Subgroups — C₅×#33797 #11956517

Order 1280.

460 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3170	C₂	1	1	yes	maximal, characteristic
2	C₅×#3160	C₂	1	1	yes	maximal, characteristic
3	C₅×#2254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2252	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2241	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2241	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2237	C₂	1	4	yes	maximal
8	C₅×#2229	C₂	1	4	yes	maximal, complemented
9	C₅×#2162	C₂	1	1	yes	maximal, characteristic
10	C₅×#533	—	2	1	no	—
11	C₅×#533	—	2	1	no	—
12	C₅×#500	C₂²	1	1	yes	characteristic
13	C₅×#500	C₂²	1	1	yes	characteristic
14	C₅×#500	C₂²	1	1	yes	characteristic
15	C₅×#499	—	2	1	no	—
16	C₅×#499	C₂²	1	2	yes	—
17	C₅×#498	—	2	1	no	—
18	C₅×#494	C₂²	1	1	yes	characteristic
19	C₅×#487	—	2	1	no	—
20	C₅×#467	—	2	1	no	—
21	C₅×#467	C₂²	1	2	yes	—
22	C₄×C₅×Q₁₆	—	2	1	no	—
23	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
24	C₅×#427	—	2	1	no	—
25	C₅×#427	C₂²	1	2	yes	—
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₅×#367	C₂²	1	4	yes	—
28	C₅×#366	C₂²	1	4	yes	—
29	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
30	C₅×#358	C₂²	1	4	yes	—
31	C₅×#358	C₂²	1	4	yes	—
32	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
33	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
35	#33797	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₅×Q₁₆	—	2	1	no	—
37	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
38	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
40	C₅×C₄⋊Q₈	—	2	1	no	—
41	C₅×C₄⋊Q₈	—	2	1	no	—
42	C₅×C₄⋊Q₈	—	2	1	no	—
43	C₅×C₄⋊Q₈	—	2	1	no	—
44	C₅×#125	—	2	2	no	—
45	C₅×#125	—	4	1	no	—
46	C₅×C₂²⋊Q₈	—	2	2	no	—
47	C₅×C₂²⋊Q₈	—	4	1	no	—
48	C₅×C₂²⋊Q₈	—	4	1	no	—
49	C₅×C₂²⋊Q₈	—	4	1	no	—
50	C₄×C₅×Q₈	—	2	2	no	—
51	C₄×C₅×Q₈	—	4	1	no	—
52	C₄×C₅×Q₈	—	4	1	no	—
53	C₄×C₅×Q₈	—	4	1	no	—
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	4	1	no	—
56	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
57	C₂×C₅×C₁₆	C₂³	1	2	yes	—
58	C₂×C₅×C₁₆	C₂³	1	2	yes	—
59	C₅×#107	—	2	1	no	—
60	C₅×#107	—	2	1	no	—
61	C₅×#107	—	2	1	no	—
62	C₅×#107	C₂³	1	2	yes	—
63	C₅×#107	C₂³	1	2	yes	—
64	C₅×#107	C₂³	1	2	yes	—
65	C₅×#106	—	2	2	no	—
66	C₅×#106	—	2	2	no	—
67	C₅×#103	—	2	2	no	—
68	C₅×#103	—	2	2	no	—
69	C₄×C₅×C₈	D₄	1	1	yes	characteristic
70	C₄×C₅×C₈	D₄	1	1	yes	characteristic
71	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
73	#3170	C₂×C₅	1	1	yes	characteristic
74	#3160	C₂×C₅	1	1	yes	characteristic
75	#2254	C₂×C₅	1	1	yes	characteristic, complemented
76	#2252	C₂×C₅	1	1	yes	characteristic, complemented
77	#2241	C₂×C₅	1	1	yes	characteristic, complemented
78	#2241	C₂×C₅	1	1	yes	characteristic, complemented
79	#2237	C₂×C₅	1	4	yes	—
80	#2229	C₂×C₅	1	4	yes	complemented
81	#2162	C₂×C₅	1	1	yes	characteristic
82	C₂×C₅×Q₈	—	2	2	no	—
83	C₂×C₅×Q₈	—	4	1	no	—
84	C₂×C₅×Q₈	—	4	1	no	—
85	C₂×C₅×Q₈	—	4	1	no	—
86	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₅×Q₁₆	—	2	4	no	—
90	C₅×Q₁₆	—	4	2	no	—
91	C₂×C₅×C₈	—	2	2	no	—
92	C₂×C₅×C₈	—	2	2	no	—
93	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
94	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
95	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
96	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
97	C₅×C₄⋊C₄	—	2	2	no	—
98	C₅×C₄⋊C₄	—	2	2	no	—
99	C₅×C₄⋊C₄	—	2	2	no	—
100	C₅×C₄⋊C₄	—	4	1	no	—
101	C₅×C₄⋊C₄	—	4	1	no	—
102	C₅×C₄⋊C₄	—	4	2	no	—
103	C₅×C₄⋊C₄	—	4	2	no	—
104	C₅×C₄⋊C₄	—	4	2	no	—
105	C₅×C₄⋊C₄	—	4	2	no	—
106	C₅×C₄⋊C₄	—	4	1	no	—
107	C₅×C₄⋊C₄	—	4	1	no	—
108	C₅×C₄⋊C₄	—	4	1	no	—
109	C₅×C₂²⋊C₄	—	4	2	no	—
110	C₅×C₂²⋊C₄	—	4	2	no	—
111	C₄²×C₅	—	4	2	no	—
112	C₄²×C₅	—	4	2	no	—
113	C₄²×C₅	D₈	1	1	yes	characteristic
114	C₄²×C₅	D₈	1	1	yes	characteristic
115	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
117	C₅×C₁₆	—	2	2	no	—
118	C₅×C₁₆	—	2	2	no	—
119	#533	—	2	1	no	—
120	#533	—	2	1	no	—
121	#500	C₂²×C₅	1	1	yes	characteristic
122	#500	C₂²×C₅	1	1	yes	characteristic
123	#500	C₂²×C₅	1	1	yes	characteristic
124	#499	—	2	1	no	—
125	#499	C₂²×C₅	1	2	yes	—
126	#498	—	2	1	no	—
127	#494	C₂²×C₅	1	1	yes	characteristic
128	#487	—	2	1	no	—
129	#467	—	2	1	no	—
130	#467	C₂²×C₅	1	2	yes	—
131	C₄×Q₁₆	—	2	1	no	—
132	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
133	#427	—	2	1	no	—
134	#427	C₂²×C₅	1	2	yes	—
135	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
136	#367	C₂²×C₅	1	4	yes	—
137	#366	C₂²×C₅	1	4	yes	—
138	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
139	#358	C₂²×C₅	1	4	yes	—
140	#358	C₂²×C₅	1	4	yes	—
141	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
142	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
143	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
145	C₅×Q₈	—	4	2	no	—
146	C₅×Q₈	—	4	2	no	—
147	C₅×Q₈	—	8	2	no	—
148	C₅×Q₈	—	8	2	no	—
149	C₅×Q₈	—	8	2	no	—
150	C₂×C₄×C₅	—	2	1	no	—
151	C₂×C₄×C₅	—	2	1	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	4	2	no	—
155	C₂×C₄×C₅	—	4	2	no	—
156	C₂×C₄×C₅	—	4	2	no	—
157	C₂×C₄×C₅	—	4	2	no	—
158	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
164	C₅×C₈	—	2	1	no	—
165	C₅×C₈	—	2	1	no	—
166	C₅×C₈	#137	1	2	yes	—
167	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
168	C₂×Q₁₆	—	2	1	no	—
169	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
170	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
171	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
172	C₄⋊Q₈	—	2	1	no	—
173	C₄⋊Q₈	—	2	1	no	—
174	C₄⋊Q₈	—	2	1	no	—
175	C₄⋊Q₈	—	2	1	no	—
176	#125	—	2	2	no	—
177	#125	—	4	1	no	—
178	C₂²⋊Q₈	—	2	2	no	—
179	C₂²⋊Q₈	—	4	1	no	—
180	C₂²⋊Q₈	—	4	1	no	—
181	C₂²⋊Q₈	—	4	1	no	—
182	C₄×Q₈	—	2	2	no	—
183	C₄×Q₈	—	4	1	no	—
184	C₄×Q₈	—	4	1	no	—
185	C₄×Q₈	—	4	1	no	—
186	#117	—	2	2	no	—
187	#117	—	4	1	no	—
188	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
189	C₂×C₁₆	C₂³×C₅	1	2	yes	—
190	C₂×C₁₆	C₂³×C₅	1	2	yes	—
191	#107	—	2	1	no	—
192	#107	—	2	1	no	—
193	#107	—	2	1	no	—
194	#107	C₂³×C₅	1	2	yes	—
195	#107	C₂³×C₅	1	2	yes	—
196	#107	C₂³×C₅	1	2	yes	—
197	#106	—	2	2	no	—
198	#106	—	2	2	no	—
199	#103	—	2	2	no	—
200	#103	—	2	2	no	—
201	C₄×C₈	C₅×D₄	1	1	yes	characteristic
202	C₄×C₈	C₅×D₄	1	1	yes	characteristic
203	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
204	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
205	C₂²×C₅	—	2	1	no	—
206	C₂²×C₅	—	2	1	no	—
207	C₂²×C₅	—	2	1	no	—
208	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
209	C₄×C₅	—	2	1	no	—
210	C₄×C₅	—	2	1	no	—
211	C₄×C₅	—	2	1	no	—
212	C₄×C₅	—	8	2	no	—
213	C₄×C₅	—	8	2	no	—
214	C₄×C₅	—	8	2	no	—
215	C₄×C₅	—	8	2	no	—
216	C₄×C₅	#508	1	2	yes	—
217	C₄×C₅	#510	1	2	yes	—
218	C₄×C₅	#536	1	1	yes	characteristic
219	C₄×C₅	C₂×#137	1	1	yes	characteristic
220	C₂×Q₈	—	2	2	no	—
221	C₂×Q₈	—	4	1	no	—
222	C₂×Q₈	—	4	1	no	—
223	C₂×Q₈	—	4	1	no	—
224	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
225	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
226	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
227	Q₁₆	—	2	4	no	—
228	Q₁₆	—	4	2	no	—
229	C₂×C₈	—	2	2	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
232	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
233	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	4	1	no	—
239	C₄⋊C₄	—	4	1	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₄⋊C₄	—	4	2	no	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	—	4	2	no	—
244	C₄⋊C₄	—	4	1	no	—
245	C₄⋊C₄	—	4	1	no	—
246	C₄⋊C₄	—	4	1	no	—
247	C₂²⋊C₄	—	4	2	no	—
248	C₂²⋊C₄	—	4	2	no	—
249	C₄²	—	4	2	no	—
250	C₄²	—	4	2	no	—
251	C₄²	C₅×D₈	1	1	yes	characteristic
252	C₄²	C₅×D₈	1	1	yes	characteristic
253	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
254	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
255	C₁₆	—	2	2	no	—
256	C₁₆	—	2	2	no	—
257	C₂×C₅	—	4	1	no	—
258	C₂×C₅	#3226	1	1	yes	characteristic
259	C₂×C₅	C₂×#508	1	1	yes	characteristic
260	C₂×C₅	C₂×#510	1	1	yes	characteristic
261	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
262	Q₈	—	4	2	no	—
263	Q₈	—	4	2	no	—
264	Q₈	—	8	2	no	—
265	Q₈	—	8	2	no	—
266	Q₈	—	8	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
276	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
277	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
278	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
279	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
280	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
281	C₈	—	2	1	no	—
282	C₈	—	2	1	no	—
283	C₈	C₅×#137	1	2	yes	—
284	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
285	C₅	#33797	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²	—	2	1	no	—
287	C₂²	—	2	1	no	—
288	C₂²	—	2	1	no	—
289	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	2	1	no	—
293	C₄	—	8	2	no	—
294	C₄	—	8	2	no	—
295	C₄	—	8	2	no	—
296	C₄	—	8	2	no	—
297	C₄	C₅×#508	1	2	yes	—
298	C₄	C₅×#510	1	2	yes	—
299	C₄	C₅×#536	1	1	yes	characteristic
300	C₄	C₂×C₅×#137	1	1	yes	characteristic
301	C₂	—	4	1	no	—
302	C₂	C₅×#3226	1	1	yes	characteristic
303	C₂	C₂×C₅×#508	1	1	yes	characteristic
304	C₂	C₂×C₅×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₂³×C₅	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2254	C₂	semidirect
4. C₅×#2252	C₂	semidirect
5. C₅×#2241	C₂	semidirect
6. C₅×#2241	C₂	semidirect
8. C₅×#2229	C₂	semidirect
35. #33797	C₅	direct (N × H)
75. #2254	C₂×C₅	semidirect
76. #2252	C₂×C₅	semidirect
77. #2241	C₂×C₅	semidirect
78. #2241	C₂×C₅	semidirect
80. #2229	C₂×C₅	semidirect
285. C₅	#33797	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3170	2
C₅×#3160	2
C₅×#2254	2
C₅×#2252	2
C₅×#2241	2
C₅×#2237	2
C₅×#2229	2
C₅×#2162	2
#33797	5

Subgroups — C5×#33797 #11956517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33797 #11956517