Subgroups — #7298382

Order 512.

1440 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#42698	C₂	1	1	yes	maximal, characteristic, complemented
2	#42481	C₂	1	1	yes	maximal, characteristic, complemented
3	#32813	C₂	1	1	yes	maximal, characteristic, complemented
4	#32671	C₂	1	1	yes	maximal, characteristic, complemented
5	#32638	C₂	1	1	yes	maximal, characteristic, complemented
6	#32618	C₂	1	1	yes	maximal, characteristic, complemented
7	#32575	C₂	1	1	yes	maximal, characteristic, complemented
8	#31922	C₂	1	1	yes	maximal, characteristic, complemented
9	#31829	C₂	1	1	yes	maximal, characteristic, complemented
10	#31658	C₂	1	1	yes	maximal, characteristic
11	#31525	C₂	1	1	yes	maximal, characteristic, complemented
12	#31218	C₂	1	1	yes	maximal, characteristic
13	#31177	C₂	1	1	yes	maximal, characteristic, complemented
14	#30899	C₂	1	1	yes	maximal, characteristic, complemented
15	#30739	C₂	1	1	yes	maximal, characteristic, complemented
16	#29570	C₂	1	1	yes	maximal, characteristic, complemented
17	#29568	C₂	1	1	yes	maximal, characteristic, complemented
18	#29542	C₂	1	1	yes	maximal, characteristic, complemented
19	#29075	C₂	1	1	yes	maximal, characteristic, complemented
20	#28881	C₂	1	1	yes	maximal, characteristic, complemented
21	#27007	C₂	1	1	yes	maximal, characteristic, complemented
22	#26911	C₂	1	1	yes	maximal, characteristic, complemented
23	#26846	C₂	1	1	yes	maximal, characteristic, complemented
24	#26717	C₂	1	1	yes	maximal, characteristic, complemented
25	#26588	C₂	1	1	yes	maximal, characteristic, complemented
26	#26251	C₂	1	1	yes	maximal, characteristic, complemented
27	#25939	C₂	1	1	yes	maximal, characteristic, complemented
28	#25635	C₂	1	1	yes	maximal, characteristic
29	#24330	C₂	1	1	yes	maximal, characteristic, complemented
30	#24202	C₂	1	1	yes	maximal, characteristic, complemented
31	#22310	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#559	C₂²	1	1	yes	characteristic
33	C₂×D₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×#495	C₂²	1	1	yes	characteristic
35	C₂×#489	C₂²	1	1	yes	characteristic
36	C₂×#475	C₂²	1	1	yes	characteristic
37	C₂×#460	C₂²	1	1	yes	characteristic
38	C₂×#463	C₂²	1	1	yes	characteristic
39	C₂×#463	C₂²	1	1	yes	characteristic
40	C₂×#441	C₂²	1	1	yes	characteristic
41	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
42	#2838	—	2	1	no	—
43	#2814	—	2	1	no	—
44	#2747	—	2	1	no	—
45	#2745	—	2	1	no	—
46	#2742	—	2	1	no	—
47	#2738	—	2	1	no	—
48	#2700	—	2	1	no	—
49	#2700	—	2	1	no	—
50	#2680	—	2	1	no	—
51	#2680	—	2	1	no	—
52	#2654	—	2	1	no	—
53	#2650	—	2	1	no	—
54	#2642	C₂²	1	1	yes	characteristic
55	#2640	C₂²	1	1	yes	characteristic
56	#2638	—	2	1	no	—
57	#2614	—	2	1	no	—
58	#2592	C₂²	1	1	yes	characteristic
59	#2592	C₂²	1	1	yes	characteristic
60	#2592	C₂²	1	1	yes	characteristic
61	#2582	C₂²	1	1	yes	characteristic
62	#2581	C₂²	1	1	yes	characteristic
63	#2567	C₂²	1	1	yes	characteristic
64	#2566	C₂²	1	1	yes	characteristic
65	#2547	C₂²	1	1	yes	characteristic
66	#2525	—	2	1	no	—
67	#2514	C₂²	1	1	yes	characteristic
68	#2511	C₂²	1	1	yes	characteristic
69	#2452	C₂²	1	1	yes	characteristic
70	#2452	C₂²	1	1	yes	characteristic
71	#2451	C₂²	1	1	yes	characteristic
72	#2451	C₂²	1	1	yes	characteristic
73	#2448	C₂²	1	1	yes	characteristic
74	#2448	C₂²	1	1	yes	characteristic
75	#2447	C₂²	1	1	yes	characteristic
76	#2447	C₂²	1	1	yes	characteristic
77	#2445	C₂²	1	1	yes	characteristic
78	#2445	C₂²	1	1	yes	characteristic
79	#2409	—	2	1	no	—
80	#2399	C₂²	1	1	yes	characteristic
81	#2370	C₂²	1	1	yes	characteristic
82	#2365	C₂²	1	1	yes	characteristic
83	#2319	C₂²	1	1	yes	characteristic
84	#2319	C₂²	1	1	yes	characteristic
85	#2101	C₂²	1	1	yes	characteristic
86	#2095	C₂²	1	1	yes	characteristic
87	#2088	C₂²	1	1	yes	characteristic
88	#2088	C₂²	1	1	yes	characteristic
89	#2085	C₂²	1	1	yes	characteristic
90	#2071	C₂²	1	1	yes	characteristic
91	#2068	C₂²	1	1	yes	characteristic
92	#2067	C₂²	1	1	yes	characteristic
93	#2067	C₂²	1	1	yes	characteristic
94	#2067	C₂²	1	1	yes	characteristic
95	#2066	C₂²	1	1	yes	characteristic
96	#2065	C₂²	1	1	yes	characteristic
97	#2059	C₂²	1	1	yes	characteristic
98	#2058	C₂²	1	1	yes	characteristic
99	#2058	C₂²	1	1	yes	characteristic
100	#2056	C₂²	1	1	yes	characteristic
101	#2056	C₂²	1	1	yes	characteristic
102	#2056	C₂²	1	1	yes	characteristic
103	#2056	C₂²	1	1	yes	characteristic
104	#2055	C₂²	1	1	yes	characteristic
105	#2055	C₂²	1	1	yes	characteristic
106	#2054	C₂²	1	1	yes	characteristic
107	#2054	C₂²	1	1	yes	characteristic
108	#2043	C₂²	1	1	yes	characteristic
109	#2042	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2042	C₂²	1	1	yes	characteristic
112	#2042	C₂²	1	1	yes	characteristic
113	#2026	C₂²	1	1	yes	characteristic
114	#2025	C₂²	1	1	yes	characteristic
115	#2025	C₂²	1	1	yes	characteristic
116	#2024	C₂²	1	1	yes	characteristic
117	#2024	C₂²	1	1	yes	characteristic
118	#2024	C₂²	1	1	yes	characteristic
119	#2024	C₂²	1	1	yes	characteristic
120	#2023	C₂²	1	1	yes	characteristic
121	#2023	C₂²	1	1	yes	characteristic
122	#2016	C₂²	1	1	yes	characteristic
123	#2015	C₂²	1	1	yes	characteristic
124	#2015	C₂²	1	1	yes	characteristic
125	#2015	C₂²	1	1	yes	characteristic
126	#2015	C₂²	1	1	yes	characteristic
127	#2014	C₂²	1	1	yes	characteristic
128	#2013	C₂²	1	1	yes	characteristic
129	#2013	C₂²	1	1	yes	characteristic
130	#2012	C₂²	1	1	yes	characteristic
131	#2012	C₂²	1	1	yes	characteristic
132	#2011	C₂²	1	1	yes	characteristic
133	#1990	C₂²	1	1	yes	characteristic
134	#1987	C₂²	1	1	yes	characteristic
135	#1985	C₂²	1	1	yes	characteristic
136	#1985	C₂²	1	1	yes	characteristic
137	#1984	C₂²	1	1	yes	characteristic
138	#1984	C₂²	1	1	yes	characteristic
139	#1983	C₂²	1	1	yes	characteristic
140	#1973	C₂²	1	1	yes	characteristic
141	#1973	C₂²	1	1	yes	characteristic
142	#1972	C₂²	1	1	yes	characteristic
143	#1968	C₂²	1	1	yes	characteristic
144	#1968	C₂²	1	1	yes	characteristic
145	#1968	C₂²	1	1	yes	characteristic
146	#1968	C₂²	1	1	yes	characteristic
147	#1961	C₂²	1	1	yes	characteristic
148	#1941	C₂²	1	1	yes	characteristic
149	#1940	C₂²	1	1	yes	characteristic
150	#1940	C₂²	1	1	yes	characteristic
151	#1936	C₂²	1	1	yes	characteristic
152	#1935	C₂²	1	1	yes	characteristic
153	#1935	C₂²	1	1	yes	characteristic
154	#1935	C₂²	1	1	yes	characteristic
155	#1935	C₂²	1	1	yes	characteristic
156	#1934	C₂²	1	1	yes	characteristic
157	#1933	C₂²	1	1	yes	characteristic
158	#1933	C₂²	1	1	yes	characteristic
159	#1928	C₂²	1	1	yes	characteristic
160	#1927	C₂²	1	1	yes	characteristic
161	#1927	C₂²	1	1	yes	characteristic
162	#1927	C₂²	1	1	yes	characteristic
163	#1926	C₂²	1	1	yes	characteristic
164	#1926	C₂²	1	1	yes	characteristic
165	#1926	C₂²	1	1	yes	characteristic
166	#1926	C₂²	1	1	yes	characteristic
167	#1920	C₂²	1	1	yes	characteristic
168	#1919	C₂²	1	1	yes	characteristic
169	#1918	C₂²	1	1	yes	characteristic
170	#1918	C₂²	1	1	yes	characteristic
171	#1917	C₂²	1	1	yes	characteristic
172	#1917	C₂²	1	1	yes	characteristic
173	#1916	C₂²	1	1	yes	characteristic
174	#1916	C₂²	1	1	yes	characteristic
175	#1880	C₂²	1	1	yes	characteristic
176	#1880	C₂²	1	1	yes	characteristic
177	#1879	C₂²	1	1	yes	characteristic
178	#1879	C₂²	1	1	yes	characteristic
179	#1879	C₂²	1	1	yes	characteristic
180	#1879	C₂²	1	1	yes	characteristic
181	#1878	C₂²	1	1	yes	characteristic
182	#1878	C₂²	1	1	yes	characteristic
183	#1877	C₂²	1	1	yes	characteristic
184	#1877	C₂²	1	1	yes	characteristic
185	#1877	C₂²	1	1	yes	characteristic
186	#1877	C₂²	1	1	yes	characteristic
187	#1877	C₂²	1	1	yes	characteristic
188	#1877	C₂²	1	1	yes	characteristic
189	#1865	C₂²	1	1	yes	characteristic
190	#1865	C₂²	1	1	yes	characteristic
191	#1864	C₂²	1	1	yes	characteristic
192	#1864	C₂²	1	1	yes	characteristic
193	#1864	C₂²	1	1	yes	characteristic
194	#1862	C₂²	1	1	yes	characteristic
195	#1832	C₂²	1	1	yes	characteristic
196	#1805	C₂²	1	1	yes	characteristic
197	#1802	C₂²	1	1	yes	characteristic
198	#1770	C₂²	1	1	yes	characteristic
199	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
200	#1762	C₂²	1	1	yes	characteristic
201	C₄×#102	C₂²	1	1	yes	characteristic
202	#1746	C₂²	1	1	yes	characteristic
203	C₂³×Q₈	—	2	1	no	—
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
211	C₂²×D₈	C₂³	1	1	yes	characteristic
212	C₂²×D₈	C₂³	1	1	yes	characteristic
213	#559	—	4	2	no	—
214	#559	—	4	2	no	—
215	D₄×Q₈	—	4	2	no	—
216	D₄×Q₈	—	4	2	no	—
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×#127	C₂³	1	1	yes	characteristic
222	C₂×#125	C₂³	1	1	yes	characteristic
223	C₂×#124	—	2	1	no	—
224	C₂×#124	C₂³	1	1	yes	characteristic
225	C₂×#124	C₂³	1	1	yes	characteristic
226	C₂×#124	C₂³	1	1	yes	characteristic
227	C₂×#124	C₂³	1	1	yes	characteristic
228	C₂×#123	—	2	1	no	—
229	C₂×#123	—	2	1	no	—
230	C₂×#123	—	2	1	no	—
231	C₂×#123	—	2	1	no	—
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	—	2	1	no	—
234	C₂×C₂²⋊Q₈	—	2	1	no	—
235	C₂×C₂²⋊Q₈	—	2	1	no	—
236	C₂×C₂²⋊Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₄	—	2	1	no	—
243	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
248	#495	—	4	2	no	—
249	#489	—	4	2	no	—
250	#475	—	4	2	no	—
251	#463	—	4	2	no	—
252	#463	—	4	2	no	—
253	#460	—	4	2	no	—
254	#441	—	4	2	no	—
255	C₄×SD₁₆	—	4	2	no	—
256	C₂×#107	C₂³	1	1	yes	characteristic
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×#106	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	C₂×#106	C₂³	1	1	yes	characteristic
262	C₂×#106	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#97	C₂³	1	1	yes	characteristic
300	C₂×#97	C₂³	1	1	yes	characteristic
301	C₂×#97	C₂³	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
304	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
305	#401	—	2	1	no	—
306	#400	—	2	1	no	—
307	#400	—	2	1	no	—
308	#400	—	2	1	no	—
309	#400	—	2	1	no	—
310	#400	—	2	1	no	—
311	#400	—	2	1	no	—
312	#400	—	2	1	no	—
313	#400	—	2	1	no	—
314	#399	—	2	1	no	—
315	#399	—	2	1	no	—
316	#398	—	2	1	no	—
317	#398	—	2	1	no	—
318	#398	—	2	1	no	—
319	#398	—	2	1	no	—
320	#398	D₄	1	1	yes	characteristic
321	#398	D₄	1	1	yes	characteristic
322	#398	D₄	1	1	yes	characteristic
323	#398	D₄	1	1	yes	characteristic
324	#397	—	2	1	no	—
325	#397	—	2	1	no	—
326	#397	—	2	1	no	—
327	#397	—	2	1	no	—
328	#397	—	2	1	no	—
329	#397	—	2	1	no	—
330	#397	—	2	1	no	—
331	#397	—	2	1	no	—
332	#397	—	2	1	no	—
333	#397	—	2	1	no	—
334	#397	—	2	1	no	—
335	#397	—	2	1	no	—
336	#397	—	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	D₄	1	1	yes	characteristic
347	#395	D₄	1	1	yes	characteristic
348	#395	D₄	1	1	yes	characteristic
349	#395	D₄	1	1	yes	characteristic
350	#394	—	2	1	no	—
351	#394	—	2	1	no	—
352	#394	—	2	1	no	—
353	#394	—	2	1	no	—
354	#393	—	2	1	no	—
355	#393	—	2	1	no	—
356	#393	—	2	1	no	—
357	#393	—	2	1	no	—
358	#393	—	2	1	no	—
359	#393	—	2	1	no	—
360	#393	—	2	1	no	—
361	#391	—	2	1	no	—
362	#391	—	2	1	no	—
363	#391	—	2	1	no	—
364	#391	—	2	1	no	—
365	#391	C₂³	1	1	yes	characteristic
366	#391	C₂³	1	1	yes	characteristic
367	#391	C₂³	1	1	yes	characteristic
368	#391	C₂³	1	1	yes	characteristic
369	#391	C₂³	1	1	yes	characteristic
370	#391	C₂³	1	1	yes	characteristic
371	#391	C₂³	1	1	yes	characteristic
372	#391	C₂³	1	1	yes	characteristic
373	#391	C₂³	1	1	yes	characteristic
374	#391	C₂³	1	1	yes	characteristic
375	#391	C₂³	1	1	yes	characteristic
376	#391	C₂³	1	1	yes	characteristic
377	#390	C₂³	1	1	yes	characteristic
378	#390	C₂³	1	1	yes	characteristic
379	#390	C₂³	1	1	yes	characteristic
380	#390	C₂³	1	1	yes	characteristic
381	#390	C₂³	1	1	yes	characteristic
382	#390	C₂³	1	1	yes	characteristic
383	#390	C₂³	1	1	yes	characteristic
384	#390	C₂³	1	1	yes	characteristic
385	#390	C₂³	1	1	yes	characteristic
386	#390	C₂³	1	1	yes	characteristic
387	#389	—	2	1	no	—
388	#389	—	2	1	no	—
389	#389	—	2	1	no	—
390	#389	C₂³	1	1	yes	characteristic
391	#389	C₂³	1	1	yes	characteristic
392	#389	C₂³	1	1	yes	characteristic
393	#389	C₂³	1	1	yes	characteristic
394	#389	C₂³	1	1	yes	characteristic
395	#389	C₂³	1	1	yes	characteristic
396	#389	C₂³	1	1	yes	characteristic
397	#389	C₂³	1	1	yes	characteristic
398	#389	C₂³	1	1	yes	characteristic
399	#389	C₂³	1	1	yes	characteristic
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	—	2	1	no	—
404	#388	—	2	1	no	—
405	#388	—	2	1	no	—
406	#388	—	2	1	no	—
407	#388	—	2	1	no	—
408	#388	—	2	1	no	—
409	#388	—	2	1	no	—
410	#388	—	2	1	no	—
411	#388	—	2	1	no	—
412	#388	—	2	1	no	—
413	#388	—	2	1	no	—
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	—	2	1	no	—
421	#387	—	2	1	no	—
422	#387	—	2	1	no	—
423	#387	—	2	1	no	—
424	#387	—	2	1	no	—
425	#386	—	2	1	no	—
426	#386	—	2	1	no	—
427	#385	—	2	1	no	—
428	#385	—	2	1	no	—
429	#385	—	2	1	no	—
430	#385	—	2	1	no	—
431	#385	—	2	1	no	—
432	#385	—	2	1	no	—
433	#384	—	2	1	no	—
434	#384	C₂³	1	1	yes	characteristic
435	#383	—	2	1	no	—
436	#382	C₂³	1	1	yes	characteristic
437	#381	—	2	1	no	—
438	#381	—	2	1	no	—
439	#381	—	2	1	no	—
440	#381	—	2	1	no	—
441	#380	—	2	1	no	—
442	#380	—	2	1	no	—
443	#380	—	2	1	no	—
444	#380	—	2	1	no	—
445	C₄×C₄⋊C₄	—	2	1	no	—
446	C₄×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
455	#376	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
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	#336	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	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	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	—	4	4	no	—
494	C₂²×Q₈	—	8	2	no	—
495	C₂²×Q₈	—	8	2	no	—
496	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
497	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
498	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
500	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	C₂⁴	1	1	yes	characteristic
504	C₂²×D₄	C₂⁴	1	1	yes	characteristic
505	C₂²×D₄	C₂⁴	1	1	yes	characteristic
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂×Q₁₆	—	4	1	no	—
512	C₂×Q₁₆	—	4	1	no	—
513	C₂×Q₁₆	—	4	1	no	—
514	C₂×Q₁₆	—	4	1	no	—
515	C₂×Q₁₆	—	4	1	no	—
516	C₂×Q₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×SD₁₆	—	4	1	no	—
528	C₂×SD₁₆	—	4	1	no	—
529	C₂×SD₁₆	—	4	1	no	—
530	C₂×SD₁₆	—	4	1	no	—
531	C₂×SD₁₆	—	4	1	no	—
532	C₂×D₈	—	2	2	no	—
533	C₂×D₈	—	4	1	no	—
534	C₂×D₈	—	4	1	no	—
535	C₂×D₈	—	4	1	no	—
536	C₂×D₈	—	4	1	no	—
537	C₂×D₈	—	4	1	no	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	2	2	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	1	no	—
554	#127	—	2	2	no	—
555	#127	—	4	1	no	—
556	#125	—	4	1	no	—
557	#125	—	4	1	no	—
558	#124	—	2	2	no	—
559	#124	—	4	1	no	—
560	#124	—	4	1	no	—
561	#124	—	4	1	no	—
562	#124	—	4	1	no	—
563	#124	—	4	1	no	—
564	#124	—	4	1	no	—
565	#124	—	4	1	no	—
566	#124	—	4	4	no	—
567	#123	—	4	4	no	—
568	#123	—	4	4	no	—
569	#123	—	8	2	no	—
570	#123	—	8	2	no	—
571	C₂²⋊Q₈	—	4	4	no	—
572	C₂²⋊Q₈	—	4	4	no	—
573	C₂²⋊Q₈	—	4	4	no	—
574	C₂²⋊Q₈	—	8	2	no	—
575	C₂²⋊Q₈	—	8	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	4	1	no	—
578	C₄×Q₈	—	4	1	no	—
579	C₄×Q₈	—	4	1	no	—
580	C₄×Q₈	—	4	1	no	—
581	C₄×Q₈	—	4	1	no	—
582	C₄×Q₈	—	4	1	no	—
583	C₄×Q₈	—	4	1	no	—
584	C₄×Q₈	—	4	1	no	—
585	C₄×Q₈	—	4	1	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	4	1	no	—
592	C₄×D₄	—	4	1	no	—
593	C₄×D₄	—	4	1	no	—
594	C₄×D₄	—	4	1	no	—
595	C₄×D₄	—	4	1	no	—
596	C₄×D₄	—	4	4	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	C₂×D₄	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	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	C₂⁴	1	1	yes	characteristic
684	C₂×C₄²	C₂⁴	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	—	4	1	no	—
691	#107	—	4	1	no	—
692	#106	—	2	2	no	—
693	#106	—	4	1	no	—
694	#106	—	4	1	no	—
695	#106	—	4	1	no	—
696	#106	—	4	1	no	—
697	C₄⋊C₈	—	4	1	no	—
698	C₄⋊C₈	—	4	1	no	—
699	C₄⋊C₈	—	4	1	no	—
700	C₄⋊C₈	—	4	1	no	—
701	C₄⋊C₈	—	4	1	no	—
702	C₄⋊C₈	—	4	1	no	—
703	#103	—	2	2	no	—
704	#103	—	2	2	no	—
705	#103	—	2	2	no	—
706	#103	—	4	1	no	—
707	#103	—	4	1	no	—
708	#103	—	4	1	no	—
709	#103	—	4	1	no	—
710	#103	—	4	1	no	—
711	#103	—	4	1	no	—
712	#103	—	4	1	no	—
713	#103	—	4	1	no	—
714	#103	—	4	1	no	—
715	#103	—	4	1	no	—
716	#103	—	4	1	no	—
717	#103	—	4	1	no	—
718	#102	—	2	2	no	—
719	#102	—	2	2	no	—
720	#102	—	2	2	no	—
721	#102	—	4	1	no	—
722	#102	—	4	1	no	—
723	#102	—	4	1	no	—
724	#102	—	4	1	no	—
725	#102	—	4	1	no	—
726	#102	—	4	1	no	—
727	#102	—	4	1	no	—
728	#102	—	4	1	no	—
729	#102	—	4	1	no	—
730	#102	—	4	1	no	—
731	#102	—	4	1	no	—
732	#102	—	4	1	no	—
733	#97	—	4	1	no	—
734	#97	—	4	1	no	—
735	#97	—	4	1	no	—
736	C₄×C₈	—	2	2	no	—
737	C₄×C₈	—	4	1	no	—
738	C₄×C₈	—	4	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
781	#95	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	C₂⁴	—	2	1	no	—
792	C₂⁴	—	2	1	no	—
793	C₂⁴	—	2	1	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
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	—	4	1	no	—
814	C₂×Q₈	—	4	1	no	—
815	C₂×Q₈	—	4	1	no	—
816	C₂×Q₈	—	4	1	no	—
817	C₂×Q₈	—	4	1	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×Q₈	—	4	2	no	—
820	C₂×Q₈	—	4	2	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×Q₈	—	8	1	no	—
824	C₂×Q₈	—	8	1	no	—
825	C₂×Q₈	—	8	1	no	—
826	C₂×Q₈	—	8	1	no	—
827	C₂×Q₈	—	8	16	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	1	no	—
838	C₂×D₄	—	2	1	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	8	1	no	—
849	C₂×D₄	—	8	1	no	—
850	C₂×D₄	—	8	1	no	—
851	C₂×D₄	H(5,𝔽₂)	1	2	yes	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	4	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	1	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	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	8	1	no	—
873	C₂²×C₄	—	8	1	no	—
874	C₂²×C₄	—	8	1	no	—
875	C₂²×C₄	—	8	1	no	—
876	C₂²×C₄	—	8	1	no	—
877	C₂²×C₄	—	8	1	no	—
878	C₂²×C₄	—	8	1	no	—
879	C₂²×C₄	—	8	1	no	—
880	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂⁵	1	1	yes	characteristic
895	Q₁₆	—	4	4	no	—
896	Q₁₆	—	8	2	no	—
897	SD₁₆	—	4	4	no	—
898	SD₁₆	—	8	2	no	—
899	SD₁₆	—	8	2	no	—
900	SD₁₆	—	8	2	no	—
901	SD₁₆	—	8	2	no	—
902	D₈	—	8	2	no	—
903	D₈	—	8	2	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
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⁺⁴	1	2	yes	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	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	—	4	1	no	—
950	C₄⋊C₄	—	4	1	no	—
951	C₄⋊C₄	—	4	1	no	—
952	C₄⋊C₄	—	4	1	no	—
953	C₄⋊C₄	—	4	1	no	—
954	C₄⋊C₄	—	4	1	no	—
955	C₄⋊C₄	—	4	1	no	—
956	C₄⋊C₄	—	4	1	no	—
957	C₄⋊C₄	—	4	1	no	—
958	C₄⋊C₄	—	4	1	no	—
959	C₄⋊C₄	—	4	1	no	—
960	C₄⋊C₄	—	4	1	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	8	1	no	—
970	C₄⋊C₄	—	8	1	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	—	8	1	no	—
973	C₄⋊C₄	—	8	1	no	—
974	C₄⋊C₄	—	8	1	no	—
975	C₄⋊C₄	—	8	1	no	—
976	C₄⋊C₄	—	8	1	no	—
977	C₄⋊C₄	—	8	1	no	—
978	C₄⋊C₄	—	8	1	no	—
979	C₄⋊C₄	—	8	1	no	—
980	C₄⋊C₄	—	8	1	no	—
981	C₄⋊C₄	—	8	1	no	—
982	C₄⋊C₄	—	8	1	no	—
983	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	1	no	—
1006	C₂²⋊C₄	—	8	1	no	—
1007	C₂²⋊C₄	—	8	1	no	—
1008	C₂²⋊C₄	—	8	1	no	—
1009	C₂²⋊C₄	—	8	1	no	—
1010	C₂²⋊C₄	—	8	1	no	—
1011	C₂²⋊C₄	—	8	1	no	—
1012	C₂²⋊C₄	—	8	1	no	—
1013	C₂²⋊C₄	—	8	1	no	—
1014	C₂²⋊C₄	—	8	1	no	—
1015	C₂²⋊C₄	—	8	1	no	—
1016	C₂²⋊C₄	—	8	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	4	2	no	—
1032	C₄²	—	8	1	no	—
1033	C₄²	—	8	1	no	—
1034	C₄²	—	8	1	no	—
1035	C₄²	—	8	1	no	—
1036	C₄²	—	8	1	no	—
1037	C₄²	—	8	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	—	4	1	no	—
1045	C₂³	—	4	1	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	1	no	—
1055	C₂³	—	4	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	C₂³×D₄	1	1	yes	characteristic
1060	Q₈	—	4	4	no	—
1061	Q₈	—	4	1	no	—
1062	Q₈	—	4	1	no	—
1063	Q₈	—	4	1	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	4	1	no	—
1066	Q₈	—	4	1	no	—
1067	Q₈	—	4	1	no	—
1068	Q₈	—	4	1	no	—
1069	Q₈	—	4	1	no	—
1070	Q₈	—	4	1	no	—
1071	Q₈	—	4	1	no	—
1072	Q₈	—	4	1	no	—
1073	Q₈	—	8	4	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	—	8	4	no	—
1076	Q₈	—	8	4	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	4	1	no	—
1080	D₄	—	4	1	no	—
1081	D₄	—	4	1	no	—
1082	D₄	—	4	1	no	—
1083	D₄	—	4	1	no	—
1084	D₄	—	4	1	no	—
1085	D₄	—	4	1	no	—
1086	D₄	—	4	1	no	—
1087	D₄	—	4	1	no	—
1088	D₄	—	4	1	no	—
1089	D₄	—	8	4	no	—
1090	D₄	—	16	2	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	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	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	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	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	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	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	—	8	4	no	—
1172	C₂×C₄	—	8	4	no	—
1173	C₂×C₄	—	8	4	no	—
1174	C₂×C₄	—	16	2	no	—
1175	C₂×C₄	—	16	2	no	—
1176	C₂×C₄	#577	1	2	yes	—
1177	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1178	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1179	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1180	C₂×C₄	#585	1	1	yes	characteristic
1181	C₂×C₄	#585	1	1	yes	characteristic
1182	C₂×C₄	#585	1	1	yes	characteristic
1183	C₈	—	2	2	no	—
1184	C₈	—	4	1	no	—
1185	C₈	—	4	1	no	—
1186	C₈	—	4	1	no	—
1187	C₈	—	4	1	no	—
1188	C₈	—	4	1	no	—
1189	C₈	—	4	1	no	—
1190	C₈	—	4	1	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	1	no	—
1196	C₂²	—	8	1	no	—
1197	C₂²	—	8	1	no	—
1198	C₂²	—	8	1	no	—
1199	C₂²	—	8	1	no	—
1200	C₂²	—	8	1	no	—
1201	C₂²	—	8	1	no	—
1202	C₂²	—	8	1	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	—	8	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	8	1	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	#3484	1	1	yes	characteristic
1213	C₂²	#3487	1	1	yes	characteristic
1214	C₂²	#3497	1	1	yes	characteristic
1215	C₂²	C₂×#577	1	1	yes	characteristic
1216	C₂²	#3584	1	1	yes	characteristic
1217	C₂²	#3585	1	1	yes	characteristic
1218	C₂²	#3586	1	1	yes	characteristic
1219	C₄	—	2	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	8	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	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	#3535	1	1	yes	characteristic
1247	C₄	#3540	1	1	yes	characteristic
1248	C₄	#3545	1	1	yes	characteristic
1249	C₄	#3547	1	1	yes	characteristic
1250	C₂	—	8	2	no	—
1251	C₂	—	16	1	no	—
1252	C₂	—	16	1	no	—
1253	C₂	#47797	1	1	yes	characteristic
1254	C₂	#61610	1	1	yes	characteristic
1255	C₂	#61626	1	1	yes	characteristic
1256	C₂	#61916	1	1	yes	characteristic
1257	C₂	#61924	1	1	yes	characteristic
1258	C₂	#62378	1	1	yes	characteristic
1259	C₂	#62389	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2011	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2399 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #42698	C₂	semidirect
2. #42481	C₂	semidirect
3. #32813	C₂	semidirect
4. #32671	C₂	semidirect
5. #32638	C₂	semidirect
6. #32618	C₂	semidirect
7. #32575	C₂	semidirect
8. #31922	C₂	semidirect
9. #31829	C₂	semidirect
11. #31525	C₂	semidirect
13. #31177	C₂	semidirect
14. #30899	C₂	semidirect
15. #30739	C₂	semidirect
16. #29570	C₂	semidirect
17. #29568	C₂	semidirect
18. #29542	C₂	semidirect
19. #29075	C₂	semidirect
20. #28881	C₂	semidirect
21. #27007	C₂	semidirect
22. #26911	C₂	semidirect
23. #26846	C₂	semidirect
24. #26717	C₂	semidirect
25. #26588	C₂	semidirect
26. #26251	C₂	semidirect
27. #25939	C₂	semidirect
29. #24330	C₂	semidirect
30. #24202	C₂	semidirect
31. #22310	C₂	semidirect

Maximal subgroups

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

subgroup	index
#42698	2
#42481	2
#32813	2
#32671	2
#32638	2
#32618	2
#32575	2
#31922	2
#31829	2
#31658	2
#31525	2
#31218	2
#31177	2
#30899	2
#30739	2
#29570	2
#29568	2
#29542	2
#29075	2
#28881	2
#27007	2
#26911	2
#26846	2
#26717	2
#26588	2
#26251	2
#25939	2
#25635	2
#24330	2
#24202	2
#22310	2