C4C23×C3×C516yescomplemented
496C42C23×C3×C511yescharacteristic, complemented
497C42C23×C3×C513yescomplemented
498C42C23×C3×C512yescomplemented
499C3×C5#353211yescharacteristic, direct product factor, Hall
500C22×C3—26no—
501C22×C3—26no—
502C22×C3—23no—
503C22×C3—26no—
504C22×C3—23no—
505C22×C3—23no—
506C22×C3—26no—
507C22×C3—23no—
508C22×C3—412no—
509C22×C3—412no—
510C22×C3—44no—
511C22×C3—86no—
512C22×C3—82no—
513C22×C3C5×H(5,𝔽2)16yes—
514C22×C3C25×C511yescharacteristic
515C3×C4—23no—
516C3×C4—23no—
517C3×C4—26no—
518C3×C4—26no—
519C2×C5—26no—
520C2×C5—43no—
521C2×C5—41no—
522C2×C5—43no—
523C2×C5—43no—
524C2×C5C2×C3×H(5,𝔽2)13yes—
525C23—212no—
526C23—26no—
527C23—26no—
528C23—43no—
529C23—46no—
530C23—43no—
531C23—46no—
532C23—43no—
533C23—416no—
534C23C24×C3×C513yes—
535C23C24×C3×C511yescharacteristic
536C23C24×C3×C513yes—
537C23C24×C3×C513yes—
538C23C24×C3×C513yes—
539Q8—43no—
540D4—212no—
541D4—212no—
542D4—43no—
543D4—43no—
544D4—43no—
545D4—43no—
546D4—46no—
547D4—46no—
548D4—46no—
549D4—43no—
550C2×C4—26no—
551C2×C4—46no—
552C2×C4—43no—
553C2×C4—46no—
554C2×C4C24×C3×C513yes—
555C2×C4C24×C3×C516yes—
556C2×C4C24×C3×C516yes—
557C2×C4C24×C3×C513yes—
558C2×C3—26no—
559C2×C3—43no—
560C2×C3—41no—
561C2×C3—43no—
562C2×C3—43no—
563C2×C3C2×C5×H(5,𝔽2)13yes—
564C5C3×#353211yescharacteristic, direct product factor, Sylow
565C22—26no—
566C22—26no—
567C22—23no—
568C22—26no—
569C22—23no—
570C22—23no—
571C22—26no—
572C22—23no—
573C22—412no—
574C22—412no—
575C22—44no—
576C22—86no—
577C22—82no—
578C22C3×C5×H(5,𝔽2)16yes—
579C22C25×C3×C511yescharacteristic
580C4—23no—
581C4—23no—
582C4—26no—
583C4—26no—
584C3C5×#353211yescharacteristic, direct product factor, Sylow
585C2—26no—
586C2—43no—
587C2—41no—
588C2—43no—
589C2—43no—
590C2C2×C3×C5×H(5,𝔽2)13yes—
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×H(3,𝔽4)C2semidirect
2. C3×C5×#560C2semidirect
3. C3×C5×#551C2semidirect
4. C3×C5×#546C2semidirect
5. C3×C5×D42C2semidirect
6. C3×C5×#538C2semidirect
7. C3×C5×#535C2semidirect
8. C3×C5×#534C2semidirect
9. C2×C3×C5×#120C2semidirect
10. C5×#3532C3direct (N × H)
11. C25×C3×C5C22semidirect
12. C2×C3×C5×#41C22semidirect
13. C22×C3×C5×D4C22semidirect
14. C22×C3×C5×D4C22semidirect
15. C22×C3×C5×D4C22semidirect
16. C3×C5×#127C22semidirect
17. C3×C5×#127C22semidirect
18. C3×C5×#126C22semidirect
19. C3×C5×#126C22semidirect
20. C3×C5×#124C22semidirect
21. C3×C5×#124C22semidirect
22. C3×C5×#124C22semidirect
23. C3×C5×#123C22semidirect
24. C3×C5×#123C22semidirect
25. C3×C5×#123C22semidirect
26. C3×C5×#123C22semidirect
27. C3×C5×C22⋊Q8C22semidirect
28. C3×C5×#121C22semidirect
29. C3×C5×#121C22semidirect
30. C3×C5×#121C22semidirect
31. C3×C5×#121C22semidirect
32. C3×C5×#121C22semidirect
34. C3×C5×#120C22semidirect
35. C3×C5×#120C22semidirect
36. C3×C5×#120C22semidirect
37. C3×C5×#120C22semidirect
38. C3×C5×#120C22semidirect
39. C3×C5×#120C22semidirect
40. C3×C5×#120C22semidirect
41. C3×C5×#120C22semidirect
42. C3×C4×C5×D4C22semidirect
43. C3×C4×C5×D4C22semidirect
44. C3×C5×#117C22semidirect
45. C2×C3×C5×C22⋊C4C22semidirect
46. C2×C3×C5×C22⋊C4C22semidirect
47. C2×C3×C5×C22⋊C4C22semidirect
48. C3×#3532C5direct (N × H)
49. C5×H(3,𝔽4)C2×C3semidirect
50. C5×#560C2×C3semidirect
51. C5×#551C2×C3semidirect
52. C5×#546C2×C3semidirect
53. C5×D42C2×C3semidirect
54. C5×#538C2×C3semidirect
55. C5×#535C2×C3semidirect
56. C5×#534C2×C3semidirect
57. C2×C5×#120C2×C3semidirect
63. C24×C3×C5C23semidirect
65. C2×C3×C5×Q8C23semidirect
77. C2×C3×C5×D4C23semidirect
78. C2×C3×C5×D4C23semidirect
81. C22×C3×C4×C5C23semidirect
82. C22×C3×C4×C5C23semidirect
83. C3×C5×C4⋊C4C23semidirect
84. C3×C5×C4⋊C4C23semidirect
85. C3×C5×C4⋊C4C23semidirect
93. C3×C5×C22⋊C4C23semidirect
94. C3×C5×C22⋊C4C23semidirect
95. C3×C5×C22⋊C4C23semidirect
96. C3×C5×C22⋊C4C23semidirect
97. C3×C42×C5C23semidirect
98. C3×C42×C5C23semidirect
99. C3×C42×C5C23semidirect
100. C3×H(3,𝔽4)C2×C5semidirect
101. C3×#560C2×C5semidirect
102. C3×#551C2×C5semidirect
103. C3×#546C2×C5semidirect
104. C3×D42C2×C5semidirect
105. C3×#538C2×C5semidirect
106. C3×#535C2×C5semidirect
107. C3×#534C2×C5semidirect
108. C2×C3×#120C2×C5semidirect
109. C25×C5C22×C3semidirect
110. C2×C5×#41C22×C3semidirect
111. C22×C5×D4C22×C3semidirect
112. C22×C5×D4C22×C3semidirect
113. C22×C5×D4C22×C3semidirect
114. C5×#127C22×C3semidirect
115. C5×#127C22×C3semidirect
116. C5×#126C22×C3semidirect
117. C5×#126C22×C3semidirect
118. C5×#124C22×C3semidirect
119. C5×#124C22×C3semidirect
120. C5×#124C22×C3semidirect
121. C5×#123C22×C3semidirect
122. C5×#123C22×C3semidirect
123. C5×#123C22×C3semidirect
124. C5×#123C22×C3semidirect
125. C5×C22⋊Q8C22×C3semidirect
126. C5×#121C22×C3semidirect
127. C5×#121C22×C3semidirect
128. C5×#121C22×C3semidirect
129. C5×#121C22×C3semidirect
130. C5×#121C22×C3semidirect
132. C5×#120C22×C3semidirect
133. C5×#120C22×C3semidirect
134. C5×#120C22×C3semidirect
135. C5×#120C22×C3semidirect
136. C5×#120C22×C3semidirect
137. C5×#120C22×C3semidirect
138. C5×#120C22×C3semidirect
139. C5×#120C22×C3semidirect
140. C4×C5×D4C22×C3semidirect
141. C4×C5×D4C22×C3semidirect
142. C5×#117C22×C3semidirect
143. C2×C5×C22⋊C4C22×C3semidirect
144. C2×C5×C22⋊C4C22×C3semidirect
145. C2×C5×C22⋊C4C22×C3semidirect
146. #3532C3×C5direct (N × H)
180. C25×C3C22×C5semidirect
181. C2×C3×#41C22×C5semidirect
182. C22×C3×D4C22×C5semidirect
183. C22×C3×D4C22×C5semidirect
184. C22×C3×D4C22×C5semidirect
185. C3×#127C22×C5semidirect
186. C3×#127C22×C5semidirect
187. C3×#126C22×C5semidirect
188. C3×#126C22×C5semidirect
189. C3×#124C22×C5semidirect
190. C3×#124C22×C5semidirect
191. C3×#124C22×C5semidirect
192. C3×#123C22×C5semidirect
193. C3×#123C22×C5semidirect
194. C3×#123C22×C5semidirect
195. C3×#123C22×C5semidirect
196. C3×C22⋊Q8C22×C5semidirect
197. C3×#121C22×C5semidirect
198. C3×#121C22×C5semidirect
199. C3×#121C22×C5semidirect
200. C3×#121C22×C5semidirect
201. C3×#121C22×C5semidirect
203. C3×#120C22×C5semidirect
204. C3×#120C22×C5semidirect
205. C3×#120C22×C5semidirect
206. C3×#120C22×C5semidirect
207. C3×#120C22×C5semidirect
208. C3×#120C22×C5semidirect
209. C3×#120C22×C5semidirect
210. C3×#120C22×C5semidirect
211. C3×C4×D4C22×C5semidirect
212. C3×C4×D4C22×C5semidirect
213. C3×#117C22×C5semidirect
214. C2×C3×C22⋊C4C22×C5semidirect
215. C2×C3×C22⋊C4C22×C5semidirect
216. C2×C3×C22⋊C4C22×C5semidirect
222. C24×C5C23×C3semidirect
224. C2×C5×Q8C23×C3semidirect
236. C2×C5×D4C23×C3semidirect
237. C2×C5×D4C23×C3semidirect
240. C22×C4×C5C23×C3semidirect
241. C22×C4×C5C23×C3semidirect
242. C5×C4⋊C4C23×C3semidirect
243. C5×C4⋊C4C23×C3semidirect
244. C5×C4⋊C4C23×C3semidirect
252. C5×C22⋊C4C23×C3semidirect
253. C5×C22⋊C4C23×C3semidirect
254. C5×C22⋊C4C23×C3semidirect
255. C5×C22⋊C4C23×C3semidirect
256. C42×C5C23×C3semidirect
257. C42×C5C23×C3semidirect
258. C42×C5C23×C3semidirect
259. H(3,𝔽4)C2×C3×C5semidirect
260. #560C2×C3×C5semidirect
261. #551C2×C3×C5semidirect
262. #546C2×C3×C5semidirect
263. D42C2×C3×C5semidirect
264. #538C2×C3×C5semidirect
265. #535C2×C3×C5semidirect
266. #534C2×C3×C5semidirect
267. C2×#120C2×C3×C5semidirect
292. C24×C3C23×C5semidirect
294. C2×C3×Q8C23×C5semidirect
306. C2×C3×D4C23×C5semidirect
307. C2×C3×D4C23×C5semidirect
310. C22×C3×C4C23×C5semidirect
311. C22×C3×C4C23×C5semidirect
312. C3×C4⋊C4C23×C5semidirect
313. C3×C4⋊C4C23×C5semidirect
314. C3×C4⋊C4C23×C5semidirect
322. C3×C22⋊C4C23×C5semidirect
323. C3×C22⋊C4C23×C5semidirect
324. C3×C22⋊C4C23×C5semidirect
325. C3×C22⋊C4C23×C5semidirect
326. C3×C42C23×C5semidirect
327. C3×C42C23×C5semidirect
328. C3×C42C23×C5semidirect
362. C25C22×C3×C5semidirect
363. C2×#41C22×C3×C5semidirect
364. C22×D4C22×C3×C5semidirect
365. C22×D4C22×C3×C5semidirect
366. C22×D4C22×C3×C5semidirect
367. #127C22×C3×C5semidirect
368. #127C22×C3×C5semidirect
369. #126C22×C3×C5semidirect
370. #126C22×C3×C5semidirect
371. #124C22×C3×C5semidirect
372. #124C22×C3×C5semidirect
373. #124C22×C3×C5semidirect
374. #123C22×C3×C5semidirect
375. #123C22×C3×C5semidirect
376. #123C22×C3×C5semidirect
377. #123C22×C3×C5semidirect
378. C22⋊Q8C22×C3×C5semidirect
379. #121C22×C3×C5semidirect
380. #121C22×C3×C5semidirect
381. #121C22×C3×C5semidirect
382. #121C22×C3×C5semidirect
383. #121C22×C3×C5semidirect
385. #120C22×C3×C5semidirect
386. #120C22×C3×C5semidirect
387. #120C22×C3×C5semidirect
388. #120C22×C3×C5semidirect
389. #120C22×C3×C5semidirect
390. #120C22×C3×C5semidirect
391. #120C22×C3×C5semidirect
392. #120C22×C3×C5semidirect
393. C4×D4C22×C3×C5semidirect
394. C4×D4C22×C3×C5semidirect
395. #117C22×C3×C5semidirect
396. C2×C22⋊C4C22×C3×C5semidirect
397. C2×C22⋊C4C22×C3×C5semidirect
398. C2×C22⋊C4C22×C3×C5semidirect
462. C24C23×C3×C5semidirect
464. C2×Q8C23×C3×C5semidirect
476. C2×D4C23×C3×C5semidirect
477. C2×D4C23×C3×C5semidirect
480. C22×C4C23×C3×C5semidirect
481. C22×C4C23×C3×C5semidirect
482. C4⋊C4C23×C3×C5semidirect
483. C4⋊C4C23×C3×C5semidirect
484. C4⋊C4C23×C3×C5semidirect
492. C22⋊C4C23×C3×C5semidirect
493. C22⋊C4C23×C3×C5semidirect
494. C22⋊C4C23×C3×C5semidirect
495. C22⋊C4C23×C3×C5semidirect
496. C42C23×C3×C5semidirect
497. C42C23×C3×C5semidirect
498. C42C23×C3×C5semidirect
499. C3×C5#3532direct (N × H)
564. C5C3×#3532direct (N × H)
584. C3C5×#3532direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×H(3,𝔽4)2
C3×C5×#5602
C3×C5×#5512
C3×C5×#5462
C3×C5×D422
C3×C5×#5382
C3×C5×#5352
C3×C5×#5342
C2×C3×C5×#1202
C5×#35323
C3×#35325