Subgroups — #6410995

Order 512.

1241 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34552	C₂	1	1	yes	maximal, characteristic
2	#23342	C₂	1	2	yes	maximal
3	#23340	C₂	1	2	yes	maximal
4	#23262	C₂	1	2	yes	maximal, complemented
5	#23259	C₂	1	2	yes	maximal, complemented
6	#22832	C₂	1	1	yes	maximal, characteristic, complemented
7	#22830	C₂	1	1	yes	maximal, characteristic, complemented
8	#22830	C₂	1	1	yes	maximal, characteristic, complemented
9	#22828	C₂	1	1	yes	maximal, characteristic, complemented
10	#22641	C₂	1	1	yes	maximal, characteristic
11	#22641	C₂	1	1	yes	maximal, characteristic
12	#22636	C₂	1	1	yes	maximal, characteristic
13	#22632	C₂	1	1	yes	maximal, characteristic
14	#22324	C₂	1	2	yes	maximal
15	#22322	C₂	1	2	yes	maximal
16	#22316	C₂	1	2	yes	maximal, complemented
17	#22310	C₂	1	2	yes	maximal, complemented
18	#22024	C₂	1	1	yes	maximal, characteristic, complemented
19	#22022	C₂	1	1	yes	maximal, characteristic, complemented
20	#22020	C₂	1	1	yes	maximal, characteristic, complemented
21	#22018	C₂	1	1	yes	maximal, characteristic, complemented
22	#20785	C₂	1	1	yes	maximal, characteristic
23	#20784	C₂	1	1	yes	maximal, characteristic
24	#2402	C₄	1	1	yes	characteristic
25	#2402	C₄	1	1	yes	characteristic
26	#2402	C₄	1	1	yes	characteristic
27	#2402	C₄	1	1	yes	characteristic
28	#2402	C₂²	1	1	yes	characteristic
29	#2402	C₂²	1	1	yes	characteristic
30	#2399	C₄	1	1	yes	characteristic
31	#2399	C₄	1	1	yes	characteristic
32	#2399	C₄	1	1	yes	characteristic
33	#2399	C₄	1	1	yes	characteristic
34	#2399	C₂²	1	1	yes	characteristic
35	#2399	C₂²	1	1	yes	characteristic
36	#2396	C₄	1	1	yes	characteristic
37	#2396	C₄	1	1	yes	characteristic
38	#2396	C₄	1	1	yes	characteristic
39	#2396	C₄	1	1	yes	characteristic
40	#2396	C₄	1	1	yes	characteristic
41	#2396	C₄	1	1	yes	characteristic
42	#2396	C₄	1	1	yes	characteristic
43	#2396	C₄	1	1	yes	characteristic
44	#2396	C₂²	1	1	yes	characteristic
45	#2396	C₂²	1	1	yes	characteristic
46	#2396	C₂²	1	1	yes	characteristic
47	#2396	C₂²	1	1	yes	characteristic
48	C₄²×Q₈	C₂²	1	1	yes	characteristic
49	C₄²×Q₈	C₂²	1	1	yes	characteristic
50	C₄²×Q₈	C₂²	1	1	yes	characteristic
51	C₄²×Q₈	C₂²	1	1	yes	characteristic
52	C₄×#117	C₂²	1	1	yes	characteristic
53	C₄×#117	C₂²	1	1	yes	characteristic
54	C₄×#117	C₂²	1	1	yes	characteristic
55	#1985	C₂²	1	2	yes	—
56	#1985	C₂²	1	2	yes	—
57	#1985	C₂²	1	2	yes	—
58	#1985	C₂²	1	2	yes	—
59	#1984	C₂²	1	2	yes	—
60	#1984	C₂²	1	2	yes	—
61	#1984	C₂²	1	2	yes	—
62	#1984	C₂²	1	2	yes	—
63	#1940	C₂²	1	2	yes	—
64	#1940	C₂²	1	2	yes	—
65	#1940	C₂²	1	2	yes	—
66	#1940	C₂²	1	2	yes	—
67	#1939	C₂²	1	2	yes	—
68	#1939	C₂²	1	2	yes	—
69	#1939	C₂²	1	2	yes	—
70	#1939	C₂²	1	2	yes	—
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	#1923	C₂²	1	2	yes	—
76	#1923	C₂²	1	2	yes	—
77	#1923	C₂²	1	2	yes	—
78	#1923	C₂²	1	2	yes	—
79	#1917	C₂²	1	2	yes	—
80	#1917	C₂²	1	2	yes	—
81	#1917	C₂²	1	2	yes	—
82	#1917	C₂²	1	2	yes	—
83	#1917	C₂²	1	2	yes	—
84	#1917	C₂²	1	2	yes	—
85	#1917	C₂²	1	2	yes	—
86	#1917	C₂²	1	2	yes	—
87	#1916	C₂²	1	2	yes	—
88	#1916	C₂²	1	2	yes	—
89	#1916	C₂²	1	2	yes	—
90	#1916	C₂²	1	2	yes	—
91	#1916	C₂²	1	2	yes	—
92	#1916	C₂²	1	2	yes	—
93	#1916	C₂²	1	2	yes	—
94	#1916	C₂²	1	2	yes	—
95	#1839	C₂²	1	1	yes	characteristic
96	#1839	C₂²	1	1	yes	characteristic
97	#1839	C₂²	1	1	yes	characteristic
98	#1839	C₂²	1	1	yes	characteristic
99	#1839	C₂²	1	1	yes	characteristic
100	#1839	C₂²	1	1	yes	characteristic
101	#1839	C₂²	1	1	yes	characteristic
102	#1839	C₂²	1	1	yes	characteristic
103	#1832	C₂²	1	2	yes	—
104	#1831	C₂²	1	1	yes	characteristic
105	#1831	C₂²	1	1	yes	characteristic
106	#1831	C₂²	1	1	yes	characteristic
107	#1831	C₂²	1	1	yes	characteristic
108	#1831	C₂²	1	1	yes	characteristic
109	#1831	C₂²	1	1	yes	characteristic
110	#1818	C₂²	1	2	yes	—
111	#1818	C₂²	1	2	yes	—
112	#1798	C₂²	1	2	yes	—
113	#1797	C₂²	1	1	yes	characteristic
114	#1797	C₂²	1	1	yes	characteristic
115	#1771	C₂²	1	2	yes	—
116	#1771	C₂²	1	2	yes	—
117	#1771	C₂²	1	2	yes	—
118	#1771	C₂²	1	2	yes	—
119	#1770	C₂²	1	2	yes	—
120	#1770	C₂²	1	2	yes	—
121	C₈×C₄⋊C₄	C₂²	1	2	yes	—
122	C₈×C₄⋊C₄	C₂²	1	2	yes	—
123	#1768	C₂²	1	2	yes	—
124	#1768	C₂²	1	2	yes	—
125	#1767	C₂²	1	1	yes	characteristic
126	#1767	C₂²	1	1	yes	characteristic
127	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
128	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
129	#1750	C₂²	1	2	yes	—
130	#1749	C₂²	1	1	yes	characteristic
131	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
132	#1746	C₂²	1	2	yes	—
133	#1745	C₂²	1	1	yes	characteristic
134	#1745	C₂²	1	1	yes	characteristic
135	#1745	C₂²	1	1	yes	characteristic
136	#1744	C₂²	1	1	yes	characteristic
137	#1744	C₂²	1	1	yes	characteristic
138	#1744	C₂²	1	1	yes	characteristic
139	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	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×C₄×Q₈	C₂³	1	1	yes	characteristic
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	C₂²×C₄²	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂³	1	2	yes	—
159	C₂×C₄⋊C₈	C₂³	1	2	yes	—
160	C₂×C₄⋊C₈	C₂³	1	2	yes	—
161	C₂×C₄⋊C₈	C₂³	1	2	yes	—
162	C₂×C₄⋊C₈	C₂³	1	2	yes	—
163	C₂×C₄⋊C₈	C₂³	1	2	yes	—
164	C₂×C₄⋊C₈	C₂³	1	2	yes	—
165	C₂×C₄⋊C₈	C₂³	1	2	yes	—
166	C₂×C₄⋊C₈	C₂³	1	2	yes	—
167	C₂×C₄⋊C₈	C₂³	1	2	yes	—
168	C₂×C₄⋊C₈	C₂³	1	2	yes	—
169	C₂×C₄⋊C₈	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
174	C₂×#97	C₂³	1	2	yes	—
175	C₂×#97	C₂³	1	2	yes	—
176	C₂×#97	C₂³	1	2	yes	—
177	C₂×#97	C₂³	1	2	yes	—
178	C₂×#97	C₂³	1	2	yes	—
179	C₂×#97	C₂³	1	2	yes	—
180	C₂×C₄×C₈	C₂³	1	2	yes	—
181	C₂×C₄×C₈	C₂³	1	2	yes	—
182	C₂×C₄×C₈	C₂³	1	2	yes	—
183	C₂×C₄×C₈	C₂³	1	2	yes	—
184	C₂×C₄×C₈	C₂³	1	2	yes	—
185	C₂×C₄×C₈	C₂³	1	2	yes	—
186	#400	C₂×C₄	1	1	yes	characteristic
187	#400	C₂×C₄	1	1	yes	characteristic
188	#400	C₂×C₄	1	1	yes	characteristic
189	#400	C₂×C₄	1	1	yes	characteristic
190	#400	C₂×C₄	1	1	yes	characteristic
191	#400	C₂×C₄	1	1	yes	characteristic
192	#400	C₂×C₄	1	1	yes	characteristic
193	#400	C₂×C₄	1	1	yes	characteristic
194	#400	C₂×C₄	1	1	yes	characteristic
195	#400	C₂×C₄	1	1	yes	characteristic
196	#400	C₂×C₄	1	1	yes	characteristic
197	#400	C₂×C₄	1	1	yes	characteristic
198	#399	C₂×C₄	1	1	yes	characteristic
199	#399	C₂×C₄	1	1	yes	characteristic
200	#399	C₂×C₄	1	1	yes	characteristic
201	#399	C₂×C₄	1	1	yes	characteristic
202	#398	C₂×C₄	1	1	yes	characteristic
203	#398	C₂×C₄	1	1	yes	characteristic
204	#398	C₂×C₄	1	1	yes	characteristic
205	#398	C₂×C₄	1	1	yes	characteristic
206	#398	C₂×C₄	1	1	yes	characteristic
207	#398	C₂×C₄	1	1	yes	characteristic
208	#398	C₂×C₄	1	1	yes	characteristic
209	#398	C₂×C₄	1	1	yes	characteristic
210	#398	C₂×C₄	1	1	yes	characteristic
211	#398	C₂×C₄	1	1	yes	characteristic
212	#398	C₂×C₄	1	1	yes	characteristic
213	#398	C₂×C₄	1	1	yes	characteristic
214	#398	C₂×C₄	1	1	yes	characteristic
215	#398	C₂×C₄	1	1	yes	characteristic
216	#398	C₂×C₄	1	1	yes	characteristic
217	#398	C₂×C₄	1	1	yes	characteristic
218	#398	C₂×C₄	1	1	yes	characteristic
219	#398	C₂×C₄	1	1	yes	characteristic
220	#398	C₂×C₄	1	1	yes	characteristic
221	#398	C₂×C₄	1	1	yes	characteristic
222	#398	C₂×C₄	1	1	yes	characteristic
223	#398	C₂×C₄	1	1	yes	characteristic
224	#398	C₂×C₄	1	1	yes	characteristic
225	#398	C₂×C₄	1	1	yes	characteristic
226	#396	C₂×C₄	1	1	yes	characteristic
227	#396	C₂×C₄	1	1	yes	characteristic
228	#396	C₂×C₄	1	1	yes	characteristic
229	#396	C₂×C₄	1	1	yes	characteristic
230	#396	C₂×C₄	1	1	yes	characteristic
231	#396	C₂×C₄	1	1	yes	characteristic
232	#396	C₂×C₄	1	1	yes	characteristic
233	#396	C₂×C₄	1	1	yes	characteristic
234	#395	C₂×C₄	1	1	yes	characteristic
235	#395	C₂×C₄	1	1	yes	characteristic
236	#395	C₂×C₄	1	1	yes	characteristic
237	#395	C₂×C₄	1	1	yes	characteristic
238	#395	C₂×C₄	1	1	yes	characteristic
239	#395	C₂×C₄	1	1	yes	characteristic
240	#395	C₂×C₄	1	1	yes	characteristic
241	#395	C₂×C₄	1	1	yes	characteristic
242	#395	C₂×C₄	1	1	yes	characteristic
243	#395	C₂×C₄	1	1	yes	characteristic
244	#395	C₂×C₄	1	1	yes	characteristic
245	#395	C₂×C₄	1	1	yes	characteristic
246	#393	C₂×C₄	1	1	yes	characteristic
247	#393	C₂×C₄	1	1	yes	characteristic
248	#393	C₂×C₄	1	1	yes	characteristic
249	#393	C₂×C₄	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
265	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
269	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
279	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
282	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
299	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
304	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
305	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
306	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	#376	C₂×C₄	1	1	yes	characteristic
311	#376	C₂×C₄	1	1	yes	characteristic
312	#376	C₂×C₄	1	1	yes	characteristic
313	#376	C₂×C₄	1	1	yes	characteristic
314	#376	C₂³	1	1	yes	characteristic
315	#376	C₂³	1	1	yes	characteristic
316	C₄³	C₂³	1	1	yes	characteristic
317	C₄³	C₂³	1	1	yes	characteristic
318	C₄³	C₂³	1	1	yes	characteristic
319	C₄³	C₂³	1	1	yes	characteristic
320	C₄³	C₂³	1	1	yes	characteristic
321	C₄³	C₂³	1	1	yes	characteristic
322	#336	C₂³	1	1	yes	characteristic
323	#336	C₂³	1	1	yes	characteristic
324	#336	C₂³	1	1	yes	characteristic
325	#336	C₂³	1	1	yes	characteristic
326	#336	C₂³	1	2	yes	—
327	#336	C₂³	1	2	yes	—
328	#336	C₂³	1	2	yes	—
329	#336	C₂³	1	2	yes	—
330	#336	C₂³	1	2	yes	—
331	#336	C₂³	1	2	yes	—
332	#336	C₂³	1	2	yes	—
333	#336	C₂³	1	2	yes	—
334	#336	C₂³	1	2	yes	—
335	#336	C₂³	1	2	yes	—
336	#336	C₂³	1	1	yes	characteristic
337	#336	C₂³	1	1	yes	characteristic
338	#336	C₂³	1	1	yes	characteristic
339	#336	C₂³	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	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
359	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
360	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
361	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
362	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
363	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
364	C₂³×C₄	C₂⁴	1	1	yes	characteristic
365	C₂²×C₈	C₂⁴	1	2	yes	—
366	C₂²×C₈	C₂⁴	1	2	yes	—
367	C₂²×C₈	C₂⁴	1	2	yes	—
368	C₂²×C₈	C₂⁴	1	2	yes	—
369	C₂²×C₈	C₂⁴	1	2	yes	—
370	C₂²×C₈	C₂⁴	1	2	yes	—
371	C₂²×C₈	C₂⁴	1	2	yes	—
372	C₂²×C₈	C₂⁴	1	2	yes	—
373	C₄×Q₈	—	2	4	no	—
374	C₄×Q₈	—	2	4	no	—
375	C₄×Q₈	—	4	2	no	—
376	C₄×Q₈	—	4	2	no	—
377	C₄×Q₈	—	4	1	no	—
378	C₄×Q₈	—	4	1	no	—
379	C₄×Q₈	—	4	2	no	—
380	C₄×Q₈	—	4	2	no	—
381	C₄×Q₈	—	4	1	no	—
382	C₄×Q₈	—	4	1	no	—
383	C₄×Q₈	—	4	2	no	—
384	C₄×Q₈	—	4	2	no	—
385	C₄×Q₈	—	4	2	no	—
386	C₄×Q₈	—	4	2	no	—
387	#117	—	2	4	no	—
388	#117	—	4	2	no	—
389	#117	—	4	2	no	—
390	#117	—	4	1	no	—
391	#117	—	4	1	no	—
392	#117	—	4	2	no	—
393	#117	—	4	2	no	—
394	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
454	C₂×C₄²	—	2	4	no	—
455	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
456	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
457	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
458	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
459	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
460	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
461	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
462	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
463	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
464	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
465	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
466	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
467	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
468	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
469	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
470	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
471	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
472	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
473	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
474	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
475	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
476	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
477	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
478	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
479	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
480	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
481	C₂×C₄²	C₂⁴	1	1	yes	characteristic
482	C₂×C₄²	C₂⁴	1	1	yes	characteristic
483	C₂×C₄²	C₂⁴	1	1	yes	characteristic
484	C₂×C₄²	C₂⁴	1	1	yes	characteristic
485	C₂×C₄²	C₂⁴	1	1	yes	characteristic
486	C₂×C₄²	C₂⁴	1	1	yes	characteristic
487	C₂×C₄²	C₂⁴	1	1	yes	characteristic
488	C₂×C₄²	C₂⁴	1	1	yes	characteristic
489	C₂×C₄²	C₂⁴	1	1	yes	characteristic
490	C₂×C₄²	C₂⁴	1	1	yes	characteristic
491	C₂×C₄²	C₂⁴	1	1	yes	characteristic
492	C₂×C₄²	C₂⁴	1	1	yes	characteristic
493	C₂×C₄²	C₂⁴	1	1	yes	characteristic
494	C₂×C₄²	C₂⁴	1	1	yes	characteristic
495	C₄⋊C₈	—	2	4	no	—
496	C₄⋊C₈	—	2	4	no	—
497	C₄⋊C₈	—	4	2	no	—
498	C₄⋊C₈	—	4	2	no	—
499	C₄⋊C₈	—	4	2	no	—
500	C₄⋊C₈	—	4	2	no	—
501	C₄⋊C₈	—	4	2	no	—
502	C₄⋊C₈	—	4	2	no	—
503	C₄⋊C₈	—	4	2	no	—
504	C₄⋊C₈	—	4	2	no	—
505	C₄⋊C₈	—	4	2	no	—
506	C₄⋊C₈	—	4	2	no	—
507	C₂²⋊C₈	—	4	2	no	—
508	C₂²⋊C₈	—	4	2	no	—
509	C₂²⋊C₈	—	4	2	no	—
510	C₂²⋊C₈	—	4	2	no	—
511	#97	—	2	4	no	—
512	#97	—	4	2	no	—
513	#97	—	4	2	no	—
514	#97	—	4	2	no	—
515	#97	—	4	2	no	—
516	#97	—	4	2	no	—
517	C₄×C₈	—	2	4	no	—
518	C₄×C₈	—	4	2	no	—
519	C₄×C₈	—	4	2	no	—
520	C₄×C₈	—	4	2	no	—
521	C₄×C₈	—	4	2	no	—
522	C₄×C₈	—	4	2	no	—
523	#95	C₂²×C₄	1	1	yes	characteristic
524	#95	C₂²×C₄	1	1	yes	characteristic
525	#95	C₂²×C₄	1	1	yes	characteristic
526	#95	C₂²×C₄	1	1	yes	characteristic
527	#95	C₂²×C₄	1	1	yes	characteristic
528	#95	C₂²×C₄	1	1	yes	characteristic
529	#95	C₂²×C₄	1	1	yes	characteristic
530	#95	C₂²×C₄	1	1	yes	characteristic
531	#95	C₂²×C₄	1	1	yes	characteristic
532	#95	C₂²×C₄	1	1	yes	characteristic
533	#95	C₂²×C₄	1	1	yes	characteristic
534	#95	C₂²×C₄	1	1	yes	characteristic
535	#95	C₂²×C₄	1	1	yes	characteristic
536	#95	C₂²×C₄	1	1	yes	characteristic
537	#95	C₂²×C₄	1	1	yes	characteristic
538	#95	C₂²×C₄	1	1	yes	characteristic
539	#95	C₂²×C₄	1	1	yes	characteristic
540	#95	C₂²×C₄	1	1	yes	characteristic
541	#95	C₂²×C₄	1	1	yes	characteristic
542	#95	C₂²×C₄	1	1	yes	characteristic
543	#95	C₂²×C₄	1	1	yes	characteristic
544	#95	C₂²×C₄	1	1	yes	characteristic
545	#95	C₂²×C₄	1	1	yes	characteristic
546	#95	C₂²×C₄	1	1	yes	characteristic
547	#95	C₂²×C₄	1	1	yes	characteristic
548	#95	C₂²×C₄	1	1	yes	characteristic
549	#95	C₂²×C₄	1	1	yes	characteristic
550	#95	C₂²×C₄	1	1	yes	characteristic
551	#95	C₂²×C₄	1	1	yes	characteristic
552	#95	C₂²×C₄	1	1	yes	characteristic
553	#95	C₂²×C₄	1	1	yes	characteristic
554	#95	C₂²×C₄	1	1	yes	characteristic
555	#95	C₂²×C₄	1	1	yes	characteristic
556	#95	C₂²×C₄	1	1	yes	characteristic
557	#95	C₂²×C₄	1	1	yes	characteristic
558	#95	C₂²×C₄	1	1	yes	characteristic
559	#95	C₂²×C₄	1	1	yes	characteristic
560	#95	C₂²×C₄	1	1	yes	characteristic
561	#95	C₂²×C₄	1	1	yes	characteristic
562	#95	C₂²×C₄	1	1	yes	characteristic
563	#95	C₂²×C₄	1	1	yes	characteristic
564	#95	C₂²×C₄	1	1	yes	characteristic
565	#95	C₂²×C₄	1	1	yes	characteristic
566	#95	C₂²×C₄	1	1	yes	characteristic
567	#95	C₂²×C₄	1	1	yes	characteristic
568	#95	C₂²×C₄	1	1	yes	characteristic
569	#95	C₂²×C₄	1	1	yes	characteristic
570	#95	C₂²×C₄	1	1	yes	characteristic
571	C₂⁴	C₂³×C₄	1	1	yes	characteristic
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	4	1	no	—
577	C₂×Q₈	—	4	1	no	—
578	C₂×Q₈	—	4	1	no	—
579	C₂×Q₈	—	4	1	no	—
580	C₂×Q₈	—	4	1	no	—
581	C₂×Q₈	—	4	1	no	—
582	C₂×Q₈	—	4	1	no	—
583	C₂×Q₈	—	4	1	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	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
595	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
596	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
597	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
598	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
599	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
600	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
601	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
602	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
603	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
604	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
605	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
606	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
607	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
608	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
609	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
610	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
611	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
612	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
613	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
614	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
615	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
616	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
617	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
618	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
619	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
620	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
621	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
622	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
623	C₂²×C₄	C₂⁵	1	1	yes	characteristic
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	—	2	2	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	1	no	—
668	C₄⋊C₄	—	4	1	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	1	no	—
672	C₄⋊C₄	—	4	1	no	—
673	C₄⋊C₄	—	4	1	no	—
674	C₄⋊C₄	—	4	1	no	—
675	C₄⋊C₄	—	4	1	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	1	no	—
682	C₄⋊C₄	—	4	1	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	1	no	—
685	C₄⋊C₄	—	4	1	no	—
686	C₄⋊C₄	—	4	1	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₄⋊C₄	—	4	1	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	1	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	4	1	no	—
701	C₂²⋊C₄	—	4	1	no	—
702	C₂²⋊C₄	—	4	1	no	—
703	C₂²⋊C₄	—	4	1	no	—
704	C₂²⋊C₄	—	4	1	no	—
705	C₂²⋊C₄	—	4	1	no	—
706	C₂²⋊C₄	—	4	1	no	—
707	C₂²⋊C₄	—	4	1	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	2	no	—
712	C₄²	—	2	2	no	—
713	C₄²	—	2	2	no	—
714	C₄²	—	2	2	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	1	no	—
730	C₄²	—	2	1	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	1	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	4	1	no	—
743	C₄²	—	4	1	no	—
744	C₄²	—	4	1	no	—
745	C₄²	—	4	1	no	—
746	C₄²	—	4	1	no	—
747	C₄²	—	4	1	no	—
748	C₄²	—	4	1	no	—
749	C₄²	—	4	1	no	—
750	C₄²	—	4	1	no	—
751	C₄²	—	4	1	no	—
752	C₄²	#131	1	4	yes	—
753	C₄²	2₋¹⁺⁴	1	4	yes	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	C₂⁴×C₄	1	1	yes	characteristic
762	Q₈	—	4	4	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	4	4	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	#519	1	2	yes	—
850	C₂×C₄	#519	1	2	yes	—
851	C₂×C₄	C₂×#131	1	2	yes	—
852	C₂×C₄	C₂×#131	1	2	yes	—
853	C₂×C₄	C₂×#131	1	2	yes	—
854	C₂×C₄	#568	1	2	yes	—
855	C₂×C₄	#568	1	2	yes	—
856	C₂×C₄	#568	1	2	yes	—
857	C₂×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
858	C₂×C₄	#585	1	2	yes	—
859	C₂×C₄	#585	1	1	yes	characteristic
860	C₂×C₄	#585	1	1	yes	characteristic
861	C₈	—	4	2	no	—
862	C₈	—	4	2	no	—
863	C₈	—	4	2	no	—
864	C₈	—	4	2	no	—
865	C₈	—	4	2	no	—
866	C₈	—	4	2	no	—
867	C₈	—	4	2	no	—
868	C₈	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	C₂×#519	1	1	yes	characteristic
877	C₂²	#3428	1	1	yes	characteristic
878	C₂²	#3428	1	1	yes	characteristic
879	C₂²	C₂²×#131	1	1	yes	characteristic
880	C₂²	C₂×#568	1	1	yes	characteristic
881	C₂²	C₂×#568	1	1	yes	characteristic
882	C₂²	C₂×#568	1	1	yes	characteristic
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	#3565	1	2	yes	—
913	C₄	#3565	1	2	yes	—
914	C₂	—	8	1	no	—
915	C₂	#34403	1	1	yes	characteristic
916	C₂	#60250	1	1	yes	characteristic
917	C₂	#60251	1	1	yes	characteristic
918	C₂	#60279	1	1	yes	characteristic
919	C₂	#60285	1	1	yes	characteristic
920	C₂	#60294	1	1	yes	characteristic
921	C₂	#60295	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₄	C₂⁵
commutator, socle	C₂³	C₂⁴×C₄
prime radical	C₂⁴	C₂³×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
4. #23262	C₂	semidirect
5. #23259	C₂	semidirect
6. #22832	C₂	semidirect
7. #22830	C₂	semidirect
8. #22830	C₂	semidirect
9. #22828	C₂	semidirect
16. #22316	C₂	semidirect
17. #22310	C₂	semidirect
18. #22024	C₂	semidirect
19. #22022	C₂	semidirect
20. #22020	C₂	semidirect
21. #22018	C₂	semidirect

Maximal subgroups

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

subgroup	index
#34552	2
#23342	2
#23340	2
#23262	2
#23259	2
#22832	2
#22830	2
#22828	2
#22641	2
#22636	2
#22632	2
#22324	2
#22322	2
#22316	2
#22310	2
#22024	2
#22022	2
#22020	2
#22018	2
#20785	2
#20784	2