Subgroups — C₅×#34490 #11957210

Order 1280.

1840 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#557	C₂	1	1	yes	maximal, characteristic
2	C₅×#2382	C₂	1	2	yes	maximal
3	C₅×#2381	C₂	1	2	yes	maximal
4	C₅×#2371	C₂	1	2	yes	maximal
5	C₅×#2370	C₂	1	1	yes	maximal, characteristic
6	C₅×#2370	C₂	1	1	yes	maximal, characteristic
7	C₅×#2369	C₂	1	1	yes	maximal, characteristic
8	C₅×#2356	C₂	1	2	yes	maximal
9	C₅×#2356	C₂	1	1	yes	maximal, characteristic
10	C₅×#2356	C₂	1	1	yes	maximal, characteristic
11	C₅×#2355	C₂	1	1	yes	maximal, characteristic
12	C₅×#2355	C₂	1	1	yes	maximal, characteristic
13	C₅×#2336	C₂	1	2	yes	maximal
14	C₅×#2336	C₂	1	2	yes	maximal
15	C₅×#2331	C₂	1	1	yes	maximal, characteristic
16	C₅×#2331	C₂	1	2	yes	maximal
17	C₅×#2330	C₂	1	1	yes	maximal, characteristic
18	C₅×#2320	C₂	1	1	yes	maximal, characteristic
19	C₅×#2320	C₂	1	1	yes	maximal, characteristic
20	C₅×#2320	C₂	1	2	yes	maximal
21	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic
22	C₅×#2295	C₂	1	1	yes	maximal, characteristic
23	C₅×#2295	C₂	1	1	yes	maximal, characteristic
24	C₅×#557	C₄	1	16	yes	complemented
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₅×#125	C₂²	1	1	yes	characteristic
28	C₂×C₅×#125	C₂²	1	1	yes	characteristic
29	C₂×C₅×#125	C₂²	1	2	yes	—
30	C₂×C₅×#125	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
35	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
36	C₅×#391	C₂²	1	1	yes	characteristic
37	C₅×#391	C₂²	1	1	yes	characteristic
38	C₅×#391	C₂²	1	1	yes	characteristic
39	C₅×#391	C₂²	1	1	yes	characteristic
40	C₅×#391	C₂²	1	2	yes	—
41	C₅×#391	C₂²	1	1	yes	characteristic
42	C₅×#391	C₂²	1	1	yes	characteristic
43	C₅×#391	C₂²	1	2	yes	—
44	C₅×#391	C₂²	1	2	yes	—
45	C₅×#391	C₂²	1	2	yes	—
46	C₅×#391	C₂²	1	2	yes	—
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#389	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	C₂²	1	2	yes	—
54	C₅×#389	C₂²	1	1	yes	characteristic
55	C₅×#389	C₂²	1	1	yes	characteristic
56	C₅×#389	C₂²	1	2	yes	—
57	C₅×#389	C₂²	1	2	yes	—
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#389	C₂²	1	2	yes	—
60	C₅×#387	C₂²	1	1	yes	characteristic
61	C₅×#387	C₂²	1	2	yes	—
62	C₅×#387	C₂²	1	1	yes	characteristic
63	C₅×#387	C₂²	1	1	yes	characteristic
64	C₅×#387	C₂²	1	1	yes	characteristic
65	C₅×#387	C₂²	1	2	yes	—
66	C₅×#387	C₂²	1	2	yes	—
67	C₅×#387	C₂²	1	2	yes	—
68	C₅×#387	C₂²	1	2	yes	—
69	C₅×#387	C₂²	1	2	yes	—
70	C₅×#387	C₂²	1	2	yes	—
71	C₅×#387	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×#384	C₂²	1	1	yes	characteristic
89	C₅×#383	C₂²	1	2	yes	—
90	C₅×#383	C₂²	1	2	yes	—
91	C₅×#383	C₂²	1	2	yes	—
92	C₅×#383	C₂²	1	2	yes	—
93	C₅×#382	C₂²	1	1	yes	characteristic
94	C₅×#382	C₂²	1	2	yes	—
95	C₅×#382	C₂²	1	2	yes	—
96	C₅×#382	C₂²	1	2	yes	—
97	C₅×#382	C₂²	1	1	yes	characteristic
98	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
113	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
118	C₅×#376	C₂²	1	1	yes	characteristic
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	2	yes	—
121	C₅×#376	C₂²	1	2	yes	—
122	C₅×#376	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#34490	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₅×Q₈	C₂³	1	2	yes	—
128	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	—
129	C₅×C₄⋊Q₈	C₂×C₄	1	16	yes	—
130	C₅×#125	C₂×C₄	1	8	yes	—
131	C₅×#125	C₂×C₄	1	8	yes	—
132	C₅×#125	C₂×C₄	1	16	yes	—
133	C₅×#125	C₂×C₄	1	16	yes	—
134	C₄×C₅×Q₈	C₂×C₄	1	8	yes	—
135	C₄×C₅×Q₈	C₂×C₄	1	8	yes	—
136	C₄×C₅×Q₈	C₂×C₄	1	8	yes	—
137	C₄×C₅×Q₈	C₂×C₄	1	16	yes	—
138	C₄×C₅×Q₈	C₂×C₄	1	8	yes	—
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	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₄²×C₅	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₅	C₂³	1	2	yes	—
175	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₅	C₂³	1	2	yes	—
181	C₂×C₄²×C₅	C₂³	1	2	yes	—
182	C₂×C₄²×C₅	C₂³	1	2	yes	—
183	C₂×C₄²×C₅	C₂³	1	2	yes	—
184	C₂×C₄²×C₅	C₂³	1	2	yes	—
185	C₂×C₄²×C₅	C₂³	1	2	yes	—
186	C₂×C₄²×C₅	C₂³	1	2	yes	—
187	C₂×C₄²×C₅	C₂³	1	2	yes	—
188	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅	C₂³	1	2	yes	—
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	2	yes	—
193	C₂×C₄²×C₅	C₂³	1	2	yes	—
194	C₅×#95	C₂³	1	1	yes	characteristic
195	C₅×#95	C₂³	1	2	yes	—
196	C₅×#95	C₂³	1	1	yes	characteristic
197	C₅×#95	C₂³	1	2	yes	—
198	C₅×#95	C₂³	1	2	yes	—
199	C₅×#95	C₂³	1	1	yes	characteristic
200	C₅×#95	C₂³	1	2	yes	—
201	C₅×#95	C₂³	1	1	yes	characteristic
202	C₅×#95	C₂³	1	2	yes	—
203	C₅×#95	C₂³	1	2	yes	—
204	C₅×#95	C₂³	1	2	yes	—
205	C₅×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
210	C₅×#95	C₂³	1	1	yes	characteristic
211	C₅×#95	C₂³	1	2	yes	—
212	C₅×#95	C₂³	1	1	yes	characteristic
213	C₅×#95	C₂³	1	1	yes	characteristic
214	C₅×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₅×#95	C₂³	1	1	yes	characteristic
234	C₅×#95	C₂³	1	2	yes	—
235	C₂×#557	C₂×C₅	1	1	yes	characteristic
236	#2382	C₂×C₅	1	2	yes	—
237	#2381	C₂×C₅	1	2	yes	—
238	#2371	C₂×C₅	1	2	yes	—
239	#2370	C₂×C₅	1	1	yes	characteristic
240	#2370	C₂×C₅	1	1	yes	characteristic
241	#2369	C₂×C₅	1	1	yes	characteristic
242	#2356	C₂×C₅	1	1	yes	characteristic
243	#2356	C₂×C₅	1	2	yes	—
244	#2356	C₂×C₅	1	1	yes	characteristic
245	#2355	C₂×C₅	1	1	yes	characteristic
246	#2355	C₂×C₅	1	1	yes	characteristic
247	#2336	C₂×C₅	1	2	yes	—
248	#2336	C₂×C₅	1	2	yes	—
249	#2331	C₂×C₅	1	1	yes	characteristic
250	#2331	C₂×C₅	1	2	yes	—
251	#2330	C₂×C₅	1	1	yes	characteristic
252	#2320	C₂×C₅	1	1	yes	characteristic
253	#2320	C₂×C₅	1	1	yes	characteristic
254	#2320	C₂×C₅	1	2	yes	—
255	C₄×#125	C₂×C₅	1	1	yes	characteristic
256	#2295	C₂×C₅	1	1	yes	characteristic
257	#2295	C₂×C₅	1	1	yes	characteristic
258	C₂×C₅×Q₈	—	2	2	no	—
259	C₂×C₅×Q₈	—	2	2	no	—
260	C₂×C₅×Q₈	—	4	1	no	—
261	C₂×C₅×Q₈	—	4	2	no	—
262	C₂×C₅×Q₈	—	4	2	no	—
263	C₂×C₅×Q₈	—	4	1	no	—
264	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
265	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
266	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
267	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	C₅×C₄⋊C₄	—	2	2	no	—
291	C₅×C₄⋊C₄	—	2	2	no	—
292	C₅×C₄⋊C₄	—	2	2	no	—
293	C₅×C₄⋊C₄	—	2	2	no	—
294	C₅×C₄⋊C₄	—	2	2	no	—
295	C₅×C₄⋊C₄	—	2	2	no	—
296	C₅×C₄⋊C₄	—	4	1	no	—
297	C₅×C₄⋊C₄	—	4	2	no	—
298	C₅×C₄⋊C₄	—	4	2	no	—
299	C₅×C₄⋊C₄	—	4	1	no	—
300	C₅×C₄⋊C₄	—	4	1	no	—
301	C₅×C₄⋊C₄	—	4	2	no	—
302	C₅×C₄⋊C₄	—	4	2	no	—
303	C₅×C₄⋊C₄	—	4	2	no	—
304	C₅×C₄⋊C₄	—	4	1	no	—
305	C₅×C₄⋊C₄	—	4	2	no	—
306	C₅×C₄⋊C₄	—	4	2	no	—
307	C₅×C₄⋊C₄	—	4	2	no	—
308	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
309	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
310	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
311	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
312	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
313	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
314	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
315	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
316	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
317	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
318	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
319	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
320	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
321	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
322	C₄²×C₅	—	2	2	no	—
323	C₄²×C₅	—	2	4	no	—
324	C₄²×C₅	—	2	2	no	—
325	C₄²×C₅	—	2	2	no	—
326	C₄²×C₅	—	2	2	no	—
327	C₄²×C₅	—	2	2	no	—
328	C₄²×C₅	—	4	2	no	—
329	C₄²×C₅	—	4	1	no	—
330	C₄²×C₅	—	4	2	no	—
331	C₄²×C₅	—	4	1	no	—
332	C₄²×C₅	—	4	2	no	—
333	C₄²×C₅	—	4	2	no	—
334	C₄²×C₅	—	4	2	no	—
335	C₄²×C₅	—	4	2	no	—
336	C₄²×C₅	—	4	2	no	—
337	C₄²×C₅	—	4	2	no	—
338	C₄²×C₅	—	4	1	no	—
339	C₄²×C₅	C₂²×C₄	1	8	yes	—
340	C₄²×C₅	C₂²×C₄	1	8	yes	—
341	C₄²×C₅	C₂²×C₄	1	4	yes	—
342	C₄²×C₅	C₂²×C₄	1	4	yes	—
343	C₄²×C₅	C₂²×C₄	1	8	yes	—
344	C₄²×C₅	C₂²×C₄	1	4	yes	—
345	#557	C₄×C₅	1	16	yes	complemented
346	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
347	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
348	C₂×#125	C₂²×C₅	1	1	yes	characteristic
349	C₂×#125	C₂²×C₅	1	1	yes	characteristic
350	C₂×#125	C₂²×C₅	1	2	yes	—
351	C₂×#125	C₂²×C₅	1	2	yes	—
352	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
353	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
354	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
355	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
356	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
357	#391	C₂²×C₅	1	1	yes	characteristic
358	#391	C₂²×C₅	1	2	yes	—
359	#391	C₂²×C₅	1	1	yes	characteristic
360	#391	C₂²×C₅	1	1	yes	characteristic
361	#391	C₂²×C₅	1	2	yes	—
362	#391	C₂²×C₅	1	1	yes	characteristic
363	#391	C₂²×C₅	1	2	yes	—
364	#391	C₂²×C₅	1	2	yes	—
365	#391	C₂²×C₅	1	2	yes	—
366	#391	C₂²×C₅	1	1	yes	characteristic
367	#391	C₂²×C₅	1	1	yes	characteristic
368	#389	C₂²×C₅	1	1	yes	characteristic
369	#389	C₂²×C₅	1	1	yes	characteristic
370	#389	C₂²×C₅	1	2	yes	—
371	#389	C₂²×C₅	1	1	yes	characteristic
372	#389	C₂²×C₅	1	1	yes	characteristic
373	#389	C₂²×C₅	1	2	yes	—
374	#389	C₂²×C₅	1	2	yes	—
375	#389	C₂²×C₅	1	1	yes	characteristic
376	#389	C₂²×C₅	1	2	yes	—
377	#389	C₂²×C₅	1	1	yes	characteristic
378	#389	C₂²×C₅	1	2	yes	—
379	#389	C₂²×C₅	1	1	yes	characteristic
380	#389	C₂²×C₅	1	1	yes	characteristic
381	#387	C₂²×C₅	1	2	yes	—
382	#387	C₂²×C₅	1	2	yes	—
383	#387	C₂²×C₅	1	1	yes	characteristic
384	#387	C₂²×C₅	1	2	yes	—
385	#387	C₂²×C₅	1	2	yes	—
386	#387	C₂²×C₅	1	2	yes	—
387	#387	C₂²×C₅	1	2	yes	—
388	#387	C₂²×C₅	1	2	yes	—
389	#387	C₂²×C₅	1	2	yes	—
390	#387	C₂²×C₅	1	2	yes	—
391	#387	C₂²×C₅	1	2	yes	—
392	#387	C₂²×C₅	1	2	yes	—
393	#387	C₂²×C₅	1	2	yes	—
394	#387	C₂²×C₅	1	2	yes	—
395	#387	C₂²×C₅	1	2	yes	—
396	#387	C₂²×C₅	1	2	yes	—
397	#387	C₂²×C₅	1	1	yes	characteristic
398	#387	C₂²×C₅	1	2	yes	—
399	#387	C₂²×C₅	1	2	yes	—
400	#387	C₂²×C₅	1	2	yes	—
401	#387	C₂²×C₅	1	2	yes	—
402	#387	C₂²×C₅	1	2	yes	—
403	#387	C₂²×C₅	1	2	yes	—
404	#387	C₂²×C₅	1	2	yes	—
405	#387	C₂²×C₅	1	2	yes	—
406	#387	C₂²×C₅	1	1	yes	characteristic
407	#387	C₂²×C₅	1	1	yes	characteristic
408	#387	C₂²×C₅	1	2	yes	—
409	#384	C₂²×C₅	1	1	yes	characteristic
410	#383	C₂²×C₅	1	2	yes	—
411	#383	C₂²×C₅	1	2	yes	—
412	#383	C₂²×C₅	1	2	yes	—
413	#383	C₂²×C₅	1	2	yes	—
414	#382	C₂²×C₅	1	1	yes	characteristic
415	#382	C₂²×C₅	1	2	yes	—
416	#382	C₂²×C₅	1	2	yes	—
417	#382	C₂²×C₅	1	2	yes	—
418	#382	C₂²×C₅	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
439	#376	C₂²×C₅	1	1	yes	characteristic
440	#376	C₂²×C₅	1	1	yes	characteristic
441	#376	C₂²×C₅	1	2	yes	—
442	#376	C₂²×C₅	1	2	yes	—
443	#376	C₂²×C₅	1	2	yes	—
444	C₄³	C₂²×C₅	1	1	yes	characteristic
445	C₂³×C₅	C₂⁵	1	1	yes	characteristic
446	C₅×Q₈	—	2	8	no	—
447	C₅×Q₈	—	4	4	no	—
448	C₅×Q₈	—	4	8	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	2	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	2	no	—
455	C₂×C₄×C₅	—	2	2	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	2	no	—
461	C₂×C₄×C₅	—	2	2	no	—
462	C₂×C₄×C₅	—	2	2	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	2	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	2	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	2	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	2	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	2	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	2	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	2	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	2	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	2	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	2	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
505	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
506	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
507	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
508	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
509	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
510	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
511	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
512	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
513	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
514	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
515	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
516	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
517	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
518	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
519	C₂²×Q₈	C₂³×C₅	1	2	yes	—
520	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
521	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	—
522	C₄⋊Q₈	C₂×C₄×C₅	1	16	yes	—
523	#125	C₂×C₄×C₅	1	8	yes	—
524	#125	C₂×C₄×C₅	1	8	yes	—
525	#125	C₂×C₄×C₅	1	16	yes	—
526	#125	C₂×C₄×C₅	1	16	yes	—
527	C₄×Q₈	C₂×C₄×C₅	1	8	yes	—
528	C₄×Q₈	C₂×C₄×C₅	1	8	yes	—
529	C₄×Q₈	C₂×C₄×C₅	1	16	yes	—
530	C₄×Q₈	C₂×C₄×C₅	1	8	yes	—
531	C₄×Q₈	C₂×C₄×C₅	1	8	yes	—
532	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
564	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₅	1	2	yes	—
568	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₅	1	2	yes	—
574	C₂×C₄²	C₂³×C₅	1	2	yes	—
575	C₂×C₄²	C₂³×C₅	1	2	yes	—
576	C₂×C₄²	C₂³×C₅	1	2	yes	—
577	C₂×C₄²	C₂³×C₅	1	2	yes	—
578	C₂×C₄²	C₂³×C₅	1	2	yes	—
579	C₂×C₄²	C₂³×C₅	1	2	yes	—
580	C₂×C₄²	C₂³×C₅	1	2	yes	—
581	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₅	1	2	yes	—
583	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₅	1	2	yes	—
585	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₅	1	2	yes	—
587	#95	C₂³×C₅	1	1	yes	characteristic
588	#95	C₂³×C₅	1	2	yes	—
589	#95	C₂³×C₅	1	1	yes	characteristic
590	#95	C₂³×C₅	1	2	yes	—
591	#95	C₂³×C₅	1	2	yes	—
592	#95	C₂³×C₅	1	1	yes	characteristic
593	#95	C₂³×C₅	1	2	yes	—
594	#95	C₂³×C₅	1	1	yes	characteristic
595	#95	C₂³×C₅	1	2	yes	—
596	#95	C₂³×C₅	1	2	yes	—
597	#95	C₂³×C₅	1	2	yes	—
598	#95	C₂³×C₅	1	2	yes	—
599	#95	C₂³×C₅	1	1	yes	characteristic
600	#95	C₂³×C₅	1	1	yes	characteristic
601	#95	C₂³×C₅	1	1	yes	characteristic
602	#95	C₂³×C₅	1	1	yes	characteristic
603	#95	C₂³×C₅	1	1	yes	characteristic
604	#95	C₂³×C₅	1	2	yes	—
605	#95	C₂³×C₅	1	1	yes	characteristic
606	#95	C₂³×C₅	1	1	yes	characteristic
607	#95	C₂³×C₅	1	1	yes	characteristic
608	#95	C₂³×C₅	1	2	yes	—
609	#95	C₂³×C₅	1	2	yes	—
610	#95	C₂³×C₅	1	2	yes	—
611	#95	C₂³×C₅	1	2	yes	—
612	#95	C₂³×C₅	1	2	yes	—
613	#95	C₂³×C₅	1	2	yes	—
614	#95	C₂³×C₅	1	2	yes	—
615	#95	C₂³×C₅	1	2	yes	—
616	#95	C₂³×C₅	1	2	yes	—
617	#95	C₂³×C₅	1	1	yes	characteristic
618	#95	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
627	#95	C₂³×C₅	1	2	yes	—
628	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
629	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
630	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
631	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
632	C₂²×C₅	#585	1	1	yes	characteristic
633	C₂²×C₅	#585	1	1	yes	characteristic
634	C₂²×C₅	#585	1	1	yes	characteristic
635	C₄×C₅	—	2	4	no	—
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	4	no	—
638	C₄×C₅	—	2	4	no	—
639	C₄×C₅	—	2	2	no	—
640	C₄×C₅	—	2	2	no	—
641	C₄×C₅	—	2	2	no	—
642	C₄×C₅	—	2	4	no	—
643	C₄×C₅	—	2	2	no	—
644	C₄×C₅	—	2	2	no	—
645	C₄×C₅	—	2	2	no	—
646	C₄×C₅	—	4	1	no	—
647	C₄×C₅	—	4	2	no	—
648	C₄×C₅	—	4	1	no	—
649	C₄×C₅	—	4	2	no	—
650	C₄×C₅	—	4	2	no	—
651	C₄×C₅	—	4	1	no	—
652	C₄×C₅	—	4	1	no	—
653	C₄×C₅	—	4	1	no	—
654	C₄×C₅	—	4	1	no	—
655	C₄×C₅	—	4	1	no	—
656	C₄×C₅	—	4	2	no	—
657	C₄×C₅	#519	1	4	yes	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	4	1	no	—
661	C₂×Q₈	—	4	2	no	—
662	C₂×Q₈	—	4	2	no	—
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
665	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
666	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
667	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
709	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
710	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
711	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
712	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
713	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
714	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
715	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
716	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
717	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
718	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
719	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
720	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
721	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	1	no	—
730	C₄²	—	4	2	no	—
731	C₄²	—	4	1	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	2	no	—
737	C₄²	—	4	2	no	—
738	C₄²	—	4	1	no	—
739	C₄²	C₂²×C₄×C₅	1	8	yes	—
740	C₄²	C₂²×C₄×C₅	1	8	yes	—
741	C₄²	C₂²×C₄×C₅	1	4	yes	—
742	C₄²	C₂²×C₄×C₅	1	4	yes	—
743	C₄²	C₂²×C₄×C₅	1	8	yes	—
744	C₄²	C₂²×C₄×C₅	1	4	yes	—
745	C₂×C₅	C₂×#519	1	1	yes	characteristic
746	C₂×C₅	#3428	1	1	yes	characteristic
747	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
748	C₂×C₅	#3555	1	1	yes	characteristic
749	C₂×C₅	#3557	1	1	yes	characteristic
750	C₂×C₅	#3563	1	1	yes	characteristic
751	C₂×C₅	#3565	1	1	yes	characteristic
752	C₂³	C₂⁵×C₅	1	1	yes	characteristic
753	Q₈	—	2	8	no	—
754	Q₈	—	4	4	no	—
755	Q₈	—	4	8	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
812	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
813	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
814	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
815	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
816	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
817	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
818	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
819	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
820	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
821	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
822	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
823	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
824	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
825	C₅	#34490	1	1	yes	characteristic, direct product factor, Sylow
826	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
827	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
828	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
829	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
830	C₂²	C₅×#585	1	1	yes	characteristic
831	C₂²	C₅×#585	1	1	yes	characteristic
832	C₂²	C₅×#585	1	1	yes	characteristic
833	C₄	—	2	4	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	4	no	—
837	C₄	—	2	4	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	C₅×#519	1	4	yes	—
856	C₂	C₂×C₅×#519	1	1	yes	characteristic
857	C₂	C₅×#3428	1	1	yes	characteristic
858	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂	C₅×#3555	1	1	yes	characteristic
860	C₂	C₅×#3557	1	1	yes	characteristic
861	C₂	C₅×#3563	1	1	yes	characteristic
862	C₂	C₅×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
24. C₅×#557	C₄	semidirect
124. #34490	C₅	direct (N × H)
345. #557	C₄×C₅	semidirect
825. C₅	#34490	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×#557	2
C₅×#2382	2
C₅×#2381	2
C₅×#2371	2
C₅×#2370	2
C₅×#2369	2
C₅×#2356	2
C₅×#2355	2
C₅×#2336	2
C₅×#2331	2
C₅×#2330	2
C₅×#2320	2
C₄×C₅×#125	2
C₅×#2295	2
#34490	5

Subgroups — C5×#34490 #11957210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34490 #11957210