Subgroups — C₂×#10618658 #13006649

Order 1280.

7258 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#66150	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#4093	C₂	1	1	yes	maximal, characteristic, complemented
6	#10618658	C₂	1	32	yes	maximal, direct product factor
7	C₂×#66069	C₂	1	2	yes	maximal, complemented
8	C₂×#66067	C₂	1	2	yes	maximal, complemented
9	C₂×#66058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66066	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65981	C₂	1	2	yes	maximal, complemented
12	C₂×#65971	C₂	1	2	yes	maximal, complemented
13	C₂×#65967	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#65964	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#65968	C₂	1	2	yes	maximal, complemented
16	C₂×#65974	C₂	1	2	yes	maximal, complemented
17	C₂×#65977	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65956	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#65916	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#65902	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#65890	C₂	1	2	yes	maximal, complemented
22	C₂×#65884	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#65894	C₂	1	2	yes	maximal, complemented
24	C₂×#65872	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#713	C₂²	1	1	yes	characteristic
28	C₂²×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#709	C₂²	1	1	yes	characteristic
30	C₂³×D₂₀	C₂²	1	1	yes	characteristic
31	C₅×D₄×Q₈	C₂²	1	16	yes	complemented
32	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
41	#66151	C₂²	1	16	yes	complemented
42	#66150	C₂²	1	16	yes	complemented
43	Q₈×C₂²⋊D₅	C₂²	1	16	yes	complemented
44	C₂×#4093	C₂²	1	2	yes	—
45	C₂×#4093	C₂²	1	1	yes	characteristic
46	C₂×#4093	C₂²	1	2	yes	—
47	C₂×#4093	C₂²	1	1	yes	characteristic
48	C₂×#4093	C₂²	1	1	yes	characteristic
49	C₂×#4093	C₂²	1	1	yes	characteristic
50	C₂×#4093	C₂²	1	1	yes	characteristic
51	C₂×#4093	C₂²	1	16	yes	complemented
52	C₂×#4093	C₂²	1	2	yes	complemented
53	C₂×#4092	C₂²	1	2	yes	complemented
54	C₂×#4092	C₂²	1	2	yes	complemented
55	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
56	C₂×#4092	C₂²	1	2	yes	complemented
57	C₂×#4092	C₂²	1	2	yes	complemented
58	C₂×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	C₂×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
60	C₂×#4090	C₂²	1	1	yes	characteristic, complemented
61	C₂×#4090	C₂²	1	2	yes	complemented
62	C₂×#4090	C₂²	1	1	yes	characteristic, complemented
63	C₂×#4085	C₂²	1	1	yes	characteristic
64	C₂×#4083	C₂²	1	2	yes	—
65	C₂×#4081	C₂²	1	1	yes	characteristic
66	C₂×#4076	C₂²	1	1	yes	characteristic
67	C₂×#4076	C₂²	1	2	yes	complemented
68	C₂×#4075	C₂²	1	2	yes	complemented
69	C₂×#4075	C₂²	1	2	yes	complemented
70	C₂×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
71	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
72	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
73	C₂×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
74	C₂²×#685	C₂²	1	2	yes	—
75	C₂²×#685	C₂²	1	2	yes	—
76	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
77	C₂×#4070	C₂²	1	1	yes	characteristic
78	C₂×#4070	C₂²	1	2	yes	—
79	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
80	#66069	C₂²	1	32	yes	complemented
81	#66067	C₂²	1	32	yes	complemented
82	#66066	C₂²	1	16	yes	complemented
83	#66058	C₂²	1	16	yes	complemented
84	#65981	C₂²	1	32	yes	complemented
85	#65977	C₂²	1	16	yes	complemented
86	#65974	C₂²	1	32	yes	complemented
87	#65971	C₂²	1	32	yes	complemented
88	#65968	C₂²	1	32	yes	complemented
89	#65967	C₂²	1	16	yes	complemented
90	#65964	C₂²	1	16	yes	complemented
91	#65956	C₂²	1	16	yes	complemented
92	#65916	C₂²	1	16	yes	complemented
93	#65902	C₂²	1	16	yes	complemented
94	#65894	C₂²	1	32	yes	complemented
95	#65890	C₂²	1	32	yes	complemented
96	#65884	C₂²	1	16	yes	complemented
97	#65872	C₂²	1	16	yes	complemented
98	C₂×#4044	C₂²	1	2	yes	complemented
99	C₂×#4044	C₂²	1	2	yes	complemented
100	C₂×#4044	C₂²	1	2	yes	complemented
101	C₂×#4044	C₂²	1	1	yes	characteristic, complemented
102	C₂×#4044	C₂²	1	2	yes	complemented
103	C₂×#4043	C₂²	1	2	yes	complemented
104	C₂×#4043	C₂²	1	2	yes	complemented
105	C₂×#4042	C₂²	1	2	yes	complemented
106	C₂×#4042	C₂²	1	2	yes	complemented
107	C₂×#4042	C₂²	1	2	yes	complemented
108	C₂×#4042	C₂²	1	2	yes	complemented
109	C₂×#4042	C₂²	1	2	yes	complemented
110	C₂×#4041	C₂²	1	1	yes	characteristic
111	C₂×#4041	C₂²	1	2	yes	—
112	C₂×#4040	C₂²	1	2	yes	—
113	C₂×#4040	C₂²	1	2	yes	—
114	C₂×#4040	C₂²	1	2	yes	complemented
115	C₂×#4040	C₂²	1	2	yes	complemented
116	C₂×#4040	C₂²	1	2	yes	complemented
117	C₂×#4039	C₂²	1	1	yes	characteristic
118	C₂×#4039	C₂²	1	2	yes	complemented
119	C₂×#4038	C₂²	1	2	yes	complemented
120	C₂×#4035	C₂²	1	2	yes	complemented
121	C₂×#4035	C₂²	1	1	yes	characteristic, complemented
122	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
123	C₂×#4033	C₂²	1	2	yes	complemented
124	C₂×#4033	C₂²	1	1	yes	characteristic, complemented
125	C₂×#4032	C₂²	1	1	yes	characteristic
126	C₂×#4031	C₂²	1	2	yes	complemented
127	C₂×#4031	C₂²	1	2	yes	complemented
128	C₂×#4031	C₂²	1	1	yes	characteristic, complemented
129	C₂×#4030	C₂²	1	2	yes	—
130	C₂×#4030	C₂²	1	2	yes	complemented
131	C₂×#4029	C₂²	1	2	yes	complemented
132	C₂×#4028	C₂²	1	2	yes	—
133	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
134	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
135	C₂×#4025	C₂²	1	1	yes	characteristic, complemented
136	C₂×#4024	C₂²	1	2	yes	—
137	C₂×#4024	C₂²	1	1	yes	characteristic
138	C₂×#4023	C₂²	1	2	yes	—
139	C₂×#4022	C₂²	1	2	yes	complemented
140	C₂×#4022	C₂²	1	2	yes	complemented
141	C₂×#4021	C₂²	1	1	yes	characteristic
142	C₂×#4021	C₂²	1	2	yes	complemented
143	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
144	C₂×#4018	C₂²	1	1	yes	characteristic, complemented
145	C₂×#4018	C₂²	1	2	yes	complemented
146	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
147	C₂×#3561	—	5	1	no	maximal, Sylow
148	C₂⁴×D₅	C₂³	1	2	yes	—
149	C₂²×C₅×Q₈	—	4	4	no	—
150	C₂²×C₅×Q₈	—	4	4	no	—
151	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₅×Q₈	C₂³	1	2	yes	—
155	C₂²×C₅×Q₈	C₂³	1	2	yes	—
156	C₂²×C₅×Q₈	C₂³	1	8	yes	—
157	C₂²×C₅×Q₈	C₂³	1	8	yes	complemented
158	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
160	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₅	C₂³	1	2	yes	—
162	C₂³×C₄×C₅	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	2	yes	—
166	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
167	C₂³×Dic₅	C₂³	1	1	yes	characteristic
168	C₂³×Dic₅	C₂³	1	1	yes	characteristic
169	C₂×#713	—	4	4	no	—
170	C₂×#713	C₂³	1	8	yes	—
171	C₂×Q₈×D₅	—	4	4	no	—
172	C₂×Q₈×D₅	C₂³	1	8	yes	complemented
173	C₂×#709	—	4	4	no	—
174	C₂×#709	C₂³	1	8	yes	—
175	C₂²×D₂₀	—	4	4	no	—
176	C₂²×D₂₀	C₂³	1	1	yes	characteristic
177	C₂²×D₂₀	C₂³	1	1	yes	characteristic
178	C₂²×D₂₀	C₂³	1	2	yes	—
179	C₂²×D₂₀	C₂³	1	2	yes	—
180	C₂²×D₂₀	C₂³	1	2	yes	—
181	C₂²×D₂₀	C₂³	1	8	yes	—
182	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₅	C₂³	1	2	yes	—
184	C₂²×C₄×D₅	C₂³	1	2	yes	—
185	C₂²×C₄×D₅	C₂³	1	2	yes	—
186	C₂²×C₄×D₅	C₂³	1	2	yes	—
187	C₂²×C₄×D₅	C₂³	1	2	yes	—
188	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀	C₂³	1	2	yes	—
191	C₂²×Dic₁₀	C₂³	1	2	yes	—
192	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
193	C₅×C₄⋊Q₈	C₂³	1	16	yes	complemented
194	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
195	C₅×C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
197	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
199	C₄×C₅×D₄	C₂³	1	8	yes	—
200	C₄×C₅×D₄	C₂³	1	16	yes	—
201	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅	C₂³	1	2	yes	—
214	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
215	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
219	#4093	C₂³	1	8	yes	—
220	#4093	C₂³	1	8	yes	—
221	#4093	C₂³	1	8	yes	—
222	#4093	C₂³	1	16	yes	—
223	#4093	C₂³	1	16	yes	—
224	#4093	C₂³	1	8	yes	—
225	#4093	C₂³	1	8	yes	—
226	#4093	C₂³	1	16	yes	complemented
227	#4092	C₂³	1	16	yes	complemented
228	#4092	C₂³	1	16	yes	complemented
229	#4092	C₂³	1	16	yes	complemented
230	#4092	C₂³	1	16	yes	complemented
231	#4092	C₂³	1	8	yes	complemented
232	Q₈×Dic₅	C₂³	1	8	yes	complemented
233	Q₈×Dic₅	C₂³	1	8	yes	complemented
234	#4090	C₂³	1	8	yes	complemented
235	#4090	C₂³	1	16	yes	complemented
236	#4090	C₂³	1	8	yes	complemented
237	#4085	C₂³	1	8	yes	—
238	#4083	C₂³	1	16	yes	—
239	#4081	C₂³	1	8	yes	—
240	#4076	C₂³	1	8	yes	—
241	#4076	C₂³	1	16	yes	complemented
242	#4075	C₂³	1	16	yes	complemented
243	#4075	C₂³	1	16	yes	complemented
244	C₄×C₂²⋊D₅	C₂³	1	8	yes	—
245	C₄×C₂²⋊D₅	C₂³	1	16	yes	—
246	C₄×C₂²⋊D₅	C₂³	1	8	yes	complemented
247	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
248	C₂×#685	C₂³	1	2	yes	—
249	C₂×#685	C₂³	1	1	yes	characteristic
250	C₂×#685	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
268	C₂×#685	C₂³	1	1	yes	characteristic
269	C₂×#685	C₂³	1	16	yes	—
270	C₂×#685	C₂³	1	16	yes	—
271	#4072	C₂³	1	8	yes	complemented
272	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
275	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
277	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
278	#4070	C₂³	1	8	yes	—
279	#4070	C₂³	1	16	yes	—
280	C₂×#683	C₂³	1	1	yes	characteristic
281	C₂×#683	C₂³	1	1	yes	characteristic
282	C₂×#683	C₂³	1	1	yes	characteristic
283	C₂×#683	C₂³	1	1	yes	characteristic
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×#683	C₂³	1	2	yes	—
290	C₂×#683	C₂³	1	2	yes	—
291	C₂×#683	C₂³	1	1	yes	characteristic
292	C₂×#683	C₂³	1	1	yes	characteristic
293	C₂×#683	C₂³	1	2	yes	—
294	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₅	C₂³	1	2	yes	—
297	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅	C₂³	1	2	yes	—
299	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅	C₂³	1	2	yes	—
302	C₂×C₄×Dic₅	C₂³	1	8	yes	—
303	#4044	C₂³	1	16	yes	complemented
304	#4044	C₂³	1	16	yes	complemented
305	#4044	C₂³	1	8	yes	complemented
306	#4044	C₂³	1	16	yes	complemented
307	#4044	C₂³	1	16	yes	complemented
308	#4043	C₂³	1	16	yes	complemented
309	#4043	C₂³	1	16	yes	complemented
310	#4042	C₂³	1	16	yes	complemented
311	#4042	C₂³	1	16	yes	complemented
312	#4042	C₂³	1	16	yes	complemented
313	#4042	C₂³	1	16	yes	complemented
314	#4042	C₂³	1	16	yes	complemented
315	#4041	C₂³	1	16	yes	—
316	#4041	C₂³	1	8	yes	—
317	#4040	C₂³	1	16	yes	—
318	#4040	C₂³	1	16	yes	—
319	#4040	C₂³	1	16	yes	complemented
320	#4040	C₂³	1	16	yes	complemented
321	#4040	C₂³	1	16	yes	complemented
322	#4039	C₂³	1	8	yes	—
323	#4039	C₂³	1	16	yes	complemented
324	#4038	C₂³	1	16	yes	complemented
325	#4035	C₂³	1	8	yes	complemented
326	#4035	C₂³	1	16	yes	complemented
327	#4034	C₂³	1	8	yes	complemented
328	#4033	C₂³	1	16	yes	complemented
329	#4033	C₂³	1	8	yes	complemented
330	#4032	C₂³	1	8	yes	—
331	#4031	C₂³	1	8	yes	complemented
332	#4031	C₂³	1	16	yes	complemented
333	#4031	C₂³	1	16	yes	complemented
334	#4030	C₂³	1	16	yes	—
335	#4030	C₂³	1	16	yes	complemented
336	#4029	C₂³	1	16	yes	complemented
337	#4028	C₂³	1	16	yes	—
338	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
339	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
340	#4025	C₂³	1	8	yes	complemented
341	#4024	C₂³	1	8	yes	—
342	#4024	C₂³	1	16	yes	—
343	#4023	C₂³	1	16	yes	—
344	#4022	C₂³	1	16	yes	complemented
345	#4022	C₂³	1	16	yes	complemented
346	#4021	C₂³	1	8	yes	—
347	#4021	C₂³	1	16	yes	complemented
348	C₄×D₂₀	C₂³	1	8	yes	—
349	#4018	C₂³	1	8	yes	complemented
350	#4018	C₂³	1	16	yes	complemented
351	C₄×Dic₁₀	C₂³	1	8	yes	complemented
352	#3561	—	5	32	no	—
353	C₂×#563	—	5	2	no	—
354	C₂×#562	—	5	2	no	—
355	C₂×#556	—	5	1	no	—
356	C₂×#556	—	5	1	no	—
357	C₂×#551	—	5	2	no	—
358	C₂×#551	—	5	2	no	—
359	C₂×D₄×Q₈	—	5	1	no	—
360	C₂×D₄×Q₈	D₅	1	1	yes	characteristic, complemented
361	C₂×#548	—	5	1	no	—
362	C₂×#548	—	5	1	no	—
363	C₂×#546	—	5	1	no	—
364	C₂×#546	—	5	1	no	—
365	C₂×#543	—	5	2	no	—
366	C₂×#542	—	5	2	no	—
367	C₂×#542	—	5	1	no	—
368	C₂×#542	—	5	2	no	—
369	C₂×#542	—	5	1	no	—
370	C₂×#538	—	5	2	no	—
371	C₂×#536	—	5	1	no	—
372	C₂×#536	—	5	1	no	—
373	C₂×#533	—	5	1	no	—
374	C₂×#529	—	5	1	no	—
375	C₂²×#124	—	5	1	no	—
376	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
377	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
378	C₂³×D₅	—	2	8	no	—
379	C₂³×D₅	—	4	4	no	—
380	C₂³×D₅	—	4	4	no	—
381	C₂³×D₅	C₂⁴	1	1	yes	characteristic
382	C₂³×D₅	C₂⁴	1	2	yes	—
383	C₂³×D₅	C₂⁴	1	2	yes	—
384	C₂³×D₅	C₂⁴	1	8	yes	—
385	C₂×C₅×Q₈	—	2	4	no	—
386	C₂×C₅×Q₈	—	2	4	no	—
387	C₂×C₅×Q₈	—	2	4	no	—
388	C₂×C₅×Q₈	—	4	4	no	—
389	C₂×C₅×Q₈	—	4	4	no	—
390	C₂×C₅×Q₈	—	4	16	no	—
391	C₂×C₅×Q₈	—	4	16	no	—
392	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
393	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
394	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
395	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
396	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
397	C₂×C₅×D₄	—	2	4	no	—
398	C₂×C₅×D₄	C₂⁴	1	4	yes	—
399	C₂²×C₄×C₅	—	2	4	no	—
400	C₂²×C₄×C₅	—	2	4	no	—
401	C₂²×C₄×C₅	—	4	4	no	—
402	C₂²×C₄×C₅	—	4	4	no	—
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	2	yes	—
407	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
410	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
412	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
413	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
414	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
415	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
416	C₂×C₂²⋊D₅	—	2	4	no	—
417	C₂×C₂²⋊D₅	—	4	4	no	—
418	C₂×C₂²⋊D₅	—	4	4	no	—
419	C₂×C₂²⋊D₅	—	4	2	no	—
420	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
421	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
422	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
423	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
424	C₂²×Dic₅	—	2	4	no	—
425	C₂²×Dic₅	—	4	2	no	—
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	1	yes	characteristic
433	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
434	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅	C₂⁴	1	4	yes	—
436	C₂²×Dic₅	C₂⁴	1	4	yes	—
437	#713	—	4	16	no	—
438	Q₈×D₅	—	4	16	no	—
439	#709	—	4	16	no	—
440	C₂×D₂₀	—	2	4	no	—
441	C₂×D₂₀	—	2	4	no	—
442	C₂×D₂₀	—	4	16	no	—
443	C₂×D₂₀	—	4	4	no	—
444	C₂×D₂₀	—	4	4	no	—
445	C₂×D₂₀	—	4	4	no	—
446	C₂×D₂₀	C₂⁴	1	4	yes	—
447	C₂×D₂₀	C₂⁴	1	4	yes	—
448	C₂×D₂₀	C₂⁴	1	8	yes	—
449	C₂×D₂₀	C₂⁴	1	8	yes	—
450	C₂×D₂₀	C₂⁴	1	8	yes	—
451	C₂×C₄×D₅	—	2	4	no	—
452	C₂×C₄×D₅	—	4	4	no	—
453	C₂×C₄×D₅	—	4	4	no	—
454	C₂×C₄×D₅	—	4	4	no	—
455	C₂×C₄×D₅	—	4	4	no	—
456	C₂×C₄×D₅	—	4	4	no	—
457	C₂×C₄×D₅	C₂⁴	1	4	yes	—
458	C₂×C₄×D₅	C₂⁴	1	8	yes	—
459	C₂×C₄×D₅	C₂⁴	1	8	yes	—
460	C₂×C₄×D₅	C₂⁴	1	8	yes	—
461	C₂×C₄×D₅	C₂⁴	1	8	yes	—
462	C₂×C₄×D₅	C₂⁴	1	8	yes	—
463	C₂×Dic₁₀	—	2	4	no	—
464	C₂×Dic₁₀	—	4	4	no	—
465	C₂×Dic₁₀	—	4	2	no	—
466	C₂×Dic₁₀	—	4	4	no	—
467	C₂×Dic₁₀	C₂⁴	1	4	yes	—
468	C₂×Dic₁₀	C₂⁴	1	8	yes	—
469	C₂×Dic₁₀	C₂⁴	1	4	yes	—
470	C₂×Dic₁₀	C₂⁴	1	8	yes	—
471	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
472	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
473	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
474	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
475	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
476	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
477	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
478	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
479	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
480	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
481	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
482	C₄²×C₅	C₂⁴	1	4	yes	—
483	C₄²×C₅	C₂⁴	1	8	yes	—
484	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
485	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
486	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
487	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
488	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
489	#685	C₂⁴	1	8	yes	—
490	#685	C₂⁴	1	4	yes	—
491	#685	C₂⁴	1	4	yes	—
492	#685	C₂⁴	1	8	yes	—
493	#685	C₂⁴	1	8	yes	—
494	#685	C₂⁴	1	8	yes	—
495	#685	C₂⁴	1	8	yes	—
496	#685	C₂⁴	1	8	yes	—
497	#685	C₂⁴	1	8	yes	—
498	#685	C₂⁴	1	8	yes	—
499	#685	C₂⁴	1	8	yes	—
500	#685	C₂⁴	1	8	yes	—
501	#685	C₂⁴	1	8	yes	—
502	#685	C₂⁴	1	8	yes	—
503	#685	C₂⁴	1	8	yes	—
504	#685	C₂⁴	1	8	yes	—
505	#685	C₂⁴	1	8	yes	—
506	#685	C₂⁴	1	8	yes	—
507	#685	C₂⁴	1	8	yes	—
508	#685	C₂⁴	1	4	yes	—
509	#685	C₂⁴	1	4	yes	—
510	C₄⋊Dic₅	C₂⁴	1	4	yes	—
511	C₄⋊Dic₅	C₂⁴	1	4	yes	—
512	C₄⋊Dic₅	C₂⁴	1	8	yes	—
513	C₄⋊Dic₅	C₂⁴	1	4	yes	—
514	C₄⋊Dic₅	C₂⁴	1	8	yes	—
515	C₄⋊Dic₅	C₂⁴	1	4	yes	—
516	#683	C₂⁴	1	4	yes	—
517	#683	C₂⁴	1	4	yes	—
518	#683	C₂⁴	1	4	yes	—
519	#683	C₂⁴	1	4	yes	—
520	#683	C₂⁴	1	8	yes	—
521	#683	C₂⁴	1	8	yes	—
522	#683	C₂⁴	1	8	yes	—
523	#683	C₂⁴	1	8	yes	—
524	#683	C₂⁴	1	8	yes	—
525	#683	C₂⁴	1	8	yes	—
526	#683	C₂⁴	1	8	yes	—
527	#683	C₂⁴	1	4	yes	—
528	#683	C₂⁴	1	4	yes	—
529	#683	C₂⁴	1	8	yes	—
530	C₄×Dic₅	C₂⁴	1	4	yes	—
531	C₄×Dic₅	C₂⁴	1	4	yes	—
532	C₄×Dic₅	C₂⁴	1	8	yes	—
533	C₄×Dic₅	C₂⁴	1	4	yes	—
534	C₄×Dic₅	C₂⁴	1	8	yes	—
535	C₄×Dic₅	C₂⁴	1	4	yes	—
536	C₄×Dic₅	C₂⁴	1	4	yes	—
537	C₄×Dic₅	C₂⁴	1	8	yes	—
538	C₂²×#41	—	5	1	no	—
539	C₂²×#41	—	5	1	no	—
540	C₂³×Q₈	—	5	1	no	—
541	C₂³×Q₈	C₂×D₅	1	1	yes	characteristic
542	C₂³×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
543	C₂³×D₄	—	5	1	no	—
544	#563	—	5	32	no	—
545	#562	—	5	32	no	—
546	#556	—	5	16	no	—
547	#556	—	5	16	no	—
548	#551	—	5	32	no	—
549	#551	—	5	32	no	—
550	D₄×Q₈	—	5	16	no	—
551	D₄×Q₈	C₂×D₅	1	16	yes	complemented
552	#548	—	5	16	no	—
553	#548	—	5	16	no	—
554	#546	—	5	16	no	—
555	#546	—	5	16	no	—
556	#543	—	5	32	no	—
557	#542	—	5	32	no	—
558	#542	—	5	32	no	—
559	#542	—	5	16	no	—
560	#542	—	5	16	no	—
561	#538	—	5	32	no	—
562	#536	—	5	16	no	—
563	#536	—	5	16	no	—
564	#533	—	5	16	no	—
565	C₂×C₄⋊Q₈	—	5	1	no	—
566	C₂×C₄⋊Q₈	—	5	1	no	—
567	C₂×C₄⋊Q₈	—	5	2	no	—
568	C₂×C₄⋊Q₈	—	5	1	no	—
569	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
570	C₂×C₄⋊Q₈	C₂×D₅	1	2	yes	complemented
571	#529	—	5	16	no	—
572	C₂×#126	—	5	1	no	—
573	C₂×#126	—	5	2	no	—
574	C₂×#126	—	5	2	no	—
575	C₂×#126	—	5	2	no	—
576	C₂×#126	—	5	2	no	—
577	C₂×#126	—	5	1	no	—
578	C₂×#126	—	5	2	no	—
579	C₂×#126	—	5	2	no	—
580	C₂×#125	—	5	1	no	—
581	C₂×#125	—	5	2	no	—
582	C₂×#124	—	5	1	no	—
583	C₂×#124	—	5	1	no	—
584	C₂×#124	—	5	2	no	—
585	C₂×#124	—	5	1	no	—
586	C₂×#124	—	5	1	no	—
587	C₂×#124	—	5	2	no	—
588	C₂×#124	—	5	1	no	—
589	C₂×#124	—	5	16	no	—
590	C₂×#124	—	5	2	no	—
591	C₂×#124	—	5	1	no	—
592	C₂×#124	—	5	2	no	—
593	C₂×#124	—	5	2	no	—
594	C₂×#124	—	5	1	no	—
595	C₂×#124	—	5	2	no	—
596	C₂×#123	—	5	1	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	—	5	1	no	—
606	C₂×C₂²⋊Q₈	—	5	2	no	—
607	C₂×C₂²⋊Q₈	—	5	2	no	—
608	C₂×C₂²⋊Q₈	—	5	1	no	—
609	C₂×C₂²⋊Q₈	—	5	2	no	—
610	C₂×C₂²⋊Q₈	—	5	2	no	—
611	C₂×C₂²⋊Q₈	—	5	1	no	—
612	C₂×C₂²⋊Q₈	—	5	2	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	—	5	2	no	—
617	C₂×C₂²⋊Q₈	—	5	2	no	—
618	C₂×C₂²⋊Q₈	—	5	2	no	—
619	C₂×C₂²⋊Q₈	—	5	2	no	—
620	C₂×C₂²⋊Q₈	—	5	1	no	—
621	C₂×C₂²⋊Q₈	—	5	2	no	—
622	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
623	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
624	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
625	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
626	C₂×#121	—	5	1	no	—
627	C₂×#121	—	5	1	no	—
628	C₂×#121	—	5	2	no	—
629	C₂×#121	—	5	1	no	—
630	C₂×#121	—	5	2	no	—
631	C₂×#121	—	5	2	no	—
632	C₂×#121	—	5	2	no	—
633	C₂×#120	—	5	2	no	—
634	C₂×#120	—	5	2	no	—
635	C₂×C₄×Q₈	—	5	1	no	—
636	C₂×C₄×Q₈	—	5	1	no	—
637	C₂×C₄×Q₈	—	5	2	no	—
638	C₂×C₄×Q₈	—	5	1	no	—
639	C₂×C₄×Q₈	—	5	1	no	—
640	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
641	C₂×C₄×D₄	—	5	1	no	—
642	C₂×C₄×D₄	—	5	2	no	—
643	C₂×C₄×D₄	—	5	1	no	—
644	C₂×C₄×D₄	—	5	2	no	—
645	C₂×C₄×D₄	—	5	1	no	—
646	C₂×C₄×D₄	—	5	2	no	—
647	C₂×C₄×D₄	—	5	1	no	—
648	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
649	C₂×C₄×D₄	C₂×D₅	1	2	yes	—
650	C₂×#117	—	5	1	no	—
651	C₂×#117	—	5	2	no	—
652	C₂×#117	—	5	2	no	—
653	C₂×#117	—	5	1	no	—
654	C₂×#117	—	5	2	no	—
655	C₂²×C₂²⋊C₄	—	5	2	no	—
656	C₂²×C₂²⋊C₄	—	5	2	no	—
657	C₂²×C₂²⋊C₄	—	5	2	no	—
658	C₂²×C₂²⋊C₄	—	5	2	no	—
659	C₂²×C₄²	—	5	1	no	—
660	C₂³×C₅	—	2	2	no	—
661	C₂³×C₅	—	2	2	no	—
662	C₂³×C₅	—	2	2	no	—
663	C₂³×C₅	—	2	2	no	—
664	C₂³×C₅	—	2	2	no	—
665	C₂³×C₅	2₋¹⁺⁴	1	4	yes	—
666	C₂³×C₅	C₂⁵	1	2	yes	—
667	C₂³×C₅	C₂⁵	1	2	yes	—
668	C₂³×C₅	C₂⁵	1	1	yes	characteristic
669	C₂²×D₅	—	2	2	no	—
670	C₂²×D₅	—	2	4	no	—
671	C₂²×D₅	—	2	4	no	—
672	C₂²×D₅	—	2	2	no	—
673	C₂²×D₅	—	2	4	no	—
674	C₂²×D₅	—	2	4	no	—
675	C₂²×D₅	—	2	4	no	—
676	C₂²×D₅	—	2	4	no	—
677	C₂²×D₅	—	2	2	no	—
678	C₂²×D₅	—	2	16	no	—
679	C₂²×D₅	—	4	8	no	—
680	C₂²×D₅	—	4	8	no	—
681	C₂²×D₅	—	8	16	no	—
682	C₂²×D₅	C₂⁵	1	4	yes	—
683	C₂²×D₅	C₂⁵	1	4	yes	—
684	C₂²×D₅	C₂⁵	1	2	yes	—
685	C₅×Q₈	—	2	8	no	—
686	C₅×Q₈	—	2	8	no	—
687	C₅×Q₈	—	2	8	no	—
688	C₅×Q₈	—	4	8	no	—
689	C₅×Q₈	—	4	8	no	—
690	C₅×D₄	—	2	8	no	—
691	C₂×C₄×C₅	—	2	4	no	—
692	C₂×C₄×C₅	—	2	2	no	—
693	C₂×C₄×C₅	—	2	4	no	—
694	C₂×C₄×C₅	—	2	2	no	—
695	C₂×C₄×C₅	—	2	4	no	—
696	C₂×C₄×C₅	—	2	2	no	—
697	C₂×C₄×C₅	—	2	2	no	—
698	C₂×C₄×C₅	—	2	4	no	—
699	C₂×C₄×C₅	—	2	8	no	—
700	C₂×C₄×C₅	—	2	8	no	—
701	C₂×C₄×C₅	—	4	8	no	—
702	C₂×C₄×C₅	—	4	8	no	—
703	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
704	C₂×C₄×C₅	C₂⁵	1	2	yes	—
705	C₂×C₄×C₅	C₂⁵	1	4	yes	—
706	C₂×C₄×C₅	C₂⁵	1	4	yes	—
707	C₂×C₄×C₅	C₂⁵	1	4	yes	—
708	C₂×C₄×C₅	C₂⁵	1	2	yes	—
709	C₂×C₄×C₅	C₂⁵	1	4	yes	—
710	C₂×C₄×C₅	C₂⁵	1	2	yes	—
711	C₂×C₄×C₅	C₂⁵	1	2	yes	—
712	C₂×C₄×C₅	C₂⁵	1	2	yes	—
713	C₂²⋊D₅	—	2	8	no	—
714	C₂²⋊D₅	—	4	8	no	—
715	C₂²⋊D₅	—	4	8	no	—
716	C₂²⋊D₅	—	4	4	no	—
717	C₂×Dic₅	—	2	4	no	—
718	C₂×Dic₅	—	2	2	no	—
719	C₂×Dic₅	—	2	8	no	—
720	C₂×Dic₅	—	2	2	no	—
721	C₂×Dic₅	—	2	2	no	—
722	C₂×Dic₅	—	2	2	no	—
723	C₂×Dic₅	—	2	2	no	—
724	C₂×Dic₅	—	2	2	no	—
725	C₂×Dic₅	—	2	4	no	—
726	C₂×Dic₅	—	2	2	no	—
727	C₂×Dic₅	—	4	4	no	—
728	C₂×Dic₅	C₂⁵	1	2	yes	—
729	C₂×Dic₅	C₂⁵	1	2	yes	—
730	C₂×Dic₅	C₂⁵	1	2	yes	—
731	C₂×Dic₅	C₂⁵	1	2	yes	—
732	C₂×Dic₅	C₂⁵	1	4	yes	—
733	C₂×Dic₅	C₂⁵	1	2	yes	—
734	C₂×Dic₅	C₂⁵	1	4	yes	—
735	C₂×Dic₅	C₂⁵	1	2	yes	—
736	C₂×Dic₅	C₂⁵	1	2	yes	—
737	D₂₀	—	2	8	no	—
738	D₂₀	—	2	8	no	—
739	D₂₀	—	4	8	no	—
740	D₂₀	—	4	8	no	—
741	D₂₀	—	4	8	no	—
742	C₄×D₅	—	2	8	no	—
743	C₄×D₅	—	4	8	no	—
744	C₄×D₅	—	4	8	no	—
745	C₄×D₅	—	4	8	no	—
746	C₄×D₅	—	4	8	no	—
747	C₄×D₅	—	4	8	no	—
748	Dic₁₀	—	2	8	no	—
749	Dic₁₀	—	4	8	no	—
750	Dic₁₀	—	4	4	no	—
751	Dic₁₀	—	4	8	no	—
752	C₂⁵	—	5	2	no	—
753	C₂×#41	—	5	8	no	—
754	C₂×#41	—	5	8	no	—
755	C₂×#41	—	20	4	no	—
756	C₂×#41	—	20	4	no	—
757	C₂²×Q₈	—	4	4	no	—
758	C₂²×Q₈	—	4	4	no	—
759	C₂²×Q₈	—	5	8	no	—
760	C₂²×Q₈	—	5	1	no	—
761	C₂²×Q₈	—	5	1	no	—
762	C₂²×Q₈	—	5	2	no	—
763	C₂²×Q₈	—	5	2	no	—
764	C₂²×Q₈	—	20	4	no	—
765	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
766	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
767	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
768	C₂²×Q₈	C₂²×D₅	1	2	yes	—
769	C₂²×Q₈	C₂²×D₅	1	2	yes	—
770	C₂²×Q₈	C₂²×D₅	1	8	yes	—
771	C₂²×Q₈	C₂²×D₅	1	8	yes	complemented
772	C₂²×D₄	—	5	1	no	—
773	C₂²×D₄	—	5	2	no	—
774	C₂²×D₄	—	5	1	no	—
775	C₂²×D₄	—	5	2	no	—
776	C₂²×D₄	—	5	1	no	—
777	C₂²×D₄	—	5	1	no	—
778	C₂²×D₄	—	5	2	no	—
779	C₂²×D₄	—	5	2	no	—
780	C₂²×D₄	—	5	2	no	—
781	C₂²×D₄	—	5	8	no	—
782	C₂²×D₄	—	20	4	no	—
783	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
784	C₂³×C₄	—	5	1	no	—
785	C₂³×C₄	—	5	1	no	—
786	C₂³×C₄	—	5	1	no	—
787	C₂³×C₄	—	5	2	no	—
788	C₂³×C₄	—	5	2	no	—
789	C₂³×C₄	—	5	2	no	—
790	C₂³×C₄	—	5	2	no	—
791	C₂³×C₄	—	5	2	no	—
792	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
793	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
794	C₂³×C₄	C₂²×D₅	1	2	yes	—
795	C₂³×C₄	C₂²×D₅	1	2	yes	—
796	C₄⋊Q₈	—	5	8	no	—
797	C₄⋊Q₈	—	5	8	no	—
798	C₄⋊Q₈	—	5	16	no	—
799	C₄⋊Q₈	—	5	8	no	—
800	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
801	C₄⋊Q₈	C₂²×D₅	1	16	yes	complemented
802	#126	—	5	8	no	—
803	#126	—	5	16	no	—
804	#126	—	5	16	no	—
805	#126	—	5	16	no	—
806	#126	—	5	16	no	—
807	#126	—	5	8	no	—
808	#126	—	5	16	no	—
809	#126	—	5	16	no	—
810	#125	—	5	8	no	—
811	#125	—	5	16	no	—
812	#124	—	5	8	no	—
813	#124	—	5	8	no	—
814	#124	—	5	16	no	—
815	#124	—	5	8	no	—
816	#124	—	5	8	no	—
817	#124	—	5	16	no	—
818	#124	—	5	8	no	—
819	#124	—	5	16	no	—
820	#124	—	5	8	no	—
821	#124	—	5	16	no	—
822	#124	—	5	16	no	—
823	#124	—	5	8	no	—
824	#124	—	5	16	no	—
825	#123	—	5	8	no	—
826	#123	—	5	16	no	—
827	#123	—	5	16	no	—
828	#123	—	5	16	no	—
829	#123	—	5	16	no	—
830	#123	—	5	16	no	—
831	#123	—	5	16	no	—
832	#123	—	5	16	no	—
833	#123	—	5	8	no	—
834	#123	—	5	16	no	—
835	C₂²⋊Q₈	—	5	16	no	—
836	C₂²⋊Q₈	—	5	16	no	—
837	C₂²⋊Q₈	—	5	8	no	—
838	C₂²⋊Q₈	—	5	16	no	—
839	C₂²⋊Q₈	—	5	16	no	—
840	C₂²⋊Q₈	—	5	8	no	—
841	C₂²⋊Q₈	—	5	16	no	—
842	C₂²⋊Q₈	—	5	16	no	—
843	C₂²⋊Q₈	—	5	16	no	—
844	C₂²⋊Q₈	—	5	16	no	—
845	C₂²⋊Q₈	—	5	16	no	—
846	C₂²⋊Q₈	—	5	16	no	—
847	C₂²⋊Q₈	—	5	16	no	—
848	C₂²⋊Q₈	—	5	16	no	—
849	C₂²⋊Q₈	—	5	8	no	—
850	C₂²⋊Q₈	—	5	16	no	—
851	C₂²⋊Q₈	C₂²×D₅	1	8	yes	—
852	C₂²⋊Q₈	C₂²×D₅	1	16	yes	—
853	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
854	C₂²⋊Q₈	C₂²×D₅	1	16	yes	complemented
855	#121	—	5	8	no	—
856	#121	—	5	16	no	—
857	#121	—	5	8	no	—
858	#121	—	5	8	no	—
859	#121	—	5	16	no	—
860	#121	—	5	16	no	—
861	#121	—	5	16	no	—
862	#120	—	5	16	no	—
863	#120	—	5	16	no	—
864	C₄×Q₈	—	5	8	no	—
865	C₄×Q₈	—	5	8	no	—
866	C₄×Q₈	—	5	16	no	—
867	C₄×Q₈	—	5	8	no	—
868	C₄×Q₈	—	5	8	no	—
869	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
870	C₄×D₄	—	5	8	no	—
871	C₄×D₄	—	5	8	no	—
872	C₄×D₄	—	5	16	no	—
873	C₄×D₄	—	5	16	no	—
874	C₄×D₄	—	5	8	no	—
875	C₄×D₄	—	5	16	no	—
876	C₄×D₄	—	5	8	no	—
877	C₄×D₄	C₂²×D₅	1	8	yes	—
878	C₄×D₄	C₂²×D₅	1	16	yes	—
879	#117	—	5	8	no	—
880	#117	—	5	16	no	—
881	#117	—	5	16	no	—
882	#117	—	5	8	no	—
883	#117	—	5	16	no	—
884	C₂×C₄⋊C₄	—	5	1	no	—
885	C₂×C₄⋊C₄	—	5	1	no	—
886	C₂×C₄⋊C₄	—	5	1	no	—
887	C₂×C₄⋊C₄	—	5	1	no	—
888	C₂×C₄⋊C₄	—	5	2	no	—
889	C₂×C₄⋊C₄	—	5	2	no	—
890	C₂×C₄⋊C₄	—	5	1	no	—
891	C₂×C₄⋊C₄	—	5	1	no	—
892	C₂×C₄⋊C₄	—	5	2	no	—
893	C₂×C₄⋊C₄	—	5	1	no	—
894	C₂×C₄⋊C₄	—	5	1	no	—
895	C₂×C₄⋊C₄	—	5	2	no	—
896	C₂×C₄⋊C₄	—	5	2	no	—
897	C₂×C₄⋊C₄	—	5	1	no	—
898	C₂×C₄⋊C₄	—	5	2	no	—
899	C₂×C₄⋊C₄	—	5	2	no	—
900	C₂×C₄⋊C₄	—	5	2	no	—
901	C₂×C₄⋊C₄	—	5	1	no	—
902	C₂×C₄⋊C₄	—	5	2	no	—
903	C₂×C₄⋊C₄	—	5	2	no	—
904	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
905	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
907	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
908	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
910	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
911	C₂×C₂²⋊C₄	—	5	1	no	—
912	C₂×C₂²⋊C₄	—	5	2	no	—
913	C₂×C₂²⋊C₄	—	5	1	no	—
914	C₂×C₂²⋊C₄	—	5	1	no	—
915	C₂×C₂²⋊C₄	—	5	1	no	—
916	C₂×C₂²⋊C₄	—	5	2	no	—
917	C₂×C₂²⋊C₄	—	5	2	no	—
918	C₂×C₂²⋊C₄	—	5	2	no	—
919	C₂×C₂²⋊C₄	—	5	2	no	—
920	C₂×C₂²⋊C₄	—	5	2	no	—
921	C₂×C₂²⋊C₄	—	5	2	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	2	no	—
927	C₂×C₂²⋊C₄	—	5	2	no	—
928	C₂×C₂²⋊C₄	—	5	16	no	—
929	C₂×C₂²⋊C₄	—	5	16	no	—
930	C₂×C₂²⋊C₄	—	5	2	no	—
931	C₂×C₂²⋊C₄	—	5	2	no	—
932	C₂×C₂²⋊C₄	—	5	1	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	1	no	—
938	C₂×C₂²⋊C₄	—	5	2	no	—
939	C₂×C₂²⋊C₄	—	5	16	no	—
940	C₂×C₂²⋊C₄	—	5	16	no	—
941	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
942	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
943	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
944	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
945	C₂×C₄²	—	5	2	no	—
946	C₂×C₄²	—	5	2	no	—
947	C₂×C₄²	—	5	1	no	—
948	C₂×C₄²	—	5	1	no	—
949	C₂×C₄²	—	5	2	no	—
950	C₂×C₄²	—	5	1	no	—
951	C₂×C₄²	—	5	1	no	—
952	C₂×C₄²	—	5	1	no	—
953	C₂×C₄²	—	5	8	no	—
954	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
955	C₂×C₄²	C₂²×D₅	1	2	yes	—
956	C₂²×C₅	—	2	2	no	—
957	C₂²×C₅	—	2	2	no	—
958	C₂²×C₅	—	2	8	no	—
959	C₂²×C₅	—	2	2	no	—
960	C₂²×C₅	—	2	2	no	—
961	C₂²×C₅	—	2	2	no	—
962	C₂²×C₅	—	4	4	no	—
963	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
964	C₂²×C₅	C₂×2₋¹⁺⁴	1	4	yes	—
965	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
966	C₂²×C₅	#585	1	2	yes	—
967	C₂²×C₅	C₂⁶	1	1	yes	characteristic
968	C₂×D₅	—	2	2	no	—
969	C₂×D₅	—	2	4	no	—
970	C₂×D₅	—	2	4	no	—
971	C₂×D₅	—	2	2	no	—
972	C₂×D₅	—	2	4	no	—
973	C₂×D₅	—	2	4	no	—
974	C₂×D₅	—	2	4	no	—
975	C₂×D₅	—	2	4	no	—
976	C₂×D₅	—	2	2	no	—
977	C₂×D₅	—	4	4	no	—
978	C₂×D₅	—	4	8	no	—
979	C₂×D₅	—	4	8	no	—
980	C₂×D₅	—	8	16	no	—
981	C₄×C₅	—	2	4	no	—
982	C₄×C₅	—	2	2	no	—
983	C₄×C₅	—	2	4	no	—
984	C₄×C₅	—	2	2	no	—
985	C₄×C₅	—	2	4	no	—
986	C₄×C₅	—	2	2	no	—
987	C₄×C₅	—	2	2	no	—
988	C₄×C₅	—	2	4	no	—
989	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
990	Dic₅	—	2	4	no	—
991	Dic₅	—	2	2	no	—
992	Dic₅	—	2	2	no	—
993	Dic₅	—	2	2	no	—
994	Dic₅	—	2	2	no	—
995	Dic₅	—	2	2	no	—
996	Dic₅	—	2	2	no	—
997	Dic₅	—	2	4	no	—
998	Dic₅	—	2	2	no	—
999	C₂⁴	—	5	2	no	—
1000	C₂⁴	—	5	2	no	—
1001	C₂⁴	—	5	1	no	—
1002	C₂⁴	—	5	8	no	—
1003	C₂⁴	—	10	8	no	—
1004	C₂⁴	—	20	4	no	—
1005	C₂⁴	—	20	4	no	—
1006	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1007	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1008	#41	—	20	16	no	—
1009	#41	—	20	16	no	—
1010	C₂×Q₈	—	2	4	no	—
1011	C₂×Q₈	—	2	4	no	—
1012	C₂×Q₈	—	2	4	no	—
1013	C₂×Q₈	—	4	4	no	—
1014	C₂×Q₈	—	4	4	no	—
1015	C₂×Q₈	—	4	16	no	—
1016	C₂×Q₈	—	4	16	no	—
1017	C₂×Q₈	—	5	4	no	—
1018	C₂×Q₈	—	5	4	no	—
1019	C₂×Q₈	—	5	8	no	—
1020	C₂×Q₈	—	5	8	no	—
1021	C₂×Q₈	—	10	4	no	—
1022	C₂×Q₈	—	20	4	no	—
1023	C₂×Q₈	—	20	2	no	—
1024	C₂×Q₈	—	20	4	no	—
1025	C₂×Q₈	—	20	16	no	—
1026	C₂×Q₈	C₂³×D₅	1	4	yes	—
1027	C₂×Q₈	C₂³×D₅	1	4	yes	—
1028	C₂×Q₈	C₂³×D₅	1	4	yes	—
1029	C₂×Q₈	C₂³×D₅	1	8	yes	—
1030	C₂×Q₈	C₂³×D₅	1	8	yes	—
1031	C₂×D₄	—	2	4	no	—
1032	C₂×D₄	—	5	4	no	—
1033	C₂×D₄	—	5	8	no	—
1034	C₂×D₄	—	5	4	no	—
1035	C₂×D₄	—	5	8	no	—
1036	C₂×D₄	—	5	4	no	—
1037	C₂×D₄	—	5	4	no	—
1038	C₂×D₄	—	5	8	no	—
1039	C₂×D₄	—	5	8	no	—
1040	C₂×D₄	—	5	8	no	—
1041	C₂×D₄	—	10	4	no	—
1042	C₂×D₄	—	10	4	no	—
1043	C₂×D₄	—	10	4	no	—
1044	C₂×D₄	—	20	16	no	—
1045	C₂×D₄	—	20	4	no	—
1046	C₂×D₄	—	20	4	no	—
1047	C₂×D₄	—	20	4	no	—
1048	C₂×D₄	—	20	4	no	—
1049	C₂×D₄	—	20	4	no	—
1050	C₂×D₄	—	20	2	no	—
1051	C₂×D₄	C₂³×D₅	1	4	yes	—
1052	C₂²×C₄	—	2	4	no	—
1053	C₂²×C₄	—	2	4	no	—
1054	C₂²×C₄	—	4	4	no	—
1055	C₂²×C₄	—	4	4	no	—
1056	C₂²×C₄	—	5	4	no	—
1057	C₂²×C₄	—	5	1	no	—
1058	C₂²×C₄	—	5	1	no	—
1059	C₂²×C₄	—	5	1	no	—
1060	C₂²×C₄	—	5	1	no	—
1061	C₂²×C₄	—	5	2	no	—
1062	C₂²×C₄	—	5	1	no	—
1063	C₂²×C₄	—	5	1	no	—
1064	C₂²×C₄	—	5	2	no	—
1065	C₂²×C₄	—	5	1	no	—
1066	C₂²×C₄	—	5	4	no	—
1067	C₂²×C₄	—	5	4	no	—
1068	C₂²×C₄	—	5	8	no	—
1069	C₂²×C₄	—	5	8	no	—
1070	C₂²×C₄	—	5	8	no	—
1071	C₂²×C₄	—	5	8	no	—
1072	C₂²×C₄	—	5	8	no	—
1073	C₂²×C₄	—	10	4	no	—
1074	C₂²×C₄	—	10	4	no	—
1075	C₂²×C₄	—	20	4	no	—
1076	C₂²×C₄	—	20	4	no	—
1077	C₂²×C₄	—	20	4	no	—
1078	C₂²×C₄	—	20	4	no	—
1079	C₂²×C₄	—	20	4	no	—
1080	C₂²×C₄	—	20	2	no	—
1081	C₂²×C₄	C₂³×D₅	1	4	yes	—
1082	C₂²×C₄	C₂³×D₅	1	4	yes	—
1083	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1084	C₂²×C₄	C₂³×D₅	1	2	yes	—
1085	C₂²×C₄	C₂³×D₅	1	2	yes	—
1086	C₂²×C₄	C₂³×D₅	1	2	yes	—
1087	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1088	C₂²×C₄	C₂³×D₅	1	2	yes	—
1089	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1090	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1091	C₂²×C₄	C₂³×D₅	1	8	yes	—
1092	C₂²×C₄	C₂³×D₅	1	8	yes	—
1093	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1094	C₄⋊C₄	—	5	4	no	—
1095	C₄⋊C₄	—	5	4	no	—
1096	C₄⋊C₄	—	5	4	no	—
1097	C₄⋊C₄	—	5	4	no	—
1098	C₄⋊C₄	—	5	8	no	—
1099	C₄⋊C₄	—	5	8	no	—
1100	C₄⋊C₄	—	5	4	no	—
1101	C₄⋊C₄	—	5	4	no	—
1102	C₄⋊C₄	—	5	8	no	—
1103	C₄⋊C₄	—	5	4	no	—
1104	C₄⋊C₄	—	5	4	no	—
1105	C₄⋊C₄	—	5	8	no	—
1106	C₄⋊C₄	—	5	8	no	—
1107	C₄⋊C₄	—	5	4	no	—
1108	C₄⋊C₄	—	5	8	no	—
1109	C₄⋊C₄	—	5	8	no	—
1110	C₄⋊C₄	—	5	8	no	—
1111	C₄⋊C₄	—	5	4	no	—
1112	C₄⋊C₄	—	5	8	no	—
1113	C₄⋊C₄	—	5	8	no	—
1114	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1115	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1116	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1117	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1118	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1119	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1120	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1121	C₂²⋊C₄	—	5	4	no	—
1122	C₂²⋊C₄	—	5	8	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	8	no	—
1131	C₂²⋊C₄	—	5	8	no	—
1132	C₂²⋊C₄	—	5	8	no	—
1133	C₂²⋊C₄	—	5	8	no	—
1134	C₂²⋊C₄	—	5	8	no	—
1135	C₂²⋊C₄	—	5	8	no	—
1136	C₂²⋊C₄	—	5	8	no	—
1137	C₂²⋊C₄	—	5	8	no	—
1138	C₂²⋊C₄	—	5	8	no	—
1139	C₂²⋊C₄	—	5	8	no	—
1140	C₂²⋊C₄	—	5	4	no	—
1141	C₂²⋊C₄	—	5	4	no	—
1142	C₂²⋊C₄	—	5	4	no	—
1143	C₂²⋊C₄	—	5	8	no	—
1144	C₂²⋊C₄	—	5	8	no	—
1145	C₂²⋊C₄	—	5	4	no	—
1146	C₂²⋊C₄	—	5	8	no	—
1147	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1148	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1149	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1150	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1151	C₄²	—	5	4	no	—
1152	C₄²	—	5	4	no	—
1153	C₄²	—	5	4	no	—
1154	C₄²	—	5	4	no	—
1155	C₄²	—	5	8	no	—
1156	C₄²	—	5	8	no	—
1157	C₄²	—	5	4	no	—
1158	C₄²	—	5	8	no	—
1159	C₄²	C₂³×D₅	1	4	yes	—
1160	C₄²	C₂³×D₅	1	8	yes	—
1161	C₂×C₅	—	2	4	no	—
1162	C₂×C₅	—	4	2	no	—
1163	C₂×C₅	#3561	1	4	yes	complemented
1164	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₂×C₅	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
1166	C₂×C₅	C₂×#585	1	1	yes	characteristic
1167	D₅	—	4	2	no	—
1168	D₅	—	4	4	no	—
1169	D₅	—	4	4	no	—
1170	C₂³	—	2	2	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	2	2	no	—
1174	C₂³	—	2	2	no	—
1175	C₂³	—	5	4	no	—
1176	C₂³	—	5	4	no	—
1177	C₂³	—	5	2	no	—
1178	C₂³	—	10	2	no	—
1179	C₂³	—	10	4	no	—
1180	C₂³	—	10	4	no	—
1181	C₂³	—	10	2	no	—
1182	C₂³	—	10	4	no	—
1183	C₂³	—	10	4	no	—
1184	C₂³	—	10	4	no	—
1185	C₂³	—	10	4	no	—
1186	C₂³	—	10	2	no	—
1187	C₂³	—	10	16	no	—
1188	C₂³	—	20	8	no	—
1189	C₂³	—	20	8	no	—
1190	C₂³	—	40	16	no	—
1191	C₂³	#4147	1	4	yes	—
1192	C₂³	C₂⁴×D₅	1	2	yes	—
1193	C₂³	C₂⁴×D₅	1	2	yes	—
1194	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1195	Q₈	—	2	8	no	—
1196	Q₈	—	2	8	no	—
1197	Q₈	—	2	8	no	—
1198	Q₈	—	4	8	no	—
1199	Q₈	—	4	8	no	—
1200	Q₈	—	10	8	no	—
1201	Q₈	—	20	8	no	—
1202	Q₈	—	20	4	no	—
1203	Q₈	—	20	8	no	—
1204	D₄	—	2	8	no	—
1205	D₄	—	10	8	no	—
1206	D₄	—	10	8	no	—
1207	D₄	—	10	8	no	—
1208	D₄	—	20	8	no	—
1209	D₄	—	20	8	no	—
1210	D₄	—	20	8	no	—
1211	D₄	—	20	8	no	—
1212	D₄	—	20	8	no	—
1213	D₄	—	20	4	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	4	no	—
1217	C₂×C₄	—	2	4	no	—
1218	C₂×C₄	—	2	4	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	4	no	—
1222	C₂×C₄	—	2	8	no	—
1223	C₂×C₄	—	2	8	no	—
1224	C₂×C₄	—	4	8	no	—
1225	C₂×C₄	—	4	8	no	—
1226	C₂×C₄	—	5	2	no	—
1227	C₂×C₄	—	5	2	no	—
1228	C₂×C₄	—	5	2	no	—
1229	C₂×C₄	—	5	2	no	—
1230	C₂×C₄	—	5	2	no	—
1231	C₂×C₄	—	5	4	no	—
1232	C₂×C₄	—	5	2	no	—
1233	C₂×C₄	—	5	4	no	—
1234	C₂×C₄	—	5	2	no	—
1235	C₂×C₄	—	10	2	no	—
1236	C₂×C₄	—	10	4	no	—
1237	C₂×C₄	—	10	8	no	—
1238	C₂×C₄	—	10	2	no	—
1239	C₂×C₄	—	10	2	no	—
1240	C₂×C₄	—	10	2	no	—
1241	C₂×C₄	—	10	2	no	—
1242	C₂×C₄	—	10	4	no	—
1243	C₂×C₄	—	10	2	no	—
1244	C₂×C₄	—	10	2	no	—
1245	C₂×C₄	—	10	8	no	—
1246	C₂×C₄	—	20	8	no	—
1247	C₂×C₄	—	20	8	no	—
1248	C₂×C₄	—	20	8	no	—
1249	C₂×C₄	—	20	8	no	—
1250	C₂×C₄	—	20	8	no	—
1251	C₂×C₄	—	20	4	no	—
1252	C₂×C₄	#4144	1	4	yes	—
1253	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1254	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1255	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1256	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1257	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1258	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1259	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1260	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1261	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1262	C₅	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
1263	C₂²	—	2	8	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	2	no	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	4	4	no	—
1270	C₂²	—	10	2	no	—
1271	C₂²	—	10	4	no	—
1272	C₂²	—	10	4	no	—
1273	C₂²	—	10	2	no	—
1274	C₂²	—	10	4	no	—
1275	C₂²	—	10	4	no	—
1276	C₂²	—	10	4	no	—
1277	C₂²	—	10	4	no	—
1278	C₂²	—	10	2	no	—
1279	C₂²	—	20	8	no	—
1280	C₂²	—	20	8	no	—
1281	C₂²	—	20	4	no	—
1282	C₂²	—	40	16	no	—
1283	C₂²	C₂×#4144	1	2	yes	—
1284	C₂²	C₂×#4147	1	4	yes	—
1285	C₂²	C₂×#4147	1	2	yes	—
1286	C₂²	#66287	1	2	yes	—
1287	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1288	C₄	—	2	2	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	4	no	—
1291	C₄	—	2	4	no	—
1292	C₄	—	2	4	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	4	no	—
1296	C₄	—	10	2	no	—
1297	C₄	—	10	4	no	—
1298	C₄	—	10	2	no	—
1299	C₄	—	10	2	no	—
1300	C₄	—	10	2	no	—
1301	C₄	—	10	2	no	—
1302	C₄	—	10	4	no	—
1303	C₄	—	10	2	no	—
1304	C₄	—	10	2	no	—
1305	C₄	C₂×#4144	1	4	yes	—
1306	C₂	—	2	4	no	—
1307	C₂	—	4	2	no	—
1308	C₂	—	20	4	no	—
1309	C₂	—	20	4	no	—
1310	C₂	—	20	2	no	—
1311	C₂	#10618658	1	4	yes	direct product factor
1312	C₂	C₂²×#4144	1	1	yes	characteristic
1313	C₂	C₂²×#4147	1	1	yes	characteristic
1314	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×D₄×Q₈	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×D₄×Q₈	D₅
hypocenter	C₅	C₂×#3561
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₄×Q₈	C₂	semidirect
2. C₂×#66151	C₂	semidirect
3. C₂×#66150	C₂	semidirect
4. C₂×Q₈×C₂²⋊D₅	C₂	semidirect
5. C₂²×#4093	C₂	semidirect
6. #10618658	C₂	direct (N × H)
7. C₂×#66069	C₂	semidirect
8. C₂×#66067	C₂	semidirect
9. C₂×#66058	C₂	semidirect
10. C₂×#66066	C₂	semidirect
11. C₂×#65981	C₂	semidirect
12. C₂×#65971	C₂	semidirect
13. C₂×#65967	C₂	semidirect
14. C₂×#65964	C₂	semidirect
15. C₂×#65968	C₂	semidirect
16. C₂×#65974	C₂	semidirect
17. C₂×#65977	C₂	semidirect
18. C₂×#65956	C₂	semidirect
19. C₂×#65916	C₂	semidirect
20. C₂×#65902	C₂	semidirect
21. C₂×#65890	C₂	semidirect
22. C₂×#65884	C₂	semidirect
23. C₂×#65894	C₂	semidirect
24. C₂×#65872	C₂	semidirect
26. C₂³×C₅×Q₈	C₂²	semidirect
28. C₂²×Q₈×D₅	C₂²	semidirect
31. C₅×D₄×Q₈	C₂²	semidirect
32. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄×C₅×Q₈	C₂²	semidirect
41. #66151	C₂²	semidirect
42. #66150	C₂²	semidirect
43. Q₈×C₂²⋊D₅	C₂²	semidirect
51. C₂×#4093	C₂²	semidirect
52. C₂×#4093	C₂²	semidirect
53. C₂×#4092	C₂²	semidirect
54. C₂×#4092	C₂²	semidirect
55. C₂×#4092	C₂²	semidirect
56. C₂×#4092	C₂²	semidirect
57. C₂×#4092	C₂²	semidirect
58. C₂×Q₈×Dic₅	C₂²	semidirect
59. C₂×Q₈×Dic₅	C₂²	semidirect
60. C₂×#4090	C₂²	semidirect
61. C₂×#4090	C₂²	semidirect
62. C₂×#4090	C₂²	semidirect
67. C₂×#4076	C₂²	semidirect
68. C₂×#4075	C₂²	semidirect
69. C₂×#4075	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
76. C₂×#4072	C₂²	semidirect
80. #66069	C₂²	semidirect
81. #66067	C₂²	semidirect
82. #66066	C₂²	semidirect
83. #66058	C₂²	semidirect
84. #65981	C₂²	semidirect
85. #65977	C₂²	semidirect
86. #65974	C₂²	semidirect
87. #65971	C₂²	semidirect
88. #65968	C₂²	semidirect
89. #65967	C₂²	semidirect
90. #65964	C₂²	semidirect
91. #65956	C₂²	semidirect
92. #65916	C₂²	semidirect
93. #65902	C₂²	semidirect
94. #65894	C₂²	semidirect
95. #65890	C₂²	semidirect
96. #65884	C₂²	semidirect
97. #65872	C₂²	semidirect
98. C₂×#4044	C₂²	semidirect
99. C₂×#4044	C₂²	semidirect
100. C₂×#4044	C₂²	semidirect
101. C₂×#4044	C₂²	semidirect
102. C₂×#4044	C₂²	semidirect
103. C₂×#4043	C₂²	semidirect
104. C₂×#4043	C₂²	semidirect
105. C₂×#4042	C₂²	semidirect
106. C₂×#4042	C₂²	semidirect
107. C₂×#4042	C₂²	semidirect
108. C₂×#4042	C₂²	semidirect
109. C₂×#4042	C₂²	semidirect
114. C₂×#4040	C₂²	semidirect
115. C₂×#4040	C₂²	semidirect
116. C₂×#4040	C₂²	semidirect
118. C₂×#4039	C₂²	semidirect
119. C₂×#4038	C₂²	semidirect
120. C₂×#4035	C₂²	semidirect
121. C₂×#4035	C₂²	semidirect
122. C₂×#4034	C₂²	semidirect
123. C₂×#4033	C₂²	semidirect
124. C₂×#4033	C₂²	semidirect
126. C₂×#4031	C₂²	semidirect
127. C₂×#4031	C₂²	semidirect
128. C₂×#4031	C₂²	semidirect
130. C₂×#4030	C₂²	semidirect
131. C₂×#4029	C₂²	semidirect
135. C₂×#4025	C₂²	semidirect
139. C₂×#4022	C₂²	semidirect
140. C₂×#4022	C₂²	semidirect
142. C₂×#4021	C₂²	semidirect
144. C₂×#4018	C₂²	semidirect
145. C₂×#4018	C₂²	semidirect
146. C₂×C₄×Dic₁₀	C₂²	semidirect
157. C₂²×C₅×Q₈	C₂³	semidirect
172. C₂×Q₈×D₅	C₂³	semidirect
192. C₅×C₄⋊Q₈	C₂³	semidirect
193. C₅×C₄⋊Q₈	C₂³	semidirect
196. C₅×C₂²⋊Q₈	C₂³	semidirect
197. C₅×C₂²⋊Q₈	C₂³	semidirect
198. C₄×C₅×Q₈	C₂³	semidirect
226. #4093	C₂³	semidirect
227. #4092	C₂³	semidirect
228. #4092	C₂³	semidirect
229. #4092	C₂³	semidirect
230. #4092	C₂³	semidirect
231. #4092	C₂³	semidirect
232. Q₈×Dic₅	C₂³	semidirect
233. Q₈×Dic₅	C₂³	semidirect
234. #4090	C₂³	semidirect
235. #4090	C₂³	semidirect
236. #4090	C₂³	semidirect
241. #4076	C₂³	semidirect
242. #4075	C₂³	semidirect
243. #4075	C₂³	semidirect
246. C₄×C₂²⋊D₅	C₂³	semidirect
247. C₄×C₂²⋊D₅	C₂³	semidirect
271. #4072	C₂³	semidirect
303. #4044	C₂³	semidirect
304. #4044	C₂³	semidirect
305. #4044	C₂³	semidirect
306. #4044	C₂³	semidirect
307. #4044	C₂³	semidirect
308. #4043	C₂³	semidirect
309. #4043	C₂³	semidirect
310. #4042	C₂³	semidirect
311. #4042	C₂³	semidirect
312. #4042	C₂³	semidirect
313. #4042	C₂³	semidirect
314. #4042	C₂³	semidirect
319. #4040	C₂³	semidirect
320. #4040	C₂³	semidirect
321. #4040	C₂³	semidirect
323. #4039	C₂³	semidirect
324. #4038	C₂³	semidirect
325. #4035	C₂³	semidirect
326. #4035	C₂³	semidirect
327. #4034	C₂³	semidirect
328. #4033	C₂³	semidirect
329. #4033	C₂³	semidirect
331. #4031	C₂³	semidirect
332. #4031	C₂³	semidirect
333. #4031	C₂³	semidirect
335. #4030	C₂³	semidirect
336. #4029	C₂³	semidirect
340. #4025	C₂³	semidirect
344. #4022	C₂³	semidirect
345. #4022	C₂³	semidirect
347. #4021	C₂³	semidirect
349. #4018	C₂³	semidirect
350. #4018	C₂³	semidirect
351. C₄×Dic₁₀	C₂³	semidirect
360. C₂×D₄×Q₈	D₅	semidirect
542. C₂³×Q₈	C₂×D₅	semidirect
551. D₄×Q₈	C₂×D₅	semidirect
569. C₂×C₄⋊Q₈	C₂×D₅	semidirect
570. C₂×C₄⋊Q₈	C₂×D₅	semidirect
624. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
625. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
640. C₂×C₄×Q₈	C₂×D₅	semidirect
771. C₂²×Q₈	C₂²×D₅	semidirect
800. C₄⋊Q₈	C₂²×D₅	semidirect
801. C₄⋊Q₈	C₂²×D₅	semidirect
853. C₂²⋊Q₈	C₂²×D₅	semidirect
854. C₂²⋊Q₈	C₂²×D₅	semidirect
869. C₄×Q₈	C₂²×D₅	semidirect
1163. C₂×C₅	#3561	semidirect
1262. C₅	C₂×#3561	semidirect
1311. C₂	#10618658	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×D₄×Q₈	2
C₂×#66151	2
C₂×#66150	2
C₂×Q₈×C₂²⋊D₅	2
C₂²×#4093	2
#10618658	2
C₂×#66069	2
C₂×#66067	2
C₂×#66058	2
C₂×#66066	2
C₂×#65981	2
C₂×#65971	2
C₂×#65967	2
C₂×#65964	2
C₂×#65968	2
C₂×#65974	2
C₂×#65977	2
C₂×#65956	2
C₂×#65916	2
C₂×#65902	2
C₂×#65890	2
C₂×#65884	2
C₂×#65894	2
C₂×#65872	2
C₂×#3561	5

Subgroups — C2×#10618658 #13006649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618658 #13006649