Finite Group Databasebeta

← C5×#9929 #11932649

Subgroups — C5×#9929 #11932649

Order 1280.

610 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#484C211yesmaximal, characteristic
2C5×#2627C211yesmaximal, characteristic
3C2×C5×#400C211yesmaximal, characteristic
4C5×#1824C211yesmaximal, characteristic
5C2×C5×#328C211yesmaximal, characteristic
6C2×C5×#324C211yesmaximal, characteristic
7C5×#1294C211yesmaximal, characteristic
8C2×C5×C22⋊Q8C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C5×#484—22no—
12C5×#484—22no—
13C2×C5×#107—21no—
14C2×C5×#103—21no—
15C2×C5×C22⋊C8C2211yescharacteristic
16C2×C5×C22⋊C8C2211yescharacteristic
17C5×#400—22no—
18C5×#400—21no—
19C5×#400—22no—
20C5×#398—22no—
21C5×#395—21no—
22C5×#385—21no—
23C5×#381—21no—
24C5×#380C2211yescharacteristic
25C2×C5×#95—21no—
26C2×C5×#95—21no—
27C2×C5×#95C2211yescharacteristic
28C5×#340—22no—
29C5×#328—22no—
30C5×#324—22no—
31#9929C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8D411yescharacteristic
33C23×C4×C5—21no—
34C23×C4×C5—21no—
35C23×C4×C5D411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C22×C5×C8—21no—
39C22×C5×C8—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4D411yescharacteristic
58C2×C5×C4⋊C4D412yes—
59C2×C5×C4⋊C4D412yes—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C5×#107—24no—
63C5×#103—24no—
64C5×C22⋊C8—21no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8—21no—
67C5×C22⋊C8D412yes—
68C5×#95—24no—
69C5×#95—24no—
70C5×#95—22no—
71C5×#95—22no—
72C5×#95—22no—
73C5×#95—21no—
74C5×#95—21no—
75C5×#95D412yes—
76C2×#484C2×C511yescharacteristic
77#2627C2×C511yescharacteristic
78C2×#400C2×C511yescharacteristic
79#1824C2×C511yescharacteristic
80C2×#328C2×C511yescharacteristic
81C2×#324C2×C511yescharacteristic
82#1294C2×C511yescharacteristic
83C24×C5C2×D411yescharacteristic
84C2×C5×Q8—21no—
85C2×C5×Q8—21no—
86C2×C5×Q8—42no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—22no—
95C22×C4×C5—22no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—22no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—42no—
102C22×C4×C5—42no—
103C22×C4×C5—42no—
104C22×C4×C5—42no—
105C22×C4×C5—44no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5—41no—
110C22×C4×C5Q1612yes—
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5C2×D411yescharacteristic
115C22×C4×C5C2×D411yescharacteristic
116C22×C4×C5#4111yescharacteristic
117C2×C5×C8—22no—
118C2×C5×C8—42no—
119C2×C5×C8—42no—
120C2×C5×C8—41no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—22no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—42no—
126C5×C4⋊C4—41no—
127C5×C4⋊C4—41no—
128C5×C4⋊C4—41no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4—41no—
131C5×C4⋊C4—41no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—41no—
134C5×C4⋊C4—82no—
135C5×C22⋊C4—41no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—41no—
138C5×C22⋊C4—41no—
139C2×C22⋊Q8C22×C511yescharacteristic
140C22×C4⋊C4C22×C511yescharacteristic
141C22×C4⋊C4C22×C511yescharacteristic
142#484—22no—
143#484—22no—
144C2×#107—21no—
145C2×#103—21no—
146C2×C22⋊C8C22×C511yescharacteristic
147C2×C22⋊C8C22×C511yescharacteristic
148#400—21no—
149#400—22no—
150#400—22no—
151#398—22no—
152#395—21no—
153#385—21no—
154#381—21no—
155#380C22×C511yescharacteristic
156C2×#95—21no—
157C2×#95—21no—
158C2×#95C22×C511yescharacteristic
159#340—22no—
160#328—22no—
161#324—22no—
162C23×C5—22no—
163C23×C5—22no—
164C23×C5#12011yescharacteristic
165C23×C5#12011yescharacteristic
166C23×C5#12111yescharacteristic
167C23×C5C2×Q1611yescharacteristic
168C23×C5#13511yescharacteristic
169C23×C5#13711yescharacteristic
170C23×C5#13711yescharacteristic
171C5×Q8—42no—
172C5×Q8—81no—
173C2×C4×C5—22no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—22no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—42no—
187C2×C4×C5—42no—
188C2×C4×C5—44no—
189C2×C4×C5—42no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—42no—
193C2×C4×C5—41no—
194C2×C4×C5—42no—
195C2×C4×C5—42no—
196C2×C4×C5—42no—
197C2×C4×C5—42no—
198C2×C4×C5—42no—
199C2×C4×C5—42no—
200C2×C4×C5—42no—
201C2×C4×C5—82no—
202C2×C4×C5—82no—
203C2×C4×C5—82no—
204C2×C4×C5—82no—
205C2×C4×C5—81no—
206C2×C4×C5#12011yescharacteristic
207C2×C4×C5#12111yescharacteristic
208C2×C4×C5#12111yescharacteristic
209C2×C4×C5#12711yescharacteristic
210C5×C8—42no—
211C5×C8—81no—
212C22×Q8C5×D411yescharacteristic
213C23×C4—21no—
214C23×C4—21no—
215C23×C4C5×D411yescharacteristic
216C23×C4C5×D411yescharacteristic
217C23×C4C23×C511yescharacteristic
218C22×C8—21no—
219C22×C8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4C5×D412yes—
238C2×C4⋊C4C5×D411yescharacteristic
239C2×C4⋊C4C5×D412yes—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242#107—24no—
243#103—24no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8C5×D412yes—
248#95—24no—
249#95—24no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95—21no—
254#95—21no—
255#95C5×D412yes—
256C22×C5—22no—
257C22×C5—22no—
258C22×C5—22no—
259C22×C5—22no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5#39211yescharacteristic
265C22×C5#45111yescharacteristic
266C22×C5#45111yescharacteristic
267C22×C5#45211yescharacteristic
268C22×C5#45211yescharacteristic
269C22×C5#45412yes—
270C22×C5#45812yes—
271C22×C5#46711yescharacteristic
272C22×C5#47011yescharacteristic
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—42no—
278C4×C5—82no—
279C4×C5—82no—
280C4×C5—81no—
281C4×C5—82no—
282C4×C5—81no—
283C4×C5—81no—
284C24C2×C5×D411yescharacteristic
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—42no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—44no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C5×Q1612yes—
312C22×C4C2×C5×D411yescharacteristic
313C22×C4C2×C5×D411yescharacteristic
314C22×C4C2×C5×D411yescharacteristic
315C22×C4C2×C5×D411yescharacteristic
316C22×C4C2×C5×D411yescharacteristic
317C22×C4C5×#4111yescharacteristic
318C2×C8—22no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—41no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—82no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5—21no—
343C2×C5—21no—
344C2×C5#161512yes—
345C2×C5#161712yes—
346C2×C5#200111yescharacteristic
347C2×C5#200311yescharacteristic
348C2×C5#202211yescharacteristic
349C23—22no—
350C23—22no—
351C23C5×#12011yescharacteristic
352C23C5×#12011yescharacteristic
353C23C5×#12111yescharacteristic
354C23C2×C5×Q1611yescharacteristic
355C23C5×#13511yescharacteristic
356C23C5×#13711yescharacteristic
357C23C5×#13711yescharacteristic
358Q8—42no—
359Q8—81no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4C5×#12011yescharacteristic
394C2×C4C5×#12111yescharacteristic
395C2×C4C5×#12111yescharacteristic
396C2×C4C5×#12711yescharacteristic
397C8—42no—
398C8—81no—
399C5#992911yescharacteristic, direct product factor, Sylow
400C22—21no—
401C22—21no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22C5×#39211yescharacteristic
409C22C5×#45111yescharacteristic
410C22C5×#45111yescharacteristic
411C22C5×#45211yescharacteristic
412C22C5×#45211yescharacteristic
413C22C5×#45412yes—
414C22C5×#45812yes—
415C22C5×#46711yescharacteristic
416C22C5×#47011yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—82no—
423C4—81no—
424C4—81no—
425C4—82no—
426C4—82no—
427C4—81no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2C5×#161512yes—
433C2C5×#161712yes—
434C2C5×#200111yescharacteristic
435C2C5×#200311yescharacteristic
436C2C5×#202211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
31. #9929C5direct (N × H)
399. C5#9929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4842
C5×#26272
C2×C5×#4002
C5×#18242
C2×C5×#3282
C2×C5×#3242
C5×#12942
#99295