Subgroups — #6370604

Order 512.

2166 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2990	C₂	1	1	yes	maximal, characteristic
2	C₂×#2970	C₂	1	1	yes	maximal, characteristic
3	#34060	C₂	1	1	yes	maximal, characteristic
4	#20576	C₂	1	1	yes	maximal, characteristic, complemented
5	#20575	C₂	1	1	yes	maximal, characteristic, complemented
6	#20566	C₂	1	1	yes	maximal, characteristic, complemented
7	#20563	C₂	1	1	yes	maximal, characteristic, complemented
8	#20560	C₂	1	1	yes	maximal, characteristic, complemented
9	#20560	C₂	1	1	yes	maximal, characteristic, complemented
10	#20557	C₂	1	1	yes	maximal, characteristic, complemented
11	#20557	C₂	1	1	yes	maximal, characteristic, complemented
12	#20551	C₂	1	1	yes	maximal, characteristic, complemented
13	#20546	C₂	1	1	yes	maximal, characteristic, complemented
14	#20544	C₂	1	1	yes	maximal, characteristic, complemented
15	#20539	C₂	1	1	yes	maximal, characteristic, complemented
16	#20537	C₂	1	1	yes	maximal, characteristic, complemented
17	#20534	C₂	1	1	yes	maximal, characteristic, complemented
18	#20519	C₂	1	1	yes	maximal, characteristic, complemented
19	#20518	C₂	1	1	yes	maximal, characteristic, complemented
20	#20493	C₂	1	1	yes	maximal, characteristic, complemented
21	#20493	C₂	1	1	yes	maximal, characteristic, complemented
22	#20492	C₂	1	1	yes	maximal, characteristic, complemented
23	#20488	C₂	1	1	yes	maximal, characteristic, complemented
24	#20484	C₂	1	1	yes	maximal, characteristic, complemented
25	#20484	C₂	1	1	yes	maximal, characteristic, complemented
26	#20481	C₂	1	1	yes	maximal, characteristic, complemented
27	#20479	C₂	1	1	yes	maximal, characteristic, complemented
28	#20477	C₂	1	1	yes	maximal, characteristic, complemented
29	#20441	C₂	1	1	yes	maximal, characteristic, complemented
30	#20438	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#1771	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₄×#41	C₂²	1	1	yes	characteristic
33	#2990	C₄	1	16	yes	complemented
34	#2970	C₄	1	16	yes	complemented
35	C₂×#446	C₂²	1	1	yes	characteristic
36	C₂×#446	C₂²	1	1	yes	characteristic
37	C₂×#446	C₂²	1	1	yes	characteristic
38	C₂×#446	C₂²	1	1	yes	characteristic
39	C₂×#435	C₂²	1	1	yes	characteristic
40	C₂×#435	C₂²	1	1	yes	characteristic
41	C₂×#435	C₂²	1	1	yes	characteristic
42	C₂×#435	C₂²	1	1	yes	characteristic
43	C₂×#435	C₂²	1	1	yes	characteristic
44	C₂×#435	C₂²	1	1	yes	characteristic
45	C₂×#435	C₂²	1	1	yes	characteristic
46	C₂×#435	C₂²	1	1	yes	characteristic
47	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
51	C₂×#432	C₂²	1	1	yes	characteristic
52	C₂×#432	C₂²	1	1	yes	characteristic
53	C₂×#432	C₂²	1	1	yes	characteristic
54	C₂×#432	C₂²	1	1	yes	characteristic
55	C₂×#432	C₂²	1	1	yes	characteristic
56	C₂×#431	C₂²	1	1	yes	characteristic
57	C₂×#423	C₂²	1	1	yes	characteristic
58	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₂×#405	C₂²	1	1	yes	characteristic
61	C₂×#405	C₂²	1	1	yes	characteristic
62	C₂×#405	C₂²	1	1	yes	characteristic
63	C₂×#405	C₂²	1	1	yes	characteristic
64	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
65	C₂²×#97	C₂²	1	1	yes	characteristic
66	C₂²×#97	C₂²	1	1	yes	characteristic
67	C₂²×#97	C₂²	1	1	yes	characteristic
68	C₂²×C₄×C₈	C₂²	1	1	yes	characteristic
69	#2320	C₄	1	2	yes	—
70	#2319	C₄	1	2	yes	—
71	#2318	C₄	1	2	yes	—
72	#2318	C₄	1	2	yes	—
73	#2317	C₄	1	2	yes	—
74	#2314	C₄	1	2	yes	—
75	#2314	C₄	1	2	yes	—
76	#2311	C₄	1	2	yes	—
77	#2295	C₂²	1	1	yes	characteristic
78	#2295	C₂²	1	1	yes	characteristic
79	#2293	C₂²	1	1	yes	characteristic
80	#2293	C₂²	1	1	yes	characteristic
81	#2290	C₂²	1	1	yes	characteristic
82	#2290	C₂²	1	1	yes	characteristic
83	#2290	C₂²	1	1	yes	characteristic
84	#2290	C₂²	1	1	yes	characteristic
85	#2285	C₂²	1	1	yes	characteristic
86	#2285	C₂²	1	1	yes	characteristic
87	#2283	C₂²	1	1	yes	characteristic
88	#2283	C₂²	1	1	yes	characteristic
89	C₄×#117	C₂²	1	1	yes	characteristic
90	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	#1771	C₂²	1	1	yes	characteristic
92	#1771	C₂²	1	1	yes	characteristic
93	#1771	C₂²	1	1	yes	characteristic
94	#1771	C₂²	1	1	yes	characteristic
95	#1771	C₂²	1	1	yes	characteristic
96	#1771	C₂²	1	1	yes	characteristic
97	#1771	C₂²	1	1	yes	characteristic
98	#1771	C₂²	1	1	yes	characteristic
99	#1771	C₂²	1	1	yes	characteristic
100	#1771	C₂²	1	1	yes	characteristic
101	#1771	C₂²	1	1	yes	characteristic
102	#1771	C₂²	1	1	yes	characteristic
103	#1771	C₂²	1	1	yes	characteristic
104	#1771	C₂²	1	1	yes	characteristic
105	#1771	C₂²	1	1	yes	characteristic
106	#1771	C₂²	1	1	yes	characteristic
107	#1771	C₂²	1	1	yes	characteristic
108	#1771	C₂²	1	1	yes	characteristic
109	#1771	C₂²	1	1	yes	characteristic
110	#1771	C₂²	1	1	yes	characteristic
111	#1771	C₂²	1	1	yes	characteristic
112	#1771	C₂²	1	1	yes	characteristic
113	#1771	C₂²	1	1	yes	characteristic
114	#1771	C₂²	1	1	yes	characteristic
115	#1771	C₂²	1	1	yes	characteristic
116	#1771	C₂²	1	1	yes	characteristic
117	#1771	C₂²	1	1	yes	characteristic
118	#1771	C₂²	1	1	yes	characteristic
119	#1771	C₂²	1	1	yes	characteristic
120	#1771	C₂²	1	1	yes	characteristic
121	#1771	C₂²	1	1	yes	characteristic
122	#1771	C₂²	1	1	yes	characteristic
123	#1770	C₂²	1	1	yes	characteristic
124	#1770	C₂²	1	1	yes	characteristic
125	#1770	C₂²	1	1	yes	characteristic
126	#1770	C₂²	1	1	yes	characteristic
127	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
128	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
129	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
130	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
131	#1768	C₂²	1	1	yes	characteristic
132	#1768	C₂²	1	1	yes	characteristic
133	#1768	C₂²	1	1	yes	characteristic
134	#1768	C₂²	1	1	yes	characteristic
135	#1768	C₂²	1	1	yes	characteristic
136	#1768	C₂²	1	1	yes	characteristic
137	#1768	C₂²	1	1	yes	characteristic
138	#1768	C₂²	1	1	yes	characteristic
139	#1767	C₂²	1	1	yes	characteristic
140	#1767	C₂²	1	1	yes	characteristic
141	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
142	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
143	#1753	C₂²	1	1	yes	characteristic
144	#1753	C₂²	1	1	yes	characteristic
145	#1753	C₂²	1	1	yes	characteristic
146	#1753	C₂²	1	1	yes	characteristic
147	#1753	C₂²	1	1	yes	characteristic
148	#1753	C₂²	1	1	yes	characteristic
149	#1753	C₂²	1	1	yes	characteristic
150	#1753	C₂²	1	1	yes	characteristic
151	#1752	C₂²	1	1	yes	characteristic
152	#1752	C₂²	1	1	yes	characteristic
153	#1752	C₂²	1	1	yes	characteristic
154	#1752	C₂²	1	1	yes	characteristic
155	#1752	C₂²	1	1	yes	characteristic
156	#1752	C₂²	1	1	yes	characteristic
157	#1752	C₂²	1	1	yes	characteristic
158	#1752	C₂²	1	1	yes	characteristic
159	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
160	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
161	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
162	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
163	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
164	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
165	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
166	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
167	#1750	C₂²	1	1	yes	characteristic
168	#1750	C₂²	1	1	yes	characteristic
169	#1750	C₂²	1	1	yes	characteristic
170	#1750	C₂²	1	1	yes	characteristic
171	#1750	C₂²	1	1	yes	characteristic
172	#1750	C₂²	1	1	yes	characteristic
173	#1750	C₂²	1	1	yes	characteristic
174	#1750	C₂²	1	1	yes	characteristic
175	#1749	C₂²	1	1	yes	characteristic
176	#1749	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
179	#1746	C₂²	1	1	yes	characteristic
180	#1746	C₂²	1	1	yes	characteristic
181	#1746	C₂²	1	1	yes	characteristic
182	#1746	C₂²	1	1	yes	characteristic
183	#1745	C₂²	1	1	yes	characteristic
184	#1745	C₂²	1	1	yes	characteristic
185	#1729	C₂²	1	1	yes	characteristic
186	#1729	C₂²	1	1	yes	characteristic
187	#1729	C₂²	1	1	yes	characteristic
188	#1729	C₂²	1	1	yes	characteristic
189	C₂×#336	C₂²	1	1	yes	characteristic
190	C₂×#336	C₂²	1	1	yes	characteristic
191	#1726	C₂²	1	1	yes	characteristic
192	#1726	C₂²	1	1	yes	characteristic
193	#1726	C₂²	1	1	yes	characteristic
194	#1726	C₂²	1	1	yes	characteristic
195	C₄×#97	C₂²	1	1	yes	characteristic
196	C₄×#97	C₂²	1	1	yes	characteristic
197	C₂²×#41	C₂×C₄	1	1	yes	characteristic
198	C₂²×M₁₆	C₂³	1	1	yes	characteristic
199	C₂²×M₁₆	C₂³	1	1	yes	characteristic
200	C₂²×M₁₆	C₂³	1	1	yes	characteristic
201	C₂²×M₁₆	C₂³	1	1	yes	characteristic
202	C₂³×C₈	C₂³	1	1	yes	characteristic
203	C₂³×C₈	C₂³	1	1	yes	characteristic
204	C₂³×C₈	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂³×C₈	C₂³	1	1	yes	characteristic
210	C₄×#41	C₂×C₄	1	8	yes	—
211	C₄×#41	C₂×C₄	1	8	yes	—
212	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
220	C₂×#117	C₂×C₄	1	2	yes	—
221	C₂×#117	C₂×C₄	1	1	yes	characteristic
222	C₂×#117	C₂×C₄	1	1	yes	characteristic
223	C₂×#117	C₂×C₄	1	1	yes	characteristic
224	C₂×#117	C₂³	1	1	yes	characteristic
225	C₂×#117	C₂³	1	1	yes	characteristic
226	C₂×#117	C₂³	1	1	yes	characteristic
227	C₂×#117	C₂³	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂×C₄	1	2	yes	—
229	C₂²×C₄²	C₂³	1	1	yes	characteristic
230	C₂²×C₄²	C₂³	1	1	yes	characteristic
231	C₂²×C₄²	C₂³	1	1	yes	characteristic
232	C₂²×C₄²	C₂³	1	1	yes	characteristic
233	C₂²×C₄²	C₂³	1	1	yes	characteristic
234	#446	C₂×C₄	1	8	yes	complemented
235	#446	C₂×C₄	1	8	yes	complemented
236	#446	C₂×C₄	1	8	yes	complemented
237	#446	C₂×C₄	1	8	yes	complemented
238	#435	C₂×C₄	1	8	yes	—
239	#435	C₂×C₄	1	8	yes	—
240	#435	C₂×C₄	1	8	yes	—
241	#435	C₂×C₄	1	8	yes	—
242	#435	C₂×C₄	1	8	yes	complemented
243	#435	C₂×C₄	1	8	yes	complemented
244	#435	C₂×C₄	1	8	yes	complemented
245	#435	C₂×C₄	1	8	yes	complemented
246	C₈×D₄	C₂×C₄	1	8	yes	—
247	C₈×D₄	C₂×C₄	1	8	yes	—
248	C₈×D₄	C₂×C₄	1	8	yes	—
249	C₈×D₄	C₂×C₄	1	8	yes	—
250	#432	C₂×C₄	1	8	yes	—
251	#432	C₂×C₄	1	8	yes	—
252	#432	C₂×C₄	1	8	yes	complemented
253	#432	C₂×C₄	1	8	yes	complemented
254	#432	C₂×C₄	1	8	yes	complemented
255	#431	C₂×C₄	1	8	yes	complemented
256	#423	C₂×C₄	1	8	yes	complemented
257	C₂×C₄⋊C₈	C₂×C₄	1	8	yes	—
258	C₂×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	#405	—	4	2	no	—
288	#405	—	4	2	no	—
289	#405	—	4	2	no	—
290	#405	—	4	2	no	—
291	C₄×M₁₆	C₂×C₄	1	8	yes	complemented
292	C₂×#97	—	4	2	no	—
293	C₂×#97	C₂×C₄	1	8	yes	—
294	C₂×#97	C₂×C₄	1	8	yes	complemented
295	C₂×#97	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×#97	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×#97	C₂³	1	1	yes	characteristic
300	C₂×#97	C₂³	1	1	yes	characteristic
301	C₂×#97	C₂³	1	1	yes	characteristic
302	C₂×#97	C₂³	1	1	yes	characteristic
303	C₂×#97	C₂³	1	1	yes	characteristic
304	C₂×#97	C₂³	1	1	yes	characteristic
305	C₂×#97	C₂³	1	1	yes	characteristic
306	C₂×#97	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×#97	C₂³	1	1	yes	characteristic
310	C₂×#97	C₂³	1	1	yes	characteristic
311	C₂×#97	C₂³	1	1	yes	characteristic
312	C₂×#97	C₂³	1	1	yes	characteristic
313	C₂×#97	C₂³	1	1	yes	characteristic
314	C₂×#97	C₂³	1	1	yes	characteristic
315	C₂×#97	C₂³	1	1	yes	characteristic
316	C₂×#97	C₂³	1	1	yes	characteristic
317	C₂×#97	C₂³	1	1	yes	characteristic
318	C₂×#97	C₂³	1	1	yes	characteristic
319	C₂×#97	C₂³	1	1	yes	characteristic
320	C₂×#97	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	—	4	2	no	—
324	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
328	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
329	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
330	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
337	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
342	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
344	#391	C₂×C₄	1	2	yes	—
345	#391	C₂×C₄	1	2	yes	—
346	#390	C₂×C₄	1	2	yes	—
347	#390	C₂×C₄	1	2	yes	—
348	#389	C₂×C₄	1	2	yes	—
349	#389	C₂×C₄	1	2	yes	—
350	#389	C₂×C₄	1	2	yes	—
351	#389	C₂×C₄	1	2	yes	—
352	#388	C₂×C₄	1	2	yes	—
353	#388	C₂×C₄	1	2	yes	—
354	#388	C₂×C₄	1	2	yes	—
355	#388	C₂×C₄	1	2	yes	—
356	#388	C₂×C₄	1	2	yes	—
357	#388	C₂×C₄	1	2	yes	—
358	#388	C₂×C₄	1	2	yes	—
359	#388	C₂×C₄	1	2	yes	—
360	#387	C₂×C₄	1	2	yes	—
361	#387	C₂×C₄	1	2	yes	—
362	#387	C₂×C₄	1	2	yes	—
363	#387	C₂×C₄	1	2	yes	—
364	#387	C₂×C₄	1	2	yes	—
365	#387	C₂×C₄	1	2	yes	—
366	#387	C₂×C₄	1	2	yes	—
367	#387	C₂×C₄	1	2	yes	—
368	#386	C₂×C₄	1	2	yes	—
369	#386	C₂×C₄	1	2	yes	—
370	#386	C₂×C₄	1	2	yes	—
371	#386	C₂×C₄	1	2	yes	—
372	#385	C₂×C₄	1	2	yes	—
373	#385	C₂×C₄	1	2	yes	—
374	#385	C₂×C₄	1	2	yes	—
375	#385	C₂×C₄	1	2	yes	—
376	#384	C₂×C₄	1	2	yes	—
377	#384	C₂×C₄	1	2	yes	—
378	#383	C₂×C₄	1	2	yes	—
379	#383	C₂×C₄	1	2	yes	—
380	#382	C₂×C₄	1	2	yes	—
381	#382	C₂×C₄	1	2	yes	—
382	#382	C₂×C₄	1	2	yes	—
383	#382	C₂×C₄	1	2	yes	—
384	#381	C₂×C₄	1	2	yes	—
385	#381	C₂×C₄	1	2	yes	—
386	#380	C₂×C₄	1	2	yes	—
387	#380	C₂×C₄	1	2	yes	—
388	#380	C₂×C₄	1	2	yes	—
389	#380	C₂×C₄	1	2	yes	—
390	#380	C₂×C₄	1	2	yes	—
391	#380	C₂×C₄	1	2	yes	—
392	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
393	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
394	C₄×C₄⋊C₄	C₂×C₄	1	2	yes	—
395	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
396	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
397	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
400	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
401	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
404	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
405	C₄×C₂²⋊C₄	C₂×C₄	1	2	yes	—
406	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
407	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
408	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
409	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
412	#376	C₂×C₄	1	2	yes	—
413	#376	C₂³	1	1	yes	characteristic
414	#376	C₂³	1	1	yes	characteristic
415	#376	C₂³	1	1	yes	characteristic
416	#376	C₂³	1	1	yes	characteristic
417	C₂×#95	C₂×C₄	1	2	yes	—
418	C₄³	C₂³	1	1	yes	characteristic
419	C₄³	C₂³	1	1	yes	characteristic
420	#336	C₂³	1	1	yes	characteristic
421	#336	C₂³	1	1	yes	characteristic
422	#336	C₂³	1	1	yes	characteristic
423	#336	C₂³	1	1	yes	characteristic
424	#336	C₂³	1	1	yes	characteristic
425	#336	C₂³	1	1	yes	characteristic
426	#336	C₂³	1	1	yes	characteristic
427	#336	C₂³	1	1	yes	characteristic
428	#336	C₂³	1	1	yes	characteristic
429	#336	C₂³	1	1	yes	characteristic
430	#336	C₂³	1	1	yes	characteristic
431	#336	C₂³	1	1	yes	characteristic
432	#336	C₂³	1	1	yes	characteristic
433	#336	C₂³	1	1	yes	characteristic
434	#336	C₂³	1	1	yes	characteristic
435	#336	C₂³	1	1	yes	characteristic
436	#336	C₂³	1	1	yes	characteristic
437	#336	C₂³	1	1	yes	characteristic
438	#336	C₂³	1	1	yes	characteristic
439	#336	C₂³	1	1	yes	characteristic
440	#336	C₂³	1	1	yes	characteristic
441	#336	C₂³	1	1	yes	characteristic
442	#336	C₂³	1	1	yes	characteristic
443	#336	C₂³	1	1	yes	characteristic
444	#336	C₂³	1	1	yes	characteristic
445	#336	C₂³	1	1	yes	characteristic
446	#336	C₂³	1	1	yes	characteristic
447	#336	C₂³	1	1	yes	characteristic
448	#336	C₂³	1	1	yes	characteristic
449	#336	C₂³	1	1	yes	characteristic
450	#336	C₂³	1	1	yes	characteristic
451	#336	C₂³	1	1	yes	characteristic
452	C₂×#41	—	4	4	no	—
453	C₂×#41	C₄²	1	8	yes	—
454	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
455	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
456	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
457	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
458	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
459	C₂³×C₄	C₂²×C₄	1	2	yes	—
460	C₂³×C₄	C₂²×C₄	1	2	yes	—
461	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
462	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
463	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
464	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
465	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
466	C₂³×C₄	C₂⁴	1	1	yes	characteristic
467	C₂³×C₄	C₂⁴	1	1	yes	characteristic
468	C₂³×C₄	C₂⁴	1	1	yes	characteristic
469	C₂×M₁₆	—	2	2	no	—
470	C₂×M₁₆	—	2	2	no	—
471	C₂×M₁₆	—	4	1	no	—
472	C₂×M₁₆	—	4	1	no	—
473	C₂×M₁₆	—	4	1	no	—
474	C₂×M₁₆	—	4	1	no	—
475	C₂×M₁₆	—	4	1	no	—
476	C₂×M₁₆	—	4	1	no	—
477	C₂×M₁₆	C₂²×C₄	1	4	yes	—
478	C₂×M₁₆	C₂²×C₄	1	4	yes	—
479	C₂×M₁₆	C₂²×C₄	1	4	yes	—
480	C₂×M₁₆	C₂²×C₄	1	4	yes	—
481	C₂²×C₈	—	2	2	no	—
482	C₂²×C₈	—	2	2	no	—
483	C₂²×C₈	—	2	2	no	—
484	C₂²×C₈	—	2	2	no	—
485	C₂²×C₈	—	4	1	no	—
486	C₂²×C₈	—	4	1	no	—
487	C₂²×C₈	—	4	1	no	—
488	C₂²×C₈	—	4	1	no	—
489	C₂²×C₈	—	4	1	no	—
490	C₂²×C₈	—	4	1	no	—
491	C₂²×C₈	—	4	1	no	—
492	C₂²×C₈	—	4	1	no	—
493	C₂²×C₈	—	4	1	no	—
494	C₂²×C₈	—	4	1	no	—
495	C₂²×C₈	—	4	1	no	—
496	C₂²×C₈	—	4	1	no	—
497	C₂²×C₈	C₂²×C₄	1	4	yes	—
498	C₂²×C₈	C₂²×C₄	1	4	yes	—
499	C₂²×C₈	C₂²×C₄	1	4	yes	—
500	C₂²×C₈	C₂²×C₄	1	4	yes	—
501	C₂²×C₈	C₂²×C₄	1	4	yes	—
502	C₂²×C₈	C₂²×C₄	1	4	yes	—
503	C₂²×C₈	C₂²×C₄	1	4	yes	—
504	C₂²×C₈	C₂²×C₄	1	4	yes	—
505	C₂²×C₈	C₂⁴	1	1	yes	characteristic
506	C₂²×C₈	C₂⁴	1	1	yes	characteristic
507	C₂²×C₈	C₂⁴	1	1	yes	characteristic
508	C₂²×C₈	C₂⁴	1	1	yes	characteristic
509	C₂²×C₈	C₂⁴	1	1	yes	characteristic
510	C₂²×C₈	C₂⁴	1	1	yes	characteristic
511	C₂²×C₈	C₂⁴	1	1	yes	characteristic
512	C₂²×C₈	C₂⁴	1	1	yes	characteristic
513	C₂²×C₈	C₂⁴	1	1	yes	characteristic
514	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄×Q₈	C₄²	1	8	yes	—
522	C₄×Q₈	C₂²×C₄	1	4	yes	—
523	C₄×Q₈	C₂²×C₄	1	4	yes	—
524	C₄×D₄	C₄²	1	8	yes	—
525	C₄×D₄	C₄²	1	8	yes	—
526	C₄×D₄	C₄²	1	8	yes	—
527	C₄×D₄	C₂²×C₄	1	4	yes	—
528	C₄×D₄	C₂²×C₄	1	4	yes	—
529	C₄×D₄	C₂²×C₄	1	4	yes	—
530	C₄×D₄	C₂²×C₄	1	4	yes	—
531	C₄×D₄	C₂²×C₄	1	4	yes	—
532	C₄×D₄	C₂²×C₄	1	4	yes	—
533	#117	—	4	1	no	—
534	#117	—	4	1	no	—
535	#117	—	4	1	no	—
536	#117	—	4	1	no	—
537	#117	—	4	1	no	—
538	#117	—	4	1	no	—
539	#117	—	4	1	no	—
540	#117	—	4	1	no	—
541	#117	—	4	4	no	—
542	#117	C₄²	1	8	yes	—
543	#117	C₄²	1	8	yes	—
544	#117	C₄²	1	8	yes	—
545	C₂×C₄⋊C₄	—	4	4	no	—
546	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
547	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
548	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
549	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
550	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
551	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
552	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
553	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
554	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
555	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
556	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
557	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
558	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
559	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
560	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
582	C₂×C₄²	—	4	1	no	—
583	C₂×C₄²	—	4	1	no	—
584	C₂×C₄²	—	4	1	no	—
585	C₂×C₄²	—	4	1	no	—
586	C₂×C₄²	C₂²×C₄	1	2	yes	—
587	C₂×C₄²	C₂²×C₄	1	2	yes	—
588	C₂×C₄²	C₂²×C₄	1	2	yes	—
589	C₂×C₄²	C₂²×C₄	1	2	yes	—
590	C₂×C₄²	C₂²×C₄	1	2	yes	—
591	C₂×C₄²	C₂²×C₄	1	2	yes	—
592	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
593	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
594	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
595	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
596	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
597	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
598	C₂×C₄²	C₂²×C₄	1	4	yes	—
599	C₂×C₄²	C₂²×C₄	1	4	yes	—
600	C₂×C₄²	C₂²×C₄	1	4	yes	—
601	C₂×C₄²	C₂²×C₄	1	4	yes	—
602	C₂×C₄²	C₂²×C₄	1	4	yes	—
603	C₂×C₄²	C₂²×C₄	1	4	yes	—
604	C₂×C₄²	C₂⁴	1	1	yes	characteristic
605	C₂×C₄²	C₂⁴	1	1	yes	characteristic
606	C₂×C₄²	C₂⁴	1	1	yes	characteristic
607	C₂×C₄²	C₂⁴	1	1	yes	characteristic
608	C₂×C₄²	C₂⁴	1	1	yes	characteristic
609	C₂×C₄²	C₂⁴	1	1	yes	characteristic
610	C₂×C₄²	C₂⁴	1	1	yes	characteristic
611	C₂×C₄²	C₂⁴	1	1	yes	characteristic
612	C₂×C₄²	C₂⁴	1	1	yes	characteristic
613	C₂×C₄²	C₂⁴	1	1	yes	characteristic
614	C₂×C₄²	C₂⁴	1	1	yes	characteristic
615	C₂×C₄²	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₈	C₂²×C₄	1	4	yes	—
617	C₄⋊C₈	C₂²×C₄	1	4	yes	—
618	C₄⋊C₈	C₂²×C₄	1	4	yes	—
619	C₄⋊C₈	C₂²×C₄	1	4	yes	—
620	C₄⋊C₈	C₂²×C₄	1	4	yes	—
621	C₄⋊C₈	C₂²×C₄	1	4	yes	—
622	C₄⋊C₈	C₂²×C₄	1	4	yes	—
623	C₄⋊C₈	C₂²×C₄	1	4	yes	—
624	C₄⋊C₈	C₂²×C₄	1	4	yes	—
625	C₄⋊C₈	C₂²×C₄	1	4	yes	—
626	C₄⋊C₈	C₂²×C₄	1	4	yes	—
627	C₄⋊C₈	C₂²×C₄	1	4	yes	—
628	C₄⋊C₈	C₂²×C₄	1	4	yes	—
629	C₄⋊C₈	C₂²×C₄	1	4	yes	—
630	C₄⋊C₈	C₂²×C₄	1	4	yes	—
631	C₄⋊C₈	C₂²×C₄	1	4	yes	—
632	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
633	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
634	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
635	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
636	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
637	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
638	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
639	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
640	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
641	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
642	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
643	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
644	#97	—	2	2	no	—
645	#97	—	2	2	no	—
646	#97	—	2	2	no	—
647	#97	—	2	2	no	—
648	#97	—	4	1	no	—
649	#97	—	4	1	no	—
650	#97	—	4	1	no	—
651	#97	—	4	1	no	—
652	#97	—	4	1	no	—
653	#97	—	4	1	no	—
654	#97	—	4	1	no	—
655	#97	—	4	1	no	—
656	#97	—	4	1	no	—
657	#97	—	4	1	no	—
658	#97	—	4	1	no	—
659	#97	—	4	1	no	—
660	#97	C₂²×C₄	1	4	yes	—
661	#97	C₂²×C₄	1	4	yes	—
662	#97	C₂²×C₄	1	4	yes	—
663	#97	C₂²×C₄	1	4	yes	—
664	#97	C₂²×C₄	1	4	yes	—
665	#97	C₂²×C₄	1	4	yes	—
666	#97	C₂²×C₄	1	4	yes	—
667	#97	C₂²×C₄	1	4	yes	—
668	#97	C₂²×C₄	1	4	yes	—
669	#97	C₂²×C₄	1	4	yes	—
670	#97	C₂²×C₄	1	4	yes	—
671	#97	C₂²×C₄	1	4	yes	—
672	C₄×C₈	—	2	2	no	—
673	C₄×C₈	—	2	2	no	—
674	C₄×C₈	—	2	2	no	—
675	C₄×C₈	—	2	2	no	—
676	C₄×C₈	—	4	1	no	—
677	C₄×C₈	—	4	1	no	—
678	C₄×C₈	—	4	1	no	—
679	C₄×C₈	—	4	1	no	—
680	C₄×C₈	—	4	1	no	—
681	C₄×C₈	—	4	1	no	—
682	C₄×C₈	—	4	1	no	—
683	C₄×C₈	—	4	1	no	—
684	C₄×C₈	—	4	1	no	—
685	C₄×C₈	—	4	1	no	—
686	C₄×C₈	—	4	1	no	—
687	C₄×C₈	—	4	1	no	—
688	C₄×C₈	C₂²×C₄	1	4	yes	—
689	C₄×C₈	C₂²×C₄	1	4	yes	—
690	C₄×C₈	C₂²×C₄	1	4	yes	—
691	C₄×C₈	C₂²×C₄	1	4	yes	—
692	#95	C₂²×C₄	1	2	yes	—
693	#95	C₂²×C₄	1	2	yes	—
694	#95	C₂²×C₄	1	2	yes	—
695	#95	C₂²×C₄	1	2	yes	—
696	#95	C₂²×C₄	1	2	yes	—
697	#95	C₂²×C₄	1	2	yes	—
698	#95	C₂²×C₄	1	2	yes	—
699	#95	C₂²×C₄	1	2	yes	—
700	#95	C₂²×C₄	1	2	yes	—
701	#95	C₂²×C₄	1	2	yes	—
702	#95	C₂²×C₄	1	2	yes	—
703	#95	C₂²×C₄	1	2	yes	—
704	#95	C₂²×C₄	1	2	yes	—
705	#95	C₂²×C₄	1	2	yes	—
706	#95	C₂²×C₄	1	2	yes	—
707	#95	C₂²×C₄	1	2	yes	—
708	#95	C₂²×C₄	1	2	yes	—
709	#95	C₂²×C₄	1	2	yes	—
710	#95	C₂²×C₄	1	2	yes	—
711	#95	C₂²×C₄	1	2	yes	—
712	#95	C₂²×C₄	1	2	yes	—
713	#95	C₂²×C₄	1	2	yes	—
714	#95	C₂²×C₄	1	2	yes	—
715	#95	C₂²×C₄	1	2	yes	—
716	C₂⁴	C₂³×C₄	1	1	yes	characteristic
717	C₂⁴	C₂³×C₄	1	1	yes	characteristic
718	C₂⁴	C₂³×C₄	1	1	yes	characteristic
719	#41	—	4	16	no	—
720	C₂×Q₈	—	4	2	no	—
721	C₂×Q₈	C₂×C₄²	1	4	yes	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	C₂×C₄²	1	4	yes	—
726	C₂×D₄	C₂×C₄²	1	4	yes	—
727	C₂×D₄	C₂×C₄²	1	4	yes	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	C₂×C₄²	1	4	yes	—
753	C₂²×C₄	C₂×C₄²	1	4	yes	—
754	C₂²×C₄	C₂×C₄²	1	4	yes	—
755	C₂²×C₄	C₂×C₄²	1	4	yes	—
756	C₂²×C₄	C₂×C₄²	1	4	yes	—
757	C₂²×C₄	C₂×C₄²	1	4	yes	—
758	C₂²×C₄	C₂³×C₄	1	2	yes	—
759	C₂²×C₄	C₂³×C₄	1	2	yes	—
760	C₂²×C₄	C₂³×C₄	1	2	yes	—
761	C₂²×C₄	C₂³×C₄	1	2	yes	—
762	C₂²×C₄	C₂³×C₄	1	2	yes	—
763	C₂²×C₄	C₂³×C₄	1	2	yes	—
764	C₂²×C₄	C₂³×C₄	1	2	yes	—
765	C₂²×C₄	C₂³×C₄	1	2	yes	—
766	C₂²×C₄	C₂³×C₄	1	2	yes	—
767	C₂²×C₄	C₂³×C₄	1	2	yes	—
768	C₂²×C₄	C₂³×C₄	1	2	yes	—
769	C₂²×C₄	C₂³×C₄	1	2	yes	—
770	C₂²×C₄	C₂³×C₄	1	2	yes	—
771	C₂²×C₄	C₂³×C₄	1	2	yes	—
772	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
773	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
774	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
775	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
776	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
777	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
778	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
779	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
780	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
781	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
782	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
783	C₂²×C₄	C₂⁵	1	1	yes	characteristic
784	M₁₆	—	2	8	no	—
785	M₁₆	—	4	4	no	—
786	M₁₆	—	4	4	no	—
787	M₁₆	—	4	4	no	—
788	C₂×C₈	—	2	1	no	—
789	C₂×C₈	—	2	1	no	—
790	C₂×C₈	—	2	1	no	—
791	C₂×C₈	—	2	1	no	—
792	C₂×C₈	—	2	1	no	—
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	1	no	—
796	C₂×C₈	—	2	1	no	—
797	C₂×C₈	—	2	1	no	—
798	C₂×C₈	—	2	1	no	—
799	C₂×C₈	—	2	1	no	—
800	C₂×C₈	—	2	1	no	—
801	C₂×C₈	—	2	1	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	2	1	no	—
806	C₂×C₈	—	2	1	no	—
807	C₂×C₈	—	2	1	no	—
808	C₂×C₈	—	2	1	no	—
809	C₂×C₈	—	2	1	no	—
810	C₂×C₈	—	2	1	no	—
811	C₂×C₈	—	2	1	no	—
812	C₂×C₈	—	2	1	no	—
813	C₂×C₈	—	2	1	no	—
814	C₂×C₈	—	2	1	no	—
815	C₂×C₈	—	2	1	no	—
816	C₂×C₈	—	2	1	no	—
817	C₂×C₈	—	2	1	no	—
818	C₂×C₈	—	2	8	no	—
819	C₂×C₈	—	2	8	no	—
820	C₂×C₈	—	4	4	no	—
821	C₂×C₈	—	4	4	no	—
822	C₂×C₈	—	4	4	no	—
823	C₂×C₈	—	4	4	no	—
824	C₂×C₈	—	4	4	no	—
825	C₂×C₈	—	4	4	no	—
826	C₂×C₈	C₂³×C₄	1	2	yes	—
827	C₂×C₈	C₂³×C₄	1	2	yes	—
828	C₂×C₈	C₂³×C₄	1	2	yes	—
829	C₂×C₈	C₂³×C₄	1	2	yes	—
830	C₂×C₈	C₂³×C₄	1	2	yes	—
831	C₂×C₈	C₂³×C₄	1	2	yes	—
832	C₂×C₈	C₂³×C₄	1	2	yes	—
833	C₂×C₈	C₂³×C₄	1	2	yes	—
834	C₂×C₈	C₂³×C₄	1	2	yes	—
835	C₂×C₈	C₂³×C₄	1	2	yes	—
836	C₂×C₈	C₂³×C₄	1	2	yes	—
837	C₂×C₈	C₂³×C₄	1	2	yes	—
838	C₂×C₈	C₂³×C₄	1	2	yes	—
839	C₂×C₈	C₂³×C₄	1	2	yes	—
840	C₂×C₈	C₂³×C₄	1	2	yes	—
841	C₂×C₈	C₂³×C₄	1	2	yes	—
842	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
843	C₂×C₈	2₋¹⁺⁴	1	2	yes	—
844	C₄⋊C₄	—	4	2	no	—
845	C₄⋊C₄	—	4	2	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	C₂×C₄²	1	4	yes	—
859	C₄⋊C₄	C₂×C₄²	1	4	yes	—
860	C₄⋊C₄	C₂×C₄²	1	4	yes	—
861	C₄⋊C₄	C₂×C₄²	1	4	yes	—
862	C₄⋊C₄	C₂×C₄²	1	4	yes	—
863	C₄⋊C₄	C₂×C₄²	1	4	yes	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
875	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
876	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
877	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
878	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
879	C₂²⋊C₄	C₂×C₄²	1	4	yes	—
880	C₄²	—	2	1	no	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	1	no	—
885	C₄²	—	2	1	no	—
886	C₄²	—	2	1	no	—
887	C₄²	—	2	1	no	—
888	C₄²	—	2	1	no	—
889	C₄²	—	2	1	no	—
890	C₄²	—	2	1	no	—
891	C₄²	—	2	1	no	—
892	C₄²	—	2	1	no	—
893	C₄²	—	2	1	no	—
894	C₄²	—	2	1	no	—
895	C₄²	—	2	1	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	—	4	2	no	—
900	C₄²	—	4	2	no	—
901	C₄²	—	4	2	no	—
902	C₄²	C₂×C₄²	1	4	yes	—
903	C₄²	C₂×C₄²	1	4	yes	—
904	C₄²	C₂×C₄²	1	4	yes	—
905	C₄²	C₂×C₄²	1	4	yes	—
906	C₄²	C₂×C₄²	1	4	yes	—
907	C₄²	C₂×C₄²	1	4	yes	—
908	C₄²	C₂³×C₄	1	2	yes	—
909	C₄²	C₂³×C₄	1	2	yes	—
910	C₄²	C₂³×C₄	1	2	yes	—
911	C₄²	C₂³×C₄	1	2	yes	—
912	C₄²	C₂³×C₄	1	2	yes	—
913	C₄²	C₂³×C₄	1	2	yes	—
914	C₄²	C₂³×C₄	1	2	yes	—
915	C₄²	C₂³×C₄	1	2	yes	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	C₂²×C₄²	1	2	yes	—
928	C₂³	C₂²×C₄²	1	2	yes	—
929	C₂³	C₂²×C₄²	1	2	yes	—
930	C₂³	#568	1	4	yes	—
931	C₂³	C₂⁴×C₄	1	1	yes	characteristic
932	Q₈	—	4	4	no	—
933	D₄	—	2	8	no	—
934	D₄	—	2	8	no	—
935	D₄	—	4	4	no	—
936	C₂×C₄	—	2	8	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	8	4	no	—
994	C₂×C₄	C₂²×C₄²	1	2	yes	—
995	C₂×C₄	C₂²×C₄²	1	2	yes	—
996	C₂×C₄	C₂²×C₄²	1	2	yes	—
997	C₂×C₄	C₂²×C₄²	1	2	yes	—
998	C₂×C₄	C₂²×C₄²	1	2	yes	—
999	C₂×C₄	C₂²×C₄²	1	2	yes	—
1000	C₂×C₄	C₂²×C₄²	1	2	yes	—
1001	C₂×C₄	C₂²×C₄²	1	2	yes	—
1002	C₂×C₄	C₂²×C₄²	1	2	yes	—
1003	C₂×C₄	C₂²×C₄²	1	2	yes	—
1004	C₂×C₄	C₂²×C₄²	1	2	yes	—
1005	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1006	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1007	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1008	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1009	C₂×C₄	#585	1	1	yes	characteristic
1010	C₂×C₄	#585	1	1	yes	characteristic
1011	C₈	—	2	2	no	—
1012	C₈	—	2	2	no	—
1013	C₈	—	2	2	no	—
1014	C₈	—	2	2	no	—
1015	C₈	—	2	2	no	—
1016	C₈	—	2	2	no	—
1017	C₈	—	2	2	no	—
1018	C₈	—	2	2	no	—
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	2	2	no	—
1024	C₈	—	2	2	no	—
1025	C₈	—	2	2	no	—
1026	C₈	#520	1	4	yes	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	4	no	—
1029	C₂²	—	2	4	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	#2873	1	4	yes	—
1042	C₂²	C₂³×C₄²	1	1	yes	characteristic
1043	C₂²	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1044	C₂²	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1045	C₂²	C₂×#568	1	2	yes	—
1046	C₂²	#3573	1	2	yes	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	C₂×#520	1	1	yes	characteristic
1067	C₄	#3428	1	1	yes	characteristic
1068	C₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1069	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1070	C₂	—	2	4	no	—
1071	C₂	—	4	2	no	—
1072	C₂	—	4	2	no	—
1073	C₂	C₄×#520	1	1	yes	characteristic
1074	C₂	C₂×#2873	1	1	yes	characteristic
1075	C₂	#60058	1	1	yes	characteristic
1076	C₂	#60316	1	2	yes	—
1077	C₂	#60340	1	2	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₄	C₂⁵
commutator	C₂²	C₂³×C₄²
socle	C₂³	C₂⁴×C₄
prime radical	C₂²×#41	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #20576	C₂	semidirect
5. #20575	C₂	semidirect
6. #20566	C₂	semidirect
7. #20563	C₂	semidirect
8. #20560	C₂	semidirect
9. #20560	C₂	semidirect
10. #20557	C₂	semidirect
11. #20557	C₂	semidirect
12. #20551	C₂	semidirect
13. #20546	C₂	semidirect
14. #20544	C₂	semidirect
15. #20539	C₂	semidirect
16. #20537	C₂	semidirect
17. #20534	C₂	semidirect
18. #20519	C₂	semidirect
19. #20518	C₂	semidirect
20. #20493	C₂	semidirect
21. #20493	C₂	semidirect
22. #20492	C₂	semidirect
23. #20488	C₂	semidirect
24. #20484	C₂	semidirect
25. #20484	C₂	semidirect
26. #20481	C₂	semidirect
27. #20479	C₂	semidirect
28. #20477	C₂	semidirect
29. #20441	C₂	semidirect
30. #20438	C₂	semidirect
31. C₂×#1771	C₂	semidirect
33. #2990	C₄	semidirect
34. #2970	C₄	semidirect
234. #446	C₂×C₄	semidirect
235. #446	C₂×C₄	semidirect
236. #446	C₂×C₄	semidirect
237. #446	C₂×C₄	semidirect
242. #435	C₂×C₄	semidirect
243. #435	C₂×C₄	semidirect
244. #435	C₂×C₄	semidirect
245. #435	C₂×C₄	semidirect
252. #432	C₂×C₄	semidirect
253. #432	C₂×C₄	semidirect
254. #432	C₂×C₄	semidirect
255. #431	C₂×C₄	semidirect
256. #423	C₂×C₄	semidirect
258. C₂×C₄⋊C₈	C₂×C₄	semidirect
291. C₄×M₁₆	C₂×C₄	semidirect
294. C₂×#97	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2990	2
C₂×#2970	2
#34060	2
#20576	2
#20575	2
#20566	2
#20563	2
#20560	2
#20557	2
#20551	2
#20546	2
#20544	2
#20539	2
#20537	2
#20534	2
#20519	2
#20518	2
#20493	2
#20492	2
#20488	2
#20484	2
#20481	2
#20479	2
#20477	2
#20441	2
#20438	2
C₂×#1771	2