Subgroups — C₅×#35008 #11957728

Order 1280.

2284 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#539	C₂	1	2	yes	maximal, complemented
2	C₅×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2854	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2664	C₂	1	2	yes	maximal, complemented
7	C₅×#2663	C₂	1	2	yes	maximal, complemented
8	C₅×#2556	C₂	1	2	yes	maximal, complemented
9	C₅×#2553	C₂	1	2	yes	maximal, complemented
10	C₅×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2501	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2496	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2488	C₂	1	2	yes	maximal, complemented
14	C₅×#2486	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2452	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2440	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2425	C₂	1	2	yes	maximal, complemented
18	C₅×#2422	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2416	C₂	1	1	yes	maximal, characteristic
20	C₅×#2322	C₂	1	2	yes	maximal, complemented
21	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#539	—	2	16	no	—
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#126	C₂²	1	2	yes	—
27	C₂×C₅×#126	C₂²	1	2	yes	—
28	C₂×C₅×#125	C₂²	1	2	yes	—
29	C₂×C₅×#125	C₂²	1	2	yes	—
30	C₂×C₅×#123	C₂²	1	2	yes	—
31	C₂×C₅×#123	C₂²	1	2	yes	—
32	C₂×C₅×#123	C₂²	1	2	yes	—
33	C₂×C₅×#123	C₂²	1	2	yes	—
34	C₂×C₅×#123	C₂²	1	2	yes	—
35	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₅×#121	C₂²	1	1	yes	characteristic
39	C₂×C₅×#121	C₂²	1	2	yes	—
40	C₂×C₅×#121	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
44	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
46	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
48	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
51	C₅×#400	C₂²	1	2	yes	—
52	C₅×#400	C₂²	1	2	yes	—
53	C₅×#399	C₂²	1	2	yes	—
54	C₅×#399	C₂²	1	2	yes	—
55	C₅×#398	C₂²	1	2	yes	—
56	C₅×#398	C₂²	1	2	yes	—
57	C₅×#398	C₂²	1	2	yes	—
58	C₅×#397	C₂²	1	2	yes	—
59	C₅×#397	C₂²	1	2	yes	—
60	C₅×#397	C₂²	1	2	yes	—
61	C₅×#396	C₂²	1	2	yes	—
62	C₅×#396	C₂²	1	2	yes	—
63	C₅×#395	C₂²	1	2	yes	—
64	C₅×#394	C₂²	1	2	yes	—
65	C₅×#394	C₂²	1	2	yes	—
66	C₅×#393	C₂²	1	2	yes	—
67	C₅×#391	C₂²	1	2	yes	—
68	C₅×#390	C₂²	1	1	yes	characteristic
69	C₅×#390	C₂²	1	1	yes	characteristic
70	C₅×#390	C₂²	1	1	yes	characteristic
71	C₅×#390	C₂²	1	1	yes	characteristic
72	C₅×#389	C₂²	1	1	yes	characteristic
73	C₅×#389	C₂²	1	1	yes	characteristic
74	C₅×#389	C₂²	1	1	yes	characteristic
75	C₅×#389	C₂²	1	1	yes	characteristic
76	C₅×#389	C₂²	1	1	yes	characteristic
77	C₅×#389	C₂²	1	1	yes	characteristic
78	C₅×#389	C₂²	1	1	yes	characteristic
79	C₅×#389	C₂²	1	2	yes	—
80	C₅×#389	C₂²	1	1	yes	characteristic
81	C₅×#389	C₂²	1	1	yes	characteristic
82	C₅×#389	C₂²	1	2	yes	—
83	C₅×#389	C₂²	1	1	yes	characteristic
84	C₅×#389	C₂²	1	2	yes	—
85	C₅×#389	C₂²	1	2	yes	—
86	C₅×#389	C₂²	1	2	yes	—
87	C₅×#388	C₂²	1	2	yes	—
88	C₅×#388	C₂²	1	2	yes	—
89	C₅×#388	C₂²	1	2	yes	—
90	C₅×#388	C₂²	1	2	yes	—
91	C₅×#388	C₂²	1	2	yes	—
92	C₅×#388	C₂²	1	2	yes	—
93	C₅×#387	C₂²	1	2	yes	—
94	C₅×#387	C₂²	1	2	yes	—
95	C₅×#386	C₂²	1	2	yes	—
96	C₅×#386	C₂²	1	2	yes	—
97	C₅×#386	C₂²	1	2	yes	—
98	C₅×#385	C₂²	1	2	yes	—
99	C₅×#385	C₂²	1	2	yes	—
100	C₅×#385	C₂²	1	2	yes	—
101	C₅×#384	C₂²	1	1	yes	characteristic
102	C₅×#384	C₂²	1	1	yes	characteristic
103	C₅×#384	C₂²	1	1	yes	characteristic
104	C₅×#382	C₂²	1	2	yes	—
105	C₅×#381	C₂²	1	2	yes	—
106	C₅×#380	C₂²	1	1	yes	characteristic
107	C₅×#380	C₂²	1	1	yes	characteristic
108	C₅×#380	C₂²	1	1	yes	characteristic
109	C₅×#380	C₂²	1	1	yes	characteristic
110	C₅×#380	C₂²	1	2	yes	—
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	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	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#35008	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	2	yes	—
126	C₂²×C₅×D₄	C₂³	1	2	yes	—
127	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₅×D₄	C₂³	1	2	yes	—
130	C₂³×C₄×C₅	C₂³	1	2	yes	—
131	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂³	1	2	yes	—
136	C₂³×C₄×C₅	C₂³	1	2	yes	—
137	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₅×C₄⋊Q₈	—	4	2	no	—
140	C₅×#126	—	2	8	no	—
141	C₅×#126	—	2	8	no	—
142	C₅×#125	—	2	8	no	—
143	C₅×#125	—	2	8	no	—
144	C₅×#123	—	2	8	no	—
145	C₅×#123	—	2	8	no	—
146	C₅×#123	—	2	8	no	—
147	C₅×#123	—	2	8	no	—
148	C₅×#123	—	2	8	no	—
149	C₅×C₂²⋊Q₈	—	2	8	no	—
150	C₅×C₂²⋊Q₈	—	2	8	no	—
151	C₅×C₂²⋊Q₈	—	2	8	no	—
152	C₅×#121	—	2	8	no	—
153	C₅×#121	—	2	4	no	—
154	C₅×#121	—	4	2	no	—
155	C₄×C₅×D₄	—	2	8	no	—
156	C₄×C₅×D₄	—	2	4	no	—
157	C₄×C₅×D₄	—	2	4	no	—
158	C₄×C₅×D₄	—	4	2	no	—
159	C₄×C₅×D₄	D₄	1	8	yes	complemented
160	C₂×C₅×C₄⋊C₄	—	2	8	no	—
161	C₂×C₅×C₄⋊C₄	—	2	4	no	—
162	C₂×C₅×C₄⋊C₄	—	4	2	no	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅	—	4	2	no	—
214	C₂×C₄²×C₅	—	4	2	no	—
215	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅	C₂³	1	2	yes	—
223	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
235	C₅×#95	C₂³	1	1	yes	characteristic
236	C₅×#95	C₂³	1	1	yes	characteristic
237	C₅×#95	C₂³	1	1	yes	characteristic
238	C₅×#95	C₂³	1	1	yes	characteristic
239	C₅×#95	C₂³	1	2	yes	—
240	C₅×#95	C₂³	1	2	yes	—
241	C₅×#95	C₂³	1	2	yes	—
242	C₅×#95	C₂³	1	2	yes	—
243	C₅×#95	C₂³	1	2	yes	—
244	C₅×#95	C₂³	1	2	yes	—
245	C₅×#95	C₂³	1	2	yes	—
246	C₅×#95	C₂³	1	2	yes	—
247	C₅×#95	C₂³	1	2	yes	—
248	C₅×#95	C₂³	1	2	yes	—
249	C₅×#95	C₂³	1	2	yes	—
250	C₂×#539	C₂×C₅	1	2	yes	complemented
251	#2860	C₂×C₅	1	1	yes	characteristic, complemented
252	#2859	C₂×C₅	1	1	yes	characteristic, complemented
253	#2857	C₂×C₅	1	1	yes	characteristic, complemented
254	#2854	C₂×C₅	1	1	yes	characteristic, complemented
255	#2664	C₂×C₅	1	2	yes	complemented
256	#2663	C₂×C₅	1	2	yes	complemented
257	#2556	C₂×C₅	1	2	yes	complemented
258	#2553	C₂×C₅	1	2	yes	complemented
259	#2506	C₂×C₅	1	1	yes	characteristic, complemented
260	#2501	C₂×C₅	1	1	yes	characteristic, complemented
261	#2496	C₂×C₅	1	1	yes	characteristic, complemented
262	#2488	C₂×C₅	1	2	yes	complemented
263	#2486	C₂×C₅	1	1	yes	characteristic, complemented
264	#2452	C₂×C₅	1	1	yes	characteristic, complemented
265	#2440	C₂×C₅	1	1	yes	characteristic, complemented
266	#2425	C₂×C₅	1	2	yes	complemented
267	#2422	C₂×C₅	1	1	yes	characteristic, complemented
268	#2416	C₂×C₅	1	1	yes	characteristic
269	#2322	C₂×C₅	1	2	yes	complemented
270	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
271	C₂×#389	C₂×C₅	1	1	yes	characteristic, complemented
272	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
273	C₂⁴×C₅	C₂⁴	1	2	yes	—
274	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
275	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₅×Q₈	—	2	4	no	—
277	C₂×C₅×Q₈	—	4	2	no	—
278	C₂×C₅×Q₈	—	4	2	no	—
279	C₂×C₅×D₄	—	2	2	no	—
280	C₂×C₅×D₄	—	2	2	no	—
281	C₂×C₅×D₄	—	2	4	no	—
282	C₂×C₅×D₄	—	2	4	no	—
283	C₂×C₅×D₄	—	2	4	no	—
284	C₂×C₅×D₄	—	2	4	no	—
285	C₂×C₅×D₄	—	2	2	no	—
286	C₂×C₅×D₄	—	2	2	no	—
287	C₂×C₅×D₄	—	2	2	no	—
288	C₂×C₅×D₄	—	4	2	no	—
289	C₂×C₅×D₄	—	4	2	no	—
290	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
291	C₂²×C₄×C₅	—	2	2	no	—
292	C₂²×C₄×C₅	—	2	2	no	—
293	C₂²×C₄×C₅	—	2	4	no	—
294	C₂²×C₄×C₅	—	2	4	no	—
295	C₂²×C₄×C₅	—	2	2	no	—
296	C₂²×C₄×C₅	—	2	4	no	—
297	C₂²×C₄×C₅	—	2	4	no	—
298	C₂²×C₄×C₅	—	2	2	no	—
299	C₂²×C₄×C₅	—	2	2	no	—
300	C₂²×C₄×C₅	—	2	2	no	—
301	C₂²×C₄×C₅	—	2	2	no	—
302	C₂²×C₄×C₅	—	2	2	no	—
303	C₂²×C₄×C₅	—	2	2	no	—
304	C₂²×C₄×C₅	—	2	4	no	—
305	C₂²×C₄×C₅	—	4	1	no	—
306	C₂²×C₄×C₅	—	4	1	no	—
307	C₂²×C₄×C₅	—	4	1	no	—
308	C₂²×C₄×C₅	—	4	1	no	—
309	C₂²×C₄×C₅	—	4	1	no	—
310	C₂²×C₄×C₅	—	4	1	no	—
311	C₂²×C₄×C₅	—	4	2	no	—
312	C₂²×C₄×C₅	—	4	2	no	—
313	C₂²×C₄×C₅	—	4	2	no	—
314	C₂²×C₄×C₅	—	4	2	no	—
315	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
316	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
317	C₂²×C₄×C₅	#41	1	4	yes	—
318	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
338	C₅×C₄⋊C₄	—	2	4	no	—
339	C₅×C₄⋊C₄	—	2	4	no	—
340	C₅×C₄⋊C₄	—	2	4	no	—
341	C₅×C₄⋊C₄	—	2	4	no	—
342	C₅×C₄⋊C₄	—	2	4	no	—
343	C₅×C₄⋊C₄	—	2	4	no	—
344	C₅×C₄⋊C₄	—	2	4	no	—
345	C₅×C₄⋊C₄	—	2	4	no	—
346	C₅×C₄⋊C₄	—	2	4	no	—
347	C₅×C₄⋊C₄	—	2	4	no	—
348	C₅×C₄⋊C₄	—	2	4	no	—
349	C₅×C₄⋊C₄	—	2	4	no	—
350	C₅×C₄⋊C₄	—	2	4	no	—
351	C₅×C₄⋊C₄	—	2	4	no	—
352	C₅×C₄⋊C₄	—	2	2	no	—
353	C₅×C₄⋊C₄	—	2	2	no	—
354	C₅×C₄⋊C₄	—	2	2	no	—
355	C₅×C₄⋊C₄	—	2	2	no	—
356	C₅×C₄⋊C₄	—	2	2	no	—
357	C₅×C₄⋊C₄	—	2	4	no	—
358	C₅×C₄⋊C₄	—	2	4	no	—
359	C₅×C₄⋊C₄	—	2	2	no	—
360	C₅×C₄⋊C₄	—	2	2	no	—
361	C₅×C₄⋊C₄	—	2	2	no	—
362	C₅×C₄⋊C₄	—	2	2	no	—
363	C₅×C₄⋊C₄	—	4	2	no	—
364	C₅×C₄⋊C₄	—	4	2	no	—
365	C₅×C₄⋊C₄	—	4	2	no	—
366	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
367	C₅×C₂²⋊C₄	—	2	4	no	—
368	C₅×C₂²⋊C₄	—	2	4	no	—
369	C₅×C₂²⋊C₄	—	2	4	no	—
370	C₅×C₂²⋊C₄	—	2	4	no	—
371	C₅×C₂²⋊C₄	—	2	2	no	—
372	C₅×C₂²⋊C₄	—	2	4	no	—
373	C₅×C₂²⋊C₄	—	2	4	no	—
374	C₅×C₂²⋊C₄	—	2	4	no	—
375	C₅×C₂²⋊C₄	—	2	4	no	—
376	C₅×C₂²⋊C₄	—	2	2	no	—
377	C₅×C₂²⋊C₄	—	2	2	no	—
378	C₅×C₂²⋊C₄	—	2	4	no	—
379	C₅×C₂²⋊C₄	—	2	4	no	—
380	C₅×C₂²⋊C₄	—	2	4	no	—
381	C₅×C₂²⋊C₄	—	2	4	no	—
382	C₅×C₂²⋊C₄	—	4	2	no	—
383	C₅×C₂²⋊C₄	—	4	2	no	—
384	C₅×C₂²⋊C₄	—	4	2	no	—
385	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
386	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
387	C₅×C₂²⋊C₄	#41	1	4	yes	—
388	C₄²×C₅	—	2	4	no	—
389	C₄²×C₅	—	2	2	no	—
390	C₄²×C₅	—	2	2	no	—
391	C₄²×C₅	—	2	2	no	—
392	C₄²×C₅	—	2	2	no	—
393	C₄²×C₅	—	2	2	no	—
394	C₄²×C₅	—	2	2	no	—
395	C₄²×C₅	—	2	2	no	—
396	C₄²×C₅	—	4	1	no	—
397	C₄²×C₅	—	4	1	no	—
398	C₄²×C₅	—	4	1	no	—
399	C₄²×C₅	—	4	1	no	—
400	C₄²×C₅	—	4	1	no	—
401	C₄²×C₅	C₂×D₄	1	4	yes	—
402	#539	—	2	16	no	—
403	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
404	C₂×#126	C₂²×C₅	1	2	yes	—
405	C₂×#126	C₂²×C₅	1	2	yes	—
406	C₂×#125	C₂²×C₅	1	2	yes	—
407	C₂×#125	C₂²×C₅	1	2	yes	—
408	C₂×#123	C₂²×C₅	1	2	yes	—
409	C₂×#123	C₂²×C₅	1	2	yes	—
410	C₂×#123	C₂²×C₅	1	2	yes	—
411	C₂×#123	C₂²×C₅	1	2	yes	—
412	C₂×#123	C₂²×C₅	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
416	C₂×#121	C₂²×C₅	1	2	yes	—
417	C₂×#121	C₂²×C₅	1	1	yes	characteristic
418	C₂×#121	C₂²×C₅	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
425	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
427	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
428	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
429	#400	C₂²×C₅	1	2	yes	—
430	#400	C₂²×C₅	1	2	yes	—
431	#399	C₂²×C₅	1	2	yes	—
432	#399	C₂²×C₅	1	2	yes	—
433	#398	C₂²×C₅	1	2	yes	—
434	#398	C₂²×C₅	1	2	yes	—
435	#398	C₂²×C₅	1	2	yes	—
436	#397	C₂²×C₅	1	2	yes	—
437	#397	C₂²×C₅	1	2	yes	—
438	#397	C₂²×C₅	1	2	yes	—
439	#396	C₂²×C₅	1	2	yes	—
440	#396	C₂²×C₅	1	2	yes	—
441	#395	C₂²×C₅	1	2	yes	—
442	#394	C₂²×C₅	1	2	yes	—
443	#394	C₂²×C₅	1	2	yes	—
444	#393	C₂²×C₅	1	2	yes	—
445	#391	C₂²×C₅	1	2	yes	—
446	#390	C₂²×C₅	1	1	yes	characteristic
447	#390	C₂²×C₅	1	1	yes	characteristic
448	#390	C₂²×C₅	1	1	yes	characteristic
449	#390	C₂²×C₅	1	1	yes	characteristic
450	#389	C₂²×C₅	1	2	yes	—
451	#389	C₂²×C₅	1	2	yes	—
452	#389	C₂²×C₅	1	1	yes	characteristic
453	#389	C₂²×C₅	1	1	yes	characteristic
454	#389	C₂²×C₅	1	1	yes	characteristic
455	#389	C₂²×C₅	1	1	yes	characteristic
456	#389	C₂²×C₅	1	1	yes	characteristic
457	#389	C₂²×C₅	1	2	yes	—
458	#389	C₂²×C₅	1	1	yes	characteristic
459	#389	C₂²×C₅	1	1	yes	characteristic
460	#389	C₂²×C₅	1	1	yes	characteristic
461	#389	C₂²×C₅	1	2	yes	—
462	#389	C₂²×C₅	1	1	yes	characteristic
463	#389	C₂²×C₅	1	1	yes	characteristic
464	#389	C₂²×C₅	1	2	yes	—
465	#388	C₂²×C₅	1	2	yes	—
466	#388	C₂²×C₅	1	2	yes	—
467	#388	C₂²×C₅	1	2	yes	—
468	#388	C₂²×C₅	1	2	yes	—
469	#388	C₂²×C₅	1	2	yes	—
470	#388	C₂²×C₅	1	2	yes	—
471	#387	C₂²×C₅	1	2	yes	—
472	#387	C₂²×C₅	1	2	yes	—
473	#386	C₂²×C₅	1	2	yes	—
474	#386	C₂²×C₅	1	2	yes	—
475	#386	C₂²×C₅	1	2	yes	—
476	#385	C₂²×C₅	1	2	yes	—
477	#385	C₂²×C₅	1	2	yes	—
478	#385	C₂²×C₅	1	2	yes	—
479	#384	C₂²×C₅	1	1	yes	characteristic
480	#384	C₂²×C₅	1	1	yes	characteristic
481	#384	C₂²×C₅	1	1	yes	characteristic
482	#382	C₂²×C₅	1	2	yes	—
483	#381	C₂²×C₅	1	2	yes	—
484	#380	C₂²×C₅	1	1	yes	characteristic
485	#380	C₂²×C₅	1	1	yes	characteristic
486	#380	C₂²×C₅	1	1	yes	characteristic
487	#380	C₂²×C₅	1	2	yes	—
488	#380	C₂²×C₅	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
490	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
491	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
493	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
494	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
496	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
497	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
498	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
499	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
500	C₂×#95	C₂²×C₅	1	2	yes	—
501	C₄³	C₂²×C₅	1	1	yes	characteristic
502	C₂³×C₅	—	2	1	no	—
503	C₂³×C₅	—	2	1	no	—
504	C₂³×C₅	—	2	1	no	—
505	C₂³×C₅	—	2	1	no	—
506	C₂³×C₅	—	2	1	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	—	2	1	no	—
510	C₂³×C₅	—	2	1	no	—
511	C₂³×C₅	—	2	1	no	—
512	C₂³×C₅	—	2	2	no	—
513	C₂³×C₅	—	2	2	no	—
514	C₂³×C₅	—	2	2	no	—
515	C₂³×C₅	—	2	2	no	—
516	C₂³×C₅	—	2	2	no	—
517	C₂³×C₅	—	2	2	no	—
518	C₂³×C₅	—	2	2	no	—
519	C₂³×C₅	C₂²×D₄	1	2	yes	—
520	C₂³×C₅	C₂²×D₄	1	2	yes	—
521	C₂³×C₅	C₂×#41	1	2	yes	—
522	C₂³×C₅	C₂×#41	1	2	yes	—
523	C₂³×C₅	C₂⁵	1	1	yes	characteristic
524	C₅×Q₈	—	8	4	no	—
525	C₅×D₄	—	2	8	no	—
526	C₅×D₄	—	4	8	no	—
527	C₅×D₄	—	4	4	no	—
528	C₅×D₄	—	8	4	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	1	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	8	no	—
548	C₂×C₄×C₅	—	2	2	no	—
549	C₂×C₄×C₅	—	2	2	no	—
550	C₂×C₄×C₅	—	2	2	no	—
551	C₂×C₄×C₅	—	2	2	no	—
552	C₂×C₄×C₅	—	2	2	no	—
553	C₂×C₄×C₅	—	2	2	no	—
554	C₂×C₄×C₅	—	2	2	no	—
555	C₂×C₄×C₅	—	2	1	no	—
556	C₂×C₄×C₅	—	2	2	no	—
557	C₂×C₄×C₅	—	2	2	no	—
558	C₂×C₄×C₅	—	2	1	no	—
559	C₂×C₄×C₅	—	2	1	no	—
560	C₂×C₄×C₅	—	2	2	no	—
561	C₂×C₄×C₅	—	2	2	no	—
562	C₂×C₄×C₅	—	2	2	no	—
563	C₂×C₄×C₅	—	2	2	no	—
564	C₂×C₄×C₅	—	2	1	no	—
565	C₂×C₄×C₅	—	2	1	no	—
566	C₂×C₄×C₅	—	2	2	no	—
567	C₂×C₄×C₅	—	2	2	no	—
568	C₂×C₄×C₅	—	2	2	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	2	no	—
571	C₂×C₄×C₅	—	2	2	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	1	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	2	2	no	—
576	C₂×C₄×C₅	—	2	2	no	—
577	C₂×C₄×C₅	—	2	2	no	—
578	C₂×C₄×C₅	—	4	4	no	—
579	C₂×C₄×C₅	—	4	4	no	—
580	C₂×C₄×C₅	—	4	4	no	—
581	C₂×C₄×C₅	—	4	4	no	—
582	C₂×C₄×C₅	—	4	8	no	—
583	C₂×C₄×C₅	—	4	4	no	—
584	C₂×C₄×C₅	—	8	4	no	—
585	C₂×C₄×C₅	—	8	4	no	—
586	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
587	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
588	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
589	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
590	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
591	C₂×C₄×C₅	C₂×#41	1	2	yes	—
592	C₂×C₄×C₅	C₂×#41	1	2	yes	—
593	C₂×C₄×C₅	C₂×#41	1	2	yes	—
594	C₂×C₄×C₅	C₂×#41	1	2	yes	—
595	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
596	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
597	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
598	C₂²×Q₈	C₂³×C₅	1	2	yes	—
599	C₂²×D₄	C₂³×C₅	1	2	yes	—
600	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
602	C₂²×D₄	C₂³×C₅	1	2	yes	—
603	C₂³×C₄	C₂³×C₅	1	2	yes	—
604	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₅	1	2	yes	—
609	C₂³×C₄	C₂³×C₅	1	2	yes	—
610	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
612	C₄⋊Q₈	—	4	2	no	—
613	#126	—	2	8	no	—
614	#126	—	2	8	no	—
615	#125	—	2	8	no	—
616	#125	—	2	8	no	—
617	#123	—	2	8	no	—
618	#123	—	2	8	no	—
619	#123	—	2	8	no	—
620	#123	—	2	8	no	—
621	#123	—	2	8	no	—
622	C₂²⋊Q₈	—	2	8	no	—
623	C₂²⋊Q₈	—	2	8	no	—
624	C₂²⋊Q₈	—	2	8	no	—
625	#121	—	2	8	no	—
626	#121	—	2	4	no	—
627	#121	—	4	2	no	—
628	C₄×D₄	—	2	8	no	—
629	C₄×D₄	—	2	4	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	4	2	no	—
632	C₄×D₄	C₅×D₄	1	8	yes	complemented
633	C₂×C₄⋊C₄	—	2	8	no	—
634	C₂×C₄⋊C₄	—	2	4	no	—
635	C₂×C₄⋊C₄	—	4	2	no	—
636	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
686	C₂×C₄²	—	4	2	no	—
687	C₂×C₄²	—	4	2	no	—
688	C₂×C₄²	C₂³×C₅	1	2	yes	—
689	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
702	#95	C₂³×C₅	1	2	yes	—
703	#95	C₂³×C₅	1	2	yes	—
704	#95	C₂³×C₅	1	2	yes	—
705	#95	C₂³×C₅	1	2	yes	—
706	#95	C₂³×C₅	1	1	yes	characteristic
707	#95	C₂³×C₅	1	1	yes	characteristic
708	#95	C₂³×C₅	1	1	yes	characteristic
709	#95	C₂³×C₅	1	1	yes	characteristic
710	#95	C₂³×C₅	1	1	yes	characteristic
711	#95	C₂³×C₅	1	1	yes	characteristic
712	#95	C₂³×C₅	1	2	yes	—
713	#95	C₂³×C₅	1	2	yes	—
714	#95	C₂³×C₅	1	2	yes	—
715	#95	C₂³×C₅	1	2	yes	—
716	#95	C₂³×C₅	1	2	yes	—
717	#95	C₂³×C₅	1	2	yes	—
718	#95	C₂³×C₅	1	2	yes	—
719	#95	C₂³×C₅	1	2	yes	—
720	#95	C₂³×C₅	1	2	yes	—
721	#95	C₂³×C₅	1	2	yes	—
722	#95	C₂³×C₅	1	2	yes	—
723	C₂²×C₅	—	2	2	no	—
724	C₂²×C₅	—	2	2	no	—
725	C₂²×C₅	—	2	2	no	—
726	C₂²×C₅	—	2	2	no	—
727	C₂²×C₅	—	2	2	no	—
728	C₂²×C₅	—	2	2	no	—
729	C₂²×C₅	—	2	2	no	—
730	C₂²×C₅	—	2	2	no	—
731	C₂²×C₅	—	2	2	no	—
732	C₂²×C₅	—	4	1	no	—
733	C₂²×C₅	—	4	1	no	—
734	C₂²×C₅	—	4	1	no	—
735	C₂²×C₅	—	4	1	no	—
736	C₂²×C₅	—	4	2	no	—
737	C₂²×C₅	—	4	2	no	—
738	C₂²×C₅	—	4	2	no	—
739	C₂²×C₅	—	4	2	no	—
740	C₂²×C₅	—	4	2	no	—
741	C₂²×C₅	—	4	2	no	—
742	C₂²×C₅	—	4	2	no	—
743	C₂²×C₅	#532	1	4	yes	—
744	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
745	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
746	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
747	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
749	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
750	C₂²×C₅	#585	1	1	yes	characteristic
751	C₄×C₅	—	2	2	no	—
752	C₄×C₅	—	2	2	no	—
753	C₄×C₅	—	2	2	no	—
754	C₄×C₅	—	2	2	no	—
755	C₄×C₅	—	2	2	no	—
756	C₄×C₅	—	2	2	no	—
757	C₄×C₅	—	2	2	no	—
758	C₄×C₅	—	2	2	no	—
759	C₄×C₅	—	2	2	no	—
760	C₄×C₅	—	4	2	no	—
761	C₄×C₅	—	4	2	no	—
762	C₄×C₅	—	4	2	no	—
763	C₄×C₅	—	4	1	no	—
764	C₄×C₅	—	4	1	no	—
765	C₄×C₅	—	4	2	no	—
766	C₄×C₅	—	4	2	no	—
767	C₄×C₅	—	4	2	no	—
768	C₄×C₅	—	4	2	no	—
769	C₄×C₅	—	4	1	no	—
770	C₄×C₅	#539	1	4	yes	complemented
771	C₂⁴	C₂⁴×C₅	1	2	yes	—
772	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
774	C₂×Q₈	—	2	4	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	4	1	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	1	no	—
807	C₂²×C₄	—	4	1	no	—
808	C₂²×C₄	—	4	1	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
814	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
815	C₂²×C₄	C₅×#41	1	4	yes	—
816	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	4	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	4	no	—
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	4	2	no	—
862	C₄⋊C₄	—	4	2	no	—
863	C₄⋊C₄	—	4	2	no	—
864	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	4	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
884	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
885	C₂²⋊C₄	C₅×#41	1	4	yes	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	1	no	—
896	C₄²	—	4	1	no	—
897	C₄²	—	4	1	no	—
898	C₄²	—	4	1	no	—
899	C₄²	C₂×C₅×D₄	1	4	yes	—
900	C₂×C₅	—	2	4	no	—
901	C₂×C₅	—	4	2	no	—
902	C₂×C₅	—	8	2	no	—
903	C₂×C₅	C₂×#532	1	1	yes	characteristic
904	C₂×C₅	C₂×#539	1	1	yes	characteristic
905	C₂×C₅	#3461	1	1	yes	characteristic
906	C₂×C₅	#3496	1	1	yes	characteristic
907	C₂×C₅	#3499	1	1	yes	characteristic
908	C₂×C₅	#3515	1	1	yes	characteristic
909	C₂×C₅	#3520	1	1	yes	characteristic
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	C₂²×C₅×D₄	1	2	yes	—
928	C₂³	C₂²×C₅×D₄	1	2	yes	—
929	C₂³	C₂×C₅×#41	1	2	yes	—
930	C₂³	C₂×C₅×#41	1	2	yes	—
931	C₂³	C₂⁵×C₅	1	1	yes	characteristic
932	Q₈	—	8	4	no	—
933	D₄	—	2	8	no	—
934	D₄	—	4	8	no	—
935	D₄	—	4	4	no	—
936	D₄	—	8	4	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	8	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	4	4	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	8	4	no	—
993	C₂×C₄	—	8	4	no	—
994	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
995	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
996	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
997	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
998	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
999	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1000	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1001	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1002	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1003	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1004	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
1005	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
1006	C₅	#35008	1	1	yes	characteristic, direct product factor, Sylow
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	C₅×#532	1	4	yes	—
1028	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1029	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1030	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1031	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1033	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1034	C₂²	C₅×#585	1	1	yes	characteristic
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	C₅×#539	1	4	yes	complemented
1055	C₂	—	2	4	no	—
1056	C₂	—	4	2	no	—
1057	C₂	—	8	2	no	—
1058	C₂	C₂×C₅×#532	1	1	yes	characteristic
1059	C₂	C₂×C₅×#539	1	1	yes	characteristic
1060	C₂	C₅×#3461	1	1	yes	characteristic
1061	C₂	C₅×#3496	1	1	yes	characteristic
1062	C₂	C₅×#3499	1	1	yes	characteristic
1063	C₂	C₅×#3515	1	1	yes	characteristic
1064	C₂	C₅×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₅×#2416	C₂
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×#539	C₂	semidirect
2. C₅×#2860	C₂	semidirect
3. C₅×#2859	C₂	semidirect
4. C₅×#2857	C₂	semidirect
5. C₅×#2854	C₂	semidirect
6. C₅×#2664	C₂	semidirect
7. C₅×#2663	C₂	semidirect
8. C₅×#2556	C₂	semidirect
9. C₅×#2553	C₂	semidirect
10. C₅×#2506	C₂	semidirect
11. C₅×#2501	C₂	semidirect
12. C₅×#2496	C₂	semidirect
13. C₅×#2488	C₂	semidirect
14. C₅×#2486	C₂	semidirect
15. C₅×#2452	C₂	semidirect
16. C₅×#2440	C₂	semidirect
17. C₅×#2425	C₂	semidirect
18. C₅×#2422	C₂	semidirect
20. C₅×#2322	C₂	semidirect
21. C₄×C₅×#121	C₂	semidirect
22. C₂×C₅×#389	C₂	semidirect
23. C₄²×C₅×D₄	C₂	semidirect
124. #35008	C₅	direct (N × H)
159. C₄×C₅×D₄	D₄	semidirect
250. C₂×#539	C₂×C₅	semidirect
251. #2860	C₂×C₅	semidirect
252. #2859	C₂×C₅	semidirect
253. #2857	C₂×C₅	semidirect
254. #2854	C₂×C₅	semidirect
255. #2664	C₂×C₅	semidirect
256. #2663	C₂×C₅	semidirect
257. #2556	C₂×C₅	semidirect
258. #2553	C₂×C₅	semidirect
259. #2506	C₂×C₅	semidirect
260. #2501	C₂×C₅	semidirect
261. #2496	C₂×C₅	semidirect
262. #2488	C₂×C₅	semidirect
263. #2486	C₂×C₅	semidirect
264. #2452	C₂×C₅	semidirect
265. #2440	C₂×C₅	semidirect
266. #2425	C₂×C₅	semidirect
267. #2422	C₂×C₅	semidirect
269. #2322	C₂×C₅	semidirect
270. C₄×#121	C₂×C₅	semidirect
271. C₂×#389	C₂×C₅	semidirect
272. C₄²×D₄	C₂×C₅	semidirect
632. C₄×D₄	C₅×D₄	semidirect
770. C₄×C₅	#539	semidirect
1006. C₅	#35008	direct (N × H)
1054. C₄	C₅×#539	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#539	2
C₅×#2860	2
C₅×#2859	2
C₅×#2857	2
C₅×#2854	2
C₅×#2664	2
C₅×#2663	2
C₅×#2556	2
C₅×#2553	2
C₅×#2506	2
C₅×#2501	2
C₅×#2496	2
C₅×#2488	2
C₅×#2486	2
C₅×#2452	2
C₅×#2440	2
C₅×#2425	2
C₅×#2422	2
C₅×#2416	2
C₅×#2322	2
C₄×C₅×#121	2
C₂×C₅×#389	2
C₄²×C₅×D₄	2
#35008	5

Subgroups — C5×#35008 #11957728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35008 #11957728