Subgroups — #36220

Order 256.

1563 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#2852	C₂	1	1	yes	maximal, characteristic, complemented
4	#2849	C₂	1	1	yes	maximal, characteristic, complemented
5	#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	#2603	C₂	1	1	yes	maximal, characteristic, complemented
7	#2602	C₂	1	1	yes	maximal, characteristic, complemented
8	#2600	C₂	1	1	yes	maximal, characteristic, complemented
9	#2598	C₂	1	1	yes	maximal, characteristic, complemented
10	#2564	C₂	1	1	yes	maximal, characteristic, complemented
11	#2534	C₂	1	1	yes	maximal, characteristic, complemented
12	#2481	C₂	1	1	yes	maximal, characteristic, complemented
13	#2472	C₂	1	1	yes	maximal, characteristic, complemented
14	#2467	C₂	1	1	yes	maximal, characteristic, complemented
15	#2463	C₂	1	1	yes	maximal, characteristic, complemented
16	#2461	C₂	1	1	yes	maximal, characteristic, complemented
17	#2457	C₂	1	1	yes	maximal, characteristic, complemented
18	#2449	C₂	1	1	yes	maximal, characteristic, complemented
19	#2419	C₂	1	1	yes	maximal, characteristic, complemented
20	#2418	C₂	1	1	yes	maximal, characteristic, complemented
21	#2418	C₂	1	1	yes	maximal, characteristic, complemented
22	#2405	C₂	1	1	yes	maximal, characteristic, complemented
23	#2403	C₂	1	1	yes	maximal, characteristic
24	#2359	C₂	1	1	yes	maximal, characteristic, complemented
25	#2358	C₂	1	1	yes	maximal, characteristic, complemented
26	#2353	C₂	1	1	yes	maximal, characteristic, complemented
27	#2342	C₂	1	1	yes	maximal, characteristic, complemented
28	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#120	C₂	1	1	yes	maximal, characteristic, complemented
30	#2290	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#386	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×D₄	C₂²	1	1	yes	characteristic
33	C₂³×D₄	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄	C₂²	1	1	yes	characteristic
35	C₂⁴×C₄	C₂²	1	1	yes	characteristic, complemented
36	#551	—	2	8	no	—
37	C₂×#126	C₂²	1	1	yes	characteristic, complemented
38	C₂×#126	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124	C₂²	1	1	yes	characteristic, complemented
40	C₂×#123	C₂²	1	1	yes	characteristic
41	C₂×#123	C₂²	1	1	yes	characteristic
42	C₂×#123	C₂²	1	1	yes	characteristic, complemented
43	C₂×#123	C₂²	1	1	yes	characteristic, complemented
44	C₂×#123	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×#120	C₂²	1	1	yes	characteristic
50	C₂×#120	C₂²	1	1	yes	characteristic
51	C₂×#120	C₂²	1	1	yes	characteristic
52	C₂×#120	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄	—	2	8	no	—
54	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
60	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
66	C₂×#117	C₂²	1	1	yes	characteristic, complemented
67	C₂×#117	C₂²	1	1	yes	characteristic, complemented
68	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
73	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
74	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
76	#400	C₂²	1	1	yes	characteristic, complemented
77	#400	C₂²	1	1	yes	characteristic, complemented
78	#399	C₂²	1	1	yes	characteristic, complemented
79	#399	C₂²	1	1	yes	characteristic, complemented
80	#398	C₂²	1	1	yes	characteristic, complemented
81	#397	C₂²	1	1	yes	characteristic, complemented
82	#397	C₂²	1	1	yes	characteristic, complemented
83	#397	C₂²	1	1	yes	characteristic, complemented
84	#396	C₂²	1	1	yes	characteristic, complemented
85	#396	C₂²	1	1	yes	characteristic, complemented
86	#395	C₂²	1	1	yes	characteristic, complemented
87	#394	C₂²	1	1	yes	characteristic, complemented
88	#394	C₂²	1	1	yes	characteristic, complemented
89	#394	C₂²	1	1	yes	characteristic, complemented
90	#394	C₂²	1	1	yes	characteristic, complemented
91	#394	C₂²	1	1	yes	characteristic, complemented
92	#394	C₂²	1	1	yes	characteristic, complemented
93	#394	C₂²	1	1	yes	characteristic, complemented
94	#394	C₂²	1	1	yes	characteristic, complemented
95	#393	C₂²	1	1	yes	characteristic, complemented
96	#392	C₂²	1	1	yes	characteristic
97	#392	C₂²	1	1	yes	characteristic
98	#392	C₂²	1	1	yes	characteristic
99	#392	C₂²	1	1	yes	characteristic
100	#390	C₂²	1	1	yes	characteristic, complemented
101	#390	C₂²	1	1	yes	characteristic, complemented
102	#390	C₂²	1	1	yes	characteristic, complemented
103	#389	C₂²	1	1	yes	characteristic, complemented
104	#388	C₂²	1	1	yes	characteristic, complemented
105	#388	C₂²	1	1	yes	characteristic, complemented
106	#388	C₂²	1	1	yes	characteristic, complemented
107	#388	C₂²	1	1	yes	characteristic, complemented
108	#388	C₂²	1	1	yes	characteristic, complemented
109	#388	C₂²	1	1	yes	characteristic, complemented
110	#388	C₂²	1	1	yes	characteristic, complemented
111	#388	C₂²	1	1	yes	characteristic, complemented
112	#388	C₂²	1	1	yes	characteristic, complemented
113	#388	C₂²	1	1	yes	characteristic, complemented
114	#388	C₂²	1	1	yes	characteristic, complemented
115	#388	C₂²	1	1	yes	characteristic, complemented
116	#388	C₂²	1	1	yes	characteristic, complemented
117	#388	C₂²	1	1	yes	characteristic, complemented
118	#387	C₂²	1	1	yes	characteristic, complemented
119	#387	C₂²	1	1	yes	characteristic, complemented
120	#387	C₂²	1	1	yes	characteristic, complemented
121	#387	C₂²	1	1	yes	characteristic, complemented
122	#387	C₂²	1	1	yes	characteristic, complemented
123	#387	C₂²	1	1	yes	characteristic, complemented
124	#387	C₂²	1	1	yes	characteristic, complemented
125	#387	C₂²	1	1	yes	characteristic, complemented
126	#386	C₂²	1	1	yes	characteristic
127	#386	C₂²	1	1	yes	characteristic
128	#386	C₂²	1	1	yes	characteristic
129	#386	C₂²	1	1	yes	characteristic
130	#386	C₂²	1	1	yes	characteristic
131	#386	C₂²	1	1	yes	characteristic
132	#386	C₂²	1	1	yes	characteristic
133	#386	C₂²	1	1	yes	characteristic
134	#386	C₂²	1	1	yes	characteristic
135	#386	C₂²	1	1	yes	characteristic
136	#386	C₂²	1	1	yes	characteristic
137	#386	C₂²	1	1	yes	characteristic
138	#386	C₂²	1	1	yes	characteristic, complemented
139	#386	C₂²	1	1	yes	characteristic, complemented
140	#386	C₂²	1	1	yes	characteristic, complemented
141	#386	C₂²	1	1	yes	characteristic, complemented
142	#386	C₂²	1	1	yes	characteristic, complemented
143	#386	C₂²	1	1	yes	characteristic, complemented
144	#386	C₂²	1	1	yes	characteristic, complemented
145	#386	C₂²	1	1	yes	characteristic, complemented
146	#386	C₂²	1	1	yes	characteristic, complemented
147	#386	C₂²	1	1	yes	characteristic, complemented
148	#386	C₂²	1	1	yes	characteristic, complemented
149	#385	C₂²	1	1	yes	characteristic, complemented
150	#385	C₂²	1	1	yes	characteristic, complemented
151	#385	C₂²	1	1	yes	characteristic, complemented
152	#385	C₂²	1	1	yes	characteristic, complemented
153	#385	C₂²	1	1	yes	characteristic, complemented
154	#385	C₂²	1	1	yes	characteristic, complemented
155	#385	C₂²	1	1	yes	characteristic, complemented
156	#385	C₂²	1	1	yes	characteristic, complemented
157	#385	C₂²	1	1	yes	characteristic, complemented
158	#385	C₂²	1	1	yes	characteristic, complemented
159	#385	C₂²	1	1	yes	characteristic, complemented
160	#385	C₂²	1	1	yes	characteristic, complemented
161	#385	C₂²	1	1	yes	characteristic, complemented
162	#385	C₂²	1	1	yes	characteristic, complemented
163	#385	C₂²	1	1	yes	characteristic, complemented
164	#383	C₂²	1	1	yes	characteristic, complemented
165	#381	C₂²	1	1	yes	characteristic, complemented
166	#381	C₂²	1	1	yes	characteristic, complemented
167	#381	C₂²	1	1	yes	characteristic, complemented
168	#380	C₂²	1	1	yes	characteristic, complemented
169	#380	C₂²	1	1	yes	characteristic, complemented
170	#380	C₂²	1	1	yes	characteristic, complemented
171	#380	C₂²	1	1	yes	characteristic, complemented
172	#380	C₂²	1	1	yes	characteristic, complemented
173	#379	C₂²	1	1	yes	characteristic
174	#379	C₂²	1	1	yes	characteristic
175	#379	C₂²	1	1	yes	characteristic, complemented
176	#379	C₂²	1	1	yes	characteristic, complemented
177	#379	C₂²	1	1	yes	characteristic, complemented
178	C₄×C₄⋊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	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	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
186	#376	C₂²	1	1	yes	characteristic, complemented
187	C₂×#95	C₂²	1	1	yes	characteristic, complemented
188	C₂×#95	C₂²	1	1	yes	characteristic, complemented
189	C₂⁵	C₂³	1	1	yes	characteristic
190	C₂⁵	C₂³	1	1	yes	characteristic
191	C₂⁵	C₂³	1	1	yes	characteristic
192	C₂²×Q₈	C₂³	1	1	yes	characteristic
193	C₂²×D₄	—	2	4	no	—
194	C₂²×D₄	—	2	4	no	—
195	C₂²×D₄	—	2	4	no	—
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	—	2	4	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	C₂³×C₄	—	2	4	no	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	4	2	no	—
214	C₂³×C₄	—	4	2	no	—
215	C₂³×C₄	—	4	2	no	—
216	C₂³×C₄	—	4	2	no	—
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	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	#126	—	2	4	no	—
236	#126	—	2	4	no	—
237	#124	—	2	4	no	—
238	#123	—	2	4	no	—
239	#123	—	2	4	no	—
240	#123	—	2	4	no	—
241	#123	—	2	4	no	—
242	#123	—	4	2	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	C₂²⋊Q₈	—	4	2	no	—
247	#120	—	2	4	no	—
248	#120	—	2	4	no	—
249	#120	—	2	4	no	—
250	#120	—	4	2	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	4	no	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	4	2	no	—
261	C₄×D₄	—	4	2	no	—
262	C₄×D₄	D₄	1	8	yes	complemented
263	#117	—	2	4	no	—
264	#117	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₂²⋊C₄	—	2	4	no	—
292	C₂×C₂²⋊C₄	—	2	4	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	4	2	no	—
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×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×C₄²	—	2	4	no	—
350	C₂×C₄²	C₂³	1	1	yes	characteristic
351	C₂×C₄²	C₂³	1	1	yes	characteristic
352	C₂×C₄²	C₂³	1	1	yes	characteristic
353	C₂×C₄²	C₂³	1	1	yes	characteristic
354	C₂×C₄²	C₂³	1	1	yes	characteristic
355	C₂×C₄²	C₂³	1	1	yes	characteristic
356	C₂×C₄²	C₂³	1	1	yes	characteristic
357	C₂×C₄²	C₂³	1	1	yes	characteristic
358	C₂×C₄²	C₂³	1	1	yes	characteristic
359	C₂×C₄²	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	#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	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	2	no	—
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	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	4	1	no	—
408	C₂⁴	—	4	1	no	—
409	C₂⁴	—	4	1	no	—
410	C₂⁴	—	4	1	no	—
411	C₂⁴	—	4	1	no	—
412	C₂⁴	—	4	1	no	—
413	C₂⁴	—	4	1	no	—
414	C₂⁴	#41	1	4	yes	—
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	C₂⁴	C₂⁴	1	1	yes	characteristic
420	C₂⁴	C₂⁴	1	1	yes	characteristic
421	C₂⁴	C₂⁴	1	1	yes	characteristic
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×D₄	—	2	32	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	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	16	no	—
460	C₂×D₄	C₂×D₄	1	4	yes	—
461	C₂×D₄	#41	1	4	yes	—
462	C₂×D₄	#41	1	4	yes	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	4	1	no	—
504	C₂²×C₄	—	4	1	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	1	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	16	no	—
516	C₂²×C₄	—	4	16	no	—
517	C₂²×C₄	C₂×D₄	1	4	yes	—
518	C₂²×C₄	C₂×D₄	1	4	yes	complemented
519	C₂²×C₄	C₂⁴	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	4	1	no	—
559	C₄⋊C₄	—	4	1	no	—
560	C₄⋊C₄	—	4	1	no	—
561	C₄⋊C₄	—	4	1	no	—
562	C₄⋊C₄	—	4	1	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	—	4	1	no	—
565	C₄⋊C₄	C₂×D₄	1	4	yes	complemented
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	2	no	—
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	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₂²⋊C₄	—	4	1	no	—
607	C₂²⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₂²⋊C₄	—	4	1	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₂²⋊C₄	—	4	1	no	—
616	C₂²⋊C₄	—	4	1	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	C₂×D₄	1	4	yes	—
619	C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
620	C₄²	—	2	2	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	2	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	4	1	no	—
627	C₄²	—	4	1	no	—
628	C₄²	—	4	1	no	—
629	C₄²	C₂×D₄	1	4	yes	complemented
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	1	no	—
638	C₂³	—	2	8	no	—
639	C₂³	—	2	8	no	—
640	C₂³	—	2	8	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	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	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	4	no	—
678	C₂³	—	4	4	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	4	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	4	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	4	4	no	—
687	C₂³	—	8	2	no	—
688	C₂³	—	8	2	no	—
689	C₂³	—	8	2	no	—
690	C₂³	C₂²×D₄	1	2	yes	—
691	C₂³	C₂²×D₄	1	2	yes	—
692	C₂³	C₂×#41	1	2	yes	—
693	C₂³	C₂×#41	1	2	yes	—
694	C₂³	C₂×#41	1	2	yes	—
695	C₂³	C₂×#41	1	2	yes	—
696	C₂³	C₂×#41	1	2	yes	—
697	C₂³	C₂×#41	1	2	yes	—
698	C₂³	C₂×#41	1	2	yes	—
699	C₂³	H(5,𝔽₂)	1	2	yes	—
700	C₂³	C₂⁵	1	1	yes	characteristic
701	Q₈	—	8	2	no	—
702	D₄	—	2	8	no	—
703	D₄	—	2	8	no	—
704	D₄	—	2	8	no	—
705	D₄	—	2	8	no	—
706	D₄	—	2	8	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	4	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	4	no	—
712	D₄	—	8	2	no	—
713	D₄	—	8	2	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	8	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	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	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	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	2	no	—
796	C₂×C₄	C₂²×D₄	1	2	yes	—
797	C₂×C₄	C₂²×D₄	1	2	yes	—
798	C₂×C₄	C₂²×D₄	1	2	yes	—
799	C₂×C₄	C₂²×D₄	1	2	yes	—
800	C₂×C₄	C₂²×D₄	1	2	yes	—
801	C₂×C₄	C₂×#41	1	2	yes	—
802	C₂×C₄	C₂×#41	1	2	yes	—
803	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	4	16	no	—
829	C₂²	—	4	16	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	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	—	8	8	no	—
854	C₂²	#525	1	4	yes	—
855	C₂²	#551	1	4	yes	complemented
856	C₂²	C₂³×D₄	1	1	yes	characteristic
857	C₂²	C₂²×#41	1	1	yes	characteristic
858	C₂²	C₂²×#41	1	1	yes	characteristic
859	C₂²	C₂²×#41	1	1	yes	characteristic
860	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²	#585	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₂	—	2	4	no	—
888	C₂	—	2	4	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	4	2	no	—
892	C₂	—	4	2	no	—
893	C₂	—	8	1	no	—
894	C₂	C₂×#525	1	1	yes	characteristic
895	C₂	D₄×#41	1	1	yes	characteristic
896	C₂	C₂×#551	1	1	yes	characteristic
897	C₂	#3481	1	1	yes	characteristic
898	C₂	#3484	1	1	yes	characteristic
899	C₂	#3505	1	1	yes	characteristic
900	C₂	#3513	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	#2403	C₂
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×#551	C₂	semidirect
2. C₂²×C₄×D₄	C₂	semidirect
3. #2852	C₂	semidirect
4. #2849	C₂	semidirect
5. #2848	C₂	semidirect
6. #2603	C₂	semidirect
7. #2602	C₂	semidirect
8. #2600	C₂	semidirect
9. #2598	C₂	semidirect
10. #2564	C₂	semidirect
11. #2534	C₂	semidirect
12. #2481	C₂	semidirect
13. #2472	C₂	semidirect
14. #2467	C₂	semidirect
15. #2463	C₂	semidirect
16. #2461	C₂	semidirect
17. #2457	C₂	semidirect
18. #2449	C₂	semidirect
19. #2419	C₂	semidirect
20. #2418	C₂	semidirect
21. #2418	C₂	semidirect
22. #2405	C₂	semidirect
24. #2359	C₂	semidirect
25. #2358	C₂	semidirect
26. #2353	C₂	semidirect
27. #2342	C₂	semidirect
28. D₄×C₂²⋊C₄	C₂	semidirect
29. C₄×#120	C₂	semidirect
30. #2290	C₂	semidirect
31. C₂×#386	C₂	semidirect
35. C₂⁴×C₄	C₂²	semidirect
37. C₂×#126	C₂²	semidirect
38. C₂×#126	C₂²	semidirect
39. C₂×#124	C₂²	semidirect
42. C₂×#123	C₂²	semidirect
43. C₂×#123	C₂²	semidirect
44. C₂×#123	C₂²	semidirect
45. C₂×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₄×D₄	C₂²	semidirect
61. C₂×C₄×D₄	C₂²	semidirect
62. C₂×C₄×D₄	C₂²	semidirect
63. C₂×C₄×D₄	C₂²	semidirect
64. C₂×C₄×D₄	C₂²	semidirect
65. C₂×C₄×D₄	C₂²	semidirect
66. C₂×#117	C₂²	semidirect
67. C₂×#117	C₂²	semidirect
68. C₂²×C₄⋊C₄	C₂²	semidirect
71. C₂²×C₂²⋊C₄	C₂²	semidirect
72. C₂²×C₂²⋊C₄	C₂²	semidirect
73. C₂²×C₂²⋊C₄	C₂²	semidirect
74. C₂²×C₂²⋊C₄	C₂²	semidirect
75. C₂²×C₄²	C₂²	semidirect
76. #400	C₂²	semidirect
77. #400	C₂²	semidirect
78. #399	C₂²	semidirect
79. #399	C₂²	semidirect
80. #398	C₂²	semidirect
81. #397	C₂²	semidirect
82. #397	C₂²	semidirect
83. #397	C₂²	semidirect
84. #396	C₂²	semidirect
85. #396	C₂²	semidirect
86. #395	C₂²	semidirect
87. #394	C₂²	semidirect
88. #394	C₂²	semidirect
89. #394	C₂²	semidirect
90. #394	C₂²	semidirect
91. #394	C₂²	semidirect
92. #394	C₂²	semidirect
93. #394	C₂²	semidirect
94. #394	C₂²	semidirect
95. #393	C₂²	semidirect
100. #390	C₂²	semidirect
101. #390	C₂²	semidirect
102. #390	C₂²	semidirect
103. #389	C₂²	semidirect
104. #388	C₂²	semidirect
105. #388	C₂²	semidirect
106. #388	C₂²	semidirect
107. #388	C₂²	semidirect
108. #388	C₂²	semidirect
109. #388	C₂²	semidirect
110. #388	C₂²	semidirect
111. #388	C₂²	semidirect
112. #388	C₂²	semidirect
113. #388	C₂²	semidirect
114. #388	C₂²	semidirect
115. #388	C₂²	semidirect
116. #388	C₂²	semidirect
117. #388	C₂²	semidirect
118. #387	C₂²	semidirect
119. #387	C₂²	semidirect
120. #387	C₂²	semidirect
121. #387	C₂²	semidirect
122. #387	C₂²	semidirect
123. #387	C₂²	semidirect
124. #387	C₂²	semidirect
125. #387	C₂²	semidirect
138. #386	C₂²	semidirect
139. #386	C₂²	semidirect
140. #386	C₂²	semidirect
141. #386	C₂²	semidirect
142. #386	C₂²	semidirect
143. #386	C₂²	semidirect
144. #386	C₂²	semidirect
145. #386	C₂²	semidirect
146. #386	C₂²	semidirect
147. #386	C₂²	semidirect
148. #386	C₂²	semidirect
149. #385	C₂²	semidirect
150. #385	C₂²	semidirect
151. #385	C₂²	semidirect
152. #385	C₂²	semidirect
153. #385	C₂²	semidirect
154. #385	C₂²	semidirect
155. #385	C₂²	semidirect
156. #385	C₂²	semidirect
157. #385	C₂²	semidirect
158. #385	C₂²	semidirect
159. #385	C₂²	semidirect
160. #385	C₂²	semidirect
161. #385	C₂²	semidirect
162. #385	C₂²	semidirect
163. #385	C₂²	semidirect
164. #383	C₂²	semidirect
165. #381	C₂²	semidirect
166. #381	C₂²	semidirect
167. #381	C₂²	semidirect
168. #380	C₂²	semidirect
169. #380	C₂²	semidirect
170. #380	C₂²	semidirect
171. #380	C₂²	semidirect
172. #380	C₂²	semidirect
175. #379	C₂²	semidirect
176. #379	C₂²	semidirect
177. #379	C₂²	semidirect
178. C₄×C₄⋊C₄	C₂²	semidirect
179. C₄×C₂²⋊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. C₄×C₂²⋊C₄	C₂²	semidirect
186. #376	C₂²	semidirect
187. C₂×#95	C₂²	semidirect
188. C₂×#95	C₂²	semidirect
262. C₄×D₄	D₄	semidirect
518. C₂²×C₄	C₂×D₄	semidirect
565. C₄⋊C₄	C₂×D₄	semidirect
619. C₂²⋊C₄	C₂×D₄	semidirect
629. C₄²	C₂×D₄	semidirect
855. C₂²	#551	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551	2
C₂²×C₄×D₄	2
#2852	2
#2849	2
#2848	2
#2603	2
#2602	2
#2600	2
#2598	2
#2564	2
#2534	2
#2481	2
#2472	2
#2467	2
#2463	2
#2461	2
#2457	2
#2449	2
#2419	2
#2418	2
#2405	2
#2403	2
#2359	2
#2358	2
#2353	2
#2342	2
D₄×C₂²⋊C₄	2
C₄×#120	2
#2290	2
C₂×#386	2