Subgroups — C₅×#12665 #11935385

Order 1280.

326 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic
2	C₅×#2108	C₂	1	2	yes	maximal
3	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic
4	C₅×#1772	C₂	1	1	yes	maximal, characteristic
5	C₅×#1379	C₂	1	2	yes	maximal
6	C₂×C₅×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₅×#108	C₄	1	1	yes	characteristic
10	C₅×#427	C₄	1	1	yes	characteristic
11	C₅×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#364	C₄	1	4	yes	complemented
14	C₅×#346	—	2	2	no	—
15	C₅×#346	C₄	1	4	yes	complemented
16	C₄×C₅×C₁₆	—	2	2	no	—
17	C₅×#339	C₄	1	2	yes	—
18	#12665	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
20	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₅×#117	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
24	C₅×M₃₂	—	2	2	no	—
25	C₅×M₃₂	C₂×C₄	1	4	yes	—
26	C₂×C₅×C₁₆	—	2	2	no	—
27	C₂×C₅×C₁₆	—	2	1	no	—
28	C₂×C₅×C₁₆	—	2	1	no	—
29	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
30	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
31	C₂×C₅×C₁₆	D₄	1	2	yes	—
32	C₂×C₅×C₁₆	Q₈	1	2	yes	—
33	C₅×#108	C₈	1	4	yes	—
34	C₅×#107	C₈	1	2	yes	—
35	C₅×#106	C₈	1	2	yes	—
36	C₅×#97	—	2	2	no	—
37	C₄×C₅×C₈	—	2	2	no	—
38	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₂×#364	C₂×C₅	1	1	yes	characteristic
41	#2108	C₂×C₅	1	2	yes	—
42	C₂×#346	C₂×C₅	1	1	yes	characteristic
43	#1772	C₂×C₅	1	1	yes	characteristic
44	#1379	C₂×C₅	1	2	yes	—
45	C₂²×C₄×C₅	—	2	1	no	—
46	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
47	C₅×M₁₆	—	2	2	no	—
48	C₅×M₁₆	C₂×C₈	1	4	yes	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	C₄²	1	2	yes	—
51	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
52	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
53	C₂×C₅×C₈	C₂×C₈	1	2	yes	—
54	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
57	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₅×C₈	#41	1	1	yes	characteristic
59	C₂×C₅×C₈	#41	1	1	yes	characteristic
60	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
61	C₅×C₂²⋊C₄	—	2	2	no	—
62	C₄²×C₅	—	2	2	no	—
63	C₄²×C₅	—	2	1	no	—
64	C₄²×C₅	C₄²	1	2	yes	—
65	C₅×C₁₆	—	2	2	no	—
66	C₅×C₁₆	—	2	4	no	—
67	C₅×C₁₆	C₄⋊C₄	1	4	yes	—
68	C₂×M₃₂	C₂²×C₅	1	2	yes	—
69	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
70	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
71	C₂×#108	C₄×C₅	1	1	yes	characteristic
72	#427	C₄×C₅	1	1	yes	characteristic
73	#405	C₂²×C₅	1	2	yes	—
74	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
75	#364	C₄×C₅	1	4	yes	complemented
76	#346	—	2	2	no	—
77	#346	C₄×C₅	1	4	yes	complemented
78	C₄×C₁₆	—	2	2	no	—
79	#339	C₄×C₅	1	2	yes	—
80	C₂³×C₅	#131	1	1	yes	characteristic
81	C₂×C₄×C₅	—	2	2	no	—
82	C₂×C₄×C₅	—	2	4	no	—
83	C₂×C₄×C₅	—	4	2	no	—
84	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
87	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
88	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₅	#131	1	1	yes	characteristic
90	C₅×C₈	—	2	4	no	—
91	C₅×C₈	C₄×C₈	1	2	yes	—
92	C₅×C₈	C₄×C₈	1	2	yes	—
93	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
94	C₅×C₈	#117	1	1	yes	characteristic
95	C₅×C₈	C₄×D₄	1	1	yes	characteristic
96	C₅×C₈	C₄×Q₈	1	1	yes	characteristic
97	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
98	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
99	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
100	#117	C₂×C₄×C₅	1	2	yes	—
101	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
102	M₃₂	—	2	2	no	—
103	M₃₂	C₂×C₄×C₅	1	4	yes	—
104	C₂×C₁₆	—	2	2	no	—
105	C₂×C₁₆	—	2	1	no	—
106	C₂×C₁₆	—	2	1	no	—
107	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
108	C₂×C₁₆	C₂×C₄×C₅	1	2	yes	—
109	C₂×C₁₆	C₅×D₄	1	2	yes	—
110	C₂×C₁₆	C₅×Q₈	1	2	yes	—
111	#108	C₅×C₈	1	4	yes	—
112	#107	C₅×C₈	1	2	yes	—
113	#106	C₅×C₈	1	2	yes	—
114	#97	—	2	2	no	—
115	C₄×C₈	—	2	2	no	—
116	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
117	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
118	C₂²×C₅	—	2	2	no	—
119	C₂²×C₅	#405	1	1	yes	characteristic
120	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
121	C₂²×C₅	C₈×Q₈	1	1	yes	characteristic
122	C₄×C₅	—	4	2	no	—
123	C₄×C₅	—	4	4	no	—
124	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
125	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
126	C₄×C₅	C₈×D₄	1	1	yes	characteristic
127	C₄×C₅	C₈×Q₈	1	1	yes	characteristic
128	C₂²×C₄	—	2	1	no	—
129	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
130	M₁₆	—	2	2	no	—
131	M₁₆	C₂×C₅×C₈	1	4	yes	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	C₄²×C₅	1	2	yes	—
134	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
135	C₂×C₈	C₂×C₅×C₈	1	1	yes	characteristic
136	C₂×C₈	C₂×C₅×C₈	1	2	yes	—
137	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
138	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
139	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
140	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
141	C₂×C₈	C₅×#41	1	1	yes	characteristic
142	C₂×C₈	C₅×#41	1	1	yes	characteristic
143	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
144	C₂²⋊C₄	—	2	2	no	—
145	C₄²	—	2	2	no	—
146	C₄²	—	2	1	no	—
147	C₄²	C₄²×C₅	1	2	yes	—
148	C₁₆	—	2	2	no	—
149	C₁₆	—	2	4	no	—
150	C₁₆	C₅×C₄⋊C₄	1	4	yes	—
151	C₂×C₅	—	2	1	no	—
152	C₂×C₅	—	2	1	no	—
153	C₂×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₅	#2171	1	2	yes	—
155	C₂³	C₅×#131	1	1	yes	characteristic
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
160	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
161	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
162	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
163	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
164	C₂×C₄	C₅×#131	1	1	yes	characteristic
165	C₈	—	2	4	no	—
166	C₈	C₄×C₅×C₈	1	2	yes	—
167	C₈	C₄×C₅×C₈	1	2	yes	—
168	C₈	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
169	C₈	C₅×#117	1	1	yes	characteristic
170	C₈	C₄×C₅×D₄	1	1	yes	characteristic
171	C₈	C₄×C₅×Q₈	1	1	yes	characteristic
172	C₅	#12665	1	1	yes	characteristic, direct product factor, Sylow
173	C₂²	—	2	2	no	—
174	C₂²	C₅×#405	1	1	yes	characteristic
175	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
176	C₂²	C₅×C₈×Q₈	1	1	yes	characteristic
177	C₄	—	4	2	no	—
178	C₄	—	4	4	no	—
179	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
180	C₄	C₂×C₄×C₅×C₈	1	1	yes	characteristic
181	C₄	C₅×C₈×D₄	1	1	yes	characteristic
182	C₄	C₅×C₈×Q₈	1	1	yes	characteristic
183	C₂	—	2	1	no	—
184	C₂	—	2	1	no	—
185	C₂	C₅×C₈×C₄⋊C₄	1	1	yes	characteristic
186	C₂	C₅×#2171	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₄	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₈×D₄
prime radical	C₂³×C₅	#131
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂²×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₅×#364	C₄	semidirect
15. C₅×#346	C₄	semidirect
18. #12665	C₅	direct (N × H)
75. #364	C₄×C₅	semidirect
77. #346	C₄×C₅	semidirect
172. C₅	#12665	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#364	2
C₅×#2108	2
C₂×C₅×#346	2
C₅×#1772	2
C₅×#1379	2
#12665	5

Subgroups — C5×#12665 #11935385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#12665 #11935385