Subgroups — C₂×#10617765 #13007389

Order 1280.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#66140	C₂	1	1	yes	maximal, characteristic, complemented
4	#10617765	C₂	1	32	yes	maximal, direct product factor
5	C₂×#65890	C₂	1	2	yes	maximal, complemented
6	C₂×#65888	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#65894	C₂	1	2	yes	maximal, complemented
9	C₂×#65882	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65897	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#65886	C₂	1	2	yes	maximal, complemented
15	C₂×#65872	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#65867	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65866	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#65868	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#65862	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#65824	C₂	1	2	yes	maximal, complemented
22	C₂×#65828	C₂	1	2	yes	maximal, complemented
23	C₂×#65829	C₂	1	2	yes	maximal, complemented
24	C₂²×#4031	C₂	1	2	yes	maximal, complemented
25	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂³×C₂²⋊D₅	C₂²	1	2	yes	—
27	C₂²×#711	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₅	C₂²	1	1	yes	characteristic
29	C₂²×#709	C₂²	1	2	yes	complemented
30	C₂³×Dic₁₀	C₂²	1	2	yes	complemented
31	C₅×#518	C₂²	1	16	yes	complemented
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
36	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
42	C₂×#4099	C₂²	1	2	yes	—
43	C₂×#4099	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
45	#66140	C₂²	1	16	yes	complemented
46	C₂×#4086	C₂²	1	1	yes	characteristic
47	C₂×#4085	C₂²	1	2	yes	—
48	C₂×#4085	C₂²	1	2	yes	complemented
49	D₄×C₂²⋊D₅	C₂²	1	16	yes	complemented
50	C₂×#4084	C₂²	1	1	yes	characteristic
51	C₂×#4084	C₂²	1	1	yes	characteristic, complemented
52	C₂×#4083	C₂²	1	2	yes	—
53	C₂×#4082	C₂²	1	1	yes	characteristic, complemented
54	C₂×#4081	C₂²	1	2	yes	complemented
55	C₂×D₄×Dic₅	C₂²	1	1	yes	characteristic
56	C₂×D₄×Dic₅	C₂²	1	1	yes	characteristic
57	C₂×#4076	C₂²	1	1	yes	characteristic
58	C₂×#4076	C₂²	1	2	yes	complemented
59	C₂×#4076	C₂²	1	2	yes	complemented
60	C₂×#4075	C₂²	1	2	yes	complemented
61	C₂×#4075	C₂²	1	2	yes	complemented
62	C₂×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
65	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
66	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
67	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
68	C₂²×#685	C₂²	1	2	yes	complemented
69	C₂²×#685	C₂²	1	2	yes	complemented
70	C₂×#4072	C₂²	1	2	yes	complemented
71	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
72	C₂×#4070	C₂²	1	2	yes	complemented
73	C₂×#4070	C₂²	1	2	yes	complemented
74	C₂²×C₄×Dic₅	C₂²	1	2	yes	complemented
75	#65897	C₂²	1	16	yes	complemented
76	#65895	C₂²	1	16	yes	complemented
77	#65894	C₂²	1	32	yes	complemented
78	#65893	C₂²	1	16	yes	complemented
79	#65890	C₂²	1	32	yes	complemented
80	#65888	C₂²	1	16	yes	complemented
81	#65886	C₂²	1	32	yes	complemented
82	#65882	C₂²	1	16	yes	complemented
83	#65879	C₂²	1	16	yes	complemented
84	#65872	C₂²	1	32	yes	complemented
85	D₄×Dic₁₀	C₂²	1	16	yes	complemented
86	C₄×#711	C₂²	1	16	yes	complemented
87	#65868	C₂²	1	16	yes	complemented
88	#65867	C₂²	1	16	yes	complemented
89	#65866	C₂²	1	16	yes	complemented
90	#65862	C₂²	1	16	yes	complemented
91	C₂×#4044	C₂²	1	1	yes	characteristic, complemented
92	C₂×#4044	C₂²	1	2	yes	complemented
93	C₂×#4043	C₂²	1	1	yes	characteristic, complemented
94	C₂×#4042	C₂²	1	1	yes	characteristic, complemented
95	C₂×#4042	C₂²	1	2	yes	complemented
96	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
97	C₂×#4040	C₂²	1	1	yes	characteristic, complemented
98	C₂×#4039	C₂²	1	1	yes	characteristic, complemented
99	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
100	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
101	C₂×#4035	C₂²	1	1	yes	characteristic, complemented
102	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
103	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
104	C₂×#4033	C₂²	1	1	yes	characteristic, complemented
105	#65829	C₂²	1	32	yes	complemented
106	#65828	C₂²	1	32	yes	complemented
107	C₂×#4032	C₂²	1	2	yes	complemented
108	C₂×#4031	C₂²	1	1	yes	characteristic
109	C₂×#4031	C₂²	1	2	yes	—
110	C₂×#4031	C₂²	1	2	yes	complemented
111	C₂×#4031	C₂²	1	2	yes	complemented
112	C₂×#4031	C₂²	1	2	yes	complemented
113	C₂×#4031	C₂²	1	2	yes	complemented
114	C₂×#4031	C₂²	1	2	yes	complemented
115	C₂×#4031	C₂²	1	2	yes	complemented
116	C₂×#4031	C₂²	1	2	yes	complemented
117	C₂×#4031	C₂²	1	32	yes	complemented
118	#65824	C₂²	1	32	yes	complemented
119	C₂×#4030	C₂²	1	1	yes	characteristic
120	C₂×#4030	C₂²	1	2	yes	complemented
121	C₂×#4030	C₂²	1	2	yes	complemented
122	C₂×#4029	C₂²	1	1	yes	characteristic, complemented
123	C₂×#4029	C₂²	1	2	yes	complemented
124	C₂×#4029	C₂²	1	2	yes	complemented
125	C₂×#4028	C₂²	1	2	yes	complemented
126	C₂×#4027	C₂²	1	2	yes	complemented
127	C₂×#4027	C₂²	1	2	yes	complemented
128	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
129	C₂×#4025	C₂²	1	1	yes	characteristic, complemented
130	C₂×#4025	C₂²	1	2	yes	complemented
131	C₂×#4025	C₂²	1	2	yes	complemented
132	C₂×#4024	C₂²	1	2	yes	complemented
133	C₂×#4024	C₂²	1	2	yes	complemented
134	C₂×#4023	C₂²	1	2	yes	complemented
135	C₂×#4022	C₂²	1	2	yes	complemented
136	C₂×#4021	C₂²	1	1	yes	characteristic, complemented
137	C₂×#4021	C₂²	1	2	yes	complemented
138	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
139	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
140	C₂×#4018	C₂²	1	1	yes	characteristic, complemented
141	C₂×#4018	C₂²	1	2	yes	complemented
142	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
143	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
144	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
147	C₂×#3514	—	5	1	no	maximal, Sylow
148	C₂⁵×C₅	C₂³	1	2	yes	—
149	C₂⁴×D₅	C₂³	1	2	yes	—
150	C₂²×C₅×D₄	—	2	8	no	—
151	C₂²×C₅×D₄	C₂³	1	2	yes	—
152	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₅×D₄	C₂³	1	8	yes	—
154	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₅	C₂³	1	2	yes	—
157	C₂³×C₄×C₅	C₂³	1	2	yes	—
158	C₂³×C₄×C₅	C₂³	1	2	yes	—
159	C₂³×C₄×C₅	C₂³	1	2	yes	—
160	C₂²×C₂²⋊D₅	—	4	8	no	—
161	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
163	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
164	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
165	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
166	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
167	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
168	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
169	C₂²×C₂²⋊D₅	C₂³	1	16	yes	—
170	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
171	C₂³×Dic₅	C₂³	1	2	yes	—
172	C₂³×Dic₅	C₂³	1	2	yes	—
173	C₂³×Dic₅	C₂³	1	2	yes	—
174	C₂×#711	—	2	8	no	—
175	C₂×#711	C₂³	1	8	yes	—
176	C₂×D₄×D₅	—	2	8	no	—
177	C₂×D₄×D₅	C₂³	1	8	yes	—
178	C₂×#709	—	4	8	no	—
179	C₂×#709	C₂³	1	16	yes	complemented
180	C₂²×D₂₀	C₂³	1	1	yes	characteristic
181	C₂²×D₂₀	C₂³	1	1	yes	characteristic
182	C₂²×D₂₀	C₂³	1	2	yes	—
183	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
185	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
186	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
187	C₂²×C₄×D₅	C₂³	1	2	yes	—
188	C₂²×C₄×D₅	C₂³	1	2	yes	—
189	C₂²×Dic₁₀	—	4	8	no	—
190	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀	C₂³	1	2	yes	—
192	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
193	C₂²×Dic₁₀	C₂³	1	2	yes	—
194	C₂²×Dic₁₀	C₂³	1	2	yes	—
195	C₂²×Dic₁₀	C₂³	1	16	yes	complemented
196	C₄×C₅×D₄	C₂³	1	8	yes	—
197	C₄×C₅×D₄	C₂³	1	8	yes	—
198	C₄×C₅×D₄	C₂³	1	16	yes	complemented
199	C₄×C₅×D₄	C₂³	1	8	yes	complemented
200	C₄×C₅×D₄	C₂³	1	16	yes	complemented
201	C₄×C₅×D₄	C₂³	1	8	yes	complemented
202	C₅×#117	C₂³	1	8	yes	complemented
203	C₅×#117	C₂³	1	8	yes	complemented
204	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
216	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	2	yes	—
220	#4099	C₂³	1	16	yes	—
221	#4099	C₂³	1	16	yes	complemented
222	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
223	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
224	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
226	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
227	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
229	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
230	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
231	C₂×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
232	#4086	C₂³	1	8	yes	—
233	#4085	C₂³	1	16	yes	—
234	#4085	C₂³	1	16	yes	complemented
235	#4084	C₂³	1	8	yes	—
236	#4084	C₂³	1	8	yes	complemented
237	#4083	C₂³	1	16	yes	—
238	#4082	C₂³	1	8	yes	complemented
239	#4081	C₂³	1	16	yes	complemented
240	D₄×Dic₅	C₂³	1	8	yes	—
241	D₄×Dic₅	C₂³	1	8	yes	—
242	#4076	C₂³	1	8	yes	—
243	#4076	C₂³	1	16	yes	complemented
244	#4076	C₂³	1	16	yes	complemented
245	#4075	C₂³	1	16	yes	complemented
246	#4075	C₂³	1	16	yes	complemented
247	C₄×C₂²⋊D₅	C₂³	1	8	yes	—
248	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
249	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
250	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
251	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
252	C₄×C₂²⋊D₅	C₂³	1	8	yes	complemented
253	C₂×#685	C₂³	1	2	yes	—
254	C₂×#685	C₂³	1	1	yes	characteristic
255	C₂×#685	C₂³	1	1	yes	characteristic
256	C₂×#685	C₂³	1	2	yes	—
257	C₂×#685	C₂³	1	1	yes	characteristic
258	C₂×#685	C₂³	1	2	yes	—
259	C₂×#685	C₂³	1	1	yes	characteristic
260	C₂×#685	C₂³	1	1	yes	characteristic
261	C₂×#685	C₂³	1	2	yes	—
262	C₂×#685	C₂³	1	2	yes	—
263	C₂×#685	C₂³	1	2	yes	—
264	C₂×#685	C₂³	1	2	yes	—
265	C₂×#685	C₂³	1	1	yes	characteristic
266	C₂×#685	C₂³	1	2	yes	—
267	C₂×#685	C₂³	1	2	yes	—
268	C₂×#685	C₂³	1	16	yes	complemented
269	C₂×#685	C₂³	1	16	yes	complemented
270	#4072	C₂³	1	16	yes	complemented
271	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
273	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
276	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
277	#4070	C₂³	1	16	yes	complemented
278	#4070	C₂³	1	16	yes	complemented
279	#4070	C₂³	1	8	yes	complemented
280	C₂×#683	C₂³	1	1	yes	characteristic
281	C₂×#683	C₂³	1	2	yes	—
282	C₂×#683	C₂³	1	2	yes	—
283	C₂×#683	C₂³	1	1	yes	characteristic
284	C₂×#683	C₂³	1	1	yes	characteristic
285	C₂×#683	C₂³	1	1	yes	characteristic
286	C₂×#683	C₂³	1	2	yes	—
287	C₂×#683	C₂³	1	1	yes	characteristic
288	C₂×#683	C₂³	1	1	yes	characteristic
289	C₂×#683	C₂³	1	2	yes	—
290	C₂×#683	C₂³	1	2	yes	—
291	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅	C₂³	1	2	yes	—
294	C₂×C₄×Dic₅	C₂³	1	2	yes	—
295	C₂×C₄×Dic₅	C₂³	1	2	yes	—
296	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅	C₂³	1	2	yes	—
299	C₂×C₄×Dic₅	C₂³	1	16	yes	complemented
300	#4044	C₂³	1	8	yes	complemented
301	#4044	C₂³	1	16	yes	complemented
302	#4043	C₂³	1	8	yes	complemented
303	#4042	C₂³	1	8	yes	complemented
304	#4042	C₂³	1	16	yes	complemented
305	#4041	C₂³	1	8	yes	complemented
306	#4040	C₂³	1	8	yes	complemented
307	#4039	C₂³	1	8	yes	complemented
308	#4038	C₂³	1	8	yes	complemented
309	#4038	C₂³	1	8	yes	complemented
310	#4035	C₂³	1	8	yes	complemented
311	#4034	C₂³	1	8	yes	complemented
312	#4034	C₂³	1	8	yes	complemented
313	#4033	C₂³	1	8	yes	complemented
314	#4032	C₂³	1	16	yes	complemented
315	#4031	C₂³	1	16	yes	—
316	#4031	C₂³	1	8	yes	—
317	#4031	C₂³	1	16	yes	complemented
318	#4031	C₂³	1	16	yes	complemented
319	#4031	C₂³	1	16	yes	complemented
320	#4031	C₂³	1	16	yes	complemented
321	#4031	C₂³	1	16	yes	complemented
322	#4031	C₂³	1	16	yes	complemented
323	#4031	C₂³	1	16	yes	complemented
324	#4030	C₂³	1	8	yes	—
325	#4030	C₂³	1	16	yes	complemented
326	#4030	C₂³	1	16	yes	complemented
327	#4029	C₂³	1	16	yes	complemented
328	#4029	C₂³	1	8	yes	complemented
329	#4029	C₂³	1	16	yes	complemented
330	#4028	C₂³	1	16	yes	complemented
331	#4027	C₂³	1	16	yes	complemented
332	#4027	C₂³	1	16	yes	complemented
333	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
334	#4025	C₂³	1	16	yes	complemented
335	#4025	C₂³	1	16	yes	complemented
336	#4025	C₂³	1	8	yes	complemented
337	#4024	C₂³	1	16	yes	complemented
338	#4024	C₂³	1	16	yes	complemented
339	#4023	C₂³	1	16	yes	complemented
340	#4022	C₂³	1	16	yes	complemented
341	#4021	C₂³	1	16	yes	complemented
342	#4021	C₂³	1	8	yes	complemented
343	C₄×D₂₀	C₂³	1	8	yes	complemented
344	C₄×D₂₀	C₂³	1	8	yes	complemented
345	#4018	C₂³	1	8	yes	complemented
346	#4018	C₂³	1	16	yes	complemented
347	C₄²×D₅	C₂³	1	8	yes	complemented
348	#4015	C₂³	1	8	yes	complemented
349	C₄×Dic₁₀	C₂³	1	8	yes	complemented
350	C₄×Dic₁₀	C₂³	1	16	yes	complemented
351	C₄×Dic₁₀	C₂³	1	8	yes	complemented
352	#3514	—	5	32	no	—
353	C₂×#559	—	5	1	no	—
354	C₂×#556	—	5	1	no	—
355	C₂×#555	—	5	1	no	—
356	C₂×#555	—	5	1	no	—
357	C₂×#551	—	5	2	no	—
358	C₂×#551	—	5	2	no	—
359	C₂×D₄×Q₈	—	5	1	no	—
360	C₂×#548	—	5	2	no	—
361	C₂×#546	—	5	1	no	—
362	C₂×#546	—	5	1	no	—
363	C₂×#546	—	5	2	no	—
364	C₂×D₄²	—	5	1	no	—
365	C₂×#542	—	5	1	no	—
366	C₂×#542	—	5	1	no	—
367	C₂×#538	—	5	2	no	—
368	C₂×#538	—	5	2	no	—
369	C₂×#532	—	5	1	no	—
370	C₂×#529	—	5	2	no	—
371	C₂×#529	—	5	1	no	—
372	C₂²×#124	—	5	2	no	—
373	C₂×#518	—	5	1	no	—
374	C₂×#518	D₅	1	1	yes	characteristic, complemented
375	C₂×C₄×#41	—	5	1	no	—
376	C₂⁴×C₅	—	2	8	no	—
377	C₂⁴×C₅	—	4	4	no	—
378	C₂⁴×C₅	—	4	4	no	—
379	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₅	C₂⁴	1	2	yes	—
381	C₂⁴×C₅	C₂⁴	1	2	yes	—
382	C₂⁴×C₅	C₂⁴	1	8	yes	—
383	C₂³×D₅	—	2	8	no	—
384	C₂³×D₅	—	4	4	no	—
385	C₂³×D₅	—	4	4	no	—
386	C₂³×D₅	C₂⁴	1	1	yes	characteristic
387	C₂³×D₅	C₂⁴	1	2	yes	—
388	C₂³×D₅	C₂⁴	1	1	yes	characteristic
389	C₂³×D₅	C₂⁴	1	8	yes	—
390	C₂×C₅×D₄	—	2	8	no	—
391	C₂×C₅×D₄	—	2	32	no	—
392	C₂×C₅×D₄	—	2	4	no	—
393	C₂×C₅×D₄	#41	1	8	yes	complemented
394	C₂×C₅×D₄	C₂⁴	1	8	yes	—
395	C₂×C₅×D₄	C₂⁴	1	4	yes	—
396	C₂×C₅×D₄	C₂⁴	1	4	yes	—
397	C₂²×C₄×C₅	—	2	4	no	—
398	C₂²×C₄×C₅	—	4	4	no	—
399	C₂²×C₄×C₅	—	4	4	no	—
400	C₂²×C₄×C₅	—	4	4	no	—
401	C₂²×C₄×C₅	—	4	4	no	—
402	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
410	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
411	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
412	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
413	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
414	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
415	C₂×C₂²⋊D₅	—	2	8	no	—
416	C₂×C₂²⋊D₅	—	2	8	no	—
417	C₂×C₂²⋊D₅	—	2	8	no	—
418	C₂×C₂²⋊D₅	—	2	4	no	—
419	C₂×C₂²⋊D₅	—	4	32	no	—
420	C₂×C₂²⋊D₅	—	4	4	no	—
421	C₂×C₂²⋊D₅	—	4	4	no	—
422	C₂×C₂²⋊D₅	—	4	4	no	—
423	C₂×C₂²⋊D₅	—	4	2	no	—
424	C₂×C₂²⋊D₅	—	4	4	no	—
425	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
426	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
427	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
428	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
429	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
430	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
431	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
432	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
433	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
434	C₂²×Dic₅	—	2	8	no	—
435	C₂²×Dic₅	—	2	8	no	—
436	C₂²×Dic₅	—	4	4	no	—
437	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
438	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅	C₂⁴	1	2	yes	—
440	C₂²×Dic₅	C₂⁴	1	2	yes	—
441	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
442	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
443	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
444	C₂²×Dic₅	C₂⁴	1	2	yes	—
445	C₂²×Dic₅	C₂⁴	1	8	yes	—
446	C₂²×Dic₅	C₂⁴	1	8	yes	—
447	C₂²×Dic₅	C₂⁴	1	8	yes	—
448	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
449	#711	—	2	32	no	—
450	D₄×D₅	—	2	32	no	—
451	#709	—	4	32	no	—
452	C₂×D₂₀	—	2	4	no	—
453	C₂×D₂₀	—	4	2	no	—
454	C₂×D₂₀	—	4	4	no	—
455	C₂×D₂₀	C₂⁴	1	4	yes	—
456	C₂×D₂₀	C₂⁴	1	8	yes	—
457	C₂×D₂₀	C₂⁴	1	4	yes	—
458	C₂×C₄×D₅	—	2	4	no	—
459	C₂×C₄×D₅	—	2	4	no	—
460	C₂×C₄×D₅	—	2	4	no	—
461	C₂×C₄×D₅	—	4	4	no	—
462	C₂×C₄×D₅	—	4	2	no	—
463	C₂×C₄×D₅	—	4	4	no	—
464	C₂×C₄×D₅	C₂⁴	1	4	yes	—
465	C₂×C₄×D₅	C₂⁴	1	4	yes	—
466	C₂×C₄×D₅	C₂⁴	1	4	yes	—
467	C₂×C₄×D₅	C₂⁴	1	8	yes	—
468	C₂×C₄×D₅	C₂⁴	1	4	yes	—
469	C₂×C₄×D₅	C₂⁴	1	8	yes	—
470	C₂×Dic₁₀	—	2	4	no	—
471	C₂×Dic₁₀	—	2	4	no	—
472	C₂×Dic₁₀	—	2	8	no	—
473	C₂×Dic₁₀	—	4	32	no	—
474	C₂×Dic₁₀	—	4	4	no	—
475	C₂×Dic₁₀	—	4	4	no	—
476	C₂×Dic₁₀	C₂⁴	1	4	yes	—
477	C₂×Dic₁₀	C₂⁴	1	8	yes	—
478	C₂×Dic₁₀	C₂⁴	1	4	yes	—
479	C₂×Dic₁₀	C₂⁴	1	8	yes	—
480	C₂×Dic₁₀	C₂⁴	1	8	yes	—
481	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
482	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
483	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
484	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
485	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
486	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
487	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
488	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
489	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
490	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
491	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
492	C₄²×C₅	C₂⁴	1	4	yes	—
493	C₄²×C₅	C₂⁴	1	4	yes	—
494	C₄²×C₅	C₂⁴	1	8	yes	—
495	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
496	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
497	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
498	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
499	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
500	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
501	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
502	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
503	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
504	#685	C₂⁴	1	8	yes	—
505	#685	C₂⁴	1	4	yes	—
506	#685	C₂⁴	1	4	yes	—
507	#685	C₂⁴	1	8	yes	—
508	#685	C₂⁴	1	4	yes	—
509	#685	C₂⁴	1	8	yes	—
510	#685	C₂⁴	1	4	yes	—
511	#685	C₂⁴	1	4	yes	—
512	#685	C₂⁴	1	8	yes	—
513	#685	C₂⁴	1	8	yes	—
514	#685	C₂⁴	1	8	yes	—
515	#685	C₂⁴	1	8	yes	—
516	#685	C₂⁴	1	4	yes	—
517	#685	C₂⁴	1	8	yes	—
518	#685	C₂⁴	1	8	yes	—
519	C₄⋊Dic₅	C₂⁴	1	4	yes	—
520	C₄⋊Dic₅	C₂⁴	1	8	yes	—
521	C₄⋊Dic₅	C₂⁴	1	4	yes	—
522	C₄⋊Dic₅	C₂⁴	1	4	yes	—
523	C₄⋊Dic₅	C₂⁴	1	8	yes	—
524	C₄⋊Dic₅	C₂⁴	1	4	yes	—
525	#683	C₂⁴	1	4	yes	—
526	#683	C₂⁴	1	8	yes	—
527	#683	C₂⁴	1	8	yes	—
528	#683	C₂⁴	1	4	yes	—
529	#683	C₂⁴	1	4	yes	—
530	#683	C₂⁴	1	4	yes	—
531	#683	C₂⁴	1	8	yes	—
532	#683	C₂⁴	1	4	yes	—
533	#683	C₂⁴	1	4	yes	—
534	#683	C₂⁴	1	8	yes	—
535	#683	C₂⁴	1	8	yes	—
536	C₄×Dic₅	C₂⁴	1	4	yes	—
537	C₄×Dic₅	C₂⁴	1	4	yes	—
538	C₄×Dic₅	C₂⁴	1	8	yes	—
539	C₄×Dic₅	C₂⁴	1	8	yes	—
540	C₄×Dic₅	C₂⁴	1	8	yes	—
541	C₄×Dic₅	C₂⁴	1	4	yes	—
542	C₄×Dic₅	C₂⁴	1	4	yes	—
543	C₄×Dic₅	C₂⁴	1	8	yes	—
544	C₂²×#41	—	5	1	no	—
545	C₂²×#41	—	5	2	no	—
546	C₂³×Q₈	—	5	2	no	—
547	C₂³×D₄	—	5	2	no	—
548	C₂³×D₄	—	5	1	no	—
549	C₂³×D₄	C₂×D₅	1	1	yes	characteristic
550	#559	—	5	16	no	—
551	#556	—	5	16	no	—
552	#555	—	5	16	no	—
553	#555	—	5	16	no	—
554	#551	—	5	32	no	—
555	#551	—	5	32	no	—
556	D₄×Q₈	—	5	16	no	—
557	#548	—	5	32	no	—
558	#546	—	5	16	no	—
559	#546	—	5	16	no	—
560	#546	—	5	32	no	—
561	D₄²	—	5	16	no	—
562	#542	—	5	16	no	—
563	#542	—	5	16	no	—
564	#538	—	5	32	no	—
565	#538	—	5	32	no	—
566	#532	—	5	16	no	—
567	C₂×C₄⋊Q₈	—	5	1	no	—
568	C₂×C₄⋊Q₈	—	5	1	no	—
569	C₂×C₄⋊Q₈	—	5	1	no	—
570	C₂×#127	—	5	1	no	—
571	#529	—	5	32	no	—
572	#529	—	5	16	no	—
573	C₂×#126	—	5	2	no	—
574	C₂×#126	—	5	1	no	—
575	C₂×#126	—	5	2	no	—
576	C₂×#126	—	5	1	no	—
577	C₂×#126	—	5	2	no	—
578	C₂×#126	—	5	2	no	—
579	C₂×#125	—	5	1	no	—
580	C₂×#124	—	5	1	no	—
581	C₂×#124	—	5	1	no	—
582	C₂×#124	—	5	2	no	—
583	C₂×#124	—	5	2	no	—
584	C₂×#124	—	5	2	no	—
585	C₂×#124	—	5	2	no	—
586	C₂×#124	—	5	2	no	—
587	C₂×#124	—	5	2	no	—
588	C₂×#124	—	5	2	no	—
589	C₂×#124	—	5	2	no	—
590	C₂×#124	—	5	32	no	—
591	C₂×#124	—	5	2	no	—
592	C₂×#124	—	5	1	no	—
593	C₂×#123	—	5	2	no	—
594	C₂×#123	—	5	2	no	—
595	C₂×#123	—	5	2	no	—
596	C₂×#123	—	5	1	no	—
597	C₂×#123	—	5	1	no	—
598	C₂×#123	—	5	2	no	—
599	C₂×#123	—	5	2	no	—
600	C₂×#123	—	5	2	no	—
601	C₂×C₂²⋊Q₈	—	5	2	no	—
602	C₂×C₂²⋊Q₈	—	5	1	no	—
603	C₂×C₂²⋊Q₈	—	5	2	no	—
604	C₂×C₂²⋊Q₈	—	5	1	no	—
605	C₂×C₂²⋊Q₈	—	5	2	no	—
606	C₂×C₂²⋊Q₈	—	5	1	no	—
607	C₂×C₂²⋊Q₈	—	5	2	no	—
608	C₂×C₂²⋊Q₈	—	5	2	no	—
609	C₂×#121	—	5	1	no	—
610	C₂×#121	—	5	1	no	—
611	C₂×#121	—	5	2	no	—
612	C₂×#121	—	5	2	no	—
613	C₂×#121	—	5	1	no	—
614	C₂×#121	—	5	2	no	—
615	C₂×#121	—	5	2	no	—
616	C₂×#121	—	5	1	no	—
617	C₂×#121	—	5	1	no	—
618	C₂×#121	—	5	2	no	—
619	C₂×#121	—	5	2	no	—
620	C₂×#120	—	5	2	no	—
621	C₂×#120	—	5	2	no	—
622	C₂×#120	—	5	2	no	—
623	C₂×#120	—	5	2	no	—
624	#518	—	5	16	no	—
625	#518	C₂×D₅	1	16	yes	complemented
626	C₄×#41	—	5	16	no	—
627	C₂×C₄×Q₈	—	5	1	no	—
628	C₂×C₄×Q₈	—	5	1	no	—
629	C₂×C₄×Q₈	—	5	2	no	—
630	C₂×C₄×Q₈	—	5	1	no	—
631	C₂×C₄×D₄	—	5	1	no	—
632	C₂×C₄×D₄	—	5	1	no	—
633	C₂×C₄×D₄	—	5	1	no	—
634	C₂×C₄×D₄	—	5	2	no	—
635	C₂×C₄×D₄	—	5	2	no	—
636	C₂×C₄×D₄	—	5	1	no	—
637	C₂×C₄×D₄	—	5	2	no	—
638	C₂×C₄×D₄	—	5	2	no	—
639	C₂×C₄×D₄	—	5	1	no	—
640	C₂×C₄×D₄	—	5	2	no	—
641	C₂×C₄×D₄	—	5	2	no	—
642	C₂×C₄×D₄	—	5	1	no	—
643	C₂×C₄×D₄	—	5	1	no	—
644	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
645	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
647	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
648	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
649	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
650	C₂×#117	—	5	2	no	—
651	C₂×#117	—	5	1	no	—
652	C₂×#117	—	5	1	no	—
653	C₂×#117	—	5	2	no	—
654	C₂×#117	—	5	1	no	—
655	C₂×#117	—	5	2	no	—
656	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
657	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
658	C₂²×C₂²⋊C₄	—	5	2	no	—
659	C₂²×C₂²⋊C₄	—	5	2	no	—
660	C₂²×C₂²⋊C₄	—	5	2	no	—
661	C₂²×C₂²⋊C₄	—	5	2	no	—
662	C₂²×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
663	C₂²×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
664	C₂²×C₄²	—	5	2	no	—
665	C₂²×C₄²	—	5	1	no	—
666	C₂³×C₅	—	2	4	no	—
667	C₂³×C₅	—	2	4	no	—
668	C₂³×C₅	—	2	2	no	—
669	C₂³×C₅	—	2	4	no	—
670	C₂³×C₅	—	2	4	no	—
671	C₂³×C₅	—	2	2	no	—
672	C₂³×C₅	—	2	4	no	—
673	C₂³×C₅	—	2	2	no	—
674	C₂³×C₅	—	2	16	no	—
675	C₂³×C₅	—	4	8	no	—
676	C₂³×C₅	—	4	8	no	—
677	C₂³×C₅	—	8	16	no	—
678	C₂³×C₅	C₂×#41	1	8	yes	—
679	C₂³×C₅	C₂⁵	1	2	yes	—
680	C₂³×C₅	C₂⁵	1	4	yes	—
681	C₂³×C₅	C₂⁵	1	4	yes	—
682	C₂³×C₅	C₂⁵	1	1	yes	characteristic
683	C₂²×D₅	—	2	2	no	—
684	C₂²×D₅	—	2	2	no	—
685	C₂²×D₅	—	2	4	no	—
686	C₂²×D₅	—	2	2	no	—
687	C₂²×D₅	—	2	4	no	—
688	C₂²×D₅	—	2	2	no	—
689	C₂²×D₅	—	2	2	no	—
690	C₂²×D₅	—	2	4	no	—
691	C₂²×D₅	—	2	2	no	—
692	C₂²×D₅	—	2	16	no	—
693	C₂²×D₅	—	4	8	no	—
694	C₂²×D₅	—	4	8	no	—
695	C₂²×D₅	—	8	16	no	—
696	C₂²×D₅	C₂⁵	1	2	yes	—
697	C₂²×D₅	C₂⁵	1	4	yes	—
698	C₂²×D₅	C₂⁵	1	2	yes	—
699	C₅×D₄	—	2	16	no	—
700	C₅×D₄	—	2	8	no	—
701	C₅×D₄	C₂×#41	1	16	yes	complemented
702	C₂×C₄×C₅	—	2	2	no	—
703	C₂×C₄×C₅	—	2	2	no	—
704	C₂×C₄×C₅	—	2	4	no	—
705	C₂×C₄×C₅	—	2	2	no	—
706	C₂×C₄×C₅	—	2	4	no	—
707	C₂×C₄×C₅	—	2	2	no	—
708	C₂×C₄×C₅	—	2	2	no	—
709	C₂×C₄×C₅	—	2	8	no	—
710	C₂×C₄×C₅	—	4	8	no	—
711	C₂×C₄×C₅	—	4	8	no	—
712	C₂×C₄×C₅	—	4	8	no	—
713	C₂×C₄×C₅	—	4	8	no	—
714	C₂×C₄×C₅	C₂×#41	1	4	yes	—
715	C₂×C₄×C₅	C₂⁵	1	4	yes	—
716	C₂×C₄×C₅	C₂⁵	1	2	yes	—
717	C₂×C₄×C₅	C₂⁵	1	2	yes	—
718	C₂×C₄×C₅	C₂⁵	1	2	yes	—
719	C₂×C₄×C₅	C₂⁵	1	2	yes	—
720	C₂×C₄×C₅	C₂⁵	1	4	yes	—
721	C₂×C₄×C₅	C₂⁵	1	2	yes	—
722	C₂×C₄×C₅	C₂⁵	1	2	yes	—
723	C₂²⋊D₅	—	2	16	no	—
724	C₂²⋊D₅	—	2	16	no	—
725	C₂²⋊D₅	—	2	16	no	—
726	C₂²⋊D₅	—	2	8	no	—
727	C₂²⋊D₅	—	4	8	no	—
728	C₂²⋊D₅	—	4	8	no	—
729	C₂²⋊D₅	—	4	8	no	—
730	C₂²⋊D₅	—	4	4	no	—
731	C₂²⋊D₅	—	4	8	no	—
732	C₂×Dic₅	—	2	4	no	—
733	C₂×Dic₅	—	2	2	no	—
734	C₂×Dic₅	—	2	2	no	—
735	C₂×Dic₅	—	2	16	no	—
736	C₂×Dic₅	—	2	2	no	—
737	C₂×Dic₅	—	2	4	no	—
738	C₂×Dic₅	—	2	4	no	—
739	C₂×Dic₅	—	2	2	no	—
740	C₂×Dic₅	—	2	2	no	—
741	C₂×Dic₅	—	2	16	no	—
742	C₂×Dic₅	—	4	8	no	—
743	C₂×Dic₅	H(5,𝔽₂)	1	4	yes	—
744	C₂×Dic₅	C₂⁵	1	2	yes	—
745	C₂×Dic₅	C₂⁵	1	2	yes	—
746	C₂×Dic₅	C₂⁵	1	2	yes	—
747	C₂×Dic₅	C₂⁵	1	4	yes	—
748	C₂×Dic₅	C₂⁵	1	4	yes	—
749	C₂×Dic₅	C₂⁵	1	2	yes	—
750	C₂×Dic₅	C₂⁵	1	4	yes	—
751	C₂×Dic₅	C₂⁵	1	2	yes	—
752	C₂×Dic₅	C₂⁵	1	2	yes	—
753	D₂₀	—	2	8	no	—
754	D₂₀	—	4	4	no	—
755	D₂₀	—	4	8	no	—
756	C₄×D₅	—	2	8	no	—
757	C₄×D₅	—	2	8	no	—
758	C₄×D₅	—	2	8	no	—
759	C₄×D₅	—	4	8	no	—
760	C₄×D₅	—	4	4	no	—
761	C₄×D₅	—	4	8	no	—
762	Dic₁₀	—	2	8	no	—
763	Dic₁₀	—	2	8	no	—
764	Dic₁₀	—	2	16	no	—
765	Dic₁₀	—	4	8	no	—
766	Dic₁₀	—	4	8	no	—
767	C₂⁵	—	5	2	no	—
768	C₂⁵	C₂²×D₅	1	2	yes	—
769	C₂×#41	—	5	8	no	—
770	C₂×#41	—	5	16	no	—
771	C₂×#41	—	10	8	no	—
772	C₂×#41	—	20	8	no	—
773	C₂²×Q₈	—	5	1	no	—
774	C₂²×Q₈	—	5	1	no	—
775	C₂²×Q₈	—	5	2	no	—
776	C₂²×Q₈	—	5	2	no	—
777	C₂²×Q₈	—	5	2	no	—
778	C₂²×Q₈	—	5	16	no	—
779	C₂²×Q₈	—	20	8	no	—
780	C₂²×D₄	—	2	8	no	—
781	C₂²×D₄	—	5	2	no	—
782	C₂²×D₄	—	5	2	no	—
783	C₂²×D₄	—	5	1	no	—
784	C₂²×D₄	—	5	2	no	—
785	C₂²×D₄	—	5	1	no	—
786	C₂²×D₄	—	5	2	no	—
787	C₂²×D₄	—	5	2	no	—
788	C₂²×D₄	—	5	2	no	—
789	C₂²×D₄	—	5	2	no	—
790	C₂²×D₄	—	5	16	no	—
791	C₂²×D₄	—	5	8	no	—
792	C₂²×D₄	—	5	1	no	—
793	C₂²×D₄	—	5	1	no	—
794	C₂²×D₄	—	5	2	no	—
795	C₂²×D₄	—	10	8	no	—
796	C₂²×D₄	—	20	8	no	—
797	C₂²×D₄	C₂²×D₅	1	2	yes	—
798	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
799	C₂²×D₄	C₂²×D₅	1	8	yes	—
800	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
801	C₂³×C₄	—	5	2	no	—
802	C₂³×C₄	—	5	2	no	—
803	C₂³×C₄	—	5	2	no	—
804	C₂³×C₄	—	5	1	no	—
805	C₂³×C₄	—	5	1	no	—
806	C₂³×C₄	—	5	1	no	—
807	C₂³×C₄	—	5	2	no	—
808	C₂³×C₄	—	5	2	no	—
809	C₂³×C₄	—	5	1	no	—
810	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
811	C₂³×C₄	C₂²×D₅	1	2	yes	—
812	C₂³×C₄	C₂²×D₅	1	2	yes	—
813	C₂³×C₄	C₂²×D₅	1	2	yes	—
814	C₂³×C₄	C₂²×D₅	1	2	yes	—
815	C₄⋊Q₈	—	5	8	no	—
816	C₄⋊Q₈	—	5	8	no	—
817	C₄⋊Q₈	—	5	8	no	—
818	#127	—	5	8	no	—
819	#126	—	5	16	no	—
820	#126	—	5	8	no	—
821	#126	—	5	16	no	—
822	#126	—	5	8	no	—
823	#126	—	5	16	no	—
824	#126	—	5	16	no	—
825	#125	—	5	8	no	—
826	#124	—	5	8	no	—
827	#124	—	5	8	no	—
828	#124	—	5	16	no	—
829	#124	—	5	16	no	—
830	#124	—	5	16	no	—
831	#124	—	5	16	no	—
832	#124	—	5	16	no	—
833	#124	—	5	16	no	—
834	#124	—	5	16	no	—
835	#124	—	5	16	no	—
836	#124	—	5	16	no	—
837	#124	—	5	8	no	—
838	#123	—	5	16	no	—
839	#123	—	5	16	no	—
840	#123	—	5	16	no	—
841	#123	—	5	8	no	—
842	#123	—	5	8	no	—
843	#123	—	5	16	no	—
844	#123	—	5	16	no	—
845	#123	—	5	16	no	—
846	C₂²⋊Q₈	—	5	16	no	—
847	C₂²⋊Q₈	—	5	8	no	—
848	C₂²⋊Q₈	—	5	16	no	—
849	C₂²⋊Q₈	—	5	8	no	—
850	C₂²⋊Q₈	—	5	8	no	—
851	C₂²⋊Q₈	—	5	16	no	—
852	C₂²⋊Q₈	—	5	16	no	—
853	C₂²⋊Q₈	—	5	16	no	—
854	#121	—	5	16	no	—
855	#121	—	5	8	no	—
856	#121	—	5	16	no	—
857	#121	—	5	8	no	—
858	#121	—	5	16	no	—
859	#121	—	5	16	no	—
860	#121	—	5	8	no	—
861	#121	—	5	8	no	—
862	#121	—	5	8	no	—
863	#121	—	5	16	no	—
864	#121	—	5	16	no	—
865	#120	—	5	16	no	—
866	#120	—	5	16	no	—
867	#120	—	5	16	no	—
868	#120	—	5	16	no	—
869	C₄×Q₈	—	5	8	no	—
870	C₄×Q₈	—	5	8	no	—
871	C₄×Q₈	—	5	16	no	—
872	C₄×Q₈	—	5	8	no	—
873	C₄×D₄	—	5	8	no	—
874	C₄×D₄	—	5	8	no	—
875	C₄×D₄	—	5	16	no	—
876	C₄×D₄	—	5	16	no	—
877	C₄×D₄	—	5	8	no	—
878	C₄×D₄	—	5	8	no	—
879	C₄×D₄	—	5	16	no	—
880	C₄×D₄	—	5	16	no	—
881	C₄×D₄	—	5	8	no	—
882	C₄×D₄	—	5	16	no	—
883	C₄×D₄	—	5	16	no	—
884	C₄×D₄	—	5	8	no	—
885	C₄×D₄	—	5	8	no	—
886	C₄×D₄	C₂²×D₅	1	8	yes	—
887	C₄×D₄	C₂²×D₅	1	8	yes	—
888	C₄×D₄	C₂²×D₅	1	16	yes	complemented
889	C₄×D₄	C₂²×D₅	1	8	yes	complemented
890	C₄×D₄	C₂²×D₅	1	16	yes	complemented
891	C₄×D₄	C₂²×D₅	1	8	yes	complemented
892	#117	—	5	16	no	—
893	#117	—	5	8	no	—
894	#117	—	5	8	no	—
895	#117	—	5	16	no	—
896	#117	—	5	8	no	—
897	#117	—	5	16	no	—
898	#117	C₂²×D₅	1	8	yes	complemented
899	#117	C₂²×D₅	1	8	yes	complemented
900	C₂×C₄⋊C₄	—	5	1	no	—
901	C₂×C₄⋊C₄	—	5	1	no	—
902	C₂×C₄⋊C₄	—	5	1	no	—
903	C₂×C₄⋊C₄	—	5	1	no	—
904	C₂×C₄⋊C₄	—	5	1	no	—
905	C₂×C₄⋊C₄	—	5	1	no	—
906	C₂×C₄⋊C₄	—	5	2	no	—
907	C₂×C₄⋊C₄	—	5	2	no	—
908	C₂×C₄⋊C₄	—	5	2	no	—
909	C₂×C₄⋊C₄	—	5	2	no	—
910	C₂×C₄⋊C₄	—	5	1	no	—
911	C₂×C₄⋊C₄	—	5	1	no	—
912	C₂×C₄⋊C₄	—	5	2	no	—
913	C₂×C₄⋊C₄	—	5	2	no	—
914	C₂×C₄⋊C₄	—	5	2	no	—
915	C₂×C₄⋊C₄	—	5	1	no	—
916	C₂×C₄⋊C₄	—	5	1	no	—
917	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
921	C₂×C₂²⋊C₄	—	5	1	no	—
922	C₂×C₂²⋊C₄	—	5	2	no	—
923	C₂×C₂²⋊C₄	—	5	2	no	—
924	C₂×C₂²⋊C₄	—	5	2	no	—
925	C₂×C₂²⋊C₄	—	5	2	no	—
926	C₂×C₂²⋊C₄	—	5	16	no	—
927	C₂×C₂²⋊C₄	—	5	2	no	—
928	C₂×C₂²⋊C₄	—	5	2	no	—
929	C₂×C₂²⋊C₄	—	5	1	no	—
930	C₂×C₂²⋊C₄	—	5	2	no	—
931	C₂×C₂²⋊C₄	—	5	1	no	—
932	C₂×C₂²⋊C₄	—	5	2	no	—
933	C₂×C₂²⋊C₄	—	5	1	no	—
934	C₂×C₂²⋊C₄	—	5	1	no	—
935	C₂×C₂²⋊C₄	—	5	2	no	—
936	C₂×C₂²⋊C₄	—	5	2	no	—
937	C₂×C₂²⋊C₄	—	5	2	no	—
938	C₂×C₂²⋊C₄	—	5	16	no	—
939	C₂×C₂²⋊C₄	—	5	2	no	—
940	C₂×C₂²⋊C₄	—	5	2	no	—
941	C₂×C₂²⋊C₄	—	5	16	no	—
942	C₂×C₂²⋊C₄	—	5	2	no	—
943	C₂×C₂²⋊C₄	—	5	2	no	—
944	C₂×C₂²⋊C₄	—	5	1	no	—
945	C₂×C₂²⋊C₄	—	5	2	no	—
946	C₂×C₂²⋊C₄	—	5	1	no	—
947	C₂×C₂²⋊C₄	—	5	1	no	—
948	C₂×C₂²⋊C₄	—	5	16	no	—
949	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
950	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
951	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
952	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
953	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
954	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
955	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
956	C₂×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
957	C₂×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
958	C₂×C₄²	—	5	2	no	—
959	C₂×C₄²	—	5	2	no	—
960	C₂×C₄²	—	5	1	no	—
961	C₂×C₄²	—	5	1	no	—
962	C₂×C₄²	—	5	2	no	—
963	C₂×C₄²	—	5	1	no	—
964	C₂×C₄²	—	5	2	no	—
965	C₂×C₄²	—	5	16	no	—
966	C₂×C₄²	—	5	1	no	—
967	C₂×C₄²	—	5	8	no	—
968	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
969	C₂×C₄²	C₂²×D₅	1	2	yes	—
970	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
971	C₂²×C₅	—	2	4	no	—
972	C₂²×C₅	—	2	4	no	—
973	C₂²×C₅	—	2	16	no	—
974	C₂²×C₅	—	2	2	no	—
975	C₂²×C₅	—	2	4	no	—
976	C₂²×C₅	—	2	4	no	—
977	C₂²×C₅	—	2	2	no	—
978	C₂²×C₅	—	2	4	no	—
979	C₂²×C₅	—	2	2	no	—
980	C₂²×C₅	—	4	8	no	—
981	C₂²×C₅	—	4	4	no	—
982	C₂²×C₅	—	8	16	no	—
983	C₂²×C₅	C₂²×#41	1	8	yes	—
984	C₂²×C₅	C₂²×#41	1	2	yes	—
985	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
986	C₂²×C₅	#585	1	2	yes	—
987	C₂²×C₅	C₂⁶	1	1	yes	characteristic
988	C₂×D₅	—	2	2	no	—
989	C₂×D₅	—	2	2	no	—
990	C₂×D₅	—	2	4	no	—
991	C₂×D₅	—	2	2	no	—
992	C₂×D₅	—	2	4	no	—
993	C₂×D₅	—	2	2	no	—
994	C₂×D₅	—	2	2	no	—
995	C₂×D₅	—	2	4	no	—
996	C₂×D₅	—	2	2	no	—
997	C₂×D₅	—	4	4	no	—
998	C₂×D₅	—	4	8	no	—
999	C₂×D₅	—	4	4	no	—
1000	C₂×D₅	—	8	16	no	—
1001	C₄×C₅	—	2	2	no	—
1002	C₄×C₅	—	2	2	no	—
1003	C₄×C₅	—	2	4	no	—
1004	C₄×C₅	—	2	2	no	—
1005	C₄×C₅	—	2	4	no	—
1006	C₄×C₅	—	2	2	no	—
1007	C₄×C₅	—	2	2	no	—
1008	C₄×C₅	C₂²×#41	1	4	yes	—
1009	Dic₅	—	2	4	no	—
1010	Dic₅	—	2	2	no	—
1011	Dic₅	—	2	2	no	—
1012	Dic₅	—	2	2	no	—
1013	Dic₅	—	2	4	no	—
1014	Dic₅	—	2	4	no	—
1015	Dic₅	—	2	2	no	—
1016	Dic₅	—	2	2	no	—
1017	Dic₅	C₂×H(5,𝔽₂)	1	4	yes	—
1018	C₂⁴	—	2	8	no	—
1019	C₂⁴	—	4	4	no	—
1020	C₂⁴	—	4	4	no	—
1021	C₂⁴	—	5	1	no	—
1022	C₂⁴	—	5	2	no	—
1023	C₂⁴	—	5	1	no	—
1024	C₂⁴	—	5	8	no	—
1025	C₂⁴	—	10	8	no	—
1026	C₂⁴	—	20	4	no	—
1027	C₂⁴	—	20	4	no	—
1028	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1029	C₂⁴	C₂³×D₅	1	2	yes	—
1030	C₂⁴	C₂³×D₅	1	2	yes	—
1031	C₂⁴	C₂³×D₅	1	8	yes	—
1032	#41	—	10	32	no	—
1033	#41	—	20	32	no	—
1034	C₂×Q₈	—	5	4	no	—
1035	C₂×Q₈	—	5	4	no	—
1036	C₂×Q₈	—	5	8	no	—
1037	C₂×Q₈	—	5	8	no	—
1038	C₂×Q₈	—	5	8	no	—
1039	C₂×Q₈	—	10	4	no	—
1040	C₂×Q₈	—	10	8	no	—
1041	C₂×Q₈	—	10	4	no	—
1042	C₂×Q₈	—	20	4	no	—
1043	C₂×Q₈	—	20	4	no	—
1044	C₂×Q₈	—	20	32	no	—
1045	C₂×D₄	—	2	8	no	—
1046	C₂×D₄	—	2	32	no	—
1047	C₂×D₄	—	2	4	no	—
1048	C₂×D₄	—	5	8	no	—
1049	C₂×D₄	—	5	8	no	—
1050	C₂×D₄	—	5	4	no	—
1051	C₂×D₄	—	5	8	no	—
1052	C₂×D₄	—	5	4	no	—
1053	C₂×D₄	—	5	8	no	—
1054	C₂×D₄	—	5	8	no	—
1055	C₂×D₄	—	5	8	no	—
1056	C₂×D₄	—	5	8	no	—
1057	C₂×D₄	—	5	4	no	—
1058	C₂×D₄	—	5	4	no	—
1059	C₂×D₄	—	5	8	no	—
1060	C₂×D₄	—	10	4	no	—
1061	C₂×D₄	—	10	8	no	—
1062	C₂×D₄	—	10	8	no	—
1063	C₂×D₄	—	10	8	no	—
1064	C₂×D₄	—	10	32	no	—
1065	C₂×D₄	—	10	4	no	—
1066	C₂×D₄	—	20	4	no	—
1067	C₂×D₄	—	20	2	no	—
1068	C₂×D₄	—	20	32	no	—
1069	C₂×D₄	—	20	4	no	—
1070	C₂×D₄	—	20	4	no	—
1071	C₂×D₄	—	20	4	no	—
1072	C₂×D₄	—	20	2	no	—
1073	C₂×D₄	—	20	4	no	—
1074	C₂×D₄	#709	1	8	yes	complemented
1075	C₂×D₄	C₂³×D₅	1	8	yes	—
1076	C₂×D₄	C₂³×D₅	1	4	yes	—
1077	C₂×D₄	C₂³×D₅	1	4	yes	—
1078	C₂²×C₄	—	2	4	no	—
1079	C₂²×C₄	—	4	4	no	—
1080	C₂²×C₄	—	4	4	no	—
1081	C₂²×C₄	—	4	4	no	—
1082	C₂²×C₄	—	4	4	no	—
1083	C₂²×C₄	—	5	1	no	—
1084	C₂²×C₄	—	5	8	no	—
1085	C₂²×C₄	—	5	8	no	—
1086	C₂²×C₄	—	5	1	no	—
1087	C₂²×C₄	—	5	2	no	—
1088	C₂²×C₄	—	5	1	no	—
1089	C₂²×C₄	—	5	1	no	—
1090	C₂²×C₄	—	5	2	no	—
1091	C₂²×C₄	—	5	1	no	—
1092	C₂²×C₄	—	5	1	no	—
1093	C₂²×C₄	—	5	2	no	—
1094	C₂²×C₄	—	5	8	no	—
1095	C₂²×C₄	—	5	4	no	—
1096	C₂²×C₄	—	5	4	no	—
1097	C₂²×C₄	—	5	4	no	—
1098	C₂²×C₄	—	5	4	no	—
1099	C₂²×C₄	—	5	8	no	—
1100	C₂²×C₄	—	5	8	no	—
1101	C₂²×C₄	—	10	4	no	—
1102	C₂²×C₄	—	10	8	no	—
1103	C₂²×C₄	—	10	8	no	—
1104	C₂²×C₄	—	10	4	no	—
1105	C₂²×C₄	—	10	4	no	—
1106	C₂²×C₄	—	20	4	no	—
1107	C₂²×C₄	—	20	4	no	—
1108	C₂²×C₄	—	20	2	no	—
1109	C₂²×C₄	—	20	4	no	—
1110	C₂²×C₄	C₂³×D₅	1	4	yes	—
1111	C₂²×C₄	C₂³×D₅	1	2	yes	—
1112	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1113	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1114	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1115	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1116	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1117	C₂²×C₄	C₂³×D₅	1	2	yes	—
1118	C₂²×C₄	C₂³×D₅	1	8	yes	—
1119	C₂²×C₄	C₂³×D₅	1	8	yes	—
1120	C₂²×C₄	C₂³×D₅	1	8	yes	—
1121	C₂²×C₄	C₂³×D₅	1	8	yes	—
1122	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1123	C₄⋊C₄	—	5	4	no	—
1124	C₄⋊C₄	—	5	4	no	—
1125	C₄⋊C₄	—	5	4	no	—
1126	C₄⋊C₄	—	5	4	no	—
1127	C₄⋊C₄	—	5	4	no	—
1128	C₄⋊C₄	—	5	4	no	—
1129	C₄⋊C₄	—	5	8	no	—
1130	C₄⋊C₄	—	5	8	no	—
1131	C₄⋊C₄	—	5	8	no	—
1132	C₄⋊C₄	—	5	8	no	—
1133	C₄⋊C₄	—	5	4	no	—
1134	C₄⋊C₄	—	5	4	no	—
1135	C₄⋊C₄	—	5	8	no	—
1136	C₄⋊C₄	—	5	8	no	—
1137	C₄⋊C₄	—	5	8	no	—
1138	C₄⋊C₄	—	5	4	no	—
1139	C₄⋊C₄	—	5	4	no	—
1140	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1141	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1142	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1143	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1144	C₂²⋊C₄	—	5	4	no	—
1145	C₂²⋊C₄	—	5	8	no	—
1146	C₂²⋊C₄	—	5	8	no	—
1147	C₂²⋊C₄	—	5	8	no	—
1148	C₂²⋊C₄	—	5	8	no	—
1149	C₂²⋊C₄	—	5	8	no	—
1150	C₂²⋊C₄	—	5	8	no	—
1151	C₂²⋊C₄	—	5	4	no	—
1152	C₂²⋊C₄	—	5	8	no	—
1153	C₂²⋊C₄	—	5	4	no	—
1154	C₂²⋊C₄	—	5	8	no	—
1155	C₂²⋊C₄	—	5	4	no	—
1156	C₂²⋊C₄	—	5	4	no	—
1157	C₂²⋊C₄	—	5	8	no	—
1158	C₂²⋊C₄	—	5	8	no	—
1159	C₂²⋊C₄	—	5	8	no	—
1160	C₂²⋊C₄	—	5	8	no	—
1161	C₂²⋊C₄	—	5	8	no	—
1162	C₂²⋊C₄	—	5	8	no	—
1163	C₂²⋊C₄	—	5	8	no	—
1164	C₂²⋊C₄	—	5	4	no	—
1165	C₂²⋊C₄	—	5	8	no	—
1166	C₂²⋊C₄	—	5	4	no	—
1167	C₂²⋊C₄	—	5	4	no	—
1168	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1169	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1170	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1171	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1172	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1173	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1174	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1175	C₄²	—	5	4	no	—
1176	C₄²	—	5	8	no	—
1177	C₄²	—	5	4	no	—
1178	C₄²	—	5	8	no	—
1179	C₄²	—	5	4	no	—
1180	C₄²	—	5	8	no	—
1181	C₄²	—	5	8	no	—
1182	C₄²	—	5	4	no	—
1183	C₄²	C₂³×D₅	1	4	yes	—
1184	C₄²	C₂³×D₅	1	8	yes	—
1185	C₄²	C₂³×D₅	1	4	yes	—
1186	C₂×C₅	—	2	8	no	—
1187	C₂×C₅	—	4	4	no	—
1188	C₂×C₅	—	4	2	no	—
1189	C₂×C₅	#3514	1	4	yes	complemented
1190	C₂×C₅	C₂³×#41	1	1	yes	characteristic
1191	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₂×C₅	C₂×#585	1	1	yes	characteristic
1193	D₅	—	4	2	no	—
1194	D₅	—	4	4	no	—
1195	D₅	—	4	2	no	—
1196	C₂³	—	2	4	no	—
1197	C₂³	—	2	4	no	—
1198	C₂³	—	2	2	no	—
1199	C₂³	—	2	4	no	—
1200	C₂³	—	2	4	no	—
1201	C₂³	—	2	2	no	—
1202	C₂³	—	2	4	no	—
1203	C₂³	—	2	2	no	—
1204	C₂³	—	2	16	no	—
1205	C₂³	—	4	8	no	—
1206	C₂³	—	4	8	no	—
1207	C₂³	—	5	2	no	—
1208	C₂³	—	5	4	no	—
1209	C₂³	—	5	2	no	—
1210	C₂³	—	8	16	no	—
1211	C₂³	—	10	2	no	—
1212	C₂³	—	10	2	no	—
1213	C₂³	—	10	4	no	—
1214	C₂³	—	10	2	no	—
1215	C₂³	—	10	4	no	—
1216	C₂³	—	10	2	no	—
1217	C₂³	—	10	2	no	—
1218	C₂³	—	10	4	no	—
1219	C₂³	—	10	2	no	—
1220	C₂³	—	10	16	no	—
1221	C₂³	—	20	8	no	—
1222	C₂³	—	20	8	no	—
1223	C₂³	—	40	16	no	—
1224	C₂³	C₂×#709	1	8	yes	—
1225	C₂³	C₂⁴×D₅	1	2	yes	—
1226	C₂³	C₂⁴×D₅	1	4	yes	—
1227	C₂³	C₂⁴×D₅	1	4	yes	—
1228	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1229	Q₈	—	10	8	no	—
1230	Q₈	—	10	16	no	—
1231	Q₈	—	10	8	no	—
1232	Q₈	—	20	8	no	—
1233	Q₈	—	20	8	no	—
1234	D₄	—	2	16	no	—
1235	D₄	—	2	8	no	—
1236	D₄	—	10	8	no	—
1237	D₄	—	10	16	no	—
1238	D₄	—	10	16	no	—
1239	D₄	—	10	16	no	—
1240	D₄	—	10	8	no	—
1241	D₄	—	20	8	no	—
1242	D₄	—	20	4	no	—
1243	D₄	—	20	8	no	—
1244	D₄	—	20	8	no	—
1245	D₄	—	20	8	no	—
1246	D₄	—	20	4	no	—
1247	D₄	—	20	8	no	—
1248	D₄	C₂×#709	1	16	yes	complemented
1249	C₂×C₄	—	2	2	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	4	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	8	no	—
1257	C₂×C₄	—	4	8	no	—
1258	C₂×C₄	—	4	8	no	—
1259	C₂×C₄	—	4	8	no	—
1260	C₂×C₄	—	4	8	no	—
1261	C₂×C₄	—	5	4	no	—
1262	C₂×C₄	—	5	2	no	—
1263	C₂×C₄	—	5	2	no	—
1264	C₂×C₄	—	5	4	no	—
1265	C₂×C₄	—	5	2	no	—
1266	C₂×C₄	—	5	2	no	—
1267	C₂×C₄	—	5	4	no	—
1268	C₂×C₄	—	5	2	no	—
1269	C₂×C₄	—	5	2	no	—
1270	C₂×C₄	—	5	4	no	—
1271	C₂×C₄	—	10	8	no	—
1272	C₂×C₄	—	10	16	no	—
1273	C₂×C₄	—	10	2	no	—
1274	C₂×C₄	—	10	2	no	—
1275	C₂×C₄	—	10	4	no	—
1276	C₂×C₄	—	10	16	no	—
1277	C₂×C₄	—	10	4	no	—
1278	C₂×C₄	—	10	4	no	—
1279	C₂×C₄	—	10	2	no	—
1280	C₂×C₄	—	10	2	no	—
1281	C₂×C₄	—	10	2	no	—
1282	C₂×C₄	—	10	8	no	—
1283	C₂×C₄	—	10	8	no	—
1284	C₂×C₄	—	20	8	no	—
1285	C₂×C₄	—	20	8	no	—
1286	C₂×C₄	—	20	4	no	—
1287	C₂×C₄	—	20	8	no	—
1288	C₂×C₄	C₂×#709	1	4	yes	—
1289	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1290	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1291	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1292	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1293	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1294	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1295	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1296	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1297	C₅	C₂×#3514	1	1	yes	characteristic, complemented, Sylow
1298	C₂²	—	2	4	no	—
1299	C₂²	—	2	4	no	—
1300	C₂²	—	2	16	no	—
1301	C₂²	—	2	2	no	—
1302	C₂²	—	2	4	no	—
1303	C₂²	—	2	4	no	—
1304	C₂²	—	2	2	no	—
1305	C₂²	—	2	4	no	—
1306	C₂²	—	2	2	no	—
1307	C₂²	—	4	4	no	—
1308	C₂²	—	4	8	no	—
1309	C₂²	—	8	16	no	—
1310	C₂²	—	10	2	no	—
1311	C₂²	—	10	2	no	—
1312	C₂²	—	10	4	no	—
1313	C₂²	—	10	2	no	—
1314	C₂²	—	10	4	no	—
1315	C₂²	—	10	2	no	—
1316	C₂²	—	10	2	no	—
1317	C₂²	—	10	4	no	—
1318	C₂²	—	10	2	no	—
1319	C₂²	—	20	4	no	—
1320	C₂²	—	20	8	no	—
1321	C₂²	—	20	4	no	—
1322	C₂²	—	40	16	no	—
1323	C₂²	C₂²×#709	1	8	yes	—
1324	C₂²	C₂²×#709	1	2	yes	—
1325	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
1326	C₂²	#66285	1	2	yes	—
1327	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1328	C₄	—	2	2	no	—
1329	C₄	—	2	2	no	—
1330	C₄	—	2	4	no	—
1331	C₄	—	2	2	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	4	no	—
1334	C₄	—	2	2	no	—
1335	C₄	—	5	4	no	—
1336	C₄	—	10	2	no	—
1337	C₄	—	10	2	no	—
1338	C₄	—	10	4	no	—
1339	C₄	—	10	2	no	—
1340	C₄	—	10	2	no	—
1341	C₄	—	10	4	no	—
1342	C₄	—	10	4	no	—
1343	C₄	—	10	2	no	—
1344	C₄	C₂²×#709	1	4	yes	—
1345	C₂	—	2	8	no	—
1346	C₂	—	4	2	no	—
1347	C₂	—	4	4	no	—
1348	C₂	—	20	2	no	—
1349	C₂	—	20	4	no	—
1350	C₂	—	20	2	no	—
1351	C₂	#10617765	1	4	yes	direct product factor
1352	C₂	C₂³×#709	1	1	yes	characteristic
1353	C₂	C₂×#66285	1	1	yes	characteristic
1354	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#518	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#518	D₅
hypocenter	C₅	C₂×#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#518	C₂	semidirect
2. C₂×D₄×C₂²⋊D₅	C₂	semidirect
3. C₂×#66140	C₂	semidirect
4. #10617765	C₂	direct (N × H)
5. C₂×#65890	C₂	semidirect
6. C₂×#65888	C₂	semidirect
7. C₂×#65895	C₂	semidirect
8. C₂×#65894	C₂	semidirect
9. C₂×#65882	C₂	semidirect
10. C₂×#65879	C₂	semidirect
11. C₂×#65893	C₂	semidirect
12. C₂×#65897	C₂	semidirect
13. C₂×D₄×Dic₁₀	C₂	semidirect
14. C₂×#65886	C₂	semidirect
15. C₂×#65872	C₂	semidirect
16. C₂×C₄×#711	C₂	semidirect
17. C₂×#65867	C₂	semidirect
18. C₂×#65866	C₂	semidirect
19. C₂×#65868	C₂	semidirect
20. C₂×#65862	C₂	semidirect
21. C₂×#65824	C₂	semidirect
22. C₂×#65828	C₂	semidirect
23. C₂×#65829	C₂	semidirect
24. C₂²×#4031	C₂	semidirect
29. C₂²×#709	C₂²	semidirect
30. C₂³×Dic₁₀	C₂²	semidirect
31. C₅×#518	C₂²	semidirect
34. C₂×C₄×C₅×D₄	C₂²	semidirect
35. C₂×C₄×C₅×D₄	C₂²	semidirect
36. C₂×C₄×C₅×D₄	C₂²	semidirect
37. C₂×C₄×C₅×D₄	C₂²	semidirect
38. C₂×C₅×#117	C₂²	semidirect
39. C₂×C₅×#117	C₂²	semidirect
40. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
41. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
43. C₂×#4099	C₂²	semidirect
44. C₂²×C₂²⋊Dic₅	C₂²	semidirect
45. #66140	C₂²	semidirect
48. C₂×#4085	C₂²	semidirect
49. D₄×C₂²⋊D₅	C₂²	semidirect
51. C₂×#4084	C₂²	semidirect
53. C₂×#4082	C₂²	semidirect
54. C₂×#4081	C₂²	semidirect
58. C₂×#4076	C₂²	semidirect
59. C₂×#4076	C₂²	semidirect
60. C₂×#4075	C₂²	semidirect
61. C₂×#4075	C₂²	semidirect
63. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
64. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
65. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
67. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
68. C₂²×#685	C₂²	semidirect
69. C₂²×#685	C₂²	semidirect
70. C₂×#4072	C₂²	semidirect
71. C₂×#4070	C₂²	semidirect
72. C₂×#4070	C₂²	semidirect
73. C₂×#4070	C₂²	semidirect
74. C₂²×C₄×Dic₅	C₂²	semidirect
75. #65897	C₂²	semidirect
76. #65895	C₂²	semidirect
77. #65894	C₂²	semidirect
78. #65893	C₂²	semidirect
79. #65890	C₂²	semidirect
80. #65888	C₂²	semidirect
81. #65886	C₂²	semidirect
82. #65882	C₂²	semidirect
83. #65879	C₂²	semidirect
84. #65872	C₂²	semidirect
85. D₄×Dic₁₀	C₂²	semidirect
86. C₄×#711	C₂²	semidirect
87. #65868	C₂²	semidirect
88. #65867	C₂²	semidirect
89. #65866	C₂²	semidirect
90. #65862	C₂²	semidirect
91. C₂×#4044	C₂²	semidirect
92. C₂×#4044	C₂²	semidirect
93. C₂×#4043	C₂²	semidirect
94. C₂×#4042	C₂²	semidirect
95. C₂×#4042	C₂²	semidirect
96. C₂×#4041	C₂²	semidirect
97. C₂×#4040	C₂²	semidirect
98. C₂×#4039	C₂²	semidirect
99. C₂×#4038	C₂²	semidirect
100. C₂×#4038	C₂²	semidirect
101. C₂×#4035	C₂²	semidirect
102. C₂×#4034	C₂²	semidirect
103. C₂×#4034	C₂²	semidirect
104. C₂×#4033	C₂²	semidirect
105. #65829	C₂²	semidirect
106. #65828	C₂²	semidirect
107. C₂×#4032	C₂²	semidirect
110. C₂×#4031	C₂²	semidirect
111. C₂×#4031	C₂²	semidirect
112. C₂×#4031	C₂²	semidirect
113. C₂×#4031	C₂²	semidirect
114. C₂×#4031	C₂²	semidirect
115. C₂×#4031	C₂²	semidirect
116. C₂×#4031	C₂²	semidirect
117. C₂×#4031	C₂²	semidirect
118. #65824	C₂²	semidirect
120. C₂×#4030	C₂²	semidirect
121. C₂×#4030	C₂²	semidirect
122. C₂×#4029	C₂²	semidirect
123. C₂×#4029	C₂²	semidirect
124. C₂×#4029	C₂²	semidirect
125. C₂×#4028	C₂²	semidirect
126. C₂×#4027	C₂²	semidirect
127. C₂×#4027	C₂²	semidirect
128. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
129. C₂×#4025	C₂²	semidirect
130. C₂×#4025	C₂²	semidirect
131. C₂×#4025	C₂²	semidirect
132. C₂×#4024	C₂²	semidirect
133. C₂×#4024	C₂²	semidirect
134. C₂×#4023	C₂²	semidirect
135. C₂×#4022	C₂²	semidirect
136. C₂×#4021	C₂²	semidirect
137. C₂×#4021	C₂²	semidirect
138. C₂×C₄×D₂₀	C₂²	semidirect
139. C₂×C₄×D₂₀	C₂²	semidirect
140. C₂×#4018	C₂²	semidirect
141. C₂×#4018	C₂²	semidirect
142. C₂×C₄²×D₅	C₂²	semidirect
143. C₂×#4015	C₂²	semidirect
144. C₂×C₄×Dic₁₀	C₂²	semidirect
145. C₂×C₄×Dic₁₀	C₂²	semidirect
146. C₂×C₄×Dic₁₀	C₂²	semidirect
179. C₂×#709	C₂³	semidirect
195. C₂²×Dic₁₀	C₂³	semidirect
198. C₄×C₅×D₄	C₂³	semidirect
199. C₄×C₅×D₄	C₂³	semidirect
200. C₄×C₅×D₄	C₂³	semidirect
201. C₄×C₅×D₄	C₂³	semidirect
202. C₅×#117	C₂³	semidirect
203. C₅×#117	C₂³	semidirect
215. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
216. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
221. #4099	C₂³	semidirect
231. C₂×C₂²⋊Dic₅	C₂³	semidirect
234. #4085	C₂³	semidirect
236. #4084	C₂³	semidirect
238. #4082	C₂³	semidirect
239. #4081	C₂³	semidirect
243. #4076	C₂³	semidirect
244. #4076	C₂³	semidirect
245. #4075	C₂³	semidirect
246. #4075	C₂³	semidirect
248. C₄×C₂²⋊D₅	C₂³	semidirect
249. C₄×C₂²⋊D₅	C₂³	semidirect
250. C₄×C₂²⋊D₅	C₂³	semidirect
251. C₄×C₂²⋊D₅	C₂³	semidirect
252. C₄×C₂²⋊D₅	C₂³	semidirect
268. C₂×#685	C₂³	semidirect
269. C₂×#685	C₂³	semidirect
270. #4072	C₂³	semidirect
277. #4070	C₂³	semidirect
278. #4070	C₂³	semidirect
279. #4070	C₂³	semidirect
299. C₂×C₄×Dic₅	C₂³	semidirect
300. #4044	C₂³	semidirect
301. #4044	C₂³	semidirect
302. #4043	C₂³	semidirect
303. #4042	C₂³	semidirect
304. #4042	C₂³	semidirect
305. #4041	C₂³	semidirect
306. #4040	C₂³	semidirect
307. #4039	C₂³	semidirect
308. #4038	C₂³	semidirect
309. #4038	C₂³	semidirect
310. #4035	C₂³	semidirect
311. #4034	C₂³	semidirect
312. #4034	C₂³	semidirect
313. #4033	C₂³	semidirect
314. #4032	C₂³	semidirect
317. #4031	C₂³	semidirect
318. #4031	C₂³	semidirect
319. #4031	C₂³	semidirect
320. #4031	C₂³	semidirect
321. #4031	C₂³	semidirect
322. #4031	C₂³	semidirect
323. #4031	C₂³	semidirect
325. #4030	C₂³	semidirect
326. #4030	C₂³	semidirect
327. #4029	C₂³	semidirect
328. #4029	C₂³	semidirect
329. #4029	C₂³	semidirect
330. #4028	C₂³	semidirect
331. #4027	C₂³	semidirect
332. #4027	C₂³	semidirect
333. D₅×C₂²⋊C₄	C₂³	semidirect
334. #4025	C₂³	semidirect
335. #4025	C₂³	semidirect
336. #4025	C₂³	semidirect
337. #4024	C₂³	semidirect
338. #4024	C₂³	semidirect
339. #4023	C₂³	semidirect
340. #4022	C₂³	semidirect
341. #4021	C₂³	semidirect
342. #4021	C₂³	semidirect
343. C₄×D₂₀	C₂³	semidirect
344. C₄×D₂₀	C₂³	semidirect
345. #4018	C₂³	semidirect
346. #4018	C₂³	semidirect
347. C₄²×D₅	C₂³	semidirect
348. #4015	C₂³	semidirect
349. C₄×Dic₁₀	C₂³	semidirect
350. C₄×Dic₁₀	C₂³	semidirect
351. C₄×Dic₁₀	C₂³	semidirect
374. C₂×#518	D₅	semidirect
393. C₂×C₅×D₄	#41	semidirect
625. #518	C₂×D₅	semidirect
646. C₂×C₄×D₄	C₂×D₅	semidirect
647. C₂×C₄×D₄	C₂×D₅	semidirect
648. C₂×C₄×D₄	C₂×D₅	semidirect
649. C₂×C₄×D₄	C₂×D₅	semidirect
656. C₂×#117	C₂×D₅	semidirect
657. C₂×#117	C₂×D₅	semidirect
662. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
663. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
701. C₅×D₄	C₂×#41	semidirect
888. C₄×D₄	C₂²×D₅	semidirect
889. C₄×D₄	C₂²×D₅	semidirect
890. C₄×D₄	C₂²×D₅	semidirect
891. C₄×D₄	C₂²×D₅	semidirect
898. #117	C₂²×D₅	semidirect
899. #117	C₂²×D₅	semidirect
956. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
957. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
1074. C₂×D₄	#709	semidirect
1189. C₂×C₅	#3514	semidirect
1248. D₄	C₂×#709	semidirect
1297. C₅	C₂×#3514	semidirect
1351. C₂	#10617765	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×#518	2
C₂×D₄×C₂²⋊D₅	2
C₂×#66140	2
#10617765	2
C₂×#65890	2
C₂×#65888	2
C₂×#65895	2
C₂×#65894	2
C₂×#65882	2
C₂×#65879	2
C₂×#65893	2
C₂×#65897	2
C₂×D₄×Dic₁₀	2
C₂×#65886	2
C₂×#65872	2
C₂×C₄×#711	2
C₂×#65867	2
C₂×#65866	2
C₂×#65868	2
C₂×#65862	2
C₂×#65824	2
C₂×#65828	2
C₂×#65829	2
C₂²×#4031	2
C₂×#3514	5

Subgroups — C2×#10617765 #13007389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10617765 #13007389