Subgroups — #6484412

Order 512.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34625	C₂	1	1	yes	maximal, characteristic, complemented
2	#34211	C₂	1	1	yes	maximal, characteristic
3	#32967	C₂	1	1	yes	maximal, characteristic, complemented
4	#32966	C₂	1	1	yes	maximal, characteristic
5	#32964	C₂	1	1	yes	maximal, characteristic, complemented
6	#32962	C₂	1	1	yes	maximal, characteristic
7	#29963	C₂	1	1	yes	maximal, characteristic, complemented
8	#29962	C₂	1	1	yes	maximal, characteristic
9	#29960	C₂	1	1	yes	maximal, characteristic, complemented
10	#29959	C₂	1	1	yes	maximal, characteristic
11	#29262	C₂	1	1	yes	maximal, characteristic, complemented
12	#29261	C₂	1	1	yes	maximal, characteristic, complemented
13	#29261	C₂	1	1	yes	maximal, characteristic, complemented
14	#29260	C₂	1	1	yes	maximal, characteristic, complemented
15	#29203	C₂	1	1	yes	maximal, characteristic, complemented
16	#29203	C₂	1	1	yes	maximal, characteristic, complemented
17	#29200	C₂	1	1	yes	maximal, characteristic, complemented
18	#29199	C₂	1	1	yes	maximal, characteristic, complemented
19	#29151	C₂	1	1	yes	maximal, characteristic, complemented
20	#29151	C₂	1	1	yes	maximal, characteristic, complemented
21	#28524	C₂	1	1	yes	maximal, characteristic, complemented
22	#28523	C₂	1	1	yes	maximal, characteristic, complemented
23	#28285	C₂	1	1	yes	maximal, characteristic, complemented
24	#28285	C₂	1	1	yes	maximal, characteristic, complemented
25	#28282	C₂	1	1	yes	maximal, characteristic, complemented
26	#28281	C₂	1	1	yes	maximal, characteristic, complemented
27	#21989	C₂	1	1	yes	maximal, characteristic, complemented
28	#21984	C₂	1	1	yes	maximal, characteristic, complemented
29	#21808	C₂	1	1	yes	maximal, characteristic
30	#21806	C₂	1	1	yes	maximal, characteristic
31	#20815	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#124	C₂²	1	1	yes	characteristic
33	C₂×#519	C₂²	1	1	yes	characteristic
34	C₂×#518	C₂²	1	1	yes	characteristic
35	C₂×#479	C₂²	1	1	yes	characteristic, complemented
36	C₂×#479	C₂²	1	1	yes	characteristic, complemented
37	C₂×#477	C₂²	1	1	yes	characteristic, complemented
38	C₂×#475	C₂²	1	1	yes	characteristic, complemented
39	C₂×#478	C₂²	1	1	yes	characteristic
40	C₂×#478	C₂²	1	1	yes	characteristic
41	C₂×#476	C₂²	1	1	yes	characteristic
42	C₂×#474	C₂²	1	1	yes	characteristic
43	C₂×#432	C₂²	1	1	yes	characteristic
44	C₂×#431	C₂²	1	1	yes	characteristic
45	#2667	—	2	1	no	—
46	#2666	—	2	1	no	—
47	#2666	—	2	1	no	—
48	#2665	—	2	1	no	—
49	#2660	C₂²	1	1	yes	characteristic, complemented
50	#2660	C₂²	1	1	yes	characteristic, complemented
51	#2647	C₂²	1	1	yes	characteristic, complemented
52	#2647	C₂²	1	1	yes	characteristic, complemented
53	#2629	C₂²	1	1	yes	characteristic
54	#2629	C₂²	1	1	yes	characteristic
55	#2628	C₂²	1	1	yes	characteristic
56	#2628	C₂²	1	1	yes	characteristic
57	#2402	—	2	1	no	—
58	#2399	—	2	1	no	—
59	#2396	—	2	1	no	—
60	#2396	—	2	1	no	—
61	#2367	—	2	1	no	—
62	#2367	—	2	1	no	—
63	#2367	—	2	1	no	—
64	#2367	—	2	1	no	—
65	#2342	—	2	1	no	—
66	#2342	—	2	1	no	—
67	#2342	—	2	1	no	—
68	#2342	—	2	1	no	—
69	#2326	C₂²	1	1	yes	characteristic
70	#2326	C₂²	1	1	yes	characteristic
71	#2326	C₂²	1	1	yes	characteristic
72	#2326	C₂²	1	1	yes	characteristic
73	#2310	C₂²	1	1	yes	characteristic
74	#2309	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×#125	C₂²	1	1	yes	characteristic, complemented
78	C₄×#125	C₂²	1	1	yes	characteristic, complemented
79	C₄×#124	C₂²	1	1	yes	characteristic
80	C₄×#124	C₂²	1	1	yes	characteristic
81	C₄×#124	C₂²	1	1	yes	characteristic
82	C₄×#124	C₂²	1	1	yes	characteristic
83	#2285	C₂²	1	1	yes	characteristic
84	#2285	C₂²	1	1	yes	characteristic
85	#2283	C₂²	1	1	yes	characteristic
86	C₄×#117	C₂²	1	1	yes	characteristic
87	#2097	C₂²	1	1	yes	characteristic, complemented
88	#2097	C₂²	1	1	yes	characteristic, complemented
89	#2096	C₂²	1	1	yes	characteristic, complemented
90	#2095	C₂²	1	1	yes	characteristic, complemented
91	#2094	C₂²	1	1	yes	characteristic
92	#2093	C₂²	1	1	yes	characteristic
93	#2092	C₂²	1	1	yes	characteristic
94	#2092	C₂²	1	1	yes	characteristic
95	#2068	C₂²	1	1	yes	characteristic, complemented
96	#2068	C₂²	1	1	yes	characteristic, complemented
97	#2068	C₂²	1	1	yes	characteristic, complemented
98	#2068	C₂²	1	1	yes	characteristic, complemented
99	#2067	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, complemented
104	#2066	C₂²	1	1	yes	characteristic, complemented
105	#2066	C₂²	1	1	yes	characteristic, complemented
106	#2066	C₂²	1	1	yes	characteristic, complemented
107	#2065	C₂²	1	1	yes	characteristic
108	#2065	C₂²	1	1	yes	characteristic
109	#2065	C₂²	1	1	yes	characteristic
110	#2065	C₂²	1	1	yes	characteristic
111	#2026	C₂²	1	1	yes	characteristic, complemented
112	#2026	C₂²	1	1	yes	characteristic, complemented
113	#2025	C₂²	1	1	yes	characteristic
114	#2025	C₂²	1	1	yes	characteristic
115	#2024	C₂²	1	1	yes	characteristic, complemented
116	#2024	C₂²	1	1	yes	characteristic, complemented
117	#2023	C₂²	1	1	yes	characteristic
118	#2023	C₂²	1	1	yes	characteristic
119	#1983	C₂²	1	1	yes	characteristic
120	#1983	C₂²	1	1	yes	characteristic
121	#1983	C₂²	1	1	yes	characteristic
122	#1983	C₂²	1	1	yes	characteristic
123	#1983	C₂²	1	1	yes	characteristic
124	#1983	C₂²	1	1	yes	characteristic
125	#1983	C₂²	1	1	yes	characteristic
126	#1983	C₂²	1	1	yes	characteristic
127	#1959	C₂²	1	1	yes	characteristic
128	#1959	C₂²	1	1	yes	characteristic
129	#1959	C₂²	1	1	yes	characteristic
130	#1959	C₂²	1	1	yes	characteristic
131	#1958	C₂²	1	1	yes	characteristic
132	#1958	C₂²	1	1	yes	characteristic
133	#1958	C₂²	1	1	yes	characteristic
134	#1958	C₂²	1	1	yes	characteristic
135	#1949	C₂²	1	1	yes	characteristic, complemented
136	#1949	C₂²	1	1	yes	characteristic, complemented
137	#1949	C₂²	1	1	yes	characteristic, complemented
138	#1949	C₂²	1	1	yes	characteristic, complemented
139	#1949	C₂²	1	1	yes	characteristic, complemented
140	#1949	C₂²	1	1	yes	characteristic, complemented
141	#1949	C₂²	1	1	yes	characteristic, complemented
142	#1949	C₂²	1	1	yes	characteristic, complemented
143	#1865	C₂²	1	1	yes	characteristic, complemented
144	#1865	C₂²	1	1	yes	characteristic, complemented
145	#1865	C₂²	1	1	yes	characteristic, complemented
146	#1865	C₂²	1	1	yes	characteristic, complemented
147	#1864	C₂²	1	1	yes	characteristic
148	#1864	C₂²	1	1	yes	characteristic
149	#1864	C₂²	1	1	yes	characteristic
150	#1864	C₂²	1	1	yes	characteristic
151	#1863	C₂²	1	1	yes	characteristic, complemented
152	#1863	C₂²	1	1	yes	characteristic, complemented
153	#1863	C₂²	1	1	yes	characteristic, complemented
154	#1863	C₂²	1	1	yes	characteristic, complemented
155	#1862	C₂²	1	1	yes	characteristic
156	#1862	C₂²	1	1	yes	characteristic
157	#1862	C₂²	1	1	yes	characteristic
158	#1862	C₂²	1	1	yes	characteristic
159	#1854	C₂²	1	1	yes	characteristic
160	#1854	C₂²	1	1	yes	characteristic
161	#1854	C₂²	1	1	yes	characteristic
162	#1854	C₂²	1	1	yes	characteristic
163	#1854	C₂²	1	1	yes	characteristic
164	#1854	C₂²	1	1	yes	characteristic
165	#1854	C₂²	1	1	yes	characteristic
166	#1854	C₂²	1	1	yes	characteristic
167	#1847	C₂²	1	1	yes	characteristic, complemented
168	#1847	C₂²	1	1	yes	characteristic, complemented
169	#1845	C₂²	1	1	yes	characteristic, complemented
170	#1844	C₂²	1	1	yes	characteristic, complemented
171	#1842	C₂²	1	1	yes	characteristic, complemented
172	#1842	C₂²	1	1	yes	characteristic, complemented
173	#1836	C₂²	1	1	yes	characteristic, complemented
174	#1836	C₂²	1	1	yes	characteristic, complemented
175	#1834	C₂²	1	1	yes	characteristic, complemented
176	#1834	C₂²	1	1	yes	characteristic, complemented
177	#1831	C₂²	1	1	yes	characteristic, complemented
178	#1831	C₂²	1	1	yes	characteristic, complemented
179	#1805	C₂²	1	1	yes	characteristic, complemented
180	#1805	C₂²	1	1	yes	characteristic, complemented
181	#1804	C₂²	1	1	yes	characteristic
182	#1804	C₂²	1	1	yes	characteristic
183	#1803	C₂²	1	1	yes	characteristic, complemented
184	#1803	C₂²	1	1	yes	characteristic, complemented
185	#1802	C₂²	1	1	yes	characteristic
186	#1802	C₂²	1	1	yes	characteristic
187	#1798	C₂²	1	1	yes	characteristic
188	#1798	C₂²	1	1	yes	characteristic
189	#1798	C₂²	1	1	yes	characteristic
190	#1798	C₂²	1	1	yes	characteristic
191	#1787	C₂²	1	1	yes	characteristic
192	#1787	C₂²	1	1	yes	characteristic
193	#1787	C₂²	1	1	yes	characteristic
194	#1787	C₂²	1	1	yes	characteristic
195	#1786	C₂²	1	1	yes	characteristic
196	#1786	C₂²	1	1	yes	characteristic
197	#1786	C₂²	1	1	yes	characteristic
198	#1786	C₂²	1	1	yes	characteristic
199	#1768	C₂²	1	1	yes	characteristic, complemented
200	#1768	C₂²	1	1	yes	characteristic, complemented
201	#1768	C₂²	1	1	yes	characteristic, complemented
202	#1768	C₂²	1	1	yes	characteristic, complemented
203	C₂³×Q₈	C₂³	1	1	yes	characteristic
204	C₂³×D₄	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂×#125	C₂³	1	1	yes	characteristic
208	C₂×#125	C₂³	1	1	yes	characteristic
209	C₂×#124	—	2	1	no	—
210	C₂×#124	—	2	1	no	—
211	C₂×#124	—	2	4	no	—
212	C₂×#124	Q₈	1	8	yes	complemented
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×#124	C₂³	1	1	yes	characteristic
217	#519	—	4	2	no	—
218	#519	—	4	2	no	—
219	#518	—	4	2	no	—
220	#518	—	4	2	no	—
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×C₄×Q₈	—	2	1	no	—
223	C₂×C₄×Q₈	—	2	1	no	—
224	C₂×C₄×Q₈	—	2	1	no	—
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	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×#117	—	2	1	no	—
236	C₂×#117	—	2	1	no	—
237	C₂×#117	—	2	1	no	—
238	C₂×#117	C₂³	1	1	yes	characteristic
239	C₂×#117	C₂³	1	1	yes	characteristic
240	C₂×#117	C₂³	1	1	yes	characteristic
241	C₂×#117	C₂³	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	—	2	1	no	—
243	C₂²×C₂²⋊C₄	—	2	1	no	—
244	C₂²×C₂²⋊C₄	—	2	1	no	—
245	C₂²×C₂²⋊C₄	—	2	1	no	—
246	C₂²×C₄²	C₂³	1	1	yes	characteristic
247	#479	—	4	2	no	—
248	#479	—	4	2	no	—
249	#478	—	4	2	no	—
250	#478	—	4	2	no	—
251	#477	—	4	2	no	—
252	#476	—	4	2	no	—
253	#475	—	4	2	no	—
254	#474	—	4	2	no	—
255	#432	—	2	4	no	—
256	#431	—	2	4	no	—
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#107	C₂³	1	1	yes	characteristic
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×#102	C₂³	1	1	yes	characteristic
303	C₂×#102	C₂³	1	1	yes	characteristic
304	C₂×#102	C₂³	1	1	yes	characteristic
305	C₂×#102	C₂³	1	1	yes	characteristic
306	C₂×#102	C₂³	1	1	yes	characteristic
307	C₂×#102	C₂³	1	1	yes	characteristic
308	C₂×#102	C₂³	1	1	yes	characteristic
309	C₂×#102	C₂³	1	1	yes	characteristic
310	C₂×#102	C₂³	1	1	yes	characteristic
311	C₂×#102	C₂³	1	1	yes	characteristic
312	C₂×#102	C₂³	1	1	yes	characteristic
313	C₂×#102	C₂³	1	1	yes	characteristic
314	C₂×#102	C₂³	1	1	yes	characteristic
315	C₂×#102	C₂³	1	1	yes	characteristic
316	C₂×#102	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
321	C₂×#97	C₂³	1	1	yes	characteristic
322	C₂×#97	C₂³	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
325	#400	—	2	1	no	—
326	#400	—	2	1	no	—
327	#400	—	2	1	no	—
328	#400	—	2	1	no	—
329	#400	—	2	1	no	—
330	#400	—	2	1	no	—
331	#399	—	2	1	no	—
332	#399	—	2	1	no	—
333	#398	—	2	1	no	—
334	#398	—	2	1	no	—
335	#398	—	2	1	no	—
336	#398	—	2	1	no	—
337	#398	—	2	1	no	—
338	#398	—	2	1	no	—
339	#398	—	2	1	no	—
340	#398	—	2	1	no	—
341	#398	—	2	1	no	—
342	#398	—	2	1	no	—
343	#398	—	2	1	no	—
344	#398	—	2	1	no	—
345	#396	—	2	1	no	—
346	#396	—	2	1	no	—
347	#396	—	2	1	no	—
348	#396	—	2	1	no	—
349	#395	—	2	1	no	—
350	#395	—	2	1	no	—
351	#395	—	2	1	no	—
352	#395	—	2	1	no	—
353	#395	—	2	1	no	—
354	#395	—	2	1	no	—
355	#393	—	2	1	no	—
356	#393	—	2	1	no	—
357	#391	—	2	1	no	—
358	#391	—	2	1	no	—
359	#391	—	2	1	no	—
360	#391	—	2	1	no	—
361	#391	C₂³	1	1	yes	characteristic
362	#391	C₂³	1	1	yes	characteristic
363	#391	C₂³	1	1	yes	characteristic
364	#391	C₂³	1	1	yes	characteristic
365	#390	—	2	1	no	—
366	#390	—	2	1	no	—
367	#390	C₂³	1	1	yes	characteristic
368	#390	C₂³	1	1	yes	characteristic
369	#390	C₂³	1	1	yes	characteristic
370	#390	C₂³	1	1	yes	characteristic
371	#389	—	2	1	no	—
372	#389	—	2	1	no	—
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	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	—	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	#384	C₂³	1	1	yes	characteristic
410	#384	C₂³	1	1	yes	characteristic
411	#384	C₂³	1	1	yes	characteristic
412	#384	C₂³	1	1	yes	characteristic
413	#384	C₂³	1	1	yes	characteristic
414	#384	C₂³	1	1	yes	characteristic
415	#383	—	2	1	no	—
416	#382	—	2	1	no	—
417	#382	C₂³	1	1	yes	characteristic
418	#382	C₂³	1	1	yes	characteristic
419	#382	C₂³	1	1	yes	characteristic
420	#382	C₂³	1	1	yes	characteristic
421	#382	C₂³	1	1	yes	characteristic
422	#382	C₂³	1	1	yes	characteristic
423	#381	—	2	1	no	—
424	#381	—	2	1	no	—
425	#381	—	2	1	no	—
426	#380	—	2	1	no	—
427	#380	—	2	1	no	—
428	#380	—	2	1	no	—
429	#380	C₂³	1	1	yes	characteristic
430	#380	C₂³	1	1	yes	characteristic
431	#380	C₂³	1	1	yes	characteristic
432	#380	C₂³	1	1	yes	characteristic
433	#379	—	2	1	no	—
434	#379	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	—	2	1	no	—
439	C₄×C₄⋊C₄	—	2	1	no	—
440	C₄×C₄⋊C₄	—	2	1	no	—
441	C₄×C₄⋊C₄	—	2	1	no	—
442	C₄×C₄⋊C₄	—	2	1	no	—
443	C₄×C₄⋊C₄	—	2	1	no	—
444	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
445	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
446	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
447	C₄×C₄⋊C₄	D₄	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×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	C₄×C₂²⋊C₄	—	2	1	no	—
457	C₄×C₂²⋊C₄	—	2	1	no	—
458	C₄×C₂²⋊C₄	—	2	1	no	—
459	C₄×C₂²⋊C₄	—	2	1	no	—
460	C₄×C₂²⋊C₄	—	2	1	no	—
461	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
462	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
463	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
465	#376	—	2	1	no	—
466	#376	C₂³	1	1	yes	characteristic
467	#376	C₂³	1	1	yes	characteristic
468	C₄³	C₂³	1	1	yes	characteristic
469	C₄³	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	C₂⁵	—	2	1	no	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	—	2	1	no	—
498	C₂²×Q₈	—	2	2	no	—
499	C₂²×Q₈	—	4	1	no	—
500	C₂²×Q₈	—	4	1	no	—
501	C₂²×Q₈	—	4	1	no	—
502	C₂²×Q₈	—	4	1	no	—
503	C₂²×Q₈	C₂×Q₈	1	4	yes	—
504	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
505	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	—	4	1	no	—
509	C₂²×D₄	—	4	1	no	—
510	C₂²×D₄	—	4	1	no	—
511	C₂²×D₄	—	4	1	no	—
512	C₂²×D₄	C₂×Q₈	1	4	yes	—
513	C₂²×D₄	C₂⁴	1	1	yes	characteristic
514	C₂²×D₄	C₂⁴	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
521	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
522	C₂³×C₄	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	4	1	no	—
534	C₄⋊Q₈	—	4	1	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	4	1	no	—
538	#125	—	4	1	no	—
539	#124	—	2	8	no	—
540	#124	—	2	8	no	—
541	#124	—	2	2	no	—
542	#124	—	2	2	no	—
543	#124	—	2	2	no	—
544	#124	—	2	2	no	—
545	#124	C₂×Q₈	1	4	yes	—
546	#124	C₂×Q₈	1	4	yes	—
547	#124	C₂×Q₈	1	4	yes	—
548	#124	C₂×Q₈	1	4	yes	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	4	1	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	4	1	no	—
557	C₄×Q₈	—	4	4	no	—
558	C₄×Q₈	—	4	4	no	—
559	C₄×Q₈	—	8	2	no	—
560	C₄×Q₈	—	8	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	4	1	no	—
566	C₄×D₄	—	4	1	no	—
567	C₄×D₄	—	4	1	no	—
568	C₄×D₄	—	4	1	no	—
569	C₄×D₄	—	4	4	no	—
570	C₄×D₄	—	4	4	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	4	1	no	—
574	#117	—	4	1	no	—
575	#117	—	4	4	no	—
576	#117	—	4	4	no	—
577	#117	—	4	1	no	—
578	#117	—	4	1	no	—
579	#117	—	4	1	no	—
580	#117	—	4	1	no	—
581	#117	—	8	2	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	—	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	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	C₂⁴	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×C₂²⋊C₄	—	2	8	no	—
629	C₂×C₂²⋊C₄	—	2	8	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
657	C₂×C₂²⋊C₄	—	4	4	no	—
658	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
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	—	2	1	no	—
672	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
677	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
678	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
679	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
680	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
681	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
682	C₂×C₄²	C₂×Q₈	1	4	yes	—
683	C₂×C₄²	#41	1	4	yes	—
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	#107	—	4	1	no	—
693	#107	—	4	1	no	—
694	#107	—	4	1	no	—
695	#107	—	4	1	no	—
696	#107	—	4	1	no	—
697	#107	—	4	1	no	—
698	#106	—	4	1	no	—
699	#106	—	4	1	no	—
700	#106	—	4	1	no	—
701	#106	—	4	1	no	—
702	#106	—	4	1	no	—
703	#106	—	4	1	no	—
704	#106	—	4	1	no	—
705	#106	—	4	1	no	—
706	C₄⋊C₈	—	2	2	no	—
707	C₄⋊C₈	—	2	2	no	—
708	C₄⋊C₈	—	2	2	no	—
709	C₄⋊C₈	—	2	2	no	—
710	C₄⋊C₈	—	2	2	no	—
711	C₄⋊C₈	—	2	2	no	—
712	C₄⋊C₈	—	2	2	no	—
713	C₄⋊C₈	—	2	2	no	—
714	C₄⋊C₈	—	4	1	no	—
715	C₄⋊C₈	—	4	1	no	—
716	C₄⋊C₈	—	4	1	no	—
717	C₄⋊C₈	—	4	1	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#103	—	4	1	no	—
724	#103	—	4	1	no	—
725	#103	—	4	1	no	—
726	#103	—	4	1	no	—
727	#103	—	4	1	no	—
728	#103	—	4	1	no	—
729	#103	—	4	1	no	—
730	#103	—	4	1	no	—
731	#103	—	4	1	no	—
732	#103	—	4	1	no	—
733	#103	—	4	1	no	—
734	#102	—	4	1	no	—
735	#102	—	4	1	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	—	4	1	no	—
739	#102	—	4	1	no	—
740	#102	—	4	1	no	—
741	#102	—	4	1	no	—
742	#102	—	4	1	no	—
743	#102	—	4	1	no	—
744	#102	—	4	1	no	—
745	#102	—	4	1	no	—
746	#102	—	4	1	no	—
747	#102	—	4	1	no	—
748	#102	—	4	1	no	—
749	#102	—	4	1	no	—
750	C₂²⋊C₈	—	2	2	no	—
751	C₂²⋊C₈	—	2	2	no	—
752	C₂²⋊C₈	—	2	2	no	—
753	C₂²⋊C₈	—	2	2	no	—
754	#97	—	2	2	no	—
755	#97	—	2	2	no	—
756	C₄×C₈	—	2	2	no	—
757	C₄×C₈	—	2	2	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	C₂×D₄	1	1	yes	characteristic
795	#95	C₂×D₄	1	1	yes	characteristic
796	#95	C₂×D₄	1	1	yes	characteristic
797	#95	C₂×D₄	1	1	yes	characteristic
798	#95	C₂×D₄	1	1	yes	characteristic
799	#95	C₂×D₄	1	1	yes	characteristic
800	#95	C₂×D₄	1	1	yes	characteristic
801	#95	C₂×D₄	1	1	yes	characteristic
802	C₂⁴	—	2	1	no	—
803	C₂⁴	—	2	1	no	—
804	C₂⁴	—	2	4	no	—
805	C₂⁴	—	4	2	no	—
806	C₂⁴	—	4	2	no	—
807	C₂⁴	—	8	1	no	—
808	C₂⁴	—	8	1	no	—
809	C₂⁴	—	8	1	no	—
810	C₂⁴	—	8	1	no	—
811	C₂⁴	C₂²×D₄	1	1	yes	characteristic
812	C₂×Q₈	—	2	4	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	4	4	no	—
824	C₂×Q₈	—	4	4	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×Q₈	—	4	2	no	—
827	C₂×Q₈	—	4	4	no	—
828	C₂×Q₈	—	4	4	no	—
829	C₂×Q₈	—	4	2	no	—
830	C₂×Q₈	—	4	2	no	—
831	C₂×Q₈	—	8	1	no	—
832	C₂×Q₈	—	8	1	no	—
833	C₂×Q₈	—	8	1	no	—
834	C₂×Q₈	—	8	1	no	—
835	C₂×Q₈	C₂²×Q₈	1	2	yes	—
836	C₂×Q₈	C₂²×Q₈	1	2	yes	—
837	C₂×D₄	—	2	4	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	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	4	4	no	—
849	C₂×D₄	—	4	4	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	4	no	—
853	C₂×D₄	—	4	4	no	—
854	C₂×D₄	C₂²×Q₈	1	2	yes	—
855	C₂×D₄	C₂²×Q₈	1	2	yes	—
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	4	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	1	no	—
877	C₂²×C₄	—	4	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	8	1	no	—
886	C₂²×C₄	—	8	1	no	—
887	C₂²×C₄	—	8	1	no	—
888	C₂²×C₄	—	8	1	no	—
889	C₂²×C₄	—	8	1	no	—
890	C₂²×C₄	—	8	1	no	—
891	C₂²×C₄	—	8	1	no	—
892	C₂²×C₄	—	8	1	no	—
893	C₂²×C₄	C₂²⋊Q₈	1	4	yes	—
894	C₂²×C₄	C₂²⋊Q₈	1	4	yes	—
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
901	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
902	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
904	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂²×Q₈	1	2	yes	—
909	C₂²×C₄	C₂×#41	1	2	yes	—
910	C₂²×C₄	C₂⁵	1	1	yes	characteristic
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	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	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	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	4	1	no	—
962	C₄⋊C₄	—	4	1	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	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	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	—	8	1	no	—
984	C₄⋊C₄	—	8	1	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	—	8	1	no	—
992	C₄⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	4	no	—
996	C₂²⋊C₄	—	2	4	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	4	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	4	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	4	1	no	—
1004	C₂²⋊C₄	—	4	1	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	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	C₂²⋊C₄	—	8	1	no	—
1018	C₂²⋊C₄	—	8	1	no	—
1019	C₂²⋊C₄	—	8	1	no	—
1020	C₂²⋊C₄	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	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	—	4	1	no	—
1030	C₄²	—	4	1	no	—
1031	C₄²	—	4	1	no	—
1032	C₄²	—	4	1	no	—
1033	C₄²	—	4	1	no	—
1034	C₄²	—	4	1	no	—
1035	C₄²	—	4	1	no	—
1036	C₄²	—	4	1	no	—
1037	C₄²	—	4	2	no	—
1038	C₄²	—	4	2	no	—
1039	C₄²	—	4	2	no	—
1040	C₄²	—	4	2	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	—	4	2	no	—
1044	C₄²	—	4	2	no	—
1045	C₄²	—	4	2	no	—
1046	C₄²	—	4	2	no	—
1047	C₄²	C₂²⋊Q₈	1	4	yes	—
1048	C₄²	C₂²⋊Q₈	1	4	yes	—
1049	C₄²	C₂²×Q₈	1	2	yes	—
1050	C₄²	C₂²×Q₈	1	2	yes	—
1051	C₄²	C₂×#41	1	2	yes	—
1052	C₄²	C₂×#41	1	2	yes	—
1053	C₄²	H(5,𝔽₂)	1	2	yes	—
1054	C₄²	H(5,𝔽₂)	1	2	yes	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	4	8	no	—
1064	C₂³	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	4	1	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	8	4	no	—
1077	C₂³	—	8	4	no	—
1078	C₂³	—	16	2	no	—
1079	C₂³	—	16	2	no	—
1080	C₂³	—	16	2	no	—
1081	C₂³	—	16	2	no	—
1082	C₂³	C₂×C₂²⋊Q₈	1	2	yes	—
1083	C₂³	C₂³×D₄	1	1	yes	characteristic
1084	Q₈	—	2	2	no	—
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	4	8	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	8	4	no	—
1094	Q₈	—	8	4	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	4	8	no	—
1100	D₄	—	4	1	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	4	1	no	—
1103	D₄	—	4	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	2	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	1	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	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	4	4	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	8	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	16	2	no	—
1186	C₂×C₄	—	16	2	no	—
1187	C₂×C₄	—	16	2	no	—
1188	C₂×C₄	—	16	2	no	—
1189	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1190	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1191	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1192	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1193	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1194	C₂×C₄	#535	1	2	yes	—
1195	C₂×C₄	#535	1	2	yes	—
1196	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
1197	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1198	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1199	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1200	C₂×C₄	#585	1	1	yes	characteristic
1201	C₂×C₄	#585	1	1	yes	characteristic
1202	C₈	—	4	1	no	—
1203	C₈	—	4	1	no	—
1204	C₈	—	4	1	no	—
1205	C₈	—	4	1	no	—
1206	C₈	—	4	1	no	—
1207	C₈	—	4	1	no	—
1208	C₈	—	4	1	no	—
1209	C₈	—	4	1	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	—	8	1	no	—
1229	C₂²	—	8	1	no	—
1230	C₂²	—	8	1	no	—
1231	C₂²	—	16	8	no	—
1232	C₂²	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
1233	C₂²	C₂×#535	1	1	yes	characteristic
1234	C₂²	#3449	1	1	yes	characteristic
1235	C₂²	#3584	1	1	yes	characteristic
1236	C₂²	#3584	1	1	yes	characteristic
1237	C₂²	#3585	1	1	yes	characteristic
1238	C₂²	#3586	1	1	yes	characteristic
1239	C₄	—	2	2	no	—
1240	C₄	—	2	2	no	—
1241	C₄	—	2	2	no	—
1242	C₄	—	2	2	no	—
1243	C₄	—	2	2	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	2	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	—	8	1	no	—
1266	C₄	#3501	1	1	yes	characteristic
1267	C₄	#3501	1	1	yes	characteristic
1268	C₄	#3506	1	1	yes	characteristic
1269	C₄	#3506	1	1	yes	characteristic
1270	C₂	—	4	2	no	—
1271	C₂	—	8	2	no	—
1272	C₂	—	8	2	no	—
1273	C₂	#35172	1	1	yes	characteristic
1274	C₂	#60489	1	1	yes	characteristic
1275	C₂	#60493	1	1	yes	characteristic
1276	C₂	#60834	1	1	yes	characteristic
1277	C₂	#60835	1	1	yes	characteristic
1278	C₂	#60996	1	1	yes	characteristic
1279	C₂	#60998	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×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #34625	C₂	semidirect
3. #32967	C₂	semidirect
5. #32964	C₂	semidirect
7. #29963	C₂	semidirect
9. #29960	C₂	semidirect
11. #29262	C₂	semidirect
12. #29261	C₂	semidirect
13. #29261	C₂	semidirect
14. #29260	C₂	semidirect
15. #29203	C₂	semidirect
16. #29203	C₂	semidirect
17. #29200	C₂	semidirect
18. #29199	C₂	semidirect
19. #29151	C₂	semidirect
20. #29151	C₂	semidirect
21. #28524	C₂	semidirect
22. #28523	C₂	semidirect
23. #28285	C₂	semidirect
24. #28285	C₂	semidirect
25. #28282	C₂	semidirect
26. #28281	C₂	semidirect
27. #21989	C₂	semidirect
28. #21984	C₂	semidirect
31. #20815	C₂	semidirect
35. C₂×#479	C₂²	semidirect
36. C₂×#479	C₂²	semidirect
37. C₂×#477	C₂²	semidirect
38. C₂×#475	C₂²	semidirect
49. #2660	C₂²	semidirect
50. #2660	C₂²	semidirect
51. #2647	C₂²	semidirect
52. #2647	C₂²	semidirect
75. C₄×C₄⋊Q₈	C₂²	semidirect
76. C₄×C₄⋊Q₈	C₂²	semidirect
77. C₄×#125	C₂²	semidirect
78. C₄×#125	C₂²	semidirect
87. #2097	C₂²	semidirect
88. #2097	C₂²	semidirect
89. #2096	C₂²	semidirect
90. #2095	C₂²	semidirect
95. #2068	C₂²	semidirect
96. #2068	C₂²	semidirect
97. #2068	C₂²	semidirect
98. #2068	C₂²	semidirect
103. #2066	C₂²	semidirect
104. #2066	C₂²	semidirect
105. #2066	C₂²	semidirect
106. #2066	C₂²	semidirect
111. #2026	C₂²	semidirect
112. #2026	C₂²	semidirect
115. #2024	C₂²	semidirect
116. #2024	C₂²	semidirect
135. #1949	C₂²	semidirect
136. #1949	C₂²	semidirect
137. #1949	C₂²	semidirect
138. #1949	C₂²	semidirect
139. #1949	C₂²	semidirect
140. #1949	C₂²	semidirect
141. #1949	C₂²	semidirect
142. #1949	C₂²	semidirect
143. #1865	C₂²	semidirect
144. #1865	C₂²	semidirect
145. #1865	C₂²	semidirect
146. #1865	C₂²	semidirect
151. #1863	C₂²	semidirect
152. #1863	C₂²	semidirect
153. #1863	C₂²	semidirect
154. #1863	C₂²	semidirect
167. #1847	C₂²	semidirect
168. #1847	C₂²	semidirect
169. #1845	C₂²	semidirect
170. #1844	C₂²	semidirect
171. #1842	C₂²	semidirect
172. #1842	C₂²	semidirect
173. #1836	C₂²	semidirect
174. #1836	C₂²	semidirect
175. #1834	C₂²	semidirect
176. #1834	C₂²	semidirect
177. #1831	C₂²	semidirect
178. #1831	C₂²	semidirect
179. #1805	C₂²	semidirect
180. #1805	C₂²	semidirect
183. #1803	C₂²	semidirect
184. #1803	C₂²	semidirect
199. #1768	C₂²	semidirect
200. #1768	C₂²	semidirect
201. #1768	C₂²	semidirect
202. #1768	C₂²	semidirect
212. C₂×#124	Q₈	semidirect

Maximal subgroups

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

subgroup	index
#34625	2
#34211	2
#32967	2
#32966	2
#32964	2
#32962	2
#29963	2
#29962	2
#29960	2
#29959	2
#29262	2
#29261	2
#29260	2
#29203	2
#29200	2
#29199	2
#29151	2
#28524	2
#28523	2
#28285	2
#28282	2
#28281	2
#21989	2
#21984	2
#21808	2
#21806	2
#20815	2