Subgroups — #12963703

Order 1280.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10618175	C₂	1	1	yes	maximal, characteristic
2	C₅×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	#10615061	C₂	1	1	yes	maximal, characteristic, complemented
4	#10611692	C₂	1	2	yes	maximal, complemented
5	#10611692	C₂	1	2	yes	maximal, complemented
6	#10611691	C₂	1	2	yes	maximal, complemented
7	#10611690	C₂	1	2	yes	maximal, complemented
8	#10611690	C₂	1	2	yes	maximal, complemented
9	#10611689	C₂	1	2	yes	maximal, complemented
10	#10611649	C₂	1	2	yes	maximal, complemented
11	#10611648	C₂	1	2	yes	maximal, complemented
12	#10610811	C₂	1	1	yes	maximal, characteristic
13	D₅×#424	C₂	1	1	yes	maximal, characteristic
14	#10610809	C₂	1	1	yes	maximal, characteristic, complemented
15	#10610809	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#65128	C₂	1	1	yes	maximal, characteristic
17	#10610739	C₂	1	1	yes	maximal, characteristic, complemented
18	#10610279	C₂	1	1	yes	maximal, characteristic
19	D₅×#405	C₂	1	1	yes	maximal, characteristic
20	#10610275	C₂	1	1	yes	maximal, characteristic, complemented
21	#10610275	C₂	1	1	yes	maximal, characteristic, complemented
22	#10610245	C₂	1	1	yes	maximal, characteristic
23	#10610239	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#533	C₂²	1	1	yes	characteristic
25	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
27	C₂²×#676	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
29	#66063	C₄	1	1	yes	characteristic
30	#66063	C₄	1	1	yes	characteristic
31	#66063	C₄	1	1	yes	characteristic
32	#66063	C₄	1	1	yes	characteristic
33	#66023	C₄	1	1	yes	characteristic
34	#66023	C₄	1	1	yes	characteristic
35	#66023	C₄	1	1	yes	characteristic
36	#66023	C₄	1	1	yes	characteristic
37	#65968	C₄	1	2	yes	—
38	#65968	C₄	1	2	yes	—
39	#65957	C₄	1	2	yes	—
40	#65957	C₄	1	2	yes	—
41	#65912	C₂²	1	2	yes	—
42	#65912	C₂²	1	2	yes	—
43	#65912	C₂²	1	2	yes	—
44	#65912	C₂²	1	2	yes	—
45	D₅×#117	C₂²	1	1	yes	characteristic
46	D₅×#117	C₂²	1	1	yes	characteristic
47	#65851	C₂²	1	1	yes	characteristic
48	#65851	C₂²	1	1	yes	characteristic
49	C₂×#4018	C₂²	1	1	yes	characteristic
50	#65804	C₂²	1	1	yes	characteristic
51	C₅×#446	C₂²	1	2	yes	complemented
52	C₅×#446	C₂²	1	2	yes	complemented
53	C₅×#446	C₂²	1	2	yes	complemented
54	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
55	C₅×#424	C₂²	1	1	yes	characteristic
56	C₅×#424	C₂²	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×#405	C₂²	1	1	yes	characteristic
59	C₅×#405	C₂²	1	1	yes	characteristic
60	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
61	#65411	C₂²	1	1	yes	characteristic
62	#65411	C₂²	1	1	yes	characteristic
63	#65408	C₂²	1	1	yes	characteristic
64	#65408	C₂²	1	1	yes	characteristic
65	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
66	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
67	#65391	C₂²	1	1	yes	characteristic
68	#65391	C₂²	1	1	yes	characteristic
69	#65390	C₂²	1	1	yes	characteristic
70	#65390	C₂²	1	1	yes	characteristic
71	C₂×#3946	C₂²	1	1	yes	characteristic
72	C₂×#3946	C₂²	1	1	yes	characteristic
73	#65313	C₂²	1	2	yes	complemented
74	#65313	C₂²	1	2	yes	complemented
75	#65313	C₂²	1	2	yes	complemented
76	Q₈×#168	C₂²	1	2	yes	complemented
77	#65288	C₂²	1	1	yes	characteristic
78	#65288	C₂²	1	1	yes	characteristic
79	#65286	C₂²	1	1	yes	characteristic
80	#65286	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
82	C₄×#681	C₂²	1	1	yes	characteristic
83	#65128	C₂²	1	1	yes	characteristic
84	#65128	C₂²	1	1	yes	characteristic
85	#65128	C₂²	1	1	yes	characteristic
86	#65128	C₂²	1	1	yes	characteristic
87	#65128	C₂²	1	1	yes	characteristic
88	#65128	C₂²	1	1	yes	characteristic
89	#65128	C₂²	1	1	yes	characteristic
90	#65128	C₂²	1	1	yes	characteristic
91	#65128	C₂²	1	2	yes	—
92	#65128	C₂²	1	2	yes	—
93	#65128	C₂²	1	2	yes	—
94	#65128	C₂²	1	2	yes	—
95	#65126	C₂²	1	2	yes	—
96	#65126	C₂²	1	2	yes	—
97	D₅×C₄⋊C₈	C₂²	1	2	yes	—
98	D₅×C₄⋊C₈	C₂²	1	2	yes	—
99	#65120	C₂²	1	2	yes	complemented
100	#65120	C₂²	1	2	yes	complemented
101	#65120	C₂²	1	2	yes	complemented
102	#65119	C₂²	1	2	yes	complemented
103	#65119	C₂²	1	2	yes	complemented
104	#65119	C₂²	1	2	yes	complemented
105	#65117	C₂²	1	2	yes	complemented
106	#65117	C₂²	1	2	yes	complemented
107	#65117	C₂²	1	2	yes	complemented
108	#65117	C₂²	1	2	yes	complemented
109	#65117	C₂²	1	2	yes	complemented
110	#65117	C₂²	1	2	yes	complemented
111	#64997	C₂²	1	2	yes	—
112	#64997	C₂²	1	2	yes	—
113	#64997	C₂²	1	2	yes	—
114	#64997	C₂²	1	2	yes	—
115	#64996	C₂²	1	2	yes	—
116	D₅×#97	C₂²	1	2	yes	—
117	#64990	C₂²	1	2	yes	complemented
118	#64990	C₂²	1	2	yes	complemented
119	#64990	C₂²	1	2	yes	complemented
120	#64990	C₂²	1	2	yes	complemented
121	#64990	C₂²	1	2	yes	complemented
122	#64990	C₂²	1	2	yes	complemented
123	#64978	C₂²	1	2	yes	—
124	#64978	C₂²	1	2	yes	—
125	#64978	C₂²	1	2	yes	—
126	#64978	C₂²	1	2	yes	—
127	C₄×#676	C₂²	1	2	yes	—
128	C₄×C₈×D₅	C₂²	1	2	yes	—
129	#64968	C₂²	1	2	yes	complemented
130	#64968	C₂²	1	2	yes	complemented
131	#64968	C₂²	1	2	yes	complemented
132	C₈×Dic₁₀	C₂²	1	2	yes	complemented
133	C₈×Dic₁₀	C₂²	1	2	yes	complemented
134	C₈×Dic₁₀	C₂²	1	2	yes	complemented
135	#60193	—	5	1	no	maximal, Sylow
136	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
137	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
138	C₂×C₅×M₁₆	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×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
142	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
143	C₅×#125	C₂×C₄	1	1	yes	characteristic
144	C₅×#125	C₂×C₄	1	1	yes	characteristic
145	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
146	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
147	C₄×C₅×Q₈	C₂³	1	2	yes	—
148	C₄×C₅×Q₈	C₂³	1	2	yes	—
149	C₅×#117	C₂³	1	1	yes	characteristic
150	C₅×#117	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
152	#4092	C₂×C₄	1	2	yes	—
153	#4092	C₂×C₄	1	2	yes	—
154	#4092	C₂×C₄	1	2	yes	—
155	#4092	C₂×C₄	1	2	yes	—
156	#4090	C₂×C₄	1	2	yes	—
157	#4090	C₂×C₄	1	2	yes	—
158	#4090	C₂×C₄	1	2	yes	—
159	#4090	C₂×C₄	1	2	yes	—
160	C₂×#685	C₂×C₄	1	1	yes	characteristic
161	C₂×#685	C₂×C₄	1	1	yes	characteristic
162	#4072	C₂³	1	1	yes	characteristic
163	#4072	C₂³	1	1	yes	characteristic
164	#4070	C₂×C₄	1	2	yes	—
165	#4070	C₂×C₄	1	2	yes	—
166	C₂×#683	C₂×C₄	1	1	yes	characteristic
167	C₂×#683	C₂×C₄	1	1	yes	characteristic
168	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
169	C₂×#681	C₂³	1	1	yes	characteristic
170	C₂×#681	C₂³	1	1	yes	characteristic
171	C₂²×#168	C₂³	1	1	yes	characteristic
172	C₂²×#168	C₂³	1	1	yes	characteristic
173	D₅×M₁₆	—	2	4	no	—
174	D₅×M₁₆	Q₈	1	8	yes	complemented
175	C₂×#676	—	2	4	no	—
176	C₂×#676	C₂³	1	1	yes	characteristic
177	C₂×#676	C₂³	1	1	yes	characteristic
178	C₂×#676	C₂³	1	1	yes	characteristic
179	C₂×#676	C₂³	1	1	yes	characteristic
180	C₂×#676	C₂³	1	2	yes	—
181	C₂×#676	C₂³	1	2	yes	—
182	C₂×C₈×D₅	—	2	4	no	—
183	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
184	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
185	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
186	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
187	C₂×C₈×D₅	C₂³	1	2	yes	—
188	C₂×C₈×D₅	C₂³	1	2	yes	—
189	#4043	C₂×C₄	1	2	yes	—
190	#4043	C₂×C₄	1	2	yes	—
191	#4043	C₂×C₄	1	2	yes	—
192	#4043	C₂×C₄	1	2	yes	—
193	#4042	C₂×C₄	1	2	yes	—
194	#4042	C₂×C₄	1	2	yes	—
195	#4042	C₂×C₄	1	2	yes	—
196	#4042	C₂×C₄	1	2	yes	—
197	#4042	C₂×C₄	1	2	yes	—
198	#4042	C₂×C₄	1	2	yes	—
199	#4042	C₂×C₄	1	2	yes	—
200	#4042	C₂×C₄	1	2	yes	—
201	#4038	C₂×C₄	1	1	yes	characteristic
202	#4038	C₂×C₄	1	1	yes	characteristic
203	#4038	C₂×C₄	1	1	yes	characteristic
204	#4038	C₂×C₄	1	1	yes	characteristic
205	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
206	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
207	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
208	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
209	#4036	C₂×C₄	1	1	yes	characteristic
210	#4036	C₂×C₄	1	1	yes	characteristic
211	#4036	C₂×C₄	1	1	yes	characteristic
212	#4036	C₂×C₄	1	1	yes	characteristic
213	#4035	C₂×C₄	1	2	yes	—
214	#4035	C₂×C₄	1	2	yes	—
215	#4035	C₂×C₄	1	2	yes	—
216	#4035	C₂×C₄	1	2	yes	—
217	#4035	C₂×C₄	1	2	yes	—
218	#4035	C₂×C₄	1	2	yes	—
219	#4035	C₂×C₄	1	2	yes	—
220	#4035	C₂×C₄	1	2	yes	—
221	#4034	C₂×C₄	1	1	yes	characteristic
222	#4034	C₂×C₄	1	1	yes	characteristic
223	#4034	C₂×C₄	1	1	yes	characteristic
224	#4034	C₂×C₄	1	1	yes	characteristic
225	#4034	C₂×C₄	1	2	yes	—
226	#4034	C₂×C₄	1	2	yes	—
227	#4034	C₂×C₄	1	2	yes	—
228	#4034	C₂×C₄	1	2	yes	—
229	D₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
230	D₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
231	#4024	C₂×C₄	1	2	yes	—
232	#4024	C₂×C₄	1	2	yes	—
233	#4024	C₂×C₄	1	2	yes	—
234	#4024	C₂×C₄	1	2	yes	—
235	#4023	C₂×C₄	1	2	yes	—
236	#4023	C₂×C₄	1	2	yes	—
237	#4018	C₂×C₄	1	1	yes	characteristic
238	#4018	C₂×C₄	1	1	yes	characteristic
239	#4018	C₂×C₄	1	1	yes	characteristic
240	#4018	C₂×C₄	1	1	yes	characteristic
241	#4018	C₂³	1	1	yes	characteristic
242	#4018	C₂³	1	1	yes	characteristic
243	#4018	C₂³	1	1	yes	characteristic
244	#4018	C₂³	1	1	yes	characteristic
245	#4018	C₂³	1	2	yes	—
246	#4018	C₂³	1	2	yes	—
247	C₄²×D₅	C₂³	1	2	yes	—
248	C₄²×D₅	C₂³	1	2	yes	—
249	#4016	C₂×C₄	1	1	yes	characteristic
250	#4016	C₂×C₄	1	1	yes	characteristic
251	#4015	C₂×C₄	1	1	yes	characteristic
252	#4015	C₂×C₄	1	1	yes	characteristic
253	C₄×Dic₁₀	C₂³	1	2	yes	—
254	C₄×Dic₁₀	C₂³	1	2	yes	—
255	C₄×Dic₁₀	C₂³	1	2	yes	—
256	C₄×Dic₁₀	C₂³	1	2	yes	—
257	C₄×Dic₁₀	C₂³	1	2	yes	—
258	C₄×Dic₁₀	C₂³	1	2	yes	—
259	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₅×C₄⋊C₈	C₂³	1	2	yes	—
264	C₅×C₄⋊C₈	C₂³	1	2	yes	—
265	C₅×C₄⋊C₈	C₂³	1	2	yes	—
266	C₅×C₄⋊C₈	C₂³	1	2	yes	—
267	C₅×#97	C₂³	1	2	yes	—
268	C₅×#97	C₂³	1	2	yes	—
269	C₅×#97	C₂³	1	2	yes	—
270	C₄×C₅×C₈	C₂³	1	2	yes	—
271	C₄×C₅×C₈	C₂³	1	2	yes	—
272	C₄×C₅×C₈	C₂³	1	2	yes	—
273	#3947	C₂³	1	2	yes	—
274	#3947	C₂³	1	2	yes	—
275	#3947	C₂³	1	2	yes	—
276	#3947	C₂³	1	2	yes	—
277	#3947	C₂³	1	2	yes	—
278	#3947	C₂³	1	2	yes	—
279	#3946	C₂³	1	2	yes	—
280	#3946	C₂³	1	2	yes	—
281	#3946	C₂³	1	1	yes	characteristic
282	#3946	C₂³	1	1	yes	characteristic
283	#3946	C₂³	1	1	yes	characteristic
284	#3946	C₂³	1	1	yes	characteristic
285	#3946	C₂³	1	2	yes	—
286	#3946	C₂³	1	2	yes	—
287	#3946	C₂³	1	2	yes	—
288	#3946	C₂³	1	2	yes	—
289	#3946	C₂³	1	1	yes	characteristic
290	#3946	C₂³	1	1	yes	characteristic
291	#3946	C₂³	1	2	yes	—
292	#3946	C₂³	1	2	yes	—
293	#3946	C₂³	1	1	yes	characteristic
294	#3946	C₂³	1	1	yes	characteristic
295	C₈×Dic₅	C₂³	1	2	yes	—
296	C₈×Dic₅	C₂³	1	2	yes	—
297	C₈×Dic₅	C₂³	1	2	yes	—
298	C₈×Dic₅	C₂³	1	2	yes	—
299	C₈×Dic₅	C₂³	1	2	yes	—
300	C₈×Dic₅	C₂³	1	2	yes	—
301	C₄⋊#168	C₂³	1	2	yes	—
302	C₄⋊#168	C₂³	1	2	yes	—
303	C₄⋊#168	C₂³	1	2	yes	—
304	C₄⋊#168	C₂³	1	2	yes	—
305	C₄⋊#168	C₂³	1	1	yes	characteristic
306	C₄⋊#168	C₂³	1	1	yes	characteristic
307	C₄⋊#168	C₂³	1	1	yes	characteristic
308	C₄⋊#168	C₂³	1	1	yes	characteristic
309	#3935	C₂³	1	2	yes	—
310	#3935	C₂³	1	2	yes	—
311	#3935	C₂³	1	2	yes	—
312	C₄×#168	C₂³	1	2	yes	—
313	C₄×#168	C₂³	1	2	yes	—
314	C₄×#168	C₂³	1	2	yes	—
315	#3458	—	5	1	no	—
316	#2962	—	5	2	no	—
317	#2962	—	5	2	no	—
318	#2962	—	5	2	no	—
319	#2962	—	5	2	no	—
320	#2962	—	5	1	no	—
321	#2962	—	5	1	no	—
322	#2962	—	5	1	no	—
323	#2962	—	5	1	no	—
324	#2962	—	5	1	no	—
325	#2962	—	5	1	no	—
326	#2962	—	5	1	no	—
327	#2962	D₅	1	1	yes	characteristic, complemented
328	#2961	—	5	2	no	—
329	#2961	—	5	2	no	—
330	#2960	—	5	2	no	—
331	#2960	—	5	2	no	—
332	#2905	—	5	1	no	—
333	C₂×#424	—	5	1	no	—
334	C₂×#424	—	5	1	no	—
335	#2873	—	5	1	no	—
336	#2873	—	5	1	no	—
337	C₂×#405	—	5	1	no	—
338	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
340	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
341	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
344	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
345	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
346	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
348	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
349	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
350	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
351	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₄×D₅	C₂×Q₈	1	4	yes	—
354	C₂×C₄×D₅	#41	1	4	yes	—
355	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
357	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
358	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
359	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
360	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
361	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
362	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
363	C₅×M₁₆	—	2	2	no	—
364	C₅×M₁₆	C₂×Q₈	1	4	yes	—
365	C₂×C₅×C₈	—	2	2	no	—
366	C₂×C₅×C₈	—	2	2	no	—
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	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₅×C₈	C₂⁴	1	2	yes	—
372	C₂×C₅×C₈	C₂⁴	1	2	yes	—
373	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
374	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
378	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
379	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
380	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
382	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
384	C₅×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
385	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
386	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
387	C₄²×C₅	C₂⁴	1	1	yes	characteristic
388	C₄²×C₅	C₂⁴	1	1	yes	characteristic
389	C₄²×C₅	C₂⁴	1	2	yes	—
390	C₄²×C₅	C₂⁴	1	2	yes	—
391	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
392	C₂²⋊Dic₅	C₂²×C₄	1	2	yes	—
393	#685	C₂²×C₄	1	1	yes	characteristic
394	#685	C₂²×C₄	1	1	yes	characteristic
395	#685	C₂²×C₄	1	1	yes	characteristic
396	#685	C₂²×C₄	1	1	yes	characteristic
397	#685	C₂²×C₄	1	1	yes	characteristic
398	#685	C₂²×C₄	1	1	yes	characteristic
399	#685	C₂²×C₄	1	1	yes	characteristic
400	#685	C₂²×C₄	1	1	yes	characteristic
401	#685	C₂²×C₄	1	2	yes	—
402	#685	C₂²×C₄	1	2	yes	—
403	#685	C₂²×C₄	1	2	yes	—
404	#685	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
406	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
407	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
408	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
409	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
410	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
411	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
412	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
414	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
415	#683	C₂²×C₄	1	2	yes	—
416	#683	C₂²×C₄	1	2	yes	—
417	#683	C₂²×C₄	1	2	yes	—
418	#683	C₂²×C₄	1	2	yes	—
419	#683	C₂²×C₄	1	2	yes	—
420	#683	C₂²×C₄	1	2	yes	—
421	#683	C₂²×C₄	1	2	yes	—
422	#683	C₂²×C₄	1	2	yes	—
423	#683	C₂²×C₄	1	2	yes	—
424	#683	C₂²×C₄	1	2	yes	—
425	#683	C₂²×C₄	1	2	yes	—
426	#683	C₂²×C₄	1	2	yes	—
427	#683	C₂²×C₄	1	1	yes	characteristic
428	#683	C₂²×C₄	1	1	yes	characteristic
429	#683	C₂²×C₄	1	1	yes	characteristic
430	#683	C₂²×C₄	1	1	yes	characteristic
431	#683	C₂²×C₄	1	1	yes	characteristic
432	#683	C₂²×C₄	1	1	yes	characteristic
433	#683	C₂²×C₄	1	1	yes	characteristic
434	#683	C₂²×C₄	1	1	yes	characteristic
435	#683	C₂²×C₄	1	2	yes	—
436	#683	C₂²×C₄	1	2	yes	—
437	#683	C₂²×C₄	1	2	yes	—
438	#683	C₂²×C₄	1	2	yes	—
439	C₄×Dic₅	C₂²×C₄	1	2	yes	—
440	C₄×Dic₅	C₂²×C₄	1	2	yes	—
441	C₄×Dic₅	C₂²×C₄	1	2	yes	—
442	C₄×Dic₅	C₂²×C₄	1	2	yes	—
443	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
444	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
445	C₄×Dic₅	C₂⁴	1	2	yes	—
446	C₄×Dic₅	C₂⁴	1	2	yes	—
447	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
448	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
449	#681	—	2	2	no	—
450	#681	C₂×Q₈	1	4	yes	—
451	C₂×#168	—	2	2	no	—
452	C₂×#168	—	2	2	no	—
453	C₂×#168	C₂⁴	1	1	yes	characteristic
454	C₂×#168	C₂⁴	1	1	yes	characteristic
455	C₂×#168	C₂⁴	1	2	yes	—
456	C₂×#168	C₂⁴	1	1	yes	characteristic
457	C₂×#168	C₂⁴	1	1	yes	characteristic
458	C₂×#168	C₂⁴	1	2	yes	—
459	#676	—	2	2	no	—
460	#676	—	2	2	no	—
461	#676	—	2	2	no	—
462	#676	—	2	2	no	—
463	#676	—	2	4	no	—
464	#676	C₂×Q₈	1	8	yes	—
465	C₈×D₅	—	2	2	no	—
466	C₈×D₅	—	2	2	no	—
467	C₈×D₅	—	2	2	no	—
468	C₈×D₅	—	2	2	no	—
469	C₈×D₅	—	2	4	no	—
470	C₈×D₅	C₂×Q₈	1	8	yes	—
471	C₂²×M₁₆	—	5	1	no	—
472	C₂²×M₁₆	—	5	1	no	—
473	C₂²×M₁₆	—	5	1	no	—
474	C₂³×C₈	—	5	1	no	—
475	#544	—	5	1	no	—
476	#544	—	5	1	no	—
477	#544	—	5	1	no	—
478	#544	—	5	1	no	—
479	#544	—	5	1	no	—
480	#544	—	5	1	no	—
481	#544	—	5	1	no	—
482	#544	—	5	1	no	—
483	#544	—	5	2	no	—
484	#544	—	5	2	no	—
485	#543	—	5	2	no	—
486	#543	—	5	2	no	—
487	#533	—	5	2	no	—
488	#533	—	5	2	no	—
489	#533	—	5	2	no	—
490	#533	—	5	2	no	—
491	#533	—	5	1	no	—
492	#533	—	5	1	no	—
493	#533	—	5	1	no	—
494	#533	C₂×D₅	1	1	yes	characteristic
495	C₂×#117	—	5	1	no	—
496	C₂×#117	—	5	1	no	—
497	C₂×#117	—	5	1	no	—
498	#446	—	5	2	no	—
499	#446	—	5	2	no	—
500	#446	—	5	2	no	—
501	#446	—	5	2	no	—
502	#446	—	5	2	no	—
503	#446	—	5	2	no	—
504	#446	—	5	2	no	—
505	#446	—	5	2	no	—
506	#446	—	5	2	no	—
507	#446	—	5	2	no	—
508	#446	—	5	2	no	—
509	#446	—	5	2	no	—
510	#446	—	5	2	no	—
511	#446	—	5	2	no	—
512	#446	—	5	2	no	—
513	#446	—	5	2	no	—
514	#446	—	5	2	no	—
515	#446	—	5	2	no	—
516	#446	—	5	2	no	—
517	#446	—	5	2	no	—
518	#446	—	5	2	no	—
519	#446	C₂×D₅	1	2	yes	complemented
520	#446	C₂×D₅	1	2	yes	complemented
521	#446	C₂×D₅	1	2	yes	complemented
522	C₈×Q₈	—	5	2	no	—
523	C₈×Q₈	—	5	2	no	—
524	C₈×Q₈	—	5	2	no	—
525	C₈×Q₈	—	5	2	no	—
526	C₈×Q₈	—	5	2	no	—
527	C₈×Q₈	—	5	2	no	—
528	C₈×Q₈	—	5	2	no	—
529	C₈×Q₈	C₂×D₅	1	2	yes	complemented
530	#424	—	5	1	no	—
531	#424	—	5	1	no	—
532	#424	—	5	1	no	—
533	#424	—	5	1	no	—
534	#424	—	5	1	no	—
535	#424	—	5	1	no	—
536	#424	—	5	2	no	—
537	#424	—	5	1	no	—
538	#424	—	5	1	no	—
539	#424	—	5	2	no	—
540	#424	—	5	1	no	—
541	#424	—	5	1	no	—
542	#424	—	5	1	no	—
543	#424	—	5	1	no	—
544	#424	—	5	1	no	—
545	#424	—	5	1	no	—
546	#424	—	5	2	no	—
547	#424	—	5	2	no	—
548	#424	C₂×D₅	1	1	yes	characteristic
549	#424	C₂×D₅	1	1	yes	characteristic
550	#423	—	5	2	no	—
551	#423	—	5	2	no	—
552	C₂×C₄⋊C₈	—	5	1	no	—
553	C₂×C₄⋊C₈	—	5	1	no	—
554	C₂×C₄⋊C₈	—	5	1	no	—
555	C₂×C₄⋊C₈	—	5	2	no	—
556	C₂×C₄⋊C₈	—	5	2	no	—
557	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
558	#405	—	5	1	no	—
559	#405	—	5	1	no	—
560	#405	—	5	1	no	—
561	#405	—	5	1	no	—
562	#405	—	5	1	no	—
563	#405	—	5	1	no	—
564	#405	—	5	2	no	—
565	#405	—	5	2	no	—
566	#405	—	5	2	no	—
567	#405	—	5	2	no	—
568	#405	—	5	2	no	—
569	#405	—	5	2	no	—
570	#405	—	5	2	no	—
571	#405	—	5	2	no	—
572	#405	C₂×D₅	1	1	yes	characteristic
573	#405	C₂×D₅	1	1	yes	characteristic
574	C₄×M₁₆	—	5	1	no	—
575	C₄×M₁₆	—	5	1	no	—
576	C₄×M₁₆	—	5	1	no	—
577	C₄×M₁₆	—	5	2	no	—
578	C₄×M₁₆	—	5	2	no	—
579	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
580	C₂×#97	—	5	2	no	—
581	C₂×C₄×C₈	—	5	2	no	—
582	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
583	C₂²×D₅	—	4	1	no	—
584	C₂²×D₅	—	4	1	no	—
585	C₂²×D₅	C₄×Q₈	1	4	yes	—
586	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
587	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
588	C₅×Q₈	—	4	2	no	—
589	C₅×Q₈	—	4	2	no	—
590	C₂×C₄×C₅	—	4	1	no	—
591	C₂×C₄×C₅	—	4	1	no	—
592	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
593	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
594	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
595	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
596	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
597	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
598	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
599	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
600	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
601	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
602	C₂×C₄×C₅	C₂×#41	1	2	yes	—
603	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
604	C₂×Dic₅	—	4	1	no	—
605	C₂×Dic₅	—	4	1	no	—
606	C₂×Dic₅	C₄×Q₈	1	4	yes	—
607	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
608	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
609	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
610	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
611	C₂×Dic₅	C₂³×C₄	1	2	yes	—
612	C₂×Dic₅	C₂³×C₄	1	2	yes	—
613	C₂×Dic₅	C₂³×C₄	1	2	yes	—
614	C₂×Dic₅	C₂³×C₄	1	2	yes	—
615	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
616	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
617	C₄×D₅	—	4	2	no	—
618	C₄×D₅	—	4	2	no	—
619	C₄×D₅	—	4	2	no	—
620	C₄×D₅	—	4	2	no	—
621	C₄×D₅	C₄×Q₈	1	4	yes	—
622	C₄×D₅	C₄×Q₈	1	4	yes	—
623	C₄×D₅	C₂²×Q₈	1	2	yes	—
624	C₄×D₅	C₂²×Q₈	1	2	yes	—
625	C₄×D₅	C₂×#41	1	2	yes	—
626	C₄×D₅	C₂×#41	1	2	yes	—
627	Dic₁₀	—	4	2	no	—
628	Dic₁₀	—	4	2	no	—
629	Dic₁₀	—	4	2	no	—
630	Dic₁₀	—	4	2	no	—
631	Dic₁₀	—	4	2	no	—
632	Dic₁₀	—	4	2	no	—
633	C₅×C₈	—	2	1	no	—
634	C₅×C₈	—	2	1	no	—
635	C₅×C₈	—	2	2	no	—
636	C₅×C₈	—	2	1	no	—
637	C₅×C₈	—	2	1	no	—
638	C₅×C₈	C₂²×Q₈	1	4	yes	—
639	#168	—	2	1	no	—
640	#168	—	2	1	no	—
641	#168	—	2	2	no	—
642	#168	—	2	1	no	—
643	#168	—	2	1	no	—
644	#168	C₂²×Q₈	1	4	yes	—
645	C₂³×C₄	—	5	1	no	—
646	C₂×M₁₆	—	5	1	no	—
647	C₂×M₁₆	—	5	8	no	—
648	C₂×M₁₆	—	5	1	no	—
649	C₂×M₁₆	—	5	2	no	—
650	C₂×M₁₆	—	5	1	no	—
651	C₂×M₁₆	—	5	1	no	—
652	C₂×M₁₆	—	5	1	no	—
653	C₂×M₁₆	—	5	2	no	—
654	C₂×M₁₆	—	5	1	no	—
655	C₂×M₁₆	—	10	4	no	—
656	C₂×M₁₆	—	10	4	no	—
657	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
658	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
659	C₂²×C₈	—	5	2	no	—
660	C₂²×C₈	—	5	1	no	—
661	C₂²×C₈	—	5	1	no	—
662	C₂²×C₈	—	5	1	no	—
663	C₂²×C₈	—	5	1	no	—
664	C₂²×C₈	—	5	1	no	—
665	C₂²×C₈	—	5	1	no	—
666	C₂²×C₈	—	5	2	no	—
667	C₂²×C₈	—	10	4	no	—
668	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
669	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
670	C₄⋊Q₈	—	5	2	no	—
671	C₄⋊Q₈	—	5	2	no	—
672	C₄⋊Q₈	—	5	2	no	—
673	C₄⋊Q₈	—	5	2	no	—
674	C₄⋊Q₈	—	5	2	no	—
675	C₄⋊Q₈	—	5	2	no	—
676	C₄⋊Q₈	—	5	2	no	—
677	C₄⋊Q₈	—	5	2	no	—
678	C₄⋊Q₈	—	5	1	no	—
679	C₄⋊Q₈	—	5	1	no	—
680	C₄⋊Q₈	—	5	1	no	—
681	C₄⋊Q₈	—	5	1	no	—
682	C₄⋊Q₈	—	5	1	no	—
683	C₄⋊Q₈	—	5	1	no	—
684	C₄⋊Q₈	C₄×D₅	1	1	yes	characteristic
685	C₄⋊Q₈	C₄×D₅	1	1	yes	characteristic
686	#125	—	5	2	no	—
687	#125	—	5	2	no	—
688	#125	—	5	2	no	—
689	#125	—	5	2	no	—
690	#125	—	5	2	no	—
691	#125	—	5	2	no	—
692	#125	—	5	2	no	—
693	#125	—	5	2	no	—
694	#125	—	5	1	no	—
695	#125	—	5	1	no	—
696	#125	—	5	1	no	—
697	#125	—	5	1	no	—
698	#125	—	5	1	no	—
699	#125	—	5	1	no	—
700	#125	C₄×D₅	1	1	yes	characteristic
701	#125	C₄×D₅	1	1	yes	characteristic
702	C₂²⋊Q₈	—	5	2	no	—
703	C₂²⋊Q₈	—	5	2	no	—
704	C₂²⋊Q₈	—	5	2	no	—
705	C₂²⋊Q₈	—	5	2	no	—
706	C₂²⋊Q₈	—	5	2	no	—
707	C₂²⋊Q₈	—	5	2	no	—
708	C₂²⋊Q₈	—	5	2	no	—
709	C₂²⋊Q₈	—	5	2	no	—
710	C₂²⋊Q₈	—	5	2	no	—
711	C₂²⋊Q₈	—	5	2	no	—
712	C₂²⋊Q₈	—	5	2	no	—
713	C₂²⋊Q₈	—	5	2	no	—
714	C₂²⋊Q₈	—	5	2	no	—
715	C₂²⋊Q₈	—	5	2	no	—
716	C₂²⋊Q₈	—	5	2	no	—
717	C₂²⋊Q₈	—	5	2	no	—
718	C₂²⋊Q₈	—	5	2	no	—
719	C₂²⋊Q₈	—	5	2	no	—
720	C₂²⋊Q₈	—	5	2	no	—
721	C₂²⋊Q₈	—	5	2	no	—
722	C₂²⋊Q₈	—	5	2	no	—
723	C₂²⋊Q₈	—	5	2	no	—
724	C₂²⋊Q₈	C₄×D₅	1	2	yes	—
725	C₂²⋊Q₈	C₄×D₅	1	2	yes	—
726	C₄×Q₈	—	5	2	no	—
727	C₄×Q₈	—	5	2	no	—
728	C₄×Q₈	—	5	2	no	—
729	C₄×Q₈	—	5	2	no	—
730	C₄×Q₈	—	5	2	no	—
731	C₄×Q₈	—	5	2	no	—
732	C₄×Q₈	C₂²×D₅	1	2	yes	—
733	C₄×Q₈	C₂²×D₅	1	2	yes	—
734	#117	—	5	1	no	—
735	#117	—	5	1	no	—
736	#117	—	5	1	no	—
737	#117	—	5	1	no	—
738	#117	—	5	1	no	—
739	#117	—	5	1	no	—
740	#117	—	5	2	no	—
741	#117	—	5	2	no	—
742	#117	—	5	1	no	—
743	#117	—	5	1	no	—
744	#117	—	5	1	no	—
745	#117	—	5	1	no	—
746	#117	—	5	1	no	—
747	#117	—	5	1	no	—
748	#117	—	5	2	no	—
749	#117	—	5	2	no	—
750	#117	—	5	1	no	—
751	#117	—	5	1	no	—
752	#117	C₂²×D₅	1	1	yes	characteristic
753	#117	C₂²×D₅	1	1	yes	characteristic
754	C₂×C₄⋊C₄	—	5	1	no	—
755	C₂×C₄⋊C₄	—	5	1	no	—
756	C₂×C₄⋊C₄	—	5	1	no	—
757	C₂×C₄⋊C₄	—	5	1	no	—
758	C₂×C₄⋊C₄	—	5	1	no	—
759	C₂×C₄⋊C₄	—	5	1	no	—
760	C₂×C₂²⋊C₄	—	5	1	no	—
761	C₂×C₂²⋊C₄	—	5	1	no	—
762	C₂×C₂²⋊C₄	—	5	2	no	—
763	C₂×C₂²⋊C₄	—	5	2	no	—
764	C₂×C₄²	—	5	1	no	—
765	C₂×C₄²	—	5	2	no	—
766	C₂×C₄²	—	5	2	no	—
767	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
768	C₄⋊C₈	—	5	1	no	—
769	C₄⋊C₈	—	5	2	no	—
770	C₄⋊C₈	—	5	1	no	—
771	C₄⋊C₈	—	5	1	no	—
772	C₄⋊C₈	—	5	2	no	—
773	C₄⋊C₈	—	5	1	no	—
774	C₄⋊C₈	—	5	1	no	—
775	C₄⋊C₈	—	5	2	no	—
776	C₄⋊C₈	—	5	1	no	—
777	C₄⋊C₈	—	5	1	no	—
778	C₄⋊C₈	—	5	2	no	—
779	C₄⋊C₈	—	5	1	no	—
780	C₄⋊C₈	—	5	2	no	—
781	C₄⋊C₈	—	5	2	no	—
782	C₄⋊C₈	—	5	2	no	—
783	C₄⋊C₈	—	5	2	no	—
784	C₄⋊C₈	—	5	1	no	—
785	C₄⋊C₈	—	5	2	no	—
786	C₄⋊C₈	—	5	1	no	—
787	C₄⋊C₈	—	5	1	no	—
788	C₄⋊C₈	—	5	2	no	—
789	C₄⋊C₈	—	5	1	no	—
790	C₄⋊C₈	—	5	2	no	—
791	C₄⋊C₈	—	5	2	no	—
792	C₄⋊C₈	C₂²×D₅	1	2	yes	—
793	C₄⋊C₈	C₂²×D₅	1	2	yes	—
794	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
795	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
796	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
797	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
798	C₄⋊C₈	C₂²×D₅	1	2	yes	—
799	C₄⋊C₈	C₂²×D₅	1	2	yes	—
800	#97	—	5	2	no	—
801	#97	—	5	2	no	—
802	#97	—	5	2	no	—
803	#97	—	5	2	no	—
804	#97	—	5	2	no	—
805	#97	—	5	2	no	—
806	#97	—	5	2	no	—
807	#97	—	5	2	no	—
808	#97	—	5	2	no	—
809	#97	C₂²×D₅	1	2	yes	—
810	#97	C₂²×D₅	1	2	yes	—
811	#97	C₂²×D₅	1	2	yes	—
812	C₄×C₈	—	5	2	no	—
813	C₄×C₈	—	5	2	no	—
814	C₄×C₈	—	5	2	no	—
815	C₄×C₈	—	5	2	no	—
816	C₄×C₈	—	5	2	no	—
817	C₄×C₈	—	5	2	no	—
818	C₄×C₈	—	5	2	no	—
819	C₄×C₈	—	5	2	no	—
820	C₄×C₈	—	5	2	no	—
821	C₄×C₈	C₂²×D₅	1	2	yes	—
822	C₄×C₈	C₂²×D₅	1	2	yes	—
823	C₄×C₈	C₂²×D₅	1	2	yes	—
824	C₂²×C₅	—	2	1	no	—
825	C₂²×C₅	—	2	1	no	—
826	C₂²×C₅	C₂×C₄×Q₈	1	2	yes	—
827	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
828	C₂×D₅	—	2	1	no	—
829	C₂×D₅	—	2	1	no	—
830	C₂×D₅	—	2	1	no	—
831	C₂×D₅	—	2	1	no	—
832	C₂×D₅	—	4	4	no	—
833	C₂×D₅	C₂×C₄×Q₈	1	2	yes	—
834	C₂×D₅	C₂×C₄×Q₈	1	2	yes	—
835	C₄×C₅	—	2	1	no	—
836	C₄×C₅	—	2	1	no	—
837	C₄×C₅	—	2	2	no	—
838	C₄×C₅	—	2	2	no	—
839	C₄×C₅	—	2	2	no	—
840	C₄×C₅	—	2	2	no	—
841	C₄×C₅	—	2	1	no	—
842	C₄×C₅	—	2	1	no	—
843	C₄×C₅	C₂×C₄×Q₈	1	2	yes	—
844	C₄×C₅	C₂³×Q₈	1	1	yes	characteristic
845	C₄×C₅	C₂²×#41	1	1	yes	characteristic
846	Dic₅	—	2	2	no	—
847	Dic₅	—	2	2	no	—
848	Dic₅	—	2	2	no	—
849	Dic₅	—	2	2	no	—
850	Dic₅	—	2	1	no	—
851	Dic₅	—	2	1	no	—
852	Dic₅	—	2	1	no	—
853	Dic₅	—	2	1	no	—
854	Dic₅	C₂×C₄×Q₈	1	2	yes	—
855	Dic₅	C₂×C₄×Q₈	1	2	yes	—
856	C₂⁴	—	5	1	no	—
857	C₂×Q₈	—	5	2	no	—
858	C₂×Q₈	—	5	2	no	—
859	C₂×Q₈	—	5	2	no	—
860	C₂×Q₈	—	5	2	no	—
861	C₂×Q₈	—	5	2	no	—
862	C₂×Q₈	—	5	2	no	—
863	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
864	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
865	C₂²×C₄	—	5	1	no	—
866	C₂²×C₄	—	5	1	no	—
867	C₂²×C₄	—	5	1	no	—
868	C₂²×C₄	—	5	4	no	—
869	C₂²×C₄	—	5	4	no	—
870	C₂²×C₄	—	5	1	no	—
871	C₂²×C₄	—	5	1	no	—
872	C₂²×C₄	—	5	1	no	—
873	C₂²×C₄	—	5	1	no	—
874	C₂²×C₄	—	5	2	no	—
875	C₂²×C₄	—	5	2	no	—
876	C₂²×C₄	—	5	2	no	—
877	C₂²×C₄	—	5	2	no	—
878	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
879	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
880	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
881	M₁₆	—	2	2	no	—
882	M₁₆	—	5	4	no	—
883	M₁₆	—	5	8	no	—
884	M₁₆	—	10	2	no	—
885	M₁₆	—	10	2	no	—
886	M₁₆	—	10	2	no	—
887	M₁₆	—	10	2	no	—
888	M₁₆	—	10	4	no	—
889	M₁₆	—	10	2	no	—
890	M₁₆	Q₈×D₅	1	4	yes	—
891	C₂×C₈	—	2	2	no	—
892	C₂×C₈	—	2	2	no	—
893	C₂×C₈	—	5	2	no	—
894	C₂×C₈	—	5	8	no	—
895	C₂×C₈	—	5	1	no	—
896	C₂×C₈	—	5	1	no	—
897	C₂×C₈	—	5	2	no	—
898	C₂×C₈	—	5	1	no	—
899	C₂×C₈	—	5	1	no	—
900	C₂×C₈	—	10	2	no	—
901	C₂×C₈	—	10	2	no	—
902	C₂×C₈	—	10	2	no	—
903	C₂×C₈	—	10	2	no	—
904	C₂×C₈	—	10	4	no	—
905	C₂×C₈	—	10	2	no	—
906	C₂×C₈	—	10	2	no	—
907	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
908	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
909	C₂×C₈	C₂³×D₅	1	2	yes	—
910	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
911	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
912	C₂×C₈	C₂³×D₅	1	2	yes	—
913	C₄⋊C₄	—	5	2	no	—
914	C₄⋊C₄	—	5	2	no	—
915	C₄⋊C₄	—	5	2	no	—
916	C₄⋊C₄	—	5	2	no	—
917	C₄⋊C₄	—	5	1	no	—
918	C₄⋊C₄	—	5	1	no	—
919	C₄⋊C₄	—	5	1	no	—
920	C₄⋊C₄	—	5	1	no	—
921	C₄⋊C₄	—	5	1	no	—
922	C₄⋊C₄	—	5	1	no	—
923	C₄⋊C₄	—	5	1	no	—
924	C₄⋊C₄	—	5	1	no	—
925	C₄⋊C₄	—	5	1	no	—
926	C₄⋊C₄	—	5	1	no	—
927	C₄⋊C₄	—	5	1	no	—
928	C₄⋊C₄	—	5	1	no	—
929	C₄⋊C₄	—	5	2	no	—
930	C₄⋊C₄	—	5	2	no	—
931	C₄⋊C₄	—	5	2	no	—
932	C₄⋊C₄	—	5	2	no	—
933	C₄⋊C₄	—	5	2	no	—
934	C₄⋊C₄	—	5	2	no	—
935	C₄⋊C₄	—	5	2	no	—
936	C₄⋊C₄	—	5	2	no	—
937	C₄⋊C₄	—	5	2	no	—
938	C₄⋊C₄	—	5	2	no	—
939	C₄⋊C₄	—	5	2	no	—
940	C₄⋊C₄	—	5	2	no	—
941	C₄⋊C₄	—	5	2	no	—
942	C₄⋊C₄	—	5	2	no	—
943	C₄⋊C₄	—	5	2	no	—
944	C₄⋊C₄	—	5	2	no	—
945	C₄⋊C₄	—	5	2	no	—
946	C₄⋊C₄	—	5	2	no	—
947	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
948	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
949	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
950	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
951	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
952	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
953	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
954	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
955	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
956	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
957	C₂²⋊C₄	—	5	2	no	—
958	C₂²⋊C₄	—	5	2	no	—
959	C₂²⋊C₄	—	5	2	no	—
960	C₂²⋊C₄	—	5	2	no	—
961	C₂²⋊C₄	—	5	2	no	—
962	C₂²⋊C₄	—	5	2	no	—
963	C₂²⋊C₄	—	5	1	no	—
964	C₂²⋊C₄	—	5	1	no	—
965	C₂²⋊C₄	—	5	1	no	—
966	C₂²⋊C₄	—	5	1	no	—
967	C₂²⋊C₄	—	5	1	no	—
968	C₂²⋊C₄	—	5	1	no	—
969	C₂²⋊C₄	—	5	1	no	—
970	C₂²⋊C₄	—	5	1	no	—
971	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
972	C₂²⋊C₄	C₂×C₄×D₅	1	2	yes	—
973	C₄²	—	5	2	no	—
974	C₄²	—	5	2	no	—
975	C₄²	—	5	2	no	—
976	C₄²	—	5	2	no	—
977	C₄²	—	5	1	no	—
978	C₄²	—	5	1	no	—
979	C₄²	—	5	2	no	—
980	C₄²	—	5	1	no	—
981	C₄²	—	5	1	no	—
982	C₄²	—	5	2	no	—
983	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
984	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
985	C₄²	C₂³×D₅	1	1	yes	characteristic
986	C₄²	C₂³×D₅	1	2	yes	—
987	C₄²	C₂³×D₅	1	2	yes	—
988	C₄²	C₂³×D₅	1	1	yes	characteristic
989	C₂×C₅	—	2	2	no	—
990	C₂×C₅	C₂²×C₄×Q₈	1	1	yes	characteristic
991	C₂×C₅	#3573	1	1	yes	characteristic
992	C₂×C₅	#3573	1	1	yes	characteristic
993	D₅	—	2	2	no	—
994	D₅	—	2	2	no	—
995	C₂³	—	5	1	no	—
996	C₂³	—	5	1	no	—
997	C₂³	—	5	4	no	—
998	C₂³	—	20	1	no	—
999	C₂³	—	20	1	no	—
1000	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
1001	Q₈	—	4	2	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	20	2	no	—
1004	Q₈	—	20	2	no	—
1005	Q₈	—	20	2	no	—
1006	Q₈	—	20	2	no	—
1007	Q₈	—	20	2	no	—
1008	Q₈	—	20	2	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	5	4	no	—
1012	C₂×C₄	—	5	1	no	—
1013	C₂×C₄	—	5	1	no	—
1014	C₂×C₄	—	5	4	no	—
1015	C₂×C₄	—	5	4	no	—
1016	C₂×C₄	—	5	2	no	—
1017	C₂×C₄	—	5	2	no	—
1018	C₂×C₄	—	5	2	no	—
1019	C₂×C₄	—	5	2	no	—
1020	C₂×C₄	—	5	2	no	—
1021	C₂×C₄	—	5	2	no	—
1022	C₂×C₄	—	5	1	no	—
1023	C₂×C₄	—	5	1	no	—
1024	C₂×C₄	—	5	2	no	—
1025	C₂×C₄	—	5	2	no	—
1026	C₂×C₄	—	5	1	no	—
1027	C₂×C₄	—	5	1	no	—
1028	C₂×C₄	—	20	2	no	—
1029	C₂×C₄	—	20	2	no	—
1030	C₂×C₄	—	20	2	no	—
1031	C₂×C₄	—	20	2	no	—
1032	C₂×C₄	—	20	1	no	—
1033	C₂×C₄	—	20	1	no	—
1034	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1035	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1036	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1037	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
1038	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1039	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1040	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1041	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1042	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
1043	C₂×C₄	C₂×Q₈×D₅	1	2	yes	—
1044	C₂×C₄	D₅×#41	1	2	yes	—
1045	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	1	no	—
1050	C₈	—	2	2	no	—
1051	C₈	—	5	4	no	—
1052	C₈	—	10	1	no	—
1053	C₈	—	10	1	no	—
1054	C₈	—	10	2	no	—
1055	C₈	—	10	1	no	—
1056	C₈	—	10	1	no	—
1057	C₈	C₂×Q₈×D₅	1	4	yes	—
1058	C₅	#60193	1	1	yes	characteristic, complemented, Sylow
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	5	2	no	—
1062	C₂²	—	5	2	no	—
1063	C₂²	—	10	1	no	—
1064	C₂²	—	10	1	no	—
1065	C₂²	—	10	1	no	—
1066	C₂²	—	10	1	no	—
1067	C₂²	—	20	4	no	—
1068	C₂²	C₄×Q₈×D₅	1	2	yes	—
1069	C₂²	C₂³×C₄×D₅	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	5	2	no	—
1079	C₄	—	5	2	no	—
1080	C₄	—	10	2	no	—
1081	C₄	—	10	2	no	—
1082	C₄	—	10	1	no	—
1083	C₄	—	10	1	no	—
1084	C₄	—	10	2	no	—
1085	C₄	—	10	2	no	—
1086	C₄	—	10	1	no	—
1087	C₄	—	10	1	no	—
1088	C₄	C₄×Q₈×D₅	1	2	yes	—
1089	C₄	C₂²×Q₈×D₅	1	1	yes	characteristic
1090	C₄	C₂×D₅×#41	1	1	yes	characteristic
1091	C₂	—	2	2	no	—
1092	C₂	—	10	2	no	—
1093	C₂	—	10	2	no	—
1094	C₂	C₂×C₄×Q₈×D₅	1	1	yes	characteristic
1095	C₂	#10619061	1	1	yes	characteristic
1096	C₂	#10619067	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅
commutator, socle	C₂²×C₅	C₂⁴×C₄
Fitting	C₅×#2962	C₂
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	#2962	D₅
hypocenter	C₅	#60193
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. C₅×#2962	C₂	semidirect
3. #10615061	C₂	semidirect
4. #10611692	C₂	semidirect
5. #10611692	C₂	semidirect
6. #10611691	C₂	semidirect
7. #10611690	C₂	semidirect
8. #10611690	C₂	semidirect
9. #10611689	C₂	semidirect
10. #10611649	C₂	semidirect
11. #10611648	C₂	semidirect
14. #10610809	C₂	semidirect
15. #10610809	C₂	semidirect
17. #10610739	C₂	semidirect
20. #10610275	C₂	semidirect
21. #10610275	C₂	semidirect
23. #10610239	C₂	semidirect
51. C₅×#446	C₂²	semidirect
52. C₅×#446	C₂²	semidirect
53. C₅×#446	C₂²	semidirect
54. C₅×C₈×Q₈	C₂²	semidirect
73. #65313	C₂²	semidirect
74. #65313	C₂²	semidirect
75. #65313	C₂²	semidirect
76. Q₈×#168	C₂²	semidirect
99. #65120	C₂²	semidirect
100. #65120	C₂²	semidirect
101. #65120	C₂²	semidirect
102. #65119	C₂²	semidirect
103. #65119	C₂²	semidirect
104. #65119	C₂²	semidirect
105. #65117	C₂²	semidirect
106. #65117	C₂²	semidirect
107. #65117	C₂²	semidirect
108. #65117	C₂²	semidirect
109. #65117	C₂²	semidirect
110. #65117	C₂²	semidirect
117. #64990	C₂²	semidirect
118. #64990	C₂²	semidirect
119. #64990	C₂²	semidirect
120. #64990	C₂²	semidirect
121. #64990	C₂²	semidirect
122. #64990	C₂²	semidirect
129. #64968	C₂²	semidirect
130. #64968	C₂²	semidirect
131. #64968	C₂²	semidirect
132. C₈×Dic₁₀	C₂²	semidirect
133. C₈×Dic₁₀	C₂²	semidirect
134. C₈×Dic₁₀	C₂²	semidirect
174. D₅×M₁₆	Q₈	semidirect
327. #2962	D₅	semidirect
519. #446	C₂×D₅	semidirect
520. #446	C₂×D₅	semidirect
521. #446	C₂×D₅	semidirect
529. C₈×Q₈	C₂×D₅	semidirect
1058. C₅	#60193	semidirect

Maximal subgroups

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

subgroup	index
#10618175	2
C₅×#2962	2
#10615061	2
#10611692	2
#10611691	2
#10611690	2
#10611689	2
#10611649	2
#10611648	2
#10610811	2
D₅×#424	2
#10610809	2
C₂×#65128	2
#10610739	2
#10610279	2
D₅×#405	2
#10610275	2
#10610245	2
#10610239	2
#60193	5