Subgroups — C₂×#10618059 #13007220

Order 1280.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618059	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66039	C₂	1	2	yes	maximal, complemented
4	C₂×#66043	C₂	1	2	yes	maximal, complemented
5	C₂×#66029	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66028	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#66010	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65987	C₂	1	2	yes	maximal, complemented
10	C₂×#65999	C₂	1	2	yes	maximal, complemented
11	C₂×D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65961	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#65940	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#65915	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#65910	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#65892	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65888	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#65894	C₂	1	2	yes	maximal, complemented
20	C₂×#65879	C₂	1	2	yes	maximal, complemented
21	C₂×#65864	C₂	1	2	yes	maximal, complemented
22	C₂×#65861	C₂	1	2	yes	maximal, complemented
23	C₂×#65813	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#713	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#711	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄×D₅	C₂²	1	2	yes	—
29	C₂²×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
30	C₂³×D₂₀	C₂²	1	1	yes	characteristic
31	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic
32	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
33	C₅×#529	C₂²	1	16	yes	complemented
34	C₂×C₅×#126	C₂²	1	2	yes	complemented
35	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#123	C₂²	1	2	yes	complemented
38	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
42	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×#117	C₂²	1	2	yes	complemented
44	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
45	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
46	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
47	C₂×#4085	C₂²	1	2	yes	—
48	C₂×#4084	C₂²	1	1	yes	characteristic, complemented
49	C₂×#4084	C₂²	1	1	yes	characteristic, complemented
50	C₂×#4083	C₂²	1	2	yes	complemented
51	C₂×D₄×Dic₅	C₂²	1	2	yes	complemented
52	C₂×#4076	C₂²	1	1	yes	characteristic
53	C₂×#4076	C₂²	1	2	yes	complemented
54	C₂×#4075	C₂²	1	2	yes	complemented
55	C₂×#4075	C₂²	1	2	yes	complemented
56	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
57	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
58	C₂²×#685	C₂²	1	1	yes	characteristic
59	C₂²×#685	C₂²	1	2	yes	complemented
60	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
62	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
63	#66043	C₂²	1	32	yes	complemented
64	#66039	C₂²	1	32	yes	complemented
65	#66029	C₂²	1	16	yes	complemented
66	#66028	C₂²	1	16	yes	complemented
67	#66011	C₂²	1	16	yes	complemented
68	#66010	C₂²	1	16	yes	complemented
69	#65999	C₂²	1	32	yes	complemented
70	#65987	C₂²	1	32	yes	complemented
71	#65961	C₂²	1	16	yes	complemented
72	D₅×C₂²⋊Q₈	C₂²	1	16	yes	complemented
73	#65940	C₂²	1	16	yes	complemented
74	D₅×#121	C₂²	1	16	yes	complemented
75	#65915	C₂²	1	16	yes	complemented
76	#65910	C₂²	1	16	yes	complemented
77	#65894	C₂²	1	32	yes	complemented
78	#65892	C₂²	1	16	yes	complemented
79	#65888	C₂²	1	16	yes	complemented
80	#65879	C₂²	1	32	yes	complemented
81	#65864	C₂²	1	32	yes	complemented
82	#65861	C₂²	1	32	yes	complemented
83	C₂×#4044	C₂²	1	2	yes	complemented
84	C₂×#4044	C₂²	1	2	yes	complemented
85	C₂×#4043	C₂²	1	1	yes	characteristic, complemented
86	C₂×#4043	C₂²	1	2	yes	complemented
87	C₂×#4043	C₂²	1	1	yes	characteristic, complemented
88	C₂×#4042	C₂²	1	2	yes	complemented
89	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
90	C₂×#4041	C₂²	1	2	yes	complemented
91	C₂×#4041	C₂²	1	2	yes	complemented
92	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
93	C₂×#4040	C₂²	1	2	yes	—
94	C₂×#4040	C₂²	1	2	yes	—
95	C₂×#4040	C₂²	1	2	yes	complemented
96	C₂×#4040	C₂²	1	2	yes	complemented
97	C₂×#4039	C₂²	1	2	yes	complemented
98	C₂×#4039	C₂²	1	2	yes	complemented
99	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
100	C₂×#4038	C₂²	1	2	yes	complemented
101	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
102	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
103	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₂×#4036	C₂²	1	2	yes	complemented
106	C₂×#4035	C₂²	1	2	yes	complemented
107	C₂×#4032	C₂²	1	2	yes	complemented
108	C₂×#4031	C₂²	1	2	yes	complemented
109	C₂×#4030	C₂²	1	2	yes	complemented
110	C₂×#4030	C₂²	1	2	yes	complemented
111	C₂×#4030	C₂²	1	2	yes	complemented
112	C₂×#4030	C₂²	1	2	yes	complemented
113	C₂×#4029	C₂²	1	2	yes	complemented
114	C₂×#4029	C₂²	1	2	yes	complemented
115	C₂×#4028	C₂²	1	2	yes	—
116	C₂×#4028	C₂²	1	2	yes	—
117	C₂×#4028	C₂²	1	2	yes	complemented
118	C₂×#4027	C₂²	1	2	yes	complemented
119	C₂×#4027	C₂²	1	2	yes	complemented
120	C₂×#4027	C₂²	1	2	yes	complemented
121	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₂×#4025	C₂²	1	2	yes	complemented
125	C₂×#4024	C₂²	1	2	yes	complemented
126	C₂×#4024	C₂²	1	2	yes	complemented
127	#65813	C₂²	1	16	yes	complemented
128	C₂×#4022	C₂²	1	2	yes	complemented
129	C₂×#4022	C₂²	1	2	yes	complemented
130	C₂×#4021	C₂²	1	2	yes	complemented
131	C₂×#4021	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
134	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
135	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
136	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₄×D₂₀	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×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
141	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₄×D₂₀	C₂²	1	16	yes	complemented
143	C₂×#4018	C₂²	1	2	yes	complemented
144	C₂×#4018	C₂²	1	2	yes	complemented
145	C₂×#4016	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
147	C₂×#3505	—	5	1	no	maximal, Sylow
148	C₂⁴×D₅	C₂³	1	2	yes	—
149	C₂⁴×D₅	C₂³	1	1	yes	characteristic
150	C₂⁴×D₅	C₂³	1	1	yes	characteristic
151	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₅×D₄	C₂³	1	2	yes	—
153	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₅	C₂³	1	2	yes	—
158	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
159	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
161	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
163	C₂³×Dic₅	C₂³	1	1	yes	characteristic
164	C₂³×Dic₅	C₂³	1	2	yes	—
165	C₂³×Dic₅	C₂³	1	1	yes	characteristic
166	C₂×#713	—	4	4	no	—
167	C₂×#713	C₂³	1	8	yes	complemented
168	C₂×Q₈×D₅	—	4	4	no	—
169	C₂×Q₈×D₅	C₂³	1	8	yes	complemented
170	C₂×#711	—	4	4	no	—
171	C₂×#711	C₂³	1	8	yes	complemented
172	C₂×D₄×D₅	—	2	16	no	—
173	C₂×D₄×D₅	—	4	4	no	—
174	C₂×D₄×D₅	C₂³	1	16	yes	—
175	C₂×D₄×D₅	C₂³	1	8	yes	complemented
176	C₂²×D₂₀	—	2	8	no	—
177	C₂²×D₂₀	C₂³	1	1	yes	characteristic
178	C₂²×D₂₀	C₂³	1	1	yes	characteristic
179	C₂²×D₂₀	C₂³	1	1	yes	characteristic
180	C₂²×D₂₀	C₂³	1	1	yes	characteristic
181	C₂²×D₂₀	C₂³	1	8	yes	—
182	C₂²×D₂₀	C₂³	1	1	yes	characteristic
183	C₂²×D₂₀	C₂³	1	2	yes	—
184	C₂²×D₂₀	C₂³	1	2	yes	—
185	C₂²×D₂₀	C₂³	1	2	yes	—
186	C₂²×C₄×D₅	—	4	4	no	—
187	C₂²×C₄×D₅	—	4	4	no	—
188	C₂²×C₄×D₅	C₂³	1	2	yes	—
189	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₅	C₂³	1	2	yes	—
194	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅	C₂³	1	8	yes	—
199	C₂²×C₄×D₅	C₂³	1	2	yes	—
200	C₂²×C₄×D₅	C₂³	1	2	yes	—
201	C₂²×C₄×D₅	C₂³	1	2	yes	—
202	C₂²×C₄×D₅	C₂³	1	8	yes	complemented
203	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
204	C₂²×Dic₁₀	C₂³	1	2	yes	—
205	C₅×#126	C₂³	1	16	yes	complemented
206	C₅×#125	C₂³	1	8	yes	complemented
207	C₅×#124	C₂³	1	8	yes	complemented
208	C₅×#123	C₂³	1	16	yes	complemented
209	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
210	C₅×#121	C₂³	1	8	yes	—
211	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
212	C₄×C₅×D₄	C₂³	1	16	yes	complemented
213	C₄×C₅×D₄	C₂³	1	8	yes	complemented
214	C₅×#117	C₂³	1	16	yes	complemented
215	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅	C₂³	1	2	yes	—
230	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
232	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
233	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
234	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
235	#4092	C₂³	1	8	yes	complemented
236	#4092	C₂³	1	8	yes	complemented
237	#4085	C₂³	1	16	yes	—
238	#4084	C₂³	1	8	yes	complemented
239	#4084	C₂³	1	8	yes	complemented
240	#4083	C₂³	1	16	yes	complemented
241	D₄×Dic₅	C₂³	1	16	yes	complemented
242	#4076	C₂³	1	8	yes	—
243	#4076	C₂³	1	16	yes	complemented
244	#4075	C₂³	1	16	yes	complemented
245	#4075	C₂³	1	16	yes	complemented
246	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
247	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
248	C₂×#685	C₂³	1	1	yes	characteristic
249	C₂×#685	C₂³	1	2	yes	—
250	C₂×#685	C₂³	1	2	yes	—
251	C₂×#685	C₂³	1	2	yes	—
252	C₂×#685	C₂³	1	1	yes	characteristic
253	C₂×#685	C₂³	1	1	yes	characteristic
254	C₂×#685	C₂³	1	1	yes	characteristic
255	C₂×#685	C₂³	1	1	yes	characteristic
256	C₂×#685	C₂³	1	1	yes	characteristic
257	C₂×#685	C₂³	1	1	yes	characteristic
258	C₂×#685	C₂³	1	1	yes	characteristic
259	C₂×#685	C₂³	1	8	yes	—
260	C₂×#685	C₂³	1	2	yes	—
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	2	yes	—
266	C₂×#685	C₂³	1	2	yes	—
267	C₂×#685	C₂³	1	2	yes	—
268	C₂×#685	C₂³	1	2	yes	—
269	C₂×#685	C₂³	1	8	yes	complemented
270	C₂×#685	C₂³	1	16	yes	complemented
271	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
278	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
279	C₂×C₄⋊Dic₅	C₂³	1	8	yes	complemented
280	#4070	C₂³	1	8	yes	complemented
281	C₂×#683	C₂³	1	2	yes	—
282	C₂×#683	C₂³	1	2	yes	—
283	C₂×#683	C₂³	1	2	yes	—
284	C₂×#683	C₂³	1	2	yes	—
285	C₂×#683	C₂³	1	2	yes	—
286	C₂×#683	C₂³	1	2	yes	—
287	C₂×#683	C₂³	1	2	yes	—
288	C₂×#683	C₂³	1	2	yes	—
289	C₂×C₄×Dic₅	C₂³	1	2	yes	—
290	C₂×C₄×Dic₅	C₂³	1	2	yes	—
291	C₂×C₄×Dic₅	C₂³	1	2	yes	—
292	#4044	C₂³	1	16	yes	complemented
293	#4044	C₂³	1	16	yes	complemented
294	#4043	C₂³	1	8	yes	complemented
295	#4043	C₂³	1	8	yes	complemented
296	#4043	C₂³	1	16	yes	complemented
297	#4042	C₂³	1	16	yes	complemented
298	#4041	C₂³	1	16	yes	complemented
299	#4041	C₂³	1	8	yes	complemented
300	#4041	C₂³	1	8	yes	complemented
301	#4041	C₂³	1	16	yes	complemented
302	#4040	C₂³	1	16	yes	—
303	#4040	C₂³	1	16	yes	—
304	#4040	C₂³	1	16	yes	complemented
305	#4040	C₂³	1	16	yes	complemented
306	#4039	C₂³	1	16	yes	complemented
307	#4039	C₂³	1	16	yes	complemented
308	#4038	C₂³	1	16	yes	complemented
309	#4038	C₂³	1	8	yes	complemented
310	#4038	C₂³	1	8	yes	complemented
311	D₅×C₄⋊C₄	C₂³	1	16	yes	complemented
312	D₅×C₄⋊C₄	C₂³	1	8	yes	complemented
313	D₅×C₄⋊C₄	C₂³	1	8	yes	complemented
314	#4036	C₂³	1	16	yes	complemented
315	#4035	C₂³	1	16	yes	complemented
316	#4032	C₂³	1	16	yes	complemented
317	#4031	C₂³	1	16	yes	complemented
318	#4030	C₂³	1	16	yes	complemented
319	#4030	C₂³	1	16	yes	complemented
320	#4030	C₂³	1	16	yes	complemented
321	#4030	C₂³	1	16	yes	complemented
322	#4029	C₂³	1	16	yes	complemented
323	#4029	C₂³	1	16	yes	complemented
324	#4028	C₂³	1	16	yes	—
325	#4028	C₂³	1	16	yes	—
326	#4028	C₂³	1	16	yes	complemented
327	#4027	C₂³	1	16	yes	complemented
328	#4027	C₂³	1	16	yes	complemented
329	#4027	C₂³	1	16	yes	complemented
330	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
331	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
332	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
333	#4025	C₂³	1	16	yes	complemented
334	#4024	C₂³	1	16	yes	complemented
335	#4024	C₂³	1	16	yes	complemented
336	#4022	C₂³	1	16	yes	complemented
337	#4022	C₂³	1	16	yes	complemented
338	#4021	C₂³	1	8	yes	complemented
339	#4021	C₂³	1	16	yes	complemented
340	C₄×D₂₀	C₂³	1	8	yes	—
341	C₄×D₂₀	C₂³	1	8	yes	—
342	C₄×D₂₀	C₂³	1	8	yes	—
343	C₄×D₂₀	C₂³	1	8	yes	—
344	C₄×D₂₀	C₂³	1	8	yes	complemented
345	C₄×D₂₀	C₂³	1	8	yes	complemented
346	C₄×D₂₀	C₂³	1	8	yes	complemented
347	C₄×D₂₀	C₂³	1	8	yes	complemented
348	C₄×D₂₀	C₂³	1	8	yes	complemented
349	C₄×D₂₀	C₂³	1	16	yes	complemented
350	#4018	C₂³	1	16	yes	complemented
351	#4018	C₂³	1	16	yes	complemented
352	#4016	C₂³	1	8	yes	complemented
353	C₄×Dic₁₀	C₂³	1	8	yes	complemented
354	#3505	—	5	32	no	—
355	C₂×#553	—	5	2	no	—
356	C₂×#553	—	5	1	no	—
357	C₂×#553	—	5	1	no	—
358	C₂×#553	—	5	2	no	—
359	C₂×#552	—	5	1	no	—
360	C₂×#552	—	5	1	no	—
361	C₂×#551	—	5	2	no	—
362	C₂×#551	—	5	2	no	—
363	C₂×#548	—	5	1	no	—
364	C₂×#548	—	5	1	no	—
365	C₂×#546	—	5	1	no	—
366	C₂×#546	—	5	1	no	—
367	C₂×#539	—	5	2	no	—
368	C₂×#538	—	5	2	no	—
369	C₂×#534	—	5	2	no	—
370	C₂×#529	—	5	1	no	—
371	C₂×#529	D₅	1	1	yes	characteristic, complemented
372	C₂×#525	—	5	1	no	—
373	C₂×#525	—	5	1	no	—
374	C₂²×C₂²⋊Q₈	—	5	1	no	—
375	C₂²×#121	—	5	1	no	—
376	C₂×#518	—	5	2	no	—
377	C₂²×C₄×D₄	—	5	1	no	—
378	C₂⁴×C₅	C₂⁴	1	2	yes	—
379	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
380	C₂³×D₅	—	2	4	no	—
381	C₂³×D₅	—	2	8	no	—
382	C₂³×D₅	—	4	2	no	—
383	C₂³×D₅	—	4	2	no	—
384	C₂³×D₅	—	4	2	no	—
385	C₂³×D₅	—	4	2	no	—
386	C₂³×D₅	—	4	4	no	—
387	C₂³×D₅	—	4	4	no	—
388	C₂³×D₅	#41	1	8	yes	complemented
389	C₂³×D₅	C₂⁴	1	1	yes	characteristic
390	C₂³×D₅	C₂⁴	1	1	yes	characteristic
391	C₂³×D₅	C₂⁴	1	2	yes	—
392	C₂³×D₅	C₂⁴	1	1	yes	characteristic
393	C₂³×D₅	C₂⁴	1	1	yes	characteristic
394	C₂³×D₅	C₂⁴	1	4	yes	—
395	C₂³×D₅	C₂⁴	1	8	yes	—
396	C₂³×D₅	C₂⁴	1	4	yes	—
397	C₂×C₅×Q₈	—	2	4	no	—
398	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
399	C₂×C₅×D₄	—	2	8	no	—
400	C₂×C₅×D₄	—	2	4	no	—
401	C₂×C₅×D₄	C₂⁴	1	8	yes	—
402	C₂×C₅×D₄	C₂⁴	1	4	yes	—
403	C₂²×C₄×C₅	—	2	4	no	—
404	C₂²×C₄×C₅	—	2	4	no	—
405	C₂²×C₄×C₅	—	4	2	no	—
406	C₂²×C₄×C₅	—	4	4	no	—
407	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
414	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
415	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
416	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
418	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
419	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
420	C₂×C₂²⋊D₅	—	2	8	no	—
421	C₂×C₂²⋊D₅	—	2	8	no	—
422	C₂×C₂²⋊D₅	—	4	4	no	—
423	C₂×C₂²⋊D₅	—	4	4	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	8	yes	—
429	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
430	C₂²×Dic₅	—	4	2	no	—
431	C₂²×Dic₅	—	4	2	no	—
432	C₂²×Dic₅	—	4	4	no	—
433	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
434	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅	C₂⁴	1	2	yes	—
436	C₂²×Dic₅	C₂⁴	1	2	yes	—
437	C₂²×Dic₅	C₂⁴	1	2	yes	—
438	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
440	C₂²×Dic₅	C₂⁴	1	4	yes	—
441	C₂²×Dic₅	C₂⁴	1	4	yes	—
442	C₂²×Dic₅	C₂⁴	1	8	yes	—
443	#713	—	4	16	no	—
444	Q₈×D₅	—	4	16	no	—
445	#711	—	4	16	no	—
446	D₄×D₅	—	2	64	no	—
447	D₄×D₅	—	4	16	no	—
448	C₂×D₂₀	—	2	4	no	—
449	C₂×D₂₀	—	2	4	no	—
450	C₂×D₂₀	—	2	4	no	—
451	C₂×D₂₀	—	2	4	no	—
452	C₂×D₂₀	—	2	8	no	—
453	C₂×D₂₀	—	2	32	no	—
454	C₂×D₂₀	—	2	4	no	—
455	C₂×D₂₀	—	4	4	no	—
456	C₂×D₂₀	—	4	4	no	—
457	C₂×D₂₀	C₂⁴	1	4	yes	—
458	C₂×D₂₀	C₂⁴	1	4	yes	—
459	C₂×D₂₀	C₂⁴	1	4	yes	—
460	C₂×D₂₀	C₂⁴	1	4	yes	—
461	C₂×D₂₀	C₂⁴	1	8	yes	—
462	C₂×D₂₀	C₂⁴	1	4	yes	—
463	C₂×D₂₀	C₂⁴	1	8	yes	—
464	C₂×D₂₀	C₂⁴	1	8	yes	—
465	C₂×C₄×D₅	—	2	8	no	—
466	C₂×C₄×D₅	—	2	4	no	—
467	C₂×C₄×D₅	—	2	4	no	—
468	C₂×C₄×D₅	—	2	4	no	—
469	C₂×C₄×D₅	—	2	4	no	—
470	C₂×C₄×D₅	—	4	16	no	—
471	C₂×C₄×D₅	—	4	16	no	—
472	C₂×C₄×D₅	—	4	2	no	—
473	C₂×C₄×D₅	—	4	2	no	—
474	C₂×C₄×D₅	—	4	2	no	—
475	C₂×C₄×D₅	—	4	2	no	—
476	C₂×C₄×D₅	—	4	4	no	—
477	C₂×C₄×D₅	—	4	4	no	—
478	C₂×C₄×D₅	—	4	4	no	—
479	C₂×C₄×D₅	—	4	4	no	—
480	C₂×C₄×D₅	C₂⁴	1	4	yes	—
481	C₂×C₄×D₅	C₂⁴	1	4	yes	—
482	C₂×C₄×D₅	C₂⁴	1	4	yes	—
483	C₂×C₄×D₅	C₂⁴	1	4	yes	—
484	C₂×C₄×D₅	C₂⁴	1	8	yes	—
485	C₂×C₄×D₅	C₂⁴	1	4	yes	—
486	C₂×C₄×D₅	C₂⁴	1	4	yes	—
487	C₂×C₄×D₅	C₂⁴	1	4	yes	—
488	C₂×C₄×D₅	C₂⁴	1	4	yes	—
489	C₂×C₄×D₅	C₂⁴	1	8	yes	—
490	C₂×C₄×D₅	C₂⁴	1	8	yes	—
491	C₂×C₄×D₅	C₂⁴	1	8	yes	—
492	C₂×C₄×D₅	C₂⁴	1	8	yes	—
493	C₂×Dic₁₀	—	2	4	no	—
494	C₂×Dic₁₀	—	4	4	no	—
495	C₂×Dic₁₀	C₂⁴	1	4	yes	—
496	C₂×Dic₁₀	C₂⁴	1	8	yes	—
497	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
498	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
499	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
500	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
501	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
502	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
503	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
504	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
505	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
506	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
507	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
508	C₄²×C₅	C₂⁴	1	4	yes	—
509	C₄²×C₅	C₂⁴	1	4	yes	—
510	C₄²×C₅	C₂⁴	1	4	yes	—
511	C₄²×C₅	C₂⁴	1	4	yes	—
512	C₄²×C₅	C₂⁴	1	8	yes	—
513	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
514	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
515	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
516	#685	C₂⁴	1	4	yes	—
517	#685	C₂⁴	1	8	yes	—
518	#685	C₂⁴	1	8	yes	—
519	#685	C₂⁴	1	8	yes	—
520	#685	C₂⁴	1	4	yes	—
521	#685	C₂⁴	1	4	yes	—
522	#685	C₂⁴	1	4	yes	—
523	#685	C₂⁴	1	4	yes	—
524	#685	C₂⁴	1	4	yes	—
525	#685	C₂⁴	1	4	yes	—
526	#685	C₂⁴	1	4	yes	—
527	#685	C₂⁴	1	8	yes	—
528	#685	C₂⁴	1	8	yes	—
529	#685	C₂⁴	1	8	yes	—
530	#685	C₂⁴	1	8	yes	—
531	#685	C₂⁴	1	8	yes	—
532	#685	C₂⁴	1	8	yes	—
533	#685	C₂⁴	1	8	yes	—
534	#685	C₂⁴	1	8	yes	—
535	#685	C₂⁴	1	8	yes	—
536	C₄⋊Dic₅	C₂⁴	1	4	yes	—
537	C₄⋊Dic₅	C₂⁴	1	4	yes	—
538	C₄⋊Dic₅	C₂⁴	1	4	yes	—
539	C₄⋊Dic₅	C₂⁴	1	4	yes	—
540	C₄⋊Dic₅	C₂⁴	1	4	yes	—
541	C₄⋊Dic₅	C₂⁴	1	4	yes	—
542	C₄⋊Dic₅	C₂⁴	1	8	yes	—
543	C₄⋊Dic₅	C₂⁴	1	8	yes	—
544	#683	C₂⁴	1	8	yes	—
545	#683	C₂⁴	1	8	yes	—
546	#683	C₂⁴	1	8	yes	—
547	#683	C₂⁴	1	8	yes	—
548	#683	C₂⁴	1	8	yes	—
549	#683	C₂⁴	1	8	yes	—
550	#683	C₂⁴	1	8	yes	—
551	#683	C₂⁴	1	8	yes	—
552	C₄×Dic₅	C₂⁴	1	8	yes	—
553	C₄×Dic₅	C₂⁴	1	8	yes	—
554	C₄×Dic₅	C₂⁴	1	8	yes	—
555	C₂²×#41	—	5	1	no	—
556	C₂²×#41	—	5	1	no	—
557	C₂³×Q₈	—	5	1	no	—
558	C₂³×D₄	—	5	2	no	—
559	C₂³×D₄	—	5	1	no	—
560	C₂³×D₄	—	5	1	no	—
561	C₂⁴×C₄	—	5	1	no	—
562	C₂⁴×C₄	—	5	1	no	—
563	#553	—	5	32	no	—
564	#553	—	5	16	no	—
565	#553	—	5	16	no	—
566	#553	—	5	32	no	—
567	#552	—	5	16	no	—
568	#552	—	5	16	no	—
569	#551	—	5	32	no	—
570	#551	—	5	32	no	—
571	#548	—	5	16	no	—
572	#548	—	5	16	no	—
573	#546	—	5	16	no	—
574	#546	—	5	16	no	—
575	#539	—	5	32	no	—
576	#538	—	5	32	no	—
577	#534	—	5	32	no	—
578	#529	—	5	16	no	—
579	#529	C₂×D₅	1	16	yes	complemented
580	C₂×#126	—	5	2	no	—
581	C₂×#126	—	5	2	no	—
582	C₂×#126	—	5	2	no	—
583	C₂×#126	—	5	2	no	—
584	C₂×#126	—	5	2	no	—
585	C₂×#126	C₂×D₅	1	2	yes	complemented
586	C₂×#125	—	5	2	no	—
587	C₂×#125	—	5	2	no	—
588	C₂×#125	—	5	1	no	—
589	C₂×#125	C₂×D₅	1	1	yes	characteristic, complemented
590	C₂×#124	—	5	2	no	—
591	C₂×#124	—	5	1	no	—
592	C₂×#124	—	5	2	no	—
593	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
594	#525	—	5	16	no	—
595	#525	—	5	16	no	—
596	C₂×#123	—	5	2	no	—
597	C₂×#123	—	5	2	no	—
598	C₂×#123	—	5	2	no	—
599	C₂×#123	—	5	2	no	—
600	C₂×#123	—	5	2	no	—
601	C₂×#123	—	5	2	no	—
602	C₂×#123	—	5	2	no	—
603	C₂×#123	—	5	2	no	—
604	C₂×#123	—	5	2	no	—
605	C₂×#123	C₂×D₅	1	2	yes	complemented
606	C₂×C₂²⋊Q₈	—	5	1	no	—
607	C₂×C₂²⋊Q₈	—	5	1	no	—
608	C₂×C₂²⋊Q₈	—	5	1	no	—
609	C₂×C₂²⋊Q₈	—	5	16	no	—
610	C₂×C₂²⋊Q₈	—	5	2	no	—
611	C₂×C₂²⋊Q₈	—	5	1	no	—
612	C₂×C₂²⋊Q₈	—	5	1	no	—
613	C₂×C₂²⋊Q₈	—	5	2	no	—
614	C₂×C₂²⋊Q₈	—	5	2	no	—
615	C₂×C₂²⋊Q₈	—	5	2	no	—
616	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
617	C₂×#121	—	5	1	no	—
618	C₂×#121	—	5	1	no	—
619	C₂×#121	—	5	2	no	—
620	C₂×#121	—	5	1	no	—
621	C₂×#121	—	5	2	no	—
622	C₂×#121	—	5	16	no	—
623	C₂×#121	—	5	1	no	—
624	C₂×#121	—	5	1	no	—
625	C₂×#121	—	5	2	no	—
626	C₂×#121	—	5	2	no	—
627	C₂×#121	—	5	2	no	—
628	C₂×#121	—	5	2	no	—
629	C₂×#121	—	5	2	no	—
630	C₂×#121	—	5	2	no	—
631	C₂×#121	C₂×D₅	1	1	yes	characteristic
632	C₂×#120	—	5	2	no	—
633	C₂×#120	—	5	2	no	—
634	C₂×#120	—	5	2	no	—
635	C₂×#120	—	5	2	no	—
636	#518	—	5	32	no	—
637	C₂×C₄×Q₈	—	5	1	no	—
638	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
639	C₂×C₄×D₄	—	5	2	no	—
640	C₂×C₄×D₄	—	5	2	no	—
641	C₂×C₄×D₄	—	5	2	no	—
642	C₂×C₄×D₄	—	5	2	no	—
643	C₂×C₄×D₄	—	5	2	no	—
644	C₂×C₄×D₄	—	5	2	no	—
645	C₂×C₄×D₄	—	5	2	no	—
646	C₂×C₄×D₄	—	5	2	no	—
647	C₂×C₄×D₄	—	5	1	no	—
648	C₂×C₄×D₄	—	5	1	no	—
649	C₂×C₄×D₄	—	5	1	no	—
650	C₂×C₄×D₄	—	5	1	no	—
651	C₂×C₄×D₄	—	5	1	no	—
652	C₂×C₄×D₄	—	5	1	no	—
653	C₂×C₄×D₄	—	5	1	no	—
654	C₂×C₄×D₄	—	5	1	no	—
655	C₂×C₄×D₄	—	5	2	no	—
656	C₂×C₄×D₄	—	5	1	no	—
657	C₂×C₄×D₄	—	5	16	no	—
658	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
659	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
660	C₂×#117	—	5	2	no	—
661	C₂×#117	—	5	1	no	—
662	C₂×#117	—	5	1	no	—
663	C₂×#117	—	5	2	no	—
664	C₂×#117	—	5	2	no	—
665	C₂×#117	C₂×D₅	1	2	yes	complemented
666	C₂²×C₄⋊C₄	—	5	1	no	—
667	C₂²×C₄⋊C₄	—	5	1	no	—
668	C₂²×C₄⋊C₄	—	5	1	no	—
669	C₂²×C₄⋊C₄	—	5	2	no	—
670	C₂²×C₂²⋊C₄	—	5	1	no	—
671	C₂²×C₂²⋊C₄	—	5	1	no	—
672	C₂²×C₂²⋊C₄	—	5	2	no	—
673	C₂²×C₂²⋊C₄	—	5	2	no	—
674	C₂²×C₂²⋊C₄	—	5	2	no	—
675	C₂²×C₂²⋊C₄	—	5	2	no	—
676	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
677	C₂³×C₅	—	2	2	no	—
678	C₂³×C₅	—	2	2	no	—
679	C₂³×C₅	—	2	4	no	—
680	C₂³×C₅	—	2	4	no	—
681	C₂³×C₅	—	2	4	no	—
682	C₂³×C₅	C₂×#41	1	4	yes	—
683	C₂³×C₅	C₂⁵	1	4	yes	—
684	C₂³×C₅	C₂⁵	1	2	yes	—
685	C₂³×C₅	C₂⁵	1	1	yes	characteristic
686	C₂²×D₅	—	2	2	no	—
687	C₂²×D₅	—	2	2	no	—
688	C₂²×D₅	—	2	2	no	—
689	C₂²×D₅	—	2	2	no	—
690	C₂²×D₅	—	2	8	no	—
691	C₂²×D₅	—	2	2	no	—
692	C₂²×D₅	—	2	2	no	—
693	C₂²×D₅	—	2	4	no	—
694	C₂²×D₅	—	2	2	no	—
695	C₂²×D₅	—	2	2	no	—
696	C₂²×D₅	—	2	4	no	—
697	C₂²×D₅	—	2	4	no	—
698	C₂²×D₅	—	2	2	no	—
699	C₂²×D₅	—	2	2	no	—
700	C₂²×D₅	—	2	16	no	—
701	C₂²×D₅	—	4	4	no	—
702	C₂²×D₅	—	4	4	no	—
703	C₂²×D₅	—	4	16	no	—
704	C₂²×D₅	—	4	4	no	—
705	C₂²×D₅	—	4	4	no	—
706	C₂²×D₅	—	4	8	no	—
707	C₂²×D₅	—	4	8	no	—
708	C₂²×D₅	—	4	16	no	—
709	C₂²×D₅	—	8	16	no	—
710	C₂²×D₅	C₂×#41	1	4	yes	—
711	C₂²×D₅	C₂×#41	1	4	yes	—
712	C₂²×D₅	C₂×#41	1	16	yes	complemented
713	C₂²×D₅	C₂⁵	1	2	yes	—
714	C₂²×D₅	C₂⁵	1	2	yes	—
715	C₂²×D₅	C₂⁵	1	4	yes	—
716	C₂²×D₅	C₂⁵	1	2	yes	—
717	C₂²×D₅	C₂⁵	1	2	yes	—
718	C₅×Q₈	—	2	8	no	—
719	C₅×D₄	—	2	16	no	—
720	C₅×D₄	—	2	8	no	—
721	C₂×C₄×C₅	—	2	4	no	—
722	C₂×C₄×C₅	—	2	8	no	—
723	C₂×C₄×C₅	—	2	2	no	—
724	C₂×C₄×C₅	—	2	2	no	—
725	C₂×C₄×C₅	—	2	4	no	—
726	C₂×C₄×C₅	—	2	2	no	—
727	C₂×C₄×C₅	—	2	2	no	—
728	C₂×C₄×C₅	—	2	4	no	—
729	C₂×C₄×C₅	—	2	2	no	—
730	C₂×C₄×C₅	—	2	8	no	—
731	C₂×C₄×C₅	—	4	4	no	—
732	C₂×C₄×C₅	—	4	8	no	—
733	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
734	C₂×C₄×C₅	C₂⁵	1	2	yes	—
735	C₂×C₄×C₅	C₂⁵	1	4	yes	—
736	C₂×C₄×C₅	C₂⁵	1	4	yes	—
737	C₂×C₄×C₅	C₂⁵	1	2	yes	—
738	C₂×C₄×C₅	C₂⁵	1	2	yes	—
739	C₂×C₄×C₅	C₂⁵	1	2	yes	—
740	C₂×C₄×C₅	C₂⁵	1	2	yes	—
741	C₂×C₄×C₅	C₂⁵	1	4	yes	—
742	C₂×C₄×C₅	C₂⁵	1	2	yes	—
743	C₂²⋊D₅	—	2	16	no	—
744	C₂²⋊D₅	—	2	16	no	—
745	C₂²⋊D₅	—	4	8	no	—
746	C₂²⋊D₅	—	4	8	no	—
747	C₂²⋊D₅	—	4	8	no	—
748	C₂×Dic₅	—	2	4	no	—
749	C₂×Dic₅	—	2	4	no	—
750	C₂×Dic₅	—	2	2	no	—
751	C₂×Dic₅	—	2	2	no	—
752	C₂×Dic₅	—	2	2	no	—
753	C₂×Dic₅	—	2	2	no	—
754	C₂×Dic₅	—	2	4	no	—
755	C₂×Dic₅	—	4	4	no	—
756	C₂×Dic₅	—	4	4	no	—
757	C₂×Dic₅	—	4	8	no	—
758	C₂×Dic₅	C₂⁵	1	4	yes	—
759	C₂×Dic₅	C₂⁵	1	2	yes	—
760	C₂×Dic₅	C₂⁵	1	2	yes	—
761	C₂×Dic₅	C₂⁵	1	4	yes	—
762	C₂×Dic₅	C₂⁵	1	4	yes	—
763	C₂×Dic₅	C₂⁵	1	2	yes	—
764	C₂×Dic₅	C₂⁵	1	2	yes	—
765	D₂₀	—	2	8	no	—
766	D₂₀	—	2	8	no	—
767	D₂₀	—	2	8	no	—
768	D₂₀	—	2	8	no	—
769	D₂₀	—	2	16	no	—
770	D₂₀	—	2	8	no	—
771	D₂₀	—	4	8	no	—
772	D₂₀	—	4	8	no	—
773	C₄×D₅	—	2	16	no	—
774	C₄×D₅	—	2	8	no	—
775	C₄×D₅	—	2	8	no	—
776	C₄×D₅	—	2	8	no	—
777	C₄×D₅	—	2	8	no	—
778	C₄×D₅	—	4	4	no	—
779	C₄×D₅	—	4	4	no	—
780	C₄×D₅	—	4	4	no	—
781	C₄×D₅	—	4	4	no	—
782	C₄×D₅	—	4	8	no	—
783	C₄×D₅	—	4	8	no	—
784	C₄×D₅	—	4	8	no	—
785	C₄×D₅	—	4	8	no	—
786	Dic₁₀	—	2	8	no	—
787	Dic₁₀	—	4	8	no	—
788	C₂⁵	—	5	1	no	—
789	C₂⁵	—	5	2	no	—
790	C₂⁵	—	5	1	no	—
791	C₂×#41	—	5	8	no	—
792	C₂×#41	—	5	8	no	—
793	C₂×#41	—	20	4	no	—
794	C₂×#41	—	20	4	no	—
795	C₂²×Q₈	—	5	8	no	—
796	C₂²×Q₈	—	5	1	no	—
797	C₂²×Q₈	—	5	2	no	—
798	C₂²×Q₈	—	20	4	no	—
799	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
800	C₂²×D₄	—	5	2	no	—
801	C₂²×D₄	—	5	2	no	—
802	C₂²×D₄	—	5	2	no	—
803	C₂²×D₄	—	5	2	no	—
804	C₂²×D₄	—	5	2	no	—
805	C₂²×D₄	—	5	16	no	—
806	C₂²×D₄	—	5	8	no	—
807	C₂²×D₄	—	5	1	no	—
808	C₂²×D₄	—	5	1	no	—
809	C₂²×D₄	—	5	2	no	—
810	C₂²×D₄	—	5	1	no	—
811	C₂²×D₄	—	5	1	no	—
812	C₂²×D₄	—	5	8	no	—
813	C₂²×D₄	—	5	1	no	—
814	C₂²×D₄	—	5	2	no	—
815	C₂²×D₄	—	5	2	no	—
816	C₂²×D₄	—	10	8	no	—
817	C₂²×D₄	—	10	16	no	—
818	C₂²×D₄	—	20	4	no	—
819	C₂²×D₄	C₂²×D₅	1	2	yes	—
820	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
821	C₂³×C₄	—	5	1	no	—
822	C₂³×C₄	—	5	1	no	—
823	C₂³×C₄	—	5	2	no	—
824	C₂³×C₄	—	5	2	no	—
825	C₂³×C₄	—	5	1	no	—
826	C₂³×C₄	—	5	1	no	—
827	C₂³×C₄	—	5	1	no	—
828	C₂³×C₄	—	5	1	no	—
829	C₂³×C₄	—	5	1	no	—
830	C₂³×C₄	—	5	2	no	—
831	C₂³×C₄	—	5	2	no	—
832	C₂³×C₄	—	5	2	no	—
833	C₂³×C₄	—	5	2	no	—
834	C₂³×C₄	—	5	1	no	—
835	C₂³×C₄	—	5	1	no	—
836	C₂³×C₄	—	5	1	no	—
837	C₂³×C₄	—	5	8	no	—
838	C₂³×C₄	—	5	8	no	—
839	C₂³×C₄	—	20	4	no	—
840	C₂³×C₄	—	20	4	no	—
841	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
842	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
843	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
844	C₂³×C₄	C₂²×D₅	1	2	yes	—
845	#126	—	5	16	no	—
846	#126	—	5	16	no	—
847	#126	—	5	16	no	—
848	#126	—	5	16	no	—
849	#126	—	5	16	no	—
850	#126	C₂²×D₅	1	16	yes	complemented
851	#125	—	5	16	no	—
852	#125	—	5	16	no	—
853	#125	—	5	8	no	—
854	#125	C₂²×D₅	1	8	yes	complemented
855	#124	—	5	16	no	—
856	#124	—	5	8	no	—
857	#124	—	5	16	no	—
858	#124	C₂²×D₅	1	8	yes	complemented
859	#123	—	5	16	no	—
860	#123	—	5	16	no	—
861	#123	—	5	16	no	—
862	#123	—	5	16	no	—
863	#123	—	5	16	no	—
864	#123	—	5	16	no	—
865	#123	—	5	16	no	—
866	#123	—	5	16	no	—
867	#123	—	5	16	no	—
868	#123	C₂²×D₅	1	16	yes	complemented
869	C₂²⋊Q₈	—	5	8	no	—
870	C₂²⋊Q₈	—	5	8	no	—
871	C₂²⋊Q₈	—	5	8	no	—
872	C₂²⋊Q₈	—	5	8	no	—
873	C₂²⋊Q₈	—	5	16	no	—
874	C₂²⋊Q₈	—	5	8	no	—
875	C₂²⋊Q₈	—	5	16	no	—
876	C₂²⋊Q₈	—	5	16	no	—
877	C₂²⋊Q₈	—	5	16	no	—
878	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
879	#121	—	5	16	no	—
880	#121	—	5	8	no	—
881	#121	—	5	8	no	—
882	#121	—	5	8	no	—
883	#121	—	5	16	no	—
884	#121	—	5	8	no	—
885	#121	—	5	8	no	—
886	#121	—	5	16	no	—
887	#121	—	5	16	no	—
888	#121	—	5	16	no	—
889	#121	—	5	16	no	—
890	#121	—	5	16	no	—
891	#121	—	5	16	no	—
892	#121	C₂²×D₅	1	8	yes	—
893	#120	—	5	16	no	—
894	#120	—	5	16	no	—
895	#120	—	5	16	no	—
896	#120	—	5	16	no	—
897	C₄×Q₈	—	5	8	no	—
898	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
899	C₄×D₄	—	5	16	no	—
900	C₄×D₄	—	5	16	no	—
901	C₄×D₄	—	5	16	no	—
902	C₄×D₄	—	5	16	no	—
903	C₄×D₄	—	5	16	no	—
904	C₄×D₄	—	5	16	no	—
905	C₄×D₄	—	5	16	no	—
906	C₄×D₄	—	5	16	no	—
907	C₄×D₄	—	5	8	no	—
908	C₄×D₄	—	5	8	no	—
909	C₄×D₄	—	5	8	no	—
910	C₄×D₄	—	5	8	no	—
911	C₄×D₄	—	5	8	no	—
912	C₄×D₄	—	5	8	no	—
913	C₄×D₄	—	5	8	no	—
914	C₄×D₄	—	5	8	no	—
915	C₄×D₄	—	5	16	no	—
916	C₄×D₄	—	5	8	no	—
917	C₄×D₄	C₂²×D₅	1	16	yes	complemented
918	C₄×D₄	C₂²×D₅	1	8	yes	complemented
919	#117	—	5	16	no	—
920	#117	—	5	8	no	—
921	#117	—	5	8	no	—
922	#117	—	5	16	no	—
923	#117	—	5	16	no	—
924	#117	C₂²×D₅	1	16	yes	complemented
925	C₂×C₄⋊C₄	—	5	1	no	—
926	C₂×C₄⋊C₄	—	5	2	no	—
927	C₂×C₄⋊C₄	—	5	1	no	—
928	C₂×C₄⋊C₄	—	5	1	no	—
929	C₂×C₄⋊C₄	—	5	1	no	—
930	C₂×C₄⋊C₄	—	5	1	no	—
931	C₂×C₄⋊C₄	—	5	1	no	—
932	C₂×C₄⋊C₄	—	5	8	no	—
933	C₂×C₄⋊C₄	—	5	2	no	—
934	C₂×C₄⋊C₄	—	5	2	no	—
935	C₂×C₄⋊C₄	—	5	2	no	—
936	C₂×C₄⋊C₄	—	5	2	no	—
937	C₂×C₄⋊C₄	—	5	2	no	—
938	C₂×C₄⋊C₄	—	5	2	no	—
939	C₂×C₄⋊C₄	—	5	2	no	—
940	C₂×C₄⋊C₄	—	5	2	no	—
941	C₂×C₄⋊C₄	—	5	2	no	—
942	C₂×C₄⋊C₄	—	5	8	no	—
943	C₂×C₄⋊C₄	—	5	8	no	—
944	C₂×C₄⋊C₄	—	5	16	no	—
945	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
948	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
949	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
950	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
951	C₂×C₂²⋊C₄	—	5	2	no	—
952	C₂×C₂²⋊C₄	—	5	2	no	—
953	C₂×C₂²⋊C₄	—	5	2	no	—
954	C₂×C₂²⋊C₄	—	5	1	no	—
955	C₂×C₂²⋊C₄	—	5	1	no	—
956	C₂×C₂²⋊C₄	—	5	2	no	—
957	C₂×C₂²⋊C₄	—	5	2	no	—
958	C₂×C₂²⋊C₄	—	5	2	no	—
959	C₂×C₂²⋊C₄	—	5	1	no	—
960	C₂×C₂²⋊C₄	—	5	1	no	—
961	C₂×C₂²⋊C₄	—	5	8	no	—
962	C₂×C₂²⋊C₄	—	5	1	no	—
963	C₂×C₂²⋊C₄	—	5	1	no	—
964	C₂×C₂²⋊C₄	—	5	2	no	—
965	C₂×C₂²⋊C₄	—	5	2	no	—
966	C₂×C₂²⋊C₄	—	5	1	no	—
967	C₂×C₂²⋊C₄	—	5	1	no	—
968	C₂×C₂²⋊C₄	—	5	8	no	—
969	C₂×C₂²⋊C₄	—	5	16	no	—
970	C₂×C₂²⋊C₄	—	5	2	no	—
971	C₂×C₂²⋊C₄	—	5	2	no	—
972	C₂×C₂²⋊C₄	—	5	2	no	—
973	C₂×C₂²⋊C₄	—	5	2	no	—
974	C₂×C₂²⋊C₄	—	5	2	no	—
975	C₂×C₂²⋊C₄	—	5	2	no	—
976	C₂×C₂²⋊C₄	—	5	2	no	—
977	C₂×C₂²⋊C₄	—	5	16	no	—
978	C₂×C₂²⋊C₄	—	5	16	no	—
979	C₂×C₂²⋊C₄	—	5	16	no	—
980	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
981	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
982	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
983	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
984	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
985	C₂×C₄²	—	5	2	no	—
986	C₂×C₄²	—	5	2	no	—
987	C₂×C₄²	—	5	2	no	—
988	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
989	C₂×C₄²	C₂²×D₅	1	2	yes	—
990	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
991	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
992	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
993	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
994	C₂²×C₅	—	2	2	no	—
995	C₂²×C₅	—	2	2	no	—
996	C₂²×C₅	—	2	8	no	—
997	C₂²×C₅	—	2	4	no	—
998	C₂²×C₅	—	2	4	no	—
999	C₂²×C₅	—	2	4	no	—
1000	C₂²×C₅	—	4	8	no	—
1001	C₂²×C₅	C₂²×#41	1	4	yes	—
1002	C₂²×C₅	C₂²×#41	1	2	yes	—
1003	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
1004	C₂²×C₅	#585	1	2	yes	—
1005	C₂²×C₅	C₂⁶	1	1	yes	characteristic
1006	C₂×D₅	—	2	2	no	—
1007	C₂×D₅	—	2	2	no	—
1008	C₂×D₅	—	2	2	no	—
1009	C₂×D₅	—	2	2	no	—
1010	C₂×D₅	—	2	8	no	—
1011	C₂×D₅	—	2	8	no	—
1012	C₂×D₅	—	2	2	no	—
1013	C₂×D₅	—	2	2	no	—
1014	C₂×D₅	—	2	4	no	—
1015	C₂×D₅	—	2	2	no	—
1016	C₂×D₅	—	2	2	no	—
1017	C₂×D₅	—	2	4	no	—
1018	C₂×D₅	—	2	4	no	—
1019	C₂×D₅	—	2	2	no	—
1020	C₂×D₅	—	2	2	no	—
1021	C₂×D₅	—	4	16	no	—
1022	C₂×D₅	—	4	16	no	—
1023	C₂×D₅	—	4	4	no	—
1024	C₂×D₅	—	4	4	no	—
1025	C₂×D₅	—	4	8	no	—
1026	C₂×D₅	—	8	16	no	—
1027	C₂×D₅	C₂²×#41	1	4	yes	—
1028	C₂×D₅	C₂²×#41	1	4	yes	—
1029	C₄×C₅	—	2	4	no	—
1030	C₄×C₅	—	2	2	no	—
1031	C₄×C₅	—	2	2	no	—
1032	C₄×C₅	—	2	4	no	—
1033	C₄×C₅	—	2	2	no	—
1034	C₄×C₅	—	2	2	no	—
1035	C₄×C₅	—	2	4	no	—
1036	C₄×C₅	—	2	2	no	—
1037	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
1038	Dic₅	—	2	4	no	—
1039	Dic₅	—	2	4	no	—
1040	Dic₅	—	2	2	no	—
1041	Dic₅	—	2	2	no	—
1042	Dic₅	—	2	2	no	—
1043	Dic₅	—	2	2	no	—
1044	Dic₅	—	2	4	no	—
1045	C₂⁴	—	5	1	no	—
1046	C₂⁴	—	5	1	no	—
1047	C₂⁴	—	5	8	no	—
1048	C₂⁴	—	5	4	no	—
1049	C₂⁴	—	5	1	no	—
1050	C₂⁴	—	5	1	no	—
1051	C₂⁴	—	5	2	no	—
1052	C₂⁴	—	5	8	no	—
1053	C₂⁴	—	5	4	no	—
1054	C₂⁴	—	10	8	no	—
1055	C₂⁴	—	10	4	no	—
1056	C₂⁴	—	20	2	no	—
1057	C₂⁴	—	20	2	no	—
1058	C₂⁴	—	20	2	no	—
1059	C₂⁴	—	20	2	no	—
1060	C₂⁴	—	20	4	no	—
1061	C₂⁴	—	20	4	no	—
1062	C₂⁴	C₂³×D₅	1	2	yes	—
1063	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1064	#41	—	20	16	no	—
1065	#41	—	20	16	no	—
1066	C₂×Q₈	—	2	4	no	—
1067	C₂×Q₈	—	5	4	no	—
1068	C₂×Q₈	—	5	8	no	—
1069	C₂×Q₈	—	10	4	no	—
1070	C₂×Q₈	—	20	4	no	—
1071	C₂×Q₈	—	20	16	no	—
1072	C₂×Q₈	C₂³×D₅	1	4	yes	—
1073	C₂×D₄	—	2	8	no	—
1074	C₂×D₄	—	2	4	no	—
1075	C₂×D₄	—	5	8	no	—
1076	C₂×D₄	—	5	8	no	—
1077	C₂×D₄	—	5	8	no	—
1078	C₂×D₄	—	5	8	no	—
1079	C₂×D₄	—	5	8	no	—
1080	C₂×D₄	—	5	4	no	—
1081	C₂×D₄	—	5	4	no	—
1082	C₂×D₄	—	5	8	no	—
1083	C₂×D₄	—	5	4	no	—
1084	C₂×D₄	—	5	4	no	—
1085	C₂×D₄	—	5	4	no	—
1086	C₂×D₄	—	5	8	no	—
1087	C₂×D₄	—	5	8	no	—
1088	C₂×D₄	—	10	4	no	—
1089	C₂×D₄	—	10	4	no	—
1090	C₂×D₄	—	10	4	no	—
1091	C₂×D₄	—	10	4	no	—
1092	C₂×D₄	—	10	32	no	—
1093	C₂×D₄	—	10	8	no	—
1094	C₂×D₄	—	10	64	no	—
1095	C₂×D₄	—	10	8	no	—
1096	C₂×D₄	—	10	8	no	—
1097	C₂×D₄	—	10	4	no	—
1098	C₂×D₄	—	20	4	no	—
1099	C₂×D₄	—	20	4	no	—
1100	C₂×D₄	—	20	16	no	—
1101	C₂×D₄	—	20	4	no	—
1102	C₂×D₄	—	20	4	no	—
1103	C₂×D₄	—	20	4	no	—
1104	C₂×D₄	C₂³×D₅	1	8	yes	—
1105	C₂×D₄	C₂³×D₅	1	4	yes	—
1106	C₂²×C₄	—	2	4	no	—
1107	C₂²×C₄	—	2	4	no	—
1108	C₂²×C₄	—	4	2	no	—
1109	C₂²×C₄	—	4	4	no	—
1110	C₂²×C₄	—	5	2	no	—
1111	C₂²×C₄	—	5	1	no	—
1112	C₂²×C₄	—	5	1	no	—
1113	C₂²×C₄	—	5	2	no	—
1114	C₂²×C₄	—	5	2	no	—
1115	C₂²×C₄	—	5	1	no	—
1116	C₂²×C₄	—	5	1	no	—
1117	C₂²×C₄	—	5	4	no	—
1118	C₂²×C₄	—	5	4	no	—
1119	C₂²×C₄	—	5	8	no	—
1120	C₂²×C₄	—	5	8	no	—
1121	C₂²×C₄	—	5	4	no	—
1122	C₂²×C₄	—	5	4	no	—
1123	C₂²×C₄	—	5	4	no	—
1124	C₂²×C₄	—	5	4	no	—
1125	C₂²×C₄	—	5	4	no	—
1126	C₂²×C₄	—	5	8	no	—
1127	C₂²×C₄	—	5	8	no	—
1128	C₂²×C₄	—	5	8	no	—
1129	C₂²×C₄	—	5	8	no	—
1130	C₂²×C₄	—	5	4	no	—
1131	C₂²×C₄	—	5	4	no	—
1132	C₂²×C₄	—	5	4	no	—
1133	C₂²×C₄	—	10	8	no	—
1134	C₂²×C₄	—	10	4	no	—
1135	C₂²×C₄	—	10	4	no	—
1136	C₂²×C₄	—	10	4	no	—
1137	C₂²×C₄	—	10	4	no	—
1138	C₂²×C₄	—	20	16	no	—
1139	C₂²×C₄	—	20	16	no	—
1140	C₂²×C₄	—	20	2	no	—
1141	C₂²×C₄	—	20	2	no	—
1142	C₂²×C₄	—	20	2	no	—
1143	C₂²×C₄	—	20	2	no	—
1144	C₂²×C₄	—	20	4	no	—
1145	C₂²×C₄	—	20	4	no	—
1146	C₂²×C₄	—	20	4	no	—
1147	C₂²×C₄	—	20	4	no	—
1148	C₂²×C₄	—	20	2	no	—
1149	C₂²×C₄	—	20	2	no	—
1150	C₂²×C₄	—	20	4	no	—
1151	C₂²×C₄	C₂³×D₅	1	4	yes	—
1152	C₂²×C₄	C₂³×D₅	1	4	yes	—
1153	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1154	C₂²×C₄	C₂³×D₅	1	2	yes	—
1155	C₂²×C₄	C₂³×D₅	1	2	yes	—
1156	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1157	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1158	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1159	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₅	1	2	yes	—
1161	C₂²×C₄	C₂³×D₅	1	4	yes	—
1162	C₂²×C₄	C₂³×D₅	1	8	yes	—
1163	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1164	C₄⋊C₄	—	5	4	no	—
1165	C₄⋊C₄	—	5	8	no	—
1166	C₄⋊C₄	—	5	4	no	—
1167	C₄⋊C₄	—	5	4	no	—
1168	C₄⋊C₄	—	5	4	no	—
1169	C₄⋊C₄	—	5	4	no	—
1170	C₄⋊C₄	—	5	4	no	—
1171	C₄⋊C₄	—	5	8	no	—
1172	C₄⋊C₄	—	5	8	no	—
1173	C₄⋊C₄	—	5	8	no	—
1174	C₄⋊C₄	—	5	8	no	—
1175	C₄⋊C₄	—	5	8	no	—
1176	C₄⋊C₄	—	5	8	no	—
1177	C₄⋊C₄	—	5	8	no	—
1178	C₄⋊C₄	—	5	8	no	—
1179	C₄⋊C₄	—	5	8	no	—
1180	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1181	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1182	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1183	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1184	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1185	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1186	C₂²⋊C₄	—	5	8	no	—
1187	C₂²⋊C₄	—	5	8	no	—
1188	C₂²⋊C₄	—	5	8	no	—
1189	C₂²⋊C₄	—	5	4	no	—
1190	C₂²⋊C₄	—	5	4	no	—
1191	C₂²⋊C₄	—	5	8	no	—
1192	C₂²⋊C₄	—	5	8	no	—
1193	C₂²⋊C₄	—	5	8	no	—
1194	C₂²⋊C₄	—	5	4	no	—
1195	C₂²⋊C₄	—	5	4	no	—
1196	C₂²⋊C₄	—	5	4	no	—
1197	C₂²⋊C₄	—	5	4	no	—
1198	C₂²⋊C₄	—	5	8	no	—
1199	C₂²⋊C₄	—	5	8	no	—
1200	C₂²⋊C₄	—	5	4	no	—
1201	C₂²⋊C₄	—	5	4	no	—
1202	C₂²⋊C₄	—	5	8	no	—
1203	C₂²⋊C₄	—	5	8	no	—
1204	C₂²⋊C₄	—	5	8	no	—
1205	C₂²⋊C₄	—	5	8	no	—
1206	C₂²⋊C₄	—	5	8	no	—
1207	C₂²⋊C₄	—	5	8	no	—
1208	C₂²⋊C₄	—	5	8	no	—
1209	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1210	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1211	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1212	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1213	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1214	C₄²	—	5	8	no	—
1215	C₄²	—	5	8	no	—
1216	C₄²	—	5	8	no	—
1217	C₄²	C₂³×D₅	1	4	yes	—
1218	C₄²	C₂³×D₅	1	4	yes	—
1219	C₄²	C₂³×D₅	1	4	yes	—
1220	C₄²	C₂³×D₅	1	4	yes	—
1221	C₄²	C₂³×D₅	1	8	yes	—
1222	C₂×C₅	—	2	4	no	—
1223	C₂×C₅	—	4	4	no	—
1224	C₂×C₅	#3505	1	4	yes	complemented
1225	C₂×C₅	C₂³×#41	1	1	yes	characteristic
1226	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1227	C₂×C₅	C₂×#585	1	1	yes	characteristic
1228	D₅	—	2	4	no	—
1229	D₅	—	2	4	no	—
1230	D₅	—	4	2	no	—
1231	D₅	—	4	2	no	—
1232	D₅	—	4	4	no	—
1233	C₂³	—	2	2	no	—
1234	C₂³	—	2	2	no	—
1235	C₂³	—	2	4	no	—
1236	C₂³	—	2	4	no	—
1237	C₂³	—	2	4	no	—
1238	C₂³	—	5	4	no	—
1239	C₂³	—	5	4	no	—
1240	C₂³	—	5	2	no	—
1241	C₂³	—	5	2	no	—
1242	C₂³	—	5	16	no	—
1243	C₂³	—	5	2	no	—
1244	C₂³	—	5	2	no	—
1245	C₂³	—	5	4	no	—
1246	C₂³	—	10	16	no	—
1247	C₂³	—	10	2	no	—
1248	C₂³	—	10	2	no	—
1249	C₂³	—	10	2	no	—
1250	C₂³	—	10	2	no	—
1251	C₂³	—	10	8	no	—
1252	C₂³	—	10	2	no	—
1253	C₂³	—	10	2	no	—
1254	C₂³	—	10	4	no	—
1255	C₂³	—	10	2	no	—
1256	C₂³	—	10	2	no	—
1257	C₂³	—	10	4	no	—
1258	C₂³	—	10	4	no	—
1259	C₂³	—	10	2	no	—
1260	C₂³	—	10	2	no	—
1261	C₂³	—	20	4	no	—
1262	C₂³	—	20	4	no	—
1263	C₂³	—	20	4	no	—
1264	C₂³	—	20	4	no	—
1265	C₂³	—	20	16	no	—
1266	C₂³	—	20	8	no	—
1267	C₂³	—	20	8	no	—
1268	C₂³	—	20	16	no	—
1269	C₂³	—	40	16	no	—
1270	C₂³	D₅×#41	1	4	yes	—
1271	C₂³	C₂⁴×D₅	1	4	yes	—
1272	C₂³	C₂⁴×D₅	1	2	yes	—
1273	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1274	Q₈	—	2	8	no	—
1275	Q₈	—	10	8	no	—
1276	Q₈	—	20	8	no	—
1277	D₄	—	2	16	no	—
1278	D₄	—	2	8	no	—
1279	D₄	—	10	8	no	—
1280	D₄	—	10	8	no	—
1281	D₄	—	10	8	no	—
1282	D₄	—	10	8	no	—
1283	D₄	—	10	16	no	—
1284	D₄	—	10	16	no	—
1285	D₄	—	10	16	no	—
1286	D₄	—	10	8	no	—
1287	D₄	—	20	8	no	—
1288	D₄	—	20	8	no	—
1289	D₄	—	20	8	no	—
1290	D₄	—	20	8	no	—
1291	D₄	—	20	8	no	—
1292	C₂×C₄	—	2	8	no	—
1293	C₂×C₄	—	2	2	no	—
1294	C₂×C₄	—	2	2	no	—
1295	C₂×C₄	—	2	4	no	—
1296	C₂×C₄	—	2	2	no	—
1297	C₂×C₄	—	2	4	no	—
1298	C₂×C₄	—	2	2	no	—
1299	C₂×C₄	—	2	2	no	—
1300	C₂×C₄	—	2	4	no	—
1301	C₂×C₄	—	2	8	no	—
1302	C₂×C₄	—	4	4	no	—
1303	C₂×C₄	—	4	8	no	—
1304	C₂×C₄	—	5	4	no	—
1305	C₂×C₄	—	5	2	no	—
1306	C₂×C₄	—	5	2	no	—
1307	C₂×C₄	—	5	4	no	—
1308	C₂×C₄	—	5	4	no	—
1309	C₂×C₄	—	5	2	no	—
1310	C₂×C₄	—	5	2	no	—
1311	C₂×C₄	—	10	16	no	—
1312	C₂×C₄	—	10	4	no	—
1313	C₂×C₄	—	10	2	no	—
1314	C₂×C₄	—	10	2	no	—
1315	C₂×C₄	—	10	2	no	—
1316	C₂×C₄	—	10	2	no	—
1317	C₂×C₄	—	10	4	no	—
1318	C₂×C₄	—	10	4	no	—
1319	C₂×C₄	—	10	8	no	—
1320	C₂×C₄	—	10	8	no	—
1321	C₂×C₄	—	10	8	no	—
1322	C₂×C₄	—	10	8	no	—
1323	C₂×C₄	—	20	4	no	—
1324	C₂×C₄	—	20	4	no	—
1325	C₂×C₄	—	20	4	no	—
1326	C₂×C₄	—	20	4	no	—
1327	C₂×C₄	—	20	8	no	—
1328	C₂×C₄	—	20	8	no	—
1329	C₂×C₄	—	20	8	no	—
1330	C₂×C₄	—	20	8	no	—
1331	C₂×C₄	—	20	4	no	—
1332	C₂×C₄	—	20	4	no	—
1333	C₂×C₄	—	20	8	no	—
1334	C₂×C₄	#4149	1	4	yes	—
1335	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1336	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1337	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1338	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1339	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1340	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1341	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1342	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1343	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1344	C₅	C₂×#3505	1	1	yes	characteristic, complemented, Sylow
1345	C₂²	—	2	2	no	—
1346	C₂²	—	2	2	no	—
1347	C₂²	—	2	8	no	—
1348	C₂²	—	2	4	no	—
1349	C₂²	—	2	4	no	—
1350	C₂²	—	2	4	no	—
1351	C₂²	—	4	8	no	—
1352	C₂²	—	5	4	no	—
1353	C₂²	—	5	4	no	—
1354	C₂²	—	10	2	no	—
1355	C₂²	—	10	2	no	—
1356	C₂²	—	10	2	no	—
1357	C₂²	—	10	2	no	—
1358	C₂²	—	10	8	no	—
1359	C₂²	—	10	8	no	—
1360	C₂²	—	10	2	no	—
1361	C₂²	—	10	2	no	—
1362	C₂²	—	10	4	no	—
1363	C₂²	—	10	2	no	—
1364	C₂²	—	10	2	no	—
1365	C₂²	—	10	4	no	—
1366	C₂²	—	10	4	no	—
1367	C₂²	—	10	2	no	—
1368	C₂²	—	10	2	no	—
1369	C₂²	—	20	16	no	—
1370	C₂²	—	20	16	no	—
1371	C₂²	—	20	4	no	—
1372	C₂²	—	20	4	no	—
1373	C₂²	—	20	8	no	—
1374	C₂²	—	40	16	no	—
1375	C₂²	C₂×D₅×#41	1	4	yes	—
1376	C₂²	C₂×D₅×#41	1	2	yes	—
1377	C₂²	C₂×#4149	1	2	yes	—
1378	C₂²	#66283	1	2	yes	—
1379	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1380	C₄	—	2	2	no	—
1381	C₄	—	2	2	no	—
1382	C₄	—	2	4	no	—
1383	C₄	—	2	2	no	—
1384	C₄	—	2	4	no	—
1385	C₄	—	2	2	no	—
1386	C₄	—	2	2	no	—
1387	C₄	—	2	4	no	—
1388	C₄	—	10	4	no	—
1389	C₄	—	10	2	no	—
1390	C₄	—	10	2	no	—
1391	C₄	—	10	2	no	—
1392	C₄	—	10	2	no	—
1393	C₄	—	10	4	no	—
1394	C₄	—	10	4	no	—
1395	C₄	C₂×#4149	1	4	yes	—
1396	C₂	—	2	4	no	—
1397	C₂	—	4	4	no	—
1398	C₂	—	10	4	no	—
1399	C₂	—	10	4	no	—
1400	C₂	—	20	2	no	—
1401	C₂	—	20	2	no	—
1402	C₂	—	20	4	no	—
1403	C₂	#10618059	1	4	yes	direct product factor
1404	C₂	C₂²×D₅×#41	1	1	yes	characteristic
1405	C₂	C₂²×#4149	1	1	yes	characteristic
1406	C₂	C₂×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#529	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#529	D₅
hypocenter	C₅	C₂×#3505
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#529	C₂	semidirect
2. #10618059	C₂	direct (N × H)
3. C₂×#66039	C₂	semidirect
4. C₂×#66043	C₂	semidirect
5. C₂×#66029	C₂	semidirect
6. C₂×#66028	C₂	semidirect
7. C₂×#66011	C₂	semidirect
8. C₂×#66010	C₂	semidirect
9. C₂×#65987	C₂	semidirect
10. C₂×#65999	C₂	semidirect
11. C₂×D₅×C₂²⋊Q₈	C₂	semidirect
12. C₂×#65961	C₂	semidirect
13. C₂×D₅×#121	C₂	semidirect
14. C₂×#65940	C₂	semidirect
15. C₂×#65915	C₂	semidirect
16. C₂×#65910	C₂	semidirect
17. C₂×#65892	C₂	semidirect
18. C₂×#65888	C₂	semidirect
19. C₂×#65894	C₂	semidirect
20. C₂×#65879	C₂	semidirect
21. C₂×#65864	C₂	semidirect
22. C₂×#65861	C₂	semidirect
23. C₂×#65813	C₂	semidirect
24. C₂²×C₄×D₂₀	C₂	semidirect
25. C₂²×#713	C₂²	semidirect
26. C₂²×Q₈×D₅	C₂²	semidirect
27. C₂²×#711	C₂²	semidirect
29. C₂²×D₄×D₅	C₂²	semidirect
32. C₂³×C₄×D₅	C₂²	semidirect
33. C₅×#529	C₂²	semidirect
34. C₂×C₅×#126	C₂²	semidirect
35. C₂×C₅×#125	C₂²	semidirect
36. C₂×C₅×#124	C₂²	semidirect
37. C₂×C₅×#123	C₂²	semidirect
38. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×C₅×Q₈	C₂²	semidirect
41. C₂×C₄×C₅×D₄	C₂²	semidirect
42. C₂×C₄×C₅×D₄	C₂²	semidirect
43. C₂×C₅×#117	C₂²	semidirect
44. C₂²×C₄²×C₅	C₂²	semidirect
45. C₂×#4092	C₂²	semidirect
46. C₂×#4092	C₂²	semidirect
48. C₂×#4084	C₂²	semidirect
49. C₂×#4084	C₂²	semidirect
50. C₂×#4083	C₂²	semidirect
51. C₂×D₄×Dic₅	C₂²	semidirect
53. C₂×#4076	C₂²	semidirect
54. C₂×#4075	C₂²	semidirect
55. C₂×#4075	C₂²	semidirect
56. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
57. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
59. C₂²×#685	C₂²	semidirect
60. C₂²×#685	C₂²	semidirect
61. C₂²×C₄⋊Dic₅	C₂²	semidirect
62. C₂×#4070	C₂²	semidirect
63. #66043	C₂²	semidirect
64. #66039	C₂²	semidirect
65. #66029	C₂²	semidirect
66. #66028	C₂²	semidirect
67. #66011	C₂²	semidirect
68. #66010	C₂²	semidirect
69. #65999	C₂²	semidirect
70. #65987	C₂²	semidirect
71. #65961	C₂²	semidirect
72. D₅×C₂²⋊Q₈	C₂²	semidirect
73. #65940	C₂²	semidirect
74. D₅×#121	C₂²	semidirect
75. #65915	C₂²	semidirect
76. #65910	C₂²	semidirect
77. #65894	C₂²	semidirect
78. #65892	C₂²	semidirect
79. #65888	C₂²	semidirect
80. #65879	C₂²	semidirect
81. #65864	C₂²	semidirect
82. #65861	C₂²	semidirect
83. C₂×#4044	C₂²	semidirect
84. C₂×#4044	C₂²	semidirect
85. C₂×#4043	C₂²	semidirect
86. C₂×#4043	C₂²	semidirect
87. C₂×#4043	C₂²	semidirect
88. C₂×#4042	C₂²	semidirect
89. C₂×#4041	C₂²	semidirect
90. C₂×#4041	C₂²	semidirect
91. C₂×#4041	C₂²	semidirect
92. C₂×#4041	C₂²	semidirect
95. C₂×#4040	C₂²	semidirect
96. C₂×#4040	C₂²	semidirect
97. C₂×#4039	C₂²	semidirect
98. C₂×#4039	C₂²	semidirect
99. C₂×#4038	C₂²	semidirect
100. C₂×#4038	C₂²	semidirect
101. C₂×#4038	C₂²	semidirect
102. C₂×D₅×C₄⋊C₄	C₂²	semidirect
103. C₂×D₅×C₄⋊C₄	C₂²	semidirect
104. C₂×D₅×C₄⋊C₄	C₂²	semidirect
105. C₂×#4036	C₂²	semidirect
106. C₂×#4035	C₂²	semidirect
107. C₂×#4032	C₂²	semidirect
108. C₂×#4031	C₂²	semidirect
109. C₂×#4030	C₂²	semidirect
110. C₂×#4030	C₂²	semidirect
111. C₂×#4030	C₂²	semidirect
112. C₂×#4030	C₂²	semidirect
113. C₂×#4029	C₂²	semidirect
114. C₂×#4029	C₂²	semidirect
117. C₂×#4028	C₂²	semidirect
118. C₂×#4027	C₂²	semidirect
119. C₂×#4027	C₂²	semidirect
120. C₂×#4027	C₂²	semidirect
122. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
123. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
124. C₂×#4025	C₂²	semidirect
125. C₂×#4024	C₂²	semidirect
126. C₂×#4024	C₂²	semidirect
127. #65813	C₂²	semidirect
128. C₂×#4022	C₂²	semidirect
129. C₂×#4022	C₂²	semidirect
130. C₂×#4021	C₂²	semidirect
131. C₂×#4021	C₂²	semidirect
136. C₂×C₄×D₂₀	C₂²	semidirect
137. C₂×C₄×D₂₀	C₂²	semidirect
138. C₂×C₄×D₂₀	C₂²	semidirect
139. C₂×C₄×D₂₀	C₂²	semidirect
140. C₂×C₄×D₂₀	C₂²	semidirect
141. C₂×C₄×D₂₀	C₂²	semidirect
142. C₂×C₄×D₂₀	C₂²	semidirect
143. C₂×#4018	C₂²	semidirect
144. C₂×#4018	C₂²	semidirect
145. C₂×#4016	C₂²	semidirect
146. C₂×C₄×Dic₁₀	C₂²	semidirect
167. C₂×#713	C₂³	semidirect
169. C₂×Q₈×D₅	C₂³	semidirect
171. C₂×#711	C₂³	semidirect
175. C₂×D₄×D₅	C₂³	semidirect
202. C₂²×C₄×D₅	C₂³	semidirect
205. C₅×#126	C₂³	semidirect
206. C₅×#125	C₂³	semidirect
207. C₅×#124	C₂³	semidirect
208. C₅×#123	C₂³	semidirect
209. C₅×C₂²⋊Q₈	C₂³	semidirect
211. C₄×C₅×Q₈	C₂³	semidirect
212. C₄×C₅×D₄	C₂³	semidirect
213. C₄×C₅×D₄	C₂³	semidirect
214. C₅×#117	C₂³	semidirect
231. C₂×C₄²×C₅	C₂³	semidirect
235. #4092	C₂³	semidirect
236. #4092	C₂³	semidirect
238. #4084	C₂³	semidirect
239. #4084	C₂³	semidirect
240. #4083	C₂³	semidirect
241. D₄×Dic₅	C₂³	semidirect
243. #4076	C₂³	semidirect
244. #4075	C₂³	semidirect
245. #4075	C₂³	semidirect
246. C₄×C₂²⋊D₅	C₂³	semidirect
247. C₄×C₂²⋊D₅	C₂³	semidirect
269. C₂×#685	C₂³	semidirect
270. C₂×#685	C₂³	semidirect
279. C₂×C₄⋊Dic₅	C₂³	semidirect
280. #4070	C₂³	semidirect
292. #4044	C₂³	semidirect
293. #4044	C₂³	semidirect
294. #4043	C₂³	semidirect
295. #4043	C₂³	semidirect
296. #4043	C₂³	semidirect
297. #4042	C₂³	semidirect
298. #4041	C₂³	semidirect
299. #4041	C₂³	semidirect
300. #4041	C₂³	semidirect
301. #4041	C₂³	semidirect
304. #4040	C₂³	semidirect
305. #4040	C₂³	semidirect
306. #4039	C₂³	semidirect
307. #4039	C₂³	semidirect
308. #4038	C₂³	semidirect
309. #4038	C₂³	semidirect
310. #4038	C₂³	semidirect
311. D₅×C₄⋊C₄	C₂³	semidirect
312. D₅×C₄⋊C₄	C₂³	semidirect
313. D₅×C₄⋊C₄	C₂³	semidirect
314. #4036	C₂³	semidirect
315. #4035	C₂³	semidirect
316. #4032	C₂³	semidirect
317. #4031	C₂³	semidirect
318. #4030	C₂³	semidirect
319. #4030	C₂³	semidirect
320. #4030	C₂³	semidirect
321. #4030	C₂³	semidirect
322. #4029	C₂³	semidirect
323. #4029	C₂³	semidirect
326. #4028	C₂³	semidirect
327. #4027	C₂³	semidirect
328. #4027	C₂³	semidirect
329. #4027	C₂³	semidirect
331. D₅×C₂²⋊C₄	C₂³	semidirect
332. D₅×C₂²⋊C₄	C₂³	semidirect
333. #4025	C₂³	semidirect
334. #4024	C₂³	semidirect
335. #4024	C₂³	semidirect
336. #4022	C₂³	semidirect
337. #4022	C₂³	semidirect
338. #4021	C₂³	semidirect
339. #4021	C₂³	semidirect
344. C₄×D₂₀	C₂³	semidirect
345. C₄×D₂₀	C₂³	semidirect
346. C₄×D₂₀	C₂³	semidirect
347. C₄×D₂₀	C₂³	semidirect
348. C₄×D₂₀	C₂³	semidirect
349. C₄×D₂₀	C₂³	semidirect
350. #4018	C₂³	semidirect
351. #4018	C₂³	semidirect
352. #4016	C₂³	semidirect
353. C₄×Dic₁₀	C₂³	semidirect
371. C₂×#529	D₅	semidirect
388. C₂³×D₅	#41	semidirect
579. #529	C₂×D₅	semidirect
585. C₂×#126	C₂×D₅	semidirect
589. C₂×#125	C₂×D₅	semidirect
593. C₂×#124	C₂×D₅	semidirect
605. C₂×#123	C₂×D₅	semidirect
616. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
638. C₂×C₄×Q₈	C₂×D₅	semidirect
658. C₂×C₄×D₄	C₂×D₅	semidirect
659. C₂×C₄×D₄	C₂×D₅	semidirect
665. C₂×#117	C₂×D₅	semidirect
676. C₂²×C₄²	C₂×D₅	semidirect
712. C₂²×D₅	C₂×#41	semidirect
850. #126	C₂²×D₅	semidirect
854. #125	C₂²×D₅	semidirect
858. #124	C₂²×D₅	semidirect
868. #123	C₂²×D₅	semidirect
878. C₂²⋊Q₈	C₂²×D₅	semidirect
898. C₄×Q₈	C₂²×D₅	semidirect
917. C₄×D₄	C₂²×D₅	semidirect
918. C₄×D₄	C₂²×D₅	semidirect
924. #117	C₂²×D₅	semidirect
993. C₂×C₄²	C₂²×D₅	semidirect
1224. C₂×C₅	#3505	semidirect
1344. C₅	C₂×#3505	semidirect
1403. C₂	#10618059	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×#529	2
#10618059	2
C₂×#66039	2
C₂×#66043	2
C₂×#66029	2
C₂×#66028	2
C₂×#66011	2
C₂×#66010	2
C₂×#65987	2
C₂×#65999	2
C₂×D₅×C₂²⋊Q₈	2
C₂×#65961	2
C₂×D₅×#121	2
C₂×#65940	2
C₂×#65915	2
C₂×#65910	2
C₂×#65892	2
C₂×#65888	2
C₂×#65894	2
C₂×#65879	2
C₂×#65864	2
C₂×#65861	2
C₂×#65813	2
C₂²×C₄×D₂₀	2
C₂×#3505	5

Subgroups — C2×#10618059 #13007220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618059 #13007220