Subgroups — #7622754

Order 512.

1245 conjugacy classes of subgroups.

The subgroup lattice has 807 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	#33509	C₂	1	2	yes	maximal, complemented
3	#33508	C₂	1	1	yes	maximal, characteristic, complemented
4	#33507	C₂	1	1	yes	maximal, characteristic, complemented
5	#33507	C₂	1	2	yes	maximal, complemented
6	#33505	C₂	1	1	yes	maximal, characteristic, complemented
7	#33503	C₂	1	1	yes	maximal, characteristic, complemented
8	#33500	C₂	1	1	yes	maximal, characteristic, complemented
9	#33499	C₂	1	1	yes	maximal, characteristic, complemented
10	#33492	C₂	1	2	yes	maximal, complemented
11	#33490	C₂	1	2	yes	maximal, complemented
12	#33489	C₂	1	1	yes	maximal, characteristic, complemented
13	#33488	C₂	1	1	yes	maximal, characteristic, complemented
14	#33485	C₂	1	1	yes	maximal, characteristic, complemented
15	#33483	C₂	1	1	yes	maximal, characteristic, complemented
16	#33483	C₂	1	2	yes	maximal, complemented
17	#33481	C₂	1	2	yes	maximal, complemented
18	#33480	C₂	1	1	yes	maximal, characteristic, complemented
19	#33479	C₂	1	1	yes	maximal, characteristic, complemented
20	#33423	C₂	1	1	yes	maximal, characteristic, complemented
21	#33422	C₂	1	2	yes	maximal, complemented
22	#33420	C₂	1	1	yes	maximal, characteristic, complemented
23	#33419	C₂	1	2	yes	maximal, complemented
24	#3475	C₄	1	1	yes	characteristic
25	#2970	C₄	1	1	yes	characteristic
26	#2970	C₄	1	1	yes	characteristic
27	#2969	C₄	1	1	yes	characteristic
28	#2969	C₄	1	1	yes	characteristic
29	#2968	C₄	1	2	yes	—
30	#2968	C₄	1	2	yes	—
31	#2966	C₂²	1	1	yes	characteristic
32	#2966	C₂²	1	2	yes	—
33	#2966	C₂²	1	1	yes	characteristic
34	#2966	C₂²	1	2	yes	—
35	C₈×#41	C₂²	1	1	yes	characteristic
36	C₈×#41	C₂²	1	1	yes	characteristic
37	#2962	C₄	1	1	yes	characteristic
38	#2960	C₂²	1	1	yes	characteristic
39	D₄×M₁₆	C₄	1	1	yes	characteristic
40	#2933	C₄	1	2	yes	—
41	#2929	C₂²	1	2	yes	—
42	C₂×C₈×D₄	C₂²	1	1	yes	characteristic
43	#2925	C₄	1	1	yes	characteristic
44	#2924	C₄	1	2	yes	—
45	C₄×#131	C₂²	1	1	yes	characteristic
46	C₂×#405	C₂²	1	2	yes	—
47	#2183	C₂²	1	1	yes	characteristic, complemented
48	#2183	C₂²	1	1	yes	characteristic, complemented
49	#2183	C₂²	1	1	yes	characteristic, complemented
50	#2183	C₂²	1	2	yes	complemented
51	#2183	C₂²	1	2	yes	complemented
52	#2183	C₂²	1	2	yes	complemented
53	#2183	C₂²	1	1	yes	characteristic, complemented
54	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
55	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
56	Q₈×C₁₆	C₂²	1	2	yes	complemented
57	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
58	Q₈×C₁₆	C₂²	1	1	yes	characteristic, complemented
59	#2169	C₂²	1	1	yes	characteristic
60	#2169	C₂²	1	1	yes	characteristic
61	#2169	C₂²	1	1	yes	characteristic
62	#2169	C₂²	1	2	yes	—
63	#2169	C₂²	1	1	yes	characteristic
64	#2169	C₂²	1	2	yes	—
65	#2169	C₂²	1	1	yes	characteristic
66	#2169	C₂²	1	1	yes	characteristic
67	#2169	C₂²	1	2	yes	complemented
68	#2169	C₂²	1	2	yes	complemented
69	#2169	C₂²	1	2	yes	complemented
70	#2169	C₂²	1	2	yes	complemented
71	#2169	C₂²	1	2	yes	complemented
72	#2169	C₂²	1	2	yes	complemented
73	#2168	C₂²	1	2	yes	—
74	#2168	C₂²	1	2	yes	—
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	D₄×C₁₆	C₂²	1	1	yes	characteristic
84	D₄×C₁₆	C₂²	1	1	yes	characteristic
85	D₄×C₁₆	C₂²	1	2	yes	complemented
86	D₄×C₁₆	C₂²	1	2	yes	complemented
87	#2164	C₂²	1	1	yes	characteristic
88	#2164	C₂²	1	2	yes	—
89	#2164	C₂²	1	2	yes	—
90	#2164	C₂²	1	2	yes	—
91	#2164	C₂²	1	1	yes	characteristic
92	#2164	C₂²	1	2	yes	—
93	#2164	C₂²	1	2	yes	—
94	#2164	C₂²	1	2	yes	complemented
95	#2164	C₂²	1	2	yes	complemented
96	#2164	C₂²	1	2	yes	complemented
97	#2164	C₂²	1	2	yes	complemented
98	#2164	C₂²	1	1	yes	characteristic, complemented
99	#2164	C₂²	1	1	yes	characteristic, complemented
100	#2164	C₂²	1	2	yes	complemented
101	#2163	C₂²	1	1	yes	characteristic
102	#2163	C₂²	1	2	yes	complemented
103	#2163	C₂²	1	2	yes	complemented
104	#2163	C₂²	1	1	yes	characteristic, complemented
105	#2162	C₂²	1	1	yes	characteristic
106	#2162	C₂²	1	1	yes	characteristic
107	#2162	C₂²	1	1	yes	characteristic
108	#2162	C₂²	1	1	yes	characteristic, complemented
109	#2162	C₂²	1	1	yes	characteristic, complemented
110	#2162	C₂²	1	2	yes	complemented
111	#2162	C₂²	1	2	yes	complemented
112	#2162	C₂²	1	1	yes	characteristic, complemented
113	#2151	C₂²	1	1	yes	characteristic, complemented
114	#2151	C₂²	1	1	yes	characteristic, complemented
115	#2151	C₂²	1	2	yes	complemented
116	#2151	C₂²	1	2	yes	complemented
117	#2150	C₂²	1	2	yes	complemented
118	#2150	C₂²	1	2	yes	complemented
119	#2150	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
121	#2113	C₂²	1	1	yes	characteristic
122	#2113	C₂²	1	1	yes	characteristic
123	#2113	C₂²	1	2	yes	—
124	#2112	C₂²	1	2	yes	—
125	#2112	C₂²	1	2	yes	—
126	#2112	C₂²	1	2	yes	—
127	C₂×C₂²⋊C₁₆	C₂²	1	2	yes	—
128	#2108	C₂²	1	2	yes	complemented
129	#2108	C₂²	1	2	yes	complemented
130	#2108	C₂²	1	2	yes	complemented
131	C₄×M₃₂	C₂²	1	2	yes	complemented
132	C₄×M₃₂	C₂²	1	2	yes	complemented
133	C₄×M₃₂	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×#131	C₂×C₄	1	1	yes	characteristic
136	C₂×#131	C₂³	1	1	yes	characteristic
137	C₂²×M₁₆	C₂×C₄	1	2	yes	—
138	C₂³×C₈	C₂³	1	2	yes	—
139	#556	C₈	1	1	yes	characteristic
140	#555	C₈	1	1	yes	characteristic
141	#554	C₈	1	1	yes	characteristic
142	#553	C₈	1	2	yes	—
143	#552	C₈	1	2	yes	—
144	#552	C₈	1	1	yes	characteristic
145	#552	C₈	1	1	yes	characteristic
146	#551	C₈	1	2	yes	—
147	#551	C₈	1	2	yes	—
148	#547	C₈	1	1	yes	characteristic
149	#546	C₈	1	1	yes	characteristic
150	#546	C₈	1	1	yes	characteristic
151	#533	C₂×C₄	1	1	yes	characteristic
152	#529	C₂×C₄	1	2	yes	—
153	#529	C₂×C₄	1	2	yes	—
154	#529	C₂×C₄	1	1	yes	characteristic
155	#529	C₂×C₄	1	1	yes	characteristic
156	#525	C₂×C₄	1	2	yes	—
157	C₄×#41	C₂×C₄	1	1	yes	characteristic
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	C₂×#117	C₂×C₄	1	2	yes	—
162	C₂×M₃₂	C₂³	1	2	yes	—
163	C₂×M₃₂	C₂³	1	2	yes	—
164	C₂×M₃₂	C₂³	1	2	yes	—
165	C₂×M₃₂	C₂³	1	2	yes	—
166	C₂×M₃₂	C₂³	1	1	yes	characteristic
167	C₂×M₃₂	C₂³	1	1	yes	characteristic
168	C₂×M₃₂	C₂³	1	2	yes	—
169	C₂×M₃₂	C₂³	1	2	yes	—
170	C₂×M₃₂	C₂³	1	2	yes	—
171	C₂²×C₁₆	C₂³	1	1	yes	characteristic
172	C₂²×C₁₆	C₂³	1	1	yes	characteristic
173	C₂²×C₁₆	C₂³	1	2	yes	—
174	C₂²×C₁₆	C₂³	1	2	yes	—
175	C₂²×C₁₆	C₂³	1	2	yes	—
176	#446	C₂×C₄	1	2	yes	—
177	#446	C₂×C₄	1	1	yes	characteristic
178	#446	C₂×C₄	1	1	yes	characteristic
179	#446	C₂×C₄	1	2	yes	—
180	#446	C₂×C₄	1	2	yes	—
181	#446	C₂×C₄	1	1	yes	characteristic
182	#446	C₂×C₄	1	1	yes	characteristic
183	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
184	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
185	C₈×Q₈	C₂³	1	1	yes	characteristic
186	C₈×Q₈	C₂³	1	1	yes	characteristic
187	C₈×Q₈	C₂³	1	2	yes	—
188	#436	C₂×C₄	1	2	yes	—
189	#436	C₂×C₄	1	2	yes	—
190	#436	C₂×C₄	1	1	yes	characteristic
191	#436	C₂×C₄	1	1	yes	characteristic
192	#435	C₂×C₄	1	2	yes	—
193	#435	C₂×C₄	1	2	yes	—
194	#435	C₂×C₄	1	2	yes	—
195	#435	C₂×C₄	1	2	yes	—
196	#435	C₂×C₄	1	2	yes	—
197	#435	C₂×C₄	1	2	yes	—
198	#435	C₂×C₄	1	2	yes	—
199	#435	C₂×C₄	1	2	yes	—
200	#435	C₂×C₄	1	2	yes	—
201	#435	C₂×C₄	1	2	yes	—
202	C₈×D₄	C₂×C₄	1	2	yes	—
203	C₈×D₄	C₂×C₄	1	1	yes	characteristic
204	C₈×D₄	C₂×C₄	1	1	yes	characteristic
205	C₈×D₄	C₂×C₄	1	2	yes	—
206	C₈×D₄	C₂×C₄	1	2	yes	—
207	C₈×D₄	C₂×C₄	1	1	yes	characteristic
208	C₈×D₄	C₂×C₄	1	1	yes	characteristic
209	C₈×D₄	C₂³	1	1	yes	characteristic
210	C₈×D₄	C₂³	1	2	yes	—
211	C₈×D₄	C₂³	1	1	yes	characteristic
212	C₈×D₄	C₂³	1	2	yes	—
213	C₈×D₄	C₂³	1	2	yes	—
214	C₈×D₄	C₂³	1	2	yes	—
215	C₈×D₄	C₂³	1	2	yes	—
216	#433	C₂×C₄	1	2	yes	—
217	#433	C₂×C₄	1	2	yes	—
218	#433	C₂×C₄	1	2	yes	—
219	#433	C₂×C₄	1	2	yes	—
220	#433	C₂×C₄	1	2	yes	—
221	#433	C₂×C₄	1	2	yes	—
222	#432	C₂×C₄	1	2	yes	—
223	#432	C₂×C₄	1	2	yes	—
224	#432	C₂×C₄	1	1	yes	characteristic
225	#432	C₂×C₄	1	1	yes	characteristic
226	#431	C₂×C₄	1	2	yes	—
227	#431	C₂×C₄	1	2	yes	—
228	#431	C₂×C₄	1	1	yes	characteristic
229	#431	C₂×C₄	1	1	yes	characteristic
230	#424	C₂×C₄	1	2	yes	—
231	#424	C₂×C₄	1	2	yes	—
232	#423	C₂×C₄	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
234	#408	C₂×C₄	1	2	yes	—
235	#407	C₂×C₄	1	2	yes	—
236	C₂×C₂²⋊C₈	C₂×C₄	1	2	yes	—
237	#405	C₂×C₄	1	2	yes	—
238	#405	C₂×C₄	1	2	yes	—
239	#405	C₂×C₄	1	2	yes	—
240	#405	C₂×C₄	1	2	yes	—
241	#405	C₂×C₄	1	1	yes	characteristic
242	#405	C₂×C₄	1	1	yes	characteristic
243	#405	C₂×C₄	1	1	yes	characteristic
244	#405	C₂³	1	1	yes	characteristic
245	#405	C₂³	1	2	yes	—
246	#405	C₂³	1	2	yes	—
247	#405	C₂³	1	2	yes	—
248	#405	C₂³	1	1	yes	characteristic
249	#405	C₂³	1	1	yes	characteristic
250	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
251	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
252	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
253	C₂×#97	C₂×C₄	1	2	yes	—
254	C₂×#97	C₂×C₄	1	2	yes	—
255	C₂×C₄×C₈	C₂³	1	2	yes	—
256	C₂×C₄×C₈	C₂³	1	2	yes	—
257	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
260	C₄⋊C₁₆	C₂³	1	2	yes	—
261	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
262	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
264	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
265	C₄⋊C₁₆	C₂³	1	2	yes	—
266	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
267	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
268	C₄⋊C₁₆	C₂³	1	2	yes	—
269	C₄⋊C₁₆	C₂³	1	2	yes	—
270	C₄⋊C₁₆	C₂³	1	2	yes	—
271	C₄⋊C₁₆	C₂³	1	2	yes	—
272	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
273	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
274	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
275	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
276	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
277	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
278	C₄⋊C₁₆	C₂³	1	2	yes	—
279	C₄⋊C₁₆	C₂³	1	2	yes	—
280	C₄⋊C₁₆	C₂³	1	2	yes	—
281	C₄⋊C₁₆	C₂³	1	2	yes	—
282	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
283	C₂²⋊C₁₆	C₂³	1	2	yes	—
284	C₂²⋊C₁₆	C₂³	1	2	yes	—
285	C₂²⋊C₁₆	C₂³	1	2	yes	—
286	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
287	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
288	C₂²⋊C₁₆	C₂³	1	2	yes	—
289	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
290	C₂²⋊C₁₆	C₂³	1	2	yes	—
291	C₂²⋊C₁₆	C₂³	1	2	yes	—
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	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	1	yes	characteristic
301	C₂²⋊C₁₆	C₂³	1	2	yes	—
302	#346	C₂³	1	1	yes	characteristic
303	#346	C₂³	1	2	yes	—
304	#346	C₂³	1	1	yes	characteristic
305	#346	C₂³	1	2	yes	—
306	#346	C₂³	1	2	yes	—
307	#346	C₂³	1	2	yes	—
308	#346	C₂³	1	2	yes	—
309	#346	C₂³	1	2	yes	—
310	C₄×C₁₆	C₂³	1	1	yes	characteristic
311	C₄×C₁₆	C₂³	1	1	yes	characteristic
312	C₄×C₁₆	C₂³	1	1	yes	characteristic
313	C₄×C₁₆	C₂³	1	1	yes	characteristic
314	C₄×C₁₆	C₂³	1	2	yes	—
315	C₄×C₁₆	C₂³	1	1	yes	characteristic
316	C₄×C₁₆	C₂³	1	1	yes	characteristic
317	C₄×C₁₆	C₂³	1	2	yes	—
318	C₄×C₁₆	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	C₂×#41	C₂×C₈	1	1	yes	characteristic
323	C₂×#41	C₂×C₈	1	1	yes	characteristic
324	C₂×#41	C₂²×C₄	1	1	yes	characteristic
325	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
326	C₂³×C₄	C₂²×C₄	1	2	yes	—
327	#131	—	4	1	no	—
328	#131	—	4	1	no	—
329	#131	—	4	2	no	—
330	C₂×M₁₆	—	4	4	no	—
331	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
332	C₂×M₁₆	C₂²×C₄	1	2	yes	—
333	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×C₄	1	2	yes	—
335	C₂×M₁₆	C₂²×C₄	1	2	yes	—
336	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
337	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
339	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
340	C₂²×C₈	—	4	2	no	—
341	C₂²×C₈	—	4	2	no	—
342	C₂²×C₈	C₂²×C₄	1	2	yes	—
343	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₈	C₂²×C₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
351	C₂²×C₈	C₂⁴	1	2	yes	—
352	C₂²×C₈	C₂⁴	1	2	yes	—
353	C₂²×C₈	C₂⁴	1	1	yes	characteristic
354	C₂²×C₈	C₂⁴	1	1	yes	characteristic
355	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
356	C₄⋊Q₈	C₂×C₈	1	1	yes	characteristic
357	#126	C₂×C₈	1	2	yes	—
358	#126	C₂×C₈	1	2	yes	—
359	#126	C₂×C₈	1	2	yes	—
360	#126	C₂×C₈	1	2	yes	—
361	#126	C₂×C₈	1	2	yes	—
362	#126	C₂×C₈	1	2	yes	—
363	#125	C₂×C₈	1	2	yes	—
364	#125	C₂×C₈	1	2	yes	—
365	#125	C₂×C₈	1	1	yes	characteristic
366	#125	C₂×C₈	1	1	yes	characteristic
367	#125	C₂×C₈	1	2	yes	—
368	#124	C₂×C₈	1	1	yes	characteristic
369	#124	C₂×C₈	1	1	yes	characteristic
370	#124	C₂×C₈	1	2	yes	—
371	#124	C₂×C₈	1	2	yes	—
372	#123	C₂×C₈	1	2	yes	—
373	#123	C₂×C₈	1	2	yes	—
374	#123	C₂×C₈	1	2	yes	—
375	#123	C₂×C₈	1	2	yes	—
376	#123	C₂×C₈	1	2	yes	—
377	#123	C₂×C₈	1	2	yes	—
378	#123	C₂×C₈	1	2	yes	—
379	#123	C₂×C₈	1	2	yes	—
380	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
381	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
382	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
383	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
385	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
386	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
387	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
388	C₂²⋊Q₈	C₂×C₈	1	2	yes	—
389	#121	C₂×C₈	1	2	yes	—
390	#121	C₂×C₈	1	2	yes	—
391	#121	C₂×C₈	1	2	yes	—
392	#121	C₂×C₈	1	2	yes	—
393	#121	C₂×C₈	1	1	yes	characteristic
394	#121	C₂×C₈	1	1	yes	characteristic
395	#120	C₂×C₈	1	2	yes	—
396	#120	C₂×C₈	1	2	yes	—
397	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
398	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
399	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
400	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
401	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
402	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
403	C₄×Q₈	C₂²×C₄	1	2	yes	—
404	C₄×D₄	C₂×C₈	1	1	yes	characteristic
405	C₄×D₄	C₂×C₈	1	2	yes	—
406	C₄×D₄	C₂×C₈	1	1	yes	characteristic
407	C₄×D₄	C₂×C₈	1	1	yes	characteristic
408	C₄×D₄	C₂×C₈	1	1	yes	characteristic
409	C₄×D₄	C₂×C₈	1	1	yes	characteristic
410	C₄×D₄	C₂×C₈	1	1	yes	characteristic
411	C₄×D₄	C₂×C₈	1	1	yes	characteristic
412	C₄×D₄	C₂×C₈	1	1	yes	characteristic
413	C₄×D₄	C₂×C₈	1	1	yes	characteristic
414	C₄×D₄	C₂×C₈	1	2	yes	—
415	C₄×D₄	C₂×C₈	1	2	yes	—
416	C₄×D₄	C₂×C₈	1	1	yes	characteristic
417	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
418	C₄×D₄	C₂²×C₄	1	2	yes	—
419	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
420	C₄×D₄	C₂²×C₄	1	2	yes	—
421	C₄×D₄	C₂²×C₄	1	2	yes	—
422	C₄×D₄	C₂²×C₄	1	2	yes	—
423	C₄×D₄	C₂²×C₄	1	2	yes	—
424	#117	C₂×C₈	1	2	yes	—
425	#117	C₂×C₈	1	2	yes	—
426	#117	C₂×C₈	1	2	yes	—
427	#117	C₂×C₈	1	2	yes	—
428	#117	C₂×C₈	1	2	yes	—
429	#117	C₂×C₈	1	2	yes	—
430	#117	C₂×C₈	1	1	yes	characteristic
431	#117	C₂×C₈	1	1	yes	characteristic
432	#117	C₂²×C₄	1	1	yes	characteristic
433	#117	C₂²×C₄	1	2	yes	—
434	#117	C₂²×C₄	1	2	yes	—
435	#117	C₂²×C₄	1	2	yes	—
436	#117	C₂²×C₄	1	1	yes	characteristic
437	#117	C₂²×C₄	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
439	C₂×C₄⋊C₄	C₂×C₈	1	2	yes	—
440	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂×C₈	1	2	yes	—
444	C₂×C₄²	C₂²×C₄	1	2	yes	—
445	C₂×C₄²	C₂²×C₄	1	2	yes	—
446	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
447	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
448	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
449	M₃₂	—	4	1	no	—
450	M₃₂	—	4	2	no	—
451	M₃₂	—	4	2	no	—
452	M₃₂	—	4	2	no	—
453	M₃₂	—	4	2	no	—
454	M₃₂	—	4	2	no	—
455	M₃₂	—	4	2	no	—
456	M₃₂	—	4	1	no	—
457	M₃₂	—	4	2	no	—
458	C₂×C₁₆	—	4	2	no	—
459	C₂×C₁₆	—	4	1	no	—
460	C₂×C₁₆	—	4	2	no	—
461	C₂×C₁₆	—	4	2	no	—
462	C₂×C₁₆	—	4	1	no	—
463	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
464	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
465	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
466	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
467	C₂×C₁₆	C₂⁴	1	2	yes	—
468	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
469	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
470	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
471	C₂×C₁₆	C₂⁴	1	2	yes	—
472	C₂×C₁₆	C₂⁴	1	2	yes	—
473	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
474	C₂×C₁₆	C₂⁴	1	2	yes	—
475	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
476	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
477	C₄⋊C₈	C₂²×C₄	1	2	yes	—
478	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
479	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
480	C₄⋊C₈	C₂²×C₄	1	2	yes	—
481	C₄⋊C₈	C₂²×C₄	1	2	yes	—
482	C₄⋊C₈	C₂²×C₄	1	2	yes	—
483	C₄⋊C₈	C₂²×C₄	1	2	yes	—
484	C₄⋊C₈	C₂²×C₄	1	2	yes	—
485	C₄⋊C₈	C₂²×C₄	1	2	yes	—
486	C₄⋊C₈	C₂²×C₄	1	2	yes	—
487	C₄⋊C₈	C₂²×C₄	1	2	yes	—
488	C₄⋊C₈	C₂²×C₄	1	2	yes	—
489	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
490	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
491	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
492	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
493	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
494	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
495	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
496	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
497	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
498	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
499	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
500	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
501	#97	C₂²×C₄	1	1	yes	characteristic
502	#97	C₂²×C₄	1	1	yes	characteristic
503	#97	C₂²×C₄	1	2	yes	—
504	#97	C₂²×C₄	1	2	yes	—
505	#97	C₂²×C₄	1	2	yes	—
506	#97	C₂²×C₄	1	2	yes	—
507	#97	C₂²×C₄	1	2	yes	—
508	#97	C₂²×C₄	1	2	yes	—
509	#97	C₂²×C₄	1	1	yes	characteristic
510	#97	C₂²×C₄	1	1	yes	characteristic
511	#97	C₂²×C₄	1	1	yes	characteristic
512	#97	C₂²×C₄	1	1	yes	characteristic
513	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
514	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
515	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
516	C₄×C₈	C₂²×C₄	1	2	yes	—
517	C₄×C₈	C₂²×C₄	1	2	yes	—
518	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
519	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
520	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
521	C₄×C₈	C₂²×C₄	1	2	yes	—
522	C₄×C₈	C₂²×C₄	1	2	yes	—
523	C₄×C₈	C₂⁴	1	1	yes	characteristic
524	C₄×C₈	C₂⁴	1	1	yes	characteristic
525	C₄×C₈	C₂⁴	1	2	yes	—
526	C₄×C₈	C₂⁴	1	1	yes	characteristic
527	C₄×C₈	C₂⁴	1	2	yes	—
528	C₄×C₈	C₂⁴	1	1	yes	characteristic
529	C₂⁴	C₂²×C₈	1	2	yes	—
530	#41	—	4	1	no	—
531	#41	—	4	1	no	—
532	#41	—	4	2	no	—
533	#41	—	4	2	no	—
534	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
535	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
536	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
537	C₂×Q₈	C₂²×C₈	1	2	yes	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
540	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
541	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
542	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
543	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
544	C₂×D₄	C₂²×C₈	1	2	yes	—
545	C₂×D₄	C₂²×C₈	1	2	yes	—
546	C₂×D₄	C₂²×C₈	1	2	yes	—
547	C₂×D₄	C₂²×C₈	1	2	yes	—
548	C₂×D₄	C₂²×C₈	1	2	yes	—
549	C₂²×C₄	—	4	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
554	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
555	C₂²×C₄	C₂²×C₈	1	2	yes	—
556	C₂²×C₄	C₂²×C₈	1	2	yes	—
557	C₂²×C₄	C₂²×C₈	1	2	yes	—
558	C₂²×C₄	C₂²×C₈	1	2	yes	—
559	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₈	1	2	yes	—
562	C₂²×C₄	C₂²×C₈	1	2	yes	—
563	C₂²×C₄	C₂²×C₈	1	2	yes	—
564	C₂²×C₄	C₂³×C₄	1	2	yes	—
565	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
566	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
567	C₂²×C₄	C₂³×C₄	1	2	yes	—
568	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
569	M₁₆	—	2	2	no	—
570	M₁₆	—	2	4	no	—
571	M₁₆	—	2	2	no	—
572	M₁₆	—	4	2	no	—
573	M₁₆	—	4	2	no	—
574	M₁₆	—	4	1	no	—
575	M₁₆	—	4	1	no	—
576	M₁₆	—	4	1	no	—
577	M₁₆	—	4	1	no	—
578	C₂×C₈	—	2	4	no	—
579	C₂×C₈	—	2	2	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	2	no	—
582	C₂×C₈	—	2	2	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	4	2	no	—
591	C₂×C₈	—	4	2	no	—
592	C₂×C₈	—	4	2	no	—
593	C₂×C₈	—	4	2	no	—
594	C₂×C₈	—	4	1	no	—
595	C₂×C₈	—	4	1	no	—
596	C₂×C₈	C₂³×C₄	1	2	yes	—
597	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
598	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
599	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
600	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
601	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
602	C₂×C₈	C₂³×C₄	1	2	yes	—
603	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
604	C₂×C₈	C₂³×C₄	1	2	yes	—
605	C₂×C₈	C₂³×C₄	1	2	yes	—
606	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
607	C₂×C₈	C₂⁵	1	1	yes	characteristic
608	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
609	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
610	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
611	C₄⋊C₄	C₂²×C₈	1	2	yes	—
612	C₄⋊C₄	C₂²×C₈	1	2	yes	—
613	C₄⋊C₄	C₂²×C₈	1	2	yes	—
614	C₄⋊C₄	C₂²×C₈	1	2	yes	—
615	C₄⋊C₄	C₂²×C₈	1	2	yes	—
616	C₄⋊C₄	C₂²×C₈	1	2	yes	—
617	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
618	C₄⋊C₄	C₂²×C₈	1	2	yes	—
619	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
620	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
621	C₄⋊C₄	C₂²×C₈	1	2	yes	—
622	C₄⋊C₄	C₂²×C₈	1	2	yes	—
623	C₄⋊C₄	C₂²×C₈	1	2	yes	—
624	C₄⋊C₄	C₂²×C₈	1	2	yes	—
625	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
627	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
628	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
629	C₄⋊C₄	C₂²×C₈	1	2	yes	—
630	C₄⋊C₄	C₂²×C₈	1	2	yes	—
631	C₄⋊C₄	C₂²×C₈	1	2	yes	—
632	C₄⋊C₄	C₂²×C₈	1	2	yes	—
633	C₄⋊C₄	C₂²×C₈	1	2	yes	—
634	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
635	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
636	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
637	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
638	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
639	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
640	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
641	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
642	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
643	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
644	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
645	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
646	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
647	C₂²⋊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	1	yes	characteristic
651	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
652	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
653	C₂²⋊C₄	C₂²×C₈	1	1	yes	characteristic
654	C₂²⋊C₄	C₂²×C₈	1	2	yes	—
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	C₄²	C₂²×C₈	1	2	yes	—
659	C₄²	C₂²×C₈	1	2	yes	—
660	C₄²	C₂²×C₈	1	2	yes	—
661	C₄²	C₂²×C₈	1	2	yes	—
662	C₄²	C₂²×C₈	1	1	yes	characteristic
663	C₄²	C₂²×C₈	1	1	yes	characteristic
664	C₄²	C₂²×C₈	1	1	yes	characteristic
665	C₄²	C₂²×C₈	1	1	yes	characteristic
666	C₄²	C₂²×C₈	1	1	yes	characteristic
667	C₄²	C₂²×C₈	1	1	yes	characteristic
668	C₄²	C₂³×C₄	1	1	yes	characteristic
669	C₄²	C₂³×C₄	1	1	yes	characteristic
670	C₄²	C₂³×C₄	1	1	yes	characteristic
671	C₄²	C₂³×C₄	1	1	yes	characteristic
672	C₄²	C₂³×C₄	1	2	yes	—
673	C₄²	C₂³×C₄	1	2	yes	—
674	C₁₆	—	2	1	no	—
675	C₁₆	—	2	2	no	—
676	C₁₆	—	2	1	no	—
677	C₁₆	—	2	1	no	—
678	C₁₆	—	2	2	no	—
679	C₁₆	—	2	2	no	—
680	C₁₆	—	2	1	no	—
681	C₁₆	—	2	1	no	—
682	C₁₆	—	2	1	no	—
683	C₁₆	—	2	1	no	—
684	C₁₆	—	2	1	no	—
685	C₁₆	—	2	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	C₂³×C₈	1	2	yes	—
690	C₂³	C₂³×C₈	1	1	yes	characteristic
691	C₂³	C₂³×C₈	1	1	yes	characteristic
692	C₂³	C₂³×C₈	1	1	yes	characteristic
693	C₂³	C₂³×C₈	1	2	yes	—
694	Q₈	—	2	2	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	1	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	C₂³×C₈	1	2	yes	—
732	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
733	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
734	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
735	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
736	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
737	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
738	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
739	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
740	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
741	C₂×C₄	C₂³×C₈	1	2	yes	—
742	C₂×C₄	C₂³×C₈	1	2	yes	—
743	C₂×C₄	C₂³×C₈	1	2	yes	—
744	C₂×C₄	C₂³×C₈	1	2	yes	—
745	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
746	C₂×C₄	C₂³×C₈	1	2	yes	—
747	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
748	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
749	C₈	—	2	1	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	2	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	1	no	—
754	C₈	—	2	1	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	1	no	—
757	C₈	—	2	2	no	—
758	C₈	—	2	1	no	—
759	C₈	#568	1	2	yes	—
760	C₈	#585	1	1	yes	characteristic
761	C₈	#585	1	1	yes	characteristic
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	8	4	no	—
778	C₂²	C₂⁴×C₈	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	1	no	—
795	C₄	#3407	1	2	yes	—
796	C₄	#3428	1	1	yes	characteristic
797	C₄	C₂×#568	1	1	yes	characteristic
798	C₂	—	4	1	no	—
799	C₂	—	4	1	no	—
800	C₂	—	4	2	no	—
801	C₂	—	4	2	no	—
802	C₂	—	4	1	no	—
803	C₂	#60276	1	1	yes	characteristic
804	C₂	C₂×#3407	1	1	yes	characteristic
805	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. #33509	C₂	semidirect
3. #33508	C₂	semidirect
4. #33507	C₂	semidirect
5. #33507	C₂	semidirect
6. #33505	C₂	semidirect
7. #33503	C₂	semidirect
8. #33500	C₂	semidirect
9. #33499	C₂	semidirect
10. #33492	C₂	semidirect
11. #33490	C₂	semidirect
12. #33489	C₂	semidirect
13. #33488	C₂	semidirect
14. #33485	C₂	semidirect
15. #33483	C₂	semidirect
16. #33483	C₂	semidirect
17. #33481	C₂	semidirect
18. #33480	C₂	semidirect
19. #33479	C₂	semidirect
20. #33423	C₂	semidirect
21. #33422	C₂	semidirect
22. #33420	C₂	semidirect
23. #33419	C₂	semidirect
47. #2183	C₂²	semidirect
48. #2183	C₂²	semidirect
49. #2183	C₂²	semidirect
50. #2183	C₂²	semidirect
51. #2183	C₂²	semidirect
52. #2183	C₂²	semidirect
53. #2183	C₂²	semidirect
54. Q₈×C₁₆	C₂²	semidirect
55. Q₈×C₁₆	C₂²	semidirect
56. Q₈×C₁₆	C₂²	semidirect
57. Q₈×C₁₆	C₂²	semidirect
58. Q₈×C₁₆	C₂²	semidirect
67. #2169	C₂²	semidirect
68. #2169	C₂²	semidirect
69. #2169	C₂²	semidirect
70. #2169	C₂²	semidirect
71. #2169	C₂²	semidirect
72. #2169	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
85. D₄×C₁₆	C₂²	semidirect
86. D₄×C₁₆	C₂²	semidirect
94. #2164	C₂²	semidirect
95. #2164	C₂²	semidirect
96. #2164	C₂²	semidirect
97. #2164	C₂²	semidirect
98. #2164	C₂²	semidirect
99. #2164	C₂²	semidirect
100. #2164	C₂²	semidirect
102. #2163	C₂²	semidirect
103. #2163	C₂²	semidirect
104. #2163	C₂²	semidirect
108. #2162	C₂²	semidirect
109. #2162	C₂²	semidirect
110. #2162	C₂²	semidirect
111. #2162	C₂²	semidirect
112. #2162	C₂²	semidirect
113. #2151	C₂²	semidirect
114. #2151	C₂²	semidirect
115. #2151	C₂²	semidirect
116. #2151	C₂²	semidirect
117. #2150	C₂²	semidirect
118. #2150	C₂²	semidirect
119. #2150	C₂²	semidirect
120. C₂×C₄⋊C₁₆	C₂²	semidirect
128. #2108	C₂²	semidirect
129. #2108	C₂²	semidirect
130. #2108	C₂²	semidirect
131. C₄×M₃₂	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
#60215	2
#33509	2
#33508	2
#33507	2
#33505	2
#33503	2
#33500	2
#33499	2
#33492	2
#33490	2
#33489	2
#33488	2
#33485	2
#33483	2
#33481	2
#33480	2
#33479	2
#33423	2
#33422	2
#33420	2
#33419	2