Subgroups — #6817805

Order 512.

1521 conjugacy classes of subgroups.

The subgroup lattice has 1243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39983	C₂	1	1	yes	maximal, characteristic, complemented
2	#39367	C₂	1	1	yes	maximal, characteristic
3	#33210	C₂	1	1	yes	maximal, characteristic, complemented
4	#32593	C₂	1	1	yes	maximal, characteristic, complemented
5	#32581	C₂	1	1	yes	maximal, characteristic, complemented
6	#32342	C₂	1	1	yes	maximal, characteristic, complemented
7	#32342	C₂	1	1	yes	maximal, characteristic, complemented
8	#31891	C₂	1	1	yes	maximal, characteristic, complemented
9	#31882	C₂	1	1	yes	maximal, characteristic, complemented
10	#30954	C₂	1	1	yes	maximal, characteristic, complemented
11	#30947	C₂	1	1	yes	maximal, characteristic, complemented
12	#29971	C₂	1	1	yes	maximal, characteristic, complemented
13	#29950	C₂	1	1	yes	maximal, characteristic
14	#28974	C₂	1	1	yes	maximal, characteristic, complemented
15	#28968	C₂	1	1	yes	maximal, characteristic, complemented
16	#28959	C₂	1	1	yes	maximal, characteristic, complemented
17	#28943	C₂	1	1	yes	maximal, characteristic, complemented
18	#28784	C₂	1	1	yes	maximal, characteristic, complemented
19	#28781	C₂	1	1	yes	maximal, characteristic, complemented
20	#27830	C₂	1	1	yes	maximal, characteristic, complemented
21	#27813	C₂	1	1	yes	maximal, characteristic, complemented
22	#26011	C₂	1	1	yes	maximal, characteristic, complemented
23	#26005	C₂	1	1	yes	maximal, characteristic, complemented
24	#25976	C₂	1	1	yes	maximal, characteristic
25	#25974	C₂	1	1	yes	maximal, characteristic
26	#25482	C₂	1	1	yes	maximal, characteristic, complemented
27	#25477	C₂	1	1	yes	maximal, characteristic, complemented
28	#22584	C₂	1	1	yes	maximal, characteristic
29	#22580	C₂	1	1	yes	maximal, characteristic
30	#21600	C₂	1	1	yes	maximal, characteristic, complemented
31	#21095	C₂	1	1	yes	maximal, characteristic
32	C₂×#543	—	2	1	no	—
33	C₂×#498	C₂²	1	1	yes	characteristic, complemented
34	C₂×#478	C₂²	1	1	yes	characteristic
35	C₂×#476	C₂²	1	1	yes	characteristic
36	C₂×#446	C₂²	1	1	yes	characteristic, complemented
37	C₂×#418	C₂²	1	1	yes	characteristic
38	C₂×#418	C₂²	1	1	yes	characteristic
39	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
40	#2857	C₂²	1	1	yes	characteristic
41	#2857	C₂²	1	1	yes	characteristic
42	#2742	—	2	1	no	—
43	#2732	—	2	1	no	—
44	#2729	—	2	1	no	—
45	#2720	—	2	1	no	—
46	#2704	—	2	1	no	—
47	#2692	—	2	1	no	—
48	#2692	—	2	1	no	—
49	#2683	—	2	1	no	—
50	#2666	—	2	1	no	—
51	#2626	—	2	1	no	—
52	#2605	—	2	1	no	—
53	#2584	C₂²	1	1	yes	characteristic, complemented
54	#2567	C₂²	1	1	yes	characteristic, complemented
55	#2551	C₂²	1	1	yes	characteristic, complemented
56	#2550	—	2	1	no	—
57	#2550	C₂²	1	1	yes	characteristic, complemented
58	#2542	C₂²	1	1	yes	characteristic
59	#2542	C₂²	1	1	yes	characteristic
60	#2538	C₂²	1	1	yes	characteristic
61	#2538	C₂²	1	1	yes	characteristic
62	#2509	C₂²	1	1	yes	characteristic, complemented
63	#2507	C₂²	1	1	yes	characteristic, complemented
64	#2506	C₂²	1	1	yes	characteristic, complemented
65	#2506	C₂²	1	1	yes	characteristic, complemented
66	#2452	C₂²	1	1	yes	characteristic
67	#2452	C₂²	1	1	yes	characteristic
68	#2452	C₂²	1	1	yes	characteristic
69	#2452	C₂²	1	1	yes	characteristic
70	#2441	C₂²	1	1	yes	characteristic
71	#2440	C₂²	1	1	yes	characteristic
72	#2440	C₂²	1	1	yes	characteristic
73	#2439	C₂²	1	1	yes	characteristic
74	#2437	—	2	1	no	—
75	#2437	—	2	1	no	—
76	#2347	C₂²	1	1	yes	characteristic
77	#2346	C₂²	1	1	yes	characteristic
78	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
79	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
80	#2330	—	2	1	no	—
81	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
82	#2296	C₂²	1	1	yes	characteristic
83	C₂×#390	C₂²	1	1	yes	characteristic
84	#2100	C₂²	1	1	yes	characteristic, complemented
85	#2099	C₂²	1	1	yes	characteristic, complemented
86	#2099	C₂²	1	1	yes	characteristic, complemented
87	#2099	C₂²	1	1	yes	characteristic, complemented
88	#2094	C₂²	1	1	yes	characteristic
89	#2093	C₂²	1	1	yes	characteristic
90	#2093	C₂²	1	1	yes	characteristic
91	#2092	C₂²	1	1	yes	characteristic
92	#2088	C₂²	1	1	yes	characteristic, complemented
93	#2088	C₂²	1	1	yes	characteristic, complemented
94	#2088	C₂²	1	1	yes	characteristic, complemented
95	#2088	C₂²	1	1	yes	characteristic, complemented
96	#2087	C₂²	1	1	yes	characteristic, complemented
97	#2087	C₂²	1	1	yes	characteristic, complemented
98	#2087	C₂²	1	1	yes	characteristic, complemented
99	#2086	C₂²	1	1	yes	characteristic, complemented
100	#2085	C₂²	1	1	yes	characteristic, complemented
101	#2084	C₂²	1	1	yes	characteristic, complemented
102	#2083	C₂²	1	1	yes	characteristic, complemented
103	#2083	C₂²	1	1	yes	characteristic, complemented
104	#2067	C₂²	1	1	yes	characteristic
105	#2067	C₂²	1	1	yes	characteristic
106	#2067	C₂²	1	1	yes	characteristic
107	#2067	C₂²	1	1	yes	characteristic
108	#2067	C₂²	1	1	yes	characteristic
109	#2067	C₂²	1	1	yes	characteristic
110	#2067	C₂²	1	1	yes	characteristic
111	#2065	C₂²	1	1	yes	characteristic
112	#2059	C₂²	1	1	yes	characteristic, complemented
113	#2058	C₂²	1	1	yes	characteristic, complemented
114	#2058	C₂²	1	1	yes	characteristic, complemented
115	#2057	C₂²	1	1	yes	characteristic, complemented
116	#2057	C₂²	1	1	yes	characteristic, complemented
117	#2057	C₂²	1	1	yes	characteristic, complemented
118	#2057	C₂²	1	1	yes	characteristic, complemented
119	#2057	C₂²	1	1	yes	characteristic, complemented
120	#2025	C₂²	1	1	yes	characteristic
121	#2023	C₂²	1	1	yes	characteristic
122	#2023	C₂²	1	1	yes	characteristic
123	#2023	C₂²	1	1	yes	characteristic
124	#1993	C₂²	1	1	yes	characteristic, complemented
125	#1992	C₂²	1	1	yes	characteristic, complemented
126	#1990	C₂²	1	1	yes	characteristic, complemented
127	#1990	C₂²	1	1	yes	characteristic, complemented
128	#1990	C₂²	1	1	yes	characteristic, complemented
129	#1990	C₂²	1	1	yes	characteristic, complemented
130	#1988	C₂²	1	1	yes	characteristic, complemented
131	#1987	C₂²	1	1	yes	characteristic, complemented
132	#1985	C₂²	1	1	yes	characteristic, complemented
133	#1947	C₂²	1	1	yes	characteristic, complemented
134	#1947	C₂²	1	1	yes	characteristic, complemented
135	#1944	C₂²	1	1	yes	characteristic, complemented
136	#1943	C₂²	1	1	yes	characteristic, complemented
137	#1943	C₂²	1	1	yes	characteristic, complemented
138	#1943	C₂²	1	1	yes	characteristic, complemented
139	#1943	C₂²	1	1	yes	characteristic, complemented
140	#1943	C₂²	1	1	yes	characteristic, complemented
141	#1942	C₂²	1	1	yes	characteristic, complemented
142	#1942	C₂²	1	1	yes	characteristic, complemented
143	#1940	C₂²	1	1	yes	characteristic, complemented
144	#1936	C₂²	1	1	yes	characteristic
145	#1936	C₂²	1	1	yes	characteristic
146	#1936	C₂²	1	1	yes	characteristic
147	#1936	C₂²	1	1	yes	characteristic
148	#1936	C₂²	1	1	yes	characteristic
149	#1936	C₂²	1	1	yes	characteristic
150	#1934	C₂²	1	1	yes	characteristic
151	#1934	C₂²	1	1	yes	characteristic
152	#1934	C₂²	1	1	yes	characteristic
153	#1934	C₂²	1	1	yes	characteristic
154	#1934	C₂²	1	1	yes	characteristic
155	#1934	C₂²	1	1	yes	characteristic
156	#1926	C₂²	1	1	yes	characteristic
157	#1926	C₂²	1	1	yes	characteristic
158	#1925	C₂²	1	1	yes	characteristic
159	#1925	C₂²	1	1	yes	characteristic
160	#1921	C₂²	1	1	yes	characteristic, complemented
161	#1920	C₂²	1	1	yes	characteristic, complemented
162	#1919	C₂²	1	1	yes	characteristic, complemented
163	#1918	C₂²	1	1	yes	characteristic, complemented
164	#1916	C₂²	1	1	yes	characteristic, complemented
165	#1916	C₂²	1	1	yes	characteristic, complemented
166	#1864	C₂²	1	1	yes	characteristic
167	#1864	C₂²	1	1	yes	characteristic
168	#1864	C₂²	1	1	yes	characteristic
169	#1862	C₂²	1	1	yes	characteristic
170	#1862	C₂²	1	1	yes	characteristic
171	#1862	C₂²	1	1	yes	characteristic
172	#1862	C₂²	1	1	yes	characteristic
173	#1862	C₂²	1	1	yes	characteristic
174	#1854	C₂²	1	1	yes	characteristic
175	#1854	C₂²	1	1	yes	characteristic
176	#1852	C₂²	1	1	yes	characteristic
177	#1852	C₂²	1	1	yes	characteristic
178	#1851	C₂²	1	1	yes	characteristic
179	#1851	C₂²	1	1	yes	characteristic
180	#1845	C₂²	1	1	yes	characteristic, complemented
181	#1825	C₂²	1	1	yes	characteristic
182	#1825	C₂²	1	1	yes	characteristic
183	#1809	C₂²	1	1	yes	characteristic
184	#1809	C₂²	1	1	yes	characteristic
185	#1809	C₂²	1	1	yes	characteristic
186	#1809	C₂²	1	1	yes	characteristic
187	#1804	C₂²	1	1	yes	characteristic
188	#1802	C₂²	1	1	yes	characteristic
189	#1797	C₂²	1	1	yes	characteristic
190	#1786	C₂²	1	1	yes	characteristic
191	#1786	C₂²	1	1	yes	characteristic
192	#1771	C₂²	1	1	yes	characteristic, complemented
193	#1771	C₂²	1	1	yes	characteristic, complemented
194	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
195	#1762	C₂²	1	1	yes	characteristic
196	#1762	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	#1753	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	#1736	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	#543	—	4	8	no	—
207	C₂×C₄⋊Q₈	—	2	1	no	—
208	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×#125	—	2	1	no	—
214	C₂×#125	—	2	1	no	—
215	C₂×#125	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	—	2	1	no	—
217	C₂×C₂²⋊Q₈	—	2	1	no	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
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	—	2	1	no	—
228	C₂×C₂²⋊Q₈	—	2	1	no	—
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂×#117	C₂³	1	1	yes	characteristic
237	C₂×#117	C₂³	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	—	2	1	no	—
240	C₂²×C₂²⋊C₄	—	2	1	no	—
241	C₂²×C₂²⋊C₄	—	2	1	no	—
242	C₂²×C₂²⋊C₄	—	2	1	no	—
243	C₂²×C₄²	C₂³	1	1	yes	characteristic
244	#498	—	4	2	no	—
245	#478	—	4	2	no	—
246	#476	—	4	2	no	—
247	#446	—	4	2	no	—
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#107	C₂³	1	1	yes	characteristic
253	C₂×#107	C₂³	1	1	yes	characteristic
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×#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×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	#418	—	4	2	no	—
271	#418	Q₈	1	8	yes	complemented
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	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×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₄×M₁₆	—	4	2	no	—
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×#97	C₂³	1	1	yes	characteristic
293	C₂×#97	C₂³	1	1	yes	characteristic
294	C₂×#97	C₂³	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
296	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#400	—	2	1	no	—
302	#400	—	2	1	no	—
303	#399	—	2	1	no	—
304	#399	—	2	1	no	—
305	#399	—	2	1	no	—
306	#399	—	2	1	no	—
307	#399	—	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	#396	—	2	1	no	—
317	#396	—	2	1	no	—
318	#396	—	2	1	no	—
319	#396	—	2	1	no	—
320	#396	—	2	1	no	—
321	#396	—	2	1	no	—
322	#396	—	2	1	no	—
323	#396	—	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	#395	—	2	1	no	—
332	#395	—	2	1	no	—
333	#395	—	2	1	no	—
334	#393	—	2	1	no	—
335	#393	—	2	1	no	—
336	#393	—	2	1	no	—
337	#393	—	2	1	no	—
338	#393	—	2	1	no	—
339	#391	—	2	1	no	—
340	#391	—	2	1	no	—
341	#391	—	2	1	no	—
342	#391	—	2	1	no	—
343	#391	—	2	1	no	—
344	#391	D₄	1	1	yes	characteristic
345	#390	—	2	1	no	—
346	#390	—	2	1	no	—
347	#390	C₂³	1	1	yes	characteristic
348	#390	C₂³	1	1	yes	characteristic
349	#390	C₂³	1	1	yes	characteristic
350	#390	C₂³	1	1	yes	characteristic
351	#390	C₂³	1	1	yes	characteristic
352	#390	C₂³	1	1	yes	characteristic
353	#390	C₂³	1	1	yes	characteristic
354	#390	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
362	#389	—	2	1	no	—
363	#389	—	2	1	no	—
364	#389	D₄	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	#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	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	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	D₄	1	1	yes	characteristic
396	#387	D₄	1	1	yes	characteristic
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#386	—	2	1	no	—
401	#385	—	2	1	no	—
402	#385	—	2	1	no	—
403	#385	—	2	1	no	—
404	#385	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	D₄	1	1	yes	characteristic
410	#385	D₄	1	1	yes	characteristic
411	#384	—	2	1	no	—
412	#384	C₂³	1	1	yes	characteristic
413	#384	C₂³	1	1	yes	characteristic
414	#384	C₂³	1	1	yes	characteristic
415	#384	C₂³	1	1	yes	characteristic
416	#384	C₂³	1	1	yes	characteristic
417	#383	—	2	1	no	—
418	#382	—	2	1	no	—
419	#382	C₂³	1	1	yes	characteristic
420	#380	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	—	2	1	no	—
423	#380	—	2	1	no	—
424	#380	D₄	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	#380	C₂³	1	1	yes	characteristic
427	#380	C₂³	1	1	yes	characteristic
428	#380	C₂³	1	1	yes	characteristic
429	#379	—	2	1	no	—
430	#379	—	2	1	no	—
431	C₄×C₄⋊C₄	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
443	#376	—	2	1	no	—
444	#340	C₂³	1	1	yes	characteristic
445	#340	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
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	#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	C₂⁵	—	2	1	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	C₂×Q₈	1	4	yes	—
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂⁴	1	1	yes	characteristic
510	C₂×M₁₆	—	2	2	no	—
511	C₂×M₁₆	—	2	2	no	—
512	C₂×M₁₆	—	4	1	no	—
513	C₂×M₁₆	—	4	1	no	—
514	C₂×M₁₆	—	4	1	no	—
515	C₂×M₁₆	C₂×Q₈	1	4	yes	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
530	C₄⋊Q₈	—	4	1	no	—
531	C₄⋊Q₈	—	4	1	no	—
532	C₄⋊Q₈	—	4	1	no	—
533	C₄⋊Q₈	—	4	1	no	—
534	C₄⋊Q₈	—	8	2	no	—
535	#125	—	4	1	no	—
536	#125	—	4	1	no	—
537	#125	—	4	4	no	—
538	#125	—	8	2	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	4	4	no	—
541	C₂²⋊Q₈	—	4	4	no	—
542	C₂²⋊Q₈	—	4	4	no	—
543	C₂²⋊Q₈	—	4	4	no	—
544	C₂²⋊Q₈	—	4	4	no	—
545	C₂²⋊Q₈	—	4	4	no	—
546	C₂²⋊Q₈	—	4	4	no	—
547	C₂²⋊Q₈	—	4	4	no	—
548	C₂²⋊Q₈	—	4	4	no	—
549	C₂²⋊Q₈	—	4	4	no	—
550	C₂²⋊Q₈	—	4	4	no	—
551	C₂²⋊Q₈	—	8	2	no	—
552	C₂²⋊Q₈	—	8	2	no	—
553	C₂²⋊Q₈	—	8	2	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×D₄	—	4	1	no	—
557	C₄×D₄	—	4	1	no	—
558	C₄×D₄	—	4	1	no	—
559	C₄×D₄	—	4	1	no	—
560	C₄×D₄	—	4	1	no	—
561	C₄×D₄	—	4	1	no	—
562	C₄×D₄	—	4	1	no	—
563	C₄×D₄	—	4	1	no	—
564	#117	—	2	2	no	—
565	#117	—	4	1	no	—
566	#117	—	4	1	no	—
567	#117	C₂×Q₈	1	4	yes	—
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	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
607	C₂×C₄⋊C₄	—	4	1	no	—
608	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
658	C₂×C₂²⋊C₄	—	4	4	no	—
659	C₂×C₂²⋊C₄	—	4	4	no	—
660	C₂×C₂²⋊C₄	—	8	2	no	—
661	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	4	1	no	—
672	C₂×C₄²	—	4	1	no	—
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	C₂×C₄²	C₂⁴	1	1	yes	characteristic
678	C₂×C₄²	C₂⁴	1	1	yes	characteristic
679	C₂×C₄²	C₂⁴	1	1	yes	characteristic
680	C₂×C₄²	C₂⁴	1	1	yes	characteristic
681	#107	—	4	1	no	—
682	#107	—	4	1	no	—
683	#107	—	4	1	no	—
684	#107	—	4	1	no	—
685	#107	—	4	1	no	—
686	#107	—	4	1	no	—
687	#107	—	4	1	no	—
688	#107	—	4	1	no	—
689	#107	—	4	1	no	—
690	#107	—	4	1	no	—
691	#106	—	2	2	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	—	2	2	no	—
698	C₄⋊C₈	—	2	2	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	#102	—	2	2	no	—
704	#102	—	2	2	no	—
705	#102	—	4	1	no	—
706	#102	—	4	1	no	—
707	#102	—	4	1	no	—
708	#102	—	4	1	no	—
709	#102	—	4	1	no	—
710	#102	—	4	1	no	—
711	#102	—	4	1	no	—
712	#102	—	4	1	no	—
713	#102	—	4	1	no	—
714	#102	—	4	1	no	—
715	#102	C₂×Q₈	1	4	yes	—
716	#102	C₂×Q₈	1	4	yes	—
717	#102	C₂×Q₈	1	4	yes	—
718	#102	C₂×Q₈	1	4	yes	—
719	C₂²⋊C₈	—	2	2	no	—
720	C₂²⋊C₈	—	2	2	no	—
721	#97	—	2	2	no	—
722	#97	—	4	1	no	—
723	#97	—	4	1	no	—
724	#97	—	4	1	no	—
725	C₄×C₈	—	2	2	no	—
726	C₄×C₈	—	4	1	no	—
727	C₄×C₈	—	4	1	no	—
728	C₄×C₈	—	4	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	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
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	#95	C₂×D₄	1	1	yes	characteristic
767	#95	C₂×D₄	1	1	yes	characteristic
768	#95	C₂×D₄	1	1	yes	characteristic
769	C₂⁴	—	2	1	no	—
770	C₂⁴	—	2	1	no	—
771	C₂⁴	—	2	4	no	—
772	C₂⁴	—	4	2	no	—
773	C₂⁴	—	4	2	no	—
774	C₂⁴	—	8	1	no	—
775	C₂⁴	—	8	1	no	—
776	C₂⁴	—	8	1	no	—
777	C₂⁴	—	8	1	no	—
778	C₂⁴	C₂²×D₄	1	1	yes	characteristic
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	4	1	no	—
781	C₂×Q₈	—	4	1	no	—
782	C₂×Q₈	—	4	2	no	—
783	C₂×Q₈	—	4	2	no	—
784	C₂×Q₈	—	4	2	no	—
785	C₂×Q₈	—	4	2	no	—
786	C₂×Q₈	—	8	1	no	—
787	C₂×Q₈	—	8	1	no	—
788	C₂×Q₈	—	8	1	no	—
789	C₂×Q₈	—	8	1	no	—
790	C₂×Q₈	—	8	1	no	—
791	C₂×Q₈	—	8	1	no	—
792	C₂×Q₈	—	8	1	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×D₄	—	2	4	no	—
798	C₂×D₄	—	2	1	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	—	2	1	no	—
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	4	4	no	—
809	C₂×D₄	—	4	4	no	—
810	C₂×D₄	—	8	2	no	—
811	C₂×D₄	—	8	2	no	—
812	C₂×D₄	—	8	1	no	—
813	C₂×D₄	—	8	1	no	—
814	C₂×D₄	C₂²×Q₈	1	2	yes	—
815	C₂×D₄	C₂²×Q₈	1	2	yes	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	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	2	no	—
823	C₂²×C₄	—	2	2	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	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	1	no	—
838	C₂²×C₄	—	4	1	no	—
839	C₂²×C₄	—	4	1	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	8	1	no	—
846	C₂²×C₄	—	8	1	no	—
847	C₂²×C₄	—	8	1	no	—
848	C₂²×C₄	—	8	1	no	—
849	C₂²×C₄	—	8	1	no	—
850	C₂²×C₄	—	8	1	no	—
851	C₂²×C₄	—	8	1	no	—
852	C₂²×C₄	—	8	1	no	—
853	C₂²×C₄	—	8	1	no	—
854	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
865	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
866	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
867	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
868	C₂²×C₄	C₂²×Q₈	1	2	yes	—
869	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
870	C₂²×C₄	C₂⁵	1	1	yes	characteristic
871	M₁₆	—	4	4	no	—
872	M₁₆	—	4	4	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	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	C₂²×Q₈	1	2	yes	—
895	C₂×C₈	C₂²×Q₈	1	2	yes	—
896	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	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	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	4	1	no	—
928	C₄⋊C₄	—	4	1	no	—
929	C₄⋊C₄	—	4	1	no	—
930	C₄⋊C₄	—	4	1	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	2	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	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	no	—
958	C₄⋊C₄	—	8	1	no	—
959	C₄⋊C₄	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₄⋊C₄	—	8	1	no	—
962	C₄⋊C₄	—	8	1	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	—	8	1	no	—
967	C₄⋊C₄	—	8	1	no	—
968	C₄⋊C₄	—	8	1	no	—
969	C₄⋊C₄	AGL(1,ℤ/8)	1	4	yes	—
970	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
971	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	4	1	no	—
976	C₂²⋊C₄	—	4	1	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	no	—
995	C₂²⋊C₄	—	8	1	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	C₄²	—	2	4	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	4	1	no	—
1016	C₄²	—	4	1	no	—
1017	C₄²	—	4	2	no	—
1018	C₄²	—	8	1	no	—
1019	C₄²	—	8	1	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	4	8	no	—
1031	C₂³	—	4	1	no	—
1032	C₂³	—	4	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	8	4	no	—
1044	C₂³	—	8	4	no	—
1045	C₂³	—	16	2	no	—
1046	C₂³	—	16	2	no	—
1047	C₂³	—	16	2	no	—
1048	C₂³	—	16	2	no	—
1049	C₂³	D₄×Q₈	1	2	yes	—
1050	C₂³	C₂³×D₄	1	1	yes	characteristic
1051	Q₈	—	8	2	no	—
1052	Q₈	—	16	2	no	—
1053	Q₈	—	16	2	no	—
1054	Q₈	—	16	2	no	—
1055	Q₈	—	16	2	no	—
1056	Q₈	—	16	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	4	1	no	—
1062	D₄	—	4	1	no	—
1063	D₄	—	4	1	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	8	4	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	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	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	—	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	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	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	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	16	2	no	—
1149	C₂×C₄	—	16	2	no	—
1150	C₂×C₄	—	16	2	no	—
1151	C₂×C₄	—	16	2	no	—
1152	C₂×C₄	—	16	2	no	—
1153	C₂×C₄	D₄×Q₈	1	2	yes	—
1154	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
1155	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
1156	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
1157	C₂×C₄	#576	1	2	yes	—
1158	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
1159	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1160	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1161	C₂×C₄	#585	1	1	yes	characteristic
1162	C₂×C₄	#585	1	1	yes	characteristic
1163	C₂×C₄	#585	1	1	yes	characteristic
1164	C₈	—	2	2	no	—
1165	C₈	—	2	2	no	—
1166	C₈	—	2	2	no	—
1167	C₈	—	4	1	no	—
1168	C₈	—	4	1	no	—
1169	C₈	—	4	1	no	—
1170	C₈	—	4	1	no	—
1171	C₈	—	4	1	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	8	1	no	—
1186	C₂²	—	8	1	no	—
1187	C₂²	—	8	1	no	—
1188	C₂²	—	8	1	no	—
1189	C₂²	—	8	1	no	—
1190	C₂²	—	8	1	no	—
1191	C₂²	—	8	1	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	16	8	no	—
1194	C₂²	C₂×D₄×Q₈	1	1	yes	characteristic
1195	C₂²	#3496	1	1	yes	characteristic
1196	C₂²	#3500	1	1	yes	characteristic
1197	C₂²	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
1198	C₂²	C₂×#576	1	1	yes	characteristic
1199	C₂²	#3586	1	1	yes	characteristic
1200	C₂²	#3586	1	1	yes	characteristic
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	2	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	8	1	no	—
1217	C₄	—	8	1	no	—
1218	C₄	—	8	1	no	—
1219	C₄	—	8	1	no	—
1220	C₄	—	8	1	no	—
1221	C₄	—	8	1	no	—
1222	C₄	—	8	1	no	—
1223	C₄	—	8	1	no	—
1224	C₄	—	8	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	—	8	1	no	—
1228	C₄	#3458	1	1	yes	characteristic
1229	C₄	#3501	1	1	yes	characteristic
1230	C₄	#3535	1	1	yes	characteristic
1231	C₄	#3564	1	1	yes	characteristic
1232	C₂	—	4	2	no	—
1233	C₂	—	8	2	no	—
1234	C₂	—	8	2	no	—
1235	C₂	#39364	1	1	yes	characteristic
1236	C₂	Q₈×AGL(1,ℤ/8)	1	1	yes	characteristic
1237	C₂	#61381	1	1	yes	characteristic
1238	C₂	#62295	1	1	yes	characteristic
1239	C₂	#62311	1	1	yes	characteristic
1240	C₂	#62535	1	1	yes	characteristic
1241	C₂	#62571	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	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. #39983	C₂	semidirect
3. #33210	C₂	semidirect
4. #32593	C₂	semidirect
5. #32581	C₂	semidirect
6. #32342	C₂	semidirect
7. #32342	C₂	semidirect
8. #31891	C₂	semidirect
9. #31882	C₂	semidirect
10. #30954	C₂	semidirect
11. #30947	C₂	semidirect
12. #29971	C₂	semidirect
14. #28974	C₂	semidirect
15. #28968	C₂	semidirect
16. #28959	C₂	semidirect
17. #28943	C₂	semidirect
18. #28784	C₂	semidirect
19. #28781	C₂	semidirect
20. #27830	C₂	semidirect
21. #27813	C₂	semidirect
22. #26011	C₂	semidirect
23. #26005	C₂	semidirect
26. #25482	C₂	semidirect
27. #25477	C₂	semidirect
30. #21600	C₂	semidirect
33. C₂×#498	C₂²	semidirect
36. C₂×#446	C₂²	semidirect
53. #2584	C₂²	semidirect
54. #2567	C₂²	semidirect
55. #2551	C₂²	semidirect
57. #2550	C₂²	semidirect
62. #2509	C₂²	semidirect
63. #2507	C₂²	semidirect
64. #2506	C₂²	semidirect
65. #2506	C₂²	semidirect
84. #2100	C₂²	semidirect
85. #2099	C₂²	semidirect
86. #2099	C₂²	semidirect
87. #2099	C₂²	semidirect
92. #2088	C₂²	semidirect
93. #2088	C₂²	semidirect
94. #2088	C₂²	semidirect
95. #2088	C₂²	semidirect
96. #2087	C₂²	semidirect
97. #2087	C₂²	semidirect
98. #2087	C₂²	semidirect
99. #2086	C₂²	semidirect
100. #2085	C₂²	semidirect
101. #2084	C₂²	semidirect
102. #2083	C₂²	semidirect
103. #2083	C₂²	semidirect
112. #2059	C₂²	semidirect
113. #2058	C₂²	semidirect
114. #2058	C₂²	semidirect
115. #2057	C₂²	semidirect
116. #2057	C₂²	semidirect
117. #2057	C₂²	semidirect
118. #2057	C₂²	semidirect
119. #2057	C₂²	semidirect
124. #1993	C₂²	semidirect
125. #1992	C₂²	semidirect
126. #1990	C₂²	semidirect
127. #1990	C₂²	semidirect
128. #1990	C₂²	semidirect
129. #1990	C₂²	semidirect
130. #1988	C₂²	semidirect
131. #1987	C₂²	semidirect
132. #1985	C₂²	semidirect
133. #1947	C₂²	semidirect
134. #1947	C₂²	semidirect
135. #1944	C₂²	semidirect
136. #1943	C₂²	semidirect
137. #1943	C₂²	semidirect
138. #1943	C₂²	semidirect
139. #1943	C₂²	semidirect
140. #1943	C₂²	semidirect
141. #1942	C₂²	semidirect
142. #1942	C₂²	semidirect
143. #1940	C₂²	semidirect
160. #1921	C₂²	semidirect
161. #1920	C₂²	semidirect
162. #1919	C₂²	semidirect
163. #1918	C₂²	semidirect
164. #1916	C₂²	semidirect
165. #1916	C₂²	semidirect
180. #1845	C₂²	semidirect
192. #1771	C₂²	semidirect
193. #1771	C₂²	semidirect
194. C₈×C₄⋊C₄	C₂²	semidirect
271. #418	Q₈	semidirect

Maximal subgroups

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

subgroup	index
#39983	2
#39367	2
#33210	2
#32593	2
#32581	2
#32342	2
#31891	2
#31882	2
#30954	2
#30947	2
#29971	2
#29950	2
#28974	2
#28968	2
#28959	2
#28943	2
#28784	2
#28781	2
#27830	2
#27813	2
#26011	2
#26005	2
#25976	2
#25974	2
#25482	2
#25477	2
#22584	2
#22580	2
#21600	2
#21095	2