Subgroups — #181106

Order 512.

1762 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
4	#7938	C₂	1	4	yes	maximal, complemented
5	#7937	C₂	1	4	yes	maximal, complemented
6	#7932	C₂	1	4	yes	maximal, complemented
7	C₂³×M₁₆	C₄	1	2	yes	—
8	C₂³×C₄²	C₂²	1	1	yes	characteristic
9	#2920	—	2	1	no	—
10	#2920	—	2	1	no	—
11	#2920	—	2	1	no	—
12	#2920	—	2	1	no	—
13	#2920	—	2	1	no	—
14	#2920	—	2	1	no	—
15	#2920	—	2	1	no	—
16	#2920	—	2	1	no	—
17	#2920	—	2	1	no	—
18	#2920	—	2	1	no	—
19	#2920	—	2	1	no	—
20	#2920	—	2	1	no	—
21	#2920	C₄	1	2	yes	—
22	#2920	C₄	1	2	yes	—
23	#2920	C₂²	1	2	yes	—
24	#2920	C₂²	1	2	yes	—
25	C₂×#432	—	2	1	no	—
26	C₂×#432	C₄	1	2	yes	—
27	C₂×#432	C₄	1	2	yes	—
28	C₂×#432	C₂²	1	2	yes	—
29	C₂×#431	—	2	1	no	—
30	C₂×#431	C₄	1	2	yes	—
31	C₂×#431	C₂²	1	2	yes	—
32	C₂×#431	C₂²	1	2	yes	—
33	C₂×#423	—	2	1	no	—
34	C₂×#423	C₂²	1	2	yes	—
35	C₂×#407	C₄	1	2	yes	—
36	C₂×#407	C₄	1	2	yes	—
37	C₂×C₄×M₁₆	—	2	1	no	—
38	C₂×C₄×M₁₆	—	2	1	no	—
39	C₂×C₄×M₁₆	—	2	1	no	—
40	C₂×C₄×M₁₆	—	2	1	no	—
41	C₂×C₄×M₁₆	—	2	1	no	—
42	C₂×C₄×M₁₆	—	2	1	no	—
43	C₂×C₄×M₁₆	—	2	1	no	—
44	C₂×C₄×M₁₆	C₄	1	2	yes	—
45	C₂×C₄×M₁₆	C₄	1	2	yes	—
46	C₂×C₄×M₁₆	C₄	1	2	yes	—
47	C₂×C₄×M₁₆	C₄	1	2	yes	—
48	C₂×C₄×M₁₆	C₂²	1	2	yes	—
49	C₂×C₄×M₁₆	C₂²	1	2	yes	—
50	C₂×C₄×M₁₆	C₂²	1	2	yes	—
51	C₂²×#97	—	2	1	no	—
52	C₂²×C₄×C₈	—	2	1	no	—
53	#1283	C₂²	1	16	yes	complemented
54	C₂⁴×C₄	C₂×C₄	1	1	yes	characteristic
55	C₂⁴×C₄	C₂×C₄	1	1	yes	characteristic
56	C₂⁴×C₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×M₁₆	—	2	2	no	—
58	C₂²×M₁₆	—	2	2	no	—
59	C₂²×M₁₆	—	2	2	no	—
60	C₂²×M₁₆	—	2	16	no	—
61	C₂²×M₁₆	—	2	2	no	—
62	C₂²×M₁₆	C₂×C₄	1	4	yes	—
63	C₂²×M₁₆	C₂×C₄	1	4	yes	—
64	C₂²×M₁₆	C₂×C₄	1	4	yes	—
65	C₂²×M₁₆	C₂×C₄	1	4	yes	—
66	C₂³×C₈	—	2	2	no	—
67	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₄²	D₄	1	1	yes	characteristic
77	C₂²×C₄²	D₄	1	1	yes	characteristic
78	C₂²×C₄²	D₄	1	1	yes	characteristic
79	C₂²×C₄²	D₄	1	1	yes	characteristic
80	C₂²×C₄²	D₄	1	1	yes	characteristic
81	C₂²×C₄²	D₄	1	1	yes	characteristic
82	C₂²×C₄²	D₄	1	1	yes	characteristic
83	C₂²×C₄²	D₄	1	1	yes	characteristic
84	C₂²×C₄²	D₄	1	1	yes	characteristic
85	C₂²×C₄²	D₄	1	1	yes	characteristic
86	C₂²×C₄²	D₄	1	1	yes	characteristic
87	C₂²×C₄²	D₄	1	1	yes	characteristic
88	C₂²×C₄²	Q₈	1	1	yes	characteristic
89	C₂²×C₄²	Q₈	1	1	yes	characteristic
90	C₂²×C₄²	Q₈	1	1	yes	characteristic
91	C₂²×C₄²	Q₈	1	1	yes	characteristic
92	C₂²×C₄²	C₂³	1	1	yes	characteristic
93	C₂²×C₄²	C₂³	1	1	yes	characteristic
94	C₂²×C₄²	C₂³	1	1	yes	characteristic
95	#432	—	2	2	no	—
96	#432	—	2	2	no	—
97	#432	—	2	2	no	—
98	#432	—	2	2	no	—
99	#432	—	2	2	no	—
100	#432	—	2	2	no	—
101	#432	—	2	2	no	—
102	#432	—	2	2	no	—
103	#432	—	2	2	no	—
104	#432	—	2	2	no	—
105	#432	—	2	2	no	—
106	#432	—	2	2	no	—
107	#432	—	2	2	no	—
108	#432	—	2	2	no	—
109	#432	C₂×C₄	1	4	yes	—
110	#432	C₂×C₄	1	4	yes	—
111	#431	—	2	2	no	—
112	#431	—	2	2	no	—
113	#431	—	2	2	no	—
114	#431	—	2	2	no	—
115	#431	—	2	2	no	—
116	#431	—	2	2	no	—
117	#431	—	2	2	no	—
118	#431	—	2	2	no	—
119	#431	—	2	2	no	—
120	#431	—	2	2	no	—
121	#431	—	2	2	no	—
122	#431	—	2	2	no	—
123	#431	—	2	2	no	—
124	#431	—	2	2	no	—
125	#431	C₂×C₄	1	4	yes	—
126	#431	C₂³	1	4	yes	—
127	#423	—	2	2	no	—
128	#423	—	2	2	no	—
129	#423	—	2	2	no	—
130	#423	—	2	2	no	—
131	#423	—	2	2	no	—
132	#423	—	2	2	no	—
133	#423	—	2	2	no	—
134	#423	—	2	2	no	—
135	C₂×C₄⋊C₈	—	2	2	no	—
136	C₂×C₄⋊C₈	—	2	2	no	—
137	C₂×C₄⋊C₈	C₂×C₄	1	4	yes	—
138	C₂×C₄⋊C₈	C₂³	1	4	yes	—
139	#407	—	2	2	no	—
140	#407	—	2	2	no	—
141	#407	—	2	2	no	—
142	#407	—	2	2	no	—
143	#407	—	2	2	no	—
144	#407	—	2	2	no	—
145	#407	C₂×C₄	1	4	yes	—
146	#407	C₂×C₄	1	4	yes	—
147	C₂×C₂²⋊C₈	—	2	2	no	—
148	C₂×C₂²⋊C₈	C₂×C₄	1	4	yes	—
149	C₂×C₂²⋊C₈	C₂×C₄	1	4	yes	—
150	C₂×C₂²⋊C₈	C₂×C₄	1	4	yes	—
151	C₄×M₁₆	—	2	2	no	—
152	C₄×M₁₆	—	2	2	no	—
153	C₄×M₁₆	—	2	2	no	—
154	C₄×M₁₆	—	2	2	no	—
155	C₄×M₁₆	—	2	2	no	—
156	C₄×M₁₆	—	2	2	no	—
157	C₄×M₁₆	—	2	2	no	—
158	C₄×M₁₆	—	2	2	no	—
159	C₄×M₁₆	—	2	2	no	—
160	C₄×M₁₆	—	2	2	no	—
161	C₄×M₁₆	—	2	2	no	—
162	C₄×M₁₆	—	2	2	no	—
163	C₄×M₁₆	—	2	2	no	—
164	C₄×M₁₆	—	2	2	no	—
165	C₄×M₁₆	—	2	2	no	—
166	C₄×M₁₆	—	2	2	no	—
167	C₄×M₁₆	—	2	2	no	—
168	C₄×M₁₆	—	2	2	no	—
169	C₄×M₁₆	—	2	2	no	—
170	C₄×M₁₆	—	2	2	no	—
171	C₄×M₁₆	C₂×C₄	1	4	yes	—
172	C₄×M₁₆	C₂×C₄	1	4	yes	—
173	C₄×M₁₆	C₂×C₄	1	4	yes	—
174	C₄×M₁₆	C₂³	1	4	yes	—
175	C₂×#97	—	2	2	no	—
176	C₂×#97	—	2	2	no	—
177	C₂×#97	—	2	2	no	—
178	C₂×#97	—	2	2	no	—
179	C₂×#97	—	2	2	no	—
180	C₂×#97	—	2	2	no	—
181	C₂×#97	—	2	2	no	—
182	C₂×#97	C₂×C₄	1	4	yes	—
183	C₂×C₄×C₈	—	2	2	no	—
184	C₂×C₄×C₈	—	2	2	no	—
185	C₂×C₄×C₈	—	2	2	no	—
186	C₂×C₄×C₈	—	2	2	no	—
187	C₂×C₄×C₈	—	2	2	no	—
188	C₂×C₄×C₈	—	2	2	no	—
189	C₂×C₄×C₈	—	2	2	no	—
190	C₂×C₄×C₈	C₂×C₄	1	4	yes	—
191	C₂⁵	C₄²	1	1	yes	characteristic
192	C₂³×C₄	—	2	8	no	—
193	C₂³×C₄	—	4	4	no	—
194	C₂³×C₄	—	4	4	no	—
195	C₂³×C₄	C₄²	1	1	yes	characteristic
196	C₂³×C₄	C₄²	1	1	yes	characteristic
197	C₂³×C₄	C₄²	1	1	yes	characteristic
198	C₂³×C₄	C₄²	1	1	yes	characteristic
199	C₂³×C₄	C₄²	1	1	yes	characteristic
200	C₂³×C₄	C₄²	1	1	yes	characteristic
201	C₂³×C₄	C₄²	1	1	yes	characteristic
202	C₂³×C₄	C₄²	1	1	yes	characteristic
203	C₂³×C₄	C₄²	1	1	yes	characteristic
204	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
217	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
218	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
219	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
220	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
221	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
222	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
223	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
224	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
225	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
226	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
227	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
228	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
229	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
230	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
231	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
232	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
233	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
234	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
235	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
236	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
237	C₂×M₁₆	—	2	16	no	—
238	C₂×M₁₆	—	2	16	no	—
239	C₂×M₁₆	—	2	16	no	—
240	C₂×M₁₆	—	2	4	no	—
241	C₂×M₁₆	—	2	4	no	—
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	8	no	—
244	C₂×M₁₆	—	2	16	no	—
245	C₂×M₁₆	—	2	16	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	—	4	8	no	—
251	C₂×M₁₆	—	4	8	no	—
252	C₂×M₁₆	M₁₆	1	16	yes	complemented
253	C₂×M₁₆	C₂²×C₄	1	8	yes	—
254	C₂²×C₈	—	2	16	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	—	2	4	no	—
257	C₂²×C₈	—	2	4	no	—
258	C₂²×C₈	—	2	4	no	—
259	C₂²×C₈	C₂²×C₄	1	8	yes	—
260	C₂×C₄²	C₄²	1	1	yes	characteristic
261	C₂×C₄²	C₄²	1	1	yes	characteristic
262	C₂×C₄²	C₄²	1	1	yes	characteristic
263	C₂×C₄²	C₄²	1	1	yes	characteristic
264	C₂×C₄²	C₄²	1	1	yes	characteristic
265	C₂×C₄²	C₄²	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
288	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
303	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
305	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
306	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
307	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
308	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
309	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
310	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
311	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
312	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
313	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
314	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
315	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
317	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
318	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
319	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
321	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
322	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
324	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
328	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
329	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
330	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
332	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
335	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
336	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
337	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
338	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
346	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
348	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
349	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
350	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
351	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
352	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
353	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
354	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
355	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
356	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
357	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
358	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
359	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
360	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
361	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
362	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
363	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
364	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
365	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
366	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
367	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
368	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
369	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
370	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
371	C₂×C₄²	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₈	—	2	4	no	—
373	C₄⋊C₈	—	2	4	no	—
374	C₄⋊C₈	—	2	4	no	—
375	C₄⋊C₈	—	2	4	no	—
376	C₄⋊C₈	—	2	4	no	—
377	C₄⋊C₈	—	2	4	no	—
378	C₄⋊C₈	—	2	4	no	—
379	C₄⋊C₈	—	2	4	no	—
380	C₂²⋊C₈	—	2	4	no	—
381	C₂²⋊C₈	—	2	4	no	—
382	C₂²⋊C₈	—	2	4	no	—
383	C₂²⋊C₈	—	2	4	no	—
384	C₂²⋊C₈	—	2	4	no	—
385	C₂²⋊C₈	—	2	4	no	—
386	C₂²⋊C₈	—	2	4	no	—
387	C₂²⋊C₈	C₂²×C₄	1	8	yes	—
388	#97	—	2	4	no	—
389	#97	—	2	4	no	—
390	#97	—	2	4	no	—
391	#97	—	2	4	no	—
392	#97	—	2	4	no	—
393	#97	—	2	4	no	—
394	#97	—	2	4	no	—
395	#97	—	2	4	no	—
396	C₄×C₈	—	2	4	no	—
397	C₄×C₈	—	2	4	no	—
398	C₄×C₈	—	2	4	no	—
399	C₄×C₈	—	2	4	no	—
400	C₄×C₈	—	2	4	no	—
401	C₄×C₈	—	2	4	no	—
402	C₄×C₈	—	2	4	no	—
403	C₄×C₈	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	4	2	no	—
406	C₂⁴	—	4	2	no	—
407	C₂⁴	#95	1	1	yes	characteristic
408	C₂⁴	#95	1	1	yes	characteristic
409	C₂⁴	#95	1	1	yes	characteristic
410	C₂⁴	#95	1	1	yes	characteristic
411	C₂⁴	C₂×C₄²	1	1	yes	characteristic
412	C₂⁴	C₂×C₄²	1	1	yes	characteristic
413	C₂⁴	C₂×C₄²	1	1	yes	characteristic
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	#95	1	1	yes	characteristic
456	C₂²×C₄	#95	1	1	yes	characteristic
457	C₂²×C₄	#95	1	1	yes	characteristic
458	C₂²×C₄	#95	1	1	yes	characteristic
459	C₂²×C₄	#95	1	1	yes	characteristic
460	C₂²×C₄	#95	1	1	yes	characteristic
461	C₂²×C₄	#95	1	1	yes	characteristic
462	C₂²×C₄	#95	1	1	yes	characteristic
463	C₂²×C₄	#95	1	1	yes	characteristic
464	C₂²×C₄	#95	1	1	yes	characteristic
465	C₂²×C₄	#95	1	1	yes	characteristic
466	C₂²×C₄	#95	1	1	yes	characteristic
467	C₂²×C₄	#95	1	1	yes	characteristic
468	C₂²×C₄	#95	1	1	yes	characteristic
469	C₂²×C₄	#95	1	1	yes	characteristic
470	C₂²×C₄	#95	1	1	yes	characteristic
471	C₂²×C₄	#95	1	1	yes	characteristic
472	C₂²×C₄	#95	1	1	yes	characteristic
473	C₂²×C₄	#95	1	1	yes	characteristic
474	C₂²×C₄	#95	1	1	yes	characteristic
475	C₂²×C₄	#95	1	1	yes	characteristic
476	C₂²×C₄	#95	1	1	yes	characteristic
477	C₂²×C₄	#95	1	1	yes	characteristic
478	C₂²×C₄	#95	1	1	yes	characteristic
479	C₂²×C₄	#95	1	1	yes	characteristic
480	C₂²×C₄	#95	1	1	yes	characteristic
481	C₂²×C₄	#95	1	1	yes	characteristic
482	C₂²×C₄	#95	1	1	yes	characteristic
483	C₂²×C₄	#95	1	1	yes	characteristic
484	C₂²×C₄	#95	1	1	yes	characteristic
485	C₂²×C₄	#95	1	1	yes	characteristic
486	C₂²×C₄	#95	1	1	yes	characteristic
487	C₂²×C₄	#95	1	1	yes	characteristic
488	C₂²×C₄	#95	1	1	yes	characteristic
489	C₂²×C₄	#95	1	1	yes	characteristic
490	C₂²×C₄	#95	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
493	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₄²	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
527	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
528	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
529	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
530	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
531	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
532	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
533	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×M₁₆	1	8	yes	—
537	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
538	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
539	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
540	M₁₆	—	2	16	no	—
541	M₁₆	—	2	16	no	—
542	M₁₆	—	2	8	no	—
543	M₁₆	—	2	16	no	—
544	M₁₆	—	4	8	no	—
545	M₁₆	—	4	8	no	—
546	M₁₆	—	4	8	no	—
547	M₁₆	—	4	8	no	—
548	M₁₆	C₂×M₁₆	1	16	yes	complemented
549	C₂×C₈	—	2	16	no	—
550	C₂×C₈	—	2	16	no	—
551	C₂×C₈	—	2	8	no	—
552	C₂×C₈	—	2	16	no	—
553	C₂×C₈	—	2	8	no	—
554	C₂×C₈	—	2	8	no	—
555	C₂×C₈	—	4	8	no	—
556	C₂×C₈	—	4	8	no	—
557	C₄²	#95	1	1	yes	characteristic
558	C₄²	#95	1	1	yes	characteristic
559	C₄²	#95	1	1	yes	characteristic
560	C₄²	#95	1	1	yes	characteristic
561	C₄²	#95	1	1	yes	characteristic
562	C₄²	#95	1	1	yes	characteristic
563	C₄²	#95	1	1	yes	characteristic
564	C₄²	#95	1	1	yes	characteristic
565	C₄²	#95	1	1	yes	characteristic
566	C₄²	#95	1	1	yes	characteristic
567	C₄²	#95	1	1	yes	characteristic
568	C₄²	#95	1	1	yes	characteristic
569	C₄²	#95	1	1	yes	characteristic
570	C₄²	#95	1	1	yes	characteristic
571	C₄²	#95	1	1	yes	characteristic
572	C₄²	#95	1	1	yes	characteristic
573	C₄²	#95	1	1	yes	characteristic
574	C₄²	#95	1	1	yes	characteristic
575	C₄²	#95	1	1	yes	characteristic
576	C₄²	#95	1	1	yes	characteristic
577	C₄²	#95	1	1	yes	characteristic
578	C₄²	#95	1	1	yes	characteristic
579	C₄²	#95	1	1	yes	characteristic
580	C₄²	#95	1	1	yes	characteristic
581	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
582	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
583	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
584	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
585	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
586	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
587	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
588	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
589	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
590	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
591	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
592	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
593	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
594	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
595	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
596	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
597	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
598	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
599	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
600	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
601	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
602	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
603	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
604	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
605	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
606	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
607	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
608	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
609	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
610	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
611	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
612	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
613	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
614	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
615	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
616	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
617	C₄²	C₂²×D₄	1	1	yes	characteristic
618	C₄²	C₂²×D₄	1	1	yes	characteristic
619	C₄²	C₂²×D₄	1	1	yes	characteristic
620	C₄²	C₂²×Q₈	1	1	yes	characteristic
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	16	no	—
642	C₂³	C₂×#95	1	1	yes	characteristic
643	C₂³	C₂×#95	1	1	yes	characteristic
644	C₂³	C₂×#95	1	1	yes	characteristic
645	C₂³	C₂×#95	1	1	yes	characteristic
646	C₂³	C₂×#95	1	1	yes	characteristic
647	C₂³	C₂×#95	1	1	yes	characteristic
648	C₂³	C₄×M₁₆	1	4	yes	—
649	C₂³	C₂²×C₄²	1	1	yes	characteristic
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	#344	1	4	yes	—
727	C₂×C₄	C₂×#95	1	1	yes	characteristic
728	C₂×C₄	C₂×#95	1	1	yes	characteristic
729	C₂×C₄	C₂×#95	1	1	yes	characteristic
730	C₂×C₄	C₂×#95	1	1	yes	characteristic
731	C₂×C₄	C₂×#95	1	1	yes	characteristic
732	C₂×C₄	C₂×#95	1	1	yes	characteristic
733	C₂×C₄	C₂×#95	1	1	yes	characteristic
734	C₂×C₄	C₂×#95	1	1	yes	characteristic
735	C₂×C₄	C₂×#95	1	1	yes	characteristic
736	C₂×C₄	C₂×#95	1	1	yes	characteristic
737	C₂×C₄	C₂×#95	1	1	yes	characteristic
738	C₂×C₄	C₂×#95	1	1	yes	characteristic
739	C₂×C₄	C₂×#95	1	1	yes	characteristic
740	C₂×C₄	C₂×#95	1	1	yes	characteristic
741	C₂×C₄	C₂×#95	1	1	yes	characteristic
742	C₂×C₄	C₂×#95	1	1	yes	characteristic
743	C₂×C₄	C₂×#95	1	1	yes	characteristic
744	C₂×C₄	C₂×#95	1	1	yes	characteristic
745	C₂×C₄	C₄×M₁₆	1	4	yes	—
746	C₂×C₄	#407	1	4	yes	—
747	C₂×C₄	#407	1	4	yes	—
748	C₂×C₄	#413	1	4	yes	—
749	C₂×C₄	#423	1	4	yes	—
750	C₂×C₄	#423	1	4	yes	—
751	C₂×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
752	C₂×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
753	C₂×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
754	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
755	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
756	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
757	C₂×C₄	C₂²×M₁₆	1	4	yes	—
758	C₈	—	2	16	no	—
759	C₈	—	4	8	no	—
760	C₈	—	4	8	no	—
761	C₂²	—	2	8	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	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	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	4	no	—
784	C₂²	#1728	1	2	yes	—
785	C₂²	#1728	1	2	yes	—
786	C₂²	#1742	1	2	yes	—
787	C₂²	C₂×#344	1	2	yes	—
788	C₂²	C₂²×#95	1	1	yes	characteristic
789	C₂²	C₂×C₄×M₁₆	1	2	yes	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	#1728	1	2	yes	—
807	C₄	#1728	1	2	yes	—
808	C₄	#1742	1	2	yes	—
809	C₄	C₂×#344	1	2	yes	—
810	C₄	C₂×#344	1	2	yes	—
811	C₄	C₂×#407	1	2	yes	—
812	C₄	C₂×#413	1	2	yes	—
813	C₄	C₂×#423	1	2	yes	—
814	C₂	—	2	2	no	—
815	C₂	—	2	2	no	—
816	C₂	—	2	2	no	—
817	C₂	—	2	2	no	—
818	C₂	—	2	2	no	—
819	C₂	—	4	1	no	—
820	C₂	—	4	1	no	—
821	C₂	C₂×#1728	1	1	yes	characteristic
822	C₂	C₂×#1742	1	1	yes	characteristic
823	C₂	C₂²×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄²
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂²	C₂²×#95
prime radical	C₂⁵	C₄²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄² ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #7938	C₂	semidirect
5. #7937	C₂	semidirect
6. #7932	C₂	semidirect
53. #1283	C₂²	semidirect
252. C₂×M₁₆	M₁₆	semidirect
548. M₁₆	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2920	2
C₂²×C₄×M₁₆	2
#7938	2
#7937	2
#7932	2