Subgroups — C₅×#34499 #11957219

Order 1280.

2032 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#556	C₂	1	1	yes	maximal, characteristic
2	C₅×#2383	C₂	1	2	yes	maximal, complemented
3	C₅×#2378	C₂	1	2	yes	maximal, complemented
4	C₅×#2373	C₂	1	2	yes	maximal, complemented
5	C₅×#2367	C₂	1	1	yes	maximal, characteristic
6	C₅×#2367	C₂	1	1	yes	maximal, characteristic
7	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2349	C₂	1	1	yes	maximal, characteristic
12	C₅×#2343	C₂	1	2	yes	maximal, complemented
13	C₅×#2334	C₂	1	2	yes	maximal, complemented
14	C₅×#2334	C₂	1	2	yes	maximal, complemented
15	C₅×#2329	C₂	1	2	yes	maximal, complemented
16	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2326	C₂	1	1	yes	maximal, characteristic
18	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2319	C₂	1	1	yes	maximal, characteristic
20	C₅×#2314	C₂	1	2	yes	maximal, complemented
21	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
22	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#556	C₄	1	16	yes	complemented
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×#124	C₂²	1	1	yes	characteristic
29	C₂×C₅×#124	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×#117	C₂²	1	2	yes	—
42	C₅×#391	C₂²	1	1	yes	characteristic
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#391	C₂²	1	1	yes	characteristic
47	C₅×#391	C₂²	1	1	yes	characteristic
48	C₅×#391	C₂²	1	2	yes	—
49	C₅×#390	C₂²	1	1	yes	characteristic
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#389	C₂²	1	1	yes	characteristic
55	C₅×#389	C₂²	1	1	yes	characteristic
56	C₅×#389	C₂²	1	1	yes	characteristic
57	C₅×#389	C₂²	1	2	yes	—
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#389	C₂²	1	2	yes	—
60	C₅×#389	C₂²	1	2	yes	—
61	C₅×#389	C₂²	1	2	yes	—
62	C₅×#388	C₂²	1	2	yes	—
63	C₅×#388	C₂²	1	2	yes	—
64	C₅×#388	C₂²	1	2	yes	—
65	C₅×#388	C₂²	1	2	yes	—
66	C₅×#388	C₂²	1	2	yes	—
67	C₅×#388	C₂²	1	2	yes	—
68	C₅×#388	C₂²	1	2	yes	—
69	C₅×#388	C₂²	1	2	yes	—
70	C₅×#388	C₂²	1	2	yes	—
71	C₅×#388	C₂²	1	2	yes	—
72	C₅×#387	C₂²	1	1	yes	characteristic
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	1	yes	characteristic
75	C₅×#387	C₂²	1	1	yes	characteristic
76	C₅×#387	C₂²	1	1	yes	characteristic
77	C₅×#387	C₂²	1	2	yes	—
78	C₅×#387	C₂²	1	2	yes	—
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#387	C₂²	1	2	yes	—
83	C₅×#387	C₂²	1	2	yes	—
84	C₅×#387	C₂²	1	2	yes	—
85	C₅×#387	C₂²	1	2	yes	—
86	C₅×#387	C₂²	1	2	yes	—
87	C₅×#387	C₂²	1	2	yes	—
88	C₅×#385	C₂²	1	2	yes	—
89	C₅×#385	C₂²	1	2	yes	—
90	C₅×#385	C₂²	1	2	yes	—
91	C₅×#385	C₂²	1	2	yes	—
92	C₅×#385	C₂²	1	2	yes	—
93	C₅×#385	C₂²	1	2	yes	—
94	C₅×#384	C₂²	1	2	yes	—
95	C₅×#384	C₂²	1	1	yes	characteristic
96	C₅×#383	C₂²	1	2	yes	—
97	C₅×#382	C₂²	1	1	yes	characteristic
98	C₅×#382	C₂²	1	2	yes	—
99	C₅×#382	C₂²	1	1	yes	characteristic
100	C₅×#382	C₂²	1	2	yes	—
101	C₅×#381	C₂²	1	2	yes	—
102	C₅×#380	C₂²	1	2	yes	—
103	C₅×#380	C₂²	1	2	yes	—
104	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	1	yes	characteristic
121	C₅×#376	C₂²	1	2	yes	—
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#34499	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅	C₂³	1	2	yes	—
130	C₂³×C₄×C₅	C₂³	1	2	yes	—
131	C₂³×C₄×C₅	C₂³	1	2	yes	—
132	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
133	C₅×#126	C₂×C₄	1	16	yes	complemented
134	C₅×#126	C₂×C₄	1	16	yes	complemented
135	C₅×#124	C₂×C₄	1	8	yes	—
136	C₅×#124	C₂×C₄	1	8	yes	—
137	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
138	C₄×C₅×Q₈	—	4	2	no	—
139	C₄×C₅×Q₈	—	4	2	no	—
140	C₄×C₅×Q₈	—	4	2	no	—
141	C₄×C₅×Q₈	—	4	2	no	—
142	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
143	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
144	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
145	C₄×C₅×D₄	—	4	2	no	—
146	C₄×C₅×D₄	—	4	2	no	—
147	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
148	C₅×#117	C₂×C₄	1	16	yes	complemented
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	2	yes	—
197	C₂×C₄²×C₅	C₂³	1	2	yes	—
198	C₂×C₄²×C₅	C₂³	1	2	yes	—
199	C₂×C₄²×C₅	C₂³	1	2	yes	—
200	C₂×C₄²×C₅	C₂³	1	2	yes	—
201	C₂×C₄²×C₅	C₂³	1	2	yes	—
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅	C₂³	1	2	yes	—
205	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₅×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	C₅×#95	C₂³	1	1	yes	characteristic
215	C₅×#95	C₂³	1	2	yes	—
216	C₅×#95	C₂³	1	1	yes	characteristic
217	C₅×#95	C₂³	1	1	yes	characteristic
218	C₅×#95	C₂³	1	1	yes	characteristic
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	1	yes	characteristic
221	C₅×#95	C₂³	1	1	yes	characteristic
222	C₅×#95	C₂³	1	1	yes	characteristic
223	C₅×#95	C₂³	1	1	yes	characteristic
224	C₅×#95	C₂³	1	1	yes	characteristic
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	2	yes	—
230	C₅×#95	C₂³	1	1	yes	characteristic
231	C₅×#95	C₂³	1	1	yes	characteristic
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	2	yes	—
236	C₅×#95	C₂³	1	2	yes	—
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	2	yes	—
240	C₅×#95	C₂³	1	1	yes	characteristic
241	C₂×#556	C₂×C₅	1	1	yes	characteristic
242	#2383	C₂×C₅	1	2	yes	complemented
243	#2378	C₂×C₅	1	2	yes	complemented
244	#2373	C₂×C₅	1	2	yes	complemented
245	#2367	C₂×C₅	1	1	yes	characteristic
246	#2367	C₂×C₅	1	1	yes	characteristic
247	#2365	C₂×C₅	1	1	yes	characteristic, complemented
248	#2355	C₂×C₅	1	1	yes	characteristic, complemented
249	#2351	C₂×C₅	1	1	yes	characteristic, complemented
250	Q₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
251	#2349	C₂×C₅	1	1	yes	characteristic
252	#2343	C₂×C₅	1	2	yes	complemented
253	#2334	C₂×C₅	1	2	yes	complemented
254	#2334	C₂×C₅	1	2	yes	complemented
255	#2329	C₂×C₅	1	2	yes	complemented
256	#2327	C₂×C₅	1	1	yes	characteristic, complemented
257	#2326	C₂×C₅	1	1	yes	characteristic
258	#2320	C₂×C₅	1	1	yes	characteristic, complemented
259	#2319	C₂×C₅	1	1	yes	characteristic
260	#2314	C₂×C₅	1	2	yes	complemented
261	C₄×#124	C₂×C₅	1	1	yes	characteristic
262	#2295	C₂×C₅	1	1	yes	characteristic, complemented
263	#2295	C₂×C₅	1	1	yes	characteristic, complemented
264	C₂⁴×C₅	C₂⁴	1	2	yes	—
265	C₂×C₅×Q₈	—	2	2	no	—
266	C₂×C₅×Q₈	—	2	2	no	—
267	C₂×C₅×Q₈	—	2	2	no	—
268	C₂×C₅×Q₈	—	2	2	no	—
269	C₂×C₅×Q₈	—	4	1	no	—
270	C₂×C₅×Q₈	—	4	1	no	—
271	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
272	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
273	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
274	C₂×C₅×D₄	—	2	2	no	—
275	C₂×C₅×D₄	—	2	2	no	—
276	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₅	—	2	4	no	—
278	C₂²×C₄×C₅	—	4	2	no	—
279	C₂²×C₄×C₅	—	4	2	no	—
280	C₂²×C₄×C₅	—	4	2	no	—
281	C₂²×C₄×C₅	—	4	2	no	—
282	C₂²×C₄×C₅	—	4	2	no	—
283	C₂²×C₄×C₅	—	4	2	no	—
284	C₂²×C₄×C₅	—	4	2	no	—
285	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
286	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	2	2	no	—
310	C₅×C₄⋊C₄	—	2	2	no	—
311	C₅×C₄⋊C₄	—	2	2	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	2	2	no	—
314	C₅×C₄⋊C₄	—	4	1	no	—
315	C₅×C₄⋊C₄	—	4	1	no	—
316	C₅×C₄⋊C₄	—	4	1	no	—
317	C₅×C₄⋊C₄	—	4	2	no	—
318	C₅×C₄⋊C₄	—	4	1	no	—
319	C₅×C₄⋊C₄	—	4	2	no	—
320	C₅×C₄⋊C₄	—	4	2	no	—
321	C₅×C₄⋊C₄	—	4	2	no	—
322	C₅×C₄⋊C₄	—	4	2	no	—
323	C₅×C₄⋊C₄	—	4	2	no	—
324	C₅×C₄⋊C₄	—	4	2	no	—
325	C₅×C₄⋊C₄	—	4	2	no	—
326	C₅×C₄⋊C₄	—	4	2	no	—
327	C₅×C₄⋊C₄	—	4	2	no	—
328	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
329	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
330	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
331	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
332	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
333	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
334	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
335	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
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	C₂²×C₄	1	8	yes	—
343	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
344	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
345	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
346	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
347	C₄²×C₅	—	2	2	no	—
348	C₄²×C₅	—	2	2	no	—
349	C₄²×C₅	—	2	2	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	2	2	no	—
352	C₄²×C₅	—	4	2	no	—
353	C₄²×C₅	—	4	1	no	—
354	C₄²×C₅	—	4	2	no	—
355	C₄²×C₅	—	4	2	no	—
356	C₄²×C₅	—	4	1	no	—
357	C₄²×C₅	—	4	1	no	—
358	C₄²×C₅	—	4	2	no	—
359	C₄²×C₅	—	4	2	no	—
360	C₄²×C₅	—	4	2	no	—
361	C₄²×C₅	—	4	2	no	—
362	C₄²×C₅	C₂²×C₄	1	8	yes	—
363	C₄²×C₅	C₂²×C₄	1	8	yes	—
364	C₄²×C₅	C₂²×C₄	1	4	yes	—
365	C₄²×C₅	C₂²×C₄	1	4	yes	—
366	C₄²×C₅	C₂²×C₄	1	4	yes	—
367	#556	C₄×C₅	1	16	yes	complemented
368	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
369	C₂×#126	C₂²×C₅	1	2	yes	—
370	C₂×#126	C₂²×C₅	1	2	yes	—
371	C₂×#124	C₂²×C₅	1	1	yes	characteristic
372	C₂×#124	C₂²×C₅	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
374	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
375	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
376	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
384	C₂×#117	C₂²×C₅	1	2	yes	—
385	#391	C₂²×C₅	1	1	yes	characteristic
386	#391	C₂²×C₅	1	1	yes	characteristic
387	#391	C₂²×C₅	1	1	yes	characteristic
388	#391	C₂²×C₅	1	1	yes	characteristic
389	#391	C₂²×C₅	1	2	yes	—
390	#391	C₂²×C₅	1	1	yes	characteristic
391	#391	C₂²×C₅	1	1	yes	characteristic
392	#390	C₂²×C₅	1	1	yes	characteristic
393	#390	C₂²×C₅	1	1	yes	characteristic
394	#389	C₂²×C₅	1	1	yes	characteristic
395	#389	C₂²×C₅	1	1	yes	characteristic
396	#389	C₂²×C₅	1	1	yes	characteristic
397	#389	C₂²×C₅	1	2	yes	—
398	#389	C₂²×C₅	1	2	yes	—
399	#389	C₂²×C₅	1	1	yes	characteristic
400	#389	C₂²×C₅	1	2	yes	—
401	#389	C₂²×C₅	1	2	yes	—
402	#389	C₂²×C₅	1	2	yes	—
403	#389	C₂²×C₅	1	1	yes	characteristic
404	#389	C₂²×C₅	1	1	yes	characteristic
405	#388	C₂²×C₅	1	2	yes	—
406	#388	C₂²×C₅	1	2	yes	—
407	#388	C₂²×C₅	1	2	yes	—
408	#388	C₂²×C₅	1	2	yes	—
409	#388	C₂²×C₅	1	2	yes	—
410	#388	C₂²×C₅	1	2	yes	—
411	#388	C₂²×C₅	1	2	yes	—
412	#388	C₂²×C₅	1	2	yes	—
413	#388	C₂²×C₅	1	2	yes	—
414	#388	C₂²×C₅	1	2	yes	—
415	#387	C₂²×C₅	1	1	yes	characteristic
416	#387	C₂²×C₅	1	2	yes	—
417	#387	C₂²×C₅	1	2	yes	—
418	#387	C₂²×C₅	1	2	yes	—
419	#387	C₂²×C₅	1	2	yes	—
420	#387	C₂²×C₅	1	2	yes	—
421	#387	C₂²×C₅	1	2	yes	—
422	#387	C₂²×C₅	1	2	yes	—
423	#387	C₂²×C₅	1	2	yes	—
424	#387	C₂²×C₅	1	2	yes	—
425	#387	C₂²×C₅	1	2	yes	—
426	#387	C₂²×C₅	1	1	yes	characteristic
427	#387	C₂²×C₅	1	2	yes	—
428	#387	C₂²×C₅	1	1	yes	characteristic
429	#387	C₂²×C₅	1	1	yes	characteristic
430	#387	C₂²×C₅	1	2	yes	—
431	#385	C₂²×C₅	1	2	yes	—
432	#385	C₂²×C₅	1	2	yes	—
433	#385	C₂²×C₅	1	2	yes	—
434	#385	C₂²×C₅	1	2	yes	—
435	#385	C₂²×C₅	1	2	yes	—
436	#385	C₂²×C₅	1	2	yes	—
437	#384	C₂²×C₅	1	2	yes	—
438	#384	C₂²×C₅	1	1	yes	characteristic
439	#383	C₂²×C₅	1	2	yes	—
440	#382	C₂²×C₅	1	2	yes	—
441	#382	C₂²×C₅	1	1	yes	characteristic
442	#382	C₂²×C₅	1	2	yes	—
443	#382	C₂²×C₅	1	1	yes	characteristic
444	#381	C₂²×C₅	1	2	yes	—
445	#380	C₂²×C₅	1	2	yes	—
446	#380	C₂²×C₅	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
462	#376	C₂²×C₅	1	1	yes	characteristic
463	#376	C₂²×C₅	1	1	yes	characteristic
464	#376	C₂²×C₅	1	2	yes	—
465	C₂×#95	C₂²×C₅	1	2	yes	—
466	C₄³	C₂²×C₅	1	1	yes	characteristic
467	C₂³×C₅	—	2	2	no	—
468	C₂³×C₅	—	2	2	no	—
469	C₂³×C₅	—	2	2	no	—
470	C₂³×C₅	—	2	2	no	—
471	C₂³×C₅	—	2	2	no	—
472	C₂³×C₅	—	2	2	no	—
473	C₂³×C₅	C₂³×C₄	1	4	yes	—
474	C₂³×C₅	C₂⁵	1	1	yes	characteristic
475	C₅×Q₈	—	2	8	no	—
476	C₅×Q₈	—	2	8	no	—
477	C₅×Q₈	—	4	4	no	—
478	C₅×D₄	—	2	8	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	2	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	2	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	2	no	—
495	C₂×C₄×C₅	—	2	2	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	2	no	—
506	C₂×C₄×C₅	—	2	2	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	2	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	2	no	—
523	C₂×C₄×C₅	—	2	2	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	1	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	2	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	4	8	no	—
533	C₂×C₄×C₅	—	8	4	no	—
534	C₂×C₄×C₅	—	8	4	no	—
535	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
536	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
538	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
539	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
540	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
541	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
542	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
543	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
544	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
545	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
546	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
547	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
548	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₅	1	2	yes	—
553	C₂³×C₄	C₂³×C₅	1	2	yes	—
554	C₂³×C₄	C₂³×C₅	1	2	yes	—
555	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
556	#126	C₂×C₄×C₅	1	16	yes	complemented
557	#126	C₂×C₄×C₅	1	16	yes	complemented
558	#124	C₂×C₄×C₅	1	8	yes	—
559	#124	C₂×C₄×C₅	1	8	yes	—
560	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
561	C₄×Q₈	—	4	2	no	—
562	C₄×Q₈	—	4	2	no	—
563	C₄×Q₈	—	4	2	no	—
564	C₄×Q₈	—	4	2	no	—
565	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
566	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
567	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
568	C₄×D₄	—	4	2	no	—
569	C₄×D₄	—	4	2	no	—
570	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
571	#117	C₂×C₄×C₅	1	16	yes	complemented
572	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₅	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
599	C₂×C₄⋊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×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
611	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₅	1	2	yes	—
617	C₂×C₄²	C₂³×C₅	1	2	yes	—
618	C₂×C₄²	C₂³×C₅	1	2	yes	—
619	C₂×C₄²	C₂³×C₅	1	2	yes	—
620	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₅	1	2	yes	—
624	C₂×C₄²	C₂³×C₅	1	2	yes	—
625	C₂×C₄²	C₂³×C₅	1	2	yes	—
626	C₂×C₄²	C₂³×C₅	1	2	yes	—
627	C₂×C₄²	C₂³×C₅	1	2	yes	—
628	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
631	#95	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
637	#95	C₂³×C₅	1	1	yes	characteristic
638	#95	C₂³×C₅	1	2	yes	—
639	#95	C₂³×C₅	1	1	yes	characteristic
640	#95	C₂³×C₅	1	1	yes	characteristic
641	#95	C₂³×C₅	1	1	yes	characteristic
642	#95	C₂³×C₅	1	2	yes	—
643	#95	C₂³×C₅	1	1	yes	characteristic
644	#95	C₂³×C₅	1	1	yes	characteristic
645	#95	C₂³×C₅	1	1	yes	characteristic
646	#95	C₂³×C₅	1	1	yes	characteristic
647	#95	C₂³×C₅	1	1	yes	characteristic
648	#95	C₂³×C₅	1	2	yes	—
649	#95	C₂³×C₅	1	2	yes	—
650	#95	C₂³×C₅	1	2	yes	—
651	#95	C₂³×C₅	1	2	yes	—
652	#95	C₂³×C₅	1	2	yes	—
653	#95	C₂³×C₅	1	1	yes	characteristic
654	#95	C₂³×C₅	1	1	yes	characteristic
655	#95	C₂³×C₅	1	2	yes	—
656	#95	C₂³×C₅	1	2	yes	—
657	#95	C₂³×C₅	1	2	yes	—
658	#95	C₂³×C₅	1	2	yes	—
659	#95	C₂³×C₅	1	2	yes	—
660	#95	C₂³×C₅	1	2	yes	—
661	#95	C₂³×C₅	1	2	yes	—
662	#95	C₂³×C₅	1	2	yes	—
663	#95	C₂³×C₅	1	1	yes	characteristic
664	C₂²×C₅	—	2	4	no	—
665	C₂²×C₅	—	2	4	no	—
666	C₂²×C₅	—	2	4	no	—
667	C₂²×C₅	—	4	2	no	—
668	C₂²×C₅	—	4	2	no	—
669	C₂²×C₅	—	4	2	no	—
670	C₂²×C₅	—	4	2	no	—
671	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
672	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
675	C₂²×C₅	#585	1	1	yes	characteristic
676	C₂²×C₅	#585	1	1	yes	characteristic
677	C₂²×C₅	#585	1	1	yes	characteristic
678	C₄×C₅	—	2	4	no	—
679	C₄×C₅	—	2	4	no	—
680	C₄×C₅	—	2	2	no	—
681	C₄×C₅	—	2	4	no	—
682	C₄×C₅	—	2	2	no	—
683	C₄×C₅	—	2	2	no	—
684	C₄×C₅	—	2	2	no	—
685	C₄×C₅	—	2	2	no	—
686	C₄×C₅	—	2	2	no	—
687	C₄×C₅	—	2	2	no	—
688	C₄×C₅	—	4	1	no	—
689	C₄×C₅	—	4	1	no	—
690	C₄×C₅	—	4	2	no	—
691	C₄×C₅	—	4	1	no	—
692	C₄×C₅	—	4	1	no	—
693	C₄×C₅	—	4	2	no	—
694	C₄×C₅	—	4	1	no	—
695	C₄×C₅	—	4	1	no	—
696	C₄×C₅	—	4	2	no	—
697	C₄×C₅	—	4	2	no	—
698	C₄×C₅	—	4	1	no	—
699	C₄×C₅	#520	1	4	yes	—
700	C₂⁴	C₂⁴×C₅	1	2	yes	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	4	1	no	—
706	C₂×Q₈	—	4	1	no	—
707	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
708	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
709	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
722	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	1	no	—
755	C₄⋊C₄	—	4	1	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
765	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
766	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
767	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
768	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
769	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
770	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
771	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
779	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
780	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
781	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
782	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	1	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	1	no	—
798	C₄²	C₂²×C₄×C₅	1	8	yes	—
799	C₄²	C₂²×C₄×C₅	1	8	yes	—
800	C₄²	C₂²×C₄×C₅	1	4	yes	—
801	C₄²	C₂²×C₄×C₅	1	4	yes	—
802	C₄²	C₂²×C₄×C₅	1	4	yes	—
803	C₂×C₅	—	4	4	no	—
804	C₂×C₅	C₂×#520	1	1	yes	characteristic
805	C₂×C₅	#3428	1	1	yes	characteristic
806	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
807	C₂×C₅	#3555	1	1	yes	characteristic
808	C₂×C₅	#3557	1	1	yes	characteristic
809	C₂×C₅	#3561	1	1	yes	characteristic
810	C₂×C₅	#3562	1	1	yes	characteristic
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	C₂³×C₄×C₅	1	4	yes	—
818	C₂³	C₂⁵×C₅	1	1	yes	characteristic
819	Q₈	—	2	8	no	—
820	Q₈	—	2	8	no	—
821	Q₈	—	4	4	no	—
822	D₄	—	2	8	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	4	8	no	—
877	C₂×C₄	—	8	4	no	—
878	C₂×C₄	—	8	4	no	—
879	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
881	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
882	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
883	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
884	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
885	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
888	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
889	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
890	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
891	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
892	C₅	#34499	1	1	yes	characteristic, direct product factor, Sylow
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
901	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
903	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
904	C₂²	C₅×#585	1	1	yes	characteristic
905	C₂²	C₅×#585	1	1	yes	characteristic
906	C₂²	C₅×#585	1	1	yes	characteristic
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	C₅×#520	1	4	yes	—
929	C₂	—	4	4	no	—
930	C₂	C₂×C₅×#520	1	1	yes	characteristic
931	C₂	C₅×#3428	1	1	yes	characteristic
932	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
933	C₂	C₅×#3555	1	1	yes	characteristic
934	C₂	C₅×#3557	1	1	yes	characteristic
935	C₂	C₅×#3561	1	1	yes	characteristic
936	C₂	C₅×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×D₄	C₂³
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×#2378	C₂	semidirect
4. C₅×#2373	C₂	semidirect
7. C₅×#2365	C₂	semidirect
8. C₅×#2355	C₂	semidirect
9. C₅×#2351	C₂	semidirect
10. C₅×Q₈×C₄⋊C₄	C₂	semidirect
12. C₅×#2343	C₂	semidirect
13. C₅×#2334	C₂	semidirect
14. C₅×#2334	C₂	semidirect
15. C₅×#2329	C₂	semidirect
16. C₅×#2327	C₂	semidirect
18. C₅×#2320	C₂	semidirect
20. C₅×#2314	C₂	semidirect
22. C₅×#2295	C₂	semidirect
23. C₅×#2295	C₂	semidirect
24. C₅×#556	C₄	semidirect
124. #34499	C₅	direct (N × H)
132. C₅×C₄⋊Q₈	C₂×C₄	semidirect
133. C₅×#126	C₂×C₄	semidirect
134. C₅×#126	C₂×C₄	semidirect
137. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
142. C₄×C₅×Q₈	C₂×C₄	semidirect
143. C₄×C₅×Q₈	C₂×C₄	semidirect
144. C₄×C₅×Q₈	C₂×C₄	semidirect
148. C₅×#117	C₂×C₄	semidirect
242. #2383	C₂×C₅	semidirect
243. #2378	C₂×C₅	semidirect
244. #2373	C₂×C₅	semidirect
247. #2365	C₂×C₅	semidirect
248. #2355	C₂×C₅	semidirect
249. #2351	C₂×C₅	semidirect
250. Q₈×C₄⋊C₄	C₂×C₅	semidirect
252. #2343	C₂×C₅	semidirect
253. #2334	C₂×C₅	semidirect
254. #2334	C₂×C₅	semidirect
255. #2329	C₂×C₅	semidirect
256. #2327	C₂×C₅	semidirect
258. #2320	C₂×C₅	semidirect
260. #2314	C₂×C₅	semidirect
262. #2295	C₂×C₅	semidirect
263. #2295	C₂×C₅	semidirect
367. #556	C₄×C₅	semidirect
555. C₄⋊Q₈	C₂×C₄×C₅	semidirect
556. #126	C₂×C₄×C₅	semidirect
557. #126	C₂×C₄×C₅	semidirect
560. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
565. C₄×Q₈	C₂×C₄×C₅	semidirect
566. C₄×Q₈	C₂×C₄×C₅	semidirect
567. C₄×Q₈	C₂×C₄×C₅	semidirect
571. #117	C₂×C₄×C₅	semidirect
892. C₅	#34499	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×#556	2
C₅×#2383	2
C₅×#2378	2
C₅×#2373	2
C₅×#2367	2
C₅×#2365	2
C₅×#2355	2
C₅×#2351	2
C₅×Q₈×C₄⋊C₄	2
C₅×#2349	2
C₅×#2343	2
C₅×#2334	2
C₅×#2329	2
C₅×#2327	2
C₅×#2326	2
C₅×#2320	2
C₅×#2319	2
C₅×#2314	2
C₄×C₅×#124	2
C₅×#2295	2
#34499	5

Subgroups — C5×#34499 #11957219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34499 #11957219