Subgroups — #7622694

Order 512.

1553 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#131	C₂	1	1	yes	maximal, characteristic
2	#33495	C₂	1	2	yes	maximal, complemented
3	#33494	C₂	1	2	yes	maximal, complemented
4	#33492	C₂	1	2	yes	maximal, complemented
5	#33491	C₂	1	2	yes	maximal, complemented
6	#33490	C₂	1	2	yes	maximal, complemented
7	#33490	C₂	1	2	yes	maximal, complemented
8	#33488	C₂	1	2	yes	maximal, complemented
9	#33487	C₂	1	2	yes	maximal, complemented
10	#33438	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	#33436	C₂	1	1	yes	maximal, characteristic, complemented
13	#33436	C₂	1	1	yes	maximal, characteristic, complemented
14	#33435	C₂	1	1	yes	maximal, characteristic, complemented
15	#33433	C₂	1	1	yes	maximal, characteristic, complemented
16	#33432	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#2168	C₂	1	1	yes	maximal, characteristic, complemented
18	#33423	C₂	1	1	yes	maximal, characteristic, complemented
19	#33421	C₂	1	1	yes	maximal, characteristic, complemented
20	#33334	C₂	1	1	yes	maximal, characteristic, complemented
21	#33334	C₂	1	1	yes	maximal, characteristic, complemented
22	#33333	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#2113	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#131	C₂²	1	1	yes	characteristic
25	C₂²×#131	C₂²	1	1	yes	characteristic
26	D₄×#41	C₄	1	1	yes	characteristic
27	C₂×#504	C₂²	1	1	yes	characteristic, complemented
28	C₂×#504	C₂²	1	1	yes	characteristic, complemented
29	C₂×#504	C₂²	1	1	yes	characteristic, complemented
30	C₂×#504	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₃₂	C₂²	1	1	yes	characteristic, complemented
32	C₂²×M₃₂	C₂²	1	1	yes	characteristic, complemented
33	C₂²×M₃₂	C₂²	1	1	yes	characteristic, complemented
34	C₂³×C₁₆	C₂²	1	1	yes	characteristic, complemented
35	#2935	C₄	1	1	yes	characteristic
36	#2935	C₄	1	2	yes	—
37	D₄×M₁₆	C₄	1	1	yes	characteristic
38	D₄×M₁₆	C₄	1	2	yes	—
39	#2933	C₄	1	1	yes	characteristic
40	#2933	C₄	1	1	yes	characteristic
41	#2933	C₄	1	2	yes	—
42	#2933	C₄	1	2	yes	—
43	#2931	C₂²	1	1	yes	characteristic
44	#2931	C₂²	1	2	yes	—
45	#2929	C₂²	1	1	yes	characteristic
46	#2929	C₂²	1	1	yes	characteristic
47	#2929	C₂²	1	2	yes	—
48	#2929	C₂²	1	2	yes	—
49	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₈×D₄	C₂²	1	2	yes	—
51	#2906	C₄	1	1	yes	characteristic
52	#2880	C₄	1	1	yes	characteristic
53	#2880	C₄	1	1	yes	characteristic
54	C₄×#131	C₂²	1	1	yes	characteristic
55	#2169	C₂²	1	2	yes	complemented
56	#2169	C₂²	1	2	yes	complemented
57	#2169	C₂²	1	2	yes	complemented
58	#2169	C₂²	1	2	yes	complemented
59	#2169	C₂²	1	2	yes	complemented
60	#2169	C₂²	1	2	yes	complemented
61	#2168	C₂²	1	1	yes	characteristic
62	#2168	C₂²	1	1	yes	characteristic
63	#2168	C₂²	1	2	yes	—
64	#2168	C₂²	1	1	yes	characteristic, complemented
65	#2168	C₂²	1	1	yes	characteristic, complemented
66	#2168	C₂²	1	1	yes	characteristic, complemented
67	#2168	C₂²	1	1	yes	characteristic, complemented
68	#2168	C₂²	1	1	yes	characteristic, complemented
69	#2168	C₂²	1	1	yes	characteristic, complemented
70	#2168	C₂²	1	2	yes	complemented
71	#2168	C₂²	1	2	yes	complemented
72	#2168	C₂²	1	2	yes	complemented
73	#2168	C₂²	1	2	yes	complemented
74	#2168	C₂²	1	2	yes	complemented
75	#2168	C₂²	1	2	yes	complemented
76	#2168	C₂²	1	2	yes	complemented
77	#2168	C₂²	1	2	yes	complemented
78	#2168	C₂²	1	2	yes	complemented
79	#2168	C₂²	1	2	yes	complemented
80	#2168	C₂²	1	2	yes	complemented
81	#2168	C₂²	1	2	yes	complemented
82	#2168	C₂²	1	2	yes	complemented
83	#2168	C₂²	1	2	yes	complemented
84	#2168	C₂²	1	2	yes	complemented
85	D₄×C₁₆	C₂²	1	2	yes	complemented
86	D₄×C₁₆	C₂²	1	2	yes	complemented
87	D₄×C₁₆	C₂²	1	2	yes	complemented
88	D₄×C₁₆	C₂²	1	2	yes	complemented
89	D₄×C₁₆	C₂²	1	2	yes	complemented
90	D₄×C₁₆	C₂²	1	2	yes	complemented
91	#2164	C₂²	1	2	yes	complemented
92	#2164	C₂²	1	2	yes	complemented
93	#2164	C₂²	1	2	yes	complemented
94	#2164	C₂²	1	2	yes	complemented
95	#2163	C₂²	1	2	yes	complemented
96	#2163	C₂²	1	2	yes	complemented
97	#2163	C₂²	1	2	yes	complemented
98	#2162	C₂²	1	2	yes	complemented
99	#2151	C₂²	1	1	yes	characteristic, complemented
100	#2151	C₂²	1	1	yes	characteristic, complemented
101	#2150	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
103	#2113	C₂²	1	1	yes	characteristic
104	#2113	C₂²	1	1	yes	characteristic
105	#2113	C₂²	1	1	yes	characteristic
106	#2113	C₂²	1	1	yes	characteristic
107	#2113	C₂²	1	1	yes	characteristic, complemented
108	#2113	C₂²	1	1	yes	characteristic, complemented
109	#2113	C₂²	1	2	yes	complemented
110	#2113	C₂²	1	2	yes	complemented
111	#2113	C₂²	1	1	yes	characteristic, complemented
112	#2113	C₂²	1	1	yes	characteristic, complemented
113	#2113	C₂²	1	2	yes	complemented
114	#2113	C₂²	1	2	yes	complemented
115	#2113	C₂²	1	2	yes	complemented
116	#2113	C₂²	1	2	yes	complemented
117	#2113	C₂²	1	2	yes	complemented
118	#2113	C₂²	1	2	yes	complemented
119	#2112	C₂²	1	2	yes	complemented
120	#2112	C₂²	1	2	yes	complemented
121	#2112	C₂²	1	1	yes	characteristic, complemented
122	#2112	C₂²	1	1	yes	characteristic, complemented
123	#2112	C₂²	1	2	yes	complemented
124	#2112	C₂²	1	2	yes	complemented
125	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
126	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
131	#2108	C₂²	1	1	yes	characteristic, complemented
132	#2108	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₃₂	C₂²	1	1	yes	characteristic, complemented
134	C₂×#346	C₂²	1	1	yes	characteristic, complemented
135	C₂²×#41	C₂×C₄	1	1	yes	characteristic
136	C₂²×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×#131	—	4	2	no	—
138	C₂×#131	—	4	2	no	—
139	C₂×#131	—	4	2	no	—
140	C₂×#131	—	4	2	no	—
141	C₂×#131	C₂×C₄	1	1	yes	characteristic
142	C₂×#131	C₂×C₄	1	1	yes	characteristic
143	C₂×#131	C₂×C₄	1	1	yes	characteristic
144	C₂×#131	C₂×C₄	1	1	yes	characteristic
145	C₂×#131	C₂×C₄	1	1	yes	characteristic
146	C₂×#131	C₂×C₄	1	2	yes	—
147	C₂×#131	C₂×C₄	1	2	yes	—
148	C₂×#131	C₂³	1	1	yes	characteristic
149	C₂×#131	C₂³	1	1	yes	characteristic
150	C₂×#131	C₂³	1	1	yes	characteristic
151	C₂×#131	C₂³	1	2	yes	—
152	C₂×#131	C₂³	1	2	yes	—
153	C₂²×M₁₆	C₂×C₄	1	2	yes	—
154	C₂²×M₁₆	C₂×C₄	1	2	yes	—
155	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
156	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
157	C₂³×C₈	C₂³	1	1	yes	characteristic
158	C₂³×C₈	C₂³	1	1	yes	characteristic
159	C₂³×C₈	C₂³	1	2	yes	—
160	C₂³×C₈	C₂³	1	2	yes	—
161	#550	C₈	1	1	yes	characteristic
162	D₄×Q₈	C₈	1	1	yes	characteristic
163	#548	C₈	1	1	yes	characteristic
164	#548	C₈	1	1	yes	characteristic
165	#547	C₈	1	2	yes	—
166	#547	C₈	1	1	yes	characteristic
167	#546	C₈	1	2	yes	—
168	#546	C₈	1	2	yes	—
169	#546	C₈	1	1	yes	characteristic
170	#546	C₈	1	1	yes	characteristic
171	D₄²	C₈	1	1	yes	characteristic
172	D₄²	C₈	1	2	yes	—
173	#532	C₂×C₄	1	1	yes	characteristic
174	#532	C₂×C₄	1	2	yes	—
175	#525	C₂×C₄	1	1	yes	characteristic
176	#525	C₂×C₄	1	1	yes	characteristic
177	#525	C₂×C₄	1	2	yes	—
178	#525	C₂×C₄	1	2	yes	—
179	C₄×#41	C₂×C₄	1	1	yes	characteristic
180	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂×C₄	1	2	yes	—
182	#504	—	4	2	no	—
183	#504	—	4	2	no	—
184	#504	—	4	2	no	—
185	#504	—	4	2	no	—
186	C₂×M₃₂	—	4	2	no	—
187	C₂×M₃₂	—	4	2	no	—
188	C₂×M₃₂	—	4	2	no	—
189	C₂×M₃₂	C₂³	1	1	yes	characteristic
190	C₂×M₃₂	C₂³	1	1	yes	characteristic
191	C₂×M₃₂	C₂³	1	1	yes	characteristic
192	C₂×M₃₂	C₂³	1	1	yes	characteristic
193	C₂×M₃₂	C₂³	1	1	yes	characteristic
194	C₂×M₃₂	C₂³	1	1	yes	characteristic
195	C₂×M₃₂	C₂³	1	2	yes	—
196	C₂×M₃₂	C₂³	1	2	yes	—
197	C₂×M₃₂	C₂³	1	2	yes	—
198	C₂×M₃₂	C₂³	1	2	yes	—
199	C₂×M₃₂	C₂³	1	2	yes	—
200	C₂×M₃₂	C₂³	1	1	yes	characteristic
201	C₂×M₃₂	C₂³	1	1	yes	characteristic
202	C₂×M₃₂	C₂³	1	2	yes	—
203	C₂²×C₁₆	—	4	2	no	—
204	C₂²×C₁₆	C₂³	1	1	yes	characteristic
205	C₂²×C₁₆	C₂³	1	1	yes	characteristic
206	C₂²×C₁₆	C₂³	1	1	yes	characteristic
207	C₂²×C₁₆	C₂³	1	1	yes	characteristic
208	C₂²×C₁₆	C₂³	1	1	yes	characteristic
209	C₂²×C₁₆	C₂³	1	1	yes	characteristic
210	C₂²×C₁₆	C₂³	1	2	yes	—
211	C₂²×C₁₆	C₂³	1	2	yes	—
212	C₂²×C₁₆	C₂³	1	2	yes	—
213	C₂²×C₁₆	C₂³	1	2	yes	—
214	C₂²×C₁₆	C₂³	1	2	yes	—
215	C₂²×C₁₆	C₂³	1	1	yes	characteristic
216	C₂²×C₁₆	C₂³	1	1	yes	characteristic
217	C₂²×C₁₆	C₂³	1	2	yes	—
218	#436	C₂×C₄	1	2	yes	—
219	#436	C₂×C₄	1	2	yes	—
220	#436	C₂×C₄	1	2	yes	—
221	#436	C₂×C₄	1	2	yes	—
222	#436	C₂×C₄	1	2	yes	—
223	#436	C₂×C₄	1	2	yes	—
224	#435	C₂×C₄	1	2	yes	—
225	#435	C₂×C₄	1	2	yes	—
226	#435	C₂×C₄	1	2	yes	—
227	#435	C₂×C₄	1	2	yes	—
228	#435	C₂×C₄	1	2	yes	—
229	#435	C₂×C₄	1	2	yes	—
230	#435	C₂×C₄	1	2	yes	—
231	#435	C₂×C₄	1	2	yes	—
232	#435	C₂×C₄	1	2	yes	—
233	#435	C₂×C₄	1	2	yes	—
234	#435	C₂×C₄	1	2	yes	—
235	#435	C₂×C₄	1	2	yes	—
236	C₈×D₄	C₂×C₄	1	1	yes	characteristic
237	C₈×D₄	C₂×C₄	1	1	yes	characteristic
238	C₈×D₄	C₂×C₄	1	2	yes	—
239	C₈×D₄	C₂×C₄	1	2	yes	—
240	C₈×D₄	C₂×C₄	1	1	yes	characteristic
241	C₈×D₄	C₂×C₄	1	2	yes	—
242	C₈×D₄	C₂×C₄	1	1	yes	characteristic
243	C₈×D₄	C₂×C₄	1	2	yes	—
244	C₈×D₄	C₂³	1	1	yes	characteristic
245	C₈×D₄	C₂³	1	1	yes	characteristic
246	C₈×D₄	C₂³	1	2	yes	—
247	C₈×D₄	C₂³	1	1	yes	characteristic
248	C₈×D₄	C₂³	1	2	yes	—
249	C₈×D₄	C₂³	1	1	yes	characteristic
250	C₈×D₄	C₂³	1	2	yes	—
251	C₈×D₄	C₂³	1	2	yes	—
252	C₈×D₄	C₂³	1	2	yes	—
253	C₈×D₄	C₂³	1	2	yes	—
254	#424	C₂×C₄	1	1	yes	characteristic
255	#424	C₂×C₄	1	1	yes	characteristic
256	#424	C₂×C₄	1	2	yes	—
257	#424	C₂×C₄	1	2	yes	—
258	#423	C₂×C₄	1	1	yes	characteristic
259	#423	C₂×C₄	1	2	yes	—
260	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂×C₄	1	2	yes	—
262	#408	C₂×C₄	1	1	yes	characteristic
263	#408	C₂×C₄	1	1	yes	characteristic
264	#408	C₂×C₄	1	2	yes	—
265	#408	C₂×C₄	1	2	yes	—
266	#408	C₂×C₄	1	1	yes	characteristic
267	#408	C₂×C₄	1	1	yes	characteristic
268	#408	C₂×C₄	1	2	yes	—
269	#408	C₂×C₄	1	2	yes	—
270	#407	C₂×C₄	1	1	yes	characteristic
271	#407	C₂×C₄	1	1	yes	characteristic
272	#407	C₂×C₄	1	2	yes	—
273	#407	C₂×C₄	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
278	#405	C₂×C₄	1	1	yes	characteristic
279	#405	C₂×C₄	1	2	yes	—
280	#405	C₂³	1	1	yes	characteristic
281	#405	C₂³	1	2	yes	—
282	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
283	C₄×M₁₆	C₂×C₄	1	2	yes	—
284	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂³	1	2	yes	—
286	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
287	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
288	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
289	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
290	C₄⋊C₁₆	C₂³	1	2	yes	—
291	C₄⋊C₁₆	C₂³	1	2	yes	—
292	C₄⋊C₁₆	C₂³	1	2	yes	—
293	C₄⋊C₁₆	C₂³	1	2	yes	—
294	C₄⋊C₁₆	C₂³	1	2	yes	—
295	C₄⋊C₁₆	C₂³	1	2	yes	—
296	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
297	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
298	C₂²⋊C₁₆	C₂³	1	2	yes	—
299	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
300	C₂²⋊C₁₆	C₂³	1	2	yes	—
301	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
302	C₂²⋊C₁₆	C₂³	1	2	yes	—
303	C₂²⋊C₁₆	C₂³	1	2	yes	—
304	C₂²⋊C₁₆	C₂³	1	2	yes	—
305	C₂²⋊C₁₆	C₂³	1	2	yes	—
306	C₂²⋊C₁₆	C₂³	1	2	yes	—
307	C₂²⋊C₁₆	C₂³	1	2	yes	—
308	C₂²⋊C₁₆	C₂³	1	2	yes	—
309	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
310	C₂²⋊C₁₆	C₂³	1	2	yes	—
311	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
312	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
313	C₂²⋊C₁₆	C₂³	1	2	yes	—
314	C₂²⋊C₁₆	C₂³	1	2	yes	—
315	C₂²⋊C₁₆	C₂³	1	2	yes	—
316	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
317	C₂²⋊C₁₆	C₂³	1	2	yes	—
318	C₂²⋊C₁₆	C₂³	1	2	yes	—
319	C₂²⋊C₁₆	C₂³	1	2	yes	—
320	C₂²⋊C₁₆	C₂³	1	2	yes	—
321	C₂²⋊C₁₆	C₂³	1	2	yes	—
322	C₂²⋊C₁₆	C₂³	1	2	yes	—
323	C₂²⋊C₁₆	C₂³	1	2	yes	—
324	#346	C₂³	1	1	yes	characteristic
325	#346	C₂³	1	1	yes	characteristic
326	#346	C₂³	1	1	yes	characteristic
327	#346	C₂³	1	1	yes	characteristic
328	#346	C₂³	1	2	yes	—
329	#346	C₂³	1	2	yes	—
330	#346	C₂³	1	2	yes	—
331	C₄×C₁₆	C₂³	1	2	yes	—
332	C₄×C₁₆	C₂³	1	2	yes	—
333	C₄×C₁₆	C₂³	1	2	yes	—
334	C₂×#41	—	4	2	no	—
335	C₂×#41	—	4	2	no	—
336	C₂×#41	—	4	2	no	—
337	C₂×#41	—	4	2	no	—
338	C₂×#41	C₂×C₈	1	2	yes	—
339	C₂×#41	C₂×C₈	1	2	yes	—
340	C₂×#41	C₂×C₈	1	1	yes	characteristic
341	C₂×#41	C₂×C₈	1	1	yes	characteristic
342	C₂×#41	C₂×C₈	1	1	yes	characteristic
343	C₂×#41	C₂×C₈	1	1	yes	characteristic
344	C₂×#41	C₂²×C₄	1	1	yes	characteristic
345	C₂×#41	C₂²×C₄	1	1	yes	characteristic
346	C₂×#41	C₂²×C₄	1	1	yes	characteristic
347	C₂×#41	C₂²×C₄	1	2	yes	—
348	C₂×#41	C₂²×C₄	1	2	yes	—
349	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
350	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
351	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
352	C₂²×D₄	C₂×C₈	1	2	yes	—
353	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
354	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
355	C₂²×D₄	C₂×C₈	1	2	yes	—
356	C₂²×D₄	C₂×C₈	1	2	yes	—
357	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
358	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
359	C₂³×C₄	C₂²×C₄	1	2	yes	—
360	C₂³×C₄	C₂²×C₄	1	2	yes	—
361	#131	—	2	2	no	—
362	#131	—	2	2	no	—
363	#131	—	2	2	no	—
364	#131	—	2	2	no	—
365	#131	—	2	2	no	—
366	#131	—	2	2	no	—
367	#131	—	4	2	no	—
368	#131	—	4	2	no	—
369	#131	—	4	2	no	—
370	#131	—	4	2	no	—
371	#131	—	4	4	no	—
372	#131	—	4	4	no	—
373	#131	—	4	2	no	—
374	#131	—	4	2	no	—
375	#131	—	4	2	no	—
376	#131	—	4	2	no	—
377	#131	—	4	2	no	—
378	C₂×M₁₆	—	4	4	no	—
379	C₂×M₁₆	—	4	4	no	—
380	C₂×M₁₆	—	4	2	no	—
381	C₂×M₁₆	—	4	2	no	—
382	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
383	C₂×M₁₆	C₂²×C₄	1	2	yes	—
384	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
385	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
386	C₂×M₁₆	C₂²×C₄	1	2	yes	—
387	C₂×M₁₆	C₂²×C₄	1	2	yes	—
388	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
389	C₂×M₁₆	C₂²×C₄	1	2	yes	—
390	C₂×M₁₆	C₂²×C₄	1	2	yes	—
391	C₂×M₁₆	C₂²×C₄	1	2	yes	—
392	C₂×M₁₆	C₂²×C₄	1	2	yes	—
393	C₂×M₁₆	C₂²×C₄	1	2	yes	—
394	C₂×M₁₆	C₂²×C₄	1	2	yes	—
395	C₂×M₁₆	C₂²×C₄	1	2	yes	—
396	C₂²×C₈	—	2	2	no	—
397	C₂²×C₈	—	2	2	no	—
398	C₂²×C₈	—	2	2	no	—
399	C₂²×C₈	—	2	2	no	—
400	C₂²×C₈	—	4	2	no	—
401	C₂²×C₈	—	4	2	no	—
402	C₂²×C₈	—	4	2	no	—
403	C₂²×C₈	—	4	2	no	—
404	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
405	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
406	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
407	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
408	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
409	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
410	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
411	C₂²×C₈	C₂²×C₄	1	2	yes	—
412	C₂²×C₈	C₂²×C₄	1	2	yes	—
413	C₂²×C₈	C₂²×C₄	1	2	yes	—
414	C₂²×C₈	C₂²×C₄	1	2	yes	—
415	C₂²×C₈	C₂²×C₄	1	2	yes	—
416	C₂²×C₈	C₂²×C₄	1	2	yes	—
417	C₂²×C₈	C₂²×C₄	1	2	yes	—
418	C₂²×C₈	C₂⁴	1	1	yes	characteristic
419	C₂²×C₈	C₂⁴	1	1	yes	characteristic
420	C₂²×C₈	C₂⁴	1	2	yes	—
421	C₂²×C₈	C₂⁴	1	1	yes	characteristic
422	C₂²×C₈	C₂⁴	1	1	yes	characteristic
423	C₂²×C₈	C₂⁴	1	2	yes	—
424	C₂²×C₈	C₂⁴	1	2	yes	—
425	C₂²×C₈	C₂⁴	1	1	yes	characteristic
426	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
427	C₄⋊Q₈	C₂×C₈	1	2	yes	—
428	#127	C₂×C₈	1	1	yes	characteristic
429	#127	C₂×C₈	1	2	yes	—
430	#124	C₂×C₈	1	1	yes	characteristic
431	#124	C₂×C₈	1	1	yes	characteristic
432	#124	C₂×C₈	1	2	yes	—
433	#124	C₂×C₈	1	2	yes	—
434	#123	C₂×C₈	1	2	yes	—
435	#123	C₂×C₈	1	2	yes	—
436	#123	C₂×C₈	1	2	yes	—
437	#123	C₂×C₈	1	2	yes	—
438	#123	C₂×C₈	1	2	yes	—
439	#123	C₂×C₈	1	2	yes	—
440	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
441	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
442	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
443	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
444	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
445	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
446	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
447	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
448	#121	C₂×C₈	1	1	yes	characteristic
449	#121	C₂×C₈	1	1	yes	characteristic
450	#121	C₂×C₈	1	2	yes	—
451	#121	C₂×C₈	1	2	yes	—
452	#121	C₂×C₈	1	1	yes	characteristic
453	#121	C₂×C₈	1	1	yes	characteristic
454	#121	C₂×C₈	1	2	yes	—
455	#121	C₂×C₈	1	2	yes	—
456	#121	C₂×C₈	1	2	yes	—
457	#121	C₂×C₈	1	2	yes	—
458	#121	C₂×C₈	1	2	yes	—
459	#121	C₂×C₈	1	2	yes	—
460	#121	C₂×C₈	1	2	yes	—
461	#121	C₂×C₈	1	2	yes	—
462	#120	C₂×C₈	1	2	yes	—
463	#120	C₂×C₈	1	2	yes	—
464	#120	C₂×C₈	1	2	yes	—
465	#120	C₂×C₈	1	2	yes	—
466	#120	C₂×C₈	1	2	yes	—
467	#120	C₂×C₈	1	2	yes	—
468	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
469	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
470	C₄×D₄	C₂×C₈	1	1	yes	characteristic
471	C₄×D₄	C₂×C₈	1	2	yes	—
472	C₄×D₄	C₂×C₈	1	1	yes	characteristic
473	C₄×D₄	C₂×C₈	1	1	yes	characteristic
474	C₄×D₄	C₂×C₈	1	2	yes	—
475	C₄×D₄	C₂×C₈	1	2	yes	—
476	C₄×D₄	C₂×C₈	1	1	yes	characteristic
477	C₄×D₄	C₂×C₈	1	2	yes	—
478	C₄×D₄	C₂×C₈	1	2	yes	—
479	C₄×D₄	C₂×C₈	1	1	yes	characteristic
480	C₄×D₄	C₂×C₈	1	2	yes	—
481	C₄×D₄	C₂×C₈	1	1	yes	characteristic
482	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
483	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
484	C₄×D₄	C₂²×C₄	1	2	yes	—
485	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
486	C₄×D₄	C₂²×C₄	1	2	yes	—
487	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
488	C₄×D₄	C₂²×C₄	1	2	yes	—
489	C₄×D₄	C₂²×C₄	1	2	yes	—
490	C₄×D₄	C₂²×C₄	1	2	yes	—
491	C₄×D₄	C₂²×C₄	1	2	yes	—
492	#117	C₂²×C₄	1	2	yes	—
493	#117	C₂²×C₄	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
500	C₂×C₄²	C₂²×C₄	1	2	yes	—
501	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
502	M₃₂	—	2	2	no	—
503	M₃₂	—	2	2	no	—
504	M₃₂	—	2	2	no	—
505	M₃₂	—	2	2	no	—
506	M₃₂	—	4	1	no	—
507	M₃₂	—	4	1	no	—
508	M₃₂	—	4	1	no	—
509	M₃₂	—	4	1	no	—
510	M₃₂	—	4	2	no	—
511	M₃₂	—	4	2	no	—
512	M₃₂	—	4	2	no	—
513	M₃₂	—	4	2	no	—
514	M₃₂	—	4	2	no	—
515	M₃₂	—	4	2	no	—
516	C₂×C₁₆	—	2	2	no	—
517	C₂×C₁₆	—	2	2	no	—
518	C₂×C₁₆	—	2	2	no	—
519	C₂×C₁₆	—	2	2	no	—
520	C₂×C₁₆	—	4	1	no	—
521	C₂×C₁₆	—	4	1	no	—
522	C₂×C₁₆	—	4	1	no	—
523	C₂×C₁₆	—	4	1	no	—
524	C₂×C₁₆	—	4	2	no	—
525	C₂×C₁₆	—	4	2	no	—
526	C₂×C₁₆	—	4	2	no	—
527	C₂×C₁₆	—	4	2	no	—
528	C₂×C₁₆	—	4	2	no	—
529	C₂×C₁₆	—	4	2	no	—
530	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
531	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
532	C₂×C₁₆	C₂⁴	1	2	yes	—
533	C₂×C₁₆	C₂⁴	1	2	yes	—
534	C₂×C₁₆	C₂⁴	1	2	yes	—
535	C₂×C₁₆	C₂⁴	1	2	yes	—
536	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
537	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
538	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
539	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
540	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
541	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
542	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
543	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
544	C₄⋊C₈	C₂²×C₄	1	2	yes	—
545	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
546	C₄⋊C₈	C₂²×C₄	1	2	yes	—
547	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
548	C₄⋊C₈	C₂²×C₄	1	2	yes	—
549	C₄⋊C₈	C₂²×C₄	1	2	yes	—
550	C₄⋊C₈	C₂²×C₄	1	2	yes	—
551	C₄⋊C₈	C₂²×C₄	1	2	yes	—
552	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
553	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
554	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
555	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
556	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
557	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
558	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
559	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
560	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
561	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
562	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
563	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
564	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
565	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
566	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
567	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
568	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
569	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
570	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
571	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
572	#97	C₂²×C₄	1	2	yes	—
573	#97	C₂²×C₄	1	2	yes	—
574	#97	C₂²×C₄	1	2	yes	—
575	C₄×C₈	C₂²×C₄	1	2	yes	—
576	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
577	C₄×C₈	C₂²×C₄	1	2	yes	—
578	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
579	C₄×C₈	C₂⁴	1	1	yes	characteristic
580	C₄×C₈	C₂⁴	1	2	yes	—
581	C₄×C₈	C₂⁴	1	1	yes	characteristic
582	C₂⁴	C₂²×C₈	1	1	yes	characteristic
583	C₂⁴	C₂²×C₈	1	2	yes	—
584	C₂⁴	C₂²×C₈	1	1	yes	characteristic
585	C₂⁴	C₂²×C₈	1	2	yes	—
586	#41	—	2	2	no	—
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	4	2	no	—
593	#41	—	4	2	no	—
594	#41	—	4	2	no	—
595	#41	—	4	2	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	2	no	—
599	#41	—	4	2	no	—
600	#41	—	4	2	no	—
601	#41	—	4	2	no	—
602	C₂×Q₈	—	4	2	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
605	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
606	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
607	C₂×Q₈	C₂²×C₈	1	2	yes	—
608	C₂×Q₈	C₂²×C₈	1	2	yes	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
616	C₂×D₄	C₂²×C₈	1	2	yes	—
617	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
618	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
619	C₂×D₄	C₂²×C₈	1	2	yes	—
620	C₂×D₄	C₂²×C₈	1	2	yes	—
621	C₂×D₄	C₂²×C₈	1	2	yes	—
622	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
623	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
624	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
625	C₂×D₄	C₂²×C₈	1	2	yes	—
626	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
627	C₂×D₄	C₂²×C₈	1	2	yes	—
628	C₂×D₄	C₂²×C₈	1	2	yes	—
629	C₂×D₄	C₂²×C₈	1	2	yes	—
630	C₂×D₄	C₂²×C₈	1	2	yes	—
631	C₂×D₄	C₂²×C₈	1	2	yes	—
632	C₂×D₄	C₂²×C₈	1	2	yes	—
633	C₂×D₄	C₂²×C₈	1	2	yes	—
634	C₂×D₄	C₂²×C₈	1	2	yes	—
635	C₂×D₄	C₂²×C₈	1	2	yes	—
636	C₂×D₄	C₂²×C₈	1	2	yes	—
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	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
647	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
648	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
649	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
650	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
651	C₂²×C₄	C₂²×C₈	1	2	yes	—
652	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
653	C₂²×C₄	C₂²×C₈	1	2	yes	—
654	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
655	C₂²×C₄	C₂²×C₈	1	2	yes	—
656	C₂²×C₄	C₂²×C₈	1	2	yes	—
657	C₂²×C₄	C₂²×C₈	1	2	yes	—
658	C₂²×C₄	C₂²×C₈	1	2	yes	—
659	C₂²×C₄	C₂²×C₈	1	2	yes	—
660	C₂²×C₄	C₂²×C₈	1	2	yes	—
661	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
662	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
663	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
664	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
665	C₂²×C₄	C₂³×C₄	1	2	yes	—
666	C₂²×C₄	C₂³×C₄	1	2	yes	—
667	C₂²×C₄	C₂³×C₄	1	2	yes	—
668	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
669	M₁₆	—	2	2	no	—
670	M₁₆	—	2	2	no	—
671	M₁₆	—	2	2	no	—
672	M₁₆	—	2	2	no	—
673	M₁₆	—	2	4	no	—
674	M₁₆	—	2	4	no	—
675	M₁₆	—	2	4	no	—
676	M₁₆	—	4	2	no	—
677	M₁₆	—	4	2	no	—
678	M₁₆	—	4	2	no	—
679	M₁₆	—	4	2	no	—
680	M₁₆	—	4	2	no	—
681	M₁₆	—	4	2	no	—
682	M₁₆	—	4	2	no	—
683	C₂×C₈	—	2	2	no	—
684	C₂×C₈	—	2	2	no	—
685	C₂×C₈	—	2	2	no	—
686	C₂×C₈	—	2	2	no	—
687	C₂×C₈	—	2	2	no	—
688	C₂×C₈	—	2	2	no	—
689	C₂×C₈	—	2	2	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	2	no	—
695	C₂×C₈	—	2	2	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	—	2	2	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	2	no	—
703	C₂×C₈	—	2	2	no	—
704	C₂×C₈	—	4	2	no	—
705	C₂×C₈	—	4	2	no	—
706	C₂×C₈	—	4	2	no	—
707	C₂×C₈	—	4	2	no	—
708	C₂×C₈	—	4	2	no	—
709	C₂×C₈	—	4	2	no	—
710	C₂×C₈	—	4	2	no	—
711	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
712	C₂×C₈	C₂³×C₄	1	2	yes	—
713	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
714	C₂×C₈	C₂³×C₄	1	2	yes	—
715	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
716	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
717	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
718	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
719	C₂×C₈	C₂³×C₄	1	2	yes	—
720	C₂×C₈	C₂³×C₄	1	2	yes	—
721	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
722	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
723	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
724	C₂×C₈	C₂⁵	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×C₈	1	2	yes	—
728	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×C₈	1	2	yes	—
731	C₄⋊C₄	C₂²×C₈	1	2	yes	—
732	C₄⋊C₄	C₂²×C₈	1	2	yes	—
733	C₄⋊C₄	C₂²×C₈	1	2	yes	—
734	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×C₈	1	2	yes	—
737	C₄⋊C₄	C₂²×C₈	1	2	yes	—
738	C₄⋊C₄	C₂²×C₈	1	2	yes	—
739	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
740	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
741	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
742	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
743	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
744	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
745	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
746	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
747	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
748	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
749	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
750	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
751	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
752	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
753	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
754	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
755	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
756	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
757	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
758	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
759	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
760	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
761	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
762	C₄²	C₂²×C₈	1	2	yes	—
763	C₄²	C₂²×C₈	1	1	yes	characteristic
764	C₄²	C₂²×C₈	1	2	yes	—
765	C₄²	C₂²×C₈	1	1	yes	characteristic
766	C₄²	C₂³×C₄	1	1	yes	characteristic
767	C₄²	C₂³×C₄	1	2	yes	—
768	C₄²	C₂³×C₄	1	1	yes	characteristic
769	C₁₆	—	2	1	no	—
770	C₁₆	—	2	1	no	—
771	C₁₆	—	2	1	no	—
772	C₁₆	—	2	1	no	—
773	C₁₆	—	2	1	no	—
774	C₁₆	—	2	1	no	—
775	C₁₆	—	2	1	no	—
776	C₁₆	—	2	1	no	—
777	C₁₆	—	2	2	no	—
778	C₁₆	—	2	2	no	—
779	C₁₆	—	2	2	no	—
780	C₁₆	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	4	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	4	2	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	2	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	C₂³×C₈	1	1	yes	characteristic
794	C₂³	C₂³×C₈	1	1	yes	characteristic
795	C₂³	C₂³×C₈	1	1	yes	characteristic
796	C₂³	C₂³×C₈	1	2	yes	—
797	C₂³	C₂³×C₈	1	2	yes	—
798	C₂³	C₂³×C₈	1	2	yes	—
799	C₂³	C₂³×C₈	1	1	yes	characteristic
800	C₂³	C₂³×C₈	1	1	yes	characteristic
801	Q₈	—	2	2	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	2	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	4	no	—
809	D₄	—	2	4	no	—
810	D₄	—	2	4	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	1	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	1	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	2	no	—
821	D₄	—	4	2	no	—
822	D₄	—	4	2	no	—
823	D₄	—	4	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	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	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	#518	1	2	yes	—
859	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
860	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
861	C₂×C₄	C₂³×C₈	1	2	yes	—
862	C₂×C₄	C₂³×C₈	1	2	yes	—
863	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
864	C₂×C₄	C₂³×C₈	1	2	yes	—
865	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
866	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
867	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
868	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
869	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
870	C₂×C₄	C₂³×C₈	1	2	yes	—
871	C₂×C₄	C₂³×C₈	1	2	yes	—
872	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
873	C₂×C₄	#568	1	2	yes	—
874	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
875	C₈	—	2	1	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	1	no	—
878	C₈	—	2	1	no	—
879	C₈	—	2	2	no	—
880	C₈	—	2	2	no	—
881	C₈	—	2	2	no	—
882	C₈	—	2	1	no	—
883	C₈	—	2	1	no	—
884	C₈	—	2	2	no	—
885	C₈	#518	1	2	yes	—
886	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
887	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	4	4	no	—
911	C₂²	—	8	4	no	—
912	C₂²	—	8	2	no	—
913	C₂²	—	8	4	no	—
914	C₂²	#2972	1	2	yes	—
915	C₂²	#3407	1	2	yes	—
916	C₂²	C₂⁴×C₈	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	2	no	—
930	C₄	#2972	1	2	yes	—
931	C₄	C₂×#518	1	1	yes	characteristic
932	C₄	C₂×#568	1	1	yes	characteristic
933	C₂	—	2	2	no	—
934	C₂	—	2	2	no	—
935	C₂	—	4	1	no	—
936	C₂	—	4	1	no	—
937	C₂	—	4	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	4	2	no	—
940	C₂	—	4	1	no	—
941	C₂	C₂×#2972	1	1	yes	characteristic
942	C₂	C₂×#3407	1	1	yes	characteristic
943	C₂	#62624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₈	C₂⁵
commutator, socle	C₂²	C₂⁴×C₈
prime radical	D₄×#41	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #33495	C₂	semidirect
3. #33494	C₂	semidirect
4. #33492	C₂	semidirect
5. #33491	C₂	semidirect
6. #33490	C₂	semidirect
7. #33490	C₂	semidirect
8. #33488	C₂	semidirect
9. #33487	C₂	semidirect
10. #33438	C₂	semidirect
11. D₄×M₃₂	C₂	semidirect
12. #33436	C₂	semidirect
13. #33436	C₂	semidirect
14. #33435	C₂	semidirect
15. #33433	C₂	semidirect
16. #33432	C₂	semidirect
17. C₂×#2168	C₂	semidirect
18. #33423	C₂	semidirect
19. #33421	C₂	semidirect
20. #33334	C₂	semidirect
21. #33334	C₂	semidirect
22. #33333	C₂	semidirect
23. C₂×#2113	C₂	semidirect
27. C₂×#504	C₂²	semidirect
28. C₂×#504	C₂²	semidirect
29. C₂×#504	C₂²	semidirect
30. C₂×#504	C₂²	semidirect
31. C₂²×M₃₂	C₂²	semidirect
32. C₂²×M₃₂	C₂²	semidirect
33. C₂²×M₃₂	C₂²	semidirect
34. C₂³×C₁₆	C₂²	semidirect
55. #2169	C₂²	semidirect
56. #2169	C₂²	semidirect
57. #2169	C₂²	semidirect
58. #2169	C₂²	semidirect
59. #2169	C₂²	semidirect
60. #2169	C₂²	semidirect
64. #2168	C₂²	semidirect
65. #2168	C₂²	semidirect
66. #2168	C₂²	semidirect
67. #2168	C₂²	semidirect
68. #2168	C₂²	semidirect
69. #2168	C₂²	semidirect
70. #2168	C₂²	semidirect
71. #2168	C₂²	semidirect
72. #2168	C₂²	semidirect
73. #2168	C₂²	semidirect
74. #2168	C₂²	semidirect
75. #2168	C₂²	semidirect
76. #2168	C₂²	semidirect
77. #2168	C₂²	semidirect
78. #2168	C₂²	semidirect
79. #2168	C₂²	semidirect
80. #2168	C₂²	semidirect
81. #2168	C₂²	semidirect
82. #2168	C₂²	semidirect
83. #2168	C₂²	semidirect
84. #2168	C₂²	semidirect
85. D₄×C₁₆	C₂²	semidirect
86. D₄×C₁₆	C₂²	semidirect
87. D₄×C₁₆	C₂²	semidirect
88. D₄×C₁₆	C₂²	semidirect
89. D₄×C₁₆	C₂²	semidirect
90. D₄×C₁₆	C₂²	semidirect
91. #2164	C₂²	semidirect
92. #2164	C₂²	semidirect
93. #2164	C₂²	semidirect
94. #2164	C₂²	semidirect
95. #2163	C₂²	semidirect
96. #2163	C₂²	semidirect
97. #2163	C₂²	semidirect
98. #2162	C₂²	semidirect
99. #2151	C₂²	semidirect
100. #2151	C₂²	semidirect
101. #2150	C₂²	semidirect
102. C₂×C₄⋊C₁₆	C₂²	semidirect
107. #2113	C₂²	semidirect
108. #2113	C₂²	semidirect
109. #2113	C₂²	semidirect
110. #2113	C₂²	semidirect
111. #2113	C₂²	semidirect
112. #2113	C₂²	semidirect
113. #2113	C₂²	semidirect
114. #2113	C₂²	semidirect
115. #2113	C₂²	semidirect
116. #2113	C₂²	semidirect
117. #2113	C₂²	semidirect
118. #2113	C₂²	semidirect
119. #2112	C₂²	semidirect
120. #2112	C₂²	semidirect
121. #2112	C₂²	semidirect
122. #2112	C₂²	semidirect
123. #2112	C₂²	semidirect
124. #2112	C₂²	semidirect
125. C₂×C₂²⋊C₁₆	C₂²	semidirect
126. C₂×C₂²⋊C₁₆	C₂²	semidirect
127. C₂×C₂²⋊C₁₆	C₂²	semidirect
128. C₂×C₂²⋊C₁₆	C₂²	semidirect
129. C₂×C₂²⋊C₁₆	C₂²	semidirect
130. C₂×C₂²⋊C₁₆	C₂²	semidirect
131. #2108	C₂²	semidirect
132. #2108	C₂²	semidirect
133. C₄×M₃₂	C₂²	semidirect
134. C₂×#346	C₂²	semidirect

Maximal subgroups

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

subgroup	index
D₄×#131	2
#33495	2
#33494	2
#33492	2
#33491	2
#33490	2
#33488	2
#33487	2
#33438	2
D₄×M₃₂	2
#33436	2
#33435	2
#33433	2
#33432	2
C₂×#2168	2
#33423	2
#33421	2
#33334	2
#33333	2
C₂×#2113	2