Subgroups — C₅×#60563 #11983283

Order 1280.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3117	C₂	1	2	yes	maximal, complemented
4	C₅×#3114	C₂	1	2	yes	maximal, complemented
5	C₅×#3111	C₂	1	4	yes	maximal, complemented
6	C₅×#3108	C₂	1	2	yes	maximal, complemented
7	C₅×#3105	C₂	1	2	yes	maximal, complemented
8	C₅×#3102	C₂	1	4	yes	maximal, complemented
9	C₅×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3080	C₂	1	2	yes	maximal, complemented
12	C₅×#3040	C₂	1	2	yes	maximal, complemented
13	C₅×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3006	C₂	1	1	yes	maximal, characteristic
15	C₄×C₅×#137	C₂	1	2	yes	maximal, complemented
16	C₄×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
17	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₅×#137	C₂²	1	2	yes	—
20	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₅×#529	—	2	1	no	—
22	C₅×#529	—	2	1	no	—
23	C₅×#529	—	2	1	no	—
24	C₅×#529	—	2	1	no	—
25	C₅×#529	C₂²	1	2	yes	—
26	C₅×#529	C₂²	1	2	yes	—
27	C₅×#529	C₂²	1	2	yes	complemented
28	C₅×#529	C₂²	1	2	yes	complemented
29	C₂×C₅×#126	—	2	1	no	—
30	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#123	—	2	1	no	—
33	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×#121	C₂²	1	1	yes	characteristic
35	C₄×C₅×#41	—	2	1	no	—
36	C₄×C₅×#41	—	2	1	no	—
37	C₄×C₅×#41	—	2	1	no	—
38	C₄×C₅×#41	—	2	1	no	—
39	C₄×C₅×#41	C₂²	1	2	yes	—
40	C₄×C₅×#41	C₂²	1	2	yes	—
41	C₄×C₅×#41	C₂²	1	2	yes	complemented
42	C₄×C₅×#41	C₂²	1	2	yes	complemented
43	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×D₄	—	2	1	no	—
47	C₂×C₄×C₅×D₄	—	2	1	no	—
48	C₂×C₄×C₅×D₄	—	2	1	no	—
49	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₅×#117	—	2	1	no	—
53	C₂×C₅×#117	—	2	1	no	—
54	C₂×C₅×#117	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₅	—	2	1	no	—
56	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
57	C₅×#485	C₂²	1	4	yes	complemented
58	C₅×#484	C₂²	1	2	yes	complemented
59	C₅×#483	C₂²	1	2	yes	complemented
60	C₅×#482	C₂²	1	4	yes	complemented
61	C₅×#481	C₂²	1	2	yes	—
62	C₅×#480	C₂²	1	2	yes	—
63	C₅×#479	C₂²	1	4	yes	complemented
64	C₅×#479	C₂²	1	4	yes	complemented
65	C₅×#478	C₂²	1	4	yes	complemented
66	C₅×#478	C₂²	1	4	yes	complemented
67	C₅×#464	C₂²	1	4	yes	complemented
68	C₅×#464	C₂²	1	4	yes	complemented
69	C₅×#463	C₂²	1	4	yes	complemented
70	C₅×#463	C₂²	1	4	yes	complemented
71	C₅×#452	C₂²	1	4	yes	complemented
72	C₅×#451	C₂²	1	2	yes	complemented
73	C₅×#450	C₂²	1	2	yes	complemented
74	C₅×#449	C₂²	1	4	yes	—
75	C₅×#448	C₂²	1	2	yes	—
76	C₅×#447	C₂²	1	2	yes	—
77	C₅×#442	C₂²	1	4	yes	complemented
78	C₅×#441	C₂²	1	4	yes	complemented
79	C₅×#440	C₂²	1	4	yes	complemented
80	C₅×#440	C₂²	1	4	yes	complemented
81	C₄×C₅×Q₁₆	C₂²	1	4	yes	complemented
82	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
83	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×C₅×D₈	C₂²	1	4	yes	complemented
85	C₅×#432	C₂²	1	2	yes	complemented
86	C₅×#432	C₂²	1	2	yes	complemented
87	C₅×#431	C₂²	1	2	yes	complemented
88	C₅×#431	C₂²	1	2	yes	complemented
89	C₅×#428	C₂²	1	2	yes	complemented
90	C₅×#428	C₂²	1	2	yes	complemented
91	C₅×#423	C₂²	1	2	yes	complemented
92	C₅×#419	C₂²	1	2	yes	complemented
93	C₅×#418	C₂²	1	2	yes	complemented
94	C₅×#417	C₂²	1	2	yes	—
95	C₅×#417	C₂²	1	2	yes	—
96	C₅×#407	C₂²	1	1	yes	characteristic
97	C₅×#407	C₂²	1	1	yes	characteristic
98	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
99	#60563	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×C₅×#41	—	2	8	no	—
101	C₂×C₅×#41	—	2	1	no	—
102	C₂×C₅×#41	—	2	1	no	—
103	C₂×C₅×#41	C₂³	1	2	yes	—
104	C₂×C₅×#41	C₂³	1	2	yes	—
105	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₅×D₄	—	2	1	no	—
108	C₂²×C₅×D₄	—	2	1	no	—
109	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
110	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅	—	2	1	no	—
112	C₂³×C₄×C₅	—	2	1	no	—
113	C₂³×C₄×C₅	—	2	1	no	—
114	C₂³×C₄×C₅	—	2	1	no	—
115	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
116	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
117	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₅×#137	—	2	8	no	—
119	C₅×AGL(1,ℤ/8)	—	2	8	no	—
120	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
121	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
123	C₂×C₅×D₈	C₂³	1	4	yes	—
124	C₂×C₅×M₁₆	C₂³	1	2	yes	—
125	C₂×C₅×M₁₆	C₂³	1	2	yes	—
126	C₅×#126	—	2	2	no	—
127	C₅×#126	—	2	2	no	—
128	C₅×#126	—	2	2	no	—
129	C₅×#126	—	2	2	no	—
130	C₅×#125	—	2	1	no	—
131	C₅×#125	—	2	1	no	—
132	C₅×#125	C₂³	1	2	yes	—
133	C₅×#125	C₂³	1	2	yes	—
134	C₅×#124	—	2	1	no	—
135	C₅×#124	—	2	1	no	—
136	C₅×#124	C₂³	1	2	yes	—
137	C₅×#124	C₂³	1	2	yes	—
138	C₅×#123	—	2	2	no	—
139	C₅×#123	—	2	2	no	—
140	C₅×#123	—	2	2	no	—
141	C₅×#123	—	2	2	no	—
142	C₅×C₂²⋊Q₈	—	2	1	no	—
143	C₅×C₂²⋊Q₈	—	2	1	no	—
144	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₅×#121	—	2	1	no	—
147	C₅×#121	—	2	1	no	—
148	C₅×#121	C₂³	1	2	yes	—
149	C₅×#121	C₂³	1	2	yes	—
150	C₄×C₅×Q₈	—	2	1	no	—
151	C₄×C₅×Q₈	—	2	1	no	—
152	C₄×C₅×Q₈	—	2	1	no	—
153	C₄×C₅×Q₈	—	2	1	no	—
154	C₄×C₅×Q₈	—	2	1	no	—
155	C₄×C₅×Q₈	—	2	1	no	—
156	C₄×C₅×Q₈	C₂³	1	2	yes	—
157	C₄×C₅×Q₈	C₂³	1	2	yes	—
158	C₄×C₅×Q₈	C₂³	1	2	yes	—
159	C₄×C₅×Q₈	C₂³	1	2	yes	—
160	C₄×C₅×Q₈	C₂³	1	2	yes	—
161	C₄×C₅×Q₈	C₂³	1	2	yes	—
162	C₄×C₅×D₄	—	2	2	no	—
163	C₄×C₅×D₄	—	2	2	no	—
164	C₄×C₅×D₄	—	2	2	no	—
165	C₄×C₅×D₄	—	2	2	no	—
166	C₄×C₅×D₄	—	2	2	no	—
167	C₄×C₅×D₄	—	2	2	no	—
168	C₄×C₅×D₄	—	2	2	no	—
169	C₄×C₅×D₄	—	2	2	no	—
170	C₄×C₅×D₄	—	2	2	no	—
171	C₄×C₅×D₄	—	2	2	no	—
172	C₄×C₅×D₄	—	2	2	no	—
173	C₄×C₅×D₄	—	2	2	no	—
174	C₄×C₅×D₄	—	2	1	no	—
175	C₄×C₅×D₄	—	2	1	no	—
176	C₄×C₅×D₄	—	2	1	no	—
177	C₄×C₅×D₄	—	2	1	no	—
178	C₄×C₅×D₄	—	2	1	no	—
179	C₄×C₅×D₄	—	2	1	no	—
180	C₄×C₅×D₄	C₂³	1	2	yes	—
181	C₄×C₅×D₄	C₂³	1	2	yes	—
182	C₄×C₅×D₄	C₂³	1	2	yes	—
183	C₄×C₅×D₄	C₂³	1	2	yes	—
184	C₄×C₅×D₄	C₂³	1	2	yes	—
185	C₄×C₅×D₄	C₂³	1	2	yes	—
186	C₅×#117	—	2	1	no	—
187	C₅×#117	—	2	1	no	—
188	C₅×#117	—	2	2	no	—
189	C₅×#117	—	2	2	no	—
190	C₅×#117	—	2	2	no	—
191	C₅×#117	—	2	2	no	—
192	C₅×#117	—	2	2	no	—
193	C₅×#117	—	2	2	no	—
194	C₅×#117	—	2	2	no	—
195	C₅×#117	—	2	2	no	—
196	C₅×#117	C₂³	1	2	yes	—
197	C₅×#117	C₂³	1	2	yes	—
198	C₂×C₅×C₄⋊C₄	—	2	1	no	—
199	C₂×C₅×C₄⋊C₄	—	2	1	no	—
200	C₂×C₅×C₄⋊C₄	—	2	1	no	—
201	C₂×C₅×C₄⋊C₄	—	2	1	no	—
202	C₂×C₅×C₄⋊C₄	—	2	1	no	—
203	C₂×C₅×C₄⋊C₄	—	2	1	no	—
204	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
210	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
211	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
213	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
214	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
216	C₂×C₄²×C₅	—	2	1	no	—
217	C₂×C₄²×C₅	—	2	1	no	—
218	C₂×C₄²×C₅	—	2	1	no	—
219	C₂×C₄²×C₅	—	2	1	no	—
220	C₂×C₄²×C₅	—	2	2	no	—
221	C₂×C₄²×C₅	—	2	2	no	—
222	C₂×C₄²×C₅	—	2	2	no	—
223	C₂×C₄²×C₅	—	2	2	no	—
224	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
236	C₅×#107	C₂³	1	4	yes	—
237	C₅×#107	C₂³	1	4	yes	—
238	C₅×#106	C₂³	1	4	yes	—
239	C₅×#106	C₂³	1	4	yes	—
240	C₅×C₄⋊C₈	C₂³	1	4	yes	—
241	C₅×C₄⋊C₈	C₂³	1	4	yes	—
242	C₅×#103	C₂³	1	4	yes	—
243	C₅×#103	C₂³	1	4	yes	—
244	C₅×#103	C₂³	1	4	yes	—
245	C₅×#103	C₂³	1	4	yes	—
246	C₅×#102	C₂³	1	4	yes	—
247	C₅×#102	C₂³	1	4	yes	—
248	C₅×#102	C₂³	1	4	yes	—
249	C₅×#102	C₂³	1	4	yes	—
250	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₅×#97	C₂³	1	4	yes	—
255	C₄×C₅×C₈	C₂³	1	4	yes	—
256	C₂×#529	C₂×C₅	1	1	yes	characteristic, complemented
257	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
258	#3117	C₂×C₅	1	2	yes	complemented
259	#3114	C₂×C₅	1	2	yes	complemented
260	#3111	C₂×C₅	1	4	yes	complemented
261	#3108	C₂×C₅	1	2	yes	complemented
262	#3105	C₂×C₅	1	2	yes	complemented
263	#3102	C₂×C₅	1	4	yes	complemented
264	#3095	C₂×C₅	1	1	yes	characteristic, complemented
265	#3094	C₂×C₅	1	1	yes	characteristic, complemented
266	#3080	C₂×C₅	1	2	yes	complemented
267	#3040	C₂×C₅	1	2	yes	complemented
268	#3007	C₂×C₅	1	1	yes	characteristic, complemented
269	#3006	C₂×C₅	1	1	yes	characteristic
270	C₄×#137	C₂×C₅	1	2	yes	complemented
271	C₄×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
272	#2920	C₂×C₅	1	1	yes	characteristic, complemented
273	C₂⁴×C₅	—	2	1	no	—
274	C₂⁴×C₅	—	2	1	no	—
275	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
276	C₅×#41	—	2	8	no	—
277	C₅×#41	—	2	8	no	—
278	C₅×#41	—	2	4	no	—
279	C₅×#41	—	2	4	no	—
280	C₅×#41	—	2	4	no	—
281	C₅×#41	#41	1	8	yes	—
282	C₂×C₅×Q₈	—	2	4	no	—
283	C₂×C₅×Q₈	—	2	1	no	—
284	C₂×C₅×Q₈	—	2	1	no	—
285	C₂×C₅×Q₈	—	2	4	no	—
286	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
287	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
288	C₂×C₅×D₄	—	2	8	no	—
289	C₂×C₅×D₄	—	2	2	no	—
290	C₂×C₅×D₄	—	2	2	no	—
291	C₂×C₅×D₄	—	2	4	no	—
292	C₂×C₅×D₄	—	2	2	no	—
293	C₂×C₅×D₄	—	2	2	no	—
294	C₂×C₅×D₄	—	2	1	no	—
295	C₂×C₅×D₄	—	2	1	no	—
296	C₂×C₅×D₄	—	2	4	no	—
297	C₂×C₅×D₄	—	4	4	no	—
298	C₂×C₅×D₄	C₂⁴	1	2	yes	—
299	C₂×C₅×D₄	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	—	2	8	no	—
301	C₂²×C₄×C₅	—	2	1	no	—
302	C₂²×C₄×C₅	—	2	2	no	—
303	C₂²×C₄×C₅	—	2	2	no	—
304	C₂²×C₄×C₅	—	2	4	no	—
305	C₂²×C₄×C₅	—	2	1	no	—
306	C₂²×C₄×C₅	—	2	1	no	—
307	C₂²×C₄×C₅	—	2	1	no	—
308	C₂²×C₄×C₅	—	2	1	no	—
309	C₂²×C₄×C₅	—	2	1	no	—
310	C₂²×C₄×C₅	—	2	2	no	—
311	C₂²×C₄×C₅	—	2	2	no	—
312	C₂²×C₄×C₅	—	2	2	no	—
313	C₂²×C₄×C₅	—	2	2	no	—
314	C₂²×C₄×C₅	—	2	2	no	—
315	C₂²×C₄×C₅	—	2	2	no	—
316	C₂²×C₄×C₅	—	4	2	no	—
317	C₂²×C₄×C₅	—	4	2	no	—
318	C₂²×C₄×C₅	—	4	4	no	—
319	C₂²×C₄×C₅	—	4	4	no	—
320	C₂²×C₄×C₅	—	4	4	no	—
321	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
339	C₅×Q₁₆	—	2	8	no	—
340	C₅×SD₁₆	—	2	8	no	—
341	C₅×SD₁₆	—	2	8	no	—
342	C₅×D₈	—	2	8	no	—
343	C₅×M₁₆	—	2	4	no	—
344	C₅×M₁₆	—	2	4	no	—
345	C₂×C₅×C₈	C₂⁴	1	4	yes	—
346	C₂×C₅×C₈	C₂⁴	1	4	yes	—
347	C₅×C₄⋊C₄	—	2	2	no	—
348	C₅×C₄⋊C₄	—	2	2	no	—
349	C₅×C₄⋊C₄	—	2	2	no	—
350	C₅×C₄⋊C₄	—	2	2	no	—
351	C₅×C₄⋊C₄	—	2	2	no	—
352	C₅×C₄⋊C₄	—	2	2	no	—
353	C₅×C₄⋊C₄	—	2	2	no	—
354	C₅×C₄⋊C₄	—	2	2	no	—
355	C₅×C₄⋊C₄	—	2	2	no	—
356	C₅×C₄⋊C₄	—	2	2	no	—
357	C₅×C₄⋊C₄	—	2	2	no	—
358	C₅×C₄⋊C₄	—	2	2	no	—
359	C₅×C₄⋊C₄	—	2	1	no	—
360	C₅×C₄⋊C₄	—	2	1	no	—
361	C₅×C₄⋊C₄	—	2	1	no	—
362	C₅×C₄⋊C₄	—	2	1	no	—
363	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₅×C₂²⋊C₄	—	2	2	no	—
368	C₅×C₂²⋊C₄	—	2	2	no	—
369	C₅×C₂²⋊C₄	—	2	2	no	—
370	C₅×C₂²⋊C₄	—	2	2	no	—
371	C₅×C₂²⋊C₄	—	2	2	no	—
372	C₅×C₂²⋊C₄	—	2	2	no	—
373	C₅×C₂²⋊C₄	—	2	2	no	—
374	C₅×C₂²⋊C₄	—	2	2	no	—
375	C₅×C₂²⋊C₄	—	2	2	no	—
376	C₅×C₂²⋊C₄	—	2	2	no	—
377	C₅×C₂²⋊C₄	—	2	2	no	—
378	C₅×C₂²⋊C₄	—	2	2	no	—
379	C₅×C₂²⋊C₄	—	2	2	no	—
380	C₅×C₂²⋊C₄	—	2	2	no	—
381	C₅×C₂²⋊C₄	—	2	2	no	—
382	C₅×C₂²⋊C₄	—	2	2	no	—
383	C₄²×C₅	—	2	2	no	—
384	C₄²×C₅	—	2	2	no	—
385	C₄²×C₅	—	2	2	no	—
386	C₄²×C₅	—	2	2	no	—
387	C₄²×C₅	—	2	2	no	—
388	C₄²×C₅	—	2	2	no	—
389	C₄²×C₅	—	2	2	no	—
390	C₄²×C₅	—	2	2	no	—
391	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₅	C₂⁴	1	1	yes	characteristic
404	C₄²×C₅	C₂⁴	1	1	yes	characteristic
405	C₄²×C₅	C₂⁴	1	1	yes	characteristic
406	C₄²×C₅	C₂⁴	1	1	yes	characteristic
407	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
408	C₂×#137	C₂²×C₅	1	2	yes	—
409	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
410	#529	—	2	1	no	—
411	#529	—	2	1	no	—
412	#529	—	2	1	no	—
413	#529	—	2	1	no	—
414	#529	C₂²×C₅	1	2	yes	—
415	#529	C₂²×C₅	1	2	yes	—
416	#529	C₂²×C₅	1	2	yes	complemented
417	#529	C₂²×C₅	1	2	yes	complemented
418	C₂×#126	—	2	1	no	—
419	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
420	C₂×#124	C₂²×C₅	1	1	yes	characteristic, complemented
421	C₂×#123	—	2	1	no	—
422	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
423	C₂×#121	C₂²×C₅	1	1	yes	characteristic
424	C₄×#41	—	2	1	no	—
425	C₄×#41	—	2	1	no	—
426	C₄×#41	—	2	1	no	—
427	C₄×#41	—	2	1	no	—
428	C₄×#41	C₂²×C₅	1	2	yes	—
429	C₄×#41	C₂²×C₅	1	2	yes	—
430	C₄×#41	C₂²×C₅	1	2	yes	complemented
431	C₄×#41	C₂²×C₅	1	2	yes	complemented
432	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
433	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
434	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
435	C₂×C₄×D₄	—	2	1	no	—
436	C₂×C₄×D₄	—	2	1	no	—
437	C₂×C₄×D₄	—	2	1	no	—
438	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
439	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
441	C₂×#117	—	2	1	no	—
442	C₂×#117	—	2	1	no	—
443	C₂×#117	C₂²×C₅	1	1	yes	characteristic
444	C₂²×C₄²	—	2	1	no	—
445	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
446	#485	C₂²×C₅	1	4	yes	complemented
447	#484	C₂²×C₅	1	2	yes	complemented
448	#483	C₂²×C₅	1	2	yes	complemented
449	#482	C₂²×C₅	1	4	yes	complemented
450	#481	C₂²×C₅	1	2	yes	—
451	#480	C₂²×C₅	1	2	yes	—
452	#479	C₂²×C₅	1	4	yes	complemented
453	#479	C₂²×C₅	1	4	yes	complemented
454	#478	C₂²×C₅	1	4	yes	complemented
455	#478	C₂²×C₅	1	4	yes	complemented
456	#464	C₂²×C₅	1	4	yes	complemented
457	#464	C₂²×C₅	1	4	yes	complemented
458	#463	C₂²×C₅	1	4	yes	complemented
459	#463	C₂²×C₅	1	4	yes	complemented
460	#452	C₂²×C₅	1	4	yes	complemented
461	#451	C₂²×C₅	1	2	yes	complemented
462	#450	C₂²×C₅	1	2	yes	complemented
463	#449	C₂²×C₅	1	4	yes	—
464	#448	C₂²×C₅	1	2	yes	—
465	#447	C₂²×C₅	1	2	yes	—
466	#442	C₂²×C₅	1	4	yes	complemented
467	#441	C₂²×C₅	1	4	yes	complemented
468	#440	C₂²×C₅	1	4	yes	complemented
469	#440	C₂²×C₅	1	4	yes	complemented
470	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
471	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
472	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
473	C₄×D₈	C₂²×C₅	1	4	yes	complemented
474	#432	C₂²×C₅	1	2	yes	complemented
475	#432	C₂²×C₅	1	2	yes	complemented
476	#431	C₂²×C₅	1	2	yes	complemented
477	#431	C₂²×C₅	1	2	yes	complemented
478	#428	C₂²×C₅	1	2	yes	complemented
479	#428	C₂²×C₅	1	2	yes	complemented
480	#423	C₂²×C₅	1	2	yes	complemented
481	#419	C₂²×C₅	1	2	yes	complemented
482	#418	C₂²×C₅	1	2	yes	complemented
483	#417	C₂²×C₅	1	2	yes	—
484	#417	C₂²×C₅	1	2	yes	—
485	#407	C₂²×C₅	1	1	yes	characteristic
486	#407	C₂²×C₅	1	1	yes	characteristic
487	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
488	C₂³×C₅	—	2	4	no	—
489	C₂³×C₅	—	2	2	no	—
490	C₂³×C₅	—	2	2	no	—
491	C₂³×C₅	—	2	2	no	—
492	C₂³×C₅	—	2	2	no	—
493	C₂³×C₅	—	4	1	no	—
494	C₂³×C₅	—	4	2	no	—
495	C₂³×C₅	—	4	2	no	—
496	C₂³×C₅	—	4	2	no	—
497	C₂³×C₅	—	4	2	no	—
498	C₂³×C₅	—	4	2	no	—
499	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
500	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
502	C₅×Q₈	—	2	4	no	—
503	C₅×Q₈	—	2	2	no	—
504	C₅×Q₈	—	2	4	no	—
505	C₅×Q₈	—	4	2	no	—
506	C₅×Q₈	C₂×#41	1	4	yes	—
507	C₅×D₄	—	2	8	no	—
508	C₅×D₄	—	2	4	no	—
509	C₅×D₄	—	2	8	no	—
510	C₅×D₄	—	2	2	no	—
511	C₅×D₄	—	2	4	no	—
512	C₅×D₄	—	4	4	no	—
513	C₅×D₄	—	4	4	no	—
514	C₅×D₄	—	4	2	no	—
515	C₅×D₄	C₂×#41	1	4	yes	—
516	C₂×C₄×C₅	—	2	4	no	—
517	C₂×C₄×C₅	—	2	8	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	2	no	—
522	C₂×C₄×C₅	—	2	2	no	—
523	C₂×C₄×C₅	—	2	8	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	2	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	2	no	—
529	C₂×C₄×C₅	—	2	2	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	2	no	—
532	C₂×C₄×C₅	—	2	2	no	—
533	C₂×C₄×C₅	—	2	2	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	4	1	no	—
536	C₂×C₄×C₅	—	4	1	no	—
537	C₂×C₄×C₅	—	4	1	no	—
538	C₂×C₄×C₅	—	4	1	no	—
539	C₂×C₄×C₅	—	4	1	no	—
540	C₂×C₄×C₅	—	4	1	no	—
541	C₂×C₄×C₅	—	4	1	no	—
542	C₂×C₄×C₅	—	4	4	no	—
543	C₂×C₄×C₅	—	4	4	no	—
544	C₂×C₄×C₅	—	4	4	no	—
545	C₂×C₄×C₅	—	4	4	no	—
546	C₂×C₄×C₅	—	4	2	no	—
547	C₂×C₄×C₅	—	4	2	no	—
548	C₂×C₄×C₅	—	4	2	no	—
549	C₂×C₄×C₅	—	4	2	no	—
550	C₂×C₄×C₅	—	4	2	no	—
551	C₂×C₄×C₅	—	4	4	no	—
552	C₂×C₄×C₅	—	4	4	no	—
553	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₅	C₂×#41	1	4	yes	—
565	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
566	C₅×C₈	—	2	4	no	—
567	C₅×C₈	—	2	4	no	—
568	C₂×#41	—	2	8	no	—
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	2	1	no	—
571	C₂×#41	C₂³×C₅	1	2	yes	—
572	C₂×#41	C₂³×C₅	1	2	yes	—
573	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
579	C₂³×C₄	—	2	1	no	—
580	C₂³×C₄	—	2	1	no	—
581	C₂³×C₄	—	2	1	no	—
582	C₂³×C₄	—	2	1	no	—
583	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
584	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
586	#137	—	2	8	no	—
587	AGL(1,ℤ/8)	—	2	8	no	—
588	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
589	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
590	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
591	C₂×D₈	C₂³×C₅	1	4	yes	—
592	C₂×M₁₆	C₂³×C₅	1	2	yes	—
593	C₂×M₁₆	C₂³×C₅	1	2	yes	—
594	#126	—	2	2	no	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#125	—	2	1	no	—
599	#125	—	2	1	no	—
600	#125	C₂³×C₅	1	2	yes	—
601	#125	C₂³×C₅	1	2	yes	—
602	#124	—	2	1	no	—
603	#124	—	2	1	no	—
604	#124	C₂³×C₅	1	2	yes	—
605	#124	C₂³×C₅	1	2	yes	—
606	#123	—	2	2	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
613	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
614	#121	—	2	1	no	—
615	#121	—	2	1	no	—
616	#121	C₂³×C₅	1	2	yes	—
617	#121	C₂³×C₅	1	2	yes	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	—	2	1	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	C₂³×C₅	1	2	yes	—
625	C₄×Q₈	C₂³×C₅	1	2	yes	—
626	C₄×Q₈	C₂³×C₅	1	2	yes	—
627	C₄×Q₈	C₂³×C₅	1	2	yes	—
628	C₄×Q₈	C₂³×C₅	1	2	yes	—
629	C₄×Q₈	C₂³×C₅	1	2	yes	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	C₂³×C₅	1	2	yes	—
649	C₄×D₄	C₂³×C₅	1	2	yes	—
650	C₄×D₄	C₂³×C₅	1	2	yes	—
651	C₄×D₄	C₂³×C₅	1	2	yes	—
652	C₄×D₄	C₂³×C₅	1	2	yes	—
653	C₄×D₄	C₂³×C₅	1	2	yes	—
654	#117	—	2	1	no	—
655	#117	—	2	1	no	—
656	#117	—	2	2	no	—
657	#117	—	2	2	no	—
658	#117	—	2	2	no	—
659	#117	—	2	2	no	—
660	#117	—	2	2	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	C₂³×C₅	1	2	yes	—
665	#117	C₂³×C₅	1	2	yes	—
666	C₂×C₄⋊C₄	—	2	1	no	—
667	C₂×C₄⋊C₄	—	2	1	no	—
668	C₂×C₄⋊C₄	—	2	1	no	—
669	C₂×C₄⋊C₄	—	2	1	no	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	—	2	1	no	—
672	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	2	no	—
689	C₂×C₄²	—	2	2	no	—
690	C₂×C₄²	—	2	2	no	—
691	C₂×C₄²	—	2	2	no	—
692	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
693	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
694	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
695	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
696	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
697	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
704	#107	C₂³×C₅	1	4	yes	—
705	#107	C₂³×C₅	1	4	yes	—
706	#106	C₂³×C₅	1	4	yes	—
707	#106	C₂³×C₅	1	4	yes	—
708	C₄⋊C₈	C₂³×C₅	1	4	yes	—
709	C₄⋊C₈	C₂³×C₅	1	4	yes	—
710	#103	C₂³×C₅	1	4	yes	—
711	#103	C₂³×C₅	1	4	yes	—
712	#103	C₂³×C₅	1	4	yes	—
713	#103	C₂³×C₅	1	4	yes	—
714	#102	C₂³×C₅	1	4	yes	—
715	#102	C₂³×C₅	1	4	yes	—
716	#102	C₂³×C₅	1	4	yes	—
717	#102	C₂³×C₅	1	4	yes	—
718	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
722	#97	C₂³×C₅	1	4	yes	—
723	C₄×C₈	C₂³×C₅	1	4	yes	—
724	C₂²×C₅	—	2	1	no	—
725	C₂²×C₅	—	2	1	no	—
726	C₂²×C₅	—	2	1	no	—
727	C₂²×C₅	—	2	1	no	—
728	C₂²×C₅	—	2	1	no	—
729	C₂²×C₅	—	2	4	no	—
730	C₂²×C₅	—	2	1	no	—
731	C₂²×C₅	—	2	1	no	—
732	C₂²×C₅	—	4	4	no	—
733	C₂²×C₅	—	4	8	no	—
734	C₂²×C₅	—	4	2	no	—
735	C₂²×C₅	—	4	2	no	—
736	C₂²×C₅	—	4	2	no	—
737	C₂²×C₅	—	4	2	no	—
738	C₂²×C₅	—	4	2	no	—
739	C₂²×C₅	—	8	4	no	—
740	C₂²×C₅	#525	1	2	yes	—
741	C₂²×C₅	#575	1	2	yes	—
742	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
743	C₄×C₅	—	2	1	no	—
744	C₄×C₅	—	2	4	no	—
745	C₄×C₅	—	2	1	no	—
746	C₄×C₅	—	2	1	no	—
747	C₄×C₅	—	2	1	no	—
748	C₄×C₅	—	2	1	no	—
749	C₄×C₅	—	2	1	no	—
750	C₄×C₅	—	2	1	no	—
751	C₄×C₅	—	2	1	no	—
752	C₄×C₅	—	2	1	no	—
753	C₄×C₅	—	4	2	no	—
754	C₄×C₅	—	4	2	no	—
755	C₄×C₅	—	4	2	no	—
756	C₄×C₅	—	4	2	no	—
757	C₄×C₅	—	4	2	no	—
758	C₄×C₅	#525	1	2	yes	—
759	C₄×C₅	#575	1	2	yes	—
760	C₄×C₅	C₂²×#41	1	2	yes	—
761	C₂⁴	—	2	1	no	—
762	C₂⁴	—	2	1	no	—
763	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
764	#41	—	2	8	no	—
765	#41	—	2	8	no	—
766	#41	—	2	4	no	—
767	#41	—	2	4	no	—
768	#41	—	2	4	no	—
769	#41	C₅×#41	1	8	yes	—
770	C₂×Q₈	—	2	4	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	4	no	—
774	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
775	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
776	C₂×D₄	—	2	8	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	C₂⁴×C₅	1	2	yes	—
787	C₂×D₄	C₂⁴×C₅	1	2	yes	—
788	C₂²×C₄	—	2	8	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	4	no	—
807	C₂²×C₄	—	4	4	no	—
808	C₂²×C₄	—	4	4	no	—
809	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
810	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
811	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
812	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
813	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
814	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
815	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
816	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
817	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
818	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
819	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
820	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
821	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
822	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
823	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
827	Q₁₆	—	2	8	no	—
828	SD₁₆	—	2	8	no	—
829	SD₁₆	—	2	8	no	—
830	D₈	—	2	8	no	—
831	M₁₆	—	2	4	no	—
832	M₁₆	—	2	4	no	—
833	C₂×C₈	C₂⁴×C₅	1	4	yes	—
834	C₂×C₈	C₂⁴×C₅	1	4	yes	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
880	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
881	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
882	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
883	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
884	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
885	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
886	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
887	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
888	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
889	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
890	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
891	C₄²	C₂⁴×C₅	1	1	yes	characteristic
892	C₄²	C₂⁴×C₅	1	1	yes	characteristic
893	C₄²	C₂⁴×C₅	1	1	yes	characteristic
894	C₄²	C₂⁴×C₅	1	1	yes	characteristic
895	C₂×C₅	—	2	2	no	—
896	C₂×C₅	—	2	2	no	—
897	C₂×C₅	—	4	1	no	—
898	C₂×C₅	—	4	4	no	—
899	C₂×C₅	—	8	2	no	—
900	C₂×C₅	C₂×#525	1	1	yes	characteristic
901	C₂×C₅	C₂×#575	1	1	yes	characteristic
902	C₂×C₅	C₂×#575	1	1	yes	characteristic
903	C₂³	—	2	4	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	4	1	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	4	2	no	—
911	C₂³	—	4	2	no	—
912	C₂³	—	4	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
915	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
916	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
917	Q₈	—	2	4	no	—
918	Q₈	—	2	2	no	—
919	Q₈	—	2	4	no	—
920	Q₈	—	4	2	no	—
921	Q₈	C₂×C₅×#41	1	4	yes	—
922	D₄	—	2	8	no	—
923	D₄	—	2	4	no	—
924	D₄	—	2	8	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	4	no	—
927	D₄	—	4	4	no	—
928	D₄	—	4	4	no	—
929	D₄	—	4	2	no	—
930	D₄	C₂×C₅×#41	1	4	yes	—
931	C₂×C₄	—	2	4	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	8	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	1	no	—
952	C₂×C₄	—	4	1	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	4	1	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	—	4	4	no	—
961	C₂×C₄	—	4	2	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
969	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
970	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
971	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
972	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
973	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
974	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
975	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
976	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
977	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
978	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
979	C₂×C₄	C₂×C₅×#41	1	4	yes	—
980	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
981	C₈	—	2	4	no	—
982	C₈	—	2	4	no	—
983	C₅	#60563	1	1	yes	characteristic, direct product factor, Sylow
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	4	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	4	4	no	—
993	C₂²	—	4	8	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	8	4	no	—
1000	C₂²	C₅×#525	1	2	yes	—
1001	C₂²	C₅×#575	1	2	yes	—
1002	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1003	C₄	—	2	1	no	—
1004	C₄	—	2	4	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	C₅×#525	1	2	yes	—
1019	C₄	C₅×#575	1	2	yes	—
1020	C₄	C₂²×C₅×#41	1	2	yes	—
1021	C₂	—	2	2	no	—
1022	C₂	—	2	2	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	4	4	no	—
1025	C₂	—	8	2	no	—
1026	C₂	C₂×C₅×#525	1	1	yes	characteristic
1027	C₂	C₂×C₅×#575	1	1	yes	characteristic
1028	C₂	C₂×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
prime radical	C₅×#3006	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#529	C₂	semidirect
2. C₂×C₄×C₅×#41	C₂	semidirect
3. C₅×#3117	C₂	semidirect
4. C₅×#3114	C₂	semidirect
5. C₅×#3111	C₂	semidirect
6. C₅×#3108	C₂	semidirect
7. C₅×#3105	C₂	semidirect
8. C₅×#3102	C₂	semidirect
9. C₅×#3095	C₂	semidirect
10. C₅×#3094	C₂	semidirect
11. C₅×#3080	C₂	semidirect
12. C₅×#3040	C₂	semidirect
13. C₅×#3007	C₂	semidirect
15. C₄×C₅×#137	C₂	semidirect
16. C₄×C₅×AGL(1,ℤ/8)	C₂	semidirect
17. C₅×#2920	C₂	semidirect
27. C₅×#529	C₂²	semidirect
28. C₅×#529	C₂²	semidirect
30. C₂×C₅×#125	C₂²	semidirect
31. C₂×C₅×#124	C₂²	semidirect
41. C₄×C₅×#41	C₂²	semidirect
42. C₄×C₅×#41	C₂²	semidirect
43. C₂×C₄×C₅×Q₈	C₂²	semidirect
44. C₂×C₄×C₅×Q₈	C₂²	semidirect
45. C₂×C₄×C₅×Q₈	C₂²	semidirect
49. C₂×C₄×C₅×D₄	C₂²	semidirect
50. C₂×C₄×C₅×D₄	C₂²	semidirect
51. C₂×C₄×C₅×D₄	C₂²	semidirect
57. C₅×#485	C₂²	semidirect
58. C₅×#484	C₂²	semidirect
59. C₅×#483	C₂²	semidirect
60. C₅×#482	C₂²	semidirect
63. C₅×#479	C₂²	semidirect
64. C₅×#479	C₂²	semidirect
65. C₅×#478	C₂²	semidirect
66. C₅×#478	C₂²	semidirect
67. C₅×#464	C₂²	semidirect
68. C₅×#464	C₂²	semidirect
69. C₅×#463	C₂²	semidirect
70. C₅×#463	C₂²	semidirect
71. C₅×#452	C₂²	semidirect
72. C₅×#451	C₂²	semidirect
73. C₅×#450	C₂²	semidirect
77. C₅×#442	C₂²	semidirect
78. C₅×#441	C₂²	semidirect
79. C₅×#440	C₂²	semidirect
80. C₅×#440	C₂²	semidirect
81. C₄×C₅×Q₁₆	C₂²	semidirect
82. C₄×C₅×SD₁₆	C₂²	semidirect
83. C₄×C₅×SD₁₆	C₂²	semidirect
84. C₄×C₅×D₈	C₂²	semidirect
85. C₅×#432	C₂²	semidirect
86. C₅×#432	C₂²	semidirect
87. C₅×#431	C₂²	semidirect
88. C₅×#431	C₂²	semidirect
89. C₅×#428	C₂²	semidirect
90. C₅×#428	C₂²	semidirect
91. C₅×#423	C₂²	semidirect
92. C₅×#419	C₂²	semidirect
93. C₅×#418	C₂²	semidirect
98. C₄×C₅×M₁₆	C₂²	semidirect
99. #60563	C₅	direct (N × H)
256. C₂×#529	C₂×C₅	semidirect
257. C₂×C₄×#41	C₂×C₅	semidirect
258. #3117	C₂×C₅	semidirect
259. #3114	C₂×C₅	semidirect
260. #3111	C₂×C₅	semidirect
261. #3108	C₂×C₅	semidirect
262. #3105	C₂×C₅	semidirect
263. #3102	C₂×C₅	semidirect
264. #3095	C₂×C₅	semidirect
265. #3094	C₂×C₅	semidirect
266. #3080	C₂×C₅	semidirect
267. #3040	C₂×C₅	semidirect
268. #3007	C₂×C₅	semidirect
270. C₄×#137	C₂×C₅	semidirect
271. C₄×AGL(1,ℤ/8)	C₂×C₅	semidirect
272. #2920	C₂×C₅	semidirect
416. #529	C₂²×C₅	semidirect
417. #529	C₂²×C₅	semidirect
419. C₂×#125	C₂²×C₅	semidirect
420. C₂×#124	C₂²×C₅	semidirect
430. C₄×#41	C₂²×C₅	semidirect
431. C₄×#41	C₂²×C₅	semidirect
432. C₂×C₄×Q₈	C₂²×C₅	semidirect
433. C₂×C₄×Q₈	C₂²×C₅	semidirect
434. C₂×C₄×Q₈	C₂²×C₅	semidirect
438. C₂×C₄×D₄	C₂²×C₅	semidirect
439. C₂×C₄×D₄	C₂²×C₅	semidirect
440. C₂×C₄×D₄	C₂²×C₅	semidirect
446. #485	C₂²×C₅	semidirect
447. #484	C₂²×C₅	semidirect
448. #483	C₂²×C₅	semidirect
449. #482	C₂²×C₅	semidirect
452. #479	C₂²×C₅	semidirect
453. #479	C₂²×C₅	semidirect
454. #478	C₂²×C₅	semidirect
455. #478	C₂²×C₅	semidirect
456. #464	C₂²×C₅	semidirect
457. #464	C₂²×C₅	semidirect
458. #463	C₂²×C₅	semidirect
459. #463	C₂²×C₅	semidirect
460. #452	C₂²×C₅	semidirect
461. #451	C₂²×C₅	semidirect
462. #450	C₂²×C₅	semidirect
466. #442	C₂²×C₅	semidirect
467. #441	C₂²×C₅	semidirect
468. #440	C₂²×C₅	semidirect
469. #440	C₂²×C₅	semidirect
470. C₄×Q₁₆	C₂²×C₅	semidirect
471. C₄×SD₁₆	C₂²×C₅	semidirect
472. C₄×SD₁₆	C₂²×C₅	semidirect
473. C₄×D₈	C₂²×C₅	semidirect
474. #432	C₂²×C₅	semidirect
475. #432	C₂²×C₅	semidirect
476. #431	C₂²×C₅	semidirect
477. #431	C₂²×C₅	semidirect
478. #428	C₂²×C₅	semidirect
479. #428	C₂²×C₅	semidirect
480. #423	C₂²×C₅	semidirect
481. #419	C₂²×C₅	semidirect
482. #418	C₂²×C₅	semidirect
487. C₄×M₁₆	C₂²×C₅	semidirect
983. C₅	#60563	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×#529	2
C₂×C₄×C₅×#41	2
C₅×#3117	2
C₅×#3114	2
C₅×#3111	2
C₅×#3108	2
C₅×#3105	2
C₅×#3102	2
C₅×#3095	2
C₅×#3094	2
C₅×#3080	2
C₅×#3040	2
C₅×#3007	2
C₅×#3006	2
C₄×C₅×#137	2
C₄×C₅×AGL(1,ℤ/8)	2
C₅×#2920	2
#60563	5

Subgroups — C5×#60563 #11983283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60563 #11983283