Finite Group Databasebeta

← C5×#75492 #14330997

Subgroups — C5×#75492 #14330997

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#878C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic
3C5×#4978C211yesmaximal, characteristic, complemented
4C5×#4972C211yesmaximal, characteristic, complemented
5C5×#4951C211yesmaximal, characteristic
6C5×#4945C211yesmaximal, characteristic
7C5×#4945C211yesmaximal, characteristic
8C5×#4943C211yesmaximal, characteristic
9C5×#4942C211yesmaximal, characteristic
10C5×#4933C211yesmaximal, characteristic, complemented
11C5×#4929C211yesmaximal, characteristic, complemented
12C5×#4653C211yesmaximal, characteristic, complemented
13C5×#4652C211yesmaximal, characteristic, complemented
14C5×#4647C211yesmaximal, characteristic, complemented
15C5×#4646C211yesmaximal, characteristic, complemented
16C5×#2378—31nomaximal, Hall
17C23×C5×Dic3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C4×C5×Dic3C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C5×#878C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53#75492C511yesmaximal, characteristic, direct product factor, Hall
54C2×C5×C22⋊Q8—31no—
55C5×#391—31no—
56C5×#391—31no—
57C5×#389—31no—
58C5×#389—31no—
59C5×#388—31no—
60C5×#388—31no—
61C5×#388—31no—
62C5×#388D311yescharacteristic
63C5×#387—31no—
64C5×#387—31no—
65C5×#387—31no—
66C5×#387—31no—
67C5×#381—31no—
68C5×#380—31no—
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C5×Dic3—41no—
77C22×C5×Dic3—41no—
78C22×C5×Dic3C2×C414yes—
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C2×C5×Dic6—41no—
88C2×C5×Dic6—41no—
89C2×C5×Dic6C2×C414yes—
90C3×C5×C4⋊C4—41no—
91C3×C5×C22⋊C4—41no—
92C3×C5×C22⋊C4—41no—
93C3×C5×C22⋊C4C2×C414yes—
94C3×C42×C5—41no—
95C5×#217—41no—
96C5×#217—41no—
97C5×#217C2×C414yes—
98C5×C4⋊Dic3—41no—
99C5×C4⋊Dic3C2×C414yes—
100C5×Dic3⋊C4—41no—
101C5×Dic3⋊C4—41no—
102C5×Dic3⋊C4—41no—
103C5×Dic3⋊C4—41no—
104C5×Dic3⋊C4C2×C414yes—
105C5×Dic3⋊C4C2×C414yes—
106C4×C5×Dic3—41no—
107C4×C5×Dic3—41no—
108C4×C5×Dic3—41no—
109C2×#878C2×C511yescharacteristic
110C3×#388C2×C511yescharacteristic
111#4978C2×C511yescharacteristic, complemented
112#4972C2×C511yescharacteristic, complemented
113#4951C2×C511yescharacteristic
114#4945C2×C511yescharacteristic
115#4945C2×C511yescharacteristic
116#4943C2×C511yescharacteristic
117#4942C2×C511yescharacteristic
118#4933C2×C511yescharacteristic, complemented
119#4929C2×C511yescharacteristic, complemented
120#4653C2×C511yescharacteristic, complemented
121#4652C2×C511yescharacteristic, complemented
122#4647C2×C511yescharacteristic, complemented
123#4646C2×C511yescharacteristic, complemented
124C22×C5×Q8—31no—
125C23×C4×C5—31no—
126C5×C22⋊Q8—38no—
127C2×C5×C4⋊C4—31no—
128C2×C5×C4⋊C4—31no—
129C2×C5×C4⋊C4—31no—
130C2×C5×C4⋊C4—31no—
131C2×C5×C4⋊C4—31no—
132C2×C5×C4⋊C4—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4C2×D311yescharacteristic
136C2×C5×C22⋊C4—31no—
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4—31no—
139C2×C5×C22⋊C4C2×D311yescharacteristic
140C2×C5×C22⋊C4C2×D311yescharacteristic
141C2×C5×C22⋊C4C2×D311yescharacteristic
142C2×C42×C5—31no—
143C2×C42×C5—31no—
144C2×C42×C5—31no—
145C2×C42×C5C2×D311yescharacteristic
146C5×#95—31no—
147C5×#95—31no—
148C5×#95—31no—
149C5×#95—31no—
150C5×#95—31no—
151C5×#95—31no—
152C5×#95—31no—
153C5×#95—31no—
154C5×#95—31no—
155C5×#95—31no—
156C5×#95—31no—
157C5×#95—31no—
158C5×#95C2×D311yescharacteristic
159C5×#95C2×D311yescharacteristic
160#2378—31noSylow
161C23×C3×C5—21no—
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5—21no—
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5C22×C412yes—
168C23×C3×C5C2411yescharacteristic
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C22×C412yes—
186C2×C3×C4×C5C22×C412yes—
187C2×C5×Dic3—21no—
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—44no—
208C2×C5×Dic3C22×C412yes—
209C2×C5×Dic3C22×C412yes—
210C2×C5×Dic3C22×C412yes—
211C2×C5×Dic3C22×C412yes—
212C5×Dic6—44no—
213C23×Dic3C22×C511yescharacteristic
214C22×Dic6C22×C511yescharacteristic
215C2×C3×C4⋊C4C22×C511yescharacteristic
216C2×C3×C22⋊C4C22×C511yescharacteristic
217C2×C3×C22⋊C4C22×C511yescharacteristic
218C2×C3×C22⋊C4C22×C511yescharacteristic
219C2×C3×C42C22×C511yescharacteristic
220C2×#217C22×C511yescharacteristic
221C2×#217C22×C511yescharacteristic
222C2×#217C22×C511yescharacteristic
223C2×C4⋊Dic3C22×C511yescharacteristic
224C2×C4⋊Dic3C22×C511yescharacteristic
225C2×Dic3⋊C4C22×C511yescharacteristic
226C2×Dic3⋊C4C22×C511yescharacteristic
227C2×Dic3⋊C4C22×C511yescharacteristic
228C2×Dic3⋊C4C22×C511yescharacteristic
229C2×Dic3⋊C4C22×C511yescharacteristic
230C2×Dic3⋊C4C22×C511yescharacteristic
231C2×C4×Dic3C22×C511yescharacteristic
232C2×C4×Dic3C22×C511yescharacteristic
233C2×C4×Dic3C22×C511yescharacteristic
234#878C4×C518yescomplemented
235C3×#95C22×C511yescharacteristic
236C3×#95C22×C511yescharacteristic
237C3⋊#95C22×C511yescharacteristic
238C3⋊#95C22×C511yescharacteristic
239C3⋊#95C22×C511yescharacteristic
240C3⋊#95C22×C511yescharacteristic
241C3⋊#95C22×C511yescharacteristic
242C3⋊#95C22×C511yescharacteristic
243C3⋊#95C22×C511yescharacteristic
244C3⋊#95C22×C511yescharacteristic
245C3⋊#95C22×C511yescharacteristic
246C3⋊#95C22×C511yescharacteristic
247C3⋊#95C22×C511yescharacteristic
248C3⋊#95C22×C511yescharacteristic
249C24×C5C22×D311yescharacteristic
250C2×C5×Q8—34no—
251C2×C5×Q8—121no—
252C2×C5×Q8—121no—
253C22×C4×C5—31no—
254C22×C4×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—31no—
257C22×C4×C5—34no—
258C22×C4×C5—31no—
259C22×C4×C5—31no—
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—121no—
263C22×C4×C5—121no—
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×C4×C5C22×D311yescharacteristic
267C22×C4×C5C22×D311yescharacteristic
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C5×C4⋊C4—34no—
271C5×C4⋊C4—34no—
272C5×C4⋊C4—34no—
273C5×C4⋊C4—41no—
274C5×C4⋊C4—121no—
275C5×C4⋊C4—121no—
276C5×C4⋊C4—121no—
277C5×C4⋊C4—121no—
278C5×C4⋊C4—121no—
279C5×C22⋊C4—34no—
280C5×C22⋊C4—41no—
281C5×C22⋊C4—41no—
282C5×C22⋊C4—121no—
283C5×C22⋊C4—121no—
284C5×C22⋊C4C4×D314yes—
285C42×C5—41no—
286C42×C5—121no—
287C42×C5—121no—
288C42×C5—121no—
289C2×C22⋊Q8—31no—
290#391—31no—
291#391—31no—
292#389—31no—
293#389—31no—
294#388—31no—
295#388—31no—
296#388—31no—
297#388C5×D311yescharacteristic
298#387—31no—
299#387—31no—
300#387—31no—
301#387—31no—
302#381—31no—
303#380—31no—
304C22×C3×C5—22no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5—41no—
308C22×C3×C5—41no—
309C22×C3×C5—41no—
310C22×C3×C5—41no—
311C22×C3×C5C23×C411yescharacteristic
312C22×C3×C5H(5,𝔽2)11yescharacteristic
313C22×C3×C5H(5,𝔽2)11yescharacteristic
314C22×C3×C5H(5,𝔽2)11yescharacteristic
315C22×C3×C52−1+411yescharacteristic
316C22×C3×C52−1+411yescharacteristic
317C22×C3×C52−1+411yescharacteristic
318C3×C4×C5—22no—
319C3×C4×C5—22no—
320C3×C4×C5—41no—
321C3×C4×C5—41no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C5×Dic3—22no—
325C5×Dic3—22no—
326C5×Dic3—22no—
327C5×Dic3—22no—
328C5×Dic3—41no—
329C5×Dic3—41no—
330C5×Dic3—41no—
331C5×Dic3—41no—
332C24×C3C23×C511yescharacteristic
333C22×C3×C4C23×C511yescharacteristic
334C22×C3×C4C23×C511yescharacteristic
335C22×C3×C4C23×C511yescharacteristic
336C22×C3×C4C23×C511yescharacteristic
337C22×C3×C4C23×C511yescharacteristic
338C22×C3×C4C23×C511yescharacteristic
339C22×Dic3—41no—
340C22×Dic3—41no—
341C22×Dic3C2×C4×C514yes—
342C22×Dic3C23×C511yescharacteristic
343C22×Dic3C23×C511yescharacteristic
344C22×Dic3C23×C511yescharacteristic
345C22×Dic3C23×C511yescharacteristic
346C22×Dic3C23×C511yescharacteristic
347C22×Dic3C23×C511yescharacteristic
348C22×Dic3C23×C511yescharacteristic
349C22×Dic3C23×C511yescharacteristic
350C2×Dic6—41no—
351C2×Dic6—41no—
352C2×Dic6C2×C4×C514yes—
353C3×C4⋊C4—41no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4C2×C4×C514yes—
357C3×C42—41no—
358#217—41no—
359#217—41no—
360#217C2×C4×C514yes—
361C4⋊Dic3—41no—
362C4⋊Dic3C2×C4×C514yes—
363Dic3⋊C4—41no—
364Dic3⋊C4—41no—
365Dic3⋊C4—41no—
366Dic3⋊C4—41no—
367Dic3⋊C4C2×C4×C514yes—
368Dic3⋊C4C2×C4×C514yes—
369C4×Dic3—41no—
370C4×Dic3—41no—
371C4×Dic3—41no—
372C23×C5—21no—
373C23×C5—21no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—21no—
377C23×C5—21no—
378C23×C5C2×C4×D312yes—
379C23×C5C23×D311yescharacteristic
380C5×Q8—124no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—32no—
398C2×C4×C5—32no—
399C2×C4×C5—32no—
400C2×C4×C5—32no—
401C2×C4×C5—61no—
402C2×C4×C5—61no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—61no—
416C2×C4×C5—61no—
417C2×C4×C5—61no—
418C2×C4×C5—61no—
419C2×C4×C5—61no—
420C2×C4×C5—61no—
421C2×C4×C5—124no—
422C2×C4×C5C2×C4×D312yes—
423C2×C4×C5C2×C4×D312yes—
424C22×Q8—31no—
425C23×C4—31no—
426C22⋊Q8—38no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4C2×C5×D311yescharacteristic
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4C2×C5×D311yescharacteristic
440C2×C22⋊C4C2×C5×D311yescharacteristic
441C2×C22⋊C4C2×C5×D311yescharacteristic
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—31no—
445C2×C42C2×C5×D311yescharacteristic
446#95—31no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95C2×C5×D311yescharacteristic
459#95C2×C5×D311yescharacteristic
460C2×C3×C5—42no—
461C2×C3×C5#51811yescharacteristic
462C2×C3×C5#51911yescharacteristic
463C2×C3×C5#52011yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56211yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C2×C3×C5#56311yescharacteristic
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3C22×C4×C512yes—
475C23×C3C24×C511yescharacteristic
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4C22×C4×C512yes—
493C2×C3×C4C22×C4×C512yes—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—44no—
515C2×Dic3C22×C4×C512yes—
516C2×Dic3C22×C4×C512yes—
517C2×Dic3C22×C4×C512yes—
518C2×Dic3C22×C4×C512yes—
519Dic6—44no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5C22×C4×D311yescharacteristic
528C22×C5#100411yescharacteristic
529C22×C5#100411yescharacteristic
530C22×C5#100911yescharacteristic
531C22×C5#101011yescharacteristic
532C22×C5#101011yescharacteristic
533C22×C5#101011yescharacteristic
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—41no—
537C4×C5—41no—
538C4×C5—41no—
539C4×C5—41no—
540C4×C5—62no—
541C4×C5—62no—
542C4×C5—62no—
543C4×C5—62no—
544C4×C5—121no—
545C4×C5—121no—
546C4×C5—121no—
547C4×C5—121no—
548C24C22×C5×D311yescharacteristic
549C2×Q8—34no—
550C2×Q8—121no—
551C2×Q8—121no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—34no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—121no—
562C22×C4—121no—
563C22×C4C22×C5×D311yescharacteristic
564C22×C4C22×C5×D311yescharacteristic
565C22×C4C22×C5×D311yescharacteristic
566C22×C4C22×C5×D311yescharacteristic
567C22×C4C22×C5×D311yescharacteristic
568C22×C4C22×C5×D311yescharacteristic
569C4⋊C4—34no—
570C4⋊C4—34no—
571C4⋊C4—34no—
572C4⋊C4—41no—
573C4⋊C4—121no—
574C4⋊C4—121no—
575C4⋊C4—121no—
576C4⋊C4—121no—
577C4⋊C4—121no—
578C22⋊C4—34no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—121no—
582C22⋊C4—121no—
583C22⋊C4C4×C5×D314yes—
584C42—41no—
585C42—121no—
586C42—121no—
587C42—121no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3C23×C4×C511yescharacteristic
597C22×C3C5×H(5,𝔽2)11yescharacteristic
598C22×C3C5×H(5,𝔽2)11yescharacteristic
599C22×C3C5×H(5,𝔽2)11yescharacteristic
600C22×C3C5×2−1+411yescharacteristic
601C22×C3C5×2−1+411yescharacteristic
602C22×C3C5×2−1+411yescharacteristic
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609Dic3—22no—
610Dic3—22no—
611Dic3—22no—
612Dic3—22no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617C2×C5—42no—
618C2×C5#551611yescharacteristic
619C2×C5#554511yescharacteristic
620C2×C5#554611yescharacteristic
621C2×C5#562111yescharacteristic
622C2×C5#565111yescharacteristic
623C2×C5#568411yescharacteristic
624C2×C5#571211yescharacteristic
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23C2×C4×C5×D312yes—
632C23C23×C5×D311yescharacteristic
633Q8—124no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—32no—
651C2×C4—32no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—124no—
675C2×C4C2×C4×C5×D312yes—
676C2×C4C2×C4×C5×D312yes—
677C2×C3—42no—
678C2×C3C5×#51811yescharacteristic
679C2×C3C5×#51911yescharacteristic
680C2×C3C5×#52011yescharacteristic
681C2×C3C5×#56211yescharacteristic
682C2×C3C5×#56211yescharacteristic
683C2×C3C5×#56311yescharacteristic
684C2×C3C5×#56311yescharacteristic
685C5#7549211yescharacteristic, direct product factor, Sylow
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22C22×C4×C5×D311yescharacteristic
694C22C5×#100411yescharacteristic
695C22C5×#100411yescharacteristic
696C22C5×#100911yescharacteristic
697C22C5×#101011yescharacteristic
698C22C5×#101011yescharacteristic
699C22C5×#101011yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—62no—
707C4—62no—
708C4—62no—
709C4—62no—
710C4—121no—
711C4—121no—
712C4—121no—
713C4—121no—
714C3C5×#237811yescharacteristic, complemented, Sylow
715C2—42no—
716C2C5×#551611yescharacteristic
717C2C5×#554511yescharacteristic
718C2C5×#554611yescharacteristic
719C2C5×#562111yescharacteristic
720C2C5×#565111yescharacteristic
721C2C5×#568411yescharacteristic
722C2C5×#571211yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC5×#388D3
hypocenterC3C5×#2378
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#388

Complements

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

NH ≅ G/Ntype
3. C5×#4978C2semidirect
4. C5×#4972C2semidirect
10. C5×#4933C2semidirect
11. C5×#4929C2semidirect
12. C5×#4653C2semidirect
13. C5×#4652C2semidirect
14. C5×#4647C2semidirect
15. C5×#4646C2semidirect
38. C5×#878C4semidirect
53. #75492C5direct (N × H)
111. #4978C2×C5semidirect
112. #4972C2×C5semidirect
118. #4933C2×C5semidirect
119. #4929C2×C5semidirect
120. #4653C2×C5semidirect
121. #4652C2×C5semidirect
122. #4647C2×C5semidirect
123. #4646C2×C5semidirect
234. #878C4×C5semidirect
588. C3×C5#2378semidirect
685. C5#75492direct (N × H)
714. C3C5×#2378semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8782
C3×C5×#3882
C5×#49782
C5×#49722
C5×#49512
C5×#49452
C5×#49432
C5×#49422
C5×#49332
C5×#49292
C5×#46532
C5×#46522
C5×#46472
C5×#46462
C5×#23783
#754925