Subgroups — C₅×#22038 #11944758

Order 1280.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#120	C₂	1	1	yes	maximal, characteristic
4	C₅×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1851	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1779	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	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	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×#120	C₄	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₅×#436	—	2	4	no	—
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×#407	—	2	4	no	—
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
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, complemented
40	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
45	C₅×#386	C₄	1	1	yes	characteristic
46	C₅×#386	C₄	1	1	yes	characteristic
47	C₅×#386	C₄	1	1	yes	characteristic
48	C₅×#385	C₄	1	1	yes	characteristic
49	C₅×#385	C₄	1	1	yes	characteristic
50	C₅×#385	C₄	1	1	yes	characteristic
51	C₅×#379	C₄	1	1	yes	characteristic
52	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic, complemented
56	C₅×#336	C₂²	1	1	yes	characteristic, complemented
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	#22038	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	2	no	—
67	C₂³×C₄×C₅	—	2	2	no	—
68	C₂³×C₄×C₅	—	4	1	no	—
69	C₂³×C₄×C₅	—	4	1	no	—
70	C₂³×C₄×C₅	—	4	1	no	—
71	C₂³×C₄×C₅	—	4	1	no	—
72	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	2	2	no	—
80	C₂×C₅×M₁₆	—	2	2	no	—
81	C₂×C₅×M₁₆	—	4	1	no	—
82	C₂×C₅×M₁₆	—	4	1	no	—
83	C₂×C₅×M₁₆	—	4	1	no	—
84	C₂×C₅×M₁₆	—	4	1	no	—
85	C₂×C₅×M₁₆	—	4	1	no	—
86	C₂×C₅×M₁₆	—	4	1	no	—
87	C₂×C₅×M₁₆	D₄	1	4	yes	complemented
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₅×#120	—	2	4	no	—
97	C₄×C₅×D₄	—	2	2	no	—
98	C₄×C₅×D₄	—	2	2	no	—
99	C₄×C₅×D₄	—	4	1	no	—
100	C₄×C₅×D₄	—	4	1	no	—
101	C₄×C₅×D₄	—	4	1	no	—
102	C₄×C₅×D₄	—	4	1	no	—
103	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊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×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	—	2	2	no	—
122	C₅×C₄⋊C₈	—	4	1	no	—
123	C₅×C₄⋊C₈	—	4	1	no	—
124	C₅×C₂²⋊C₈	—	2	2	no	—
125	C₅×C₂²⋊C₈	—	2	2	no	—
126	C₅×C₂²⋊C₈	—	2	2	no	—
127	C₅×C₂²⋊C₈	—	2	2	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	2	2	no	—
131	C₅×C₂²⋊C₈	—	4	1	no	—
132	C₅×C₂²⋊C₈	—	4	1	no	—
133	C₅×C₂²⋊C₈	—	4	1	no	—
134	C₅×C₂²⋊C₈	—	4	1	no	—
135	C₅×C₂²⋊C₈	—	4	1	no	—
136	C₅×C₂²⋊C₈	—	4	1	no	—
137	C₅×#97	—	4	1	no	—
138	C₄×C₅×C₈	—	2	2	no	—
139	C₄×C₅×C₈	—	4	1	no	—
140	C₅×#95	C₂×C₄	1	1	yes	characteristic
141	C₅×#95	C₂×C₄	1	1	yes	characteristic
142	C₅×#95	C₂×C₄	1	1	yes	characteristic
143	C₅×#95	C₂×C₄	1	1	yes	characteristic
144	C₅×#95	C₂×C₄	1	1	yes	characteristic
145	C₅×#95	C₂×C₄	1	1	yes	characteristic
146	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×#407	C₂×C₅	1	1	yes	characteristic, complemented
148	C₄×#120	C₂×C₅	1	1	yes	characteristic
149	#1955	C₂×C₅	1	1	yes	characteristic, complemented
150	#1954	C₂×C₅	1	1	yes	characteristic, complemented
151	#1924	C₂×C₅	1	1	yes	characteristic, complemented
152	#1923	C₂×C₅	1	1	yes	characteristic, complemented
153	#1923	C₂×C₅	1	1	yes	characteristic, complemented
154	#1923	C₂×C₅	1	1	yes	characteristic, complemented
155	#1870	C₂×C₅	1	1	yes	characteristic, complemented
156	#1870	C₂×C₅	1	1	yes	characteristic, complemented
157	#1870	C₂×C₅	1	1	yes	characteristic, complemented
158	#1851	C₂×C₅	1	1	yes	characteristic, complemented
159	#1779	C₂×C₅	1	1	yes	characteristic, complemented
160	#1753	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁴×C₅	—	2	2	no	—
162	C₂⁴×C₅	—	2	2	no	—
163	C₂⁴×C₅	—	2	2	no	—
164	C₂⁴×C₅	—	4	1	no	—
165	C₂⁴×C₅	—	4	1	no	—
166	C₂⁴×C₅	—	4	1	no	—
167	C₂⁴×C₅	—	4	1	no	—
168	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₅×D₄	—	2	2	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	—	2	2	no	—
176	C₂×C₅×D₄	—	2	2	no	—
177	C₂×C₅×D₄	—	4	1	no	—
178	C₂×C₅×D₄	—	4	1	no	—
179	C₂×C₅×D₄	—	4	1	no	—
180	C₂×C₅×D₄	—	4	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	2	no	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂²×C₄×C₅	—	2	2	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	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	2	1	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	—	4	1	no	—
207	C₂²×C₄×C₅	—	4	1	no	—
208	C₂²×C₄×C₅	—	4	1	no	—
209	C₂²×C₄×C₅	—	4	1	no	—
210	C₂²×C₄×C₅	—	4	1	no	—
211	C₂²×C₄×C₅	—	4	1	no	—
212	C₂²×C₄×C₅	—	4	4	no	—
213	C₂²×C₄×C₅	—	4	4	no	—
214	C₂²×C₄×C₅	—	4	4	no	—
215	C₂²×C₄×C₅	—	4	4	no	—
216	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₅	#41	1	2	yes	—
228	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₅×M₁₆	—	4	4	no	—
230	C₅×M₁₆	—	4	4	no	—
231	C₅×M₁₆	—	4	4	no	—
232	C₂×C₅×C₈	—	2	1	no	—
233	C₂×C₅×C₈	—	2	1	no	—
234	C₂×C₅×C₈	—	2	1	no	—
235	C₂×C₅×C₈	—	2	1	no	—
236	C₂×C₅×C₈	—	2	1	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	C₂×D₄	1	2	yes	—
255	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
256	C₅×C₄⋊C₄	—	2	2	no	—
257	C₅×C₄⋊C₄	—	4	1	no	—
258	C₅×C₄⋊C₄	—	4	1	no	—
259	C₅×C₂²⋊C₄	—	2	2	no	—
260	C₅×C₂²⋊C₄	—	2	2	no	—
261	C₅×C₂²⋊C₄	—	2	2	no	—
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	—	2	2	no	—
264	C₅×C₂²⋊C₄	—	4	1	no	—
265	C₅×C₂²⋊C₄	—	4	1	no	—
266	C₅×C₂²⋊C₄	—	4	1	no	—
267	C₅×C₂²⋊C₄	—	4	1	no	—
268	C₅×C₂²⋊C₄	—	4	1	no	—
269	C₅×C₂²⋊C₄	—	4	1	no	—
270	C₅×C₂²⋊C₄	M₁₆	1	4	yes	complemented
271	C₄²×C₅	—	2	1	no	—
272	C₄²×C₅	—	2	1	no	—
273	C₄²×C₅	—	2	1	no	—
274	C₄²×C₅	—	2	1	no	—
275	C₄²×C₅	—	2	1	no	—
276	C₄²×C₅	—	2	1	no	—
277	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
279	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
280	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂×#120	C₄×C₅	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
285	#436	—	2	4	no	—
286	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
289	#407	—	2	4	no	—
290	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
306	#386	C₄×C₅	1	1	yes	characteristic
307	#386	C₄×C₅	1	1	yes	characteristic
308	#386	C₄×C₅	1	1	yes	characteristic
309	#385	C₄×C₅	1	1	yes	characteristic
310	#385	C₄×C₅	1	1	yes	characteristic
311	#385	C₄×C₅	1	1	yes	characteristic
312	#379	C₄×C₅	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	#336	C₂²×C₅	1	1	yes	characteristic, complemented
317	#336	C₂²×C₅	1	1	yes	characteristic, complemented
318	#336	C₂²×C₅	1	1	yes	characteristic, complemented
319	#336	C₂²×C₅	1	1	yes	characteristic, complemented
320	#336	C₂²×C₅	1	1	yes	characteristic, complemented
321	#336	C₂²×C₅	1	1	yes	characteristic, complemented
322	C₂³×C₅	—	2	1	no	—
323	C₂³×C₅	—	2	1	no	—
324	C₂³×C₅	—	2	1	no	—
325	C₂³×C₅	—	2	1	no	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	2	1	no	—
328	C₂³×C₅	—	2	1	no	—
329	C₂³×C₅	—	2	1	no	—
330	C₂³×C₅	—	2	1	no	—
331	C₂³×C₅	—	2	1	no	—
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	1	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	—	4	4	no	—
348	C₂³×C₅	—	4	4	no	—
349	C₂³×C₅	—	4	4	no	—
350	C₂³×C₅	—	4	4	no	—
351	C₂³×C₅	—	4	4	no	—
352	C₂³×C₅	—	4	4	no	—
353	C₂³×C₅	—	4	4	no	—
354	C₂³×C₅	C₄×D₄	1	2	yes	—
355	C₂³×C₅	C₂×M₁₆	1	2	yes	—
356	C₂³×C₅	#131	1	2	yes	—
357	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
358	C₅×D₄	—	4	4	no	—
359	C₅×D₄	—	4	4	no	—
360	C₅×D₄	—	4	4	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	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	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
393	C₂×C₄×C₅	—	4	4	no	—
394	C₂×C₄×C₅	—	4	4	no	—
395	C₂×C₄×C₅	—	4	1	no	—
396	C₂×C₄×C₅	—	4	1	no	—
397	C₂×C₄×C₅	—	4	1	no	—
398	C₂×C₄×C₅	—	4	1	no	—
399	C₂×C₄×C₅	—	4	1	no	—
400	C₂×C₄×C₅	—	4	1	no	—
401	C₂×C₄×C₅	—	4	1	no	—
402	C₂×C₄×C₅	—	4	1	no	—
403	C₂×C₄×C₅	—	4	1	no	—
404	C₂×C₄×C₅	—	4	1	no	—
405	C₂×C₄×C₅	—	4	1	no	—
406	C₂×C₄×C₅	—	4	1	no	—
407	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
408	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
409	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
410	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
412	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
415	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
416	C₅×C₈	—	2	2	no	—
417	C₅×C₈	—	2	2	no	—
418	C₅×C₈	—	4	1	no	—
419	C₅×C₈	—	4	1	no	—
420	C₅×C₈	—	4	1	no	—
421	C₅×C₈	—	4	1	no	—
422	C₅×C₈	—	4	1	no	—
423	C₅×C₈	—	4	1	no	—
424	C₂⁵	C₂×C₄×C₅	1	1	yes	characteristic
425	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
426	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
427	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
428	C₂³×C₄	—	2	2	no	—
429	C₂³×C₄	—	2	2	no	—
430	C₂³×C₄	—	4	1	no	—
431	C₂³×C₄	—	4	1	no	—
432	C₂³×C₄	—	4	1	no	—
433	C₂³×C₄	—	4	1	no	—
434	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
435	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
436	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂×M₁₆	—	2	2	no	—
442	C₂×M₁₆	—	2	2	no	—
443	C₂×M₁₆	—	4	1	no	—
444	C₂×M₁₆	—	4	1	no	—
445	C₂×M₁₆	—	4	1	no	—
446	C₂×M₁₆	—	4	1	no	—
447	C₂×M₁₆	—	4	1	no	—
448	C₂×M₁₆	—	4	1	no	—
449	C₂×M₁₆	C₅×D₄	1	4	yes	complemented
450	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
458	#120	—	2	4	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	4	1	no	—
462	C₄×D₄	—	4	1	no	—
463	C₄×D₄	—	4	1	no	—
464	C₄×D₄	—	4	1	no	—
465	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
483	C₄⋊C₈	—	2	2	no	—
484	C₄⋊C₈	—	4	1	no	—
485	C₄⋊C₈	—	4	1	no	—
486	C₂²⋊C₈	—	2	2	no	—
487	C₂²⋊C₈	—	2	2	no	—
488	C₂²⋊C₈	—	2	2	no	—
489	C₂²⋊C₈	—	2	2	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	C₂²⋊C₈	—	2	2	no	—
492	C₂²⋊C₈	—	2	2	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	C₂²⋊C₈	—	4	1	no	—
495	C₂²⋊C₈	—	4	1	no	—
496	C₂²⋊C₈	—	4	1	no	—
497	C₂²⋊C₈	—	4	1	no	—
498	C₂²⋊C₈	—	4	1	no	—
499	#97	—	4	1	no	—
500	C₄×C₈	—	2	2	no	—
501	C₄×C₈	—	4	1	no	—
502	#95	C₂×C₄×C₅	1	1	yes	characteristic
503	#95	C₂×C₄×C₅	1	1	yes	characteristic
504	#95	C₂×C₄×C₅	1	1	yes	characteristic
505	#95	C₂×C₄×C₅	1	1	yes	characteristic
506	#95	C₂×C₄×C₅	1	1	yes	characteristic
507	#95	C₂×C₄×C₅	1	1	yes	characteristic
508	C₂²×C₅	—	2	2	no	—
509	C₂²×C₅	—	2	2	no	—
510	C₂²×C₅	—	2	2	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	2	2	no	—
513	C₂²×C₅	—	2	2	no	—
514	C₂²×C₅	—	2	2	no	—
515	C₂²×C₅	—	2	2	no	—
516	C₂²×C₅	—	2	2	no	—
517	C₂²×C₅	—	4	16	no	—
518	C₂²×C₅	—	4	1	no	—
519	C₂²×C₅	—	4	1	no	—
520	C₂²×C₅	—	4	1	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	4	1	no	—
523	C₂²×C₅	—	4	1	no	—
524	C₂²×C₅	—	4	1	no	—
525	C₂²×C₅	—	4	1	no	—
526	C₂²×C₅	—	4	1	no	—
527	C₂²×C₅	—	4	1	no	—
528	C₂²×C₅	—	4	1	no	—
529	C₂²×C₅	—	4	1	no	—
530	C₂²×C₅	—	4	1	no	—
531	C₂²×C₅	—	4	1	no	—
532	C₂²×C₅	—	4	1	no	—
533	C₂²×C₅	—	4	1	no	—
534	C₂²×C₅	—	4	1	no	—
535	C₂²×C₅	—	4	1	no	—
536	C₂²×C₅	—	4	1	no	—
537	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
538	C₂²×C₅	#518	1	1	yes	characteristic
539	C₂²×C₅	#518	1	1	yes	characteristic
540	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
541	C₂²×C₅	C₂×#131	1	1	yes	characteristic
542	C₂²×C₅	#568	1	1	yes	characteristic
543	C₂²×C₅	#568	1	1	yes	characteristic
544	C₄×C₅	—	2	2	no	—
545	C₄×C₅	—	2	2	no	—
546	C₄×C₅	—	2	2	no	—
547	C₄×C₅	—	4	1	no	—
548	C₄×C₅	—	4	1	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	4	1	no	—
554	C₄×C₅	#534	1	1	yes	characteristic
555	C₄×C₅	#535	1	1	yes	characteristic
556	C₄×C₅	#538	1	1	yes	characteristic
557	C₄×C₅	#538	1	1	yes	characteristic
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	4	1	no	—
562	C₂⁴	—	4	1	no	—
563	C₂⁴	—	4	1	no	—
564	C₂⁴	—	4	1	no	—
565	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
566	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
567	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
568	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
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	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	—	4	4	no	—
611	C₂²×C₄	—	4	4	no	—
612	C₂²×C₄	—	4	4	no	—
613	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
614	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
616	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
618	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
619	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
620	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
621	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
623	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
624	C₂²×C₄	C₅×#41	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
626	M₁₆	—	4	4	no	—
627	M₁₆	—	4	4	no	—
628	M₁₆	—	4	4	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	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	C₂×C₅×D₄	1	2	yes	—
652	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	4	1	no	—
655	C₄⋊C₄	—	4	1	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₂²⋊C₄	—	4	1	no	—
664	C₂²⋊C₄	—	4	1	no	—
665	C₂²⋊C₄	—	4	1	no	—
666	C₂²⋊C₄	—	4	1	no	—
667	C₂²⋊C₄	C₅×M₁₆	1	4	yes	complemented
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	2	1	no	—
674	C₂×C₅	—	4	2	no	—
675	C₂×C₅	—	4	2	no	—
676	C₂×C₅	—	4	2	no	—
677	C₂×C₅	—	8	1	no	—
678	C₂×C₅	#2321	1	1	yes	characteristic
679	C₂×C₅	#2933	1	1	yes	characteristic
680	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
681	C₂×C₅	#2974	1	1	yes	characteristic
682	C₂×C₅	#2975	1	1	yes	characteristic
683	C₂×C₅	#2976	1	1	yes	characteristic
684	C₂×C₅	#2978	1	1	yes	characteristic
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	4	4	no	—
711	C₂³	—	4	4	no	—
712	C₂³	—	4	4	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	C₄×C₅×D₄	1	2	yes	—
718	C₂³	C₂×C₅×M₁₆	1	2	yes	—
719	C₂³	C₅×#131	1	2	yes	—
720	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
721	D₄	—	4	4	no	—
722	D₄	—	4	4	no	—
723	D₄	—	4	4	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	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	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
771	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
772	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
773	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
774	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
775	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
777	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
778	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	4	1	no	—
782	C₈	—	4	1	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₅	#22038	1	1	yes	characteristic, direct product factor, Sylow
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	4	16	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
818	C₂²	C₅×#518	1	1	yes	characteristic
819	C₂²	C₅×#518	1	1	yes	characteristic
820	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
821	C₂²	C₂×C₅×#131	1	1	yes	characteristic
822	C₂²	C₅×#568	1	1	yes	characteristic
823	C₂²	C₅×#568	1	1	yes	characteristic
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	C₅×#534	1	1	yes	characteristic
835	C₄	C₅×#535	1	1	yes	characteristic
836	C₄	C₅×#538	1	1	yes	characteristic
837	C₄	C₅×#538	1	1	yes	characteristic
838	C₂	—	4	2	no	—
839	C₂	—	4	2	no	—
840	C₂	—	4	2	no	—
841	C₂	—	8	1	no	—
842	C₂	C₅×#2321	1	1	yes	characteristic
843	C₂	C₅×#2933	1	1	yes	characteristic
844	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
845	C₂	C₅×#2974	1	1	yes	characteristic
846	C₂	C₅×#2975	1	1	yes	characteristic
847	C₂	C₅×#2976	1	1	yes	characteristic
848	C₂	C₅×#2978	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×#436	C₂	semidirect
2. C₂×C₅×#407	C₂	semidirect
4. C₅×#1955	C₂	semidirect
5. C₅×#1954	C₂	semidirect
6. C₅×#1924	C₂	semidirect
7. C₅×#1923	C₂	semidirect
8. C₅×#1923	C₂	semidirect
9. C₅×#1923	C₂	semidirect
10. C₅×#1870	C₂	semidirect
11. C₅×#1870	C₂	semidirect
12. C₅×#1870	C₂	semidirect
13. C₅×#1851	C₂	semidirect
14. C₅×#1779	C₂	semidirect
15. C₅×#1753	C₂	semidirect
19. C₂²×C₅×M₁₆	C₂²	semidirect
25. C₂×C₅×C₄⋊C₈	C₂²	semidirect
26. C₂×C₅×C₄⋊C₈	C₂²	semidirect
27. C₂×C₅×C₄⋊C₈	C₂²	semidirect
39. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
40. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
41. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
42. C₂×C₅×#97	C₂²	semidirect
43. C₂×C₄×C₅×C₈	C₂²	semidirect
44. C₂×C₄×C₅×C₈	C₂²	semidirect
55. C₅×#336	C₂²	semidirect
56. C₅×#336	C₂²	semidirect
57. C₅×#336	C₂²	semidirect
58. C₅×#336	C₂²	semidirect
59. C₅×#336	C₂²	semidirect
60. C₅×#336	C₂²	semidirect
61. #22038	C₅	direct (N × H)
87. C₂×C₅×M₁₆	D₄	semidirect
146. C₂×#436	C₂×C₅	semidirect
147. C₂×#407	C₂×C₅	semidirect
149. #1955	C₂×C₅	semidirect
150. #1954	C₂×C₅	semidirect
151. #1924	C₂×C₅	semidirect
152. #1923	C₂×C₅	semidirect
153. #1923	C₂×C₅	semidirect
154. #1923	C₂×C₅	semidirect
155. #1870	C₂×C₅	semidirect
156. #1870	C₂×C₅	semidirect
157. #1870	C₂×C₅	semidirect
158. #1851	C₂×C₅	semidirect
159. #1779	C₂×C₅	semidirect
160. #1753	C₂×C₅	semidirect
270. C₅×C₂²⋊C₄	M₁₆	semidirect
280. C₂²×M₁₆	C₂²×C₅	semidirect
286. C₂×C₄⋊C₈	C₂²×C₅	semidirect
287. C₂×C₄⋊C₈	C₂²×C₅	semidirect
288. C₂×C₄⋊C₈	C₂²×C₅	semidirect
300. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
301. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
302. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
303. C₂×#97	C₂²×C₅	semidirect
304. C₂×C₄×C₈	C₂²×C₅	semidirect
305. C₂×C₄×C₈	C₂²×C₅	semidirect
316. #336	C₂²×C₅	semidirect
317. #336	C₂²×C₅	semidirect
318. #336	C₂²×C₅	semidirect
319. #336	C₂²×C₅	semidirect
320. #336	C₂²×C₅	semidirect
321. #336	C₂²×C₅	semidirect
449. C₂×M₁₆	C₅×D₄	semidirect
667. C₂²⋊C₄	C₅×M₁₆	semidirect
787. C₅	#22038	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×C₅×#436	2
C₂×C₅×#407	2
C₄×C₅×#120	2
C₅×#1955	2
C₅×#1954	2
C₅×#1924	2
C₅×#1923	2
C₅×#1870	2
C₅×#1851	2
C₅×#1779	2
C₅×#1753	2
#22038	5

Subgroups — C5×#22038 #11944758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22038 #11944758