Subgroups — #7622778

Order 512.

1305 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60306	C₂	1	1	yes	maximal, characteristic
2	#33508	C₂	1	1	yes	maximal, characteristic, complemented
3	#33507	C₂	1	1	yes	maximal, characteristic, complemented
4	#33506	C₂	1	2	yes	maximal, complemented
5	#33504	C₂	1	1	yes	maximal, characteristic, complemented
6	#33503	C₂	1	1	yes	maximal, characteristic, complemented
7	#33495	C₂	1	1	yes	maximal, characteristic, complemented
8	#33494	C₂	1	2	yes	maximal, complemented
9	#33493	C₂	1	1	yes	maximal, characteristic, complemented
10	#33492	C₂	1	2	yes	maximal, complemented
11	#33490	C₂	1	2	yes	maximal, complemented
12	#33488	C₂	1	1	yes	maximal, characteristic, complemented
13	#33485	C₂	1	1	yes	maximal, characteristic, complemented
14	#33483	C₂	1	1	yes	maximal, characteristic, complemented
15	#33481	C₂	1	2	yes	maximal, complemented
16	#33480	C₂	1	1	yes	maximal, characteristic, complemented
17	#33479	C₂	1	1	yes	maximal, characteristic, complemented
18	#33438	C₂	1	1	yes	maximal, characteristic, complemented
19	#33438	C₂	1	2	yes	maximal, complemented
20	D₄×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
21	#33436	C₂	1	2	yes	maximal, complemented
22	#33434	C₂	1	1	yes	maximal, characteristic, complemented
23	#33433	C₂	1	2	yes	maximal, complemented
24	#3460	C₄	1	1	yes	characteristic
25	C₂×#504	C₂²	1	2	yes	complemented
26	C₂×#504	C₂²	1	2	yes	complemented
27	C₂²×M₃₂	C₂²	1	2	yes	—
28	#2993	C₄	1	1	yes	characteristic
29	#2993	C₄	1	2	yes	—
30	#2993	C₄	1	1	yes	characteristic
31	#2989	C₄	1	1	yes	characteristic
32	#2989	C₄	1	1	yes	characteristic
33	#2981	C₄	1	1	yes	characteristic
34	#2981	C₄	1	1	yes	characteristic
35	#2981	C₄	1	2	yes	—
36	#2976	C₄	1	2	yes	—
37	#2976	C₄	1	2	yes	—
38	#2975	C₄	1	1	yes	characteristic
39	#2966	C₂²	1	1	yes	characteristic
40	#2966	C₂²	1	2	yes	—
41	#2966	C₂²	1	1	yes	characteristic
42	C₈×#41	C₂²	1	1	yes	characteristic
43	C₈×#41	C₂²	1	1	yes	characteristic
44	#2931	C₂²	1	1	yes	characteristic
45	#2931	C₂²	1	1	yes	characteristic
46	#2931	C₂²	1	2	yes	—
47	#2929	C₂²	1	2	yes	—
48	#2929	C₂²	1	2	yes	—
49	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
50	#2183	C₂²	1	1	yes	characteristic, complemented
51	#2183	C₂²	1	1	yes	characteristic, complemented
52	#2183	C₂²	1	1	yes	characteristic, complemented
53	#2183	C₂²	1	2	yes	complemented
54	#2183	C₂²	1	1	yes	characteristic, complemented
55	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
56	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
57	#2169	C₂²	1	1	yes	characteristic
58	#2169	C₂²	1	2	yes	—
59	#2169	C₂²	1	1	yes	characteristic
60	#2169	C₂²	1	2	yes	—
61	#2169	C₂²	1	1	yes	characteristic
62	#2169	C₂²	1	1	yes	characteristic
63	#2169	C₂²	1	1	yes	characteristic
64	#2169	C₂²	1	1	yes	characteristic
65	#2169	C₂²	1	2	yes	—
66	#2169	C₂²	1	2	yes	complemented
67	#2169	C₂²	1	2	yes	complemented
68	#2169	C₂²	1	1	yes	characteristic, complemented
69	#2169	C₂²	1	2	yes	complemented
70	#2169	C₂²	1	2	yes	complemented
71	#2169	C₂²	1	1	yes	characteristic, complemented
72	#2168	C₂²	1	2	yes	—
73	#2168	C₂²	1	2	yes	—
74	#2168	C₂²	1	1	yes	characteristic
75	#2168	C₂²	1	2	yes	—
76	#2168	C₂²	1	2	yes	—
77	#2168	C₂²	1	2	yes	—
78	#2168	C₂²	1	2	yes	—
79	#2168	C₂²	1	1	yes	characteristic
80	#2168	C₂²	1	2	yes	—
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	#2168	C₂²	1	1	yes	characteristic, complemented
86	#2168	C₂²	1	2	yes	complemented
87	#2168	C₂²	1	2	yes	complemented
88	#2168	C₂²	1	1	yes	characteristic, complemented
89	#2168	C₂²	1	2	yes	complemented
90	#2168	C₂²	1	2	yes	complemented
91	#2168	C₂²	1	2	yes	complemented
92	D₄×C₁₆	C₂²	1	1	yes	characteristic
93	D₄×C₁₆	C₂²	1	1	yes	characteristic
94	D₄×C₁₆	C₂²	1	1	yes	characteristic
95	D₄×C₁₆	C₂²	1	1	yes	characteristic
96	D₄×C₁₆	C₂²	1	2	yes	complemented
97	D₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
98	D₄×C₁₆	C₂²	1	2	yes	complemented
99	D₄×C₁₆	C₂²	1	2	yes	complemented
100	D₄×C₁₆	C₂²	1	2	yes	complemented
101	D₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
102	#2164	C₂²	1	2	yes	complemented
103	#2164	C₂²	1	2	yes	complemented
104	#2164	C₂²	1	2	yes	complemented
105	#2164	C₂²	1	2	yes	complemented
106	#2163	C₂²	1	1	yes	characteristic
107	#2163	C₂²	1	1	yes	characteristic, complemented
108	#2163	C₂²	1	2	yes	complemented
109	#2163	C₂²	1	2	yes	complemented
110	#2162	C₂²	1	1	yes	characteristic
111	#2162	C₂²	1	1	yes	characteristic, complemented
112	#2162	C₂²	1	1	yes	characteristic, complemented
113	#2162	C₂²	1	1	yes	characteristic, complemented
114	#2151	C₂²	1	2	yes	complemented
115	#2151	C₂²	1	2	yes	complemented
116	#2150	C₂²	1	1	yes	characteristic
117	#2150	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₁₆	C₂²	1	2	yes	complemented
120	#2113	C₂²	1	2	yes	complemented
121	#2113	C₂²	1	2	yes	complemented
122	#2113	C₂²	1	2	yes	complemented
123	#2113	C₂²	1	2	yes	complemented
124	#2113	C₂²	1	2	yes	complemented
125	#2113	C₂²	1	2	yes	complemented
126	#2112	C₂²	1	2	yes	—
127	#2112	C₂²	1	2	yes	—
128	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	—
129	#2108	C₂²	1	2	yes	complemented
130	#2108	C₂²	1	2	yes	complemented
131	C₄×M₃₂	C₂²	1	1	yes	characteristic
132	C₄×M₃₂	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₃₂	C₂²	1	2	yes	complemented
134	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×#131	C₂³	1	2	yes	—
136	C₂×#131	C₂³	1	2	yes	—
137	C₂³×C₈	C₂³	1	2	yes	—
138	#544	C₈	1	1	yes	characteristic
139	#542	C₈	1	1	yes	characteristic
140	#542	C₈	1	1	yes	characteristic
141	#542	C₈	1	2	yes	—
142	#540	C₈	1	1	yes	characteristic
143	#540	C₈	1	1	yes	characteristic
144	#540	C₈	1	2	yes	—
145	#538	C₈	1	2	yes	—
146	#538	C₈	1	2	yes	—
147	#537	C₈	1	1	yes	characteristic
148	#535	C₈	1	1	yes	characteristic
149	#535	C₈	1	1	yes	characteristic
150	#532	C₂×C₄	1	1	yes	characteristic
151	#532	C₂×C₄	1	1	yes	characteristic
152	#532	C₂×C₄	1	2	yes	—
153	#529	C₂×C₄	1	1	yes	characteristic
154	#529	C₂×C₄	1	2	yes	—
155	#529	C₂×C₄	1	1	yes	characteristic
156	#525	C₂×C₄	1	2	yes	—
157	#525	C₂×C₄	1	2	yes	—
158	C₄×#41	C₂×C₄	1	1	yes	characteristic
159	C₄×#41	C₂×C₄	1	1	yes	characteristic
160	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
161	#504	—	4	4	no	—
162	#504	—	4	4	no	—
163	C₂×M₃₂	—	4	4	no	—
164	C₂×M₃₂	C₂³	1	1	yes	characteristic
165	C₂×M₃₂	C₂³	1	1	yes	characteristic
166	C₂×M₃₂	C₂³	1	2	yes	—
167	C₂×M₃₂	C₂³	1	2	yes	—
168	C₂×M₃₂	C₂³	1	1	yes	characteristic
169	C₂×M₃₂	C₂³	1	1	yes	characteristic
170	C₂×M₃₂	C₂³	1	2	yes	—
171	C₂×M₃₂	C₂³	1	2	yes	—
172	C₂×M₃₂	C₂³	1	2	yes	—
173	C₂×M₃₂	C₂³	1	2	yes	—
174	C₂×M₃₂	C₂³	1	2	yes	—
175	C₂×M₃₂	C₂³	1	2	yes	—
176	C₂²×C₁₆	C₂³	1	1	yes	characteristic
177	C₂²×C₁₆	C₂³	1	2	yes	—
178	C₂²×C₁₆	C₂³	1	1	yes	characteristic
179	C₂²×C₁₆	C₂³	1	2	yes	—
180	C₂²×C₁₆	C₂³	1	2	yes	—
181	C₂²×C₁₆	C₂³	1	2	yes	—
182	C₂²×C₁₆	C₂³	1	2	yes	—
183	C₂²×C₁₆	C₂³	1	2	yes	—
184	C₂²×C₁₆	C₂³	1	2	yes	—
185	#446	C₂×C₄	1	1	yes	characteristic
186	#446	C₂×C₄	1	2	yes	—
187	#446	C₂×C₄	1	1	yes	characteristic
188	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
189	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
190	C₈×Q₈	C₂³	1	1	yes	characteristic
191	C₈×Q₈	C₂³	1	1	yes	characteristic
192	#436	C₂×C₄	1	1	yes	characteristic
193	#436	C₂×C₄	1	1	yes	characteristic
194	#436	C₂×C₄	1	2	yes	—
195	#436	C₂×C₄	1	2	yes	—
196	#436	C₂×C₄	1	2	yes	—
197	#436	C₂×C₄	1	2	yes	—
198	#436	C₂×C₄	1	2	yes	—
199	#436	C₂×C₄	1	1	yes	characteristic
200	#436	C₂×C₄	1	1	yes	characteristic
201	#436	C₂×C₄	1	2	yes	—
202	#436	C₂×C₄	1	1	yes	characteristic
203	#436	C₂×C₄	1	2	yes	—
204	#436	C₂×C₄	1	1	yes	characteristic
205	#435	C₂×C₄	1	2	yes	—
206	#435	C₂×C₄	1	2	yes	—
207	#435	C₂×C₄	1	2	yes	—
208	#435	C₂×C₄	1	2	yes	—
209	#435	C₂×C₄	1	2	yes	—
210	#435	C₂×C₄	1	2	yes	—
211	#435	C₂×C₄	1	2	yes	—
212	#435	C₂×C₄	1	2	yes	—
213	#435	C₂×C₄	1	2	yes	—
214	#435	C₂×C₄	1	2	yes	—
215	#435	C₂×C₄	1	2	yes	—
216	#435	C₂×C₄	1	2	yes	—
217	C₈×D₄	C₂×C₄	1	2	yes	—
218	C₈×D₄	C₂×C₄	1	1	yes	characteristic
219	C₈×D₄	C₂×C₄	1	1	yes	characteristic
220	C₈×D₄	C₂×C₄	1	1	yes	characteristic
221	C₈×D₄	C₂×C₄	1	1	yes	characteristic
222	C₈×D₄	C₂×C₄	1	2	yes	—
223	C₈×D₄	C₂×C₄	1	1	yes	characteristic
224	C₈×D₄	C₂×C₄	1	1	yes	characteristic
225	C₈×D₄	C₂³	1	1	yes	characteristic
226	C₈×D₄	C₂³	1	1	yes	characteristic
227	C₈×D₄	C₂³	1	2	yes	—
228	C₈×D₄	C₂³	1	1	yes	characteristic
229	C₈×D₄	C₂³	1	2	yes	—
230	C₈×D₄	C₂³	1	1	yes	characteristic
231	C₈×D₄	C₂³	1	2	yes	—
232	C₈×D₄	C₂³	1	2	yes	—
233	C₈×D₄	C₂³	1	2	yes	—
234	C₈×D₄	C₂³	1	2	yes	—
235	C₈×D₄	C₂³	1	1	yes	characteristic
236	C₈×D₄	C₂³	1	1	yes	characteristic
237	#433	C₂×C₄	1	2	yes	—
238	#433	C₂×C₄	1	2	yes	—
239	#433	C₂×C₄	1	2	yes	—
240	#433	C₂×C₄	1	2	yes	—
241	#432	C₂×C₄	1	1	yes	characteristic
242	#432	C₂×C₄	1	2	yes	—
243	#432	C₂×C₄	1	1	yes	characteristic
244	#431	C₂×C₄	1	1	yes	characteristic
245	#431	C₂×C₄	1	1	yes	characteristic
246	#431	C₂×C₄	1	1	yes	characteristic
247	#431	C₂×C₄	1	1	yes	characteristic
248	#431	C₂×C₄	1	2	yes	—
249	#424	C₂×C₄	1	2	yes	—
250	#424	C₂×C₄	1	2	yes	—
251	#423	C₂×C₄	1	1	yes	characteristic
252	#423	C₂×C₄	1	1	yes	characteristic
253	#423	C₂×C₄	1	2	yes	—
254	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
255	#408	C₂×C₄	1	2	yes	—
256	#408	C₂×C₄	1	2	yes	—
257	#408	C₂×C₄	1	2	yes	—
258	#408	C₂×C₄	1	2	yes	—
259	#408	C₂×C₄	1	2	yes	—
260	#408	C₂×C₄	1	2	yes	—
261	#407	C₂×C₄	1	2	yes	—
262	#407	C₂×C₄	1	2	yes	—
263	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
264	#405	C₂³	1	2	yes	—
265	#405	C₂³	1	2	yes	—
266	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄×C₈	C₂³	1	2	yes	—
270	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
271	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
272	C₄⋊C₁₆	C₂³	1	2	yes	—
273	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
274	C₄⋊C₁₆	C₂³	1	2	yes	—
275	C₄⋊C₁₆	C₂³	1	2	yes	—
276	C₄⋊C₁₆	C₂³	1	2	yes	—
277	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
278	C₄⋊C₁₆	C₂³	1	2	yes	—
279	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
280	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
281	C₄⋊C₁₆	C₂³	1	2	yes	—
282	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
283	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
284	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
285	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
286	C₄⋊C₁₆	C₂³	1	2	yes	—
287	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
288	C₂²⋊C₁₆	C₂³	1	2	yes	—
289	C₂²⋊C₁₆	C₂³	1	2	yes	—
290	C₂²⋊C₁₆	C₂³	1	2	yes	—
291	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
292	C₂²⋊C₁₆	C₂³	1	2	yes	—
293	C₂²⋊C₁₆	C₂³	1	2	yes	—
294	C₂²⋊C₁₆	C₂³	1	2	yes	—
295	C₂²⋊C₁₆	C₂³	1	2	yes	—
296	C₂²⋊C₁₆	C₂³	1	2	yes	—
297	C₂²⋊C₁₆	C₂³	1	2	yes	—
298	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	#346	C₂³	1	1	yes	characteristic
309	#346	C₂³	1	1	yes	characteristic
310	#346	C₂³	1	1	yes	characteristic
311	#346	C₂³	1	2	yes	—
312	#346	C₂³	1	1	yes	characteristic
313	#346	C₂³	1	2	yes	—
314	#346	C₂³	1	2	yes	—
315	#346	C₂³	1	2	yes	—
316	C₄×C₁₆	C₂³	1	1	yes	characteristic
317	C₄×C₁₆	C₂³	1	1	yes	characteristic
318	C₄×C₁₆	C₂³	1	1	yes	characteristic
319	C₄×C₁₆	C₂³	1	1	yes	characteristic
320	C₄×C₁₆	C₂³	1	1	yes	characteristic
321	C₄×C₁₆	C₂³	1	2	yes	—
322	C₄×C₁₆	C₂³	1	1	yes	characteristic
323	C₄×C₁₆	C₂³	1	2	yes	—
324	C₄×C₁₆	C₂³	1	2	yes	—
325	C₂×#41	C₂×C₈	1	1	yes	characteristic
326	C₂×#41	C₂×C₈	1	1	yes	characteristic
327	C₂×#41	C₂²×C₄	1	2	yes	—
328	C₂×#41	C₂²×C₄	1	2	yes	—
329	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
330	C₂³×C₄	C₂²×C₄	1	2	yes	—
331	#131	—	4	2	no	—
332	#131	—	4	2	no	—
333	#131	—	4	2	no	—
334	#131	—	4	2	no	—
335	C₂×M₁₆	C₂²×C₄	1	2	yes	—
336	C₂×M₁₆	C₂²×C₄	1	2	yes	—
337	C₂×M₁₆	C₂²×C₄	1	2	yes	—
338	C₂×M₁₆	C₂²×C₄	1	2	yes	—
339	C₂×M₁₆	C₂²×C₄	1	2	yes	—
340	C₂×M₁₆	C₂²×C₄	1	2	yes	—
341	C₂×M₁₆	C₂²×C₄	1	2	yes	—
342	C₂×M₁₆	C₂²×C₄	1	2	yes	—
343	C₂²×C₈	—	4	2	no	—
344	C₂²×C₈	—	4	2	no	—
345	C₂²×C₈	C₂²×C₄	1	2	yes	—
346	C₂²×C₈	C₂²×C₄	1	2	yes	—
347	C₂²×C₈	C₂²×C₄	1	2	yes	—
348	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
350	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₈	C₂²×C₄	1	2	yes	—
352	C₂²×C₈	C₂⁴	1	1	yes	characteristic
353	C₂²×C₈	C₂⁴	1	2	yes	—
354	C₂²×C₈	C₂⁴	1	2	yes	—
355	C₂²×C₈	C₂⁴	1	1	yes	characteristic
356	C₂²×C₈	C₂⁴	1	1	yes	characteristic
357	C₂²×C₈	C₂⁴	1	2	yes	—
358	C₄⋊Q₈	C₂×C₈	1	2	yes	—
359	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
360	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
361	#127	C₂×C₈	1	1	yes	characteristic
362	#127	C₂×C₈	1	1	yes	characteristic
363	#127	C₂×C₈	1	2	yes	—
364	#126	C₂×C₈	1	2	yes	—
365	#126	C₂×C₈	1	2	yes	—
366	#126	C₂×C₈	1	2	yes	—
367	#126	C₂×C₈	1	2	yes	—
368	#125	C₂×C₈	1	2	yes	—
369	#125	C₂×C₈	1	1	yes	characteristic
370	#125	C₂×C₈	1	1	yes	characteristic
371	#124	C₂×C₈	1	1	yes	characteristic
372	#124	C₂×C₈	1	1	yes	characteristic
373	#124	C₂×C₈	1	2	yes	—
374	#124	C₂×C₈	1	2	yes	—
375	#124	C₂×C₈	1	2	yes	—
376	#124	C₂×C₈	1	2	yes	—
377	#124	C₂×C₈	1	2	yes	—
378	#123	C₂×C₈	1	2	yes	—
379	#123	C₂×C₈	1	2	yes	—
380	#123	C₂×C₈	1	2	yes	—
381	#123	C₂×C₈	1	2	yes	—
382	#123	C₂×C₈	1	2	yes	—
383	#123	C₂×C₈	1	2	yes	—
384	#123	C₂×C₈	1	2	yes	—
385	#123	C₂×C₈	1	2	yes	—
386	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
387	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
388	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
389	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
390	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
393	#121	C₂×C₈	1	2	yes	—
394	#121	C₂×C₈	1	2	yes	—
395	#121	C₂×C₈	1	2	yes	—
396	#121	C₂×C₈	1	2	yes	—
397	#121	C₂×C₈	1	1	yes	characteristic
398	#121	C₂×C₈	1	1	yes	characteristic
399	#121	C₂×C₈	1	2	yes	—
400	#121	C₂×C₈	1	1	yes	characteristic
401	#121	C₂×C₈	1	1	yes	characteristic
402	#121	C₂×C₈	1	2	yes	—
403	#121	C₂×C₈	1	1	yes	characteristic
404	#121	C₂×C₈	1	1	yes	characteristic
405	#121	C₂×C₈	1	2	yes	—
406	#121	C₂×C₈	1	2	yes	—
407	#121	C₂×C₈	1	2	yes	—
408	#121	C₂×C₈	1	2	yes	—
409	#121	C₂×C₈	1	2	yes	—
410	#120	C₂×C₈	1	2	yes	—
411	#120	C₂×C₈	1	2	yes	—
412	#120	C₂×C₈	1	2	yes	—
413	#120	C₂×C₈	1	2	yes	—
414	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
415	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
416	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
417	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
418	C₄×D₄	C₂×C₈	1	1	yes	characteristic
419	C₄×D₄	C₂×C₈	1	1	yes	characteristic
420	C₄×D₄	C₂×C₈	1	2	yes	—
421	C₄×D₄	C₂×C₈	1	1	yes	characteristic
422	C₄×D₄	C₂×C₈	1	1	yes	characteristic
423	C₄×D₄	C₂×C₈	1	2	yes	—
424	C₄×D₄	C₂×C₈	1	1	yes	characteristic
425	C₄×D₄	C₂×C₈	1	1	yes	characteristic
426	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
427	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
428	C₄×D₄	C₂²×C₄	1	2	yes	—
429	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
430	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
431	C₄×D₄	C₂²×C₄	1	2	yes	—
432	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
433	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
434	C₄×D₄	C₂²×C₄	1	2	yes	—
435	C₄×D₄	C₂²×C₄	1	2	yes	—
436	C₄×D₄	C₂²×C₄	1	2	yes	—
437	C₄×D₄	C₂²×C₄	1	2	yes	—
438	#117	C₂×C₈	1	1	yes	characteristic
439	#117	C₂×C₈	1	1	yes	characteristic
440	#117	C₂×C₈	1	1	yes	characteristic
441	#117	C₂×C₈	1	1	yes	characteristic
442	#117	C₂×C₈	1	2	yes	—
443	#117	C₂²×C₄	1	2	yes	—
444	#117	C₂²×C₄	1	2	yes	—
445	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
447	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
448	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
449	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
450	C₂×C₄²	C₂²×C₄	1	2	yes	—
451	M₃₂	—	2	2	no	—
452	M₃₂	—	2	4	no	—
453	M₃₂	—	2	2	no	—
454	M₃₂	—	2	4	no	—
455	M₃₂	—	4	2	no	—
456	M₃₂	—	4	2	no	—
457	M₃₂	—	4	1	no	—
458	M₃₂	—	4	2	no	—
459	M₃₂	—	4	1	no	—
460	M₃₂	—	4	2	no	—
461	M₃₂	—	4	2	no	—
462	M₃₂	—	4	2	no	—
463	C₂×C₁₆	—	2	4	no	—
464	C₂×C₁₆	—	2	2	no	—
465	C₂×C₁₆	—	4	2	no	—
466	C₂×C₁₆	—	4	1	no	—
467	C₂×C₁₆	—	4	2	no	—
468	C₂×C₁₆	—	4	2	no	—
469	C₂×C₁₆	—	4	2	no	—
470	C₂×C₁₆	—	4	2	no	—
471	C₂×C₁₆	—	4	2	no	—
472	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
473	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
474	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
475	C₂×C₁₆	C₂⁴	1	2	yes	—
476	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
477	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
478	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
479	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
480	C₂×C₁₆	C₂⁴	1	2	yes	—
481	C₂×C₁₆	C₂⁴	1	2	yes	—
482	C₂×C₁₆	C₂⁴	1	2	yes	—
483	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
484	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
485	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
486	C₄⋊C₈	C₂²×C₄	1	2	yes	—
487	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
488	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
489	C₄⋊C₈	C₂²×C₄	1	2	yes	—
490	C₄⋊C₈	C₂²×C₄	1	2	yes	—
491	C₄⋊C₈	C₂²×C₄	1	2	yes	—
492	C₄⋊C₈	C₂²×C₄	1	2	yes	—
493	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
494	C₄⋊C₈	C₂²×C₄	1	2	yes	—
495	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
496	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
497	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
498	C₄⋊C₈	C₂²×C₄	1	2	yes	—
499	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
500	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
501	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
502	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
503	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
504	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
505	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
506	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
507	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
508	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
509	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
510	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
511	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
512	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
513	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
514	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
515	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
516	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
517	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
518	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
519	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
520	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
521	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
522	#97	C₂²×C₄	1	2	yes	—
523	#97	C₂²×C₄	1	2	yes	—
524	#97	C₂²×C₄	1	2	yes	—
525	#97	C₂²×C₄	1	2	yes	—
526	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
527	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
528	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
529	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
530	C₄×C₈	C₂²×C₄	1	2	yes	—
531	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
532	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
533	C₄×C₈	C₂²×C₄	1	2	yes	—
534	C₄×C₈	C₂⁴	1	1	yes	characteristic
535	C₄×C₈	C₂⁴	1	1	yes	characteristic
536	C₄×C₈	C₂⁴	1	2	yes	—
537	C₄×C₈	C₂⁴	1	1	yes	characteristic
538	C₄×C₈	C₂⁴	1	1	yes	characteristic
539	C₂⁴	C₂²×C₈	1	2	yes	—
540	#41	—	4	2	no	—
541	#41	—	4	2	no	—
542	#41	—	4	2	no	—
543	#41	—	4	2	no	—
544	#41	—	4	2	no	—
545	#41	—	4	2	no	—
546	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
547	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
548	C₂×Q₈	C₂²×C₈	1	2	yes	—
549	C₂×Q₈	C₂²×C₈	1	2	yes	—
550	C₂×D₄	—	4	2	no	—
551	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
552	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
553	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
554	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
555	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
556	C₂×D₄	C₂²×C₈	1	2	yes	—
557	C₂×D₄	C₂²×C₈	1	2	yes	—
558	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
559	C₂×D₄	C₂²×C₈	1	2	yes	—
560	C₂×D₄	C₂²×C₈	1	2	yes	—
561	C₂×D₄	C₂²×C₈	1	2	yes	—
562	C₂×D₄	C₂²×C₈	1	2	yes	—
563	C₂×D₄	C₂²×C₈	1	2	yes	—
564	C₂×D₄	C₂²×C₈	1	2	yes	—
565	C₂×D₄	C₂²×C₈	1	2	yes	—
566	C₂×D₄	C₂²×C₈	1	2	yes	—
567	C₂×D₄	C₂²×C₈	1	2	yes	—
568	C₂×D₄	C₂²×C₈	1	2	yes	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
572	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
573	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
574	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
575	C₂²×C₄	C₂²×C₈	1	2	yes	—
576	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
577	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
578	C₂²×C₄	C₂²×C₈	1	2	yes	—
579	C₂²×C₄	C₂²×C₈	1	2	yes	—
580	C₂²×C₄	C₂²×C₈	1	2	yes	—
581	C₂²×C₄	C₂²×C₈	1	2	yes	—
582	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
583	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
584	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
585	C₂²×C₄	C₂³×C₄	1	2	yes	—
586	C₂²×C₄	C₂³×C₄	1	2	yes	—
587	C₂²×C₄	C₂³×C₄	1	2	yes	—
588	M₁₆	—	4	2	no	—
589	M₁₆	—	4	2	no	—
590	M₁₆	—	4	2	no	—
591	M₁₆	—	4	2	no	—
592	M₁₆	—	4	2	no	—
593	M₁₆	—	4	2	no	—
594	M₁₆	—	4	2	no	—
595	M₁₆	—	4	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	2	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	2	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	4	2	no	—
609	C₂×C₈	—	4	2	no	—
610	C₂×C₈	—	4	2	no	—
611	C₂×C₈	—	4	1	no	—
612	C₂×C₈	—	4	1	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	—	4	2	no	—
615	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
616	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
617	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
618	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
619	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
620	C₂×C₈	C₂³×C₄	1	2	yes	—
621	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
622	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
623	C₂×C₈	C₂³×C₄	1	2	yes	—
624	C₂×C₈	C₂³×C₄	1	2	yes	—
625	C₂×C₈	C₂³×C₄	1	2	yes	—
626	C₂×C₈	C₂⁵	1	1	yes	characteristic
627	C₄⋊C₄	C₂²×C₈	1	2	yes	—
628	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
629	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
630	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
631	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
632	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
633	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
634	C₄⋊C₄	C₂²×C₈	1	2	yes	—
635	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
636	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
637	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
638	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
639	C₄⋊C₄	C₂²×C₈	1	2	yes	—
640	C₄⋊C₄	C₂²×C₈	1	2	yes	—
641	C₄⋊C₄	C₂²×C₈	1	2	yes	—
642	C₄⋊C₄	C₂²×C₈	1	2	yes	—
643	C₄⋊C₄	C₂²×C₈	1	2	yes	—
644	C₄⋊C₄	C₂²×C₈	1	2	yes	—
645	C₄⋊C₄	C₂²×C₈	1	2	yes	—
646	C₄⋊C₄	C₂²×C₈	1	2	yes	—
647	C₄⋊C₄	C₂²×C₈	1	2	yes	—
648	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
649	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
650	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
651	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
652	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
653	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
654	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
655	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
656	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
657	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
658	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
659	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
660	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
661	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
662	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
663	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
664	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
665	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
666	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
667	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
668	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
669	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
670	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
671	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
672	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
673	C₄²	C₂²×C₈	1	1	yes	characteristic
674	C₄²	C₂²×C₈	1	1	yes	characteristic
675	C₄²	C₂²×C₈	1	2	yes	—
676	C₄²	C₂²×C₈	1	1	yes	characteristic
677	C₄²	C₂²×C₈	1	1	yes	characteristic
678	C₄²	C₂²×C₈	1	1	yes	characteristic
679	C₄²	C₂²×C₈	1	1	yes	characteristic
680	C₄²	C₂²×C₈	1	2	yes	—
681	C₄²	C₂³×C₄	1	1	yes	characteristic
682	C₄²	C₂³×C₄	1	1	yes	characteristic
683	C₄²	C₂³×C₄	1	1	yes	characteristic
684	C₄²	C₂³×C₄	1	1	yes	characteristic
685	C₄²	C₂³×C₄	1	2	yes	—
686	C₁₆	—	2	1	no	—
687	C₁₆	—	2	2	no	—
688	C₁₆	—	2	1	no	—
689	C₁₆	—	2	2	no	—
690	C₁₆	—	2	2	no	—
691	C₁₆	—	2	1	no	—
692	C₁₆	—	2	1	no	—
693	C₁₆	—	2	2	no	—
694	C₁₆	—	2	1	no	—
695	C₁₆	—	2	1	no	—
696	C₁₆	—	2	1	no	—
697	C₁₆	H(5,𝔽₂)	1	2	yes	—
698	C₂³	—	4	2	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	C₂³×C₈	1	2	yes	—
702	C₂³	C₂³×C₈	1	2	yes	—
703	C₂³	C₂³×C₈	1	1	yes	characteristic
704	C₂³	C₂³×C₈	1	1	yes	characteristic
705	C₂³	C₂³×C₈	1	1	yes	characteristic
706	C₂³	C₂³×C₈	1	2	yes	—
707	Q₈	—	2	2	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	1	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
753	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
754	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
755	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
756	C₂×C₄	C₂³×C₈	1	2	yes	—
757	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
758	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
759	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
760	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
761	C₂×C₄	C₂³×C₈	1	2	yes	—
762	C₂×C₄	C₂³×C₈	1	2	yes	—
763	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
764	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
765	C₂×C₄	C₂³×C₈	1	2	yes	—
766	C₂×C₄	C₂³×C₈	1	2	yes	—
767	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
768	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
769	C₈	—	2	1	no	—
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	1	no	—
773	C₈	—	2	2	no	—
774	C₈	—	2	1	no	—
775	C₈	—	2	1	no	—
776	C₈	—	2	1	no	—
777	C₈	—	2	1	no	—
778	C₈	—	2	1	no	—
779	C₈	—	2	2	no	—
780	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
781	C₈	#585	1	1	yes	characteristic
782	C₂²	—	2	1	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	1	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	8	4	no	—
801	C₂²	C₂⁴×C₈	1	1	yes	characteristic
802	C₄	—	2	1	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	#3407	1	2	yes	—
818	C₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
819	C₄	#3573	1	1	yes	characteristic
820	C₂	—	4	1	no	—
821	C₂	—	4	1	no	—
822	C₂	—	4	2	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	2	no	—
825	C₂	—	4	1	no	—
826	C₂	C₈×H(5,𝔽₂)	1	1	yes	characteristic
827	C₂	C₂×#3407	1	1	yes	characteristic
828	C₂	#62624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₈	C₂⁵
commutator, socle	C₂²	C₂⁴×C₈
prime radical	#3460	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. #33508	C₂	semidirect
3. #33507	C₂	semidirect
4. #33506	C₂	semidirect
5. #33504	C₂	semidirect
6. #33503	C₂	semidirect
7. #33495	C₂	semidirect
8. #33494	C₂	semidirect
9. #33493	C₂	semidirect
10. #33492	C₂	semidirect
11. #33490	C₂	semidirect
12. #33488	C₂	semidirect
13. #33485	C₂	semidirect
14. #33483	C₂	semidirect
15. #33481	C₂	semidirect
16. #33480	C₂	semidirect
17. #33479	C₂	semidirect
18. #33438	C₂	semidirect
19. #33438	C₂	semidirect
20. D₄×M₃₂	C₂	semidirect
21. #33436	C₂	semidirect
22. #33434	C₂	semidirect
23. #33433	C₂	semidirect
25. C₂×#504	C₂²	semidirect
26. C₂×#504	C₂²	semidirect
50. #2183	C₂²	semidirect
51. #2183	C₂²	semidirect
52. #2183	C₂²	semidirect
53. #2183	C₂²	semidirect
54. #2183	C₂²	semidirect
55. Q₈×C₁₆	C₂²	semidirect
56. Q₈×C₁₆	C₂²	semidirect
66. #2169	C₂²	semidirect
67. #2169	C₂²	semidirect
68. #2169	C₂²	semidirect
69. #2169	C₂²	semidirect
70. #2169	C₂²	semidirect
71. #2169	C₂²	semidirect
81. #2168	C₂²	semidirect
82. #2168	C₂²	semidirect
83. #2168	C₂²	semidirect
84. #2168	C₂²	semidirect
85. #2168	C₂²	semidirect
86. #2168	C₂²	semidirect
87. #2168	C₂²	semidirect
88. #2168	C₂²	semidirect
89. #2168	C₂²	semidirect
90. #2168	C₂²	semidirect
91. #2168	C₂²	semidirect
96. D₄×C₁₆	C₂²	semidirect
97. D₄×C₁₆	C₂²	semidirect
98. D₄×C₁₆	C₂²	semidirect
99. D₄×C₁₆	C₂²	semidirect
100. D₄×C₁₆	C₂²	semidirect
101. D₄×C₁₆	C₂²	semidirect
102. #2164	C₂²	semidirect
103. #2164	C₂²	semidirect
104. #2164	C₂²	semidirect
105. #2164	C₂²	semidirect
107. #2163	C₂²	semidirect
108. #2163	C₂²	semidirect
109. #2163	C₂²	semidirect
111. #2162	C₂²	semidirect
112. #2162	C₂²	semidirect
113. #2162	C₂²	semidirect
114. #2151	C₂²	semidirect
115. #2151	C₂²	semidirect
117. #2150	C₂²	semidirect
118. C₂×C₄⋊C₁₆	C₂²	semidirect
119. C₂×C₄⋊C₁₆	C₂²	semidirect
120. #2113	C₂²	semidirect
121. #2113	C₂²	semidirect
122. #2113	C₂²	semidirect
123. #2113	C₂²	semidirect
124. #2113	C₂²	semidirect
125. #2113	C₂²	semidirect
129. #2108	C₂²	semidirect
130. #2108	C₂²	semidirect
132. C₄×M₃₂	C₂²	semidirect
133. C₄×M₃₂	C₂²	semidirect
134. C₂×C₄×C₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#60306	2
#33508	2
#33507	2
#33506	2
#33504	2
#33503	2
#33495	2
#33494	2
#33493	2
#33492	2
#33490	2
#33488	2
#33485	2
#33483	2
#33481	2
#33480	2
#33479	2
#33438	2
D₄×M₃₂	2
#33436	2
#33434	2
#33433	2