Subgroups — C₂×#10618451 #13007645

Order 1280.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618451	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66063	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66059	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66039	C₂	1	2	yes	maximal, complemented
6	C₂×#66043	C₂	1	2	yes	maximal, complemented
7	C₂×#66010	C₂	1	2	yes	maximal, complemented
8	C₂×#66008	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66004	C₂	1	2	yes	maximal, complemented
10	C₂×#66014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65988	C₂	1	2	yes	maximal, complemented
12	C₂×#65995	C₂	1	2	yes	maximal, complemented
13	C₂×#65971	C₂	1	2	yes	maximal, complemented
14	C₂×#65965	C₂	1	2	yes	maximal, complemented
15	C₂×#65977	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#65961	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65953	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#65914	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#65908	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#65882	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#65879	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#65869	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#713	C₂²	1	1	yes	characteristic
26	C₂²×#713	C₂²	1	2	yes	complemented
27	C₂²×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₅	C₂²	1	2	yes	—
29	C₂²×#709	C₂²	1	2	yes	complemented
30	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic
31	C₅×#542	C₂²	1	16	yes	complemented
32	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#126	C₂²	1	2	yes	complemented
34	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#124	C₂²	1	2	yes	complemented
36	C₂×C₅×#123	C₂²	1	2	yes	complemented
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	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	1	yes	characteristic, complemented
42	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×#4093	C₂²	1	1	yes	characteristic, complemented
44	C₂×#4093	C₂²	1	2	yes	complemented
45	C₂×#4092	C₂²	1	2	yes	—
46	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
47	C₂×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
48	C₂×#4090	C₂²	1	2	yes	complemented
49	C₂×#4086	C₂²	1	1	yes	characteristic, complemented
50	C₂×#4085	C₂²	1	2	yes	—
51	C₂×#4085	C₂²	1	2	yes	complemented
52	C₂×#4084	C₂²	1	1	yes	characteristic
53	C₂×#4084	C₂²	1	2	yes	complemented
54	C₂×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
55	C₂×#4076	C₂²	1	1	yes	characteristic
56	C₂×#4076	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
58	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
59	C₂²×#685	C₂²	1	2	yes	—
60	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
61	#66063	C₂²	1	16	yes	complemented
62	#66059	C₂²	1	16	yes	complemented
63	#66043	C₂²	1	32	yes	complemented
64	#66039	C₂²	1	32	yes	complemented
65	#66014	C₂²	1	16	yes	complemented
66	#66010	C₂²	1	32	yes	complemented
67	#66008	C₂²	1	16	yes	complemented
68	#66004	C₂²	1	32	yes	complemented
69	#65995	C₂²	1	32	yes	complemented
70	#65988	C₂²	1	32	yes	complemented
71	#65977	C₂²	1	16	yes	complemented
72	#65971	C₂²	1	32	yes	complemented
73	#65965	C₂²	1	32	yes	complemented
74	#65961	C₂²	1	16	yes	complemented
75	#65953	C₂²	1	16	yes	complemented
76	D₅×#121	C₂²	1	16	yes	complemented
77	#65914	C₂²	1	16	yes	complemented
78	#65908	C₂²	1	16	yes	complemented
79	#65882	C₂²	1	16	yes	complemented
80	#65879	C₂²	1	16	yes	complemented
81	#65869	C₂²	1	16	yes	complemented
82	D₅×#117	C₂²	1	16	yes	complemented
83	C₂×#4044	C₂²	1	2	yes	complemented
84	C₂×#4044	C₂²	1	2	yes	complemented
85	C₂×#4043	C₂²	1	2	yes	complemented
86	C₂×#4042	C₂²	1	2	yes	—
87	C₂×#4041	C₂²	1	1	yes	characteristic
88	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
89	C₂×#4041	C₂²	1	2	yes	complemented
90	C₂×#4040	C₂²	1	2	yes	—
91	C₂×#4040	C₂²	1	2	yes	complemented
92	C₂×#4040	C₂²	1	2	yes	complemented
93	C₂×#4040	C₂²	1	2	yes	complemented
94	C₂×#4039	C₂²	1	2	yes	—
95	C₂×#4039	C₂²	1	2	yes	complemented
96	C₂×#4039	C₂²	1	1	yes	characteristic, complemented
97	C₂×#4039	C₂²	1	2	yes	complemented
98	C₂×#4039	C₂²	1	1	yes	characteristic, complemented
99	C₂×#4038	C₂²	1	1	yes	characteristic
100	C₂×#4038	C₂²	1	1	yes	characteristic
101	C₂×#4038	C₂²	1	1	yes	characteristic
102	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
105	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₂×#4036	C₂²	1	1	yes	characteristic, complemented
107	C₂×#4035	C₂²	1	2	yes	complemented
108	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
109	C₂×#4032	C₂²	1	2	yes	complemented
110	C₂×#4031	C₂²	1	2	yes	complemented
111	C₂×#4031	C₂²	1	2	yes	complemented
112	C₂×#4030	C₂²	1	2	yes	—
113	C₂×#4030	C₂²	1	2	yes	complemented
114	C₂×#4030	C₂²	1	2	yes	complemented
115	C₂×#4030	C₂²	1	2	yes	complemented
116	C₂×#4030	C₂²	1	2	yes	complemented
117	C₂×#4030	C₂²	1	2	yes	complemented
118	C₂×#4029	C₂²	1	2	yes	complemented
119	C₂×#4029	C₂²	1	2	yes	complemented
120	C₂×#4029	C₂²	1	2	yes	complemented
121	C₂×#4028	C₂²	1	2	yes	—
122	C₂×#4028	C₂²	1	2	yes	—
123	C₂×#4028	C₂²	1	2	yes	—
124	C₂×#4027	C₂²	1	2	yes	complemented
125	C₂×#4027	C₂²	1	2	yes	complemented
126	C₂×#4027	C₂²	1	2	yes	complemented
127	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
128	C₂×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
129	C₂×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
130	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
131	C₂×#4025	C₂²	1	2	yes	complemented
132	C₂×#4023	C₂²	1	2	yes	complemented
133	C₂×#4023	C₂²	1	1	yes	characteristic, complemented
134	C₂×#4023	C₂²	1	1	yes	characteristic, complemented
135	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄×D₂₀	C₂²	1	2	yes	—
137	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
139	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
140	C₂×#4018	C₂²	1	1	yes	characteristic
141	C₂×#4018	C₂²	1	1	yes	characteristic
142	C₂×#4018	C₂²	1	2	yes	complemented
143	C₂×#4018	C₂²	1	2	yes	complemented
144	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
146	C₂×#4016	C₂²	1	1	yes	characteristic, complemented
147	C₂×#3494	—	5	1	no	maximal, Sylow
148	C₂⁴×D₅	C₂³	1	1	yes	characteristic
149	C₂⁴×D₅	C₂³	1	2	yes	—
150	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₅×Q₈	C₂³	1	2	yes	—
152	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₅×D₄	C₂³	1	2	yes	—
154	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₅	C₂³	1	2	yes	—
156	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂²×C₂²⋊D₅	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	C₂³×Dic₅	C₂³	1	1	yes	characteristic
163	C₂³×Dic₅	C₂³	1	2	yes	—
164	C₂×#713	—	2	8	no	—
165	C₂×#713	—	4	8	no	—
166	C₂×#713	C₂³	1	8	yes	—
167	C₂×#713	C₂³	1	16	yes	complemented
168	C₂×D₄×D₅	—	2	8	no	—
169	C₂×D₄×D₅	—	4	8	no	—
170	C₂×D₄×D₅	C₂³	1	8	yes	—
171	C₂×D₄×D₅	C₂³	1	16	yes	—
172	C₂×#709	—	4	8	no	—
173	C₂×#709	C₂³	1	16	yes	complemented
174	C₂²×D₂₀	C₂³	1	2	yes	—
175	C₂²×D₂₀	C₂³	1	1	yes	characteristic
176	C₂²×D₂₀	C₂³	1	1	yes	characteristic
177	C₂²×D₂₀	C₂³	1	2	yes	—
178	C₂²×D₂₀	C₂³	1	2	yes	—
179	C₂²×D₂₀	C₂³	1	2	yes	—
180	C₂²×D₂₀	C₂³	1	2	yes	—
181	C₂²×C₄×D₅	—	2	8	no	—
182	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
185	C₂²×C₄×D₅	C₂³	1	2	yes	—
186	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
187	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₅	C₂³	1	8	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	2	yes	—
192	C₂²×C₄×D₅	C₂³	1	2	yes	—
193	C₂²×C₄×D₅	C₂³	1	2	yes	—
194	C₂²×C₄×D₅	C₂³	1	2	yes	—
195	C₂²×C₄×D₅	C₂³	1	2	yes	—
196	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
197	C₂²×Dic₁₀	C₂³	1	2	yes	—
198	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
199	C₅×#126	C₂³	1	16	yes	complemented
200	C₅×#124	C₂³	1	16	yes	complemented
201	C₅×#124	C₂³	1	8	yes	complemented
202	C₅×#123	C₂³	1	16	yes	complemented
203	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
204	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₅×#121	C₂³	1	8	yes	—
206	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
207	C₄×C₅×D₄	C₂³	1	8	yes	complemented
208	C₅×#117	C₂³	1	8	yes	complemented
209	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₅×C₂²⋊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×C₄²×C₅	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅	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	1	yes	characteristic
229	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
230	#4093	C₂³	1	16	yes	complemented
231	#4093	C₂³	1	8	yes	complemented
232	#4092	C₂³	1	16	yes	—
233	#4092	C₂³	1	8	yes	complemented
234	Q₈×Dic₅	C₂³	1	8	yes	complemented
235	#4090	C₂³	1	16	yes	complemented
236	#4086	C₂³	1	8	yes	complemented
237	#4085	C₂³	1	16	yes	—
238	#4085	C₂³	1	16	yes	complemented
239	#4084	C₂³	1	8	yes	—
240	#4084	C₂³	1	16	yes	complemented
241	D₄×Dic₅	C₂³	1	8	yes	complemented
242	#4076	C₂³	1	8	yes	—
243	#4076	C₂³	1	8	yes	complemented
244	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
245	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
246	C₂×#685	C₂³	1	1	yes	characteristic
247	C₂×#685	C₂³	1	1	yes	characteristic
248	C₂×#685	C₂³	1	1	yes	characteristic
249	C₂×#685	C₂³	1	1	yes	characteristic
250	C₂×#685	C₂³	1	2	yes	—
251	C₂×#685	C₂³	1	2	yes	—
252	C₂×#685	C₂³	1	2	yes	—
253	C₂×#685	C₂³	1	2	yes	—
254	C₂×#685	C₂³	1	2	yes	—
255	C₂×#685	C₂³	1	2	yes	—
256	C₂×#685	C₂³	1	2	yes	—
257	C₂×#685	C₂³	1	2	yes	—
258	C₂×#685	C₂³	1	2	yes	—
259	C₂×#685	C₂³	1	2	yes	—
260	C₂×#685	C₂³	1	2	yes	—
261	C₂×#685	C₂³	1	2	yes	—
262	C₂×#685	C₂³	1	16	yes	—
263	#4072	C₂³	1	8	yes	complemented
264	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
267	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
268	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
270	C₂×#683	C₂³	1	2	yes	—
271	C₂×#683	C₂³	1	2	yes	—
272	C₂×#683	C₂³	1	1	yes	characteristic
273	C₂×#683	C₂³	1	1	yes	characteristic
274	C₂×#683	C₂³	1	1	yes	characteristic
275	C₂×#683	C₂³	1	1	yes	characteristic
276	C₂×#683	C₂³	1	2	yes	—
277	C₂×#683	C₂³	1	2	yes	—
278	C₂×#683	C₂³	1	2	yes	—
279	C₂×#683	C₂³	1	2	yes	—
280	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅	C₂³	1	2	yes	—
287	C₂×C₄×Dic₅	C₂³	1	2	yes	—
288	#4044	C₂³	1	16	yes	complemented
289	#4044	C₂³	1	16	yes	complemented
290	#4043	C₂³	1	16	yes	complemented
291	#4042	C₂³	1	16	yes	—
292	#4041	C₂³	1	8	yes	—
293	#4041	C₂³	1	8	yes	complemented
294	#4041	C₂³	1	16	yes	complemented
295	#4040	C₂³	1	16	yes	—
296	#4040	C₂³	1	16	yes	complemented
297	#4040	C₂³	1	16	yes	complemented
298	#4040	C₂³	1	16	yes	complemented
299	#4039	C₂³	1	16	yes	—
300	#4039	C₂³	1	8	yes	complemented
301	#4039	C₂³	1	8	yes	complemented
302	#4039	C₂³	1	16	yes	complemented
303	#4039	C₂³	1	16	yes	complemented
304	#4038	C₂³	1	8	yes	—
305	#4038	C₂³	1	8	yes	—
306	#4038	C₂³	1	8	yes	—
307	D₅×C₄⋊C₄	C₂³	1	8	yes	—
308	D₅×C₄⋊C₄	C₂³	1	8	yes	complemented
309	D₅×C₄⋊C₄	C₂³	1	8	yes	complemented
310	D₅×C₄⋊C₄	C₂³	1	16	yes	complemented
311	#4036	C₂³	1	8	yes	complemented
312	#4035	C₂³	1	16	yes	complemented
313	#4034	C₂³	1	8	yes	complemented
314	#4032	C₂³	1	16	yes	complemented
315	#4031	C₂³	1	16	yes	complemented
316	#4031	C₂³	1	16	yes	complemented
317	#4030	C₂³	1	16	yes	—
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	#4030	C₂³	1	16	yes	complemented
323	#4029	C₂³	1	16	yes	complemented
324	#4029	C₂³	1	16	yes	complemented
325	#4029	C₂³	1	16	yes	complemented
326	#4028	C₂³	1	16	yes	—
327	#4028	C₂³	1	16	yes	—
328	#4028	C₂³	1	16	yes	—
329	#4027	C₂³	1	16	yes	complemented
330	#4027	C₂³	1	16	yes	complemented
331	#4027	C₂³	1	16	yes	complemented
332	D₅×C₂²⋊C₄	C₂³	1	8	yes	—
333	D₅×C₂²⋊C₄	C₂³	1	8	yes	—
334	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
335	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
336	#4025	C₂³	1	16	yes	complemented
337	#4023	C₂³	1	8	yes	complemented
338	#4023	C₂³	1	8	yes	complemented
339	#4023	C₂³	1	16	yes	complemented
340	#4020	C₂³	1	8	yes	complemented
341	C₄×D₂₀	C₂³	1	16	yes	—
342	C₄×D₂₀	C₂³	1	8	yes	complemented
343	C₄×D₂₀	C₂³	1	8	yes	complemented
344	C₄×D₂₀	C₂³	1	16	yes	complemented
345	#4018	C₂³	1	8	yes	—
346	#4018	C₂³	1	8	yes	—
347	#4018	C₂³	1	16	yes	complemented
348	#4018	C₂³	1	16	yes	complemented
349	C₄²×D₅	C₂³	1	8	yes	complemented
350	C₄²×D₅	C₂³	1	8	yes	complemented
351	#4016	C₂³	1	8	yes	complemented
352	#3494	—	5	32	no	—
353	C₂×#555	—	5	2	no	—
354	C₂×#553	—	5	2	no	—
355	C₂×#553	—	5	2	no	—
356	C₂×#551	—	5	2	no	—
357	C₂×#551	—	5	2	no	—
358	C₂×#547	—	5	2	no	—
359	C₂×#546	—	5	2	no	—
360	C₂×#546	—	5	2	no	—
361	C₂×#544	—	5	1	no	—
362	C₂×#542	—	5	1	no	—
363	C₂×#542	D₅	1	1	yes	characteristic, complemented
364	C₂×#540	—	5	1	no	—
365	C₂×#540	—	5	1	no	—
366	C₂×#535	—	5	1	no	—
367	C₂×#532	—	5	1	no	—
368	C₂×#532	—	5	1	no	—
369	C₂×#529	—	5	1	no	—
370	C₂×#529	—	5	1	no	—
371	C₂×#525	—	5	1	no	—
372	C₂²×#121	—	5	1	no	—
373	C₂×#520	—	5	1	no	—
374	C₂×#518	—	5	1	no	—
375	C₂²×#117	—	5	1	no	—
376	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
377	C₂⁴×C₅	C₂⁴	1	2	yes	—
378	C₂³×D₅	—	2	4	no	—
379	C₂³×D₅	—	2	4	no	—
380	C₂³×D₅	—	2	8	no	—
381	C₂³×D₅	—	4	2	no	—
382	C₂³×D₅	—	4	4	no	—
383	C₂³×D₅	—	4	4	no	—
384	C₂³×D₅	C₂⁴	1	2	yes	—
385	C₂³×D₅	C₂⁴	1	2	yes	—
386	C₂³×D₅	C₂⁴	1	4	yes	—
387	C₂³×D₅	C₂⁴	1	1	yes	characteristic
388	C₂³×D₅	C₂⁴	1	1	yes	characteristic
389	C₂³×D₅	C₂⁴	1	8	yes	—
390	C₂×C₅×Q₈	—	2	4	no	—
391	C₂×C₅×Q₈	—	4	4	no	—
392	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
393	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
394	C₂×C₅×D₄	—	2	4	no	—
395	C₂×C₅×D₄	—	4	4	no	—
396	C₂×C₅×D₄	C₂⁴	1	4	yes	—
397	C₂×C₅×D₄	C₂⁴	1	8	yes	—
398	C₂²×C₄×C₅	—	2	4	no	—
399	C₂²×C₄×C₅	—	4	4	no	—
400	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
409	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
410	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
411	C₂×C₂²⋊D₅	—	2	8	no	—
412	C₂×C₂²⋊D₅	—	2	8	no	—
413	C₂×C₂²⋊D₅	—	4	4	no	—
414	C₂×C₂²⋊D₅	—	4	4	no	—
415	C₂×C₂²⋊D₅	—	4	4	no	—
416	C₂×C₂²⋊D₅	—	4	4	no	—
417	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
418	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
419	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
420	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
421	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
422	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
423	C₂²×Dic₅	—	2	4	no	—
424	C₂²×Dic₅	—	4	4	no	—
425	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₅	C₂⁴	1	2	yes	—
429	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₅	C₂⁴	1	2	yes	—
431	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
432	C₂²×Dic₅	C₂⁴	1	4	yes	—
433	C₂²×Dic₅	C₂⁴	1	8	yes	—
434	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
435	#713	—	2	32	no	—
436	#713	—	4	32	no	—
437	D₄×D₅	—	2	32	no	—
438	D₄×D₅	—	4	32	no	—
439	#709	—	4	32	no	—
440	C₂×D₂₀	—	2	8	no	—
441	C₂×D₂₀	—	2	8	no	—
442	C₂×D₂₀	—	2	8	no	—
443	C₂×D₂₀	—	2	4	no	—
444	C₂×D₂₀	—	2	4	no	—
445	C₂×D₂₀	—	4	4	no	—
446	C₂×D₂₀	—	4	4	no	—
447	C₂×D₂₀	C₂⁴	1	8	yes	—
448	C₂×D₂₀	C₂⁴	1	8	yes	—
449	C₂×D₂₀	C₂⁴	1	4	yes	—
450	C₂×D₂₀	C₂⁴	1	8	yes	—
451	C₂×D₂₀	C₂⁴	1	4	yes	—
452	C₂×D₂₀	C₂⁴	1	8	yes	—
453	C₂×D₂₀	C₂⁴	1	8	yes	—
454	C₂×C₄×D₅	—	2	4	no	—
455	C₂×C₄×D₅	—	2	4	no	—
456	C₂×C₄×D₅	—	2	4	no	—
457	C₂×C₄×D₅	—	2	4	no	—
458	C₂×C₄×D₅	—	2	4	no	—
459	C₂×C₄×D₅	—	2	8	no	—
460	C₂×C₄×D₅	—	2	32	no	—
461	C₂×C₄×D₅	—	4	2	no	—
462	C₂×C₄×D₅	—	4	4	no	—
463	C₂×C₄×D₅	—	4	2	no	—
464	C₂×C₄×D₅	—	4	4	no	—
465	C₂×C₄×D₅	—	4	4	no	—
466	C₂×C₄×D₅	—	4	4	no	—
467	C₂×C₄×D₅	—	4	4	no	—
468	C₂×C₄×D₅	#41	1	8	yes	complemented
469	C₂×C₄×D₅	C₂⁴	1	4	yes	—
470	C₂×C₄×D₅	C₂⁴	1	4	yes	—
471	C₂×C₄×D₅	C₂⁴	1	4	yes	—
472	C₂×C₄×D₅	C₂⁴	1	4	yes	—
473	C₂×C₄×D₅	C₂⁴	1	8	yes	—
474	C₂×C₄×D₅	C₂⁴	1	4	yes	—
475	C₂×C₄×D₅	C₂⁴	1	8	yes	—
476	C₂×C₄×D₅	C₂⁴	1	8	yes	—
477	C₂×C₄×D₅	C₂⁴	1	8	yes	—
478	C₂×C₄×D₅	C₂⁴	1	8	yes	—
479	C₂×C₄×D₅	C₂⁴	1	4	yes	—
480	C₂×C₄×D₅	C₂⁴	1	4	yes	—
481	C₂×C₄×D₅	C₂⁴	1	8	yes	—
482	C₂×C₄×D₅	C₂⁴	1	4	yes	—
483	C₂×Dic₁₀	—	4	4	no	—
484	C₂×Dic₁₀	C₂⁴	1	8	yes	—
485	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
486	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
487	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
488	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
489	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
490	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
491	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
492	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
493	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
494	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
495	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
496	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
497	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
498	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
499	C₄²×C₅	C₂⁴	1	4	yes	—
500	C₄²×C₅	C₂⁴	1	4	yes	—
501	C₄²×C₅	C₂⁴	1	8	yes	—
502	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
503	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
504	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
505	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
506	#685	C₂⁴	1	4	yes	—
507	#685	C₂⁴	1	4	yes	—
508	#685	C₂⁴	1	4	yes	—
509	#685	C₂⁴	1	4	yes	—
510	#685	C₂⁴	1	8	yes	—
511	#685	C₂⁴	1	8	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	8	yes	—
517	#685	C₂⁴	1	8	yes	—
518	#685	C₂⁴	1	8	yes	—
519	#685	C₂⁴	1	8	yes	—
520	#685	C₂⁴	1	8	yes	—
521	#685	C₂⁴	1	8	yes	—
522	C₄⋊Dic₅	C₂⁴	1	4	yes	—
523	C₄⋊Dic₅	C₂⁴	1	4	yes	—
524	C₄⋊Dic₅	C₂⁴	1	8	yes	—
525	C₄⋊Dic₅	C₂⁴	1	8	yes	—
526	C₄⋊Dic₅	C₂⁴	1	4	yes	—
527	C₄⋊Dic₅	C₂⁴	1	4	yes	—
528	#683	C₂⁴	1	8	yes	—
529	#683	C₂⁴	1	8	yes	—
530	#683	C₂⁴	1	4	yes	—
531	#683	C₂⁴	1	4	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	#683	C₂⁴	1	8	yes	—
537	#683	C₂⁴	1	8	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	4	yes	—
543	C₄×Dic₅	C₂⁴	1	4	yes	—
544	C₄×Dic₅	C₂⁴	1	8	yes	—
545	C₄×Dic₅	C₂⁴	1	8	yes	—
546	C₂²×#41	—	5	1	no	—
547	C₂²×#41	—	5	2	no	—
548	C₂²×#41	—	5	2	no	—
549	C₂³×D₄	—	5	1	no	—
550	C₂³×D₄	—	5	2	no	—
551	C₂⁴×C₄	—	5	1	no	—
552	#555	—	5	32	no	—
553	#553	—	5	32	no	—
554	#553	—	5	32	no	—
555	#551	—	5	32	no	—
556	#551	—	5	32	no	—
557	#547	—	5	32	no	—
558	#546	—	5	32	no	—
559	#546	—	5	32	no	—
560	#544	—	5	16	no	—
561	#542	—	5	16	no	—
562	#542	C₂×D₅	1	16	yes	complemented
563	#540	—	5	16	no	—
564	#540	—	5	16	no	—
565	#535	—	5	16	no	—
566	#532	—	5	16	no	—
567	#532	—	5	16	no	—
568	C₂×C₄⋊Q₈	—	5	2	no	—
569	C₂×C₄⋊Q₈	—	5	1	no	—
570	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
571	C₂×#127	—	5	1	no	—
572	C₂×#127	—	5	1	no	—
573	#529	—	5	16	no	—
574	#529	—	5	16	no	—
575	C₂×#126	—	5	2	no	—
576	C₂×#126	—	5	2	no	—
577	C₂×#126	—	5	2	no	—
578	C₂×#126	C₂×D₅	1	2	yes	complemented
579	C₂×#125	—	5	2	no	—
580	C₂×#125	—	5	1	no	—
581	C₂×#125	—	5	1	no	—
582	C₂×#124	—	5	1	no	—
583	C₂×#124	—	5	2	no	—
584	C₂×#124	—	5	2	no	—
585	C₂×#124	—	5	2	no	—
586	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
587	C₂×#124	C₂×D₅	1	2	yes	complemented
588	#525	—	5	16	no	—
589	C₂×#123	—	5	2	no	—
590	C₂×#123	—	5	2	no	—
591	C₂×#123	—	5	2	no	—
592	C₂×#123	—	5	2	no	—
593	C₂×#123	—	5	2	no	—
594	C₂×#123	—	5	2	no	—
595	C₂×#123	—	5	2	no	—
596	C₂×#123	—	5	2	no	—
597	C₂×#123	C₂×D₅	1	2	yes	complemented
598	C₂×C₂²⋊Q₈	—	5	2	no	—
599	C₂×C₂²⋊Q₈	—	5	1	no	—
600	C₂×C₂²⋊Q₈	—	5	2	no	—
601	C₂×C₂²⋊Q₈	—	5	2	no	—
602	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
603	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
604	C₂×#121	—	5	1	no	—
605	C₂×#121	—	5	2	no	—
606	C₂×#121	—	5	2	no	—
607	C₂×#121	—	5	2	no	—
608	C₂×#121	—	5	1	no	—
609	C₂×#121	—	5	1	no	—
610	C₂×#121	—	5	16	no	—
611	C₂×#121	—	5	1	no	—
612	C₂×#121	—	5	1	no	—
613	C₂×#121	—	5	2	no	—
614	C₂×#121	—	5	2	no	—
615	C₂×#121	—	5	2	no	—
616	C₂×#121	—	5	2	no	—
617	C₂×#121	—	5	2	no	—
618	C₂×#121	—	5	2	no	—
619	C₂×#121	—	5	2	no	—
620	C₂×#121	C₂×D₅	1	1	yes	characteristic
621	C₂×#120	—	5	2	no	—
622	C₂×#120	—	5	2	no	—
623	C₂×#120	—	5	2	no	—
624	#520	—	5	16	no	—
625	#518	—	5	16	no	—
626	C₂×C₄×Q₈	—	5	1	no	—
627	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
628	C₂×C₄×D₄	—	5	1	no	—
629	C₂×C₄×D₄	—	5	2	no	—
630	C₂×C₄×D₄	—	5	2	no	—
631	C₂×C₄×D₄	—	5	2	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	2	no	—
637	C₂×C₄×D₄	—	5	2	no	—
638	C₂×C₄×D₄	—	5	2	no	—
639	C₂×C₄×D₄	—	5	2	no	—
640	C₂×C₄×D₄	—	5	1	no	—
641	C₂×C₄×D₄	—	5	1	no	—
642	C₂×C₄×D₄	—	5	2	no	—
643	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
644	C₂×#117	—	5	1	no	—
645	C₂×#117	—	5	16	no	—
646	C₂×#117	—	5	1	no	—
647	C₂×#117	—	5	1	no	—
648	C₂×#117	—	5	1	no	—
649	C₂×#117	—	5	1	no	—
650	C₂×#117	—	5	1	no	—
651	C₂×#117	—	5	2	no	—
652	C₂×#117	—	5	1	no	—
653	C₂×#117	—	5	1	no	—
654	C₂×#117	—	5	2	no	—
655	C₂×#117	—	5	2	no	—
656	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
657	C₂²×C₄⋊C₄	—	5	1	no	—
658	C₂²×C₄⋊C₄	—	5	1	no	—
659	C₂²×C₄⋊C₄	—	5	1	no	—
660	C₂²×C₄⋊C₄	—	5	2	no	—
661	C₂²×C₂²⋊C₄	—	5	2	no	—
662	C₂²×C₂²⋊C₄	—	5	1	no	—
663	C₂²×C₂²⋊C₄	—	5	1	no	—
664	C₂²×C₂²⋊C₄	—	5	2	no	—
665	C₂²×C₂²⋊C₄	—	5	2	no	—
666	C₂²×C₄²	—	5	1	no	—
667	C₂²×C₄²	—	5	1	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	C₂⁵	1	2	yes	—
675	C₂³×C₅	C₂⁵	1	4	yes	—
676	C₂³×C₅	C₂⁵	1	1	yes	characteristic
677	C₂²×D₅	—	2	2	no	—
678	C₂²×D₅	—	2	2	no	—
679	C₂²×D₅	—	2	2	no	—
680	C₂²×D₅	—	2	2	no	—
681	C₂²×D₅	—	2	4	no	—
682	C₂²×D₅	—	2	4	no	—
683	C₂²×D₅	—	2	4	no	—
684	C₂²×D₅	—	2	4	no	—
685	C₂²×D₅	—	2	4	no	—
686	C₂²×D₅	—	2	4	no	—
687	C₂²×D₅	—	2	8	no	—
688	C₂²×D₅	—	2	8	no	—
689	C₂²×D₅	—	2	16	no	—
690	C₂²×D₅	—	4	4	no	—
691	C₂²×D₅	—	4	16	no	—
692	C₂²×D₅	—	4	8	no	—
693	C₂²×D₅	—	4	8	no	—
694	C₂²×D₅	—	8	16	no	—
695	C₂²×D₅	C₂×#41	1	4	yes	—
696	C₂²×D₅	H(5,𝔽₂)	1	4	yes	—
697	C₂²×D₅	C₂⁵	1	4	yes	—
698	C₂²×D₅	C₂⁵	1	4	yes	—
699	C₂²×D₅	C₂⁵	1	2	yes	—
700	C₂²×D₅	C₂⁵	1	2	yes	—
701	C₅×Q₈	—	2	8	no	—
702	C₅×Q₈	—	4	8	no	—
703	C₅×D₄	—	2	8	no	—
704	C₅×D₄	—	4	8	no	—
705	C₂×C₄×C₅	—	2	2	no	—
706	C₂×C₄×C₅	—	2	4	no	—
707	C₂×C₄×C₅	—	2	4	no	—
708	C₂×C₄×C₅	—	2	2	no	—
709	C₂×C₄×C₅	—	2	2	no	—
710	C₂×C₄×C₅	—	2	4	no	—
711	C₂×C₄×C₅	—	2	2	no	—
712	C₂×C₄×C₅	—	2	2	no	—
713	C₂×C₄×C₅	—	2	8	no	—
714	C₂×C₄×C₅	—	4	8	no	—
715	C₂×C₄×C₅	C₂×#41	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	4	yes	—
719	C₂×C₄×C₅	C₂⁵	1	2	yes	—
720	C₂×C₄×C₅	C₂⁵	1	2	yes	—
721	C₂×C₄×C₅	C₂⁵	1	4	yes	—
722	C₂×C₄×C₅	C₂⁵	1	4	yes	—
723	C₂×C₄×C₅	C₂⁵	1	2	yes	—
724	C₂×C₄×C₅	C₂⁵	1	2	yes	—
725	C₂²⋊D₅	—	2	16	no	—
726	C₂²⋊D₅	—	2	16	no	—
727	C₂²⋊D₅	—	4	8	no	—
728	C₂²⋊D₅	—	4	8	no	—
729	C₂²⋊D₅	—	4	8	no	—
730	C₂²⋊D₅	—	4	8	no	—
731	C₂×Dic₅	—	2	2	no	—
732	C₂×Dic₅	—	2	2	no	—
733	C₂×Dic₅	—	2	4	no	—
734	C₂×Dic₅	—	2	2	no	—
735	C₂×Dic₅	—	2	2	no	—
736	C₂×Dic₅	—	2	4	no	—
737	C₂×Dic₅	—	2	2	no	—
738	C₂×Dic₅	—	2	8	no	—
739	C₂×Dic₅	—	4	8	no	—
740	C₂×Dic₅	C₂×#41	1	4	yes	—
741	C₂×Dic₅	C₂⁵	1	2	yes	—
742	C₂×Dic₅	C₂⁵	1	2	yes	—
743	C₂×Dic₅	C₂⁵	1	2	yes	—
744	C₂×Dic₅	C₂⁵	1	2	yes	—
745	C₂×Dic₅	C₂⁵	1	2	yes	—
746	C₂×Dic₅	C₂⁵	1	4	yes	—
747	C₂×Dic₅	C₂⁵	1	4	yes	—
748	C₂×Dic₅	C₂⁵	1	2	yes	—
749	D₂₀	—	2	16	no	—
750	D₂₀	—	2	16	no	—
751	D₂₀	—	2	16	no	—
752	D₂₀	—	2	8	no	—
753	D₂₀	—	2	8	no	—
754	D₂₀	—	4	8	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	—	2	8	no	—
760	C₄×D₅	—	2	8	no	—
761	C₄×D₅	—	2	16	no	—
762	C₄×D₅	—	4	4	no	—
763	C₄×D₅	—	4	8	no	—
764	C₄×D₅	—	4	4	no	—
765	C₄×D₅	—	4	8	no	—
766	C₄×D₅	—	4	8	no	—
767	C₄×D₅	—	4	8	no	—
768	C₄×D₅	—	4	8	no	—
769	C₄×D₅	C₂×#41	1	16	yes	complemented
770	Dic₁₀	—	4	8	no	—
771	C₂⁵	—	5	1	no	—
772	C₂⁵	—	5	2	no	—
773	C₂×#41	—	5	8	no	—
774	C₂×#41	—	5	16	no	—
775	C₂×#41	—	5	16	no	—
776	C₂×#41	—	10	8	no	—
777	C₂×#41	—	20	8	no	—
778	C₂×#41	—	20	8	no	—
779	C₂²×Q₈	—	5	2	no	—
780	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
781	C₂²×Q₈	C₂²×D₅	1	2	yes	—
782	C₂²×D₄	—	5	2	no	—
783	C₂²×D₄	—	5	2	no	—
784	C₂²×D₄	—	5	2	no	—
785	C₂²×D₄	—	5	2	no	—
786	C₂²×D₄	—	5	2	no	—
787	C₂²×D₄	—	5	2	no	—
788	C₂²×D₄	—	5	8	no	—
789	C₂²×D₄	—	5	16	no	—
790	C₂²×D₄	—	5	2	no	—
791	C₂²×D₄	—	5	1	no	—
792	C₂²×D₄	—	5	1	no	—
793	C₂²×D₄	—	5	2	no	—
794	C₂²×D₄	—	5	2	no	—
795	C₂²×D₄	—	5	2	no	—
796	C₂²×D₄	—	5	2	no	—
797	C₂²×D₄	—	10	8	no	—
798	C₂²×D₄	—	20	8	no	—
799	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
800	C₂²×D₄	C₂²×D₅	1	2	yes	—
801	C₂³×C₄	—	5	1	no	—
802	C₂³×C₄	—	5	1	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	1	no	—
808	C₂³×C₄	—	5	2	no	—
809	C₂³×C₄	—	5	8	no	—
810	C₂³×C₄	—	5	1	no	—
811	C₂³×C₄	—	5	1	no	—
812	C₂³×C₄	—	5	1	no	—
813	C₂³×C₄	—	5	2	no	—
814	C₂³×C₄	—	5	2	no	—
815	C₂³×C₄	—	5	2	no	—
816	C₂³×C₄	—	5	2	no	—
817	C₂³×C₄	—	5	2	no	—
818	C₂³×C₄	—	10	8	no	—
819	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
820	C₂³×C₄	C₂²×D₅	1	2	yes	—
821	C₄⋊Q₈	—	5	16	no	—
822	C₄⋊Q₈	—	5	8	no	—
823	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
824	#127	—	5	8	no	—
825	#127	—	5	8	no	—
826	#126	—	5	16	no	—
827	#126	—	5	16	no	—
828	#126	—	5	16	no	—
829	#126	C₂²×D₅	1	16	yes	complemented
830	#125	—	5	8	no	—
831	#125	—	5	16	no	—
832	#125	—	5	8	no	—
833	#124	—	5	8	no	—
834	#124	—	5	16	no	—
835	#124	—	5	16	no	—
836	#124	—	5	16	no	—
837	#124	C₂²×D₅	1	8	yes	complemented
838	#124	C₂²×D₅	1	16	yes	complemented
839	#123	—	5	16	no	—
840	#123	—	5	16	no	—
841	#123	—	5	16	no	—
842	#123	—	5	16	no	—
843	#123	—	5	16	no	—
844	#123	—	5	16	no	—
845	#123	—	5	16	no	—
846	#123	—	5	16	no	—
847	#123	C₂²×D₅	1	16	yes	complemented
848	C₂²⋊Q₈	—	5	8	no	—
849	C₂²⋊Q₈	—	5	16	no	—
850	C₂²⋊Q₈	—	5	16	no	—
851	C₂²⋊Q₈	—	5	16	no	—
852	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
853	C₂²⋊Q₈	C₂²×D₅	1	16	yes	complemented
854	#121	—	5	8	no	—
855	#121	—	5	16	no	—
856	#121	—	5	16	no	—
857	#121	—	5	16	no	—
858	#121	—	5	8	no	—
859	#121	—	5	8	no	—
860	#121	—	5	8	no	—
861	#121	—	5	8	no	—
862	#121	—	5	16	no	—
863	#121	—	5	16	no	—
864	#121	—	5	16	no	—
865	#121	—	5	16	no	—
866	#121	—	5	16	no	—
867	#121	—	5	16	no	—
868	#121	—	5	16	no	—
869	#121	C₂²×D₅	1	8	yes	—
870	#120	—	5	16	no	—
871	#120	—	5	16	no	—
872	#120	—	5	16	no	—
873	C₄×Q₈	—	5	8	no	—
874	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
875	C₄×D₄	—	5	8	no	—
876	C₄×D₄	—	5	16	no	—
877	C₄×D₄	—	5	16	no	—
878	C₄×D₄	—	5	8	no	—
879	C₄×D₄	—	5	8	no	—
880	C₄×D₄	—	5	16	no	—
881	C₄×D₄	—	5	16	no	—
882	C₄×D₄	—	5	16	no	—
883	C₄×D₄	—	5	16	no	—
884	C₄×D₄	—	5	16	no	—
885	C₄×D₄	—	5	16	no	—
886	C₄×D₄	—	5	8	no	—
887	C₄×D₄	—	5	8	no	—
888	C₄×D₄	—	5	16	no	—
889	C₄×D₄	—	5	16	no	—
890	C₄×D₄	C₂²×D₅	1	8	yes	complemented
891	#117	—	5	8	no	—
892	#117	—	5	8	no	—
893	#117	—	5	8	no	—
894	#117	—	5	8	no	—
895	#117	—	5	8	no	—
896	#117	—	5	8	no	—
897	#117	—	5	16	no	—
898	#117	—	5	8	no	—
899	#117	—	5	8	no	—
900	#117	—	5	16	no	—
901	#117	—	5	16	no	—
902	#117	C₂²×D₅	1	8	yes	complemented
903	C₂×C₄⋊C₄	—	5	1	no	—
904	C₂×C₄⋊C₄	—	5	2	no	—
905	C₂×C₄⋊C₄	—	5	1	no	—
906	C₂×C₄⋊C₄	—	5	1	no	—
907	C₂×C₄⋊C₄	—	5	1	no	—
908	C₂×C₄⋊C₄	—	5	1	no	—
909	C₂×C₄⋊C₄	—	5	1	no	—
910	C₂×C₄⋊C₄	—	5	1	no	—
911	C₂×C₄⋊C₄	—	5	2	no	—
912	C₂×C₄⋊C₄	—	5	2	no	—
913	C₂×C₄⋊C₄	—	5	1	no	—
914	C₂×C₄⋊C₄	—	5	2	no	—
915	C₂×C₄⋊C₄	—	5	2	no	—
916	C₂×C₄⋊C₄	—	5	2	no	—
917	C₂×C₄⋊C₄	—	5	2	no	—
918	C₂×C₄⋊C₄	—	5	2	no	—
919	C₂×C₄⋊C₄	—	5	8	no	—
920	C₂×C₄⋊C₄	—	5	8	no	—
921	C₂×C₄⋊C₄	—	5	8	no	—
922	C₂×C₄⋊C₄	—	5	16	no	—
923	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
924	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
925	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
926	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
927	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
928	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
929	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
930	C₂×C₂²⋊C₄	—	5	1	no	—
931	C₂×C₂²⋊C₄	—	5	1	no	—
932	C₂×C₂²⋊C₄	—	5	2	no	—
933	C₂×C₂²⋊C₄	—	5	2	no	—
934	C₂×C₂²⋊C₄	—	5	1	no	—
935	C₂×C₂²⋊C₄	—	5	1	no	—
936	C₂×C₂²⋊C₄	—	5	2	no	—
937	C₂×C₂²⋊C₄	—	5	1	no	—
938	C₂×C₂²⋊C₄	—	5	1	no	—
939	C₂×C₂²⋊C₄	—	5	2	no	—
940	C₂×C₂²⋊C₄	—	5	2	no	—
941	C₂×C₂²⋊C₄	—	5	2	no	—
942	C₂×C₂²⋊C₄	—	5	16	no	—
943	C₂×C₂²⋊C₄	—	5	2	no	—
944	C₂×C₂²⋊C₄	—	5	2	no	—
945	C₂×C₂²⋊C₄	—	5	2	no	—
946	C₂×C₂²⋊C₄	—	5	2	no	—
947	C₂×C₂²⋊C₄	—	5	2	no	—
948	C₂×C₂²⋊C₄	—	5	2	no	—
949	C₂×C₂²⋊C₄	—	5	2	no	—
950	C₂×C₂²⋊C₄	—	5	2	no	—
951	C₂×C₂²⋊C₄	—	5	8	no	—
952	C₂×C₂²⋊C₄	—	5	8	no	—
953	C₂×C₂²⋊C₄	—	5	16	no	—
954	C₂×C₂²⋊C₄	—	5	16	no	—
955	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
957	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
958	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
959	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
960	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
961	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
962	C₂×C₄²	—	5	1	no	—
963	C₂×C₄²	—	5	1	no	—
964	C₂×C₄²	—	5	1	no	—
965	C₂×C₄²	—	5	2	no	—
966	C₂×C₄²	—	5	1	no	—
967	C₂×C₄²	—	5	1	no	—
968	C₂×C₄²	—	5	1	no	—
969	C₂×C₄²	—	5	2	no	—
970	C₂×C₄²	—	5	8	no	—
971	C₂×C₄²	—	5	8	no	—
972	C₂×C₄²	C₂²×D₅	1	2	yes	—
973	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
974	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
975	C₂²×C₅	—	2	2	no	—
976	C₂²×C₅	—	2	4	no	—
977	C₂²×C₅	—	2	4	no	—
978	C₂²×C₅	—	2	2	no	—
979	C₂²×C₅	—	2	4	no	—
980	C₂²×C₅	—	2	2	no	—
981	C₂²×C₅	—	4	4	no	—
982	C₂²×C₅	—	4	8	no	—
983	C₂²×C₅	C₂²×#41	1	2	yes	—
984	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
985	C₂²×C₅	#585	1	2	yes	—
986	C₂²×C₅	C₂⁶	1	1	yes	characteristic
987	C₂×D₅	—	2	2	no	—
988	C₂×D₅	—	2	2	no	—
989	C₂×D₅	—	2	2	no	—
990	C₂×D₅	—	2	2	no	—
991	C₂×D₅	—	2	8	no	—
992	C₂×D₅	—	2	8	no	—
993	C₂×D₅	—	2	4	no	—
994	C₂×D₅	—	2	4	no	—
995	C₂×D₅	—	2	4	no	—
996	C₂×D₅	—	2	4	no	—
997	C₂×D₅	—	2	4	no	—
998	C₂×D₅	—	2	4	no	—
999	C₂×D₅	—	4	16	no	—
1000	C₂×D₅	—	4	8	no	—
1001	C₂×D₅	—	4	8	no	—
1002	C₂×D₅	—	8	16	no	—
1003	C₂×D₅	C₂²×#41	1	4	yes	—
1004	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
1005	C₄×C₅	—	2	2	no	—
1006	C₄×C₅	—	2	4	no	—
1007	C₄×C₅	—	2	4	no	—
1008	C₄×C₅	—	2	2	no	—
1009	C₄×C₅	—	2	2	no	—
1010	C₄×C₅	—	2	4	no	—
1011	C₄×C₅	—	2	2	no	—
1012	C₄×C₅	—	2	2	no	—
1013	C₄×C₅	C₂²×#41	1	4	yes	—
1014	Dic₅	—	2	2	no	—
1015	Dic₅	—	2	2	no	—
1016	Dic₅	—	2	4	no	—
1017	Dic₅	—	2	2	no	—
1018	Dic₅	—	2	2	no	—
1019	Dic₅	—	2	4	no	—
1020	Dic₅	—	2	2	no	—
1021	Dic₅	C₂²×#41	1	4	yes	—
1022	C₂⁴	—	5	1	no	—
1023	C₂⁴	—	5	1	no	—
1024	C₂⁴	—	5	2	no	—
1025	C₂⁴	—	5	2	no	—
1026	C₂⁴	—	5	4	no	—
1027	C₂⁴	—	5	8	no	—
1028	C₂⁴	—	10	4	no	—
1029	C₂⁴	—	10	4	no	—
1030	C₂⁴	—	10	8	no	—
1031	C₂⁴	—	20	2	no	—
1032	C₂⁴	—	20	4	no	—
1033	C₂⁴	—	20	4	no	—
1034	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1035	C₂⁴	C₂³×D₅	1	2	yes	—
1036	#41	—	10	32	no	—
1037	#41	—	20	32	no	—
1038	#41	—	20	32	no	—
1039	C₂×Q₈	—	2	4	no	—
1040	C₂×Q₈	—	4	4	no	—
1041	C₂×Q₈	—	5	8	no	—
1042	C₂×Q₈	—	20	4	no	—
1043	C₂×Q₈	C₂³×D₅	1	4	yes	—
1044	C₂×Q₈	C₂³×D₅	1	8	yes	—
1045	C₂×D₄	—	2	4	no	—
1046	C₂×D₄	—	4	4	no	—
1047	C₂×D₄	—	5	8	no	—
1048	C₂×D₄	—	5	8	no	—
1049	C₂×D₄	—	5	8	no	—
1050	C₂×D₄	—	5	8	no	—
1051	C₂×D₄	—	5	8	no	—
1052	C₂×D₄	—	5	8	no	—
1053	C₂×D₄	—	5	8	no	—
1054	C₂×D₄	—	5	4	no	—
1055	C₂×D₄	—	5	4	no	—
1056	C₂×D₄	—	5	8	no	—
1057	C₂×D₄	—	5	8	no	—
1058	C₂×D₄	—	5	8	no	—
1059	C₂×D₄	—	5	8	no	—
1060	C₂×D₄	—	10	8	no	—
1061	C₂×D₄	—	10	8	no	—
1062	C₂×D₄	—	10	8	no	—
1063	C₂×D₄	—	10	32	no	—
1064	C₂×D₄	—	10	8	no	—
1065	C₂×D₄	—	10	8	no	—
1066	C₂×D₄	—	10	4	no	—
1067	C₂×D₄	—	10	4	no	—
1068	C₂×D₄	—	20	4	no	—
1069	C₂×D₄	—	20	4	no	—
1070	C₂×D₄	—	20	4	no	—
1071	C₂×D₄	—	20	4	no	—
1072	C₂×D₄	—	20	4	no	—
1073	C₂×D₄	—	20	4	no	—
1074	C₂×D₄	—	20	32	no	—
1075	C₂×D₄	C₂³×D₅	1	4	yes	—
1076	C₂×D₄	C₂³×D₅	1	8	yes	—
1077	C₂²×C₄	—	2	4	no	—
1078	C₂²×C₄	—	4	4	no	—
1079	C₂²×C₄	—	5	1	no	—
1080	C₂²×C₄	—	5	8	no	—
1081	C₂²×C₄	—	5	4	no	—
1082	C₂²×C₄	—	5	4	no	—
1083	C₂²×C₄	—	5	1	no	—
1084	C₂²×C₄	—	5	1	no	—
1085	C₂²×C₄	—	5	1	no	—
1086	C₂²×C₄	—	5	1	no	—
1087	C₂²×C₄	—	5	1	no	—
1088	C₂²×C₄	—	5	2	no	—
1089	C₂²×C₄	—	5	2	no	—
1090	C₂²×C₄	—	5	8	no	—
1091	C₂²×C₄	—	5	4	no	—
1092	C₂²×C₄	—	5	4	no	—
1093	C₂²×C₄	—	5	4	no	—
1094	C₂²×C₄	—	5	4	no	—
1095	C₂²×C₄	—	5	4	no	—
1096	C₂²×C₄	—	5	8	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	—	5	8	no	—
1102	C₂²×C₄	—	5	8	no	—
1103	C₂²×C₄	—	5	8	no	—
1104	C₂²×C₄	—	10	4	no	—
1105	C₂²×C₄	—	10	32	no	—
1106	C₂²×C₄	—	10	8	no	—
1107	C₂²×C₄	—	10	4	no	—
1108	C₂²×C₄	—	10	4	no	—
1109	C₂²×C₄	—	10	4	no	—
1110	C₂²×C₄	—	10	4	no	—
1111	C₂²×C₄	—	10	4	no	—
1112	C₂²×C₄	—	20	4	no	—
1113	C₂²×C₄	—	20	4	no	—
1114	C₂²×C₄	—	20	4	no	—
1115	C₂²×C₄	—	20	4	no	—
1116	C₂²×C₄	—	20	4	no	—
1117	C₂²×C₄	—	20	2	no	—
1118	C₂²×C₄	—	20	2	no	—
1119	C₂²×C₄	—	20	4	no	—
1120	C₂²×C₄	C₂³×D₅	1	4	yes	—
1121	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1122	C₂²×C₄	C₂³×D₅	1	2	yes	—
1123	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1124	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅	1	2	yes	—
1127	C₂²×C₄	C₂³×D₅	1	2	yes	—
1128	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1129	C₂²×C₄	C₂³×D₅	1	8	yes	—
1130	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1131	C₄⋊C₄	—	5	4	no	—
1132	C₄⋊C₄	—	5	8	no	—
1133	C₄⋊C₄	—	5	4	no	—
1134	C₄⋊C₄	—	5	4	no	—
1135	C₄⋊C₄	—	5	4	no	—
1136	C₄⋊C₄	—	5	4	no	—
1137	C₄⋊C₄	—	5	4	no	—
1138	C₄⋊C₄	—	5	4	no	—
1139	C₄⋊C₄	—	5	8	no	—
1140	C₄⋊C₄	—	5	8	no	—
1141	C₄⋊C₄	—	5	4	no	—
1142	C₄⋊C₄	—	5	8	no	—
1143	C₄⋊C₄	—	5	8	no	—
1144	C₄⋊C₄	—	5	8	no	—
1145	C₄⋊C₄	—	5	8	no	—
1146	C₄⋊C₄	—	5	8	no	—
1147	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1148	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1149	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1150	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1151	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1152	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1153	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1154	C₂²⋊C₄	—	5	4	no	—
1155	C₂²⋊C₄	—	5	4	no	—
1156	C₂²⋊C₄	—	5	8	no	—
1157	C₂²⋊C₄	—	5	8	no	—
1158	C₂²⋊C₄	—	5	4	no	—
1159	C₂²⋊C₄	—	5	4	no	—
1160	C₂²⋊C₄	—	5	8	no	—
1161	C₂²⋊C₄	—	5	4	no	—
1162	C₂²⋊C₄	—	5	4	no	—
1163	C₂²⋊C₄	—	5	8	no	—
1164	C₂²⋊C₄	—	5	8	no	—
1165	C₂²⋊C₄	—	5	8	no	—
1166	C₂²⋊C₄	—	5	8	no	—
1167	C₂²⋊C₄	—	5	8	no	—
1168	C₂²⋊C₄	—	5	8	no	—
1169	C₂²⋊C₄	—	5	8	no	—
1170	C₂²⋊C₄	—	5	8	no	—
1171	C₂²⋊C₄	—	5	8	no	—
1172	C₂²⋊C₄	—	5	8	no	—
1173	C₂²⋊C₄	—	5	8	no	—
1174	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1175	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1176	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1177	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1178	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1179	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1180	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1181	C₄²	—	5	4	no	—
1182	C₄²	—	5	4	no	—
1183	C₄²	—	5	4	no	—
1184	C₄²	—	5	4	no	—
1185	C₄²	—	5	4	no	—
1186	C₄²	—	5	4	no	—
1187	C₄²	—	5	8	no	—
1188	C₄²	—	5	8	no	—
1189	C₄²	C₂³×D₅	1	4	yes	—
1190	C₄²	C₂³×D₅	1	4	yes	—
1191	C₄²	C₂³×D₅	1	8	yes	—
1192	C₂×C₅	—	4	2	no	—
1193	C₂×C₅	—	4	4	no	—
1194	C₂×C₅	#3494	1	4	yes	complemented
1195	C₂×C₅	C₂³×#41	1	1	yes	characteristic
1196	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1197	C₂×C₅	C₂×#585	1	1	yes	characteristic
1198	D₅	—	2	4	no	—
1199	D₅	—	2	4	no	—
1200	D₅	—	4	4	no	—
1201	D₅	—	4	4	no	—
1202	C₂³	—	2	2	no	—
1203	C₂³	—	2	4	no	—
1204	C₂³	—	2	4	no	—
1205	C₂³	—	2	2	no	—
1206	C₂³	—	2	4	no	—
1207	C₂³	—	2	2	no	—
1208	C₂³	—	5	4	no	—
1209	C₂³	—	5	4	no	—
1210	C₂³	—	5	2	no	—
1211	C₂³	—	5	2	no	—
1212	C₂³	—	5	4	no	—
1213	C₂³	—	5	4	no	—
1214	C₂³	—	10	8	no	—
1215	C₂³	—	10	8	no	—
1216	C₂³	—	10	16	no	—
1217	C₂³	—	10	2	no	—
1218	C₂³	—	10	2	no	—
1219	C₂³	—	10	2	no	—
1220	C₂³	—	10	2	no	—
1221	C₂³	—	10	4	no	—
1222	C₂³	—	10	4	no	—
1223	C₂³	—	10	4	no	—
1224	C₂³	—	10	4	no	—
1225	C₂³	—	10	4	no	—
1226	C₂³	—	10	4	no	—
1227	C₂³	—	20	4	no	—
1228	C₂³	—	20	8	no	—
1229	C₂³	—	20	8	no	—
1230	C₂³	—	20	16	no	—
1231	C₂³	—	40	16	no	—
1232	C₂³	C₂⁴×D₅	1	2	yes	—
1233	C₂³	C₂⁴×D₅	1	4	yes	—
1234	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1235	Q₈	—	2	8	no	—
1236	Q₈	—	4	8	no	—
1237	Q₈	—	20	8	no	—
1238	D₄	—	2	8	no	—
1239	D₄	—	4	8	no	—
1240	D₄	—	10	16	no	—
1241	D₄	—	10	16	no	—
1242	D₄	—	10	16	no	—
1243	D₄	—	10	16	no	—
1244	D₄	—	10	16	no	—
1245	D₄	—	10	8	no	—
1246	D₄	—	10	8	no	—
1247	D₄	—	20	8	no	—
1248	D₄	—	20	8	no	—
1249	D₄	—	20	8	no	—
1250	D₄	—	20	8	no	—
1251	D₄	—	20	8	no	—
1252	D₄	—	20	8	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	4	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	4	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	2	4	no	—
1259	C₂×C₄	—	2	2	no	—
1260	C₂×C₄	—	2	2	no	—
1261	C₂×C₄	—	2	8	no	—
1262	C₂×C₄	—	4	8	no	—
1263	C₂×C₄	—	5	4	no	—
1264	C₂×C₄	—	5	2	no	—
1265	C₂×C₄	—	5	16	no	—
1266	C₂×C₄	—	5	2	no	—
1267	C₂×C₄	—	5	2	no	—
1268	C₂×C₄	—	5	2	no	—
1269	C₂×C₄	—	5	2	no	—
1270	C₂×C₄	—	5	2	no	—
1271	C₂×C₄	—	5	4	no	—
1272	C₂×C₄	—	5	4	no	—
1273	C₂×C₄	—	10	8	no	—
1274	C₂×C₄	—	10	16	no	—
1275	C₂×C₄	—	10	8	no	—
1276	C₂×C₄	—	10	8	no	—
1277	C₂×C₄	—	10	8	no	—
1278	C₂×C₄	—	10	8	no	—
1279	C₂×C₄	—	10	2	no	—
1280	C₂×C₄	—	10	2	no	—
1281	C₂×C₄	—	10	2	no	—
1282	C₂×C₄	—	10	4	no	—
1283	C₂×C₄	—	10	2	no	—
1284	C₂×C₄	—	10	4	no	—
1285	C₂×C₄	—	10	2	no	—
1286	C₂×C₄	—	10	8	no	—
1287	C₂×C₄	—	20	8	no	—
1288	C₂×C₄	—	20	8	no	—
1289	C₂×C₄	—	20	8	no	—
1290	C₂×C₄	—	20	8	no	—
1291	C₂×C₄	—	20	8	no	—
1292	C₂×C₄	—	20	4	no	—
1293	C₂×C₄	—	20	4	no	—
1294	C₂×C₄	—	20	8	no	—
1295	C₂×C₄	D₅×#41	1	4	yes	—
1296	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1297	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1298	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1299	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1300	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1301	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1302	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1303	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1304	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1305	C₅	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
1306	C₂²	—	2	2	no	—
1307	C₂²	—	2	4	no	—
1308	C₂²	—	2	4	no	—
1309	C₂²	—	2	2	no	—
1310	C₂²	—	2	4	no	—
1311	C₂²	—	2	2	no	—
1312	C₂²	—	4	4	no	—
1313	C₂²	—	4	8	no	—
1314	C₂²	—	5	4	no	—
1315	C₂²	—	5	4	no	—
1316	C₂²	—	10	2	no	—
1317	C₂²	—	10	2	no	—
1318	C₂²	—	10	2	no	—
1319	C₂²	—	10	2	no	—
1320	C₂²	—	10	8	no	—
1321	C₂²	—	10	8	no	—
1322	C₂²	—	10	4	no	—
1323	C₂²	—	10	4	no	—
1324	C₂²	—	10	4	no	—
1325	C₂²	—	10	4	no	—
1326	C₂²	—	10	4	no	—
1327	C₂²	—	10	4	no	—
1328	C₂²	—	20	16	no	—
1329	C₂²	—	20	8	no	—
1330	C₂²	—	20	8	no	—
1331	C₂²	—	40	16	no	—
1332	C₂²	C₂×D₅×#41	1	2	yes	—
1333	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
1334	C₂²	#66287	1	2	yes	—
1335	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1336	C₄	—	2	2	no	—
1337	C₄	—	2	4	no	—
1338	C₄	—	2	2	no	—
1339	C₄	—	2	4	no	—
1340	C₄	—	2	2	no	—
1341	C₄	—	2	4	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	—	5	4	no	—
1345	C₄	—	10	2	no	—
1346	C₄	—	10	2	no	—
1347	C₄	—	10	2	no	—
1348	C₄	—	10	4	no	—
1349	C₄	—	10	2	no	—
1350	C₄	—	10	4	no	—
1351	C₄	—	10	2	no	—
1352	C₄	C₂×D₅×#41	1	4	yes	—
1353	C₂	—	4	2	no	—
1354	C₂	—	4	4	no	—
1355	C₂	—	10	4	no	—
1356	C₂	—	10	4	no	—
1357	C₂	—	20	4	no	—
1358	C₂	—	20	4	no	—
1359	C₂	#10618451	1	4	yes	direct product factor
1360	C₂	C₂²×D₅×#41	1	1	yes	characteristic
1361	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic
1362	C₂	C₂×#66287	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#542	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#542	D₅
hypocenter	C₅	C₂×#3494
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#542	C₂	semidirect
2. #10618451	C₂	direct (N × H)
3. C₂×#66063	C₂	semidirect
4. C₂×#66059	C₂	semidirect
5. C₂×#66039	C₂	semidirect
6. C₂×#66043	C₂	semidirect
7. C₂×#66010	C₂	semidirect
8. C₂×#66008	C₂	semidirect
9. C₂×#66004	C₂	semidirect
10. C₂×#66014	C₂	semidirect
11. C₂×#65988	C₂	semidirect
12. C₂×#65995	C₂	semidirect
13. C₂×#65971	C₂	semidirect
14. C₂×#65965	C₂	semidirect
15. C₂×#65977	C₂	semidirect
16. C₂×#65961	C₂	semidirect
17. C₂×D₅×#121	C₂	semidirect
18. C₂×#65953	C₂	semidirect
19. C₂×#65914	C₂	semidirect
20. C₂×#65908	C₂	semidirect
21. C₂×#65882	C₂	semidirect
22. C₂×#65879	C₂	semidirect
23. C₂×#65869	C₂	semidirect
24. C₂×D₅×#117	C₂	semidirect
26. C₂²×#713	C₂²	semidirect
29. C₂²×#709	C₂²	semidirect
31. C₅×#542	C₂²	semidirect
32. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₅×#126	C₂²	semidirect
34. C₂×C₅×#124	C₂²	semidirect
35. C₂×C₅×#124	C₂²	semidirect
36. C₂×C₅×#123	C₂²	semidirect
37. C₂×C₅×C₂²⋊Q₈	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×C₅×#117	C₂²	semidirect
43. C₂×#4093	C₂²	semidirect
44. C₂×#4093	C₂²	semidirect
46. C₂×#4092	C₂²	semidirect
47. C₂×Q₈×Dic₅	C₂²	semidirect
48. C₂×#4090	C₂²	semidirect
49. C₂×#4086	C₂²	semidirect
51. C₂×#4085	C₂²	semidirect
53. C₂×#4084	C₂²	semidirect
54. C₂×D₄×Dic₅	C₂²	semidirect
56. C₂×#4076	C₂²	semidirect
57. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
58. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
60. C₂×#4072	C₂²	semidirect
61. #66063	C₂²	semidirect
62. #66059	C₂²	semidirect
63. #66043	C₂²	semidirect
64. #66039	C₂²	semidirect
65. #66014	C₂²	semidirect
66. #66010	C₂²	semidirect
67. #66008	C₂²	semidirect
68. #66004	C₂²	semidirect
69. #65995	C₂²	semidirect
70. #65988	C₂²	semidirect
71. #65977	C₂²	semidirect
72. #65971	C₂²	semidirect
73. #65965	C₂²	semidirect
74. #65961	C₂²	semidirect
75. #65953	C₂²	semidirect
76. D₅×#121	C₂²	semidirect
77. #65914	C₂²	semidirect
78. #65908	C₂²	semidirect
79. #65882	C₂²	semidirect
80. #65879	C₂²	semidirect
81. #65869	C₂²	semidirect
82. D₅×#117	C₂²	semidirect
83. C₂×#4044	C₂²	semidirect
84. C₂×#4044	C₂²	semidirect
85. C₂×#4043	C₂²	semidirect
88. C₂×#4041	C₂²	semidirect
89. C₂×#4041	C₂²	semidirect
91. C₂×#4040	C₂²	semidirect
92. C₂×#4040	C₂²	semidirect
93. C₂×#4040	C₂²	semidirect
95. C₂×#4039	C₂²	semidirect
96. C₂×#4039	C₂²	semidirect
97. C₂×#4039	C₂²	semidirect
98. C₂×#4039	C₂²	semidirect
103. C₂×D₅×C₄⋊C₄	C₂²	semidirect
104. C₂×D₅×C₄⋊C₄	C₂²	semidirect
105. C₂×D₅×C₄⋊C₄	C₂²	semidirect
106. C₂×#4036	C₂²	semidirect
107. C₂×#4035	C₂²	semidirect
108. C₂×#4034	C₂²	semidirect
109. C₂×#4032	C₂²	semidirect
110. C₂×#4031	C₂²	semidirect
111. C₂×#4031	C₂²	semidirect
113. C₂×#4030	C₂²	semidirect
114. C₂×#4030	C₂²	semidirect
115. C₂×#4030	C₂²	semidirect
116. C₂×#4030	C₂²	semidirect
117. C₂×#4030	C₂²	semidirect
118. C₂×#4029	C₂²	semidirect
119. C₂×#4029	C₂²	semidirect
120. C₂×#4029	C₂²	semidirect
124. C₂×#4027	C₂²	semidirect
125. C₂×#4027	C₂²	semidirect
126. C₂×#4027	C₂²	semidirect
131. C₂×#4025	C₂²	semidirect
132. C₂×#4023	C₂²	semidirect
133. C₂×#4023	C₂²	semidirect
134. C₂×#4023	C₂²	semidirect
135. C₂×#4020	C₂²	semidirect
137. C₂×C₄×D₂₀	C₂²	semidirect
138. C₂×C₄×D₂₀	C₂²	semidirect
139. C₂×C₄×D₂₀	C₂²	semidirect
142. C₂×#4018	C₂²	semidirect
143. C₂×#4018	C₂²	semidirect
144. C₂×C₄²×D₅	C₂²	semidirect
145. C₂×C₄²×D₅	C₂²	semidirect
146. C₂×#4016	C₂²	semidirect
167. C₂×#713	C₂³	semidirect
173. C₂×#709	C₂³	semidirect
198. C₅×C₄⋊Q₈	C₂³	semidirect
199. C₅×#126	C₂³	semidirect
200. C₅×#124	C₂³	semidirect
201. C₅×#124	C₂³	semidirect
202. C₅×#123	C₂³	semidirect
203. C₅×C₂²⋊Q₈	C₂³	semidirect
204. C₅×C₂²⋊Q₈	C₂³	semidirect
206. C₄×C₅×Q₈	C₂³	semidirect
207. C₄×C₅×D₄	C₂³	semidirect
208. C₅×#117	C₂³	semidirect
230. #4093	C₂³	semidirect
231. #4093	C₂³	semidirect
233. #4092	C₂³	semidirect
234. Q₈×Dic₅	C₂³	semidirect
235. #4090	C₂³	semidirect
236. #4086	C₂³	semidirect
238. #4085	C₂³	semidirect
240. #4084	C₂³	semidirect
241. D₄×Dic₅	C₂³	semidirect
243. #4076	C₂³	semidirect
244. C₄×C₂²⋊D₅	C₂³	semidirect
245. C₄×C₂²⋊D₅	C₂³	semidirect
263. #4072	C₂³	semidirect
288. #4044	C₂³	semidirect
289. #4044	C₂³	semidirect
290. #4043	C₂³	semidirect
293. #4041	C₂³	semidirect
294. #4041	C₂³	semidirect
296. #4040	C₂³	semidirect
297. #4040	C₂³	semidirect
298. #4040	C₂³	semidirect
300. #4039	C₂³	semidirect
301. #4039	C₂³	semidirect
302. #4039	C₂³	semidirect
303. #4039	C₂³	semidirect
308. D₅×C₄⋊C₄	C₂³	semidirect
309. D₅×C₄⋊C₄	C₂³	semidirect
310. D₅×C₄⋊C₄	C₂³	semidirect
311. #4036	C₂³	semidirect
312. #4035	C₂³	semidirect
313. #4034	C₂³	semidirect
314. #4032	C₂³	semidirect
315. #4031	C₂³	semidirect
316. #4031	C₂³	semidirect
318. #4030	C₂³	semidirect
319. #4030	C₂³	semidirect
320. #4030	C₂³	semidirect
321. #4030	C₂³	semidirect
322. #4030	C₂³	semidirect
323. #4029	C₂³	semidirect
324. #4029	C₂³	semidirect
325. #4029	C₂³	semidirect
329. #4027	C₂³	semidirect
330. #4027	C₂³	semidirect
331. #4027	C₂³	semidirect
336. #4025	C₂³	semidirect
337. #4023	C₂³	semidirect
338. #4023	C₂³	semidirect
339. #4023	C₂³	semidirect
340. #4020	C₂³	semidirect
342. C₄×D₂₀	C₂³	semidirect
343. C₄×D₂₀	C₂³	semidirect
344. C₄×D₂₀	C₂³	semidirect
347. #4018	C₂³	semidirect
348. #4018	C₂³	semidirect
349. C₄²×D₅	C₂³	semidirect
350. C₄²×D₅	C₂³	semidirect
351. #4016	C₂³	semidirect
363. C₂×#542	D₅	semidirect
468. C₂×C₄×D₅	#41	semidirect
562. #542	C₂×D₅	semidirect
570. C₂×C₄⋊Q₈	C₂×D₅	semidirect
578. C₂×#126	C₂×D₅	semidirect
586. C₂×#124	C₂×D₅	semidirect
587. C₂×#124	C₂×D₅	semidirect
597. C₂×#123	C₂×D₅	semidirect
602. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
603. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
627. C₂×C₄×Q₈	C₂×D₅	semidirect
643. C₂×C₄×D₄	C₂×D₅	semidirect
656. C₂×#117	C₂×D₅	semidirect
769. C₄×D₅	C₂×#41	semidirect
823. C₄⋊Q₈	C₂²×D₅	semidirect
829. #126	C₂²×D₅	semidirect
837. #124	C₂²×D₅	semidirect
838. #124	C₂²×D₅	semidirect
847. #123	C₂²×D₅	semidirect
852. C₂²⋊Q₈	C₂²×D₅	semidirect
853. C₂²⋊Q₈	C₂²×D₅	semidirect
874. C₄×Q₈	C₂²×D₅	semidirect
890. C₄×D₄	C₂²×D₅	semidirect
902. #117	C₂²×D₅	semidirect
1194. C₂×C₅	#3494	semidirect
1305. C₅	C₂×#3494	semidirect
1359. C₂	#10618451	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×#542	2
#10618451	2
C₂×#66063	2
C₂×#66059	2
C₂×#66039	2
C₂×#66043	2
C₂×#66010	2
C₂×#66008	2
C₂×#66004	2
C₂×#66014	2
C₂×#65988	2
C₂×#65995	2
C₂×#65971	2
C₂×#65965	2
C₂×#65977	2
C₂×#65961	2
C₂×D₅×#121	2
C₂×#65953	2
C₂×#65914	2
C₂×#65908	2
C₂×#65882	2
C₂×#65879	2
C₂×#65869	2
C₂×D₅×#117	2
C₂×#3494	5

Subgroups — C2×#10618451 #13007645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618451 #13007645