Subgroups — #38428

Order 256.

1335 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	#2731	C₂	1	1	yes	maximal, characteristic, complemented
5	#2730	C₂	1	1	yes	maximal, characteristic, complemented
6	#2729	C₂	1	1	yes	maximal, characteristic, complemented
7	#2728	C₂	1	1	yes	maximal, characteristic, complemented
8	#2701	C₂	1	1	yes	maximal, characteristic, complemented
9	#2699	C₂	1	1	yes	maximal, characteristic, complemented
10	#2697	C₂	1	1	yes	maximal, characteristic, complemented
11	#2678	C₂	1	1	yes	maximal, characteristic, complemented
12	#2663	C₂	1	1	yes	maximal, characteristic, complemented
13	#2661	C₂	1	1	yes	maximal, characteristic, complemented
14	#2602	C₂	1	1	yes	maximal, characteristic, complemented
15	#2602	C₂	1	1	yes	maximal, characteristic, complemented
16	#2591	C₂	1	1	yes	maximal, characteristic, complemented
17	#2561	C₂	1	1	yes	maximal, characteristic, complemented
18	#2444	C₂	1	1	yes	maximal, characteristic, complemented
19	#2444	C₂	1	1	yes	maximal, characteristic, complemented
20	#2430	C₂	1	1	yes	maximal, characteristic, complemented
21	#2419	C₂	1	1	yes	maximal, characteristic, complemented
22	#2418	C₂	1	1	yes	maximal, characteristic, complemented
23	#2413	C₂	1	1	yes	maximal, characteristic, complemented
24	#2411	C₂	1	1	yes	maximal, characteristic, complemented
25	#2410	C₂	1	1	yes	maximal, characteristic, complemented
26	#2405	C₂	1	1	yes	maximal, characteristic, complemented
27	#2404	C₂	1	1	yes	maximal, characteristic, complemented
28	#2322	C₂	1	1	yes	maximal, characteristic, complemented
29	#2321	C₂	1	1	yes	maximal, characteristic, complemented
30	#2297	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#388	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41	C₂²	1	1	yes	characteristic
33	C₂²×#41	C₂²	1	1	yes	characteristic, complemented
34	C₂³×D₄	C₂²	1	1	yes	characteristic
35	#547	—	2	8	no	—
36	#546	—	2	8	no	—
37	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×#124	C₂²	1	1	yes	characteristic
39	C₂×#123	C₂²	1	1	yes	characteristic
40	C₂×#123	C₂²	1	1	yes	characteristic
41	C₂×#123	C₂²	1	1	yes	characteristic
42	C₂×#123	C₂²	1	1	yes	characteristic
43	C₂×#123	C₂²	1	1	yes	characteristic
44	C₂×#123	C₂²	1	1	yes	characteristic, complemented
45	C₂×#123	C₂²	1	1	yes	characteristic, complemented
46	C₂×#123	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×#121	C₂²	1	1	yes	characteristic
51	C₂×#121	C₂²	1	1	yes	characteristic
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, complemented
56	C₂×#120	C₂²	1	1	yes	characteristic
57	C₂×#120	C₂²	1	1	yes	characteristic
58	C₂×#120	C₂²	1	1	yes	characteristic
59	C₂×#120	C₂²	1	1	yes	characteristic
60	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117	C₂²	1	1	yes	characteristic, complemented
65	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
66	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
72	#400	C₂²	1	1	yes	characteristic, complemented
73	#400	C₂²	1	1	yes	characteristic, complemented
74	#400	C₂²	1	1	yes	characteristic, complemented
75	#399	C₂²	1	1	yes	characteristic, complemented
76	#398	C₂²	1	1	yes	characteristic, complemented
77	#398	C₂²	1	1	yes	characteristic, complemented
78	#398	C₂²	1	1	yes	characteristic, complemented
79	#397	C₂²	1	1	yes	characteristic
80	#397	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	#397	C₂²	1	1	yes	characteristic, complemented
85	#397	C₂²	1	1	yes	characteristic, complemented
86	#396	C₂²	1	1	yes	characteristic
87	#396	C₂²	1	1	yes	characteristic, complemented
88	#396	C₂²	1	1	yes	characteristic, complemented
89	#396	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
94	#394	C₂²	1	1	yes	characteristic
95	#394	C₂²	1	1	yes	characteristic
96	#394	C₂²	1	1	yes	characteristic
97	#394	C₂²	1	1	yes	characteristic
98	#394	C₂²	1	1	yes	characteristic
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	#394	C₂²	1	1	yes	characteristic, complemented
103	#394	C₂²	1	1	yes	characteristic, complemented
104	#393	C₂²	1	1	yes	characteristic
105	#393	C₂²	1	1	yes	characteristic, complemented
106	#393	C₂²	1	1	yes	characteristic, complemented
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	#391	C₂²	1	1	yes	characteristic, complemented
113	#391	C₂²	1	1	yes	characteristic, complemented
114	#390	C₂²	1	1	yes	characteristic
115	#390	C₂²	1	1	yes	characteristic, complemented
116	#390	C₂²	1	1	yes	characteristic, complemented
117	#390	C₂²	1	1	yes	characteristic, complemented
118	#390	C₂²	1	1	yes	characteristic, complemented
119	#390	C₂²	1	1	yes	characteristic, complemented
120	#389	C₂²	1	1	yes	characteristic, complemented
121	#389	C₂²	1	1	yes	characteristic, complemented
122	#389	C₂²	1	1	yes	characteristic, complemented
123	#389	C₂²	1	1	yes	characteristic, complemented
124	#388	C₂²	1	1	yes	characteristic
125	#388	C₂²	1	1	yes	characteristic
126	#388	C₂²	1	1	yes	characteristic
127	#388	C₂²	1	1	yes	characteristic
128	#388	C₂²	1	1	yes	characteristic
129	#388	C₂²	1	1	yes	characteristic
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	#388	C₂²	1	1	yes	characteristic, complemented
142	#388	C₂²	1	1	yes	characteristic, complemented
143	#388	C₂²	1	1	yes	characteristic, complemented
144	#387	C₂²	1	1	yes	characteristic, complemented
145	#387	C₂²	1	1	yes	characteristic, complemented
146	#387	C₂²	1	1	yes	characteristic, complemented
147	#387	C₂²	1	1	yes	characteristic, complemented
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	#386	C₂²	1	1	yes	characteristic, complemented
166	#385	C₂²	1	1	yes	characteristic
167	#385	C₂²	1	1	yes	characteristic
168	#385	C₂²	1	1	yes	characteristic
169	#385	C₂²	1	1	yes	characteristic, complemented
170	#385	C₂²	1	1	yes	characteristic, complemented
171	#385	C₂²	1	1	yes	characteristic, complemented
172	#385	C₂²	1	1	yes	characteristic, complemented
173	#385	C₂²	1	1	yes	characteristic, complemented
174	#381	C₂²	1	1	yes	characteristic, complemented
175	#381	C₂²	1	1	yes	characteristic, complemented
176	#381	C₂²	1	1	yes	characteristic, complemented
177	#381	C₂²	1	1	yes	characteristic, complemented
178	#380	C₂²	1	1	yes	characteristic, complemented
179	#379	C₂²	1	1	yes	characteristic
180	#379	C₂²	1	1	yes	characteristic
181	#379	C₂²	1	1	yes	characteristic
182	#379	C₂²	1	1	yes	characteristic
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	C₄×C₂²⋊C₄	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	C₂×#41	—	2	4	no	—
192	C₂×#41	—	4	2	no	—
193	C₂×#41	—	4	2	no	—
194	C₂×#41	—	4	2	no	—
195	C₂×#41	—	4	2	no	—
196	C₂×#41	D₄	1	8	yes	complemented
197	C₂²×Q₈	C₂³	1	1	yes	characteristic
198	C₂²×Q₈	C₂³	1	1	yes	characteristic
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	—	4	2	no	—
201	C₂²×D₄	—	4	2	no	—
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	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	C₄⋊Q₈	—	2	4	no	—
231	#124	—	2	4	no	—
232	#123	—	2	4	no	—
233	#123	—	2	4	no	—
234	#123	—	2	4	no	—
235	#123	—	2	4	no	—
236	#123	—	2	4	no	—
237	#123	—	2	4	no	—
238	#123	—	2	4	no	—
239	#123	—	4	2	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	—	2	4	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	#121	—	2	4	no	—
244	#121	—	2	4	no	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	#121	—	2	4	no	—
248	#121	—	4	2	no	—
249	#120	—	2	4	no	—
250	#120	—	2	4	no	—
251	#120	—	2	4	no	—
252	#120	—	4	2	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	#117	—	4	2	no	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
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×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×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	4	2	no	—
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×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×C₄²	—	4	2	no	—
346	C₂×C₄²	C₂³	1	1	yes	characteristic
347	C₂×C₄²	C₂³	1	1	yes	characteristic
348	C₂×C₄²	C₂³	1	1	yes	characteristic
349	C₂×C₄²	C₂³	1	1	yes	characteristic
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	#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	#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	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	4	1	no	—
395	C₂⁴	—	4	1	no	—
396	C₂⁴	—	4	1	no	—
397	C₂⁴	—	4	1	no	—
398	C₂⁴	—	4	1	no	—
399	C₂⁴	—	4	1	no	—
400	C₂⁴	—	4	1	no	—
401	C₂⁴	—	4	1	no	—
402	C₂⁴	C₂⁴	1	1	yes	characteristic
403	C₂⁴	C₂⁴	1	1	yes	characteristic
404	C₂⁴	C₂⁴	1	1	yes	characteristic
405	C₂⁴	C₂⁴	1	1	yes	characteristic
406	C₂⁴	C₂⁴	1	1	yes	characteristic
407	C₂⁴	C₂⁴	1	1	yes	characteristic
408	C₂⁴	C₂⁴	1	1	yes	characteristic
409	#41	—	4	16	no	—
410	#41	—	4	16	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	—	4	1	no	—
414	C₂×Q₈	—	4	1	no	—
415	C₂×Q₈	—	4	1	no	—
416	C₂×Q₈	C₂×D₄	1	4	yes	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	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	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	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	C₂×D₄	1	4	yes	—
462	C₂×D₄	C₂×D₄	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	—	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	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	—	4	1	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	C₂×D₄	1	4	yes	—
500	C₂²×C₄	C₂×D₄	1	4	yes	—
501	C₂²×C₄	C₂×D₄	1	4	yes	—
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	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	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	4	1	no	—
545	C₄⋊C₄	—	4	1	no	—
546	C₄⋊C₄	—	4	1	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₄⋊C₄	—	4	1	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	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	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
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	—	4	1	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	1	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	4	1	no	—
585	C₂²⋊C₄	—	4	1	no	—
586	C₂²⋊C₄	—	4	1	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	—	4	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₂²⋊C₄	—	4	1	no	—
595	C₂²⋊C₄	—	4	1	no	—
596	C₂²⋊C₄	—	4	1	no	—
597	C₂²⋊C₄	—	4	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	4	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₂²⋊C₄	#41	1	4	yes	complemented
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	4	1	no	—
610	C₄²	—	4	1	no	—
611	C₄²	—	4	1	no	—
612	C₄²	—	4	1	no	—
613	C₄²	—	4	1	no	—
614	C₄²	—	4	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	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	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	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	4	no	—
662	C₂³	—	4	4	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	8	2	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	2	no	—
668	C₂³	—	8	2	no	—
669	C₂³	—	8	2	no	—
670	C₂³	—	8	2	no	—
671	C₂³	—	8	2	no	—
672	C₂³	C₂²×D₄	1	2	yes	—
673	C₂³	C₂²×D₄	1	2	yes	—
674	C₂³	C₂²×D₄	1	2	yes	—
675	C₂³	C₂×#41	1	2	yes	—
676	C₂³	H(5,𝔽₂)	1	2	yes	—
677	C₂³	H(5,𝔽₂)	1	2	yes	—
678	C₂³	C₂⁵	1	1	yes	characteristic
679	Q₈	—	4	4	no	—
680	Q₈	—	4	4	no	—
681	D₄	—	2	8	no	—
682	D₄	—	2	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	4	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	D₄	—	4	4	no	—
690	D₄	—	4	4	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	2	no	—
694	D₄	—	8	2	no	—
695	D₄	—	8	2	no	—
696	C₂×C₄	—	2	8	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	—	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	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	C₂²×D₄	1	2	yes	—
776	C₂×C₄	C₂²×D₄	1	2	yes	—
777	C₂×C₄	C₂²×D₄	1	2	yes	—
778	C₂×C₄	C₂²×D₄	1	2	yes	—
779	C₂×C₄	C₂×#41	1	2	yes	—
780	C₂×C₄	C₂×#41	1	2	yes	—
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	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	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	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	8	8	no	—
830	C₂²	—	8	8	no	—
831	C₂²	#534	1	4	yes	—
832	C₂²	C₂³×D₄	1	1	yes	characteristic
833	C₂²	C₂²×#41	1	1	yes	characteristic
834	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
835	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂²	#585	1	1	yes	characteristic
837	C₂²	#585	1	1	yes	characteristic
838	C₂²	#585	1	1	yes	characteristic
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₂	—	2	4	no	—
864	C₂	—	4	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	4	2	no	—
867	C₂	—	8	1	no	—
868	C₂	—	8	1	no	—
869	C₂	—	8	1	no	—
870	C₂	C₂×#534	1	1	yes	characteristic
871	C₂	D₄×#41	1	1	yes	characteristic
872	C₂	#3494	1	1	yes	characteristic
873	C₂	#3500	1	1	yes	characteristic
874	C₂	#3513	1	1	yes	characteristic
875	C₂	#3533	1	1	yes	characteristic
876	C₂	#3560	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×#547	C₂	semidirect
2. C₂×#546	C₂	semidirect
3. #2854	C₂	semidirect
4. #2731	C₂	semidirect
5. #2730	C₂	semidirect
6. #2729	C₂	semidirect
7. #2728	C₂	semidirect
8. #2701	C₂	semidirect
9. #2699	C₂	semidirect
10. #2697	C₂	semidirect
11. #2678	C₂	semidirect
12. #2663	C₂	semidirect
13. #2661	C₂	semidirect
14. #2602	C₂	semidirect
15. #2602	C₂	semidirect
16. #2591	C₂	semidirect
17. #2561	C₂	semidirect
18. #2444	C₂	semidirect
19. #2444	C₂	semidirect
20. #2430	C₂	semidirect
21. #2419	C₂	semidirect
22. #2418	C₂	semidirect
23. #2413	C₂	semidirect
24. #2411	C₂	semidirect
25. #2410	C₂	semidirect
26. #2405	C₂	semidirect
27. #2404	C₂	semidirect
28. #2322	C₂	semidirect
29. #2321	C₂	semidirect
30. #2297	C₂	semidirect
31. C₂×#388	C₂	semidirect
33. C₂²×#41	C₂²	semidirect
37. C₂×C₄⋊Q₈	C₂²	semidirect
44. C₂×#123	C₂²	semidirect
45. C₂×#123	C₂²	semidirect
46. C₂×#123	C₂²	semidirect
48. C₂×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₂²⋊Q₈	C₂²	semidirect
55. C₂×#121	C₂²	semidirect
62. C₂×C₄×D₄	C₂²	semidirect
63. C₂×C₄×D₄	C₂²	semidirect
64. C₂×#117	C₂²	semidirect
65. C₂²×C₄⋊C₄	C₂²	semidirect
66. C₂²×C₄⋊C₄	C₂²	semidirect
71. C₂²×C₄²	C₂²	semidirect
72. #400	C₂²	semidirect
73. #400	C₂²	semidirect
74. #400	C₂²	semidirect
75. #399	C₂²	semidirect
76. #398	C₂²	semidirect
77. #398	C₂²	semidirect
78. #398	C₂²	semidirect
80. #397	C₂²	semidirect
81. #397	C₂²	semidirect
82. #397	C₂²	semidirect
83. #397	C₂²	semidirect
84. #397	C₂²	semidirect
85. #397	C₂²	semidirect
87. #396	C₂²	semidirect
88. #396	C₂²	semidirect
89. #396	C₂²	semidirect
90. #395	C₂²	semidirect
99. #394	C₂²	semidirect
100. #394	C₂²	semidirect
101. #394	C₂²	semidirect
102. #394	C₂²	semidirect
103. #394	C₂²	semidirect
105. #393	C₂²	semidirect
106. #393	C₂²	semidirect
110. #392	C₂²	semidirect
111. #392	C₂²	semidirect
112. #391	C₂²	semidirect
113. #391	C₂²	semidirect
115. #390	C₂²	semidirect
116. #390	C₂²	semidirect
117. #390	C₂²	semidirect
118. #390	C₂²	semidirect
119. #390	C₂²	semidirect
120. #389	C₂²	semidirect
121. #389	C₂²	semidirect
122. #389	C₂²	semidirect
123. #389	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. #388	C₂²	semidirect
142. #388	C₂²	semidirect
143. #388	C₂²	semidirect
144. #387	C₂²	semidirect
145. #387	C₂²	semidirect
146. #387	C₂²	semidirect
147. #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
165. #386	C₂²	semidirect
169. #385	C₂²	semidirect
170. #385	C₂²	semidirect
171. #385	C₂²	semidirect
172. #385	C₂²	semidirect
173. #385	C₂²	semidirect
174. #381	C₂²	semidirect
175. #381	C₂²	semidirect
176. #381	C₂²	semidirect
177. #381	C₂²	semidirect
178. #380	C₂²	semidirect
183. C₄×C₂²⋊C₄	C₂²	semidirect
184. C₄×C₂²⋊C₄	C₂²	semidirect
185. C₄×C₂²⋊C₄	C₂²	semidirect
186. C₄×C₂²⋊C₄	C₂²	semidirect
187. C₂×#95	C₂²	semidirect
188. C₂×#95	C₂²	semidirect
196. C₂×#41	D₄	semidirect
606. C₂²⋊C₄	#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547	2
C₂×#546	2
#2854	2
#2731	2
#2730	2
#2729	2
#2728	2
#2701	2
#2699	2
#2697	2
#2678	2
#2663	2
#2661	2
#2602	2
#2591	2
#2561	2
#2444	2
#2430	2
#2419	2
#2418	2
#2413	2
#2411	2
#2410	2
#2405	2
#2404	2
#2322	2
#2321	2
#2297	2
C₂×#388	2