Subgroups — C₅×#33657 #11956377

Order 1280.

566 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3058	C₂	1	1	yes	maximal, characteristic
2	C₅×#2916	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2238	C₂	1	8	yes	maximal, complemented
4	C₅×#2155	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#361	C₂	1	2	yes	maximal, complemented
6	C₅×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
8	C₅×#568	—	2	1	no	—
9	C₂×C₅×#131	C₂²	1	1	yes	characteristic
10	C₅×#535	—	2	1	no	—
11	C₂×C₅×M₃₂	C₂²	1	2	yes	—
12	C₅×#469	C₂²	1	4	yes	—
13	C₅×#466	—	2	2	no	—
14	C₅×#430	—	2	1	no	—
15	C₅×#430	C₂²	1	4	yes	complemented
16	C₂×C₅×#108	—	2	2	no	—
17	C₂×C₅×#108	C₂²	1	2	yes	—
18	C₅×#427	C₂²	1	1	yes	characteristic
19	C₅×#418	—	2	1	no	—
20	C₅×#365	C₂²	1	8	yes	complemented
21	C₅×#361	C₂²	1	8	yes	—
22	C₅×#349	C₂²	1	4	yes	complemented
23	#33657	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂×C₅×#41	D₄	1	1	yes	characteristic
25	C₂²×C₅×D₄	—	2	1	no	—
26	C₂×C₅×D₈	—	2	1	no	—
27	C₂×C₅×D₈	—	2	2	no	—
28	C₂×C₅×D₈	—	2	2	no	—
29	C₂×C₅×D₈	C₂³	1	2	yes	—
30	C₅×#131	—	2	2	no	—
31	C₅×#131	—	2	2	no	—
32	C₅×#131	—	4	4	no	—
33	C₂×C₅×M₁₆	—	2	4	no	—
34	C₂×C₅×M₁₆	—	2	2	no	—
35	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
36	C₂×C₅×M₁₆	C₂³	1	2	yes	—
37	C₂²×C₅×C₈	D₄	1	2	yes	—
38	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
39	C₅×#127	—	4	1	no	—
40	C₅×#124	—	4	1	no	—
41	C₅×#121	—	2	4	no	—
42	C₅×#120	—	4	2	no	—
43	C₅×#117	—	2	1	no	—
44	C₅×M₃₂	—	2	2	no	—
45	C₅×M₃₂	C₂³	1	4	yes	—
46	C₂×C₅×C₁₆	—	2	2	no	—
47	C₅×#108	—	2	2	no	—
48	C₅×#108	—	2	4	no	—
49	C₅×#108	C₂³	1	4	yes	—
50	C₅×#107	—	2	1	no	—
51	C₅×#106	C₂³	1	2	yes	—
52	C₅×#102	—	2	4	no	—
53	#3058	C₂×C₅	1	1	yes	characteristic
54	#2916	C₂×C₅	1	1	yes	characteristic, complemented
55	#2238	C₂×C₅	1	8	yes	complemented
56	#2155	C₂×C₅	1	2	yes	complemented
57	C₂×#361	C₂×C₅	1	2	yes	complemented
58	#2115	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂⁴×C₅	—	4	1	no	—
60	C₅×#41	—	2	2	no	—
61	C₅×#41	—	2	2	no	—
62	C₂×C₅×Q₈	SD₁₆	1	1	yes	characteristic
63	C₂×C₅×D₄	—	2	2	no	—
64	C₂×C₅×D₄	—	4	4	no	—
65	C₂×C₅×D₄	—	4	2	no	—
66	C₂×C₅×D₄	—	4	1	no	—
67	C₂×C₅×D₄	—	4	2	no	—
68	C₂×C₅×D₄	SD₁₆	1	2	yes	—
69	C₂×C₅×D₄	SD₁₆	1	1	yes	characteristic
70	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
72	C₅×D₈	—	2	4	no	—
73	C₅×D₈	—	4	1	no	—
74	C₅×D₈	—	4	1	no	—
75	C₅×M₁₆	—	2	2	no	—
76	C₅×M₁₆	—	2	4	no	—
77	C₅×M₁₆	—	2	4	no	—
78	C₅×M₁₆	—	4	4	no	—
79	C₅×M₁₆	—	4	2	no	—
80	C₂×C₅×C₈	—	2	2	no	—
81	C₂×C₅×C₈	—	2	2	no	—
82	C₂×C₅×C₈	—	4	4	no	—
83	C₂×C₅×C₈	—	4	2	no	—
84	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
85	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
86	C₂×C₅×C₈	#41	1	2	yes	—
87	C₂×C₅×C₈	#41	1	2	yes	—
88	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
89	C₅×C₄⋊C₄	—	2	2	no	—
90	C₅×C₂²⋊C₄	—	4	1	no	—
91	C₅×C₂²⋊C₄	—	4	4	no	—
92	C₄²×C₅	—	4	1	no	—
93	C₅×C₁₆	—	2	4	no	—
94	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
95	#568	—	2	1	no	—
96	C₂×#131	C₂²×C₅	1	1	yes	characteristic
97	#535	—	2	1	no	—
98	C₂×M₃₂	C₂²×C₅	1	2	yes	—
99	#469	C₂²×C₅	1	4	yes	—
100	#466	—	2	2	no	—
101	#430	—	2	1	no	—
102	#430	C₂²×C₅	1	4	yes	complemented
103	C₂×#108	—	2	2	no	—
104	C₂×#108	C₂²×C₅	1	2	yes	—
105	#427	C₂²×C₅	1	1	yes	characteristic
106	#418	—	2	1	no	—
107	#365	C₂²×C₅	1	8	yes	complemented
108	#361	C₂²×C₅	1	8	yes	—
109	#349	C₂²×C₅	1	4	yes	complemented
110	C₂³×C₅	—	4	2	no	—
111	C₂³×C₅	—	8	2	no	—
112	C₂³×C₅	—	16	2	no	—
113	C₂³×C₅	C₂×SD₁₆	1	2	yes	—
114	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
115	C₅×Q₈	—	2	2	no	—
116	C₅×D₄	—	2	4	no	—
117	C₅×D₄	—	2	2	no	—
118	C₅×D₄	—	4	2	no	—
119	C₅×D₄	—	4	2	no	—
120	C₅×D₄	—	8	2	no	—
121	C₅×D₄	—	16	4	no	—
122	C₂×C₄×C₅	—	2	2	no	—
123	C₂×C₄×C₅	—	2	2	no	—
124	C₂×C₄×C₅	—	4	2	no	—
125	C₂×C₄×C₅	#123	1	2	yes	—
126	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
127	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
128	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
129	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
130	C₅×C₈	—	2	2	no	—
131	C₅×C₈	—	4	4	no	—
132	C₅×C₈	#123	1	1	yes	characteristic
133	C₅×C₈	#123	1	1	yes	characteristic
134	C₅×C₈	C₂×#41	1	2	yes	—
135	C₂×#41	C₅×D₄	1	1	yes	characteristic
136	C₂²×D₄	—	2	1	no	—
137	C₂×D₈	—	2	1	no	—
138	C₂×D₈	—	2	2	no	—
139	C₂×D₈	—	2	2	no	—
140	C₂×D₈	C₂³×C₅	1	2	yes	—
141	#131	—	2	2	no	—
142	#131	—	2	2	no	—
143	#131	—	4	4	no	—
144	C₂×M₁₆	—	2	4	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
147	C₂×M₁₆	C₂³×C₅	1	2	yes	—
148	C₂²×C₈	C₅×D₄	1	2	yes	—
149	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
150	#127	—	4	1	no	—
151	#124	—	4	1	no	—
152	#121	—	2	4	no	—
153	#120	—	4	2	no	—
154	#117	—	2	1	no	—
155	M₃₂	—	2	2	no	—
156	M₃₂	C₂³×C₅	1	4	yes	—
157	C₂×C₁₆	—	2	2	no	—
158	#108	—	2	2	no	—
159	#108	—	2	4	no	—
160	#108	C₂³×C₅	1	4	yes	—
161	#107	—	2	1	no	—
162	#106	C₂³×C₅	1	2	yes	—
163	#102	—	2	4	no	—
164	C₂²×C₅	—	2	2	no	—
165	C₂²×C₅	—	4	1	no	—
166	C₂²×C₅	—	4	2	no	—
167	C₂²×C₅	—	8	4	no	—
168	C₂²×C₅	—	8	2	no	—
169	C₂²×C₅	—	16	4	no	—
170	C₂²×C₅	#481	1	2	yes	—
171	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
172	C₄×C₅	—	2	2	no	—
173	C₄×C₅	—	8	2	no	—
174	C₄×C₅	#481	1	2	yes	—
175	C₄×C₅	C₂×#123	1	1	yes	characteristic
176	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂⁴	—	4	1	no	—
178	#41	—	2	2	no	—
179	#41	—	2	2	no	—
180	C₂×Q₈	C₅×SD₁₆	1	1	yes	characteristic
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	—	4	4	no	—
183	C₂×D₄	—	4	2	no	—
184	C₂×D₄	—	4	1	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	C₅×SD₁₆	1	2	yes	—
187	C₂×D₄	C₅×SD₁₆	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
189	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
190	D₈	—	2	4	no	—
191	D₈	—	4	1	no	—
192	D₈	—	4	1	no	—
193	M₁₆	—	2	2	no	—
194	M₁₆	—	2	4	no	—
195	M₁₆	—	2	4	no	—
196	M₁₆	—	4	4	no	—
197	M₁₆	—	4	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	4	4	no	—
201	C₂×C₈	—	4	2	no	—
202	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
203	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
204	C₂×C₈	C₅×#41	1	2	yes	—
205	C₂×C₈	C₅×#41	1	2	yes	—
206	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
207	C₄⋊C₄	—	2	2	no	—
208	C₂²⋊C₄	—	4	1	no	—
209	C₂²⋊C₄	—	4	4	no	—
210	C₄²	—	4	1	no	—
211	C₁₆	—	2	4	no	—
212	C₂×C₅	—	2	1	no	—
213	C₂×C₅	—	2	2	no	—
214	C₂×C₅	—	4	2	no	—
215	C₂×C₅	—	16	2	no	—
216	C₂×C₅	C₂×#481	1	1	yes	characteristic
217	C₂³	—	4	2	no	—
218	C₂³	—	8	2	no	—
219	C₂³	—	16	2	no	—
220	C₂³	C₂×C₅×SD₁₆	1	2	yes	—
221	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
222	Q₈	—	2	2	no	—
223	D₄	—	2	4	no	—
224	D₄	—	2	2	no	—
225	D₄	—	4	2	no	—
226	D₄	—	4	2	no	—
227	D₄	—	8	2	no	—
228	D₄	—	16	4	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	C₅×#123	1	2	yes	—
233	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
234	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
235	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
237	C₈	—	2	2	no	—
238	C₈	—	4	4	no	—
239	C₈	C₅×#123	1	1	yes	characteristic
240	C₈	C₅×#123	1	1	yes	characteristic
241	C₈	C₂×C₅×#41	1	2	yes	—
242	C₅	#33657	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²	—	2	2	no	—
244	C₂²	—	4	1	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	8	4	no	—
247	C₂²	—	8	2	no	—
248	C₂²	—	16	4	no	—
249	C₂²	C₅×#481	1	2	yes	—
250	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	8	2	no	—
253	C₄	C₅×#481	1	2	yes	—
254	C₄	C₂×C₅×#123	1	1	yes	characteristic
255	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	2	no	—
258	C₂	—	4	2	no	—
259	C₂	—	16	2	no	—
260	C₂	C₂×C₅×#481	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×#481
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2916	C₂	semidirect
3. C₅×#2238	C₂	semidirect
4. C₅×#2155	C₂	semidirect
5. C₂×C₅×#361	C₂	semidirect
6. C₅×#2115	C₂	semidirect
15. C₅×#430	C₂²	semidirect
20. C₅×#365	C₂²	semidirect
22. C₅×#349	C₂²	semidirect
23. #33657	C₅	direct (N × H)
54. #2916	C₂×C₅	semidirect
55. #2238	C₂×C₅	semidirect
56. #2155	C₂×C₅	semidirect
57. C₂×#361	C₂×C₅	semidirect
58. #2115	C₂×C₅	semidirect
102. #430	C₂²×C₅	semidirect
107. #365	C₂²×C₅	semidirect
109. #349	C₂²×C₅	semidirect
242. C₅	#33657	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×#3058	2
C₅×#2916	2
C₅×#2238	2
C₅×#2155	2
C₂×C₅×#361	2
C₅×#2115	2
#33657	5

Subgroups — C5×#33657 #11956377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33657 #11956377