Subgroups — C₅×#35282 #11958002

Order 1280.

1638 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2857	C₂	1	1	yes	maximal, characteristic
4	C₅×#2851	C₂	1	1	yes	maximal, characteristic
5	C₅×#2660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2660	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2629	C₂	1	1	yes	maximal, characteristic
8	C₅×#2628	C₂	1	1	yes	maximal, characteristic
9	C₅×#2586	C₂	1	2	yes	maximal, complemented
10	C₅×#2585	C₂	1	2	yes	maximal, complemented
11	C₅×#2574	C₂	1	2	yes	maximal
12	C₅×#2556	C₂	1	2	yes	maximal
13	C₅×#2522	C₂	1	2	yes	maximal
14	C₅×#2520	C₂	1	2	yes	maximal, complemented
15	C₅×#2465	C₂	1	2	yes	maximal
16	C₅×#2462	C₂	1	2	yes	maximal, complemented
17	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2314	C₂	1	1	yes	maximal, characteristic
20	C₅×#2314	C₂	1	1	yes	maximal, characteristic
21	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#125	C₂²	1	1	yes	characteristic
27	C₂×C₅×#125	C₂²	1	1	yes	characteristic
28	C₂×C₅×#125	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
31	C₂×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₅×#400	C₂²	1	2	yes	—
35	C₅×#399	C₂²	1	2	yes	—
36	C₅×#398	C₂²	1	2	yes	—
37	C₅×#398	C₂²	1	2	yes	—
38	C₅×#398	C₂²	1	2	yes	—
39	C₅×#398	C₂²	1	2	yes	—
40	C₅×#398	C₂²	1	2	yes	—
41	C₅×#398	C₂²	1	2	yes	—
42	C₅×#396	C₂²	1	2	yes	—
43	C₅×#396	C₂²	1	2	yes	—
44	C₅×#395	C₂²	1	2	yes	—
45	C₅×#395	C₂²	1	2	yes	—
46	C₅×#395	C₂²	1	2	yes	—
47	C₅×#395	C₂²	1	2	yes	—
48	C₅×#395	C₂²	1	2	yes	—
49	C₅×#393	C₂²	1	2	yes	—
50	C₅×#391	C₂²	1	2	yes	—
51	C₅×#391	C₂²	1	2	yes	—
52	C₅×#391	C₂²	1	2	yes	—
53	C₅×#391	C₂²	1	2	yes	—
54	C₅×#389	C₂²	1	2	yes	—
55	C₅×#389	C₂²	1	2	yes	—
56	C₅×#389	C₂²	1	2	yes	—
57	C₅×#389	C₂²	1	2	yes	—
58	C₅×#389	C₂²	1	1	yes	characteristic
59	C₅×#389	C₂²	1	1	yes	characteristic
60	C₅×#389	C₂²	1	1	yes	characteristic
61	C₅×#389	C₂²	1	1	yes	characteristic
62	C₅×#389	C₂²	1	2	yes	—
63	C₅×#389	C₂²	1	2	yes	—
64	C₅×#389	C₂²	1	1	yes	characteristic
65	C₅×#389	C₂²	1	1	yes	characteristic
66	C₅×#389	C₂²	1	1	yes	characteristic
67	C₅×#389	C₂²	1	1	yes	characteristic
68	C₅×#388	C₂²	1	2	yes	—
69	C₅×#388	C₂²	1	2	yes	—
70	C₅×#388	C₂²	1	2	yes	—
71	C₅×#388	C₂²	1	2	yes	—
72	C₅×#387	C₂²	1	2	yes	—
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	2	yes	—
75	C₅×#387	C₂²	1	2	yes	—
76	C₅×#387	C₂²	1	2	yes	—
77	C₅×#387	C₂²	1	2	yes	—
78	C₅×#387	C₂²	1	2	yes	—
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#387	C₂²	1	2	yes	—
83	C₅×#387	C₂²	1	2	yes	—
84	C₅×#387	C₂²	1	2	yes	—
85	C₅×#387	C₂²	1	2	yes	—
86	C₅×#387	C₂²	1	2	yes	—
87	C₅×#387	C₂²	1	2	yes	—
88	C₅×#385	C₂²	1	2	yes	—
89	C₅×#385	C₂²	1	2	yes	—
90	C₅×#384	C₂²	1	1	yes	characteristic
91	C₅×#384	C₂²	1	1	yes	characteristic
92	C₅×#384	C₂²	1	1	yes	characteristic
93	C₅×#384	C₂²	1	1	yes	characteristic
94	C₅×#382	C₂²	1	2	yes	—
95	C₅×#382	C₂²	1	1	yes	characteristic
96	C₅×#382	C₂²	1	1	yes	characteristic
97	C₅×#382	C₂²	1	1	yes	characteristic
98	C₅×#382	C₂²	1	1	yes	characteristic
99	C₅×#380	C₂²	1	2	yes	—
100	C₅×#380	C₂²	1	1	yes	characteristic
101	C₅×#380	C₂²	1	1	yes	characteristic
102	C₅×#380	C₂²	1	1	yes	characteristic
103	C₅×#380	C₂²	1	1	yes	characteristic
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	1	yes	characteristic
121	C₄³×C₅	C₂²	1	1	yes	characteristic
122	C₄³×C₅	C₂²	1	1	yes	characteristic
123	#35282	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₅×Q₈	C₂³	1	2	yes	—
125	C₂²×C₅×Q₈	C₂³	1	2	yes	—
126	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₅×C₄⋊Q₈	—	2	4	no	—
130	C₅×C₄⋊Q₈	—	2	4	no	—
131	C₅×#125	—	2	4	no	—
132	C₅×#125	—	2	4	no	—
133	C₅×#125	—	4	4	no	—
134	C₅×C₂²⋊Q₈	—	4	4	no	—
135	C₄×C₅×Q₈	—	4	4	no	—
136	C₅×#117	—	2	4	no	—
137	C₅×#117	Q₈	1	8	yes	complemented
138	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₅	—	2	4	no	—
181	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	2	yes	—
194	C₂×C₄²×C₅	C₂³	1	2	yes	—
195	C₂×C₄²×C₅	C₂³	1	2	yes	—
196	C₂×C₄²×C₅	C₂³	1	2	yes	—
197	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₅×#95	C₂³	1	1	yes	characteristic
202	C₅×#95	C₂³	1	1	yes	characteristic
203	C₅×#95	C₂³	1	1	yes	characteristic
204	C₅×#95	C₂³	1	1	yes	characteristic
205	C₅×#95	C₂³	1	1	yes	characteristic
206	C₅×#95	C₂³	1	1	yes	characteristic
207	C₅×#95	C₂³	1	1	yes	characteristic
208	C₅×#95	C₂³	1	1	yes	characteristic
209	C₅×#95	C₂³	1	2	yes	—
210	C₅×#95	C₂³	1	2	yes	—
211	C₅×#95	C₂³	1	2	yes	—
212	C₅×#95	C₂³	1	2	yes	—
213	C₅×#95	C₂³	1	2	yes	—
214	C₅×#95	C₂³	1	2	yes	—
215	C₅×#95	C₂³	1	2	yes	—
216	C₅×#95	C₂³	1	2	yes	—
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	2	yes	—
221	C₅×#95	C₂³	1	2	yes	—
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	2	yes	—
230	C₅×#95	C₂³	1	2	yes	—
231	C₅×#95	C₂³	1	2	yes	—
232	C₅×#95	C₂³	1	2	yes	—
233	#2864	C₂×C₅	1	1	yes	characteristic, complemented
234	#2859	C₂×C₅	1	1	yes	characteristic, complemented
235	#2857	C₂×C₅	1	1	yes	characteristic
236	#2851	C₂×C₅	1	1	yes	characteristic
237	#2660	C₂×C₅	1	1	yes	characteristic, complemented
238	#2660	C₂×C₅	1	1	yes	characteristic, complemented
239	#2629	C₂×C₅	1	1	yes	characteristic
240	#2628	C₂×C₅	1	1	yes	characteristic
241	#2586	C₂×C₅	1	2	yes	complemented
242	#2585	C₂×C₅	1	2	yes	complemented
243	#2574	C₂×C₅	1	2	yes	—
244	#2556	C₂×C₅	1	2	yes	—
245	#2522	C₂×C₅	1	2	yes	—
246	#2520	C₂×C₅	1	2	yes	complemented
247	#2465	C₂×C₅	1	2	yes	—
248	#2462	C₂×C₅	1	2	yes	complemented
249	#2331	C₂×C₅	1	1	yes	characteristic, complemented
250	#2330	C₂×C₅	1	1	yes	characteristic, complemented
251	#2314	C₂×C₅	1	1	yes	characteristic
252	#2314	C₂×C₅	1	1	yes	characteristic
253	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
254	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
255	C₄×#117	C₂×C₅	1	1	yes	characteristic
256	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₅×Q₈	—	2	4	no	—
258	C₂×C₅×Q₈	—	2	4	no	—
259	C₂×C₅×Q₈	—	4	2	no	—
260	C₂×C₅×Q₈	—	4	2	no	—
261	C₂×C₅×Q₈	—	4	2	no	—
262	C₂×C₅×Q₈	—	4	2	no	—
263	C₂²×C₄×C₅	—	2	2	no	—
264	C₂²×C₄×C₅	—	2	2	no	—
265	C₂²×C₄×C₅	—	2	2	no	—
266	C₂²×C₄×C₅	—	2	2	no	—
267	C₂²×C₄×C₅	—	2	2	no	—
268	C₂²×C₄×C₅	—	2	2	no	—
269	C₂²×C₄×C₅	—	4	1	no	—
270	C₂²×C₄×C₅	—	4	1	no	—
271	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
272	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₅×C₄⋊C₄	—	2	2	no	—
295	C₅×C₄⋊C₄	—	2	2	no	—
296	C₅×C₄⋊C₄	—	2	4	no	—
297	C₅×C₄⋊C₄	—	2	4	no	—
298	C₅×C₄⋊C₄	—	2	4	no	—
299	C₅×C₄⋊C₄	—	2	4	no	—
300	C₅×C₄⋊C₄	—	2	2	no	—
301	C₅×C₄⋊C₄	—	2	2	no	—
302	C₅×C₄⋊C₄	—	2	2	no	—
303	C₅×C₄⋊C₄	—	2	2	no	—
304	C₅×C₄⋊C₄	—	2	4	no	—
305	C₅×C₄⋊C₄	—	2	4	no	—
306	C₅×C₄⋊C₄	—	2	2	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	2	2	no	—
310	C₅×C₄⋊C₄	—	2	4	no	—
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	2	4	no	—
313	C₅×C₄⋊C₄	—	2	4	no	—
314	C₅×C₄⋊C₄	—	4	2	no	—
315	C₅×C₄⋊C₄	—	4	2	no	—
316	C₅×C₄⋊C₄	—	4	2	no	—
317	C₅×C₄⋊C₄	—	4	2	no	—
318	C₅×C₄⋊C₄	—	4	2	no	—
319	C₅×C₄⋊C₄	—	4	2	no	—
320	C₅×C₄⋊C₄	—	4	2	no	—
321	C₅×C₄⋊C₄	—	4	2	no	—
322	C₅×C₄⋊C₄	—	4	2	no	—
323	C₅×C₄⋊C₄	—	4	2	no	—
324	C₅×C₄⋊C₄	—	4	2	no	—
325	C₅×C₄⋊C₄	—	4	2	no	—
326	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
327	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
328	C₅×C₂²⋊C₄	—	2	2	no	—
329	C₅×C₂²⋊C₄	—	2	2	no	—
330	C₅×C₂²⋊C₄	—	4	2	no	—
331	C₅×C₂²⋊C₄	—	4	2	no	—
332	C₅×C₂²⋊C₄	—	4	2	no	—
333	C₅×C₂²⋊C₄	—	4	2	no	—
334	C₅×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
335	C₅×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
336	C₄²×C₅	—	2	2	no	—
337	C₄²×C₅	—	2	2	no	—
338	C₄²×C₅	—	2	2	no	—
339	C₄²×C₅	—	2	2	no	—
340	C₄²×C₅	—	2	2	no	—
341	C₄²×C₅	—	2	2	no	—
342	C₄²×C₅	—	2	2	no	—
343	C₄²×C₅	—	2	2	no	—
344	C₄²×C₅	—	4	1	no	—
345	C₄²×C₅	—	4	1	no	—
346	C₄²×C₅	—	4	2	no	—
347	C₄²×C₅	—	4	2	no	—
348	C₄²×C₅	—	4	1	no	—
349	C₄²×C₅	—	4	1	no	—
350	C₄²×C₅	—	4	2	no	—
351	C₄²×C₅	—	4	2	no	—
352	C₄²×C₅	C₂×Q₈	1	4	yes	—
353	C₄²×C₅	C₂×Q₈	1	4	yes	—
354	C₄²×C₅	#41	1	4	yes	—
355	C₄²×C₅	#41	1	4	yes	—
356	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
357	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
358	C₂×#125	C₂²×C₅	1	1	yes	characteristic
359	C₂×#125	C₂²×C₅	1	1	yes	characteristic
360	C₂×#125	C₂²×C₅	1	2	yes	—
361	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
362	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
363	C₂×#117	C₂²×C₅	1	1	yes	characteristic
364	C₂×#117	C₂²×C₅	1	1	yes	characteristic
365	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
366	#400	C₂²×C₅	1	2	yes	—
367	#399	C₂²×C₅	1	2	yes	—
368	#398	C₂²×C₅	1	2	yes	—
369	#398	C₂²×C₅	1	2	yes	—
370	#398	C₂²×C₅	1	2	yes	—
371	#398	C₂²×C₅	1	2	yes	—
372	#398	C₂²×C₅	1	2	yes	—
373	#398	C₂²×C₅	1	2	yes	—
374	#396	C₂²×C₅	1	2	yes	—
375	#396	C₂²×C₅	1	2	yes	—
376	#395	C₂²×C₅	1	2	yes	—
377	#395	C₂²×C₅	1	2	yes	—
378	#395	C₂²×C₅	1	2	yes	—
379	#395	C₂²×C₅	1	2	yes	—
380	#395	C₂²×C₅	1	2	yes	—
381	#393	C₂²×C₅	1	2	yes	—
382	#391	C₂²×C₅	1	2	yes	—
383	#391	C₂²×C₅	1	2	yes	—
384	#391	C₂²×C₅	1	2	yes	—
385	#391	C₂²×C₅	1	2	yes	—
386	#389	C₂²×C₅	1	1	yes	characteristic
387	#389	C₂²×C₅	1	1	yes	characteristic
388	#389	C₂²×C₅	1	2	yes	—
389	#389	C₂²×C₅	1	1	yes	characteristic
390	#389	C₂²×C₅	1	1	yes	characteristic
391	#389	C₂²×C₅	1	2	yes	—
392	#389	C₂²×C₅	1	2	yes	—
393	#389	C₂²×C₅	1	2	yes	—
394	#389	C₂²×C₅	1	1	yes	characteristic
395	#389	C₂²×C₅	1	1	yes	characteristic
396	#389	C₂²×C₅	1	2	yes	—
397	#389	C₂²×C₅	1	2	yes	—
398	#389	C₂²×C₅	1	1	yes	characteristic
399	#389	C₂²×C₅	1	1	yes	characteristic
400	#388	C₂²×C₅	1	2	yes	—
401	#388	C₂²×C₅	1	2	yes	—
402	#388	C₂²×C₅	1	2	yes	—
403	#388	C₂²×C₅	1	2	yes	—
404	#387	C₂²×C₅	1	2	yes	—
405	#387	C₂²×C₅	1	2	yes	—
406	#387	C₂²×C₅	1	2	yes	—
407	#387	C₂²×C₅	1	2	yes	—
408	#387	C₂²×C₅	1	2	yes	—
409	#387	C₂²×C₅	1	2	yes	—
410	#387	C₂²×C₅	1	2	yes	—
411	#387	C₂²×C₅	1	2	yes	—
412	#387	C₂²×C₅	1	2	yes	—
413	#387	C₂²×C₅	1	2	yes	—
414	#387	C₂²×C₅	1	2	yes	—
415	#387	C₂²×C₅	1	2	yes	—
416	#387	C₂²×C₅	1	2	yes	—
417	#387	C₂²×C₅	1	2	yes	—
418	#387	C₂²×C₅	1	2	yes	—
419	#387	C₂²×C₅	1	2	yes	—
420	#385	C₂²×C₅	1	2	yes	—
421	#385	C₂²×C₅	1	2	yes	—
422	#384	C₂²×C₅	1	1	yes	characteristic
423	#384	C₂²×C₅	1	1	yes	characteristic
424	#384	C₂²×C₅	1	1	yes	characteristic
425	#384	C₂²×C₅	1	1	yes	characteristic
426	#382	C₂²×C₅	1	1	yes	characteristic
427	#382	C₂²×C₅	1	1	yes	characteristic
428	#382	C₂²×C₅	1	1	yes	characteristic
429	#382	C₂²×C₅	1	2	yes	—
430	#382	C₂²×C₅	1	1	yes	characteristic
431	#380	C₂²×C₅	1	1	yes	characteristic
432	#380	C₂²×C₅	1	1	yes	characteristic
433	#380	C₂²×C₅	1	1	yes	characteristic
434	#380	C₂²×C₅	1	1	yes	characteristic
435	#380	C₂²×C₅	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
451	#376	C₂²×C₅	1	1	yes	characteristic
452	#376	C₂²×C₅	1	1	yes	characteristic
453	C₄³	C₂²×C₅	1	1	yes	characteristic
454	C₄³	C₂²×C₅	1	1	yes	characteristic
455	C₂³×C₅	—	2	1	no	—
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	—	2	1	no	—
458	C₂³×C₅	—	2	1	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	2	1	no	—
461	C₂³×C₅	C₂²×Q₈	1	2	yes	—
462	C₂³×C₅	C₂⁵	1	1	yes	characteristic
463	C₅×Q₈	—	4	8	no	—
464	C₅×Q₈	—	8	4	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	8	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	2	2	no	—
493	C₂×C₄×C₅	—	2	2	no	—
494	C₂×C₄×C₅	—	2	2	no	—
495	C₂×C₄×C₅	—	2	2	no	—
496	C₂×C₄×C₅	—	2	2	no	—
497	C₂×C₄×C₅	—	2	2	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	2	no	—
500	C₂×C₄×C₅	—	2	2	no	—
501	C₂×C₄×C₅	—	2	2	no	—
502	C₂×C₄×C₅	—	2	2	no	—
503	C₂×C₄×C₅	—	2	2	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	2	no	—
507	C₂×C₄×C₅	—	2	2	no	—
508	C₂×C₄×C₅	—	2	2	no	—
509	C₂×C₄×C₅	—	2	2	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	2	2	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	4	4	no	—
519	C₂×C₄×C₅	—	4	4	no	—
520	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
521	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
522	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
523	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
524	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
525	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
526	C₂×C₄×C₅	C₂×#41	1	2	yes	—
527	C₂×C₄×C₅	C₂×#41	1	2	yes	—
528	C₂×C₄×C₅	C₂×#41	1	2	yes	—
529	C₂×C₄×C₅	C₂×#41	1	2	yes	—
530	C₂×C₄×C₅	C₂×#41	1	2	yes	—
531	C₂×C₄×C₅	C₂×#41	1	2	yes	—
532	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
533	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
534	C₂²×Q₈	C₂³×C₅	1	2	yes	—
535	C₂²×Q₈	C₂³×C₅	1	2	yes	—
536	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
539	C₄⋊Q₈	—	2	4	no	—
540	C₄⋊Q₈	—	2	4	no	—
541	#125	—	2	4	no	—
542	#125	—	2	4	no	—
543	#125	—	4	4	no	—
544	C₂²⋊Q₈	—	4	4	no	—
545	C₄×Q₈	—	4	4	no	—
546	#117	—	2	4	no	—
547	#117	C₅×Q₈	1	8	yes	complemented
548	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄²	—	2	4	no	—
591	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₅	1	2	yes	—
600	C₂×C₄²	C₂³×C₅	1	2	yes	—
601	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₅	1	2	yes	—
606	C₂×C₄²	C₂³×C₅	1	2	yes	—
607	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
611	#95	C₂³×C₅	1	1	yes	characteristic
612	#95	C₂³×C₅	1	1	yes	characteristic
613	#95	C₂³×C₅	1	1	yes	characteristic
614	#95	C₂³×C₅	1	1	yes	characteristic
615	#95	C₂³×C₅	1	1	yes	characteristic
616	#95	C₂³×C₅	1	1	yes	characteristic
617	#95	C₂³×C₅	1	1	yes	characteristic
618	#95	C₂³×C₅	1	1	yes	characteristic
619	#95	C₂³×C₅	1	2	yes	—
620	#95	C₂³×C₅	1	2	yes	—
621	#95	C₂³×C₅	1	2	yes	—
622	#95	C₂³×C₅	1	2	yes	—
623	#95	C₂³×C₅	1	2	yes	—
624	#95	C₂³×C₅	1	2	yes	—
625	#95	C₂³×C₅	1	2	yes	—
626	#95	C₂³×C₅	1	2	yes	—
627	#95	C₂³×C₅	1	2	yes	—
628	#95	C₂³×C₅	1	2	yes	—
629	#95	C₂³×C₅	1	2	yes	—
630	#95	C₂³×C₅	1	2	yes	—
631	#95	C₂³×C₅	1	2	yes	—
632	#95	C₂³×C₅	1	2	yes	—
633	#95	C₂³×C₅	1	2	yes	—
634	#95	C₂³×C₅	1	2	yes	—
635	#95	C₂³×C₅	1	2	yes	—
636	#95	C₂³×C₅	1	2	yes	—
637	#95	C₂³×C₅	1	2	yes	—
638	#95	C₂³×C₅	1	2	yes	—
639	#95	C₂³×C₅	1	2	yes	—
640	#95	C₂³×C₅	1	2	yes	—
641	#95	C₂³×C₅	1	2	yes	—
642	#95	C₂³×C₅	1	2	yes	—
643	C₂²×C₅	—	2	2	no	—
644	C₂²×C₅	—	2	2	no	—
645	C₂²×C₅	—	2	2	no	—
646	C₂²×C₅	—	4	1	no	—
647	C₂²×C₅	—	4	1	no	—
648	C₂²×C₅	—	4	1	no	—
649	C₂²×C₅	—	4	1	no	—
650	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
651	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
652	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
653	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
655	C₂²×C₅	#585	1	1	yes	characteristic
656	C₂²×C₅	#585	1	1	yes	characteristic
657	C₄×C₅	—	2	2	no	—
658	C₄×C₅	—	2	2	no	—
659	C₄×C₅	—	2	2	no	—
660	C₄×C₅	—	2	2	no	—
661	C₄×C₅	—	2	2	no	—
662	C₄×C₅	—	2	2	no	—
663	C₄×C₅	—	2	2	no	—
664	C₄×C₅	—	2	2	no	—
665	C₄×C₅	—	2	2	no	—
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	—	2	2	no	—
668	C₄×C₅	—	4	1	no	—
669	C₄×C₅	—	4	2	no	—
670	C₄×C₅	—	4	2	no	—
671	C₄×C₅	—	4	2	no	—
672	C₄×C₅	—	4	1	no	—
673	C₄×C₅	—	4	2	no	—
674	C₄×C₅	—	4	2	no	—
675	C₄×C₅	—	4	2	no	—
676	C₄×C₅	—	4	2	no	—
677	C₄×C₅	—	4	2	no	—
678	C₄×C₅	#533	1	4	yes	—
679	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	1	no	—
694	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
695	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
750	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	C₂×C₅×Q₈	1	4	yes	—
758	C₂²⋊C₄	C₂×C₅×Q₈	1	4	yes	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	1	no	—
770	C₄²	—	4	1	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	1	no	—
774	C₄²	—	4	1	no	—
775	C₄²	C₂×C₅×Q₈	1	4	yes	—
776	C₄²	C₂×C₅×Q₈	1	4	yes	—
777	C₄²	C₅×#41	1	4	yes	—
778	C₄²	C₅×#41	1	4	yes	—
779	C₂×C₅	—	4	2	no	—
780	C₂×C₅	C₂×#533	1	1	yes	characteristic
781	C₂×C₅	#3460	1	1	yes	characteristic
782	C₂×C₅	#3461	1	1	yes	characteristic
783	C₂×C₅	#3494	1	1	yes	characteristic
784	C₂×C₅	#3495	1	1	yes	characteristic
785	C₂×C₅	#3503	1	1	yes	characteristic
786	C₂×C₅	#3504	1	1	yes	characteristic
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	C₂²×C₅×Q₈	1	2	yes	—
794	C₂³	C₂⁵×C₅	1	1	yes	characteristic
795	Q₈	—	4	8	no	—
796	Q₈	—	8	4	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
853	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
854	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
855	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
856	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
857	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
858	C₂×C₄	C₂×C₅×#41	1	2	yes	—
859	C₂×C₄	C₂×C₅×#41	1	2	yes	—
860	C₂×C₄	C₂×C₅×#41	1	2	yes	—
861	C₂×C₄	C₂×C₅×#41	1	2	yes	—
862	C₂×C₄	C₂×C₅×#41	1	2	yes	—
863	C₂×C₄	C₂×C₅×#41	1	2	yes	—
864	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
865	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
866	C₅	#35282	1	1	yes	characteristic, direct product factor, Sylow
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
875	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
876	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
877	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
878	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
879	C₂²	C₅×#585	1	1	yes	characteristic
880	C₂²	C₅×#585	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	C₅×#533	1	4	yes	—
903	C₂	—	4	2	no	—
904	C₂	C₂×C₅×#533	1	1	yes	characteristic
905	C₂	C₅×#3460	1	1	yes	characteristic
906	C₂	C₅×#3461	1	1	yes	characteristic
907	C₂	C₅×#3494	1	1	yes	characteristic
908	C₂	C₅×#3495	1	1	yes	characteristic
909	C₂	C₅×#3503	1	1	yes	characteristic
910	C₂	C₅×#3504	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂⁴
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. C₅×#2864	C₂	semidirect
2. C₅×#2859	C₂	semidirect
5. C₅×#2660	C₂	semidirect
6. C₅×#2660	C₂	semidirect
9. C₅×#2586	C₂	semidirect
10. C₅×#2585	C₂	semidirect
14. C₅×#2520	C₂	semidirect
16. C₅×#2462	C₂	semidirect
17. C₅×#2331	C₂	semidirect
18. C₅×#2330	C₂	semidirect
21. C₄×C₅×C₄⋊Q₈	C₂	semidirect
22. C₄×C₅×#125	C₂	semidirect
123. #35282	C₅	direct (N × H)
137. C₅×#117	Q₈	semidirect
233. #2864	C₂×C₅	semidirect
234. #2859	C₂×C₅	semidirect
237. #2660	C₂×C₅	semidirect
238. #2660	C₂×C₅	semidirect
241. #2586	C₂×C₅	semidirect
242. #2585	C₂×C₅	semidirect
246. #2520	C₂×C₅	semidirect
248. #2462	C₂×C₅	semidirect
249. #2331	C₂×C₅	semidirect
250. #2330	C₂×C₅	semidirect
253. C₄×C₄⋊Q₈	C₂×C₅	semidirect
254. C₄×#125	C₂×C₅	semidirect
547. #117	C₅×Q₈	semidirect
866. C₅	#35282	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#2864	2
C₅×#2859	2
C₅×#2857	2
C₅×#2851	2
C₅×#2660	2
C₅×#2629	2
C₅×#2628	2
C₅×#2586	2
C₅×#2585	2
C₅×#2574	2
C₅×#2556	2
C₅×#2522	2
C₅×#2520	2
C₅×#2465	2
C₅×#2462	2
C₅×#2331	2
C₅×#2330	2
C₅×#2314	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#125	2
C₄×C₅×#117	2
#35282	5

Subgroups — C5×#35282 #11958002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35282 #11958002