Subgroups — C₅×#35034 #11957754

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2852	C₂	1	2	yes	maximal, complemented
2	C₅×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2847	C₂	1	1	yes	maximal, characteristic
4	C₅×#2646	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2639	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2622	C₂	1	2	yes	maximal, complemented
7	C₅×#2578	C₂	1	2	yes	maximal, complemented
8	C₅×#2577	C₂	1	2	yes	maximal, complemented
9	C₅×#2560	C₂	1	2	yes	maximal, complemented
10	C₅×#2559	C₂	1	2	yes	maximal, complemented
11	C₅×#2531	C₂	1	2	yes	maximal, complemented
12	C₅×#2530	C₂	1	2	yes	maximal, complemented
13	C₅×#2477	C₂	1	2	yes	maximal, complemented
14	C₅×#2476	C₂	1	2	yes	maximal, complemented
15	C₅×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2325	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2321	C₂	1	2	yes	maximal, complemented
18	C₅×#2290	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#126	C₂²	1	2	yes	complemented
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#121	C₂²	1	1	yes	characteristic
26	C₂×C₅×#121	C₂²	1	1	yes	characteristic
27	C₂×C₅×#121	C₂²	1	1	yes	characteristic
28	C₂×C₅×#120	C₂²	1	2	yes	—
29	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₂×C₅×#117	C₂²	1	2	yes	complemented
31	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₅×#400	C₂²	1	2	yes	complemented
36	C₅×#400	C₂²	1	2	yes	complemented
37	C₅×#400	C₂²	1	2	yes	complemented
38	C₅×#398	C₂²	1	2	yes	complemented
39	C₅×#398	C₂²	1	2	yes	complemented
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	complemented
45	C₅×#394	C₂²	1	2	yes	—
46	C₅×#394	C₂²	1	2	yes	—
47	C₅×#394	C₂²	1	2	yes	—
48	C₅×#394	C₂²	1	2	yes	—
49	C₅×#394	C₂²	1	2	yes	complemented
50	C₅×#393	C₂²	1	2	yes	complemented
51	C₅×#391	C₂²	1	2	yes	complemented
52	C₅×#390	C₂²	1	2	yes	—
53	C₅×#390	C₂²	1	2	yes	—
54	C₅×#389	C₂²	1	2	yes	complemented
55	C₅×#388	C₂²	1	2	yes	—
56	C₅×#388	C₂²	1	2	yes	—
57	C₅×#388	C₂²	1	2	yes	—
58	C₅×#388	C₂²	1	2	yes	—
59	C₅×#388	C₂²	1	2	yes	complemented
60	C₅×#388	C₂²	1	2	yes	complemented
61	C₅×#388	C₂²	1	2	yes	complemented
62	C₅×#388	C₂²	1	2	yes	complemented
63	C₅×#388	C₂²	1	2	yes	complemented
64	C₅×#388	C₂²	1	2	yes	complemented
65	C₅×#387	C₂²	1	2	yes	complemented
66	C₅×#387	C₂²	1	2	yes	complemented
67	C₅×#387	C₂²	1	2	yes	complemented
68	C₅×#387	C₂²	1	2	yes	complemented
69	C₅×#387	C₂²	1	2	yes	complemented
70	C₅×#387	C₂²	1	2	yes	complemented
71	C₅×#387	C₂²	1	2	yes	complemented
72	C₅×#387	C₂²	1	2	yes	complemented
73	C₅×#386	C₂²	1	2	yes	—
74	C₅×#386	C₂²	1	2	yes	—
75	C₅×#386	C₂²	1	2	yes	—
76	C₅×#386	C₂²	1	2	yes	—
77	C₅×#386	C₂²	1	2	yes	—
78	C₅×#386	C₂²	1	2	yes	—
79	C₅×#386	C₂²	1	2	yes	—
80	C₅×#386	C₂²	1	2	yes	—
81	C₅×#386	C₂²	1	2	yes	complemented
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#385	C₂²	1	2	yes	—
84	C₅×#385	C₂²	1	2	yes	—
85	C₅×#385	C₂²	1	2	yes	—
86	C₅×#385	C₂²	1	2	yes	—
87	C₅×#385	C₂²	1	2	yes	—
88	C₅×#385	C₂²	1	2	yes	complemented
89	C₅×#383	C₂²	1	2	yes	complemented
90	C₅×#380	C₂²	1	1	yes	characteristic
91	C₅×#380	C₂²	1	1	yes	characteristic
92	C₅×#380	C₂²	1	1	yes	characteristic
93	C₅×#380	C₂²	1	1	yes	characteristic
94	C₅×#380	C₂²	1	1	yes	characteristic
95	C₅×#380	C₂²	1	1	yes	characteristic
96	C₅×#379	C₂²	1	2	yes	—
97	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	C₅×#376	C₂²	1	2	yes	complemented
105	C₂×C₅×#95	C₂²	1	1	yes	characteristic
106	C₂×C₅×#95	C₂²	1	1	yes	characteristic
107	#35034	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₅×D₄	C₂³	1	2	yes	—
111	C₂²×C₅×D₄	C₂³	1	2	yes	—
112	C₂²×C₅×D₄	C₂³	1	2	yes	—
113	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅	—	2	4	no	—
115	C₂³×C₄×C₅	—	4	2	no	—
116	C₂³×C₄×C₅	—	4	2	no	—
117	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₅	C₂³	1	2	yes	—
126	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₅×#126	—	4	4	no	—
129	C₅×C₂²⋊Q₈	—	2	4	no	—
130	C₅×C₂²⋊Q₈	—	4	2	no	—
131	C₅×C₂²⋊Q₈	—	4	2	no	—
132	C₅×#121	—	2	4	no	—
133	C₅×#121	—	4	2	no	—
134	C₅×#121	—	4	2	no	—
135	C₅×#120	—	2	8	no	—
136	C₄×C₅×D₄	—	2	8	no	—
137	C₅×#117	—	4	4	no	—
138	C₂×C₅×C₄⋊C₄	C₂³	1	2	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	2	yes	—
142	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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×C₂²⋊C₄	—	2	4	no	—
155	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
156	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₅	—	4	2	no	—
180	C₂×C₄²×C₅	—	4	2	no	—
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	C₅×#95	C₂³	1	2	yes	—
189	C₅×#95	C₂³	1	2	yes	—
190	C₅×#95	C₂³	1	2	yes	—
191	C₅×#95	C₂³	1	2	yes	—
192	C₅×#95	C₂³	1	2	yes	—
193	C₅×#95	C₂³	1	2	yes	—
194	C₅×#95	C₂³	1	2	yes	—
195	C₅×#95	C₂³	1	2	yes	—
196	C₅×#95	C₂³	1	2	yes	—
197	C₅×#95	C₂³	1	2	yes	—
198	C₅×#95	C₂³	1	2	yes	—
199	C₅×#95	C₂³	1	2	yes	—
200	C₅×#95	C₂³	1	2	yes	—
201	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
207	C₅×#95	C₂³	1	2	yes	—
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	#2852	C₂×C₅	1	2	yes	complemented
213	#2848	C₂×C₅	1	1	yes	characteristic, complemented
214	#2847	C₂×C₅	1	1	yes	characteristic
215	#2646	C₂×C₅	1	1	yes	characteristic, complemented
216	#2639	C₂×C₅	1	1	yes	characteristic, complemented
217	#2622	C₂×C₅	1	2	yes	complemented
218	#2578	C₂×C₅	1	2	yes	complemented
219	#2577	C₂×C₅	1	2	yes	complemented
220	#2560	C₂×C₅	1	2	yes	complemented
221	#2559	C₂×C₅	1	2	yes	complemented
222	#2531	C₂×C₅	1	2	yes	complemented
223	#2530	C₂×C₅	1	2	yes	complemented
224	#2477	C₂×C₅	1	2	yes	complemented
225	#2476	C₂×C₅	1	2	yes	complemented
226	#2329	C₂×C₅	1	1	yes	characteristic, complemented
227	#2325	C₂×C₅	1	1	yes	characteristic, complemented
228	#2321	C₂×C₅	1	2	yes	complemented
229	#2290	C₂×C₅	1	2	yes	complemented
230	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
231	C₂⁴×C₅	—	2	2	no	—
232	C₂⁴×C₅	—	2	2	no	—
233	C₂⁴×C₅	—	4	1	no	—
234	C₂⁴×C₅	—	4	1	no	—
235	C₂⁴×C₅	—	4	1	no	—
236	C₂⁴×C₅	—	4	1	no	—
237	C₂⁴×C₅	#41	1	4	yes	—
238	C₂⁴×C₅	C₂⁴	1	2	yes	—
239	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
242	C₂×C₅×Q₈	—	2	2	no	—
243	C₂×C₅×Q₈	—	4	1	no	—
244	C₂×C₅×Q₈	—	4	1	no	—
245	C₂×C₅×D₄	—	2	4	no	—
246	C₂×C₅×D₄	—	2	4	no	—
247	C₂×C₅×D₄	—	2	4	no	—
248	C₂×C₅×D₄	—	2	4	no	—
249	C₂×C₅×D₄	—	2	4	no	—
250	C₂×C₅×D₄	—	2	2	no	—
251	C₂×C₅×D₄	—	4	1	no	—
252	C₂×C₅×D₄	—	4	1	no	—
253	C₂×C₅×D₄	—	4	2	no	—
254	C₂×C₅×D₄	—	4	2	no	—
255	C₂×C₅×D₄	—	4	2	no	—
256	C₂×C₅×D₄	—	4	2	no	—
257	C₂²×C₄×C₅	—	2	2	no	—
258	C₂²×C₄×C₅	—	2	2	no	—
259	C₂²×C₄×C₅	—	2	2	no	—
260	C₂²×C₄×C₅	—	2	2	no	—
261	C₂²×C₄×C₅	—	2	2	no	—
262	C₂²×C₄×C₅	—	2	2	no	—
263	C₂²×C₄×C₅	—	2	4	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	—	2	2	no	—
270	C₂²×C₄×C₅	—	2	2	no	—
271	C₂²×C₄×C₅	—	2	2	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	1	no	—
276	C₂²×C₄×C₅	—	4	2	no	—
277	C₂²×C₄×C₅	—	4	1	no	—
278	C₂²×C₄×C₅	—	4	1	no	—
279	C₂²×C₄×C₅	—	4	1	no	—
280	C₂²×C₄×C₅	—	4	1	no	—
281	C₂²×C₄×C₅	—	4	1	no	—
282	C₂²×C₄×C₅	—	4	1	no	—
283	C₂²×C₄×C₅	—	4	1	no	—
284	C₂²×C₄×C₅	—	4	2	no	—
285	C₂²×C₄×C₅	—	4	1	no	—
286	C₂²×C₄×C₅	—	4	1	no	—
287	C₂²×C₄×C₅	—	4	1	no	—
288	C₂²×C₄×C₅	—	4	16	no	—
289	C₂²×C₄×C₅	#41	1	4	yes	—
290	C₂²×C₄×C₅	#41	1	4	yes	—
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₅×C₄⋊C₄	—	2	4	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	2	4	no	—
310	C₅×C₄⋊C₄	—	2	4	no	—
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	4	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	1	no	—
317	C₅×C₄⋊C₄	—	4	1	no	—
318	C₅×C₄⋊C₄	—	4	1	no	—
319	C₅×C₄⋊C₄	—	4	1	no	—
320	C₅×C₄⋊C₄	—	4	2	no	—
321	C₅×C₄⋊C₄	—	4	2	no	—
322	C₅×C₂²⋊C₄	—	2	4	no	—
323	C₅×C₂²⋊C₄	—	2	4	no	—
324	C₅×C₂²⋊C₄	—	2	4	no	—
325	C₅×C₂²⋊C₄	—	2	4	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	—	2	4	no	—
331	C₅×C₂²⋊C₄	—	2	4	no	—
332	C₅×C₂²⋊C₄	—	2	4	no	—
333	C₅×C₂²⋊C₄	—	2	4	no	—
334	C₅×C₂²⋊C₄	—	2	4	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	C₅×C₂²⋊C₄	—	4	2	no	—
341	C₅×C₂²⋊C₄	—	4	2	no	—
342	C₅×C₂²⋊C₄	—	4	2	no	—
343	C₅×C₂²⋊C₄	—	4	2	no	—
344	C₅×C₂²⋊C₄	—	4	2	no	—
345	C₄²×C₅	—	2	4	no	—
346	C₄²×C₅	—	2	4	no	—
347	C₄²×C₅	—	2	4	no	—
348	C₄²×C₅	—	4	2	no	—
349	C₄²×C₅	—	4	2	no	—
350	C₄²×C₅	—	4	2	no	—
351	C₄²×C₅	—	4	2	no	—
352	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
353	C₂×#126	C₂²×C₅	1	2	yes	complemented
354	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
355	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
356	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
357	C₂×#121	C₂²×C₅	1	1	yes	characteristic
358	C₂×#121	C₂²×C₅	1	1	yes	characteristic
359	C₂×#121	C₂²×C₅	1	1	yes	characteristic
360	C₂×#120	C₂²×C₅	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
362	C₂×#117	C₂²×C₅	1	2	yes	complemented
363	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
365	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
366	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
367	#400	C₂²×C₅	1	2	yes	complemented
368	#400	C₂²×C₅	1	2	yes	complemented
369	#400	C₂²×C₅	1	2	yes	complemented
370	#398	C₂²×C₅	1	2	yes	complemented
371	#398	C₂²×C₅	1	2	yes	complemented
372	#397	C₂²×C₅	1	2	yes	—
373	#397	C₂²×C₅	1	2	yes	—
374	#397	C₂²×C₅	1	2	yes	—
375	#397	C₂²×C₅	1	2	yes	—
376	#397	C₂²×C₅	1	2	yes	complemented
377	#394	C₂²×C₅	1	2	yes	—
378	#394	C₂²×C₅	1	2	yes	—
379	#394	C₂²×C₅	1	2	yes	—
380	#394	C₂²×C₅	1	2	yes	—
381	#394	C₂²×C₅	1	2	yes	complemented
382	#393	C₂²×C₅	1	2	yes	complemented
383	#391	C₂²×C₅	1	2	yes	complemented
384	#390	C₂²×C₅	1	2	yes	—
385	#390	C₂²×C₅	1	2	yes	—
386	#389	C₂²×C₅	1	2	yes	complemented
387	#388	C₂²×C₅	1	2	yes	—
388	#388	C₂²×C₅	1	2	yes	—
389	#388	C₂²×C₅	1	2	yes	—
390	#388	C₂²×C₅	1	2	yes	—
391	#388	C₂²×C₅	1	2	yes	complemented
392	#388	C₂²×C₅	1	2	yes	complemented
393	#388	C₂²×C₅	1	2	yes	complemented
394	#388	C₂²×C₅	1	2	yes	complemented
395	#388	C₂²×C₅	1	2	yes	complemented
396	#388	C₂²×C₅	1	2	yes	complemented
397	#387	C₂²×C₅	1	2	yes	complemented
398	#387	C₂²×C₅	1	2	yes	complemented
399	#387	C₂²×C₅	1	2	yes	complemented
400	#387	C₂²×C₅	1	2	yes	complemented
401	#387	C₂²×C₅	1	2	yes	complemented
402	#387	C₂²×C₅	1	2	yes	complemented
403	#387	C₂²×C₅	1	2	yes	complemented
404	#387	C₂²×C₅	1	2	yes	complemented
405	#386	C₂²×C₅	1	2	yes	—
406	#386	C₂²×C₅	1	2	yes	—
407	#386	C₂²×C₅	1	2	yes	—
408	#386	C₂²×C₅	1	2	yes	—
409	#386	C₂²×C₅	1	2	yes	—
410	#386	C₂²×C₅	1	2	yes	—
411	#386	C₂²×C₅	1	2	yes	—
412	#386	C₂²×C₅	1	2	yes	—
413	#386	C₂²×C₅	1	2	yes	complemented
414	#385	C₂²×C₅	1	2	yes	—
415	#385	C₂²×C₅	1	2	yes	—
416	#385	C₂²×C₅	1	2	yes	—
417	#385	C₂²×C₅	1	2	yes	—
418	#385	C₂²×C₅	1	2	yes	—
419	#385	C₂²×C₅	1	2	yes	—
420	#385	C₂²×C₅	1	2	yes	complemented
421	#383	C₂²×C₅	1	2	yes	complemented
422	#380	C₂²×C₅	1	1	yes	characteristic
423	#380	C₂²×C₅	1	1	yes	characteristic
424	#380	C₂²×C₅	1	1	yes	characteristic
425	#380	C₂²×C₅	1	1	yes	characteristic
426	#380	C₂²×C₅	1	1	yes	characteristic
427	#380	C₂²×C₅	1	1	yes	characteristic
428	#379	C₂²×C₅	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
430	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
436	#376	C₂²×C₅	1	2	yes	complemented
437	C₂×#95	C₂²×C₅	1	1	yes	characteristic
438	C₂×#95	C₂²×C₅	1	1	yes	characteristic
439	C₂³×C₅	—	2	1	no	—
440	C₂³×C₅	—	2	1	no	—
441	C₂³×C₅	—	2	1	no	—
442	C₂³×C₅	—	2	1	no	—
443	C₂³×C₅	—	2	8	no	—
444	C₂³×C₅	—	2	1	no	—
445	C₂³×C₅	—	2	1	no	—
446	C₂³×C₅	—	2	1	no	—
447	C₂³×C₅	—	2	1	no	—
448	C₂³×C₅	—	2	1	no	—
449	C₂³×C₅	—	2	1	no	—
450	C₂³×C₅	—	2	1	no	—
451	C₂³×C₅	—	2	1	no	—
452	C₂³×C₅	—	2	1	no	—
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	—	2	1	no	—
455	C₂³×C₅	—	2	1	no	—
456	C₂³×C₅	—	2	2	no	—
457	C₂³×C₅	—	2	2	no	—
458	C₂³×C₅	—	2	2	no	—
459	C₂³×C₅	—	2	2	no	—
460	C₂³×C₅	—	2	2	no	—
461	C₂³×C₅	—	2	2	no	—
462	C₂³×C₅	—	2	2	no	—
463	C₂³×C₅	—	4	4	no	—
464	C₂³×C₅	—	4	4	no	—
465	C₂³×C₅	—	4	4	no	—
466	C₂³×C₅	—	4	4	no	—
467	C₂³×C₅	—	4	4	no	—
468	C₂³×C₅	—	4	4	no	—
469	C₂³×C₅	C₂×#41	1	2	yes	—
470	C₂³×C₅	C₂×#41	1	2	yes	—
471	C₂³×C₅	C₂×#41	1	2	yes	—
472	C₂³×C₅	C₂×#41	1	2	yes	—
473	C₂³×C₅	C₂×#41	1	2	yes	—
474	C₂³×C₅	C₂⁵	1	1	yes	characteristic
475	C₅×Q₈	—	8	2	no	—
476	C₅×D₄	—	4	8	no	—
477	C₅×D₄	—	8	2	no	—
478	C₅×D₄	—	8	4	no	—
479	C₅×D₄	—	8	4	no	—
480	C₂×C₄×C₅	—	2	8	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	2	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	1	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	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	2	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	2	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	2	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	—	2	2	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	4	4	no	—
522	C₂×C₄×C₅	—	4	4	no	—
523	C₂×C₄×C₅	—	4	4	no	—
524	C₂×C₄×C₅	—	4	4	no	—
525	C₂×C₄×C₅	—	4	4	no	—
526	C₂×C₄×C₅	—	4	4	no	—
527	C₂×C₄×C₅	—	4	8	no	—
528	C₂×C₄×C₅	—	4	4	no	—
529	C₂×C₄×C₅	—	4	4	no	—
530	C₂×C₄×C₅	—	4	4	no	—
531	C₂×C₄×C₅	C₂×#41	1	4	yes	—
532	C₂×C₄×C₅	C₂×#41	1	2	yes	—
533	C₂×C₄×C₅	C₂×#41	1	2	yes	—
534	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
535	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
536	C₂⁵	C₂³×C₅	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₅	1	2	yes	—
539	C₂²×D₄	C₂³×C₅	1	2	yes	—
540	C₂²×D₄	C₂³×C₅	1	2	yes	—
541	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
542	C₂³×C₄	—	2	4	no	—
543	C₂³×C₄	—	4	2	no	—
544	C₂³×C₄	—	4	2	no	—
545	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₅	1	2	yes	—
554	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
556	#126	—	4	4	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	—	4	2	no	—
559	C₂²⋊Q₈	—	4	2	no	—
560	#121	—	2	4	no	—
561	#121	—	4	2	no	—
562	#121	—	4	2	no	—
563	#120	—	2	8	no	—
564	C₄×D₄	—	2	8	no	—
565	#117	—	4	4	no	—
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	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
582	C₂×C₂²⋊C₄	—	2	4	no	—
583	C₂×C₂²⋊C₄	—	2	4	no	—
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×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
607	C₂×C₄²	—	4	2	no	—
608	C₂×C₄²	—	4	2	no	—
609	C₂×C₄²	C₂³×C₅	1	2	yes	—
610	C₂×C₄²	C₂³×C₅	1	2	yes	—
611	C₂×C₄²	C₂³×C₅	1	2	yes	—
612	C₂×C₄²	C₂³×C₅	1	2	yes	—
613	C₂×C₄²	C₂³×C₅	1	2	yes	—
614	C₂×C₄²	C₂³×C₅	1	2	yes	—
615	C₂×C₄²	C₂³×C₅	1	2	yes	—
616	#95	C₂³×C₅	1	2	yes	—
617	#95	C₂³×C₅	1	2	yes	—
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	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	C₂²×C₅	—	2	2	no	—
641	C₂²×C₅	—	2	2	no	—
642	C₂²×C₅	—	2	2	no	—
643	C₂²×C₅	—	2	2	no	—
644	C₂²×C₅	—	2	2	no	—
645	C₂²×C₅	—	2	2	no	—
646	C₂²×C₅	—	2	2	no	—
647	C₂²×C₅	—	2	2	no	—
648	C₂²×C₅	—	2	2	no	—
649	C₂²×C₅	—	2	2	no	—
650	C₂²×C₅	—	2	2	no	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	4	16	no	—
653	C₂²×C₅	—	4	1	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	1	no	—
659	C₂²×C₅	—	4	1	no	—
660	C₂²×C₅	—	4	1	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	—	4	2	no	—
666	C₂²×C₅	—	4	2	no	—
667	C₂²×C₅	—	4	2	no	—
668	C₂²×C₅	#529	1	4	yes	—
669	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
670	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
671	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
672	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂²×C₅	#585	1	1	yes	characteristic
675	C₂²×C₅	#585	1	1	yes	characteristic
676	C₄×C₅	—	2	4	no	—
677	C₄×C₅	—	2	2	no	—
678	C₄×C₅	—	2	2	no	—
679	C₄×C₅	—	2	2	no	—
680	C₄×C₅	—	2	2	no	—
681	C₄×C₅	—	4	2	no	—
682	C₄×C₅	—	4	2	no	—
683	C₄×C₅	—	4	2	no	—
684	C₄×C₅	—	4	2	no	—
685	C₄×C₅	—	4	2	no	—
686	C₄×C₅	—	4	2	no	—
687	C₄×C₅	—	4	2	no	—
688	C₄×C₅	—	4	2	no	—
689	C₄×C₅	—	4	2	no	—
690	C₄×C₅	—	4	2	no	—
691	C₂⁴	—	2	2	no	—
692	C₂⁴	—	2	2	no	—
693	C₂⁴	—	4	1	no	—
694	C₂⁴	—	4	1	no	—
695	C₂⁴	—	4	1	no	—
696	C₂⁴	—	4	1	no	—
697	C₂⁴	C₅×#41	1	4	yes	—
698	C₂⁴	C₂⁴×C₅	1	2	yes	—
699	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
700	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
701	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	4	1	no	—
704	C₂×Q₈	—	4	1	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	1	no	—
748	C₂²×C₄	—	4	16	no	—
749	C₂²×C₄	C₅×#41	1	4	yes	—
750	C₂²×C₄	C₅×#41	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	4	no	—
807	C₄²	—	2	4	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	2	no	—
812	C₂×C₅	—	2	4	no	—
813	C₂×C₅	—	4	2	no	—
814	C₂×C₅	—	4	2	no	—
815	C₂×C₅	—	8	2	no	—
816	C₂×C₅	C₂×#529	1	1	yes	characteristic
817	C₂×C₅	#3459	1	1	yes	characteristic
818	C₂×C₅	#3460	1	1	yes	characteristic
819	C₂×C₅	#3490	1	1	yes	characteristic
820	C₂×C₅	#3493	1	1	yes	characteristic
821	C₂×C₅	#3505	1	1	yes	characteristic
822	C₂×C₅	#3505	1	1	yes	characteristic
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	8	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	4	4	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	4	4	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	4	no	—
853	C₂³	C₂×C₅×#41	1	2	yes	—
854	C₂³	C₂×C₅×#41	1	2	yes	—
855	C₂³	C₂×C₅×#41	1	2	yes	—
856	C₂³	C₂×C₅×#41	1	2	yes	—
857	C₂³	C₂×C₅×#41	1	2	yes	—
858	C₂³	C₂⁵×C₅	1	1	yes	characteristic
859	Q₈	—	8	2	no	—
860	D₄	—	4	8	no	—
861	D₄	—	8	2	no	—
862	D₄	—	8	4	no	—
863	D₄	—	8	4	no	—
864	C₂×C₄	—	2	8	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	4	8	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	C₂×C₅×#41	1	4	yes	—
916	C₂×C₄	C₂×C₅×#41	1	2	yes	—
917	C₂×C₄	C₂×C₅×#41	1	2	yes	—
918	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
919	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
920	C₅	#35034	1	1	yes	characteristic, direct product factor, Sylow
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	4	16	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	C₅×#529	1	4	yes	—
950	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
951	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
952	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
953	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
955	C₂²	C₅×#585	1	1	yes	characteristic
956	C₂²	C₅×#585	1	1	yes	characteristic
957	C₄	—	2	4	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₂	—	2	4	no	—
973	C₂	—	4	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₂×C₅×#529	1	1	yes	characteristic
977	C₂	C₅×#3459	1	1	yes	characteristic
978	C₂	C₅×#3460	1	1	yes	characteristic
979	C₂	C₅×#3490	1	1	yes	characteristic
980	C₂	C₅×#3493	1	1	yes	characteristic
981	C₂	C₅×#3505	1	1	yes	characteristic
982	C₂	C₅×#3505	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₅×#2847	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. C₅×#2852	C₂	semidirect
2. C₅×#2848	C₂	semidirect
4. C₅×#2646	C₂	semidirect
5. C₅×#2639	C₂	semidirect
6. C₅×#2622	C₂	semidirect
7. C₅×#2578	C₂	semidirect
8. C₅×#2577	C₂	semidirect
9. C₅×#2560	C₂	semidirect
10. C₅×#2559	C₂	semidirect
11. C₅×#2531	C₂	semidirect
12. C₅×#2530	C₂	semidirect
13. C₅×#2477	C₂	semidirect
14. C₅×#2476	C₂	semidirect
15. C₅×#2329	C₂	semidirect
16. C₅×#2325	C₂	semidirect
17. C₅×#2321	C₂	semidirect
18. C₅×#2290	C₂	semidirect
19. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
21. C₂×C₅×#126	C₂²	semidirect
30. C₂×C₅×#117	C₂²	semidirect
35. C₅×#400	C₂²	semidirect
36. C₅×#400	C₂²	semidirect
37. C₅×#400	C₂²	semidirect
38. C₅×#398	C₂²	semidirect
39. C₅×#398	C₂²	semidirect
44. C₅×#397	C₂²	semidirect
49. C₅×#394	C₂²	semidirect
50. C₅×#393	C₂²	semidirect
51. C₅×#391	C₂²	semidirect
54. C₅×#389	C₂²	semidirect
59. C₅×#388	C₂²	semidirect
60. C₅×#388	C₂²	semidirect
61. C₅×#388	C₂²	semidirect
62. C₅×#388	C₂²	semidirect
63. C₅×#388	C₂²	semidirect
64. C₅×#388	C₂²	semidirect
65. C₅×#387	C₂²	semidirect
66. C₅×#387	C₂²	semidirect
67. C₅×#387	C₂²	semidirect
68. C₅×#387	C₂²	semidirect
69. C₅×#387	C₂²	semidirect
70. C₅×#387	C₂²	semidirect
71. C₅×#387	C₂²	semidirect
72. C₅×#387	C₂²	semidirect
81. C₅×#386	C₂²	semidirect
88. C₅×#385	C₂²	semidirect
89. C₅×#383	C₂²	semidirect
97. C₄×C₅×C₄⋊C₄	C₂²	semidirect
103. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
104. C₅×#376	C₂²	semidirect
107. #35034	C₅	direct (N × H)
212. #2852	C₂×C₅	semidirect
213. #2848	C₂×C₅	semidirect
215. #2646	C₂×C₅	semidirect
216. #2639	C₂×C₅	semidirect
217. #2622	C₂×C₅	semidirect
218. #2578	C₂×C₅	semidirect
219. #2577	C₂×C₅	semidirect
220. #2560	C₂×C₅	semidirect
221. #2559	C₂×C₅	semidirect
222. #2531	C₂×C₅	semidirect
223. #2530	C₂×C₅	semidirect
224. #2477	C₂×C₅	semidirect
225. #2476	C₂×C₅	semidirect
226. #2329	C₂×C₅	semidirect
227. #2325	C₂×C₅	semidirect
228. #2321	C₂×C₅	semidirect
229. #2290	C₂×C₅	semidirect
230. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
353. C₂×#126	C₂²×C₅	semidirect
362. C₂×#117	C₂²×C₅	semidirect
367. #400	C₂²×C₅	semidirect
368. #400	C₂²×C₅	semidirect
369. #400	C₂²×C₅	semidirect
370. #398	C₂²×C₅	semidirect
371. #398	C₂²×C₅	semidirect
376. #397	C₂²×C₅	semidirect
381. #394	C₂²×C₅	semidirect
382. #393	C₂²×C₅	semidirect
383. #391	C₂²×C₅	semidirect
386. #389	C₂²×C₅	semidirect
391. #388	C₂²×C₅	semidirect
392. #388	C₂²×C₅	semidirect
393. #388	C₂²×C₅	semidirect
394. #388	C₂²×C₅	semidirect
395. #388	C₂²×C₅	semidirect
396. #388	C₂²×C₅	semidirect
397. #387	C₂²×C₅	semidirect
398. #387	C₂²×C₅	semidirect
399. #387	C₂²×C₅	semidirect
400. #387	C₂²×C₅	semidirect
401. #387	C₂²×C₅	semidirect
402. #387	C₂²×C₅	semidirect
403. #387	C₂²×C₅	semidirect
404. #387	C₂²×C₅	semidirect
413. #386	C₂²×C₅	semidirect
420. #385	C₂²×C₅	semidirect
421. #383	C₂²×C₅	semidirect
429. C₄×C₄⋊C₄	C₂²×C₅	semidirect
435. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
436. #376	C₂²×C₅	semidirect
920. C₅	#35034	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×#2852	2
C₅×#2848	2
C₅×#2847	2
C₅×#2646	2
C₅×#2639	2
C₅×#2622	2
C₅×#2578	2
C₅×#2577	2
C₅×#2560	2
C₅×#2559	2
C₅×#2531	2
C₅×#2530	2
C₅×#2477	2
C₅×#2476	2
C₅×#2329	2
C₅×#2325	2
C₅×#2321	2
C₅×#2290	2
C₂×C₄×C₅×C₂²⋊C₄	2
#35034	5

Subgroups — C5×#35034 #11957754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35034 #11957754