Finite Group Databasebeta

← C5×#9945 #11932665

Subgroups — C5×#9945 #11932665

Order 1280.

574 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3095C211yesmaximal, characteristic
2C5×#2583C211yesmaximal, characteristic
3C5×#2484C211yesmaximal, characteristic
4C5×#1826C211yesmaximal, characteristic
5C5×#1511C211yesmaximal, characteristic
6C5×#1463C211yesmaximal, characteristic
7C5×#1284C211yesmaximal, characteristic
8C2×C5×C22⋊Q8C2211yescharacteristic
9C2×C5×#117C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C5×#485—22no—
12C5×#484—21no—
13C5×#483—21no—
14C5×#428—21no—
15C5×#419—21no—
16C5×#407C2211yescharacteristic
17C5×#407C2211yescharacteristic
18C5×#400—21no—
19C5×#398—21no—
20C5×#398—21no—
21C5×#395—21no—
22C5×#389—22no—
23C5×#387—22no—
24C5×#385—21no—
25C5×#385—21no—
26C5×#385—21no—
27C5×#381—21no—
28C5×#381C2211yescharacteristic
29C4×C5×C22⋊C4C2211yescharacteristic
30C5×#339—22no—
31C5×#328—22no—
32C5×#324—22no—
33#9945C511yesmaximal, characteristic, direct product factor, Sylow
34C22×C5×Q8D411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C2×C5×M16—21no—
39C2×C5×M16—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×#117—21no—
45C5×#117—21no—
46C5×#117—21no—
47C5×#117—21no—
48C2×C5×C4⋊C4—22no—
49C2×C5×C4⋊C4—22no—
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—21no—
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4D411yescharacteristic
59C2×C5×C4⋊C4D411yescharacteristic
60C2×C5×C4⋊C4D411yescharacteristic
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C42×C5—21no—
66C2×C42×C5D412yes—
67C5×#107—22no—
68C5×#106—22no—
69C5×#103—22no—
70C5×#103—22no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8D412yes—
75C5×#95—22no—
76C5×#95—22no—
77C5×#95—22no—
78C5×#95—22no—
79C5×#95—22no—
80C5×#95—21no—
81C5×#95—21no—
82C5×#95D412yes—
83#3095C2×C511yescharacteristic
84#2583C2×C511yescharacteristic
85#2484C2×C511yescharacteristic
86#1826C2×C511yescharacteristic
87#1511C2×C511yescharacteristic
88#1463C2×C511yescharacteristic
89#1284C2×C511yescharacteristic
90C24×C5C2×D411yescharacteristic
91C2×C5×Q8—21no—
92C2×C5×Q8—21no—
93C2×C5×Q8—42no—
94C22×C4×C5—22no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—22no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—42no—
107C22×C4×C5—42no—
108C22×C4×C5—42no—
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5#4111yescharacteristic
115C5×M16—42no—
116C5×M16—42no—
117C2×C5×C8—22no—
118C2×C5×C8—41no—
119C5×C4⋊C4—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—44no—
126C5×C4⋊C4—44no—
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—82no—
134C5×C22⋊C4—24no—
135C5×C22⋊C4—42no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—41no—
138C5×C22⋊C4—41no—
139C5×C22⋊C4—41no—
140C42×C5—42no—
141C42×C5—41no—
142C42×C5—41no—
143C2×C22⋊Q8C22×C511yescharacteristic
144C2×#117C22×C511yescharacteristic
145C22×C4⋊C4C22×C511yescharacteristic
146#485—22no—
147#484—21no—
148#483—21no—
149#428—21no—
150#419—21no—
151#407C22×C511yescharacteristic
152#407C22×C511yescharacteristic
153#400—21no—
154#398—21no—
155#398—21no—
156#395—21no—
157#389—22no—
158#387—22no—
159#385—21no—
160#385—21no—
161#385—21no—
162#381—21no—
163#381C22×C511yescharacteristic
164C4×C22⋊C4C22×C511yescharacteristic
165#339—22no—
166#328—22no—
167#324—22no—
168C23×C5—22no—
169C23×C5—22no—
170C23×C5—41no—
171C23×C5#12011yescharacteristic
172C23×C5#12011yescharacteristic
173C23×C5#12111yescharacteristic
174C5×Q8—42no—
175C5×Q8—81no—
176C2×C4×C5—22no—
177C2×C4×C5—22no—
178C2×C4×C5—24no—
179C2×C4×C5—22no—
180C2×C4×C5—22no—
181C2×C4×C5—22no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—42no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—42no—
192C2×C4×C5—42no—
193C2×C4×C5—42no—
194C2×C4×C5—42no—
195C2×C4×C5—42no—
196C2×C4×C5—42no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—42no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—81no—
207C2×C4×C5#12011yescharacteristic
208C2×C4×C5#12111yescharacteristic
209C2×C4×C5#12111yescharacteristic
210C2×C4×C5#12711yescharacteristic
211C5×C8—42no—
212C5×C8—81no—
213C22×Q8C5×D411yescharacteristic
214C23×C4C5×D411yescharacteristic
215C23×C4C5×D411yescharacteristic
216C23×C4C23×C511yescharacteristic
217C2×M16—21no—
218C2×M16—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223#117—21no—
224#117—21no—
225#117—21no—
226#117—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
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×D411yescharacteristic
238C2×C4⋊C4C5×D411yescharacteristic
239C2×C4⋊C4C5×D411yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42—21no—
245C2×C42C5×D412yes—
246#107—22no—
247#106—22no—
248#103—22no—
249#103—22no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8C5×D412yes—
254#95—22no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—21no—
260#95—21no—
261#95C5×D412yes—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—44no—
270C22×C5#39211yescharacteristic
271C22×C5#45612yes—
272C22×C5#45812yes—
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—44no—
278C4×C5—42no—
279C4×C5—82no—
280C4×C5—81no—
281C4×C5—81no—
282C4×C5—81no—
283C4×C5—81no—
284C4×C5—81no—
285C24C2×C5×D411yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—42no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4C2×C5×D411yescharacteristic
305C22×C4C2×C5×D411yescharacteristic
306C22×C4C2×C5×D411yescharacteristic
307C22×C4C2×C5×D411yescharacteristic
308C22×C4C2×C5×D411yescharacteristic
309C22×C4C5×#4111yescharacteristic
310M16—42no—
311M16—42no—
312C2×C8—22no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—44no—
321C4⋊C4—44no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—82no—
329C22⋊C4—24no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—42no—
336C42—41no—
337C42—41no—
338C2×C5—22no—
339C2×C5—22no—
340C2×C5—41no—
341C2×C5#200511yescharacteristic
342C2×C5#201011yescharacteristic
343C2×C5#202211yescharacteristic
344C23—22no—
345C23—22no—
346C23—41no—
347C23C5×#12011yescharacteristic
348C23C5×#12011yescharacteristic
349C23C5×#12111yescharacteristic
350Q8—42no—
351Q8—81no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4C5×#12011yescharacteristic
384C2×C4C5×#12111yescharacteristic
385C2×C4C5×#12111yescharacteristic
386C2×C4C5×#12711yescharacteristic
387C8—42no—
388C8—81no—
389C5#994511yescharacteristic, direct product factor, Sylow
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22C5×#39211yescharacteristic
399C22C5×#45612yes—
400C22C5×#45812yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—44no—
406C4—42no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C2—22no—
414C2—22no—
415C2—41no—
416C2C5×#200511yescharacteristic
417C2C5×#201011yescharacteristic
418C2C5×#202211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
33. #9945C5direct (N × H)
389. C5#9945direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30952
C5×#25832
C5×#24842
C5×#18262
C5×#15112
C5×#14632
C5×#12842
#99455