Subgroups — #181123

Order 512.

1658 conjugacy classes of subgroups.

The subgroup lattice has 835 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	#34012	C₂	1	1	yes	maximal, characteristic
3	C₂×#2283	C₂	1	1	yes	maximal, characteristic
4	#7945	C₂	1	4	yes	maximal, complemented
5	#7943	C₂	1	4	yes	maximal
6	#7941	C₂	1	4	yes	maximal, complemented
7	C₂³×C₄²	C₂²	1	1	yes	characteristic
8	#2920	—	2	1	no	—
9	#2920	—	2	1	no	—
10	#2920	—	2	1	no	—
11	#2920	—	2	1	no	—
12	#2920	C₄	1	2	yes	complemented
13	#2920	C₄	1	2	yes	complemented
14	#2920	C₂²	1	2	yes	—
15	#2920	C₂²	1	2	yes	—
16	C₂×#432	—	2	1	no	—
17	C₂×#432	C₄	1	2	yes	complemented
18	C₂×#431	—	2	1	no	—
19	C₂×#431	C₄	1	2	yes	complemented
20	C₂×#423	—	2	1	no	—
21	C₂×#407	C₂²	1	2	yes	—
22	C₂×C₄×M₁₆	—	2	1	no	—
23	#2285	—	2	1	no	—
24	#2285	—	2	1	no	—
25	#2285	C₄	1	2	yes	complemented
26	#2283	—	2	1	no	—
27	#2283	—	2	1	no	—
28	#2283	—	2	1	no	—
29	#2283	—	2	1	no	—
30	#2283	—	2	1	no	—
31	#2283	—	2	1	no	—
32	#2283	—	2	1	no	—
33	#2283	—	2	1	no	—
34	#2283	C₄	1	2	yes	complemented
35	#2283	C₄	1	2	yes	complemented
36	#2283	C₄	1	2	yes	complemented
37	#2283	C₂²	1	2	yes	—
38	#2283	C₂²	1	2	yes	—
39	#2283	C₂²	1	2	yes	—
40	C₂×#383	C₄	1	2	yes	complemented
41	C₂×#382	—	2	1	no	—
42	#2280	—	2	1	no	—
43	#2280	—	2	1	no	—
44	#2280	C₂²	1	2	yes	—
45	C₂×#381	C₂²	1	2	yes	—
46	C₂×#380	—	2	1	no	—
47	C₄×#117	C₄	1	2	yes	complemented
48	C₄×#117	C₄	1	2	yes	complemented
49	C₄×#117	C₂²	1	2	yes	—
50	C₂×C₄×C₄⋊C₄	C₄	1	2	yes	complemented
51	C₂×C₄×C₂²⋊C₄	—	2	1	no	—
52	C₂×#376	—	2	1	no	—
53	#1284	C₂²	1	16	yes	—
54	C₂⁴×C₄	D₄	1	1	yes	characteristic
55	C₂⁴×C₄	D₄	1	1	yes	characteristic
56	C₂⁴×C₄	C₂³	1	1	yes	characteristic
57	C₂²×M₁₆	—	2	2	no	—
58	C₂×#117	—	2	2	no	—
59	C₂×#117	—	2	2	no	—
60	C₂×#117	C₂×C₄	1	4	yes	—
61	C₂²×C₄⋊C₄	—	2	2	no	—
62	C₂²×C₂²⋊C₄	—	2	2	no	—
63	C₂²×C₄²	—	2	2	no	—
64	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
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	Q₈	1	1	yes	characteristic
87	C₂²×C₄²	Q₈	1	1	yes	characteristic
88	C₂²×C₄²	Q₈	1	1	yes	characteristic
89	C₂²×C₄²	Q₈	1	1	yes	characteristic
90	C₂²×C₄²	C₂³	1	1	yes	characteristic
91	C₂²×C₄²	C₂³	1	1	yes	characteristic
92	#432	—	2	2	no	—
93	#432	—	2	2	no	—
94	#432	—	2	2	no	—
95	#432	—	2	2	no	—
96	#432	—	2	2	no	—
97	#432	—	2	2	no	—
98	#432	C₂×C₄	1	4	yes	complemented
99	#432	C₂×C₄	1	4	yes	complemented
100	#431	—	2	2	no	—
101	#431	—	2	2	no	—
102	#431	—	2	2	no	—
103	#431	—	2	2	no	—
104	#431	—	2	2	no	—
105	#431	—	2	2	no	—
106	#431	C₂×C₄	1	4	yes	complemented
107	#431	C₂×C₄	1	4	yes	complemented
108	#423	—	2	2	no	—
109	#423	—	2	2	no	—
110	#423	—	2	2	no	—
111	#423	—	2	2	no	—
112	C₂×C₄⋊C₈	—	2	2	no	—
113	C₂×C₄⋊C₈	—	2	2	no	—
114	#407	—	2	2	no	—
115	#407	—	2	2	no	—
116	#407	C₂×C₄	1	4	yes	—
117	#407	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₈	—	2	2	no	—
119	C₂×C₂²⋊C₈	C₂×C₄	1	4	yes	—
120	C₄×M₁₆	—	2	2	no	—
121	C₄×M₁₆	—	2	2	no	—
122	C₄×M₁₆	—	2	2	no	—
123	C₄×M₁₆	—	2	2	no	—
124	C₂×#97	—	2	2	no	—
125	C₂×C₄×C₈	—	2	2	no	—
126	#384	—	2	2	no	—
127	#383	—	2	2	no	—
128	#383	—	2	2	no	—
129	#383	—	2	2	no	—
130	#383	—	2	2	no	—
131	#383	C₂×C₄	1	4	yes	—
132	#383	C₂×C₄	1	4	yes	—
133	#382	—	2	2	no	—
134	#382	—	2	2	no	—
135	#382	—	2	2	no	—
136	#382	—	2	2	no	—
137	#382	—	2	2	no	—
138	#382	—	2	2	no	—
139	#382	—	2	2	no	—
140	#381	—	2	2	no	—
141	#381	—	2	2	no	—
142	#381	—	2	2	no	—
143	#381	—	2	2	no	—
144	#381	—	2	2	no	—
145	#381	C₂×C₄	1	4	yes	—
146	#381	C₂³	1	4	yes	—
147	#380	—	2	2	no	—
148	#380	—	2	2	no	—
149	#380	—	2	2	no	—
150	#380	—	2	2	no	—
151	#380	—	2	2	no	—
152	#380	—	2	2	no	—
153	#380	—	2	2	no	—
154	#380	—	2	2	no	—
155	#380	—	2	2	no	—
156	#380	—	2	2	no	—
157	#379	—	2	2	no	—
158	C₄×C₄⋊C₄	—	2	2	no	—
159	C₄×C₄⋊C₄	—	2	2	no	—
160	C₄×C₄⋊C₄	—	2	2	no	—
161	C₄×C₄⋊C₄	—	2	2	no	—
162	C₄×C₄⋊C₄	—	2	2	no	—
163	C₄×C₄⋊C₄	—	2	2	no	—
164	C₄×C₄⋊C₄	C₂×C₄	1	4	yes	—
165	C₄×C₄⋊C₄	C₂×C₄	1	4	yes	—
166	C₄×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
167	C₄×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
168	C₄×C₂²⋊C₄	—	2	2	no	—
169	C₄×C₂²⋊C₄	—	2	2	no	—
170	C₄×C₂²⋊C₄	—	2	2	no	—
171	C₄×C₂²⋊C₄	—	2	2	no	—
172	C₄×C₂²⋊C₄	—	2	2	no	—
173	C₄×C₂²⋊C₄	—	2	2	no	—
174	C₄×C₂²⋊C₄	—	2	2	no	—
175	C₄×C₂²⋊C₄	—	2	2	no	—
176	C₄×C₂²⋊C₄	C₂×C₄	1	4	yes	—
177	C₄×C₂²⋊C₄	C₂³	1	4	yes	—
178	#376	—	2	2	no	—
179	#376	—	2	2	no	—
180	#376	—	2	2	no	—
181	#376	—	2	2	no	—
182	#376	—	2	2	no	—
183	#376	—	2	2	no	—
184	#376	C₂×C₄	1	4	yes	complemented
185	C₂×#95	—	2	2	no	—
186	C₂×#95	—	2	2	no	—
187	C₂×#95	—	2	2	no	—
188	C₂×#95	C₂×C₄	1	4	yes	—
189	C₄³	C₂×C₄	1	4	yes	complemented
190	C₂⁵	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₄	—	2	4	no	—
192	C₂³×C₄	—	4	4	no	—
193	C₂³×C₄	—	4	4	no	—
194	C₂³×C₄	—	4	4	no	—
195	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₄	C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×C₄	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
212	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
213	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
214	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
215	C₂³×C₄	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
221	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
222	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
223	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
224	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
225	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
229	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
230	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
233	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
235	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
236	C₂³×C₄	C₂⁴	1	1	yes	characteristic
237	C₂×M₁₆	—	2	4	no	—
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	—	4	8	no	—
240	C₂²×C₈	—	2	4	no	—
241	#117	—	4	8	no	—
242	#117	—	4	8	no	—
243	#117	—	4	8	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	4	8	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₂²⋊C₄	—	4	8	no	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	—	2	4	no	—
258	C₂×C₄²	—	2	4	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	—	4	8	no	—
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	C₄²	1	1	yes	characteristic
267	C₂×C₄²	C₄²	1	1	yes	characteristic
268	C₂×C₄²	C₄²	1	1	yes	characteristic
269	C₂×C₄²	C₄²	1	1	yes	characteristic
270	C₂×C₄²	C₄²	1	1	yes	characteristic
271	C₂×C₄²	C₄²	1	1	yes	characteristic
272	C₂×C₄²	C₄²	1	1	yes	characteristic
273	C₂×C₄²	C₄²	1	1	yes	characteristic
274	C₂×C₄²	C₄²	1	1	yes	characteristic
275	C₂×C₄²	C₄²	1	1	yes	characteristic
276	C₂×C₄²	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄²	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
339	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
340	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
341	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
342	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
346	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
349	C₂×C₄²	C₂²×C₄	1	8	yes	—
350	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
354	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
355	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
356	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
357	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
358	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
359	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
360	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
361	C₂×C₄²	C₂²×C₄	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×D₄	1	1	yes	characteristic
366	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
367	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
368	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
369	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
370	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
371	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
372	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
373	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
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	C₂²⋊C₈	—	2	4	no	—
379	C₂²⋊C₈	—	2	4	no	—
380	C₂²⋊C₈	—	2	4	no	—
381	C₂²⋊C₈	C₂²×C₄	1	8	yes	—
382	#97	—	2	4	no	—
383	#97	—	2	4	no	—
384	C₄×C₈	—	2	4	no	—
385	C₄×C₈	—	2	4	no	—
386	#95	—	2	4	no	—
387	#95	—	2	4	no	—
388	#95	—	2	4	no	—
389	#95	—	2	4	no	—
390	#95	—	2	4	no	—
391	#95	—	2	4	no	—
392	#95	—	2	4	no	—
393	#95	—	2	4	no	—
394	#95	—	2	4	no	—
395	#95	—	2	4	no	—
396	#95	—	2	4	no	—
397	#95	—	2	4	no	—
398	#95	—	2	4	no	—
399	#95	C₂²×C₄	1	8	yes	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂⁴	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂⁴	C₂×C₂²⋊C₄	1	1	yes	characteristic
406	C₂⁴	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
408	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
409	C₂⁴	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
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	8	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	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	8	no	—
455	C₂²×C₄	—	4	8	no	—
456	C₂²×C₄	—	4	8	no	—
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	C₂×C₄²	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₄²	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×C₂²⋊C₄	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₂²⋊C₄	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×C₄⋊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	C₂³×C₄	1	1	yes	characteristic
536	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
537	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
541	M₁₆	—	4	8	no	—
542	M₁₆	—	4	8	no	—
543	C₂×C₈	—	2	8	no	—
544	C₂×C₈	—	4	8	no	—
545	C₄⋊C₄	—	4	8	no	—
546	C₄⋊C₄	—	4	8	no	—
547	C₄⋊C₄	—	4	8	no	—
548	C₄⋊C₄	—	4	8	no	—
549	C₄⋊C₄	—	4	8	no	—
550	C₂²⋊C₄	—	4	8	no	—
551	C₂²⋊C₄	—	4	8	no	—
552	C₂²⋊C₄	—	4	8	no	—
553	C₂²⋊C₄	—	4	8	no	—
554	C₂²⋊C₄	—	4	8	no	—
555	C₄²	—	4	8	no	—
556	C₄²	—	4	8	no	—
557	C₄²	—	4	8	no	—
558	C₄²	—	4	8	no	—
559	C₄²	—	4	8	no	—
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	#95	1	1	yes	characteristic
582	C₄²	#95	1	1	yes	characteristic
583	C₄²	#95	1	1	yes	characteristic
584	C₄²	#95	1	1	yes	characteristic
585	C₄²	#95	1	1	yes	characteristic
586	C₄²	#95	1	1	yes	characteristic
587	C₄²	#95	1	1	yes	characteristic
588	C₄²	#95	1	1	yes	characteristic
589	C₄²	#95	1	1	yes	characteristic
590	C₄²	#95	1	1	yes	characteristic
591	C₄²	#95	1	1	yes	characteristic
592	C₄²	C₂×C₄²	1	1	yes	characteristic
593	C₄²	C₂×C₄²	1	1	yes	characteristic
594	C₄²	C₂×C₄²	1	1	yes	characteristic
595	C₄²	C₂×C₄²	1	1	yes	characteristic
596	C₄²	C₂×C₄²	1	1	yes	characteristic
597	C₄²	C₂×C₄²	1	1	yes	characteristic
598	C₄²	C₂×C₄²	1	1	yes	characteristic
599	C₄²	C₂×C₄²	1	1	yes	characteristic
600	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
601	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
602	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
603	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
604	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
605	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
606	C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
607	C₄²	C₂×C₂²⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
618	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
619	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
620	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
621	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
622	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
623	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	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	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	16	no	—
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	C₂×#95	1	1	yes	characteristic
649	C₂³	#410	1	4	yes	—
650	C₂³	C₂²×C₂²⋊C₄	1	1	yes	characteristic
651	C₂³	C₂²×C₂²⋊C₄	1	1	yes	characteristic
652	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	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	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	8	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	4	8	no	—
739	C₂×C₄	—	4	8	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	8	16	no	—
742	C₂×C₄	H(3,ℤ/4)	1	4	yes	—
743	C₂×C₄	C₂×#95	1	1	yes	characteristic
744	C₂×C₄	C₂×#95	1	1	yes	characteristic
745	C₂×C₄	C₂×#95	1	1	yes	characteristic
746	C₂×C₄	C₂×#95	1	1	yes	characteristic
747	C₂×C₄	C₂×#95	1	1	yes	characteristic
748	C₂×C₄	C₂×#95	1	1	yes	characteristic
749	C₂×C₄	C₂×#95	1	1	yes	characteristic
750	C₂×C₄	C₂×#95	1	1	yes	characteristic
751	C₂×C₄	C₂×#95	1	1	yes	characteristic
752	C₂×C₄	C₂×#95	1	1	yes	characteristic
753	C₂×C₄	C₂×#95	1	1	yes	characteristic
754	C₂×C₄	C₂×#95	1	1	yes	characteristic
755	C₂×C₄	C₂×#95	1	1	yes	characteristic
756	C₂×C₄	C₂×#95	1	1	yes	characteristic
757	C₂×C₄	C₂×#95	1	1	yes	characteristic
758	C₂×C₄	C₂×#95	1	1	yes	characteristic
759	C₂×C₄	C₂×#95	1	1	yes	characteristic
760	C₂×C₄	C₂×#95	1	1	yes	characteristic
761	C₂×C₄	C₂×#95	1	1	yes	characteristic
762	C₂×C₄	C₂×#95	1	1	yes	characteristic
763	C₂×C₄	#421	1	4	yes	—
764	C₂×C₄	C₂²×C₄²	1	1	yes	characteristic
765	C₂×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
766	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
767	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
768	C₈	—	4	8	no	—
769	C₂²	—	2	8	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	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	C₂×H(3,ℤ/4)	1	2	yes	—
793	C₂²	#1740	1	2	yes	—
794	C₂²	#1740	1	2	yes	—
795	C₂²	C₂²×#95	1	1	yes	characteristic
796	C₂²	C₂×#410	1	2	yes	—
797	C₂²	C₂×#421	1	2	yes	—
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	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	8	8	no	—
819	C₄	—	8	8	no	—
820	C₄	C₂×H(3,ℤ/4)	1	2	yes	—
821	C₄	C₂×H(3,ℤ/4)	1	2	yes	—
822	C₄	#1733	1	2	yes	—
823	C₄	#1733	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	2	no	—
826	C₂	—	2	2	no	—
827	C₂	—	2	2	no	—
828	C₂	—	2	2	no	—
829	C₂	—	4	1	no	—
830	C₂	—	4	1	no	—
831	C₂	C₂²×H(3,ℤ/4)	1	1	yes	characteristic
832	C₂	C₂×#1733	1	1	yes	characteristic
833	C₂	C₂×#1740	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#95
commutator	C₂×C₄	C₂²×C₄²
Frattini, cosocle	C₂³×C₄	C₂⁴
socle	C₂²	C₂²×#95
prime radical	C₂⁵	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #7945	C₂	semidirect
6. #7941	C₂	semidirect
12. #2920	C₄	semidirect
13. #2920	C₄	semidirect
17. C₂×#432	C₄	semidirect
19. C₂×#431	C₄	semidirect
25. #2285	C₄	semidirect
34. #2283	C₄	semidirect
35. #2283	C₄	semidirect
36. #2283	C₄	semidirect
40. C₂×#383	C₄	semidirect
47. C₄×#117	C₄	semidirect
48. C₄×#117	C₄	semidirect
50. C₂×C₄×C₄⋊C₄	C₄	semidirect
98. #432	C₂×C₄	semidirect
99. #432	C₂×C₄	semidirect
106. #431	C₂×C₄	semidirect
107. #431	C₂×C₄	semidirect
166. C₄×C₄⋊C₄	C₂×C₄	semidirect
167. C₄×C₄⋊C₄	C₂×C₄	semidirect
184. #376	C₂×C₄	semidirect
189. C₄³	C₂×C₄	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
#34012	2
C₂×#2283	2
#7945	2
#7943	2
#7941	2