Subgroups — #6408802

Order 512.

1568 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2396	C₂	1	1	yes	maximal, characteristic
2	#23342	C₂	1	2	yes	maximal, complemented
3	#23338	C₂	1	2	yes	maximal, complemented
4	#23059	C₂	1	2	yes	maximal, complemented
5	#23057	C₂	1	2	yes	maximal, complemented
6	#22629	C₂	1	1	yes	maximal, characteristic, complemented
7	#22629	C₂	1	1	yes	maximal, characteristic, complemented
8	#22627	C₂	1	1	yes	maximal, characteristic, complemented
9	#22627	C₂	1	1	yes	maximal, characteristic, complemented
10	#22625	C₂	1	1	yes	maximal, characteristic, complemented
11	#22625	C₂	1	1	yes	maximal, characteristic, complemented
12	#22510	C₂	1	1	yes	maximal, characteristic, complemented
13	#22510	C₂	1	1	yes	maximal, characteristic, complemented
14	#22328	C₂	1	2	yes	maximal, complemented
15	#22322	C₂	1	2	yes	maximal, complemented
16	#22107	C₂	1	2	yes	maximal, complemented
17	#22103	C₂	1	2	yes	maximal, complemented
18	#21906	C₂	1	1	yes	maximal, characteristic
19	#21904	C₂	1	1	yes	maximal, characteristic
20	#21904	C₂	1	1	yes	maximal, characteristic
21	#21902	C₂	1	1	yes	maximal, characteristic
22	#20716	C₂	1	1	yes	maximal, characteristic
23	#20716	C₂	1	1	yes	maximal, characteristic
24	C₂²×C₄×Q₈	C₂²	1	1	yes	characteristic
25	C₂²×#117	C₂²	1	1	yes	characteristic
26	C₂×#446	C₂²	1	2	yes	complemented
27	C₂×#446	C₂²	1	2	yes	complemented
28	C₂×#433	C₂²	1	2	yes	—
29	C₂×#433	C₂²	1	2	yes	—
30	#2396	C₄	1	1	yes	characteristic
31	#2396	C₄	1	1	yes	characteristic
32	#2396	C₄	1	1	yes	characteristic
33	#2396	C₄	1	1	yes	characteristic
34	#2396	C₄	1	1	yes	characteristic
35	#2396	C₄	1	1	yes	characteristic
36	#2396	C₄	1	1	yes	characteristic
37	#2396	C₄	1	1	yes	characteristic
38	#2396	C₂²	1	1	yes	characteristic
39	#2396	C₂²	1	1	yes	characteristic
40	#2396	C₂²	1	1	yes	characteristic
41	#2396	C₂²	1	1	yes	characteristic
42	#2396	C₂²	1	1	yes	characteristic
43	#2396	C₂²	1	1	yes	characteristic
44	#2396	C₂²	1	1	yes	characteristic
45	#2396	C₂²	1	1	yes	characteristic
46	C₂×#400	C₄	1	1	yes	characteristic
47	C₂×#399	C₄	1	1	yes	characteristic
48	C₂×#398	C₄	1	1	yes	characteristic
49	C₂×#398	C₄	1	1	yes	characteristic
50	C₂×#396	C₄	1	1	yes	characteristic
51	C₂×#396	C₄	1	1	yes	characteristic
52	C₂×#395	C₄	1	1	yes	characteristic
53	C₂×#393	C₄	1	1	yes	characteristic
54	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	#1985	C₂²	1	2	yes	complemented
60	#1985	C₂²	1	2	yes	complemented
61	#1985	C₂²	1	2	yes	complemented
62	#1985	C₂²	1	2	yes	complemented
63	#1984	C₂²	1	2	yes	complemented
64	#1984	C₂²	1	2	yes	complemented
65	#1940	C₂²	1	2	yes	complemented
66	#1940	C₂²	1	2	yes	complemented
67	#1939	C₂²	1	2	yes	complemented
68	#1939	C₂²	1	2	yes	complemented
69	#1939	C₂²	1	2	yes	complemented
70	#1939	C₂²	1	2	yes	complemented
71	#1924	C₂²	1	2	yes	—
72	#1924	C₂²	1	2	yes	—
73	#1924	C₂²	1	2	yes	—
74	#1924	C₂²	1	2	yes	—
75	#1924	C₂²	1	2	yes	—
76	#1924	C₂²	1	2	yes	—
77	#1924	C₂²	1	2	yes	—
78	#1924	C₂²	1	2	yes	—
79	#1923	C₂²	1	2	yes	—
80	#1923	C₂²	1	2	yes	—
81	#1923	C₂²	1	2	yes	—
82	#1923	C₂²	1	2	yes	—
83	#1923	C₂²	1	2	yes	—
84	#1923	C₂²	1	2	yes	—
85	#1923	C₂²	1	2	yes	—
86	#1923	C₂²	1	2	yes	—
87	#1917	C₂²	1	2	yes	complemented
88	#1917	C₂²	1	2	yes	complemented
89	#1917	C₂²	1	2	yes	complemented
90	#1917	C₂²	1	2	yes	complemented
91	#1917	C₂²	1	2	yes	complemented
92	#1917	C₂²	1	2	yes	complemented
93	#1916	C₂²	1	2	yes	complemented
94	#1916	C₂²	1	2	yes	complemented
95	#1916	C₂²	1	2	yes	complemented
96	#1916	C₂²	1	2	yes	complemented
97	#1916	C₂²	1	2	yes	complemented
98	#1916	C₂²	1	2	yes	complemented
99	#1818	C₂²	1	2	yes	—
100	#1818	C₂²	1	2	yes	—
101	#1798	C₂²	1	2	yes	—
102	#1798	C₂²	1	2	yes	—
103	#1797	C₂²	1	1	yes	characteristic
104	#1797	C₂²	1	1	yes	characteristic
105	#1797	C₂²	1	1	yes	characteristic
106	#1797	C₂²	1	1	yes	characteristic
107	#1797	C₂²	1	1	yes	characteristic
108	#1797	C₂²	1	1	yes	characteristic
109	#1797	C₂²	1	1	yes	characteristic
110	#1797	C₂²	1	1	yes	characteristic
111	#1797	C₂²	1	1	yes	characteristic
112	#1797	C₂²	1	1	yes	characteristic
113	#1797	C₂²	1	1	yes	characteristic
114	#1797	C₂²	1	1	yes	characteristic
115	#1779	C₂²	1	1	yes	characteristic
116	#1779	C₂²	1	1	yes	characteristic
117	#1779	C₂²	1	1	yes	characteristic
118	#1779	C₂²	1	1	yes	characteristic
119	#1771	C₂²	1	2	yes	complemented
120	#1771	C₂²	1	2	yes	complemented
121	#1770	C₂²	1	2	yes	complemented
122	#1770	C₂²	1	2	yes	complemented
123	C₈×C₄⋊C₄	C₂²	1	2	yes	complemented
124	C₈×C₄⋊C₄	C₂²	1	2	yes	complemented
125	#1750	C₂²	1	2	yes	—
126	#1750	C₂²	1	2	yes	—
127	#1749	C₂²	1	1	yes	characteristic
128	#1749	C₂²	1	1	yes	characteristic
129	#1749	C₂²	1	1	yes	characteristic
130	#1749	C₂²	1	1	yes	characteristic
131	#1749	C₂²	1	1	yes	characteristic
132	#1749	C₂²	1	1	yes	characteristic
133	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
135	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
136	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
137	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
139	C₂³×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₂⁴×C₄	C₂³	1	1	yes	characteristic
141	C₂×C₄×Q₈	—	4	4	no	—
142	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
143	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
144	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
145	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
146	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
147	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
148	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
149	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
150	C₂×#117	—	4	4	no	—
151	C₂×#117	C₂×C₄	1	1	yes	characteristic
152	C₂×#117	C₂×C₄	1	1	yes	characteristic
153	C₂×#117	C₂×C₄	1	1	yes	characteristic
154	C₂×#117	C₂×C₄	1	1	yes	characteristic
155	C₂×#117	C₂³	1	1	yes	characteristic
156	C₂×#117	C₂³	1	1	yes	characteristic
157	C₂×#117	C₂³	1	1	yes	characteristic
158	C₂×#117	C₂³	1	1	yes	characteristic
159	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
160	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
161	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
162	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
163	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
165	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
166	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
167	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
168	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
169	C₂²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
170	C₂²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
171	C₂²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
172	C₂²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
173	C₂²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
174	C₂²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
175	C₂²×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
176	C₂²×C₄²	C₂³	1	1	yes	characteristic
177	C₂²×C₄²	C₂³	1	1	yes	characteristic
178	C₂²×C₄²	C₂³	1	1	yes	characteristic
179	C₂²×C₄²	C₂³	1	1	yes	characteristic
180	C₂²×C₄²	C₂³	1	1	yes	characteristic
181	C₂²×C₄²	C₂³	1	1	yes	characteristic
182	#446	—	4	4	no	—
183	#446	—	4	4	no	—
184	#433	—	4	4	no	—
185	#433	—	4	4	no	—
186	C₂×C₄⋊C₈	C₂³	1	2	yes	—
187	C₂×C₄⋊C₈	C₂³	1	2	yes	—
188	C₂×C₄⋊C₈	C₂³	1	2	yes	—
189	C₂×C₄⋊C₈	C₂³	1	2	yes	—
190	C₂×C₄⋊C₈	C₂³	1	2	yes	—
191	C₂×C₄⋊C₈	C₂³	1	2	yes	—
192	C₂×C₄⋊C₈	C₂³	1	2	yes	—
193	C₂×C₄⋊C₈	C₂³	1	2	yes	—
194	C₂×C₄⋊C₈	C₂³	1	2	yes	—
195	C₂×C₄⋊C₈	C₂³	1	2	yes	—
196	C₂×C₄⋊C₈	C₂³	1	2	yes	—
197	C₂×C₄⋊C₈	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₂×#97	C₂³	1	2	yes	—
215	C₂×#97	C₂³	1	2	yes	—
216	C₂×#97	C₂³	1	2	yes	—
217	C₂×#97	C₂³	1	2	yes	—
218	C₂×#97	C₂³	1	2	yes	—
219	C₂×#97	C₂³	1	2	yes	—
220	C₂×C₄×C₈	C₂³	1	2	yes	—
221	C₂×C₄×C₈	C₂³	1	2	yes	—
222	C₂×C₄×C₈	C₂³	1	2	yes	—
223	C₂×C₄×C₈	C₂³	1	2	yes	—
224	C₂×C₄×C₈	C₂³	1	2	yes	—
225	C₂×C₄×C₈	C₂³	1	2	yes	—
226	#400	C₂×C₄	1	1	yes	characteristic
227	#400	C₂×C₄	1	1	yes	characteristic
228	#400	C₂×C₄	1	1	yes	characteristic
229	#400	C₂×C₄	1	1	yes	characteristic
230	#400	C₂×C₄	1	1	yes	characteristic
231	#400	C₂×C₄	1	1	yes	characteristic
232	#400	C₂×C₄	1	1	yes	characteristic
233	#400	C₂×C₄	1	1	yes	characteristic
234	#399	C₂×C₄	1	1	yes	characteristic
235	#399	C₂×C₄	1	1	yes	characteristic
236	#399	C₂×C₄	1	1	yes	characteristic
237	#399	C₂×C₄	1	1	yes	characteristic
238	#399	C₂×C₄	1	1	yes	characteristic
239	#399	C₂×C₄	1	1	yes	characteristic
240	#399	C₂×C₄	1	1	yes	characteristic
241	#399	C₂×C₄	1	1	yes	characteristic
242	#398	C₂×C₄	1	1	yes	characteristic
243	#398	C₂×C₄	1	1	yes	characteristic
244	#398	C₂×C₄	1	1	yes	characteristic
245	#398	C₂×C₄	1	1	yes	characteristic
246	#398	C₂×C₄	1	1	yes	characteristic
247	#398	C₂×C₄	1	1	yes	characteristic
248	#398	C₂×C₄	1	1	yes	characteristic
249	#398	C₂×C₄	1	1	yes	characteristic
250	#398	C₂×C₄	1	1	yes	characteristic
251	#398	C₂×C₄	1	1	yes	characteristic
252	#398	C₂×C₄	1	1	yes	characteristic
253	#398	C₂×C₄	1	1	yes	characteristic
254	#398	C₂×C₄	1	1	yes	characteristic
255	#398	C₂×C₄	1	1	yes	characteristic
256	#398	C₂×C₄	1	1	yes	characteristic
257	#398	C₂×C₄	1	1	yes	characteristic
258	#396	C₂×C₄	1	1	yes	characteristic
259	#396	C₂×C₄	1	1	yes	characteristic
260	#396	C₂×C₄	1	1	yes	characteristic
261	#396	C₂×C₄	1	1	yes	characteristic
262	#396	C₂×C₄	1	1	yes	characteristic
263	#396	C₂×C₄	1	1	yes	characteristic
264	#396	C₂×C₄	1	1	yes	characteristic
265	#396	C₂×C₄	1	1	yes	characteristic
266	#396	C₂×C₄	1	1	yes	characteristic
267	#396	C₂×C₄	1	1	yes	characteristic
268	#396	C₂×C₄	1	1	yes	characteristic
269	#396	C₂×C₄	1	1	yes	characteristic
270	#396	C₂×C₄	1	1	yes	characteristic
271	#396	C₂×C₄	1	1	yes	characteristic
272	#396	C₂×C₄	1	1	yes	characteristic
273	#396	C₂×C₄	1	1	yes	characteristic
274	#395	C₂×C₄	1	1	yes	characteristic
275	#395	C₂×C₄	1	1	yes	characteristic
276	#395	C₂×C₄	1	1	yes	characteristic
277	#395	C₂×C₄	1	1	yes	characteristic
278	#395	C₂×C₄	1	1	yes	characteristic
279	#395	C₂×C₄	1	1	yes	characteristic
280	#395	C₂×C₄	1	1	yes	characteristic
281	#395	C₂×C₄	1	1	yes	characteristic
282	#393	C₂×C₄	1	1	yes	characteristic
283	#393	C₂×C₄	1	1	yes	characteristic
284	#393	C₂×C₄	1	1	yes	characteristic
285	#393	C₂×C₄	1	1	yes	characteristic
286	#393	C₂×C₄	1	1	yes	characteristic
287	#393	C₂×C₄	1	1	yes	characteristic
288	#393	C₂×C₄	1	1	yes	characteristic
289	#393	C₂×C₄	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
293	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
296	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
301	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
303	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
307	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
312	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
313	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
316	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
317	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
318	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
321	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
322	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
324	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
326	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
327	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
328	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
329	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
330	C₂×#95	C₂×C₄	1	1	yes	characteristic
331	C₂×#95	C₂×C₄	1	1	yes	characteristic
332	C₂×#95	C₂×C₄	1	1	yes	characteristic
333	C₂×#95	C₂×C₄	1	1	yes	characteristic
334	C₂×#95	C₂×C₄	1	1	yes	characteristic
335	C₂×#95	C₂×C₄	1	1	yes	characteristic
336	C₂×#95	C₂×C₄	1	1	yes	characteristic
337	C₂×#95	C₂×C₄	1	1	yes	characteristic
338	C₂×#95	C₂×C₄	1	1	yes	characteristic
339	C₂×#95	C₂×C₄	1	1	yes	characteristic
340	#336	C₂³	1	2	yes	—
341	#336	C₂³	1	2	yes	—
342	#336	C₂³	1	2	yes	—
343	#336	C₂³	1	2	yes	—
344	#336	C₂³	1	2	yes	—
345	#336	C₂³	1	2	yes	—
346	#336	C₂³	1	2	yes	—
347	#336	C₂³	1	2	yes	—
348	#336	C₂³	1	2	yes	—
349	#336	C₂³	1	2	yes	—
350	#336	C₂³	1	2	yes	—
351	#336	C₂³	1	2	yes	—
352	#336	C₂³	1	2	yes	—
353	#336	C₂³	1	2	yes	—
354	#336	C₂³	1	2	yes	—
355	#336	C₂³	1	2	yes	—
356	#336	C₂³	1	2	yes	—
357	#336	C₂³	1	2	yes	—
358	#336	C₂³	1	2	yes	—
359	#336	C₂³	1	2	yes	—
360	#336	C₂³	1	2	yes	—
361	#336	C₂³	1	2	yes	—
362	#336	C₂³	1	2	yes	—
363	#336	C₂³	1	2	yes	—
364	C₂⁵	C₂²×C₄	1	1	yes	characteristic
365	C₂²×Q₈	—	4	2	no	—
366	C₂²×Q₈	—	4	2	no	—
367	C₂²×Q₈	—	4	2	no	—
368	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
369	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
370	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
371	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
372	C₂³×C₄	—	2	2	no	—
373	C₂³×C₄	—	2	2	no	—
374	C₂³×C₄	—	4	2	no	—
375	C₂³×C₄	—	4	2	no	—
376	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
377	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
378	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
379	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
380	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
381	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
382	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
383	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
384	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
385	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
386	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
387	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
388	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
389	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
390	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
391	C₂³×C₄	C₂⁴	1	1	yes	characteristic
392	C₂³×C₄	C₂⁴	1	1	yes	characteristic
393	C₂³×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₈	C₂⁴	1	2	yes	—
395	C₂²×C₈	C₂⁴	1	2	yes	—
396	C₂²×C₈	C₂⁴	1	2	yes	—
397	C₂²×C₈	C₂⁴	1	2	yes	—
398	C₂²×C₈	C₂⁴	1	2	yes	—
399	C₂²×C₈	C₂⁴	1	2	yes	—
400	C₂²×C₈	C₂⁴	1	2	yes	—
401	C₂²×C₈	C₂⁴	1	2	yes	—
402	C₄×Q₈	—	2	4	no	—
403	C₄×Q₈	—	2	4	no	—
404	C₄×Q₈	—	4	2	no	—
405	C₄×Q₈	—	4	2	no	—
406	C₄×Q₈	—	4	2	no	—
407	C₄×Q₈	—	4	2	no	—
408	C₄×Q₈	—	4	2	no	—
409	C₄×Q₈	—	4	2	no	—
410	#117	—	2	4	no	—
411	#117	—	2	4	no	—
412	#117	—	4	2	no	—
413	#117	—	4	2	no	—
414	#117	—	4	2	no	—
415	#117	—	4	2	no	—
416	#117	—	4	2	no	—
417	#117	—	4	2	no	—
418	C₂×C₄⋊C₄	—	2	4	no	—
419	C₂×C₄⋊C₄	—	2	4	no	—
420	C₂×C₄⋊C₄	—	4	2	no	—
421	C₂×C₄⋊C₄	—	4	2	no	—
422	C₂×C₄⋊C₄	—	4	2	no	—
423	C₂×C₄⋊C₄	—	4	2	no	—
424	C₂×C₄⋊C₄	—	4	2	no	—
425	C₂×C₄⋊C₄	—	4	2	no	—
426	C₂×C₄⋊C₄	—	4	2	no	—
427	C₂×C₄⋊C₄	—	4	2	no	—
428	C₂×C₄⋊C₄	—	4	2	no	—
429	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	—	2	4	no	—
474	C₂×C₂²⋊C₄	—	4	2	no	—
475	C₂×C₂²⋊C₄	—	4	2	no	—
476	C₂×C₂²⋊C₄	—	4	2	no	—
477	C₂×C₂²⋊C₄	—	4	2	no	—
478	C₂×C₂²⋊C₄	—	4	2	no	—
479	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
503	C₂×C₄²	—	2	4	no	—
504	C₂×C₄²	—	4	2	no	—
505	C₂×C₄²	—	4	2	no	—
506	C₂×C₄²	—	4	2	no	—
507	C₂×C₄²	—	4	2	no	—
508	C₂×C₄²	—	4	2	no	—
509	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
510	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
511	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
512	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
513	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
514	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
515	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
516	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
517	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
518	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
519	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
520	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
521	C₂×C₄²	C₂⁴	1	1	yes	characteristic
522	C₂×C₄²	C₂⁴	1	1	yes	characteristic
523	C₂×C₄²	C₂⁴	1	1	yes	characteristic
524	C₂×C₄²	C₂⁴	1	1	yes	characteristic
525	C₂×C₄²	C₂⁴	1	1	yes	characteristic
526	C₂×C₄²	C₂⁴	1	1	yes	characteristic
527	C₂×C₄²	C₂⁴	1	1	yes	characteristic
528	C₂×C₄²	C₂⁴	1	1	yes	characteristic
529	C₂×C₄²	C₂⁴	1	1	yes	characteristic
530	C₂×C₄²	C₂⁴	1	1	yes	characteristic
531	C₂×C₄²	C₂⁴	1	1	yes	characteristic
532	C₂×C₄²	C₂⁴	1	1	yes	characteristic
533	C₄⋊C₈	—	2	4	no	—
534	C₄⋊C₈	—	2	4	no	—
535	C₄⋊C₈	—	4	2	no	—
536	C₄⋊C₈	—	4	2	no	—
537	C₄⋊C₈	—	4	2	no	—
538	C₄⋊C₈	—	4	2	no	—
539	C₄⋊C₈	—	4	2	no	—
540	C₄⋊C₈	—	4	2	no	—
541	C₄⋊C₈	—	4	2	no	—
542	C₄⋊C₈	—	4	2	no	—
543	C₄⋊C₈	—	4	2	no	—
544	C₄⋊C₈	—	4	2	no	—
545	C₂²⋊C₈	—	2	2	no	—
546	C₂²⋊C₈	—	2	2	no	—
547	C₂²⋊C₈	—	2	2	no	—
548	C₂²⋊C₈	—	2	2	no	—
549	C₂²⋊C₈	—	2	2	no	—
550	C₂²⋊C₈	—	2	2	no	—
551	C₂²⋊C₈	—	2	2	no	—
552	C₂²⋊C₈	—	2	2	no	—
553	C₂²⋊C₈	—	4	2	no	—
554	C₂²⋊C₈	—	4	2	no	—
555	C₂²⋊C₈	—	4	2	no	—
556	C₂²⋊C₈	—	4	2	no	—
557	C₂²⋊C₈	—	4	2	no	—
558	C₂²⋊C₈	—	4	2	no	—
559	C₂²⋊C₈	—	4	2	no	—
560	C₂²⋊C₈	—	4	2	no	—
561	#97	—	2	4	no	—
562	#97	—	4	2	no	—
563	#97	—	4	2	no	—
564	#97	—	4	2	no	—
565	#97	—	4	2	no	—
566	#97	—	4	2	no	—
567	C₄×C₈	—	2	4	no	—
568	C₄×C₈	—	4	2	no	—
569	C₄×C₈	—	4	2	no	—
570	C₄×C₈	—	4	2	no	—
571	C₄×C₈	—	4	2	no	—
572	C₄×C₈	—	4	2	no	—
573	#95	C₂²×C₄	1	1	yes	characteristic
574	#95	C₂²×C₄	1	1	yes	characteristic
575	#95	C₂²×C₄	1	1	yes	characteristic
576	#95	C₂²×C₄	1	1	yes	characteristic
577	#95	C₂²×C₄	1	1	yes	characteristic
578	#95	C₂²×C₄	1	1	yes	characteristic
579	#95	C₂²×C₄	1	1	yes	characteristic
580	#95	C₂²×C₄	1	1	yes	characteristic
581	#95	C₂²×C₄	1	1	yes	characteristic
582	#95	C₂²×C₄	1	1	yes	characteristic
583	#95	C₂²×C₄	1	1	yes	characteristic
584	#95	C₂²×C₄	1	1	yes	characteristic
585	#95	C₂²×C₄	1	1	yes	characteristic
586	#95	C₂²×C₄	1	1	yes	characteristic
587	#95	C₂²×C₄	1	1	yes	characteristic
588	#95	C₂²×C₄	1	1	yes	characteristic
589	#95	C₂²×C₄	1	1	yes	characteristic
590	#95	C₂²×C₄	1	1	yes	characteristic
591	#95	C₂²×C₄	1	1	yes	characteristic
592	#95	C₂²×C₄	1	1	yes	characteristic
593	#95	C₂²×C₄	1	1	yes	characteristic
594	#95	C₂²×C₄	1	1	yes	characteristic
595	#95	C₂²×C₄	1	1	yes	characteristic
596	#95	C₂²×C₄	1	1	yes	characteristic
597	#95	C₂²×C₄	1	1	yes	characteristic
598	#95	C₂²×C₄	1	1	yes	characteristic
599	#95	C₂²×C₄	1	1	yes	characteristic
600	#95	C₂²×C₄	1	1	yes	characteristic
601	#95	C₂²×C₄	1	1	yes	characteristic
602	#95	C₂²×C₄	1	1	yes	characteristic
603	#95	C₂²×C₄	1	1	yes	characteristic
604	#95	C₂²×C₄	1	1	yes	characteristic
605	#95	C₂²×C₄	1	1	yes	characteristic
606	#95	C₂²×C₄	1	1	yes	characteristic
607	#95	C₂²×C₄	1	1	yes	characteristic
608	#95	C₂²×C₄	1	1	yes	characteristic
609	#95	C₂²×C₄	1	1	yes	characteristic
610	#95	C₂²×C₄	1	1	yes	characteristic
611	#95	C₂²×C₄	1	1	yes	characteristic
612	#95	C₂²×C₄	1	1	yes	characteristic
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	—	2	2	no	—
616	C₂⁴	—	4	1	no	—
617	C₂⁴	—	4	1	no	—
618	C₂⁴	—	4	1	no	—
619	C₂⁴	—	4	1	no	—
620	C₂⁴	C₂³×C₄	1	1	yes	characteristic
621	C₂⁴	C₂³×C₄	1	1	yes	characteristic
622	C₂⁴	C₂³×C₄	1	1	yes	characteristic
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	2	2	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	4	1	no	—
628	C₂×Q₈	—	4	1	no	—
629	C₂×Q₈	—	4	1	no	—
630	C₂×Q₈	—	4	1	no	—
631	C₂×Q₈	—	4	1	no	—
632	C₂×Q₈	—	4	1	no	—
633	C₂×Q₈	—	4	1	no	—
634	C₂×Q₈	—	4	1	no	—
635	C₂×Q₈	—	4	16	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	1	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	1	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	—	4	1	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	—	4	8	no	—
691	C₂²×C₄	—	4	8	no	—
692	C₂²×C₄	#131	1	4	yes	—
693	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
694	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
695	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
696	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
697	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
698	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
699	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
700	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
701	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
702	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
703	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
704	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
705	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
706	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
707	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
708	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
709	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
710	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
711	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
712	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
713	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
714	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
715	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
716	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
717	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
718	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
719	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
720	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
721	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
722	C₂²×C₄	C₂⁵	1	1	yes	characteristic
723	C₂×C₈	—	2	2	no	—
724	C₂×C₈	—	2	2	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	2	no	—
727	C₂×C₈	—	2	2	no	—
728	C₂×C₈	—	2	2	no	—
729	C₂×C₈	—	2	2	no	—
730	C₂×C₈	—	2	2	no	—
731	C₂×C₈	—	2	2	no	—
732	C₂×C₈	—	2	2	no	—
733	C₂×C₈	—	2	2	no	—
734	C₂×C₈	—	2	2	no	—
735	C₂×C₈	—	2	2	no	—
736	C₂×C₈	—	2	2	no	—
737	C₂×C₈	—	2	2	no	—
738	C₂×C₈	—	2	2	no	—
739	C₂×C₈	—	2	2	no	—
740	C₂×C₈	—	2	2	no	—
741	C₂×C₈	—	2	2	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	2	no	—
745	C₂×C₈	—	2	2	no	—
746	C₂×C₈	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	4	1	no	—
772	C₄⋊C₄	—	4	1	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	1	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	—	4	1	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	1	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	1	no	—
785	C₄⋊C₄	—	4	1	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	—	4	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	4	1	no	—
806	C₂²⋊C₄	—	4	1	no	—
807	C₂²⋊C₄	—	4	1	no	—
808	C₂²⋊C₄	—	4	1	no	—
809	C₂²⋊C₄	—	4	1	no	—
810	C₂²⋊C₄	—	4	1	no	—
811	C₂²⋊C₄	—	4	1	no	—
812	C₂²⋊C₄	—	4	1	no	—
813	C₂²⋊C₄	—	4	1	no	—
814	C₂²⋊C₄	—	4	1	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	4	1	no	—
829	C₄²	—	4	1	no	—
830	C₄²	—	4	1	no	—
831	C₄²	—	4	1	no	—
832	C₄²	—	4	1	no	—
833	C₄²	—	4	1	no	—
834	C₄²	—	4	1	no	—
835	C₄²	—	4	1	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	1	no	—
838	C₄²	H(5,𝔽₂)	1	4	yes	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	4	4	no	—
860	C₂³	—	8	2	no	—
861	C₂³	—	8	2	no	—
862	C₂³	—	8	2	no	—
863	C₂³	—	8	2	no	—
864	C₂³	#519	1	2	yes	—
865	C₂³	C₂×#131	1	2	yes	—
866	C₂³	#568	1	2	yes	—
867	C₂³	C₂⁴×C₄	1	1	yes	characteristic
868	Q₈	—	4	4	no	—
869	Q₈	—	4	4	no	—
870	Q₈	—	4	4	no	—
871	Q₈	—	4	4	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	4	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	2	no	—
959	C₂×C₄	—	4	2	no	—
960	C₂×C₄	—	4	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	2	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	#518	1	2	yes	—
968	C₂×C₄	#518	1	2	yes	—
969	C₂×C₄	#519	1	2	yes	—
970	C₂×C₄	C₂×#131	1	2	yes	—
971	C₂×C₄	C₂×#131	1	2	yes	—
972	C₂×C₄	#568	1	2	yes	—
973	C₂×C₄	#568	1	2	yes	—
974	C₂×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
975	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
976	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
977	C₂×C₄	#585	1	2	yes	—
978	C₈	—	4	2	no	—
979	C₈	—	4	2	no	—
980	C₈	—	4	2	no	—
981	C₈	—	4	2	no	—
982	C₈	—	4	2	no	—
983	C₈	—	4	2	no	—
984	C₈	—	4	2	no	—
985	C₈	—	4	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	1	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	8	8	no	—
1007	C₂²	#2985	1	4	yes	—
1008	C₂²	C₂×#518	1	1	yes	characteristic
1009	C₂²	C₂×#519	1	1	yes	characteristic
1010	C₂²	#3428	1	1	yes	characteristic
1011	C₂²	C₂²×#131	1	1	yes	characteristic
1012	C₂²	C₂×#568	1	1	yes	characteristic
1013	C₂²	C₂×#568	1	1	yes	characteristic
1014	C₂²	C₂×#568	1	1	yes	characteristic
1015	C₄	—	2	2	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	#3541	1	2	yes	—
1043	C₄	#3541	1	2	yes	—
1044	C₂	—	2	4	no	—
1045	C₂	—	8	1	no	—
1046	C₂	—	8	1	no	—
1047	C₂	#34370	1	1	yes	characteristic
1048	C₂	#60234	1	1	yes	characteristic
1049	C₂	#60236	1	1	yes	characteristic
1050	C₂	C₂×#2985	1	1	yes	characteristic
1051	C₂	#60249	1	1	yes	characteristic
1052	C₂	#60288	1	1	yes	characteristic
1053	C₂	#60291	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #23342	C₂	semidirect
3. #23338	C₂	semidirect
4. #23059	C₂	semidirect
5. #23057	C₂	semidirect
6. #22629	C₂	semidirect
7. #22629	C₂	semidirect
8. #22627	C₂	semidirect
9. #22627	C₂	semidirect
10. #22625	C₂	semidirect
11. #22625	C₂	semidirect
12. #22510	C₂	semidirect
13. #22510	C₂	semidirect
14. #22328	C₂	semidirect
15. #22322	C₂	semidirect
16. #22107	C₂	semidirect
17. #22103	C₂	semidirect
26. C₂×#446	C₂²	semidirect
27. C₂×#446	C₂²	semidirect
59. #1985	C₂²	semidirect
60. #1985	C₂²	semidirect
61. #1985	C₂²	semidirect
62. #1985	C₂²	semidirect
63. #1984	C₂²	semidirect
64. #1984	C₂²	semidirect
65. #1940	C₂²	semidirect
66. #1940	C₂²	semidirect
67. #1939	C₂²	semidirect
68. #1939	C₂²	semidirect
69. #1939	C₂²	semidirect
70. #1939	C₂²	semidirect
87. #1917	C₂²	semidirect
88. #1917	C₂²	semidirect
89. #1917	C₂²	semidirect
90. #1917	C₂²	semidirect
91. #1917	C₂²	semidirect
92. #1917	C₂²	semidirect
93. #1916	C₂²	semidirect
94. #1916	C₂²	semidirect
95. #1916	C₂²	semidirect
96. #1916	C₂²	semidirect
97. #1916	C₂²	semidirect
98. #1916	C₂²	semidirect
119. #1771	C₂²	semidirect
120. #1771	C₂²	semidirect
121. #1770	C₂²	semidirect
122. #1770	C₂²	semidirect
123. C₈×C₄⋊C₄	C₂²	semidirect
124. C₈×C₄⋊C₄	C₂²	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2396	2
#23342	2
#23338	2
#23059	2
#23057	2
#22629	2
#22627	2
#22625	2
#22510	2
#22328	2
#22322	2
#22107	2
#22103	2
#21906	2
#21904	2
#21902	2
#20716	2