Subgroups — C₅×#35340 #11958060

Order 1280.

1630 conjugacy classes of subgroups.

The subgroup lattice has 944 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×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2850	C₂	1	1	yes	maximal, characteristic
5	C₅×#2645	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2644	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2625	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2624	C₂	1	1	yes	maximal, characteristic
9	C₅×#2597	C₂	1	2	yes	maximal, complemented
10	C₅×#2596	C₂	1	2	yes	maximal, complemented
11	C₅×#2595	C₂	1	2	yes	maximal, complemented
12	C₅×#2594	C₂	1	2	yes	maximal, complemented
13	C₅×#2578	C₂	1	2	yes	maximal, complemented
14	C₅×#2577	C₂	1	2	yes	maximal, complemented
15	C₅×#2576	C₂	1	2	yes	maximal, complemented
16	C₅×#2575	C₂	1	2	yes	maximal, complemented
17	C₅×#2324	C₂	1	1	yes	maximal, characteristic
18	C₅×#2323	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#125	C₂²	1	1	yes	characteristic
25	C₂×C₅×#124	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×#117	C₂²	1	1	yes	characteristic
31	C₂×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₅×#401	C₂²	1	2	yes	—
34	C₅×#400	C₂²	1	2	yes	—
35	C₅×#400	C₂²	1	2	yes	—
36	C₅×#400	C₂²	1	2	yes	—
37	C₅×#400	C₂²	1	2	yes	—
38	C₅×#399	C₂²	1	2	yes	—
39	C₅×#398	C₂²	1	2	yes	—
40	C₅×#397	C₂²	1	2	yes	—
41	C₅×#397	C₂²	1	2	yes	—
42	C₅×#397	C₂²	1	2	yes	—
43	C₅×#397	C₂²	1	2	yes	—
44	C₅×#397	C₂²	1	2	yes	—
45	C₅×#397	C₂²	1	2	yes	—
46	C₅×#396	C₂²	1	2	yes	—
47	C₅×#394	C₂²	1	2	yes	—
48	C₅×#394	C₂²	1	2	yes	—
49	C₅×#391	C₂²	1	1	yes	characteristic
50	C₅×#391	C₂²	1	1	yes	characteristic
51	C₅×#391	C₂²	1	1	yes	characteristic
52	C₅×#391	C₂²	1	1	yes	characteristic
53	C₅×#390	C₂²	1	1	yes	characteristic
54	C₅×#390	C₂²	1	1	yes	characteristic
55	C₅×#390	C₂²	1	1	yes	characteristic
56	C₅×#390	C₂²	1	2	yes	—
57	C₅×#390	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
63	C₅×#389	C₂²	1	1	yes	characteristic
64	C₅×#389	C₂²	1	2	yes	—
65	C₅×#389	C₂²	1	1	yes	characteristic
66	C₅×#389	C₂²	1	1	yes	characteristic
67	C₅×#388	C₂²	1	2	yes	—
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×#388	C₂²	1	2	yes	—
73	C₅×#388	C₂²	1	2	yes	—
74	C₅×#388	C₂²	1	2	yes	—
75	C₅×#388	C₂²	1	2	yes	—
76	C₅×#388	C₂²	1	2	yes	—
77	C₅×#388	C₂²	1	2	yes	—
78	C₅×#388	C₂²	1	2	yes	—
79	C₅×#388	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×#387	C₂²	1	2	yes	—
89	C₅×#387	C₂²	1	2	yes	—
90	C₅×#387	C₂²	1	2	yes	—
91	C₅×#386	C₂²	1	2	yes	—
92	C₅×#386	C₂²	1	2	yes	—
93	C₅×#386	C₂²	1	2	yes	—
94	C₅×#385	C₂²	1	2	yes	—
95	C₅×#385	C₂²	1	2	yes	—
96	C₅×#385	C₂²	1	2	yes	—
97	C₅×#383	C₂²	1	2	yes	—
98	C₅×#382	C₂²	1	1	yes	characteristic
99	C₅×#382	C₂²	1	1	yes	characteristic
100	C₅×#382	C₂²	1	2	yes	—
101	C₅×#381	C₂²	1	2	yes	—
102	C₅×#380	C₂²	1	2	yes	—
103	C₅×#380	C₂²	1	1	yes	characteristic
104	C₅×#380	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₅×C₂²⋊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	2	yes	—
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	#35340	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₅×D₄	C₂³	1	2	yes	—
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	2	yes	—
129	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₅×#125	—	2	4	no	—
132	C₅×#124	—	2	4	no	—
133	C₅×C₂²⋊Q₈	—	2	4	no	—
134	C₅×#121	—	2	4	no	—
135	C₄×C₅×Q₈	—	2	4	no	—
136	C₄×C₅×D₄	—	2	4	no	—
137	C₅×#117	—	2	4	no	—
138	C₅×#117	—	2	4	no	—
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	2	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	2	yes	—
197	C₂×C₄²×C₅	C₂³	1	2	yes	—
198	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₅×#95	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	2	yes	—
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	#2864	C₂×C₅	1	1	yes	characteristic, complemented
233	#2861	C₂×C₅	1	1	yes	characteristic, complemented
234	#2851	C₂×C₅	1	1	yes	characteristic, complemented
235	#2850	C₂×C₅	1	1	yes	characteristic
236	#2645	C₂×C₅	1	1	yes	characteristic, complemented
237	#2644	C₂×C₅	1	1	yes	characteristic, complemented
238	#2625	C₂×C₅	1	1	yes	characteristic, complemented
239	#2624	C₂×C₅	1	1	yes	characteristic
240	#2597	C₂×C₅	1	2	yes	complemented
241	#2596	C₂×C₅	1	2	yes	complemented
242	#2595	C₂×C₅	1	2	yes	complemented
243	#2594	C₂×C₅	1	2	yes	complemented
244	#2578	C₂×C₅	1	2	yes	complemented
245	#2577	C₂×C₅	1	2	yes	complemented
246	#2576	C₂×C₅	1	2	yes	complemented
247	#2575	C₂×C₅	1	2	yes	complemented
248	#2324	C₂×C₅	1	1	yes	characteristic
249	#2323	C₂×C₅	1	1	yes	characteristic, complemented
250	#2320	C₂×C₅	1	1	yes	characteristic, complemented
251	#2319	C₂×C₅	1	1	yes	characteristic, complemented
252	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
253	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
254	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
255	C₂⁴×C₅	C₂⁴	1	2	yes	—
256	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₅×Q₈	—	2	2	no	—
258	C₂×C₅×Q₈	—	2	2	no	—
259	C₂×C₅×Q₈	—	2	2	no	—
260	C₂×C₅×D₄	—	2	4	no	—
261	C₂×C₅×D₄	—	2	2	no	—
262	C₂×C₅×D₄	—	2	2	no	—
263	C₂×C₅×D₄	—	2	2	no	—
264	C₂×C₅×D₄	—	4	2	no	—
265	C₂×C₅×D₄	—	4	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	—	2	2	no	—
270	C₂²×C₄×C₅	—	2	4	no	—
271	C₂²×C₄×C₅	—	4	1	no	—
272	C₂²×C₄×C₅	—	4	1	no	—
273	C₂²×C₄×C₅	—	4	1	no	—
274	C₂²×C₄×C₅	—	4	1	no	—
275	C₂²×C₄×C₅	—	4	2	no	—
276	C₂²×C₄×C₅	—	4	2	no	—
277	C₂²×C₄×C₅	#41	1	4	yes	—
278	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
287	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₅×C₄⋊C₄	—	2	2	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	2	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	4	no	—
309	C₅×C₄⋊C₄	—	2	4	no	—
310	C₅×C₄⋊C₄	—	2	4	no	—
311	C₅×C₄⋊C₄	—	2	2	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	4	2	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×C₂²⋊C₄	—	2	2	no	—
322	C₅×C₂²⋊C₄	—	2	2	no	—
323	C₅×C₂²⋊C₄	—	2	4	no	—
324	C₅×C₂²⋊C₄	—	2	2	no	—
325	C₅×C₂²⋊C₄	—	2	2	no	—
326	C₅×C₂²⋊C₄	—	2	4	no	—
327	C₅×C₂²⋊C₄	—	2	4	no	—
328	C₅×C₂²⋊C₄	—	2	4	no	—
329	C₅×C₂²⋊C₄	—	2	4	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	—	4	2	no	—
335	C₅×C₂²⋊C₄	—	4	2	no	—
336	C₅×C₂²⋊C₄	—	4	2	no	—
337	C₅×C₂²⋊C₄	—	4	2	no	—
338	C₅×C₂²⋊C₄	—	4	2	no	—
339	C₅×C₂²⋊C₄	—	4	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	—	2	2	no	—
345	C₄²×C₅	—	2	2	no	—
346	C₄²×C₅	—	2	4	no	—
347	C₄²×C₅	—	4	1	no	—
348	C₄²×C₅	—	4	1	no	—
349	C₄²×C₅	—	4	2	no	—
350	C₄²×C₅	—	4	2	no	—
351	C₄²×C₅	—	4	1	no	—
352	C₄²×C₅	—	4	1	no	—
353	C₄²×C₅	—	4	1	no	—
354	C₄²×C₅	—	4	1	no	—
355	C₄²×C₅	—	4	1	no	—
356	C₄²×C₅	—	4	1	no	—
357	C₄²×C₅	#41	1	4	yes	—
358	C₄²×C₅	#41	1	4	yes	—
359	C₂×#125	C₂²×C₅	1	1	yes	characteristic
360	C₂×#124	C₂²×C₅	1	1	yes	characteristic
361	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
362	C₂×#121	C₂²×C₅	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
365	C₂×#117	C₂²×C₅	1	1	yes	characteristic
366	C₂×#117	C₂²×C₅	1	1	yes	characteristic
367	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
368	#401	C₂²×C₅	1	2	yes	—
369	#400	C₂²×C₅	1	2	yes	—
370	#400	C₂²×C₅	1	2	yes	—
371	#400	C₂²×C₅	1	2	yes	—
372	#400	C₂²×C₅	1	2	yes	—
373	#399	C₂²×C₅	1	2	yes	—
374	#398	C₂²×C₅	1	2	yes	—
375	#397	C₂²×C₅	1	2	yes	—
376	#397	C₂²×C₅	1	2	yes	—
377	#397	C₂²×C₅	1	2	yes	—
378	#397	C₂²×C₅	1	2	yes	—
379	#397	C₂²×C₅	1	2	yes	—
380	#397	C₂²×C₅	1	2	yes	—
381	#396	C₂²×C₅	1	2	yes	—
382	#394	C₂²×C₅	1	2	yes	—
383	#394	C₂²×C₅	1	2	yes	—
384	#391	C₂²×C₅	1	1	yes	characteristic
385	#391	C₂²×C₅	1	1	yes	characteristic
386	#391	C₂²×C₅	1	1	yes	characteristic
387	#391	C₂²×C₅	1	1	yes	characteristic
388	#390	C₂²×C₅	1	1	yes	characteristic
389	#390	C₂²×C₅	1	1	yes	characteristic
390	#390	C₂²×C₅	1	2	yes	—
391	#390	C₂²×C₅	1	1	yes	characteristic
392	#390	C₂²×C₅	1	1	yes	characteristic
393	#389	C₂²×C₅	1	1	yes	characteristic
394	#389	C₂²×C₅	1	1	yes	characteristic
395	#389	C₂²×C₅	1	1	yes	characteristic
396	#389	C₂²×C₅	1	1	yes	characteristic
397	#389	C₂²×C₅	1	1	yes	characteristic
398	#389	C₂²×C₅	1	1	yes	characteristic
399	#389	C₂²×C₅	1	2	yes	—
400	#389	C₂²×C₅	1	1	yes	characteristic
401	#389	C₂²×C₅	1	1	yes	characteristic
402	#388	C₂²×C₅	1	2	yes	—
403	#388	C₂²×C₅	1	2	yes	—
404	#388	C₂²×C₅	1	2	yes	—
405	#388	C₂²×C₅	1	2	yes	—
406	#388	C₂²×C₅	1	2	yes	—
407	#388	C₂²×C₅	1	2	yes	—
408	#388	C₂²×C₅	1	2	yes	—
409	#388	C₂²×C₅	1	2	yes	—
410	#388	C₂²×C₅	1	2	yes	—
411	#388	C₂²×C₅	1	2	yes	—
412	#388	C₂²×C₅	1	2	yes	—
413	#388	C₂²×C₅	1	2	yes	—
414	#388	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	#387	C₂²×C₅	1	2	yes	—
421	#387	C₂²×C₅	1	2	yes	—
422	#387	C₂²×C₅	1	2	yes	—
423	#387	C₂²×C₅	1	2	yes	—
424	#387	C₂²×C₅	1	2	yes	—
425	#387	C₂²×C₅	1	2	yes	—
426	#386	C₂²×C₅	1	2	yes	—
427	#386	C₂²×C₅	1	2	yes	—
428	#386	C₂²×C₅	1	2	yes	—
429	#385	C₂²×C₅	1	2	yes	—
430	#385	C₂²×C₅	1	2	yes	—
431	#385	C₂²×C₅	1	2	yes	—
432	#383	C₂²×C₅	1	2	yes	—
433	#382	C₂²×C₅	1	1	yes	characteristic
434	#382	C₂²×C₅	1	2	yes	—
435	#382	C₂²×C₅	1	1	yes	characteristic
436	#381	C₂²×C₅	1	2	yes	—
437	#380	C₂²×C₅	1	2	yes	—
438	#380	C₂²×C₅	1	1	yes	characteristic
439	#380	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
454	#376	C₂²×C₅	1	1	yes	characteristic
455	#376	C₂²×C₅	1	1	yes	characteristic
456	C₄³	C₂²×C₅	1	1	yes	characteristic
457	C₄³	C₂²×C₅	1	1	yes	characteristic
458	C₂³×C₅	—	2	1	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	2	1	no	—
461	C₂³×C₅	—	2	1	no	—
462	C₂³×C₅	—	2	1	no	—
463	C₂³×C₅	—	2	1	no	—
464	C₂³×C₅	—	2	2	no	—
465	C₂³×C₅	—	2	2	no	—
466	C₂³×C₅	—	2	2	no	—
467	C₂³×C₅	—	2	2	no	—
468	C₂³×C₅	—	2	2	no	—
469	C₂³×C₅	—	2	2	no	—
470	C₂³×C₅	—	2	2	no	—
471	C₂³×C₅	C₂×#41	1	2	yes	—
472	C₂³×C₅	C₂⁵	1	1	yes	characteristic
473	C₅×Q₈	—	4	4	no	—
474	C₅×D₄	—	4	4	no	—
475	C₅×D₄	—	8	4	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	8	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	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	1	no	—
494	C₂×C₄×C₅	—	2	1	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	2	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	1	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	2	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	2	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	2	no	—
532	C₂×C₄×C₅	—	4	4	no	—
533	C₂×C₄×C₅	—	4	4	no	—
534	C₂×C₄×C₅	—	8	4	no	—
535	C₂×C₄×C₅	C₂×#41	1	2	yes	—
536	C₂×C₄×C₅	C₂×#41	1	2	yes	—
537	C₂×C₄×C₅	C₂×#41	1	2	yes	—
538	C₂×C₄×C₅	C₂×#41	1	2	yes	—
539	C₂×C₄×C₅	C₂×#41	1	2	yes	—
540	C₂×C₄×C₅	C₂×#41	1	2	yes	—
541	C₂×C₄×C₅	C₂×#41	1	2	yes	—
542	C₂×C₄×C₅	C₂×#41	1	2	yes	—
543	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₅	1	2	yes	—
546	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₅	1	2	yes	—
548	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
550	#125	—	2	4	no	—
551	#124	—	2	4	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	#121	—	2	4	no	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×D₄	—	2	4	no	—
556	#117	—	2	4	no	—
557	#117	—	2	4	no	—
558	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
581	C₂×C₂²⋊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	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
599	C₂×C₄²	—	2	4	no	—
600	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₅	1	2	yes	—
604	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₅	1	2	yes	—
616	C₂×C₄²	C₂³×C₅	1	2	yes	—
617	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
619	#95	C₂³×C₅	1	1	yes	characteristic
620	#95	C₂³×C₅	1	1	yes	characteristic
621	#95	C₂³×C₅	1	1	yes	characteristic
622	#95	C₂³×C₅	1	1	yes	characteristic
623	#95	C₂³×C₅	1	1	yes	characteristic
624	#95	C₂³×C₅	1	1	yes	characteristic
625	#95	C₂³×C₅	1	1	yes	characteristic
626	#95	C₂³×C₅	1	1	yes	characteristic
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	#95	C₂³×C₅	1	2	yes	—
644	#95	C₂³×C₅	1	2	yes	—
645	#95	C₂³×C₅	1	2	yes	—
646	#95	C₂³×C₅	1	2	yes	—
647	#95	C₂³×C₅	1	2	yes	—
648	#95	C₂³×C₅	1	2	yes	—
649	#95	C₂³×C₅	1	2	yes	—
650	#95	C₂³×C₅	1	2	yes	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	2	2	no	—
653	C₂²×C₅	—	2	2	no	—
654	C₂²×C₅	—	4	1	no	—
655	C₂²×C₅	—	4	1	no	—
656	C₂²×C₅	—	4	1	no	—
657	C₂²×C₅	—	4	1	no	—
658	C₂²×C₅	—	4	2	no	—
659	C₂²×C₅	—	4	2	no	—
660	C₂²×C₅	—	4	2	no	—
661	C₂²×C₅	—	4	2	no	—
662	C₂²×C₅	—	4	2	no	—
663	C₂²×C₅	—	4	2	no	—
664	C₂²×C₅	—	4	2	no	—
665	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
666	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
667	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
668	C₂²×C₅	#585	1	1	yes	characteristic
669	C₂²×C₅	#585	1	1	yes	characteristic
670	C₂²×C₅	#585	1	1	yes	characteristic
671	C₂²×C₅	#585	1	1	yes	characteristic
672	C₄×C₅	—	2	2	no	—
673	C₄×C₅	—	2	2	no	—
674	C₄×C₅	—	2	2	no	—
675	C₄×C₅	—	2	2	no	—
676	C₄×C₅	—	2	2	no	—
677	C₄×C₅	—	4	2	no	—
678	C₄×C₅	—	4	2	no	—
679	C₄×C₅	—	4	2	no	—
680	C₄×C₅	—	4	1	no	—
681	C₄×C₅	—	4	1	no	—
682	C₄×C₅	—	4	1	no	—
683	C₄×C₅	—	4	1	no	—
684	C₄×C₅	—	4	1	no	—
685	C₄×C₅	—	4	2	no	—
686	C₄×C₅	—	4	2	no	—
687	C₄×C₅	—	4	1	no	—
688	C₄×C₅	—	4	2	no	—
689	C₄×C₅	—	4	1	no	—
690	C₄×C₅	—	4	1	no	—
691	C₄×C₅	—	4	2	no	—
692	C₄×C₅	#529	1	4	yes	—
693	C₂⁴	C₂⁴×C₅	1	2	yes	—
694	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	C₅×#41	1	4	yes	—
716	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	4	1	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	1	no	—
790	C₄²	—	4	1	no	—
791	C₄²	—	4	1	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	1	no	—
794	C₄²	—	4	1	no	—
795	C₄²	C₅×#41	1	4	yes	—
796	C₄²	C₅×#41	1	4	yes	—
797	C₂×C₅	—	4	2	no	—
798	C₂×C₅	—	8	2	no	—
799	C₂×C₅	C₂×#529	1	1	yes	characteristic
800	C₂×C₅	#3455	1	1	yes	characteristic
801	C₂×C₅	#3455	1	1	yes	characteristic
802	C₂×C₅	#3510	1	1	yes	characteristic
803	C₂×C₅	#3510	1	1	yes	characteristic
804	C₂×C₅	#3512	1	1	yes	characteristic
805	C₂×C₅	#3512	1	1	yes	characteristic
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	C₂×C₅×#41	1	2	yes	—
820	C₂³	C₂⁵×C₅	1	1	yes	characteristic
821	Q₈	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	8	4	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	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	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	8	4	no	—
883	C₂×C₄	C₂×C₅×#41	1	2	yes	—
884	C₂×C₄	C₂×C₅×#41	1	2	yes	—
885	C₂×C₄	C₂×C₅×#41	1	2	yes	—
886	C₂×C₄	C₂×C₅×#41	1	2	yes	—
887	C₂×C₄	C₂×C₅×#41	1	2	yes	—
888	C₂×C₄	C₂×C₅×#41	1	2	yes	—
889	C₂×C₄	C₂×C₅×#41	1	2	yes	—
890	C₂×C₄	C₂×C₅×#41	1	2	yes	—
891	C₅	#35340	1	1	yes	characteristic, direct product factor, Sylow
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
907	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
908	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
909	C₂²	C₅×#585	1	1	yes	characteristic
910	C₂²	C₅×#585	1	1	yes	characteristic
911	C₂²	C₅×#585	1	1	yes	characteristic
912	C₂²	C₅×#585	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	2	no	—
933	C₄	C₅×#529	1	4	yes	—
934	C₂	—	4	2	no	—
935	C₂	—	8	2	no	—
936	C₂	C₂×C₅×#529	1	1	yes	characteristic
937	C₂	C₅×#3455	1	1	yes	characteristic
938	C₂	C₅×#3455	1	1	yes	characteristic
939	C₂	C₅×#3510	1	1	yes	characteristic
940	C₂	C₅×#3510	1	1	yes	characteristic
941	C₂	C₅×#3512	1	1	yes	characteristic
942	C₂	C₅×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#121	C₂²
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×#2861	C₂	semidirect
3. C₅×#2851	C₂	semidirect
5. C₅×#2645	C₂	semidirect
6. C₅×#2644	C₂	semidirect
7. C₅×#2625	C₂	semidirect
9. C₅×#2597	C₂	semidirect
10. C₅×#2596	C₂	semidirect
11. C₅×#2595	C₂	semidirect
12. C₅×#2594	C₂	semidirect
13. C₅×#2578	C₂	semidirect
14. C₅×#2577	C₂	semidirect
15. C₅×#2576	C₂	semidirect
16. C₅×#2575	C₂	semidirect
18. C₅×#2323	C₂	semidirect
19. C₅×#2320	C₂	semidirect
20. C₅×#2319	C₂	semidirect
21. C₄×C₅×#125	C₂	semidirect
22. C₄×C₅×#124	C₂	semidirect
23. C₄×C₅×#117	C₂	semidirect
123. #35340	C₅	direct (N × H)
232. #2864	C₂×C₅	semidirect
233. #2861	C₂×C₅	semidirect
234. #2851	C₂×C₅	semidirect
236. #2645	C₂×C₅	semidirect
237. #2644	C₂×C₅	semidirect
238. #2625	C₂×C₅	semidirect
240. #2597	C₂×C₅	semidirect
241. #2596	C₂×C₅	semidirect
242. #2595	C₂×C₅	semidirect
243. #2594	C₂×C₅	semidirect
244. #2578	C₂×C₅	semidirect
245. #2577	C₂×C₅	semidirect
246. #2576	C₂×C₅	semidirect
247. #2575	C₂×C₅	semidirect
249. #2323	C₂×C₅	semidirect
250. #2320	C₂×C₅	semidirect
251. #2319	C₂×C₅	semidirect
252. C₄×#125	C₂×C₅	semidirect
253. C₄×#124	C₂×C₅	semidirect
254. C₄×#117	C₂×C₅	semidirect
891. C₅	#35340	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×#2861	2
C₅×#2851	2
C₅×#2850	2
C₅×#2645	2
C₅×#2644	2
C₅×#2625	2
C₅×#2624	2
C₅×#2597	2
C₅×#2596	2
C₅×#2595	2
C₅×#2594	2
C₅×#2578	2
C₅×#2577	2
C₅×#2576	2
C₅×#2575	2
C₅×#2324	2
C₅×#2323	2
C₅×#2320	2
C₅×#2319	2
C₄×C₅×#125	2
C₄×C₅×#124	2
C₄×C₅×#117	2
#35340	5

Subgroups — C5×#35340 #11958060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35340 #11958060