Finite Group Databasebeta

← #14284434

Subgroups — #14284434

Order 1920.

400 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 76 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
1#11754878C211yesmaximal, characteristic
2#11751828C211yesmaximal, characteristic, complemented
3#11751808C211yesmaximal, characteristic, complemented
4#11746792C211yesmaximal, characteristic, complemented
5C3×#64921C211yesmaximal, characteristic, complemented
6#11746507C211yesmaximal, characteristic, complemented
7#11746506C211yesmaximal, characteristic, complemented
8#10604399—31nomaximal, Hall
9#91827C411yescharacteristic
10C5×D4×Dic3C411yescharacteristic
11C3×#4082C2211yescharacteristic
12#91562—21no—
13#91556—21no—
14#91531—21no—
15#91529—21no—
16C4×#1200C2211yescharacteristic
17#91390C411yescharacteristic
18#91388C2211yescharacteristic
19Dic3×Dic10C411yescharacteristic
20#91231C2211yescharacteristic
21#91231C2211yescharacteristic
22C3×#4002C2211yescharacteristic
23C3×#4002C2211yescharacteristic
24#91177—21no—
25Dic3⋊#170—21no—
26#91171—21no—
27#91171—21no—
28#68348—51nomaximal, Hall
29#65891—31no—
30#65684—31no—
31#65683—31no—
32#64921—31no—
33#64921D311yescharacteristic, complemented
34#64870—31no—
35#64870—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C2×#1220—21no—
38C2×C4×D15C2×C411yescharacteristic
39C22×C5×Dic3—21no—
40C2×C3×Dic10C2×C411yescharacteristic
41C2×#1200D411yescharacteristic
42C2×#1200D411yescharacteristic
43C2×C3⋊#170—21no—
44C2×C3⋊#170—21no—
45C2×C3×#170—21no—
46C2×C3×#170—21no—
47#6719—21no—
48C4⋊Dic15C2×C411yescharacteristic
49C5×#217—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C4×C5×Dic3C2×C411yescharacteristic
52C3×C22⋊Dic5—21no—
53C3×C22⋊Dic5—21no—
54C3×C4×Dic5C2311yescharacteristic
55Dic3⋊Dic5—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6668—21no—
59#6667—21no—
60Dic3×Dic5—21no—
61Dic3×Dic5D411yescharacteristic
62Dic3×Dic5D411yescharacteristic
63#5680—51no—
64#4705—51no—
65#4705—51no—
66C3×#329—51no—
67#4540—51no—
68#4465—51no—
69#4465—51no—
70C4×C5×D4—31no—
71#4084—31no—
72#4082C2×D311yescharacteristic
73C4×C22⋊D5—61no—
74#4072—61no—
75#4043—31no—
76#4036—31no—
77#4029—61no—
78#4025—61no—
79C42×D5—31no—
80C4×Dic10—31no—
81#4004—61no—
82#4003—61no—
83#4003—61no—
84#4002—31no—
85#4002—31no—
86#4002C2×D311yescharacteristic
87#4002C2×D311yescharacteristic
88C4⋊#170—61no—
89#1535—151noSylow
90C23×C3×C5—21no—
91C22×D15C22⋊C411yescharacteristic
92C3×C5×D4—41no—
93C2×C3×C4×C5C22×C411yescharacteristic
94#1220—42no—
95C2×Dic15—21no—
96C2×Dic15C22⋊C411yescharacteristic
97C4×D15—41no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—42no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C3×Dic5—21no—
103C2×C3×Dic5C2×D411yescharacteristic
104C2×C3×Dic5C2×D411yescharacteristic
105C3×Dic10—41no—
106#1200—41no—
107#1200—41no—
108C3⋊#170—41no—
109C3⋊#170—41no—
110C3×#170—41no—
111C3×#170—41no—
112C3×#124—51no—
113#946—51no—
114Q8×Dic3—51no—
115#938—51no—
116D4×Dic3AGL(1,𝔽5)11yescharacteristic
117#883—101no—
118#67⋊C4—101no—
119#879—101no—
120#877—101no—
121C42×D3—51no—
122#870—51no—
123C3×#97—51no—
124C3×#97—51no—
125(C2×D3)⋊C8—101no—
126(C2×D3)⋊C8—101no—
127Dic3⋊C8—101no—
128Dic3⋊C8—101no—
129#803—51no—
130#803—51no—
131C2×C5×D4C4×D311yescharacteristic
132C22×C4×C5—61no—
133C2×C22⋊D5—61no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×Dic10C4×D311yescharacteristic
138C2×#170—21no—
139C2×#170—21no—
140C2×#170—61no—
141C2×#170—61no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—61no—
144C42×C5—31no—
145C22⋊Dic5—21no—
146C22⋊Dic5—21no—
147C22⋊Dic5—61no—
148#685—61no—
149C4⋊Dic5—31no—
150C4⋊Dic5—61no—
151C4⋊Dic5—61no—
152#683—61no—
153#683—61no—
154C4×Dic5—31no—
155C4×Dic5—31no—
156C4×Dic5—61no—
157C4×Dic5C22×D311yescharacteristic
158#529—151no—
159#432—151no—
160#432—151no—
161#330—151no—
162#330—151no—
163#329—51no—
164#329—151no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C2×D15—21no—
170C2×D15—21no—
171C2×D15—21no—
172C3×C4×C5—21no—
173Dic15—21no—
174Dic15—41no—
175C3×Dic5—21no—
176C3×Dic5—21no—
177C3×Dic5—41no—
178C5×Dic3—21no—
179C5×Dic3—21no—
180C5×Dic3—41no—
181C2×C3×Q8—51no—
182C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
183C2×#67—101no—
184C22×Dic3—21no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C3×C8—101no—
189C2×C3×C8—101no—
190C3×C22⋊C4—101no—
191C3×C22⋊C4—101no—
192C3×C42—51no—
193#217—21no—
194#217—101no—
195(C2×D3)⋊C4—101no—
196C4⋊Dic3—51no—
197C4⋊Dic3—101no—
198C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201Dic3⋊C4—101no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C4×Dic3—101no—
205C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—21no—
209C22×D5—31no—
210C5×D4—41no—
211C2×C4×C5—31no—
212C2×C4×C5—31no—
213C2×C4×C5—61no—
214C2×C4×C5—122no—
215C2×C4×C5C2×C4×D311yescharacteristic
216C22⋊D5—122no—
217C2×Dic5—21no—
218C2×Dic5—31no—
219C2×Dic5—61no—
220C2×Dic5D3×D411yescharacteristic
221C2×Dic5D3×D411yescharacteristic
222C4×D5—121no—
223C4×D5—121no—
224C4×D5—121no—
225Dic10—41no—
226#170—41no—
227#170—41no—
228#170—121no—
229#170—121no—
230#126—301no—
231#125—151no—
232#124—51no—
233#123—301no—
234C22⋊Q8—151no—
235#121—151no—
236C4×Q8—151no—
237C4×D4—31no—
238C4×D4—301no—
239#117—301no—
240C2×C42—151no—
241C4⋊C8—301no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244C22⋊C8—301no—
245#97—51no—
246#97—51no—
247#97—151no—
248#97—151no—
249C2×C3×C5—81no—
250C2×C3×C5#41311yescharacteristic
251C2×C3×C5#42111yescharacteristic
252C2×C3×C5#42111yescharacteristic
253D15—41no—
254C23×C3—21no—
255C22×D3—51no—
256C3×Q8—201no—
257C3×D4—41no—
258C2×C3×C4—51no—
259C2×C3×C4—51no—
260C2×C3×C4—101no—
261C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
262#67—202no—
263C2×Dic3—21no—
264C2×Dic3—42no—
265C2×Dic3—51no—
266C2×Dic3—101no—
267C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
268C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
269C4×D3—201no—
270C4×D3—201no—
271C4×D3—201no—
272C3×C8—201no—
273C3×C8—201no—
274C3⋊C8—201no—
275C3⋊C8—201no—
276C22×C5—41no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5D3×C22⋊C411yescharacteristic
280C2×D5—61no—
281C2×D5—61no—
282C2×D5—61no—
283C4×C5—21no—
284C4×C5—61no—
285C4×C5—61no—
286C4×C5—121no—
287Dic5—21no—
288Dic5—21no—
289Dic5—41no—
290Dic5—61no—
291Dic5—121no—
292C2×Q8—51no—
293C2×D4—301no—
294C2×D4D3×AGL(1,𝔽5)11yescharacteristic
295C22×C4—61no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—151no—
299C2×C8—101no—
300C2×C8—101no—
301C2×C8—301no—
302C2×C8—301no—
303C4⋊C4—31no—
304C4⋊C4—151no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C4⋊C4—301no—
309C22⋊C4—61no—
310C22⋊C4—101no—
311C22⋊C4—101no—
312C22⋊C4—301no—
313C22⋊C4—301no—
314C42—31no—
315C42—51no—
316C42—151no—
317C42—151no—
318C42—301no—
319C3×C5#153511yescharacteristic, complemented, Hall
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
324C2×D3—101no—
325C2×D3—101no—
326C2×D3—101no—
327C3×C4—21no—
328C3×C4—101no—
329C3×C4—101no—
330C3×C4—201no—
331Dic3—21no—
332Dic3—21no—
333Dic3—41no—
334Dic3—101no—
335Dic3—201no—
336C2×C5—81no—
337C2×C5#474511yescharacteristic
338C2×C5#482111yescharacteristic
339C2×C5#482111yescharacteristic
340D5—121no—
341C23—21no—
342C23—151no—
343Q8—201no—
344D4—41no—
345D4—602no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—61no—
351C2×C4—101no—
352C2×C4—122no—
353C2×C4—151no—
354C2×C4—301no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4—601no—
358C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
359C8—201no—
360C8—201no—
361C8—601no—
362C8—601no—
363C2×C3—81no—
364C2×C3#6576111yescharacteristic
365C2×C3#6576911yescharacteristic
366C2×C3#6579511yescharacteristic
367D3—201no—
368C5#6834811yescharacteristic, complemented, Sylow
369C22—41no—
370C22—41no—
371C22—41no—
372C22—301no—
373C22—301no—
374C22—301no—
375C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
376C4—21no—
377C4—61no—
378C4—61no—
379C4—101no—
380C4—101no—
381C4—121no—
382C4—201no—
383C4—301no—
384C4—601no—
385C3#1060439911yescharacteristic, complemented, Sylow
386C2—81no—
387C2—601no—
388C2#1175194911yescharacteristic
389C2#1175195011yescharacteristic
390C2#1175204911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1535
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751828C2semidirect
3. #11751808C2semidirect
4. #11746792C2semidirect
5. C3×#64921C2semidirect
6. #11746507C2semidirect
7. #11746506C2semidirect
33. #64921D3semidirect
319. C3×C5#1535semidirect
368. C5#68348semidirect
385. C3#10604399semidirect

Maximal subgroups

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

subgroupindex
#117548782
#117518282
#117518082
#117467922
C3×#649212
#117465072
#117465062
#106043993
#683485