Subgroups — #35392

Order 256.

1464 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	#2610	C₂	1	1	yes	maximal, characteristic, complemented
4	#2603	C₂	1	1	yes	maximal, characteristic, complemented
5	#2602	C₂	1	1	yes	maximal, characteristic, complemented
6	#2601	C₂	1	1	yes	maximal, characteristic, complemented
7	#2560	C₂	1	1	yes	maximal, characteristic, complemented
8	#2557	C₂	1	1	yes	maximal, characteristic, complemented
9	#2555	C₂	1	1	yes	maximal, characteristic, complemented
10	#2554	C₂	1	1	yes	maximal, characteristic, complemented
11	#2549	C₂	1	1	yes	maximal, characteristic, complemented
12	#2544	C₂	1	1	yes	maximal, characteristic, complemented
13	#2543	C₂	1	1	yes	maximal, characteristic, complemented
14	#2543	C₂	1	1	yes	maximal, characteristic, complemented
15	#2472	C₂	1	1	yes	maximal, characteristic, complemented
16	#2472	C₂	1	1	yes	maximal, characteristic, complemented
17	#2464	C₂	1	1	yes	maximal, characteristic, complemented
18	#2461	C₂	1	1	yes	maximal, characteristic, complemented
19	#2445	C₂	1	1	yes	maximal, characteristic, complemented
20	#2433	C₂	1	1	yes	maximal, characteristic, complemented
21	#2431	C₂	1	1	yes	maximal, characteristic, complemented
22	#2430	C₂	1	1	yes	maximal, characteristic, complemented
23	#2428	C₂	1	1	yes	maximal, characteristic, complemented
24	#2424	C₂	1	1	yes	maximal, characteristic, complemented
25	#2424	C₂	1	1	yes	maximal, characteristic, complemented
26	#2408	C₂	1	1	yes	maximal, characteristic, complemented
27	#2325	C₂	1	1	yes	maximal, characteristic, complemented
28	#2321	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#120	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#386	C₂	1	1	yes	maximal, characteristic, complemented
31	#2275	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41	C₂²	1	1	yes	characteristic, complemented
33	C₂³×D₄	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄	C₂²	1	1	yes	characteristic
35	#538	—	2	8	no	—
36	C₂×#127	C₂²	1	1	yes	characteristic
37	C₂×#127	C₂²	1	1	yes	characteristic
38	C₂×#126	C₂²	1	1	yes	characteristic, complemented
39	C₂×#126	C₂²	1	1	yes	characteristic, complemented
40	C₂×#124	C₂²	1	1	yes	characteristic, complemented
41	C₂×#124	C₂²	1	1	yes	characteristic, complemented
42	C₂×#124	C₂²	1	1	yes	characteristic, complemented
43	C₂×#124	C₂²	1	1	yes	characteristic, complemented
44	#525	—	2	8	no	—
45	C₂×#123	C₂²	1	1	yes	characteristic, complemented
46	C₂×#123	C₂²	1	1	yes	characteristic, complemented
47	C₂×#123	C₂²	1	1	yes	characteristic, complemented
48	C₂×#123	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×#121	C₂²	1	1	yes	characteristic
53	C₂×#121	C₂²	1	1	yes	characteristic
54	C₂×#121	C₂²	1	1	yes	characteristic
55	C₂×#121	C₂²	1	1	yes	characteristic
56	C₂×#121	C₂²	1	1	yes	characteristic
57	C₂×#121	C₂²	1	1	yes	characteristic, complemented
58	C₂×#121	C₂²	1	1	yes	characteristic, complemented
59	C₂×#121	C₂²	1	1	yes	characteristic, complemented
60	C₂×#121	C₂²	1	1	yes	characteristic, complemented
61	C₂×#121	C₂²	1	1	yes	characteristic, complemented
62	C₂×#120	C₂²	1	1	yes	characteristic
63	C₂×#120	C₂²	1	1	yes	characteristic
64	C₂×#120	C₂²	1	1	yes	characteristic
65	C₂×#120	C₂²	1	1	yes	characteristic
66	C₂×#120	C₂²	1	1	yes	characteristic
67	C₂×#120	C₂²	1	1	yes	characteristic
68	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
71	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
73	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
77	C₂×#117	C₂²	1	1	yes	characteristic, complemented
78	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
79	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
80	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	#398	C₂²	1	1	yes	characteristic, complemented
82	#398	C₂²	1	1	yes	characteristic, complemented
83	#398	C₂²	1	1	yes	characteristic, complemented
84	#397	C₂²	1	1	yes	characteristic, complemented
85	#397	C₂²	1	1	yes	characteristic, complemented
86	#397	C₂²	1	1	yes	characteristic, complemented
87	#396	C₂²	1	1	yes	characteristic, complemented
88	#396	C₂²	1	1	yes	characteristic, complemented
89	#395	C₂²	1	1	yes	characteristic, complemented
90	#395	C₂²	1	1	yes	characteristic, complemented
91	#394	C₂²	1	1	yes	characteristic
92	#394	C₂²	1	1	yes	characteristic
93	#394	C₂²	1	1	yes	characteristic, complemented
94	#394	C₂²	1	1	yes	characteristic, complemented
95	#394	C₂²	1	1	yes	characteristic, complemented
96	#394	C₂²	1	1	yes	characteristic, complemented
97	#394	C₂²	1	1	yes	characteristic, complemented
98	#394	C₂²	1	1	yes	characteristic, complemented
99	#394	C₂²	1	1	yes	characteristic, complemented
100	#394	C₂²	1	1	yes	characteristic, complemented
101	#394	C₂²	1	1	yes	characteristic, complemented
102	#393	C₂²	1	1	yes	characteristic, complemented
103	#393	C₂²	1	1	yes	characteristic, complemented
104	#392	C₂²	1	1	yes	characteristic
105	#392	C₂²	1	1	yes	characteristic
106	#392	C₂²	1	1	yes	characteristic
107	#392	C₂²	1	1	yes	characteristic
108	#392	C₂²	1	1	yes	characteristic
109	#392	C₂²	1	1	yes	characteristic
110	#392	C₂²	1	1	yes	characteristic, complemented
111	#392	C₂²	1	1	yes	characteristic, complemented
112	#392	C₂²	1	1	yes	characteristic, complemented
113	#391	C₂²	1	1	yes	characteristic, complemented
114	#391	C₂²	1	1	yes	characteristic, complemented
115	#390	C₂²	1	1	yes	characteristic
116	#390	C₂²	1	1	yes	characteristic
117	#390	C₂²	1	1	yes	characteristic
118	#390	C₂²	1	1	yes	characteristic
119	#390	C₂²	1	1	yes	characteristic, complemented
120	#390	C₂²	1	1	yes	characteristic, complemented
121	#390	C₂²	1	1	yes	characteristic, complemented
122	#390	C₂²	1	1	yes	characteristic, complemented
123	#390	C₂²	1	1	yes	characteristic, complemented
124	#390	C₂²	1	1	yes	characteristic, complemented
125	#389	C₂²	1	1	yes	characteristic, complemented
126	#389	C₂²	1	1	yes	characteristic, complemented
127	#388	C₂²	1	1	yes	characteristic, complemented
128	#388	C₂²	1	1	yes	characteristic, complemented
129	#388	C₂²	1	1	yes	characteristic, complemented
130	#388	C₂²	1	1	yes	characteristic, complemented
131	#388	C₂²	1	1	yes	characteristic, complemented
132	#388	C₂²	1	1	yes	characteristic, complemented
133	#388	C₂²	1	1	yes	characteristic, complemented
134	#388	C₂²	1	1	yes	characteristic, complemented
135	#388	C₂²	1	1	yes	characteristic, complemented
136	#388	C₂²	1	1	yes	characteristic, complemented
137	#388	C₂²	1	1	yes	characteristic, complemented
138	#388	C₂²	1	1	yes	characteristic, complemented
139	#388	C₂²	1	1	yes	characteristic, complemented
140	#388	C₂²	1	1	yes	characteristic, complemented
141	#387	C₂²	1	1	yes	characteristic, complemented
142	#387	C₂²	1	1	yes	characteristic, complemented
143	#386	C₂²	1	1	yes	characteristic
144	#386	C₂²	1	1	yes	characteristic
145	#386	C₂²	1	1	yes	characteristic
146	#386	C₂²	1	1	yes	characteristic
147	#386	C₂²	1	1	yes	characteristic
148	#386	C₂²	1	1	yes	characteristic
149	#386	C₂²	1	1	yes	characteristic
150	#386	C₂²	1	1	yes	characteristic
151	#386	C₂²	1	1	yes	characteristic
152	#386	C₂²	1	1	yes	characteristic
153	#386	C₂²	1	1	yes	characteristic
154	#386	C₂²	1	1	yes	characteristic
155	#386	C₂²	1	1	yes	characteristic, complemented
156	#386	C₂²	1	1	yes	characteristic, complemented
157	#386	C₂²	1	1	yes	characteristic, complemented
158	#386	C₂²	1	1	yes	characteristic, complemented
159	#386	C₂²	1	1	yes	characteristic, complemented
160	#386	C₂²	1	1	yes	characteristic, complemented
161	#386	C₂²	1	1	yes	characteristic, complemented
162	#386	C₂²	1	1	yes	characteristic, complemented
163	#386	C₂²	1	1	yes	characteristic, complemented
164	#386	C₂²	1	1	yes	characteristic, complemented
165	#385	C₂²	1	1	yes	characteristic
166	#385	C₂²	1	1	yes	characteristic
167	#385	C₂²	1	1	yes	characteristic, complemented
168	#385	C₂²	1	1	yes	characteristic, complemented
169	#385	C₂²	1	1	yes	characteristic, complemented
170	#385	C₂²	1	1	yes	characteristic, complemented
171	#380	C₂²	1	1	yes	characteristic
172	#379	C₂²	1	1	yes	characteristic
173	#379	C₂²	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
175	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
176	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
177	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
185	#376	C₂²	1	1	yes	characteristic, complemented
186	C₂×#95	C₂²	1	1	yes	characteristic
187	C₂×#95	C₂²	1	1	yes	characteristic
188	C₂×#95	C₂²	1	1	yes	characteristic, complemented
189	C₂⁵	C₂³	1	1	yes	characteristic
190	C₂⁵	C₂³	1	1	yes	characteristic
191	C₂×#41	—	2	4	no	—
192	C₂×#41	—	4	2	no	—
193	C₂×#41	—	4	2	no	—
194	C₂²×Q₈	C₂³	1	1	yes	characteristic
195	C₂²×Q₈	C₂³	1	1	yes	characteristic
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	—	4	2	no	—
198	C₂²×D₄	—	4	2	no	—
199	C₂²×D₄	C₂³	1	1	yes	characteristic
200	C₂²×D₄	C₂³	1	1	yes	characteristic
201	C₂²×D₄	C₂³	1	1	yes	characteristic
202	C₂²×D₄	C₂³	1	1	yes	characteristic
203	C₂²×D₄	C₂³	1	1	yes	characteristic
204	C₂²×D₄	C₂³	1	1	yes	characteristic
205	C₂²×D₄	C₂³	1	1	yes	characteristic
206	C₂²×D₄	C₂³	1	1	yes	characteristic
207	C₂²×D₄	C₂³	1	1	yes	characteristic
208	C₂²×D₄	C₂³	1	1	yes	characteristic
209	C₂²×D₄	C₂³	1	1	yes	characteristic
210	C₂²×D₄	C₂³	1	1	yes	characteristic
211	C₂²×D₄	C₂³	1	1	yes	characteristic
212	C₂²×D₄	C₂³	1	1	yes	characteristic
213	C₂²×D₄	C₂³	1	1	yes	characteristic
214	C₂²×D₄	C₂³	1	1	yes	characteristic
215	C₂²×D₄	C₂³	1	1	yes	characteristic
216	C₂²×D₄	C₂³	1	1	yes	characteristic
217	C₂²×D₄	C₂³	1	1	yes	characteristic
218	C₂²×D₄	C₂³	1	1	yes	characteristic
219	C₂²×D₄	C₂³	1	1	yes	characteristic
220	C₂²×D₄	C₂³	1	1	yes	characteristic
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	4	2	no	—
223	C₂³×C₄	—	4	2	no	—
224	C₂³×C₄	C₂³	1	1	yes	characteristic
225	C₂³×C₄	C₂³	1	1	yes	characteristic
226	C₂³×C₄	C₂³	1	1	yes	characteristic
227	C₂³×C₄	C₂³	1	1	yes	characteristic
228	C₂³×C₄	C₂³	1	1	yes	characteristic
229	C₂³×C₄	C₂³	1	1	yes	characteristic
230	C₂³×C₄	C₂³	1	1	yes	characteristic
231	C₂³×C₄	C₂³	1	1	yes	characteristic
232	C₂³×C₄	C₂³	1	1	yes	characteristic
233	C₂³×C₄	C₂³	1	1	yes	characteristic
234	C₂³×C₄	C₂³	1	1	yes	characteristic
235	C₂³×C₄	C₂³	1	1	yes	characteristic
236	C₂³×C₄	C₂³	1	1	yes	characteristic
237	C₂³×C₄	C₂³	1	1	yes	characteristic
238	#127	—	4	2	no	—
239	#127	—	4	2	no	—
240	#126	—	2	4	no	—
241	#126	—	2	4	no	—
242	#124	—	2	4	no	—
243	#124	—	2	4	no	—
244	#124	—	4	2	no	—
245	#124	—	4	2	no	—
246	#123	—	2	4	no	—
247	#123	—	2	4	no	—
248	#123	—	2	4	no	—
249	#123	—	2	4	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	#121	—	2	4	no	—
254	#121	—	2	4	no	—
255	#121	—	2	4	no	—
256	#121	—	2	4	no	—
257	#121	—	2	4	no	—
258	#121	—	2	4	no	—
259	#121	—	4	2	no	—
260	#121	—	4	2	no	—
261	#121	—	4	2	no	—
262	#121	—	4	2	no	—
263	#120	—	2	4	no	—
264	#120	—	2	4	no	—
265	#120	—	2	4	no	—
266	#120	—	2	4	no	—
267	#120	—	2	4	no	—
268	#120	—	2	4	no	—
269	C₄×D₄	—	2	4	no	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	4	2	no	—
276	C₄×D₄	—	4	2	no	—
277	C₄×D₄	D₄	1	8	yes	complemented
278	#117	—	2	4	no	—
279	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	—	4	2	no	—
301	C₂×C₂²⋊C₄	—	4	2	no	—
302	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
358	C₂×C₄²	C₂³	1	1	yes	characteristic
359	C₂×C₄²	C₂³	1	1	yes	characteristic
360	C₂×C₄²	C₂³	1	1	yes	characteristic
361	C₂×C₄²	C₂³	1	1	yes	characteristic
362	C₂×C₄²	C₂³	1	1	yes	characteristic
363	C₂×C₄²	C₂³	1	1	yes	characteristic
364	C₂×C₄²	C₂³	1	1	yes	characteristic
365	C₂×C₄²	C₂³	1	1	yes	characteristic
366	C₂×C₄²	C₂³	1	1	yes	characteristic
367	C₂×C₄²	C₂³	1	1	yes	characteristic
368	C₂×C₄²	C₂³	1	1	yes	characteristic
369	#95	C₂³	1	1	yes	characteristic
370	#95	C₂³	1	1	yes	characteristic
371	#95	C₂³	1	1	yes	characteristic
372	#95	C₂³	1	1	yes	characteristic
373	#95	C₂³	1	1	yes	characteristic
374	#95	C₂³	1	1	yes	characteristic
375	#95	C₂³	1	1	yes	characteristic
376	#95	C₂³	1	1	yes	characteristic
377	#95	C₂³	1	1	yes	characteristic
378	#95	C₂³	1	1	yes	characteristic
379	#95	C₂³	1	1	yes	characteristic
380	#95	C₂³	1	1	yes	characteristic
381	#95	C₂³	1	1	yes	characteristic
382	#95	C₂³	1	1	yes	characteristic
383	#95	C₂³	1	1	yes	characteristic
384	#95	C₂³	1	1	yes	characteristic
385	#95	C₂³	1	1	yes	characteristic
386	#95	C₂³	1	1	yes	characteristic
387	#95	C₂³	1	1	yes	characteristic
388	#95	C₂³	1	1	yes	characteristic
389	#95	C₂³	1	1	yes	characteristic
390	#95	C₂³	1	1	yes	characteristic
391	#95	C₂³	1	1	yes	characteristic
392	#95	C₂³	1	1	yes	characteristic
393	#95	C₂³	1	1	yes	characteristic
394	#95	C₂³	1	1	yes	characteristic
395	#95	C₂³	1	1	yes	characteristic
396	#95	C₂³	1	1	yes	characteristic
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	4	1	no	—
406	C₂⁴	—	4	1	no	—
407	C₂⁴	—	4	1	no	—
408	C₂⁴	—	4	1	no	—
409	C₂⁴	—	4	1	no	—
410	C₂⁴	—	4	1	no	—
411	C₂⁴	C₂⁴	1	1	yes	characteristic
412	C₂⁴	C₂⁴	1	1	yes	characteristic
413	C₂⁴	C₂⁴	1	1	yes	characteristic
414	C₂⁴	C₂⁴	1	1	yes	characteristic
415	C₂⁴	C₂⁴	1	1	yes	characteristic
416	C₂⁴	C₂⁴	1	1	yes	characteristic
417	C₂⁴	C₂⁴	1	1	yes	characteristic
418	C₂⁴	C₂⁴	1	1	yes	characteristic
419	#41	—	4	16	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	—	4	1	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	4	16	no	—
492	C₂×D₄	C₂×D₄	1	4	yes	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	—	4	1	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	4	1	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	—	4	1	no	—
520	C₂²×C₄	—	4	1	no	—
521	C₂²×C₄	—	4	1	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	—	4	1	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	1	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	16	no	—
533	C₂²×C₄	C₂×D₄	1	4	yes	—
534	C₂²×C₄	C₂×D₄	1	4	yes	complemented
535	C₂²×C₄	#41	1	4	yes	complemented
536	C₂²×C₄	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴	1	1	yes	characteristic
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	1	no	—
576	C₄⋊C₄	—	4	1	no	—
577	C₄⋊C₄	—	4	1	no	—
578	C₄⋊C₄	C₂×D₄	1	4	yes	complemented
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	4	1	no	—
616	C₂²⋊C₄	—	4	1	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₂²⋊C₄	—	4	1	no	—
620	C₂²⋊C₄	—	4	1	no	—
621	C₂²⋊C₄	—	4	1	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	1	no	—
624	C₂²⋊C₄	—	4	1	no	—
625	C₂²⋊C₄	—	4	1	no	—
626	C₂²⋊C₄	—	4	1	no	—
627	C₂²⋊C₄	—	4	1	no	—
628	C₂²⋊C₄	—	4	1	no	—
629	C₂²⋊C₄	—	4	1	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	C₂×D₄	1	4	yes	—
633	C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
634	C₂²⋊C₄	#41	1	4	yes	complemented
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	4	1	no	—
640	C₄²	—	4	1	no	—
641	C₄²	—	4	1	no	—
642	C₄²	—	4	1	no	—
643	C₄²	—	4	1	no	—
644	C₄²	—	4	1	no	—
645	C₄²	C₂×D₄	1	4	yes	complemented
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	8	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	4	4	no	—
701	C₂³	—	4	4	no	—
702	C₂³	—	4	4	no	—
703	C₂³	—	4	4	no	—
704	C₂³	—	4	4	no	—
705	C₂³	—	4	4	no	—
706	C₂³	—	8	2	no	—
707	C₂³	—	8	2	no	—
708	C₂³	—	8	2	no	—
709	C₂³	—	8	2	no	—
710	C₂³	C₂²×D₄	1	2	yes	—
711	C₂³	C₂²×D₄	1	2	yes	—
712	C₂³	C₂×#41	1	2	yes	—
713	C₂³	C₂×#41	1	2	yes	—
714	C₂³	H(5,𝔽₂)	1	2	yes	—
715	C₂³	H(5,𝔽₂)	1	2	yes	—
716	C₂³	C₂⁵	1	1	yes	characteristic
717	Q₈	—	4	4	no	—
718	Q₈	—	8	2	no	—
719	D₄	—	2	8	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	4	no	—
723	D₄	—	4	4	no	—
724	D₄	—	4	4	no	—
725	D₄	—	4	4	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	4	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	4	no	—
733	D₄	—	8	2	no	—
734	D₄	—	8	2	no	—
735	D₄	—	8	2	no	—
736	D₄	—	8	2	no	—
737	D₄	—	8	2	no	—
738	D₄	—	8	2	no	—
739	D₄	—	8	2	no	—
740	D₄	—	8	2	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	2	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	C₂²×D₄	1	2	yes	—
815	C₂×C₄	C₂²×D₄	1	2	yes	—
816	C₂×C₄	C₂²×D₄	1	2	yes	—
817	C₂×C₄	C₂²×D₄	1	2	yes	—
818	C₂×C₄	C₂²×D₄	1	2	yes	—
819	C₂×C₄	C₂×#41	1	2	yes	—
820	C₂×C₄	C₂×#41	1	2	yes	—
821	C₂×C₄	C₂×#41	1	2	yes	—
822	C₂×C₄	C₂×#41	1	2	yes	—
823	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	16	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	8	8	no	—
881	C₂²	#532	1	4	yes	—
882	C₂²	C₂³×D₄	1	1	yes	characteristic
883	C₂²	C₂²×#41	1	1	yes	characteristic
884	C₂²	C₂²×#41	1	1	yes	characteristic
885	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
888	C₂²	#585	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₂	—	2	4	no	—
913	C₂	—	4	2	no	—
914	C₂	—	4	2	no	—
915	C₂	—	4	2	no	—
916	C₂	—	8	1	no	—
917	C₂	—	8	1	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	1	no	—
920	C₂	C₂×#532	1	1	yes	characteristic
921	C₂	#3484	1	1	yes	characteristic
922	C₂	#3488	1	1	yes	characteristic
923	C₂	#3490	1	1	yes	characteristic
924	C₂	#3506	1	1	yes	characteristic
925	C₂	#3513	1	1	yes	characteristic
926	C₂	#3519	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#538	C₂	semidirect
2. C₂×#525	C₂	semidirect
3. #2610	C₂	semidirect
4. #2603	C₂	semidirect
5. #2602	C₂	semidirect
6. #2601	C₂	semidirect
7. #2560	C₂	semidirect
8. #2557	C₂	semidirect
9. #2555	C₂	semidirect
10. #2554	C₂	semidirect
11. #2549	C₂	semidirect
12. #2544	C₂	semidirect
13. #2543	C₂	semidirect
14. #2543	C₂	semidirect
15. #2472	C₂	semidirect
16. #2472	C₂	semidirect
17. #2464	C₂	semidirect
18. #2461	C₂	semidirect
19. #2445	C₂	semidirect
20. #2433	C₂	semidirect
21. #2431	C₂	semidirect
22. #2430	C₂	semidirect
23. #2428	C₂	semidirect
24. #2424	C₂	semidirect
25. #2424	C₂	semidirect
26. #2408	C₂	semidirect
27. #2325	C₂	semidirect
28. #2321	C₂	semidirect
29. C₄×#120	C₂	semidirect
30. C₂×#386	C₂	semidirect
31. #2275	C₂	semidirect
32. C₂²×#41	C₂²	semidirect
38. C₂×#126	C₂²	semidirect
39. C₂×#126	C₂²	semidirect
40. C₂×#124	C₂²	semidirect
41. C₂×#124	C₂²	semidirect
42. C₂×#124	C₂²	semidirect
43. C₂×#124	C₂²	semidirect
45. C₂×#123	C₂²	semidirect
46. C₂×#123	C₂²	semidirect
47. C₂×#123	C₂²	semidirect
48. C₂×#123	C₂²	semidirect
51. C₂×C₂²⋊Q₈	C₂²	semidirect
57. C₂×#121	C₂²	semidirect
58. C₂×#121	C₂²	semidirect
59. C₂×#121	C₂²	semidirect
60. C₂×#121	C₂²	semidirect
61. C₂×#121	C₂²	semidirect
73. C₂×C₄×D₄	C₂²	semidirect
74. C₂×C₄×D₄	C₂²	semidirect
75. C₂×C₄×D₄	C₂²	semidirect
76. C₂×C₄×D₄	C₂²	semidirect
77. C₂×#117	C₂²	semidirect
81. #398	C₂²	semidirect
82. #398	C₂²	semidirect
83. #398	C₂²	semidirect
84. #397	C₂²	semidirect
85. #397	C₂²	semidirect
86. #397	C₂²	semidirect
87. #396	C₂²	semidirect
88. #396	C₂²	semidirect
89. #395	C₂²	semidirect
90. #395	C₂²	semidirect
93. #394	C₂²	semidirect
94. #394	C₂²	semidirect
95. #394	C₂²	semidirect
96. #394	C₂²	semidirect
97. #394	C₂²	semidirect
98. #394	C₂²	semidirect
99. #394	C₂²	semidirect
100. #394	C₂²	semidirect
101. #394	C₂²	semidirect
102. #393	C₂²	semidirect
103. #393	C₂²	semidirect
110. #392	C₂²	semidirect
111. #392	C₂²	semidirect
112. #392	C₂²	semidirect
113. #391	C₂²	semidirect
114. #391	C₂²	semidirect
119. #390	C₂²	semidirect
120. #390	C₂²	semidirect
121. #390	C₂²	semidirect
122. #390	C₂²	semidirect
123. #390	C₂²	semidirect
124. #390	C₂²	semidirect
125. #389	C₂²	semidirect
126. #389	C₂²	semidirect
127. #388	C₂²	semidirect
128. #388	C₂²	semidirect
129. #388	C₂²	semidirect
130. #388	C₂²	semidirect
131. #388	C₂²	semidirect
132. #388	C₂²	semidirect
133. #388	C₂²	semidirect
134. #388	C₂²	semidirect
135. #388	C₂²	semidirect
136. #388	C₂²	semidirect
137. #388	C₂²	semidirect
138. #388	C₂²	semidirect
139. #388	C₂²	semidirect
140. #388	C₂²	semidirect
141. #387	C₂²	semidirect
142. #387	C₂²	semidirect
155. #386	C₂²	semidirect
156. #386	C₂²	semidirect
157. #386	C₂²	semidirect
158. #386	C₂²	semidirect
159. #386	C₂²	semidirect
160. #386	C₂²	semidirect
161. #386	C₂²	semidirect
162. #386	C₂²	semidirect
163. #386	C₂²	semidirect
164. #386	C₂²	semidirect
167. #385	C₂²	semidirect
168. #385	C₂²	semidirect
169. #385	C₂²	semidirect
170. #385	C₂²	semidirect
174. C₄×C₄⋊C₄	C₂²	semidirect
175. C₄×C₄⋊C₄	C₂²	semidirect
176. C₄×C₄⋊C₄	C₂²	semidirect
180. C₄×C₂²⋊C₄	C₂²	semidirect
181. C₄×C₂²⋊C₄	C₂²	semidirect
182. C₄×C₂²⋊C₄	C₂²	semidirect
183. C₄×C₂²⋊C₄	C₂²	semidirect
184. C₄×C₂²⋊C₄	C₂²	semidirect
185. #376	C₂²	semidirect
188. C₂×#95	C₂²	semidirect
277. C₄×D₄	D₄	semidirect
534. C₂²×C₄	C₂×D₄	semidirect
535. C₂²×C₄	#41	semidirect
578. C₄⋊C₄	C₂×D₄	semidirect
633. C₂²⋊C₄	C₂×D₄	semidirect
634. C₂²⋊C₄	#41	semidirect
645. C₄²	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#538	2
C₂×#525	2
#2610	2
#2603	2
#2602	2
#2601	2
#2560	2
#2557	2
#2555	2
#2554	2
#2549	2
#2544	2
#2543	2
#2472	2
#2464	2
#2461	2
#2445	2
#2433	2
#2431	2
#2430	2
#2428	2
#2424	2
#2408	2
#2325	2
#2321	2
C₄×#120	2
C₂×#386	2
#2275	2