Finite Group Databasebeta

← #14284048

Subgroups — #14284048

Order 1920.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C3×D5×#124C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic, complemented
3C4×#6758C211yesmaximal, characteristic, complemented
4#11746798C212yesmaximal, complemented
5#11746792C212yesmaximal, complemented
6#10604542—31nomaximal, Hall
7C2×C3×Q8×D5C411yescharacteristic
8C2×C3×D4×D5C411yescharacteristic
9C2×#6758—21no—
10C3×C5×#124C411yescharacteristic
11C3×#4093C2211yescharacteristic
12C3×#4082C2211yescharacteristic
13C3×#4031—21no—
14C3×#4031—21no—
15C3×D5×C22⋊C4—21no—
16C3×D5×C22⋊C4—21no—
17C3×#4021C411yescharacteristic
18C3×C42×D5C2211yescharacteristic
19#91233—21no—
20#91232—21no—
21#91231C2212yescomplemented
22#91231C2212yescomplemented
23C4×C3⋊#170—21no—
24#71718—51nomaximal, Hall
25D5×#124D311yescharacteristic
26#65684—31no—
27C4×#700—31no—
28#64927—32no—
29#64921—32no—
30C23×C3×D5—21no—
31C2×C3×C5×Q8C2×C411yescharacteristic
32C2×C3×C5×D4C2×C411yescharacteristic
33C2×C3×C22⋊D5—21no—
34C3×Q8×D5—42no—
35C3×D4×D5—42no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×Dic10—21no—
42C2×C3×Dic10C2×C411yescharacteristic
43C2×C3⋊#170—22no—
44C2×C3⋊#170—22no—
45#6758—24no—
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5C2×C411yescharacteristic
49C3×C22⋊Dic5—21no—
50C3×C22⋊Dic5—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57C3×C4×Dic5C2311yescharacteristic
58C2×C3×#124—51no—
59#4926—51no—
60C4×#208—51no—
61#4540—52no—
62#4540—52no—
63C2×Q8×D5Dic311yescharacteristic
64C2×D4×D5Dic311yescharacteristic
65C2×#700—61no—
66C5×#124Dic311yescharacteristic
67#4093C2×D311yescharacteristic
68#4082C2×D311yescharacteristic
69#4031—21no—
70#4031—21no—
71D5×C22⋊C4—21no—
72D5×C22⋊C4—21no—
73#4021Dic311yescharacteristic
74C42×D5C2×D311yescharacteristic
75#4004—61no—
76#4003—61no—
77#4002—32no—
78#4002—32no—
79C4×#170—61no—
80#1527—151noSylow
81C23×C3×C5—21no—
82C22×C3×D5—21no—
83C22×C3×D5—42no—
84C22×C3×D5—42no—
85C22×C3×D5—42no—
86C22×C3×D5C22⋊C411yescharacteristic
87C3×C5×Q8—41no—
88C3×C5×D4—41no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C3×C22⋊D5—42no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C2×D411yescharacteristic
97C2×C3×Dic5C2×D411yescharacteristic
98C3×D20—41no—
99C3×C4×D5—22no—
100C3×C4×D5—22no—
101C3×C4×D5—41no—
102C3×C4×D5—42no—
103C3×Dic10—42no—
104C3×Dic10—41no—
105C3⋊#170—24no—
106C3⋊#170—42no—
107C22×C3×Q8—51no—
108C22×C3×D4—51no—
109C3×#124—51no—
110C3×#124—51no—
111C3×#124—51no—
112C3×#124—101no—
113C3×#124—101no—
114C3×#124AGL(1,𝔽5)11yescharacteristic
115C2×C3×C22⋊C4—101no—
116C2×C3×C22⋊C4—101no—
117C2×C3×C42—51no—
118C2×#208—101no—
119#830—101no—
120C4⋊(C3⋊C8)—101no—
121#803—52no—
122#803—52no—
123C4×C3⋊C8—101no—
124C23×D5—21no—
125C2×C5×Q8C2×Dic311yescharacteristic
126C2×C5×D4C2×Dic311yescharacteristic
127C2×C22⋊D5—21no—
128Q8×D5—42no—
129D4×D5—42no—
130C2×D20C2×Dic311yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5C2×Dic311yescharacteristic
133C2×C4×D5#6711yescharacteristic
134C2×C4×D5#6711yescharacteristic
135C2×Dic10—21no—
136C2×Dic10C2×Dic311yescharacteristic
137C2×#170—62no—
138C2×#170—62no—
139#700—64no—
140C5×C22⋊C4—21no—
141C5×C22⋊C4—21no—
142C42×C5C2×Dic311yescharacteristic
143C22⋊Dic5—21no—
144C22⋊Dic5—21no—
145#685—21no—
146#685—21no—
147#685—21no—
148#685—21no—
149C4×Dic5#6711yescharacteristic
150C4×Dic5#6711yescharacteristic
151C4×Dic5C22×D311yescharacteristic
152C2×#124—51no—
153#432—151no—
154C4×M16—151no—
155#329—152no—
156#329—152no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5C2×C22⋊C411yescharacteristic
161C2×C3×D5—21no—
162C2×C3×D5—21no—
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C2×C3×D5—84no—
167C2×C3×D5#10412yes—
168C3×C4×C5—21no—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×Dic5—21no—
173C3×Dic5—21no—
174C3×Dic5—41no—
175C3×Dic5#10012yes—
176C24×C3—101no—
177C2×C3×Q8—51no—
178C2×C3×Q8—101no—
179C2×C3×Q8—202no—
180C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
181C2×C3×D4—51no—
182C2×C3×D4—101no—
183C2×C3×D4—202no—
184C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
185C22×C3×C4—51no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4—101no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—101no—
192C3×C22⋊C4—101no—
193C3×C22⋊C4—101no—
194C3×C22⋊C4—101no—
195C3×C22⋊C4—101no—
196C3×C22⋊C4—101no—
197C3×C42—51no—
198C3×C42—51no—
199C3×C42—51no—
200C3×C42C2×AGL(1,𝔽5)11yescharacteristic
201#208—104no—
202C2×C3⋊C8—102no—
203C2×C3⋊C8—102no—
204C23×C5—21no—
205C22×D5—21no—
206C22×D5—42no—
207C22×D5—42no—
208C22×D5—42no—
209C22×D5#21711yescharacteristic
210C5×Q8—41no—
211C5×D4—41no—
212C2×C4×C5—21no—
213C2×C4×C5#21711yescharacteristic
214C2×C4×C5#21711yescharacteristic
215C2×C4×C5C22×Dic311yescharacteristic
216C22⋊D5—42no—
217C2×Dic5—21no—
218C2×Dic5#21711yescharacteristic
219C2×Dic5C2×#6711yescharacteristic
220C2×Dic5C2×#6711yescharacteristic
221D20—41no—
222C4×D5—22no—
223C4×D5—22no—
224C4×D5—41no—
225C4×D5—42no—
226Dic10—42no—
227Dic10—41no—
228#170—64no—
229#170—122no—
230C22×Q8—51no—
231C22×D4—51no—
232C2×M16—301no—
233#124—51no—
234#124—51no—
235#124—51no—
236#124—101no—
237#124—101no—
238#124ΓL(1,𝔽16)11yescharacteristic
239C2×C22⋊C4—101no—
240C2×C22⋊C4—101no—
241C2×C42—51no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244#97—152no—
245#97—152no—
246C4×C8—301no—
247C2×C3×C5—81no—
248C2×C3×C5C2×#10011yescharacteristic
249C2×C3×C5C2×#10411yescharacteristic
250C2×C3×C5#42111yescharacteristic
251C3×D5—22no—
252C3×D5—81no—
253C23×C3—21no—
254C23×C3—51no—
255C23×C3—101no—
256C23×C3—202no—
257C23×C3—202no—
258C23×C3—202no—
259C3×Q8—41no—
260C3×Q8—201no—
261C3×Q8—202no—
262C3×D4—41no—
263C3×D4—201no—
264C3×D4—202no—
265C2×C3×C4—21no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—51no—
269C2×C3×C4—102no—
270C2×C3×C4—102no—
271C2×C3×C4—101no—
272C2×C3×C4—201no—
273C2×C3×C4—202no—
274C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
275C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
276C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
277C3⋊C8—104no—
278C3⋊C8—202no—
279C22×C5—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5C2×#21711yescharacteristic
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—41no—
286C2×D5—41no—
287C2×D5—41no—
288C2×D5—84no—
289C2×D5#83712yes—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—41no—
294Dic5—21no—
295Dic5—21no—
296Dic5—41no—
297Dic5#83312yes—
298C24—101no—
299C2×Q8—51no—
300C2×Q8—101no—
301C2×Q8—202no—
302C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
303C2×D4—51no—
304C2×D4—101no—
305C2×D4—202no—
306C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
307C22×C4—51no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—101no—
311M16—304no—
312C2×C8—302no—
313C2×C8—302no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—101no—
317C22⋊C4—101no—
318C22⋊C4—101no—
319C22⋊C4—101no—
320C22⋊C4—101no—
321C22⋊C4—101no—
322C42—51no—
323C42—51no—
324C42—51no—
325C42C2×ΓL(1,𝔽16)11yescharacteristic
326C3×C5#152711yescharacteristic, complemented, Hall
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—52no—
331C22×C3—101no—
332C22×C3—101no—
333C22×C3—201no—
334C22×C3—201no—
335C22×C3—201no—
336C22×C3—404no—
337C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—41no—
342C3×C4—52no—
343C3×C4—101no—
344C3×C4—101no—
345C3×C4—201no—
346C2×C5—81no—
347C2×C5C2×#83311yescharacteristic
348C2×C5C2×#83711yescharacteristic
349C2×C5#523611yescharacteristic
350D5—22no—
351D5—81no—
352C23—21no—
353C23—51no—
354C23—101no—
355C23—202no—
356C23—202no—
357C23—202no—
358Q8—41no—
359Q8—201no—
360Q8—202no—
361D4—41no—
362D4—201no—
363D4—202no—
364C2×C4—21no—
365C2×C4—51no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4—101no—
371C2×C4—201no—
372C2×C4—202no—
373C2×C4#676311yescharacteristic
374C2×C4#676311yescharacteristic
375C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
376C8—304no—
377C8—602no—
378C2×C3—81no—
379C2×C3—102no—
380C2×C3—401no—
381C2×C3D5⋊#10011yescharacteristic
382C2×C3D5⋊#10411yescharacteristic
383C2×C3#6579511yescharacteristic
384C5#7171811yescharacteristic, complemented, Sylow
385C22—41no—
386C22—41no—
387C22—41no—
388C22—52no—
389C22—101no—
390C22—101no—
391C22—201no—
392C22—201no—
393C22—201no—
394C22—404no—
395C22C2×#676311yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—52no—
401C4—101no—
402C4—101no—
403C4—201no—
404C3#1060454211yescharacteristic, complemented, Sylow
405C2—81no—
406C2—102no—
407C2—401no—
408C2D5⋊#83311yescharacteristic
409C2D5⋊#83711yescharacteristic
410C2#1175245411yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#124C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC3×C4×Dic5C23
hypercenter#124ΓL(1,𝔽16)
hypocenterC3×C5#1527
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752343C2semidirect
3. C4×#6758C2semidirect
4. #11746798C2semidirect
5. #11746792C2semidirect
21. #91231C22semidirect
22. #91231C22semidirect
326. C3×C5#1527semidirect
384. C5#71718semidirect
404. C3#10604542semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
#117523432
C4×#67582
#117467982
#117467922
#106045423
#717185