Subgroups — C₅×#35269 #11957989

Order 1280.

1714 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2860	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2629	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2625	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2624	C₂	1	1	yes	maximal, characteristic
8	C₅×#2620	C₂	1	1	yes	maximal, characteristic
9	C₅×#2525	C₂	1	2	yes	maximal, complemented
10	C₅×#2522	C₂	1	2	yes	maximal, complemented
11	C₅×#2519	C₂	1	2	yes	maximal, complemented
12	C₅×#2518	C₂	1	2	yes	maximal, complemented
13	C₅×#2518	C₂	1	2	yes	maximal, complemented
14	C₅×#2515	C₂	1	2	yes	maximal, complemented
15	C₅×#2466	C₂	1	2	yes	maximal, complemented
16	C₅×#2460	C₂	1	2	yes	maximal, complemented
17	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#126	C₂²	1	2	yes	—
25	C₂×C₅×#125	C₂²	1	1	yes	characteristic
26	C₂×C₅×#125	C₂²	1	2	yes	—
27	C₂×C₅×#124	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₅×#117	C₂²	1	1	yes	characteristic
34	C₂×C₅×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₅×#400	C₂²	1	2	yes	—
37	C₅×#399	C₂²	1	2	yes	—
38	C₅×#398	C₂²	1	2	yes	—
39	C₅×#398	C₂²	1	2	yes	—
40	C₅×#398	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×#396	C₂²	1	2	yes	—
45	C₅×#396	C₂²	1	2	yes	—
46	C₅×#396	C₂²	1	2	yes	—
47	C₅×#396	C₂²	1	2	yes	—
48	C₅×#394	C₂²	1	2	yes	—
49	C₅×#394	C₂²	1	2	yes	—
50	C₅×#394	C₂²	1	2	yes	—
51	C₅×#394	C₂²	1	2	yes	—
52	C₅×#391	C₂²	1	1	yes	characteristic
53	C₅×#391	C₂²	1	1	yes	characteristic
54	C₅×#391	C₂²	1	1	yes	characteristic
55	C₅×#391	C₂²	1	1	yes	characteristic
56	C₅×#390	C₂²	1	1	yes	characteristic
57	C₅×#390	C₂²	1	1	yes	characteristic
58	C₅×#390	C₂²	1	1	yes	characteristic
59	C₅×#390	C₂²	1	1	yes	characteristic
60	C₅×#389	C₂²	1	2	yes	—
61	C₅×#389	C₂²	1	2	yes	—
62	C₅×#389	C₂²	1	2	yes	—
63	C₅×#389	C₂²	1	2	yes	—
64	C₅×#389	C₂²	1	1	yes	characteristic
65	C₅×#389	C₂²	1	1	yes	characteristic
66	C₅×#389	C₂²	1	1	yes	characteristic
67	C₅×#389	C₂²	1	1	yes	characteristic
68	C₅×#389	C₂²	1	1	yes	characteristic
69	C₅×#389	C₂²	1	1	yes	characteristic
70	C₅×#389	C₂²	1	1	yes	characteristic
71	C₅×#389	C₂²	1	1	yes	characteristic
72	C₅×#388	C₂²	1	2	yes	—
73	C₅×#388	C₂²	1	2	yes	—
74	C₅×#388	C₂²	1	2	yes	—
75	C₅×#388	C₂²	1	2	yes	—
76	C₅×#388	C₂²	1	2	yes	—
77	C₅×#388	C₂²	1	2	yes	—
78	C₅×#388	C₂²	1	2	yes	—
79	C₅×#388	C₂²	1	2	yes	—
80	C₅×#388	C₂²	1	2	yes	—
81	C₅×#388	C₂²	1	2	yes	—
82	C₅×#388	C₂²	1	2	yes	—
83	C₅×#388	C₂²	1	2	yes	—
84	C₅×#387	C₂²	1	2	yes	—
85	C₅×#387	C₂²	1	2	yes	—
86	C₅×#387	C₂²	1	2	yes	—
87	C₅×#387	C₂²	1	2	yes	—
88	C₅×#387	C₂²	1	2	yes	—
89	C₅×#387	C₂²	1	2	yes	—
90	C₅×#387	C₂²	1	2	yes	—
91	C₅×#387	C₂²	1	2	yes	—
92	C₅×#386	C₂²	1	2	yes	—
93	C₅×#385	C₂²	1	2	yes	—
94	C₅×#385	C₂²	1	2	yes	—
95	C₅×#385	C₂²	1	2	yes	—
96	C₅×#384	C₂²	1	1	yes	characteristic
97	C₅×#384	C₂²	1	1	yes	characteristic
98	C₅×#383	C₂²	1	2	yes	—
99	C₅×#383	C₂²	1	2	yes	—
100	C₅×#382	C₂²	1	2	yes	—
101	C₅×#382	C₂²	1	2	yes	—
102	C₅×#381	C₂²	1	2	yes	—
103	C₅×#380	C₂²	1	2	yes	—
104	C₅×#380	C₂²	1	1	yes	characteristic
105	C₅×#380	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	2	yes	—
109	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	1	yes	characteristic
121	C₄³×C₅	C₂²	1	1	yes	characteristic
122	C₄³×C₅	C₂²	1	1	yes	characteristic
123	#35269	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₅×D₄	C₂³	1	2	yes	—
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂³	1	2	yes	—
131	C₅×#126	—	4	4	no	—
132	C₅×#125	—	2	4	no	—
133	C₅×#125	—	4	4	no	—
134	C₅×#124	—	2	4	no	—
135	C₅×C₂²⋊Q₈	—	2	4	no	—
136	C₅×#121	—	2	4	no	—
137	C₄×C₅×Q₈	—	2	4	no	—
138	C₄×C₅×D₄	—	2	4	no	—
139	C₄×C₅×D₄	—	4	4	no	—
140	C₅×#117	—	2	4	no	—
141	C₅×#117	—	2	4	no	—
142	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×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	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×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×C₄²×C₅	—	2	4	no	—
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	1	yes	characteristic
197	C₂×C₄²×C₅	C₂³	1	2	yes	—
198	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
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	C₅×#95	C₂³	1	1	yes	characteristic
208	C₅×#95	C₂³	1	1	yes	characteristic
209	C₅×#95	C₂³	1	1	yes	characteristic
210	C₅×#95	C₂³	1	1	yes	characteristic
211	C₅×#95	C₂³	1	1	yes	characteristic
212	C₅×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	2	yes	—
221	C₅×#95	C₂³	1	2	yes	—
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	2	yes	—
230	C₅×#95	C₂³	1	2	yes	—
231	C₅×#95	C₂³	1	2	yes	—
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	#2863	C₂×C₅	1	1	yes	characteristic, complemented
236	#2861	C₂×C₅	1	1	yes	characteristic, complemented
237	#2860	C₂×C₅	1	1	yes	characteristic, complemented
238	#2859	C₂×C₅	1	1	yes	characteristic, complemented
239	#2629	C₂×C₅	1	1	yes	characteristic, complemented
240	#2625	C₂×C₅	1	1	yes	characteristic, complemented
241	#2624	C₂×C₅	1	1	yes	characteristic
242	#2620	C₂×C₅	1	1	yes	characteristic
243	#2525	C₂×C₅	1	2	yes	complemented
244	#2522	C₂×C₅	1	2	yes	complemented
245	#2519	C₂×C₅	1	2	yes	complemented
246	#2518	C₂×C₅	1	2	yes	complemented
247	#2518	C₂×C₅	1	2	yes	complemented
248	#2515	C₂×C₅	1	2	yes	complemented
249	#2466	C₂×C₅	1	2	yes	complemented
250	#2460	C₂×C₅	1	2	yes	complemented
251	#2330	C₂×C₅	1	1	yes	characteristic, complemented
252	#2326	C₂×C₅	1	1	yes	characteristic, complemented
253	#2320	C₂×C₅	1	1	yes	characteristic, complemented
254	#2319	C₂×C₅	1	1	yes	characteristic, complemented
255	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
256	C₄×#121	C₂×C₅	1	1	yes	characteristic
257	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
258	C₂⁴×C₅	C₂⁴	1	2	yes	—
259	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
260	C₂×C₅×Q₈	—	2	2	no	—
261	C₂×C₅×Q₈	—	2	2	no	—
262	C₂×C₅×Q₈	—	2	2	no	—
263	C₂×C₅×D₄	—	2	4	no	—
264	C₂×C₅×D₄	—	2	2	no	—
265	C₂×C₅×D₄	—	2	2	no	—
266	C₂×C₅×D₄	—	2	2	no	—
267	C₂×C₅×D₄	—	4	2	no	—
268	C₂×C₅×D₄	—	4	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	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	2	no	—
274	C₂²×C₄×C₅	—	2	2	no	—
275	C₂²×C₄×C₅	—	2	4	no	—
276	C₂²×C₄×C₅	—	4	1	no	—
277	C₂²×C₄×C₅	—	4	1	no	—
278	C₂²×C₄×C₅	—	4	2	no	—
279	C₂²×C₄×C₅	—	4	2	no	—
280	C₂²×C₄×C₅	#41	1	4	yes	—
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
302	C₅×C₄⋊C₄	—	2	2	no	—
303	C₅×C₄⋊C₄	—	2	2	no	—
304	C₅×C₄⋊C₄	—	2	2	no	—
305	C₅×C₄⋊C₄	—	2	2	no	—
306	C₅×C₄⋊C₄	—	2	2	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	2	4	no	—
309	C₅×C₄⋊C₄	—	2	2	no	—
310	C₅×C₄⋊C₄	—	2	2	no	—
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	2	4	no	—
313	C₅×C₄⋊C₄	—	2	4	no	—
314	C₅×C₄⋊C₄	—	2	2	no	—
315	C₅×C₄⋊C₄	—	2	2	no	—
316	C₅×C₄⋊C₄	—	2	4	no	—
317	C₅×C₄⋊C₄	—	2	4	no	—
318	C₅×C₄⋊C₄	—	4	2	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×C₂²⋊C₄	—	2	2	no	—
329	C₅×C₂²⋊C₄	—	2	2	no	—
330	C₅×C₂²⋊C₄	—	2	4	no	—
331	C₅×C₂²⋊C₄	—	2	2	no	—
332	C₅×C₂²⋊C₄	—	2	2	no	—
333	C₅×C₂²⋊C₄	—	2	4	no	—
334	C₅×C₂²⋊C₄	—	2	4	no	—
335	C₅×C₂²⋊C₄	—	2	4	no	—
336	C₅×C₂²⋊C₄	—	2	4	no	—
337	C₅×C₂²⋊C₄	—	2	4	no	—
338	C₅×C₂²⋊C₄	—	2	4	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	C₅×C₂²⋊C₄	—	4	2	no	—
346	C₅×C₂²⋊C₄	—	4	2	no	—
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	—	2	2	no	—
353	C₄²×C₅	—	2	4	no	—
354	C₄²×C₅	—	2	2	no	—
355	C₄²×C₅	—	2	2	no	—
356	C₄²×C₅	—	2	2	no	—
357	C₄²×C₅	—	2	2	no	—
358	C₄²×C₅	—	4	1	no	—
359	C₄²×C₅	—	4	1	no	—
360	C₄²×C₅	—	4	1	no	—
361	C₄²×C₅	—	4	1	no	—
362	C₄²×C₅	—	4	2	no	—
363	C₄²×C₅	—	4	2	no	—
364	C₄²×C₅	#41	1	4	yes	—
365	C₄²×C₅	#41	1	4	yes	—
366	C₂×#126	C₂²×C₅	1	2	yes	—
367	C₂×#125	C₂²×C₅	1	1	yes	characteristic
368	C₂×#125	C₂²×C₅	1	2	yes	—
369	C₂×#124	C₂²×C₅	1	1	yes	characteristic
370	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
371	C₂×#121	C₂²×C₅	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
375	C₂×#117	C₂²×C₅	1	1	yes	characteristic
376	C₂×#117	C₂²×C₅	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
378	#400	C₂²×C₅	1	2	yes	—
379	#399	C₂²×C₅	1	2	yes	—
380	#398	C₂²×C₅	1	2	yes	—
381	#398	C₂²×C₅	1	2	yes	—
382	#398	C₂²×C₅	1	2	yes	—
383	#397	C₂²×C₅	1	2	yes	—
384	#397	C₂²×C₅	1	2	yes	—
385	#397	C₂²×C₅	1	2	yes	—
386	#396	C₂²×C₅	1	2	yes	—
387	#396	C₂²×C₅	1	2	yes	—
388	#396	C₂²×C₅	1	2	yes	—
389	#396	C₂²×C₅	1	2	yes	—
390	#394	C₂²×C₅	1	2	yes	—
391	#394	C₂²×C₅	1	2	yes	—
392	#394	C₂²×C₅	1	2	yes	—
393	#394	C₂²×C₅	1	2	yes	—
394	#391	C₂²×C₅	1	1	yes	characteristic
395	#391	C₂²×C₅	1	1	yes	characteristic
396	#391	C₂²×C₅	1	1	yes	characteristic
397	#391	C₂²×C₅	1	1	yes	characteristic
398	#390	C₂²×C₅	1	1	yes	characteristic
399	#390	C₂²×C₅	1	1	yes	characteristic
400	#390	C₂²×C₅	1	1	yes	characteristic
401	#390	C₂²×C₅	1	1	yes	characteristic
402	#389	C₂²×C₅	1	1	yes	characteristic
403	#389	C₂²×C₅	1	1	yes	characteristic
404	#389	C₂²×C₅	1	1	yes	characteristic
405	#389	C₂²×C₅	1	1	yes	characteristic
406	#389	C₂²×C₅	1	1	yes	characteristic
407	#389	C₂²×C₅	1	1	yes	characteristic
408	#389	C₂²×C₅	1	2	yes	—
409	#389	C₂²×C₅	1	2	yes	—
410	#389	C₂²×C₅	1	1	yes	characteristic
411	#389	C₂²×C₅	1	1	yes	characteristic
412	#389	C₂²×C₅	1	2	yes	—
413	#389	C₂²×C₅	1	2	yes	—
414	#388	C₂²×C₅	1	2	yes	—
415	#388	C₂²×C₅	1	2	yes	—
416	#388	C₂²×C₅	1	2	yes	—
417	#388	C₂²×C₅	1	2	yes	—
418	#388	C₂²×C₅	1	2	yes	—
419	#388	C₂²×C₅	1	2	yes	—
420	#388	C₂²×C₅	1	2	yes	—
421	#388	C₂²×C₅	1	2	yes	—
422	#388	C₂²×C₅	1	2	yes	—
423	#388	C₂²×C₅	1	2	yes	—
424	#388	C₂²×C₅	1	2	yes	—
425	#388	C₂²×C₅	1	2	yes	—
426	#387	C₂²×C₅	1	2	yes	—
427	#387	C₂²×C₅	1	2	yes	—
428	#387	C₂²×C₅	1	2	yes	—
429	#387	C₂²×C₅	1	2	yes	—
430	#387	C₂²×C₅	1	2	yes	—
431	#387	C₂²×C₅	1	2	yes	—
432	#387	C₂²×C₅	1	2	yes	—
433	#387	C₂²×C₅	1	2	yes	—
434	#386	C₂²×C₅	1	2	yes	—
435	#385	C₂²×C₅	1	2	yes	—
436	#385	C₂²×C₅	1	2	yes	—
437	#385	C₂²×C₅	1	2	yes	—
438	#384	C₂²×C₅	1	1	yes	characteristic
439	#384	C₂²×C₅	1	1	yes	characteristic
440	#383	C₂²×C₅	1	2	yes	—
441	#383	C₂²×C₅	1	2	yes	—
442	#382	C₂²×C₅	1	2	yes	—
443	#382	C₂²×C₅	1	2	yes	—
444	#381	C₂²×C₅	1	2	yes	—
445	#380	C₂²×C₅	1	2	yes	—
446	#380	C₂²×C₅	1	1	yes	characteristic
447	#380	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
456	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
461	#376	C₂²×C₅	1	1	yes	characteristic
462	#376	C₂²×C₅	1	1	yes	characteristic
463	C₄³	C₂²×C₅	1	1	yes	characteristic
464	C₄³	C₂²×C₅	1	1	yes	characteristic
465	C₂³×C₅	—	2	1	no	—
466	C₂³×C₅	—	2	1	no	—
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	—	2	1	no	—
469	C₂³×C₅	—	2	1	no	—
470	C₂³×C₅	—	2	1	no	—
471	C₂³×C₅	—	2	2	no	—
472	C₂³×C₅	—	2	2	no	—
473	C₂³×C₅	—	2	2	no	—
474	C₂³×C₅	—	2	2	no	—
475	C₂³×C₅	—	2	2	no	—
476	C₂³×C₅	—	2	2	no	—
477	C₂³×C₅	—	2	2	no	—
478	C₂³×C₅	C₂×#41	1	2	yes	—
479	C₂³×C₅	C₂⁵	1	1	yes	characteristic
480	C₅×Q₈	—	4	4	no	—
481	C₅×D₄	—	4	8	no	—
482	C₅×D₄	—	4	4	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	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	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	8	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	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	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	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	2	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	2	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	2	2	no	—
536	C₂×C₄×C₅	—	2	2	no	—
537	C₂×C₄×C₅	—	4	4	no	—
538	C₂×C₄×C₅	—	4	4	no	—
539	C₂×C₄×C₅	—	8	4	no	—
540	C₂×C₄×C₅	C₂×#41	1	2	yes	—
541	C₂×C₄×C₅	C₂×#41	1	2	yes	—
542	C₂×C₄×C₅	C₂×#41	1	2	yes	—
543	C₂×C₄×C₅	C₂×#41	1	2	yes	—
544	C₂×C₄×C₅	C₂×#41	1	2	yes	—
545	C₂×C₄×C₅	C₂×#41	1	2	yes	—
546	C₂×C₄×C₅	C₂×#41	1	2	yes	—
547	C₂×C₄×C₅	C₂×#41	1	2	yes	—
548	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
550	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₅	1	2	yes	—
553	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₅	1	2	yes	—
557	#126	—	4	4	no	—
558	#125	—	2	4	no	—
559	#125	—	4	4	no	—
560	#124	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	#121	—	2	4	no	—
563	C₄×Q₈	—	2	4	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	4	4	no	—
566	#117	—	2	4	no	—
567	#117	—	2	4	no	—
568	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×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×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₄²	—	2	4	no	—
614	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₅	1	2	yes	—
618	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
624	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₅	1	2	yes	—
626	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₅	1	2	yes	—
631	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
633	#95	C₂³×C₅	1	1	yes	characteristic
634	#95	C₂³×C₅	1	1	yes	characteristic
635	#95	C₂³×C₅	1	1	yes	characteristic
636	#95	C₂³×C₅	1	1	yes	characteristic
637	#95	C₂³×C₅	1	1	yes	characteristic
638	#95	C₂³×C₅	1	1	yes	characteristic
639	#95	C₂³×C₅	1	1	yes	characteristic
640	#95	C₂³×C₅	1	1	yes	characteristic
641	#95	C₂³×C₅	1	2	yes	—
642	#95	C₂³×C₅	1	2	yes	—
643	#95	C₂³×C₅	1	2	yes	—
644	#95	C₂³×C₅	1	2	yes	—
645	#95	C₂³×C₅	1	2	yes	—
646	#95	C₂³×C₅	1	2	yes	—
647	#95	C₂³×C₅	1	2	yes	—
648	#95	C₂³×C₅	1	2	yes	—
649	#95	C₂³×C₅	1	2	yes	—
650	#95	C₂³×C₅	1	2	yes	—
651	#95	C₂³×C₅	1	2	yes	—
652	#95	C₂³×C₅	1	2	yes	—
653	#95	C₂³×C₅	1	2	yes	—
654	#95	C₂³×C₅	1	2	yes	—
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	C₂²×C₅	—	2	2	no	—
662	C₂²×C₅	—	2	2	no	—
663	C₂²×C₅	—	2	2	no	—
664	C₂²×C₅	—	4	1	no	—
665	C₂²×C₅	—	4	1	no	—
666	C₂²×C₅	—	4	1	no	—
667	C₂²×C₅	—	4	1	no	—
668	C₂²×C₅	—	4	2	no	—
669	C₂²×C₅	—	4	2	no	—
670	C₂²×C₅	—	4	2	no	—
671	C₂²×C₅	—	4	2	no	—
672	C₂²×C₅	—	4	2	no	—
673	C₂²×C₅	—	4	2	no	—
674	C₂²×C₅	—	4	2	no	—
675	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
676	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
677	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
678	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂²×C₅	#585	1	1	yes	characteristic
681	C₂²×C₅	#585	1	1	yes	characteristic
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	—	2	2	no	—
689	C₄×C₅	—	4	2	no	—
690	C₄×C₅	—	4	1	no	—
691	C₄×C₅	—	4	1	no	—
692	C₄×C₅	—	4	2	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	—	4	2	no	—
700	C₄×C₅	—	4	1	no	—
701	C₄×C₅	—	4	2	no	—
702	C₄×C₅	#529	1	4	yes	—
703	C₂⁴	C₂⁴×C₅	1	2	yes	—
704	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	4	1	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	C₅×#41	1	4	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	2	yes	—
729	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
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	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	4	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	4	2	no	—
804	C₄²	—	4	1	no	—
805	C₄²	—	4	1	no	—
806	C₄²	—	4	1	no	—
807	C₄²	—	4	1	no	—
808	C₄²	—	4	2	no	—
809	C₄²	C₅×#41	1	4	yes	—
810	C₄²	C₅×#41	1	4	yes	—
811	C₂×C₅	—	4	2	no	—
812	C₂×C₅	—	8	2	no	—
813	C₂×C₅	C₂×#529	1	1	yes	characteristic
814	C₂×C₅	#3460	1	1	yes	characteristic
815	C₂×C₅	#3461	1	1	yes	characteristic
816	C₂×C₅	#3494	1	1	yes	characteristic
817	C₂×C₅	#3495	1	1	yes	characteristic
818	C₂×C₅	#3511	1	1	yes	characteristic
819	C₂×C₅	#3512	1	1	yes	characteristic
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	C₂×C₅×#41	1	2	yes	—
834	C₂³	C₂⁵×C₅	1	1	yes	characteristic
835	Q₈	—	4	4	no	—
836	D₄	—	4	8	no	—
837	D₄	—	4	4	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	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	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	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	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	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	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	8	4	no	—
895	C₂×C₄	C₂×C₅×#41	1	2	yes	—
896	C₂×C₄	C₂×C₅×#41	1	2	yes	—
897	C₂×C₄	C₂×C₅×#41	1	2	yes	—
898	C₂×C₄	C₂×C₅×#41	1	2	yes	—
899	C₂×C₄	C₂×C₅×#41	1	2	yes	—
900	C₂×C₄	C₂×C₅×#41	1	2	yes	—
901	C₂×C₄	C₂×C₅×#41	1	2	yes	—
902	C₂×C₄	C₂×C₅×#41	1	2	yes	—
903	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
904	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
905	C₅	#35269	1	1	yes	characteristic, direct product factor, Sylow
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
921	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
922	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
923	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
924	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
925	C₂²	C₅×#585	1	1	yes	characteristic
926	C₂²	C₅×#585	1	1	yes	characteristic
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	C₅×#529	1	4	yes	—
948	C₂	—	4	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₂×C₅×#529	1	1	yes	characteristic
951	C₂	C₅×#3460	1	1	yes	characteristic
952	C₂	C₅×#3461	1	1	yes	characteristic
953	C₂	C₅×#3494	1	1	yes	characteristic
954	C₂	C₅×#3495	1	1	yes	characteristic
955	C₂	C₅×#3511	1	1	yes	characteristic
956	C₂	C₅×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2863	C₂	semidirect
2. C₅×#2861	C₂	semidirect
3. C₅×#2860	C₂	semidirect
4. C₅×#2859	C₂	semidirect
5. C₅×#2629	C₂	semidirect
6. C₅×#2625	C₂	semidirect
9. C₅×#2525	C₂	semidirect
10. C₅×#2522	C₂	semidirect
11. C₅×#2519	C₂	semidirect
12. C₅×#2518	C₂	semidirect
13. C₅×#2518	C₂	semidirect
14. C₅×#2515	C₂	semidirect
15. C₅×#2466	C₂	semidirect
16. C₅×#2460	C₂	semidirect
17. C₅×#2330	C₂	semidirect
18. C₅×#2326	C₂	semidirect
19. C₅×#2320	C₂	semidirect
20. C₅×#2319	C₂	semidirect
21. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
23. C₄×C₅×#117	C₂	semidirect
123. #35269	C₅	direct (N × H)
235. #2863	C₂×C₅	semidirect
236. #2861	C₂×C₅	semidirect
237. #2860	C₂×C₅	semidirect
238. #2859	C₂×C₅	semidirect
239. #2629	C₂×C₅	semidirect
240. #2625	C₂×C₅	semidirect
243. #2525	C₂×C₅	semidirect
244. #2522	C₂×C₅	semidirect
245. #2519	C₂×C₅	semidirect
246. #2518	C₂×C₅	semidirect
247. #2518	C₂×C₅	semidirect
248. #2515	C₂×C₅	semidirect
249. #2466	C₂×C₅	semidirect
250. #2460	C₂×C₅	semidirect
251. #2330	C₂×C₅	semidirect
252. #2326	C₂×C₅	semidirect
253. #2320	C₂×C₅	semidirect
254. #2319	C₂×C₅	semidirect
255. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
257. C₄×#117	C₂×C₅	semidirect
905. C₅	#35269	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×#2863	2
C₅×#2861	2
C₅×#2860	2
C₅×#2859	2
C₅×#2629	2
C₅×#2625	2
C₅×#2624	2
C₅×#2620	2
C₅×#2525	2
C₅×#2522	2
C₅×#2519	2
C₅×#2518	2
C₅×#2515	2
C₅×#2466	2
C₅×#2460	2
C₅×#2330	2
C₅×#2326	2
C₅×#2320	2
C₅×#2319	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#121	2
C₄×C₅×#117	2
#35269	5

Subgroups — C5×#35269 #11957989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35269 #11957989