Subgroups — D₅×#2957 #12963615

Order 1280.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×#135	C₂	1	1	yes	maximal, characteristic
2	D₅×#568	C₂	1	2	yes	maximal, complemented
3	C₅×#2957	C₂	1	1	yes	maximal, characteristic, complemented
4	#10615641	C₂	1	1	yes	maximal, characteristic, complemented
5	#10615543	C₂	1	2	yes	maximal, complemented
6	#10611630	C₂	1	4	yes	maximal, complemented
7	D₅×#444	C₂	1	4	yes	maximal, complemented
8	#10611621	C₂	1	4	yes	maximal, complemented
9	D₅×#443	C₂	1	4	yes	maximal, complemented
10	C₂×D₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	#10610980	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#421	C₂	1	2	yes	maximal, complemented
13	#10610721	C₂	1	2	yes	maximal, complemented
14	#10610311	C₂	1	1	yes	maximal, characteristic, complemented
15	D₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅×#41	C₂²	1	2	yes	—
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₅×#568	C₂²	1	2	yes	complemented
19	C₂×#4096	C₂²	1	2	yes	—
20	#66153	C₂²	1	2	yes	complemented
21	D₅×#135	C₄	1	2	yes	complemented
22	D₅×#135	C₄	1	2	yes	complemented
23	D₅×#135	C₄	1	2	yes	complemented
24	D₅×#135	C₄	1	2	yes	complemented
25	D₅×#135	C₂²	1	2	yes	—
26	D₅×#135	C₂²	1	2	yes	—
27	D₅×#135	C₂²	1	2	yes	—
28	D₅×#135	C₂²	1	2	yes	—
29	C₂×#4065	C₄	1	1	yes	characteristic, complemented
30	C₂×D₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
31	C₂×#4062	C₄	1	2	yes	complemented
32	C₂×D₅×SD₁₆	C₄	1	2	yes	complemented
33	C₂×#4058	C₄	1	1	yes	characteristic, complemented
34	C₂×D₅×D₈	C₄	1	1	yes	characteristic, complemented
35	#66084	—	2	4	no	—
36	#66084	C₂²	1	8	yes	complemented
37	D₅×#131	—	2	4	no	—
38	D₅×#131	C₂²	1	8	yes	complemented
39	#66079	—	2	4	no	—
40	#66079	C₂²	1	2	yes	complemented
41	#66079	C₂²	1	2	yes	complemented
42	C₂×D₅×M₁₆	—	2	4	no	—
43	C₂×D₅×M₁₆	C₂²	1	2	yes	—
44	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
45	C₂×#4050	C₂²	1	1	yes	characteristic
46	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
47	D₅×#117	C₂²	1	1	yes	characteristic
48	C₅×#444	C₂²	1	4	yes	complemented
49	C₅×#443	C₂²	1	4	yes	complemented
50	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
51	C₅×#421	C₂²	1	2	yes	complemented
52	C₅×#405	C₂²	1	1	yes	characteristic, complemented
53	#65525	C₂²	1	2	yes	complemented
54	#65486	C₂²	1	4	yes	complemented
55	#65485	C₂²	1	4	yes	complemented
56	#65434	C₂²	1	8	yes	complemented
57	#65433	C₂²	1	8	yes	complemented
58	#65428	C₂²	1	2	yes	complemented
59	C₂×#3954	C₂²	1	2	yes	complemented
60	#65411	C₂²	1	1	yes	characteristic, complemented
61	C₂×#3951	C₂²	1	1	yes	characteristic, complemented
62	#65390	C₂²	1	1	yes	characteristic, complemented
63	#65294	C₂²	1	2	yes	complemented
64	#65286	C₂²	1	1	yes	characteristic, complemented
65	#65184	C₂²	1	4	yes	complemented
66	#65183	C₂²	1	4	yes	complemented
67	D₅×#108	C₂²	1	2	yes	complemented
68	D₅×#108	C₂²	1	2	yes	complemented
69	D₅×#108	C₂²	1	2	yes	complemented
70	D₅×#108	C₂²	1	2	yes	complemented
71	#65113	C₂²	1	8	yes	complemented
72	#65112	C₂²	1	8	yes	complemented
73	#65110	C₂²	1	8	yes	complemented
74	D₅×#104	C₂²	1	8	yes	complemented
75	#65006	C₂²	1	4	yes	complemented
76	#64997	C₂²	1	2	yes	complemented
77	D₅×#97	C₂²	1	2	yes	complemented
78	#64989	C₂²	1	4	yes	complemented
79	#64978	C₂²	1	2	yes	complemented
80	C₄×C₈×D₅	C₂²	1	2	yes	complemented
81	C₂×#2957	—	5	1	no	maximal, Sylow
82	C₂×C₅×#41	C₂³	1	2	yes	—
83	D₅×#41	—	2	2	no	—
84	D₅×#41	—	2	2	no	—
85	D₅×#41	—	2	2	no	—
86	D₅×#41	—	2	2	no	—
87	D₅×#41	C₂×C₄	1	4	yes	—
88	D₅×#41	C₂×C₄	1	4	yes	—
89	D₅×#41	C₂³	1	4	yes	—
90	D₅×#41	C₂³	1	4	yes	—
91	C₂×#713	C₂×C₄	1	2	yes	—
92	C₂×Q₈×D₅	C₂×C₄	1	2	yes	—
93	C₂×#711	—	2	2	no	—
94	C₂×#711	C₂×C₄	1	2	yes	—
95	C₂×D₄×D₅	—	2	2	no	—
96	C₂×D₄×D₅	C₂×C₄	1	2	yes	—
97	C₂×#709	—	2	2	no	—
98	C₂×#709	C₂³	1	2	yes	—
99	C₂²×C₄×D₅	—	2	2	no	—
100	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
101	C₅×#135	C₂×C₄	1	2	yes	complemented
102	C₅×#135	C₂×C₄	1	2	yes	complemented
103	C₅×#135	C₂³	1	2	yes	—
104	C₅×#135	C₂³	1	2	yes	—
105	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
106	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
107	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
108	C₅×#131	—	2	4	no	—
109	C₅×#131	C₂³	1	8	yes	complemented
110	C₂×C₅×M₁₆	—	2	4	no	—
111	C₂×C₅×M₁₆	C₂³	1	2	yes	—
112	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
113	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₅×#117	C₂³	1	1	yes	characteristic
115	#4096	C₂×C₄	1	4	yes	complemented
116	#4096	C₂×C₄	1	4	yes	complemented
117	#4096	C₂³	1	4	yes	—
118	#4096	C₂³	1	4	yes	—
119	#4094	—	2	4	no	—
120	#4094	C₂³	1	8	yes	complemented
121	C₂×#689	C₂×C₄	1	2	yes	complemented
122	C₂×#688	C₂×C₄	1	2	yes	complemented
123	C₂×#687	C₂×C₄	1	2	yes	complemented
124	C₂×#686	C₂×C₄	1	2	yes	complemented
125	#4072	C₂³	1	1	yes	characteristic
126	C₂×#681	—	2	4	no	—
127	C₂×#681	C₂³	1	2	yes	—
128	C₂×#681	C₂³	1	1	yes	characteristic
129	C₂²×#168	C₂³	1	1	yes	characteristic
130	#4065	C₂×C₄	1	2	yes	—
131	#4065	C₂×C₄	1	2	yes	—
132	#4065	C₂×C₄	1	2	yes	complemented
133	#4065	C₂×C₄	1	2	yes	complemented
134	D₅×Q₁₆	C₂×C₄	1	2	yes	—
135	D₅×Q₁₆	C₂×C₄	1	2	yes	—
136	D₅×Q₁₆	C₂×C₄	1	2	yes	complemented
137	D₅×Q₁₆	C₂×C₄	1	2	yes	complemented
138	#4062	C₂×C₄	1	4	yes	—
139	#4062	C₂×C₄	1	4	yes	—
140	#4062	C₂×C₄	1	4	yes	complemented
141	#4062	C₂×C₄	1	4	yes	complemented
142	D₅×SD₁₆	C₂×C₄	1	4	yes	—
143	D₅×SD₁₆	C₂×C₄	1	4	yes	—
144	D₅×SD₁₆	C₂×C₄	1	4	yes	complemented
145	D₅×SD₁₆	C₂×C₄	1	4	yes	complemented
146	#4058	C₂×C₄	1	2	yes	—
147	#4058	C₂×C₄	1	2	yes	—
148	#4058	C₂×C₄	1	2	yes	complemented
149	#4058	C₂×C₄	1	2	yes	complemented
150	D₅×D₈	C₂×C₄	1	2	yes	—
151	D₅×D₈	C₂×C₄	1	2	yes	—
152	D₅×D₈	C₂×C₄	1	2	yes	complemented
153	D₅×D₈	C₂×C₄	1	2	yes	complemented
154	#4053	—	2	4	no	—
155	#4053	—	2	8	no	—
156	#4053	—	2	8	no	—
157	#4053	C₂³	1	8	yes	complemented
158	D₅×M₁₆	—	2	2	no	—
159	D₅×M₁₆	—	2	2	no	—
160	D₅×M₁₆	—	2	4	no	—
161	D₅×M₁₆	—	2	4	no	—
162	D₅×M₁₆	—	2	8	no	—
163	D₅×M₁₆	—	2	8	no	—
164	D₅×M₁₆	D₄	1	2	yes	—
165	D₅×M₁₆	D₄	1	2	yes	—
166	D₅×M₁₆	D₄	1	2	yes	—
167	D₅×M₁₆	D₄	1	2	yes	—
168	D₅×M₁₆	C₂³	1	4	yes	—
169	D₅×M₁₆	C₂³	1	4	yes	—
170	C₂×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
171	#4050	C₂×C₄	1	2	yes	complemented
172	#4050	C₂×C₄	1	2	yes	complemented
173	#4050	C₂³	1	2	yes	—
174	#4050	C₂³	1	2	yes	—
175	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
176	C₂×#677	C₂×C₄	1	2	yes	complemented
177	#4047	—	2	4	no	—
178	#4047	—	2	8	no	—
179	#4047	—	2	8	no	—
180	#4047	C₂³	1	8	yes	complemented
181	C₂×#676	—	2	2	no	—
182	C₂×#676	—	2	8	no	—
183	C₂×#676	C₂³	1	2	yes	—
184	C₂×C₈×D₅	—	2	2	no	—
185	C₂×C₈×D₅	—	2	8	no	—
186	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
187	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
188	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
189	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
190	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
191	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
192	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
193	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
194	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
195	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
196	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
197	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
198	C₂×C₈×D₅	C₂³	1	2	yes	—
199	#4038	—	2	1	no	—
200	D₅×C₄⋊C₄	—	2	1	no	—
201	D₅×C₂²⋊C₄	—	2	1	no	—
202	#4023	—	2	1	no	—
203	#4018	C₂³	1	2	yes	—
204	C₄²×D₅	C₂³	1	2	yes	—
205	C₅×#108	C₂³	1	2	yes	complemented
206	C₅×#108	C₂³	1	2	yes	complemented
207	C₅×#104	C₂³	1	8	yes	complemented
208	C₅×#97	C₂³	1	2	yes	complemented
209	C₄×C₅×C₈	C₂³	1	2	yes	complemented
210	#3969	C₂³	1	8	yes	complemented
211	#3957	C₂³	1	8	yes	complemented
212	#3954	C₂³	1	4	yes	complemented
213	#3954	C₂³	1	4	yes	complemented
214	#3951	C₂³	1	2	yes	complemented
215	#3951	C₂³	1	2	yes	complemented
216	#3947	C₂³	1	2	yes	complemented
217	#3947	C₂³	1	2	yes	complemented
218	C₈×Dic₅	C₂³	1	2	yes	complemented
219	C₈×Dic₅	C₂³	1	2	yes	complemented
220	#3937	C₂³	1	8	yes	complemented
221	#3935	C₂³	1	2	yes	complemented
222	C₄×#168	C₂³	1	2	yes	complemented
223	C₂²×#135	—	5	1	no	—
224	C₂×#568	—	5	2	no	—
225	#2957	—	5	4	no	—
226	#2957	—	5	4	no	—
227	#2957	—	5	1	no	—
228	#2957	—	5	2	no	—
229	#2957	—	5	1	no	—
230	#2957	—	5	1	no	—
231	#2957	—	5	2	no	—
232	#2957	D₅	1	1	yes	characteristic, direct product factor
233	C₂×#444	—	5	4	no	—
234	C₂×#443	—	5	4	no	—
235	C₂²×#108	—	5	1	no	—
236	C₂×#421	—	5	2	no	—
237	C₂×#405	—	5	1	no	—
238	C₂³×D₅	—	2	2	no	—
239	C₂³×D₅	#41	1	1	yes	characteristic
240	C₅×#41	—	2	2	no	—
241	C₅×#41	—	2	2	no	—
242	C₅×#41	C₂²×C₄	1	4	yes	—
243	C₅×#41	C₂⁴	1	4	yes	—
244	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
245	C₂×C₅×D₄	—	2	2	no	—
246	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
247	C₂²×C₄×C₅	—	2	2	no	—
248	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₂×C₂²⋊D₅	—	2	2	no	—
250	C₂×C₂²⋊D₅	—	2	2	no	—
251	C₂×C₂²⋊D₅	—	2	2	no	—
252	C₂²×Dic₅	—	2	2	no	—
253	C₂²×Dic₅	#41	1	1	yes	characteristic
254	#713	—	2	2	no	—
255	#713	—	2	2	no	—
256	#713	C₂²×C₄	1	4	yes	—
257	#713	C₂²×C₄	1	4	yes	—
258	Q₈×D₅	—	2	2	no	—
259	Q₈×D₅	—	2	2	no	—
260	Q₈×D₅	C₂²×C₄	1	4	yes	—
261	Q₈×D₅	C₂²×C₄	1	4	yes	—
262	#711	—	2	4	no	—
263	#711	—	2	4	no	—
264	#711	—	2	4	no	—
265	#711	—	2	4	no	—
266	#711	—	2	2	no	—
267	#711	—	2	2	no	—
268	#711	C₂²×C₄	1	4	yes	—
269	#711	C₂²×C₄	1	4	yes	—
270	D₄×D₅	—	2	4	no	—
271	D₄×D₅	—	2	4	no	—
272	D₄×D₅	—	2	4	no	—
273	D₄×D₅	—	2	4	no	—
274	D₄×D₅	—	2	2	no	—
275	D₄×D₅	—	2	2	no	—
276	D₄×D₅	C₂²×C₄	1	4	yes	—
277	D₄×D₅	C₂²×C₄	1	4	yes	—
278	#709	—	2	2	no	—
279	#709	—	2	2	no	—
280	#709	—	2	4	no	—
281	#709	—	2	4	no	—
282	#709	—	2	4	no	—
283	#709	—	2	4	no	—
284	#709	C₂²×C₄	1	4	yes	—
285	#709	C₂⁴	1	4	yes	—
286	C₂×D₂₀	—	2	2	no	—
287	C₂×D₂₀	C₂²×C₄	1	2	yes	—
288	C₂×C₄×D₅	—	2	2	no	—
289	C₂×C₄×D₅	—	2	2	no	—
290	C₂×C₄×D₅	—	2	2	no	—
291	C₂×C₄×D₅	—	2	4	no	—
292	C₂×C₄×D₅	—	2	4	no	—
293	C₂×C₄×D₅	—	2	4	no	—
294	C₂×C₄×D₅	—	2	4	no	—
295	C₂×C₄×D₅	—	2	2	no	—
296	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
298	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
299	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
300	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
301	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
302	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
303	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
304	C₂×C₄×D₅	#41	1	1	yes	characteristic
305	C₂×C₄×D₅	#41	1	1	yes	characteristic
306	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
307	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₁₀	—	2	2	no	—
309	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
310	C₅×Q₁₆	C₂²×C₄	1	2	yes	—
311	C₅×Q₁₆	C₂²×C₄	1	2	yes	—
312	C₅×SD₁₆	C₂²×C₄	1	4	yes	—
313	C₅×SD₁₆	C₂²×C₄	1	4	yes	—
314	C₅×D₈	C₂²×C₄	1	2	yes	—
315	C₅×D₈	C₂²×C₄	1	2	yes	—
316	C₅×M₁₆	—	2	2	no	—
317	C₅×M₁₆	—	2	8	no	—
318	C₅×M₁₆	C₂×D₄	1	2	yes	—
319	C₅×M₁₆	C₂×D₄	1	2	yes	—
320	C₅×M₁₆	C₂⁴	1	4	yes	—
321	C₂×C₅×C₈	—	2	2	no	—
322	C₂×C₅×C₈	—	2	8	no	—
323	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
325	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
328	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₅×C₈	C₂⁴	1	2	yes	—
330	C₅×C₄⋊C₄	—	2	1	no	—
331	C₅×C₂²⋊C₄	—	2	1	no	—
332	C₄²×C₅	C₂⁴	1	2	yes	—
333	C₂²⋊Dic₅	—	2	1	no	—
334	#689	C₂²×C₄	1	4	yes	—
335	#689	C₂²×C₄	1	4	yes	—
336	#688	C₂²×C₄	1	4	yes	—
337	#688	C₂²×C₄	1	4	yes	—
338	#687	C₂²×C₄	1	4	yes	—
339	#687	C₂²×C₄	1	4	yes	—
340	#686	C₂²×C₄	1	4	yes	—
341	#686	C₂²×C₄	1	4	yes	—
342	#685	—	2	2	no	—
343	C₄⋊Dic₅	—	2	1	no	—
344	#683	—	2	2	no	—
345	C₄×Dic₅	—	2	2	no	—
346	C₄×Dic₅	C₂⁴	1	2	yes	—
347	#681	—	2	2	no	—
348	#681	—	2	8	no	—
349	#681	C₂×D₄	1	2	yes	—
350	#681	C₂×D₄	1	2	yes	—
351	#681	C₂⁴	1	4	yes	—
352	C₂×#168	—	2	2	no	—
353	C₂×#168	—	2	8	no	—
354	C₂×#168	C₂²×C₄	1	1	yes	characteristic
355	C₂×#168	C₂²×C₄	1	1	yes	characteristic
356	C₂×#168	C₂²×C₄	1	1	yes	characteristic
357	C₂×#168	C₂²×C₄	1	1	yes	characteristic
358	C₂×#168	C₂⁴	1	1	yes	characteristic
359	C₂×#168	C₂⁴	1	1	yes	characteristic
360	C₂×#168	C₂⁴	1	2	yes	—
361	Dic₂₀	C₂²×C₄	1	2	yes	—
362	Dic₂₀	C₂²×C₄	1	2	yes	—
363	D₄₀	C₂²×C₄	1	2	yes	—
364	D₄₀	C₂²×C₄	1	2	yes	—
365	#677	C₂²×C₄	1	4	yes	—
366	#677	C₂²×C₄	1	4	yes	—
367	#676	—	2	4	no	—
368	#676	—	2	4	no	—
369	#676	—	2	8	no	—
370	#676	—	2	8	no	—
371	#676	C₂×D₄	1	4	yes	—
372	#676	C₂×D₄	1	4	yes	—
373	C₈×D₅	—	2	4	no	—
374	C₈×D₅	—	2	4	no	—
375	C₈×D₅	—	2	8	no	—
376	C₈×D₅	—	2	8	no	—
377	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
378	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
379	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
380	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
381	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
382	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
383	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
384	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
385	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
386	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
387	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
388	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
389	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
390	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
391	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
392	C₈×D₅	C₂²×C₄	1	1	yes	characteristic
393	C₈×D₅	C₂×D₄	1	4	yes	—
394	C₈×D₅	C₂×D₄	1	4	yes	—
395	C₂²×#41	—	5	2	no	—
396	C₂×#135	—	5	2	no	—
397	C₂×#135	—	5	2	no	—
398	C₂×#135	—	5	2	no	—
399	C₂×#135	—	5	2	no	—
400	C₂×#135	—	5	2	no	—
401	C₂×#135	—	5	2	no	—
402	C₂×#135	—	5	2	no	—
403	C₂×#135	—	5	2	no	—
404	C₂×#135	—	5	2	no	—
405	C₂×#135	—	5	1	no	—
406	C₂×#135	—	5	2	no	—
407	C₂×#135	—	5	1	no	—
408	C₂×#135	—	5	1	no	—
409	C₂×#135	C₂×D₅	1	1	yes	characteristic
410	C₂²×Q₁₆	—	5	1	no	—
411	C₂²×SD₁₆	—	5	2	no	—
412	C₂²×D₈	—	5	1	no	—
413	#568	—	5	2	no	—
414	#568	—	5	8	no	—
415	#568	—	5	2	no	—
416	#568	—	5	2	no	—
417	#568	—	10	4	no	—
418	#568	—	10	4	no	—
419	#568	C₂×D₅	1	2	yes	complemented
420	C₂×#131	—	5	8	no	—
421	C₂×#131	—	10	4	no	—
422	C₂²×M₁₆	—	5	1	no	—
423	C₂²×M₁₆	—	5	2	no	—
424	C₂²×M₁₆	—	10	4	no	—
425	C₂³×C₈	—	5	1	no	—
426	C₂×#117	—	5	1	no	—
427	#444	—	5	4	no	—
428	#444	—	5	8	no	—
429	#444	—	5	4	no	—
430	#444	—	5	8	no	—
431	#444	—	5	4	no	—
432	#444	C₂×D₅	1	4	yes	complemented
433	#443	—	5	4	no	—
434	#443	—	5	8	no	—
435	#443	—	5	4	no	—
436	#443	—	5	8	no	—
437	#443	—	5	4	no	—
438	#443	C₂×D₅	1	4	yes	complemented
439	C₂×#108	—	5	2	no	—
440	C₂×#108	—	5	1	no	—
441	C₂×#108	—	5	2	no	—
442	C₂×#108	—	5	2	no	—
443	C₂×#108	—	5	2	no	—
444	C₂×#108	—	5	2	no	—
445	C₂×#108	C₂×D₅	1	1	yes	characteristic, complemented
446	#421	—	5	2	no	—
447	#421	—	5	2	no	—
448	#421	—	5	2	no	—
449	#421	—	5	8	no	—
450	#421	C₂×D₅	1	2	yes	complemented
451	C₂×#104	—	5	8	no	—
452	#405	—	5	1	no	—
453	#405	—	5	1	no	—
454	#405	—	5	1	no	—
455	#405	—	5	2	no	—
456	#405	—	5	2	no	—
457	#405	C₂×D₅	1	1	yes	characteristic, complemented
458	C₂×#97	—	5	2	no	—
459	C₂×C₄×C₈	—	5	2	no	—
460	C₂³×C₅	—	2	2	no	—
461	C₂³×C₅	C₂×#41	1	1	yes	characteristic
462	C₂²×D₅	—	2	2	no	—
463	C₂²×D₅	—	2	4	no	—
464	C₂²×D₅	—	2	4	no	—
465	C₂²×D₅	—	4	2	no	—
466	C₂²×D₅	—	8	4	no	—
467	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
468	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
469	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
470	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
471	C₂²×D₅	C₂×#41	1	1	yes	characteristic
472	C₂²×D₅	C₂×#41	1	1	yes	characteristic
473	C₅×Q₈	—	2	2	no	—
474	C₅×Q₈	C₂³×C₄	1	4	yes	—
475	C₅×D₄	—	2	4	no	—
476	C₅×D₄	—	2	4	no	—
477	C₅×D₄	—	2	2	no	—
478	C₅×D₄	C₂³×C₄	1	4	yes	—
479	C₂×C₄×C₅	—	2	2	no	—
480	C₂×C₄×C₅	—	2	4	no	—
481	C₂×C₄×C₅	—	2	4	no	—
482	C₂×C₄×C₅	—	2	2	no	—
483	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
484	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
485	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
488	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
489	C₂²⋊D₅	—	2	4	no	—
490	C₂²⋊D₅	—	2	4	no	—
491	C₂²⋊D₅	—	2	4	no	—
492	C₂²⋊D₅	—	2	4	no	—
493	C₂²⋊D₅	—	2	4	no	—
494	C₂²⋊D₅	—	2	4	no	—
495	C₂×Dic₅	—	2	2	no	—
496	C₂×Dic₅	—	2	4	no	—
497	C₂×Dic₅	—	2	4	no	—
498	C₂×Dic₅	—	2	2	no	—
499	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
500	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
501	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
502	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
503	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
504	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
505	D₂₀	—	2	4	no	—
506	D₂₀	—	2	4	no	—
507	D₂₀	—	2	2	no	—
508	D₂₀	C₂³×C₄	1	4	yes	—
509	C₄×D₅	—	2	4	no	—
510	C₄×D₅	—	2	4	no	—
511	C₄×D₅	—	2	4	no	—
512	C₄×D₅	—	2	4	no	—
513	C₄×D₅	—	2	4	no	—
514	C₄×D₅	—	2	4	no	—
515	C₄×D₅	—	4	4	no	—
516	C₄×D₅	C₄×D₄	1	1	yes	characteristic
517	C₄×D₅	C₄×D₄	1	1	yes	characteristic
518	C₄×D₅	C₄×D₄	1	1	yes	characteristic
519	C₄×D₅	C₄×D₄	1	1	yes	characteristic
520	C₄×D₅	C₄×D₄	1	1	yes	characteristic
521	C₄×D₅	C₄×D₄	1	1	yes	characteristic
522	C₄×D₅	C₄×D₄	1	1	yes	characteristic
523	C₄×D₅	C₄×D₄	1	1	yes	characteristic
524	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
525	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
526	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
527	C₄×D₅	C₂³×C₄	1	1	yes	characteristic
528	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
529	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
530	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
531	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
532	Dic₁₀	—	2	2	no	—
533	Dic₁₀	—	2	4	no	—
534	Dic₁₀	—	2	4	no	—
535	Dic₁₀	C₂³×C₄	1	4	yes	—
536	C₅×C₈	—	2	4	no	—
537	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
538	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
539	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
540	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
541	C₅×C₈	C₂²×D₄	1	4	yes	—
542	#168	—	2	4	no	—
543	#168	C₂³×C₄	1	1	yes	characteristic
544	#168	C₂³×C₄	1	1	yes	characteristic
545	#168	C₂³×C₄	1	1	yes	characteristic
546	#168	C₂³×C₄	1	1	yes	characteristic
547	#168	C₂²×D₄	1	4	yes	—
548	C₂×#41	—	5	4	no	—
549	C₂×#41	—	5	4	no	—
550	C₂×#41	—	5	4	no	—
551	C₂×#41	—	5	4	no	—
552	C₂×#41	—	5	2	no	—
553	C₂×#41	—	5	2	no	—
554	C₂×#41	—	5	2	no	—
555	C₂×#41	—	10	2	no	—
556	C₂×#41	—	10	2	no	—
557	C₂×#41	—	10	2	no	—
558	C₂×#41	—	10	2	no	—
559	C₂×#41	—	10	2	no	—
560	C₂×#41	—	10	2	no	—
561	C₂×#41	C₂²×D₅	1	2	yes	—
562	C₂²×Q₈	—	5	2	no	—
563	C₂²×D₄	—	5	2	no	—
564	C₂²×D₄	—	10	2	no	—
565	C₂³×C₄	—	5	1	no	—
566	C₂³×C₄	—	10	2	no	—
567	#135	—	5	4	no	—
568	#135	—	5	4	no	—
569	#135	—	5	4	no	—
570	#135	—	5	4	no	—
571	#135	—	5	2	no	—
572	#135	—	5	2	no	—
573	#135	—	5	2	no	—
574	#135	—	5	2	no	—
575	#135	—	5	4	no	—
576	#135	—	5	4	no	—
577	#135	—	5	4	no	—
578	#135	—	5	4	no	—
579	#135	—	5	2	no	—
580	#135	—	5	2	no	—
581	#135	—	5	2	no	—
582	#135	—	5	2	no	—
583	#135	—	5	2	no	—
584	#135	—	5	2	no	—
585	#135	—	5	2	no	—
586	#135	—	5	2	no	—
587	#135	C₄×D₅	1	2	yes	complemented
588	#135	C₄×D₅	1	2	yes	complemented
589	#135	C₂²×D₅	1	2	yes	—
590	#135	C₂²×D₅	1	2	yes	—
591	C₂×Q₁₆	—	5	2	no	—
592	C₂×Q₁₆	—	5	2	no	—
593	C₂×Q₁₆	—	5	2	no	—
594	C₂×Q₁₆	—	5	2	no	—
595	C₂×Q₁₆	—	5	2	no	—
596	C₂×Q₁₆	—	5	1	no	—
597	C₂×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
598	C₂×SD₁₆	—	5	2	no	—
599	C₂×SD₁₆	—	5	2	no	—
600	C₂×SD₁₆	—	5	4	no	—
601	C₂×SD₁₆	—	5	4	no	—
602	C₂×SD₁₆	—	5	4	no	—
603	C₂×SD₁₆	—	5	4	no	—
604	C₂×SD₁₆	—	5	2	no	—
605	C₂×SD₁₆	C₄×D₅	1	2	yes	complemented
606	C₂×D₈	—	5	2	no	—
607	C₂×D₈	—	5	2	no	—
608	C₂×D₈	—	5	2	no	—
609	C₂×D₈	—	5	2	no	—
610	C₂×D₈	—	5	2	no	—
611	C₂×D₈	—	5	1	no	—
612	C₂×D₈	C₄×D₅	1	1	yes	characteristic, complemented
613	#131	—	2	4	no	—
614	#131	—	5	8	no	—
615	#131	—	5	8	no	—
616	#131	—	5	8	no	—
617	#131	—	10	8	no	—
618	#131	—	10	4	no	—
619	#131	—	10	8	no	—
620	#131	—	10	8	no	—
621	#131	—	10	8	no	—
622	#131	—	10	4	no	—
623	#131	—	10	4	no	—
624	#131	C₂²×D₅	1	8	yes	complemented
625	C₂×M₁₆	—	2	4	no	—
626	C₂×M₁₆	—	5	1	no	—
627	C₂×M₁₆	—	5	2	no	—
628	C₂×M₁₆	—	5	2	no	—
629	C₂×M₁₆	—	5	2	no	—
630	C₂×M₁₆	—	5	2	no	—
631	C₂×M₁₆	—	5	2	no	—
632	C₂×M₁₆	—	5	2	no	—
633	C₂×M₁₆	—	5	4	no	—
634	C₂×M₁₆	—	5	4	no	—
635	C₂×M₁₆	—	10	8	no	—
636	C₂×M₁₆	—	10	2	no	—
637	C₂×M₁₆	—	10	8	no	—
638	C₂×M₁₆	—	10	4	no	—
639	C₂×M₁₆	—	10	8	no	—
640	C₂×M₁₆	—	10	2	no	—
641	C₂×M₁₆	—	10	2	no	—
642	C₂×M₁₆	—	10	4	no	—
643	C₂×M₁₆	—	10	4	no	—
644	C₂×M₁₆	C₂²×D₅	1	2	yes	—
645	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
646	C₂²×C₈	—	5	1	no	—
647	C₂²×C₈	—	5	1	no	—
648	C₂²×C₈	—	5	1	no	—
649	C₂²×C₈	—	5	1	no	—
650	C₂²×C₈	—	5	1	no	—
651	C₂²×C₈	—	5	1	no	—
652	C₂²×C₈	—	5	1	no	—
653	C₂²×C₈	—	5	1	no	—
654	C₂²×C₈	—	5	1	no	—
655	C₂²×C₈	—	5	1	no	—
656	C₂²×C₈	—	5	1	no	—
657	C₂²×C₈	—	5	1	no	—
658	C₂²×C₈	—	5	1	no	—
659	C₂²×C₈	—	5	2	no	—
660	C₂²×C₈	—	10	8	no	—
661	C₂²×C₈	—	10	2	no	—
662	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
663	#117	—	5	1	no	—
664	#117	—	5	2	no	—
665	#117	—	10	1	no	—
666	#117	—	10	1	no	—
667	#117	C₂²×D₅	1	1	yes	characteristic
668	C₂×C₄⋊C₄	—	10	1	no	—
669	C₂×C₂²⋊C₄	—	10	1	no	—
670	C₂×C₄²	—	5	2	no	—
671	#108	—	5	4	no	—
672	#108	—	5	4	no	—
673	#108	—	5	2	no	—
674	#108	—	5	2	no	—
675	#108	C₂²×D₅	1	2	yes	complemented
676	#108	C₂²×D₅	1	2	yes	complemented
677	#104	—	5	8	no	—
678	#104	—	5	8	no	—
679	#104	—	5	8	no	—
680	#104	C₂²×D₅	1	8	yes	complemented
681	#97	—	5	2	no	—
682	#97	—	5	2	no	—
683	#97	—	5	2	no	—
684	#97	C₂²×D₅	1	2	yes	complemented
685	C₄×C₈	—	5	2	no	—
686	C₄×C₈	—	5	2	no	—
687	C₄×C₈	—	5	2	no	—
688	C₄×C₈	C₂²×D₅	1	2	yes	complemented
689	C₂²×C₅	—	2	4	no	—
690	C₂²×C₅	—	4	1	no	—
691	C₂²×C₅	—	8	2	no	—
692	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
693	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
694	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
695	C₂×D₅	—	2	2	no	—
696	C₂×D₅	—	2	2	no	—
697	C₂×D₅	—	2	2	no	—
698	C₂×D₅	—	2	4	no	—
699	C₂×D₅	—	4	1	no	—
700	C₂×D₅	—	4	1	no	—
701	C₂×D₅	—	4	1	no	—
702	C₂×D₅	—	4	8	no	—
703	C₂×D₅	—	8	4	no	—
704	C₂×D₅	—	8	2	no	—
705	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
706	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
707	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
708	C₂×D₅	C₂×C₄×D₄	1	1	yes	characteristic
709	C₄×C₅	—	2	4	no	—
710	C₄×C₅	—	4	2	no	—
711	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
712	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
713	C₄×C₅	C₂⁴×C₄	1	1	yes	characteristic
714	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
715	Dic₅	—	2	4	no	—
716	Dic₅	—	4	2	no	—
717	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
718	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
719	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
720	Dic₅	C₂×C₄×D₄	1	1	yes	characteristic
721	C₂⁴	—	5	1	no	—
722	C₂⁴	—	10	2	no	—
723	#41	—	2	2	no	—
724	#41	—	2	2	no	—
725	#41	—	5	4	no	—
726	#41	—	5	4	no	—
727	#41	—	5	4	no	—
728	#41	—	5	4	no	—
729	#41	—	5	4	no	—
730	#41	—	5	4	no	—
731	#41	—	10	4	no	—
732	#41	—	10	4	no	—
733	#41	—	10	4	no	—
734	#41	—	10	4	no	—
735	#41	—	10	4	no	—
736	#41	—	10	4	no	—
737	#41	—	10	4	no	—
738	#41	—	10	4	no	—
739	#41	—	10	2	no	—
740	#41	—	10	2	no	—
741	#41	—	10	2	no	—
742	#41	—	10	2	no	—
743	#41	—	10	2	no	—
744	#41	—	10	2	no	—
745	#41	C₂×C₄×D₅	1	4	yes	—
746	#41	C₂³×D₅	1	4	yes	—
747	C₂×Q₈	—	5	4	no	—
748	C₂×Q₈	—	5	4	no	—
749	C₂×Q₈	—	5	2	no	—
750	C₂×Q₈	—	10	2	no	—
751	C₂×Q₈	—	10	2	no	—
752	C₂×Q₈	—	10	2	no	—
753	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	5	4	no	—
756	C₂×D₄	—	5	4	no	—
757	C₂×D₄	—	5	2	no	—
758	C₂×D₄	—	10	2	no	—
759	C₂×D₄	—	10	2	no	—
760	C₂×D₄	—	10	2	no	—
761	C₂×D₄	—	10	2	no	—
762	C₂×D₄	—	10	4	no	—
763	C₂×D₄	—	10	4	no	—
764	C₂×D₄	—	10	4	no	—
765	C₂×D₄	—	10	4	no	—
766	C₂×D₄	—	10	2	no	—
767	C₂×D₄	—	10	2	no	—
768	C₂×D₄	C₂×C₄×D₅	1	2	yes	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	5	1	no	—
771	C₂²×C₄	—	5	1	no	—
772	C₂²×C₄	—	5	1	no	—
773	C₂²×C₄	—	5	1	no	—
774	C₂²×C₄	—	5	1	no	—
775	C₂²×C₄	—	5	1	no	—
776	C₂²×C₄	—	5	1	no	—
777	C₂²×C₄	—	5	1	no	—
778	C₂²×C₄	—	5	1	no	—
779	C₂²×C₄	—	5	1	no	—
780	C₂²×C₄	—	5	1	no	—
781	C₂²×C₄	—	5	1	no	—
782	C₂²×C₄	—	5	1	no	—
783	C₂²×C₄	—	10	4	no	—
784	C₂²×C₄	—	10	4	no	—
785	C₂²×C₄	—	10	2	no	—
786	C₂²×C₄	—	10	4	no	—
787	C₂²×C₄	—	10	4	no	—
788	C₂²×C₄	—	10	2	no	—
789	C₂²×C₄	—	10	2	no	—
790	C₂²×C₄	—	10	2	no	—
791	C₂²×C₄	—	10	2	no	—
792	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
793	Q₁₆	—	5	4	no	—
794	Q₁₆	—	5	4	no	—
795	Q₁₆	—	5	2	no	—
796	Q₁₆	—	5	2	no	—
797	Q₁₆	C₂×C₄×D₅	1	2	yes	—
798	Q₁₆	C₂×C₄×D₅	1	2	yes	—
799	SD₁₆	—	5	4	no	—
800	SD₁₆	—	5	4	no	—
801	SD₁₆	—	5	4	no	—
802	SD₁₆	—	5	4	no	—
803	SD₁₆	—	5	4	no	—
804	SD₁₆	—	5	4	no	—
805	SD₁₆	C₂×C₄×D₅	1	4	yes	—
806	SD₁₆	C₂×C₄×D₅	1	4	yes	—
807	D₈	—	5	4	no	—
808	D₈	—	5	4	no	—
809	D₈	—	5	2	no	—
810	D₈	—	5	2	no	—
811	D₈	C₂×C₄×D₅	1	2	yes	—
812	D₈	C₂×C₄×D₅	1	2	yes	—
813	M₁₆	—	2	2	no	—
814	M₁₆	—	2	8	no	—
815	M₁₆	—	5	2	no	—
816	M₁₆	—	5	2	no	—
817	M₁₆	—	5	4	no	—
818	M₁₆	—	5	4	no	—
819	M₁₆	—	5	4	no	—
820	M₁₆	—	10	8	no	—
821	M₁₆	—	10	4	no	—
822	M₁₆	—	10	4	no	—
823	M₁₆	—	10	8	no	—
824	M₁₆	—	10	2	no	—
825	M₁₆	—	10	8	no	—
826	M₁₆	D₄×D₅	1	2	yes	—
827	M₁₆	D₄×D₅	1	2	yes	—
828	M₁₆	C₂³×D₅	1	4	yes	—
829	C₂×C₈	—	2	2	no	—
830	C₂×C₈	—	2	8	no	—
831	C₂×C₈	—	5	1	no	—
832	C₂×C₈	—	5	1	no	—
833	C₂×C₈	—	5	1	no	—
834	C₂×C₈	—	5	1	no	—
835	C₂×C₈	—	5	1	no	—
836	C₂×C₈	—	5	2	no	—
837	C₂×C₈	—	5	1	no	—
838	C₂×C₈	—	5	1	no	—
839	C₂×C₈	—	5	1	no	—
840	C₂×C₈	—	5	1	no	—
841	C₂×C₈	—	5	1	no	—
842	C₂×C₈	—	5	1	no	—
843	C₂×C₈	—	5	1	no	—
844	C₂×C₈	—	5	1	no	—
845	C₂×C₈	—	5	1	no	—
846	C₂×C₈	—	5	1	no	—
847	C₂×C₈	—	5	1	no	—
848	C₂×C₈	—	5	1	no	—
849	C₂×C₈	—	5	1	no	—
850	C₂×C₈	—	5	1	no	—
851	C₂×C₈	—	5	1	no	—
852	C₂×C₈	—	5	1	no	—
853	C₂×C₈	—	5	1	no	—
854	C₂×C₈	—	5	4	no	—
855	C₂×C₈	—	5	4	no	—
856	C₂×C₈	—	10	8	no	—
857	C₂×C₈	—	10	4	no	—
858	C₂×C₈	—	10	4	no	—
859	C₂×C₈	—	10	8	no	—
860	C₂×C₈	—	10	2	no	—
861	C₂×C₈	—	10	8	no	—
862	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
863	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
864	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
865	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
866	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
867	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
868	C₂×C₈	C₂³×D₅	1	2	yes	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	10	2	no	—
871	C₄⋊C₄	—	10	1	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	10	2	no	—
874	C₂²⋊C₄	—	10	1	no	—
875	C₄²	—	5	2	no	—
876	C₄²	—	10	2	no	—
877	C₄²	C₂³×D₅	1	2	yes	—
878	C₂×C₅	—	2	1	no	—
879	C₂×C₅	—	2	1	no	—
880	C₂×C₅	—	2	1	no	—
881	C₂×C₅	—	4	4	no	—
882	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
883	D₅	—	2	1	no	—
884	D₅	—	2	1	no	—
885	D₅	—	2	1	no	—
886	D₅	—	4	4	no	—
887	D₅	#2957	1	2	yes	direct product factor
888	C₂³	—	2	2	no	—
889	C₂³	—	5	1	no	—
890	C₂³	—	5	1	no	—
891	C₂³	—	5	1	no	—
892	C₂³	—	5	1	no	—
893	C₂³	—	5	1	no	—
894	C₂³	—	5	1	no	—
895	C₂³	—	10	4	no	—
896	C₂³	—	10	4	no	—
897	C₂³	—	10	2	no	—
898	C₂³	—	20	2	no	—
899	C₂³	—	40	4	no	—
900	C₂³	D₅×#41	1	1	yes	characteristic
901	Q₈	—	2	2	no	—
902	Q₈	—	5	4	no	—
903	Q₈	—	10	4	no	—
904	Q₈	—	10	4	no	—
905	Q₈	—	10	2	no	—
906	Q₈	C₂²×C₄×D₅	1	4	yes	—
907	D₄	—	2	4	no	—
908	D₄	—	2	4	no	—
909	D₄	—	2	2	no	—
910	D₄	—	5	4	no	—
911	D₄	—	10	4	no	—
912	D₄	—	10	4	no	—
913	D₄	—	10	4	no	—
914	D₄	—	10	4	no	—
915	D₄	—	10	4	no	—
916	D₄	—	10	4	no	—
917	D₄	—	10	4	no	—
918	D₄	—	10	4	no	—
919	D₄	—	10	2	no	—
920	D₄	C₂²×C₄×D₅	1	4	yes	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	4	no	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	5	1	no	—
926	C₂×C₄	—	5	1	no	—
927	C₂×C₄	—	5	1	no	—
928	C₂×C₄	—	5	1	no	—
929	C₂×C₄	—	5	1	no	—
930	C₂×C₄	—	5	1	no	—
931	C₂×C₄	—	5	1	no	—
932	C₂×C₄	—	5	1	no	—
933	C₂×C₄	—	5	1	no	—
934	C₂×C₄	—	5	1	no	—
935	C₂×C₄	—	5	1	no	—
936	C₂×C₄	—	5	1	no	—
937	C₂×C₄	—	5	1	no	—
938	C₂×C₄	—	5	1	no	—
939	C₂×C₄	—	5	1	no	—
940	C₂×C₄	—	5	1	no	—
941	C₂×C₄	—	5	1	no	—
942	C₂×C₄	—	5	1	no	—
943	C₂×C₄	—	5	1	no	—
944	C₂×C₄	—	5	1	no	—
945	C₂×C₄	—	5	1	no	—
946	C₂×C₄	—	5	1	no	—
947	C₂×C₄	—	10	4	no	—
948	C₂×C₄	—	10	4	no	—
949	C₂×C₄	—	10	4	no	—
950	C₂×C₄	—	10	4	no	—
951	C₂×C₄	—	10	4	no	—
952	C₂×C₄	—	10	4	no	—
953	C₂×C₄	—	10	2	no	—
954	C₂×C₄	—	10	4	no	—
955	C₂×C₄	—	10	4	no	—
956	C₂×C₄	—	10	2	no	—
957	C₂×C₄	—	20	4	no	—
958	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
959	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
960	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
961	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
962	C₂×C₄	D₅×#41	1	1	yes	characteristic
963	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
964	C₈	—	2	4	no	—
965	C₈	—	5	1	no	—
966	C₈	—	5	1	no	—
967	C₈	—	5	1	no	—
968	C₈	—	5	1	no	—
969	C₈	—	5	4	no	—
970	C₈	—	10	4	no	—
971	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
972	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
973	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
974	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
975	C₈	C₂×D₄×D₅	1	4	yes	—
976	C₅	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
977	C₂²	—	2	4	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	5	1	no	—
980	C₂²	—	5	1	no	—
981	C₂²	—	5	1	no	—
982	C₂²	—	5	1	no	—
983	C₂²	—	8	2	no	—
984	C₂²	—	10	2	no	—
985	C₂²	—	10	2	no	—
986	C₂²	—	10	2	no	—
987	C₂²	—	10	4	no	—
988	C₂²	—	20	1	no	—
989	C₂²	—	20	1	no	—
990	C₂²	—	20	1	no	—
991	C₂²	—	20	8	no	—
992	C₂²	—	40	2	no	—
993	C₂²	—	40	4	no	—
994	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
995	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
996	C₂²	C₂×D₅×#41	1	1	yes	characteristic
997	C₄	—	2	4	no	—
998	C₄	—	4	2	no	—
999	C₄	—	5	1	no	—
1000	C₄	—	5	1	no	—
1001	C₄	—	5	1	no	—
1002	C₄	—	5	1	no	—
1003	C₄	—	10	4	no	—
1004	C₄	—	20	2	no	—
1005	C₄	C₄×D₄×D₅	1	1	yes	characteristic
1006	C₄	C₄×D₄×D₅	1	1	yes	characteristic
1007	C₄	C₂³×C₄×D₅	1	1	yes	characteristic
1008	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
1009	C₂	—	2	1	no	—
1010	C₂	—	2	1	no	—
1011	C₂	—	2	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	5	2	no	—
1014	C₂	—	10	1	no	—
1015	C₂	—	10	1	no	—
1016	C₂	—	10	1	no	—
1017	C₂	—	20	4	no	—
1018	C₂	C₂×C₄×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₅
commutator	C₄×C₅	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₅×#2957	C₂
socle	C₂×C₅	C₂²×C₄×D₄
prime radical	C₂×D₅×#135	C₂
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	#2957	D₅
hypocenter	C₅	C₂×#2957
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. D₅×#568	C₂	semidirect
3. C₅×#2957	C₂	semidirect
4. #10615641	C₂	semidirect
5. #10615543	C₂	semidirect
6. #10611630	C₂	semidirect
7. D₅×#444	C₂	semidirect
8. #10611621	C₂	semidirect
9. D₅×#443	C₂	semidirect
10. C₂×D₅×#108	C₂	semidirect
11. #10610980	C₂	semidirect
12. D₅×#421	C₂	semidirect
13. #10610721	C₂	semidirect
14. #10610311	C₂	semidirect
15. D₅×#405	C₂	semidirect
18. C₅×#568	C₂²	semidirect
20. #66153	C₂²	semidirect
21. D₅×#135	C₄	semidirect
22. D₅×#135	C₄	semidirect
23. D₅×#135	C₄	semidirect
24. D₅×#135	C₄	semidirect
29. C₂×#4065	C₄	semidirect
30. C₂×D₅×Q₁₆	C₄	semidirect
31. C₂×#4062	C₄	semidirect
32. C₂×D₅×SD₁₆	C₄	semidirect
33. C₂×#4058	C₄	semidirect
34. C₂×D₅×D₈	C₄	semidirect
36. #66084	C₂²	semidirect
38. D₅×#131	C₂²	semidirect
40. #66079	C₂²	semidirect
41. #66079	C₂²	semidirect
48. C₅×#444	C₂²	semidirect
49. C₅×#443	C₂²	semidirect
50. C₂×C₅×#108	C₂²	semidirect
51. C₅×#421	C₂²	semidirect
52. C₅×#405	C₂²	semidirect
53. #65525	C₂²	semidirect
54. #65486	C₂²	semidirect
55. #65485	C₂²	semidirect
56. #65434	C₂²	semidirect
57. #65433	C₂²	semidirect
58. #65428	C₂²	semidirect
59. C₂×#3954	C₂²	semidirect
60. #65411	C₂²	semidirect
61. C₂×#3951	C₂²	semidirect
62. #65390	C₂²	semidirect
63. #65294	C₂²	semidirect
64. #65286	C₂²	semidirect
65. #65184	C₂²	semidirect
66. #65183	C₂²	semidirect
67. D₅×#108	C₂²	semidirect
68. D₅×#108	C₂²	semidirect
69. D₅×#108	C₂²	semidirect
70. D₅×#108	C₂²	semidirect
71. #65113	C₂²	semidirect
72. #65112	C₂²	semidirect
73. #65110	C₂²	semidirect
74. D₅×#104	C₂²	semidirect
75. #65006	C₂²	semidirect
76. #64997	C₂²	semidirect
77. D₅×#97	C₂²	semidirect
78. #64989	C₂²	semidirect
79. #64978	C₂²	semidirect
80. C₄×C₈×D₅	C₂²	semidirect
101. C₅×#135	C₂×C₄	semidirect
102. C₅×#135	C₂×C₄	semidirect
105. C₂×C₅×Q₁₆	C₂×C₄	semidirect
106. C₂×C₅×SD₁₆	C₂×C₄	semidirect
107. C₂×C₅×D₈	C₂×C₄	semidirect
109. C₅×#131	C₂³	semidirect
115. #4096	C₂×C₄	semidirect
116. #4096	C₂×C₄	semidirect
120. #4094	C₂³	semidirect
121. C₂×#689	C₂×C₄	semidirect
122. C₂×#688	C₂×C₄	semidirect
123. C₂×#687	C₂×C₄	semidirect
124. C₂×#686	C₂×C₄	semidirect
132. #4065	C₂×C₄	semidirect
133. #4065	C₂×C₄	semidirect
136. D₅×Q₁₆	C₂×C₄	semidirect
137. D₅×Q₁₆	C₂×C₄	semidirect
140. #4062	C₂×C₄	semidirect
141. #4062	C₂×C₄	semidirect
144. D₅×SD₁₆	C₂×C₄	semidirect
145. D₅×SD₁₆	C₂×C₄	semidirect
148. #4058	C₂×C₄	semidirect
149. #4058	C₂×C₄	semidirect
152. D₅×D₈	C₂×C₄	semidirect
153. D₅×D₈	C₂×C₄	semidirect
157. #4053	C₂³	semidirect
170. C₂×Dic₂₀	C₂×C₄	semidirect
171. #4050	C₂×C₄	semidirect
172. #4050	C₂×C₄	semidirect
175. C₂×D₄₀	C₂×C₄	semidirect
176. C₂×#677	C₂×C₄	semidirect
180. #4047	C₂³	semidirect
205. C₅×#108	C₂³	semidirect
206. C₅×#108	C₂³	semidirect
207. C₅×#104	C₂³	semidirect
208. C₅×#97	C₂³	semidirect
209. C₄×C₅×C₈	C₂³	semidirect
210. #3969	C₂³	semidirect
211. #3957	C₂³	semidirect
212. #3954	C₂³	semidirect
213. #3954	C₂³	semidirect
214. #3951	C₂³	semidirect
215. #3951	C₂³	semidirect
216. #3947	C₂³	semidirect
217. #3947	C₂³	semidirect
218. C₈×Dic₅	C₂³	semidirect
219. C₈×Dic₅	C₂³	semidirect
220. #3937	C₂³	semidirect
221. #3935	C₂³	semidirect
222. C₄×#168	C₂³	semidirect
232. #2957	D₅	direct (N × H)
419. #568	C₂×D₅	semidirect
432. #444	C₂×D₅	semidirect
438. #443	C₂×D₅	semidirect
445. C₂×#108	C₂×D₅	semidirect
450. #421	C₂×D₅	semidirect
457. #405	C₂×D₅	semidirect
587. #135	C₄×D₅	semidirect
588. #135	C₄×D₅	semidirect
597. C₂×Q₁₆	C₄×D₅	semidirect
605. C₂×SD₁₆	C₄×D₅	semidirect
612. C₂×D₈	C₄×D₅	semidirect
624. #131	C₂²×D₅	semidirect
675. #108	C₂²×D₅	semidirect
676. #108	C₂²×D₅	semidirect
680. #104	C₂²×D₅	semidirect
684. #97	C₂²×D₅	semidirect
688. C₄×C₈	C₂²×D₅	semidirect
887. D₅	#2957	direct (N × H)
976. C₅	C₂×#2957	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×#135	2
D₅×#568	2
C₅×#2957	2
#10615641	2
#10615543	2
#10611630	2
D₅×#444	2
#10611621	2
D₅×#443	2
C₂×D₅×#108	2
#10610980	2
D₅×#421	2
#10610721	2
#10610311	2
D₅×#405	2
C₂×#2957	5

Subgroups — D5×#2957 #12963615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#2957 #12963615