Subgroups — C₂×#10617928 #13007648

Order 1280.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66164	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#66161	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#4076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#4072	C₂	1	1	yes	maximal, characteristic, complemented
6	#10617928	C₂	1	32	yes	maximal, direct product factor
7	C₂×#65992	C₂	1	4	yes	maximal, complemented
8	C₂×#65977	C₂	1	2	yes	maximal, complemented
9	C₂×#65958	C₂	1	2	yes	maximal, complemented
10	C₂×#65953	C₂	1	2	yes	maximal, complemented
11	C₂×#65930	C₂	1	2	yes	maximal, complemented
12	C₂×#65925	C₂	1	4	yes	maximal, complemented
13	C₂×#65897	C₂	1	2	yes	maximal, complemented
14	C₂×#65899	C₂	1	2	yes	maximal, complemented
15	C₂×#65899	C₂	1	2	yes	maximal, complemented
16	C₂×#65889	C₂	1	2	yes	maximal, complemented
17	C₂×#65855	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65853	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂³×C₂²⋊D₅	C₂²	1	2	yes	—
22	C₂²×#711	C₂²	1	4	yes	complemented
23	C₂³×D₂₀	C₂²	1	1	yes	characteristic
24	C₅×#525	C₂²	1	16	yes	complemented
25	C₂×C₅×#123	C₂²	1	2	yes	—
26	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#121	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#121	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#120	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
33	C₂×C₅×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊Dic₅	C₂²	1	2	yes	—
35	#66164	C₂²	1	16	yes	complemented
36	#66161	C₂²	1	16	yes	complemented
37	C₂×#4093	C₂²	1	2	yes	complemented
38	C₂×Q₈×Dic₅	C₂²	1	2	yes	complemented
39	C₂×#4086	C₂²	1	2	yes	complemented
40	C₂×#4085	C₂²	1	4	yes	complemented
41	C₂×#4085	C₂²	1	4	yes	complemented
42	C₂×#4084	C₂²	1	4	yes	complemented
43	C₂×#4083	C₂²	1	4	yes	—
44	C₂×D₄×Dic₅	C₂²	1	4	yes	—
45	C₂×D₄×Dic₅	C₂²	1	2	yes	complemented
46	C₂×#4076	C₂²	1	2	yes	—
47	C₂×#4076	C₂²	1	2	yes	—
48	C₂×#4076	C₂²	1	2	yes	—
49	C₂×#4076	C₂²	1	2	yes	—
50	C₂×#4076	C₂²	1	16	yes	complemented
51	C₂×#4076	C₂²	1	2	yes	complemented
52	C₂×#4076	C₂²	1	2	yes	complemented
53	C₂²×#685	C₂²	1	2	yes	—
54	C₂×#4072	C₂²	1	1	yes	characteristic
55	C₂×#4072	C₂²	1	1	yes	characteristic
56	C₂×#4072	C₂²	1	2	yes	—
57	C₂×#4072	C₂²	1	2	yes	complemented
58	C₂×#4072	C₂²	1	2	yes	complemented
59	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
60	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
61	C₂×#4072	C₂²	1	16	yes	complemented
62	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
63	C₂²×C₄⋊Dic₅	C₂²	1	2	yes	complemented
64	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
65	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₄×Dic₅	C₂²	1	2	yes	complemented
67	#65992	C₂²	1	64	yes	complemented
68	#65977	C₂²	1	32	yes	complemented
69	#65958	C₂²	1	32	yes	complemented
70	#65953	C₂²	1	32	yes	complemented
71	#65930	C₂²	1	32	yes	complemented
72	#65925	C₂²	1	64	yes	complemented
73	#65899	C₂²	1	32	yes	complemented
74	#65899	C₂²	1	32	yes	complemented
75	#65897	C₂²	1	32	yes	complemented
76	#65889	C₂²	1	32	yes	complemented
77	#65855	C₂²	1	16	yes	complemented
78	#65853	C₂²	1	16	yes	complemented
79	C₂×#4044	C₂²	1	4	yes	complemented
80	C₂×#4044	C₂²	1	4	yes	complemented
81	C₂×#4043	C₂²	1	4	yes	complemented
82	C₂×#4039	C₂²	1	2	yes	complemented
83	C₂×#4039	C₂²	1	2	yes	complemented
84	C₂×#4038	C₂²	1	4	yes	complemented
85	C₂×#4036	C₂²	1	2	yes	complemented
86	C₂×#4034	C₂²	1	2	yes	complemented
87	C₂×#4032	C₂²	1	4	yes	complemented
88	C₂×#4032	C₂²	1	4	yes	complemented
89	C₂×#4031	C₂²	1	4	yes	complemented
90	C₂×#4031	C₂²	1	4	yes	complemented
91	C₂×#4029	C₂²	1	4	yes	complemented
92	C₂×#4029	C₂²	1	4	yes	complemented
93	C₂×#4027	C₂²	1	4	yes	complemented
94	C₂×#4027	C₂²	1	4	yes	complemented
95	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
96	C₂×#4024	C₂²	1	4	yes	—
97	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
98	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
99	C₂×#4016	C₂²	1	2	yes	complemented
100	C₂×#4015	C₂²	1	2	yes	complemented
101	C₂×#3494	—	5	1	no	maximal, Sylow
102	C₂⁵×C₅	C₂³	1	1	yes	characteristic
103	C₂⁴×D₅	C₂³	1	2	yes	—
104	C₂×C₅×#41	—	2	8	no	—
105	C₂×C₅×#41	C₂³	1	8	yes	—
106	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₅×D₄	C₂³	1	2	yes	—
108	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₂²×C₅×D₄	C₂³	1	2	yes	—
110	C₂²×C₅×D₄	C₂³	1	2	yes	—
111	C₂³×C₄×C₅	—	2	8	no	—
112	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅	C₂³	1	2	yes	—
115	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅	C₂³	1	8	yes	—
119	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
120	C₂²×C₂²⋊D₅	—	4	8	no	—
121	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
123	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
124	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
125	C₂²×C₂²⋊D₅	C₂³	1	16	yes	—
126	C₂³×Dic₅	C₂³	1	2	yes	—
127	C₂³×Dic₅	C₂³	1	2	yes	—
128	C₂³×Dic₅	C₂³	1	2	yes	—
129	C₂³×Dic₅	C₂³	1	4	yes	—
130	C₂×#711	—	4	16	no	—
131	C₂×#711	C₂³	1	32	yes	complemented
132	C₂²×D₂₀	—	2	8	no	—
133	C₂²×D₂₀	C₂³	1	2	yes	—
134	C₂²×D₂₀	C₂³	1	2	yes	—
135	C₂²×D₂₀	C₂³	1	8	yes	—
136	C₂²×C₄×D₅	C₂³	1	4	yes	—
137	C₂²×C₄×D₅	C₂³	1	4	yes	—
138	C₂²×Dic₁₀	C₂³	1	4	yes	—
139	C₅×#123	C₂³	1	16	yes	—
140	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
141	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
142	C₅×#121	C₂³	1	8	yes	complemented
143	C₅×#121	C₂³	1	8	yes	complemented
144	C₅×#120	C₂³	1	16	yes	—
145	C₄×C₅×D₄	C₂³	1	16	yes	complemented
146	C₄×C₅×D₄	C₂³	1	16	yes	complemented
147	C₅×#117	C₂³	1	8	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₄²×C₅	C₂³	1	2	yes	—
158	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
159	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
160	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
161	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
162	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
163	C₂×C₂²⋊Dic₅	C₂³	1	16	yes	—
164	#4093	C₂³	1	16	yes	complemented
165	Q₈×Dic₅	C₂³	1	16	yes	complemented
166	#4086	C₂³	1	16	yes	complemented
167	#4085	C₂³	1	32	yes	complemented
168	#4085	C₂³	1	32	yes	complemented
169	#4084	C₂³	1	32	yes	complemented
170	#4083	C₂³	1	32	yes	—
171	D₄×Dic₅	C₂³	1	32	yes	—
172	D₄×Dic₅	C₂³	1	16	yes	complemented
173	#4076	C₂³	1	16	yes	—
174	#4076	C₂³	1	16	yes	—
175	#4076	C₂³	1	16	yes	—
176	#4076	C₂³	1	16	yes	—
177	#4076	C₂³	1	16	yes	complemented
178	#4076	C₂³	1	16	yes	complemented
179	C₂×#685	C₂³	1	4	yes	—
180	C₂×#685	C₂³	1	4	yes	—
181	C₂×#685	C₂³	1	4	yes	—
182	C₂×#685	C₂³	1	4	yes	—
183	C₂×#685	C₂³	1	4	yes	—
184	C₂×#685	C₂³	1	4	yes	—
185	C₂×#685	C₂³	1	16	yes	—
186	#4072	C₂³	1	8	yes	—
187	#4072	C₂³	1	8	yes	—
188	#4072	C₂³	1	16	yes	—
189	#4072	C₂³	1	8	yes	complemented
190	#4072	C₂³	1	8	yes	complemented
191	#4072	C₂³	1	16	yes	complemented
192	#4072	C₂³	1	16	yes	complemented
193	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
195	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
196	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
200	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
201	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
202	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
203	C₂×C₄⋊Dic₅	C₂³	1	8	yes	—
204	C₂×C₄⋊Dic₅	C₂³	1	8	yes	complemented
205	C₂×C₄⋊Dic₅	C₂³	1	8	yes	complemented
206	C₂×C₄⋊Dic₅	C₂³	1	16	yes	complemented
207	C₂×#683	C₂³	1	4	yes	—
208	C₂×#683	C₂³	1	4	yes	—
209	C₂×C₄×Dic₅	C₂³	1	2	yes	—
210	C₂×C₄×Dic₅	C₂³	1	4	yes	—
211	C₂×C₄×Dic₅	C₂³	1	2	yes	—
212	C₂×C₄×Dic₅	C₂³	1	2	yes	—
213	C₂×C₄×Dic₅	C₂³	1	2	yes	—
214	C₂×C₄×Dic₅	C₂³	1	16	yes	complemented
215	#4044	C₂³	1	32	yes	complemented
216	#4044	C₂³	1	32	yes	complemented
217	#4043	C₂³	1	32	yes	complemented
218	#4039	C₂³	1	16	yes	complemented
219	#4039	C₂³	1	16	yes	complemented
220	#4038	C₂³	1	32	yes	complemented
221	#4036	C₂³	1	16	yes	complemented
222	#4034	C₂³	1	16	yes	complemented
223	#4032	C₂³	1	32	yes	complemented
224	#4032	C₂³	1	32	yes	complemented
225	#4031	C₂³	1	32	yes	complemented
226	#4031	C₂³	1	32	yes	complemented
227	#4029	C₂³	1	32	yes	complemented
228	#4029	C₂³	1	32	yes	complemented
229	#4027	C₂³	1	32	yes	complemented
230	#4027	C₂³	1	32	yes	complemented
231	D₅×C₂²⋊C₄	C₂³	1	32	yes	—
232	#4024	C₂³	1	32	yes	—
233	C₄×D₂₀	C₂³	1	16	yes	complemented
234	C₄×D₂₀	C₂³	1	16	yes	complemented
235	#4016	C₂³	1	16	yes	complemented
236	#4015	C₂³	1	16	yes	complemented
237	#3494	—	5	32	no	—
238	C₂×#555	—	5	2	no	—
239	C₂×#553	—	5	2	no	—
240	C₂×#553	—	5	2	no	—
241	C₂×#551	—	5	4	no	—
242	C₂×#547	—	5	2	no	—
243	C₂×#546	—	5	4	no	—
244	C₂×#544	—	5	1	no	—
245	C₂×#542	—	5	2	no	—
246	C₂×#540	—	5	2	no	—
247	C₂×#535	—	5	1	no	—
248	C₂×#532	—	5	2	no	—
249	C₂×#529	—	5	2	no	—
250	C₂×#525	D₅	1	1	yes	characteristic, complemented
251	C₂²×#121	—	5	1	no	—
252	C₂×#520	—	5	1	no	—
253	C₂×#518	—	5	1	no	—
254	C₂²×#117	—	5	1	no	—
255	C₂⁴×C₅	—	2	4	no	—
256	C₂⁴×C₅	—	2	4	no	—
257	C₂⁴×C₅	—	4	2	no	—
258	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₅	C₂⁴	1	2	yes	—
260	C₂⁴×C₅	C₂⁴	1	4	yes	—
261	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
263	C₂³×D₅	—	2	8	no	—
264	C₂³×D₅	—	4	4	no	—
265	C₂³×D₅	—	4	4	no	—
266	C₂³×D₅	C₂⁴	1	4	yes	—
267	C₂³×D₅	C₂⁴	1	8	yes	—
268	C₅×#41	—	2	32	no	—
269	C₂×C₅×Q₈	—	2	4	no	—
270	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
271	C₂×C₅×D₄	—	2	8	no	—
272	C₂×C₅×D₄	—	2	8	no	—
273	C₂×C₅×D₄	—	2	4	no	—
274	C₂×C₅×D₄	—	4	4	no	—
275	C₂×C₅×D₄	C₂⁴	1	8	yes	—
276	C₂×C₅×D₄	C₂⁴	1	8	yes	—
277	C₂×C₅×D₄	C₂⁴	1	4	yes	—
278	C₂×C₅×D₄	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₅	—	2	4	no	—
280	C₂²×C₄×C₅	—	2	4	no	—
281	C₂²×C₄×C₅	—	2	4	no	—
282	C₂²×C₄×C₅	—	2	4	no	—
283	C₂²×C₄×C₅	—	2	4	no	—
284	C₂²×C₄×C₅	—	2	8	no	—
285	C₂²×C₄×C₅	—	2	32	no	—
286	C₂²×C₄×C₅	#41	1	8	yes	complemented
287	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
294	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
295	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
301	C₂×C₂²⋊D₅	—	2	16	no	—
302	C₂×C₂²⋊D₅	—	4	8	no	—
303	C₂×C₂²⋊D₅	—	4	8	no	—
304	C₂×C₂²⋊D₅	—	4	8	no	—
305	C₂×C₂²⋊D₅	—	4	32	no	—
306	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
307	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
308	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
309	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
310	C₂²×Dic₅	—	2	8	no	—
311	C₂²×Dic₅	—	4	8	no	—
312	C₂²×Dic₅	—	4	4	no	—
313	C₂²×Dic₅	—	4	4	no	—
314	C₂²×Dic₅	C₂⁴	1	2	yes	—
315	C₂²×Dic₅	C₂⁴	1	2	yes	—
316	C₂²×Dic₅	C₂⁴	1	2	yes	—
317	C₂²×Dic₅	C₂⁴	1	8	yes	—
318	C₂²×Dic₅	C₂⁴	1	2	yes	—
319	C₂²×Dic₅	C₂⁴	1	4	yes	—
320	C₂²×Dic₅	C₂⁴	1	8	yes	—
321	C₂²×Dic₅	C₂⁴	1	16	yes	—
322	C₂²×Dic₅	C₂⁴	1	8	yes	—
323	#711	—	4	64	no	—
324	C₂×D₂₀	—	2	8	no	—
325	C₂×D₂₀	—	2	8	no	—
326	C₂×D₂₀	—	2	32	no	—
327	C₂×D₂₀	C₂⁴	1	8	yes	—
328	C₂×D₂₀	C₂⁴	1	8	yes	—
329	C₂×C₄×D₅	—	4	8	no	—
330	C₂×C₄×D₅	—	4	8	no	—
331	C₂×C₄×D₅	C₂⁴	1	16	yes	—
332	C₂×C₄×D₅	C₂⁴	1	16	yes	—
333	C₂×Dic₁₀	—	4	8	no	—
334	C₂×Dic₁₀	C₂⁴	1	16	yes	—
335	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
336	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
337	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
338	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
339	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
340	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
341	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
342	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
343	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₄²×C₅	C₂⁴	1	8	yes	—
345	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
346	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
347	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
348	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
349	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
350	#685	C₂⁴	1	16	yes	—
351	#685	C₂⁴	1	16	yes	—
352	#685	C₂⁴	1	16	yes	—
353	#685	C₂⁴	1	16	yes	—
354	#685	C₂⁴	1	16	yes	—
355	#685	C₂⁴	1	16	yes	—
356	C₄⋊Dic₅	C₂⁴	1	4	yes	—
357	C₄⋊Dic₅	C₂⁴	1	8	yes	—
358	C₄⋊Dic₅	C₂⁴	1	16	yes	—
359	C₄⋊Dic₅	C₂⁴	1	4	yes	—
360	C₄⋊Dic₅	C₂⁴	1	4	yes	—
361	C₄⋊Dic₅	C₂⁴	1	4	yes	—
362	C₄⋊Dic₅	C₂⁴	1	8	yes	—
363	C₄⋊Dic₅	C₂⁴	1	16	yes	—
364	C₄⋊Dic₅	C₂⁴	1	8	yes	—
365	C₄⋊Dic₅	C₂⁴	1	8	yes	—
366	#683	C₂⁴	1	16	yes	—
367	#683	C₂⁴	1	16	yes	—
368	C₄×Dic₅	C₂⁴	1	8	yes	—
369	C₄×Dic₅	C₂⁴	1	16	yes	—
370	C₄×Dic₅	C₂⁴	1	8	yes	—
371	C₄×Dic₅	C₂⁴	1	8	yes	—
372	C₄×Dic₅	C₂⁴	1	8	yes	—
373	C₂²×#41	—	5	4	no	—
374	C₂²×#41	C₂×D₅	1	1	yes	characteristic
375	C₂³×D₄	—	5	2	no	—
376	C₂³×D₄	—	5	1	no	—
377	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic
378	#555	—	5	32	no	—
379	#553	—	5	32	no	—
380	#553	—	5	32	no	—
381	#551	—	5	64	no	—
382	#547	—	5	32	no	—
383	#546	—	5	64	no	—
384	#544	—	5	16	no	—
385	#542	—	5	32	no	—
386	#540	—	5	32	no	—
387	#535	—	5	16	no	—
388	#532	—	5	32	no	—
389	C₂×C₄⋊Q₈	—	5	2	no	—
390	C₂×C₄⋊Q₈	—	5	2	no	—
391	C₂×#127	—	5	2	no	—
392	#529	—	5	32	no	—
393	C₂×#126	—	5	4	no	—
394	C₂×#126	—	5	4	no	—
395	C₂×#125	—	5	2	no	—
396	C₂×#125	—	5	2	no	—
397	C₂×#124	—	5	2	no	—
398	C₂×#124	—	5	4	no	—
399	C₂×#124	—	5	4	no	—
400	#525	C₂×D₅	1	16	yes	complemented
401	C₂×#123	—	5	4	no	—
402	C₂×#123	—	5	4	no	—
403	C₂×#123	—	5	4	no	—
404	C₂×#123	—	5	4	no	—
405	C₂×#123	C₂×D₅	1	2	yes	—
406	C₂×C₂²⋊Q₈	—	5	4	no	—
407	C₂×C₂²⋊Q₈	—	5	4	no	—
408	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
409	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
410	C₂×#121	—	5	4	no	—
411	C₂×#121	—	5	4	no	—
412	C₂×#121	—	5	4	no	—
413	C₂×#121	—	5	2	no	—
414	C₂×#121	—	5	2	no	—
415	C₂×#121	—	5	2	no	—
416	C₂×#121	—	5	2	no	—
417	C₂×#121	—	5	16	no	—
418	C₂×#121	—	5	2	no	—
419	C₂×#121	—	5	2	no	—
420	C₂×#121	C₂×D₅	1	1	yes	characteristic, complemented
421	C₂×#121	C₂×D₅	1	1	yes	characteristic, complemented
422	C₂×#120	—	5	4	no	—
423	C₂×#120	C₂×D₅	1	2	yes	—
424	#520	—	5	16	no	—
425	#518	—	5	16	no	—
426	C₂×C₄×Q₈	—	5	2	no	—
427	C₂×C₄×D₄	—	5	4	no	—
428	C₂×C₄×D₄	—	5	2	no	—
429	C₂×C₄×D₄	—	5	2	no	—
430	C₂×C₄×D₄	—	5	2	no	—
431	C₂×C₄×D₄	—	5	4	no	—
432	C₂×C₄×D₄	—	5	4	no	—
433	C₂×C₄×D₄	—	5	2	no	—
434	C₂×C₄×D₄	—	5	2	no	—
435	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
436	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
437	C₂×#117	—	5	1	no	—
438	C₂×#117	—	5	1	no	—
439	C₂×#117	—	5	2	no	—
440	C₂×#117	—	5	2	no	—
441	C₂×#117	—	5	1	no	—
442	C₂×#117	—	5	1	no	—
443	C₂×#117	—	5	16	no	—
444	C₂×#117	—	5	2	no	—
445	C₂×#117	—	5	4	no	—
446	C₂×#117	C₂×D₅	1	1	yes	characteristic
447	C₂²×C₄⋊C₄	—	5	1	no	—
448	C₂²×C₄⋊C₄	—	5	1	no	—
449	C₂²×C₄⋊C₄	—	5	1	no	—
450	C₂²×C₄⋊C₄	—	5	2	no	—
451	C₂²×C₂²⋊C₄	—	5	2	no	—
452	C₂²×C₂²⋊C₄	—	5	2	no	—
453	C₂²×C₂²⋊C₄	—	5	4	no	—
454	C₂²×C₄²	—	5	2	no	—
455	C₂³×C₅	—	2	2	no	—
456	C₂³×C₅	—	2	2	no	—
457	C₂³×C₅	—	2	2	no	—
458	C₂³×C₅	—	2	2	no	—
459	C₂³×C₅	—	2	8	no	—
460	C₂³×C₅	—	2	2	no	—
461	C₂³×C₅	—	2	4	no	—
462	C₂³×C₅	—	2	4	no	—
463	C₂³×C₅	—	2	8	no	—
464	C₂³×C₅	—	2	2	no	—
465	C₂³×C₅	—	2	4	no	—
466	C₂³×C₅	—	2	2	no	—
467	C₂³×C₅	—	4	4	no	—
468	C₂³×C₅	—	4	16	no	—
469	C₂³×C₅	C₂×#41	1	4	yes	—
470	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
471	C₂³×C₅	C₂⁵	1	2	yes	—
472	C₂³×C₅	C₂⁵	1	4	yes	—
473	C₂³×C₅	C₂⁵	1	2	yes	—
474	C₂³×C₅	C₂⁵	1	2	yes	—
475	C₂³×C₅	C₂⁵	1	1	yes	characteristic
476	C₂²×D₅	—	2	8	no	—
477	C₂²×D₅	—	2	8	no	—
478	C₂²×D₅	—	2	8	no	—
479	C₂²×D₅	—	2	16	no	—
480	C₂²×D₅	—	4	8	no	—
481	C₂²×D₅	—	4	8	no	—
482	C₂²×D₅	—	8	16	no	—
483	C₂²×D₅	C₂⁵	1	8	yes	—
484	C₅×Q₈	—	2	8	no	—
485	C₅×D₄	—	2	16	no	—
486	C₅×D₄	—	2	16	no	—
487	C₅×D₄	—	2	8	no	—
488	C₅×D₄	—	4	8	no	—
489	C₂×C₄×C₅	—	2	8	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	2	4	no	—
493	C₂×C₄×C₅	—	2	4	no	—
494	C₂×C₄×C₅	—	2	4	no	—
495	C₂×C₄×C₅	—	2	8	no	—
496	C₂×C₄×C₅	—	2	8	no	—
497	C₂×C₄×C₅	—	2	8	no	—
498	C₂×C₄×C₅	—	2	8	no	—
499	C₂×C₄×C₅	—	2	16	no	—
500	C₂×C₄×C₅	C₂×#41	1	4	yes	—
501	C₂×C₄×C₅	C₂×#41	1	4	yes	—
502	C₂×C₄×C₅	C₂×#41	1	16	yes	complemented
503	C₂×C₄×C₅	C₂⁵	1	2	yes	—
504	C₂×C₄×C₅	C₂⁵	1	4	yes	—
505	C₂×C₄×C₅	C₂⁵	1	4	yes	—
506	C₂×C₄×C₅	C₂⁵	1	4	yes	—
507	C₂×C₄×C₅	C₂⁵	1	2	yes	—
508	C₂×C₄×C₅	C₂⁵	1	2	yes	—
509	C₂×C₄×C₅	C₂⁵	1	2	yes	—
510	C₂²⋊D₅	—	2	32	no	—
511	C₂²⋊D₅	—	4	16	no	—
512	C₂²⋊D₅	—	4	16	no	—
513	C₂²⋊D₅	—	4	16	no	—
514	C₂×Dic₅	—	2	4	no	—
515	C₂×Dic₅	—	2	8	no	—
516	C₂×Dic₅	—	2	4	no	—
517	C₂×Dic₅	—	2	16	no	—
518	C₂×Dic₅	—	2	4	no	—
519	C₂×Dic₅	—	2	4	no	—
520	C₂×Dic₅	—	4	16	no	—
521	C₂×Dic₅	—	4	8	no	—
522	C₂×Dic₅	—	4	8	no	—
523	C₂×Dic₅	C₂⁵	1	4	yes	—
524	C₂×Dic₅	C₂⁵	1	4	yes	—
525	C₂×Dic₅	C₂⁵	1	4	yes	—
526	C₂×Dic₅	C₂⁵	1	4	yes	—
527	C₂×Dic₅	C₂⁵	1	8	yes	—
528	D₂₀	—	2	16	no	—
529	D₂₀	—	2	16	no	—
530	C₄×D₅	—	4	16	no	—
531	C₄×D₅	—	4	16	no	—
532	Dic₁₀	—	4	16	no	—
533	C₂⁵	—	5	2	no	—
534	C₂⁵	C₂²×D₅	1	1	yes	characteristic
535	C₂×#41	—	2	8	no	—
536	C₂×#41	—	5	32	no	—
537	C₂×#41	—	20	16	no	—
538	C₂×#41	C₂²×D₅	1	8	yes	—
539	C₂²×Q₈	—	5	4	no	—
540	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
541	C₂²×D₄	—	5	4	no	—
542	C₂²×D₄	—	5	4	no	—
543	C₂²×D₄	—	5	4	no	—
544	C₂²×D₄	—	5	4	no	—
545	C₂²×D₄	—	5	16	no	—
546	C₂²×D₄	—	5	2	no	—
547	C₂²×D₄	—	5	2	no	—
548	C₂²×D₄	—	5	8	no	—
549	C₂²×D₄	—	10	8	no	—
550	C₂²×D₄	—	20	8	no	—
551	C₂²×D₄	C₂²×D₅	1	2	yes	—
552	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
553	C₂²×D₄	C₂²×D₅	1	2	yes	—
554	C₂²×D₄	C₂²×D₅	1	2	yes	—
555	C₂³×C₄	—	2	8	no	—
556	C₂³×C₄	—	5	2	no	—
557	C₂³×C₄	—	5	2	no	—
558	C₂³×C₄	—	5	2	no	—
559	C₂³×C₄	—	5	4	no	—
560	C₂³×C₄	—	5	4	no	—
561	C₂³×C₄	—	5	4	no	—
562	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
563	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
564	C₂³×C₄	C₂²×D₅	1	2	yes	—
565	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
566	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
567	C₂³×C₄	C₂²×D₅	1	8	yes	—
568	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
569	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
570	C₄⋊Q₈	—	5	16	no	—
571	C₄⋊Q₈	—	5	16	no	—
572	#127	—	5	16	no	—
573	#126	—	5	32	no	—
574	#126	—	5	32	no	—
575	#125	—	5	16	no	—
576	#125	—	5	16	no	—
577	#124	—	5	16	no	—
578	#124	—	5	32	no	—
579	#124	—	5	32	no	—
580	#123	—	5	32	no	—
581	#123	—	5	32	no	—
582	#123	—	5	32	no	—
583	#123	—	5	32	no	—
584	#123	C₂²×D₅	1	16	yes	—
585	C₂²⋊Q₈	—	5	32	no	—
586	C₂²⋊Q₈	—	5	32	no	—
587	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
588	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
589	#121	—	5	32	no	—
590	#121	—	5	32	no	—
591	#121	—	5	32	no	—
592	#121	—	5	16	no	—
593	#121	—	5	16	no	—
594	#121	—	5	16	no	—
595	#121	—	5	16	no	—
596	#121	—	5	16	no	—
597	#121	—	5	16	no	—
598	#121	C₂²×D₅	1	8	yes	complemented
599	#121	C₂²×D₅	1	8	yes	complemented
600	#120	—	5	32	no	—
601	#120	C₂²×D₅	1	16	yes	—
602	C₄×Q₈	—	5	16	no	—
603	C₄×D₄	—	5	16	no	—
604	C₄×D₄	—	5	32	no	—
605	C₄×D₄	—	5	16	no	—
606	C₄×D₄	—	5	16	no	—
607	C₄×D₄	—	5	32	no	—
608	C₄×D₄	—	5	32	no	—
609	C₄×D₄	—	5	16	no	—
610	C₄×D₄	—	5	16	no	—
611	C₄×D₄	C₂²×D₅	1	16	yes	complemented
612	C₄×D₄	C₂²×D₅	1	16	yes	complemented
613	#117	—	5	8	no	—
614	#117	—	5	8	no	—
615	#117	—	5	16	no	—
616	#117	—	5	16	no	—
617	#117	—	5	8	no	—
618	#117	—	5	8	no	—
619	#117	—	5	16	no	—
620	#117	—	5	32	no	—
621	#117	C₂²×D₅	1	8	yes	—
622	C₂×C₄⋊C₄	—	5	1	no	—
623	C₂×C₄⋊C₄	—	5	2	no	—
624	C₂×C₄⋊C₄	—	5	1	no	—
625	C₂×C₄⋊C₄	—	5	1	no	—
626	C₂×C₄⋊C₄	—	5	1	no	—
627	C₂×C₄⋊C₄	—	5	2	no	—
628	C₂×C₄⋊C₄	—	5	2	no	—
629	C₂×C₄⋊C₄	—	5	8	no	—
630	C₂×C₄⋊C₄	—	5	8	no	—
631	C₂×C₄⋊C₄	—	5	2	no	—
632	C₂×C₄⋊C₄	—	5	4	no	—
633	C₂×C₄⋊C₄	—	5	8	no	—
634	C₂×C₄⋊C₄	—	5	16	no	—
635	C₂×C₄⋊C₄	—	5	4	no	—
636	C₂×C₄⋊C₄	—	5	4	no	—
637	C₂×C₄⋊C₄	—	5	4	no	—
638	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
639	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
642	C₂×C₂²⋊C₄	—	5	2	no	—
643	C₂×C₂²⋊C₄	—	5	2	no	—
644	C₂×C₂²⋊C₄	—	5	2	no	—
645	C₂×C₂²⋊C₄	—	5	2	no	—
646	C₂×C₂²⋊C₄	—	5	16	no	—
647	C₂×C₂²⋊C₄	—	5	4	no	—
648	C₂×C₂²⋊C₄	—	5	4	no	—
649	C₂×C₂²⋊C₄	—	5	4	no	—
650	C₂×C₂²⋊C₄	—	5	4	no	—
651	C₂×C₂²⋊C₄	—	5	4	no	—
652	C₂×C₂²⋊C₄	—	5	16	no	—
653	C₂×C₂²⋊C₄	—	5	4	no	—
654	C₂×C₂²⋊C₄	—	5	4	no	—
655	C₂×C₂²⋊C₄	—	5	32	no	—
656	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
661	C₂×C₄²	—	5	2	no	—
662	C₂×C₄²	—	5	2	no	—
663	C₂×C₄²	—	5	4	no	—
664	C₂×C₄²	—	5	2	no	—
665	C₂×C₄²	—	5	2	no	—
666	C₂×C₄²	—	5	16	no	—
667	C₂×C₄²	C₂²×D₅	1	2	yes	—
668	C₂²×C₅	—	2	2	no	—
669	C₂²×C₅	—	2	2	no	—
670	C₂²×C₅	—	2	2	no	—
671	C₂²×C₅	—	2	2	no	—
672	C₂²×C₅	—	2	8	no	—
673	C₂²×C₅	—	2	8	no	—
674	C₂²×C₅	—	2	2	no	—
675	C₂²×C₅	—	2	4	no	—
676	C₂²×C₅	—	2	4	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	4	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	4	16	no	—
681	C₂²×C₅	—	4	8	no	—
682	C₂²×C₅	—	4	4	no	—
683	C₂²×C₅	C₂²×#41	1	4	yes	—
684	C₂²×C₅	C₂²×#41	1	2	yes	—
685	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
686	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
687	C₂²×C₅	#585	1	2	yes	—
688	C₂²×C₅	C₂⁶	1	1	yes	characteristic
689	C₂×D₅	—	2	8	no	—
690	C₂×D₅	—	2	8	no	—
691	C₂×D₅	—	2	8	no	—
692	C₂×D₅	—	4	16	no	—
693	C₂×D₅	—	8	16	no	—
694	C₄×C₅	—	2	2	no	—
695	C₄×C₅	—	2	2	no	—
696	C₄×C₅	—	2	4	no	—
697	C₄×C₅	—	2	4	no	—
698	C₄×C₅	—	2	4	no	—
699	C₄×C₅	C₂²×#41	1	4	yes	—
700	C₄×C₅	C₂²×#41	1	4	yes	—
701	Dic₅	—	2	4	no	—
702	Dic₅	—	2	8	no	—
703	Dic₅	—	2	4	no	—
704	Dic₅	—	2	4	no	—
705	Dic₅	—	2	4	no	—
706	C₂⁴	—	2	4	no	—
707	C₂⁴	—	2	4	no	—
708	C₂⁴	—	4	2	no	—
709	C₂⁴	—	5	4	no	—
710	C₂⁴	—	5	8	no	—
711	C₂⁴	—	10	8	no	—
712	C₂⁴	—	20	4	no	—
713	C₂⁴	—	20	4	no	—
714	C₂⁴	C₂³×D₅	1	1	yes	characteristic
715	C₂⁴	C₂³×D₅	1	2	yes	—
716	C₂⁴	C₂³×D₅	1	4	yes	—
717	C₂⁴	C₂³×D₅	1	1	yes	characteristic
718	C₂⁴	C₂³×D₅	1	1	yes	characteristic
719	#41	—	2	32	no	—
720	#41	—	20	64	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	5	16	no	—
723	C₂×Q₈	—	20	8	no	—
724	C₂×Q₈	C₂³×D₅	1	4	yes	—
725	C₂×D₄	—	2	8	no	—
726	C₂×D₄	—	2	8	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	5	16	no	—
730	C₂×D₄	—	5	16	no	—
731	C₂×D₄	—	5	16	no	—
732	C₂×D₄	—	5	16	no	—
733	C₂×D₄	—	5	8	no	—
734	C₂×D₄	—	5	8	no	—
735	C₂×D₄	—	10	16	no	—
736	C₂×D₄	—	10	8	no	—
737	C₂×D₄	—	10	8	no	—
738	C₂×D₄	—	10	32	no	—
739	C₂×D₄	—	20	8	no	—
740	C₂×D₄	—	20	8	no	—
741	C₂×D₄	—	20	8	no	—
742	C₂×D₄	—	20	32	no	—
743	C₂×D₄	C₂³×D₅	1	8	yes	—
744	C₂×D₄	C₂³×D₅	1	4	yes	—
745	C₂×D₄	C₂³×D₅	1	8	yes	—
746	C₂×D₄	C₂³×D₅	1	8	yes	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	8	no	—
753	C₂²×C₄	—	2	32	no	—
754	C₂²×C₄	—	5	8	no	—
755	C₂²×C₄	—	5	2	no	—
756	C₂²×C₄	—	5	2	no	—
757	C₂²×C₄	—	5	2	no	—
758	C₂²×C₄	—	5	2	no	—
759	C₂²×C₄	—	5	4	no	—
760	C₂²×C₄	—	5	8	no	—
761	C₂²×C₄	—	5	8	no	—
762	C₂²×C₄	—	5	16	no	—
763	C₂²×C₄	—	5	16	no	—
764	C₂²×C₄	—	5	16	no	—
765	C₂²×C₄	—	10	8	no	—
766	C₂²×C₄	—	20	8	no	—
767	C₂²×C₄	—	20	8	no	—
768	C₂²×C₄	—	20	4	no	—
769	C₂²×C₄	—	20	8	no	—
770	C₂²×C₄	—	20	4	no	—
771	C₂²×C₄	#711	1	8	yes	complemented
772	C₂²×C₄	C₂³×D₅	1	4	yes	—
773	C₂²×C₄	C₂³×D₅	1	4	yes	—
774	C₂²×C₄	C₂³×D₅	1	4	yes	—
775	C₂²×C₄	C₂³×D₅	1	8	yes	—
776	C₂²×C₄	C₂³×D₅	1	4	yes	—
777	C₂²×C₄	C₂³×D₅	1	4	yes	—
778	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
779	C₂²×C₄	C₂³×D₅	1	2	yes	—
780	C₂²×C₄	C₂³×D₅	1	2	yes	—
781	C₂²×C₄	C₂³×D₅	1	2	yes	—
782	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
783	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
784	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
785	C₂²×C₄	C₂³×D₅	1	4	yes	—
786	C₄⋊C₄	—	5	4	no	—
787	C₄⋊C₄	—	5	8	no	—
788	C₄⋊C₄	—	5	4	no	—
789	C₄⋊C₄	—	5	4	no	—
790	C₄⋊C₄	—	5	4	no	—
791	C₄⋊C₄	—	5	8	no	—
792	C₄⋊C₄	—	5	8	no	—
793	C₄⋊C₄	—	5	8	no	—
794	C₄⋊C₄	—	5	16	no	—
795	C₄⋊C₄	—	5	16	no	—
796	C₄⋊C₄	—	5	16	no	—
797	C₄⋊C₄	—	5	16	no	—
798	C₄⋊C₄	C₂³×D₅	1	8	yes	—
799	C₄⋊C₄	C₂³×D₅	1	4	yes	—
800	C₄⋊C₄	C₂³×D₅	1	4	yes	—
801	C₄⋊C₄	C₂³×D₅	1	8	yes	—
802	C₂²⋊C₄	—	5	8	no	—
803	C₂²⋊C₄	—	5	8	no	—
804	C₂²⋊C₄	—	5	8	no	—
805	C₂²⋊C₄	—	5	8	no	—
806	C₂²⋊C₄	—	5	16	no	—
807	C₂²⋊C₄	—	5	16	no	—
808	C₂²⋊C₄	—	5	16	no	—
809	C₂²⋊C₄	—	5	16	no	—
810	C₂²⋊C₄	—	5	16	no	—
811	C₂²⋊C₄	—	5	16	no	—
812	C₂²⋊C₄	—	5	16	no	—
813	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
814	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
815	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
816	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
817	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
818	C₄²	—	5	8	no	—
819	C₄²	—	5	8	no	—
820	C₄²	—	5	8	no	—
821	C₄²	—	5	8	no	—
822	C₄²	—	5	16	no	—
823	C₄²	C₂³×D₅	1	8	yes	—
824	C₂×C₅	—	2	4	no	—
825	C₂×C₅	—	2	4	no	—
826	C₂×C₅	—	4	4	no	—
827	C₂×C₅	—	4	2	no	—
828	C₂×C₅	#3494	1	4	yes	complemented
829	C₂×C₅	C₂³×#41	1	1	yes	characteristic
830	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₅	C₂×#585	1	1	yes	characteristic
832	D₅	—	4	8	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	8	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	4	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	8	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	16	no	—
847	C₂³	—	5	8	no	—
848	C₂³	—	10	8	no	—
849	C₂³	—	10	8	no	—
850	C₂³	—	10	8	no	—
851	C₂³	—	10	16	no	—
852	C₂³	—	20	8	no	—
853	C₂³	—	20	8	no	—
854	C₂³	—	40	16	no	—
855	C₂³	C₂×#711	1	4	yes	—
856	C₂³	#4149	1	4	yes	—
857	C₂³	C₂⁴×D₅	1	2	yes	—
858	C₂³	C₂⁴×D₅	1	4	yes	—
859	C₂³	C₂⁴×D₅	1	2	yes	—
860	C₂³	C₂⁴×D₅	1	2	yes	—
861	C₂³	C₂⁴×D₅	1	1	yes	characteristic
862	Q₈	—	2	8	no	—
863	Q₈	—	20	16	no	—
864	D₄	—	2	16	no	—
865	D₄	—	2	16	no	—
866	D₄	—	2	8	no	—
867	D₄	—	4	8	no	—
868	D₄	—	10	32	no	—
869	D₄	—	10	16	no	—
870	D₄	—	10	16	no	—
871	D₄	—	20	16	no	—
872	D₄	—	20	16	no	—
873	D₄	—	20	16	no	—
874	C₂×C₄	—	2	8	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	4	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	8	no	—
882	C₂×C₄	—	2	8	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	16	no	—
885	C₂×C₄	—	5	4	no	—
886	C₂×C₄	—	5	4	no	—
887	C₂×C₄	—	5	4	no	—
888	C₂×C₄	—	5	4	no	—
889	C₂×C₄	—	5	8	no	—
890	C₂×C₄	—	10	4	no	—
891	C₂×C₄	—	10	4	no	—
892	C₂×C₄	—	10	16	no	—
893	C₂×C₄	—	10	8	no	—
894	C₂×C₄	—	10	4	no	—
895	C₂×C₄	—	10	4	no	—
896	C₂×C₄	—	20	16	no	—
897	C₂×C₄	—	20	16	no	—
898	C₂×C₄	—	20	8	no	—
899	C₂×C₄	—	20	16	no	—
900	C₂×C₄	—	20	8	no	—
901	C₂×C₄	C₂×#711	1	4	yes	—
902	C₂×C₄	C₂×#711	1	4	yes	—
903	C₂×C₄	C₂×#711	1	16	yes	complemented
904	C₂×C₄	C₂⁴×D₅	1	2	yes	—
905	C₂×C₄	C₂⁴×D₅	1	4	yes	—
906	C₂×C₄	C₂⁴×D₅	1	4	yes	—
907	C₂×C₄	C₂⁴×D₅	1	4	yes	—
908	C₂×C₄	C₂⁴×D₅	1	2	yes	—
909	C₂×C₄	C₂⁴×D₅	1	2	yes	—
910	C₂×C₄	C₂⁴×D₅	1	2	yes	—
911	C₅	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	8	no	—
917	C₂²	—	2	8	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	4	no	—
924	C₂²	—	4	16	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	8	no	—
927	C₂²	—	10	8	no	—
928	C₂²	—	10	8	no	—
929	C₂²	—	10	8	no	—
930	C₂²	—	20	16	no	—
931	C₂²	—	40	16	no	—
932	C₂²	C₂²×#711	1	4	yes	—
933	C₂²	C₂²×#711	1	2	yes	—
934	C₂²	C₂×#4149	1	4	yes	—
935	C₂²	C₂×#4149	1	2	yes	—
936	C₂²	#66283	1	2	yes	—
937	C₂²	C₂⁵×D₅	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	4	no	—
943	C₄	—	10	4	no	—
944	C₄	—	10	4	no	—
945	C₄	—	10	8	no	—
946	C₄	—	10	4	no	—
947	C₄	—	10	4	no	—
948	C₄	C₂²×#711	1	4	yes	—
949	C₄	C₂²×#711	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	2	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	4	no	—
954	C₂	—	20	8	no	—
955	C₂	#10617928	1	4	yes	direct product factor
956	C₂	C₂³×#711	1	1	yes	characteristic
957	C₂	C₂²×#4149	1	1	yes	characteristic
958	C₂	C₂×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#525	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#525	D₅
hypocenter	C₅	C₂×#3494
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#525	C₂	semidirect
2. C₂×#66164	C₂	semidirect
3. C₂×#66161	C₂	semidirect
4. C₂²×#4076	C₂	semidirect
5. C₂²×#4072	C₂	semidirect
6. #10617928	C₂	direct (N × H)
7. C₂×#65992	C₂	semidirect
8. C₂×#65977	C₂	semidirect
9. C₂×#65958	C₂	semidirect
10. C₂×#65953	C₂	semidirect
11. C₂×#65930	C₂	semidirect
12. C₂×#65925	C₂	semidirect
13. C₂×#65897	C₂	semidirect
14. C₂×#65899	C₂	semidirect
15. C₂×#65899	C₂	semidirect
16. C₂×#65889	C₂	semidirect
17. C₂×#65855	C₂	semidirect
18. C₂×#65853	C₂	semidirect
22. C₂²×#711	C₂²	semidirect
24. C₅×#525	C₂²	semidirect
26. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₅×#121	C₂²	semidirect
29. C₂×C₅×#121	C₂²	semidirect
31. C₂×C₄×C₅×D₄	C₂²	semidirect
32. C₂×C₄×C₅×D₄	C₂²	semidirect
35. #66164	C₂²	semidirect
36. #66161	C₂²	semidirect
37. C₂×#4093	C₂²	semidirect
38. C₂×Q₈×Dic₅	C₂²	semidirect
39. C₂×#4086	C₂²	semidirect
40. C₂×#4085	C₂²	semidirect
41. C₂×#4085	C₂²	semidirect
42. C₂×#4084	C₂²	semidirect
45. C₂×D₄×Dic₅	C₂²	semidirect
50. C₂×#4076	C₂²	semidirect
51. C₂×#4076	C₂²	semidirect
52. C₂×#4076	C₂²	semidirect
57. C₂×#4072	C₂²	semidirect
58. C₂×#4072	C₂²	semidirect
59. C₂×#4072	C₂²	semidirect
60. C₂×#4072	C₂²	semidirect
61. C₂×#4072	C₂²	semidirect
63. C₂²×C₄⋊Dic₅	C₂²	semidirect
64. C₂²×C₄⋊Dic₅	C₂²	semidirect
65. C₂²×C₄⋊Dic₅	C₂²	semidirect
66. C₂²×C₄×Dic₅	C₂²	semidirect
67. #65992	C₂²	semidirect
68. #65977	C₂²	semidirect
69. #65958	C₂²	semidirect
70. #65953	C₂²	semidirect
71. #65930	C₂²	semidirect
72. #65925	C₂²	semidirect
73. #65899	C₂²	semidirect
74. #65899	C₂²	semidirect
75. #65897	C₂²	semidirect
76. #65889	C₂²	semidirect
77. #65855	C₂²	semidirect
78. #65853	C₂²	semidirect
79. C₂×#4044	C₂²	semidirect
80. C₂×#4044	C₂²	semidirect
81. C₂×#4043	C₂²	semidirect
82. C₂×#4039	C₂²	semidirect
83. C₂×#4039	C₂²	semidirect
84. C₂×#4038	C₂²	semidirect
85. C₂×#4036	C₂²	semidirect
86. C₂×#4034	C₂²	semidirect
87. C₂×#4032	C₂²	semidirect
88. C₂×#4032	C₂²	semidirect
89. C₂×#4031	C₂²	semidirect
90. C₂×#4031	C₂²	semidirect
91. C₂×#4029	C₂²	semidirect
92. C₂×#4029	C₂²	semidirect
93. C₂×#4027	C₂²	semidirect
94. C₂×#4027	C₂²	semidirect
97. C₂×C₄×D₂₀	C₂²	semidirect
98. C₂×C₄×D₂₀	C₂²	semidirect
99. C₂×#4016	C₂²	semidirect
100. C₂×#4015	C₂²	semidirect
131. C₂×#711	C₂³	semidirect
140. C₅×C₂²⋊Q₈	C₂³	semidirect
141. C₅×C₂²⋊Q₈	C₂³	semidirect
142. C₅×#121	C₂³	semidirect
143. C₅×#121	C₂³	semidirect
145. C₄×C₅×D₄	C₂³	semidirect
146. C₄×C₅×D₄	C₂³	semidirect
164. #4093	C₂³	semidirect
165. Q₈×Dic₅	C₂³	semidirect
166. #4086	C₂³	semidirect
167. #4085	C₂³	semidirect
168. #4085	C₂³	semidirect
169. #4084	C₂³	semidirect
172. D₄×Dic₅	C₂³	semidirect
177. #4076	C₂³	semidirect
178. #4076	C₂³	semidirect
189. #4072	C₂³	semidirect
190. #4072	C₂³	semidirect
191. #4072	C₂³	semidirect
192. #4072	C₂³	semidirect
204. C₂×C₄⋊Dic₅	C₂³	semidirect
205. C₂×C₄⋊Dic₅	C₂³	semidirect
206. C₂×C₄⋊Dic₅	C₂³	semidirect
214. C₂×C₄×Dic₅	C₂³	semidirect
215. #4044	C₂³	semidirect
216. #4044	C₂³	semidirect
217. #4043	C₂³	semidirect
218. #4039	C₂³	semidirect
219. #4039	C₂³	semidirect
220. #4038	C₂³	semidirect
221. #4036	C₂³	semidirect
222. #4034	C₂³	semidirect
223. #4032	C₂³	semidirect
224. #4032	C₂³	semidirect
225. #4031	C₂³	semidirect
226. #4031	C₂³	semidirect
227. #4029	C₂³	semidirect
228. #4029	C₂³	semidirect
229. #4027	C₂³	semidirect
230. #4027	C₂³	semidirect
233. C₄×D₂₀	C₂³	semidirect
234. C₄×D₂₀	C₂³	semidirect
235. #4016	C₂³	semidirect
236. #4015	C₂³	semidirect
250. C₂×#525	D₅	semidirect
286. C₂²×C₄×C₅	#41	semidirect
400. #525	C₂×D₅	semidirect
408. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
409. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
420. C₂×#121	C₂×D₅	semidirect
421. C₂×#121	C₂×D₅	semidirect
435. C₂×C₄×D₄	C₂×D₅	semidirect
436. C₂×C₄×D₄	C₂×D₅	semidirect
502. C₂×C₄×C₅	C₂×#41	semidirect
587. C₂²⋊Q₈	C₂²×D₅	semidirect
588. C₂²⋊Q₈	C₂²×D₅	semidirect
598. #121	C₂²×D₅	semidirect
599. #121	C₂²×D₅	semidirect
611. C₄×D₄	C₂²×D₅	semidirect
612. C₄×D₄	C₂²×D₅	semidirect
771. C₂²×C₄	#711	semidirect
828. C₂×C₅	#3494	semidirect
903. C₂×C₄	C₂×#711	semidirect
911. C₅	C₂×#3494	semidirect
955. C₂	#10617928	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×#525	2
C₂×#66164	2
C₂×#66161	2
C₂²×#4076	2
C₂²×#4072	2
#10617928	2
C₂×#65992	2
C₂×#65977	2
C₂×#65958	2
C₂×#65953	2
C₂×#65930	2
C₂×#65925	2
C₂×#65897	2
C₂×#65899	2
C₂×#65889	2
C₂×#65855	2
C₂×#65853	2
C₂×#3494	5

Subgroups — C2×#10617928 #13007648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10617928 #13007648