Subgroups — #7082441

Order 512.

1556 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59291	C₂	1	1	yes	maximal, characteristic
2	#59096	C₂	1	1	yes	maximal, characteristic
3	#32200	C₂	1	1	yes	maximal, characteristic, complemented
4	#32084	C₂	1	1	yes	maximal, characteristic, complemented
5	#31968	C₂	1	1	yes	maximal, characteristic, complemented
6	#31872	C₂	1	1	yes	maximal, characteristic, complemented
7	#31576	C₂	1	1	yes	maximal, characteristic, complemented
8	#31492	C₂	1	1	yes	maximal, characteristic, complemented
9	#31292	C₂	1	1	yes	maximal, characteristic, complemented
10	#30635	C₂	1	1	yes	maximal, characteristic, complemented
11	#27586	C₂	1	1	yes	maximal, characteristic, complemented
12	#27524	C₂	1	1	yes	maximal, characteristic, complemented
13	#27332	C₂	1	1	yes	maximal, characteristic, complemented
14	#27258	C₂	1	1	yes	maximal, characteristic, complemented
15	#27004	C₂	1	1	yes	maximal, characteristic, complemented
16	#26758	C₂	1	1	yes	maximal, characteristic, complemented
17	#26532	C₂	1	1	yes	maximal, characteristic, complemented
18	#26342	C₂	1	1	yes	maximal, characteristic, complemented
19	#26132	C₂	1	1	yes	maximal, characteristic
20	#25963	C₂	1	1	yes	maximal, characteristic, complemented
21	#25278	C₂	1	1	yes	maximal, characteristic, complemented
22	#25234	C₂	1	1	yes	maximal, characteristic
23	#24482	C₂	1	1	yes	maximal, characteristic, complemented
24	#24482	C₂	1	1	yes	maximal, characteristic, complemented
25	#24064	C₂	1	1	yes	maximal, characteristic, complemented
26	#24042	C₂	1	1	yes	maximal, characteristic
27	C₂×#2068	C₂	1	1	yes	maximal, characteristic, complemented
28	#22922	C₂	1	1	yes	maximal, characteristic, complemented
29	D₄×#103	C₂	1	1	yes	maximal, characteristic
30	#22063	C₂	1	1	yes	maximal, characteristic
31	#21885	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×D₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×#533	C₂²	1	1	yes	characteristic
34	C₂×#487	C₂²	1	1	yes	characteristic
35	C₂×#484	C₂²	1	1	yes	characteristic
36	C₂×#484	C₂²	1	1	yes	characteristic
37	C₂×#484	C₂²	1	1	yes	characteristic
38	C₂×#477	C₂²	1	1	yes	characteristic
39	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
40	C₂²×#107	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂²×#103	C₂²	1	1	yes	characteristic
43	C₂²×#103	C₂²	1	1	yes	characteristic
44	C₂²×#103	C₂²	1	1	yes	characteristic
45	#2774	—	2	1	no	—
46	#2768	—	2	1	no	—
47	#2713	—	2	1	no	—
48	#2704	—	2	1	no	—
49	#2590	—	2	1	no	—
50	#2556	—	2	1	no	—
51	#2552	C₂²	1	1	yes	characteristic
52	#2549	—	2	1	no	—
53	#2546	C₂²	1	1	yes	characteristic
54	#2507	C₂²	1	1	yes	characteristic
55	#2507	C₂²	1	1	yes	characteristic
56	#2497	C₂²	1	1	yes	characteristic
57	#2497	C₂²	1	1	yes	characteristic
58	#2492	C₂²	1	1	yes	characteristic
59	#2487	C₂²	1	1	yes	characteristic
60	#2473	—	2	1	no	—
61	#2465	—	2	1	no	—
62	#2451	—	2	1	no	—
63	#2451	C₂²	1	1	yes	characteristic
64	#2450	—	2	1	no	—
65	#2446	C₂²	1	1	yes	characteristic
66	#2440	C₂²	1	1	yes	characteristic
67	#2440	C₂²	1	1	yes	characteristic
68	#2438	—	2	1	no	—
69	#2438	—	2	1	no	—
70	#2434	C₂²	1	1	yes	characteristic
71	#2434	C₂²	1	1	yes	characteristic
72	#2429	C₂²	1	1	yes	characteristic
73	#2417	—	2	1	no	—
74	#2417	C₂²	1	1	yes	characteristic
75	#2369	C₂²	1	1	yes	characteristic
76	#2365	C₂²	1	1	yes	characteristic
77	#2360	C₂²	1	1	yes	characteristic
78	#2359	—	2	1	no	—
79	#2359	—	2	1	no	—
80	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#2345	C₂²	1	1	yes	characteristic
82	#2345	C₂²	1	1	yes	characteristic
83	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
84	C₄×#123	C₂²	1	1	yes	characteristic
85	C₂×#391	C₂²	1	1	yes	characteristic
86	C₂×#389	C₂²	1	1	yes	characteristic
87	#2285	C₂²	1	1	yes	characteristic
88	#2095	C₂²	1	1	yes	characteristic
89	#2095	C₂²	1	1	yes	characteristic
90	#2095	C₂²	1	1	yes	characteristic
91	#2095	C₂²	1	1	yes	characteristic
92	#2087	C₂²	1	1	yes	characteristic
93	#2087	C₂²	1	1	yes	characteristic
94	#2083	C₂²	1	1	yes	characteristic
95	#2076	C₂²	1	1	yes	characteristic
96	#2076	C₂²	1	1	yes	characteristic
97	#2072	C₂²	1	1	yes	characteristic
98	#2072	C₂²	1	1	yes	characteristic
99	#2072	C₂²	1	1	yes	characteristic
100	#2068	C₂²	1	1	yes	characteristic
101	#2068	C₂²	1	1	yes	characteristic
102	#2068	C₂²	1	1	yes	characteristic
103	#2068	C₂²	1	1	yes	characteristic
104	#2068	C₂²	1	1	yes	characteristic
105	#2068	C₂²	1	1	yes	characteristic
106	#2068	C₂²	1	1	yes	characteristic
107	#2068	C₂²	1	1	yes	characteristic
108	#2068	C₂²	1	1	yes	characteristic
109	#2068	C₂²	1	1	yes	characteristic
110	#2068	C₂²	1	1	yes	characteristic
111	#2068	C₂²	1	1	yes	characteristic
112	#2057	C₂²	1	1	yes	characteristic
113	#2057	C₂²	1	1	yes	characteristic
114	#2057	C₂²	1	1	yes	characteristic
115	#2043	C₂²	1	1	yes	characteristic
116	#2043	C₂²	1	1	yes	characteristic
117	#2043	C₂²	1	1	yes	characteristic
118	#2043	C₂²	1	1	yes	characteristic
119	#2043	C₂²	1	1	yes	characteristic
120	#2043	C₂²	1	1	yes	characteristic
121	#2043	C₂²	1	1	yes	characteristic
122	#2043	C₂²	1	1	yes	characteristic
123	#2036	C₂²	1	1	yes	characteristic
124	#2036	C₂²	1	1	yes	characteristic
125	#2036	C₂²	1	1	yes	characteristic
126	#2036	C₂²	1	1	yes	characteristic
127	#2024	C₂²	1	1	yes	characteristic
128	#1987	C₂²	1	1	yes	characteristic
129	#1987	C₂²	1	1	yes	characteristic
130	#1981	C₂²	1	1	yes	characteristic
131	#1981	C₂²	1	1	yes	characteristic
132	#1981	C₂²	1	1	yes	characteristic
133	#1981	C₂²	1	1	yes	characteristic
134	#1981	C₂²	1	1	yes	characteristic
135	#1956	C₂²	1	1	yes	characteristic
136	#1956	C₂²	1	1	yes	characteristic
137	#1947	C₂²	1	1	yes	characteristic
138	#1942	C₂²	1	1	yes	characteristic
139	#1942	C₂²	1	1	yes	characteristic
140	#1939	C₂²	1	1	yes	characteristic
141	#1939	C₂²	1	1	yes	characteristic
142	#1933	C₂²	1	1	yes	characteristic
143	#1933	C₂²	1	1	yes	characteristic
144	#1933	C₂²	1	1	yes	characteristic
145	#1933	C₂²	1	1	yes	characteristic
146	#1928	C₂²	1	1	yes	characteristic
147	#1928	C₂²	1	1	yes	characteristic
148	#1928	C₂²	1	1	yes	characteristic
149	#1928	C₂²	1	1	yes	characteristic
150	#1928	C₂²	1	1	yes	characteristic
151	#1928	C₂²	1	1	yes	characteristic
152	#1928	C₂²	1	1	yes	characteristic
153	#1928	C₂²	1	1	yes	characteristic
154	#1923	C₂²	1	1	yes	characteristic
155	#1923	C₂²	1	1	yes	characteristic
156	#1921	C₂²	1	1	yes	characteristic
157	#1921	C₂²	1	1	yes	characteristic
158	#1921	C₂²	1	1	yes	characteristic
159	#1921	C₂²	1	1	yes	characteristic
160	#1916	C₂²	1	1	yes	characteristic
161	#1916	C₂²	1	1	yes	characteristic
162	#1892	C₂²	1	1	yes	characteristic
163	#1892	C₂²	1	1	yes	characteristic
164	#1892	C₂²	1	1	yes	characteristic
165	#1892	C₂²	1	1	yes	characteristic
166	#1892	C₂²	1	1	yes	characteristic
167	#1892	C₂²	1	1	yes	characteristic
168	#1872	C₂²	1	1	yes	characteristic
169	#1872	C₂²	1	1	yes	characteristic
170	#1872	C₂²	1	1	yes	characteristic
171	#1869	C₂²	1	1	yes	characteristic
172	#1863	C₂²	1	1	yes	characteristic
173	#1863	C₂²	1	1	yes	characteristic
174	#1863	C₂²	1	1	yes	characteristic
175	#1863	C₂²	1	1	yes	characteristic
176	#1863	C₂²	1	1	yes	characteristic
177	#1863	C₂²	1	1	yes	characteristic
178	#1863	C₂²	1	1	yes	characteristic
179	#1863	C₂²	1	1	yes	characteristic
180	#1852	C₂²	1	1	yes	characteristic
181	#1852	C₂²	1	1	yes	characteristic
182	#1852	C₂²	1	1	yes	characteristic
183	#1850	C₂²	1	1	yes	characteristic
184	#1850	C₂²	1	1	yes	characteristic
185	#1850	C₂²	1	1	yes	characteristic
186	#1817	C₂²	1	1	yes	characteristic
187	#1808	C₂²	1	1	yes	characteristic
188	#1803	C₂²	1	1	yes	characteristic
189	#1803	C₂²	1	1	yes	characteristic
190	#1803	C₂²	1	1	yes	characteristic
191	#1803	C₂²	1	1	yes	characteristic
192	#1803	C₂²	1	1	yes	characteristic
193	#1787	C₂²	1	1	yes	characteristic
194	#1787	C₂²	1	1	yes	characteristic
195	#1787	C₂²	1	1	yes	characteristic
196	#1787	C₂²	1	1	yes	characteristic
197	#1787	C₂²	1	1	yes	characteristic
198	C₄×#107	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	C₄×#103	C₂²	1	1	yes	characteristic
201	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
202	C₂×#340	C₂²	1	1	yes	characteristic
203	C₂³×Q₈	C₂³	1	1	yes	characteristic
204	C₂³×Q₈	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	D₄×Q₈	—	2	4	no	—
209	D₄×Q₈	—	4	2	no	—
210	#533	—	2	4	no	—
211	#533	—	4	2	no	—
212	C₂×C₄⋊Q₈	—	2	1	no	—
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×#125	—	2	1	no	—
220	C₂×#125	—	2	1	no	—
221	C₂×#123	D₄	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	—	2	1	no	—
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×C₂²⋊Q₈	—	2	1	no	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	—	2	1	no	—
232	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	—	2	1	no	—
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×#117	—	2	1	no	—
240	C₂×#117	—	2	1	no	—
241	C₂²×C₄⋊C₄	—	2	1	no	—
242	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂²×C₄²	C₂³	1	1	yes	characteristic
247	#487	—	4	2	no	—
248	#484	—	2	4	no	—
249	#484	—	4	2	no	—
250	#484	—	4	2	no	—
251	#477	—	4	2	no	—
252	C₈×D₄	—	4	2	no	—
253	C₂×#107	—	4	2	no	—
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#107	C₂³	1	1	yes	characteristic
256	C₂×#107	C₂³	1	1	yes	characteristic
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#107	C₂³	1	1	yes	characteristic
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#107	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	—	4	2	no	—
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×#103	—	4	2	no	—
275	C₂×#103	—	4	2	no	—
276	C₂×#103	—	4	2	no	—
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#103	C₂³	1	1	yes	characteristic
302	C₂×#103	C₂³	1	1	yes	characteristic
303	C₂×#103	C₂³	1	1	yes	characteristic
304	C₂×#103	C₂³	1	1	yes	characteristic
305	C₂×#103	C₂³	1	1	yes	characteristic
306	C₂×#103	C₂³	1	1	yes	characteristic
307	C₂×#103	C₂³	1	1	yes	characteristic
308	C₂×#103	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
317	#400	—	2	1	no	—
318	#400	—	2	1	no	—
319	#400	—	2	1	no	—
320	#400	—	2	1	no	—
321	#400	—	2	1	no	—
322	#399	—	2	1	no	—
323	#398	—	2	1	no	—
324	#398	—	2	1	no	—
325	#398	—	2	1	no	—
326	#398	—	2	1	no	—
327	#398	—	2	1	no	—
328	#398	—	2	1	no	—
329	#398	—	2	1	no	—
330	#398	—	2	1	no	—
331	#398	—	2	1	no	—
332	#398	—	2	1	no	—
333	#398	—	2	1	no	—
334	#398	—	2	1	no	—
335	#398	—	2	1	no	—
336	#398	—	2	1	no	—
337	#396	—	2	1	no	—
338	#396	—	2	1	no	—
339	#396	—	2	1	no	—
340	#396	—	2	1	no	—
341	#395	—	2	1	no	—
342	#395	—	2	1	no	—
343	#395	—	2	1	no	—
344	#395	—	2	1	no	—
345	#395	—	2	1	no	—
346	#395	—	2	1	no	—
347	#395	—	2	1	no	—
348	#393	—	2	1	no	—
349	#391	—	2	1	no	—
350	#391	—	2	1	no	—
351	#391	—	2	1	no	—
352	#391	—	2	1	no	—
353	#391	—	2	1	no	—
354	#391	—	2	1	no	—
355	#391	—	2	1	no	—
356	#391	—	2	1	no	—
357	#391	C₂³	1	1	yes	characteristic
358	#391	C₂³	1	1	yes	characteristic
359	#391	C₂³	1	1	yes	characteristic
360	#391	C₂³	1	1	yes	characteristic
361	#391	C₂³	1	1	yes	characteristic
362	#391	C₂³	1	1	yes	characteristic
363	#391	C₂³	1	1	yes	characteristic
364	#391	C₂³	1	1	yes	characteristic
365	#389	—	2	1	no	—
366	#389	—	2	1	no	—
367	#389	—	2	1	no	—
368	#389	—	2	1	no	—
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	—	2	1	no	—
372	#389	—	2	1	no	—
373	#389	—	2	1	no	—
374	#389	—	2	1	no	—
375	#389	—	2	1	no	—
376	#389	—	2	1	no	—
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#389	C₂³	1	1	yes	characteristic
381	#389	C₂³	1	1	yes	characteristic
382	#389	C₂³	1	1	yes	characteristic
383	#389	C₂³	1	1	yes	characteristic
384	#389	C₂³	1	1	yes	characteristic
385	#389	C₂³	1	1	yes	characteristic
386	#389	C₂³	1	1	yes	characteristic
387	#389	C₂³	1	1	yes	characteristic
388	#389	C₂³	1	1	yes	characteristic
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	D₄	1	1	yes	characteristic
394	#388	D₄	1	1	yes	characteristic
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	D₄	1	1	yes	characteristic
410	#387	D₄	1	1	yes	characteristic
411	#386	—	2	1	no	—
412	#386	—	2	1	no	—
413	#386	D₄	1	1	yes	characteristic
414	#385	—	2	1	no	—
415	#385	—	2	1	no	—
416	#385	—	2	1	no	—
417	#385	—	2	1	no	—
418	#385	—	2	1	no	—
419	#385	—	2	1	no	—
420	#385	—	2	1	no	—
421	#385	—	2	1	no	—
422	#385	—	2	1	no	—
423	#385	—	2	1	no	—
424	#385	D₄	1	1	yes	characteristic
425	#384	C₂³	1	1	yes	characteristic
426	#384	C₂³	1	1	yes	characteristic
427	#384	C₂³	1	1	yes	characteristic
428	#384	C₂³	1	1	yes	characteristic
429	#382	—	2	1	no	—
430	#381	D₄	1	1	yes	characteristic
431	#380	—	2	1	no	—
432	#380	—	2	1	no	—
433	#380	—	2	1	no	—
434	#380	—	2	1	no	—
435	#380	—	2	1	no	—
436	#380	C₂³	1	1	yes	characteristic
437	#380	C₂³	1	1	yes	characteristic
438	#380	C₂³	1	1	yes	characteristic
439	#380	C₂³	1	1	yes	characteristic
440	#380	C₂³	1	1	yes	characteristic
441	#380	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	—	2	1	no	—
443	C₄×C₄⋊C₄	—	2	1	no	—
444	C₄×C₄⋊C₄	—	2	1	no	—
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	C₄×C₂²⋊C₄	—	2	1	no	—
457	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
460	C₂×#95	—	2	1	no	—
461	C₂×#95	—	2	1	no	—
462	C₂×#95	—	2	1	no	—
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	—	2	2	no	—
498	C₂²×Q₈	—	2	2	no	—
499	C₂²×Q₈	—	2	2	no	—
500	C₂²×Q₈	—	2	2	no	—
501	C₂²×Q₈	—	2	2	no	—
502	C₂²×Q₈	—	4	1	no	—
503	C₂²×Q₈	—	4	1	no	—
504	C₂²×Q₈	—	4	1	no	—
505	C₂²×Q₈	—	4	1	no	—
506	C₂²×Q₈	—	4	1	no	—
507	C₂²×Q₈	—	4	1	no	—
508	C₂²×Q₈	—	4	1	no	—
509	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
510	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
511	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
512	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
513	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
521	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
522	C₂³×C₄	C₂⁴	1	1	yes	characteristic
523	C₂³×C₄	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	—	2	2	no	—
525	C₂²×C₈	—	2	2	no	—
526	C₂²×C₈	—	4	1	no	—
527	C₂²×C₈	—	4	1	no	—
528	C₂²×C₈	—	4	1	no	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	—	4	1	no	—
532	C₂²×C₈	—	4	1	no	—
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₂²×C₈	C₂⁴	1	1	yes	characteristic
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	—	4	1	no	—
547	C₄⋊Q₈	—	4	1	no	—
548	C₄⋊Q₈	—	4	1	no	—
549	C₄⋊Q₈	—	4	1	no	—
550	C₄⋊Q₈	—	4	1	no	—
551	C₄⋊Q₈	—	4	1	no	—
552	C₄⋊Q₈	—	4	1	no	—
553	C₄⋊Q₈	—	4	4	no	—
554	#125	—	4	4	no	—
555	#125	—	8	2	no	—
556	#123	Q₁₆	1	8	yes	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	4	4	no	—
562	C₂²⋊Q₈	—	4	4	no	—
563	C₂²⋊Q₈	—	4	4	no	—
564	C₂²⋊Q₈	—	4	1	no	—
565	C₂²⋊Q₈	—	4	1	no	—
566	C₂²⋊Q₈	—	4	1	no	—
567	C₂²⋊Q₈	—	8	2	no	—
568	C₂²⋊Q₈	—	8	2	no	—
569	C₂²⋊Q₈	#41	1	4	yes	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	4	1	no	—
574	C₄×Q₈	—	4	1	no	—
575	C₄×Q₈	—	4	1	no	—
576	C₄×Q₈	—	4	4	no	—
577	C₄×Q₈	—	4	1	no	—
578	C₄×Q₈	—	4	1	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	4	4	no	—
582	C₄×D₄	—	8	2	no	—
583	#117	—	4	4	no	—
584	#117	—	8	2	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	2	no	—
587	C₂×C₄⋊C₄	—	2	2	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	—	2	2	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	4	1	no	—
632	C₂×C₄⋊C₄	—	4	1	no	—
633	C₂×C₄⋊C₄	—	4	1	no	—
634	C₂×C₄⋊C₄	—	4	1	no	—
635	C₂×C₄⋊C₄	—	8	2	no	—
636	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	—	2	2	no	—
672	C₂×C₄²	—	2	2	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
684	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
685	C₂×C₄²	C₂⁴	1	1	yes	characteristic
686	C₂×C₄²	C₂⁴	1	1	yes	characteristic
687	C₂×C₄²	C₂⁴	1	1	yes	characteristic
688	C₂×C₄²	C₂⁴	1	1	yes	characteristic
689	C₂×C₄²	C₂⁴	1	1	yes	characteristic
690	#107	—	2	2	no	—
691	#107	—	2	2	no	—
692	#107	—	2	2	no	—
693	#107	—	2	2	no	—
694	#107	—	4	1	no	—
695	#107	—	4	1	no	—
696	#107	—	4	1	no	—
697	#107	—	4	1	no	—
698	#107	—	4	1	no	—
699	#107	—	4	1	no	—
700	#107	—	4	1	no	—
701	#107	—	4	1	no	—
702	C₄⋊C₈	—	4	1	no	—
703	C₄⋊C₈	—	4	1	no	—
704	C₄⋊C₈	—	4	1	no	—
705	C₄⋊C₈	—	4	1	no	—
706	C₄⋊C₈	—	4	1	no	—
707	C₄⋊C₈	—	4	1	no	—
708	C₄⋊C₈	—	4	1	no	—
709	#103	—	2	2	no	—
710	#103	—	2	2	no	—
711	#103	—	2	2	no	—
712	#103	—	2	2	no	—
713	#103	—	2	2	no	—
714	#103	—	2	2	no	—
715	#103	—	2	2	no	—
716	#103	—	2	2	no	—
717	#103	—	4	1	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#103	—	4	1	no	—
724	#103	—	4	1	no	—
725	#103	—	4	1	no	—
726	#103	—	4	1	no	—
727	#103	—	4	1	no	—
728	#103	—	4	1	no	—
729	#103	—	4	1	no	—
730	#103	—	4	1	no	—
731	#103	—	4	1	no	—
732	#103	—	4	1	no	—
733	#103	—	4	1	no	—
734	#103	—	4	1	no	—
735	#103	—	4	1	no	—
736	#103	—	4	1	no	—
737	#103	—	4	1	no	—
738	#103	—	4	1	no	—
739	#103	—	4	1	no	—
740	#103	—	4	1	no	—
741	C₂²⋊C₈	—	2	2	no	—
742	C₂²⋊C₈	—	2	2	no	—
743	C₂²⋊C₈	—	4	1	no	—
744	C₂²⋊C₈	—	4	1	no	—
745	C₂²⋊C₈	—	4	1	no	—
746	C₄×C₈	—	4	1	no	—
747	C₄×C₈	—	4	1	no	—
748	C₄×C₈	—	4	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	#95	C₂×D₄	1	1	yes	characteristic
792	#95	C₂×D₄	1	1	yes	characteristic
793	#95	C₂×D₄	1	1	yes	characteristic
794	#95	C₂×D₄	1	1	yes	characteristic
795	#95	C₂×D₄	1	1	yes	characteristic
796	#95	C₂×D₄	1	1	yes	characteristic
797	#95	C₂×D₄	1	1	yes	characteristic
798	#95	C₂×D₄	1	1	yes	characteristic
799	C₂⁴	C₂²×D₄	1	1	yes	characteristic
800	C₂⁴	C₂²×D₄	1	1	yes	characteristic
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	—	4	2	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×Q₈	—	4	2	no	—
827	C₂×Q₈	—	4	2	no	—
828	C₂×Q₈	—	4	2	no	—
829	C₂×Q₈	—	4	4	no	—
830	C₂×Q₈	—	4	4	no	—
831	C₂×Q₈	—	4	2	no	—
832	C₂×Q₈	—	4	4	no	—
833	C₂×Q₈	—	8	1	no	—
834	C₂×Q₈	—	8	1	no	—
835	C₂×Q₈	—	8	1	no	—
836	C₂×Q₈	—	8	1	no	—
837	C₂×Q₈	—	8	1	no	—
838	C₂×Q₈	—	8	2	no	—
839	C₂×Q₈	—	8	2	no	—
840	C₂×Q₈	—	8	2	no	—
841	C₂×Q₈	—	8	2	no	—
842	C₂×Q₈	—	8	2	no	—
843	C₂×Q₈	C₂×#41	1	2	yes	—
844	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	C₂×Q₁₆	1	4	yes	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	4	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	8	1	no	—
889	C₂²×C₄	—	8	1	no	—
890	C₂²×C₄	—	8	1	no	—
891	C₂²×C₄	—	8	1	no	—
892	C₂²×C₄	—	8	1	no	—
893	C₂²×C₄	—	8	1	no	—
894	C₂²×C₄	—	8	1	no	—
895	C₂²×C₄	—	8	1	no	—
896	C₂²×C₄	—	8	1	no	—
897	C₂²×C₄	C₂×Q₁₆	1	4	yes	—
898	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
901	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
902	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
904	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
909	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
910	C₂²×C₄	C₂×#41	1	2	yes	—
911	C₂²×C₄	H(5,𝔽₂)	1	2	yes	—
912	C₂²×C₄	C₂⁵	1	1	yes	characteristic
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	2	1	no	—
936	C₂×C₈	—	2	1	no	—
937	C₂×C₈	—	4	4	no	—
938	C₂×C₈	—	8	2	no	—
939	C₂×C₈	—	8	2	no	—
940	C₄⋊C₄	—	2	4	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	4	1	no	—
965	C₄⋊C₄	—	4	1	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	—	4	2	no	—
982	C₄⋊C₄	—	4	2	no	—
983	C₄⋊C₄	—	4	2	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	—	8	1	no	—
992	C₄⋊C₄	—	8	1	no	—
993	C₄⋊C₄	—	8	1	no	—
994	C₄⋊C₄	—	8	1	no	—
995	C₄⋊C₄	—	8	1	no	—
996	C₄⋊C₄	—	8	1	no	—
997	C₄⋊C₄	—	8	1	no	—
998	C₄⋊C₄	—	8	1	no	—
999	C₄⋊C₄	—	8	1	no	—
1000	C₄⋊C₄	—	8	1	no	—
1001	C₄⋊C₄	—	8	1	no	—
1002	C₄⋊C₄	—	8	1	no	—
1003	C₄⋊C₄	—	8	1	no	—
1004	C₄⋊C₄	—	8	1	no	—
1005	C₄⋊C₄	—	8	1	no	—
1006	C₄⋊C₄	—	8	1	no	—
1007	C₄⋊C₄	C₂×Q₁₆	1	4	yes	—
1008	C₄⋊C₄	C₂×Q₁₆	1	4	yes	—
1009	C₄⋊C₄	C₂×#41	1	2	yes	—
1010	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1011	C₂²⋊C₄	—	2	4	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	4	1	no	—
1016	C₂²⋊C₄	—	4	1	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	—	4	2	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	C₂×Q₁₆	1	4	yes	—
1027	C₂²⋊C₄	C₂×Q₁₆	1	4	yes	—
1028	C₂²⋊C₄	C₂×Q₁₆	1	4	yes	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	—	4	2	no	—
1044	C₄²	—	8	1	no	—
1045	C₄²	—	8	1	no	—
1046	C₄²	—	8	1	no	—
1047	C₄²	—	8	1	no	—
1048	C₄²	—	8	1	no	—
1049	C₄²	—	8	1	no	—
1050	C₄²	—	8	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	#546	1	2	yes	—
1062	C₂³	C₂²×Q₁₆	1	2	yes	—
1063	C₂³	C₂²×Q₁₆	1	2	yes	—
1064	C₂³	#577	1	2	yes	—
1065	C₂³	C₂³×D₄	1	1	yes	characteristic
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	4	1	no	—
1071	Q₈	—	4	1	no	—
1072	Q₈	—	4	1	no	—
1073	Q₈	—	4	1	no	—
1074	Q₈	—	4	1	no	—
1075	Q₈	—	4	1	no	—
1076	Q₈	—	4	1	no	—
1077	Q₈	—	4	1	no	—
1078	Q₈	—	4	1	no	—
1079	Q₈	—	4	1	no	—
1080	Q₈	—	4	1	no	—
1081	Q₈	—	4	1	no	—
1082	Q₈	—	8	4	no	—
1083	Q₈	—	8	4	no	—
1084	Q₈	—	8	4	no	—
1085	Q₈	—	16	2	no	—
1086	D₄	—	2	8	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	8	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	—	8	4	no	—
1176	C₂×C₄	—	8	4	no	—
1177	C₂×C₄	—	8	4	no	—
1178	C₂×C₄	—	16	2	no	—
1179	C₂×C₄	—	16	2	no	—
1180	C₂×C₄	—	16	2	no	—
1181	C₂×C₄	#546	1	2	yes	—
1182	C₂×C₄	C₂²×Q₁₆	1	2	yes	—
1183	C₂×C₄	C₂²×Q₁₆	1	2	yes	—
1184	C₂×C₄	C₂²×Q₁₆	1	2	yes	—
1185	C₂×C₄	C₂²×Q₁₆	1	2	yes	—
1186	C₂×C₄	C₂²×Q₁₆	1	2	yes	—
1187	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1188	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1191	C₂×C₄	#585	1	1	yes	characteristic
1192	C₂×C₄	#585	1	1	yes	characteristic
1193	C₈	—	4	1	no	—
1194	C₈	—	4	1	no	—
1195	C₈	—	4	1	no	—
1196	C₈	—	4	1	no	—
1197	C₈	—	4	1	no	—
1198	C₈	—	4	1	no	—
1199	C₈	—	4	1	no	—
1200	C₈	—	4	1	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	#3299	1	4	yes	—
1215	C₂²	C₂×#546	1	1	yes	characteristic
1216	C₂²	#3488	1	1	yes	characteristic
1217	C₂²	#3489	1	1	yes	characteristic
1218	C₂²	C₂³×Q₁₆	1	1	yes	characteristic
1219	C₂²	C₂×#577	1	1	yes	characteristic
1220	C₂²	#3585	1	1	yes	characteristic
1221	C₂²	#3586	1	1	yes	characteristic
1222	C₄	—	2	2	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	2	2	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	2	no	—
1230	C₄	—	4	2	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	2	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	—	8	1	no	—
1249	C₄	—	8	1	no	—
1250	C₄	#3520	1	1	yes	characteristic
1251	C₄	#3521	1	1	yes	characteristic
1252	C₄	#3535	1	1	yes	characteristic
1253	C₄	#3542	1	1	yes	characteristic
1254	C₂	—	2	4	no	—
1255	C₂	—	4	2	no	—
1256	C₂	#44044	1	1	yes	characteristic
1257	C₂	C₂×#3299	1	1	yes	characteristic
1258	C₂	#61182	1	1	yes	characteristic
1259	C₂	#61952	1	1	yes	characteristic
1260	C₂	#62016	1	1	yes	characteristic
1261	C₂	#62100	1	1	yes	characteristic
1262	C₂	#62167	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×D₄	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#123 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #32200	C₂	semidirect
4. #32084	C₂	semidirect
5. #31968	C₂	semidirect
6. #31872	C₂	semidirect
7. #31576	C₂	semidirect
8. #31492	C₂	semidirect
9. #31292	C₂	semidirect
10. #30635	C₂	semidirect
11. #27586	C₂	semidirect
12. #27524	C₂	semidirect
13. #27332	C₂	semidirect
14. #27258	C₂	semidirect
15. #27004	C₂	semidirect
16. #26758	C₂	semidirect
17. #26532	C₂	semidirect
18. #26342	C₂	semidirect
20. #25963	C₂	semidirect
21. #25278	C₂	semidirect
23. #24482	C₂	semidirect
24. #24482	C₂	semidirect
25. #24064	C₂	semidirect
27. C₂×#2068	C₂	semidirect
28. #22922	C₂	semidirect
31. #21885	C₂	semidirect

Maximal subgroups

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

subgroup	index
#59291	2
#59096	2
#32200	2
#32084	2
#31968	2
#31872	2
#31576	2
#31492	2
#31292	2
#30635	2
#27586	2
#27524	2
#27332	2
#27258	2
#27004	2
#26758	2
#26532	2
#26342	2
#26132	2
#25963	2
#25278	2
#25234	2
#24482	2
#24064	2
#24042	2
C₂×#2068	2
#22922	2
D₄×#103	2
#22063	2
#21885	2