Subgroups — #34302

Order 256.

1478 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546	C₂	1	1	yes	maximal, characteristic
2	#2374	C₂	1	1	yes	maximal, characteristic, complemented
3	#2372	C₂	1	1	yes	maximal, characteristic, complemented
4	#2368	C₂	1	1	yes	maximal, characteristic, complemented
5	#2364	C₂	1	1	yes	maximal, characteristic, complemented
6	#2364	C₂	1	1	yes	maximal, characteristic, complemented
7	#2363	C₂	1	1	yes	maximal, characteristic, complemented
8	#2359	C₂	1	1	yes	maximal, characteristic, complemented
9	#2358	C₂	1	1	yes	maximal, characteristic, complemented
10	#2358	C₂	1	1	yes	maximal, characteristic, complemented
11	#2353	C₂	1	1	yes	maximal, characteristic, complemented
12	#2353	C₂	1	1	yes	maximal, characteristic, complemented
13	#2342	C₂	1	1	yes	maximal, characteristic, complemented
14	#2342	C₂	1	1	yes	maximal, characteristic, complemented
15	#2339	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	#2337	C₂	1	1	yes	maximal, characteristic, complemented
18	#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	#2333	C₂	1	1	yes	maximal, characteristic, complemented
20	#2333	C₂	1	1	yes	maximal, characteristic, complemented
21	#2329	C₂	1	1	yes	maximal, characteristic, complemented
22	#2321	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#120	C₂	1	1	yes	maximal, characteristic, complemented
26	#2297	C₂	1	1	yes	maximal, characteristic, complemented
27	#2290	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×#386	C₂	1	1	yes	maximal, characteristic, complemented
29	#2275	C₂	1	1	yes	maximal, characteristic, complemented
30	#2273	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41	C₂²	1	1	yes	characteristic
33	C₂³×D₄	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄	C₂²	1	1	yes	characteristic
35	#546	C₄	1	16	yes	complemented
36	C₂×#124	C₂²	1	1	yes	characteristic
37	C₂×#123	C₂²	1	1	yes	characteristic
38	C₂×#123	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×#121	C₂²	1	1	yes	characteristic
41	C₂×#121	C₂²	1	1	yes	characteristic
42	C₂×#121	C₂²	1	1	yes	characteristic
43	C₂×#120	C₂²	1	1	yes	characteristic
44	C₂×#120	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×#117	C₂²	1	1	yes	characteristic, complemented
56	C₂×#117	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
60	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
61	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
62	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
63	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
64	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
65	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
66	#391	C₂²	1	1	yes	characteristic, complemented
67	#391	C₂²	1	1	yes	characteristic, complemented
68	#391	C₂²	1	1	yes	characteristic, complemented
69	#391	C₂²	1	1	yes	characteristic, complemented
70	#390	C₂²	1	1	yes	characteristic
71	#390	C₂²	1	1	yes	characteristic
72	#390	C₂²	1	1	yes	characteristic, complemented
73	#390	C₂²	1	1	yes	characteristic, complemented
74	#390	C₂²	1	1	yes	characteristic, complemented
75	#390	C₂²	1	1	yes	characteristic, complemented
76	#389	C₂²	1	1	yes	characteristic, complemented
77	#389	C₂²	1	1	yes	characteristic, complemented
78	#388	C₂²	1	1	yes	characteristic, complemented
79	#388	C₂²	1	1	yes	characteristic, complemented
80	#388	C₂²	1	1	yes	characteristic, complemented
81	#388	C₂²	1	1	yes	characteristic, complemented
82	#388	C₂²	1	1	yes	characteristic, complemented
83	#388	C₂²	1	1	yes	characteristic, complemented
84	#388	C₂²	1	1	yes	characteristic, complemented
85	#388	C₂²	1	1	yes	characteristic, complemented
86	#388	C₂²	1	1	yes	characteristic, complemented
87	#388	C₂²	1	1	yes	characteristic, complemented
88	#388	C₂²	1	1	yes	characteristic, complemented
89	#388	C₂²	1	1	yes	characteristic, complemented
90	#388	C₂²	1	1	yes	characteristic, complemented
91	#388	C₂²	1	1	yes	characteristic, complemented
92	#388	C₂²	1	1	yes	characteristic, complemented
93	#388	C₂²	1	1	yes	characteristic, complemented
94	#388	C₂²	1	1	yes	characteristic, complemented
95	#388	C₂²	1	1	yes	characteristic, complemented
96	#387	C₂²	1	1	yes	characteristic, complemented
97	#387	C₂²	1	1	yes	characteristic, complemented
98	#387	C₂²	1	1	yes	characteristic, complemented
99	#387	C₂²	1	1	yes	characteristic, complemented
100	#387	C₂²	1	1	yes	characteristic, complemented
101	#387	C₂²	1	1	yes	characteristic, complemented
102	#387	C₂²	1	1	yes	characteristic, complemented
103	#387	C₂²	1	1	yes	characteristic, complemented
104	#387	C₂²	1	1	yes	characteristic, complemented
105	#387	C₂²	1	1	yes	characteristic, complemented
106	#386	C₂²	1	1	yes	characteristic
107	#386	C₂²	1	1	yes	characteristic
108	#386	C₂²	1	1	yes	characteristic
109	#386	C₂²	1	1	yes	characteristic
110	#386	C₂²	1	1	yes	characteristic
111	#386	C₂²	1	1	yes	characteristic
112	#386	C₂²	1	1	yes	characteristic
113	#386	C₂²	1	1	yes	characteristic
114	#386	C₂²	1	1	yes	characteristic
115	#386	C₂²	1	1	yes	characteristic
116	#386	C₂²	1	1	yes	characteristic
117	#386	C₂²	1	1	yes	characteristic
118	#386	C₂²	1	1	yes	characteristic
119	#386	C₂²	1	1	yes	characteristic
120	#386	C₂²	1	1	yes	characteristic, complemented
121	#386	C₂²	1	1	yes	characteristic, complemented
122	#386	C₂²	1	1	yes	characteristic, complemented
123	#386	C₂²	1	1	yes	characteristic, complemented
124	#386	C₂²	1	1	yes	characteristic, complemented
125	#386	C₂²	1	1	yes	characteristic, complemented
126	#386	C₂²	1	1	yes	characteristic, complemented
127	#386	C₂²	1	1	yes	characteristic, complemented
128	#385	C₂²	1	1	yes	characteristic
129	#385	C₂²	1	1	yes	characteristic
130	#385	C₂²	1	1	yes	characteristic
131	#385	C₂²	1	1	yes	characteristic
132	#385	C₂²	1	1	yes	characteristic, complemented
133	#385	C₂²	1	1	yes	characteristic, complemented
134	#385	C₂²	1	1	yes	characteristic, complemented
135	#385	C₂²	1	1	yes	characteristic, complemented
136	#383	C₂²	1	1	yes	characteristic, complemented
137	#381	C₂²	1	1	yes	characteristic, complemented
138	#381	C₂²	1	1	yes	characteristic, complemented
139	#381	C₂²	1	1	yes	characteristic, complemented
140	#380	C₂²	1	1	yes	characteristic
141	#380	C₂²	1	1	yes	characteristic, complemented
142	#380	C₂²	1	1	yes	characteristic, complemented
143	#379	C₂²	1	1	yes	characteristic
144	#379	C₂²	1	1	yes	characteristic
145	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
152	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
153	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
155	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
156	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
157	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
158	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
159	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
173	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
174	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
175	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
176	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
177	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
178	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
181	#376	C₂²	1	1	yes	characteristic, complemented
182	#376	C₂²	1	1	yes	characteristic, complemented
183	C₂×#95	C₂²	1	1	yes	characteristic
184	C₂×#95	C₂²	1	1	yes	characteristic
185	C₂×#95	C₂²	1	1	yes	characteristic, complemented
186	C₂×#95	C₂²	1	1	yes	characteristic, complemented
187	C₂×#95	C₂²	1	1	yes	characteristic, complemented
188	C₂⁵	C₂³	1	1	yes	characteristic
189	C₂⁵	C₂³	1	1	yes	characteristic
190	C₂×#41	—	4	2	no	—
191	C₂×#41	—	4	2	no	—
192	C₂×#41	C₂×C₄	1	8	yes	complemented
193	C₂²×Q₈	C₂³	1	1	yes	characteristic
194	C₂²×D₄	—	4	2	no	—
195	C₂²×D₄	—	4	2	no	—
196	C₂²×D₄	C₂×C₄	1	8	yes	complemented
197	C₂²×D₄	C₂³	1	1	yes	characteristic
198	C₂²×D₄	C₂³	1	1	yes	characteristic
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	C₂³×C₄	—	2	4	no	—
207	C₂³×C₄	—	4	2	no	—
208	C₂³×C₄	—	4	2	no	—
209	C₂³×C₄	C₂³	1	1	yes	characteristic
210	C₂³×C₄	C₂³	1	1	yes	characteristic
211	C₂³×C₄	C₂³	1	1	yes	characteristic
212	C₂³×C₄	C₂³	1	1	yes	characteristic
213	C₂³×C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₄	C₂³	1	1	yes	characteristic
215	C₂³×C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₄	C₂³	1	1	yes	characteristic
217	C₂³×C₄	C₂³	1	1	yes	characteristic
218	C₂³×C₄	C₂³	1	1	yes	characteristic
219	C₂³×C₄	C₂³	1	1	yes	characteristic
220	C₂³×C₄	C₂³	1	1	yes	characteristic
221	C₂³×C₄	C₂³	1	1	yes	characteristic
222	C₂³×C₄	C₂³	1	1	yes	characteristic
223	C₂³×C₄	C₂³	1	1	yes	characteristic
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	#124	C₂×C₄	1	8	yes	complemented
230	#123	C₂×C₄	1	8	yes	complemented
231	#123	C₂×C₄	1	8	yes	complemented
232	C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
233	#121	C₂×C₄	1	8	yes	complemented
234	#121	C₂×C₄	1	8	yes	complemented
235	#121	C₂×C₄	1	8	yes	complemented
236	#120	C₂×C₄	1	8	yes	complemented
237	#120	C₂×C₄	1	8	yes	complemented
238	C₄×D₄	—	2	4	no	—
239	C₄×D₄	—	2	4	no	—
240	C₄×D₄	—	4	2	no	—
241	C₄×D₄	—	4	2	no	—
242	C₄×D₄	—	4	2	no	—
243	C₄×D₄	—	4	2	no	—
244	C₄×D₄	—	4	2	no	—
245	C₄×D₄	—	4	2	no	—
246	C₄×D₄	C₂×C₄	1	8	yes	complemented
247	C₄×D₄	C₂×C₄	1	8	yes	complemented
248	#117	—	4	2	no	—
249	#117	—	4	2	no	—
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	4	no	—
269	C₂×C₂²⋊C₄	—	4	2	no	—
270	C₂×C₂²⋊C₄	—	4	2	no	—
271	C₂×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
272	C₂×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
273	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	—	4	2	no	—
320	C₂×C₄²	—	4	2	no	—
321	C₂×C₄²	C₂³	1	1	yes	characteristic
322	C₂×C₄²	C₂³	1	1	yes	characteristic
323	C₂×C₄²	C₂³	1	1	yes	characteristic
324	C₂×C₄²	C₂³	1	1	yes	characteristic
325	C₂×C₄²	C₂³	1	1	yes	characteristic
326	C₂×C₄²	C₂³	1	1	yes	characteristic
327	C₂×C₄²	C₂³	1	1	yes	characteristic
328	C₂×C₄²	C₂³	1	1	yes	characteristic
329	C₂×C₄²	C₂³	1	1	yes	characteristic
330	C₂×C₄²	C₂³	1	1	yes	characteristic
331	C₂×C₄²	C₂³	1	1	yes	characteristic
332	C₂×C₄²	C₂³	1	1	yes	characteristic
333	C₂×C₄²	C₂³	1	1	yes	characteristic
334	C₂×C₄²	C₂³	1	1	yes	characteristic
335	C₂×C₄²	C₂³	1	1	yes	characteristic
336	C₂×C₄²	C₂³	1	1	yes	characteristic
337	C₂×C₄²	C₂³	1	1	yes	characteristic
338	C₂×C₄²	C₂³	1	1	yes	characteristic
339	C₂×C₄²	C₂³	1	1	yes	characteristic
340	C₂×C₄²	C₂³	1	1	yes	characteristic
341	C₂×C₄²	C₂³	1	1	yes	characteristic
342	#95	C₂³	1	1	yes	characteristic
343	#95	C₂³	1	1	yes	characteristic
344	#95	C₂³	1	1	yes	characteristic
345	#95	C₂³	1	1	yes	characteristic
346	#95	C₂³	1	1	yes	characteristic
347	#95	C₂³	1	1	yes	characteristic
348	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	#95	C₂³	1	1	yes	characteristic
352	#95	C₂³	1	1	yes	characteristic
353	#95	C₂³	1	1	yes	characteristic
354	#95	C₂³	1	1	yes	characteristic
355	#95	C₂³	1	1	yes	characteristic
356	#95	C₂³	1	1	yes	characteristic
357	#95	C₂³	1	1	yes	characteristic
358	#95	C₂³	1	1	yes	characteristic
359	#95	C₂³	1	1	yes	characteristic
360	#95	C₂³	1	1	yes	characteristic
361	#95	C₂³	1	1	yes	characteristic
362	#95	C₂³	1	1	yes	characteristic
363	#95	C₂³	1	1	yes	characteristic
364	#95	C₂³	1	1	yes	characteristic
365	#95	C₂³	1	1	yes	characteristic
366	#95	C₂³	1	1	yes	characteristic
367	#95	C₂³	1	1	yes	characteristic
368	#95	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	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	4	1	no	—
389	C₂⁴	—	4	1	no	—
390	C₂⁴	—	4	1	no	—
391	C₂⁴	—	4	1	no	—
392	C₂⁴	—	4	1	no	—
393	C₂⁴	—	4	1	no	—
394	C₂⁴	C₂²×C₄	1	4	yes	—
395	C₂⁴	C₂²×C₄	1	4	yes	—
396	C₂⁴	C₂⁴	1	1	yes	characteristic
397	C₂⁴	C₂⁴	1	1	yes	characteristic
398	C₂⁴	C₂⁴	1	1	yes	characteristic
399	C₂⁴	C₂⁴	1	1	yes	characteristic
400	C₂⁴	C₂⁴	1	1	yes	characteristic
401	C₂⁴	C₂⁴	1	1	yes	characteristic
402	#41	—	4	16	no	—
403	C₂×Q₈	—	4	1	no	—
404	C₂×Q₈	—	4	1	no	—
405	C₂×Q₈	C₂²×C₄	1	4	yes	complemented
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	16	no	—
425	C₂×D₄	C₂²×C₄	1	4	yes	—
426	C₂×D₄	C₂²×C₄	1	4	yes	—
427	C₂×D₄	C₂²×C₄	1	4	yes	—
428	C₂×D₄	C₂²×C₄	1	4	yes	—
429	C₂×D₄	C₂²×C₄	1	4	yes	—
430	C₂×D₄	C₂²×C₄	1	4	yes	—
431	C₂×D₄	C₂²×C₄	1	4	yes	—
432	C₂×D₄	C₂²×C₄	1	4	yes	complemented
433	C₂×D₄	C₂²×C₄	1	4	yes	complemented
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	16	no	—
488	C₂²×C₄	C₂²×C₄	1	4	yes	—
489	C₂²×C₄	C₂²×C₄	1	4	yes	—
490	C₂²×C₄	C₂²×C₄	1	4	yes	—
491	C₂²×C₄	C₂²×C₄	1	4	yes	complemented
492	C₂²×C₄	C₂²×C₄	1	4	yes	complemented
493	C₂²×C₄	C₂²×C₄	1	4	yes	complemented
494	C₂²×C₄	#41	1	4	yes	complemented
495	C₂²×C₄	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴	1	1	yes	characteristic
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
533	C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
534	C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
535	C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₂²⋊C₄	—	4	1	no	—
560	C₂²⋊C₄	—	4	1	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	4	1	no	—
564	C₂²⋊C₄	—	4	1	no	—
565	C₂²⋊C₄	—	4	1	no	—
566	C₂²⋊C₄	—	4	1	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
571	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
572	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
573	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
574	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
577	C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
578	C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
579	C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
580	C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
581	C₂²⋊C₄	#41	1	4	yes	complemented
582	C₄²	—	2	2	no	—
583	C₄²	—	2	2	no	—
584	C₄²	—	2	2	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	4	1	no	—
587	C₄²	—	4	1	no	—
588	C₄²	—	4	1	no	—
589	C₄²	—	4	1	no	—
590	C₄²	—	4	1	no	—
591	C₄²	—	4	1	no	—
592	C₄²	—	4	1	no	—
593	C₄²	—	4	1	no	—
594	C₄²	—	4	1	no	—
595	C₄²	—	4	1	no	—
596	C₄²	—	4	1	no	—
597	C₄²	—	4	1	no	—
598	C₄²	—	4	1	no	—
599	C₄²	—	4	1	no	—
600	C₄²	—	4	1	no	—
601	C₄²	—	4	1	no	—
602	C₄²	C₂²×C₄	1	4	yes	complemented
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	8	no	—
612	C₂³	—	2	8	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	8	no	—
638	C₂³	—	4	4	no	—
639	C₂³	—	4	4	no	—
640	C₂³	—	4	4	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	4	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	8	2	no	—
646	C₂³	—	8	2	no	—
647	C₂³	—	8	2	no	—
648	C₂³	—	8	2	no	—
649	C₂³	C₂³×C₄	1	2	yes	—
650	C₂³	C₂³×C₄	1	2	yes	—
651	C₂³	C₂³×C₄	1	2	yes	—
652	C₂³	C₂³×C₄	1	2	yes	—
653	C₂³	C₂³×C₄	1	2	yes	—
654	C₂³	C₂³×C₄	1	2	yes	—
655	C₂³	C₂×#41	1	2	yes	—
656	C₂³	C₂×#41	1	2	yes	—
657	C₂³	H(5,𝔽₂)	1	2	yes	—
658	C₂³	H(5,𝔽₂)	1	2	yes	—
659	C₂³	C₂⁵	1	1	yes	characteristic
660	Q₈	—	4	4	no	—
661	D₄	—	2	8	no	—
662	D₄	—	2	8	no	—
663	D₄	—	2	8	no	—
664	D₄	—	2	8	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	4	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	8	2	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	2	no	—
748	C₂×C₄	—	8	2	no	—
749	C₂×C₄	—	8	2	no	—
750	C₂×C₄	—	8	2	no	—
751	C₂×C₄	C₂³×C₄	1	2	yes	—
752	C₂×C₄	C₂³×C₄	1	2	yes	—
753	C₂×C₄	C₂³×C₄	1	2	yes	—
754	C₂×C₄	C₂³×C₄	1	2	yes	—
755	C₂×C₄	C₂³×C₄	1	2	yes	—
756	C₂×C₄	C₂³×C₄	1	2	yes	—
757	C₂×C₄	C₂³×C₄	1	2	yes	—
758	C₂×C₄	C₂³×C₄	1	2	yes	—
759	C₂×C₄	C₂³×C₄	1	2	yes	—
760	C₂×C₄	C₂×#41	1	2	yes	—
761	C₂×C₄	C₂×#41	1	2	yes	—
762	C₂×C₄	C₂×#41	1	2	yes	—
763	C₂×C₄	C₂×#41	1	2	yes	—
764	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	4	16	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	8	8	no	—
807	C₂²	C₄×#41	1	4	yes	—
808	C₂²	#518	1	4	yes	—
809	C₂²	C₂⁴×C₄	1	1	yes	characteristic
810	C₂²	C₂²×#41	1	1	yes	characteristic
811	C₂²	C₂²×#41	1	1	yes	characteristic
812	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
813	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
814	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂²	#585	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₂	—	2	4	no	—
842	C₂	—	2	4	no	—
843	C₂	—	4	2	no	—
844	C₂	—	4	2	no	—
845	C₂	—	4	2	no	—
846	C₂	—	4	2	no	—
847	C₂	C₂×C₄×#41	1	1	yes	characteristic
848	C₂	C₂×#518	1	1	yes	characteristic
849	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
850	C₂	#3490	1	1	yes	characteristic
851	C₂	#3494	1	1	yes	characteristic
852	C₂	#3513	1	1	yes	characteristic
853	C₂	#3519	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂⁵
commutator	C₂²	C₂⁴×C₄
prime radical	C₂×#546	C₂
LCS	G ▷ C₂² ▷ 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
2. #2374	C₂	semidirect
3. #2372	C₂	semidirect
4. #2368	C₂	semidirect
5. #2364	C₂	semidirect
6. #2364	C₂	semidirect
7. #2363	C₂	semidirect
8. #2359	C₂	semidirect
9. #2358	C₂	semidirect
10. #2358	C₂	semidirect
11. #2353	C₂	semidirect
12. #2353	C₂	semidirect
13. #2342	C₂	semidirect
14. #2342	C₂	semidirect
15. #2339	C₂	semidirect
16. D₄×C₂²⋊C₄	C₂	semidirect
17. #2337	C₂	semidirect
18. #2335	C₂	semidirect
19. #2333	C₂	semidirect
20. #2333	C₂	semidirect
21. #2329	C₂	semidirect
22. #2321	C₂	semidirect
23. C₄×#123	C₂	semidirect
24. C₄×#121	C₂	semidirect
25. C₄×#120	C₂	semidirect
26. #2297	C₂	semidirect
27. #2290	C₂	semidirect
28. C₂×#386	C₂	semidirect
29. #2275	C₂	semidirect
30. #2273	C₂	semidirect
31. C₂×C₄×C₂²⋊C₄	C₂	semidirect
35. #546	C₄	semidirect
51. C₂×C₄×D₄	C₂²	semidirect
52. C₂×C₄×D₄	C₂²	semidirect
53. C₂×C₄×D₄	C₂²	semidirect
54. C₂×C₄×D₄	C₂²	semidirect
55. C₂×#117	C₂²	semidirect
56. C₂×#117	C₂²	semidirect
64. C₂²×C₄²	C₂²	semidirect
65. C₂²×C₄²	C₂²	semidirect
66. #391	C₂²	semidirect
67. #391	C₂²	semidirect
68. #391	C₂²	semidirect
69. #391	C₂²	semidirect
72. #390	C₂²	semidirect
73. #390	C₂²	semidirect
74. #390	C₂²	semidirect
75. #390	C₂²	semidirect
76. #389	C₂²	semidirect
77. #389	C₂²	semidirect
78. #388	C₂²	semidirect
79. #388	C₂²	semidirect
80. #388	C₂²	semidirect
81. #388	C₂²	semidirect
82. #388	C₂²	semidirect
83. #388	C₂²	semidirect
84. #388	C₂²	semidirect
85. #388	C₂²	semidirect
86. #388	C₂²	semidirect
87. #388	C₂²	semidirect
88. #388	C₂²	semidirect
89. #388	C₂²	semidirect
90. #388	C₂²	semidirect
91. #388	C₂²	semidirect
92. #388	C₂²	semidirect
93. #388	C₂²	semidirect
94. #388	C₂²	semidirect
95. #388	C₂²	semidirect
96. #387	C₂²	semidirect
97. #387	C₂²	semidirect
98. #387	C₂²	semidirect
99. #387	C₂²	semidirect
100. #387	C₂²	semidirect
101. #387	C₂²	semidirect
102. #387	C₂²	semidirect
103. #387	C₂²	semidirect
104. #387	C₂²	semidirect
105. #387	C₂²	semidirect
120. #386	C₂²	semidirect
121. #386	C₂²	semidirect
122. #386	C₂²	semidirect
123. #386	C₂²	semidirect
124. #386	C₂²	semidirect
125. #386	C₂²	semidirect
126. #386	C₂²	semidirect
127. #386	C₂²	semidirect
132. #385	C₂²	semidirect
133. #385	C₂²	semidirect
134. #385	C₂²	semidirect
135. #385	C₂²	semidirect
136. #383	C₂²	semidirect
137. #381	C₂²	semidirect
138. #381	C₂²	semidirect
139. #381	C₂²	semidirect
141. #380	C₂²	semidirect
142. #380	C₂²	semidirect
145. C₄×C₄⋊C₄	C₂²	semidirect
146. C₄×C₄⋊C₄	C₂²	semidirect
147. C₄×C₄⋊C₄	C₂²	semidirect
148. C₄×C₄⋊C₄	C₂²	semidirect
149. C₄×C₄⋊C₄	C₂²	semidirect
159. C₄×C₂²⋊C₄	C₂²	semidirect
160. C₄×C₂²⋊C₄	C₂²	semidirect
161. C₄×C₂²⋊C₄	C₂²	semidirect
162. C₄×C₂²⋊C₄	C₂²	semidirect
163. C₄×C₂²⋊C₄	C₂²	semidirect
164. C₄×C₂²⋊C₄	C₂²	semidirect
165. C₄×C₂²⋊C₄	C₂²	semidirect
166. C₄×C₂²⋊C₄	C₂²	semidirect
167. C₄×C₂²⋊C₄	C₂²	semidirect
168. C₄×C₂²⋊C₄	C₂²	semidirect
169. C₄×C₂²⋊C₄	C₂²	semidirect
170. C₄×C₂²⋊C₄	C₂²	semidirect
171. C₄×C₂²⋊C₄	C₂²	semidirect
172. C₄×C₂²⋊C₄	C₂²	semidirect
173. C₄×C₂²⋊C₄	C₂²	semidirect
174. C₄×C₂²⋊C₄	C₂²	semidirect
175. C₄×C₂²⋊C₄	C₂²	semidirect
176. C₄×C₂²⋊C₄	C₂²	semidirect
177. C₄×C₂²⋊C₄	C₂²	semidirect
178. C₄×C₂²⋊C₄	C₂²	semidirect
179. C₄×C₂²⋊C₄	C₂²	semidirect
180. C₄×C₂²⋊C₄	C₂²	semidirect
181. #376	C₂²	semidirect
182. #376	C₂²	semidirect
185. C₂×#95	C₂²	semidirect
186. C₂×#95	C₂²	semidirect
187. C₂×#95	C₂²	semidirect
192. C₂×#41	C₂×C₄	semidirect
196. C₂²×D₄	C₂×C₄	semidirect
229. #124	C₂×C₄	semidirect
230. #123	C₂×C₄	semidirect
231. #123	C₂×C₄	semidirect
232. C₂²⋊Q₈	C₂×C₄	semidirect
233. #121	C₂×C₄	semidirect
234. #121	C₂×C₄	semidirect
235. #121	C₂×C₄	semidirect
236. #120	C₂×C₄	semidirect
237. #120	C₂×C₄	semidirect
246. C₄×D₄	C₂×C₄	semidirect
247. C₄×D₄	C₂×C₄	semidirect
271. C₂×C₂²⋊C₄	C₂×C₄	semidirect
272. C₂×C₂²⋊C₄	C₂×C₄	semidirect
405. C₂×Q₈	C₂²×C₄	semidirect
432. C₂×D₄	C₂²×C₄	semidirect
433. C₂×D₄	C₂²×C₄	semidirect
491. C₂²×C₄	C₂²×C₄	semidirect
492. C₂²×C₄	C₂²×C₄	semidirect
493. C₂²×C₄	C₂²×C₄	semidirect
494. C₂²×C₄	#41	semidirect
532. C₄⋊C₄	C₂²×C₄	semidirect
533. C₄⋊C₄	C₂²×C₄	semidirect
534. C₄⋊C₄	C₂²×C₄	semidirect
535. C₄⋊C₄	C₂²×C₄	semidirect
576. C₂²⋊C₄	C₂²×C₄	semidirect
577. C₂²⋊C₄	C₂²×C₄	semidirect
578. C₂²⋊C₄	C₂²×C₄	semidirect
579. C₂²⋊C₄	C₂²×C₄	semidirect
580. C₂²⋊C₄	C₂²×C₄	semidirect
581. C₂²⋊C₄	#41	semidirect
602. C₄²	C₂²×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546	2
#2374	2
#2372	2
#2368	2
#2364	2
#2363	2
#2359	2
#2358	2
#2353	2
#2342	2
#2339	2
D₄×C₂²⋊C₄	2
#2337	2
#2335	2
#2333	2
#2329	2
#2321	2
C₄×#123	2
C₄×#121	2
C₄×#120	2
#2297	2
#2290	2
C₂×#386	2
#2275	2
#2273	2
C₂×C₄×C₂²⋊C₄	2