Subgroups — #12982021

Order 1280.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10618071	C₂	1	2	yes	maximal, complemented
2	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611705	C₂	1	2	yes	maximal, complemented
4	#10611661	C₂	1	1	yes	maximal, characteristic, complemented
5	#10611643	C₂	1	1	yes	maximal, characteristic, complemented
6	#10611285	C₂	1	2	yes	maximal, complemented
7	#10611233	C₂	1	2	yes	maximal, complemented
8	#10611231	C₂	1	2	yes	maximal, complemented
9	#10611167	C₂	1	1	yes	maximal, characteristic, complemented
10	#10611164	C₂	1	1	yes	maximal, characteristic, complemented
11	#10611164	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611150	C₂	1	1	yes	maximal, characteristic, complemented
13	#10611147	C₂	1	1	yes	maximal, characteristic, complemented
14	#10611144	C₂	1	1	yes	maximal, characteristic, complemented
15	#10611120	C₂	1	2	yes	maximal, complemented
16	#10611118	C₂	1	2	yes	maximal, complemented
17	#10611076	C₂	1	2	yes	maximal, complemented
18	#10610308	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	C₄×#4050	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#529	C₂²	1	1	yes	characteristic
25	C₂×#4050	C₂²	1	1	yes	characteristic
26	C₂×#4050	C₂²	1	1	yes	characteristic
27	C₂²×D₄₀	C₂²	1	1	yes	characteristic
28	#66040	—	2	2	no	—
29	D₅×#126	—	2	2	no	—
30	#66027	—	2	2	no	—
31	#66013	—	2	2	no	—
32	#65995	—	2	2	no	—
33	#65993	—	2	2	no	—
34	#65972	—	2	2	no	—
35	#65947	—	2	2	no	—
36	#65918	C₂²	1	2	yes	complemented
37	#65913	C₂²	1	2	yes	complemented
38	#65899	C₂²	1	2	yes	complemented
39	#65885	C₂²	1	2	yes	complemented
40	#65884	C₂²	1	2	yes	—
41	#65884	C₂²	1	2	yes	—
42	#65876	C₂²	1	2	yes	—
43	#65875	C₂²	1	2	yes	—
44	#65868	C₂²	1	2	yes	complemented
45	#65857	C₂²	1	2	yes	complemented
46	#65855	C₂²	1	2	yes	—
47	#65852	C₂²	1	2	yes	—
48	#65813	C₂²	1	2	yes	complemented
49	C₄×#709	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
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
57	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₅×#433	C₂²	1	1	yes	characteristic
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
62	C₅×#405	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
64	#65426	C₂²	1	2	yes	—
65	#65423	C₂²	1	2	yes	complemented
66	#65422	C₂²	1	2	yes	complemented
67	#65420	C₂²	1	2	yes	—
68	#65405	C₂²	1	1	yes	characteristic
69	#65405	C₂²	1	1	yes	characteristic
70	#65405	C₂²	1	1	yes	characteristic, complemented
71	#65405	C₂²	1	1	yes	characteristic, complemented
72	#65404	C₂²	1	1	yes	characteristic
73	#65404	C₂²	1	1	yes	characteristic
74	#65403	C₂²	1	2	yes	complemented
75	#65402	C₂²	1	2	yes	complemented
76	#65395	C₂²	1	1	yes	characteristic
77	#65395	C₂²	1	1	yes	characteristic, complemented
78	C₂×#3950	C₂²	1	1	yes	characteristic, complemented
79	#65140	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	#65134	C₂²	1	2	yes	complemented
84	#65134	C₂²	1	2	yes	complemented
85	#65133	C₂²	1	2	yes	—
86	#65133	C₂²	1	2	yes	—
87	#65131	C₂²	1	2	yes	complemented
88	#65130	C₂²	1	2	yes	complemented
89	#65130	C₂²	1	2	yes	complemented
90	#65118	C₂²	1	2	yes	complemented
91	#65026	C₂²	1	2	yes	complemented
92	#65024	C₂²	1	2	yes	complemented
93	#65023	C₂²	1	2	yes	—
94	#65023	C₂²	1	2	yes	—
95	#65022	C₂²	1	2	yes	complemented
96	#65022	C₂²	1	2	yes	complemented
97	#65020	C₂²	1	2	yes	—
98	#65020	C₂²	1	2	yes	—
99	#65012	C₂²	1	2	yes	—
100	#65012	C₂²	1	2	yes	—
101	#65012	C₂²	1	2	yes	complemented
102	#65010	C₂²	1	2	yes	complemented
103	#65005	C₂²	1	2	yes	complemented
104	#65003	C₂²	1	2	yes	complemented
105	#65000	C₂²	1	2	yes	—
106	#65000	C₂²	1	2	yes	—
107	#64999	C₂²	1	2	yes	complemented
108	#64999	C₂²	1	2	yes	complemented
109	#64999	C₂²	1	2	yes	complemented
110	#64992	C₂²	1	2	yes	complemented
111	#64988	C₂²	1	1	yes	characteristic, complemented
112	C₄×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
113	C₄×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
114	C₄×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
115	C₄×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
116	#64986	C₂²	1	2	yes	complemented
117	#64985	C₂²	1	1	yes	characteristic
118	#64985	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	1	yes	characteristic
122	C₄×D₄₀	C₂²	1	1	yes	characteristic
123	C₄×D₄₀	C₂²	1	1	yes	characteristic
124	C₄×D₄₀	C₂²	1	1	yes	characteristic
125	C₄×#677	C₂²	1	2	yes	complemented
126	C₄×#677	C₂²	1	2	yes	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	#61487	—	5	1	no	maximal, Sylow
132	C₂×#709	C₂³	1	2	yes	—
133	C₂×#709	C₂³	1	2	yes	—
134	C₂²×D₂₀	C₂³	1	2	yes	—
135	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
136	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
137	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₅×#126	D₄	1	1	yes	characteristic
142	C₅×#126	D₄	1	1	yes	characteristic
143	C₅×#125	D₄	1	1	yes	characteristic
144	C₅×#124	D₄	1	1	yes	characteristic
145	C₅×#123	D₄	1	1	yes	characteristic
146	C₅×#123	D₄	1	1	yes	characteristic
147	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
148	C₅×#121	D₄	1	1	yes	characteristic
149	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
151	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
152	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₅×#117	C₂³	1	1	yes	characteristic
154	C₅×#117	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
156	#4092	—	2	2	no	—
157	#4092	—	2	2	no	—
158	#4085	—	2	2	no	—
159	#4084	—	2	2	no	—
160	#4083	—	2	2	no	—
161	#4083	—	2	2	no	—
162	#4082	—	2	2	no	—
163	#4081	—	2	2	no	—
164	#4076	C₂³	1	2	yes	—
165	#4076	C₂³	1	2	yes	—
166	#4075	—	2	2	no	—
167	C₄×C₂²⋊D₅	—	2	2	no	—
168	C₄×C₂²⋊D₅	—	2	2	no	—
169	C₄×C₂²⋊D₅	—	2	2	no	—
170	#4072	C₂³	1	2	yes	—
171	#4072	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
173	#4070	C₂³	1	2	yes	—
174	#4070	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	C₂×Dic₂₀	C₂³	1	1	yes	characteristic
179	C₂×Dic₂₀	C₂³	1	2	yes	—
180	#4050	—	2	4	no	—
181	#4050	—	2	4	no	—
182	C₂×D₄₀	—	2	4	no	—
183	C₂×D₄₀	C₂³	1	2	yes	—
184	C₂×D₄₀	C₂³	1	1	yes	characteristic
185	C₂×D₄₀	C₂³	1	1	yes	characteristic
186	C₂×#677	C₂³	1	2	yes	—
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	#4044	—	2	2	no	—
193	#4044	—	2	2	no	—
194	#4042	—	2	2	no	—
195	#4042	—	2	2	no	—
196	#4042	—	2	2	no	—
197	#4040	—	2	2	no	—
198	#4040	—	2	2	no	—
199	#4039	—	2	2	no	—
200	#4039	—	2	2	no	—
201	#4038	—	2	2	no	—
202	#4038	—	2	2	no	—
203	D₅×C₄⋊C₄	—	2	2	no	—
204	D₅×C₄⋊C₄	—	2	2	no	—
205	D₅×C₄⋊C₄	—	2	2	no	—
206	#4035	—	2	2	no	—
207	#4035	—	2	2	no	—
208	#4035	—	2	2	no	—
209	#4033	—	2	2	no	—
210	#4031	—	2	2	no	—
211	#4030	—	2	2	no	—
212	#4030	—	2	2	no	—
213	#4029	—	2	2	no	—
214	#4029	—	2	2	no	—
215	#4029	—	2	2	no	—
216	#4029	—	2	2	no	—
217	#4027	—	2	2	no	—
218	#4027	—	2	2	no	—
219	#4027	—	2	2	no	—
220	D₅×C₂²⋊C₄	—	2	2	no	—
221	D₅×C₂²⋊C₄	—	2	2	no	—
222	D₅×C₂²⋊C₄	—	2	2	no	—
223	D₅×C₂²⋊C₄	—	2	2	no	—
224	#4025	—	2	2	no	—
225	#4025	—	2	2	no	—
226	#4025	—	2	2	no	—
227	#4025	—	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	C₄×D₂₀	C₂³	1	2	yes	—
234	C₄×D₂₀	C₂³	1	2	yes	—
235	C₄×D₂₀	C₂³	1	2	yes	—
236	C₄×D₂₀	C₂³	1	2	yes	—
237	C₄×D₂₀	C₂³	1	2	yes	—
238	C₄×D₂₀	C₂³	1	2	yes	—
239	#4018	—	2	2	no	—
240	#4018	—	2	2	no	—
241	C₄²×D₅	—	2	2	no	—
242	#4016	C₂³	1	2	yes	—
243	#4016	C₂³	1	2	yes	—
244	#4015	C₂³	1	2	yes	—
245	#4015	C₂³	1	2	yes	—
246	C₄×Dic₁₀	C₂³	1	2	yes	—
247	C₄×Dic₁₀	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	#3950	C₂³	1	2	yes	—
281	#3950	C₂³	1	2	yes	—
282	#3950	C₂³	1	1	yes	characteristic
283	#3950	C₂³	1	1	yes	characteristic
284	#3950	C₂³	1	1	yes	characteristic
285	#3950	C₂³	1	1	yes	characteristic
286	#3949	C₂³	1	2	yes	—
287	#3949	C₂³	1	2	yes	—
288	#3949	C₂³	1	2	yes	—
289	#3949	C₂³	1	2	yes	—
290	#3948	C₂³	1	2	yes	—
291	#3948	C₂³	1	2	yes	—
292	#3948	C₂³	1	2	yes	—
293	#3948	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	#3521	—	5	2	no	—
299	#3393	—	5	1	no	—
300	#3380	—	5	1	no	—
301	#3376	—	5	2	no	—
302	#3342	—	5	1	no	—
303	#3339	—	5	1	no	—
304	#3336	—	5	1	no	—
305	#3323	—	5	2	no	—
306	#3311	—	5	2	no	—
307	#3307	—	5	2	no	—
308	#3283	—	5	1	no	—
309	#3280	—	5	1	no	—
310	#3280	—	5	1	no	—
311	#3177	—	5	1	no	—
312	#3175	—	5	1	no	—
313	#3168	—	5	1	no	—
314	#3125	—	5	2	no	—
315	#3123	—	5	2	no	—
316	#3111	—	5	2	no	—
317	#2966	D₅	1	1	yes	characteristic, complemented
318	#2951	—	5	1	no	—
319	#2948	—	5	1	no	—
320	C₄×#135	—	5	1	no	—
321	C₂³×D₅	—	2	2	no	—
322	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
323	C₂×C₅×D₄	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	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂×C₂²⋊D₅	—	2	2	no	—
332	C₂×C₂²⋊D₅	—	2	2	no	—
333	C₂×C₂²⋊D₅	—	2	2	no	—
334	C₂×C₂²⋊D₅	—	2	2	no	—
335	C₂²×Dic₅	—	2	2	no	—
336	#709	—	2	4	no	—
337	#709	—	2	4	no	—
338	#709	—	4	2	no	—
339	#709	—	4	2	no	—
340	C₂×D₂₀	—	2	4	no	—
341	C₂×D₂₀	—	2	2	no	—
342	C₂×D₂₀	—	4	2	no	—
343	C₂×D₂₀	C₂⁴	1	2	yes	—
344	C₂×D₂₀	C₂⁴	1	2	yes	—
345	C₂×C₄×D₅	—	2	2	no	—
346	C₂×C₄×D₅	—	2	2	no	—
347	C₂×C₄×D₅	—	2	2	no	—
348	C₂×C₄×D₅	—	2	2	no	—
349	C₂×C₄×D₅	—	2	2	no	—
350	C₂×C₄×D₅	—	2	2	no	—
351	C₂×C₄×D₅	—	2	2	no	—
352	C₂×C₄×D₅	—	2	2	no	—
353	C₂×Dic₁₀	—	2	2	no	—
354	C₂×Dic₁₀	C₂⁴	1	2	yes	—
355	C₂×Dic₁₀	C₂⁴	1	2	yes	—
356	C₅×M₁₆	—	4	1	no	—
357	C₅×M₁₆	—	4	1	no	—
358	C₂×C₅×C₈	—	2	2	no	—
359	C₂×C₅×C₈	—	2	2	no	—
360	C₂×C₅×C₈	—	2	2	no	—
361	C₂×C₅×C₈	—	4	1	no	—
362	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
365	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
366	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
368	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
370	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
371	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
372	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
373	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
374	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
375	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
376	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
377	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
387	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₅	C₂⁴	1	1	yes	characteristic
393	C₄²×C₅	C₂⁴	1	1	yes	characteristic
394	C₄²×C₅	C₂⁴	1	1	yes	characteristic
395	C₄²×C₅	C₂⁴	1	1	yes	characteristic
396	C₂²⋊Dic₅	—	2	2	no	—
397	C₂²⋊Dic₅	—	2	2	no	—
398	C₂²⋊Dic₅	—	2	2	no	—
399	C₂²⋊Dic₅	—	2	2	no	—
400	C₂²⋊Dic₅	—	2	2	no	—
401	C₂²⋊Dic₅	—	2	2	no	—
402	#685	—	2	2	no	—
403	#685	—	2	2	no	—
404	#685	—	2	2	no	—
405	#685	—	2	2	no	—
406	#685	—	2	2	no	—
407	#685	—	2	2	no	—
408	#685	—	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	C₄⋊Dic₅	—	2	2	no	—
415	C₄⋊Dic₅	—	2	2	no	—
416	C₄⋊Dic₅	—	2	2	no	—
417	C₄⋊Dic₅	—	2	2	no	—
418	C₄⋊Dic₅	C₂⁴	1	2	yes	—
419	C₄⋊Dic₅	C₂⁴	1	2	yes	—
420	C₄⋊Dic₅	C₂⁴	1	2	yes	—
421	C₄⋊Dic₅	C₂⁴	1	2	yes	—
422	#683	—	2	2	no	—
423	#683	—	2	2	no	—
424	#683	—	2	2	no	—
425	#683	—	2	2	no	—
426	#683	—	2	2	no	—
427	#683	—	2	2	no	—
428	#683	—	2	2	no	—
429	#683	—	2	2	no	—
430	#683	—	2	2	no	—
431	#683	—	2	2	no	—
432	#683	—	2	2	no	—
433	#683	—	2	2	no	—
434	C₄×Dic₅	—	2	2	no	—
435	C₄×Dic₅	—	2	2	no	—
436	C₄×Dic₅	—	2	2	no	—
437	C₄×Dic₅	—	2	2	no	—
438	C₄×Dic₅	—	2	2	no	—
439	C₄×Dic₅	—	2	2	no	—
440	Dic₂₀	—	2	2	no	—
441	Dic₂₀	—	2	2	no	—
442	Dic₂₀	—	4	2	no	—
443	D₄₀	—	2	4	no	—
444	D₄₀	—	2	2	no	—
445	D₄₀	#41	1	4	yes	—
446	#677	—	2	4	no	—
447	#677	—	2	4	no	—
448	#677	—	4	2	no	—
449	#677	—	4	2	no	—
450	C₂×#135	—	5	1	no	—
451	C₂×#135	—	5	1	no	—
452	C₂²×D₈	—	5	1	no	—
453	#556	—	5	2	no	—
454	#556	—	5	2	no	—
455	#554	—	5	2	no	—
456	#553	—	5	2	no	—
457	#553	—	10	2	no	—
458	#552	—	5	2	no	—
459	#552	—	10	2	no	—
460	#551	—	10	2	no	—
461	#551	—	10	2	no	—
462	#547	—	5	2	no	—
463	#546	—	5	2	no	—
464	#546	—	5	2	no	—
465	#542	—	5	2	no	—
466	#541	—	5	2	no	—
467	#539	—	10	2	no	—
468	#538	—	10	2	no	—
469	#529	—	5	2	no	—
470	#529	—	10	2	no	—
471	#529	C₂×D₅	1	1	yes	characteristic
472	C₂×#126	—	10	2	no	—
473	#520	—	5	2	no	—
474	#518	—	5	2	no	—
475	C₄×#41	—	5	2	no	—
476	#500	—	5	1	no	—
477	#499	—	5	1	no	—
478	#499	—	5	1	no	—
479	#495	—	5	1	no	—
480	#495	—	5	1	no	—
481	#494	—	5	1	no	—
482	#491	—	5	2	no	—
483	#489	—	5	2	no	—
484	#488	—	5	2	no	—
485	#485	—	5	2	no	—
486	#485	—	5	2	no	—
487	#485	—	5	2	no	—
488	#483	—	5	2	no	—
489	#482	—	5	2	no	—
490	#481	—	5	2	no	—
491	#479	—	5	2	no	—
492	#478	—	5	2	no	—
493	#478	—	5	2	no	—
494	#478	—	5	2	no	—
495	#476	—	5	2	no	—
496	#475	—	5	2	no	—
497	#470	—	5	2	no	—
498	#468	—	5	2	no	—
499	#467	—	5	1	no	—
500	#467	—	5	1	no	—
501	#467	—	5	1	no	—
502	#467	—	5	1	no	—
503	#466	—	5	1	no	—
504	#466	—	5	1	no	—
505	#465	—	5	2	no	—
506	#464	—	5	2	no	—
507	#464	—	5	2	no	—
508	#463	—	5	2	no	—
509	#463	—	5	2	no	—
510	#461	—	5	2	no	—
511	#461	—	5	2	no	—
512	#452	—	5	2	no	—
513	#452	—	5	2	no	—
514	#450	—	5	2	no	—
515	#450	—	5	2	no	—
516	#449	—	5	2	no	—
517	#449	—	5	2	no	—
518	#446	C₂×D₅	1	1	yes	characteristic, complemented
519	C₈×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
520	#442	—	5	2	no	—
521	#442	—	5	2	no	—
522	#441	—	5	2	no	—
523	#440	—	5	2	no	—
524	#440	—	5	2	no	—
525	#440	—	5	2	no	—
526	C₄×Q₁₆	—	5	1	no	—
527	C₄×Q₁₆	—	5	1	no	—
528	C₄×Q₁₆	—	5	1	no	—
529	C₄×Q₁₆	—	5	1	no	—
530	C₄×SD₁₆	—	5	2	no	—
531	C₄×SD₁₆	—	5	2	no	—
532	C₄×SD₁₆	—	5	2	no	—
533	C₄×D₈	—	5	1	no	—
534	C₄×D₈	—	5	1	no	—
535	C₄×D₈	—	5	1	no	—
536	C₄×D₈	—	5	1	no	—
537	C₄×D₈	—	5	1	no	—
538	C₄×D₈	—	5	1	no	—
539	#436	C₂×D₅	1	1	yes	characteristic
540	#435	C₂×D₅	1	1	yes	characteristic
541	#435	C₂×D₅	1	1	yes	characteristic, complemented
542	C₈×D₄	C₂×D₅	1	1	yes	characteristic
543	C₈×D₄	C₂×D₅	1	1	yes	characteristic
544	C₈×D₄	C₂×D₅	1	1	yes	characteristic, complemented
545	#433	C₂×D₅	1	1	yes	characteristic
546	#433	C₂×D₅	1	1	yes	characteristic, complemented
547	#432	C₂×D₅	1	1	yes	characteristic, complemented
548	#427	—	5	1	no	—
549	#427	—	5	1	no	—
550	C₂×#107	—	5	1	no	—
551	#418	—	5	2	no	—
552	#417	—	5	2	no	—
553	#416	—	5	2	no	—
554	#405	C₂×D₅	1	1	yes	characteristic
555	#405	C₂×D₅	1	1	yes	characteristic, complemented
556	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
557	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
558	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
559	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
560	C₂²×D₅	—	2	2	no	—
561	C₂²×D₅	—	2	2	no	—
562	C₂²×D₅	—	4	4	no	—
563	C₂²×D₅	—	8	2	no	—
564	C₂²×D₅	—	8	2	no	—
565	C₅×Q₈	—	4	1	no	—
566	C₅×D₄	—	4	1	no	—
567	C₅×D₄	—	4	1	no	—
568	C₅×D₄	—	4	1	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	1	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	4	1	no	—
576	C₂×C₄×C₅	—	4	1	no	—
577	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
589	C₂²⋊D₅	—	4	4	no	—
590	C₂²⋊D₅	—	4	4	no	—
591	C₂²⋊D₅	—	8	2	no	—
592	C₂²⋊D₅	—	8	2	no	—
593	C₂×Dic₅	—	2	2	no	—
594	C₂×Dic₅	—	2	2	no	—
595	C₂×Dic₅	—	2	2	no	—
596	C₂×Dic₅	—	2	2	no	—
597	C₂×Dic₅	—	2	2	no	—
598	C₂×Dic₅	—	2	2	no	—
599	C₂×Dic₅	—	8	2	no	—
600	D₂₀	—	2	2	no	—
601	D₂₀	—	2	2	no	—
602	D₂₀	—	2	2	no	—
603	D₂₀	—	4	4	no	—
604	D₂₀	C₂×#41	1	4	yes	—
605	C₄×D₅	—	4	4	no	—
606	C₄×D₅	—	4	4	no	—
607	C₄×D₅	—	8	2	no	—
608	C₄×D₅	—	8	2	no	—
609	C₄×D₅	—	8	2	no	—
610	C₄×D₅	—	8	2	no	—
611	C₄×D₅	—	8	2	no	—
612	C₄×D₅	—	8	2	no	—
613	Dic₁₀	—	2	2	no	—
614	Dic₁₀	—	2	2	no	—
615	Dic₁₀	—	2	2	no	—
616	Dic₁₀	—	2	2	no	—
617	Dic₁₀	—	8	2	no	—
618	C₅×C₈	—	2	1	no	—
619	C₅×C₈	—	2	1	no	—
620	C₅×C₈	—	2	1	no	—
621	C₅×C₈	—	2	1	no	—
622	C₅×C₈	—	2	1	no	—
623	C₅×C₈	—	2	1	no	—
624	C₅×C₈	—	2	1	no	—
625	C₅×C₈	C₂×#41	1	2	yes	—
626	C₂×#41	—	5	2	no	—
627	C₂×#41	—	5	2	no	—
628	C₂²×D₄	—	5	2	no	—
629	#135	—	10	4	no	—
630	#135	—	10	4	no	—
631	C₂×Q₁₆	—	5	1	no	—
632	C₂×Q₁₆	—	5	1	no	—
633	C₂×Q₁₆	—	5	2	no	—
634	C₂×SD₁₆	—	5	2	no	—
635	C₂×SD₁₆	—	5	2	no	—
636	C₂×SD₁₆	—	5	2	no	—
637	C₂×SD₁₆	—	5	2	no	—
638	C₂×D₈	—	5	1	no	—
639	C₂×D₈	—	5	1	no	—
640	C₂×D₈	—	5	2	no	—
641	C₂×D₈	—	10	4	no	—
642	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
643	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
644	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
645	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
646	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
647	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
648	C₄⋊Q₈	—	5	2	no	—
649	C₄⋊Q₈	—	5	2	no	—
650	#126	—	10	2	no	—
651	#126	—	10	2	no	—
652	#126	—	10	2	no	—
653	#126	—	10	2	no	—
654	#126	—	10	2	no	—
655	#126	—	10	2	no	—
656	#126	—	10	2	no	—
657	#126	—	10	2	no	—
658	#126	—	10	2	no	—
659	#126	—	10	2	no	—
660	#126	D₂₀	1	1	yes	characteristic
661	#126	D₂₀	1	1	yes	characteristic
662	#125	—	5	2	no	—
663	#125	—	5	2	no	—
664	#125	—	10	2	no	—
665	#125	—	10	2	no	—
666	#125	—	10	2	no	—
667	#125	D₂₀	1	1	yes	characteristic
668	#124	—	5	2	no	—
669	#124	—	5	2	no	—
670	#124	—	10	2	no	—
671	#124	—	10	2	no	—
672	#124	D₂₀	1	1	yes	characteristic
673	#123	—	10	2	no	—
674	#123	—	10	2	no	—
675	#123	—	10	2	no	—
676	#123	—	10	2	no	—
677	#123	—	10	2	no	—
678	#123	—	10	2	no	—
679	#123	—	10	2	no	—
680	#123	—	10	2	no	—
681	#123	D₂₀	1	1	yes	characteristic
682	#123	D₂₀	1	1	yes	characteristic
683	C₂²⋊Q₈	—	5	2	no	—
684	C₂²⋊Q₈	—	5	2	no	—
685	C₂²⋊Q₈	—	5	2	no	—
686	C₂²⋊Q₈	—	5	2	no	—
687	C₂²⋊Q₈	—	10	2	no	—
688	C₂²⋊Q₈	—	10	2	no	—
689	C₂²⋊Q₈	—	10	2	no	—
690	C₂²⋊Q₈	—	10	2	no	—
691	C₂²⋊Q₈	—	10	2	no	—
692	C₂²⋊Q₈	D₂₀	1	1	yes	characteristic
693	#121	—	5	2	no	—
694	#121	—	5	2	no	—
695	#121	—	10	2	no	—
696	#121	—	10	2	no	—
697	#121	—	10	2	no	—
698	#121	—	10	2	no	—
699	#121	D₂₀	1	1	yes	characteristic
700	#120	—	10	2	no	—
701	#120	—	10	2	no	—
702	C₄×Q₈	—	5	2	no	—
703	C₄×Q₈	—	5	2	no	—
704	C₄×Q₈	—	5	2	no	—
705	C₄×Q₈	—	5	2	no	—
706	C₄×Q₈	—	10	2	no	—
707	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
708	C₄×D₄	—	5	2	no	—
709	C₄×D₄	—	5	2	no	—
710	C₄×D₄	—	5	2	no	—
711	C₄×D₄	—	5	2	no	—
712	C₄×D₄	—	5	2	no	—
713	C₄×D₄	—	5	2	no	—
714	C₄×D₄	—	10	2	no	—
715	C₄×D₄	—	10	2	no	—
716	C₄×D₄	—	10	2	no	—
717	C₄×D₄	—	10	2	no	—
718	C₄×D₄	—	10	2	no	—
719	C₄×D₄	—	10	2	no	—
720	C₄×D₄	—	10	2	no	—
721	C₄×D₄	—	10	2	no	—
722	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
723	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
724	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
725	#117	—	5	2	no	—
726	#117	—	5	2	no	—
727	#117	—	10	2	no	—
728	#117	—	10	2	no	—
729	#117	—	10	2	no	—
730	#117	—	10	2	no	—
731	#117	—	10	2	no	—
732	#117	C₂²×D₅	1	1	yes	characteristic
733	#117	C₂²×D₅	1	1	yes	characteristic
734	C₂×C₄⋊C₄	—	5	2	no	—
735	C₂×C₄⋊C₄	—	10	2	no	—
736	C₂×C₄⋊C₄	—	10	2	no	—
737	C₂×C₄⋊C₄	—	10	2	no	—
738	C₂×C₂²⋊C₄	—	10	2	no	—
739	C₂×C₂²⋊C₄	—	10	2	no	—
740	C₂×C₂²⋊C₄	—	10	2	no	—
741	C₂×C₂²⋊C₄	—	10	2	no	—
742	C₂×C₄²	—	10	2	no	—
743	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
744	#107	—	5	1	no	—
745	#107	—	5	1	no	—
746	#107	—	5	2	no	—
747	#107	—	5	1	no	—
748	#107	—	5	1	no	—
749	#107	—	5	2	no	—
750	#106	—	5	2	no	—
751	#106	—	5	2	no	—
752	#106	—	5	2	no	—
753	#106	—	5	2	no	—
754	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
755	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
756	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
757	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
758	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
759	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
760	#103	—	5	2	no	—
761	#103	—	5	2	no	—
762	#103	—	5	2	no	—
763	#103	—	5	2	no	—
764	#103	—	5	2	no	—
765	#103	—	5	2	no	—
766	#103	—	5	2	no	—
767	#103	—	5	2	no	—
768	#102	—	5	2	no	—
769	#102	—	5	2	no	—
770	#102	—	5	2	no	—
771	#102	—	5	2	no	—
772	#102	—	5	2	no	—
773	#102	—	5	2	no	—
774	#102	—	5	2	no	—
775	#102	—	5	2	no	—
776	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
777	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
778	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
779	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
780	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
781	C₂²⋊C₈	C₂²×D₅	1	1	yes	characteristic
782	#97	C₂²×D₅	1	1	yes	characteristic
783	#97	C₂²×D₅	1	1	yes	characteristic
784	#97	C₂²×D₅	1	1	yes	characteristic
785	#97	C₂²×D₅	1	1	yes	characteristic
786	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
787	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
788	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
789	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
790	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
791	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
792	C₂²×C₅	—	2	1	no	—
793	C₂²×C₅	—	2	1	no	—
794	C₂²×C₅	—	2	1	no	—
795	C₂²×C₅	—	2	1	no	—
796	C₂²×C₅	—	2	1	no	—
797	C₂²×C₅	—	2	1	no	—
798	C₂²×C₅	—	2	1	no	—
799	C₂²×C₅	—	2	1	no	—
800	C₂²×C₅	—	2	1	no	—
801	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
802	C₂×D₅	—	2	4	no	—
803	C₂×D₅	—	4	2	no	—
804	C₂×D₅	—	4	2	no	—
805	C₂×D₅	—	4	2	no	—
806	C₂×D₅	—	4	2	no	—
807	C₂×D₅	—	4	2	no	—
808	C₂×D₅	—	16	4	no	—
809	C₄×C₅	—	2	1	no	—
810	C₄×C₅	—	2	1	no	—
811	C₄×C₅	—	2	1	no	—
812	C₄×C₅	—	2	1	no	—
813	C₄×C₅	—	2	1	no	—
814	C₄×C₅	—	2	1	no	—
815	C₄×C₅	—	2	1	no	—
816	C₄×C₅	—	2	1	no	—
817	C₄×C₅	—	2	1	no	—
818	C₄×C₅	—	2	1	no	—
819	C₄×C₅	—	2	1	no	—
820	C₄×C₅	C₂²×#41	1	1	yes	characteristic
821	C₄×C₅	#585	1	1	yes	characteristic
822	Dic₅	—	4	2	no	—
823	Dic₅	—	4	2	no	—
824	Dic₅	—	4	2	no	—
825	Dic₅	—	4	2	no	—
826	Dic₅	—	4	2	no	—
827	Dic₅	—	4	2	no	—
828	C₂⁴	—	10	2	no	—
829	#41	—	10	4	no	—
830	#41	—	10	4	no	—
831	#41	—	20	2	no	—
832	#41	—	20	2	no	—
833	C₂×Q₈	—	5	2	no	—
834	C₂×Q₈	—	5	2	no	—
835	C₂×Q₈	—	10	2	no	—
836	C₂×Q₈	C₂×D₂₀	1	1	yes	characteristic
837	C₂×D₄	—	5	2	no	—
838	C₂×D₄	—	5	2	no	—
839	C₂×D₄	—	10	4	no	—
840	C₂×D₄	—	10	2	no	—
841	C₂×D₄	—	10	2	no	—
842	C₂×D₄	—	10	2	no	—
843	C₂×D₄	—	10	2	no	—
844	C₂×D₄	—	10	2	no	—
845	C₂×D₄	—	20	2	no	—
846	C₂×D₄	C₂×D₂₀	1	1	yes	characteristic
847	C₂×D₄	C₂×D₂₀	1	1	yes	characteristic
848	C₂×D₄	C₂×D₂₀	1	1	yes	characteristic
849	C₂²×C₄	—	10	2	no	—
850	C₂²×C₄	—	10	2	no	—
851	C₂²×C₄	—	10	2	no	—
852	C₂²×C₄	—	10	2	no	—
853	C₂²×C₄	—	10	2	no	—
854	C₂²×C₄	—	10	2	no	—
855	C₂²×C₄	—	10	2	no	—
856	C₂²×C₄	—	10	2	no	—
857	C₂²×C₄	—	10	2	no	—
858	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
859	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
860	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
861	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
862	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
863	Q₁₆	—	10	2	no	—
864	Q₁₆	—	10	2	no	—
865	Q₁₆	—	20	2	no	—
866	SD₁₆	—	10	4	no	—
867	SD₁₆	—	10	4	no	—
868	SD₁₆	—	20	2	no	—
869	SD₁₆	—	20	2	no	—
870	D₈	—	5	4	no	—
871	D₈	—	10	4	no	—
872	D₈	—	10	2	no	—
873	M₁₆	—	4	1	no	—
874	M₁₆	—	4	1	no	—
875	C₂×C₈	—	2	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	—	2	2	no	—
878	C₂×C₈	—	4	1	no	—
879	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
880	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
881	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
882	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
883	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
884	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
885	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
886	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
887	C₄⋊C₄	—	5	2	no	—
888	C₄⋊C₄	—	5	2	no	—
889	C₄⋊C₄	—	5	2	no	—
890	C₄⋊C₄	—	5	2	no	—
891	C₄⋊C₄	—	10	2	no	—
892	C₄⋊C₄	—	10	2	no	—
893	C₄⋊C₄	—	10	2	no	—
894	C₄⋊C₄	—	10	2	no	—
895	C₄⋊C₄	—	10	2	no	—
896	C₄⋊C₄	—	10	2	no	—
897	C₄⋊C₄	—	10	2	no	—
898	C₄⋊C₄	—	10	2	no	—
899	C₄⋊C₄	—	10	2	no	—
900	C₄⋊C₄	—	10	2	no	—
901	C₄⋊C₄	—	10	2	no	—
902	C₄⋊C₄	—	10	2	no	—
903	C₄⋊C₄	—	10	2	no	—
904	C₄⋊C₄	—	10	2	no	—
905	C₄⋊C₄	—	10	2	no	—
906	C₄⋊C₄	—	10	2	no	—
907	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
908	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
909	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
910	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
914	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
915	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
916	C₄⋊C₄	C₂×D₂₀	1	1	yes	characteristic
917	C₂²⋊C₄	—	10	2	no	—
918	C₂²⋊C₄	—	10	2	no	—
919	C₂²⋊C₄	—	10	2	no	—
920	C₂²⋊C₄	—	10	2	no	—
921	C₂²⋊C₄	—	10	2	no	—
922	C₂²⋊C₄	—	10	2	no	—
923	C₂²⋊C₄	—	10	2	no	—
924	C₂²⋊C₄	—	10	2	no	—
925	C₂²⋊C₄	—	10	2	no	—
926	C₂²⋊C₄	—	10	2	no	—
927	C₂²⋊C₄	—	10	2	no	—
928	C₂²⋊C₄	—	10	2	no	—
929	C₂²⋊C₄	—	10	2	no	—
930	C₂²⋊C₄	—	10	2	no	—
931	C₂²⋊C₄	—	10	2	no	—
932	C₂²⋊C₄	—	10	2	no	—
933	C₂²⋊C₄	—	10	2	no	—
934	C₂²⋊C₄	—	10	2	no	—
935	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
936	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
937	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
938	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
939	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
940	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
941	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
942	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
943	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
944	C₂²⋊C₄	C₂×D₂₀	1	1	yes	characteristic
945	C₄²	—	10	2	no	—
946	C₄²	—	10	2	no	—
947	C₄²	—	10	2	no	—
948	C₄²	—	10	2	no	—
949	C₄²	—	10	2	no	—
950	C₄²	—	10	2	no	—
951	C₄²	C₂×D₂₀	1	1	yes	characteristic
952	C₄²	C₂×D₂₀	1	1	yes	characteristic
953	C₄²	C₂³×D₅	1	1	yes	characteristic
954	C₄²	C₂³×D₅	1	1	yes	characteristic
955	C₄²	C₂³×D₅	1	1	yes	characteristic
956	C₄²	C₂³×D₅	1	1	yes	characteristic
957	C₂×C₅	—	4	1	no	—
958	C₂×C₅	—	4	1	no	—
959	C₂×C₅	—	4	1	no	—
960	C₂×C₅	D₄×#41	1	1	yes	characteristic
961	C₂×C₅	#3584	1	1	yes	characteristic
962	C₂×C₅	#3584	1	1	yes	characteristic
963	D₅	—	4	4	no	—
964	D₅	—	8	2	no	—
965	C₂³	—	10	2	no	—
966	C₂³	—	10	2	no	—
967	C₂³	—	20	4	no	—
968	C₂³	—	40	2	no	—
969	C₂³	—	40	2	no	—
970	C₂³	C₂²×D₂₀	1	1	yes	characteristic
971	C₂³	C₂²×D₂₀	1	1	yes	characteristic
972	C₂³	C₂²×D₂₀	1	1	yes	characteristic
973	Q₈	—	4	1	no	—
974	Q₈	—	10	2	no	—
975	Q₈	—	10	2	no	—
976	Q₈	—	10	2	no	—
977	Q₈	—	10	2	no	—
978	Q₈	—	40	2	no	—
979	D₄	—	4	1	no	—
980	D₄	—	4	1	no	—
981	D₄	—	4	1	no	—
982	D₄	—	5	4	no	—
983	D₄	—	10	2	no	—
984	D₄	—	10	2	no	—
985	D₄	—	10	2	no	—
986	D₄	—	20	4	no	—
987	D₄	—	20	4	no	—
988	D₄	—	20	4	no	—
989	D₄	—	40	2	no	—
990	D₄	—	40	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	10	2	no	—
1000	C₂×C₄	—	10	2	no	—
1001	C₂×C₄	—	10	2	no	—
1002	C₂×C₄	—	10	2	no	—
1003	C₂×C₄	—	10	2	no	—
1004	C₂×C₄	—	10	2	no	—
1005	C₂×C₄	—	20	4	no	—
1006	C₂×C₄	—	20	4	no	—
1007	C₂×C₄	—	40	2	no	—
1008	C₂×C₄	—	40	2	no	—
1009	C₂×C₄	—	40	2	no	—
1010	C₂×C₄	—	40	2	no	—
1011	C₂×C₄	—	40	2	no	—
1012	C₂×C₄	—	40	2	no	—
1013	C₂×C₄	—	40	2	no	—
1014	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
1025	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
1026	C₈	—	2	1	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	D₅×#41	1	2	yes	—
1034	C₅	#61487	1	1	yes	characteristic, complemented, Sylow
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	10	4	no	—
1045	C₂²	—	20	2	no	—
1046	C₂²	—	20	2	no	—
1047	C₂²	—	20	2	no	—
1048	C₂²	—	20	2	no	—
1049	C₂²	—	20	2	no	—
1050	C₂²	—	80	4	no	—
1051	C₂²	C₂³×D₂₀	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	20	2	no	—
1064	C₄	—	20	2	no	—
1065	C₄	—	20	2	no	—
1066	C₄	—	20	2	no	—
1067	C₄	—	20	2	no	—
1068	C₄	—	20	2	no	—
1069	C₄	C₂×D₅×#41	1	1	yes	characteristic
1070	C₄	#66283	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	20	4	no	—
1075	C₂	—	40	2	no	—
1076	C₂	#41×D₂₀	1	1	yes	characteristic
1077	C₂	#10619064	1	1	yes	characteristic
1078	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	#61487
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. #10618071	C₂	semidirect
2. C₅×#2966	C₂	semidirect
3. #10611705	C₂	semidirect
4. #10611661	C₂	semidirect
5. #10611643	C₂	semidirect
6. #10611285	C₂	semidirect
7. #10611233	C₂	semidirect
8. #10611231	C₂	semidirect
9. #10611167	C₂	semidirect
10. #10611164	C₂	semidirect
11. #10611164	C₂	semidirect
12. #10611150	C₂	semidirect
13. #10611147	C₂	semidirect
14. #10611144	C₂	semidirect
15. #10611120	C₂	semidirect
16. #10611118	C₂	semidirect
17. #10611076	C₂	semidirect
18. #10610308	C₂	semidirect
19. #10610299	C₂	semidirect
20. #10610293	C₂	semidirect
21. #10610292	C₂	semidirect
22. #10610200	C₂	semidirect
23. C₄×#4050	C₂	semidirect
36. #65918	C₂²	semidirect
37. #65913	C₂²	semidirect
38. #65899	C₂²	semidirect
39. #65885	C₂²	semidirect
44. #65868	C₂²	semidirect
45. #65857	C₂²	semidirect
48. #65813	C₂²	semidirect
49. C₄×#709	C₂²	semidirect
50. C₅×#446	C₂²	semidirect
51. C₅×C₈×Q₈	C₂²	semidirect
54. C₅×#435	C₂²	semidirect
57. C₅×C₈×D₄	C₂²	semidirect
59. C₅×#433	C₂²	semidirect
60. C₅×#432	C₂²	semidirect
62. C₅×#405	C₂²	semidirect
63. C₂×C₄×C₅×C₈	C₂²	semidirect
65. #65423	C₂²	semidirect
66. #65422	C₂²	semidirect
70. #65405	C₂²	semidirect
71. #65405	C₂²	semidirect
74. #65403	C₂²	semidirect
75. #65402	C₂²	semidirect
77. #65395	C₂²	semidirect
78. C₂×#3950	C₂²	semidirect
79. #65140	C₂²	semidirect
80. #65136	C₂²	semidirect
81. #65136	C₂²	semidirect
82. #65136	C₂²	semidirect
83. #65134	C₂²	semidirect
84. #65134	C₂²	semidirect
87. #65131	C₂²	semidirect
88. #65130	C₂²	semidirect
89. #65130	C₂²	semidirect
90. #65118	C₂²	semidirect
91. #65026	C₂²	semidirect
92. #65024	C₂²	semidirect
95. #65022	C₂²	semidirect
96. #65022	C₂²	semidirect
101. #65012	C₂²	semidirect
102. #65010	C₂²	semidirect
103. #65005	C₂²	semidirect
104. #65003	C₂²	semidirect
107. #64999	C₂²	semidirect
108. #64999	C₂²	semidirect
109. #64999	C₂²	semidirect
110. #64992	C₂²	semidirect
111. #64988	C₂²	semidirect
112. C₄×Dic₂₀	C₂²	semidirect
113. C₄×Dic₂₀	C₂²	semidirect
114. C₄×Dic₂₀	C₂²	semidirect
115. C₄×Dic₂₀	C₂²	semidirect
116. #64986	C₂²	semidirect
125. C₄×#677	C₂²	semidirect
126. C₄×#677	C₂²	semidirect
127. C₄×#677	C₂²	semidirect
128. #64972	C₂²	semidirect
129. #64972	C₂²	semidirect
130. #64971	C₂²	semidirect
317. #2966	D₅	semidirect
518. #446	C₂×D₅	semidirect
519. C₈×Q₈	C₂×D₅	semidirect
541. #435	C₂×D₅	semidirect
544. C₈×D₄	C₂×D₅	semidirect
546. #433	C₂×D₅	semidirect
547. #432	C₂×D₅	semidirect
555. #405	C₂×D₅	semidirect
556. C₂×C₄×C₈	C₂×D₅	semidirect
1034. C₅	#61487	semidirect

Maximal subgroups

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

subgroup	index
#10618071	2
C₅×#2966	2
#10611705	2
#10611661	2
#10611643	2
#10611285	2
#10611233	2
#10611231	2
#10611167	2
#10611164	2
#10611150	2
#10611147	2
#10611144	2
#10611120	2
#10611118	2
#10611076	2
#10610308	2
#10610299	2
#10610293	2
#10610292	2
#10610200	2
C₄×#4050	2
#61487	5