Subgroups — C₂×D₅×#542 #13006079

Order 1280.

7974 conjugacy classes of subgroups.

The subgroup lattice has 1332 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	D₅×#542	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66067	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅×#126	C₂	1	2	yes	maximal, complemented
6	C₂×#66044	C₂	1	2	yes	maximal, complemented
7	C₂×#66016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₅×#124	C₂	1	2	yes	maximal, complemented
10	C₂×#66003	C₂	1	2	yes	maximal, complemented
11	C₂×D₅×#123	C₂	1	2	yes	maximal, complemented
12	C₂×#65996	C₂	1	2	yes	maximal, complemented
13	C₂×D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₂×#65974	C₂	1	2	yes	maximal, complemented
16	C₂×#65977	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×D₅×#121	C₂	1	1	yes	maximal, characteristic
18	C₂×#65937	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#65916	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#65895	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#65868	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×Q₈×D₅	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×D₅	C₂²	1	2	yes	—
27	C₂²×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₅	C₂²	1	2	yes	—
29	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₂³×C₄×D₅	C₂²	1	2	yes	—
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	2	yes	complemented
35	C₂×C₅×#124	C₂²	1	1	yes	characteristic, 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	complemented
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×#4085	C₂²	1	2	yes	—
50	C₂×#4084	C₂²	1	1	yes	characteristic
51	C₂×#4082	C₂²	1	2	yes	complemented
52	C₂×#4082	C₂²	1	1	yes	characteristic, complemented
53	C₂×#4081	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×#4075	C₂²	1	2	yes	complemented
57	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
58	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
59	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
60	C₂×#4070	C₂²	1	2	yes	complemented
61	#66067	C₂²	1	16	yes	complemented
62	D₅×C₄⋊Q₈	C₂²	1	16	yes	complemented
63	#66044	C₂²	1	32	yes	complemented
64	D₅×#126	C₂²	1	32	yes	complemented
65	#66016	C₂²	1	16	yes	complemented
66	D₅×#124	C₂²	1	32	yes	complemented
67	D₅×#124	C₂²	1	16	yes	complemented
68	#66003	C₂²	1	32	yes	complemented
69	#65996	C₂²	1	32	yes	complemented
70	D₅×#123	C₂²	1	32	yes	complemented
71	#65977	C₂²	1	16	yes	complemented
72	#65974	C₂²	1	32	yes	complemented
73	D₅×C₂²⋊Q₈	C₂²	1	32	yes	complemented
74	D₅×C₂²⋊Q₈	C₂²	1	16	yes	complemented
75	D₅×#121	C₂²	1	16	yes	—
76	#65937	C₂²	1	16	yes	complemented
77	#65916	C₂²	1	16	yes	complemented
78	C₄×Q₈×D₅	C₂²	1	16	yes	complemented
79	#65895	C₂²	1	16	yes	complemented
80	C₄×D₄×D₅	C₂²	1	16	yes	complemented
81	#65868	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×#4044	C₂²	1	2	yes	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×#4042	C₂²	1	2	yes	complemented
90	C₂×#4042	C₂²	1	2	yes	complemented
91	C₂×#4041	C₂²	1	1	yes	characteristic
92	C₂×#4040	C₂²	1	2	yes	complemented
93	C₂×#4040	C₂²	1	2	yes	complemented
94	C₂×#4039	C₂²	1	1	yes	characteristic, complemented
95	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
96	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
97	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	—
100	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₂×D₅×C₄⋊C₄	C₂²	1	2	yes	—
103	C₂×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
105	C₂×#4034	C₂²	1	2	yes	complemented
106	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
107	C₂×#4033	C₂²	1	2	yes	complemented
108	C₂×#4033	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×#4031	C₂²	1	2	yes	complemented
113	C₂×#4031	C₂²	1	2	yes	complemented
114	C₂×#4031	C₂²	1	2	yes	complemented
115	C₂×#4031	C₂²	1	2	yes	complemented
116	C₂×#4030	C₂²	1	2	yes	—
117	C₂×#4029	C₂²	1	2	yes	complemented
118	C₂×#4029	C₂²	1	2	yes	complemented
119	C₂×#4027	C₂²	1	2	yes	complemented
120	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₂×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₂×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
126	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
127	C₂×#4025	C₂²	1	2	yes	complemented
128	C₂×#4025	C₂²	1	2	yes	complemented
129	C₂×#4025	C₂²	1	2	yes	complemented
130	C₂×#4024	C₂²	1	2	yes	complemented
131	C₂×#4024	C₂²	1	2	yes	complemented
132	C₂×#4024	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×#4022	C₂²	1	2	yes	complemented
136	C₂×#4021	C₂²	1	1	yes	characteristic, complemented
137	C₂×#4021	C₂²	1	2	yes	complemented
138	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
139	C₂×#4018	C₂²	1	1	yes	characteristic, complemented
140	C₂×#4018	C₂²	1	1	yes	characteristic, complemented
141	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
142	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
143	C₂×C₄²×D₅	C₂²	1	2	yes	—
144	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
147	C₂²×#542	—	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	C₂³×Dic₅	C₂³	1	1	yes	characteristic
160	C₂³×Dic₅	C₂³	1	2	yes	—
161	C₂×Q₈×D₅	—	2	8	no	—
162	C₂×Q₈×D₅	—	4	8	no	—
163	C₂×Q₈×D₅	C₂³	1	8	yes	—
164	C₂×Q₈×D₅	C₂³	1	16	yes	—
165	C₂×D₄×D₅	—	2	8	no	—
166	C₂×D₄×D₅	—	4	8	no	—
167	C₂×D₄×D₅	C₂³	1	8	yes	—
168	C₂×D₄×D₅	C₂³	1	16	yes	—
169	C₂²×D₂₀	C₂³	1	1	yes	characteristic
170	C₂²×D₂₀	C₂³	1	2	yes	—
171	C₂²×C₄×D₅	—	2	8	no	—
172	C₂²×C₄×D₅	—	4	8	no	—
173	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
175	C₂²×C₄×D₅	C₂³	1	2	yes	—
176	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
178	C₂²×C₄×D₅	C₂³	1	2	yes	—
179	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₅	C₂³	1	2	yes	—
182	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₅	C₂³	1	8	yes	—
184	C₂²×C₄×D₅	C₂³	1	2	yes	—
185	C₂²×C₄×D₅	C₂³	1	2	yes	—
186	C₂²×C₄×D₅	C₂³	1	16	yes	—
187	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀	C₂³	1	2	yes	—
190	C₂²×Dic₁₀	C₂³	1	2	yes	—
191	C₂²×Dic₁₀	C₂³	1	2	yes	—
192	C₂²×Dic₁₀	C₂³	1	2	yes	—
193	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
194	C₅×#126	C₂³	1	16	yes	complemented
195	C₅×#124	C₂³	1	16	yes	complemented
196	C₅×#124	C₂³	1	8	yes	complemented
197	C₅×#123	C₂³	1	16	yes	complemented
198	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
200	C₅×#121	C₂³	1	8	yes	—
201	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
202	C₄×C₅×D₄	C₂³	1	8	yes	complemented
203	C₅×#117	C₂³	1	8	yes	complemented
204	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	2	yes	—
220	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
224	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
225	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
226	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
227	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
228	#4093	C₂³	1	16	yes	complemented
229	#4093	C₂³	1	8	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	#4090	C₂³	1	16	yes	complemented
234	#4085	C₂³	1	16	yes	—
235	#4084	C₂³	1	8	yes	—
236	#4082	C₂³	1	8	yes	complemented
237	#4082	C₂³	1	16	yes	complemented
238	#4081	C₂³	1	16	yes	complemented
239	D₄×Dic₅	C₂³	1	8	yes	complemented
240	#4076	C₂³	1	8	yes	—
241	#4075	C₂³	1	16	yes	complemented
242	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
243	C₂×#685	C₂³	1	1	yes	characteristic
244	C₂×#685	C₂³	1	1	yes	characteristic
245	C₂×#685	C₂³	1	1	yes	characteristic
246	C₂×#685	C₂³	1	1	yes	characteristic
247	C₂×#685	C₂³	1	2	yes	—
248	C₂×#685	C₂³	1	2	yes	—
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	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	#4072	C₂³	1	8	yes	complemented
258	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
260	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
262	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
264	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
265	#4070	C₂³	1	8	yes	complemented
266	#4070	C₂³	1	16	yes	complemented
267	C₂×#683	C₂³	1	2	yes	—
268	C₂×#683	C₂³	1	2	yes	—
269	C₂×#683	C₂³	1	2	yes	—
270	C₂×#683	C₂³	1	1	yes	characteristic
271	C₂×#683	C₂³	1	1	yes	characteristic
272	C₂×#683	C₂³	1	1	yes	characteristic
273	C₂×#683	C₂³	1	1	yes	characteristic
274	C₂×#683	C₂³	1	2	yes	—
275	C₂×#683	C₂³	1	2	yes	—
276	C₂×#683	C₂³	1	2	yes	—
277	C₂×#683	C₂³	1	2	yes	—
278	C₂×#683	C₂³	1	2	yes	—
279	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅	C₂³	1	2	yes	—
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	#4044	C₂³	1	16	yes	complemented
291	#4043	C₂³	1	8	yes	complemented
292	#4043	C₂³	1	16	yes	complemented
293	#4042	C₂³	1	16	yes	complemented
294	#4042	C₂³	1	16	yes	complemented
295	#4042	C₂³	1	16	yes	complemented
296	#4041	C₂³	1	8	yes	—
297	#4040	C₂³	1	16	yes	complemented
298	#4040	C₂³	1	16	yes	complemented
299	#4039	C₂³	1	8	yes	complemented
300	#4038	C₂³	1	8	yes	complemented
301	#4038	C₂³	1	8	yes	complemented
302	D₅×C₄⋊C₄	C₂³	1	8	yes	—
303	D₅×C₄⋊C₄	C₂³	1	8	yes	—
304	D₅×C₄⋊C₄	C₂³	1	16	yes	—
305	D₅×C₄⋊C₄	C₂³	1	8	yes	—
306	D₅×C₄⋊C₄	C₂³	1	8	yes	—
307	D₅×C₄⋊C₄	C₂³	1	16	yes	—
308	D₅×C₄⋊C₄	C₂³	1	16	yes	—
309	#4034	C₂³	1	8	yes	complemented
310	#4034	C₂³	1	8	yes	complemented
311	#4034	C₂³	1	16	yes	complemented
312	#4033	C₂³	1	8	yes	complemented
313	#4033	C₂³	1	16	yes	complemented
314	#4032	C₂³	1	16	yes	complemented
315	#4031	C₂³	1	16	yes	complemented
316	#4031	C₂³	1	16	yes	complemented
317	#4031	C₂³	1	16	yes	complemented
318	#4031	C₂³	1	16	yes	complemented
319	#4031	C₂³	1	16	yes	complemented
320	#4031	C₂³	1	16	yes	complemented
321	#4030	C₂³	1	16	yes	—
322	#4029	C₂³	1	16	yes	complemented
323	#4029	C₂³	1	16	yes	complemented
324	#4027	C₂³	1	16	yes	complemented
325	D₅×C₂²⋊C₄	C₂³	1	8	yes	—
326	D₅×C₂²⋊C₄	C₂³	1	8	yes	—
327	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
328	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
329	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
330	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
331	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
332	#4025	C₂³	1	16	yes	complemented
333	#4025	C₂³	1	16	yes	complemented
334	#4025	C₂³	1	16	yes	complemented
335	#4024	C₂³	1	16	yes	complemented
336	#4024	C₂³	1	16	yes	complemented
337	#4024	C₂³	1	16	yes	complemented
338	#4023	C₂³	1	8	yes	complemented
339	#4023	C₂³	1	8	yes	complemented
340	#4022	C₂³	1	16	yes	complemented
341	#4021	C₂³	1	8	yes	complemented
342	#4021	C₂³	1	16	yes	complemented
343	C₄×D₂₀	C₂³	1	8	yes	complemented
344	#4018	C₂³	1	8	yes	complemented
345	#4018	C₂³	1	8	yes	complemented
346	C₄²×D₅	C₂³	1	8	yes	—
347	C₄²×D₅	C₂³	1	8	yes	—
348	C₄²×D₅	C₂³	1	16	yes	—
349	#4015	C₂³	1	8	yes	complemented
350	C₄×Dic₁₀	C₂³	1	8	yes	complemented
351	C₄×Dic₁₀	C₂³	1	16	yes	complemented
352	C₂×#542	—	5	32	no	—
353	C₂×#542	—	5	1	no	—
354	C₂×#542	—	5	2	no	—
355	C₂×#542	—	5	2	no	—
356	C₂×#542	—	5	1	no	—
357	C₂×#542	—	5	2	no	—
358	C₂×#542	—	5	1	no	—
359	C₂×#542	—	5	2	no	—
360	C₂×#542	—	5	1	no	—
361	C₂×#542	—	5	1	no	—
362	C₂×#542	—	5	1	no	—
363	C₂×#542	—	5	1	no	—
364	C₂×#542	D₅	1	1	yes	characteristic, direct product factor
365	C₂²×C₄⋊Q₈	—	5	1	no	—
366	C₂²×#126	—	5	2	no	—
367	C₂²×#124	—	5	2	no	—
368	C₂²×#124	—	5	1	no	—
369	C₂²×#123	—	5	2	no	—
370	C₂²×C₂²⋊Q₈	—	5	2	no	—
371	C₂²×C₂²⋊Q₈	—	5	1	no	—
372	C₂²×#121	—	5	1	no	—
373	C₂²×C₄×Q₈	—	5	1	no	—
374	C₂²×C₄×D₄	—	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	8	no	—
380	C₂³×D₅	—	2	8	no	—
381	C₂³×D₅	—	2	4	no	—
382	C₂³×D₅	—	2	4	no	—
383	C₂³×D₅	—	2	8	no	—
384	C₂³×D₅	C₂⁴	1	1	yes	characteristic
385	C₂³×D₅	C₂⁴	1	2	yes	—
386	C₂³×D₅	C₂⁴	1	4	yes	—
387	C₂³×D₅	C₂⁴	1	8	yes	—
388	C₂³×D₅	C₂⁴	1	1	yes	characteristic
389	C₂×C₅×Q₈	—	2	4	no	—
390	C₂×C₅×Q₈	—	4	4	no	—
391	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
392	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
393	C₂×C₅×D₄	—	2	4	no	—
394	C₂×C₅×D₄	—	4	4	no	—
395	C₂×C₅×D₄	C₂⁴	1	4	yes	—
396	C₂×C₅×D₄	C₂⁴	1	8	yes	—
397	C₂²×C₄×C₅	—	2	4	no	—
398	C₂²×C₄×C₅	—	4	4	no	—
399	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
409	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
410	C₂×C₂²⋊D₅	—	2	8	no	—
411	C₂×C₂²⋊D₅	—	4	4	no	—
412	C₂×C₂²⋊D₅	—	4	4	no	—
413	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
414	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
415	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
416	C₂²×Dic₅	—	2	4	no	—
417	C₂²×Dic₅	—	4	4	no	—
418	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅	C₂⁴	1	2	yes	—
420	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅	C₂⁴	1	2	yes	—
423	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅	C₂⁴	1	2	yes	—
425	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅	C₂⁴	1	4	yes	—
427	C₂²×Dic₅	C₂⁴	1	8	yes	—
428	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
429	Q₈×D₅	—	2	32	no	—
430	Q₈×D₅	—	4	32	no	—
431	D₄×D₅	—	2	32	no	—
432	D₄×D₅	—	4	32	no	—
433	C₂×D₂₀	—	2	4	no	—
434	C₂×D₂₀	—	4	4	no	—
435	C₂×D₂₀	C₂⁴	1	4	yes	—
436	C₂×D₂₀	C₂⁴	1	8	yes	—
437	C₂×C₄×D₅	—	2	4	no	—
438	C₂×C₄×D₅	—	2	8	no	—
439	C₂×C₄×D₅	—	2	4	no	—
440	C₂×C₄×D₅	—	2	8	no	—
441	C₂×C₄×D₅	—	2	8	no	—
442	C₂×C₄×D₅	—	2	4	no	—
443	C₂×C₄×D₅	—	2	4	no	—
444	C₂×C₄×D₅	—	2	4	no	—
445	C₂×C₄×D₅	—	2	4	no	—
446	C₂×C₄×D₅	—	2	4	no	—
447	C₂×C₄×D₅	—	2	32	no	—
448	C₂×C₄×D₅	—	4	32	no	—
449	C₂×C₄×D₅	—	4	4	no	—
450	C₂×C₄×D₅	—	4	4	no	—
451	C₂×C₄×D₅	#41	1	8	yes	—
452	C₂×C₄×D₅	C₂⁴	1	4	yes	—
453	C₂×C₄×D₅	C₂⁴	1	8	yes	—
454	C₂×C₄×D₅	C₂⁴	1	4	yes	—
455	C₂×C₄×D₅	C₂⁴	1	4	yes	—
456	C₂×C₄×D₅	C₂⁴	1	4	yes	—
457	C₂×C₄×D₅	C₂⁴	1	8	yes	—
458	C₂×C₄×D₅	C₂⁴	1	4	yes	—
459	C₂×C₄×D₅	C₂⁴	1	8	yes	—
460	C₂×C₄×D₅	C₂⁴	1	4	yes	—
461	C₂×C₄×D₅	C₂⁴	1	4	yes	—
462	C₂×C₄×D₅	C₂⁴	1	8	yes	—
463	C₂×C₄×D₅	C₂⁴	1	8	yes	—
464	C₂×C₄×D₅	C₂⁴	1	4	yes	—
465	C₂×Dic₁₀	—	2	4	no	—
466	C₂×Dic₁₀	—	2	8	no	—
467	C₂×Dic₁₀	—	4	4	no	—
468	C₂×Dic₁₀	—	4	4	no	—
469	C₂×Dic₁₀	—	4	4	no	—
470	C₂×Dic₁₀	C₂⁴	1	4	yes	—
471	C₂×Dic₁₀	C₂⁴	1	8	yes	—
472	C₂×Dic₁₀	C₂⁴	1	8	yes	—
473	C₂×Dic₁₀	C₂⁴	1	8	yes	—
474	C₂×Dic₁₀	C₂⁴	1	8	yes	—
475	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
476	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
477	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
478	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
479	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
480	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
481	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
482	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
483	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
484	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
485	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
486	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
487	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
488	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
489	C₄²×C₅	C₂⁴	1	4	yes	—
490	C₄²×C₅	C₂⁴	1	4	yes	—
491	C₄²×C₅	C₂⁴	1	8	yes	—
492	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
493	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
494	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
495	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
496	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
497	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
498	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
499	#685	C₂⁴	1	4	yes	—
500	#685	C₂⁴	1	4	yes	—
501	#685	C₂⁴	1	4	yes	—
502	#685	C₂⁴	1	4	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	8	yes	—
509	#685	C₂⁴	1	8	yes	—
510	#685	C₂⁴	1	8	yes	—
511	#685	C₂⁴	1	8	yes	—
512	#685	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	C₄⋊Dic₅	C₂⁴	1	8	yes	—
517	C₄⋊Dic₅	C₂⁴	1	4	yes	—
518	C₄⋊Dic₅	C₂⁴	1	8	yes	—
519	C₄⋊Dic₅	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	4	yes	—
524	#683	C₂⁴	1	4	yes	—
525	#683	C₂⁴	1	4	yes	—
526	#683	C₂⁴	1	4	yes	—
527	#683	C₂⁴	1	8	yes	—
528	#683	C₂⁴	1	8	yes	—
529	#683	C₂⁴	1	8	yes	—
530	#683	C₂⁴	1	8	yes	—
531	#683	C₂⁴	1	8	yes	—
532	C₄×Dic₅	C₂⁴	1	4	yes	—
533	C₄×Dic₅	C₂⁴	1	8	yes	—
534	C₄×Dic₅	C₂⁴	1	4	yes	—
535	C₄×Dic₅	C₂⁴	1	4	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	8	yes	—
540	C₄×Dic₅	C₂⁴	1	8	yes	—
541	C₂³×Q₈	—	5	1	no	—
542	C₂³×Q₈	—	5	2	no	—
543	C₂³×D₄	—	5	1	no	—
544	C₂³×D₄	—	5	2	no	—
545	C₂⁴×C₄	—	5	1	no	—
546	C₂⁴×C₄	—	5	2	no	—
547	#542	—	5	16	no	—
548	#542	—	5	32	no	—
549	#542	—	5	32	no	—
550	#542	—	5	16	no	—
551	#542	—	5	32	no	—
552	#542	—	5	32	no	—
553	#542	—	5	16	no	—
554	#542	—	5	16	no	—
555	#542	—	5	16	no	—
556	#542	—	5	16	no	—
557	#542	—	5	16	no	—
558	#542	C₂×D₅	1	16	yes	direct product factor
559	C₂×C₄⋊Q₈	—	5	2	no	—
560	C₂×C₄⋊Q₈	—	5	16	no	—
561	C₂×C₄⋊Q₈	—	5	2	no	—
562	C₂×C₄⋊Q₈	—	5	1	no	—
563	C₂×C₄⋊Q₈	—	5	1	no	—
564	C₂×C₄⋊Q₈	—	5	1	no	—
565	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
566	C₂×#126	—	5	32	no	—
567	C₂×#126	—	5	2	no	—
568	C₂×#126	—	5	2	no	—
569	C₂×#126	—	5	2	no	—
570	C₂×#126	—	5	2	no	—
571	C₂×#126	—	5	2	no	—
572	C₂×#126	—	5	2	no	—
573	C₂×#126	—	5	2	no	—
574	C₂×#126	C₂×D₅	1	2	yes	complemented
575	C₂×#124	—	5	1	no	—
576	C₂×#124	—	5	2	no	—
577	C₂×#124	—	5	1	no	—
578	C₂×#124	—	5	2	no	—
579	C₂×#124	—	5	16	no	—
580	C₂×#124	—	5	32	no	—
581	C₂×#124	—	5	2	no	—
582	C₂×#124	—	5	2	no	—
583	C₂×#124	—	5	2	no	—
584	C₂×#124	—	5	2	no	—
585	C₂×#124	—	5	2	no	—
586	C₂×#124	—	5	2	no	—
587	C₂×#124	—	5	1	no	—
588	C₂×#124	—	5	2	no	—
589	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
590	C₂×#124	C₂×D₅	1	2	yes	complemented
591	C₂×#123	—	5	2	no	—
592	C₂×#123	—	5	2	no	—
593	C₂×#123	—	5	32	no	—
594	C₂×#123	—	5	2	no	—
595	C₂×#123	—	5	2	no	—
596	C₂×#123	—	5	2	no	—
597	C₂×#123	—	5	2	no	—
598	C₂×#123	—	5	2	no	—
599	C₂×#123	C₂×D₅	1	2	yes	complemented
600	C₂×C₂²⋊Q₈	—	5	2	no	—
601	C₂×C₂²⋊Q₈	—	5	1	no	—
602	C₂×C₂²⋊Q₈	—	5	2	no	—
603	C₂×C₂²⋊Q₈	—	5	1	no	—
604	C₂×C₂²⋊Q₈	—	5	32	no	—
605	C₂×C₂²⋊Q₈	—	5	16	no	—
606	C₂×C₂²⋊Q₈	—	5	2	no	—
607	C₂×C₂²⋊Q₈	—	5	2	no	—
608	C₂×C₂²⋊Q₈	—	5	2	no	—
609	C₂×C₂²⋊Q₈	—	5	2	no	—
610	C₂×C₂²⋊Q₈	—	5	1	no	—
611	C₂×C₂²⋊Q₈	—	5	2	no	—
612	C₂×C₂²⋊Q₈	—	5	2	no	—
613	C₂×C₂²⋊Q₈	—	5	2	no	—
614	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
615	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
616	C₂×#121	—	5	1	no	—
617	C₂×#121	—	5	2	no	—
618	C₂×#121	—	5	1	no	—
619	C₂×#121	—	5	16	no	—
620	C₂×#121	—	5	1	no	—
621	C₂×#121	—	5	2	no	—
622	C₂×#121	C₂×D₅	1	1	yes	characteristic
623	C₂×C₄×Q₈	—	5	1	no	—
624	C₂×C₄×Q₈	—	5	16	no	—
625	C₂×C₄×Q₈	—	5	2	no	—
626	C₂×C₄×Q₈	—	5	1	no	—
627	C₂×C₄×Q₈	—	5	2	no	—
628	C₂×C₄×Q₈	—	5	1	no	—
629	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
630	C₂×C₄×D₄	—	5	1	no	—
631	C₂×C₄×D₄	—	5	2	no	—
632	C₂×C₄×D₄	—	5	16	no	—
633	C₂×C₄×D₄	—	5	1	no	—
634	C₂×C₄×D₄	—	5	2	no	—
635	C₂×C₄×D₄	—	5	1	no	—
636	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
637	C₂×#117	—	5	1	no	—
638	C₂×#117	—	5	16	no	—
639	C₂×#117	—	5	1	no	—
640	C₂×#117	—	5	1	no	—
641	C₂×#117	—	5	1	no	—
642	C₂×#117	—	5	1	no	—
643	C₂×#117	—	5	1	no	—
644	C₂×#117	—	5	1	no	—
645	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
646	C₂²×C₄⋊C₄	—	5	1	no	—
647	C₂²×C₄⋊C₄	—	5	1	no	—
648	C₂²×C₄⋊C₄	—	5	1	no	—
649	C₂²×C₄⋊C₄	—	5	1	no	—
650	C₂²×C₄⋊C₄	—	5	2	no	—
651	C₂²×C₄⋊C₄	—	5	2	no	—
652	C₂²×C₄⋊C₄	—	5	2	no	—
653	C₂²×C₂²⋊C₄	—	5	1	no	—
654	C₂²×C₂²⋊C₄	—	5	1	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×C₂²⋊C₄	—	5	2	no	—
660	C₂²×C₄²	—	5	1	no	—
661	C₂²×C₄²	—	5	1	no	—
662	C₂²×C₄²	—	5	2	no	—
663	C₂³×C₅	—	2	2	no	—
664	C₂³×C₅	—	2	4	no	—
665	C₂³×C₅	—	2	4	no	—
666	C₂³×C₅	—	2	2	no	—
667	C₂³×C₅	—	2	2	no	—
668	C₂³×C₅	—	2	4	no	—
669	C₂³×C₅	C₂⁵	1	2	yes	—
670	C₂³×C₅	C₂⁵	1	4	yes	—
671	C₂³×C₅	C₂⁵	1	1	yes	characteristic
672	C₂²×D₅	—	2	2	no	—
673	C₂²×D₅	—	2	4	no	—
674	C₂²×D₅	—	2	4	no	—
675	C₂²×D₅	—	2	2	no	—
676	C₂²×D₅	—	2	2	no	—
677	C₂²×D₅	—	2	4	no	—
678	C₂²×D₅	—	2	8	no	—
679	C₂²×D₅	—	2	16	no	—
680	C₂²×D₅	—	2	16	no	—
681	C₂²×D₅	—	2	8	no	—
682	C₂²×D₅	—	2	8	no	—
683	C₂²×D₅	—	2	16	no	—
684	C₂²×D₅	—	4	16	no	—
685	C₂²×D₅	—	4	32	no	—
686	C₂²×D₅	C₂×#41	1	4	yes	—
687	C₂²×D₅	H(5,𝔽₂)	1	4	yes	—
688	C₂²×D₅	2₋¹⁺⁴	1	4	yes	—
689	C₂²×D₅	C₂⁵	1	2	yes	—
690	C₂²×D₅	C₂⁵	1	4	yes	—
691	C₂²×D₅	C₂⁵	1	2	yes	—
692	C₅×Q₈	—	2	8	no	—
693	C₅×Q₈	—	4	8	no	—
694	C₅×D₄	—	2	8	no	—
695	C₅×D₄	—	4	8	no	—
696	C₂×C₄×C₅	—	2	4	no	—
697	C₂×C₄×C₅	—	2	2	no	—
698	C₂×C₄×C₅	—	2	2	no	—
699	C₂×C₄×C₅	—	2	4	no	—
700	C₂×C₄×C₅	—	2	4	no	—
701	C₂×C₄×C₅	—	2	2	no	—
702	C₂×C₄×C₅	—	2	2	no	—
703	C₂×C₄×C₅	—	2	2	no	—
704	C₂×C₄×C₅	—	2	8	no	—
705	C₂×C₄×C₅	—	4	8	no	—
706	C₂×C₄×C₅	C₂×#41	1	4	yes	—
707	C₂×C₄×C₅	C₂⁵	1	2	yes	—
708	C₂×C₄×C₅	C₂⁵	1	4	yes	—
709	C₂×C₄×C₅	C₂⁵	1	2	yes	—
710	C₂×C₄×C₅	C₂⁵	1	2	yes	—
711	C₂×C₄×C₅	C₂⁵	1	4	yes	—
712	C₂×C₄×C₅	C₂⁵	1	2	yes	—
713	C₂×C₄×C₅	C₂⁵	1	2	yes	—
714	C₂×C₄×C₅	C₂⁵	1	4	yes	—
715	C₂×C₄×C₅	C₂⁵	1	2	yes	—
716	C₂²⋊D₅	—	2	16	no	—
717	C₂²⋊D₅	—	4	8	no	—
718	C₂²⋊D₅	—	4	8	no	—
719	C₂×Dic₅	—	2	4	no	—
720	C₂×Dic₅	—	2	2	no	—
721	C₂×Dic₅	—	2	2	no	—
722	C₂×Dic₅	—	2	4	no	—
723	C₂×Dic₅	—	2	4	no	—
724	C₂×Dic₅	—	2	2	no	—
725	C₂×Dic₅	—	2	2	no	—
726	C₂×Dic₅	—	2	2	no	—
727	C₂×Dic₅	—	2	8	no	—
728	C₂×Dic₅	—	4	8	no	—
729	C₂×Dic₅	C₂×#41	1	4	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	C₂×Dic₅	C₂⁵	1	4	yes	—
738	C₂×Dic₅	C₂⁵	1	2	yes	—
739	D₂₀	—	2	8	no	—
740	D₂₀	—	4	8	no	—
741	C₄×D₅	—	2	8	no	—
742	C₄×D₅	—	2	16	no	—
743	C₄×D₅	—	2	8	no	—
744	C₄×D₅	—	2	16	no	—
745	C₄×D₅	—	2	16	no	—
746	C₄×D₅	—	2	8	no	—
747	C₄×D₅	—	2	8	no	—
748	C₄×D₅	—	2	8	no	—
749	C₄×D₅	—	2	8	no	—
750	C₄×D₅	—	2	8	no	—
751	C₄×D₅	—	4	8	no	—
752	C₄×D₅	—	4	8	no	—
753	C₄×D₅	C₂×#41	1	16	yes	—
754	Dic₁₀	—	2	8	no	—
755	Dic₁₀	—	2	16	no	—
756	Dic₁₀	—	4	8	no	—
757	Dic₁₀	—	4	8	no	—
758	Dic₁₀	—	4	8	no	—
759	C₂⁵	—	5	1	no	—
760	C₂⁵	—	5	2	no	—
761	C₂²×Q₈	—	5	8	no	—
762	C₂²×Q₈	—	5	16	no	—
763	C₂²×Q₈	—	5	2	no	—
764	C₂²×Q₈	—	5	1	no	—
765	C₂²×Q₈	—	5	2	no	—
766	C₂²×Q₈	—	5	2	no	—
767	C₂²×Q₈	—	5	2	no	—
768	C₂²×Q₈	—	10	8	no	—
769	C₂²×Q₈	—	20	8	no	—
770	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
771	C₂²×Q₈	C₂²×D₅	1	2	yes	—
772	C₂²×D₄	—	5	2	no	—
773	C₂²×D₄	—	5	2	no	—
774	C₂²×D₄	—	5	2	no	—
775	C₂²×D₄	—	5	8	no	—
776	C₂²×D₄	—	5	16	no	—
777	C₂²×D₄	—	5	1	no	—
778	C₂²×D₄	—	5	2	no	—
779	C₂²×D₄	—	10	8	no	—
780	C₂²×D₄	—	20	8	no	—
781	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
782	C₂²×D₄	C₂²×D₅	1	2	yes	—
783	C₂³×C₄	—	5	1	no	—
784	C₂³×C₄	—	5	1	no	—
785	C₂³×C₄	—	5	2	no	—
786	C₂³×C₄	—	5	1	no	—
787	C₂³×C₄	—	5	2	no	—
788	C₂³×C₄	—	5	1	no	—
789	C₂³×C₄	—	5	1	no	—
790	C₂³×C₄	—	5	1	no	—
791	C₂³×C₄	—	5	2	no	—
792	C₂³×C₄	—	5	1	no	—
793	C₂³×C₄	—	5	2	no	—
794	C₂³×C₄	—	5	1	no	—
795	C₂³×C₄	—	5	8	no	—
796	C₂³×C₄	—	5	1	no	—
797	C₂³×C₄	—	5	2	no	—
798	C₂³×C₄	—	5	2	no	—
799	C₂³×C₄	—	5	16	no	—
800	C₂³×C₄	—	10	8	no	—
801	C₂³×C₄	—	20	8	no	—
802	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
803	C₂³×C₄	C₂²×D₅	1	2	yes	—
804	C₄⋊Q₈	—	5	16	no	—
805	C₄⋊Q₈	—	5	16	no	—
806	C₄⋊Q₈	—	5	8	no	—
807	C₄⋊Q₈	—	5	8	no	—
808	C₄⋊Q₈	—	5	8	no	—
809	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
810	#126	—	5	16	no	—
811	#126	—	5	16	no	—
812	#126	—	5	16	no	—
813	#126	—	5	16	no	—
814	#126	—	5	16	no	—
815	#126	—	5	16	no	—
816	#126	—	5	16	no	—
817	#126	C₂²×D₅	1	16	yes	complemented
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	16	no	—
824	#124	—	5	16	no	—
825	#124	—	5	16	no	—
826	#124	—	5	16	no	—
827	#124	—	5	16	no	—
828	#124	—	5	8	no	—
829	#124	—	5	16	no	—
830	#124	C₂²×D₅	1	8	yes	complemented
831	#124	C₂²×D₅	1	16	yes	complemented
832	#123	—	5	16	no	—
833	#123	—	5	16	no	—
834	#123	—	5	16	no	—
835	#123	—	5	16	no	—
836	#123	—	5	16	no	—
837	#123	—	5	16	no	—
838	#123	—	5	16	no	—
839	#123	C₂²×D₅	1	16	yes	complemented
840	C₂²⋊Q₈	—	5	16	no	—
841	C₂²⋊Q₈	—	5	8	no	—
842	C₂²⋊Q₈	—	5	16	no	—
843	C₂²⋊Q₈	—	5	8	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	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	16	yes	complemented
853	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
854	#121	—	5	8	no	—
855	#121	—	5	16	no	—
856	#121	—	5	8	no	—
857	#121	—	5	8	no	—
858	#121	—	5	16	no	—
859	#121	C₂²×D₅	1	8	yes	—
860	C₄×Q₈	—	5	8	no	—
861	C₄×Q₈	—	5	16	no	—
862	C₄×Q₈	—	5	8	no	—
863	C₄×Q₈	—	5	16	no	—
864	C₄×Q₈	—	5	8	no	—
865	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
866	C₄×D₄	—	5	8	no	—
867	C₄×D₄	—	5	16	no	—
868	C₄×D₄	—	5	8	no	—
869	C₄×D₄	—	5	16	no	—
870	C₄×D₄	—	5	8	no	—
871	C₄×D₄	C₂²×D₅	1	8	yes	complemented
872	#117	—	5	8	no	—
873	#117	—	5	8	no	—
874	#117	—	5	8	no	—
875	#117	—	5	8	no	—
876	#117	—	5	8	no	—
877	#117	—	5	8	no	—
878	#117	—	5	8	no	—
879	#117	C₂²×D₅	1	8	yes	complemented
880	C₂×C₄⋊C₄	—	5	1	no	—
881	C₂×C₄⋊C₄	—	5	1	no	—
882	C₂×C₄⋊C₄	—	5	1	no	—
883	C₂×C₄⋊C₄	—	5	1	no	—
884	C₂×C₄⋊C₄	—	5	1	no	—
885	C₂×C₄⋊C₄	—	5	1	no	—
886	C₂×C₄⋊C₄	—	5	2	no	—
887	C₂×C₄⋊C₄	—	5	1	no	—
888	C₂×C₄⋊C₄	—	5	2	no	—
889	C₂×C₄⋊C₄	—	5	1	no	—
890	C₂×C₄⋊C₄	—	5	2	no	—
891	C₂×C₄⋊C₄	—	5	2	no	—
892	C₂×C₄⋊C₄	—	5	2	no	—
893	C₂×C₄⋊C₄	—	5	2	no	—
894	C₂×C₄⋊C₄	—	5	2	no	—
895	C₂×C₄⋊C₄	—	5	2	no	—
896	C₂×C₄⋊C₄	—	5	2	no	—
897	C₂×C₄⋊C₄	—	5	2	no	—
898	C₂×C₄⋊C₄	—	5	2	no	—
899	C₂×C₄⋊C₄	—	5	8	no	—
900	C₂×C₄⋊C₄	—	5	8	no	—
901	C₂×C₄⋊C₄	—	5	8	no	—
902	C₂×C₄⋊C₄	—	5	8	no	—
903	C₂×C₄⋊C₄	—	5	16	no	—
904	C₂×C₄⋊C₄	—	5	16	no	—
905	C₂×C₄⋊C₄	—	5	16	no	—
906	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
911	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
912	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
913	C₂×C₂²⋊C₄	—	5	1	no	—
914	C₂×C₂²⋊C₄	—	5	1	no	—
915	C₂×C₂²⋊C₄	—	5	2	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	1	no	—
921	C₂×C₂²⋊C₄	—	5	1	no	—
922	C₂×C₂²⋊C₄	—	5	1	no	—
923	C₂×C₂²⋊C₄	—	5	1	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	2	no	—
929	C₂×C₂²⋊C₄	—	5	2	no	—
930	C₂×C₂²⋊C₄	—	5	2	no	—
931	C₂×C₂²⋊C₄	—	5	2	no	—
932	C₂×C₂²⋊C₄	—	5	2	no	—
933	C₂×C₂²⋊C₄	—	5	2	no	—
934	C₂×C₂²⋊C₄	—	5	8	no	—
935	C₂×C₂²⋊C₄	—	5	8	no	—
936	C₂×C₂²⋊C₄	—	5	16	no	—
937	C₂×C₂²⋊C₄	—	5	16	no	—
938	C₂×C₂²⋊C₄	—	5	16	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	1	yes	characteristic
943	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
944	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
945	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
946	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
947	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
948	C₂×C₄²	—	5	1	no	—
949	C₂×C₄²	—	5	1	no	—
950	C₂×C₄²	—	5	1	no	—
951	C₂×C₄²	—	5	1	no	—
952	C₂×C₄²	—	5	1	no	—
953	C₂×C₄²	—	5	1	no	—
954	C₂×C₄²	—	5	2	no	—
955	C₂×C₄²	—	5	2	no	—
956	C₂×C₄²	—	5	2	no	—
957	C₂×C₄²	—	5	8	no	—
958	C₂×C₄²	—	5	8	no	—
959	C₂×C₄²	—	5	16	no	—
960	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
961	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
962	C₂×C₄²	C₂²×D₅	1	2	yes	—
963	C₂²×C₅	—	2	2	no	—
964	C₂²×C₅	—	2	4	no	—
965	C₂²×C₅	—	2	4	no	—
966	C₂²×C₅	—	2	2	no	—
967	C₂²×C₅	—	2	2	no	—
968	C₂²×C₅	—	2	4	no	—
969	C₂²×C₅	—	4	4	no	—
970	C₂²×C₅	—	4	8	no	—
971	C₂²×C₅	C₂²×#41	1	2	yes	—
972	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
973	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
974	C₂²×C₅	C₂⁶	1	1	yes	characteristic
975	C₂×D₅	—	2	2	no	—
976	C₂×D₅	—	2	4	no	—
977	C₂×D₅	—	2	4	no	—
978	C₂×D₅	—	2	2	no	—
979	C₂×D₅	—	2	2	no	—
980	C₂×D₅	—	2	4	no	—
981	C₂×D₅	—	4	4	no	—
982	C₂×D₅	—	4	8	no	—
983	C₂×D₅	—	4	16	no	—
984	C₂×D₅	—	4	32	no	—
985	C₂×D₅	#542	1	16	yes	direct product factor
986	C₂×D₅	C₂²×#41	1	4	yes	—
987	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
988	C₂×D₅	C₂×2₋¹⁺⁴	1	4	yes	—
989	C₄×C₅	—	2	4	no	—
990	C₄×C₅	—	2	2	no	—
991	C₄×C₅	—	2	2	no	—
992	C₄×C₅	—	2	4	no	—
993	C₄×C₅	—	2	4	no	—
994	C₄×C₅	—	2	2	no	—
995	C₄×C₅	—	2	2	no	—
996	C₄×C₅	—	2	2	no	—
997	C₄×C₅	C₂²×#41	1	4	yes	—
998	Dic₅	—	2	4	no	—
999	Dic₅	—	2	2	no	—
1000	Dic₅	—	2	2	no	—
1001	Dic₅	—	2	4	no	—
1002	Dic₅	—	2	4	no	—
1003	Dic₅	—	2	2	no	—
1004	Dic₅	—	2	2	no	—
1005	Dic₅	—	2	2	no	—
1006	Dic₅	C₂²×#41	1	4	yes	—
1007	C₂⁴	—	5	1	no	—
1008	C₂⁴	—	5	4	no	—
1009	C₂⁴	—	5	8	no	—
1010	C₂⁴	—	5	1	no	—
1011	C₂⁴	—	5	2	no	—
1012	C₂⁴	—	10	4	no	—
1013	C₂⁴	—	10	8	no	—
1014	C₂⁴	—	10	8	no	—
1015	C₂⁴	—	10	4	no	—
1016	C₂⁴	—	10	4	no	—
1017	C₂⁴	—	10	8	no	—
1018	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1019	C₂⁴	C₂³×D₅	1	2	yes	—
1020	C₂×Q₈	—	2	4	no	—
1021	C₂×Q₈	—	4	4	no	—
1022	C₂×Q₈	—	5	8	no	—
1023	C₂×Q₈	—	5	4	no	—
1024	C₂×Q₈	—	5	8	no	—
1025	C₂×Q₈	—	5	8	no	—
1026	C₂×Q₈	—	5	8	no	—
1027	C₂×Q₈	—	10	8	no	—
1028	C₂×Q₈	—	10	32	no	—
1029	C₂×Q₈	—	10	4	no	—
1030	C₂×Q₈	—	20	4	no	—
1031	C₂×Q₈	—	20	4	no	—
1032	C₂×Q₈	—	20	4	no	—
1033	C₂×Q₈	—	20	32	no	—
1034	C₂×Q₈	C₂³×D₅	1	4	yes	—
1035	C₂×Q₈	C₂³×D₅	1	8	yes	—
1036	C₂×D₄	—	2	4	no	—
1037	C₂×D₄	—	4	4	no	—
1038	C₂×D₄	—	5	8	no	—
1039	C₂×D₄	—	5	8	no	—
1040	C₂×D₄	—	5	8	no	—
1041	C₂×D₄	—	5	4	no	—
1042	C₂×D₄	—	5	8	no	—
1043	C₂×D₄	—	10	32	no	—
1044	C₂×D₄	—	10	8	no	—
1045	C₂×D₄	—	10	4	no	—
1046	C₂×D₄	—	20	4	no	—
1047	C₂×D₄	—	20	32	no	—
1048	C₂×D₄	—	20	4	no	—
1049	C₂×D₄	—	20	4	no	—
1050	C₂×D₄	C₂³×D₅	1	4	yes	—
1051	C₂×D₄	C₂³×D₅	1	8	yes	—
1052	C₂²×C₄	—	2	4	no	—
1053	C₂²×C₄	—	4	4	no	—
1054	C₂²×C₄	—	5	1	no	—
1055	C₂²×C₄	—	5	8	no	—
1056	C₂²×C₄	—	5	4	no	—
1057	C₂²×C₄	—	5	4	no	—
1058	C₂²×C₄	—	5	1	no	—
1059	C₂²×C₄	—	5	1	no	—
1060	C₂²×C₄	—	5	2	no	—
1061	C₂²×C₄	—	5	1	no	—
1062	C₂²×C₄	—	5	1	no	—
1063	C₂²×C₄	—	5	2	no	—
1064	C₂²×C₄	—	5	1	no	—
1065	C₂²×C₄	—	5	2	no	—
1066	C₂²×C₄	—	5	8	no	—
1067	C₂²×C₄	—	5	4	no	—
1068	C₂²×C₄	—	5	4	no	—
1069	C₂²×C₄	—	5	8	no	—
1070	C₂²×C₄	—	5	4	no	—
1071	C₂²×C₄	—	5	4	no	—
1072	C₂²×C₄	—	5	8	no	—
1073	C₂²×C₄	—	5	4	no	—
1074	C₂²×C₄	—	5	8	no	—
1075	C₂²×C₄	—	5	4	no	—
1076	C₂²×C₄	—	5	4	no	—
1077	C₂²×C₄	—	5	8	no	—
1078	C₂²×C₄	—	5	8	no	—
1079	C₂²×C₄	—	10	4	no	—
1080	C₂²×C₄	—	10	32	no	—
1081	C₂²×C₄	—	10	4	no	—
1082	C₂²×C₄	—	10	4	no	—
1083	C₂²×C₄	—	10	8	no	—
1084	C₂²×C₄	—	10	8	no	—
1085	C₂²×C₄	—	10	8	no	—
1086	C₂²×C₄	—	10	4	no	—
1087	C₂²×C₄	—	10	4	no	—
1088	C₂²×C₄	—	10	4	no	—
1089	C₂²×C₄	—	10	4	no	—
1090	C₂²×C₄	—	10	4	no	—
1091	C₂²×C₄	—	20	4	no	—
1092	C₂²×C₄	—	20	4	no	—
1093	C₂²×C₄	—	20	32	no	—
1094	C₂²×C₄	—	20	4	no	—
1095	C₂²×C₄	C₂³×D₅	1	4	yes	—
1096	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1097	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1098	C₂²×C₄	C₂³×D₅	1	2	yes	—
1099	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1100	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1101	C₂²×C₄	C₂³×D₅	1	2	yes	—
1102	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1103	C₂²×C₄	C₂³×D₅	1	2	yes	—
1104	C₂²×C₄	C₂³×D₅	1	8	yes	—
1105	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1106	C₄⋊C₄	—	5	4	no	—
1107	C₄⋊C₄	—	5	4	no	—
1108	C₄⋊C₄	—	5	4	no	—
1109	C₄⋊C₄	—	5	4	no	—
1110	C₄⋊C₄	—	5	4	no	—
1111	C₄⋊C₄	—	5	4	no	—
1112	C₄⋊C₄	—	5	8	no	—
1113	C₄⋊C₄	—	5	4	no	—
1114	C₄⋊C₄	—	5	8	no	—
1115	C₄⋊C₄	—	5	4	no	—
1116	C₄⋊C₄	—	5	8	no	—
1117	C₄⋊C₄	—	5	8	no	—
1118	C₄⋊C₄	—	5	8	no	—
1119	C₄⋊C₄	—	5	8	no	—
1120	C₄⋊C₄	—	5	8	no	—
1121	C₄⋊C₄	—	5	8	no	—
1122	C₄⋊C₄	—	5	8	no	—
1123	C₄⋊C₄	—	5	8	no	—
1124	C₄⋊C₄	—	5	8	no	—
1125	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1126	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1127	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1128	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1129	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1130	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1131	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1132	C₂²⋊C₄	—	5	4	no	—
1133	C₂²⋊C₄	—	5	4	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	4	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	8	no	—
1146	C₂²⋊C₄	—	5	8	no	—
1147	C₂²⋊C₄	—	5	8	no	—
1148	C₂²⋊C₄	—	5	8	no	—
1149	C₂²⋊C₄	—	5	8	no	—
1150	C₂²⋊C₄	—	5	8	no	—
1151	C₂²⋊C₄	—	5	8	no	—
1152	C₂²⋊C₄	—	5	8	no	—
1153	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1154	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1155	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1156	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1157	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1158	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1159	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1160	C₄²	—	5	4	no	—
1161	C₄²	—	5	4	no	—
1162	C₄²	—	5	4	no	—
1163	C₄²	—	5	4	no	—
1164	C₄²	—	5	4	no	—
1165	C₄²	—	5	4	no	—
1166	C₄²	—	5	8	no	—
1167	C₄²	—	5	8	no	—
1168	C₄²	—	5	8	no	—
1169	C₄²	C₂³×D₅	1	4	yes	—
1170	C₄²	C₂³×D₅	1	4	yes	—
1171	C₄²	C₂³×D₅	1	8	yes	—
1172	C₂×C₅	—	4	2	no	—
1173	C₂×C₅	—	4	4	no	—
1174	C₂×C₅	C₂×#542	1	4	yes	complemented
1175	C₂×C₅	C₂³×#41	1	1	yes	characteristic
1176	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₂×C₅	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
1178	D₅	—	4	2	no	—
1179	D₅	—	4	4	no	—
1180	D₅	C₂×#542	1	8	yes	direct product factor
1181	C₂³	—	2	2	no	—
1182	C₂³	—	2	4	no	—
1183	C₂³	—	2	4	no	—
1184	C₂³	—	2	2	no	—
1185	C₂³	—	2	2	no	—
1186	C₂³	—	2	4	no	—
1187	C₂³	—	5	4	no	—
1188	C₂³	—	5	4	no	—
1189	C₂³	—	5	4	no	—
1190	C₂³	—	5	2	no	—
1191	C₂³	—	5	2	no	—
1192	C₂³	—	5	4	no	—
1193	C₂³	—	10	8	no	—
1194	C₂³	—	10	16	no	—
1195	C₂³	—	10	16	no	—
1196	C₂³	—	10	8	no	—
1197	C₂³	—	10	8	no	—
1198	C₂³	—	10	16	no	—
1199	C₂³	—	10	2	no	—
1200	C₂³	—	10	4	no	—
1201	C₂³	—	10	4	no	—
1202	C₂³	—	10	2	no	—
1203	C₂³	—	10	2	no	—
1204	C₂³	—	10	4	no	—
1205	C₂³	—	20	16	no	—
1206	C₂³	—	20	32	no	—
1207	C₂³	C₂⁴×D₅	1	2	yes	—
1208	C₂³	C₂⁴×D₅	1	4	yes	—
1209	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1210	Q₈	—	2	8	no	—
1211	Q₈	—	4	8	no	—
1212	Q₈	—	10	16	no	—
1213	Q₈	—	10	8	no	—
1214	Q₈	—	20	8	no	—
1215	Q₈	—	20	8	no	—
1216	Q₈	—	20	8	no	—
1217	D₄	—	2	8	no	—
1218	D₄	—	4	8	no	—
1219	D₄	—	10	16	no	—
1220	D₄	—	10	8	no	—
1221	D₄	—	20	8	no	—
1222	D₄	—	20	8	no	—
1223	D₄	—	20	8	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	4	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	4	no	—
1228	C₂×C₄	—	2	4	no	—
1229	C₂×C₄	—	2	2	no	—
1230	C₂×C₄	—	2	2	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	8	no	—
1233	C₂×C₄	—	4	8	no	—
1234	C₂×C₄	—	5	4	no	—
1235	C₂×C₄	—	5	2	no	—
1236	C₂×C₄	—	5	16	no	—
1237	C₂×C₄	—	5	2	no	—
1238	C₂×C₄	—	5	2	no	—
1239	C₂×C₄	—	5	4	no	—
1240	C₂×C₄	—	5	2	no	—
1241	C₂×C₄	—	5	2	no	—
1242	C₂×C₄	—	5	4	no	—
1243	C₂×C₄	—	5	2	no	—
1244	C₂×C₄	—	5	4	no	—
1245	C₂×C₄	—	10	8	no	—
1246	C₂×C₄	—	10	8	no	—
1247	C₂×C₄	—	10	8	no	—
1248	C₂×C₄	—	10	16	no	—
1249	C₂×C₄	—	10	16	no	—
1250	C₂×C₄	—	10	16	no	—
1251	C₂×C₄	—	10	8	no	—
1252	C₂×C₄	—	10	8	no	—
1253	C₂×C₄	—	10	8	no	—
1254	C₂×C₄	—	10	8	no	—
1255	C₂×C₄	—	10	2	no	—
1256	C₂×C₄	—	10	4	no	—
1257	C₂×C₄	—	10	2	no	—
1258	C₂×C₄	—	10	4	no	—
1259	C₂×C₄	—	10	4	no	—
1260	C₂×C₄	—	10	2	no	—
1261	C₂×C₄	—	10	2	no	—
1262	C₂×C₄	—	10	2	no	—
1263	C₂×C₄	—	10	8	no	—
1264	C₂×C₄	—	20	8	no	—
1265	C₂×C₄	—	20	8	no	—
1266	C₂×C₄	—	20	8	no	—
1267	C₂×C₄	D₅×#41	1	4	yes	—
1268	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1269	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1270	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1271	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1272	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1273	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1274	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1275	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1276	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1277	C₅	C₂²×#542	1	1	yes	characteristic, complemented, Sylow
1278	C₂²	—	2	2	no	—
1279	C₂²	—	2	4	no	—
1280	C₂²	—	2	4	no	—
1281	C₂²	—	2	2	no	—
1282	C₂²	—	2	2	no	—
1283	C₂²	—	2	4	no	—
1284	C₂²	—	4	4	no	—
1285	C₂²	—	4	8	no	—
1286	C₂²	—	5	4	no	—
1287	C₂²	—	5	4	no	—
1288	C₂²	—	5	4	no	—
1289	C₂²	—	5	16	no	—
1290	C₂²	—	10	2	no	—
1291	C₂²	—	10	4	no	—
1292	C₂²	—	10	4	no	—
1293	C₂²	—	10	2	no	—
1294	C₂²	—	10	2	no	—
1295	C₂²	—	10	4	no	—
1296	C₂²	—	20	16	no	—
1297	C₂²	—	20	32	no	—
1298	C₂²	—	20	4	no	—
1299	C₂²	—	20	8	no	—
1300	C₂²	C₂×D₅×#41	1	2	yes	—
1301	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
1302	C₂²	D₅×2₋¹⁺⁴	1	2	yes	—
1303	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1304	C₄	—	2	2	no	—
1305	C₄	—	2	4	no	—
1306	C₄	—	2	2	no	—
1307	C₄	—	2	4	no	—
1308	C₄	—	2	4	no	—
1309	C₄	—	2	2	no	—
1310	C₄	—	2	2	no	—
1311	C₄	—	2	2	no	—
1312	C₄	—	5	4	no	—
1313	C₄	—	10	2	no	—
1314	C₄	—	10	4	no	—
1315	C₄	—	10	2	no	—
1316	C₄	—	10	4	no	—
1317	C₄	—	10	4	no	—
1318	C₄	—	10	2	no	—
1319	C₄	—	10	2	no	—
1320	C₄	—	10	2	no	—
1321	C₄	C₂×D₅×#41	1	4	yes	—
1322	C₂	—	4	2	no	—
1323	C₂	—	4	4	no	—
1324	C₂	—	5	8	no	—
1325	C₂	—	20	2	no	—
1326	C₂	—	20	4	no	—
1327	C₂	D₅×#542	1	4	yes	direct product factor
1328	C₂	C₂²×D₅×#41	1	1	yes	characteristic
1329	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic
1330	C₂	C₂×D₅×2₋¹⁺⁴	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
prime radical	C₂×D₅×#121	C₂
hypercenter	C₂×#542	D₅
hypocenter	C₅	C₂²×#542
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. D₅×#542	C₂	direct (N × H)
3. C₂×#66067	C₂	semidirect
4. C₂×D₅×C₄⋊Q₈	C₂	semidirect
5. C₂×D₅×#126	C₂	semidirect
6. C₂×#66044	C₂	semidirect
7. C₂×#66016	C₂	semidirect
8. C₂×D₅×#124	C₂	semidirect
9. C₂×D₅×#124	C₂	semidirect
10. C₂×#66003	C₂	semidirect
11. C₂×D₅×#123	C₂	semidirect
12. C₂×#65996	C₂	semidirect
13. C₂×D₅×C₂²⋊Q₈	C₂	semidirect
14. C₂×D₅×C₂²⋊Q₈	C₂	semidirect
15. C₂×#65974	C₂	semidirect
16. C₂×#65977	C₂	semidirect
18. C₂×#65937	C₂	semidirect
19. C₂×#65916	C₂	semidirect
20. C₂×C₄×Q₈×D₅	C₂	semidirect
21. C₂×#65895	C₂	semidirect
22. C₂×C₄×D₄×D₅	C₂	semidirect
23. C₂×#65868	C₂	semidirect
24. C₂×D₅×#117	C₂	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
45. C₂×#4092	C₂²	semidirect
46. C₂×#4092	C₂²	semidirect
47. C₂×Q₈×Dic₅	C₂²	semidirect
48. C₂×#4090	C₂²	semidirect
51. C₂×#4082	C₂²	semidirect
52. C₂×#4082	C₂²	semidirect
53. C₂×#4081	C₂²	semidirect
54. C₂×D₄×Dic₅	C₂²	semidirect
56. C₂×#4075	C₂²	semidirect
57. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
58. C₂×#4072	C₂²	semidirect
59. C₂×#4070	C₂²	semidirect
60. C₂×#4070	C₂²	semidirect
61. #66067	C₂²	semidirect
62. D₅×C₄⋊Q₈	C₂²	semidirect
63. #66044	C₂²	semidirect
64. D₅×#126	C₂²	semidirect
65. #66016	C₂²	semidirect
66. D₅×#124	C₂²	semidirect
67. D₅×#124	C₂²	semidirect
68. #66003	C₂²	semidirect
69. #65996	C₂²	semidirect
70. D₅×#123	C₂²	semidirect
71. #65977	C₂²	semidirect
72. #65974	C₂²	semidirect
73. D₅×C₂²⋊Q₈	C₂²	semidirect
74. D₅×C₂²⋊Q₈	C₂²	semidirect
76. #65937	C₂²	semidirect
77. #65916	C₂²	semidirect
78. C₄×Q₈×D₅	C₂²	semidirect
79. #65895	C₂²	semidirect
80. C₄×D₄×D₅	C₂²	semidirect
81. #65868	C₂²	semidirect
82. D₅×#117	C₂²	semidirect
83. C₂×#4044	C₂²	semidirect
84. C₂×#4044	C₂²	semidirect
85. C₂×#4044	C₂²	semidirect
86. C₂×#4043	C₂²	semidirect
87. C₂×#4043	C₂²	semidirect
88. C₂×#4042	C₂²	semidirect
89. C₂×#4042	C₂²	semidirect
90. C₂×#4042	C₂²	semidirect
92. C₂×#4040	C₂²	semidirect
93. C₂×#4040	C₂²	semidirect
94. C₂×#4039	C₂²	semidirect
95. C₂×#4038	C₂²	semidirect
96. C₂×#4038	C₂²	semidirect
104. C₂×#4034	C₂²	semidirect
105. C₂×#4034	C₂²	semidirect
106. C₂×#4034	C₂²	semidirect
107. C₂×#4033	C₂²	semidirect
108. C₂×#4033	C₂²	semidirect
109. C₂×#4032	C₂²	semidirect
110. C₂×#4031	C₂²	semidirect
111. C₂×#4031	C₂²	semidirect
112. C₂×#4031	C₂²	semidirect
113. C₂×#4031	C₂²	semidirect
114. C₂×#4031	C₂²	semidirect
115. C₂×#4031	C₂²	semidirect
117. C₂×#4029	C₂²	semidirect
118. C₂×#4029	C₂²	semidirect
119. C₂×#4027	C₂²	semidirect
127. C₂×#4025	C₂²	semidirect
128. C₂×#4025	C₂²	semidirect
129. C₂×#4025	C₂²	semidirect
130. C₂×#4024	C₂²	semidirect
131. C₂×#4024	C₂²	semidirect
132. C₂×#4024	C₂²	semidirect
133. C₂×#4023	C₂²	semidirect
134. C₂×#4023	C₂²	semidirect
135. C₂×#4022	C₂²	semidirect
136. C₂×#4021	C₂²	semidirect
137. C₂×#4021	C₂²	semidirect
138. C₂×C₄×D₂₀	C₂²	semidirect
139. C₂×#4018	C₂²	semidirect
140. C₂×#4018	C₂²	semidirect
144. C₂×#4015	C₂²	semidirect
145. C₂×C₄×Dic₁₀	C₂²	semidirect
146. C₂×C₄×Dic₁₀	C₂²	semidirect
193. C₅×C₄⋊Q₈	C₂³	semidirect
194. C₅×#126	C₂³	semidirect
195. C₅×#124	C₂³	semidirect
196. C₅×#124	C₂³	semidirect
197. C₅×#123	C₂³	semidirect
198. C₅×C₂²⋊Q₈	C₂³	semidirect
199. C₅×C₂²⋊Q₈	C₂³	semidirect
201. C₄×C₅×Q₈	C₂³	semidirect
202. C₄×C₅×D₄	C₂³	semidirect
203. C₅×#117	C₂³	semidirect
228. #4093	C₂³	semidirect
229. #4093	C₂³	semidirect
230. #4092	C₂³	semidirect
231. #4092	C₂³	semidirect
232. Q₈×Dic₅	C₂³	semidirect
233. #4090	C₂³	semidirect
236. #4082	C₂³	semidirect
237. #4082	C₂³	semidirect
238. #4081	C₂³	semidirect
239. D₄×Dic₅	C₂³	semidirect
241. #4075	C₂³	semidirect
242. C₄×C₂²⋊D₅	C₂³	semidirect
257. #4072	C₂³	semidirect
265. #4070	C₂³	semidirect
266. #4070	C₂³	semidirect
288. #4044	C₂³	semidirect
289. #4044	C₂³	semidirect
290. #4044	C₂³	semidirect
291. #4043	C₂³	semidirect
292. #4043	C₂³	semidirect
293. #4042	C₂³	semidirect
294. #4042	C₂³	semidirect
295. #4042	C₂³	semidirect
297. #4040	C₂³	semidirect
298. #4040	C₂³	semidirect
299. #4039	C₂³	semidirect
300. #4038	C₂³	semidirect
301. #4038	C₂³	semidirect
309. #4034	C₂³	semidirect
310. #4034	C₂³	semidirect
311. #4034	C₂³	semidirect
312. #4033	C₂³	semidirect
313. #4033	C₂³	semidirect
314. #4032	C₂³	semidirect
315. #4031	C₂³	semidirect
316. #4031	C₂³	semidirect
317. #4031	C₂³	semidirect
318. #4031	C₂³	semidirect
319. #4031	C₂³	semidirect
320. #4031	C₂³	semidirect
322. #4029	C₂³	semidirect
323. #4029	C₂³	semidirect
324. #4027	C₂³	semidirect
332. #4025	C₂³	semidirect
333. #4025	C₂³	semidirect
334. #4025	C₂³	semidirect
335. #4024	C₂³	semidirect
336. #4024	C₂³	semidirect
337. #4024	C₂³	semidirect
338. #4023	C₂³	semidirect
339. #4023	C₂³	semidirect
340. #4022	C₂³	semidirect
341. #4021	C₂³	semidirect
342. #4021	C₂³	semidirect
343. C₄×D₂₀	C₂³	semidirect
344. #4018	C₂³	semidirect
345. #4018	C₂³	semidirect
349. #4015	C₂³	semidirect
350. C₄×Dic₁₀	C₂³	semidirect
351. C₄×Dic₁₀	C₂³	semidirect
364. C₂×#542	D₅	direct (N × H)
558. #542	C₂×D₅	direct (N × H)
565. C₂×C₄⋊Q₈	C₂×D₅	semidirect
574. C₂×#126	C₂×D₅	semidirect
589. C₂×#124	C₂×D₅	semidirect
590. C₂×#124	C₂×D₅	semidirect
599. C₂×#123	C₂×D₅	semidirect
614. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
615. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
629. C₂×C₄×Q₈	C₂×D₅	semidirect
636. C₂×C₄×D₄	C₂×D₅	semidirect
645. C₂×#117	C₂×D₅	semidirect
809. C₄⋊Q₈	C₂²×D₅	semidirect
817. #126	C₂²×D₅	semidirect
830. #124	C₂²×D₅	semidirect
831. #124	C₂²×D₅	semidirect
839. #123	C₂²×D₅	semidirect
852. C₂²⋊Q₈	C₂²×D₅	semidirect
853. C₂²⋊Q₈	C₂²×D₅	semidirect
865. C₄×Q₈	C₂²×D₅	semidirect
871. C₄×D₄	C₂²×D₅	semidirect
879. #117	C₂²×D₅	semidirect
985. C₂×D₅	#542	direct (N × H)
1174. C₂×C₅	C₂×#542	semidirect
1180. D₅	C₂×#542	direct (N × H)
1277. C₅	C₂²×#542	semidirect
1327. C₂	D₅×#542	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
D₅×#542	2
C₂×#66067	2
C₂×D₅×C₄⋊Q₈	2
C₂×D₅×#126	2
C₂×#66044	2
C₂×#66016	2
C₂×D₅×#124	2
C₂×#66003	2
C₂×D₅×#123	2
C₂×#65996	2
C₂×D₅×C₂²⋊Q₈	2
C₂×#65974	2
C₂×#65977	2
C₂×D₅×#121	2
C₂×#65937	2
C₂×#65916	2
C₂×C₄×Q₈×D₅	2
C₂×#65895	2
C₂×C₄×D₄×D₅	2
C₂×#65868	2
C₂×D₅×#117	2
C₂²×#542	5

Subgroups — C2×D5×#542 #13006079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#542 #13006079