Subgroups — C₅×C₈×#107 #11931001

Order 1280.

446 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₅×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
5	C₅×#1279	C₂	1	2	yes	maximal
6	C₂×C₅×#107	C₄	1	2	yes	—
7	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₈	—	2	2	no	—
9	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₅×#340	C₄	1	2	yes	—
14	C₅×#336	—	2	2	no	—
15	C₅×#335	C₄	1	4	yes	complemented
16	C₅×C₈²	C₄	1	4	yes	complemented
17	C₈×#107	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×C₈	—	2	1	no	—
19	C₂²×C₅×C₈	—	2	2	no	—
20	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₅	—	2	2	no	—
26	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₅×#107	C₈	1	8	yes	direct product factor
28	C₅×C₄⋊C₈	—	2	2	no	—
29	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₅×C₈	—	2	1	no	—
31	C₄×C₅×C₈	—	4	4	no	—
32	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
34	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
35	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
36	C₄×C₅×C₈	Q₈	1	2	yes	—
37	C₅×#95	—	2	2	no	—
38	C₄×#107	C₂×C₅	1	1	yes	characteristic
39	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	—
40	C₂×#335	C₂×C₅	1	1	yes	characteristic
41	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
42	#1279	C₂×C₅	1	2	yes	—
43	C₂²×C₄×C₅	—	2	4	no	—
44	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅	#41	1	1	yes	characteristic
47	C₂×C₅×C₈	—	2	4	no	—
48	C₂×C₅×C₈	—	2	2	no	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	2	1	no	—
51	C₂×C₅×C₈	—	2	1	no	—
52	C₂×C₅×C₈	—	2	4	no	—
53	C₂×C₅×C₈	—	4	2	no	—
54	C₂×C₅×C₈	—	4	2	no	—
55	C₂×C₅×C₈	C₄²	1	2	yes	—
56	C₂×C₅×C₈	C₄²	1	2	yes	—
57	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
58	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
59	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
60	C₂×C₅×C₈	D₈	1	2	yes	—
61	C₂×C₅×C₈	Q₁₆	1	2	yes	—
62	C₅×C₄⋊C₄	—	2	4	no	—
63	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	—
64	C₄²×C₅	—	4	2	no	—
65	C₄²×C₅	—	4	2	no	—
66	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
69	C₄²×C₅	#41	1	1	yes	characteristic
70	C₂×#107	C₄×C₅	1	2	yes	—
71	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
72	C₂×C₄×C₈	—	2	2	no	—
73	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
74	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
75	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
76	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
77	#340	C₄×C₅	1	2	yes	—
78	#336	—	2	2	no	—
79	#335	C₄×C₅	1	4	yes	complemented
80	C₈²	C₄×C₅	1	4	yes	complemented
81	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₅	—	2	2	no	—
83	C₂×C₄×C₅	—	2	8	no	—
84	C₂×C₄×C₅	—	4	4	no	—
85	C₂×C₄×C₅	—	4	4	no	—
86	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
87	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₅	#117	1	1	yes	characteristic
89	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
90	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
91	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
92	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
93	C₂×C₄×C₅	#131	1	2	yes	—
94	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
95	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
96	C₂×C₄×C₅	#135	1	1	yes	characteristic
97	C₂×C₄×C₅	#135	1	1	yes	characteristic
98	C₅×C₈	—	2	4	no	—
99	C₅×C₈	—	2	2	no	—
100	C₅×C₈	—	2	2	no	—
101	C₅×C₈	—	4	4	no	—
102	C₅×C₈	C₄×C₈	1	4	yes	complemented
103	C₅×C₈	#107	1	4	yes	direct product factor
104	C₂²×C₈	—	2	1	no	—
105	C₂²×C₈	—	2	2	no	—
106	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
107	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
108	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
109	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
111	C₂×C₄²	—	2	2	no	—
112	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
113	#107	C₅×C₈	1	8	yes	direct product factor
114	C₄⋊C₈	—	2	2	no	—
115	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
116	C₄×C₈	—	2	1	no	—
117	C₄×C₈	—	4	4	no	—
118	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
119	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
120	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
121	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
122	C₄×C₈	C₅×Q₈	1	2	yes	—
123	#95	—	2	2	no	—
124	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₅	C₈×D₄	1	2	yes	—
126	C₂²×C₅	C₄×D₈	1	1	yes	characteristic
127	C₂²×C₅	C₄×Q₁₆	1	1	yes	characteristic
128	C₂²×C₅	#443	1	2	yes	—
129	C₄×C₅	—	2	1	no	—
130	C₄×C₅	—	2	1	no	—
131	C₄×C₅	—	4	8	no	—
132	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
133	C₄×C₅	#405	1	1	yes	characteristic
134	C₄×C₅	C₂×#107	1	1	yes	characteristic
135	C₄×C₅	#427	1	1	yes	characteristic
136	C₄×C₅	C₄×D₈	1	1	yes	characteristic
137	C₄×C₅	C₄×Q₁₆	1	1	yes	characteristic
138	C₄×C₅	C₈×Q₈	1	2	yes	—
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
141	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
142	C₂²×C₄	C₅×#41	1	1	yes	characteristic
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	—	2	2	no	—
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	1	no	—
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	4	no	—
149	C₂×C₈	—	4	2	no	—
150	C₂×C₈	—	4	2	no	—
151	C₂×C₈	C₄²×C₅	1	2	yes	—
152	C₂×C₈	C₄²×C₅	1	2	yes	—
153	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
154	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
155	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
156	C₂×C₈	C₅×D₈	1	2	yes	—
157	C₂×C₈	C₅×Q₁₆	1	2	yes	—
158	C₄⋊C₄	—	2	4	no	—
159	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	—
160	C₄²	—	4	2	no	—
161	C₄²	—	4	2	no	—
162	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
163	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
164	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
165	C₄²	C₅×#41	1	1	yes	characteristic
166	C₂×C₅	C₈×D₈	1	2	yes	—
167	C₂×C₅	C₈×Q₁₆	1	2	yes	—
168	C₂×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₅	#1772	1	1	yes	characteristic
170	C₂×C₅	C₄×#107	1	1	yes	characteristic
171	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	8	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
177	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄	C₅×#117	1	1	yes	characteristic
179	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
180	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
181	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
182	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
183	C₂×C₄	C₅×#131	1	2	yes	—
184	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
185	C₂×C₄	C₂×C₅×Q₁₆	1	1	yes	characteristic
186	C₂×C₄	C₅×#135	1	1	yes	characteristic
187	C₂×C₄	C₅×#135	1	1	yes	characteristic
188	C₈	—	2	4	no	—
189	C₈	—	2	2	no	—
190	C₈	—	2	2	no	—
191	C₈	—	4	4	no	—
192	C₈	C₄×C₅×C₈	1	4	yes	complemented
193	C₈	C₅×#107	1	4	yes	direct product factor
194	C₅	C₈×#107	1	1	yes	characteristic, direct product factor, Sylow
195	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
196	C₂²	C₅×C₈×D₄	1	2	yes	—
197	C₂²	C₄×C₅×D₈	1	1	yes	characteristic
198	C₂²	C₄×C₅×Q₁₆	1	1	yes	characteristic
199	C₂²	C₅×#443	1	2	yes	—
200	C₄	—	2	1	no	—
201	C₄	—	2	1	no	—
202	C₄	—	4	8	no	—
203	C₄	C₂×C₄×C₅×C₈	1	1	yes	characteristic
204	C₄	C₅×#405	1	1	yes	characteristic
205	C₄	C₂×C₅×#107	1	1	yes	characteristic
206	C₄	C₅×#427	1	1	yes	characteristic
207	C₄	C₄×C₅×D₈	1	1	yes	characteristic
208	C₄	C₄×C₅×Q₁₆	1	1	yes	characteristic
209	C₄	C₅×C₈×Q₈	1	2	yes	—
210	C₂	C₅×C₈×D₈	1	2	yes	—
211	C₂	C₅×C₈×Q₁₆	1	2	yes	—
212	C₂	C₅×C₈×C₄⋊C₄	1	1	yes	characteristic
213	C₂	C₅×#1772	1	1	yes	characteristic
214	C₂	C₄×C₅×#107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅×C₈	D₄
commutator	C₄	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₄×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₅×#335	C₄	semidirect
16. C₅×C₈²	C₄	semidirect
17. C₈×#107	C₅	direct (N × H)
27. C₅×#107	C₈	direct (N × H)
79. #335	C₄×C₅	semidirect
80. C₈²	C₄×C₅	semidirect
102. C₅×C₈	C₄×C₈	semidirect
103. C₅×C₈	#107	direct (N × H)
113. #107	C₅×C₈	direct (N × H)
192. C₈	C₄×C₅×C₈	semidirect
193. C₈	C₅×#107	direct (N × H)
194. C₅	C₈×#107	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#107	2
C₅×C₈×C₄⋊C₄	2
C₂×C₅×#335	2
C₂×C₅×C₈²	2
C₅×#1279	2
C₈×#107	5

Subgroups — C5×C8×#107 #11931001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈×#107 #11931001