Subgroups — #72218342

Order 6720.

760 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72218341	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#72217838	C₂	1	1	yes	maximal, characteristic, complemented
3	#72217800	C₂	1	4	yes	maximal, complemented
4	#72217799	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×D₅×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
6	C₂³×D₅×ΓL(1,𝔽₈)	—	2	1	no	—
7	C₂×C₅×D₄×ΓL(1,𝔽₈)	C₄	1	1	yes	characteristic, complemented
8	C₂×ΓL(1,𝔽₈)×C₂²⋊D₅	—	2	1	no	—
9	D₄×D₅×ΓL(1,𝔽₈)	—	2	1	no	—
10	D₄×D₅×ΓL(1,𝔽₈)	—	2	1	no	—
11	D₄×D₅×ΓL(1,𝔽₈)	C₄	1	2	yes	complemented
12	D₄×D₅×ΓL(1,𝔽₈)	C₂²	1	2	yes	—
13	C₂×ΓL(1,𝔽₈)×D₂₀	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×D₅×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
15	(C₂²⋊(C₇⋊AGL(1,𝔽₅)))⋊C₃	—	2	1	no	—
16	#10587935⋊C₃	—	2	1	no	—
17	C₄⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₅))	C₂²	1	2	yes	complemented
18	C₄×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	—	2	1	no	—
19	#10587931⋊C₃	—	2	1	no	—
20	D₅⋊(ΓL(1,𝔽₈)⋊C₈)	C₂²	1	2	yes	complemented
21	#89987⋊C₃	—	5	1	no	maximal, Hall
22	C₂×C₇×D₄×D₅	C₂×C₃	1	1	yes	characteristic
23	#11765360	C₂×C₃	1	1	yes	characteristic, complemented
24	D₅⋊#1136	C₂×C₃	1	1	yes	characteristic, complemented
25	#11764685	C₂×C₃	1	4	yes	complemented
26	C₃×#65767	—	7	1	no	maximal, Hall
27	C₂³×C₅×ΓL(1,𝔽₈)	—	2	1	no	—
28	C₂²×D₅×ΓL(1,𝔽₈)	—	2	1	no	—
29	C₂²×D₅×ΓL(1,𝔽₈)	—	2	2	no	—
30	C₂²×D₅×ΓL(1,𝔽₈)	—	2	2	no	—
31	C₂²×D₅×ΓL(1,𝔽₈)	—	4	4	no	—
32	C₂²×D₅×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
33	C₂×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	—	2	2	no	—
34	C₅×D₄×ΓL(1,𝔽₈)	—	2	1	no	—
35	C₅×D₄×ΓL(1,𝔽₈)	C₂×C₄	1	2	yes	—
36	C₂×C₄×C₅×ΓL(1,𝔽₈)	C₂×C₄	1	1	yes	characteristic
37	ΓL(1,𝔽₈)×C₂²⋊D₅	—	2	2	no	—
38	ΓL(1,𝔽₈)×C₂²⋊D₅	—	2	2	no	—
39	C₂×Dic₅×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
40	ΓL(1,𝔽₈)×D₂₀	—	2	1	no	—
41	ΓL(1,𝔽₈)×D₂₀	C₂×C₄	1	2	yes	—
42	C₄×D₅×ΓL(1,𝔽₈)	C₂×C₄	1	1	yes	characteristic
43	C₄×D₅×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
44	C₄×D₅×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
45	C₄×D₅×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
46	ΓL(1,𝔽₈)⋊#170	—	2	2	no	—
47	C₂²×D₄×ΓL(1,𝔽₈)	—	5	1	no	—
48	#6489⋊C₃	—	5	1	no	—
49	C₂×#1136⋊C₃	—	5	1	no	—
50	#6406⋊C₃	—	5	4	no	—
51	C₂³×C₇×D₅	—	2	1	no	—
52	C₂×C₅×C₇×D₄	C₃×C₄	1	1	yes	characteristic, complemented
53	C₂×C₇×C₂²⋊D₅	—	2	1	no	—
54	C₇×D₄×D₅	—	2	1	no	—
55	C₇×D₄×D₅	—	2	1	no	—
56	C₇×D₄×D₅	C₃×C₄	1	2	yes	complemented
57	C₇×D₄×D₅	C₂²×C₃	1	2	yes	—
58	C₂×C₇×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
59	C₂×C₄×C₇×D₅	C₂²×C₃	1	1	yes	characteristic
60	C₂²⋊(C₇⋊AGL(1,𝔽₅))	—	2	1	no	—
61	#10587935	—	2	1	no	—
62	C₄⋊(C₇⋊AGL(1,𝔽₅))	C₂²×C₃	1	2	yes	complemented
63	C₄×C₇⋊AGL(1,𝔽₅)	—	2	1	no	—
64	#10587931	—	2	1	no	—
65	D₅⋊(C₇⋊C₈)	C₂²×C₃	1	2	yes	complemented
66	C₂×C₃×D₄×D₅	—	7	1	no	—
67	C₃×#4130	—	7	1	no	—
68	C₃×D₅⋊M₁₆	—	7	1	no	—
69	C₃×#4007	—	7	4	no	—
70	#89987	—	5	1	no	Hall
71	C₂²×C₅×ΓL(1,𝔽₈)	—	2	2	no	—
72	C₂²×C₅×ΓL(1,𝔽₈)	—	4	2	no	—
73	C₂²×C₅×ΓL(1,𝔽₈)	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×D₅×ΓL(1,𝔽₈)	—	2	2	no	—
75	C₂×D₅×ΓL(1,𝔽₈)	—	2	2	no	—
76	C₂×D₅×ΓL(1,𝔽₈)	—	4	2	no	—
77	C₂×D₅×ΓL(1,𝔽₈)	—	4	4	no	—
78	C₂×D₅×ΓL(1,𝔽₈)	—	4	4	no	—
79	C₂×D₅×ΓL(1,𝔽₈)	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×D₅×ΓL(1,𝔽₈)	C₂×D₄	1	1	yes	characteristic
81	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	—	4	2	no	—
82	C₄×C₅×ΓL(1,𝔽₈)	C₂²⋊C₄	1	1	yes	characteristic
83	C₄×C₅×ΓL(1,𝔽₈)	C₂²×C₄	1	1	yes	characteristic
84	Dic₅×ΓL(1,𝔽₈)	C₂²⋊C₄	1	1	yes	characteristic
85	Dic₅×ΓL(1,𝔽₈)	C₂×D₄	1	1	yes	characteristic
86	C₂⁴×ΓL(1,𝔽₈)	—	10	1	no	—
87	C₂×D₄×ΓL(1,𝔽₈)	—	5	2	no	—
88	C₂×D₄×ΓL(1,𝔽₈)	—	5	2	no	—
89	C₂×D₄×ΓL(1,𝔽₈)	—	5	1	no	—
90	C₂×D₄×ΓL(1,𝔽₈)	—	10	1	no	—
91	C₂×D₄×ΓL(1,𝔽₈)	—	10	1	no	—
92	C₂×D₄×ΓL(1,𝔽₈)	—	10	1	no	—
93	C₂×D₄×ΓL(1,𝔽₈)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
94	C₂²×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
95	(C₂²⋊Dic₇)⋊C₃	—	10	1	no	—
96	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	—	5	2	no	—
97	C₄×ΓL(1,𝔽₈)⋊C₄	—	10	1	no	—
98	#1136⋊C₃	—	10	1	no	—
99	#1136⋊C₃	—	10	1	no	—
100	C₂×ΓL(1,𝔽₈)⋊C₈	—	5	2	no	—
101	#65767	—	7	1	no	Hall
102	C₂³×C₅×C₇	—	2	1	no	—
103	C₂²×C₇×D₅	—	2	1	no	—
104	C₂²×C₇×D₅	—	2	2	no	—
105	C₂²×C₇×D₅	—	2	2	no	—
106	C₂²×C₇×D₅	—	4	4	no	—
107	C₂²×C₇×D₅	C₃×D₄	1	1	yes	characteristic
108	C₂×C₇⋊AGL(1,𝔽₅)	—	2	2	no	—
109	C₅×C₇×D₄	—	2	1	no	—
110	C₅×C₇×D₄	C₂×C₃×C₄	1	2	yes	—
111	C₂×C₄×C₅×C₇	C₂×C₃×C₄	1	1	yes	characteristic
112	C₇×C₂²⋊D₅	—	2	2	no	—
113	C₇×C₂²⋊D₅	—	2	2	no	—
114	C₂×C₇×Dic₅	C₃×D₄	1	1	yes	characteristic
115	C₇×D₂₀	—	2	1	no	—
116	C₇×D₂₀	C₂×C₃×C₄	1	2	yes	—
117	C₄×C₇×D₅	C₂×C₃×C₄	1	1	yes	characteristic
118	C₄×C₇×D₅	C₃×D₄	1	1	yes	characteristic
119	C₄×C₇×D₅	C₃×D₄	1	1	yes	characteristic
120	C₄×C₇×D₅	C₂³×C₃	1	1	yes	characteristic
121	C₇⋊#170	—	2	2	no	—
122	C₂³×C₃×D₅	—	14	1	no	—
123	C₂×C₃×C₅×D₄	—	7	1	no	—
124	C₂×C₃×C₂²⋊D₅	—	14	1	no	—
125	C₃×D₄×D₅	—	7	2	no	—
126	C₃×D₄×D₅	—	7	2	no	—
127	C₃×D₄×D₅	—	14	1	no	—
128	C₃×D₄×D₅	—	14	1	no	—
129	C₂×C₃×D₂₀	—	7	1	no	—
130	C₂×C₃×C₄×D₅	—	7	1	no	—
131	C₃×C₂²⋊AGL(1,𝔽₅)	—	14	1	no	—
132	C₃×#704	—	14	1	no	—
133	C₃×C₄⋊AGL(1,𝔽₅)	—	7	2	no	—
134	C₃×C₄×AGL(1,𝔽₅)	—	14	1	no	—
135	C₃×#700	—	14	1	no	—
136	C₃×D₅⋊C₈	—	7	2	no	—
137	C₂²×C₇×D₄	—	5	1	no	—
138	#6489	—	5	1	no	—
139	C₂×#1136	—	5	1	no	—
140	#6406	—	5	4	no	—
141	C₂×C₅×ΓL(1,𝔽₈)	—	2	1	no	—
142	C₂×C₅×ΓL(1,𝔽₈)	—	4	2	no	—
143	C₂×C₅×ΓL(1,𝔽₈)	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	D₅×ΓL(1,𝔽₈)	—	2	1	no	—
145	D₅×ΓL(1,𝔽₈)	—	4	2	no	—
146	D₅×ΓL(1,𝔽₈)	AGL(1,ℤ/8)	1	2	yes	—
147	C₃×#418	—	35	1	no	Hall
148	C₂³×ΓL(1,𝔽₈)	—	2	1	no	—
149	C₂³×ΓL(1,𝔽₈)	—	5	1	no	—
150	C₂³×ΓL(1,𝔽₈)	—	10	2	no	—
151	C₂³×ΓL(1,𝔽₈)	—	10	2	no	—
152	C₂³×ΓL(1,𝔽₈)	—	10	1	no	—
153	C₂³×ΓL(1,𝔽₈)	—	20	4	no	—
154	D₄×ΓL(1,𝔽₈)	—	2	1	no	—
155	D₄×ΓL(1,𝔽₈)	—	5	2	no	—
156	D₄×ΓL(1,𝔽₈)	—	10	2	no	—
157	D₄×ΓL(1,𝔽₈)	—	10	2	no	—
158	D₄×ΓL(1,𝔽₈)	—	10	1	no	—
159	D₄×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	1	2	yes	—
160	C₂×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
161	C₂×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
162	C₂×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
163	C₂×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
164	C₂×C₄×ΓL(1,𝔽₈)	—	5	1	no	—
165	C₂×C₄×ΓL(1,𝔽₈)	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
166	C₂×ΓL(1,𝔽₈)⋊C₄	—	10	2	no	—
167	ΓL(1,𝔽₈)⋊C₈	—	10	2	no	—
168	C₂×D₄×D₅	AGL(1,𝔽₇)	1	1	yes	characteristic
169	#4130	—	7	1	no	—
170	D₅⋊M₁₆	—	7	1	no	—
171	#4007	—	7	4	no	—
172	C₂²×C₅×C₇	—	2	2	no	—
173	C₂²×C₅×C₇	—	4	2	no	—
174	C₂²×C₅×C₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₇×D₅	—	2	2	no	—
176	C₂×C₇×D₅	—	2	2	no	—
177	C₂×C₇×D₅	—	4	4	no	—
178	C₂×C₇×D₅	—	4	2	no	—
179	C₂×C₇×D₅	—	4	4	no	—
180	C₂×C₇×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₇×D₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₇⋊AGL(1,𝔽₅)	—	4	2	no	—
183	C₄×C₅×C₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
184	C₄×C₅×C₇	C₂²×C₃×C₄	1	1	yes	characteristic
185	C₇×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
186	C₇×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
187	C₂³×C₃×C₅	—	14	1	no	—
188	C₂²×C₃×D₅	—	7	1	no	—
189	C₂²×C₃×D₅	—	14	2	no	—
190	C₂²×C₃×D₅	—	14	2	no	—
191	C₂²×C₃×D₅	—	14	1	no	—
192	C₂²×C₃×D₅	—	28	4	no	—
193	C₂×C₃×AGL(1,𝔽₅)	—	14	2	no	—
194	C₃×C₅×D₄	—	7	2	no	—
195	C₃×C₅×D₄	—	14	1	no	—
196	C₂×C₃×C₄×C₅	—	7	1	no	—
197	C₃×C₂²⋊D₅	—	14	2	no	—
198	C₃×C₂²⋊D₅	—	14	2	no	—
199	C₂×C₃×Dic₅	—	7	1	no	—
200	C₃×D₂₀	—	7	2	no	—
201	C₃×D₂₀	—	14	1	no	—
202	C₃×C₄×D₅	—	7	1	no	—
203	C₃×C₄×D₅	—	7	1	no	—
204	C₃×C₄×D₅	—	7	1	no	—
205	C₃×C₄×D₅	—	7	1	no	—
206	C₃×#170	—	14	2	no	—
207	C₂⁴×C₇	—	10	1	no	—
208	C₂×C₇×D₄	—	5	2	no	—
209	C₂×C₇×D₄	—	5	2	no	—
210	C₂×C₇×D₄	—	5	1	no	—
211	C₂×C₇×D₄	—	10	1	no	—
212	C₂×C₇×D₄	—	10	1	no	—
213	C₂×C₇×D₄	—	10	1	no	—
214	C₂×C₇×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
215	C₂²×C₄×C₇	—	5	1	no	—
216	C₂²⋊Dic₇	—	10	1	no	—
217	C₄⋊Dic₇	—	5	2	no	—
218	C₄×Dic₇	—	10	1	no	—
219	#1136	—	10	1	no	—
220	#1136	—	10	1	no	—
221	C₂×C₇⋊C₈	—	5	2	no	—
222	C₅×ΓL(1,𝔽₈)	#418	1	1	yes	characteristic, complemented, Hall
223	C₂²×C₃×D₄	—	35	1	no	—
224	C₂×C₃×M₁₆	—	35	1	no	—
225	C₃×#117	—	35	1	no	—
226	C₃×#102	—	35	4	no	—
227	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
228	C₂²×ΓL(1,𝔽₈)	—	4	2	no	—
229	C₂²×ΓL(1,𝔽₈)	—	5	1	no	—
230	C₂²×ΓL(1,𝔽₈)	—	5	1	no	—
231	C₂²×ΓL(1,𝔽₈)	—	10	2	no	—
232	C₂²×ΓL(1,𝔽₈)	—	10	2	no	—
233	C₂²×ΓL(1,𝔽₈)	—	20	2	no	—
234	C₂²×ΓL(1,𝔽₈)	—	20	4	no	—
235	C₂²×ΓL(1,𝔽₈)	—	20	4	no	—
236	C₂²×ΓL(1,𝔽₈)	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
237	C₄×ΓL(1,𝔽₈)	—	5	1	no	—
238	C₄×ΓL(1,𝔽₈)	—	5	1	no	—
239	C₄×ΓL(1,𝔽₈)	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
240	C₄×ΓL(1,𝔽₈)	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
241	ΓL(1,𝔽₈)⋊C₄	—	20	2	no	—
242	C₂³×D₅	—	2	1	no	—
243	C₂×C₅×D₄	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented
244	C₂×C₂²⋊D₅	—	2	1	no	—
245	D₄×D₅	—	2	1	no	—
246	D₄×D₅	—	2	1	no	—
247	D₄×D₅	ΓL(1,𝔽₈)⋊C₄	1	2	yes	complemented
248	D₄×D₅	C₂×AGL(1,𝔽₇)	1	2	yes	—
249	C₂×D₂₀	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented
250	C₂×C₄×D₅	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
251	C₂²⋊AGL(1,𝔽₅)	—	14	1	no	—
252	#704	—	14	1	no	—
253	C₄⋊AGL(1,𝔽₅)	—	7	2	no	—
254	C₄×AGL(1,𝔽₅)	—	14	1	no	—
255	#700	—	14	1	no	—
256	D₅⋊C₈	—	7	2	no	—
257	C₂×C₅×C₇	—	2	1	no	—
258	C₂×C₅×C₇	—	4	2	no	—
259	C₂×C₅×C₇	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
260	C₇×D₅	—	2	1	no	—
261	C₇×D₅	—	4	2	no	—
262	C₇×D₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
263	#418	—	35	1	no	Sylow
264	C₂²×C₃×C₅	—	7	1	no	—
265	C₂²×C₃×C₅	—	14	2	no	—
266	C₂²×C₃×C₅	—	28	2	no	—
267	C₂×C₃×D₅	—	7	1	no	—
268	C₂×C₃×D₅	—	7	1	no	—
269	C₂×C₃×D₅	—	14	2	no	—
270	C₂×C₃×D₅	—	14	2	no	—
271	C₂×C₃×D₅	—	28	4	no	—
272	C₂×C₃×D₅	—	28	4	no	—
273	C₂×C₃×D₅	—	28	2	no	—
274	C₃×AGL(1,𝔽₅)	—	28	2	no	—
275	C₃×C₄×C₅	—	7	1	no	—
276	C₃×C₄×C₅	—	7	1	no	—
277	C₃×Dic₅	—	7	1	no	—
278	C₃×Dic₅	—	7	1	no	—
279	C₂³×C₇	—	2	1	no	—
280	C₂³×C₇	—	5	1	no	—
281	C₂³×C₇	—	10	2	no	—
282	C₂³×C₇	—	10	2	no	—
283	C₂³×C₇	—	10	1	no	—
284	C₂³×C₇	—	20	4	no	—
285	C₇×D₄	—	2	1	no	—
286	C₇×D₄	—	5	2	no	—
287	C₇×D₄	—	10	2	no	—
288	C₇×D₄	—	10	2	no	—
289	C₇×D₄	—	10	1	no	—
290	C₇×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
291	C₂×C₄×C₇	—	5	1	no	—
292	C₂×C₄×C₇	—	5	1	no	—
293	C₂×C₄×C₇	—	5	1	no	—
294	C₂×C₄×C₇	—	5	1	no	—
295	C₂×C₄×C₇	—	5	1	no	—
296	C₂×C₄×C₇	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
297	C₂×Dic₇	—	10	2	no	—
298	C₇⋊C₈	—	10	2	no	—
299	C₂⁴×C₃	—	70	1	no	—
300	C₂×C₃×D₄	—	7	1	no	—
301	C₂×C₃×D₄	—	35	1	no	—
302	C₂×C₃×D₄	—	35	2	no	—
303	C₂×C₃×D₄	—	35	2	no	—
304	C₂×C₃×D₄	—	70	1	no	—
305	C₂×C₃×D₄	—	70	1	no	—
306	C₂×C₃×D₄	—	70	1	no	—
307	C₂²×C₃×C₄	—	35	1	no	—
308	C₃×M₁₆	—	70	1	no	—
309	C₃×M₁₆	—	70	1	no	—
310	C₂×C₃×C₈	—	35	2	no	—
311	C₃×C₄⋊C₄	—	35	2	no	—
312	C₃×C₂²⋊C₄	—	70	1	no	—
313	C₃×C₄²	—	70	1	no	—
314	C₂×ΓL(1,𝔽₈)	—	2	1	no	—
315	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
316	C₂×ΓL(1,𝔽₈)	—	5	2	no	—
317	C₂×ΓL(1,𝔽₈)	—	10	1	no	—
318	C₂×ΓL(1,𝔽₈)	—	20	2	no	—
319	C₂×ΓL(1,𝔽₈)	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
320	C₂³×C₅	—	2	1	no	—
321	C₂²×D₅	—	2	1	no	—
322	C₂²×D₅	—	2	2	no	—
323	C₂²×D₅	—	2	2	no	—
324	C₂²×D₅	—	4	4	no	—
325	C₂²×D₅	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
326	C₂×AGL(1,𝔽₅)	—	14	2	no	—
327	C₅×D₄	—	2	1	no	—
328	C₅×D₄	C₂×ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
329	C₂×C₄×C₅	C₂×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
330	C₂²⋊D₅	—	2	2	no	—
331	C₂²⋊D₅	—	2	2	no	—
332	C₂×Dic₅	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
333	D₂₀	—	2	1	no	—
334	D₂₀	C₂×ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
335	C₄×D₅	C₂×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
336	C₄×D₅	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
337	C₄×D₅	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
338	C₄×D₅	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
339	#170	—	14	2	no	—
340	C₅×C₇	C₃×#418	1	1	yes	characteristic, complemented, Hall
341	C₂²×D₄	—	5	1	no	—
342	C₂×M₁₆	—	35	1	no	—
343	#117	—	35	1	no	—
344	#102	—	35	4	no	—
345	C₂×C₃×C₅	—	7	1	no	—
346	C₂×C₃×C₅	—	14	1	no	—
347	C₂×C₃×C₅	—	28	2	no	—
348	C₃×D₅	—	7	2	no	—
349	C₃×D₅	—	14	1	no	—
350	C₃×D₅	—	28	2	no	—
351	C₂²×C₇	—	2	2	no	—
352	C₂²×C₇	—	4	2	no	—
353	C₂²×C₇	—	5	1	no	—
354	C₂²×C₇	—	5	1	no	—
355	C₂²×C₇	—	10	2	no	—
356	C₂²×C₇	—	10	2	no	—
357	C₂²×C₇	—	20	2	no	—
358	C₂²×C₇	—	20	4	no	—
359	C₂²×C₇	—	20	4	no	—
360	C₂²×C₇	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₄×C₇	—	5	1	no	—
362	C₄×C₇	—	5	1	no	—
363	C₄×C₇	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₄×C₇	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
365	Dic₇	—	20	2	no	—
366	C₂³×C₃	—	14	1	no	—
367	C₂³×C₃	—	35	1	no	—
368	C₂³×C₃	—	70	1	no	—
369	C₂³×C₃	—	70	2	no	—
370	C₂³×C₃	—	70	2	no	—
371	C₂³×C₃	—	140	4	no	—
372	C₃×D₄	—	7	2	no	—
373	C₃×D₄	—	14	1	no	—
374	C₃×D₄	—	35	2	no	—
375	C₃×D₄	—	70	1	no	—
376	C₃×D₄	—	70	2	no	—
377	C₃×D₄	—	70	2	no	—
378	C₂×C₃×C₄	—	7	1	no	—
379	C₂×C₃×C₄	—	35	1	no	—
380	C₂×C₃×C₄	—	35	1	no	—
381	C₂×C₃×C₄	—	35	1	no	—
382	C₂×C₃×C₄	—	35	1	no	—
383	C₂×C₃×C₄	—	35	1	no	—
384	C₂×C₃×C₄	—	70	2	no	—
385	C₃×C₈	—	70	2	no	—
386	ΓL(1,𝔽₈)	#65767	1	1	yes	characteristic, complemented, Hall
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	4	2	no	—
389	C₂²×C₅	(C₂²⋊Dic₇)⋊C₃	1	1	yes	characteristic
390	C₂×D₅	—	2	2	no	—
391	C₂×D₅	—	2	2	no	—
392	C₂×D₅	—	4	4	no	—
393	C₂×D₅	—	4	2	no	—
394	C₂×D₅	—	4	4	no	—
395	C₂×D₅	(C₂²⋊Dic₇)⋊C₃	1	1	yes	characteristic
396	C₂×D₅	C₂×(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
397	AGL(1,𝔽₅)	—	28	2	no	—
398	C₄×C₅	(C₂²⋊Dic₇)⋊C₃	1	1	yes	characteristic
399	C₄×C₅	C₂²×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
400	Dic₅	(C₂²⋊Dic₇)⋊C₃	1	1	yes	characteristic
401	Dic₅	C₂×(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
402	C₂⁴	—	10	1	no	—
403	C₂×D₄	—	5	2	no	—
404	C₂×D₄	—	5	2	no	—
405	C₂×D₄	—	5	1	no	—
406	C₂×D₄	—	10	1	no	—
407	C₂×D₄	—	10	1	no	—
408	C₂×D₄	—	10	1	no	—
409	C₂×D₄	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
410	C₂²×C₄	—	5	1	no	—
411	M₁₆	—	70	1	no	—
412	M₁₆	—	70	1	no	—
413	C₂×C₈	—	35	2	no	—
414	C₄⋊C₄	—	35	2	no	—
415	C₂²⋊C₄	—	70	1	no	—
416	C₄²	—	70	1	no	—
417	C₃×C₅	—	7	1	no	Hall
418	C₂×C₇	—	2	1	no	—
419	C₂×C₇	—	4	2	no	—
420	C₂×C₇	—	5	2	no	—
421	C₂×C₇	—	10	1	no	—
422	C₂×C₇	—	20	2	no	—
423	C₂×C₇	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
424	C₂²×C₃	—	7	1	no	—
425	C₂²×C₃	—	14	2	no	—
426	C₂²×C₃	—	28	2	no	—
427	C₂²×C₃	—	35	1	no	—
428	C₂²×C₃	—	35	1	no	—
429	C₂²×C₃	—	70	2	no	—
430	C₂²×C₃	—	70	2	no	—
431	C₂²×C₃	—	140	2	no	—
432	C₂²×C₃	—	140	4	no	—
433	C₂²×C₃	—	140	4	no	—
434	C₃×C₄	—	7	1	no	—
435	C₃×C₄	—	7	1	no	—
436	C₃×C₄	—	35	1	no	—
437	C₃×C₄	—	35	1	no	—
438	C₃×C₄	—	140	2	no	—
439	C₂×C₅	—	2	1	no	—
440	C₂×C₅	—	4	2	no	—
441	C₂×C₅	C₂×(C₂²⋊Dic₇)⋊C₃	1	1	yes	characteristic
442	D₅	—	2	1	no	—
443	D₅	—	4	2	no	—
444	D₅	#6495⋊C₃	1	2	yes	—
445	C₂³	—	2	1	no	—
446	C₂³	—	5	1	no	—
447	C₂³	—	10	2	no	—
448	C₂³	—	10	2	no	—
449	C₂³	—	10	1	no	—
450	C₂³	—	20	4	no	—
451	D₄	—	2	1	no	—
452	D₄	—	5	2	no	—
453	D₄	—	10	2	no	—
454	D₄	—	10	2	no	—
455	D₄	—	10	1	no	—
456	D₄	C₂×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	1	2	yes	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	5	1	no	—
462	C₂×C₄	—	70	2	no	—
463	C₂×C₄	C₂×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
464	C₈	—	70	2	no	—
465	C₇	C₃×#65767	1	1	yes	characteristic, complemented, Sylow
466	C₂×C₃	—	7	1	no	—
467	C₂×C₃	—	14	1	no	—
468	C₂×C₃	—	28	2	no	—
469	C₂×C₃	—	35	2	no	—
470	C₂×C₃	—	70	1	no	—
471	C₂×C₃	—	140	2	no	—
472	C₅	#89987⋊C₃	1	1	yes	characteristic, complemented, Sylow
473	C₂²	—	2	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	5	1	no	—
476	C₂²	—	5	1	no	—
477	C₂²	—	10	2	no	—
478	C₂²	—	10	2	no	—
479	C₂²	—	20	2	no	—
480	C₂²	—	20	4	no	—
481	C₂²	—	20	4	no	—
482	C₂²	(C₂²⋊(C₇⋊AGL(1,𝔽₅)))⋊C₃	1	1	yes	characteristic
483	C₄	—	5	1	no	—
484	C₄	—	5	1	no	—
485	C₄	—	140	2	no	—
486	C₄	(C₂²⋊(C₇⋊AGL(1,𝔽₅)))⋊C₃	1	1	yes	characteristic
487	C₄	C₂²×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
488	C₃	—	7	1	no	Sylow
489	C₂	—	2	1	no	—
490	C₂	—	4	2	no	—
491	C₂	—	5	2	no	—
492	C₂	—	10	1	no	—
493	C₂	—	20	2	no	—
494	C₂	C₂×(C₂²⋊(C₇⋊AGL(1,𝔽₅)))⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×(C₂²⋊(C₇⋊AGL(1,𝔽₅)))⋊C₃
commutator	C₄×C₅×C₇	C₂²×C₃×C₄
Frattini	C₄	C₂²×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)
Fitting	C₂×C₅×C₇×D₄	C₃×C₄
socle	C₂×C₅×C₇	C₂×C₃×C₂²⋊C₄
prime radical	C₂×D₄×D₅×ΓL(1,𝔽₈)	C₂
cosocle	C₄×C₇×D₅	C₂³×C₃
hypercenter	C₂×D₄	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)
hypocenter	C₅×C₇	C₃×#418
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #72218341	C₃	semidirect
2. #72217838	C₂	semidirect
3. #72217800	C₂	semidirect
4. #72217799	C₂	semidirect
7. C₂×C₅×D₄×ΓL(1,𝔽₈)	C₄	semidirect
11. D₄×D₅×ΓL(1,𝔽₈)	C₄	semidirect
13. C₂×ΓL(1,𝔽₈)×D₂₀	C₄	semidirect
17. C₄⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₅))	C₂²	semidirect
20. D₅⋊(ΓL(1,𝔽₈)⋊C₈)	C₂²	semidirect
23. #11765360	C₂×C₃	semidirect
24. D₅⋊#1136	C₂×C₃	semidirect
25. #11764685	C₂×C₃	semidirect
52. C₂×C₅×C₇×D₄	C₃×C₄	semidirect
56. C₇×D₄×D₅	C₃×C₄	semidirect
58. C₂×C₇×D₂₀	C₃×C₄	semidirect
62. C₄⋊(C₇⋊AGL(1,𝔽₅))	C₂²×C₃	semidirect
65. D₅⋊(C₇⋊C₈)	C₂²×C₃	semidirect
93. C₂×D₄×ΓL(1,𝔽₈)	AGL(1,𝔽₅)	semidirect
214. C₂×C₇×D₄	C₃×AGL(1,𝔽₅)	semidirect
222. C₅×ΓL(1,𝔽₈)	#418	semidirect
243. C₂×C₅×D₄	ΓL(1,𝔽₈)⋊C₄	semidirect
247. D₄×D₅	ΓL(1,𝔽₈)⋊C₄	semidirect
249. C₂×D₂₀	ΓL(1,𝔽₈)⋊C₄	semidirect
340. C₅×C₇	C₃×#418	semidirect
386. ΓL(1,𝔽₈)	#65767	semidirect
409. C₂×D₄	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	semidirect
465. C₇	C₃×#65767	semidirect
472. C₅	#89987⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#72218341	3
#72217838	2
#72217800	2
#72217799	2
C₂×D₄×D₅×ΓL(1,𝔽₈)	2
#89987⋊C₃	5
C₃×#65767	7