Subgroups — #12981685

Order 1280.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10618062	C₂	1	2	yes	maximal, complemented
2	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611702	C₂	1	2	yes	maximal, complemented
4	#10611661	C₂	1	1	yes	maximal, characteristic, complemented
5	#10611646	C₂	1	1	yes	maximal, characteristic, complemented
6	#10611284	C₂	1	2	yes	maximal, complemented
7	#10611232	C₂	1	2	yes	maximal, complemented
8	#10611230	C₂	1	2	yes	maximal, complemented
9	#10611164	C₂	1	1	yes	maximal, characteristic, complemented
10	#10611164	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611147	C₂	1	1	yes	maximal, characteristic, complemented
13	#10611144	C₂	1	1	yes	maximal, characteristic, complemented
14	#10611142	C₂	1	1	yes	maximal, characteristic, complemented
15	#10611115	C₂	1	2	yes	maximal, complemented
16	#10611114	C₂	1	2	yes	maximal, complemented
17	#10611077	C₂	1	2	yes	maximal, complemented
18	#10610300	C₂	1	1	yes	maximal, characteristic, complemented
19	#10610299	C₂	1	1	yes	maximal, characteristic, complemented
20	#10610293	C₂	1	1	yes	maximal, characteristic, complemented
21	#10610292	C₂	1	1	yes	maximal, characteristic, complemented
22	#10610200	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#529	C₂²	1	1	yes	characteristic
25	C₂×#4050	C₂²	1	1	yes	characteristic
26	C₂²×D₄₀	C₂²	1	1	yes	characteristic
27	C₂²×D₄₀	C₂²	1	1	yes	characteristic
28	#66043	—	2	2	no	—
29	#66039	—	2	2	no	—
30	#66026	—	2	2	no	—
31	#66012	—	2	2	no	—
32	#65990	—	2	2	no	—
33	D₅×#123	—	2	2	no	—
34	#65971	—	2	2	no	—
35	#65944	—	2	2	no	—
36	#65919	C₂²	1	2	yes	complemented
37	#65913	C₂²	1	2	yes	complemented
38	#65899	C₂²	1	2	yes	complemented
39	#65889	C₂²	1	2	yes	complemented
40	#65884	C₂²	1	2	yes	complemented
41	#65884	C₂²	1	2	yes	complemented
42	D₄×D₂₀	C₂²	1	2	yes	—
43	#65875	C₂²	1	2	yes	—
44	#65869	C₂²	1	2	yes	complemented
45	#65868	C₂²	1	2	yes	complemented
46	#65857	C₂²	1	2	yes	complemented
47	#65855	C₂²	1	2	yes	complemented
48	#65813	C₂²	1	2	yes	complemented
49	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
50	C₅×#446	C₂²	1	1	yes	characteristic, complemented
51	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×#436	C₂²	1	1	yes	characteristic, complemented
53	C₅×#435	C₂²	1	1	yes	characteristic
54	C₅×#435	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
56	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₅×#433	C₂²	1	1	yes	characteristic, complemented
59	C₅×#433	C₂²	1	1	yes	characteristic, complemented
60	C₅×#432	C₂²	1	1	yes	characteristic, complemented
61	C₅×#405	C₂²	1	1	yes	characteristic, complemented
62	C₅×#405	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
64	#65424	C₂²	1	2	yes	complemented
65	#65423	C₂²	1	2	yes	complemented
66	#65422	C₂²	1	2	yes	complemented
67	#65420	C₂²	1	2	yes	complemented
68	#65405	C₂²	1	1	yes	characteristic, complemented
69	#65405	C₂²	1	1	yes	characteristic, complemented
70	#65404	C₂²	1	1	yes	characteristic
71	#65404	C₂²	1	1	yes	characteristic
72	#65404	C₂²	1	1	yes	characteristic, complemented
73	#65404	C₂²	1	1	yes	characteristic, complemented
74	#65403	C₂²	1	2	yes	complemented
75	C₂×#3953	C₂²	1	2	yes	complemented
76	#65395	C₂²	1	1	yes	characteristic, complemented
77	C₂×#3950	C₂²	1	1	yes	characteristic, complemented
78	C₂×#3950	C₂²	1	1	yes	characteristic, complemented
79	#65137	C₂²	1	2	yes	complemented
80	#65136	C₂²	1	2	yes	complemented
81	#65136	C₂²	1	2	yes	complemented
82	#65136	C₂²	1	2	yes	complemented
83	#65135	C₂²	1	2	yes	complemented
84	#65133	C₂²	1	2	yes	complemented
85	#65133	C₂²	1	2	yes	complemented
86	#65133	C₂²	1	2	yes	complemented
87	#65133	C₂²	1	2	yes	complemented
88	#65132	C₂²	1	2	yes	—
89	#65131	C₂²	1	2	yes	complemented
90	#65118	C₂²	1	2	yes	complemented
91	#65026	C₂²	1	2	yes	complemented
92	#65025	C₂²	1	2	yes	complemented
93	#65025	C₂²	1	2	yes	complemented
94	#65024	C₂²	1	2	yes	complemented
95	#65023	C₂²	1	2	yes	complemented
96	#65023	C₂²	1	2	yes	complemented
97	#65021	C₂²	1	2	yes	—
98	#65021	C₂²	1	2	yes	—
99	#65020	C₂²	1	2	yes	complemented
100	#65020	C₂²	1	2	yes	complemented
101	#65012	C₂²	1	2	yes	complemented
102	#65010	C₂²	1	2	yes	complemented
103	#65003	C₂²	1	2	yes	complemented
104	#65002	C₂²	1	2	yes	complemented
105	#65000	C₂²	1	2	yes	complemented
106	#65000	C₂²	1	2	yes	complemented
107	#65000	C₂²	1	2	yes	complemented
108	#64999	C₂²	1	2	yes	complemented
109	#64999	C₂²	1	2	yes	complemented
110	#64999	C₂²	1	2	yes	complemented
111	C₄×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
112	C₄×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
113	#64986	C₂²	1	2	yes	complemented
114	#64985	C₂²	1	1	yes	characteristic, complemented
115	#64985	C₂²	1	1	yes	characteristic, complemented
116	#64984	C₂²	1	1	yes	characteristic
117	C₄×D₄₀	C₂²	1	1	yes	characteristic
118	C₄×D₄₀	C₂²	1	1	yes	characteristic
119	C₄×D₄₀	C₂²	1	1	yes	characteristic
120	C₄×D₄₀	C₂²	1	1	yes	characteristic
121	C₄×D₄₀	C₂²	1	2	yes	complemented
122	C₄×D₄₀	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄₀	C₂²	1	2	yes	complemented
124	C₄×D₄₀	C₂²	1	1	yes	characteristic, complemented
125	C₄×D₄₀	C₂²	1	1	yes	characteristic, complemented
126	C₄×D₄₀	C₂²	1	1	yes	characteristic, complemented
127	C₄×#677	C₂²	1	2	yes	complemented
128	#64972	C₂²	1	1	yes	characteristic, complemented
129	#64972	C₂²	1	1	yes	characteristic, complemented
130	#64971	C₂²	1	1	yes	characteristic, complemented
131	#61471	—	5	1	no	maximal, Sylow
132	C₂×#711	—	2	2	no	—
133	C₂×D₄×D₅	—	2	2	no	—
134	C₂×#709	C₂³	1	2	yes	—
135	C₂²×D₂₀	C₂³	1	2	yes	—
136	C₂²×D₂₀	C₂³	1	2	yes	—
137	C₂²×C₄×D₅	—	2	2	no	—
138	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
140	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₅×#126	D₄	1	1	yes	characteristic
145	C₅×#126	D₄	1	1	yes	characteristic
146	C₅×#125	D₄	1	1	yes	characteristic
147	C₅×#124	D₄	1	1	yes	characteristic
148	C₅×#123	D₄	1	1	yes	characteristic
149	C₅×#123	D₄	1	1	yes	characteristic
150	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
151	C₅×#121	D₄	1	1	yes	characteristic
152	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
153	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
154	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
155	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
156	C₅×#117	C₂³	1	1	yes	characteristic
157	C₅×#117	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
159	#4093	—	2	2	no	—
160	#4092	—	2	2	no	—
161	#4085	—	2	2	no	—
162	#4083	—	2	2	no	—
163	#4083	—	2	2	no	—
164	#4081	—	2	2	no	—
165	#4076	C₂³	1	2	yes	—
166	#4076	C₂³	1	2	yes	—
167	#4076	C₂³	1	2	yes	—
168	#4076	C₂³	1	2	yes	—
169	#4075	—	2	2	no	—
170	C₄×C₂²⋊D₅	—	2	2	no	—
171	C₂×#685	—	2	2	no	—
172	#4072	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
174	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
175	#4070	C₂³	1	2	yes	—
176	#4070	C₂³	1	2	yes	—
177	C₂×Dic₂₀	C₂³	1	1	yes	characteristic
178	#4050	—	2	4	no	—
179	C₂×D₄₀	—	2	4	no	—
180	C₂×D₄₀	—	2	4	no	—
181	C₂×D₄₀	C₂³	1	2	yes	—
182	C₂×D₄₀	C₂³	1	2	yes	—
183	C₂×D₄₀	C₂³	1	1	yes	characteristic
184	C₂×D₄₀	C₂³	1	1	yes	characteristic
185	C₂×D₄₀	C₂³	1	2	yes	—
186	C₂×D₄₀	C₂³	1	1	yes	characteristic
187	C₂×#677	C₂³	1	2	yes	—
188	C₂×#677	C₂³	1	2	yes	—
189	C₂×#677	C₂³	1	2	yes	—
190	#4044	—	2	2	no	—
191	#4044	—	2	2	no	—
192	#4043	—	2	2	no	—
193	#4042	—	2	2	no	—
194	#4042	—	2	2	no	—
195	#4042	—	2	2	no	—
196	#4041	—	2	2	no	—
197	#4040	—	2	2	no	—
198	#4040	—	2	2	no	—
199	#4040	—	2	2	no	—
200	#4040	—	2	2	no	—
201	#4040	—	2	2	no	—
202	#4040	—	2	2	no	—
203	#4039	—	2	2	no	—
204	#4039	—	2	2	no	—
205	#4039	—	2	2	no	—
206	#4038	—	2	2	no	—
207	D₅×C₄⋊C₄	—	2	2	no	—
208	D₅×C₄⋊C₄	—	2	2	no	—
209	#4035	—	2	2	no	—
210	#4032	—	2	2	no	—
211	#4032	—	2	2	no	—
212	#4031	—	2	2	no	—
213	#4030	—	2	2	no	—
214	#4030	—	2	2	no	—
215	#4030	—	2	2	no	—
216	#4030	—	2	2	no	—
217	#4029	—	2	2	no	—
218	#4029	—	2	2	no	—
219	#4028	—	2	2	no	—
220	#4028	—	2	2	no	—
221	#4027	—	2	2	no	—
222	#4027	—	2	2	no	—
223	#4027	—	2	2	no	—
224	D₅×C₂²⋊C₄	—	2	2	no	—
225	D₅×C₂²⋊C₄	—	2	2	no	—
226	D₅×C₂²⋊C₄	—	2	2	no	—
227	D₅×C₂²⋊C₄	—	2	2	no	—
228	#4025	—	2	2	no	—
229	#4023	—	2	2	no	—
230	#4022	—	2	2	no	—
231	#4021	C₂³	1	2	yes	—
232	#4021	C₂³	1	2	yes	—
233	#4020	C₂³	1	2	yes	—
234	C₄×D₂₀	—	2	2	no	—
235	C₄×D₂₀	—	2	2	no	—
236	C₄×D₂₀	C₂³	1	2	yes	—
237	C₄×D₂₀	C₂³	1	2	yes	—
238	C₄×D₂₀	C₂³	1	2	yes	—
239	C₄×D₂₀	C₂³	1	2	yes	—
240	C₄×D₂₀	C₂³	1	2	yes	—
241	C₄×D₂₀	C₂³	1	2	yes	—
242	C₄×D₂₀	C₂³	1	2	yes	—
243	C₄×D₂₀	C₂³	1	2	yes	—
244	#4018	—	2	2	no	—
245	#4016	C₂³	1	2	yes	—
246	#4016	C₂³	1	2	yes	—
247	#4015	C₂³	1	2	yes	—
248	C₄×Dic₁₀	C₂³	1	2	yes	—
249	C₄×Dic₁₀	C₂³	1	2	yes	—
250	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
257	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
258	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
259	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
260	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
261	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
262	C₅×#97	C₂³	1	1	yes	characteristic
263	C₅×#97	C₂³	1	1	yes	characteristic
264	C₅×#97	C₂³	1	1	yes	characteristic
265	C₅×#97	C₂³	1	1	yes	characteristic
266	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
267	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
268	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
269	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
270	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
271	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
272	#3953	C₂³	1	2	yes	—
273	#3953	C₂³	1	2	yes	—
274	#3953	C₂³	1	2	yes	—
275	#3953	C₂³	1	2	yes	—
276	#3953	C₂³	1	2	yes	—
277	#3953	C₂³	1	2	yes	—
278	#3953	C₂³	1	2	yes	—
279	#3953	C₂³	1	2	yes	—
280	#3953	C₂³	1	2	yes	—
281	#3953	C₂³	1	2	yes	—
282	#3953	C₂³	1	2	yes	—
283	#3953	C₂³	1	2	yes	—
284	#3950	C₂³	1	2	yes	—
285	#3950	C₂³	1	2	yes	—
286	#3950	C₂³	1	2	yes	—
287	#3950	C₂³	1	1	yes	characteristic
288	#3950	C₂³	1	1	yes	characteristic
289	#3950	C₂³	1	1	yes	characteristic
290	#3950	C₂³	1	1	yes	characteristic
291	#3949	C₂³	1	2	yes	—
292	#3949	C₂³	1	2	yes	—
293	#3949	C₂³	1	2	yes	—
294	#3948	C₂³	1	2	yes	—
295	#3948	C₂³	1	2	yes	—
296	#3948	C₂³	1	2	yes	—
297	#3948	C₂³	1	2	yes	—
298	#3513	—	5	2	no	—
299	#3396	—	5	1	no	—
300	#3380	—	5	1	no	—
301	#3370	—	5	2	no	—
302	#3339	—	5	1	no	—
303	#3336	—	5	1	no	—
304	#3334	—	5	1	no	—
305	#3322	—	5	2	no	—
306	#3310	—	5	2	no	—
307	#3306	—	5	2	no	—
308	#3280	—	5	1	no	—
309	#3280	—	5	1	no	—
310	D₄×D₈	—	5	1	no	—
311	#3176	—	5	1	no	—
312	#3175	—	5	1	no	—
313	#3168	—	5	1	no	—
314	#3119	—	5	2	no	—
315	#3118	—	5	2	no	—
316	#3114	—	5	2	no	—
317	#2966	D₅	1	1	yes	characteristic, complemented
318	#2951	—	5	1	no	—
319	#2948	—	5	1	no	—
320	C₂×C₄×D₈	—	5	1	no	—
321	C₂³×D₅	—	2	2	no	—
322	C₂³×D₅	—	2	2	no	—
323	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
324	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
325	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
326	C₂×C₅×D₄	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	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₅	—	2	2	no	—
333	C₂×C₂²⋊D₅	—	2	2	no	—
334	C₂×C₂²⋊D₅	—	2	2	no	—
335	C₂×C₂²⋊D₅	—	2	2	no	—
336	C₂×C₂²⋊D₅	—	2	2	no	—
337	C₂²×Dic₅	—	2	2	no	—
338	C₂²×Dic₅	—	2	2	no	—
339	#711	—	8	4	no	—
340	D₄×D₅	—	8	4	no	—
341	#709	—	2	4	no	—
342	#709	—	4	2	no	—
343	C₂×D₂₀	—	2	4	no	—
344	C₂×D₂₀	—	2	4	no	—
345	C₂×D₂₀	—	2	2	no	—
346	C₂×D₂₀	—	2	2	no	—
347	C₂×D₂₀	—	2	2	no	—
348	C₂×D₂₀	—	2	2	no	—
349	C₂×D₂₀	—	4	2	no	—
350	C₂×D₂₀	—	4	2	no	—
351	C₂×D₂₀	C₂⁴	1	2	yes	—
352	C₂×D₂₀	C₂⁴	1	2	yes	—
353	C₂×D₂₀	C₂⁴	1	2	yes	—
354	C₂×C₄×D₅	—	2	2	no	—
355	C₂×C₄×D₅	—	2	2	no	—
356	C₂×C₄×D₅	—	2	2	no	—
357	C₂×C₄×D₅	—	2	2	no	—
358	C₂×C₄×D₅	—	2	2	no	—
359	C₂×C₄×D₅	—	2	2	no	—
360	C₂×C₄×D₅	—	2	2	no	—
361	C₂×C₄×D₅	—	2	2	no	—
362	C₂×C₄×D₅	—	2	2	no	—
363	C₂×C₄×D₅	—	8	4	no	—
364	C₂×Dic₁₀	—	2	2	no	—
365	C₂×Dic₁₀	C₂⁴	1	2	yes	—
366	C₅×M₁₆	—	4	1	no	—
367	C₅×M₁₆	—	4	1	no	—
368	C₂×C₅×C₈	—	2	2	no	—
369	C₂×C₅×C₈	—	2	2	no	—
370	C₂×C₅×C₈	—	2	2	no	—
371	C₂×C₅×C₈	—	4	1	no	—
372	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
380	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
387	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
392	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₅×C₂²⋊C₄	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	C₂⁴	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	C₂²⋊Dic₅	—	2	2	no	—
407	C₂²⋊Dic₅	—	2	2	no	—
408	C₂²⋊Dic₅	—	2	2	no	—
409	#685	—	2	2	no	—
410	#685	—	2	2	no	—
411	#685	—	2	2	no	—
412	#685	—	2	2	no	—
413	#685	—	2	2	no	—
414	#685	—	2	2	no	—
415	#685	—	2	2	no	—
416	#685	—	2	2	no	—
417	#685	—	2	2	no	—
418	#685	—	2	2	no	—
419	#685	—	2	2	no	—
420	#685	—	2	2	no	—
421	#685	—	2	2	no	—
422	#685	—	2	2	no	—
423	#685	—	2	2	no	—
424	#685	—	2	2	no	—
425	C₄⋊Dic₅	—	2	2	no	—
426	C₄⋊Dic₅	—	2	2	no	—
427	C₄⋊Dic₅	—	2	2	no	—
428	C₄⋊Dic₅	C₂⁴	1	2	yes	—
429	C₄⋊Dic₅	C₂⁴	1	2	yes	—
430	C₄⋊Dic₅	C₂⁴	1	2	yes	—
431	C₄⋊Dic₅	C₂⁴	1	2	yes	—
432	#683	—	2	2	no	—
433	#683	—	2	2	no	—
434	#683	—	2	2	no	—
435	#683	—	2	2	no	—
436	#683	—	2	2	no	—
437	#683	—	2	2	no	—
438	#683	—	2	2	no	—
439	#683	—	2	2	no	—
440	C₄×Dic₅	—	2	2	no	—
441	C₄×Dic₅	—	2	2	no	—
442	C₄×Dic₅	—	2	2	no	—
443	Dic₂₀	—	2	2	no	—
444	D₄₀	—	2	4	no	—
445	D₄₀	—	2	4	no	—
446	D₄₀	—	2	2	no	—
447	D₄₀	—	2	2	no	—
448	D₄₀	—	4	2	no	—
449	D₄₀	#41	1	4	yes	complemented
450	#677	—	2	4	no	—
451	#677	—	4	2	no	—
452	#677	—	4	2	no	—
453	C₂×#135	—	5	1	no	—
454	C₂²×D₈	—	5	1	no	—
455	C₂²×D₈	—	5	1	no	—
456	#559	—	5	2	no	—
457	#554	—	5	2	no	—
458	#553	—	5	2	no	—
459	#553	—	10	2	no	—
460	#552	—	5	2	no	—
461	#551	—	10	2	no	—
462	#551	—	10	2	no	—
463	#547	—	5	2	no	—
464	#546	—	5	2	no	—
465	#546	—	5	2	no	—
466	#546	—	10	2	no	—
467	D₄²	—	5	2	no	—
468	#542	—	5	2	no	—
469	#540	—	5	2	no	—
470	#539	—	10	2	no	—
471	#538	—	10	2	no	—
472	#529	—	5	2	no	—
473	#529	C₂×D₅	1	1	yes	characteristic
474	#525	—	10	2	no	—
475	C₂×#123	—	10	2	no	—
476	#520	—	5	2	no	—
477	#518	—	5	2	no	—
478	C₂×C₄×D₄	—	5	2	no	—
479	#500	—	5	1	no	—
480	#499	—	5	1	no	—
481	#499	—	5	1	no	—
482	#495	—	5	1	no	—
483	#495	—	5	1	no	—
484	#493	—	5	1	no	—
485	#490	—	5	2	no	—
486	#489	—	5	2	no	—
487	#488	—	5	2	no	—
488	#485	—	5	2	no	—
489	#483	—	5	2	no	—
490	#482	—	5	2	no	—
491	#481	—	5	2	no	—
492	#480	—	5	2	no	—
493	#480	—	5	2	no	—
494	#479	—	5	2	no	—
495	#478	—	5	2	no	—
496	#478	—	5	2	no	—
497	#478	—	5	2	no	—
498	#476	—	5	2	no	—
499	#474	—	5	2	no	—
500	#469	—	5	2	no	—
501	#468	—	5	2	no	—
502	#467	—	5	1	no	—
503	#467	—	5	1	no	—
504	#466	—	5	1	no	—
505	#466	—	5	1	no	—
506	#466	—	5	1	no	—
507	#466	—	5	1	no	—
508	#465	—	5	2	no	—
509	#463	—	5	2	no	—
510	#463	—	5	2	no	—
511	#463	—	5	2	no	—
512	#463	—	5	2	no	—
513	#460	—	5	2	no	—
514	#459	—	5	2	no	—
515	#450	—	5	2	no	—
516	#450	—	5	2	no	—
517	#449	—	5	2	no	—
518	#449	—	5	2	no	—
519	#447	—	5	2	no	—
520	#447	—	5	2	no	—
521	#446	C₂×D₅	1	1	yes	characteristic, complemented
522	C₈×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
523	#442	—	5	2	no	—
524	#442	—	5	2	no	—
525	#442	—	5	2	no	—
526	#440	—	5	2	no	—
527	#440	—	5	2	no	—
528	#440	—	5	2	no	—
529	C₄×Q₁₆	—	5	1	no	—
530	C₄×Q₁₆	—	5	1	no	—
531	C₄×SD₁₆	—	5	2	no	—
532	C₄×D₈	—	5	1	no	—
533	C₄×D₈	—	5	1	no	—
534	C₄×D₈	—	5	2	no	—
535	C₄×D₈	—	5	2	no	—
536	C₄×D₈	—	5	1	no	—
537	C₄×D₈	—	5	1	no	—
538	C₄×D₈	—	5	1	no	—
539	C₄×D₈	—	5	1	no	—
540	C₄×D₈	—	5	1	no	—
541	C₄×D₈	—	5	1	no	—
542	#436	C₂×D₅	1	1	yes	characteristic, complemented
543	#435	C₂×D₅	1	1	yes	characteristic
544	#435	C₂×D₅	1	1	yes	characteristic, complemented
545	C₈×D₄	C₂×D₅	1	1	yes	characteristic
546	C₈×D₄	C₂×D₅	1	1	yes	characteristic, complemented
547	C₈×D₄	C₂×D₅	1	1	yes	characteristic, complemented
548	#433	C₂×D₅	1	1	yes	characteristic, complemented
549	#433	C₂×D₅	1	1	yes	characteristic, complemented
550	#432	C₂×D₅	1	1	yes	characteristic, complemented
551	#427	—	5	1	no	—
552	C₂×#107	—	5	1	no	—
553	C₂×#107	—	5	1	no	—
554	#418	—	5	2	no	—
555	#417	—	5	2	no	—
556	C₂×#102	—	5	2	no	—
557	#405	C₂×D₅	1	1	yes	characteristic, complemented
558	#405	C₂×D₅	1	1	yes	characteristic, complemented
559	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
560	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
561	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
562	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
563	C₂²×D₅	—	2	2	no	—
564	C₂²×D₅	—	2	2	no	—
565	C₂²×D₅	—	2	2	no	—
566	C₂²×D₅	—	4	4	no	—
567	C₂²×D₅	—	4	4	no	—
568	C₂²×D₅	—	4	4	no	—
569	C₂²×D₅	—	8	2	no	—
570	C₂²×D₅	—	8	2	no	—
571	C₂²×D₅	—	8	2	no	—
572	C₅×Q₈	—	4	1	no	—
573	C₅×D₄	—	2	2	no	—
574	C₅×D₄	—	2	2	no	—
575	C₅×D₄	—	4	1	no	—
576	C₂×C₄×C₅	—	2	2	no	—
577	C₂×C₄×C₅	—	2	1	no	—
578	C₂×C₄×C₅	—	2	1	no	—
579	C₂×C₄×C₅	—	2	1	no	—
580	C₂×C₄×C₅	—	2	1	no	—
581	C₂×C₄×C₅	—	2	1	no	—
582	C₂×C₄×C₅	—	2	1	no	—
583	C₂×C₄×C₅	—	4	1	no	—
584	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
596	C₂²⋊D₅	—	4	4	no	—
597	C₂²⋊D₅	—	4	4	no	—
598	C₂²⋊D₅	—	8	2	no	—
599	C₂²⋊D₅	—	8	2	no	—
600	C₂²⋊D₅	—	8	2	no	—
601	C₂×Dic₅	—	2	2	no	—
602	C₂×Dic₅	—	2	2	no	—
603	C₂×Dic₅	—	2	2	no	—
604	C₂×Dic₅	—	2	2	no	—
605	C₂×Dic₅	—	2	2	no	—
606	C₂×Dic₅	—	4	4	no	—
607	C₂×Dic₅	—	8	2	no	—
608	D₂₀	—	2	2	no	—
609	D₂₀	—	2	2	no	—
610	D₂₀	—	2	2	no	—
611	D₂₀	—	2	2	no	—
612	D₂₀	—	2	2	no	—
613	D₂₀	—	4	4	no	—
614	D₂₀	—	4	4	no	—
615	D₂₀	—	8	2	no	—
616	D₂₀	—	8	2	no	—
617	D₂₀	C₂×#41	1	4	yes	—
618	C₄×D₅	—	4	4	no	—
619	C₄×D₅	—	8	2	no	—
620	C₄×D₅	—	8	2	no	—
621	C₄×D₅	—	8	2	no	—
622	C₄×D₅	—	8	2	no	—
623	C₄×D₅	—	8	2	no	—
624	C₄×D₅	—	8	2	no	—
625	C₄×D₅	—	8	2	no	—
626	C₄×D₅	—	8	2	no	—
627	Dic₁₀	—	2	2	no	—
628	Dic₁₀	—	2	2	no	—
629	Dic₁₀	—	8	2	no	—
630	C₅×C₈	—	2	1	no	—
631	C₅×C₈	—	2	1	no	—
632	C₅×C₈	—	2	1	no	—
633	C₅×C₈	—	2	1	no	—
634	C₅×C₈	—	2	1	no	—
635	C₅×C₈	—	2	1	no	—
636	C₅×C₈	—	2	1	no	—
637	C₅×C₈	C₂×#41	1	2	yes	—
638	C₂×#41	—	5	2	no	—
639	C₂×#41	—	10	2	no	—
640	C₂²×D₄	—	5	2	no	—
641	C₂²×D₄	—	5	2	no	—
642	C₂²×D₄	—	10	2	no	—
643	C₂³×C₄	—	10	2	no	—
644	#135	—	10	4	no	—
645	C₂×Q₁₆	—	5	1	no	—
646	C₂×SD₁₆	—	5	2	no	—
647	C₂×SD₁₆	—	5	2	no	—
648	C₂×SD₁₆	—	5	2	no	—
649	C₂×D₈	—	5	1	no	—
650	C₂×D₈	—	5	2	no	—
651	C₂×D₈	—	5	1	no	—
652	C₂×D₈	—	5	1	no	—
653	C₂×D₈	—	5	2	no	—
654	C₂×D₈	—	5	2	no	—
655	C₂×D₈	—	10	4	no	—
656	C₂×D₈	—	10	4	no	—
657	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
658	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
659	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
660	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
661	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
662	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
663	C₄⋊Q₈	—	5	2	no	—
664	#127	—	5	2	no	—
665	#126	—	10	2	no	—
666	#126	—	10	2	no	—
667	#126	—	10	2	no	—
668	#126	—	10	2	no	—
669	#126	D₂₀	1	1	yes	characteristic
670	#126	D₂₀	1	1	yes	characteristic
671	#125	—	5	2	no	—
672	#125	—	5	2	no	—
673	#125	—	10	2	no	—
674	#125	D₂₀	1	1	yes	characteristic
675	#124	—	5	2	no	—
676	#124	—	5	2	no	—
677	#124	—	10	2	no	—
678	#124	—	10	2	no	—
679	#124	D₂₀	1	1	yes	characteristic
680	#123	—	10	2	no	—
681	#123	—	10	2	no	—
682	#123	—	10	2	no	—
683	#123	—	10	2	no	—
684	#123	—	10	2	no	—
685	#123	—	10	2	no	—
686	#123	—	10	2	no	—
687	#123	—	10	2	no	—
688	#123	—	10	2	no	—
689	#123	—	10	2	no	—
690	#123	—	10	2	no	—
691	#123	—	10	2	no	—
692	#123	D₂₀	1	1	yes	characteristic
693	#123	D₂₀	1	1	yes	characteristic
694	C₂²⋊Q₈	—	5	2	no	—
695	C₂²⋊Q₈	—	5	2	no	—
696	C₂²⋊Q₈	—	10	2	no	—
697	C₂²⋊Q₈	—	10	2	no	—
698	C₂²⋊Q₈	—	10	2	no	—
699	C₂²⋊Q₈	—	10	2	no	—
700	C₂²⋊Q₈	—	10	2	no	—
701	C₂²⋊Q₈	D₂₀	1	1	yes	characteristic
702	#121	—	5	2	no	—
703	#121	—	5	2	no	—
704	#121	—	5	2	no	—
705	#121	—	5	2	no	—
706	#121	—	10	2	no	—
707	#121	—	10	2	no	—
708	#121	—	10	2	no	—
709	#121	—	10	2	no	—
710	#121	—	10	2	no	—
711	#121	—	10	2	no	—
712	#121	D₂₀	1	1	yes	characteristic
713	#120	—	10	2	no	—
714	#120	—	10	2	no	—
715	#120	—	10	2	no	—
716	#120	—	10	2	no	—
717	C₄×Q₈	—	5	2	no	—
718	C₄×Q₈	—	5	2	no	—
719	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
720	C₄×D₄	—	5	2	no	—
721	C₄×D₄	—	5	2	no	—
722	C₄×D₄	—	5	2	no	—
723	C₄×D₄	—	5	2	no	—
724	C₄×D₄	—	5	2	no	—
725	C₄×D₄	—	5	2	no	—
726	C₄×D₄	—	5	2	no	—
727	C₄×D₄	—	5	2	no	—
728	C₄×D₄	—	10	2	no	—
729	C₄×D₄	—	10	2	no	—
730	C₄×D₄	—	10	2	no	—
731	C₄×D₄	—	10	2	no	—
732	C₄×D₄	—	10	2	no	—
733	C₄×D₄	—	10	2	no	—
734	C₄×D₄	—	10	2	no	—
735	C₄×D₄	—	10	2	no	—
736	C₄×D₄	—	10	2	no	—
737	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
738	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
739	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
740	#117	—	5	2	no	—
741	#117	—	10	2	no	—
742	#117	—	10	2	no	—
743	#117	—	10	2	no	—
744	#117	C₂²×D₅	1	1	yes	characteristic
745	#117	C₂²×D₅	1	1	yes	characteristic
746	C₂×C₄⋊C₄	—	5	2	no	—
747	C₂×C₄⋊C₄	—	5	2	no	—
748	C₂×C₄⋊C₄	—	10	2	no	—
749	C₂×C₄⋊C₄	—	10	2	no	—
750	C₂×C₂²⋊C₄	—	10	2	no	—
751	C₂×C₂²⋊C₄	—	10	2	no	—
752	C₂×C₂²⋊C₄	—	10	2	no	—
753	C₂×C₂²⋊C₄	—	10	2	no	—
754	C₂×C₂²⋊C₄	—	10	2	no	—
755	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
756	#107	—	5	1	no	—
757	#107	—	5	1	no	—
758	#107	—	5	2	no	—
759	#107	—	5	1	no	—
760	#107	—	5	2	no	—
761	#107	—	5	1	no	—
762	#107	—	5	2	no	—
763	#106	—	5	2	no	—
764	#106	—	5	2	no	—
765	#106	—	5	2	no	—
766	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
767	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
768	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
769	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
770	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
771	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
772	#103	—	5	2	no	—
773	#103	—	5	2	no	—
774	#103	—	5	2	no	—
775	#103	—	5	2	no	—
776	#102	—	5	2	no	—
777	#102	—	5	2	no	—
778	#102	—	5	2	no	—
779	#102	—	5	2	no	—
780	#102	—	5	2	no	—
781	#102	—	5	2	no	—
782	#102	—	5	2	no	—
783	#102	—	5	2	no	—
784	#102	—	5	2	no	—
785	#102	—	5	2	no	—
786	#102	—	5	2	no	—
787	#102	—	5	2	no	—
788	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
789	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
790	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
791	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
792	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
793	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
794	#97	C₂²×D₅	1	1	yes	characteristic
795	#97	C₂²×D₅	1	1	yes	characteristic
796	#97	C₂²×D₅	1	1	yes	characteristic
797	#97	C₂²×D₅	1	1	yes	characteristic
798	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
799	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
800	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
801	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
802	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
803	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
804	C₂²×C₅	—	2	1	no	—
805	C₂²×C₅	—	2	1	no	—
806	C₂²×C₅	—	2	1	no	—
807	C₂²×C₅	—	2	1	no	—
808	C₂²×C₅	—	2	1	no	—
809	C₂²×C₅	—	2	1	no	—
810	C₂²×C₅	—	2	1	no	—
811	C₂²×C₅	—	2	1	no	—
812	C₂²×C₅	#576	1	2	yes	—
813	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
814	C₂×D₅	—	2	4	no	—
815	C₂×D₅	—	4	2	no	—
816	C₂×D₅	—	4	2	no	—
817	C₂×D₅	—	4	2	no	—
818	C₂×D₅	—	4	2	no	—
819	C₂×D₅	—	4	2	no	—
820	C₂×D₅	—	4	2	no	—
821	C₂×D₅	—	4	2	no	—
822	C₂×D₅	—	4	2	no	—
823	C₂×D₅	—	8	8	no	—
824	C₂×D₅	—	16	4	no	—
825	C₄×C₅	—	2	1	no	—
826	C₄×C₅	—	2	1	no	—
827	C₄×C₅	—	2	1	no	—
828	C₄×C₅	—	2	1	no	—
829	C₄×C₅	—	2	1	no	—
830	C₄×C₅	—	2	1	no	—
831	C₄×C₅	—	2	1	no	—
832	C₄×C₅	—	2	1	no	—
833	C₄×C₅	—	2	1	no	—
834	C₄×C₅	—	2	1	no	—
835	C₄×C₅	—	2	1	no	—
836	C₄×C₅	C₂²×#41	1	1	yes	characteristic
837	C₄×C₅	#585	1	1	yes	characteristic
838	Dic₅	—	4	2	no	—
839	Dic₅	—	4	2	no	—
840	Dic₅	—	4	2	no	—
841	Dic₅	—	4	2	no	—
842	Dic₅	—	4	2	no	—
843	C₂⁴	—	10	2	no	—
844	C₂⁴	—	10	2	no	—
845	#41	—	10	4	no	—
846	#41	—	20	2	no	—
847	#41	—	40	4	no	—
848	C₂×Q₈	—	5	2	no	—
849	C₂×Q₈	—	10	2	no	—
850	C₂×Q₈	C₂×D₂₀	1	1	yes	characteristic
851	C₂×D₄	—	5	2	no	—
852	C₂×D₄	—	5	2	no	—
853	C₂×D₄	—	5	2	no	—
854	C₂×D₄	—	10	4	no	—
855	C₂×D₄	—	10	4	no	—
856	C₂×D₄	—	10	2	no	—
857	C₂×D₄	—	10	2	no	—
858	C₂×D₄	—	10	2	no	—
859	C₂×D₄	—	10	2	no	—
860	C₂×D₄	—	10	2	no	—
861	C₂×D₄	—	10	2	no	—
862	C₂×D₄	—	10	2	no	—
863	C₂×D₄	—	10	2	no	—
864	C₂×D₄	—	10	2	no	—
865	C₂×D₄	—	20	2	no	—
866	C₂×D₄	—	20	2	no	—
867	C₂×D₄	—	40	4	no	—
868	C₂×D₄	C₂×D₂₀	1	1	yes	characteristic
869	C₂×D₄	C₂×D₂₀	1	1	yes	characteristic
870	C₂×D₄	C₂×D₂₀	1	1	yes	characteristic
871	C₂²×C₄	—	10	2	no	—
872	C₂²×C₄	—	10	2	no	—
873	C₂²×C₄	—	10	2	no	—
874	C₂²×C₄	—	10	2	no	—
875	C₂²×C₄	—	10	2	no	—
876	C₂²×C₄	—	10	2	no	—
877	C₂²×C₄	—	10	2	no	—
878	C₂²×C₄	—	10	2	no	—
879	C₂²×C₄	—	10	2	no	—
880	C₂²×C₄	—	10	2	no	—
881	C₂²×C₄	—	10	2	no	—
882	C₂²×C₄	—	40	4	no	—
883	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
884	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
885	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
886	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
887	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
888	Q₁₆	—	10	2	no	—
889	SD₁₆	—	10	4	no	—
890	SD₁₆	—	20	2	no	—
891	SD₁₆	—	20	2	no	—
892	D₈	—	5	4	no	—
893	D₈	—	10	4	no	—
894	D₈	—	10	4	no	—
895	D₈	—	10	2	no	—
896	D₈	—	10	2	no	—
897	D₈	—	20	2	no	—
898	M₁₆	—	4	1	no	—
899	M₁₆	—	4	1	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	2	2	no	—
902	C₂×C₈	—	2	2	no	—
903	C₂×C₈	—	4	1	no	—
904	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
905	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
906	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
907	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
908	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
909	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
910	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
911	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
912	C₄⋊C₄	—	5	2	no	—
913	C₄⋊C₄	—	5	2	no	—
914	C₄⋊C₄	—	5	2	no	—
915	C₄⋊C₄	—	5	2	no	—
916	C₄⋊C₄	—	10	2	no	—
917	C₄⋊C₄	—	10	2	no	—
918	C₄⋊C₄	—	10	2	no	—
919	C₄⋊C₄	—	10	2	no	—
920	C₄⋊C₄	—	10	2	no	—
921	C₄⋊C₄	—	10	2	no	—
922	C₄⋊C₄	—	10	2	no	—
923	C₄⋊C₄	—	10	2	no	—
924	C₄⋊C₄	—	10	2	no	—
925	C₄⋊C₄	—	10	2	no	—
926	C₄⋊C₄	—	10	2	no	—
927	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
929	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
930	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
931	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
932	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
933	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
937	C₂²⋊C₄	—	10	2	no	—
938	C₂²⋊C₄	—	10	2	no	—
939	C₂²⋊C₄	—	10	2	no	—
940	C₂²⋊C₄	—	10	2	no	—
941	C₂²⋊C₄	—	10	2	no	—
942	C₂²⋊C₄	—	10	2	no	—
943	C₂²⋊C₄	—	10	2	no	—
944	C₂²⋊C₄	—	10	2	no	—
945	C₂²⋊C₄	—	10	2	no	—
946	C₂²⋊C₄	—	10	2	no	—
947	C₂²⋊C₄	—	10	2	no	—
948	C₂²⋊C₄	—	10	2	no	—
949	C₂²⋊C₄	—	10	2	no	—
950	C₂²⋊C₄	—	10	2	no	—
951	C₂²⋊C₄	—	10	2	no	—
952	C₂²⋊C₄	—	10	2	no	—
953	C₂²⋊C₄	—	10	2	no	—
954	C₂²⋊C₄	—	10	2	no	—
955	C₂²⋊C₄	—	10	2	no	—
956	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
957	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
958	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
959	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
960	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
961	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
962	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
963	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
964	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
965	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
966	C₄²	—	10	2	no	—
967	C₄²	—	10	2	no	—
968	C₄²	—	10	2	no	—
969	C₄²	C₂×D₂₀	1	1	yes	characteristic
970	C₄²	C₂×D₂₀	1	1	yes	characteristic
971	C₄²	C₂³×D₅	1	1	yes	characteristic
972	C₄²	C₂³×D₅	1	1	yes	characteristic
973	C₄²	C₂³×D₅	1	1	yes	characteristic
974	C₄²	C₂³×D₅	1	1	yes	characteristic
975	C₂×C₅	—	2	2	no	—
976	C₂×C₅	—	4	1	no	—
977	C₂×C₅	—	4	1	no	—
978	C₂×C₅	D₄×#41	1	1	yes	characteristic
979	C₂×C₅	C₂×#576	1	1	yes	characteristic
980	C₂×C₅	#3584	1	1	yes	characteristic
981	D₅	—	4	4	no	—
982	D₅	—	8	2	no	—
983	D₅	—	8	2	no	—
984	C₂³	—	10	2	no	—
985	C₂³	—	10	2	no	—
986	C₂³	—	10	2	no	—
987	C₂³	—	20	4	no	—
988	C₂³	—	20	4	no	—
989	C₂³	—	20	4	no	—
990	C₂³	—	40	2	no	—
991	C₂³	—	40	2	no	—
992	C₂³	—	40	2	no	—
993	C₂³	C₂²×D₂₀	1	1	yes	characteristic
994	C₂³	C₂²×D₂₀	1	1	yes	characteristic
995	C₂³	C₂²×D₂₀	1	1	yes	characteristic
996	Q₈	—	4	1	no	—
997	Q₈	—	10	2	no	—
998	Q₈	—	10	2	no	—
999	Q₈	—	40	2	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	4	1	no	—
1003	D₄	—	5	4	no	—
1004	D₄	—	10	2	no	—
1005	D₄	—	10	2	no	—
1006	D₄	—	10	2	no	—
1007	D₄	—	10	2	no	—
1008	D₄	—	10	2	no	—
1009	D₄	—	20	4	no	—
1010	D₄	—	20	4	no	—
1011	D₄	—	20	4	no	—
1012	D₄	—	20	4	no	—
1013	D₄	—	40	2	no	—
1014	D₄	—	40	2	no	—
1015	D₄	—	40	2	no	—
1016	D₄	—	40	2	no	—
1017	D₄	—	40	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	4	1	no	—
1026	C₂×C₄	—	10	2	no	—
1027	C₂×C₄	—	10	2	no	—
1028	C₂×C₄	—	10	2	no	—
1029	C₂×C₄	—	10	2	no	—
1030	C₂×C₄	—	10	2	no	—
1031	C₂×C₄	—	20	4	no	—
1032	C₂×C₄	—	20	4	no	—
1033	C₂×C₄	—	40	2	no	—
1034	C₂×C₄	—	40	2	no	—
1035	C₂×C₄	—	40	2	no	—
1036	C₂×C₄	—	40	2	no	—
1037	C₂×C₄	—	40	2	no	—
1038	C₂×C₄	—	40	2	no	—
1039	C₂×C₄	—	40	2	no	—
1040	C₂×C₄	—	40	2	no	—
1041	C₂×C₄	—	40	2	no	—
1042	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1053	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	D₅×#41	1	2	yes	—
1062	C₅	#61471	1	1	yes	characteristic, complemented, Sylow
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	10	4	no	—
1072	C₂²	—	20	2	no	—
1073	C₂²	—	20	2	no	—
1074	C₂²	—	20	2	no	—
1075	C₂²	—	20	2	no	—
1076	C₂²	—	20	2	no	—
1077	C₂²	—	20	2	no	—
1078	C₂²	—	20	2	no	—
1079	C₂²	—	20	2	no	—
1080	C₂²	—	40	8	no	—
1081	C₂²	—	80	4	no	—
1082	C₂²	#66086	1	2	yes	—
1083	C₂²	C₂³×D₂₀	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	20	2	no	—
1096	C₄	—	20	2	no	—
1097	C₄	—	20	2	no	—
1098	C₄	—	20	2	no	—
1099	C₄	—	20	2	no	—
1100	C₄	C₂×D₅×#41	1	1	yes	characteristic
1101	C₄	#66283	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	1	no	—
1104	C₂	—	4	1	no	—
1105	C₂	—	20	4	no	—
1106	C₂	—	40	2	no	—
1107	C₂	—	40	2	no	—
1108	C₂	#41×D₂₀	1	1	yes	characteristic
1109	C₂	C₂×#66086	1	1	yes	characteristic
1110	C₂	#10619064	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₅×#2966	C₂
socle	C₂²×C₅	C₂³×D₄
hypercenter	#2966	D₅
hypocenter	C₅	#61471
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #10618062	C₂	semidirect
2. C₅×#2966	C₂	semidirect
3. #10611702	C₂	semidirect
4. #10611661	C₂	semidirect
5. #10611646	C₂	semidirect
6. #10611284	C₂	semidirect
7. #10611232	C₂	semidirect
8. #10611230	C₂	semidirect
9. #10611164	C₂	semidirect
10. #10611164	C₂	semidirect
11. D₄×D₄₀	C₂	semidirect
12. #10611147	C₂	semidirect
13. #10611144	C₂	semidirect
14. #10611142	C₂	semidirect
15. #10611115	C₂	semidirect
16. #10611114	C₂	semidirect
17. #10611077	C₂	semidirect
18. #10610300	C₂	semidirect
19. #10610299	C₂	semidirect
20. #10610293	C₂	semidirect
21. #10610292	C₂	semidirect
22. #10610200	C₂	semidirect
23. C₂×C₄×D₄₀	C₂	semidirect
36. #65919	C₂²	semidirect
37. #65913	C₂²	semidirect
38. #65899	C₂²	semidirect
39. #65889	C₂²	semidirect
40. #65884	C₂²	semidirect
41. #65884	C₂²	semidirect
44. #65869	C₂²	semidirect
45. #65868	C₂²	semidirect
46. #65857	C₂²	semidirect
47. #65855	C₂²	semidirect
48. #65813	C₂²	semidirect
49. C₂×C₄×D₂₀	C₂²	semidirect
50. C₅×#446	C₂²	semidirect
51. C₅×C₈×Q₈	C₂²	semidirect
52. C₅×#436	C₂²	semidirect
54. C₅×#435	C₂²	semidirect
56. C₅×C₈×D₄	C₂²	semidirect
57. C₅×C₈×D₄	C₂²	semidirect
58. C₅×#433	C₂²	semidirect
59. C₅×#433	C₂²	semidirect
60. C₅×#432	C₂²	semidirect
61. C₅×#405	C₂²	semidirect
62. C₅×#405	C₂²	semidirect
63. C₂×C₄×C₅×C₈	C₂²	semidirect
64. #65424	C₂²	semidirect
65. #65423	C₂²	semidirect
66. #65422	C₂²	semidirect
67. #65420	C₂²	semidirect
68. #65405	C₂²	semidirect
69. #65405	C₂²	semidirect
72. #65404	C₂²	semidirect
73. #65404	C₂²	semidirect
74. #65403	C₂²	semidirect
75. C₂×#3953	C₂²	semidirect
76. #65395	C₂²	semidirect
77. C₂×#3950	C₂²	semidirect
78. C₂×#3950	C₂²	semidirect
79. #65137	C₂²	semidirect
80. #65136	C₂²	semidirect
81. #65136	C₂²	semidirect
82. #65136	C₂²	semidirect
83. #65135	C₂²	semidirect
84. #65133	C₂²	semidirect
85. #65133	C₂²	semidirect
86. #65133	C₂²	semidirect
87. #65133	C₂²	semidirect
89. #65131	C₂²	semidirect
90. #65118	C₂²	semidirect
91. #65026	C₂²	semidirect
92. #65025	C₂²	semidirect
93. #65025	C₂²	semidirect
94. #65024	C₂²	semidirect
95. #65023	C₂²	semidirect
96. #65023	C₂²	semidirect
99. #65020	C₂²	semidirect
100. #65020	C₂²	semidirect
101. #65012	C₂²	semidirect
102. #65010	C₂²	semidirect
103. #65003	C₂²	semidirect
104. #65002	C₂²	semidirect
105. #65000	C₂²	semidirect
106. #65000	C₂²	semidirect
107. #65000	C₂²	semidirect
108. #64999	C₂²	semidirect
109. #64999	C₂²	semidirect
110. #64999	C₂²	semidirect
111. C₄×Dic₂₀	C₂²	semidirect
112. C₄×Dic₂₀	C₂²	semidirect
113. #64986	C₂²	semidirect
114. #64985	C₂²	semidirect
115. #64985	C₂²	semidirect
121. C₄×D₄₀	C₂²	semidirect
122. C₄×D₄₀	C₂²	semidirect
123. C₄×D₄₀	C₂²	semidirect
124. C₄×D₄₀	C₂²	semidirect
125. C₄×D₄₀	C₂²	semidirect
126. C₄×D₄₀	C₂²	semidirect
127. C₄×#677	C₂²	semidirect
128. #64972	C₂²	semidirect
129. #64972	C₂²	semidirect
130. #64971	C₂²	semidirect
317. #2966	D₅	semidirect
449. D₄₀	#41	semidirect
521. #446	C₂×D₅	semidirect
522. C₈×Q₈	C₂×D₅	semidirect
542. #436	C₂×D₅	semidirect
544. #435	C₂×D₅	semidirect
546. C₈×D₄	C₂×D₅	semidirect
547. C₈×D₄	C₂×D₅	semidirect
548. #433	C₂×D₅	semidirect
549. #433	C₂×D₅	semidirect
550. #432	C₂×D₅	semidirect
557. #405	C₂×D₅	semidirect
558. #405	C₂×D₅	semidirect
559. C₂×C₄×C₈	C₂×D₅	semidirect
1062. C₅	#61471	semidirect

Maximal subgroups

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

subgroup	index
#10618062	2
C₅×#2966	2
#10611702	2
#10611661	2
#10611646	2
#10611284	2
#10611232	2
#10611230	2
#10611164	2
D₄×D₄₀	2
#10611147	2
#10611144	2
#10611142	2
#10611115	2
#10611114	2
#10611077	2
#10610300	2
#10610299	2
#10610293	2
#10610292	2
#10610200	2
C₂×C₄×D₄₀	2
#61471	5