Subgroups — C₅×#34988 #11957708

Order 1280.

4082 conjugacy classes of subgroups.

The subgroup lattice has 852 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	C₂³×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2846	C₂	1	2	yes	maximal, complemented
6	C₅×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2622	C₂	1	2	yes	maximal, complemented
8	C₅×#2617	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2480	C₂	1	4	yes	maximal, complemented
10	C₅×#2472	C₂	1	4	yes	maximal, complemented
11	C₅×#2424	C₂	1	4	yes	maximal, complemented
12	C₅×#2418	C₂	1	4	yes	maximal, complemented
13	C₅×#2321	C₂	1	2	yes	maximal, complemented
14	C₅×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#120	C₂	1	2	yes	maximal, complemented
16	C₂⁶×C₅	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₅×#538	—	2	8	no	—
20	C₂×C₅×#126	C₂²	1	2	yes	complemented
21	C₂×C₅×#124	C₂²	1	2	yes	complemented
22	C₂×C₅×#123	C₂²	1	2	yes	complemented
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₅×#121	C₂²	1	2	yes	complemented
26	C₂×C₅×#121	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#121	C₂²	1	2	yes	complemented
28	C₂×C₅×#120	C₂²	1	2	yes	—
29	C₂×C₅×#120	C₂²	1	2	yes	—
30	C₂×C₅×#120	C₂²	1	2	yes	—
31	C₂×C₅×#120	C₂²	1	4	yes	—
32	C₂×C₅×#120	C₂²	1	4	yes	—
33	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
34	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
35	C₂²×C₅×C₂²⋊C₄	—	2	8	no	—
36	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
37	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
38	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₅×#399	C₂²	1	2	yes	complemented
43	C₅×#397	C₂²	1	4	yes	complemented
44	C₅×#397	C₂²	1	2	yes	complemented
45	C₅×#397	C₂²	1	4	yes	complemented
46	C₅×#396	C₂²	1	4	yes	complemented
47	C₅×#394	C₂²	1	4	yes	complemented
48	C₅×#394	C₂²	1	4	yes	complemented
49	C₅×#394	C₂²	1	4	yes	complemented
50	C₅×#393	C₂²	1	2	yes	complemented
51	C₅×#392	C₂²	1	2	yes	complemented
52	C₅×#390	C₂²	1	4	yes	complemented
53	C₅×#388	C₂²	1	4	yes	complemented
54	C₅×#388	C₂²	1	4	yes	complemented
55	C₅×#388	C₂²	1	4	yes	complemented
56	C₅×#388	C₂²	1	4	yes	complemented
57	C₅×#386	C₂²	1	4	yes	complemented
58	C₅×#386	C₂²	1	4	yes	complemented
59	C₅×#386	C₂²	1	4	yes	complemented
60	C₅×#386	C₂²	1	2	yes	complemented
61	C₅×#386	C₂²	1	2	yes	complemented
62	C₅×#385	C₂²	1	4	yes	complemented
63	C₅×#385	C₂²	1	4	yes	complemented
64	C₅×#385	C₂²	1	2	yes	complemented
65	C₅×#385	C₂²	1	2	yes	complemented
66	C₅×#380	C₂²	1	2	yes	complemented
67	C₅×#380	C₂²	1	1	yes	characteristic, complemented
68	C₅×#380	C₂²	1	1	yes	characteristic, complemented
69	C₅×#380	C₂²	1	2	yes	complemented
70	C₅×#379	C₂²	1	4	yes	—
71	C₅×#379	C₂²	1	4	yes	—
72	C₅×#379	C₂²	1	2	yes	—
73	C₅×#379	C₂²	1	2	yes	—
74	C₅×#379	C₂²	1	2	yes	—
75	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
76	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
77	#34988	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁵×C₅	—	2	4	no	—
79	C₂⁵×C₅	—	2	4	no	—
80	C₂⁵×C₅	—	2	4	no	—
81	C₂⁵×C₅	—	4	4	no	—
82	C₂⁵×C₅	—	4	4	no	—
83	C₂⁵×C₅	C₂³	1	1	yes	characteristic
84	C₂⁵×C₅	C₂³	1	4	yes	—
85	C₂⁵×C₅	C₂³	1	1	yes	characteristic
86	C₂⁵×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
88	C₂²×C₅×D₄	C₂³	1	2	yes	—
89	C₂²×C₅×D₄	C₂³	1	4	yes	—
90	C₂²×C₅×D₄	C₂³	1	4	yes	—
91	C₂²×C₅×D₄	C₂³	1	2	yes	—
92	C₂²×C₅×D₄	C₂³	1	2	yes	—
93	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
94	C₂³×C₄×C₅	—	2	4	no	—
95	C₂³×C₄×C₅	—	2	4	no	—
96	C₂³×C₄×C₅	—	4	4	no	—
97	C₂³×C₄×C₅	—	4	4	no	—
98	C₂³×C₄×C₅	C₂³	1	4	yes	—
99	C₂³×C₄×C₅	C₂³	1	2	yes	—
100	C₂³×C₄×C₅	C₂³	1	2	yes	—
101	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₅	C₂³	1	2	yes	complemented
106	C₅×#126	—	2	8	no	—
107	C₅×#124	—	2	8	no	—
108	C₅×#123	—	2	8	no	—
109	C₅×C₂²⋊Q₈	—	2	4	no	—
110	C₅×C₂²⋊Q₈	—	4	4	no	—
111	C₅×#121	—	2	4	no	—
112	C₅×#121	—	2	8	no	—
113	C₅×#121	—	4	4	no	—
114	C₅×#120	—	2	8	no	—
115	C₅×#120	—	2	8	no	—
116	C₅×#120	—	2	8	no	—
117	C₅×#120	—	4	8	no	—
118	C₅×#120	—	4	8	no	—
119	C₄×C₅×D₄	—	2	8	no	—
120	C₄×C₅×D₄	—	4	8	no	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
122	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
125	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
127	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
128	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
129	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
130	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
132	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
133	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
134	C₂×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
135	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₅×C₂²⋊C₄	C₂³	1	4	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	complemented
155	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
156	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
157	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
158	C₂×C₄²×C₅	C₂³	1	2	yes	complemented
159	C₂×C₄²×C₅	C₂³	1	4	yes	complemented
160	C₅×#95	C₂³	1	4	yes	complemented
161	C₅×#95	C₂³	1	4	yes	complemented
162	C₅×#95	C₂³	1	4	yes	complemented
163	C₅×#95	C₂³	1	4	yes	complemented
164	C₅×#95	C₂³	1	2	yes	complemented
165	C₅×#95	C₂³	1	2	yes	complemented
166	C₅×#95	C₂³	1	4	yes	complemented
167	C₂×#538	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂³×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
169	#2848	C₂×C₅	1	1	yes	characteristic, complemented
170	#2847	C₂×C₅	1	1	yes	characteristic, complemented
171	#2846	C₂×C₅	1	2	yes	complemented
172	#2626	C₂×C₅	1	1	yes	characteristic, complemented
173	#2622	C₂×C₅	1	2	yes	complemented
174	#2617	C₂×C₅	1	1	yes	characteristic, complemented
175	#2480	C₂×C₅	1	4	yes	complemented
176	#2472	C₂×C₅	1	4	yes	complemented
177	#2424	C₂×C₅	1	4	yes	complemented
178	#2418	C₂×C₅	1	4	yes	complemented
179	#2321	C₂×C₅	1	2	yes	complemented
180	#2312	C₂×C₅	1	1	yes	characteristic, complemented
181	C₄×#120	C₂×C₅	1	2	yes	complemented
182	C₂⁴×C₅	—	2	2	no	—
183	C₂⁴×C₅	—	2	2	no	—
184	C₂⁴×C₅	—	2	4	no	—
185	C₂⁴×C₅	—	2	4	no	—
186	C₂⁴×C₅	—	2	32	no	—
187	C₂⁴×C₅	—	2	8	no	—
188	C₂⁴×C₅	—	2	2	no	—
189	C₂⁴×C₅	—	2	8	no	—
190	C₂⁴×C₅	—	2	8	no	—
191	C₂⁴×C₅	—	2	2	no	—
192	C₂⁴×C₅	—	2	2	no	—
193	C₂⁴×C₅	—	2	2	no	—
194	C₂⁴×C₅	—	2	8	no	—
195	C₂⁴×C₅	—	2	8	no	—
196	C₂⁴×C₅	—	4	2	no	—
197	C₂⁴×C₅	—	4	2	no	—
198	C₂⁴×C₅	—	4	2	no	—
199	C₂⁴×C₅	—	4	2	no	—
200	C₂⁴×C₅	—	4	4	no	—
201	C₂⁴×C₅	—	4	4	no	—
202	C₂⁴×C₅	—	4	16	no	—
203	C₂⁴×C₅	—	4	16	no	—
204	C₂⁴×C₅	—	4	32	no	—
205	C₂⁴×C₅	—	4	32	no	—
206	C₂⁴×C₅	C₂×D₄	1	4	yes	—
207	C₂⁴×C₅	#41	1	4	yes	—
208	C₂⁴×C₅	#41	1	4	yes	—
209	C₂⁴×C₅	C₂⁴	1	2	yes	—
210	C₂⁴×C₅	C₂⁴	1	2	yes	—
211	C₂⁴×C₅	C₂⁴	1	2	yes	—
212	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₅	C₂⁴	1	2	yes	—
214	C₂×C₅×Q₈	—	2	2	no	—
215	C₂×C₅×Q₈	—	4	2	no	—
216	C₂×C₅×D₄	—	2	4	no	—
217	C₂×C₅×D₄	—	2	4	no	—
218	C₂×C₅×D₄	—	2	4	no	—
219	C₂×C₅×D₄	—	2	8	no	—
220	C₂×C₅×D₄	—	2	8	no	—
221	C₂×C₅×D₄	—	2	8	no	—
222	C₂×C₅×D₄	—	2	4	no	—
223	C₂×C₅×D₄	—	2	4	no	—
224	C₂×C₅×D₄	—	2	8	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	4	4	no	—
227	C₂×C₅×D₄	—	4	4	no	—
228	C₂×C₅×D₄	—	4	4	no	—
229	C₂×C₅×D₄	—	4	4	no	—
230	C₂×C₅×D₄	—	4	2	no	—
231	C₂²×C₄×C₅	—	2	2	no	—
232	C₂²×C₄×C₅	—	2	2	no	—
233	C₂²×C₄×C₅	—	2	8	no	—
234	C₂²×C₄×C₅	—	2	4	no	—
235	C₂²×C₄×C₅	—	2	4	no	—
236	C₂²×C₄×C₅	—	2	8	no	—
237	C₂²×C₄×C₅	—	2	4	no	—
238	C₂²×C₄×C₅	—	2	4	no	—
239	C₂²×C₄×C₅	—	2	4	no	—
240	C₂²×C₄×C₅	—	4	2	no	—
241	C₂²×C₄×C₅	—	4	4	no	—
242	C₂²×C₄×C₅	—	4	2	no	—
243	C₂²×C₄×C₅	—	4	2	no	—
244	C₂²×C₄×C₅	—	4	2	no	—
245	C₂²×C₄×C₅	—	4	2	no	—
246	C₂²×C₄×C₅	—	4	2	no	—
247	C₂²×C₄×C₅	—	4	4	no	—
248	C₂²×C₄×C₅	—	4	16	no	—
249	C₂²×C₄×C₅	—	4	16	no	—
250	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
262	C₅×C₄⋊C₄	—	2	4	no	—
263	C₅×C₄⋊C₄	—	2	4	no	—
264	C₅×C₄⋊C₄	—	2	2	no	—
265	C₅×C₄⋊C₄	—	2	2	no	—
266	C₅×C₄⋊C₄	—	4	4	no	—
267	C₅×C₄⋊C₄	—	4	2	no	—
268	C₅×C₄⋊C₄	—	4	2	no	—
269	C₅×C₄⋊C₄	—	4	4	no	—
270	C₅×C₂²⋊C₄	—	2	8	no	—
271	C₅×C₂²⋊C₄	—	2	4	no	—
272	C₅×C₂²⋊C₄	—	2	4	no	—
273	C₅×C₂²⋊C₄	—	2	4	no	—
274	C₅×C₂²⋊C₄	—	2	8	no	—
275	C₅×C₂²⋊C₄	—	2	4	no	—
276	C₅×C₂²⋊C₄	—	2	4	no	—
277	C₅×C₂²⋊C₄	—	2	8	no	—
278	C₅×C₂²⋊C₄	—	2	8	no	—
279	C₅×C₂²⋊C₄	—	2	8	no	—
280	C₅×C₂²⋊C₄	—	2	8	no	—
281	C₅×C₂²⋊C₄	—	2	4	no	—
282	C₅×C₂²⋊C₄	—	2	4	no	—
283	C₅×C₂²⋊C₄	—	2	4	no	—
284	C₅×C₂²⋊C₄	—	2	4	no	—
285	C₅×C₂²⋊C₄	—	4	4	no	—
286	C₅×C₂²⋊C₄	—	4	4	no	—
287	C₅×C₂²⋊C₄	—	4	4	no	—
288	C₅×C₂²⋊C₄	—	4	4	no	—
289	C₅×C₂²⋊C₄	—	4	4	no	—
290	C₅×C₂²⋊C₄	—	4	4	no	—
291	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
292	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
293	C₄²×C₅	—	2	4	no	—
294	C₄²×C₅	—	4	4	no	—
295	C₂⁶	C₂²×C₅	1	1	yes	characteristic
296	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
297	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
298	#538	—	2	8	no	—
299	C₂×#126	C₂²×C₅	1	2	yes	complemented
300	C₂×#124	C₂²×C₅	1	2	yes	complemented
301	C₂×#123	C₂²×C₅	1	2	yes	complemented
302	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
304	C₂×#121	C₂²×C₅	1	2	yes	complemented
305	C₂×#121	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂×#121	C₂²×C₅	1	2	yes	complemented
307	C₂×#120	C₂²×C₅	1	2	yes	—
308	C₂×#120	C₂²×C₅	1	2	yes	—
309	C₂×#120	C₂²×C₅	1	2	yes	—
310	C₂×#120	C₂²×C₅	1	4	yes	—
311	C₂×#120	C₂²×C₅	1	4	yes	—
312	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
313	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
314	C₂²×C₂²⋊C₄	—	2	8	no	—
315	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
321	#399	C₂²×C₅	1	2	yes	complemented
322	#397	C₂²×C₅	1	2	yes	complemented
323	#397	C₂²×C₅	1	4	yes	complemented
324	#397	C₂²×C₅	1	4	yes	complemented
325	#396	C₂²×C₅	1	4	yes	complemented
326	#394	C₂²×C₅	1	4	yes	complemented
327	#394	C₂²×C₅	1	4	yes	complemented
328	#394	C₂²×C₅	1	4	yes	complemented
329	#393	C₂²×C₅	1	2	yes	complemented
330	#392	C₂²×C₅	1	2	yes	complemented
331	#390	C₂²×C₅	1	4	yes	complemented
332	#388	C₂²×C₅	1	4	yes	complemented
333	#388	C₂²×C₅	1	4	yes	complemented
334	#388	C₂²×C₅	1	4	yes	complemented
335	#388	C₂²×C₅	1	4	yes	complemented
336	#386	C₂²×C₅	1	4	yes	complemented
337	#386	C₂²×C₅	1	2	yes	complemented
338	#386	C₂²×C₅	1	4	yes	complemented
339	#386	C₂²×C₅	1	2	yes	complemented
340	#386	C₂²×C₅	1	4	yes	complemented
341	#385	C₂²×C₅	1	2	yes	complemented
342	#385	C₂²×C₅	1	4	yes	complemented
343	#385	C₂²×C₅	1	2	yes	complemented
344	#385	C₂²×C₅	1	4	yes	complemented
345	#380	C₂²×C₅	1	1	yes	characteristic, complemented
346	#380	C₂²×C₅	1	1	yes	characteristic, complemented
347	#380	C₂²×C₅	1	2	yes	complemented
348	#380	C₂²×C₅	1	2	yes	complemented
349	#379	C₂²×C₅	1	2	yes	—
350	#379	C₂²×C₅	1	2	yes	—
351	#379	C₂²×C₅	1	2	yes	—
352	#379	C₂²×C₅	1	4	yes	—
353	#379	C₂²×C₅	1	4	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
355	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
356	C₂³×C₅	—	2	8	no	—
357	C₂³×C₅	—	2	8	no	—
358	C₂³×C₅	—	2	16	no	—
359	C₂³×C₅	—	2	8	no	—
360	C₂³×C₅	—	2	16	no	—
361	C₂³×C₅	—	2	2	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	2	no	—
365	C₂³×C₅	—	2	2	no	—
366	C₂³×C₅	—	2	2	no	—
367	C₂³×C₅	—	2	32	no	—
368	C₂³×C₅	—	2	8	no	—
369	C₂³×C₅	—	2	8	no	—
370	C₂³×C₅	—	2	2	no	—
371	C₂³×C₅	—	2	2	no	—
372	C₂³×C₅	—	2	2	no	—
373	C₂³×C₅	—	2	2	no	—
374	C₂³×C₅	—	2	4	no	—
375	C₂³×C₅	—	2	4	no	—
376	C₂³×C₅	—	2	4	no	—
377	C₂³×C₅	—	2	4	no	—
378	C₂³×C₅	—	2	2	no	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	—	2	4	no	—
382	C₂³×C₅	—	2	4	no	—
383	C₂³×C₅	—	4	4	no	—
384	C₂³×C₅	—	4	4	no	—
385	C₂³×C₅	—	4	8	no	—
386	C₂³×C₅	—	4	16	no	—
387	C₂³×C₅	—	4	16	no	—
388	C₂³×C₅	—	4	16	no	—
389	C₂³×C₅	—	4	16	no	—
390	C₂³×C₅	—	4	128	no	—
391	C₂³×C₅	—	4	8	no	—
392	C₂³×C₅	—	4	8	no	—
393	C₂³×C₅	—	4	16	no	—
394	C₂³×C₅	—	4	4	no	—
395	C₂³×C₅	—	4	4	no	—
396	C₂³×C₅	—	4	8	no	—
397	C₂³×C₅	—	4	16	no	—
398	C₂³×C₅	C₂²×D₄	1	4	yes	—
399	C₂³×C₅	C₂²×D₄	1	2	yes	—
400	C₂³×C₅	C₂×#41	1	4	yes	—
401	C₂³×C₅	C₂×#41	1	2	yes	—
402	C₂³×C₅	C₂×#41	1	2	yes	—
403	C₂³×C₅	C₂×#41	1	4	yes	—
404	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
405	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
406	C₂³×C₅	C₂⁵	1	1	yes	characteristic
407	C₅×Q₈	—	8	2	no	—
408	C₅×D₄	—	4	8	no	—
409	C₅×D₄	—	4	16	no	—
410	C₅×D₄	—	8	2	no	—
411	C₅×D₄	—	8	4	no	—
412	C₅×D₄	—	8	4	no	—
413	C₅×D₄	—	8	8	no	—
414	C₂×C₄×C₅	—	2	4	no	—
415	C₂×C₄×C₅	—	2	2	no	—
416	C₂×C₄×C₅	—	2	2	no	—
417	C₂×C₄×C₅	—	2	2	no	—
418	C₂×C₄×C₅	—	2	2	no	—
419	C₂×C₄×C₅	—	2	2	no	—
420	C₂×C₄×C₅	—	2	2	no	—
421	C₂×C₄×C₅	—	2	2	no	—
422	C₂×C₄×C₅	—	2	2	no	—
423	C₂×C₄×C₅	—	2	2	no	—
424	C₂×C₄×C₅	—	2	4	no	—
425	C₂×C₄×C₅	—	2	4	no	—
426	C₂×C₄×C₅	—	2	4	no	—
427	C₂×C₄×C₅	—	2	4	no	—
428	C₂×C₄×C₅	—	2	4	no	—
429	C₂×C₄×C₅	—	2	4	no	—
430	C₂×C₄×C₅	—	2	4	no	—
431	C₂×C₄×C₅	—	2	4	no	—
432	C₂×C₄×C₅	—	2	2	no	—
433	C₂×C₄×C₅	—	2	4	no	—
434	C₂×C₄×C₅	—	2	2	no	—
435	C₂×C₄×C₅	—	4	4	no	—
436	C₂×C₄×C₅	—	4	4	no	—
437	C₂×C₄×C₅	—	4	16	no	—
438	C₂×C₄×C₅	—	4	8	no	—
439	C₂×C₄×C₅	—	4	8	no	—
440	C₂×C₄×C₅	—	4	4	no	—
441	C₂×C₄×C₅	—	4	4	no	—
442	C₂×C₄×C₅	—	8	4	no	—
443	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
444	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
446	C₂⁵	—	2	4	no	—
447	C₂⁵	—	2	4	no	—
448	C₂⁵	—	2	4	no	—
449	C₂⁵	—	4	4	no	—
450	C₂⁵	—	4	4	no	—
451	C₂⁵	C₂³×C₅	1	1	yes	characteristic
452	C₂⁵	C₂³×C₅	1	4	yes	—
453	C₂⁵	C₂³×C₅	1	1	yes	characteristic
454	C₂⁵	C₂³×C₅	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic, complemented
456	C₂²×D₄	C₂³×C₅	1	2	yes	—
457	C₂²×D₄	C₂³×C₅	1	4	yes	—
458	C₂²×D₄	C₂³×C₅	1	2	yes	—
459	C₂²×D₄	C₂³×C₅	1	2	yes	—
460	C₂²×D₄	C₂³×C₅	1	4	yes	—
461	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic, complemented
462	C₂³×C₄	—	2	4	no	—
463	C₂³×C₄	—	2	4	no	—
464	C₂³×C₄	—	4	4	no	—
465	C₂³×C₄	—	4	4	no	—
466	C₂³×C₄	C₂³×C₅	1	4	yes	—
467	C₂³×C₄	C₂³×C₅	1	2	yes	—
468	C₂³×C₄	C₂³×C₅	1	2	yes	—
469	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₅	1	2	yes	complemented
474	#126	—	2	8	no	—
475	#124	—	2	8	no	—
476	#123	—	2	8	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	—	4	4	no	—
479	#121	—	2	4	no	—
480	#121	—	2	8	no	—
481	#121	—	4	4	no	—
482	#120	—	2	8	no	—
483	#120	—	2	8	no	—
484	#120	—	2	8	no	—
485	#120	—	4	8	no	—
486	#120	—	4	8	no	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	4	8	no	—
489	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
490	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
491	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic, complemented
492	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic, complemented
493	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
494	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
495	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
496	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	16	no	—
501	C₂×C₂²⋊C₄	—	2	16	no	—
502	C₂×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
503	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	complemented
523	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	complemented
524	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
525	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
526	C₂×C₄²	C₂³×C₅	1	2	yes	complemented
527	C₂×C₄²	C₂³×C₅	1	4	yes	complemented
528	#95	C₂³×C₅	1	4	yes	complemented
529	#95	C₂³×C₅	1	4	yes	complemented
530	#95	C₂³×C₅	1	4	yes	complemented
531	#95	C₂³×C₅	1	4	yes	complemented
532	#95	C₂³×C₅	1	2	yes	complemented
533	#95	C₂³×C₅	1	2	yes	complemented
534	#95	C₂³×C₅	1	4	yes	complemented
535	C₂²×C₅	—	2	32	no	—
536	C₂²×C₅	—	2	4	no	—
537	C₂²×C₅	—	2	4	no	—
538	C₂²×C₅	—	2	4	no	—
539	C₂²×C₅	—	2	2	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	2	4	no	—
542	C₂²×C₅	—	2	4	no	—
543	C₂²×C₅	—	2	4	no	—
544	C₂²×C₅	—	2	4	no	—
545	C₂²×C₅	—	2	4	no	—
546	C₂²×C₅	—	2	4	no	—
547	C₂²×C₅	—	2	4	no	—
548	C₂²×C₅	—	2	4	no	—
549	C₂²×C₅	—	2	4	no	—
550	C₂²×C₅	—	2	8	no	—
551	C₂²×C₅	—	4	16	no	—
552	C₂²×C₅	—	4	16	no	—
553	C₂²×C₅	—	4	64	no	—
554	C₂²×C₅	—	4	4	no	—
555	C₂²×C₅	—	4	4	no	—
556	C₂²×C₅	—	4	2	no	—
557	C₂²×C₅	—	4	2	no	—
558	C₂²×C₅	—	4	4	no	—
559	C₂²×C₅	—	4	2	no	—
560	C₂²×C₅	—	4	4	no	—
561	C₂²×C₅	—	4	2	no	—
562	C₂²×C₅	—	4	2	no	—
563	C₂²×C₅	—	4	4	no	—
564	C₂²×C₅	#525	1	4	yes	—
565	C₂²×C₅	#538	1	8	yes	complemented
566	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
567	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
568	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
569	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
570	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
571	C₄×C₅	—	2	4	no	—
572	C₄×C₅	—	2	2	no	—
573	C₄×C₅	—	2	2	no	—
574	C₄×C₅	—	4	2	no	—
575	C₄×C₅	—	4	4	no	—
576	C₄×C₅	—	4	2	no	—
577	C₄×C₅	—	4	2	no	—
578	C₄×C₅	—	4	2	no	—
579	C₄×C₅	—	4	2	no	—
580	C₄×C₅	—	4	4	no	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	2	4	no	—
584	C₂⁴	—	2	4	no	—
585	C₂⁴	—	2	32	no	—
586	C₂⁴	—	2	8	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	8	no	—
589	C₂⁴	—	2	8	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	8	no	—
594	C₂⁴	—	2	8	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	4	2	no	—
597	C₂⁴	—	4	2	no	—
598	C₂⁴	—	4	2	no	—
599	C₂⁴	—	4	4	no	—
600	C₂⁴	—	4	4	no	—
601	C₂⁴	—	4	16	no	—
602	C₂⁴	—	4	16	no	—
603	C₂⁴	—	4	32	no	—
604	C₂⁴	—	4	32	no	—
605	C₂⁴	C₂×C₅×D₄	1	4	yes	—
606	C₂⁴	C₅×#41	1	4	yes	—
607	C₂⁴	C₅×#41	1	4	yes	—
608	C₂⁴	C₂⁴×C₅	1	2	yes	—
609	C₂⁴	C₂⁴×C₅	1	2	yes	—
610	C₂⁴	C₂⁴×C₅	1	2	yes	—
611	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
612	C₂⁴	C₂⁴×C₅	1	2	yes	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	8	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	4	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	16	no	—
648	C₂²×C₄	—	4	16	no	—
649	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
650	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₂²⋊C₄	—	2	8	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	8	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	—	4	4	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
691	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
692	C₄²	—	2	4	no	—
693	C₄²	—	4	4	no	—
694	C₂×C₅	—	2	4	no	—
695	C₂×C₅	—	2	8	no	—
696	C₂×C₅	—	4	4	no	—
697	C₂×C₅	—	4	4	no	—
698	C₂×C₅	—	8	2	no	—
699	C₂×C₅	C₂×#525	1	1	yes	characteristic
700	C₂×C₅	C₂×#538	1	2	yes	—
701	C₂×C₅	#3484	1	1	yes	characteristic
702	C₂×C₅	#3484	1	1	yes	characteristic
703	C₂×C₅	#3490	1	2	yes	—
704	C₂³	—	2	8	no	—
705	C₂³	—	2	8	no	—
706	C₂³	—	2	16	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	16	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	32	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	8	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	4	4	no	—
732	C₂³	—	4	4	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	4	16	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	4	16	no	—
737	C₂³	—	4	16	no	—
738	C₂³	—	4	128	no	—
739	C₂³	—	4	8	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	16	no	—
742	C₂³	—	4	4	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	8	no	—
745	C₂³	—	4	16	no	—
746	C₂³	C₂²×C₅×D₄	1	4	yes	—
747	C₂³	C₂²×C₅×D₄	1	2	yes	—
748	C₂³	C₂×C₅×#41	1	4	yes	—
749	C₂³	C₂×C₅×#41	1	2	yes	—
750	C₂³	C₂×C₅×#41	1	2	yes	—
751	C₂³	C₂×C₅×#41	1	4	yes	—
752	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
753	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
754	C₂³	C₂⁵×C₅	1	1	yes	characteristic
755	Q₈	—	8	2	no	—
756	D₄	—	4	8	no	—
757	D₄	—	4	16	no	—
758	D₄	—	8	2	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	8	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	16	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
792	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
793	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
794	C₅	#34988	1	1	yes	characteristic, direct product factor, Sylow
795	C₂²	—	2	32	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	4	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	4	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	8	no	—
811	C₂²	—	4	16	no	—
812	C₂²	—	4	16	no	—
813	C₂²	—	4	64	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	4	no	—
824	C₂²	C₅×#525	1	4	yes	—
825	C₂²	C₅×#538	1	8	yes	complemented
826	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
827	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
828	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
829	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
830	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
831	C₄	—	2	4	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₂	—	2	4	no	—
842	C₂	—	2	8	no	—
843	C₂	—	4	4	no	—
844	C₂	—	4	4	no	—
845	C₂	—	8	2	no	—
846	C₂	C₂×C₅×#525	1	1	yes	characteristic
847	C₂	C₂×C₅×#538	1	2	yes	—
848	C₂	C₅×#3484	1	1	yes	characteristic
849	C₂	C₅×#3484	1	1	yes	characteristic
850	C₂	C₅×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#538	C₂	semidirect
2. C₂³×C₅×C₂²⋊C₄	C₂	semidirect
3. C₅×#2848	C₂	semidirect
4. C₅×#2847	C₂	semidirect
5. C₅×#2846	C₂	semidirect
6. C₅×#2626	C₂	semidirect
7. C₅×#2622	C₂	semidirect
8. C₅×#2617	C₂	semidirect
9. C₅×#2480	C₂	semidirect
10. C₅×#2472	C₂	semidirect
11. C₅×#2424	C₂	semidirect
12. C₅×#2418	C₂	semidirect
13. C₅×#2321	C₂	semidirect
14. C₅×#2312	C₂	semidirect
15. C₄×C₅×#120	C₂	semidirect
20. C₂×C₅×#126	C₂²	semidirect
21. C₂×C₅×#124	C₂²	semidirect
22. C₂×C₅×#123	C₂²	semidirect
23. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₅×#121	C₂²	semidirect
26. C₂×C₅×#121	C₂²	semidirect
27. C₂×C₅×#121	C₂²	semidirect
33. C₂×C₄×C₅×D₄	C₂²	semidirect
34. C₂×C₄×C₅×D₄	C₂²	semidirect
42. C₅×#399	C₂²	semidirect
43. C₅×#397	C₂²	semidirect
44. C₅×#397	C₂²	semidirect
45. C₅×#397	C₂²	semidirect
46. C₅×#396	C₂²	semidirect
47. C₅×#394	C₂²	semidirect
48. C₅×#394	C₂²	semidirect
49. C₅×#394	C₂²	semidirect
50. C₅×#393	C₂²	semidirect
51. C₅×#392	C₂²	semidirect
52. C₅×#390	C₂²	semidirect
53. C₅×#388	C₂²	semidirect
54. C₅×#388	C₂²	semidirect
55. C₅×#388	C₂²	semidirect
56. C₅×#388	C₂²	semidirect
57. C₅×#386	C₂²	semidirect
58. C₅×#386	C₂²	semidirect
59. C₅×#386	C₂²	semidirect
60. C₅×#386	C₂²	semidirect
61. C₅×#386	C₂²	semidirect
62. C₅×#385	C₂²	semidirect
63. C₅×#385	C₂²	semidirect
64. C₅×#385	C₂²	semidirect
65. C₅×#385	C₂²	semidirect
66. C₅×#380	C₂²	semidirect
67. C₅×#380	C₂²	semidirect
68. C₅×#380	C₂²	semidirect
69. C₅×#380	C₂²	semidirect
75. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
76. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
77. #34988	C₅	direct (N × H)
87. C₂²×C₅×Q₈	C₂³	semidirect
93. C₂²×C₅×D₄	C₂³	semidirect
105. C₂³×C₄×C₅	C₂³	semidirect
121. C₂×C₅×C₄⋊C₄	C₂³	semidirect
122. C₂×C₅×C₄⋊C₄	C₂³	semidirect
123. C₂×C₅×C₄⋊C₄	C₂³	semidirect
124. C₂×C₅×C₄⋊C₄	C₂³	semidirect
125. C₂×C₅×C₄⋊C₄	C₂³	semidirect
126. C₂×C₅×C₄⋊C₄	C₂³	semidirect
127. C₂×C₅×C₄⋊C₄	C₂³	semidirect
128. C₂×C₅×C₄⋊C₄	C₂³	semidirect
134. C₂×C₅×C₂²⋊C₄	D₄	semidirect
154. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
155. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
156. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
157. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
158. C₂×C₄²×C₅	C₂³	semidirect
159. C₂×C₄²×C₅	C₂³	semidirect
160. C₅×#95	C₂³	semidirect
161. C₅×#95	C₂³	semidirect
162. C₅×#95	C₂³	semidirect
163. C₅×#95	C₂³	semidirect
164. C₅×#95	C₂³	semidirect
165. C₅×#95	C₂³	semidirect
166. C₅×#95	C₂³	semidirect
167. C₂×#538	C₂×C₅	semidirect
168. C₂³×C₂²⋊C₄	C₂×C₅	semidirect
169. #2848	C₂×C₅	semidirect
170. #2847	C₂×C₅	semidirect
171. #2846	C₂×C₅	semidirect
172. #2626	C₂×C₅	semidirect
173. #2622	C₂×C₅	semidirect
174. #2617	C₂×C₅	semidirect
175. #2480	C₂×C₅	semidirect
176. #2472	C₂×C₅	semidirect
177. #2424	C₂×C₅	semidirect
178. #2418	C₂×C₅	semidirect
179. #2321	C₂×C₅	semidirect
180. #2312	C₂×C₅	semidirect
181. C₄×#120	C₂×C₅	semidirect
299. C₂×#126	C₂²×C₅	semidirect
300. C₂×#124	C₂²×C₅	semidirect
301. C₂×#123	C₂²×C₅	semidirect
302. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
303. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
304. C₂×#121	C₂²×C₅	semidirect
305. C₂×#121	C₂²×C₅	semidirect
306. C₂×#121	C₂²×C₅	semidirect
312. C₂×C₄×D₄	C₂²×C₅	semidirect
313. C₂×C₄×D₄	C₂²×C₅	semidirect
321. #399	C₂²×C₅	semidirect
322. #397	C₂²×C₅	semidirect
323. #397	C₂²×C₅	semidirect
324. #397	C₂²×C₅	semidirect
325. #396	C₂²×C₅	semidirect
326. #394	C₂²×C₅	semidirect
327. #394	C₂²×C₅	semidirect
328. #394	C₂²×C₅	semidirect
329. #393	C₂²×C₅	semidirect
330. #392	C₂²×C₅	semidirect
331. #390	C₂²×C₅	semidirect
332. #388	C₂²×C₅	semidirect
333. #388	C₂²×C₅	semidirect
334. #388	C₂²×C₅	semidirect
335. #388	C₂²×C₅	semidirect
336. #386	C₂²×C₅	semidirect
337. #386	C₂²×C₅	semidirect
338. #386	C₂²×C₅	semidirect
339. #386	C₂²×C₅	semidirect
340. #386	C₂²×C₅	semidirect
341. #385	C₂²×C₅	semidirect
342. #385	C₂²×C₅	semidirect
343. #385	C₂²×C₅	semidirect
344. #385	C₂²×C₅	semidirect
345. #380	C₂²×C₅	semidirect
346. #380	C₂²×C₅	semidirect
347. #380	C₂²×C₅	semidirect
348. #380	C₂²×C₅	semidirect
354. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
355. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
455. C₂²×Q₈	C₂³×C₅	semidirect
461. C₂²×D₄	C₂³×C₅	semidirect
473. C₂³×C₄	C₂³×C₅	semidirect
489. C₂×C₄⋊C₄	C₂³×C₅	semidirect
490. C₂×C₄⋊C₄	C₂³×C₅	semidirect
491. C₂×C₄⋊C₄	C₂³×C₅	semidirect
492. C₂×C₄⋊C₄	C₂³×C₅	semidirect
493. C₂×C₄⋊C₄	C₂³×C₅	semidirect
494. C₂×C₄⋊C₄	C₂³×C₅	semidirect
495. C₂×C₄⋊C₄	C₂³×C₅	semidirect
496. C₂×C₄⋊C₄	C₂³×C₅	semidirect
502. C₂×C₂²⋊C₄	C₅×D₄	semidirect
522. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
523. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
524. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
525. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
526. C₂×C₄²	C₂³×C₅	semidirect
527. C₂×C₄²	C₂³×C₅	semidirect
528. #95	C₂³×C₅	semidirect
529. #95	C₂³×C₅	semidirect
530. #95	C₂³×C₅	semidirect
531. #95	C₂³×C₅	semidirect
532. #95	C₂³×C₅	semidirect
533. #95	C₂³×C₅	semidirect
534. #95	C₂³×C₅	semidirect
565. C₂²×C₅	#538	semidirect
794. C₅	#34988	direct (N × H)
825. C₂²	C₅×#538	semidirect

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
C₂³×C₅×C₂²⋊C₄	2
C₅×#2848	2
C₅×#2847	2
C₅×#2846	2
C₅×#2626	2
C₅×#2622	2
C₅×#2617	2
C₅×#2480	2
C₅×#2472	2
C₅×#2424	2
C₅×#2418	2
C₅×#2321	2
C₅×#2312	2
C₄×C₅×#120	2
#34988	5

Subgroups — C5×#34988 #11957708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34988 #11957708