Subgroups — C₂×#10618315 #13007211

Order 1280.

9502 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×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618315	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66039	C₂	1	2	yes	maximal, complemented
4	C₂×#66039	C₂	1	2	yes	maximal, complemented
5	C₂×#66013	C₂	1	2	yes	maximal, complemented
6	C₂×#66010	C₂	1	2	yes	maximal, complemented
7	C₂×#65993	C₂	1	2	yes	maximal, complemented
8	C₂×#65988	C₂	1	2	yes	maximal, complemented
9	C₂×#65968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65961	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65946	C₂	1	2	yes	maximal, complemented
12	C₂×#65944	C₂	1	2	yes	maximal, complemented
13	C₂×#65939	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#65940	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₅×#120	C₂	1	2	yes	maximal, complemented
16	C₂×#65927	C₂	1	2	yes	maximal, complemented
17	C₂×#65881	C₂	1	2	yes	maximal, complemented
18	C₂×#65879	C₂	1	2	yes	maximal, complemented
19	C₂×#65828	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂⁵×D₅	C₂²	1	1	yes	characteristic
22	C₂²×#713	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#711	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₄×D₅	C₂²	1	2	yes	—
25	C₂²×D₄×D₅	C₂²	1	2	yes	complemented
26	C₂²×D₄×D₅	C₂²	1	2	yes	complemented
27	C₂²×#709	C₂²	1	2	yes	complemented
28	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
29	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
30	C₅×#538	C₂²	1	16	yes	complemented
31	C₂×C₅×#126	C₂²	1	2	yes	complemented
32	C₂×C₅×#124	C₂²	1	2	yes	complemented
33	C₂×C₅×#123	C₂²	1	2	yes	complemented
34	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#121	C₂²	1	2	yes	complemented
36	C₂×C₅×#121	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#120	C₂²	1	2	yes	complemented
38	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
39	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×#4099	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
42	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
43	C₂×#4092	C₂²	1	2	yes	complemented
44	C₂×#4085	C₂²	1	2	yes	complemented
45	C₂×#4085	C₂²	1	2	yes	complemented
46	C₂×#4084	C₂²	1	2	yes	complemented
47	C₂×#4084	C₂²	1	1	yes	characteristic, complemented
48	C₂×#4083	C₂²	1	2	yes	—
49	C₂×#4083	C₂²	1	2	yes	—
50	C₂×#4083	C₂²	1	2	yes	complemented
51	C₂×#4083	C₂²	1	2	yes	complemented
52	C₂×#4082	C₂²	1	2	yes	complemented
53	C₂×#4081	C₂²	1	2	yes	complemented
54	C₂×D₄×Dic₅	C₂²	1	2	yes	complemented
55	C₂×#4076	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	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	1	yes	characteristic
60	C₂²×#685	C₂²	1	1	yes	characteristic
61	C₂²×#685	C₂²	1	2	yes	complemented
62	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
63	#66039	C₂²	1	32	yes	complemented
64	#66039	C₂²	1	32	yes	complemented
65	#66013	C₂²	1	32	yes	complemented
66	#66010	C₂²	1	32	yes	complemented
67	#65993	C₂²	1	32	yes	complemented
68	#65988	C₂²	1	32	yes	complemented
69	#65968	C₂²	1	16	yes	complemented
70	#65961	C₂²	1	16	yes	complemented
71	#65946	C₂²	1	32	yes	complemented
72	#65944	C₂²	1	32	yes	complemented
73	#65940	C₂²	1	16	yes	complemented
74	#65939	C₂²	1	16	yes	complemented
75	#65927	C₂²	1	32	yes	complemented
76	D₅×#120	C₂²	1	32	yes	complemented
77	#65881	C₂²	1	32	yes	complemented
78	#65879	C₂²	1	32	yes	complemented
79	C₂×#4043	C₂²	1	2	yes	complemented
80	C₂×#4043	C₂²	1	1	yes	characteristic, complemented
81	C₂×#4042	C₂²	1	2	yes	complemented
82	C₂×#4042	C₂²	1	2	yes	complemented
83	C₂×#4042	C₂²	1	2	yes	complemented
84	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
85	C₂×#4040	C₂²	1	2	yes	complemented
86	C₂×#4040	C₂²	1	2	yes	complemented
87	C₂×#4040	C₂²	1	2	yes	complemented
88	C₂×#4039	C₂²	1	2	yes	complemented
89	C₂×#4039	C₂²	1	2	yes	complemented
90	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
91	C₂×#4038	C₂²	1	2	yes	complemented
92	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
93	#65828	C₂²	1	16	yes	complemented
94	C₂×#4031	C₂²	1	2	yes	complemented
95	C₂×#4031	C₂²	1	2	yes	complemented
96	C₂×#4030	C₂²	1	2	yes	complemented
97	C₂×#4030	C₂²	1	2	yes	complemented
98	C₂×#4029	C₂²	1	2	yes	complemented
99	C₂×#4029	C₂²	1	2	yes	complemented
100	C₂×#4029	C₂²	1	2	yes	complemented
101	C₂×#4029	C₂²	1	2	yes	complemented
102	C₂×#4029	C₂²	1	2	yes	complemented
103	C₂×#4028	C₂²	1	2	yes	—
104	C₂×#4028	C₂²	1	2	yes	—
105	C₂×#4028	C₂²	1	2	yes	complemented
106	C₂×#4028	C₂²	1	2	yes	complemented
107	C₂×#4027	C₂²	1	2	yes	complemented
108	C₂×#4027	C₂²	1	2	yes	complemented
109	C₂×#4027	C₂²	1	2	yes	complemented
110	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₂×D₅×C₂²⋊C₄	C₂²	1	16	yes	complemented
119	C₂×#4025	C₂²	1	2	yes	complemented
120	C₂×#4025	C₂²	1	2	yes	complemented
121	C₂×#4025	C₂²	1	2	yes	complemented
122	C₂×#4024	C₂²	1	2	yes	complemented
123	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
124	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
125	C₂×#4018	C₂²	1	2	yes	complemented
126	C₂×#4018	C₂²	1	2	yes	complemented
127	C₂×#3490	—	5	1	no	maximal, Sylow
128	C₂⁵×C₅	C₂³	1	1	yes	characteristic
129	C₂⁴×D₅	—	2	8	no	—
130	C₂⁴×D₅	—	4	4	no	—
131	C₂⁴×D₅	—	4	4	no	—
132	C₂⁴×D₅	C₂³	1	1	yes	characteristic
133	C₂⁴×D₅	C₂³	1	2	yes	—
134	C₂⁴×D₅	C₂³	1	2	yes	—
135	C₂⁴×D₅	C₂³	1	8	yes	—
136	C₂⁴×D₅	C₂³	1	2	yes	—
137	C₂⁴×D₅	C₂³	1	1	yes	characteristic
138	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
139	C₂²×C₅×D₄	C₂³	1	2	yes	—
140	C₂²×C₅×D₄	C₂³	1	2	yes	—
141	C₂²×C₅×D₄	C₂³	1	2	yes	—
142	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
143	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅	C₂³	1	2	yes	complemented
146	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
148	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
149	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
152	C₂²×C₂²⋊D₅	C₂³	1	2	yes	complemented
153	C₂³×Dic₅	C₂³	1	1	yes	characteristic
154	C₂³×Dic₅	C₂³	1	1	yes	characteristic
155	C₂³×Dic₅	C₂³	1	2	yes	complemented
156	C₂×#713	—	4	4	no	—
157	C₂×#713	C₂³	1	8	yes	complemented
158	C₂×#711	—	4	4	no	—
159	C₂×#711	C₂³	1	8	yes	complemented
160	C₂×D₄×D₅	—	2	16	no	—
161	C₂×D₄×D₅	—	4	8	no	—
162	C₂×D₄×D₅	—	4	8	no	—
163	C₂×D₄×D₅	C₂³	1	16	yes	—
164	C₂×D₄×D₅	C₂³	1	16	yes	complemented
165	C₂×D₄×D₅	C₂³	1	16	yes	complemented
166	C₂×#709	—	4	8	no	—
167	C₂×#709	C₂³	1	16	yes	complemented
168	C₂²×D₂₀	C₂³	1	2	yes	—
169	C₂²×D₂₀	C₂³	1	2	yes	—
170	C₂²×D₂₀	C₂³	1	2	yes	—
171	C₂²×D₂₀	C₂³	1	1	yes	characteristic, complemented
172	C₂²×C₄×D₅	—	4	4	no	—
173	C₂²×C₄×D₅	—	4	4	no	—
174	C₂²×C₄×D₅	C₂³	1	2	yes	—
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	2	yes	—
180	C₂²×C₄×D₅	C₂³	1	2	yes	—
181	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
182	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
183	C₂²×C₄×D₅	C₂³	1	8	yes	complemented
184	C₂²×C₄×D₅	C₂³	1	8	yes	complemented
185	C₂²×C₄×D₅	C₂³	1	2	yes	complemented
186	C₂²×C₄×D₅	C₂³	1	2	yes	complemented
187	C₂²×Dic₁₀	C₂³	1	2	yes	complemented
188	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic, complemented
189	C₅×#126	C₂³	1	16	yes	complemented
190	C₅×#124	C₂³	1	16	yes	complemented
191	C₅×#123	C₂³	1	16	yes	complemented
192	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
193	C₅×#121	C₂³	1	16	yes	complemented
194	C₅×#121	C₂³	1	8	yes	complemented
195	C₅×#120	C₂³	1	16	yes	complemented
196	C₄×C₅×D₄	C₂³	1	16	yes	complemented
197	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
198	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
199	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
200	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
209	C₂×C₄²×C₅	C₂³	1	2	yes	complemented
210	#4099	C₂³	1	16	yes	complemented
211	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
212	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
213	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
214	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
215	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
216	C₂×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
217	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	complemented
218	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	complemented
219	#4092	C₂³	1	8	yes	complemented
220	#4092	C₂³	1	16	yes	complemented
221	#4085	C₂³	1	16	yes	complemented
222	#4085	C₂³	1	16	yes	complemented
223	#4084	C₂³	1	16	yes	complemented
224	#4084	C₂³	1	8	yes	complemented
225	#4083	C₂³	1	16	yes	—
226	#4083	C₂³	1	16	yes	—
227	#4083	C₂³	1	16	yes	complemented
228	#4083	C₂³	1	16	yes	complemented
229	#4082	C₂³	1	16	yes	complemented
230	#4081	C₂³	1	16	yes	complemented
231	D₄×Dic₅	C₂³	1	16	yes	complemented
232	#4076	C₂³	1	8	yes	complemented
233	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
234	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
235	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
236	C₂×#685	C₂³	1	2	yes	—
237	C₂×#685	C₂³	1	2	yes	—
238	C₂×#685	C₂³	1	2	yes	—
239	C₂×#685	C₂³	1	2	yes	—
240	C₂×#685	C₂³	1	2	yes	—
241	C₂×#685	C₂³	1	2	yes	—
242	C₂×#685	C₂³	1	2	yes	—
243	C₂×#685	C₂³	1	2	yes	—
244	C₂×#685	C₂³	1	2	yes	—
245	C₂×#685	C₂³	1	8	yes	—
246	C₂×#685	C₂³	1	8	yes	—
247	C₂×#685	C₂³	1	2	yes	—
248	C₂×#685	C₂³	1	16	yes	complemented
249	C₂×#685	C₂³	1	2	yes	complemented
250	C₂×#685	C₂³	1	2	yes	complemented
251	C₂×#685	C₂³	1	2	yes	complemented
252	C₂×#685	C₂³	1	2	yes	complemented
253	C₂×C₄⋊Dic₅	C₂³	1	2	yes	complemented
254	C₂×C₄⋊Dic₅	C₂³	1	2	yes	complemented
255	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
256	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
257	#4070	C₂³	1	8	yes	complemented
258	C₂×#683	C₂³	1	2	yes	complemented
259	C₂×#683	C₂³	1	2	yes	complemented
260	C₂×#683	C₂³	1	2	yes	complemented
261	C₂×#683	C₂³	1	2	yes	complemented
262	C₂×#683	C₂³	1	2	yes	complemented
263	C₂×#683	C₂³	1	2	yes	complemented
264	C₂×C₄×Dic₅	C₂³	1	2	yes	complemented
265	C₂×C₄×Dic₅	C₂³	1	2	yes	complemented
266	C₂×C₄×Dic₅	C₂³	1	2	yes	complemented
267	#4043	C₂³	1	8	yes	complemented
268	#4043	C₂³	1	16	yes	complemented
269	#4042	C₂³	1	16	yes	complemented
270	#4042	C₂³	1	16	yes	complemented
271	#4042	C₂³	1	16	yes	complemented
272	#4041	C₂³	1	8	yes	complemented
273	#4040	C₂³	1	16	yes	complemented
274	#4040	C₂³	1	16	yes	complemented
275	#4040	C₂³	1	16	yes	complemented
276	#4039	C₂³	1	16	yes	complemented
277	#4039	C₂³	1	16	yes	complemented
278	#4038	C₂³	1	16	yes	complemented
279	#4038	C₂³	1	8	yes	complemented
280	#4038	C₂³	1	8	yes	complemented
281	#4031	C₂³	1	16	yes	complemented
282	#4031	C₂³	1	16	yes	complemented
283	#4030	C₂³	1	16	yes	complemented
284	#4030	C₂³	1	16	yes	complemented
285	#4029	C₂³	1	16	yes	complemented
286	#4029	C₂³	1	16	yes	complemented
287	#4029	C₂³	1	16	yes	complemented
288	#4029	C₂³	1	16	yes	complemented
289	#4029	C₂³	1	16	yes	complemented
290	#4028	C₂³	1	16	yes	—
291	#4028	C₂³	1	16	yes	—
292	#4028	C₂³	1	16	yes	complemented
293	#4028	C₂³	1	16	yes	complemented
294	#4027	C₂³	1	16	yes	complemented
295	#4027	C₂³	1	16	yes	complemented
296	#4027	C₂³	1	16	yes	complemented
297	D₅×C₂²⋊C₄	C₂³	1	16	yes	—
298	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
299	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
300	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
301	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
302	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
303	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
304	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
305	#4025	C₂³	1	16	yes	complemented
306	#4025	C₂³	1	16	yes	complemented
307	#4025	C₂³	1	16	yes	complemented
308	#4024	C₂³	1	16	yes	complemented
309	C₄×D₂₀	C₂³	1	16	yes	complemented
310	C₄×D₂₀	C₂³	1	16	yes	complemented
311	#4018	C₂³	1	16	yes	complemented
312	#4018	C₂³	1	16	yes	complemented
313	#3490	—	5	32	no	—
314	C₂×#551	—	5	2	no	—
315	C₂×#551	—	5	2	no	—
316	C₂×#551	—	5	2	no	—
317	C₂×#551	—	5	2	no	—
318	C₂×#546	—	5	2	no	—
319	C₂×#546	—	5	2	no	—
320	C₂×#546	—	5	2	no	—
321	C₂×#546	—	5	2	no	—
322	C₂×#543	—	5	1	no	—
323	C₂×#538	—	5	2	no	—
324	C₂×#538	—	5	1	no	—
325	C₂×#538	D₅	1	1	yes	characteristic, complemented
326	C₂×#534	—	5	1	no	—
327	C₂×#525	—	5	1	no	—
328	C₂×#525	—	5	1	no	—
329	C₂×#525	—	5	2	no	—
330	C₂²×#120	—	5	2	no	—
331	C₂×#518	—	5	2	no	—
332	C₂³×C₂²⋊C₄	—	5	1	no	—
333	C₂⁴×C₅	—	2	4	no	—
334	C₂⁴×C₅	—	4	2	no	—
335	C₂⁴×C₅	—	4	2	no	—
336	C₂⁴×C₅	C₂⁴	1	2	yes	—
337	C₂⁴×C₅	C₂⁴	1	2	yes	—
338	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
339	C₂⁴×C₅	C₂⁴	1	4	yes	—
340	C₂³×D₅	—	2	4	no	—
341	C₂³×D₅	—	2	4	no	—
342	C₂³×D₅	—	2	4	no	—
343	C₂³×D₅	—	2	8	no	—
344	C₂³×D₅	—	2	8	no	—
345	C₂³×D₅	—	2	32	no	—
346	C₂³×D₅	—	2	8	no	—
347	C₂³×D₅	—	2	8	no	—
348	C₂³×D₅	—	2	8	no	—
349	C₂³×D₅	—	4	16	no	—
350	C₂³×D₅	—	4	16	no	—
351	C₂³×D₅	—	4	4	no	—
352	C₂³×D₅	—	4	4	no	—
353	C₂³×D₅	—	4	2	no	—
354	C₂³×D₅	—	4	2	no	—
355	C₂³×D₅	—	4	4	no	—
356	C₂³×D₅	—	4	4	no	—
357	C₂³×D₅	—	4	64	no	—
358	C₂³×D₅	#41	1	8	yes	complemented
359	C₂³×D₅	C₂⁴	1	4	yes	—
360	C₂³×D₅	C₂⁴	1	2	yes	—
361	C₂³×D₅	C₂⁴	1	8	yes	—
362	C₂³×D₅	C₂⁴	1	8	yes	—
363	C₂³×D₅	C₂⁴	1	2	yes	—
364	C₂³×D₅	C₂⁴	1	1	yes	characteristic
365	C₂³×D₅	C₂⁴	1	1	yes	characteristic
366	C₂³×D₅	C₂⁴	1	8	yes	—
367	C₂³×D₅	C₂⁴	1	4	yes	—
368	C₂×C₅×Q₈	—	4	2	no	—
369	C₂×C₅×Q₈	C₂⁴	1	4	yes	complemented
370	C₂×C₅×D₄	—	2	8	no	—
371	C₂×C₅×D₄	—	4	4	no	—
372	C₂×C₅×D₄	—	4	4	no	—
373	C₂×C₅×D₄	—	4	2	no	—
374	C₂×C₅×D₄	C₂⁴	1	8	yes	—
375	C₂×C₅×D₄	C₂⁴	1	8	yes	—
376	C₂×C₅×D₄	C₂⁴	1	8	yes	—
377	C₂×C₅×D₄	C₂⁴	1	4	yes	complemented
378	C₂²×C₄×C₅	—	4	2	no	—
379	C₂²×C₄×C₅	—	4	2	no	—
380	C₂²×C₄×C₅	—	4	4	no	—
381	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
389	C₂²×C₄×C₅	C₂⁴	1	8	yes	complemented
390	C₂×C₂²⋊D₅	—	2	8	no	—
391	C₂×C₂²⋊D₅	—	2	8	no	—
392	C₂×C₂²⋊D₅	—	2	8	no	—
393	C₂×C₂²⋊D₅	—	2	8	no	—
394	C₂×C₂²⋊D₅	—	4	4	no	—
395	C₂×C₂²⋊D₅	—	4	4	no	—
396	C₂×C₂²⋊D₅	—	4	4	no	—
397	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
398	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
399	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
400	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
401	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
402	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
403	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	complemented
404	C₂²×Dic₅	—	4	2	no	—
405	C₂²×Dic₅	—	4	2	no	—
406	C₂²×Dic₅	—	4	4	no	—
407	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₅	C₂⁴	1	2	yes	—
409	C₂²×Dic₅	C₂⁴	1	2	yes	—
410	C₂²×Dic₅	C₂⁴	1	2	yes	—
411	C₂²×Dic₅	C₂⁴	1	2	yes	—
412	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅	C₂⁴	1	4	yes	—
414	C₂²×Dic₅	C₂⁴	1	4	yes	—
415	C₂²×Dic₅	C₂⁴	1	8	yes	complemented
416	#713	—	4	16	no	—
417	#711	—	4	16	no	—
418	D₄×D₅	—	2	64	no	—
419	D₄×D₅	—	4	32	no	—
420	D₄×D₅	—	4	32	no	—
421	#709	—	4	32	no	—
422	C₂×D₂₀	—	2	8	no	—
423	C₂×D₂₀	—	2	8	no	—
424	C₂×D₂₀	—	2	8	no	—
425	C₂×D₂₀	—	4	2	no	—
426	C₂×D₂₀	C₂⁴	1	8	yes	—
427	C₂×D₂₀	C₂⁴	1	8	yes	—
428	C₂×D₂₀	C₂⁴	1	8	yes	—
429	C₂×D₂₀	C₂⁴	1	4	yes	complemented
430	C₂×C₄×D₅	—	2	8	no	—
431	C₂×C₄×D₅	—	2	8	no	—
432	C₂×C₄×D₅	—	2	4	no	—
433	C₂×C₄×D₅	—	2	4	no	—
434	C₂×C₄×D₅	—	4	16	no	—
435	C₂×C₄×D₅	—	4	16	no	—
436	C₂×C₄×D₅	—	4	4	no	—
437	C₂×C₄×D₅	—	4	2	no	—
438	C₂×C₄×D₅	—	4	2	no	—
439	C₂×C₄×D₅	—	4	4	no	—
440	C₂×C₄×D₅	—	4	4	no	—
441	C₂×C₄×D₅	—	4	4	no	—
442	C₂×C₄×D₅	—	4	4	no	—
443	C₂×C₄×D₅	C₂⁴	1	8	yes	—
444	C₂×C₄×D₅	C₂⁴	1	4	yes	—
445	C₂×C₄×D₅	C₂⁴	1	4	yes	—
446	C₂×C₄×D₅	C₂⁴	1	8	yes	—
447	C₂×C₄×D₅	C₂⁴	1	8	yes	—
448	C₂×C₄×D₅	C₂⁴	1	4	yes	—
449	C₂×C₄×D₅	C₂⁴	1	4	yes	—
450	C₂×C₄×D₅	C₂⁴	1	8	yes	—
451	C₂×C₄×D₅	C₂⁴	1	8	yes	—
452	C₂×C₄×D₅	C₂⁴	1	8	yes	complemented
453	C₂×C₄×D₅	C₂⁴	1	8	yes	complemented
454	C₂×Dic₁₀	—	4	4	no	—
455	C₂×Dic₁₀	—	4	2	no	—
456	C₂×Dic₁₀	C₂⁴	1	8	yes	complemented
457	C₂×Dic₁₀	C₂⁴	1	4	yes	complemented
458	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
459	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
460	C₅×C₄⋊C₄	C₂⁴	1	4	yes	complemented
461	C₅×C₄⋊C₄	C₂⁴	1	4	yes	complemented
462	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
463	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
464	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
465	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
466	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
467	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	complemented
468	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	complemented
469	C₄²×C₅	C₂⁴	1	8	yes	complemented
470	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
471	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
472	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
473	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
474	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
475	C₂²⋊Dic₅	C₂⁴	1	8	yes	complemented
476	C₂²⋊Dic₅	C₂⁴	1	8	yes	complemented
477	#685	C₂⁴	1	8	yes	—
478	#685	C₂⁴	1	8	yes	—
479	#685	C₂⁴	1	8	yes	—
480	#685	C₂⁴	1	8	yes	—
481	#685	C₂⁴	1	8	yes	—
482	#685	C₂⁴	1	8	yes	—
483	#685	C₂⁴	1	8	yes	—
484	#685	C₂⁴	1	8	yes	—
485	#685	C₂⁴	1	8	yes	—
486	#685	C₂⁴	1	8	yes	—
487	#685	C₂⁴	1	8	yes	complemented
488	#685	C₂⁴	1	8	yes	complemented
489	#685	C₂⁴	1	8	yes	complemented
490	#685	C₂⁴	1	8	yes	complemented
491	C₄⋊Dic₅	C₂⁴	1	8	yes	complemented
492	C₄⋊Dic₅	C₂⁴	1	8	yes	complemented
493	C₄⋊Dic₅	C₂⁴	1	4	yes	complemented
494	C₄⋊Dic₅	C₂⁴	1	4	yes	complemented
495	#683	C₂⁴	1	8	yes	complemented
496	#683	C₂⁴	1	8	yes	complemented
497	#683	C₂⁴	1	8	yes	complemented
498	#683	C₂⁴	1	8	yes	complemented
499	#683	C₂⁴	1	8	yes	complemented
500	#683	C₂⁴	1	8	yes	complemented
501	C₄×Dic₅	C₂⁴	1	8	yes	complemented
502	C₄×Dic₅	C₂⁴	1	8	yes	complemented
503	C₄×Dic₅	C₂⁴	1	8	yes	complemented
504	C₂⁶	—	5	1	no	—
505	C₂²×#41	—	5	1	no	—
506	C₂²×#41	—	5	1	no	—
507	C₂²×#41	—	5	2	no	—
508	C₂³×D₄	—	5	2	no	—
509	C₂³×D₄	—	5	2	no	—
510	C₂³×D₄	—	5	2	no	—
511	C₂⁴×C₄	—	5	1	no	—
512	C₂⁴×C₄	—	5	1	no	—
513	#551	—	5	32	no	—
514	#551	—	5	32	no	—
515	#551	—	5	32	no	—
516	#551	—	5	32	no	—
517	#546	—	5	32	no	—
518	#546	—	5	32	no	—
519	#546	—	5	32	no	—
520	#546	—	5	32	no	—
521	#543	—	5	16	no	—
522	#538	—	5	32	no	—
523	#538	—	5	16	no	—
524	#538	C₂×D₅	1	16	yes	complemented
525	#534	—	5	16	no	—
526	C₂×#126	—	5	2	no	—
527	C₂×#126	—	5	2	no	—
528	C₂×#126	—	5	2	no	—
529	C₂×#126	C₂×D₅	1	2	yes	complemented
530	C₂×#124	—	5	2	no	—
531	C₂×#124	—	5	2	no	—
532	C₂×#124	—	5	2	no	—
533	C₂×#124	C₂×D₅	1	2	yes	complemented
534	#525	—	5	16	no	—
535	#525	—	5	16	no	—
536	#525	—	5	32	no	—
537	C₂×#123	—	5	2	no	—
538	C₂×#123	—	5	2	no	—
539	C₂×#123	—	5	2	no	—
540	C₂×#123	—	5	2	no	—
541	C₂×#123	—	5	2	no	—
542	C₂×#123	—	5	2	no	—
543	C₂×#123	—	5	2	no	—
544	C₂×#123	—	5	2	no	—
545	C₂×#123	—	5	2	no	—
546	C₂×#123	C₂×D₅	1	2	yes	complemented
547	C₂×C₂²⋊Q₈	—	5	1	no	—
548	C₂×C₂²⋊Q₈	—	5	2	no	—
549	C₂×C₂²⋊Q₈	—	5	1	no	—
550	C₂×C₂²⋊Q₈	—	5	2	no	—
551	C₂×C₂²⋊Q₈	—	5	2	no	—
552	C₂×C₂²⋊Q₈	—	5	2	no	—
553	C₂×C₂²⋊Q₈	—	5	1	no	—
554	C₂×C₂²⋊Q₈	—	5	2	no	—
555	C₂×C₂²⋊Q₈	—	5	2	no	—
556	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
557	C₂×#121	—	5	2	no	—
558	C₂×#121	—	5	2	no	—
559	C₂×#121	—	5	2	no	—
560	C₂×#121	—	5	1	no	—
561	C₂×#121	—	5	1	no	—
562	C₂×#121	—	5	1	no	—
563	C₂×#121	—	5	2	no	—
564	C₂×#121	—	5	2	no	—
565	C₂×#121	C₂×D₅	1	2	yes	complemented
566	C₂×#121	C₂×D₅	1	1	yes	characteristic, complemented
567	C₂×#120	—	5	2	no	—
568	C₂×#120	—	5	2	no	—
569	C₂×#120	—	5	2	no	—
570	C₂×#120	—	5	2	no	—
571	C₂×#120	—	5	2	no	—
572	C₂×#120	—	5	32	no	—
573	C₂×#120	—	5	2	no	—
574	C₂×#120	—	5	2	no	—
575	C₂×#120	—	5	2	no	—
576	C₂×#120	—	5	2	no	—
577	C₂×#120	C₂×D₅	1	2	yes	complemented
578	#518	—	5	32	no	—
579	C₂×C₄×D₄	—	5	2	no	—
580	C₂×C₄×D₄	—	5	2	no	—
581	C₂×C₄×D₄	—	5	2	no	—
582	C₂×C₄×D₄	—	5	2	no	—
583	C₂×C₄×D₄	—	5	2	no	—
584	C₂×C₄×D₄	—	5	2	no	—
585	C₂×C₄×D₄	—	5	2	no	—
586	C₂×C₄×D₄	—	5	2	no	—
587	C₂×C₄×D₄	—	5	2	no	—
588	C₂×C₄×D₄	—	5	2	no	—
589	C₂×C₄×D₄	—	5	2	no	—
590	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
591	C₂×#117	—	5	2	no	—
592	C₂×#117	—	5	1	no	—
593	C₂×#117	—	5	1	no	—
594	C₂×#117	—	5	2	no	—
595	C₂×#117	—	5	2	no	—
596	C₂²×C₂²⋊C₄	—	5	1	no	—
597	C₂²×C₂²⋊C₄	—	5	1	no	—
598	C₂²×C₂²⋊C₄	—	5	1	no	—
599	C₂²×C₂²⋊C₄	—	5	2	no	—
600	C₂²×C₂²⋊C₄	—	5	2	no	—
601	C₂²×C₂²⋊C₄	—	5	2	no	—
602	C₂²×C₂²⋊C₄	—	5	2	no	—
603	C₂²×C₂²⋊C₄	—	5	2	no	—
604	C₂²×C₂²⋊C₄	—	5	2	no	—
605	C₂²×C₂²⋊C₄	—	5	2	no	—
606	C₂²×C₂²⋊C₄	—	5	2	no	—
607	C₂²×C₂²⋊C₄	—	5	16	no	—
608	C₂²×C₂²⋊C₄	—	5	2	no	—
609	C₂²×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
610	C₂³×C₅	—	2	2	no	—
611	C₂³×C₅	—	2	2	no	—
612	C₂³×C₅	—	2	4	no	—
613	C₂³×C₅	—	2	8	no	—
614	C₂³×C₅	—	2	4	no	—
615	C₂³×C₅	—	2	4	no	—
616	C₂³×C₅	—	2	4	no	—
617	C₂³×C₅	—	2	4	no	—
618	C₂³×C₅	—	2	4	no	—
619	C₂³×C₅	—	4	4	no	—
620	C₂³×C₅	—	4	4	no	—
621	C₂³×C₅	—	4	16	no	—
622	C₂³×C₅	C₂×#41	1	4	yes	—
623	C₂³×C₅	C₂⁵	1	4	yes	—
624	C₂³×C₅	C₂⁵	1	4	yes	—
625	C₂³×C₅	C₂⁵	1	2	yes	—
626	C₂³×C₅	C₂⁵	1	1	yes	characteristic
627	C₂²×D₅	—	2	32	no	—
628	C₂²×D₅	—	2	8	no	—
629	C₂²×D₅	—	2	2	no	—
630	C₂²×D₅	—	2	2	no	—
631	C₂²×D₅	—	2	2	no	—
632	C₂²×D₅	—	2	2	no	—
633	C₂²×D₅	—	2	4	no	—
634	C₂²×D₅	—	2	4	no	—
635	C₂²×D₅	—	2	8	no	—
636	C₂²×D₅	—	2	8	no	—
637	C₂²×D₅	—	2	4	no	—
638	C₂²×D₅	—	2	4	no	—
639	C₂²×D₅	—	2	4	no	—
640	C₂²×D₅	—	2	16	no	—
641	C₂²×D₅	—	2	16	no	—
642	C₂²×D₅	—	2	16	no	—
643	C₂²×D₅	—	2	16	no	—
644	C₂²×D₅	—	2	16	no	—
645	C₂²×D₅	—	4	16	no	—
646	C₂²×D₅	—	4	8	no	—
647	C₂²×D₅	—	4	8	no	—
648	C₂²×D₅	—	4	4	no	—
649	C₂²×D₅	—	4	4	no	—
650	C₂²×D₅	—	4	32	no	—
651	C₂²×D₅	—	4	32	no	—
652	C₂²×D₅	—	4	8	no	—
653	C₂²×D₅	—	4	8	no	—
654	C₂²×D₅	—	4	128	no	—
655	C₂²×D₅	—	8	16	no	—
656	C₂²×D₅	C₂×#41	1	8	yes	—
657	C₂²×D₅	C₂×#41	1	16	yes	complemented
658	C₂²×D₅	H(5,𝔽₂)	1	4	yes	—
659	C₂²×D₅	H(5,𝔽₂)	1	4	yes	—
660	C₂²×D₅	C₂⁵	1	4	yes	—
661	C₂²×D₅	C₂⁵	1	4	yes	—
662	C₂²×D₅	C₂⁵	1	2	yes	—
663	C₂²×D₅	C₂⁵	1	2	yes	—
664	C₅×Q₈	—	4	4	no	—
665	C₅×D₄	—	2	16	no	—
666	C₅×D₄	—	4	8	no	—
667	C₅×D₄	—	4	8	no	—
668	C₅×D₄	—	4	4	no	—
669	C₂×C₄×C₅	—	2	4	no	—
670	C₂×C₄×C₅	—	2	2	no	—
671	C₂×C₄×C₅	—	2	4	no	—
672	C₂×C₄×C₅	—	2	4	no	—
673	C₂×C₄×C₅	—	2	2	no	—
674	C₂×C₄×C₅	—	2	4	no	—
675	C₂×C₄×C₅	—	4	4	no	—
676	C₂×C₄×C₅	—	4	4	no	—
677	C₂×C₄×C₅	—	4	8	no	—
678	C₂×C₄×C₅	C₂⁵	1	4	yes	—
679	C₂×C₄×C₅	C₂⁵	1	4	yes	—
680	C₂×C₄×C₅	C₂⁵	1	4	yes	—
681	C₂×C₄×C₅	C₂⁵	1	4	yes	—
682	C₂×C₄×C₅	C₂⁵	1	2	yes	—
683	C₂×C₄×C₅	C₂⁵	1	2	yes	—
684	C₂²⋊D₅	—	2	16	no	—
685	C₂²⋊D₅	—	2	16	no	—
686	C₂²⋊D₅	—	2	16	no	—
687	C₂²⋊D₅	—	2	16	no	—
688	C₂²⋊D₅	—	4	8	no	—
689	C₂²⋊D₅	—	4	8	no	—
690	C₂²⋊D₅	—	4	8	no	—
691	C₂×Dic₅	—	2	4	no	—
692	C₂×Dic₅	—	2	4	no	—
693	C₂×Dic₅	—	2	4	no	—
694	C₂×Dic₅	—	2	4	no	—
695	C₂×Dic₅	—	2	2	no	—
696	C₂×Dic₅	—	2	2	no	—
697	C₂×Dic₅	—	4	4	no	—
698	C₂×Dic₅	—	4	4	no	—
699	C₂×Dic₅	—	4	8	no	—
700	C₂×Dic₅	C₂⁵	1	4	yes	—
701	C₂×Dic₅	C₂⁵	1	2	yes	—
702	C₂×Dic₅	C₂⁵	1	2	yes	—
703	C₂×Dic₅	C₂⁵	1	4	yes	—
704	C₂×Dic₅	C₂⁵	1	4	yes	—
705	C₂×Dic₅	C₂⁵	1	4	yes	—
706	D₂₀	—	2	16	no	—
707	D₂₀	—	2	16	no	—
708	D₂₀	—	2	16	no	—
709	D₂₀	—	4	4	no	—
710	C₄×D₅	—	2	16	no	—
711	C₄×D₅	—	2	16	no	—
712	C₄×D₅	—	2	8	no	—
713	C₄×D₅	—	2	8	no	—
714	C₄×D₅	—	4	8	no	—
715	C₄×D₅	—	4	4	no	—
716	C₄×D₅	—	4	4	no	—
717	C₄×D₅	—	4	8	no	—
718	C₄×D₅	—	4	8	no	—
719	C₄×D₅	—	4	8	no	—
720	C₄×D₅	—	4	8	no	—
721	Dic₁₀	—	4	8	no	—
722	Dic₁₀	—	4	4	no	—
723	C₂⁵	—	5	1	no	—
724	C₂⁵	—	5	1	no	—
725	C₂⁵	—	5	2	no	—
726	C₂⁵	—	5	2	no	—
727	C₂⁵	—	5	8	no	—
728	C₂⁵	—	5	2	no	—
729	C₂⁵	—	10	8	no	—
730	C₂⁵	—	20	4	no	—
731	C₂⁵	—	20	4	no	—
732	C₂⁵	C₂²×D₅	1	1	yes	characteristic
733	C₂×#41	—	5	8	no	—
734	C₂×#41	—	5	8	no	—
735	C₂×#41	—	5	16	no	—
736	C₂×#41	—	20	8	no	—
737	C₂×#41	—	20	4	no	—
738	C₂×#41	—	20	4	no	—
739	C₂²×Q₈	—	5	1	no	—
740	C₂²×Q₈	—	5	2	no	—
741	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
742	C₂²×D₄	—	5	2	no	—
743	C₂²×D₄	—	5	2	no	—
744	C₂²×D₄	—	5	2	no	—
745	C₂²×D₄	—	5	2	no	—
746	C₂²×D₄	—	5	2	no	—
747	C₂²×D₄	—	5	2	no	—
748	C₂²×D₄	—	5	2	no	—
749	C₂²×D₄	—	5	16	no	—
750	C₂²×D₄	—	5	16	no	—
751	C₂²×D₄	—	5	16	no	—
752	C₂²×D₄	—	5	2	no	—
753	C₂²×D₄	—	5	2	no	—
754	C₂²×D₄	—	5	2	no	—
755	C₂²×D₄	—	5	1	no	—
756	C₂²×D₄	—	10	16	no	—
757	C₂²×D₄	—	20	8	no	—
758	C₂²×D₄	—	20	8	no	—
759	C₂²×D₄	C₂²×D₅	1	2	yes	—
760	C₂²×D₄	C₂²×D₅	1	2	yes	—
761	C₂²×D₄	C₂²×D₅	1	2	yes	—
762	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
763	C₂³×C₄	—	5	1	no	—
764	C₂³×C₄	—	5	1	no	—
765	C₂³×C₄	—	5	2	no	—
766	C₂³×C₄	—	5	2	no	—
767	C₂³×C₄	—	5	1	no	—
768	C₂³×C₄	—	5	1	no	—
769	C₂³×C₄	—	5	2	no	—
770	C₂³×C₄	—	5	1	no	—
771	C₂³×C₄	—	5	1	no	—
772	C₂³×C₄	—	5	2	no	—
773	C₂³×C₄	—	5	2	no	—
774	C₂³×C₄	—	5	2	no	—
775	C₂³×C₄	—	5	8	no	—
776	C₂³×C₄	—	5	8	no	—
777	C₂³×C₄	—	5	2	no	—
778	C₂³×C₄	—	5	2	no	—
779	C₂³×C₄	—	20	4	no	—
780	C₂³×C₄	—	20	4	no	—
781	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
782	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
783	C₂³×C₄	C₂²×D₅	1	2	yes	complemented
784	#126	—	5	16	no	—
785	#126	—	5	16	no	—
786	#126	—	5	16	no	—
787	#126	C₂²×D₅	1	16	yes	complemented
788	#124	—	5	16	no	—
789	#124	—	5	16	no	—
790	#124	—	5	16	no	—
791	#124	C₂²×D₅	1	16	yes	complemented
792	#123	—	5	16	no	—
793	#123	—	5	16	no	—
794	#123	—	5	16	no	—
795	#123	—	5	16	no	—
796	#123	—	5	16	no	—
797	#123	—	5	16	no	—
798	#123	—	5	16	no	—
799	#123	—	5	16	no	—
800	#123	—	5	16	no	—
801	#123	C₂²×D₅	1	16	yes	complemented
802	C₂²⋊Q₈	—	5	8	no	—
803	C₂²⋊Q₈	—	5	16	no	—
804	C₂²⋊Q₈	—	5	8	no	—
805	C₂²⋊Q₈	—	5	16	no	—
806	C₂²⋊Q₈	—	5	8	no	—
807	C₂²⋊Q₈	—	5	16	no	—
808	C₂²⋊Q₈	—	5	16	no	—
809	C₂²⋊Q₈	—	5	16	no	—
810	C₂²⋊Q₈	—	5	16	no	—
811	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
812	#121	—	5	16	no	—
813	#121	—	5	16	no	—
814	#121	—	5	16	no	—
815	#121	—	5	8	no	—
816	#121	—	5	8	no	—
817	#121	—	5	8	no	—
818	#121	—	5	16	no	—
819	#121	—	5	16	no	—
820	#121	C₂²×D₅	1	16	yes	complemented
821	#121	C₂²×D₅	1	8	yes	complemented
822	#120	—	5	16	no	—
823	#120	—	5	16	no	—
824	#120	—	5	16	no	—
825	#120	—	5	16	no	—
826	#120	—	5	16	no	—
827	#120	—	5	16	no	—
828	#120	—	5	16	no	—
829	#120	—	5	16	no	—
830	#120	—	5	16	no	—
831	#120	C₂²×D₅	1	16	yes	complemented
832	C₄×D₄	—	5	16	no	—
833	C₄×D₄	—	5	16	no	—
834	C₄×D₄	—	5	16	no	—
835	C₄×D₄	—	5	16	no	—
836	C₄×D₄	—	5	16	no	—
837	C₄×D₄	—	5	16	no	—
838	C₄×D₄	—	5	16	no	—
839	C₄×D₄	—	5	16	no	—
840	C₄×D₄	—	5	16	no	—
841	C₄×D₄	—	5	16	no	—
842	C₄×D₄	—	5	16	no	—
843	C₄×D₄	C₂²×D₅	1	16	yes	complemented
844	#117	—	5	16	no	—
845	#117	—	5	8	no	—
846	#117	—	5	8	no	—
847	#117	—	5	16	no	—
848	#117	—	5	16	no	—
849	C₂×C₄⋊C₄	—	5	2	no	—
850	C₂×C₄⋊C₄	—	5	2	no	—
851	C₂×C₄⋊C₄	—	5	2	no	—
852	C₂×C₄⋊C₄	—	5	2	no	—
853	C₂×C₄⋊C₄	—	5	1	no	—
854	C₂×C₄⋊C₄	—	5	2	no	—
855	C₂×C₄⋊C₄	—	5	1	no	—
856	C₂×C₄⋊C₄	—	5	2	no	—
857	C₂×C₄⋊C₄	—	5	2	no	—
858	C₂×C₄⋊C₄	—	5	2	no	—
859	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
860	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
861	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
862	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
863	C₂×C₂²⋊C₄	—	5	2	no	—
864	C₂×C₂²⋊C₄	—	5	2	no	—
865	C₂×C₂²⋊C₄	—	5	8	no	—
866	C₂×C₂²⋊C₄	—	5	2	no	—
867	C₂×C₂²⋊C₄	—	5	2	no	—
868	C₂×C₂²⋊C₄	—	5	2	no	—
869	C₂×C₂²⋊C₄	—	5	2	no	—
870	C₂×C₂²⋊C₄	—	5	2	no	—
871	C₂×C₂²⋊C₄	—	5	2	no	—
872	C₂×C₂²⋊C₄	—	5	2	no	—
873	C₂×C₂²⋊C₄	—	5	8	no	—
874	C₂×C₂²⋊C₄	—	5	2	no	—
875	C₂×C₂²⋊C₄	—	5	2	no	—
876	C₂×C₂²⋊C₄	—	5	8	no	—
877	C₂×C₂²⋊C₄	—	5	2	no	—
878	C₂×C₂²⋊C₄	—	5	2	no	—
879	C₂×C₂²⋊C₄	—	5	2	no	—
880	C₂×C₂²⋊C₄	—	5	2	no	—
881	C₂×C₂²⋊C₄	—	5	2	no	—
882	C₂×C₂²⋊C₄	—	5	2	no	—
883	C₂×C₂²⋊C₄	—	5	2	no	—
884	C₂×C₂²⋊C₄	—	5	2	no	—
885	C₂×C₂²⋊C₄	—	5	2	no	—
886	C₂×C₂²⋊C₄	—	5	2	no	—
887	C₂×C₂²⋊C₄	—	5	16	no	—
888	C₂×C₂²⋊C₄	—	5	16	no	—
889	C₂×C₂²⋊C₄	—	5	16	no	—
890	C₂×C₂²⋊C₄	—	5	16	no	—
891	C₂×C₂²⋊C₄	—	5	16	no	—
892	C₂×C₂²⋊C₄	—	5	16	no	—
893	C₂×C₂²⋊C₄	—	5	16	no	—
894	C₂×C₂²⋊C₄	—	5	16	no	—
895	C₂×C₂²⋊C₄	—	5	16	no	—
896	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
897	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
898	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
899	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
900	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
901	C₂×C₂²⋊C₄	C₂²×D₅	1	8	yes	complemented
902	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
903	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
904	C₂×C₄²	—	5	2	no	—
905	C₂×C₄²	—	5	2	no	—
906	C₂×C₄²	—	5	2	no	—
907	C₂×C₄²	C₂²×D₅	1	2	yes	complemented
908	C₂²×C₅	—	2	2	no	—
909	C₂²×C₅	—	2	2	no	—
910	C₂²×C₅	—	2	8	no	—
911	C₂²×C₅	—	2	4	no	—
912	C₂²×C₅	—	2	4	no	—
913	C₂²×C₅	—	2	4	no	—
914	C₂²×C₅	—	2	4	no	—
915	C₂²×C₅	—	2	4	no	—
916	C₂²×C₅	—	2	4	no	—
917	C₂²×C₅	—	4	16	no	—
918	C₂²×C₅	—	4	8	no	—
919	C₂²×C₅	—	4	8	no	—
920	C₂²×C₅	C₂²×#41	1	4	yes	—
921	C₂²×C₅	C₂²×#41	1	2	yes	—
922	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
923	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
924	C₂²×C₅	C₂⁶	1	1	yes	characteristic
925	C₂×D₅	—	2	32	no	—
926	C₂×D₅	—	2	2	no	—
927	C₂×D₅	—	2	2	no	—
928	C₂×D₅	—	2	2	no	—
929	C₂×D₅	—	2	2	no	—
930	C₂×D₅	—	2	4	no	—
931	C₂×D₅	—	2	4	no	—
932	C₂×D₅	—	2	8	no	—
933	C₂×D₅	—	2	8	no	—
934	C₂×D₅	—	2	16	no	—
935	C₂×D₅	—	2	4	no	—
936	C₂×D₅	—	2	4	no	—
937	C₂×D₅	—	2	4	no	—
938	C₂×D₅	—	4	16	no	—
939	C₂×D₅	—	4	32	no	—
940	C₂×D₅	—	4	32	no	—
941	C₂×D₅	—	4	8	no	—
942	C₂×D₅	—	8	16	no	—
943	C₂×D₅	C₂²×#41	1	8	yes	—
944	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
945	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
946	C₄×C₅	—	2	4	no	—
947	C₄×C₅	—	2	2	no	—
948	C₄×C₅	—	2	4	no	—
949	C₄×C₅	—	2	4	no	—
950	C₄×C₅	—	2	2	no	—
951	C₄×C₅	—	2	4	no	—
952	Dic₅	—	2	4	no	—
953	Dic₅	—	2	4	no	—
954	Dic₅	—	2	4	no	—
955	Dic₅	—	2	4	no	—
956	Dic₅	—	2	2	no	—
957	Dic₅	—	2	2	no	—
958	C₂⁴	—	2	4	no	—
959	C₂⁴	—	4	2	no	—
960	C₂⁴	—	4	2	no	—
961	C₂⁴	—	5	2	no	—
962	C₂⁴	—	5	1	no	—
963	C₂⁴	—	5	1	no	—
964	C₂⁴	—	5	8	no	—
965	C₂⁴	—	5	4	no	—
966	C₂⁴	—	5	4	no	—
967	C₂⁴	—	5	2	no	—
968	C₂⁴	—	5	8	no	—
969	C₂⁴	—	5	8	no	—
970	C₂⁴	—	5	8	no	—
971	C₂⁴	—	10	4	no	—
972	C₂⁴	—	10	4	no	—
973	C₂⁴	—	10	8	no	—
974	C₂⁴	—	10	8	no	—
975	C₂⁴	—	10	8	no	—
976	C₂⁴	—	10	8	no	—
977	C₂⁴	—	10	32	no	—
978	C₂⁴	—	10	8	no	—
979	C₂⁴	—	10	4	no	—
980	C₂⁴	—	20	2	no	—
981	C₂⁴	—	20	2	no	—
982	C₂⁴	—	20	4	no	—
983	C₂⁴	—	20	4	no	—
984	C₂⁴	—	20	4	no	—
985	C₂⁴	—	20	4	no	—
986	C₂⁴	—	20	16	no	—
987	C₂⁴	—	20	16	no	—
988	C₂⁴	—	20	64	no	—
989	C₂⁴	C₂³×D₅	1	2	yes	—
990	C₂⁴	C₂³×D₅	1	2	yes	—
991	C₂⁴	C₂³×D₅	1	1	yes	characteristic
992	C₂⁴	C₂³×D₅	1	4	yes	—
993	#41	—	20	32	no	—
994	#41	—	20	16	no	—
995	#41	—	20	16	no	—
996	C₂×Q₈	—	4	2	no	—
997	C₂×Q₈	—	5	4	no	—
998	C₂×Q₈	—	5	8	no	—
999	C₂×Q₈	—	20	2	no	—
1000	C₂×Q₈	—	20	4	no	—
1001	C₂×Q₈	C₂³×D₅	1	4	yes	complemented
1002	C₂×D₄	—	2	8	no	—
1003	C₂×D₄	—	4	4	no	—
1004	C₂×D₄	—	4	4	no	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	5	8	no	—
1007	C₂×D₄	—	5	8	no	—
1008	C₂×D₄	—	5	8	no	—
1009	C₂×D₄	—	5	8	no	—
1010	C₂×D₄	—	5	8	no	—
1011	C₂×D₄	—	5	8	no	—
1012	C₂×D₄	—	5	8	no	—
1013	C₂×D₄	—	5	8	no	—
1014	C₂×D₄	—	5	8	no	—
1015	C₂×D₄	—	5	8	no	—
1016	C₂×D₄	—	5	4	no	—
1017	C₂×D₄	—	10	8	no	—
1018	C₂×D₄	—	10	8	no	—
1019	C₂×D₄	—	10	8	no	—
1020	C₂×D₄	—	10	64	no	—
1021	C₂×D₄	—	10	8	no	—
1022	C₂×D₄	—	10	8	no	—
1023	C₂×D₄	—	10	8	no	—
1024	C₂×D₄	—	10	8	no	—
1025	C₂×D₄	—	20	2	no	—
1026	C₂×D₄	—	20	4	no	—
1027	C₂×D₄	—	20	4	no	—
1028	C₂×D₄	—	20	4	no	—
1029	C₂×D₄	—	20	32	no	—
1030	C₂×D₄	—	20	32	no	—
1031	C₂×D₄	C₂³×D₅	1	8	yes	—
1032	C₂×D₄	C₂³×D₅	1	8	yes	—
1033	C₂×D₄	C₂³×D₅	1	8	yes	—
1034	C₂×D₄	C₂³×D₅	1	4	yes	complemented
1035	C₂²×C₄	—	4	2	no	—
1036	C₂²×C₄	—	4	2	no	—
1037	C₂²×C₄	—	4	4	no	—
1038	C₂²×C₄	—	5	2	no	—
1039	C₂²×C₄	—	5	1	no	—
1040	C₂²×C₄	—	5	1	no	—
1041	C₂²×C₄	—	5	2	no	—
1042	C₂²×C₄	—	5	2	no	—
1043	C₂²×C₄	—	5	2	no	—
1044	C₂²×C₄	—	5	4	no	—
1045	C₂²×C₄	—	5	4	no	—
1046	C₂²×C₄	—	5	8	no	—
1047	C₂²×C₄	—	5	8	no	—
1048	C₂²×C₄	—	5	4	no	—
1049	C₂²×C₄	—	5	4	no	—
1050	C₂²×C₄	—	5	8	no	—
1051	C₂²×C₄	—	5	4	no	—
1052	C₂²×C₄	—	5	4	no	—
1053	C₂²×C₄	—	5	8	no	—
1054	C₂²×C₄	—	5	8	no	—
1055	C₂²×C₄	—	5	8	no	—
1056	C₂²×C₄	—	5	8	no	—
1057	C₂²×C₄	—	5	8	no	—
1058	C₂²×C₄	—	10	8	no	—
1059	C₂²×C₄	—	10	4	no	—
1060	C₂²×C₄	—	10	4	no	—
1061	C₂²×C₄	—	10	8	no	—
1062	C₂²×C₄	—	20	4	no	—
1063	C₂²×C₄	—	20	2	no	—
1064	C₂²×C₄	—	20	2	no	—
1065	C₂²×C₄	—	20	4	no	—
1066	C₂²×C₄	—	20	4	no	—
1067	C₂²×C₄	—	20	4	no	—
1068	C₂²×C₄	—	20	4	no	—
1069	C₂²×C₄	—	20	16	no	—
1070	C₂²×C₄	—	20	16	no	—
1071	C₂²×C₄	—	20	2	no	—
1072	C₂²×C₄	—	20	2	no	—
1073	C₂²×C₄	—	20	4	no	—
1074	C₂²×C₄	C₂³×D₅	1	2	yes	—
1075	C₂²×C₄	C₂³×D₅	1	2	yes	—
1076	C₂²×C₄	C₂³×D₅	1	2	yes	—
1077	C₂²×C₄	C₂³×D₅	1	2	yes	—
1078	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1079	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1080	C₂²×C₄	C₂³×D₅	1	4	yes	—
1081	C₂²×C₄	C₂³×D₅	1	4	yes	—
1082	C₂²×C₄	C₂³×D₅	1	8	yes	complemented
1083	C₄⋊C₄	—	5	8	no	—
1084	C₄⋊C₄	—	5	8	no	—
1085	C₄⋊C₄	—	5	8	no	—
1086	C₄⋊C₄	—	5	8	no	—
1087	C₄⋊C₄	—	5	4	no	—
1088	C₄⋊C₄	—	5	8	no	—
1089	C₄⋊C₄	—	5	4	no	—
1090	C₄⋊C₄	—	5	8	no	—
1091	C₄⋊C₄	—	5	8	no	—
1092	C₄⋊C₄	—	5	8	no	—
1093	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
1094	C₄⋊C₄	C₂³×D₅	1	4	yes	complemented
1095	C₄⋊C₄	C₂³×D₅	1	4	yes	complemented
1096	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
1097	C₂²⋊C₄	—	5	8	no	—
1098	C₂²⋊C₄	—	5	8	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	—	5	8	no	—
1105	C₂²⋊C₄	—	5	8	no	—
1106	C₂²⋊C₄	—	5	8	no	—
1107	C₂²⋊C₄	—	5	8	no	—
1108	C₂²⋊C₄	—	5	8	no	—
1109	C₂²⋊C₄	—	5	8	no	—
1110	C₂²⋊C₄	—	5	8	no	—
1111	C₂²⋊C₄	—	5	8	no	—
1112	C₂²⋊C₄	—	5	8	no	—
1113	C₂²⋊C₄	—	5	8	no	—
1114	C₂²⋊C₄	—	5	8	no	—
1115	C₂²⋊C₄	—	5	8	no	—
1116	C₂²⋊C₄	—	5	8	no	—
1117	C₂²⋊C₄	—	5	8	no	—
1118	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1119	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1120	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1121	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1122	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1123	C₂²⋊C₄	C₂³×D₅	1	8	yes	complemented
1124	C₂²⋊C₄	C₂³×D₅	1	8	yes	complemented
1125	C₄²	—	5	8	no	—
1126	C₄²	—	5	8	no	—
1127	C₄²	—	5	8	no	—
1128	C₄²	C₂³×D₅	1	8	yes	complemented
1129	C₂×C₅	—	2	4	no	—
1130	C₂×C₅	—	4	4	no	—
1131	C₂×C₅	—	4	4	no	—
1132	C₂×C₅	#3490	1	4	yes	complemented
1133	C₂×C₅	C₂³×#41	1	1	yes	characteristic
1134	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1135	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1136	D₅	—	2	4	no	—
1137	D₅	—	2	4	no	—
1138	D₅	—	2	8	no	—
1139	D₅	—	4	4	no	—
1140	C₂³	—	2	2	no	—
1141	C₂³	—	2	2	no	—
1142	C₂³	—	2	4	no	—
1143	C₂³	—	2	8	no	—
1144	C₂³	—	2	4	no	—
1145	C₂³	—	2	4	no	—
1146	C₂³	—	2	4	no	—
1147	C₂³	—	2	4	no	—
1148	C₂³	—	2	4	no	—
1149	C₂³	—	4	4	no	—
1150	C₂³	—	4	4	no	—
1151	C₂³	—	4	16	no	—
1152	C₂³	—	5	8	no	—
1153	C₂³	—	5	4	no	—
1154	C₂³	—	5	4	no	—
1155	C₂³	—	5	4	no	—
1156	C₂³	—	5	2	no	—
1157	C₂³	—	5	2	no	—
1158	C₂³	—	5	16	no	—
1159	C₂³	—	5	4	no	—
1160	C₂³	—	10	8	no	—
1161	C₂³	—	10	8	no	—
1162	C₂³	—	10	16	no	—
1163	C₂³	—	10	16	no	—
1164	C₂³	—	10	16	no	—
1165	C₂³	—	10	16	no	—
1166	C₂³	—	10	16	no	—
1167	C₂³	—	10	32	no	—
1168	C₂³	—	10	8	no	—
1169	C₂³	—	10	2	no	—
1170	C₂³	—	10	2	no	—
1171	C₂³	—	10	2	no	—
1172	C₂³	—	10	2	no	—
1173	C₂³	—	10	4	no	—
1174	C₂³	—	10	4	no	—
1175	C₂³	—	10	4	no	—
1176	C₂³	—	10	4	no	—
1177	C₂³	—	10	4	no	—
1178	C₂³	—	20	4	no	—
1179	C₂³	—	20	4	no	—
1180	C₂³	—	20	16	no	—
1181	C₂³	—	20	8	no	—
1182	C₂³	—	20	8	no	—
1183	C₂³	—	20	8	no	—
1184	C₂³	—	20	8	no	—
1185	C₂³	—	20	32	no	—
1186	C₂³	—	20	32	no	—
1187	C₂³	—	20	128	no	—
1188	C₂³	—	40	16	no	—
1189	C₂³	D₅×#41	1	4	yes	—
1190	C₂³	C₂⁴×D₅	1	4	yes	—
1191	C₂³	C₂⁴×D₅	1	4	yes	—
1192	C₂³	C₂⁴×D₅	1	2	yes	—
1193	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1194	Q₈	—	4	4	no	—
1195	Q₈	—	20	4	no	—
1196	Q₈	—	20	8	no	—
1197	D₄	—	2	16	no	—
1198	D₄	—	4	8	no	—
1199	D₄	—	4	8	no	—
1200	D₄	—	4	4	no	—
1201	D₄	—	10	16	no	—
1202	D₄	—	10	16	no	—
1203	D₄	—	10	16	no	—
1204	D₄	—	10	16	no	—
1205	D₄	—	10	16	no	—
1206	D₄	—	10	16	no	—
1207	D₄	—	10	16	no	—
1208	D₄	—	20	4	no	—
1209	D₄	—	20	8	no	—
1210	D₄	—	20	8	no	—
1211	D₄	—	20	8	no	—
1212	C₂×C₄	—	2	4	no	—
1213	C₂×C₄	—	2	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	—	4	4	no	—
1219	C₂×C₄	—	4	4	no	—
1220	C₂×C₄	—	4	8	no	—
1221	C₂×C₄	—	5	4	no	—
1222	C₂×C₄	—	5	2	no	—
1223	C₂×C₄	—	5	2	no	—
1224	C₂×C₄	—	5	4	no	—
1225	C₂×C₄	—	5	4	no	—
1226	C₂×C₄	—	5	4	no	—
1227	C₂×C₄	—	10	16	no	—
1228	C₂×C₄	—	10	8	no	—
1229	C₂×C₄	—	10	8	no	—
1230	C₂×C₄	—	10	16	no	—
1231	C₂×C₄	—	10	4	no	—
1232	C₂×C₄	—	10	2	no	—
1233	C₂×C₄	—	10	2	no	—
1234	C₂×C₄	—	10	4	no	—
1235	C₂×C₄	—	10	4	no	—
1236	C₂×C₄	—	10	4	no	—
1237	C₂×C₄	—	20	8	no	—
1238	C₂×C₄	—	20	4	no	—
1239	C₂×C₄	—	20	4	no	—
1240	C₂×C₄	—	20	8	no	—
1241	C₂×C₄	—	20	8	no	—
1242	C₂×C₄	—	20	8	no	—
1243	C₂×C₄	—	20	8	no	—
1244	C₂×C₄	—	20	4	no	—
1245	C₂×C₄	—	20	4	no	—
1246	C₂×C₄	—	20	8	no	—
1247	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1248	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1249	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1250	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1251	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1252	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1253	C₅	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
1254	C₂²	—	2	2	no	—
1255	C₂²	—	2	2	no	—
1256	C₂²	—	2	8	no	—
1257	C₂²	—	2	4	no	—
1258	C₂²	—	2	4	no	—
1259	C₂²	—	2	4	no	—
1260	C₂²	—	2	4	no	—
1261	C₂²	—	2	4	no	—
1262	C₂²	—	2	4	no	—
1263	C₂²	—	4	16	no	—
1264	C₂²	—	4	8	no	—
1265	C₂²	—	4	8	no	—
1266	C₂²	—	5	8	no	—
1267	C₂²	—	5	4	no	—
1268	C₂²	—	5	4	no	—
1269	C₂²	—	10	32	no	—
1270	C₂²	—	10	2	no	—
1271	C₂²	—	10	2	no	—
1272	C₂²	—	10	2	no	—
1273	C₂²	—	10	2	no	—
1274	C₂²	—	10	4	no	—
1275	C₂²	—	10	4	no	—
1276	C₂²	—	10	8	no	—
1277	C₂²	—	10	8	no	—
1278	C₂²	—	10	16	no	—
1279	C₂²	—	10	4	no	—
1280	C₂²	—	10	4	no	—
1281	C₂²	—	10	4	no	—
1282	C₂²	—	20	16	no	—
1283	C₂²	—	20	32	no	—
1284	C₂²	—	20	32	no	—
1285	C₂²	—	20	8	no	—
1286	C₂²	—	40	16	no	—
1287	C₂²	C₂×D₅×#41	1	4	yes	—
1288	C₂²	C₂×D₅×#41	1	2	yes	—
1289	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
1290	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
1291	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1292	C₄	—	2	4	no	—
1293	C₄	—	2	4	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	4	no	—
1297	C₄	—	2	4	no	—
1298	C₄	—	10	4	no	—
1299	C₄	—	10	2	no	—
1300	C₄	—	10	2	no	—
1301	C₄	—	10	4	no	—
1302	C₄	—	10	4	no	—
1303	C₄	—	10	4	no	—
1304	C₂	—	2	4	no	—
1305	C₂	—	4	4	no	—
1306	C₂	—	4	4	no	—
1307	C₂	—	10	4	no	—
1308	C₂	—	10	4	no	—
1309	C₂	—	10	8	no	—
1310	C₂	—	20	4	no	—
1311	C₂	#10618315	1	4	yes	direct product factor
1312	C₂	C₂²×D₅×#41	1	1	yes	characteristic
1313	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic
1314	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#538	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#538	D₅
hypocenter	C₅	C₂×#3490
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#538

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#538	C₂	semidirect
2. #10618315	C₂	direct (N × H)
3. C₂×#66039	C₂	semidirect
4. C₂×#66039	C₂	semidirect
5. C₂×#66013	C₂	semidirect
6. C₂×#66010	C₂	semidirect
7. C₂×#65993	C₂	semidirect
8. C₂×#65988	C₂	semidirect
9. C₂×#65968	C₂	semidirect
10. C₂×#65961	C₂	semidirect
11. C₂×#65946	C₂	semidirect
12. C₂×#65944	C₂	semidirect
13. C₂×#65939	C₂	semidirect
14. C₂×#65940	C₂	semidirect
15. C₂×D₅×#120	C₂	semidirect
16. C₂×#65927	C₂	semidirect
17. C₂×#65881	C₂	semidirect
18. C₂×#65879	C₂	semidirect
19. C₂×#65828	C₂	semidirect
20. C₂²×D₅×C₂²⋊C₄	C₂	semidirect
22. C₂²×#713	C₂²	semidirect
23. C₂²×#711	C₂²	semidirect
25. C₂²×D₄×D₅	C₂²	semidirect
26. C₂²×D₄×D₅	C₂²	semidirect
27. C₂²×#709	C₂²	semidirect
28. C₂³×C₄×D₅	C₂²	semidirect
29. C₂³×C₄×D₅	C₂²	semidirect
30. C₅×#538	C₂²	semidirect
31. C₂×C₅×#126	C₂²	semidirect
32. C₂×C₅×#124	C₂²	semidirect
33. C₂×C₅×#123	C₂²	semidirect
34. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₅×#121	C₂²	semidirect
36. C₂×C₅×#121	C₂²	semidirect
37. C₂×C₅×#120	C₂²	semidirect
38. C₂×C₄×C₅×D₄	C₂²	semidirect
39. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
40. C₂×#4099	C₂²	semidirect
41. C₂²×C₂²⋊Dic₅	C₂²	semidirect
42. C₂×#4092	C₂²	semidirect
43. C₂×#4092	C₂²	semidirect
44. C₂×#4085	C₂²	semidirect
45. C₂×#4085	C₂²	semidirect
46. C₂×#4084	C₂²	semidirect
47. C₂×#4084	C₂²	semidirect
50. C₂×#4083	C₂²	semidirect
51. C₂×#4083	C₂²	semidirect
52. C₂×#4082	C₂²	semidirect
53. C₂×#4081	C₂²	semidirect
54. C₂×D₄×Dic₅	C₂²	semidirect
55. C₂×#4076	C₂²	semidirect
56. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
57. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
58. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
61. C₂²×#685	C₂²	semidirect
62. C₂×#4070	C₂²	semidirect
63. #66039	C₂²	semidirect
64. #66039	C₂²	semidirect
65. #66013	C₂²	semidirect
66. #66010	C₂²	semidirect
67. #65993	C₂²	semidirect
68. #65988	C₂²	semidirect
69. #65968	C₂²	semidirect
70. #65961	C₂²	semidirect
71. #65946	C₂²	semidirect
72. #65944	C₂²	semidirect
73. #65940	C₂²	semidirect
74. #65939	C₂²	semidirect
75. #65927	C₂²	semidirect
76. D₅×#120	C₂²	semidirect
77. #65881	C₂²	semidirect
78. #65879	C₂²	semidirect
79. C₂×#4043	C₂²	semidirect
80. C₂×#4043	C₂²	semidirect
81. C₂×#4042	C₂²	semidirect
82. C₂×#4042	C₂²	semidirect
83. C₂×#4042	C₂²	semidirect
84. C₂×#4041	C₂²	semidirect
85. C₂×#4040	C₂²	semidirect
86. C₂×#4040	C₂²	semidirect
87. C₂×#4040	C₂²	semidirect
88. C₂×#4039	C₂²	semidirect
89. C₂×#4039	C₂²	semidirect
90. C₂×#4038	C₂²	semidirect
91. C₂×#4038	C₂²	semidirect
92. C₂×#4038	C₂²	semidirect
93. #65828	C₂²	semidirect
94. C₂×#4031	C₂²	semidirect
95. C₂×#4031	C₂²	semidirect
96. C₂×#4030	C₂²	semidirect
97. C₂×#4030	C₂²	semidirect
98. C₂×#4029	C₂²	semidirect
99. C₂×#4029	C₂²	semidirect
100. C₂×#4029	C₂²	semidirect
101. C₂×#4029	C₂²	semidirect
102. C₂×#4029	C₂²	semidirect
105. C₂×#4028	C₂²	semidirect
106. C₂×#4028	C₂²	semidirect
107. C₂×#4027	C₂²	semidirect
108. C₂×#4027	C₂²	semidirect
109. C₂×#4027	C₂²	semidirect
111. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
112. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
113. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
114. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
115. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
116. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
117. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
118. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
119. C₂×#4025	C₂²	semidirect
120. C₂×#4025	C₂²	semidirect
121. C₂×#4025	C₂²	semidirect
122. C₂×#4024	C₂²	semidirect
123. C₂×C₄×D₂₀	C₂²	semidirect
124. C₂×C₄×D₂₀	C₂²	semidirect
125. C₂×#4018	C₂²	semidirect
126. C₂×#4018	C₂²	semidirect
138. C₂²×C₅×Q₈	C₂³	semidirect
142. C₂²×C₅×D₄	C₂³	semidirect
145. C₂³×C₄×C₅	C₂³	semidirect
152. C₂²×C₂²⋊D₅	C₂³	semidirect
155. C₂³×Dic₅	C₂³	semidirect
157. C₂×#713	C₂³	semidirect
159. C₂×#711	C₂³	semidirect
164. C₂×D₄×D₅	C₂³	semidirect
165. C₂×D₄×D₅	C₂³	semidirect
167. C₂×#709	C₂³	semidirect
171. C₂²×D₂₀	C₂³	semidirect
183. C₂²×C₄×D₅	C₂³	semidirect
184. C₂²×C₄×D₅	C₂³	semidirect
185. C₂²×C₄×D₅	C₂³	semidirect
186. C₂²×C₄×D₅	C₂³	semidirect
187. C₂²×Dic₁₀	C₂³	semidirect
188. C₂²×Dic₁₀	C₂³	semidirect
189. C₅×#126	C₂³	semidirect
190. C₅×#124	C₂³	semidirect
191. C₅×#123	C₂³	semidirect
192. C₅×C₂²⋊Q₈	C₂³	semidirect
193. C₅×#121	C₂³	semidirect
194. C₅×#121	C₂³	semidirect
195. C₅×#120	C₂³	semidirect
196. C₄×C₅×D₄	C₂³	semidirect
197. C₂×C₅×C₄⋊C₄	C₂³	semidirect
198. C₂×C₅×C₄⋊C₄	C₂³	semidirect
199. C₂×C₅×C₄⋊C₄	C₂³	semidirect
200. C₂×C₅×C₄⋊C₄	C₂³	semidirect
206. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
207. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
208. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
209. C₂×C₄²×C₅	C₂³	semidirect
210. #4099	C₂³	semidirect
216. C₂×C₂²⋊Dic₅	C₂³	semidirect
217. C₂×C₂²⋊Dic₅	C₂³	semidirect
218. C₂×C₂²⋊Dic₅	C₂³	semidirect
219. #4092	C₂³	semidirect
220. #4092	C₂³	semidirect
221. #4085	C₂³	semidirect
222. #4085	C₂³	semidirect
223. #4084	C₂³	semidirect
224. #4084	C₂³	semidirect
227. #4083	C₂³	semidirect
228. #4083	C₂³	semidirect
229. #4082	C₂³	semidirect
230. #4081	C₂³	semidirect
231. D₄×Dic₅	C₂³	semidirect
232. #4076	C₂³	semidirect
233. C₄×C₂²⋊D₅	C₂³	semidirect
234. C₄×C₂²⋊D₅	C₂³	semidirect
235. C₄×C₂²⋊D₅	C₂³	semidirect
248. C₂×#685	C₂³	semidirect
249. C₂×#685	C₂³	semidirect
250. C₂×#685	C₂³	semidirect
251. C₂×#685	C₂³	semidirect
252. C₂×#685	C₂³	semidirect
253. C₂×C₄⋊Dic₅	C₂³	semidirect
254. C₂×C₄⋊Dic₅	C₂³	semidirect
255. C₂×C₄⋊Dic₅	C₂³	semidirect
256. C₂×C₄⋊Dic₅	C₂³	semidirect
257. #4070	C₂³	semidirect
258. C₂×#683	C₂³	semidirect
259. C₂×#683	C₂³	semidirect
260. C₂×#683	C₂³	semidirect
261. C₂×#683	C₂³	semidirect
262. C₂×#683	C₂³	semidirect
263. C₂×#683	C₂³	semidirect
264. C₂×C₄×Dic₅	C₂³	semidirect
265. C₂×C₄×Dic₅	C₂³	semidirect
266. C₂×C₄×Dic₅	C₂³	semidirect
267. #4043	C₂³	semidirect
268. #4043	C₂³	semidirect
269. #4042	C₂³	semidirect
270. #4042	C₂³	semidirect
271. #4042	C₂³	semidirect
272. #4041	C₂³	semidirect
273. #4040	C₂³	semidirect
274. #4040	C₂³	semidirect
275. #4040	C₂³	semidirect
276. #4039	C₂³	semidirect
277. #4039	C₂³	semidirect
278. #4038	C₂³	semidirect
279. #4038	C₂³	semidirect
280. #4038	C₂³	semidirect
281. #4031	C₂³	semidirect
282. #4031	C₂³	semidirect
283. #4030	C₂³	semidirect
284. #4030	C₂³	semidirect
285. #4029	C₂³	semidirect
286. #4029	C₂³	semidirect
287. #4029	C₂³	semidirect
288. #4029	C₂³	semidirect
289. #4029	C₂³	semidirect
292. #4028	C₂³	semidirect
293. #4028	C₂³	semidirect
294. #4027	C₂³	semidirect
295. #4027	C₂³	semidirect
296. #4027	C₂³	semidirect
298. D₅×C₂²⋊C₄	C₂³	semidirect
299. D₅×C₂²⋊C₄	C₂³	semidirect
300. D₅×C₂²⋊C₄	C₂³	semidirect
301. D₅×C₂²⋊C₄	C₂³	semidirect
302. D₅×C₂²⋊C₄	C₂³	semidirect
303. D₅×C₂²⋊C₄	C₂³	semidirect
304. D₅×C₂²⋊C₄	C₂³	semidirect
305. #4025	C₂³	semidirect
306. #4025	C₂³	semidirect
307. #4025	C₂³	semidirect
308. #4024	C₂³	semidirect
309. C₄×D₂₀	C₂³	semidirect
310. C₄×D₂₀	C₂³	semidirect
311. #4018	C₂³	semidirect
312. #4018	C₂³	semidirect
325. C₂×#538	D₅	semidirect
358. C₂³×D₅	#41	semidirect
369. C₂×C₅×Q₈	C₂⁴	semidirect
377. C₂×C₅×D₄	C₂⁴	semidirect
389. C₂²×C₄×C₅	C₂⁴	semidirect
403. C₂×C₂²⋊D₅	C₂⁴	semidirect
415. C₂²×Dic₅	C₂⁴	semidirect
429. C₂×D₂₀	C₂⁴	semidirect
452. C₂×C₄×D₅	C₂⁴	semidirect
453. C₂×C₄×D₅	C₂⁴	semidirect
456. C₂×Dic₁₀	C₂⁴	semidirect
457. C₂×Dic₁₀	C₂⁴	semidirect
458. C₅×C₄⋊C₄	C₂⁴	semidirect
459. C₅×C₄⋊C₄	C₂⁴	semidirect
460. C₅×C₄⋊C₄	C₂⁴	semidirect
461. C₅×C₄⋊C₄	C₂⁴	semidirect
467. C₅×C₂²⋊C₄	C₂⁴	semidirect
468. C₅×C₂²⋊C₄	C₂⁴	semidirect
469. C₄²×C₅	C₂⁴	semidirect
475. C₂²⋊Dic₅	C₂⁴	semidirect
476. C₂²⋊Dic₅	C₂⁴	semidirect
487. #685	C₂⁴	semidirect
488. #685	C₂⁴	semidirect
489. #685	C₂⁴	semidirect
490. #685	C₂⁴	semidirect
491. C₄⋊Dic₅	C₂⁴	semidirect
492. C₄⋊Dic₅	C₂⁴	semidirect
493. C₄⋊Dic₅	C₂⁴	semidirect
494. C₄⋊Dic₅	C₂⁴	semidirect
495. #683	C₂⁴	semidirect
496. #683	C₂⁴	semidirect
497. #683	C₂⁴	semidirect
498. #683	C₂⁴	semidirect
499. #683	C₂⁴	semidirect
500. #683	C₂⁴	semidirect
501. C₄×Dic₅	C₂⁴	semidirect
502. C₄×Dic₅	C₂⁴	semidirect
503. C₄×Dic₅	C₂⁴	semidirect
524. #538	C₂×D₅	semidirect
529. C₂×#126	C₂×D₅	semidirect
533. C₂×#124	C₂×D₅	semidirect
546. C₂×#123	C₂×D₅	semidirect
556. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
565. C₂×#121	C₂×D₅	semidirect
566. C₂×#121	C₂×D₅	semidirect
577. C₂×#120	C₂×D₅	semidirect
590. C₂×C₄×D₄	C₂×D₅	semidirect
609. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
657. C₂²×D₅	C₂×#41	semidirect
741. C₂²×Q₈	C₂²×D₅	semidirect
762. C₂²×D₄	C₂²×D₅	semidirect
783. C₂³×C₄	C₂²×D₅	semidirect
787. #126	C₂²×D₅	semidirect
791. #124	C₂²×D₅	semidirect
801. #123	C₂²×D₅	semidirect
811. C₂²⋊Q₈	C₂²×D₅	semidirect
820. #121	C₂²×D₅	semidirect
821. #121	C₂²×D₅	semidirect
831. #120	C₂²×D₅	semidirect
843. C₄×D₄	C₂²×D₅	semidirect
859. C₂×C₄⋊C₄	C₂²×D₅	semidirect
860. C₂×C₄⋊C₄	C₂²×D₅	semidirect
861. C₂×C₄⋊C₄	C₂²×D₅	semidirect
862. C₂×C₄⋊C₄	C₂²×D₅	semidirect
901. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
902. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
903. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
907. C₂×C₄²	C₂²×D₅	semidirect
1001. C₂×Q₈	C₂³×D₅	semidirect
1034. C₂×D₄	C₂³×D₅	semidirect
1082. C₂²×C₄	C₂³×D₅	semidirect
1093. C₄⋊C₄	C₂³×D₅	semidirect
1094. C₄⋊C₄	C₂³×D₅	semidirect
1095. C₄⋊C₄	C₂³×D₅	semidirect
1096. C₄⋊C₄	C₂³×D₅	semidirect
1123. C₂²⋊C₄	C₂³×D₅	semidirect
1124. C₂²⋊C₄	C₂³×D₅	semidirect
1128. C₄²	C₂³×D₅	semidirect
1132. C₂×C₅	#3490	semidirect
1253. C₅	C₂×#3490	semidirect
1311. C₂	#10618315	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×#538	2
#10618315	2
C₂×#66039	2
C₂×#66013	2
C₂×#66010	2
C₂×#65993	2
C₂×#65988	2
C₂×#65968	2
C₂×#65961	2
C₂×#65946	2
C₂×#65944	2
C₂×#65939	2
C₂×#65940	2
C₂×D₅×#120	2
C₂×#65927	2
C₂×#65881	2
C₂×#65879	2
C₂×#65828	2
C₂²×D₅×C₂²⋊C₄	2
C₂×#3490	5

Subgroups — C2×#10618315 #13007211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618315 #13007211