Subgroups — C₅×#17516 #11940236

Order 1280.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3480	C₂	1	1	yes	maximal, characteristic
2	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1491	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1489	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1488	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1482	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1479	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#559	—	2	1	no	—
17	C₅×#559	C₄	1	1	yes	characteristic
18	C₅×#557	C₄	1	1	yes	characteristic
19	C₅×#556	—	2	1	no	—
20	C₅×#556	C₄	1	1	yes	characteristic
21	C₅×#553	—	2	1	no	—
22	C₅×#553	—	2	1	no	—
23	C₅×#553	C₄	1	1	yes	characteristic
24	C₅×#553	C₄	1	1	yes	characteristic
25	C₅×#550	C₄	1	1	yes	characteristic
26	C₅×#548	C₄	1	1	yes	characteristic
27	C₅×#548	C₄	1	1	yes	characteristic
28	C₅×#532	—	2	1	no	—
29	C₅×#532	C₂²	1	1	yes	characteristic
30	C₅×#529	—	2	1	no	—
31	C₅×#529	—	2	1	no	—
32	C₅×#529	C₂²	1	1	yes	characteristic
33	C₅×#529	C₂²	1	1	yes	characteristic
34	C₄×C₅×#41	—	2	1	no	—
35	C₄×C₅×#41	C₂²	1	1	yes	characteristic
36	C₄×C₅×#41	C₂²	1	1	yes	characteristic
37	C₄×C₅×#41	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
39	C₅×#446	—	2	1	no	—
40	C₅×#436	—	2	1	no	—
41	C₅×#435	—	2	1	no	—
42	C₅×#435	—	2	1	no	—
43	C₅×#433	—	2	1	no	—
44	C₅×#433	—	2	1	no	—
45	C₅×#432	C₂²	1	1	yes	characteristic
46	C₅×#432	C₂²	1	1	yes	characteristic
47	C₅×#431	C₂²	1	1	yes	characteristic
48	C₅×#431	C₂²	1	1	yes	characteristic
49	C₅×#431	C₂²	1	1	yes	characteristic
50	C₅×#431	C₂²	1	1	yes	characteristic
51	C₅×#431	C₂²	1	1	yes	characteristic
52	C₅×#423	C₂²	1	1	yes	characteristic
53	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×#408	—	2	1	no	—
55	C₅×#405	—	2	1	no	—
56	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
57	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
59	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
72	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
73	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
74	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
75	#17516	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×C₅×#41	—	2	1	no	—
77	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×#41	D₄	1	1	yes	characteristic
80	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂×C₅×M₁₆	—	2	1	no	—
83	C₂×C₅×M₁₆	—	2	1	no	—
84	C₂²×C₅×C₈	—	2	1	no	—
85	C₂²×C₅×C₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	—	2	1	no	—
87	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₅×#127	—	2	1	no	—
89	C₅×#127	C₂×C₄	1	1	yes	characteristic
90	C₅×#126	—	2	1	no	—
91	C₅×#126	—	2	1	no	—
92	C₅×#126	—	2	1	no	—
93	C₅×#126	—	2	1	no	—
94	C₅×#126	—	2	1	no	—
95	C₅×#126	—	2	1	no	—
96	C₅×#125	—	2	1	no	—
97	C₅×#125	—	2	1	no	—
98	C₅×#125	C₂×C₄	1	1	yes	characteristic
99	C₅×#125	C₂×C₄	1	1	yes	characteristic
100	C₅×#124	—	2	1	no	—
101	C₅×#124	—	2	1	no	—
102	C₅×#124	—	2	1	no	—
103	C₅×#124	—	2	1	no	—
104	C₅×#124	—	2	1	no	—
105	C₅×#124	C₂×C₄	1	1	yes	characteristic
106	C₅×#124	C₂×C₄	1	1	yes	characteristic
107	C₅×#123	—	2	1	no	—
108	C₅×#123	—	2	1	no	—
109	C₅×#123	—	2	1	no	—
110	C₅×#123	—	2	1	no	—
111	C₅×#123	—	2	1	no	—
112	C₅×#123	—	2	1	no	—
113	C₅×C₂²⋊Q₈	—	2	1	no	—
114	C₅×C₂²⋊Q₈	—	2	1	no	—
115	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
116	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
117	C₅×#121	—	2	1	no	—
118	C₅×#121	—	2	1	no	—
119	C₅×#121	—	2	1	no	—
120	C₅×#121	—	2	1	no	—
121	C₅×#121	—	2	1	no	—
122	C₅×#121	—	2	1	no	—
123	C₅×#121	—	2	1	no	—
124	C₅×#121	C₂×C₄	1	1	yes	characteristic
125	C₅×#121	C₂×C₄	1	1	yes	characteristic
126	C₅×#121	C₂×C₄	1	1	yes	characteristic
127	C₅×#121	C₂×C₄	1	1	yes	characteristic
128	C₄×C₅×Q₈	—	2	1	no	—
129	C₄×C₅×Q₈	—	2	1	no	—
130	C₄×C₅×Q₈	—	2	1	no	—
131	C₄×C₅×Q₈	—	2	1	no	—
132	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
133	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
134	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
135	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
136	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
137	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
138	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
139	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
140	C₄×C₅×D₄	—	2	1	no	—
141	C₄×C₅×D₄	—	2	1	no	—
142	C₄×C₅×D₄	—	2	1	no	—
143	C₄×C₅×D₄	—	2	1	no	—
144	C₄×C₅×D₄	—	2	1	no	—
145	C₄×C₅×D₄	—	2	1	no	—
146	C₄×C₅×D₄	—	2	1	no	—
147	C₄×C₅×D₄	—	2	1	no	—
148	C₄×C₅×D₄	—	2	1	no	—
149	C₄×C₅×D₄	—	2	1	no	—
150	C₄×C₅×D₄	—	2	1	no	—
151	C₄×C₅×D₄	—	2	1	no	—
152	C₄×C₅×D₄	—	2	1	no	—
153	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
154	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
155	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
156	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
157	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
158	C₄×C₅×D₄	D₄	1	1	yes	characteristic
159	C₄×C₅×D₄	D₄	1	1	yes	characteristic
160	C₄×C₅×D₄	D₄	1	1	yes	characteristic
161	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
162	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
163	C₅×#117	—	2	1	no	—
164	C₅×#117	—	2	1	no	—
165	C₅×#117	—	2	1	no	—
166	C₅×#117	—	2	1	no	—
167	C₅×#117	C₂×C₄	1	1	yes	characteristic
168	C₅×#117	C₂×C₄	1	1	yes	characteristic
169	C₅×#117	D₄	1	1	yes	characteristic
170	C₅×#117	D₄	1	1	yes	characteristic
171	C₅×#117	D₄	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	—	2	1	no	—
173	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
174	C₂×C₄²×C₅	—	2	1	no	—
175	C₂×C₄²×C₅	—	2	1	no	—
176	C₂×C₄²×C₅	—	2	1	no	—
177	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
180	C₅×C₄⋊C₈	—	2	1	no	—
181	C₅×C₄⋊C₈	—	2	1	no	—
182	C₅×C₄⋊C₈	—	2	1	no	—
183	C₅×C₄⋊C₈	—	2	1	no	—
184	C₅×C₄⋊C₈	—	2	1	no	—
185	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
186	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
187	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
188	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
189	C₅×C₂²⋊C₈	—	2	1	no	—
190	C₅×C₂²⋊C₈	—	2	1	no	—
191	C₅×C₂²⋊C₈	—	2	1	no	—
192	C₅×C₂²⋊C₈	—	2	1	no	—
193	C₅×C₂²⋊C₈	—	2	1	no	—
194	C₅×C₂²⋊C₈	—	2	1	no	—
195	C₅×C₂²⋊C₈	—	2	1	no	—
196	C₅×#97	—	2	1	no	—
197	C₅×#97	—	2	1	no	—
198	C₅×#97	—	2	1	no	—
199	C₅×#97	—	2	1	no	—
200	C₄×C₅×C₈	—	2	1	no	—
201	C₄×C₅×C₈	—	2	1	no	—
202	C₄×C₅×C₈	—	2	1	no	—
203	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
204	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
205	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
206	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
207	#3480	C₂×C₅	1	1	yes	characteristic
208	#2965	C₂×C₅	1	1	yes	characteristic, complemented
209	#2925	C₂×C₅	1	1	yes	characteristic, complemented
210	#1496	C₂×C₅	1	1	yes	characteristic, complemented
211	#1495	C₂×C₅	1	1	yes	characteristic, complemented
212	#1494	C₂×C₅	1	1	yes	characteristic, complemented
213	#1491	C₂×C₅	1	1	yes	characteristic, complemented
214	#1489	C₂×C₅	1	1	yes	characteristic, complemented
215	#1488	C₂×C₅	1	1	yes	characteristic, complemented
216	#1484	C₂×C₅	1	1	yes	characteristic, complemented
217	#1483	C₂×C₅	1	1	yes	characteristic, complemented
218	#1482	C₂×C₅	1	1	yes	characteristic, complemented
219	#1479	C₂×C₅	1	1	yes	characteristic, complemented
220	#1477	C₂×C₅	1	1	yes	characteristic, complemented
221	#1476	C₂×C₅	1	1	yes	characteristic, complemented
222	C₅×#41	—	2	2	no	—
223	C₅×#41	—	2	2	no	—
224	C₅×#41	—	4	1	no	—
225	C₅×#41	—	4	1	no	—
226	C₅×#41	—	4	1	no	—
227	C₅×#41	—	4	1	no	—
228	C₅×#41	—	4	2	no	—
229	C₅×#41	—	4	2	no	—
230	C₂×C₅×Q₈	—	2	1	no	—
231	C₂×C₅×Q₈	—	2	1	no	—
232	C₂×C₅×Q₈	—	2	2	no	—
233	C₂×C₅×Q₈	—	4	1	no	—
234	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₅×D₄	—	2	1	no	—
238	C₂×C₅×D₄	—	2	1	no	—
239	C₂×C₅×D₄	—	2	1	no	—
240	C₂×C₅×D₄	—	2	1	no	—
241	C₂×C₅×D₄	—	2	1	no	—
242	C₂×C₅×D₄	—	2	1	no	—
243	C₂×C₅×D₄	—	2	1	no	—
244	C₂×C₅×D₄	—	2	1	no	—
245	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
249	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₄×C₅	—	2	1	no	—
251	C₂²×C₄×C₅	—	2	1	no	—
252	C₂²×C₄×C₅	—	2	1	no	—
253	C₂²×C₄×C₅	—	2	1	no	—
254	C₂²×C₄×C₅	—	2	1	no	—
255	C₂²×C₄×C₅	—	2	1	no	—
256	C₂²×C₄×C₅	—	2	1	no	—
257	C₂²×C₄×C₅	—	2	1	no	—
258	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
267	C₅×M₁₆	—	4	2	no	—
268	C₅×M₁₆	—	4	2	no	—
269	C₅×M₁₆	—	4	2	no	—
270	C₂×C₅×C₈	—	2	1	no	—
271	C₂×C₅×C₈	—	2	1	no	—
272	C₂×C₅×C₈	—	2	1	no	—
273	C₂×C₅×C₈	—	2	1	no	—
274	C₂×C₅×C₈	—	2	1	no	—
275	C₂×C₅×C₈	—	2	1	no	—
276	C₂×C₅×C₈	—	2	1	no	—
277	C₂×C₅×C₈	—	2	1	no	—
278	C₂×C₅×C₈	—	4	2	no	—
279	C₂×C₅×C₈	—	4	2	no	—
280	C₅×C₄⋊C₄	—	2	1	no	—
281	C₅×C₄⋊C₄	—	2	1	no	—
282	C₅×C₄⋊C₄	—	2	1	no	—
283	C₅×C₄⋊C₄	—	2	1	no	—
284	C₅×C₄⋊C₄	—	2	1	no	—
285	C₅×C₄⋊C₄	—	2	1	no	—
286	C₅×C₄⋊C₄	—	2	1	no	—
287	C₅×C₄⋊C₄	—	2	1	no	—
288	C₅×C₄⋊C₄	—	2	1	no	—
289	C₅×C₄⋊C₄	—	2	1	no	—
290	C₅×C₄⋊C₄	—	2	1	no	—
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	—	2	1	no	—
293	C₅×C₄⋊C₄	—	2	1	no	—
294	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
298	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
300	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
301	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
302	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
303	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	—	2	1	no	—
307	C₅×C₂²⋊C₄	—	2	1	no	—
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	—	2	1	no	—
318	C₅×C₂²⋊C₄	—	2	1	no	—
319	C₅×C₂²⋊C₄	—	2	1	no	—
320	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
322	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
324	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
325	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
326	C₄²×C₅	—	2	1	no	—
327	C₄²×C₅	—	2	1	no	—
328	C₄²×C₅	—	2	1	no	—
329	C₄²×C₅	—	2	1	no	—
330	C₄²×C₅	—	2	1	no	—
331	C₄²×C₅	—	2	1	no	—
332	C₄²×C₅	—	2	1	no	—
333	C₄²×C₅	—	2	1	no	—
334	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
335	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
336	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
337	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₅	C₂⁴	1	1	yes	characteristic
344	#559	—	2	1	no	—
345	#559	C₄×C₅	1	1	yes	characteristic
346	#557	C₄×C₅	1	1	yes	characteristic
347	#556	—	2	1	no	—
348	#556	C₄×C₅	1	1	yes	characteristic
349	#553	—	2	1	no	—
350	#553	—	2	1	no	—
351	#553	C₄×C₅	1	1	yes	characteristic
352	#553	C₄×C₅	1	1	yes	characteristic
353	#550	C₄×C₅	1	1	yes	characteristic
354	#548	C₄×C₅	1	1	yes	characteristic
355	#548	C₄×C₅	1	1	yes	characteristic
356	#532	—	2	1	no	—
357	#532	C₂²×C₅	1	1	yes	characteristic
358	#529	—	2	1	no	—
359	#529	—	2	1	no	—
360	#529	C₂²×C₅	1	1	yes	characteristic
361	#529	C₂²×C₅	1	1	yes	characteristic
362	C₄×#41	—	2	1	no	—
363	C₄×#41	C₂²×C₅	1	1	yes	characteristic
364	C₄×#41	C₂²×C₅	1	1	yes	characteristic
365	C₄×#41	C₂²×C₅	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
367	#446	—	2	1	no	—
368	#436	—	2	1	no	—
369	#435	—	2	1	no	—
370	#435	—	2	1	no	—
371	#433	—	2	1	no	—
372	#433	—	2	1	no	—
373	#432	C₂²×C₅	1	1	yes	characteristic
374	#432	C₂²×C₅	1	1	yes	characteristic
375	#431	C₂²×C₅	1	1	yes	characteristic
376	#431	C₂²×C₅	1	1	yes	characteristic
377	#431	C₂²×C₅	1	1	yes	characteristic
378	#431	C₂²×C₅	1	1	yes	characteristic
379	#431	C₂²×C₅	1	1	yes	characteristic
380	#423	C₂²×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
382	#408	—	2	1	no	—
383	#405	—	2	1	no	—
384	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
385	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
386	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
387	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
388	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
389	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
390	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
391	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
392	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
393	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
394	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
395	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
396	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
397	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
398	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
399	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
400	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
401	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
402	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
403	C₂³×C₅	—	2	1	no	—
404	C₂³×C₅	—	2	1	no	—
405	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
406	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
408	C₅×Q₈	—	2	1	no	—
409	C₅×Q₈	—	2	1	no	—
410	C₅×Q₈	—	2	1	no	—
411	C₅×Q₈	—	4	1	no	—
412	C₅×Q₈	—	4	2	no	—
413	C₅×Q₈	—	4	2	no	—
414	C₅×Q₈	#131	1	2	yes	—
415	C₅×D₄	—	2	1	no	—
416	C₅×D₄	—	2	1	no	—
417	C₅×D₄	—	2	1	no	—
418	C₅×D₄	—	2	1	no	—
419	C₅×D₄	—	4	1	no	—
420	C₅×D₄	—	4	1	no	—
421	C₅×D₄	—	4	1	no	—
422	C₅×D₄	—	4	2	no	—
423	C₅×D₄	—	4	2	no	—
424	C₅×D₄	—	4	2	no	—
425	C₅×D₄	—	4	2	no	—
426	C₅×D₄	—	4	2	no	—
427	C₅×D₄	—	8	1	no	—
428	C₅×D₄	—	8	1	no	—
429	C₅×D₄	—	8	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	4	1	no	—
449	C₂×C₄×C₅	—	4	1	no	—
450	C₂×C₄×C₅	—	4	1	no	—
451	C₂×C₄×C₅	—	4	2	no	—
452	C₂×C₄×C₅	—	4	2	no	—
453	C₂×C₄×C₅	—	4	2	no	—
454	C₂×C₄×C₅	—	4	1	no	—
455	C₂×C₄×C₅	—	4	1	no	—
456	C₂×C₄×C₅	—	4	1	no	—
457	C₂×C₄×C₅	—	4	1	no	—
458	C₂×C₄×C₅	—	8	1	no	—
459	C₂×C₄×C₅	—	8	1	no	—
460	C₂×C₄×C₅	—	8	1	no	—
461	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
471	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
473	C₅×C₈	—	2	2	no	—
474	C₅×C₈	—	4	1	no	—
475	C₅×C₈	—	4	1	no	—
476	C₅×C₈	—	4	1	no	—
477	C₅×C₈	—	4	1	no	—
478	C₅×C₈	—	4	1	no	—
479	C₅×C₈	—	4	1	no	—
480	C₅×C₈	—	4	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
483	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
484	C₂×#41	C₅×D₄	1	1	yes	characteristic
485	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
486	C₂×M₁₆	—	2	1	no	—
487	C₂×M₁₆	—	2	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂²×C₈	—	2	1	no	—
490	C₂²×C₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
493	#127	—	2	1	no	—
494	#127	C₂×C₄×C₅	1	1	yes	characteristic
495	#126	—	2	1	no	—
496	#126	—	2	1	no	—
497	#126	—	2	1	no	—
498	#126	—	2	1	no	—
499	#126	—	2	1	no	—
500	#126	—	2	1	no	—
501	#125	—	2	1	no	—
502	#125	—	2	1	no	—
503	#125	C₂×C₄×C₅	1	1	yes	characteristic
504	#125	C₂×C₄×C₅	1	1	yes	characteristic
505	#124	—	2	1	no	—
506	#124	—	2	1	no	—
507	#124	—	2	1	no	—
508	#124	—	2	1	no	—
509	#124	—	2	1	no	—
510	#124	C₂×C₄×C₅	1	1	yes	characteristic
511	#124	C₂×C₄×C₅	1	1	yes	characteristic
512	#123	—	2	1	no	—
513	#123	—	2	1	no	—
514	#123	—	2	1	no	—
515	#123	—	2	1	no	—
516	#123	—	2	1	no	—
517	#123	—	2	1	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
521	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
522	#121	—	2	1	no	—
523	#121	—	2	1	no	—
524	#121	—	2	1	no	—
525	#121	—	2	1	no	—
526	#121	—	2	1	no	—
527	#121	—	2	1	no	—
528	#121	—	2	1	no	—
529	#121	C₂×C₄×C₅	1	1	yes	characteristic
530	#121	C₂×C₄×C₅	1	1	yes	characteristic
531	#121	C₂×C₄×C₅	1	1	yes	characteristic
532	#121	C₂×C₄×C₅	1	1	yes	characteristic
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
538	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
539	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
540	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
541	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
542	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
543	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
544	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
559	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
560	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
561	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
562	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
563	C₄×D₄	C₅×D₄	1	1	yes	characteristic
564	C₄×D₄	C₅×D₄	1	1	yes	characteristic
565	C₄×D₄	C₅×D₄	1	1	yes	characteristic
566	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
567	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
568	#117	—	2	1	no	—
569	#117	—	2	1	no	—
570	#117	—	2	1	no	—
571	#117	—	2	1	no	—
572	#117	C₂×C₄×C₅	1	1	yes	characteristic
573	#117	C₂×C₄×C₅	1	1	yes	characteristic
574	#117	C₅×D₄	1	1	yes	characteristic
575	#117	C₅×D₄	1	1	yes	characteristic
576	#117	C₅×D₄	1	1	yes	characteristic
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
585	C₄⋊C₈	—	2	1	no	—
586	C₄⋊C₈	—	2	1	no	—
587	C₄⋊C₈	—	2	1	no	—
588	C₄⋊C₈	—	2	1	no	—
589	C₄⋊C₈	—	2	1	no	—
590	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
591	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
592	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
593	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
594	C₂²⋊C₈	—	2	1	no	—
595	C₂²⋊C₈	—	2	1	no	—
596	C₂²⋊C₈	—	2	1	no	—
597	C₂²⋊C₈	—	2	1	no	—
598	C₂²⋊C₈	—	2	1	no	—
599	C₂²⋊C₈	—	2	1	no	—
600	C₂²⋊C₈	—	2	1	no	—
601	#97	—	2	1	no	—
602	#97	—	2	1	no	—
603	#97	—	2	1	no	—
604	#97	—	2	1	no	—
605	C₄×C₈	—	2	1	no	—
606	C₄×C₈	—	2	1	no	—
607	C₄×C₈	—	2	1	no	—
608	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
609	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
610	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
611	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
612	C₂²×C₅	—	2	1	no	—
613	C₂²×C₅	—	2	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	2	1	no	—
618	C₂²×C₅	—	2	1	no	—
619	C₂²×C₅	—	2	1	no	—
620	C₂²×C₅	—	2	1	no	—
621	C₂²×C₅	—	4	1	no	—
622	C₂²×C₅	—	4	1	no	—
623	C₂²×C₅	—	4	1	no	—
624	C₂²×C₅	—	4	1	no	—
625	C₂²×C₅	—	4	1	no	—
626	C₂²×C₅	—	4	1	no	—
627	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
628	C₄×C₅	—	2	1	no	—
629	C₄×C₅	—	2	1	no	—
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	2	2	no	—
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	2	1	no	—
635	C₄×C₅	—	2	1	no	—
636	C₄×C₅	—	2	1	no	—
637	C₄×C₅	—	2	1	no	—
638	C₄×C₅	—	2	1	no	—
639	C₄×C₅	—	4	1	no	—
640	C₄×C₅	—	4	1	no	—
641	C₄×C₅	—	4	1	no	—
642	C₄×C₅	—	4	1	no	—
643	C₄×C₅	—	4	1	no	—
644	C₄×C₅	C₂×#131	1	1	yes	characteristic
645	C₄×C₅	#568	1	1	yes	characteristic
646	C₄×C₅	#575	1	1	yes	characteristic
647	C₄×C₅	#575	1	1	yes	characteristic
648	#41	—	2	2	no	—
649	#41	—	2	2	no	—
650	#41	—	4	1	no	—
651	#41	—	4	1	no	—
652	#41	—	4	1	no	—
653	#41	—	4	1	no	—
654	#41	—	4	2	no	—
655	#41	—	4	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	4	1	no	—
660	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
661	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
662	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
672	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
673	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
674	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
675	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
685	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
686	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
687	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
688	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
689	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
690	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
691	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
692	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
693	M₁₆	—	4	2	no	—
694	M₁₆	—	4	2	no	—
695	M₁₆	—	4	2	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	4	2	no	—
705	C₂×C₈	—	4	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
721	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
722	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
723	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
724	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
725	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
747	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
748	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
749	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
750	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
751	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
752	C₄²	—	2	1	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
761	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
762	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
763	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
764	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
765	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
766	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
767	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
768	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
769	C₄²	C₂⁴×C₅	1	1	yes	characteristic
770	C₂×C₅	—	4	1	no	—
771	C₂×C₅	—	4	1	no	—
772	C₂×C₅	—	4	1	no	—
773	C₂×C₅	—	8	1	no	—
774	C₂×C₅	—	8	1	no	—
775	C₂×C₅	#2880	1	1	yes	characteristic
776	C₂×C₅	#2896	1	1	yes	characteristic
777	C₂×C₅	#2901	1	1	yes	characteristic
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
781	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
782	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	4	1	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	4	2	no	—
789	Q₈	C₅×#131	1	2	yes	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	4	1	no	—
795	D₄	—	4	1	no	—
796	D₄	—	4	1	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	8	1	no	—
803	D₄	—	8	1	no	—
804	D₄	—	8	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	8	1	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	—	8	1	no	—
836	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
837	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
838	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
839	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
840	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
841	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
842	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
843	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
844	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
845	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
846	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
847	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
848	C₈	—	2	2	no	—
849	C₈	—	4	1	no	—
850	C₈	—	4	1	no	—
851	C₈	—	4	1	no	—
852	C₈	—	4	1	no	—
853	C₈	—	4	1	no	—
854	C₈	—	4	1	no	—
855	C₈	—	4	1	no	—
856	C₅	#17516	1	1	yes	characteristic, direct product factor, Sylow
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	C₂×C₅×#131	1	1	yes	characteristic
890	C₄	C₅×#568	1	1	yes	characteristic
891	C₄	C₅×#575	1	1	yes	characteristic
892	C₄	C₅×#575	1	1	yes	characteristic
893	C₂	—	4	1	no	—
894	C₂	—	4	1	no	—
895	C₂	—	4	1	no	—
896	C₂	—	8	1	no	—
897	C₂	—	8	1	no	—
898	C₂	C₅×#2880	1	1	yes	characteristic
899	C₂	C₅×#2896	1	1	yes	characteristic
900	C₂	C₅×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₅×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2965	C₂	semidirect
3. C₅×#2925	C₂	semidirect
4. C₅×#1496	C₂	semidirect
5. C₅×#1495	C₂	semidirect
6. C₅×#1494	C₂	semidirect
7. C₅×#1491	C₂	semidirect
8. C₅×#1489	C₂	semidirect
9. C₅×#1488	C₂	semidirect
10. C₅×#1484	C₂	semidirect
11. C₅×#1483	C₂	semidirect
12. C₅×#1482	C₂	semidirect
13. C₅×#1479	C₂	semidirect
14. C₅×#1477	C₂	semidirect
15. C₅×#1476	C₂	semidirect
75. #17516	C₅	direct (N × H)
208. #2965	C₂×C₅	semidirect
209. #2925	C₂×C₅	semidirect
210. #1496	C₂×C₅	semidirect
211. #1495	C₂×C₅	semidirect
212. #1494	C₂×C₅	semidirect
213. #1491	C₂×C₅	semidirect
214. #1489	C₂×C₅	semidirect
215. #1488	C₂×C₅	semidirect
216. #1484	C₂×C₅	semidirect
217. #1483	C₂×C₅	semidirect
218. #1482	C₂×C₅	semidirect
219. #1479	C₂×C₅	semidirect
220. #1477	C₂×C₅	semidirect
221. #1476	C₂×C₅	semidirect
856. C₅	#17516	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×#3480	2
C₅×#2965	2
C₅×#2925	2
C₅×#1496	2
C₅×#1495	2
C₅×#1494	2
C₅×#1491	2
C₅×#1489	2
C₅×#1488	2
C₅×#1484	2
C₅×#1483	2
C₅×#1482	2
C₅×#1479	2
C₅×#1477	2
C₅×#1476	2
#17516	5

Subgroups — C5×#17516 #11940236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17516 #11940236