Subgroups — C₂×D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈) #72217841

Order 6720.

1704 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×ΓL(1,𝔽₈)×C₂²⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
3	C₂×ΓL(1,𝔽₈)×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×D₅×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
5	D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂	1	2	yes	maximal, complemented
8	C₂³×D₅×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
9	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	2	8	no	—
10	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
11	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
12	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
13	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	1	8	yes	complemented
14	C₂×C₅×D₄×ΓL(1,𝔽₈)	C₄	1	1	yes	characteristic, complemented
15	C₂×ΓL(1,𝔽₈)×C₂²⋊D₅	C₄	1	2	yes	complemented
16	D₄×D₅×ΓL(1,𝔽₈)	C₄	1	4	yes	complemented
17	D₄×D₅×ΓL(1,𝔽₈)	C₂²	1	4	yes	—
18	C₂×ΓL(1,𝔽₈)×D₂₀	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×D₅×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
20	ΓL(1,𝔽₈)×C₂²⋊AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
21	ΓL(1,𝔽₈)×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
22	C₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	1	4	yes	complemented
23	C₂×C₄×D₄×ΓL(1,𝔽₈)	—	5	1	no	maximal, Hall
24	C₂³×C₇×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
25	C₂×C₇×D₄×D₅	C₂×C₃	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
27	C₇×D₄×AGL(1,𝔽₅)	C₂×C₃	1	8	yes	complemented
28	C₂×C₇×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₄×C₇×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×D₄×AGL(1,𝔽₅)	—	7	1	no	maximal, Hall
31	C₂³×C₅×ΓL(1,𝔽₈)	C₂×C₄	1	2	yes	complemented
32	C₂²×D₅×ΓL(1,𝔽₈)	—	2	4	no	—
33	C₂²×D₅×ΓL(1,𝔽₈)	—	2	4	no	—
34	C₂²×D₅×ΓL(1,𝔽₈)	C₂×C₄	1	4	yes	complemented
35	C₂²×D₅×ΓL(1,𝔽₈)	C₂×C₄	1	2	yes	complemented
36	C₂²×D₅×ΓL(1,𝔽₈)	C₂³	1	4	yes	—
37	C₂²×D₅×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
38	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	2	4	no	—
39	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	2	2	no	—
40	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	2	16	no	—
41	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	D₄	1	4	yes	direct product factor
42	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
43	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂³	1	4	yes	—
44	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
45	C₅×D₄×ΓL(1,𝔽₈)	C₂×C₄	1	4	yes	complemented
46	C₂×C₄×C₅×ΓL(1,𝔽₈)	C₂×C₄	1	1	yes	characteristic, complemented
47	ΓL(1,𝔽₈)×C₂²⋊D₅	C₂×C₄	1	8	yes	complemented
48	C₂×Dic₅×ΓL(1,𝔽₈)	C₂×C₄	1	1	yes	characteristic, complemented
49	ΓL(1,𝔽₈)×D₂₀	C₂×C₄	1	4	yes	complemented
50	C₄×D₅×ΓL(1,𝔽₈)	C₂×C₄	1	2	yes	complemented
51	C₄×D₅×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
52	C₂²×D₄×ΓL(1,𝔽₈)	—	5	1	no	—
53	C₂³×C₄×ΓL(1,𝔽₈)	—	5	2	no	—
54	C₄×D₄×ΓL(1,𝔽₈)	—	5	8	no	—
55	C₂×C₄⋊C₄×ΓL(1,𝔽₈)	—	5	1	no	—
56	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	—	5	2	no	—
57	C₂×C₄²×ΓL(1,𝔽₈)	—	5	1	no	—
58	C₂³×C₇×D₅	C₂²×C₃	1	2	yes	—
59	C₂²×C₇×AGL(1,𝔽₅)	—	2	8	no	—
60	C₂²×C₇×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₇×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
62	C₂²×C₇×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₇×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
64	C₂×C₅×C₇×D₄	C₃×C₄	1	1	yes	characteristic, complemented
65	C₂×C₇×C₂²⋊D₅	C₃×C₄	1	2	yes	complemented
66	C₇×D₄×D₅	C₃×C₄	1	4	yes	complemented
67	C₇×D₄×D₅	C₂²×C₃	1	4	yes	—
68	C₂×C₇×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
69	C₂×C₄×C₇×D₅	C₂²×C₃	1	1	yes	characteristic
70	C₇×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
71	C₇×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	complemented
72	C₄×C₇×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	complemented
73	C₂³×C₃×AGL(1,𝔽₅)	—	7	2	no	—
74	C₂×C₃×D₄×D₅	—	7	1	no	—
75	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	7	2	no	—
76	C₃×D₄×AGL(1,𝔽₅)	—	7	8	no	—
77	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	7	1	no	—
78	C₂×C₃×C₄×AGL(1,𝔽₅)	—	7	1	no	—
79	C₂×C₄×C₇×D₄	—	5	1	no	Hall
80	C₂²×C₅×ΓL(1,𝔽₈)	—	2	4	no	—
81	C₂²×C₅×ΓL(1,𝔽₈)	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₅×ΓL(1,𝔽₈)	C₂²×C₄	1	4	yes	complemented
83	C₂×D₅×ΓL(1,𝔽₈)	—	2	8	no	—
84	C₂×D₅×ΓL(1,𝔽₈)	—	2	4	no	—
85	C₂×D₅×ΓL(1,𝔽₈)	—	2	4	no	—
86	C₂×D₅×ΓL(1,𝔽₈)	—	2	4	no	—
87	C₂×D₅×ΓL(1,𝔽₈)	C₂²×C₄	1	1	yes	characteristic
88	C₂×D₅×ΓL(1,𝔽₈)	C₂²×C₄	1	4	yes	complemented
89	C₂×D₅×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
90	C₂×D₅×ΓL(1,𝔽₈)	#41	1	2	yes	—
91	C₂×D₅×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
92	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	2	4	no	—
93	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	—	2	2	no	—
94	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂×D₄	1	4	yes	direct product factor
95	C₄×C₅×ΓL(1,𝔽₈)	C₂²×C₄	1	2	yes	complemented
96	Dic₅×ΓL(1,𝔽₈)	C₂²×C₄	1	2	yes	complemented
97	C₂⁴×ΓL(1,𝔽₈)	—	5	2	no	—
98	C₂×D₄×ΓL(1,𝔽₈)	—	5	2	no	—
99	C₂×D₄×ΓL(1,𝔽₈)	—	5	4	no	—
100	C₂×D₄×ΓL(1,𝔽₈)	—	5	4	no	—
101	C₂×D₄×ΓL(1,𝔽₈)	—	5	1	no	—
102	C₂×D₄×ΓL(1,𝔽₈)	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
103	C₂²×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
104	C₂²×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
105	C₂²×C₄×ΓL(1,𝔽₈)	—	5	2	no	—
106	C₂²×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
107	C₂²×C₄×ΓL(1,𝔽₈)	—	5	8	no	—
108	C₂²×C₄×ΓL(1,𝔽₈)	—	10	8	no	—
109	C₄⋊C₄×ΓL(1,𝔽₈)	—	5	4	no	—
110	C₂²⋊C₄×ΓL(1,𝔽₈)	—	5	8	no	—
111	C₄²×ΓL(1,𝔽₈)	—	5	4	no	—
112	C₂×D₄×AGL(1,𝔽₅)	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
113	C₂³×C₅×C₇	C₂×C₃×C₄	1	2	yes	complemented
114	C₂²×C₇×D₅	—	2	4	no	—
115	C₂²×C₇×D₅	—	2	4	no	—
116	C₂²×C₇×D₅	C₂×C₃×C₄	1	4	yes	complemented
117	C₂²×C₇×D₅	C₂×C₃×C₄	1	2	yes	complemented
118	C₂²×C₇×D₅	C₂³×C₃	1	4	yes	—
119	C₂²×C₇×D₅	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₇×AGL(1,𝔽₅)	—	2	4	no	—
121	C₂×C₇×AGL(1,𝔽₅)	—	2	2	no	—
122	C₂×C₇×AGL(1,𝔽₅)	—	2	16	no	—
123	C₂×C₇×AGL(1,𝔽₅)	C₃×D₄	1	4	yes	complemented
124	C₂×C₇×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
125	C₂×C₇×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
126	C₂×C₇×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
127	C₅×C₇×D₄	C₂×C₃×C₄	1	4	yes	complemented
128	C₂×C₄×C₅×C₇	C₂×C₃×C₄	1	1	yes	characteristic, complemented
129	C₇×C₂²⋊D₅	C₂×C₃×C₄	1	8	yes	complemented
130	C₂×C₇×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
131	C₇×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
132	C₄×C₇×D₅	C₂×C₃×C₄	1	2	yes	complemented
133	C₄×C₇×D₅	C₂³×C₃	1	2	yes	—
134	C₂³×C₃×D₅	—	7	2	no	—
135	C₂²×C₃×AGL(1,𝔽₅)	—	7	1	no	—
136	C₂²×C₃×AGL(1,𝔽₅)	—	7	1	no	—
137	C₂²×C₃×AGL(1,𝔽₅)	—	7	2	no	—
138	C₂²×C₃×AGL(1,𝔽₅)	—	7	8	no	—
139	C₂²×C₃×AGL(1,𝔽₅)	—	14	8	no	—
140	C₂×C₃×C₅×D₄	—	7	1	no	—
141	C₂×C₃×C₂²⋊D₅	—	7	2	no	—
142	C₃×D₄×D₅	—	7	4	no	—
143	C₃×D₄×D₅	—	7	4	no	—
144	C₂×C₃×D₂₀	—	7	1	no	—
145	C₂×C₃×C₄×D₅	—	7	1	no	—
146	C₃×C₂²⋊AGL(1,𝔽₅)	—	7	8	no	—
147	C₃×C₄⋊AGL(1,𝔽₅)	—	7	4	no	—
148	C₃×C₄×AGL(1,𝔽₅)	—	7	4	no	—
149	C₂²×C₇×D₄	—	5	1	no	—
150	C₂³×C₄×C₇	—	5	2	no	—
151	C₄×C₇×D₄	—	5	8	no	—
152	C₂×C₇×C₄⋊C₄	—	5	1	no	—
153	C₂×C₇×C₂²⋊C₄	—	5	2	no	—
154	C₂×C₄²×C₇	—	5	1	no	—
155	C₂×C₅×ΓL(1,𝔽₈)	—	2	4	no	—
156	C₂×C₅×ΓL(1,𝔽₈)	C₄×D₄	1	2	yes	complemented
157	C₂×C₅×ΓL(1,𝔽₈)	C₂³×C₄	1	1	yes	characteristic
158	D₅×ΓL(1,𝔽₈)	—	2	4	no	—
159	D₅×ΓL(1,𝔽₈)	C₄×D₄	1	2	yes	complemented
160	D₅×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
161	D₅×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
162	C₂×C₃×C₄×D₄	—	35	1	no	Hall
163	C₂³×ΓL(1,𝔽₈)	—	5	1	no	—
164	C₂³×ΓL(1,𝔽₈)	—	5	2	no	—
165	C₂³×ΓL(1,𝔽₈)	—	5	4	no	—
166	C₂³×ΓL(1,𝔽₈)	—	5	4	no	—
167	C₂³×ΓL(1,𝔽₈)	—	10	4	no	—
168	C₂³×ΓL(1,𝔽₈)	—	10	4	no	—
169	C₂³×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
170	D₄×ΓL(1,𝔽₈)	—	5	8	no	—
171	D₄×ΓL(1,𝔽₈)	—	5	4	no	—
172	D₄×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	1	4	yes	direct product factor
173	C₂×C₄×ΓL(1,𝔽₈)	—	5	2	no	—
174	C₂×C₄×ΓL(1,𝔽₈)	—	5	4	no	—
175	C₂×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
176	C₂×C₄×ΓL(1,𝔽₈)	—	5	2	no	—
177	C₂×C₄×ΓL(1,𝔽₈)	—	5	2	no	—
178	C₂×C₄×ΓL(1,𝔽₈)	—	5	2	no	—
179	C₂×C₄×ΓL(1,𝔽₈)	—	5	4	no	—
180	C₂×C₄×ΓL(1,𝔽₈)	—	10	16	no	—
181	C₂×C₄×ΓL(1,𝔽₈)	—	10	4	no	—
182	C₂×C₄×ΓL(1,𝔽₈)	—	10	2	no	—
183	C₂×C₄×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
184	C₂³×AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
185	C₂×D₄×D₅	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
186	C₂×C₂²⋊AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
187	D₄×AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	1	8	yes	direct product factor
188	C₂×C₄⋊AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
189	C₂×C₄×AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
190	C₂²×C₅×C₇	—	2	4	no	—
191	C₂²×C₅×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
192	C₂²×C₅×C₇	C₂²×C₃×C₄	1	4	yes	complemented
193	C₂×C₇×D₅	—	2	4	no	—
194	C₂×C₇×D₅	—	2	8	no	—
195	C₂×C₇×D₅	—	2	4	no	—
196	C₂×C₇×D₅	—	2	4	no	—
197	C₂×C₇×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
198	C₂×C₇×D₅	C₂²×C₃×C₄	1	4	yes	complemented
199	C₂×C₇×D₅	C₂×C₃×D₄	1	2	yes	—
200	C₂×C₇×D₅	C₃×#41	1	2	yes	—
201	C₂×C₇×D₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₇×AGL(1,𝔽₅)	—	2	4	no	—
203	C₇×AGL(1,𝔽₅)	—	2	2	no	—
204	C₇×AGL(1,𝔽₅)	C₂×C₃×D₄	1	4	yes	complemented
205	C₄×C₅×C₇	C₂²×C₃×C₄	1	2	yes	complemented
206	C₇×Dic₅	C₂²×C₃×C₄	1	2	yes	complemented
207	C₂³×C₃×C₅	—	7	2	no	—
208	C₂²×C₃×D₅	—	7	1	no	—
209	C₂²×C₃×D₅	—	7	2	no	—
210	C₂²×C₃×D₅	—	7	4	no	—
211	C₂²×C₃×D₅	—	7	4	no	—
212	C₂²×C₃×D₅	—	14	4	no	—
213	C₂²×C₃×D₅	—	14	4	no	—
214	C₂×C₃×AGL(1,𝔽₅)	—	7	4	no	—
215	C₂×C₃×AGL(1,𝔽₅)	—	7	2	no	—
216	C₂×C₃×AGL(1,𝔽₅)	—	7	2	no	—
217	C₂×C₃×AGL(1,𝔽₅)	—	7	4	no	—
218	C₂×C₃×AGL(1,𝔽₅)	—	14	16	no	—
219	C₂×C₃×AGL(1,𝔽₅)	—	14	2	no	—
220	C₂×C₃×AGL(1,𝔽₅)	—	14	4	no	—
221	C₃×C₅×D₄	—	7	4	no	—
222	C₂×C₃×C₄×C₅	—	7	1	no	—
223	C₃×C₂²⋊D₅	—	7	8	no	—
224	C₂×C₃×Dic₅	—	7	1	no	—
225	C₃×D₂₀	—	7	4	no	—
226	C₃×C₄×D₅	—	7	2	no	—
227	C₃×C₄×D₅	—	7	2	no	—
228	C₂⁴×C₇	—	5	2	no	—
229	C₂×C₇×D₄	—	5	2	no	—
230	C₂×C₇×D₄	—	5	4	no	—
231	C₂×C₇×D₄	—	5	4	no	—
232	C₂×C₇×D₄	—	5	1	no	—
233	C₂×C₇×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
234	C₂²×C₄×C₇	—	5	1	no	—
235	C₂²×C₄×C₇	—	5	1	no	—
236	C₂²×C₄×C₇	—	5	1	no	—
237	C₂²×C₄×C₇	—	5	2	no	—
238	C₂²×C₄×C₇	—	5	8	no	—
239	C₂²×C₄×C₇	—	10	8	no	—
240	C₇×C₄⋊C₄	—	5	4	no	—
241	C₇×C₂²⋊C₄	—	5	8	no	—
242	C₄²×C₇	—	5	4	no	—
243	C₅×ΓL(1,𝔽₈)	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Hall
244	C₂²×C₃×D₄	—	35	1	no	—
245	C₂³×C₃×C₄	—	35	2	no	—
246	C₃×C₄×D₄	—	35	8	no	—
247	C₂×C₃×C₄⋊C₄	—	35	1	no	—
248	C₂×C₃×C₂²⋊C₄	—	35	2	no	—
249	C₂×C₃×C₄²	—	35	1	no	—
250	C₂²×ΓL(1,𝔽₈)	—	2	4	no	—
251	C₂²×ΓL(1,𝔽₈)	—	5	2	no	—
252	C₂²×ΓL(1,𝔽₈)	—	5	2	no	—
253	C₂²×ΓL(1,𝔽₈)	—	5	1	no	—
254	C₂²×ΓL(1,𝔽₈)	—	5	1	no	—
255	C₂²×ΓL(1,𝔽₈)	—	5	4	no	—
256	C₂²×ΓL(1,𝔽₈)	—	10	4	no	—
257	C₂²×ΓL(1,𝔽₈)	—	10	4	no	—
258	C₂²×ΓL(1,𝔽₈)	—	10	8	no	—
259	C₂²×ΓL(1,𝔽₈)	—	10	4	no	—
260	C₂²×ΓL(1,𝔽₈)	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
261	C₂²×ΓL(1,𝔽₈)	C₂²×AGL(1,𝔽₅)	1	4	yes	complemented
262	C₄×ΓL(1,𝔽₈)	—	5	4	no	—
263	C₄×ΓL(1,𝔽₈)	—	5	2	no	—
264	C₄×ΓL(1,𝔽₈)	—	10	4	no	—
265	C₄×ΓL(1,𝔽₈)	—	10	2	no	—
266	C₄×ΓL(1,𝔽₈)	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
267	C₂³×D₅	C₂²×ΓL(1,𝔽₈)	1	2	yes	—
268	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
269	C₂²×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
270	C₂²×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	2	yes	—
271	C₂²×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
272	C₂²×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	8	yes	complemented
273	C₂×C₅×D₄	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
274	C₂×C₂²⋊D₅	C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
275	D₄×D₅	C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
276	D₄×D₅	C₂²×ΓL(1,𝔽₈)	1	4	yes	—
277	C₂×D₂₀	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
278	C₂×C₄×D₅	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
279	C₂²⋊AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	8	yes	complemented
280	C₄⋊AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	4	yes	complemented
281	C₄×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	1	4	yes	complemented
282	C₂×C₅×C₇	—	2	4	no	—
283	C₂×C₅×C₇	C₃×C₄×D₄	1	2	yes	complemented
284	C₂×C₅×C₇	C₂³×C₃×C₄	1	1	yes	characteristic
285	C₇×D₅	—	2	4	no	—
286	C₇×D₅	C₃×C₄×D₄	1	2	yes	complemented
287	C₇×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
288	C₇×D₅	C₂×C₃×#41	1	1	yes	characteristic
289	C₂×C₄×D₄	—	5	1	no	Sylow
290	C₂²×C₃×C₅	—	7	1	no	—
291	C₂²×C₃×C₅	—	7	4	no	—
292	C₂²×C₃×C₅	—	14	4	no	—
293	C₂×C₃×D₅	—	7	1	no	—
294	C₂×C₃×D₅	—	7	4	no	—
295	C₂×C₃×D₅	—	7	2	no	—
296	C₂×C₃×D₅	—	7	2	no	—
297	C₂×C₃×D₅	—	7	1	no	—
298	C₂×C₃×D₅	—	14	4	no	—
299	C₂×C₃×D₅	—	14	4	no	—
300	C₂×C₃×D₅	—	14	8	no	—
301	C₂×C₃×D₅	—	14	4	no	—
302	C₃×AGL(1,𝔽₅)	—	7	4	no	—
303	C₃×AGL(1,𝔽₅)	—	14	4	no	—
304	C₃×AGL(1,𝔽₅)	—	14	2	no	—
305	C₃×C₄×C₅	—	7	2	no	—
306	C₃×Dic₅	—	7	2	no	—
307	C₂³×C₇	—	5	1	no	—
308	C₂³×C₇	—	5	2	no	—
309	C₂³×C₇	—	5	4	no	—
310	C₂³×C₇	—	5	4	no	—
311	C₂³×C₇	—	10	4	no	—
312	C₂³×C₇	—	10	4	no	—
313	C₂³×C₇	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
314	C₇×D₄	—	5	8	no	—
315	C₇×D₄	—	5	4	no	—
316	C₇×D₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
317	C₂×C₄×C₇	—	5	4	no	—
318	C₂×C₄×C₇	—	5	2	no	—
319	C₂×C₄×C₇	—	5	1	no	—
320	C₂×C₄×C₇	—	5	2	no	—
321	C₂×C₄×C₇	—	5	2	no	—
322	C₂×C₄×C₇	—	5	2	no	—
323	C₂×C₄×C₇	—	5	4	no	—
324	C₂×C₄×C₇	—	10	16	no	—
325	C₂×C₄×C₇	—	10	4	no	—
326	C₂×C₄×C₇	—	10	2	no	—
327	C₂×C₄×C₇	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
328	C₂⁴×C₃	—	35	2	no	—
329	C₂×C₃×D₄	—	7	1	no	—
330	C₂×C₃×D₄	—	35	1	no	—
331	C₂×C₃×D₄	—	35	4	no	—
332	C₂×C₃×D₄	—	35	4	no	—
333	C₂×C₃×D₄	—	35	2	no	—
334	C₂²×C₃×C₄	—	35	1	no	—
335	C₂²×C₃×C₄	—	35	1	no	—
336	C₂²×C₃×C₄	—	35	1	no	—
337	C₂²×C₃×C₄	—	35	2	no	—
338	C₂²×C₃×C₄	—	35	8	no	—
339	C₂²×C₃×C₄	—	70	8	no	—
340	C₃×C₄⋊C₄	—	35	4	no	—
341	C₃×C₂²⋊C₄	—	35	8	no	—
342	C₃×C₄²	—	35	4	no	—
343	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
344	C₂×ΓL(1,𝔽₈)	—	5	1	no	—
345	C₂×ΓL(1,𝔽₈)	—	5	1	no	—
346	C₂×ΓL(1,𝔽₈)	—	5	2	no	—
347	C₂×ΓL(1,𝔽₈)	—	10	4	no	—
348	C₂×ΓL(1,𝔽₈)	D₄×AGL(1,𝔽₅)	1	2	yes	direct product factor
349	C₂×ΓL(1,𝔽₈)	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₂³×C₅	C₂×C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
351	C₂²×D₅	—	2	4	no	—
352	C₂²×D₅	—	2	4	no	—
353	C₂²×D₅	C₂×C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
354	C₂²×D₅	C₂×C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
355	C₂²×D₅	C₂³×ΓL(1,𝔽₈)	1	4	yes	—
356	C₂²×D₅	C₂³×ΓL(1,𝔽₈)	1	1	yes	characteristic
357	C₂×AGL(1,𝔽₅)	—	2	4	no	—
358	C₂×AGL(1,𝔽₅)	—	2	2	no	—
359	C₂×AGL(1,𝔽₅)	—	2	16	no	—
360	C₂×AGL(1,𝔽₅)	D₄×ΓL(1,𝔽₈)	1	4	yes	direct product factor
361	C₂×AGL(1,𝔽₅)	C₂³×ΓL(1,𝔽₈)	1	2	yes	—
362	C₂×AGL(1,𝔽₅)	C₂³×ΓL(1,𝔽₈)	1	4	yes	—
363	C₂×AGL(1,𝔽₅)	C₂³×ΓL(1,𝔽₈)	1	2	yes	—
364	C₅×D₄	C₂×C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
365	C₂×C₄×C₅	C₂×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
366	C₂²⋊D₅	C₂×C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
367	C₂×Dic₅	C₂×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
368	D₂₀	C₂×C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
369	C₄×D₅	C₂×C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
370	C₄×D₅	C₂³×ΓL(1,𝔽₈)	1	2	yes	—
371	C₅×C₇	C₂×C₃×C₄×D₄	1	1	yes	characteristic, complemented, Hall
372	C₂²×D₄	—	5	1	no	—
373	C₂³×C₄	—	5	2	no	—
374	C₄×D₄	—	5	8	no	—
375	C₂×C₄⋊C₄	—	5	1	no	—
376	C₂×C₂²⋊C₄	—	5	2	no	—
377	C₂×C₄²	—	5	1	no	—
378	C₂×C₃×C₅	—	7	1	no	—
379	C₂×C₃×C₅	—	7	2	no	—
380	C₂×C₃×C₅	—	14	4	no	—
381	C₃×D₅	—	7	1	no	—
382	C₃×D₅	—	7	1	no	—
383	C₃×D₅	—	7	2	no	—
384	C₃×D₅	—	14	4	no	—
385	C₂²×C₇	—	2	4	no	—
386	C₂²×C₇	—	5	2	no	—
387	C₂²×C₇	—	5	2	no	—
388	C₂²×C₇	—	5	1	no	—
389	C₂²×C₇	—	5	1	no	—
390	C₂²×C₇	—	5	4	no	—
391	C₂²×C₇	—	10	4	no	—
392	C₂²×C₇	—	10	4	no	—
393	C₂²×C₇	—	10	8	no	—
394	C₂²×C₇	—	10	4	no	—
395	C₂²×C₇	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
396	C₂²×C₇	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
397	C₄×C₇	—	5	4	no	—
398	C₄×C₇	—	5	2	no	—
399	C₄×C₇	—	10	4	no	—
400	C₄×C₇	—	10	2	no	—
401	C₄×C₇	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
402	C₂³×C₃	—	7	2	no	—
403	C₂³×C₃	—	35	1	no	—
404	C₂³×C₃	—	35	4	no	—
405	C₂³×C₃	—	35	2	no	—
406	C₂³×C₃	—	35	4	no	—
407	C₂³×C₃	—	70	4	no	—
408	C₂³×C₃	—	70	4	no	—
409	C₃×D₄	—	7	4	no	—
410	C₃×D₄	—	35	4	no	—
411	C₃×D₄	—	35	8	no	—
412	C₂×C₃×C₄	—	7	1	no	—
413	C₂×C₃×C₄	—	35	2	no	—
414	C₂×C₃×C₄	—	35	2	no	—
415	C₂×C₃×C₄	—	35	1	no	—
416	C₂×C₃×C₄	—	35	2	no	—
417	C₂×C₃×C₄	—	35	4	no	—
418	C₂×C₃×C₄	—	35	2	no	—
419	C₂×C₃×C₄	—	35	4	no	—
420	C₂×C₃×C₄	—	70	16	no	—
421	C₂×C₃×C₄	—	70	2	no	—
422	C₂×C₃×C₄	—	70	4	no	—
423	ΓL(1,𝔽₈)	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
424	C₂²×C₅	—	2	4	no	—
425	C₂²×C₅	C₂²×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
426	C₂²×C₅	C₂²×C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
427	C₂×D₅	—	2	4	no	—
428	C₂×D₅	—	2	4	no	—
429	C₂×D₅	—	2	4	no	—
430	C₂×D₅	—	2	8	no	—
431	C₂×D₅	C₂²×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
432	C₂×D₅	C₂²×C₄×ΓL(1,𝔽₈)	1	4	yes	complemented
433	C₂×D₅	C₂×D₄×ΓL(1,𝔽₈)	1	2	yes	—
434	C₂×D₅	#41×ΓL(1,𝔽₈)	1	2	yes	—
435	C₂×D₅	C₂⁴×ΓL(1,𝔽₈)	1	1	yes	characteristic
436	AGL(1,𝔽₅)	—	2	4	no	—
437	AGL(1,𝔽₅)	—	2	2	no	—
438	AGL(1,𝔽₅)	C₂×D₄×ΓL(1,𝔽₈)	1	4	yes	direct product factor
439	C₄×C₅	C₂²×C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
440	Dic₅	C₂²×C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
441	C₂⁴	—	5	2	no	—
442	C₂×D₄	—	5	2	no	—
443	C₂×D₄	—	5	4	no	—
444	C₂×D₄	—	5	4	no	—
445	C₂×D₄	—	5	1	no	—
446	C₂×D₄	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
447	C₂²×C₄	—	5	1	no	—
448	C₂²×C₄	—	5	1	no	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	2	no	—
451	C₂²×C₄	—	5	8	no	—
452	C₂²×C₄	—	10	8	no	—
453	C₄⋊C₄	—	5	4	no	—
454	C₂²⋊C₄	—	5	8	no	—
455	C₄²	—	5	4	no	—
456	C₃×C₅	—	7	1	no	Hall
457	C₂×C₇	—	2	4	no	—
458	C₂×C₇	—	5	1	no	—
459	C₂×C₇	—	5	1	no	—
460	C₂×C₇	—	5	2	no	—
461	C₂×C₇	—	10	4	no	—
462	C₂×C₇	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	complemented
463	C₂×C₇	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
464	C₂²×C₃	—	7	1	no	—
465	C₂²×C₃	—	7	4	no	—
466	C₂²×C₃	—	14	4	no	—
467	C₂²×C₃	—	35	1	no	—
468	C₂²×C₃	—	35	2	no	—
469	C₂²×C₃	—	35	1	no	—
470	C₂²×C₃	—	35	2	no	—
471	C₂²×C₃	—	35	4	no	—
472	C₂²×C₃	—	70	4	no	—
473	C₂²×C₃	—	70	4	no	—
474	C₂²×C₃	—	70	4	no	—
475	C₂²×C₃	—	70	8	no	—
476	C₃×C₄	—	7	2	no	—
477	C₃×C₄	—	35	2	no	—
478	C₃×C₄	—	35	4	no	—
479	C₃×C₄	—	70	4	no	—
480	C₃×C₄	—	70	2	no	—
481	C₂×C₅	—	2	4	no	—
482	C₂×C₅	C₄×D₄×ΓL(1,𝔽₈)	1	2	yes	complemented
483	C₂×C₅	C₂³×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
484	D₅	—	2	4	no	—
485	D₅	C₄×D₄×ΓL(1,𝔽₈)	1	2	yes	complemented
486	D₅	C₂²×D₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
487	D₅	C₂×#41×ΓL(1,𝔽₈)	1	1	yes	characteristic
488	C₂³	—	5	1	no	—
489	C₂³	—	5	2	no	—
490	C₂³	—	5	4	no	—
491	C₂³	—	5	4	no	—
492	C₂³	—	10	4	no	—
493	C₂³	—	10	4	no	—
494	C₂³	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	2	yes	complemented
495	D₄	—	5	8	no	—
496	D₄	—	5	4	no	—
497	D₄	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	4	yes	direct product factor
498	C₂×C₄	—	5	2	no	—
499	C₂×C₄	—	5	4	no	—
500	C₂×C₄	—	5	1	no	—
501	C₂×C₄	—	5	2	no	—
502	C₂×C₄	—	5	2	no	—
503	C₂×C₄	—	5	2	no	—
504	C₂×C₄	—	5	4	no	—
505	C₂×C₄	—	10	16	no	—
506	C₂×C₄	—	10	4	no	—
507	C₂×C₄	—	10	2	no	—
508	C₂×C₄	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
509	C₇	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
510	C₂×C₃	—	7	1	no	—
511	C₂×C₃	—	7	2	no	—
512	C₂×C₃	—	14	4	no	—
513	C₂×C₃	—	35	1	no	—
514	C₂×C₃	—	35	1	no	—
515	C₂×C₃	—	35	2	no	—
516	C₂×C₃	—	70	4	no	—
517	C₅	C₂×C₄×D₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
518	C₂²	—	2	4	no	—
519	C₂²	—	5	1	no	—
520	C₂²	—	5	1	no	—
521	C₂²	—	5	2	no	—
522	C₂²	—	5	2	no	—
523	C₂²	—	5	4	no	—
524	C₂²	—	10	4	no	—
525	C₂²	—	10	4	no	—
526	C₂²	—	10	8	no	—
527	C₂²	—	10	4	no	—
528	C₂²	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	1	yes	characteristic
529	C₂²	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	4	yes	complemented
530	C₄	—	5	4	no	—
531	C₄	—	5	2	no	—
532	C₄	—	10	4	no	—
533	C₄	—	10	2	no	—
534	C₄	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	2	yes	complemented
535	C₃	—	7	1	no	Sylow
536	C₂	—	2	4	no	—
537	C₂	—	5	1	no	—
538	C₂	—	5	1	no	—
539	C₂	—	5	2	no	—
540	C₂	—	10	4	no	—
541	C₂	C₂³×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	1	yes	characteristic
542	C₂	D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	1	2	yes	direct product factor

	subgroup	G/H
center	C₂²	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)
commutator	C₂×C₅×C₇	C₂³×C₃×C₄
Frattini	C₂	C₂³×AGL(1,𝔽₅)×ΓL(1,𝔽₈)
Fitting	C₂×C₅×C₇×D₄	C₃×C₄
socle	C₂²×C₅×C₇	C₂²×C₃×C₄
prime radical	C₂×D₄×D₅×ΓL(1,𝔽₈)	C₂
cosocle	C₂×C₇×D₅	C₂⁴×C₃
hypercenter	C₂×D₄	AGL(1,𝔽₅)×ΓL(1,𝔽₈)
hypocenter	C₅×C₇	C₂×C₃×C₄×D₄
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×D₄×AGL(1,𝔽₅)	C₃	semidirect
2. C₂×ΓL(1,𝔽₈)×C₂²⋊AGL(1,𝔽₅)	C₂	semidirect
3. C₂×ΓL(1,𝔽₈)×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
5. D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂	direct (N × H)
6. C₂×C₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂	semidirect
7. C₂³×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂	semidirect
13. C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	semidirect
14. C₂×C₅×D₄×ΓL(1,𝔽₈)	C₄	semidirect
15. C₂×ΓL(1,𝔽₈)×C₂²⋊D₅	C₄	semidirect
16. D₄×D₅×ΓL(1,𝔽₈)	C₄	semidirect
18. C₂×ΓL(1,𝔽₈)×D₂₀	C₄	semidirect
20. ΓL(1,𝔽₈)×C₂²⋊AGL(1,𝔽₅)	C₂²	semidirect
21. ΓL(1,𝔽₈)×C₄⋊AGL(1,𝔽₅)	C₂²	semidirect
22. C₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂²	semidirect
24. C₂³×C₇×AGL(1,𝔽₅)	C₂×C₃	semidirect
26. C₂×C₇×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
27. C₇×D₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
28. C₂×C₇×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
29. C₂×C₄×C₇×AGL(1,𝔽₅)	C₂×C₃	semidirect
31. C₂³×C₅×ΓL(1,𝔽₈)	C₂×C₄	semidirect
34. C₂²×D₅×ΓL(1,𝔽₈)	C₂×C₄	semidirect
35. C₂²×D₅×ΓL(1,𝔽₈)	C₂×C₄	semidirect
41. C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	D₄	direct (N × H)
45. C₅×D₄×ΓL(1,𝔽₈)	C₂×C₄	semidirect
46. C₂×C₄×C₅×ΓL(1,𝔽₈)	C₂×C₄	semidirect
47. ΓL(1,𝔽₈)×C₂²⋊D₅	C₂×C₄	semidirect
48. C₂×Dic₅×ΓL(1,𝔽₈)	C₂×C₄	semidirect
49. ΓL(1,𝔽₈)×D₂₀	C₂×C₄	semidirect
50. C₄×D₅×ΓL(1,𝔽₈)	C₂×C₄	semidirect
63. C₂²×C₇×AGL(1,𝔽₅)	C₂²×C₃	semidirect
64. C₂×C₅×C₇×D₄	C₃×C₄	semidirect
65. C₂×C₇×C₂²⋊D₅	C₃×C₄	semidirect
66. C₇×D₄×D₅	C₃×C₄	semidirect
68. C₂×C₇×D₂₀	C₃×C₄	semidirect
70. C₇×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	semidirect
71. C₇×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	semidirect
72. C₄×C₇×AGL(1,𝔽₅)	C₂²×C₃	semidirect
82. C₂²×C₅×ΓL(1,𝔽₈)	C₂²×C₄	semidirect
88. C₂×D₅×ΓL(1,𝔽₈)	C₂²×C₄	semidirect
94. AGL(1,𝔽₅)×ΓL(1,𝔽₈)	C₂×D₄	direct (N × H)
95. C₄×C₅×ΓL(1,𝔽₈)	C₂²×C₄	semidirect
96. Dic₅×ΓL(1,𝔽₈)	C₂²×C₄	semidirect
102. C₂×D₄×ΓL(1,𝔽₈)	AGL(1,𝔽₅)	direct (N × H)
112. C₂×D₄×AGL(1,𝔽₅)	ΓL(1,𝔽₈)	direct (N × H)
113. C₂³×C₅×C₇	C₂×C₃×C₄	semidirect
116. C₂²×C₇×D₅	C₂×C₃×C₄	semidirect
117. C₂²×C₇×D₅	C₂×C₃×C₄	semidirect
123. C₂×C₇×AGL(1,𝔽₅)	C₃×D₄	semidirect
127. C₅×C₇×D₄	C₂×C₃×C₄	semidirect
128. C₂×C₄×C₅×C₇	C₂×C₃×C₄	semidirect
129. C₇×C₂²⋊D₅	C₂×C₃×C₄	semidirect
130. C₂×C₇×Dic₅	C₂×C₃×C₄	semidirect
131. C₇×D₂₀	C₂×C₃×C₄	semidirect
132. C₄×C₇×D₅	C₂×C₃×C₄	semidirect
156. C₂×C₅×ΓL(1,𝔽₈)	C₄×D₄	semidirect
159. D₅×ΓL(1,𝔽₈)	C₄×D₄	semidirect
169. C₂³×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	semidirect
172. D₄×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	direct (N × H)
183. C₂×C₄×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	semidirect
184. C₂³×AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	semidirect
186. C₂×C₂²⋊AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	semidirect
187. D₄×AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	direct (N × H)
188. C₂×C₄⋊AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	semidirect
189. C₂×C₄×AGL(1,𝔽₅)	C₂×ΓL(1,𝔽₈)	semidirect
192. C₂²×C₅×C₇	C₂²×C₃×C₄	semidirect
198. C₂×C₇×D₅	C₂²×C₃×C₄	semidirect
204. C₇×AGL(1,𝔽₅)	C₂×C₃×D₄	semidirect
205. C₄×C₅×C₇	C₂²×C₃×C₄	semidirect
206. C₇×Dic₅	C₂²×C₃×C₄	semidirect
233. C₂×C₇×D₄	C₃×AGL(1,𝔽₅)	semidirect
243. C₅×ΓL(1,𝔽₈)	C₂×C₄×D₄	semidirect
261. C₂²×ΓL(1,𝔽₈)	C₂²×AGL(1,𝔽₅)	semidirect
266. C₄×ΓL(1,𝔽₈)	C₂²×AGL(1,𝔽₅)	semidirect
272. C₂²×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	semidirect
273. C₂×C₅×D₄	C₄×ΓL(1,𝔽₈)	semidirect
274. C₂×C₂²⋊D₅	C₄×ΓL(1,𝔽₈)	semidirect
275. D₄×D₅	C₄×ΓL(1,𝔽₈)	semidirect
277. C₂×D₂₀	C₄×ΓL(1,𝔽₈)	semidirect
279. C₂²⋊AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	semidirect
280. C₄⋊AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	semidirect
281. C₄×AGL(1,𝔽₅)	C₂²×ΓL(1,𝔽₈)	semidirect
283. C₂×C₅×C₇	C₃×C₄×D₄	semidirect
286. C₇×D₅	C₃×C₄×D₄	semidirect
313. C₂³×C₇	C₂×C₃×AGL(1,𝔽₅)	semidirect
316. C₇×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
327. C₂×C₄×C₇	C₂×C₃×AGL(1,𝔽₅)	semidirect
348. C₂×ΓL(1,𝔽₈)	D₄×AGL(1,𝔽₅)	direct (N × H)
350. C₂³×C₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
353. C₂²×D₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
354. C₂²×D₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
360. C₂×AGL(1,𝔽₅)	D₄×ΓL(1,𝔽₈)	direct (N × H)
364. C₅×D₄	C₂×C₄×ΓL(1,𝔽₈)	semidirect
365. C₂×C₄×C₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
366. C₂²⋊D₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
367. C₂×Dic₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
368. D₂₀	C₂×C₄×ΓL(1,𝔽₈)	semidirect
369. C₄×D₅	C₂×C₄×ΓL(1,𝔽₈)	semidirect
371. C₅×C₇	C₂×C₃×C₄×D₄	semidirect
396. C₂²×C₇	C₂²×C₃×AGL(1,𝔽₅)	semidirect
401. C₄×C₇	C₂²×C₃×AGL(1,𝔽₅)	semidirect
423. ΓL(1,𝔽₈)	C₂×D₄×AGL(1,𝔽₅)	direct (N × H)
426. C₂²×C₅	C₂²×C₄×ΓL(1,𝔽₈)	semidirect
432. C₂×D₅	C₂²×C₄×ΓL(1,𝔽₈)	semidirect
438. AGL(1,𝔽₅)	C₂×D₄×ΓL(1,𝔽₈)	direct (N × H)
439. C₄×C₅	C₂²×C₄×ΓL(1,𝔽₈)	semidirect
440. Dic₅	C₂²×C₄×ΓL(1,𝔽₈)	semidirect
446. C₂×D₄	AGL(1,𝔽₅)×ΓL(1,𝔽₈)	direct (N × H)
462. C₂×C₇	C₃×D₄×AGL(1,𝔽₅)	semidirect
482. C₂×C₅	C₄×D₄×ΓL(1,𝔽₈)	semidirect
485. D₅	C₄×D₄×ΓL(1,𝔽₈)	semidirect
494. C₂³	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	semidirect
497. D₄	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	direct (N × H)
508. C₂×C₄	C₂×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	semidirect
509. C₇	C₂×C₃×D₄×AGL(1,𝔽₅)	semidirect
517. C₅	C₂×C₄×D₄×ΓL(1,𝔽₈)	semidirect
529. C₂²	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	semidirect
534. C₄	C₂²×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	semidirect
542. C₂	D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	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×C₇×D₄×AGL(1,𝔽₅)	3
C₂×ΓL(1,𝔽₈)×C₂²⋊AGL(1,𝔽₅)	2
C₂×ΓL(1,𝔽₈)×C₄⋊AGL(1,𝔽₅)	2
C₂×D₄×D₅×ΓL(1,𝔽₈)	2
D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	2
C₂×C₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	2
C₂³×AGL(1,𝔽₅)×ΓL(1,𝔽₈)	2
C₂×C₄×D₄×ΓL(1,𝔽₈)	5
C₂×C₃×D₄×AGL(1,𝔽₅)	7

Subgroups — C2×D4×AGL(1,𝔽5)×ΓL(1,𝔽8) #72217841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×AGL(1,𝔽₅)×ΓL(1,𝔽₈) #72217841