Subgroups — C₅×#13270 #11935990

Order 1280.

316 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2960	C₂	1	1	yes	maximal, characteristic
2	C₅×#2153	C₂	1	1	yes	maximal, characteristic
3	C₅×#2110	C₂	1	1	yes	maximal, characteristic
4	C₅×#1378	C₂	1	2	yes	maximal
5	C₅×#1376	C₂	1	2	yes	maximal
6	C₅×#533	C₄	1	1	yes	characteristic
7	C₂×C₅×M₃₂	C₂²	1	2	yes	—
8	C₂×C₅×M₃₂	C₂²	1	2	yes	—
9	C₅×#446	—	2	2	no	—
10	C₅×C₈×Q₈	—	2	2	no	—
11	C₅×#424	C₄	1	1	yes	characteristic
12	C₅×#424	C₄	1	1	yes	characteristic
13	C₅×#423	C₄	1	1	yes	characteristic
14	C₅×#405	C₂²	1	1	yes	characteristic
15	C₅×#405	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×#364	—	2	2	no	—
18	C₅×#347	—	2	2	no	—
19	#13270	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
24	C₅×C₄⋊Q₈	—	2	1	no	—
25	C₅×#125	—	2	1	no	—
26	C₅×C₂²⋊Q₈	—	2	2	no	—
27	C₄×C₅×Q₈	—	2	2	no	—
28	C₅×#117	C₂×C₄	1	1	yes	characteristic
29	C₅×#117	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
31	C₅×M₃₂	—	2	2	no	—
32	C₅×M₃₂	—	2	2	no	—
33	C₅×M₃₂	—	2	2	no	—
34	C₅×M₃₂	Q₈	1	4	yes	complemented
35	C₂×C₅×C₁₆	—	2	2	no	—
36	C₂×C₅×C₁₆	—	2	2	no	—
37	C₅×C₄⋊C₈	—	2	2	no	—
38	C₅×C₄⋊C₈	—	2	2	no	—
39	C₅×C₄⋊C₈	—	2	2	no	—
40	C₅×#97	—	2	1	no	—
41	C₅×#97	D₄	1	2	yes	—
42	C₄×C₅×C₈	—	2	1	no	—
43	C₄×C₅×C₈	—	2	1	no	—
44	C₄×C₅×C₈	—	2	1	no	—
45	C₄×C₅×C₈	D₄	1	2	yes	—
46	#2960	C₂×C₅	1	1	yes	characteristic
47	#2153	C₂×C₅	1	1	yes	characteristic
48	#2110	C₂×C₅	1	1	yes	characteristic
49	#1378	C₂×C₅	1	2	yes	—
50	#1376	C₂×C₅	1	2	yes	—
51	C₂×C₅×Q₈	—	2	2	no	—
52	C₂²×C₄×C₅	—	2	1	no	—
53	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
54	C₅×M₁₆	—	2	2	no	—
55	C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×C₈	—	2	1	no	—
57	C₂×C₅×C₈	—	2	1	no	—
58	C₂×C₅×C₈	—	2	2	no	—
59	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
60	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
61	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
62	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
63	C₂×C₅×C₈	#41	1	2	yes	—
64	C₅×C₄⋊C₄	—	2	4	no	—
65	C₅×C₄⋊C₄	—	2	2	no	—
66	C₅×C₄⋊C₄	—	2	1	no	—
67	C₅×C₄⋊C₄	—	2	1	no	—
68	C₅×C₂²⋊C₄	—	2	1	no	—
69	C₅×C₂²⋊C₄	M₁₆	1	2	yes	—
70	C₄²×C₅	—	2	1	no	—
71	C₄²×C₅	—	2	1	no	—
72	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
73	C₄²×C₅	M₁₆	1	1	yes	characteristic
74	C₄²×C₅	M₁₆	1	1	yes	characteristic
75	C₅×C₁₆	—	2	4	no	—
76	C₅×C₁₆	—	4	2	no	—
77	#533	C₄×C₅	1	1	yes	characteristic
78	C₂×M₃₂	C₂²×C₅	1	2	yes	—
79	C₂×M₃₂	C₂²×C₅	1	2	yes	—
80	#446	—	2	2	no	—
81	C₈×Q₈	—	2	2	no	—
82	#424	C₄×C₅	1	1	yes	characteristic
83	#424	C₄×C₅	1	1	yes	characteristic
84	#423	C₄×C₅	1	1	yes	characteristic
85	#405	C₂²×C₅	1	1	yes	characteristic
86	#405	C₂²×C₅	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
88	#364	—	2	2	no	—
89	#347	—	2	2	no	—
90	C₂³×C₅	C₂×M₁₆	1	1	yes	characteristic
91	C₅×Q₈	—	4	4	no	—
92	C₂×C₄×C₅	—	2	1	no	—
93	C₂×C₄×C₅	—	2	1	no	—
94	C₂×C₄×C₅	—	2	2	no	—
95	C₂×C₄×C₅	—	2	2	no	—
96	C₂×C₄×C₅	—	4	2	no	—
97	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
99	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
100	C₂×C₄×C₅	#131	1	2	yes	—
101	C₅×C₈	—	2	2	no	—
102	C₅×C₈	—	4	1	no	—
103	C₅×C₈	—	4	1	no	—
104	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
105	C₅×C₈	#124	1	1	yes	characteristic
106	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
107	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
108	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
109	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
110	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
111	C₄⋊Q₈	—	2	1	no	—
112	#125	—	2	1	no	—
113	C₂²⋊Q₈	—	2	2	no	—
114	C₄×Q₈	—	2	2	no	—
115	#117	C₂×C₄×C₅	1	1	yes	characteristic
116	#117	C₂×C₄×C₅	1	1	yes	characteristic
117	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
118	M₃₂	—	2	2	no	—
119	M₃₂	—	2	2	no	—
120	M₃₂	—	2	2	no	—
121	M₃₂	C₅×Q₈	1	4	yes	complemented
122	C₂×C₁₆	—	2	2	no	—
123	C₂×C₁₆	—	2	2	no	—
124	C₄⋊C₈	—	2	2	no	—
125	C₄⋊C₈	—	2	2	no	—
126	C₄⋊C₈	—	2	2	no	—
127	#97	—	2	1	no	—
128	#97	C₅×D₄	1	2	yes	—
129	C₄×C₈	—	2	1	no	—
130	C₄×C₈	—	2	1	no	—
131	C₄×C₈	—	2	1	no	—
132	C₄×C₈	C₅×D₄	1	2	yes	—
133	C₂²×C₅	—	4	1	no	—
134	C₂²×C₅	#407	1	1	yes	characteristic
135	C₂²×C₅	#446	1	2	yes	—
136	C₄×C₅	—	2	2	no	—
137	C₄×C₅	—	4	1	no	—
138	C₄×C₅	—	4	2	no	—
139	C₄×C₅	—	4	2	no	—
140	C₄×C₅	#391	1	1	yes	characteristic
141	C₄×C₅	#408	1	1	yes	characteristic
142	C₄×C₅	#446	1	2	yes	—
143	C₂×Q₈	—	2	2	no	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
146	M₁₆	—	2	2	no	—
147	M₁₆	—	2	2	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
152	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
153	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
154	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
155	C₂×C₈	C₅×#41	1	2	yes	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	2	1	no	—
159	C₄⋊C₄	—	2	1	no	—
160	C₂²⋊C₄	—	2	1	no	—
161	C₂²⋊C₄	C₅×M₁₆	1	2	yes	—
162	C₄²	—	2	1	no	—
163	C₄²	—	2	1	no	—
164	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
165	C₄²	C₅×M₁₆	1	1	yes	characteristic
166	C₄²	C₅×M₁₆	1	1	yes	characteristic
167	C₁₆	—	2	4	no	—
168	C₁₆	—	4	2	no	—
169	C₂×C₅	—	2	1	no	—
170	C₂×C₅	—	2	2	no	—
171	C₂×C₅	#1985	1	1	yes	characteristic
172	C₂³	C₂×C₅×M₁₆	1	1	yes	characteristic
173	Q₈	—	4	4	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
181	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
182	C₂×C₄	C₅×#131	1	2	yes	—
183	C₈	—	2	2	no	—
184	C₈	—	4	1	no	—
185	C₈	—	4	1	no	—
186	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
187	C₈	C₅×#124	1	1	yes	characteristic
188	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
189	C₅	#13270	1	1	yes	characteristic, direct product factor, Sylow
190	C₂²	—	4	1	no	—
191	C₂²	C₅×#407	1	1	yes	characteristic
192	C₂²	C₅×#446	1	2	yes	—
193	C₄	—	2	2	no	—
194	C₄	—	4	1	no	—
195	C₄	—	4	2	no	—
196	C₄	—	4	2	no	—
197	C₄	C₅×#391	1	1	yes	characteristic
198	C₄	C₅×#408	1	1	yes	characteristic
199	C₄	C₅×#446	1	2	yes	—
200	C₂	—	2	1	no	—
201	C₂	—	2	2	no	—
202	C₂	C₅×#1985	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₈	#124
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂×C₅	#1985
prime radical	C₂³×C₅	C₂×M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₅×C₈ ◁ C₂²×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
19. #13270	C₅	direct (N × H)
34. C₅×M₃₂	Q₈	semidirect
121. M₃₂	C₅×Q₈	semidirect
189. C₅	#13270	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×#2960	2
C₅×#2153	2
C₅×#2110	2
C₅×#1378	2
C₅×#1376	2
#13270	5

Subgroups — C5×#13270 #11935990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13270 #11935990