Subgroups — #7622672

Order 512.

1379 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60215	C₂	1	1	yes	maximal, characteristic
2	#33484	C₂	1	2	yes	maximal, complemented
3	#33483	C₂	1	2	yes	maximal, complemented
4	#33482	C₂	1	2	yes	maximal, complemented
5	#33482	C₂	1	2	yes	maximal, complemented
6	#33481	C₂	1	2	yes	maximal, complemented
7	#33481	C₂	1	2	yes	maximal, complemented
8	#33480	C₂	1	2	yes	maximal, complemented
9	#33479	C₂	1	2	yes	maximal, complemented
10	#33476	C₂	1	1	yes	maximal, characteristic, complemented
11	#33475	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#33436	C₂	1	1	yes	maximal, characteristic, complemented
14	#33436	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	#33422	C₂	1	1	yes	maximal, characteristic, complemented
20	#33422	C₂	1	1	yes	maximal, characteristic, complemented
21	#33326	C₂	1	1	yes	maximal, characteristic, complemented
22	#33324	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#2108	C₂	1	1	yes	maximal, characteristic, complemented
24	#3475	C₄	1	1	yes	characteristic
25	C₂×#504	C₂²	1	1	yes	characteristic
26	C₂×#504	C₂²	1	1	yes	characteristic
27	C₂²×M₃₂	C₂²	1	1	yes	characteristic
28	C₂²×M₃₂	C₂²	1	1	yes	characteristic
29	C₂²×M₃₂	C₂²	1	1	yes	characteristic
30	C₂³×C₁₆	C₂²	1	1	yes	characteristic
31	#2970	C₄	1	2	yes	—
32	#2969	C₄	1	2	yes	—
33	#2968	C₄	1	2	yes	—
34	#2968	C₄	1	2	yes	—
35	#2966	C₂²	1	2	yes	—
36	#2966	C₂²	1	2	yes	—
37	#2966	C₂²	1	2	yes	—
38	C₈×#41	C₂²	1	2	yes	—
39	#2962	C₄	1	1	yes	characteristic
40	#2960	C₂²	1	1	yes	characteristic
41	D₄×M₁₆	C₄	1	1	yes	characteristic
42	#2933	C₄	1	1	yes	characteristic
43	#2933	C₄	1	1	yes	characteristic
44	#2929	C₂²	1	1	yes	characteristic
45	#2929	C₂²	1	1	yes	characteristic
46	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
47	#2925	C₄	1	1	yes	characteristic
48	#2924	C₄	1	1	yes	characteristic
49	#2924	C₄	1	1	yes	characteristic
50	C₄×#131	C₂²	1	1	yes	characteristic
51	C₂×#405	C₂²	1	1	yes	characteristic
52	C₂×#405	C₂²	1	1	yes	characteristic
53	#2183	C₂²	1	2	yes	complemented
54	#2183	C₂²	1	2	yes	complemented
55	#2183	C₂²	1	2	yes	complemented
56	#2183	C₂²	1	2	yes	complemented
57	#2183	C₂²	1	2	yes	complemented
58	#2183	C₂²	1	2	yes	complemented
59	#2183	C₂²	1	2	yes	complemented
60	Q₈×C₁₆	C₂²	1	2	yes	complemented
61	#2169	C₂²	1	2	yes	—
62	#2169	C₂²	1	2	yes	complemented
63	#2169	C₂²	1	2	yes	complemented
64	#2169	C₂²	1	2	yes	complemented
65	#2169	C₂²	1	2	yes	complemented
66	#2168	C₂²	1	1	yes	characteristic
67	#2168	C₂²	1	1	yes	characteristic
68	#2168	C₂²	1	1	yes	characteristic
69	#2168	C₂²	1	1	yes	characteristic
70	#2168	C₂²	1	1	yes	characteristic
71	#2168	C₂²	1	1	yes	characteristic
72	#2168	C₂²	1	1	yes	characteristic
73	#2168	C₂²	1	1	yes	characteristic
74	#2168	C₂²	1	2	yes	—
75	#2168	C₂²	1	2	yes	—
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	D₄×C₁₆	C₂²	1	2	yes	—
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	#2164	C₂²	1	2	yes	complemented
90	#2164	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	#2162	C₂²	1	2	yes	complemented
100	#2162	C₂²	1	2	yes	complemented
101	#2151	C₂²	1	1	yes	characteristic
102	#2151	C₂²	1	1	yes	characteristic
103	#2151	C₂²	1	1	yes	characteristic
104	#2151	C₂²	1	1	yes	characteristic
105	#2150	C₂²	1	1	yes	characteristic
106	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
107	#2113	C₂²	1	1	yes	characteristic
108	#2113	C₂²	1	1	yes	characteristic
109	#2112	C₂²	1	1	yes	characteristic
110	#2112	C₂²	1	1	yes	characteristic
111	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
112	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
113	#2108	C₂²	1	1	yes	characteristic
114	#2108	C₂²	1	1	yes	characteristic
115	#2108	C₂²	1	1	yes	characteristic
116	#2108	C₂²	1	1	yes	characteristic
117	#2108	C₂²	1	1	yes	characteristic
118	#2108	C₂²	1	1	yes	characteristic
119	#2108	C₂²	1	1	yes	characteristic
120	#2108	C₂²	1	1	yes	characteristic
121	#2108	C₂²	1	2	yes	complemented
122	#2108	C₂²	1	2	yes	complemented
123	#2108	C₂²	1	2	yes	complemented
124	#2108	C₂²	1	2	yes	complemented
125	#2108	C₂²	1	2	yes	complemented
126	#2108	C₂²	1	2	yes	complemented
127	C₄×M₃₂	C₂²	1	1	yes	characteristic
128	C₄×M₃₂	C₂²	1	2	yes	complemented
129	C₄×M₃₂	C₂²	1	2	yes	complemented
130	C₄×M₃₂	C₂²	1	2	yes	complemented
131	C₂×#346	C₂²	1	1	yes	characteristic
132	C₂×#346	C₂²	1	2	yes	complemented
133	C₂×#346	C₂²	1	2	yes	complemented
134	C₂×C₄×C₁₆	C₂²	1	2	yes	complemented
135	C₂×#131	C₂×C₄	1	1	yes	characteristic
136	C₂×#131	C₂³	1	1	yes	characteristic
137	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
138	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
139	C₂³×C₈	C₂³	1	1	yes	characteristic
140	C₂³×C₈	C₂³	1	1	yes	characteristic
141	#556	C₈	1	1	yes	characteristic
142	#555	C₈	1	1	yes	characteristic
143	#554	C₈	1	1	yes	characteristic
144	#553	C₈	1	1	yes	characteristic
145	#553	C₈	1	1	yes	characteristic
146	#552	C₈	1	1	yes	characteristic
147	#552	C₈	1	1	yes	characteristic
148	#552	C₈	1	2	yes	—
149	#551	C₈	1	2	yes	—
150	#551	C₈	1	2	yes	—
151	#547	C₈	1	1	yes	characteristic
152	#546	C₈	1	2	yes	—
153	#533	C₂×C₄	1	1	yes	characteristic
154	#529	C₂×C₄	1	2	yes	—
155	#529	C₂×C₄	1	2	yes	—
156	#529	C₂×C₄	1	2	yes	—
157	#525	C₂×C₄	1	1	yes	characteristic
158	#525	C₂×C₄	1	1	yes	characteristic
159	C₄×#41	C₂×C₄	1	2	yes	—
160	C₄×#41	C₂×C₄	1	1	yes	characteristic
161	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
162	C₂×#117	C₂×C₄	1	1	yes	characteristic
163	C₂×#117	C₂×C₄	1	1	yes	characteristic
164	#504	—	2	4	no	—
165	#504	—	2	4	no	—
166	C₂×M₃₂	—	2	4	no	—
167	C₂×M₃₂	—	2	4	no	—
168	C₂×M₃₂	—	2	4	no	—
169	C₂×M₃₂	C₂³	1	1	yes	characteristic
170	C₂×M₃₂	C₂³	1	1	yes	characteristic
171	C₂×M₃₂	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
176	C₂×M₃₂	C₂³	1	1	yes	characteristic
177	C₂×M₃₂	C₂³	1	1	yes	characteristic
178	C₂×M₃₂	C₂³	1	1	yes	characteristic
179	C₂×M₃₂	C₂³	1	2	yes	—
180	C₂×M₃₂	C₂³	1	1	yes	characteristic
181	C₂²×C₁₆	—	2	4	no	—
182	C₂²×C₁₆	C₂³	1	1	yes	characteristic
183	C₂²×C₁₆	C₂³	1	2	yes	—
184	C₂²×C₁₆	C₂³	1	1	yes	characteristic
185	C₂²×C₁₆	C₂³	1	1	yes	characteristic
186	C₂²×C₁₆	C₂³	1	2	yes	—
187	C₂²×C₁₆	C₂³	1	2	yes	—
188	C₂²×C₁₆	C₂³	1	1	yes	characteristic
189	C₂²×C₁₆	C₂³	1	1	yes	characteristic
190	C₂²×C₁₆	C₂³	1	1	yes	characteristic
191	C₂²×C₁₆	C₂³	1	1	yes	characteristic
192	C₂²×C₁₆	C₂³	1	2	yes	—
193	C₂²×C₁₆	C₂³	1	1	yes	characteristic
194	#446	C₂×C₄	1	2	yes	—
195	#446	C₂×C₄	1	2	yes	—
196	#446	C₂×C₄	1	2	yes	—
197	#446	C₂×C₄	1	2	yes	—
198	#446	C₂×C₄	1	2	yes	—
199	C₈×Q₈	C₂×C₄	1	2	yes	—
200	C₈×Q₈	C₂³	1	2	yes	—
201	C₈×Q₈	C₂³	1	2	yes	—
202	#436	C₂×C₄	1	2	yes	—
203	#436	C₂×C₄	1	2	yes	—
204	#436	C₂×C₄	1	2	yes	—
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	C₈×D₄	C₂×C₄	1	1	yes	characteristic
216	C₈×D₄	C₂×C₄	1	1	yes	characteristic
217	C₈×D₄	C₂×C₄	1	1	yes	characteristic
218	C₈×D₄	C₂×C₄	1	1	yes	characteristic
219	C₈×D₄	C₂×C₄	1	2	yes	—
220	C₈×D₄	C₂×C₄	1	2	yes	—
221	C₈×D₄	C₂×C₄	1	2	yes	—
222	C₈×D₄	C₂³	1	1	yes	characteristic
223	C₈×D₄	C₂³	1	1	yes	characteristic
224	C₈×D₄	C₂³	1	1	yes	characteristic
225	C₈×D₄	C₂³	1	1	yes	characteristic
226	C₈×D₄	C₂³	1	2	yes	—
227	C₈×D₄	C₂³	1	2	yes	—
228	C₈×D₄	C₂³	1	2	yes	—
229	C₈×D₄	C₂³	1	2	yes	—
230	#433	C₂×C₄	1	2	yes	—
231	#433	C₂×C₄	1	2	yes	—
232	#433	C₂×C₄	1	2	yes	—
233	#433	C₂×C₄	1	2	yes	—
234	#433	C₂×C₄	1	2	yes	—
235	#433	C₂×C₄	1	2	yes	—
236	#432	C₂×C₄	1	2	yes	—
237	#432	C₂×C₄	1	2	yes	—
238	#432	C₂×C₄	1	2	yes	—
239	#431	C₂×C₄	1	2	yes	—
240	#431	C₂×C₄	1	2	yes	—
241	#431	C₂×C₄	1	2	yes	—
242	#424	C₂×C₄	1	1	yes	characteristic
243	#424	C₂×C₄	1	1	yes	characteristic
244	#424	C₂×C₄	1	1	yes	characteristic
245	#424	C₂×C₄	1	1	yes	characteristic
246	#423	C₂×C₄	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
248	#408	C₂×C₄	1	1	yes	characteristic
249	#408	C₂×C₄	1	1	yes	characteristic
250	#407	C₂×C₄	1	1	yes	characteristic
251	#407	C₂×C₄	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
254	#405	C₂×C₄	1	1	yes	characteristic
255	#405	C₂×C₄	1	1	yes	characteristic
256	#405	C₂×C₄	1	1	yes	characteristic
257	#405	C₂×C₄	1	1	yes	characteristic
258	#405	C₂×C₄	1	2	yes	—
259	#405	C₂×C₄	1	2	yes	—
260	#405	C₂×C₄	1	1	yes	characteristic
261	#405	C₂×C₄	1	2	yes	—
262	#405	C₂³	1	1	yes	characteristic
263	#405	C₂³	1	1	yes	characteristic
264	#405	C₂³	1	1	yes	characteristic
265	#405	C₂³	1	2	yes	—
266	#405	C₂³	1	2	yes	—
267	#405	C₂³	1	2	yes	—
268	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
269	C₄×M₁₆	C₂×C₄	1	2	yes	—
270	C₂×#97	C₂×C₄	1	2	yes	—
271	C₂×#97	C₂×C₄	1	2	yes	—
272	C₂×C₄×C₈	C₂³	1	2	yes	—
273	C₂×C₄×C₈	C₂³	1	2	yes	—
274	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂³	1	2	yes	—
276	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
277	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
278	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
279	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
280	C₄⋊C₁₆	C₂³	1	2	yes	—
281	C₄⋊C₁₆	C₂³	1	2	yes	—
282	C₄⋊C₁₆	C₂³	1	2	yes	—
283	C₄⋊C₁₆	C₂³	1	2	yes	—
284	C₄⋊C₁₆	C₂³	1	2	yes	—
285	C₄⋊C₁₆	C₂³	1	2	yes	—
286	C₄⋊C₁₆	C₂³	1	2	yes	—
287	C₄⋊C₁₆	C₂³	1	2	yes	—
288	C₄⋊C₁₆	C₂³	1	2	yes	—
289	C₄⋊C₁₆	C₂³	1	2	yes	—
290	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
291	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
292	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
293	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
294	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
295	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₂²⋊C₁₆	C₂³	1	2	yes	—
301	C₂²⋊C₁₆	C₂³	1	2	yes	—
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	#346	C₂³	1	1	yes	characteristic
307	#346	C₂³	1	1	yes	characteristic
308	#346	C₂³	1	1	yes	characteristic
309	#346	C₂³	1	1	yes	characteristic
310	#346	C₂³	1	2	yes	—
311	#346	C₂³	1	2	yes	—
312	#346	C₂³	1	2	yes	—
313	#346	C₂³	1	2	yes	—
314	#346	C₂³	1	2	yes	—
315	#346	C₂³	1	2	yes	—
316	#346	C₂³	1	2	yes	—
317	#346	C₂³	1	2	yes	—
318	#346	C₂³	1	2	yes	—
319	C₄×C₁₆	C₂³	1	2	yes	—
320	C₄×C₁₆	C₂³	1	2	yes	—
321	C₄×C₁₆	C₂³	1	2	yes	—
322	C₄×C₁₆	C₂³	1	2	yes	—
323	C₄×C₁₆	C₂³	1	2	yes	—
324	C₄×C₁₆	C₂³	1	2	yes	—
325	C₄×C₁₆	C₂³	1	2	yes	—
326	C₄×C₁₆	C₂³	1	2	yes	—
327	C₄×C₁₆	C₂³	1	2	yes	—
328	C₂×#41	C₂×C₈	1	2	yes	—
329	C₂×#41	C₂²×C₄	1	1	yes	characteristic
330	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
331	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
332	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
333	#131	—	2	4	no	—
334	#131	—	2	2	no	—
335	#131	—	2	2	no	—
336	C₂×M₁₆	—	2	4	no	—
337	C₂×M₁₆	—	2	4	no	—
338	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
339	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
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	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
344	C₂×M₁₆	C₂²×C₄	1	2	yes	—
345	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
353	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
354	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
355	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
356	C₂²×C₈	C₂²×C₄	1	2	yes	—
357	C₂²×C₈	C₂²×C₄	1	2	yes	—
358	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
359	C₂²×C₈	C₂²×C₄	1	2	yes	—
360	C₂²×C₈	C₂⁴	1	1	yes	characteristic
361	C₂²×C₈	C₂⁴	1	1	yes	characteristic
362	C₂²×C₈	C₂⁴	1	1	yes	characteristic
363	C₂²×C₈	C₂⁴	1	1	yes	characteristic
364	C₂²×C₈	C₂⁴	1	2	yes	—
365	C₂²×C₈	C₂⁴	1	1	yes	characteristic
366	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
367	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
368	#126	C₂×C₈	1	2	yes	—
369	#126	C₂×C₈	1	2	yes	—
370	#126	C₂×C₈	1	2	yes	—
371	#126	C₂×C₈	1	2	yes	—
372	#126	C₂×C₈	1	2	yes	—
373	#126	C₂×C₈	1	2	yes	—
374	#125	C₂×C₈	1	2	yes	—
375	#125	C₂×C₈	1	2	yes	—
376	#125	C₂×C₈	1	2	yes	—
377	#125	C₂×C₈	1	1	yes	characteristic
378	#125	C₂×C₈	1	1	yes	characteristic
379	#124	C₂×C₈	1	2	yes	—
380	#124	C₂×C₈	1	2	yes	—
381	#124	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	#123	C₂×C₈	1	2	yes	—
387	#123	C₂×C₈	1	2	yes	—
388	#123	C₂×C₈	1	2	yes	—
389	#123	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	1	yes	characteristic
393	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
395	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
396	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
397	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
398	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
399	#121	C₂×C₈	1	1	yes	characteristic
400	#121	C₂×C₈	1	1	yes	characteristic
401	#121	C₂×C₈	1	1	yes	characteristic
402	#121	C₂×C₈	1	1	yes	characteristic
403	#121	C₂×C₈	1	2	yes	—
404	#121	C₂×C₈	1	2	yes	—
405	#121	C₂×C₈	1	2	yes	—
406	#120	C₂×C₈	1	2	yes	—
407	#120	C₂×C₈	1	2	yes	—
408	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
409	C₄×Q₈	C₂×C₈	1	2	yes	—
410	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
411	C₄×Q₈	C₂²×C₄	1	2	yes	—
412	C₄×Q₈	C₂²×C₄	1	2	yes	—
413	C₄×D₄	C₂×C₈	1	1	yes	characteristic
414	C₄×D₄	C₂×C₈	1	1	yes	characteristic
415	C₄×D₄	C₂×C₈	1	1	yes	characteristic
416	C₄×D₄	C₂×C₈	1	1	yes	characteristic
417	C₄×D₄	C₂×C₈	1	2	yes	—
418	C₄×D₄	C₂×C₈	1	2	yes	—
419	C₄×D₄	C₂×C₈	1	1	yes	characteristic
420	C₄×D₄	C₂×C₈	1	2	yes	—
421	C₄×D₄	C₂×C₈	1	2	yes	—
422	C₄×D₄	C₂×C₈	1	2	yes	—
423	C₄×D₄	C₂×C₈	1	1	yes	characteristic
424	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
425	C₄×D₄	C₂²×C₄	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	2	yes	—
430	C₄×D₄	C₂²×C₄	1	2	yes	—
431	C₄×D₄	C₂²×C₄	1	2	yes	—
432	#117	C₂×C₈	1	2	yes	—
433	#117	C₂×C₈	1	2	yes	—
434	#117	C₂×C₈	1	1	yes	characteristic
435	#117	C₂×C₈	1	1	yes	characteristic
436	#117	C₂×C₈	1	1	yes	characteristic
437	#117	C₂×C₈	1	1	yes	characteristic
438	#117	C₂×C₈	1	2	yes	—
439	#117	C₂×C₈	1	2	yes	—
440	#117	C₂×C₈	1	2	yes	—
441	#117	C₂²×C₄	1	1	yes	characteristic
442	#117	C₂²×C₄	1	1	yes	characteristic
443	#117	C₂²×C₄	1	1	yes	characteristic
444	#117	C₂²×C₄	1	2	yes	—
445	#117	C₂²×C₄	1	2	yes	—
446	#117	C₂²×C₄	1	2	yes	—
447	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
456	C₂×C₄²	C₂²×C₄	1	2	yes	—
457	C₂×C₄²	C₂²×C₄	1	2	yes	—
458	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
459	C₂×C₄²	C₂²×C₄	1	2	yes	—
460	M₃₂	—	2	2	no	—
461	M₃₂	—	2	2	no	—
462	M₃₂	—	2	2	no	—
463	M₃₂	—	2	2	no	—
464	M₃₂	—	2	2	no	—
465	M₃₂	—	2	4	no	—
466	M₃₂	—	2	4	no	—
467	M₃₂	—	2	2	no	—
468	M₃₂	—	2	2	no	—
469	M₃₂	—	2	4	no	—
470	M₃₂	—	2	4	no	—
471	M₃₂	#41	1	4	yes	complemented
472	C₂×C₁₆	—	2	2	no	—
473	C₂×C₁₆	—	2	2	no	—
474	C₂×C₁₆	—	2	2	no	—
475	C₂×C₁₆	—	2	2	no	—
476	C₂×C₁₆	—	2	2	no	—
477	C₂×C₁₆	—	2	2	no	—
478	C₂×C₁₆	—	2	2	no	—
479	C₂×C₁₆	—	2	4	no	—
480	C₂×C₁₆	—	2	4	no	—
481	C₂×C₁₆	—	2	4	no	—
482	C₂×C₁₆	—	2	4	no	—
483	C₂×C₁₆	#41	1	4	yes	complemented
484	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
485	C₂×C₁₆	C₂⁴	1	2	yes	—
486	C₂×C₁₆	C₂⁴	1	2	yes	—
487	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
488	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
489	C₂×C₁₆	C₂⁴	1	2	yes	—
490	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
491	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
492	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
493	C₂×C₁₆	C₂⁴	1	2	yes	—
494	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
495	C₂×C₁₆	C₂⁴	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	1	yes	characteristic
499	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
500	C₄⋊C₈	C₂²×C₄	1	2	yes	—
501	C₄⋊C₈	C₂²×C₄	1	2	yes	—
502	C₄⋊C₈	C₂²×C₄	1	2	yes	—
503	C₄⋊C₈	C₂²×C₄	1	2	yes	—
504	C₄⋊C₈	C₂²×C₄	1	2	yes	—
505	C₄⋊C₈	C₂²×C₄	1	2	yes	—
506	C₄⋊C₈	C₂²×C₄	1	2	yes	—
507	C₄⋊C₈	C₂²×C₄	1	2	yes	—
508	C₄⋊C₈	C₂²×C₄	1	2	yes	—
509	C₄⋊C₈	C₂²×C₄	1	2	yes	—
510	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
511	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
512	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
513	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
514	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
515	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
523	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
524	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
525	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
526	#97	C₂²×C₄	1	2	yes	—
527	#97	C₂²×C₄	1	2	yes	—
528	#97	C₂²×C₄	1	2	yes	—
529	#97	C₂²×C₄	1	2	yes	—
530	#97	C₂²×C₄	1	2	yes	—
531	#97	C₂²×C₄	1	2	yes	—
532	#97	C₂²×C₄	1	2	yes	—
533	#97	C₂²×C₄	1	2	yes	—
534	#97	C₂²×C₄	1	2	yes	—
535	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
536	C₄×C₈	C₂²×C₄	1	2	yes	—
537	C₄×C₈	C₂²×C₄	1	2	yes	—
538	C₄×C₈	C₂²×C₄	1	2	yes	—
539	C₄×C₈	C₂²×C₄	1	2	yes	—
540	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
541	C₄×C₈	C₂²×C₄	1	2	yes	—
542	C₄×C₈	C₂²×C₄	1	2	yes	—
543	C₄×C₈	C₂⁴	1	2	yes	—
544	C₄×C₈	C₂⁴	1	2	yes	—
545	C₄×C₈	C₂⁴	1	1	yes	characteristic
546	C₄×C₈	C₂⁴	1	2	yes	—
547	C₄×C₈	C₂⁴	1	1	yes	characteristic
548	C₂⁴	C₂²×C₈	1	1	yes	characteristic
549	C₂⁴	C₂²×C₈	1	1	yes	characteristic
550	#41	—	2	2	no	—
551	#41	—	2	2	no	—
552	#41	—	4	4	no	—
553	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
554	C₂×Q₈	C₂²×C₈	1	2	yes	—
555	C₂×Q₈	C₂²×C₈	1	2	yes	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
558	C₂×D₄	C₂²×C₈	1	2	yes	—
559	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
560	C₂×D₄	C₂²×C₈	1	2	yes	—
561	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
562	C₂×D₄	C₂²×C₈	1	2	yes	—
563	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
564	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
565	C₂×D₄	C₂²×C₈	1	2	yes	—
566	C₂×D₄	C₂²×C₈	1	2	yes	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	C₂²×C₈	1	2	yes	—
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	1	yes	characteristic
576	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
577	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
578	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
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	C₂²×C₈	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₈	1	2	yes	—
584	C₂²×C₄	C₂²×C₈	1	2	yes	—
585	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
586	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
587	C₂²×C₄	C₂³×C₄	1	2	yes	—
588	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
589	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
590	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
591	M₁₆	—	2	2	no	—
592	M₁₆	—	2	2	no	—
593	M₁₆	—	2	2	no	—
594	M₁₆	—	2	4	no	—
595	M₁₆	—	2	4	no	—
596	M₁₆	—	2	4	no	—
597	M₁₆	—	2	4	no	—
598	M₁₆	#131	1	4	yes	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	2	no	—
602	C₂×C₈	—	2	2	no	—
603	C₂×C₈	—	2	2	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	4	no	—
607	C₂×C₈	—	2	4	no	—
608	C₂×C₈	—	2	4	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
620	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
621	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
622	C₂×C₈	C₂³×C₄	1	2	yes	—
623	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
624	C₂×C₈	C₂³×C₄	1	2	yes	—
625	C₂×C₈	C₂³×C₄	1	2	yes	—
626	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
627	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
628	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
629	C₂×C₈	C₂³×C₄	1	2	yes	—
630	C₂×C₈	C₂×#41	1	2	yes	—
631	C₂×C₈	C₂×#41	1	2	yes	—
632	C₂×C₈	C₂⁵	1	1	yes	characteristic
633	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
634	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
645	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
646	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
647	C₄⋊C₄	C₂²×C₈	1	2	yes	—
648	C₄⋊C₄	C₂²×C₈	1	2	yes	—
649	C₄⋊C₄	C₂²×C₈	1	2	yes	—
650	C₄⋊C₄	C₂²×C₈	1	2	yes	—
651	C₄⋊C₄	C₂²×C₈	1	2	yes	—
652	C₄⋊C₄	C₂²×C₈	1	2	yes	—
653	C₄⋊C₄	C₂²×C₈	1	2	yes	—
654	C₄⋊C₄	C₂²×C₈	1	2	yes	—
655	C₄⋊C₄	C₂²×C₈	1	2	yes	—
656	C₄⋊C₄	C₂²×C₈	1	2	yes	—
657	C₄⋊C₄	C₂²×C₈	1	2	yes	—
658	C₄⋊C₄	C₂²×C₈	1	2	yes	—
659	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
660	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
661	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
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	1	yes	characteristic
669	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
670	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
671	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
672	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
673	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
674	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
675	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
676	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
677	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
678	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
679	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
680	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
681	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
682	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
683	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
684	C₄²	C₂²×C₈	1	2	yes	—
685	C₄²	C₂²×C₈	1	2	yes	—
686	C₄²	C₂²×C₈	1	2	yes	—
687	C₄²	C₂²×C₈	1	2	yes	—
688	C₄²	C₂²×C₈	1	2	yes	—
689	C₄²	C₂²×C₈	1	1	yes	characteristic
690	C₄²	C₂²×C₈	1	1	yes	characteristic
691	C₄²	C₂²×C₈	1	2	yes	—
692	C₄²	C₂³×C₄	1	2	yes	—
693	C₄²	C₂³×C₄	1	1	yes	characteristic
694	C₄²	C₂³×C₄	1	1	yes	characteristic
695	C₄²	C₂³×C₄	1	2	yes	—
696	C₄²	C₂³×C₄	1	2	yes	—
697	C₁₆	—	2	1	no	—
698	C₁₆	—	2	1	no	—
699	C₁₆	—	2	1	no	—
700	C₁₆	—	2	1	no	—
701	C₁₆	—	2	1	no	—
702	C₁₆	—	2	1	no	—
703	C₁₆	—	2	2	no	—
704	C₁₆	—	2	2	no	—
705	C₁₆	—	2	2	no	—
706	C₁₆	C₂×#41	1	2	yes	—
707	C₁₆	C₂×#41	1	4	yes	—
708	C₁₆	C₂×#41	1	2	yes	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	C₂³×C₈	1	1	yes	characteristic
716	C₂³	C₂³×C₈	1	1	yes	characteristic
717	C₂³	C₂³×C₈	1	2	yes	—
718	C₂³	C₂³×C₈	1	1	yes	characteristic
719	C₂³	C₂³×C₈	1	1	yes	characteristic
720	C₂³	C₂³×C₈	1	1	yes	characteristic
721	Q₈	—	2	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	4	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	4	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	C₄×#41	1	2	yes	—
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	1	yes	characteristic
763	C₂×C₄	C₂³×C₈	1	2	yes	—
764	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
765	C₂×C₄	C₂³×C₈	1	2	yes	—
766	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
767	C₂×C₄	C₂³×C₈	1	2	yes	—
768	C₂×C₄	C₂³×C₈	1	2	yes	—
769	C₂×C₄	C₂³×C₈	1	2	yes	—
770	C₂×C₄	C₂³×C₈	1	2	yes	—
771	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
772	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
773	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
774	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
775	C₂×C₄	C₂×#131	1	2	yes	—
776	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
777	C₈	—	2	1	no	—
778	C₈	—	2	1	no	—
779	C₈	—	2	1	no	—
780	C₈	—	2	1	no	—
781	C₈	—	2	2	no	—
782	C₈	—	2	1	no	—
783	C₈	—	2	1	no	—
784	C₈	—	2	2	no	—
785	C₈	—	2	2	no	—
786	C₈	C₄×#41	1	2	yes	—
787	C₈	C₂×#131	1	4	yes	—
788	C₈	C₂²×#41	1	1	yes	characteristic
789	C₈	C₂²×#41	1	1	yes	characteristic
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	8	2	no	—
808	C₂²	C₈×#41	1	2	yes	—
809	C₂²	#3407	1	2	yes	—
810	C₂²	C₂⁴×C₈	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	1	no	—
826	C₄	C₈×#41	1	2	yes	—
827	C₄	C₂×C₄×#41	1	1	yes	characteristic
828	C₄	C₂²×#131	1	1	yes	characteristic
829	C₂	—	2	2	no	—
830	C₂	—	2	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	4	1	no	—
834	C₂	—	4	1	no	—
835	C₂	C₂×C₈×#41	1	1	yes	characteristic
836	C₂	C₂×#3407	1	1	yes	characteristic
837	C₂	#62624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₈	C₂⁵
commutator, socle	C₂²	C₂⁴×C₈
prime radical	#3475	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. #33484	C₂	semidirect
3. #33483	C₂	semidirect
4. #33482	C₂	semidirect
5. #33482	C₂	semidirect
6. #33481	C₂	semidirect
7. #33481	C₂	semidirect
8. #33480	C₂	semidirect
9. #33479	C₂	semidirect
10. #33476	C₂	semidirect
11. #33475	C₂	semidirect
12. D₄×M₃₂	C₂	semidirect
13. #33436	C₂	semidirect
14. #33436	C₂	semidirect
15. #33433	C₂	semidirect
16. #33432	C₂	semidirect
17. C₂×#2168	C₂	semidirect
18. #33423	C₂	semidirect
19. #33422	C₂	semidirect
20. #33422	C₂	semidirect
21. #33326	C₂	semidirect
22. #33324	C₂	semidirect
23. C₂×#2108	C₂	semidirect
53. #2183	C₂²	semidirect
54. #2183	C₂²	semidirect
55. #2183	C₂²	semidirect
56. #2183	C₂²	semidirect
57. #2183	C₂²	semidirect
58. #2183	C₂²	semidirect
59. #2183	C₂²	semidirect
60. Q₈×C₁₆	C₂²	semidirect
62. #2169	C₂²	semidirect
63. #2169	C₂²	semidirect
64. #2169	C₂²	semidirect
65. #2169	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
85. D₄×C₁₆	C₂²	semidirect
86. D₄×C₁₆	C₂²	semidirect
87. D₄×C₁₆	C₂²	semidirect
88. D₄×C₁₆	C₂²	semidirect
89. #2164	C₂²	semidirect
90. #2164	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. #2162	C₂²	semidirect
100. #2162	C₂²	semidirect
121. #2108	C₂²	semidirect
122. #2108	C₂²	semidirect
123. #2108	C₂²	semidirect
124. #2108	C₂²	semidirect
125. #2108	C₂²	semidirect
126. #2108	C₂²	semidirect
128. C₄×M₃₂	C₂²	semidirect
129. C₄×M₃₂	C₂²	semidirect
130. C₄×M₃₂	C₂²	semidirect
132. C₂×#346	C₂²	semidirect
133. C₂×#346	C₂²	semidirect
134. C₂×C₄×C₁₆	C₂²	semidirect
471. M₃₂	#41	semidirect
483. C₂×C₁₆	#41	semidirect

Maximal subgroups

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

subgroup	index
#60215	2
#33484	2
#33483	2
#33482	2
#33481	2
#33480	2
#33479	2
#33476	2
#33475	2
D₄×M₃₂	2
#33436	2
#33433	2
#33432	2
C₂×#2168	2
#33423	2
#33422	2
#33326	2
#33324	2
C₂×#2108	2