Finite Group Databasebeta

← #14284417

Subgroups — #14284417

Order 1920.

400 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 84 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#11756439C211yesmaximal, characteristic
2#11746940C211yesmaximal, characteristic, complemented
3#11746940C211yesmaximal, characteristic, complemented
4C5×#4540C211yesmaximal, characteristic, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745851C211yesmaximal, characteristic, complemented
8#10599141—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10#91835C411yescharacteristic
11Q8×Dic15C411yescharacteristic
12#91827C411yescharacteristic
13D4×Dic15C411yescharacteristic
14#91772—21no—
15#91770—21no—
16#91768—21no—
17#91766—21no—
18C42×D15C2211yescharacteristic
19#91759C2211yescharacteristic
20C5×#803C2211yescharacteristic
21C5×#803C2211yescharacteristic
22C3×#3935C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24#90983—21no—
25#90983—21no—
26#90957—21no—
27#90957—21no—
28#68348—51nomaximal, Hall
29#66014—31no—
30#64994—31no—
31#64994—31no—
32C5×#329—31no—
33#64760D311yescharacteristic, complemented
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×#1220—21no—
39C22×Dic15—21no—
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×C4×D15D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46#6719—21no—
47#6719—21no—
48#6714—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C4⋊Dic15C2×C411yescharacteristic
52#6712—21no—
53#6712—21no—
54#6712—21no—
55C4×Dic15—21no—
56C4×Dic15C2×C411yescharacteristic
57C4×Dic15D411yescharacteristic
58C4×Dic15D411yescharacteristic
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63#5680—51no—
64#4705—51no—
65#4705—51no—
66C3×#329—51no—
67#4540D511yescharacteristic, complemented
68#4465—51no—
69#4465—51no—
70C5×#124C2×D311yescharacteristic
71#4092—31no—
72Q8×Dic5—31no—
73#4084—31no—
74D4×Dic5—31no—
75#4029—61no—
76#4027—61no—
77#4025—61no—
78#4023—61no—
79C42×D5—31no—
80#4016—31no—
81C5×#97—31no—
82C5×#97—31no—
83#3952—61no—
84#3952—61no—
85#3946—61no—
86#3946—61no—
87#3935C2×D311yescharacteristic
88#3935C2×D311yescharacteristic
89#1535—151noSylow
90C23×C3×C5—21no—
91C22×D15C22⋊C411yescharacteristic
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98#1220—42no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15—42no—
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C4×D15—41no—
106C4×D15—41no—
107C4×D15—41no—
108C3×#168—41no—
109C3×#168—41no—
110C5×C3⋊C8—41no—
111C5×C3⋊C8—41no—
112C3×#124C2×D511yescharacteristic
113#946—51no—
114Q8×Dic3—51no—
115#938—51no—
116D4×Dic3—51no—
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#803C2×D511yescharacteristic
130#803C2×D511yescharacteristic
131C2×C5×Q8C4×D311yescharacteristic
132C2×C5×D4C4×D311yescharacteristic
133C2×C22⋊D5—61no—
134C22×Dic5—61no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140C5×C22⋊C4—21no—
141C5×C22⋊C4—21no—
142C42×C5C22×D311yescharacteristic
143C22⋊Dic5—61no—
144C22⋊Dic5—61no—
145#685—61no—
146C4⋊Dic5—31no—
147C4⋊Dic5—31no—
148C4⋊Dic5—61no—
149#683—61no—
150#683—61no—
151#683—61no—
152C4×Dic5—31no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—61no—
156C2×#168—21no—
157C2×#168—21no—
158#529—151no—
159#432—151no—
160#432—151no—
161#330—151no—
162#330—151no—
163#329—31no—
164#329—51no—
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—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176Dic15—21no—
177Dic15—21no—
178Dic15—21no—
179Dic15—41no—
180Dic15—41no—
181C2×C3×Q8C4×D511yescharacteristic
182C2×C3×D4C4×D511yescharacteristic
183C2×#67—101no—
184C22×Dic3—101no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C3×C8—101no—
189C2×C3×C8—101no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C42C22×D511yescharacteristic
193#217—101no—
194#217—101no—
195(C2×D3)⋊C4—101no—
196C4⋊Dic3—51no—
197C4⋊Dic3—51no—
198C4⋊Dic3—101no—
199Dic3⋊C4—101no—
200Dic3⋊C4—101no—
201Dic3⋊C4—101no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C4×Dic3—51no—
205C4×Dic3—101no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C23×C5—21no—
209C22×D5—31no—
210C5×Q8—41no—
211C5×D4—41no—
212C2×C4×C5—21no—
213C2×C4×C5C2×C4×D311yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C22⋊D5—122no—
217C2×Dic5—31no—
218C2×Dic5—31no—
219C2×Dic5—31no—
220C2×Dic5—61no—
221C2×Dic5—61no—
222C2×Dic5—122no—
223C4×D5—121no—
224C4×D5—121no—
225C4×D5—121no—
226C5×C8—121no—
227C5×C8—121no—
228#168—41no—
229#168—41no—
230#126—301no—
231#125—151no—
232#124D3×D511yescharacteristic
233#123—301no—
234C22⋊Q8—151no—
235#121—151no—
236C4×Q8—151no—
237C4×D4—151no—
238C4×D4—301no—
239#117—301no—
240C2×C42—151no—
241C4⋊C8—301no—
242C4⋊C8—301no—
243C22⋊C8—301no—
244C22⋊C8—301no—
245#97—31no—
246#97—31no—
247#97—51no—
248#97—51no—
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—41no—
257C3×D4—41no—
258C2×C3×C4—21no—
259C2×C3×C4C2×C4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262#67—202no—
263C2×Dic3—51no—
264C2×Dic3—51no—
265C2×Dic3—51no—
266C2×Dic3—101no—
267C2×Dic3—101no—
268C2×Dic3—202no—
269C4×D3—201no—
270C4×D3—201no—
271C4×D3—201no—
272C3×C8—201no—
273C3×C8—201no—
274C3⋊C8—41no—
275C3⋊C8—41no—
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—21no—
285C4×C5—21no—
286C4×C5—41no—
287Dic5—61no—
288Dic5—61no—
289Dic5—61no—
290Dic5—121no—
291Dic5—121no—
292C2×Q8#120011yescharacteristic
293C2×D4—301no—
294C2×D4#120011yescharacteristic
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—301no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—101no—
302C2×C8—101no—
303C4⋊C4—151no—
304C4⋊C4—151no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C4⋊C4—301no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—301no—
312C22⋊C4—301no—
313C22⋊C4—301no—
314C42—151no—
315C42—151no—
316C42—151no—
317C42—301no—
318C42C2×D3×D511yescharacteristic
319C3×C5#153511yescharacteristic, complemented, Hall
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3D5×C22⋊C411yescharacteristic
324C2×D3—101no—
325C2×D3—101no—
326C2×D3—101no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—41no—
331Dic3—101no—
332Dic3—101no—
333Dic3—101no—
334Dic3—201no—
335Dic3—201no—
336C2×C5—81no—
337C2×C5#474511yescharacteristic
338C2×C5#482111yescharacteristic
339C2×C5#482111yescharacteristic
340D5—121no—
341C23—21no—
342C23—151no—
343Q8—41no—
344D4—41no—
345D4—602no—
346C2×C4—21no—
347C2×C4—151no—
348C2×C4—151no—
349C2×C4—151no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—601no—
353C2×C4—601no—
354C2×C4—601no—
355C2×C4—602no—
356C2×C4C2×#120011yescharacteristic
357C2×C4#679011yescharacteristic
358C2×C4#679011yescharacteristic
359C8—121no—
360C8—121no—
361C8—201no—
362C8—201no—
363C2×C3—81no—
364C2×C3#6503411yescharacteristic
365C2×C3#6511011yescharacteristic
366C2×C3#6511011yescharacteristic
367D3—201no—
368C5#6834811yescharacteristic, complemented, Sylow
369C22—41no—
370C22—41no—
371C22—41no—
372C22—301no—
373C22—301no—
374C22—301no—
375C22#9156111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—301no—
381C4—301no—
382C4—301no—
383C4—601no—
384C4—601no—
385C3#1059914111yescharacteristic, complemented, Sylow
386C2—81no—
387C2—601no—
388C2#1174912811yescharacteristic
389C2#1174943111yescharacteristic
390C2#1174943111yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1535
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. #11746940C2semidirect
3. #11746940C2semidirect
4. C5×#4540C2semidirect
5. C3×#64760C2semidirect
6. #11745851C2semidirect
7. #11745851C2semidirect
33. #64760D3semidirect
67. #4540D5semidirect
319. C3×C5#1535semidirect
368. C5#68348semidirect
385. C3#10599141semidirect

Maximal subgroups

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

subgroupindex
#117564392
#117469402
C5×#45402
C3×#647602
#117458512
#105991413
#683485