Subgroups — C₅×#22846 #11945566

Order 1280.

1320 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#120	C₂	1	1	yes	maximal, characteristic
6	C₅×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×#120	C₄	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₅×#435	—	2	4	no	—
27	C₅×C₈×D₄	—	2	4	no	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#407	—	2	4	no	—
32	C₂×C₅×C₂²⋊C₈	—	2	4	no	—
33	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
47	C₅×#386	C₄	1	1	yes	characteristic
48	C₅×#386	C₄	1	1	yes	characteristic
49	C₅×#386	C₄	1	1	yes	characteristic
50	C₅×#385	C₄	1	1	yes	characteristic
51	C₅×#385	C₄	1	1	yes	characteristic
52	C₅×#385	C₄	1	1	yes	characteristic
53	C₅×#379	C₄	1	1	yes	characteristic
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic, complemented
58	C₅×#336	C₂²	1	1	yes	characteristic, complemented
59	C₅×#336	C₂²	1	1	yes	characteristic, complemented
60	C₅×#336	C₂²	1	1	yes	characteristic, complemented
61	C₅×#336	C₂²	1	1	yes	characteristic, complemented
62	C₅×#336	C₂²	1	1	yes	characteristic, complemented
63	#22846	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₅	—	2	2	no	—
69	C₂³×C₄×C₅	—	2	2	no	—
70	C₂³×C₄×C₅	—	2	2	no	—
71	C₂³×C₄×C₅	—	2	2	no	—
72	C₂³×C₄×C₅	—	4	1	no	—
73	C₂³×C₄×C₅	—	4	1	no	—
74	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₅×M₁₆	—	2	2	no	—
82	C₂×C₅×M₁₆	—	2	2	no	—
83	C₂×C₅×M₁₆	—	2	2	no	—
84	C₂×C₅×M₁₆	—	2	2	no	—
85	C₂×C₅×M₁₆	—	4	1	no	—
86	C₂×C₅×M₁₆	—	4	1	no	—
87	C₂²×C₅×C₈	—	2	2	no	—
88	C₂²×C₅×C₈	—	2	2	no	—
89	C₂²×C₅×C₈	—	2	2	no	—
90	C₂²×C₅×C₈	—	2	2	no	—
91	C₂²×C₅×C₈	—	2	2	no	—
92	C₂²×C₅×C₈	—	2	2	no	—
93	C₂²×C₅×C₈	—	4	1	no	—
94	C₂²×C₅×C₈	—	4	1	no	—
95	C₂²×C₅×C₈	—	4	1	no	—
96	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₅×#120	—	2	4	no	—
105	C₄×C₅×D₄	—	2	2	no	—
106	C₄×C₅×D₄	—	2	2	no	—
107	C₄×C₅×D₄	—	2	2	no	—
108	C₄×C₅×D₄	—	2	2	no	—
109	C₄×C₅×D₄	—	4	1	no	—
110	C₄×C₅×D₄	—	4	1	no	—
111	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₅×C₄⋊C₈	—	2	2	no	—
130	C₅×C₄⋊C₈	—	2	2	no	—
131	C₅×C₄⋊C₈	—	4	1	no	—
132	C₅×C₂²⋊C₈	—	2	2	no	—
133	C₅×C₂²⋊C₈	—	2	2	no	—
134	C₅×C₂²⋊C₈	—	2	2	no	—
135	C₅×C₂²⋊C₈	—	2	2	no	—
136	C₅×C₂²⋊C₈	—	2	2	no	—
137	C₅×C₂²⋊C₈	—	2	2	no	—
138	C₅×C₂²⋊C₈	—	2	2	no	—
139	C₅×C₂²⋊C₈	—	2	2	no	—
140	C₅×C₂²⋊C₈	—	4	1	no	—
141	C₅×C₂²⋊C₈	D₄	1	4	yes	complemented
142	C₅×C₂²⋊C₈	D₄	1	4	yes	complemented
143	C₅×#97	—	2	2	no	—
144	C₅×#97	—	4	1	no	—
145	C₄×C₅×C₈	—	2	2	no	—
146	C₅×#95	C₂×C₄	1	1	yes	characteristic
147	C₅×#95	C₂×C₄	1	1	yes	characteristic
148	C₅×#95	C₂×C₄	1	1	yes	characteristic
149	C₅×#95	C₂×C₄	1	1	yes	characteristic
150	C₅×#95	C₂×C₄	1	1	yes	characteristic
151	C₅×#95	C₂×C₄	1	1	yes	characteristic
152	C₂×#435	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#407	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂²×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
156	C₄×#120	C₂×C₅	1	1	yes	characteristic
157	#1955	C₂×C₅	1	1	yes	characteristic, complemented
158	#1924	C₂×C₅	1	1	yes	characteristic, complemented
159	#1923	C₂×C₅	1	1	yes	characteristic, complemented
160	#1870	C₂×C₅	1	1	yes	characteristic, complemented
161	#1869	C₂×C₅	1	1	yes	characteristic, complemented
162	#1869	C₂×C₅	1	1	yes	characteristic, complemented
163	#1851	C₂×C₅	1	1	yes	characteristic, complemented
164	#1850	C₂×C₅	1	1	yes	characteristic, complemented
165	#1753	C₂×C₅	1	1	yes	characteristic, complemented
166	#1752	C₂×C₅	1	1	yes	characteristic, complemented
167	C₂⁴×C₅	—	2	2	no	—
168	C₂⁴×C₅	—	2	2	no	—
169	C₂⁴×C₅	—	2	2	no	—
170	C₂⁴×C₅	—	2	2	no	—
171	C₂⁴×C₅	—	2	2	no	—
172	C₂⁴×C₅	—	4	1	no	—
173	C₂⁴×C₅	—	4	1	no	—
174	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
177	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₅×D₄	—	2	2	no	—
179	C₂×C₅×D₄	—	2	2	no	—
180	C₂×C₅×D₄	—	2	2	no	—
181	C₂×C₅×D₄	—	2	2	no	—
182	C₂×C₅×D₄	—	2	2	no	—
183	C₂×C₅×D₄	—	2	2	no	—
184	C₂×C₅×D₄	—	4	1	no	—
185	C₂×C₅×D₄	—	4	1	no	—
186	C₂×C₅×D₄	M₁₆	1	4	yes	complemented
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	2	2	no	—
197	C₂²×C₄×C₅	—	2	2	no	—
198	C₂²×C₄×C₅	—	2	2	no	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	4	1	no	—
214	C₂²×C₄×C₅	—	4	1	no	—
215	C₂²×C₄×C₅	—	4	1	no	—
216	C₂²×C₄×C₅	—	4	4	no	—
217	C₂²×C₄×C₅	—	4	4	no	—
218	C₂²×C₄×C₅	—	4	4	no	—
219	C₂²×C₄×C₅	—	4	4	no	—
220	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₅	#41	1	2	yes	—
233	C₂²×C₄×C₅	#41	1	2	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
235	C₅×M₁₆	—	4	4	no	—
236	C₅×M₁₆	—	4	4	no	—
237	C₂×C₅×C₈	—	2	1	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	—	2	1	no	—
242	C₂×C₅×C₈	—	2	1	no	—
243	C₂×C₅×C₈	—	2	1	no	—
244	C₂×C₅×C₈	—	2	1	no	—
245	C₂×C₅×C₈	—	2	1	no	—
246	C₂×C₅×C₈	—	2	1	no	—
247	C₂×C₅×C₈	—	2	1	no	—
248	C₂×C₅×C₈	—	2	1	no	—
249	C₂×C₅×C₈	—	2	1	no	—
250	C₂×C₅×C₈	—	2	1	no	—
251	C₂×C₅×C₈	—	2	1	no	—
252	C₂×C₅×C₈	—	2	1	no	—
253	C₂×C₅×C₈	—	2	1	no	—
254	C₂×C₅×C₈	—	2	1	no	—
255	C₂×C₅×C₈	—	2	1	no	—
256	C₂×C₅×C₈	—	2	1	no	—
257	C₂×C₅×C₈	—	4	4	no	—
258	C₂×C₅×C₈	—	4	4	no	—
259	C₂×C₅×C₈	—	4	4	no	—
260	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
261	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
262	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
263	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
264	C₅×C₄⋊C₄	—	2	2	no	—
265	C₅×C₄⋊C₄	—	2	2	no	—
266	C₅×C₄⋊C₄	—	4	1	no	—
267	C₅×C₂²⋊C₄	—	2	2	no	—
268	C₅×C₂²⋊C₄	—	2	2	no	—
269	C₅×C₂²⋊C₄	—	2	2	no	—
270	C₅×C₂²⋊C₄	—	2	2	no	—
271	C₅×C₂²⋊C₄	—	2	2	no	—
272	C₅×C₂²⋊C₄	—	2	2	no	—
273	C₅×C₂²⋊C₄	—	2	2	no	—
274	C₅×C₂²⋊C₄	—	2	2	no	—
275	C₅×C₂²⋊C₄	—	2	2	no	—
276	C₅×C₂²⋊C₄	—	4	1	no	—
277	C₅×C₂²⋊C₄	—	4	1	no	—
278	C₅×C₂²⋊C₄	—	4	1	no	—
279	C₄²×C₅	—	2	1	no	—
280	C₄²×C₅	—	2	1	no	—
281	C₄²×C₅	—	2	1	no	—
282	C₄²×C₅	—	2	1	no	—
283	C₄²×C₅	—	2	1	no	—
284	C₄²×C₅	—	2	1	no	—
285	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
286	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
287	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
288	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
289	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
290	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×#120	C₄×C₅	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
295	#435	—	2	4	no	—
296	C₈×D₄	—	2	4	no	—
297	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
300	#407	—	2	4	no	—
301	C₂×C₂²⋊C₈	—	2	4	no	—
302	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
311	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
314	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
315	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
316	#386	C₄×C₅	1	1	yes	characteristic
317	#386	C₄×C₅	1	1	yes	characteristic
318	#386	C₄×C₅	1	1	yes	characteristic
319	#385	C₄×C₅	1	1	yes	characteristic
320	#385	C₄×C₅	1	1	yes	characteristic
321	#385	C₄×C₅	1	1	yes	characteristic
322	#379	C₄×C₅	1	1	yes	characteristic
323	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
324	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
326	#336	C₂²×C₅	1	1	yes	characteristic, complemented
327	#336	C₂²×C₅	1	1	yes	characteristic, complemented
328	#336	C₂²×C₅	1	1	yes	characteristic, complemented
329	#336	C₂²×C₅	1	1	yes	characteristic, complemented
330	#336	C₂²×C₅	1	1	yes	characteristic, complemented
331	#336	C₂²×C₅	1	1	yes	characteristic, complemented
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	—	2	1	no	—
334	C₂³×C₅	—	2	1	no	—
335	C₂³×C₅	—	2	1	no	—
336	C₂³×C₅	—	2	8	no	—
337	C₂³×C₅	—	2	1	no	—
338	C₂³×C₅	—	2	1	no	—
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	1	no	—
342	C₂³×C₅	—	2	1	no	—
343	C₂³×C₅	—	2	1	no	—
344	C₂³×C₅	—	2	1	no	—
345	C₂³×C₅	—	2	1	no	—
346	C₂³×C₅	—	2	1	no	—
347	C₂³×C₅	—	2	1	no	—
348	C₂³×C₅	—	2	1	no	—
349	C₂³×C₅	—	2	1	no	—
350	C₂³×C₅	—	2	1	no	—
351	C₂³×C₅	—	2	1	no	—
352	C₂³×C₅	—	2	1	no	—
353	C₂³×C₅	—	2	1	no	—
354	C₂³×C₅	—	2	1	no	—
355	C₂³×C₅	—	4	4	no	—
356	C₂³×C₅	—	4	4	no	—
357	C₂³×C₅	—	4	4	no	—
358	C₂³×C₅	—	4	4	no	—
359	C₂³×C₅	—	4	4	no	—
360	C₂³×C₅	—	4	4	no	—
361	C₂³×C₅	C₄×D₄	1	2	yes	—
362	C₂³×C₅	C₄×D₄	1	2	yes	—
363	C₂³×C₅	C₂×M₁₆	1	2	yes	—
364	C₂³×C₅	C₂×M₁₆	1	2	yes	—
365	C₂³×C₅	#131	1	2	yes	—
366	C₂³×C₅	#131	1	2	yes	—
367	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
368	C₅×D₄	—	2	8	no	—
369	C₅×D₄	—	4	4	no	—
370	C₅×D₄	—	4	4	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	4	4	no	—
407	C₂×C₄×C₅	—	4	4	no	—
408	C₂×C₄×C₅	—	4	4	no	—
409	C₂×C₄×C₅	—	4	1	no	—
410	C₂×C₄×C₅	—	4	1	no	—
411	C₂×C₄×C₅	—	4	1	no	—
412	C₂×C₄×C₅	—	4	1	no	—
413	C₂×C₄×C₅	—	4	1	no	—
414	C₂×C₄×C₅	—	4	1	no	—
415	C₂×C₄×C₅	—	4	1	no	—
416	C₂×C₄×C₅	—	4	1	no	—
417	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
418	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
419	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
420	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
424	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
425	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
426	C₅×C₈	—	2	2	no	—
427	C₅×C₈	—	2	2	no	—
428	C₅×C₈	—	2	2	no	—
429	C₅×C₈	—	2	2	no	—
430	C₅×C₈	—	4	1	no	—
431	C₅×C₈	—	4	1	no	—
432	C₅×C₈	—	4	1	no	—
433	C₅×C₈	—	4	1	no	—
434	C₂⁵	C₂×C₄×C₅	1	1	yes	characteristic
435	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
436	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
437	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
438	C₂³×C₄	—	2	2	no	—
439	C₂³×C₄	—	2	2	no	—
440	C₂³×C₄	—	2	2	no	—
441	C₂³×C₄	—	2	2	no	—
442	C₂³×C₄	—	4	1	no	—
443	C₂³×C₄	—	4	1	no	—
444	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
445	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
446	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
451	C₂×M₁₆	—	2	2	no	—
452	C₂×M₁₆	—	2	2	no	—
453	C₂×M₁₆	—	2	2	no	—
454	C₂×M₁₆	—	2	2	no	—
455	C₂×M₁₆	—	4	1	no	—
456	C₂×M₁₆	—	4	1	no	—
457	C₂²×C₈	—	2	2	no	—
458	C₂²×C₈	—	2	2	no	—
459	C₂²×C₈	—	2	2	no	—
460	C₂²×C₈	—	2	2	no	—
461	C₂²×C₈	—	2	2	no	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	4	1	no	—
464	C₂²×C₈	—	4	1	no	—
465	C₂²×C₈	—	4	1	no	—
466	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
474	#120	—	2	4	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	4	1	no	—
480	C₄×D₄	—	4	1	no	—
481	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
499	C₄⋊C₈	—	2	2	no	—
500	C₄⋊C₈	—	2	2	no	—
501	C₄⋊C₈	—	4	1	no	—
502	C₂²⋊C₈	—	2	2	no	—
503	C₂²⋊C₈	—	2	2	no	—
504	C₂²⋊C₈	—	2	2	no	—
505	C₂²⋊C₈	—	2	2	no	—
506	C₂²⋊C₈	—	2	2	no	—
507	C₂²⋊C₈	—	2	2	no	—
508	C₂²⋊C₈	—	2	2	no	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	—	4	1	no	—
511	C₂²⋊C₈	C₅×D₄	1	4	yes	complemented
512	C₂²⋊C₈	C₅×D₄	1	4	yes	complemented
513	#97	—	2	2	no	—
514	#97	—	4	1	no	—
515	C₄×C₈	—	2	2	no	—
516	#95	C₂×C₄×C₅	1	1	yes	characteristic
517	#95	C₂×C₄×C₅	1	1	yes	characteristic
518	#95	C₂×C₄×C₅	1	1	yes	characteristic
519	#95	C₂×C₄×C₅	1	1	yes	characteristic
520	#95	C₂×C₄×C₅	1	1	yes	characteristic
521	#95	C₂×C₄×C₅	1	1	yes	characteristic
522	C₂²×C₅	—	2	2	no	—
523	C₂²×C₅	—	2	2	no	—
524	C₂²×C₅	—	2	2	no	—
525	C₂²×C₅	—	2	2	no	—
526	C₂²×C₅	—	2	2	no	—
527	C₂²×C₅	—	2	2	no	—
528	C₂²×C₅	—	2	2	no	—
529	C₂²×C₅	—	2	2	no	—
530	C₂²×C₅	—	2	2	no	—
531	C₂²×C₅	—	2	2	no	—
532	C₂²×C₅	—	2	2	no	—
533	C₂²×C₅	—	2	2	no	—
534	C₂²×C₅	—	2	2	no	—
535	C₂²×C₅	—	2	2	no	—
536	C₂²×C₅	—	2	2	no	—
537	C₂²×C₅	—	4	16	no	—
538	C₂²×C₅	—	4	1	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	—	4	1	no	—
544	C₂²×C₅	—	4	1	no	—
545	C₂²×C₅	—	4	1	no	—
546	C₂²×C₅	—	4	1	no	—
547	C₂²×C₅	—	4	1	no	—
548	C₂²×C₅	—	4	1	no	—
549	C₂²×C₅	—	4	1	no	—
550	C₂²×C₅	#435	1	4	yes	complemented
551	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
552	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
553	C₂²×C₅	#518	1	1	yes	characteristic
554	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
555	C₂²×C₅	C₂×#131	1	1	yes	characteristic
556	C₂²×C₅	C₂×#131	1	1	yes	characteristic
557	C₂²×C₅	#568	1	1	yes	characteristic
558	C₄×C₅	—	2	2	no	—
559	C₄×C₅	—	2	2	no	—
560	C₄×C₅	—	2	2	no	—
561	C₄×C₅	—	4	1	no	—
562	C₄×C₅	—	4	1	no	—
563	C₄×C₅	—	4	1	no	—
564	C₄×C₅	—	4	1	no	—
565	C₄×C₅	—	4	1	no	—
566	C₄×C₅	—	4	1	no	—
567	C₄×C₅	—	4	1	no	—
568	C₄×C₅	D₄²	1	1	yes	characteristic
569	C₄×C₅	#546	1	1	yes	characteristic
570	C₄×C₅	#546	1	1	yes	characteristic
571	C₄×C₅	#551	1	1	yes	characteristic
572	C₂⁴	—	2	2	no	—
573	C₂⁴	—	2	2	no	—
574	C₂⁴	—	2	2	no	—
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	2	2	no	—
577	C₂⁴	—	4	1	no	—
578	C₂⁴	—	4	1	no	—
579	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
580	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
581	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
582	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	C₅×M₁₆	1	4	yes	complemented
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	4	1	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
626	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
627	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
628	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
629	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
630	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
631	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
632	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
633	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
634	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
635	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
636	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
637	C₂²×C₄	C₅×#41	1	2	yes	—
638	C₂²×C₄	C₅×#41	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
640	M₁₆	—	4	4	no	—
641	M₁₆	—	4	4	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	4	4	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	—	4	4	no	—
665	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
666	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
667	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
668	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	4	1	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	4	1	no	—
682	C₂²⋊C₄	—	4	1	no	—
683	C₂²⋊C₄	—	4	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	1	no	—
690	C₂×C₅	—	2	4	no	—
691	C₂×C₅	—	4	2	no	—
692	C₂×C₅	—	4	2	no	—
693	C₂×C₅	—	4	2	no	—
694	C₂×C₅	#2358	1	1	yes	characteristic
695	C₂×C₅	C₂×#435	1	1	yes	characteristic
696	C₂×C₅	#2929	1	1	yes	characteristic
697	C₂×C₅	#2933	1	1	yes	characteristic
698	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
699	C₂×C₅	#2974	1	1	yes	characteristic
700	C₂×C₅	#2976	1	1	yes	characteristic
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	8	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	4	4	no	—
726	C₂³	—	4	4	no	—
727	C₂³	—	4	4	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	C₄×C₅×D₄	1	2	yes	—
731	C₂³	C₄×C₅×D₄	1	2	yes	—
732	C₂³	C₂×C₅×M₁₆	1	2	yes	—
733	C₂³	C₂×C₅×M₁₆	1	2	yes	—
734	C₂³	C₅×#131	1	2	yes	—
735	C₂³	C₅×#131	1	2	yes	—
736	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
737	D₄	—	2	8	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
787	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
788	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
789	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
790	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
791	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
792	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
793	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
794	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
795	C₈	—	2	2	no	—
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₈	—	2	2	no	—
799	C₈	—	4	1	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₅	#22846	1	1	yes	characteristic, direct product factor, Sylow
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	4	16	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	C₅×#435	1	4	yes	complemented
833	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
834	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
835	C₂²	C₅×#518	1	1	yes	characteristic
836	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
837	C₂²	C₂×C₅×#131	1	1	yes	characteristic
838	C₂²	C₂×C₅×#131	1	1	yes	characteristic
839	C₂²	C₅×#568	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	C₅×D₄²	1	1	yes	characteristic
851	C₄	C₅×#546	1	1	yes	characteristic
852	C₄	C₅×#546	1	1	yes	characteristic
853	C₄	C₅×#551	1	1	yes	characteristic
854	C₂	—	2	4	no	—
855	C₂	—	4	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	4	2	no	—
858	C₂	C₅×#2358	1	1	yes	characteristic
859	C₂	C₂×C₅×#435	1	1	yes	characteristic
860	C₂	C₅×#2929	1	1	yes	characteristic
861	C₂	C₅×#2933	1	1	yes	characteristic
862	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
863	C₂	C₅×#2974	1	1	yes	characteristic
864	C₂	C₅×#2976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂×C₅×#120	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#435	C₂	semidirect
2. C₂×C₅×C₈×D₄	C₂	semidirect
3. C₂×C₅×#407	C₂	semidirect
4. C₂²×C₅×C₂²⋊C₈	C₂	semidirect
6. C₅×#1955	C₂	semidirect
7. C₅×#1924	C₂	semidirect
8. C₅×#1923	C₂	semidirect
9. C₅×#1870	C₂	semidirect
10. C₅×#1869	C₂	semidirect
11. C₅×#1869	C₂	semidirect
12. C₅×#1851	C₂	semidirect
13. C₅×#1850	C₂	semidirect
14. C₅×#1753	C₂	semidirect
15. C₅×#1752	C₂	semidirect
21. C₂³×C₅×C₈	C₂²	semidirect
28. C₂×C₅×C₄⋊C₈	C₂²	semidirect
29. C₂×C₅×C₄⋊C₈	C₂²	semidirect
30. C₂×C₅×C₄⋊C₈	C₂²	semidirect
41. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
42. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
43. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
44. C₂×C₅×#97	C₂²	semidirect
45. C₂×C₅×#97	C₂²	semidirect
46. C₂×C₄×C₅×C₈	C₂²	semidirect
57. C₅×#336	C₂²	semidirect
58. C₅×#336	C₂²	semidirect
59. C₅×#336	C₂²	semidirect
60. C₅×#336	C₂²	semidirect
61. C₅×#336	C₂²	semidirect
62. C₅×#336	C₂²	semidirect
63. #22846	C₅	direct (N × H)
141. C₅×C₂²⋊C₈	D₄	semidirect
142. C₅×C₂²⋊C₈	D₄	semidirect
152. C₂×#435	C₂×C₅	semidirect
153. C₂×C₈×D₄	C₂×C₅	semidirect
154. C₂×#407	C₂×C₅	semidirect
155. C₂²×C₂²⋊C₈	C₂×C₅	semidirect
157. #1955	C₂×C₅	semidirect
158. #1924	C₂×C₅	semidirect
159. #1923	C₂×C₅	semidirect
160. #1870	C₂×C₅	semidirect
161. #1869	C₂×C₅	semidirect
162. #1869	C₂×C₅	semidirect
163. #1851	C₂×C₅	semidirect
164. #1850	C₂×C₅	semidirect
165. #1753	C₂×C₅	semidirect
166. #1752	C₂×C₅	semidirect
186. C₂×C₅×D₄	M₁₆	semidirect
290. C₂³×C₈	C₂²×C₅	semidirect
297. C₂×C₄⋊C₈	C₂²×C₅	semidirect
298. C₂×C₄⋊C₈	C₂²×C₅	semidirect
299. C₂×C₄⋊C₈	C₂²×C₅	semidirect
310. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
311. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
312. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
313. C₂×#97	C₂²×C₅	semidirect
314. C₂×#97	C₂²×C₅	semidirect
315. C₂×C₄×C₈	C₂²×C₅	semidirect
326. #336	C₂²×C₅	semidirect
327. #336	C₂²×C₅	semidirect
328. #336	C₂²×C₅	semidirect
329. #336	C₂²×C₅	semidirect
330. #336	C₂²×C₅	semidirect
331. #336	C₂²×C₅	semidirect
511. C₂²⋊C₈	C₅×D₄	semidirect
512. C₂²⋊C₈	C₅×D₄	semidirect
550. C₂²×C₅	#435	semidirect
591. C₂×D₄	C₅×M₁₆	semidirect
803. C₅	#22846	direct (N × H)
832. C₂²	C₅×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#435	2
C₂×C₅×C₈×D₄	2
C₂×C₅×#407	2
C₂²×C₅×C₂²⋊C₈	2
C₄×C₅×#120	2
C₅×#1955	2
C₅×#1924	2
C₅×#1923	2
C₅×#1870	2
C₅×#1869	2
C₅×#1851	2
C₅×#1850	2
C₅×#1753	2
C₅×#1752	2
#22846	5

Subgroups — C5×#22846 #11945566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22846 #11945566