Subgroups — C₅×#34457 #11957177

Order 1280.

2500 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#551	C₂	1	1	yes	maximal, characteristic
2	C₅×#2383	C₂	1	2	yes	maximal, complemented
3	C₅×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2360	C₂	1	2	yes	maximal, complemented
6	C₅×#2359	C₂	1	2	yes	maximal, complemented
7	C₅×#2358	C₂	1	1	yes	maximal, characteristic
8	C₅×D₄×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₅×#2343	C₂	1	2	yes	maximal, complemented
10	C₅×#2342	C₂	1	2	yes	maximal, complemented
11	C₅×#2334	C₂	1	2	yes	maximal, complemented
12	C₅×#2329	C₂	1	2	yes	maximal, complemented
13	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2322	C₂	1	2	yes	maximal, complemented
15	C₅×#2322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2318	C₂	1	2	yes	maximal, complemented
17	C₅×#2317	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#120	C₂	1	1	yes	maximal, characteristic
19	C₂×C₅×#385	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₅×#551	C₄	1	16	yes	complemented
22	C₂×C₅×#126	C₂²	1	2	yes	—
23	C₂×C₅×#124	C₂²	1	1	yes	characteristic
24	C₂×C₅×#123	C₂²	1	2	yes	—
25	C₂×C₅×#123	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₅×#120	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₅×#117	C₂²	1	2	yes	—
34	C₂×C₅×#117	C₂²	1	2	yes	—
35	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₅×#391	C₂²	1	1	yes	characteristic, complemented
41	C₅×#391	C₂²	1	2	yes	complemented
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	2	yes	complemented
44	C₅×#389	C₂²	1	2	yes	complemented
45	C₅×#389	C₂²	1	2	yes	complemented
46	C₅×#389	C₂²	1	2	yes	complemented
47	C₅×#389	C₂²	1	2	yes	complemented
48	C₅×#389	C₂²	1	2	yes	complemented
49	C₅×#389	C₂²	1	2	yes	complemented
50	C₅×#388	C₂²	1	2	yes	—
51	C₅×#388	C₂²	1	2	yes	—
52	C₅×#388	C₂²	1	2	yes	—
53	C₅×#388	C₂²	1	2	yes	—
54	C₅×#388	C₂²	1	2	yes	—
55	C₅×#388	C₂²	1	2	yes	complemented
56	C₅×#388	C₂²	1	2	yes	complemented
57	C₅×#388	C₂²	1	2	yes	complemented
58	C₅×#387	C₂²	1	2	yes	complemented
59	C₅×#387	C₂²	1	2	yes	complemented
60	C₅×#387	C₂²	1	2	yes	complemented
61	C₅×#387	C₂²	1	2	yes	complemented
62	C₅×#387	C₂²	1	2	yes	complemented
63	C₅×#387	C₂²	1	2	yes	complemented
64	C₅×#387	C₂²	1	2	yes	complemented
65	C₅×#387	C₂²	1	2	yes	complemented
66	C₅×#386	C₂²	1	2	yes	—
67	C₅×#386	C₂²	1	1	yes	characteristic
68	C₅×#386	C₂²	1	2	yes	—
69	C₅×#386	C₂²	1	1	yes	characteristic
70	C₅×#385	C₂²	1	2	yes	—
71	C₅×#385	C₂²	1	2	yes	—
72	C₅×#385	C₂²	1	2	yes	—
73	C₅×#385	C₂²	1	2	yes	—
74	C₅×#385	C₂²	1	2	yes	—
75	C₅×#385	C₂²	1	2	yes	—
76	C₅×#385	C₂²	1	2	yes	—
77	C₅×#385	C₂²	1	2	yes	—
78	C₅×#385	C₂²	1	2	yes	—
79	C₅×#385	C₂²	1	1	yes	characteristic
80	C₅×#385	C₂²	1	2	yes	—
81	C₅×#385	C₂²	1	2	yes	—
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#385	C₂²	1	1	yes	characteristic, complemented
84	C₅×#385	C₂²	1	2	yes	complemented
85	C₅×#385	C₂²	1	2	yes	complemented
86	C₅×#384	C₂²	1	1	yes	characteristic, complemented
87	C₅×#384	C₂²	1	2	yes	complemented
88	C₅×#383	C₂²	1	2	yes	complemented
89	C₅×#382	C₂²	1	2	yes	complemented
90	C₅×#382	C₂²	1	2	yes	complemented
91	C₅×#381	C₂²	1	2	yes	—
92	C₅×#381	C₂²	1	1	yes	characteristic, complemented
93	C₅×#380	C₂²	1	2	yes	—
94	C₅×#380	C₂²	1	2	yes	complemented
95	C₅×#379	C₂²	1	1	yes	characteristic
96	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	—
104	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₅×#376	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₅×#95	C₂²	1	2	yes	—
107	C₂×C₅×#95	C₂²	1	2	yes	—
108	#34457	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁵×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₅×D₄	C₂³	1	2	yes	—
112	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅	—	4	2	no	—
114	C₂³×C₄×C₅	—	4	4	no	—
115	C₂³×C₄×C₅	C₂³	1	2	yes	—
116	C₂³×C₄×C₅	C₂³	1	2	yes	—
117	C₂³×C₄×C₅	C₂³	1	2	yes	—
118	C₂³×C₄×C₅	C₂³	1	2	yes	—
119	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₅	C₂³	1	2	yes	—
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	2	yes	—
125	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
126	C₅×#126	C₂×C₄	1	16	yes	complemented
127	C₅×#124	C₂×C₄	1	8	yes	complemented
128	C₅×#123	C₂×C₄	1	8	yes	complemented
129	C₅×#123	C₂×C₄	1	16	yes	complemented
130	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
131	C₅×#120	C₂×C₄	1	8	yes	—
132	C₄×C₅×Q₈	—	4	2	no	—
133	C₄×C₅×D₄	—	4	2	no	—
134	C₄×C₅×D₄	—	4	4	no	—
135	C₄×C₅×D₄	—	4	4	no	—
136	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
137	C₅×#117	—	4	4	no	—
138	C₅×#117	C₂×C₄	1	16	yes	complemented
139	C₂×C₅×C₄⋊C₄	—	4	4	no	—
140	C₂×C₅×C₄⋊C₄	—	4	2	no	—
141	C₂×C₅×C₄⋊C₄	—	4	4	no	—
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	2	yes	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
163	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
169	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₅	C₂³	1	2	yes	—
187	C₂×C₄²×C₅	C₂³	1	2	yes	—
188	C₂×C₄²×C₅	C₂³	1	2	yes	—
189	C₂×C₄²×C₅	C₂³	1	2	yes	—
190	C₂×C₄²×C₅	C₂³	1	2	yes	—
191	C₂×C₄²×C₅	C₂³	1	2	yes	—
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	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	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	C₂×#551	C₂×C₅	1	1	yes	characteristic
217	#2383	C₂×C₅	1	2	yes	complemented
218	#2379	C₂×C₅	1	1	yes	characteristic, complemented
219	#2376	C₂×C₅	1	1	yes	characteristic, complemented
220	#2360	C₂×C₅	1	2	yes	complemented
221	#2359	C₂×C₅	1	2	yes	complemented
222	#2358	C₂×C₅	1	1	yes	characteristic
223	D₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
224	#2343	C₂×C₅	1	2	yes	complemented
225	#2342	C₂×C₅	1	2	yes	complemented
226	#2334	C₂×C₅	1	2	yes	complemented
227	#2329	C₂×C₅	1	2	yes	complemented
228	#2326	C₂×C₅	1	1	yes	characteristic, complemented
229	#2322	C₂×C₅	1	2	yes	complemented
230	#2322	C₂×C₅	1	1	yes	characteristic, complemented
231	#2318	C₂×C₅	1	2	yes	complemented
232	#2317	C₂×C₅	1	2	yes	complemented
233	C₄×#120	C₂×C₅	1	1	yes	characteristic
234	C₂×#385	C₂×C₅	1	2	yes	complemented
235	C₂⁴×C₅	—	2	4	no	—
236	C₂⁴×C₅	—	2	4	no	—
237	C₂⁴×C₅	—	4	1	no	—
238	C₂⁴×C₅	—	4	1	no	—
239	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
240	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₅	C₂⁴	1	2	yes	—
243	C₂×C₅×Q₈	—	4	1	no	—
244	C₂×C₅×Q₈	—	4	1	no	—
245	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
246	C₂×C₅×D₄	—	2	4	no	—
247	C₂×C₅×D₄	—	2	4	no	—
248	C₂×C₅×D₄	—	4	1	no	—
249	C₂×C₅×D₄	—	4	1	no	—
250	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
251	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₅	—	2	4	no	—
253	C₂²×C₄×C₅	—	2	4	no	—
254	C₂²×C₄×C₅	—	2	4	no	—
255	C₂²×C₄×C₅	—	2	4	no	—
256	C₂²×C₄×C₅	—	2	4	no	—
257	C₂²×C₄×C₅	—	2	4	no	—
258	C₂²×C₄×C₅	—	2	4	no	—
259	C₂²×C₄×C₅	—	2	2	no	—
260	C₂²×C₄×C₅	—	2	2	no	—
261	C₂²×C₄×C₅	—	4	2	no	—
262	C₂²×C₄×C₅	—	4	1	no	—
263	C₂²×C₄×C₅	—	4	2	no	—
264	C₂²×C₄×C₅	—	4	2	no	—
265	C₂²×C₄×C₅	—	4	2	no	—
266	C₂²×C₄×C₅	—	4	2	no	—
267	C₂²×C₄×C₅	—	4	2	no	—
268	C₂²×C₄×C₅	—	4	1	no	—
269	C₂²×C₄×C₅	—	4	2	no	—
270	C₂²×C₄×C₅	—	4	1	no	—
271	C₂²×C₄×C₅	—	4	2	no	—
272	C₂²×C₄×C₅	—	4	2	no	—
273	C₂²×C₄×C₅	—	4	2	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	—	4	2	no	—
278	C₂²×C₄×C₅	—	4	16	no	—
279	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
280	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	complemented
282	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
298	C₅×C₄⋊C₄	—	2	4	no	—
299	C₅×C₄⋊C₄	—	2	4	no	—
300	C₅×C₄⋊C₄	—	4	2	no	—
301	C₅×C₄⋊C₄	—	4	2	no	—
302	C₅×C₄⋊C₄	—	4	2	no	—
303	C₅×C₄⋊C₄	—	4	2	no	—
304	C₅×C₄⋊C₄	—	4	2	no	—
305	C₅×C₄⋊C₄	—	4	2	no	—
306	C₅×C₄⋊C₄	—	4	2	no	—
307	C₅×C₄⋊C₄	—	4	2	no	—
308	C₅×C₄⋊C₄	—	4	2	no	—
309	C₅×C₄⋊C₄	—	4	2	no	—
310	C₅×C₄⋊C₄	—	4	1	no	—
311	C₅×C₄⋊C₄	—	4	2	no	—
312	C₅×C₄⋊C₄	—	4	2	no	—
313	C₅×C₄⋊C₄	—	4	1	no	—
314	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
315	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
316	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
317	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
318	C₅×C₂²⋊C₄	—	2	4	no	—
319	C₅×C₂²⋊C₄	—	2	4	no	—
320	C₅×C₂²⋊C₄	—	2	4	no	—
321	C₅×C₂²⋊C₄	—	2	4	no	—
322	C₅×C₂²⋊C₄	—	4	2	no	—
323	C₅×C₂²⋊C₄	—	4	2	no	—
324	C₅×C₂²⋊C₄	—	4	1	no	—
325	C₅×C₂²⋊C₄	—	4	1	no	—
326	C₅×C₂²⋊C₄	—	4	1	no	—
327	C₅×C₂²⋊C₄	—	4	1	no	—
328	C₅×C₂²⋊C₄	—	4	2	no	—
329	C₅×C₂²⋊C₄	—	4	2	no	—
330	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
331	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
332	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
333	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
334	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
335	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
336	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
337	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
338	C₄²×C₅	—	2	2	no	—
339	C₄²×C₅	—	4	2	no	—
340	C₄²×C₅	—	4	1	no	—
341	C₄²×C₅	—	4	2	no	—
342	C₄²×C₅	—	4	2	no	—
343	C₄²×C₅	—	4	2	no	—
344	C₄²×C₅	—	4	2	no	—
345	C₄²×C₅	—	4	2	no	—
346	C₄²×C₅	C₂²×C₄	1	4	yes	complemented
347	C₄²×C₅	C₂²×C₄	1	8	yes	complemented
348	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
349	#551	C₄×C₅	1	16	yes	complemented
350	C₂×#126	C₂²×C₅	1	2	yes	—
351	C₂×#124	C₂²×C₅	1	1	yes	characteristic
352	C₂×#123	C₂²×C₅	1	2	yes	—
353	C₂×#123	C₂²×C₅	1	1	yes	characteristic
354	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
355	C₂×#120	C₂²×C₅	1	1	yes	characteristic
356	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
357	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
358	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
359	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
360	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
361	C₂×#117	C₂²×C₅	1	2	yes	—
362	C₂×#117	C₂²×C₅	1	2	yes	—
363	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
364	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
365	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
366	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
367	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
368	#391	C₂²×C₅	1	1	yes	characteristic, complemented
369	#391	C₂²×C₅	1	2	yes	complemented
370	#390	C₂²×C₅	1	1	yes	characteristic
371	#389	C₂²×C₅	1	2	yes	complemented
372	#389	C₂²×C₅	1	2	yes	complemented
373	#389	C₂²×C₅	1	2	yes	complemented
374	#389	C₂²×C₅	1	2	yes	complemented
375	#389	C₂²×C₅	1	2	yes	complemented
376	#389	C₂²×C₅	1	2	yes	complemented
377	#389	C₂²×C₅	1	2	yes	complemented
378	#388	C₂²×C₅	1	2	yes	—
379	#388	C₂²×C₅	1	2	yes	—
380	#388	C₂²×C₅	1	2	yes	—
381	#388	C₂²×C₅	1	2	yes	—
382	#388	C₂²×C₅	1	2	yes	—
383	#388	C₂²×C₅	1	2	yes	complemented
384	#388	C₂²×C₅	1	2	yes	complemented
385	#388	C₂²×C₅	1	2	yes	complemented
386	#387	C₂²×C₅	1	2	yes	complemented
387	#387	C₂²×C₅	1	2	yes	complemented
388	#387	C₂²×C₅	1	2	yes	complemented
389	#387	C₂²×C₅	1	2	yes	complemented
390	#387	C₂²×C₅	1	2	yes	complemented
391	#387	C₂²×C₅	1	2	yes	complemented
392	#387	C₂²×C₅	1	2	yes	complemented
393	#387	C₂²×C₅	1	2	yes	complemented
394	#386	C₂²×C₅	1	2	yes	—
395	#386	C₂²×C₅	1	2	yes	—
396	#386	C₂²×C₅	1	1	yes	characteristic
397	#386	C₂²×C₅	1	1	yes	characteristic
398	#385	C₂²×C₅	1	2	yes	—
399	#385	C₂²×C₅	1	2	yes	—
400	#385	C₂²×C₅	1	2	yes	—
401	#385	C₂²×C₅	1	2	yes	—
402	#385	C₂²×C₅	1	2	yes	—
403	#385	C₂²×C₅	1	2	yes	—
404	#385	C₂²×C₅	1	2	yes	—
405	#385	C₂²×C₅	1	2	yes	—
406	#385	C₂²×C₅	1	2	yes	—
407	#385	C₂²×C₅	1	2	yes	—
408	#385	C₂²×C₅	1	2	yes	—
409	#385	C₂²×C₅	1	2	yes	—
410	#385	C₂²×C₅	1	1	yes	characteristic
411	#385	C₂²×C₅	1	1	yes	characteristic, complemented
412	#385	C₂²×C₅	1	2	yes	complemented
413	#385	C₂²×C₅	1	2	yes	complemented
414	#384	C₂²×C₅	1	1	yes	characteristic, complemented
415	#384	C₂²×C₅	1	2	yes	complemented
416	#383	C₂²×C₅	1	2	yes	complemented
417	#382	C₂²×C₅	1	2	yes	complemented
418	#382	C₂²×C₅	1	2	yes	complemented
419	#381	C₂²×C₅	1	2	yes	—
420	#381	C₂²×C₅	1	1	yes	characteristic, complemented
421	#380	C₂²×C₅	1	2	yes	—
422	#380	C₂²×C₅	1	2	yes	complemented
423	#379	C₂²×C₅	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
425	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
426	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
429	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
430	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
433	#376	C₂²×C₅	1	1	yes	characteristic, complemented
434	C₂×#95	C₂²×C₅	1	2	yes	—
435	C₂×#95	C₂²×C₅	1	2	yes	—
436	C₂³×C₅	—	2	2	no	—
437	C₂³×C₅	—	2	2	no	—
438	C₂³×C₅	—	2	2	no	—
439	C₂³×C₅	—	2	2	no	—
440	C₂³×C₅	—	2	16	no	—
441	C₂³×C₅	—	2	2	no	—
442	C₂³×C₅	—	2	2	no	—
443	C₂³×C₅	—	2	1	no	—
444	C₂³×C₅	—	2	1	no	—
445	C₂³×C₅	—	2	2	no	—
446	C₂³×C₅	—	2	2	no	—
447	C₂³×C₅	—	2	1	no	—
448	C₂³×C₅	—	2	1	no	—
449	C₂³×C₅	—	4	4	no	—
450	C₂³×C₅	—	4	4	no	—
451	C₂³×C₅	—	4	8	no	—
452	C₂³×C₅	—	4	4	no	—
453	C₂³×C₅	C₂³×C₄	1	2	yes	—
454	C₂³×C₅	C₂³×C₄	1	2	yes	—
455	C₂³×C₅	C₂³×C₄	1	4	yes	—
456	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
457	C₂³×C₅	2₋¹⁺⁴	1	4	yes	—
458	C₂³×C₅	C₂⁵	1	1	yes	characteristic
459	C₅×Q₈	—	4	4	no	—
460	C₅×D₄	—	2	16	no	—
461	C₅×D₄	—	4	4	no	—
462	C₂×C₄×C₅	—	2	16	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	2	no	—
465	C₂×C₄×C₅	—	2	2	no	—
466	C₂×C₄×C₅	—	2	2	no	—
467	C₂×C₄×C₅	—	2	2	no	—
468	C₂×C₄×C₅	—	2	2	no	—
469	C₂×C₄×C₅	—	2	2	no	—
470	C₂×C₄×C₅	—	2	2	no	—
471	C₂×C₄×C₅	—	2	2	no	—
472	C₂×C₄×C₅	—	2	2	no	—
473	C₂×C₄×C₅	—	2	2	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	2	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	2	no	—
478	C₂×C₄×C₅	—	2	2	no	—
479	C₂×C₄×C₅	—	2	2	no	—
480	C₂×C₄×C₅	—	2	2	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	2	no	—
483	C₂×C₄×C₅	—	2	2	no	—
484	C₂×C₄×C₅	—	2	2	no	—
485	C₂×C₄×C₅	—	2	2	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	2	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	—	4	8	no	—
501	C₂×C₄×C₅	—	4	4	no	—
502	C₂×C₄×C₅	—	4	8	no	—
503	C₂×C₄×C₅	—	4	4	no	—
504	C₂×C₄×C₅	—	4	8	no	—
505	C₂×C₄×C₅	—	4	4	no	—
506	C₂×C₄×C₅	—	8	2	no	—
507	C₂×C₄×C₅	—	8	4	no	—
508	C₂×C₄×C₅	—	8	4	no	—
509	C₂×C₄×C₅	—	8	2	no	—
510	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
511	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
512	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
513	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
514	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
515	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
516	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
517	C₂⁵	C₂³×C₅	1	1	yes	characteristic
518	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₅	1	2	yes	—
520	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
521	C₂³×C₄	—	4	2	no	—
522	C₂³×C₄	—	4	4	no	—
523	C₂³×C₄	C₂³×C₅	1	2	yes	—
524	C₂³×C₄	C₂³×C₅	1	2	yes	—
525	C₂³×C₄	C₂³×C₅	1	2	yes	—
526	C₂³×C₄	C₂³×C₅	1	2	yes	—
527	C₂³×C₄	C₂³×C₅	1	2	yes	—
528	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₅	1	2	yes	—
533	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
534	#126	C₂×C₄×C₅	1	16	yes	complemented
535	#124	C₂×C₄×C₅	1	8	yes	complemented
536	#123	C₂×C₄×C₅	1	8	yes	complemented
537	#123	C₂×C₄×C₅	1	16	yes	complemented
538	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
539	#120	C₂×C₄×C₅	1	8	yes	—
540	C₄×Q₈	—	4	2	no	—
541	C₄×D₄	—	4	2	no	—
542	C₄×D₄	—	4	4	no	—
543	C₄×D₄	—	4	4	no	—
544	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
545	#117	—	4	4	no	—
546	#117	C₂×C₄×C₅	1	16	yes	complemented
547	C₂×C₄⋊C₄	—	4	4	no	—
548	C₂×C₄⋊C₄	—	4	2	no	—
549	C₂×C₄⋊C₄	—	4	4	no	—
550	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
570	C₂×C₂²⋊C₄	—	4	4	no	—
571	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
572	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₅	1	2	yes	—
594	C₂×C₄²	C₂³×C₅	1	2	yes	—
595	C₂×C₄²	C₂³×C₅	1	2	yes	—
596	C₂×C₄²	C₂³×C₅	1	2	yes	—
597	C₂×C₄²	C₂³×C₅	1	2	yes	—
598	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₅	1	2	yes	—
600	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₅	1	2	yes	—
602	#95	C₂³×C₅	1	2	yes	—
603	#95	C₂³×C₅	1	2	yes	—
604	#95	C₂³×C₅	1	2	yes	—
605	#95	C₂³×C₅	1	2	yes	—
606	#95	C₂³×C₅	1	2	yes	—
607	#95	C₂³×C₅	1	2	yes	—
608	#95	C₂³×C₅	1	2	yes	—
609	#95	C₂³×C₅	1	2	yes	—
610	#95	C₂³×C₅	1	2	yes	—
611	#95	C₂³×C₅	1	2	yes	—
612	#95	C₂³×C₅	1	2	yes	—
613	#95	C₂³×C₅	1	2	yes	—
614	#95	C₂³×C₅	1	2	yes	—
615	#95	C₂³×C₅	1	2	yes	—
616	#95	C₂³×C₅	1	2	yes	—
617	#95	C₂³×C₅	1	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	C₂²×C₅	—	2	4	no	—
625	C₂²×C₅	—	2	4	no	—
626	C₂²×C₅	—	2	4	no	—
627	C₂²×C₅	—	2	4	no	—
628	C₂²×C₅	—	2	4	no	—
629	C₂²×C₅	—	2	4	no	—
630	C₂²×C₅	—	2	4	no	—
631	C₂²×C₅	—	2	4	no	—
632	C₂²×C₅	—	2	2	no	—
633	C₂²×C₅	—	2	2	no	—
634	C₂²×C₅	—	4	16	no	—
635	C₂²×C₅	—	4	1	no	—
636	C₂²×C₅	—	4	1	no	—
637	C₂²×C₅	—	4	2	no	—
638	C₂²×C₅	—	4	2	no	—
639	C₂²×C₅	—	4	1	no	—
640	C₂²×C₅	—	4	1	no	—
641	C₂²×C₅	#520	1	8	yes	—
642	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
643	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
644	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
646	C₂²×C₅	#585	1	1	yes	characteristic
647	C₄×C₅	—	2	4	no	—
648	C₄×C₅	—	2	4	no	—
649	C₄×C₅	—	2	4	no	—
650	C₄×C₅	—	2	4	no	—
651	C₄×C₅	—	2	4	no	—
652	C₄×C₅	—	2	2	no	—
653	C₄×C₅	—	2	2	no	—
654	C₄×C₅	—	4	2	no	—
655	C₄×C₅	—	4	1	no	—
656	C₄×C₅	—	4	2	no	—
657	C₄×C₅	—	4	1	no	—
658	C₄×C₅	—	4	2	no	—
659	C₄×C₅	—	4	2	no	—
660	C₄×C₅	—	4	2	no	—
661	C₄×C₅	—	4	2	no	—
662	C₄×C₅	—	4	1	no	—
663	C₂⁴	—	2	4	no	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	4	1	no	—
666	C₂⁴	—	4	1	no	—
667	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
668	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
669	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
670	C₂⁴	C₂⁴×C₅	1	2	yes	—
671	C₂×Q₈	—	4	1	no	—
672	C₂×Q₈	—	4	1	no	—
673	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	4	1	no	—
677	C₂×D₄	—	4	1	no	—
678	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
679	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	1	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	16	no	—
707	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
708	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
709	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	complemented
710	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
743	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
744	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
745	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
759	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
760	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
761	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
762	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
763	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
764	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
765	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
766	C₄²	—	2	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	2	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	1	no	—
774	C₄²	C₂²×C₄×C₅	1	4	yes	complemented
775	C₄²	C₂²×C₄×C₅	1	8	yes	complemented
776	C₂×C₅	—	2	8	no	—
777	C₂×C₅	—	4	2	no	—
778	C₂×C₅	—	4	2	no	—
779	C₂×C₅	C₂×#520	1	2	yes	—
780	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
781	C₂×C₅	#3532	1	1	yes	characteristic
782	C₂×C₅	#3535	1	2	yes	—
783	C₂×C₅	#3538	1	1	yes	characteristic
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	16	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	4	4	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	4	4	no	—
801	C₂³	C₂³×C₄×C₅	1	2	yes	—
802	C₂³	C₂³×C₄×C₅	1	2	yes	—
803	C₂³	C₂³×C₄×C₅	1	4	yes	—
804	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
805	C₂³	C₅×2₋¹⁺⁴	1	4	yes	—
806	C₂³	C₂⁵×C₅	1	1	yes	characteristic
807	Q₈	—	4	4	no	—
808	D₄	—	2	16	no	—
809	D₄	—	4	4	no	—
810	C₂×C₄	—	2	16	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	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	—	4	8	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	—	8	4	no	—
856	C₂×C₄	—	8	4	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
859	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
860	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
861	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
862	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
863	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
864	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
865	C₅	#34457	1	1	yes	characteristic, direct product factor, Sylow
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	16	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	C₅×#520	1	8	yes	—
884	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
885	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
886	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
888	C₂²	C₅×#585	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₂	—	2	8	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	C₂×C₅×#520	1	2	yes	—
909	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂	C₅×#3532	1	1	yes	characteristic
911	C₂	C₅×#3535	1	2	yes	—
912	C₂	C₅×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#120	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2383	C₂	semidirect
3. C₅×#2379	C₂	semidirect
4. C₅×#2376	C₂	semidirect
5. C₅×#2360	C₂	semidirect
6. C₅×#2359	C₂	semidirect
8. C₅×D₄×C₄⋊C₄	C₂	semidirect
9. C₅×#2343	C₂	semidirect
10. C₅×#2342	C₂	semidirect
11. C₅×#2334	C₂	semidirect
12. C₅×#2329	C₂	semidirect
13. C₅×#2326	C₂	semidirect
14. C₅×#2322	C₂	semidirect
15. C₅×#2322	C₂	semidirect
16. C₅×#2318	C₂	semidirect
17. C₅×#2317	C₂	semidirect
19. C₂×C₅×#385	C₂	semidirect
21. C₅×#551	C₄	semidirect
28. C₂×C₄×C₅×Q₈	C₂²	semidirect
37. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
40. C₅×#391	C₂²	semidirect
41. C₅×#391	C₂²	semidirect
43. C₅×#389	C₂²	semidirect
44. C₅×#389	C₂²	semidirect
45. C₅×#389	C₂²	semidirect
46. C₅×#389	C₂²	semidirect
47. C₅×#389	C₂²	semidirect
48. C₅×#389	C₂²	semidirect
49. C₅×#389	C₂²	semidirect
55. C₅×#388	C₂²	semidirect
56. C₅×#388	C₂²	semidirect
57. C₅×#388	C₂²	semidirect
58. C₅×#387	C₂²	semidirect
59. C₅×#387	C₂²	semidirect
60. C₅×#387	C₂²	semidirect
61. C₅×#387	C₂²	semidirect
62. C₅×#387	C₂²	semidirect
63. C₅×#387	C₂²	semidirect
64. C₅×#387	C₂²	semidirect
65. C₅×#387	C₂²	semidirect
83. C₅×#385	C₂²	semidirect
84. C₅×#385	C₂²	semidirect
85. C₅×#385	C₂²	semidirect
86. C₅×#384	C₂²	semidirect
87. C₅×#384	C₂²	semidirect
88. C₅×#383	C₂²	semidirect
89. C₅×#382	C₂²	semidirect
90. C₅×#382	C₂²	semidirect
92. C₅×#381	C₂²	semidirect
94. C₅×#380	C₂²	semidirect
96. C₄×C₅×C₄⋊C₄	C₂²	semidirect
97. C₄×C₅×C₄⋊C₄	C₂²	semidirect
104. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
105. C₅×#376	C₂²	semidirect
108. #34457	C₅	direct (N × H)
126. C₅×#126	C₂×C₄	semidirect
127. C₅×#124	C₂×C₄	semidirect
128. C₅×#123	C₂×C₄	semidirect
129. C₅×#123	C₂×C₄	semidirect
130. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
136. C₄×C₅×D₄	C₂×C₄	semidirect
138. C₅×#117	C₂×C₄	semidirect
163. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
217. #2383	C₂×C₅	semidirect
218. #2379	C₂×C₅	semidirect
219. #2376	C₂×C₅	semidirect
220. #2360	C₂×C₅	semidirect
221. #2359	C₂×C₅	semidirect
223. D₄×C₄⋊C₄	C₂×C₅	semidirect
224. #2343	C₂×C₅	semidirect
225. #2342	C₂×C₅	semidirect
226. #2334	C₂×C₅	semidirect
227. #2329	C₂×C₅	semidirect
228. #2326	C₂×C₅	semidirect
229. #2322	C₂×C₅	semidirect
230. #2322	C₂×C₅	semidirect
231. #2318	C₂×C₅	semidirect
232. #2317	C₂×C₅	semidirect
234. C₂×#385	C₂×C₅	semidirect
245. C₂×C₅×Q₈	C₂²×C₄	semidirect
281. C₂²×C₄×C₅	C₂²×C₄	semidirect
314. C₅×C₄⋊C₄	C₂²×C₄	semidirect
315. C₅×C₄⋊C₄	C₂²×C₄	semidirect
316. C₅×C₄⋊C₄	C₂²×C₄	semidirect
317. C₅×C₄⋊C₄	C₂²×C₄	semidirect
336. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
337. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
346. C₄²×C₅	C₂²×C₄	semidirect
347. C₄²×C₅	C₂²×C₄	semidirect
349. #551	C₄×C₅	semidirect
356. C₂×C₄×Q₈	C₂²×C₅	semidirect
365. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
368. #391	C₂²×C₅	semidirect
369. #391	C₂²×C₅	semidirect
371. #389	C₂²×C₅	semidirect
372. #389	C₂²×C₅	semidirect
373. #389	C₂²×C₅	semidirect
374. #389	C₂²×C₅	semidirect
375. #389	C₂²×C₅	semidirect
376. #389	C₂²×C₅	semidirect
377. #389	C₂²×C₅	semidirect
383. #388	C₂²×C₅	semidirect
384. #388	C₂²×C₅	semidirect
385. #388	C₂²×C₅	semidirect
386. #387	C₂²×C₅	semidirect
387. #387	C₂²×C₅	semidirect
388. #387	C₂²×C₅	semidirect
389. #387	C₂²×C₅	semidirect
390. #387	C₂²×C₅	semidirect
391. #387	C₂²×C₅	semidirect
392. #387	C₂²×C₅	semidirect
393. #387	C₂²×C₅	semidirect
411. #385	C₂²×C₅	semidirect
412. #385	C₂²×C₅	semidirect
413. #385	C₂²×C₅	semidirect
414. #384	C₂²×C₅	semidirect
415. #384	C₂²×C₅	semidirect
416. #383	C₂²×C₅	semidirect
417. #382	C₂²×C₅	semidirect
418. #382	C₂²×C₅	semidirect
420. #381	C₂²×C₅	semidirect
422. #380	C₂²×C₅	semidirect
424. C₄×C₄⋊C₄	C₂²×C₅	semidirect
425. C₄×C₄⋊C₄	C₂²×C₅	semidirect
432. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
433. #376	C₂²×C₅	semidirect
534. #126	C₂×C₄×C₅	semidirect
535. #124	C₂×C₄×C₅	semidirect
536. #123	C₂×C₄×C₅	semidirect
537. #123	C₂×C₄×C₅	semidirect
538. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
544. C₄×D₄	C₂×C₄×C₅	semidirect
546. #117	C₂×C₄×C₅	semidirect
571. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
673. C₂×Q₈	C₂²×C₄×C₅	semidirect
709. C₂²×C₄	C₂²×C₄×C₅	semidirect
742. C₄⋊C₄	C₂²×C₄×C₅	semidirect
743. C₄⋊C₄	C₂²×C₄×C₅	semidirect
744. C₄⋊C₄	C₂²×C₄×C₅	semidirect
745. C₄⋊C₄	C₂²×C₄×C₅	semidirect
764. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
765. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
774. C₄²	C₂²×C₄×C₅	semidirect
775. C₄²	C₂²×C₄×C₅	semidirect
865. C₅	#34457	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#551	2
C₅×#2383	2
C₅×#2379	2
C₅×#2376	2
C₅×#2360	2
C₅×#2359	2
C₅×#2358	2
C₅×D₄×C₄⋊C₄	2
C₅×#2343	2
C₅×#2342	2
C₅×#2334	2
C₅×#2329	2
C₅×#2326	2
C₅×#2322	2
C₅×#2318	2
C₅×#2317	2
C₄×C₅×#120	2
C₂×C₅×#385	2
#34457	5

Subgroups — C5×#34457 #11957177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34457 #11957177