Subgroups — #6832746

Order 512.

1385 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39178	C₂	1	1	yes	maximal, characteristic, complemented
2	#38983	C₂	1	1	yes	maximal, characteristic
3	#33044	C₂	1	1	yes	maximal, characteristic
4	#32637	C₂	1	1	yes	maximal, characteristic, complemented
5	#32634	C₂	1	1	yes	maximal, characteristic, complemented
6	#32239	C₂	1	1	yes	maximal, characteristic, complemented
7	#32234	C₂	1	1	yes	maximal, characteristic, complemented
8	#32092	C₂	1	1	yes	maximal, characteristic, complemented
9	#32089	C₂	1	1	yes	maximal, characteristic, complemented
10	#31975	C₂	1	1	yes	maximal, characteristic, complemented
11	#31970	C₂	1	1	yes	maximal, characteristic, complemented
12	#29957	C₂	1	1	yes	maximal, characteristic, complemented
13	#29761	C₂	1	1	yes	maximal, characteristic
14	#29013	C₂	1	1	yes	maximal, characteristic, complemented
15	#29008	C₂	1	1	yes	maximal, characteristic, complemented
16	#28641	C₂	1	1	yes	maximal, characteristic, complemented
17	#28639	C₂	1	1	yes	maximal, characteristic, complemented
18	#28035	C₂	1	1	yes	maximal, characteristic, complemented
19	#28033	C₂	1	1	yes	maximal, characteristic, complemented
20	#27772	C₂	1	1	yes	maximal, characteristic, complemented
21	#27768	C₂	1	1	yes	maximal, characteristic, complemented
22	#27260	C₂	1	1	yes	maximal, characteristic
23	#27258	C₂	1	1	yes	maximal, characteristic, complemented
24	#26416	C₂	1	1	yes	maximal, characteristic, complemented
25	#26408	C₂	1	1	yes	maximal, characteristic
26	#24483	C₂	1	1	yes	maximal, characteristic
27	#24482	C₂	1	1	yes	maximal, characteristic, complemented
28	#22922	C₂	1	1	yes	maximal, characteristic, complemented
29	#22918	C₂	1	1	yes	maximal, characteristic
30	C₈×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#1933	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#488	C₂²	1	1	yes	characteristic
33	C₂×#488	C₂²	1	1	yes	characteristic
34	C₂×#487	C₂²	1	1	yes	characteristic
35	C₂×#484	C₂²	1	1	yes	characteristic
36	C₂×#481	C₂²	1	1	yes	characteristic
37	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
38	C₂²×#103	C₂²	1	1	yes	characteristic
39	C₂²×#103	C₂²	1	1	yes	characteristic
40	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
41	#2851	C₂²	1	1	yes	characteristic
42	#2850	C₂²	1	1	yes	characteristic
43	#2802	—	2	1	no	—
44	#2791	—	2	1	no	—
45	#2788	—	2	1	no	—
46	#2775	—	2	1	no	—
47	#2774	—	2	1	no	—
48	#2759	—	2	1	no	—
49	#2745	—	2	1	no	—
50	#2713	—	2	1	no	—
51	#2646	—	2	1	no	—
52	#2643	—	2	1	no	—
53	#2592	C₂²	1	1	yes	characteristic
54	#2584	C₂²	1	1	yes	characteristic
55	#2568	C₂²	1	1	yes	characteristic
56	#2552	C₂²	1	1	yes	characteristic
57	#2550	C₂²	1	1	yes	characteristic
58	#2547	C₂²	1	1	yes	characteristic
59	#2546	C₂²	1	1	yes	characteristic
60	#2545	C₂²	1	1	yes	characteristic
61	#2514	C₂²	1	1	yes	characteristic
62	#2514	C₂²	1	1	yes	characteristic
63	#2510	—	2	1	no	—
64	#2509	C₂²	1	1	yes	characteristic
65	#2509	C₂²	1	1	yes	characteristic
66	#2508	C₂²	1	1	yes	characteristic
67	#2506	C₂²	1	1	yes	characteristic
68	#2450	—	2	1	no	—
69	#2447	C₂²	1	1	yes	characteristic
70	#2446	C₂²	1	1	yes	characteristic
71	#2442	—	2	1	no	—
72	#2442	C₂²	1	1	yes	characteristic
73	#2440	—	2	1	no	—
74	#2440	C₂²	1	1	yes	characteristic
75	#2436	C₂²	1	1	yes	characteristic
76	#2434	C₂²	1	1	yes	characteristic
77	#2361	C₂²	1	1	yes	characteristic
78	#2360	C₂²	1	1	yes	characteristic
79	#2345	C₂²	1	1	yes	characteristic
80	#2345	C₂²	1	1	yes	characteristic
81	#2329	—	2	1	no	—
82	#2318	—	2	1	no	—
83	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
84	C₂×#391	C₂²	1	1	yes	characteristic
85	C₂×#389	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic
87	#2099	C₂²	1	1	yes	characteristic
88	#2097	C₂²	1	1	yes	characteristic
89	#2097	C₂²	1	1	yes	characteristic
90	#2088	C₂²	1	1	yes	characteristic
91	#2086	C₂²	1	1	yes	characteristic
92	#2085	C₂²	1	1	yes	characteristic
93	#2085	C₂²	1	1	yes	characteristic
94	#2074	C₂²	1	1	yes	characteristic
95	#2072	C₂²	1	1	yes	characteristic
96	#2068	C₂²	1	1	yes	characteristic
97	#2068	C₂²	1	1	yes	characteristic
98	#2068	C₂²	1	1	yes	characteristic
99	#2068	C₂²	1	1	yes	characteristic
100	#2067	C₂²	1	1	yes	characteristic
101	#2067	C₂²	1	1	yes	characteristic
102	#2067	C₂²	1	1	yes	characteristic
103	#2066	C₂²	1	1	yes	characteristic
104	#2066	C₂²	1	1	yes	characteristic
105	#2066	C₂²	1	1	yes	characteristic
106	#2066	C₂²	1	1	yes	characteristic
107	#2066	C₂²	1	1	yes	characteristic
108	#2066	C₂²	1	1	yes	characteristic
109	#2066	C₂²	1	1	yes	characteristic
110	#2043	C₂²	1	1	yes	characteristic
111	#2043	C₂²	1	1	yes	characteristic
112	#2043	C₂²	1	1	yes	characteristic
113	#2043	C₂²	1	1	yes	characteristic
114	#2042	C₂²	1	1	yes	characteristic
115	#2042	C₂²	1	1	yes	characteristic
116	#2042	C₂²	1	1	yes	characteristic
117	#2042	C₂²	1	1	yes	characteristic
118	#2042	C₂²	1	1	yes	characteristic
119	#2042	C₂²	1	1	yes	characteristic
120	#2026	C₂²	1	1	yes	characteristic
121	#2026	C₂²	1	1	yes	characteristic
122	#2026	C₂²	1	1	yes	characteristic
123	#2026	C₂²	1	1	yes	characteristic
124	#2024	C₂²	1	1	yes	characteristic
125	#2023	C₂²	1	1	yes	characteristic
126	#1991	C₂²	1	1	yes	characteristic
127	#1989	C₂²	1	1	yes	characteristic
128	#1988	C₂²	1	1	yes	characteristic
129	#1984	C₂²	1	1	yes	characteristic
130	#1983	C₂²	1	1	yes	characteristic
131	#1983	C₂²	1	1	yes	characteristic
132	#1981	C₂²	1	1	yes	characteristic
133	#1981	C₂²	1	1	yes	characteristic
134	#1958	C₂²	1	1	yes	characteristic
135	#1958	C₂²	1	1	yes	characteristic
136	#1956	C₂²	1	1	yes	characteristic
137	#1942	C₂²	1	1	yes	characteristic
138	#1941	C₂²	1	1	yes	characteristic
139	#1939	C₂²	1	1	yes	characteristic
140	#1934	C₂²	1	1	yes	characteristic
141	#1934	C₂²	1	1	yes	characteristic
142	#1934	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	#1933	C₂²	1	1	yes	characteristic
147	#1933	C₂²	1	1	yes	characteristic
148	#1933	C₂²	1	1	yes	characteristic
149	#1933	C₂²	1	1	yes	characteristic
150	#1933	C₂²	1	1	yes	characteristic
151	#1933	C₂²	1	1	yes	characteristic
152	#1933	C₂²	1	1	yes	characteristic
153	#1933	C₂²	1	1	yes	characteristic
154	#1933	C₂²	1	1	yes	characteristic
155	#1933	C₂²	1	1	yes	characteristic
156	#1933	C₂²	1	1	yes	characteristic
157	#1933	C₂²	1	1	yes	characteristic
158	#1928	C₂²	1	1	yes	characteristic
159	#1928	C₂²	1	1	yes	characteristic
160	#1928	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	#1921	C₂²	1	1	yes	characteristic
165	#1921	C₂²	1	1	yes	characteristic
166	#1920	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	#1916	C₂²	1	1	yes	characteristic
171	#1916	C₂²	1	1	yes	characteristic
172	#1893	C₂²	1	1	yes	characteristic
173	#1893	C₂²	1	1	yes	characteristic
174	#1892	C₂²	1	1	yes	characteristic
175	#1892	C₂²	1	1	yes	characteristic
176	#1874	C₂²	1	1	yes	characteristic
177	#1872	C₂²	1	1	yes	characteristic
178	#1865	C₂²	1	1	yes	characteristic
179	#1864	C₂²	1	1	yes	characteristic
180	#1863	C₂²	1	1	yes	characteristic
181	#1862	C₂²	1	1	yes	characteristic
182	#1853	C₂²	1	1	yes	characteristic
183	#1852	C₂²	1	1	yes	characteristic
184	#1850	C₂²	1	1	yes	characteristic
185	#1850	C₂²	1	1	yes	characteristic
186	#1835	C₂²	1	1	yes	characteristic
187	#1805	C₂²	1	1	yes	characteristic
188	#1802	C₂²	1	1	yes	characteristic
189	#1797	C₂²	1	1	yes	characteristic
190	#1787	C₂²	1	1	yes	characteristic
191	#1787	C₂²	1	1	yes	characteristic
192	C₄×#107	C₂²	1	1	yes	characteristic
193	C₄×#106	C₂²	1	1	yes	characteristic
194	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
195	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
196	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
197	C₄×#103	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
200	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
201	C₂×#340	C₂²	1	1	yes	characteristic
202	C₂×#340	C₂²	1	1	yes	characteristic
203	C₂³×Q₈	C₂³	1	1	yes	characteristic
204	C₂³×C₈	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	—	2	1	no	—
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#125	—	2	1	no	—
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#124	C₂³	1	1	yes	characteristic
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×#124	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	—	2	1	no	—
217	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×#121	C₂³	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	—	2	1	no	—
225	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₄²	C₂³	1	1	yes	characteristic
229	#488	—	4	2	no	—
230	#488	—	4	2	no	—
231	#487	—	4	2	no	—
232	#484	—	2	4	no	—
233	#481	—	2	4	no	—
234	C₈×Q₈	—	4	2	no	—
235	C₂×#107	C₂³	1	1	yes	characteristic
236	C₂×#107	C₂³	1	1	yes	characteristic
237	C₂×#107	C₂³	1	1	yes	characteristic
238	C₂×#107	C₂³	1	1	yes	characteristic
239	C₂×#106	C₂³	1	1	yes	characteristic
240	C₂×#106	C₂³	1	1	yes	characteristic
241	C₂×#106	C₂³	1	1	yes	characteristic
242	C₂×#106	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×#103	—	2	4	no	—
250	C₂×#103	—	4	2	no	—
251	C₂×#103	C₂³	1	1	yes	characteristic
252	C₂×#103	C₂³	1	1	yes	characteristic
253	C₂×#103	C₂³	1	1	yes	characteristic
254	C₂×#103	C₂³	1	1	yes	characteristic
255	C₂×#103	C₂³	1	1	yes	characteristic
256	C₂×#103	C₂³	1	1	yes	characteristic
257	C₂×#103	C₂³	1	1	yes	characteristic
258	C₂×#103	C₂³	1	1	yes	characteristic
259	C₂×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	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×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₄×C₈	—	4	2	no	—
286	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
291	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	#401	—	2	1	no	—
295	#401	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#400	—	2	1	no	—
302	#400	—	2	1	no	—
303	#400	—	2	1	no	—
304	#400	—	2	1	no	—
305	#400	—	2	1	no	—
306	#400	—	2	1	no	—
307	#400	—	2	1	no	—
308	#398	—	2	1	no	—
309	#398	—	2	1	no	—
310	#398	—	2	1	no	—
311	#398	—	2	1	no	—
312	#398	—	2	1	no	—
313	#398	—	2	1	no	—
314	#398	—	2	1	no	—
315	#398	—	2	1	no	—
316	#398	—	2	1	no	—
317	#398	—	2	1	no	—
318	#398	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#397	—	2	1	no	—
323	#397	—	2	1	no	—
324	#396	—	2	1	no	—
325	#396	—	2	1	no	—
326	#395	—	2	1	no	—
327	#395	—	2	1	no	—
328	#395	—	2	1	no	—
329	#395	—	2	1	no	—
330	#395	—	2	1	no	—
331	#393	—	2	1	no	—
332	#393	—	2	1	no	—
333	#393	—	2	1	no	—
334	#391	—	2	1	no	—
335	#391	—	2	1	no	—
336	#391	—	2	1	no	—
337	#391	—	2	1	no	—
338	#391	—	2	1	no	—
339	#391	D₄	1	1	yes	characteristic
340	#391	C₂³	1	1	yes	characteristic
341	#391	C₂³	1	1	yes	characteristic
342	#391	C₂³	1	1	yes	characteristic
343	#391	C₂³	1	1	yes	characteristic
344	#391	C₂³	1	1	yes	characteristic
345	#391	C₂³	1	1	yes	characteristic
346	#391	C₂³	1	1	yes	characteristic
347	#391	C₂³	1	1	yes	characteristic
348	#391	C₂³	1	1	yes	characteristic
349	#391	C₂³	1	1	yes	characteristic
350	#390	C₂³	1	1	yes	characteristic
351	#390	C₂³	1	1	yes	characteristic
352	#389	—	2	1	no	—
353	#389	—	2	1	no	—
354	#389	—	2	1	no	—
355	#389	—	2	1	no	—
356	#389	—	2	1	no	—
357	#389	—	2	1	no	—
358	#389	—	2	1	no	—
359	#389	—	2	1	no	—
360	#389	—	2	1	no	—
361	#389	D₄	1	1	yes	characteristic
362	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#389	C₂³	1	1	yes	characteristic
365	#389	C₂³	1	1	yes	characteristic
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#389	C₂³	1	1	yes	characteristic
369	#389	C₂³	1	1	yes	characteristic
370	#389	C₂³	1	1	yes	characteristic
371	#389	C₂³	1	1	yes	characteristic
372	#389	C₂³	1	1	yes	characteristic
373	#389	C₂³	1	1	yes	characteristic
374	#389	C₂³	1	1	yes	characteristic
375	#389	C₂³	1	1	yes	characteristic
376	#389	C₂³	1	1	yes	characteristic
377	#389	C₂³	1	1	yes	characteristic
378	#388	—	2	1	no	—
379	#388	—	2	1	no	—
380	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
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	D₄	1	1	yes	characteristic
401	#387	D₄	1	1	yes	characteristic
402	#386	—	2	1	no	—
403	#386	—	2	1	no	—
404	#386	—	2	1	no	—
405	#386	—	2	1	no	—
406	#386	—	2	1	no	—
407	#385	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	—	2	1	no	—
410	#385	—	2	1	no	—
411	#385	—	2	1	no	—
412	#385	—	2	1	no	—
413	#385	—	2	1	no	—
414	#385	—	2	1	no	—
415	#385	—	2	1	no	—
416	#385	D₄	1	1	yes	characteristic
417	#385	D₄	1	1	yes	characteristic
418	#384	—	2	1	no	—
419	#384	C₂³	1	1	yes	characteristic
420	#383	—	2	1	no	—
421	#383	—	2	1	no	—
422	#382	—	2	1	no	—
423	#382	—	2	1	no	—
424	#382	C₂³	1	1	yes	characteristic
425	#382	C₂³	1	1	yes	characteristic
426	#382	C₂³	1	1	yes	characteristic
427	#381	—	2	1	no	—
428	#380	—	2	1	no	—
429	#380	—	2	1	no	—
430	#380	—	2	1	no	—
431	#380	—	2	1	no	—
432	#380	—	2	1	no	—
433	#380	D₄	1	1	yes	characteristic
434	#380	C₂³	1	1	yes	characteristic
435	#380	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
450	C₂×#95	—	2	1	no	—
451	C₂×#95	—	2	1	no	—
452	C₂×#95	—	2	1	no	—
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	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	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	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	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	—	2	2	no	—
490	C₂²×Q₈	—	2	2	no	—
491	C₂²×Q₈	—	4	1	no	—
492	C₂²×Q₈	—	4	1	no	—
493	C₂²×Q₈	—	4	1	no	—
494	C₂²×Q₈	—	4	1	no	—
495	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
498	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	2	2	no	—
511	C₂²×C₈	—	2	2	no	—
512	C₂²×C₈	—	4	1	no	—
513	C₂²×C₈	—	4	1	no	—
514	C₂²×C₈	—	4	1	no	—
515	C₂²×C₈	C₂⁴	1	1	yes	characteristic
516	C₂²×C₈	C₂⁴	1	1	yes	characteristic
517	C₂²×C₈	C₂⁴	1	1	yes	characteristic
518	C₂²×C₈	C₂⁴	1	1	yes	characteristic
519	C₂²×C₈	C₂⁴	1	1	yes	characteristic
520	C₂²×C₈	C₂⁴	1	1	yes	characteristic
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₄⋊Q₈	—	4	1	no	—
524	C₄⋊Q₈	—	4	1	no	—
525	C₄⋊Q₈	—	4	1	no	—
526	C₄⋊Q₈	—	4	1	no	—
527	C₄⋊Q₈	—	4	1	no	—
528	C₄⋊Q₈	—	4	1	no	—
529	C₄⋊Q₈	—	8	2	no	—
530	#125	—	4	1	no	—
531	#125	—	4	1	no	—
532	#125	—	4	1	no	—
533	#125	—	4	1	no	—
534	#125	—	8	2	no	—
535	#124	—	4	1	no	—
536	#124	—	4	1	no	—
537	#124	—	4	1	no	—
538	#124	—	4	1	no	—
539	#124	—	4	1	no	—
540	#124	—	4	1	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	4	4	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	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×D₄	—	4	1	no	—
552	C₄×D₄	—	4	1	no	—
553	C₄×D₄	—	4	4	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	4	1	no	—
588	C₂×C₄⋊C₄	—	4	1	no	—
589	C₂×C₄⋊C₄	—	4	1	no	—
590	C₂×C₄⋊C₄	—	4	1	no	—
591	C₂×C₄⋊C₄	—	8	2	no	—
592	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₂×C₄⋊C₄	#41	1	4	yes	—
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	1	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	—	4	1	no	—
641	C₂×C₄²	—	4	1	no	—
642	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
643	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
644	C₂×C₄²	C₂⁴	1	1	yes	characteristic
645	C₂×C₄²	C₂⁴	1	1	yes	characteristic
646	C₂×C₄²	C₂⁴	1	1	yes	characteristic
647	C₂×C₄²	C₂⁴	1	1	yes	characteristic
648	C₂×C₄²	C₂⁴	1	1	yes	characteristic
649	C₂×C₄²	C₂⁴	1	1	yes	characteristic
650	#107	—	2	2	no	—
651	#107	—	2	2	no	—
652	#107	—	4	1	no	—
653	#107	—	4	1	no	—
654	#106	—	2	2	no	—
655	#106	—	2	2	no	—
656	#106	—	4	1	no	—
657	#106	—	4	1	no	—
658	C₄⋊C₈	—	4	1	no	—
659	C₄⋊C₈	—	4	1	no	—
660	C₄⋊C₈	—	4	1	no	—
661	C₄⋊C₈	—	4	1	no	—
662	C₄⋊C₈	—	4	1	no	—
663	C₄⋊C₈	—	4	1	no	—
664	#103	—	2	2	no	—
665	#103	—	2	2	no	—
666	#103	—	2	2	no	—
667	#103	—	2	2	no	—
668	#103	—	2	2	no	—
669	#103	—	2	2	no	—
670	#103	—	2	2	no	—
671	#103	—	2	2	no	—
672	#103	—	2	2	no	—
673	#103	—	4	1	no	—
674	#103	—	4	1	no	—
675	#103	—	4	1	no	—
676	#103	—	4	1	no	—
677	#103	—	4	1	no	—
678	#103	—	4	1	no	—
679	#103	—	4	1	no	—
680	#103	—	4	1	no	—
681	#103	—	4	1	no	—
682	#103	—	4	1	no	—
683	#103	—	4	1	no	—
684	#103	—	4	1	no	—
685	#103	—	4	1	no	—
686	#103	—	4	1	no	—
687	#103	—	4	1	no	—
688	#102	—	2	2	no	—
689	#102	—	2	2	no	—
690	#102	—	2	2	no	—
691	#102	—	4	1	no	—
692	#102	—	4	1	no	—
693	#102	—	4	1	no	—
694	#102	—	4	1	no	—
695	#102	—	4	1	no	—
696	C₂²⋊C₈	—	2	2	no	—
697	C₂²⋊C₈	—	2	2	no	—
698	C₄×C₈	—	2	2	no	—
699	C₄×C₈	—	2	2	no	—
700	C₄×C₈	—	2	2	no	—
701	C₄×C₈	—	2	2	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	#95	—	2	1	no	—
707	#95	—	2	1	no	—
708	#95	—	2	1	no	—
709	#95	—	2	1	no	—
710	#95	—	2	1	no	—
711	#95	—	2	1	no	—
712	#95	—	2	1	no	—
713	#95	—	2	1	no	—
714	#95	—	2	1	no	—
715	#95	—	2	1	no	—
716	#95	—	2	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
757	#95	C₂×D₄	1	1	yes	characteristic
758	#95	C₂×D₄	1	1	yes	characteristic
759	#95	C₂×D₄	1	1	yes	characteristic
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	C₂⁴	—	2	1	no	—
767	C₂⁴	C₂²×D₄	1	1	yes	characteristic
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	4	1	no	—
789	C₂×Q₈	—	4	4	no	—
790	C₂×Q₈	—	4	4	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	—	8	1	no	—
794	C₂×Q₈	—	8	1	no	—
795	C₂×Q₈	—	8	1	no	—
796	C₂×Q₈	—	8	1	no	—
797	C₂×Q₈	—	8	2	no	—
798	C₂×Q₈	—	8	2	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	4	2	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	4	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	4	1	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	8	1	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
841	C₂²×C₄	—	8	1	no	—
842	C₂²×C₄	—	8	1	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	—	8	1	no	—
845	C₂²×C₄	—	8	1	no	—
846	C₂²×C₄	—	8	1	no	—
847	C₂²×C₄	—	8	1	no	—
848	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂×#41	1	2	yes	—
862	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
863	C₂²×C₄	C₂⁵	1	1	yes	characteristic
864	C₂×C₈	—	2	1	no	—
865	C₂×C₈	—	2	1	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	4	4	no	—
888	C₂×C₈	—	4	4	no	—
889	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	1	no	—
919	C₄⋊C₄	—	4	1	no	—
920	C₄⋊C₄	—	4	1	no	—
921	C₄⋊C₄	—	4	1	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	8	1	no	—
931	C₄⋊C₄	—	8	1	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	—	8	1	no	—
945	C₄⋊C₄	—	8	1	no	—
946	C₄⋊C₄	—	8	1	no	—
947	C₄⋊C₄	—	8	1	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	—	8	1	no	—
950	C₄⋊C₄	—	8	1	no	—
951	C₄⋊C₄	—	8	1	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	C₂×#41	1	2	yes	—
954	C₄⋊C₄	C₂×#41	1	2	yes	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	8	1	no	—
965	C₂²⋊C₄	—	8	1	no	—
966	C₂²⋊C₄	—	8	1	no	—
967	C₂²⋊C₄	—	8	1	no	—
968	C₂²⋊C₄	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	#135	1	4	yes	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	4	1	no	—
987	C₄²	—	4	1	no	—
988	C₄²	—	4	2	no	—
989	C₄²	—	8	1	no	—
990	C₄²	—	8	1	no	—
991	C₄²	—	8	1	no	—
992	C₄²	—	8	1	no	—
993	C₄²	—	8	1	no	—
994	C₄²	—	8	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	4	1	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	—	4	1	no	—
1003	C₂³	—	4	1	no	—
1004	C₂³	—	4	1	no	—
1005	C₂³	—	4	1	no	—
1006	C₂³	#548	1	2	yes	—
1007	C₂³	C₂×#135	1	2	yes	—
1008	C₂³	#578	1	2	yes	—
1009	C₂³	C₂³×D₄	1	1	yes	characteristic
1010	Q₈	—	4	4	no	—
1011	Q₈	—	4	1	no	—
1012	Q₈	—	4	1	no	—
1013	Q₈	—	4	1	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	4	1	no	—
1016	Q₈	—	4	1	no	—
1017	Q₈	—	4	1	no	—
1018	Q₈	—	4	1	no	—
1019	Q₈	—	4	1	no	—
1020	Q₈	—	4	1	no	—
1021	Q₈	—	4	1	no	—
1022	Q₈	—	4	1	no	—
1023	Q₈	—	8	4	no	—
1024	Q₈	—	16	2	no	—
1025	D₄	—	4	1	no	—
1026	D₄	—	4	1	no	—
1027	D₄	—	4	1	no	—
1028	D₄	—	4	1	no	—
1029	D₄	—	8	4	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	1	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	8	4	no	—
1117	C₂×C₄	—	8	4	no	—
1118	C₂×C₄	—	16	2	no	—
1119	C₂×C₄	—	16	2	no	—
1120	C₂×C₄	—	16	2	no	—
1121	C₂×C₄	#548	1	2	yes	—
1122	C₂×C₄	C₂×#135	1	2	yes	—
1123	C₂×C₄	C₂×#135	1	2	yes	—
1124	C₂×C₄	#577	1	2	yes	—
1125	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1126	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1127	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1128	C₂×C₄	#585	1	1	yes	characteristic
1129	C₂×C₄	#585	1	1	yes	characteristic
1130	C₂×C₄	#585	1	1	yes	characteristic
1131	C₈	—	2	2	no	—
1132	C₈	—	4	1	no	—
1133	C₈	—	4	1	no	—
1134	C₈	—	4	1	no	—
1135	C₈	—	4	1	no	—
1136	C₈	—	4	1	no	—
1137	C₈	—	4	1	no	—
1138	C₈	—	4	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	8	1	no	—
1146	C₂²	—	8	1	no	—
1147	C₂²	—	8	1	no	—
1148	C₂²	—	8	1	no	—
1149	C₂²	—	8	1	no	—
1150	C₂²	—	8	1	no	—
1151	C₂²	—	8	1	no	—
1152	C₂²	#3364	1	4	yes	—
1153	C₂²	C₂×#548	1	1	yes	characteristic
1154	C₂²	#3496	1	1	yes	characteristic
1155	C₂²	#3500	1	1	yes	characteristic
1156	C₂²	C₂²×#135	1	1	yes	characteristic
1157	C₂²	C₂×#577	1	1	yes	characteristic
1158	C₂²	C₂×#578	1	1	yes	characteristic
1159	C₂²	#3584	1	1	yes	characteristic
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	2	no	—
1175	C₄	—	8	1	no	—
1176	C₄	—	8	1	no	—
1177	C₄	—	8	1	no	—
1178	C₄	—	8	1	no	—
1179	C₄	—	8	1	no	—
1180	C₄	—	8	1	no	—
1181	C₄	—	8	1	no	—
1182	C₄	—	8	1	no	—
1183	C₄	—	8	1	no	—
1184	C₄	—	8	1	no	—
1185	C₄	—	8	1	no	—
1186	C₄	—	8	1	no	—
1187	C₄	—	8	1	no	—
1188	C₄	#3460	1	1	yes	characteristic
1189	C₄	#3493	1	1	yes	characteristic
1190	C₄	#3535	1	1	yes	characteristic
1191	C₄	#3564	1	1	yes	characteristic
1192	C₂	—	2	4	no	—
1193	C₂	—	16	1	no	—
1194	C₂	#39423	1	1	yes	characteristic
1195	C₂	C₂×#3364	1	1	yes	characteristic
1196	C₂	#61326	1	1	yes	characteristic
1197	C₂	#62250	1	1	yes	characteristic
1198	C₂	#62267	1	1	yes	characteristic
1199	C₂	#62533	1	1	yes	characteristic
1200	C₂	#62553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#121	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊Q₈ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #39178	C₂	semidirect
4. #32637	C₂	semidirect
5. #32634	C₂	semidirect
6. #32239	C₂	semidirect
7. #32234	C₂	semidirect
8. #32092	C₂	semidirect
9. #32089	C₂	semidirect
10. #31975	C₂	semidirect
11. #31970	C₂	semidirect
12. #29957	C₂	semidirect
14. #29013	C₂	semidirect
15. #29008	C₂	semidirect
16. #28641	C₂	semidirect
17. #28639	C₂	semidirect
18. #28035	C₂	semidirect
19. #28033	C₂	semidirect
20. #27772	C₂	semidirect
21. #27768	C₂	semidirect
23. #27258	C₂	semidirect
24. #26416	C₂	semidirect
27. #24482	C₂	semidirect
28. #22922	C₂	semidirect
30. C₈×C₂²⋊Q₈	C₂	semidirect
31. C₂×#1933	C₂	semidirect

Maximal subgroups

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

subgroup	index
#39178	2
#38983	2
#33044	2
#32637	2
#32634	2
#32239	2
#32234	2
#32092	2
#32089	2
#31975	2
#31970	2
#29957	2
#29761	2
#29013	2
#29008	2
#28641	2
#28639	2
#28035	2
#28033	2
#27772	2
#27768	2
#27260	2
#27258	2
#26416	2
#26408	2
#24483	2
#24482	2
#22922	2
#22918	2
C₈×C₂²⋊Q₈	2
C₂×#1933	2