Subgroups — #6344358

Order 512.

1938 conjugacy classes of subgroups.

The subgroup lattice has 876 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×#423	C₂	1	1	yes	maximal, characteristic
4	#17822	C₂	1	4	yes	maximal, complemented
5	#17820	C₂	1	4	yes	maximal, complemented
6	#17817	C₂	1	4	yes	maximal, complemented
7	#17814	C₂	1	2	yes	maximal, complemented
8	#17813	C₂	1	2	yes	maximal, complemented
9	#17809	C₂	1	4	yes	maximal, complemented
10	#17807	C₂	1	4	yes	maximal, complemented
11	#17796	C₂	1	4	yes	maximal, complemented
12	C₂³×M₁₆	—	2	1	no	—
13	C₂³×C₄²	C₂²	1	1	yes	characteristic
14	#2920	—	2	1	no	—
15	#2920	—	2	1	no	—
16	#2920	—	2	1	no	—
17	#2920	—	2	1	no	—
18	#2920	C₄	1	2	yes	—
19	#2920	C₄	1	2	yes	—
20	#2920	C₄	1	2	yes	—
21	#2920	C₄	1	2	yes	—
22	#2920	C₂²	1	2	yes	—
23	#2920	C₂²	1	2	yes	—
24	#2920	C₂²	1	2	yes	—
25	#2920	C₂²	1	2	yes	—
26	#2920	C₂²	1	2	yes	—
27	#2920	C₂²	1	2	yes	—
28	#2920	C₂²	1	2	yes	—
29	#2920	C₂²	1	2	yes	—
30	C₂×#432	—	2	1	no	—
31	C₂×#432	C₄	1	2	yes	—
32	C₂×#432	C₄	1	2	yes	—
33	C₂×#432	C₂²	1	2	yes	—
34	C₂×#431	—	2	1	no	—
35	C₂×#431	C₂²	1	2	yes	—
36	C₂×#431	C₂²	1	2	yes	—
37	C₂×#431	C₂²	1	2	yes	—
38	C₂×#423	—	2	1	no	—
39	C₂×#423	—	2	1	no	—
40	C₂×#423	—	2	1	no	—
41	C₂×#423	—	2	1	no	—
42	C₂×#423	—	2	1	no	—
43	C₂×#423	—	2	1	no	—
44	C₂×#423	C₄	1	2	yes	—
45	C₂×#423	C₂²	1	2	yes	—
46	C₂×#423	C₂²	1	2	yes	—
47	C₂×#423	C₂²	1	1	yes	characteristic
48	C₂×#423	C₂²	1	2	yes	—
49	C₂×#423	C₂²	1	1	yes	characteristic
50	C₂×#423	C₂²	1	2	yes	—
51	C₂×#423	C₂²	1	2	yes	—
52	C₂×#423	C₂²	1	2	yes	—
53	C₂²×C₄⋊C₈	—	2	1	no	—
54	C₂²×C₄⋊C₈	C₂²	1	2	yes	—
55	C₂×#407	—	2	1	no	—
56	C₂×#407	C₄	1	2	yes	—
57	C₂×C₄×M₁₆	—	2	1	no	—
58	C₂×C₄×M₁₆	C₂²	1	2	yes	—
59	#1574	C₂²	1	16	yes	complemented
60	#1573	C₂²	1	16	yes	complemented
61	#1571	C₂²	1	8	yes	complemented
62	#1571	C₂²	1	8	yes	complemented
63	#1570	C₂²	1	8	yes	complemented
64	#1570	C₂²	1	8	yes	complemented
65	#1569	C₂²	1	16	yes	complemented
66	#1567	C₂²	1	8	yes	complemented
67	#1566	C₂²	1	8	yes	complemented
68	#1565	C₂²	1	16	yes	complemented
69	C₂⁴×C₄	C₂×C₄	1	1	yes	characteristic
70	C₂⁴×C₄	D₄	1	1	yes	characteristic
71	C₂⁴×C₄	Q₈	1	1	yes	characteristic
72	C₂²×M₁₆	—	2	1	no	—
73	C₂²×M₁₆	—	2	1	no	—
74	C₂²×M₁₆	—	2	2	no	—
75	C₂²×M₁₆	—	2	2	no	—
76	C₂²×M₁₆	—	2	2	no	—
77	C₂²×M₁₆	—	2	2	no	—
78	C₂²×M₁₆	—	2	2	no	—
79	C₂²×M₁₆	—	2	2	no	—
80	C₂²×M₁₆	—	4	8	no	—
81	C₂²×M₁₆	C₂×C₄	1	4	yes	—
82	C₂³×C₈	—	2	2	no	—
83	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₄²	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₄²	D₄	1	1	yes	characteristic
91	C₂²×C₄²	D₄	1	1	yes	characteristic
92	C₂²×C₄²	D₄	1	1	yes	characteristic
93	C₂²×C₄²	D₄	1	1	yes	characteristic
94	C₂²×C₄²	D₄	1	1	yes	characteristic
95	C₂²×C₄²	D₄	1	1	yes	characteristic
96	C₂²×C₄²	D₄	1	1	yes	characteristic
97	C₂²×C₄²	Q₈	1	1	yes	characteristic
98	C₂²×C₄²	Q₈	1	1	yes	characteristic
99	C₂²×C₄²	Q₈	1	1	yes	characteristic
100	C₂²×C₄²	Q₈	1	1	yes	characteristic
101	C₂²×C₄²	Q₈	1	1	yes	characteristic
102	C₂²×C₄²	Q₈	1	1	yes	characteristic
103	C₂²×C₄²	Q₈	1	1	yes	characteristic
104	C₂²×C₄²	C₂³	1	1	yes	characteristic
105	C₂²×C₄²	C₂³	1	1	yes	characteristic
106	C₂²×C₄²	C₂³	1	1	yes	characteristic
107	C₂²×C₄²	C₂³	1	1	yes	characteristic
108	C₂²×C₄²	C₂³	1	1	yes	characteristic
109	C₂²×C₄²	C₂³	1	1	yes	characteristic
110	C₂²×C₄²	C₂³	1	1	yes	characteristic
111	#432	—	2	2	no	—
112	#432	—	2	2	no	—
113	#432	—	2	2	no	—
114	#432	—	2	2	no	—
115	#432	—	2	2	no	—
116	#432	—	2	2	no	—
117	#432	C₂×C₄	1	4	yes	—
118	#432	C₂×C₄	1	4	yes	—
119	#432	C₂×C₄	1	4	yes	—
120	#432	C₂×C₄	1	4	yes	—
121	#432	C₂×C₄	1	4	yes	—
122	#432	C₂×C₄	1	4	yes	—
123	#432	C₂×C₄	1	4	yes	—
124	#432	C₂×C₄	1	4	yes	—
125	#432	C₂³	1	4	yes	—
126	#432	C₂³	1	4	yes	—
127	#431	—	2	2	no	—
128	#431	—	2	2	no	—
129	#431	—	2	2	no	—
130	#431	—	2	2	no	—
131	#431	—	2	2	no	—
132	#431	—	2	2	no	—
133	#431	C₂×C₄	1	4	yes	—
134	#431	C₂×C₄	1	4	yes	—
135	#431	C₂×C₄	1	4	yes	—
136	#431	C₂×C₄	1	4	yes	—
137	#431	C₂³	1	4	yes	—
138	#431	C₂³	1	4	yes	—
139	#431	C₂³	1	4	yes	—
140	#431	C₂³	1	4	yes	—
141	#431	C₂³	1	4	yes	—
142	#431	C₂³	1	4	yes	—
143	#423	—	2	2	no	—
144	#423	—	2	2	no	—
145	#423	—	2	2	no	—
146	#423	—	2	2	no	—
147	#423	—	2	2	no	—
148	#423	—	2	2	no	—
149	#423	—	2	2	no	—
150	#423	—	2	2	no	—
151	#423	—	2	2	no	—
152	#423	—	2	2	no	—
153	#423	—	2	2	no	—
154	#423	—	2	2	no	—
155	#423	—	2	1	no	—
156	#423	—	2	1	no	—
157	#423	—	2	1	no	—
158	#423	—	2	1	no	—
159	#423	C₂×C₄	1	4	yes	—
160	#423	C₂×C₄	1	4	yes	—
161	#423	C₂×C₄	1	4	yes	—
162	#423	C₂×C₄	1	4	yes	—
163	#423	C₂³	1	2	yes	—
164	#423	C₂³	1	4	yes	—
165	#423	C₂³	1	2	yes	—
166	#423	C₂³	1	4	yes	—
167	#423	C₂³	1	2	yes	—
168	#423	C₂³	1	4	yes	—
169	#423	C₂³	1	2	yes	—
170	#423	C₂³	1	4	yes	—
171	C₂×C₄⋊C₈	—	2	2	no	—
172	C₂×C₄⋊C₈	—	2	2	no	—
173	C₂×C₄⋊C₈	—	2	2	no	—
174	C₂×C₄⋊C₈	—	2	2	no	—
175	C₂×C₄⋊C₈	—	2	2	no	—
176	C₂×C₄⋊C₈	—	2	2	no	—
177	C₂×C₄⋊C₈	—	2	2	no	—
178	C₂×C₄⋊C₈	—	2	2	no	—
179	C₂×C₄⋊C₈	—	2	2	no	—
180	C₂×C₄⋊C₈	—	2	1	no	—
181	C₂×C₄⋊C₈	—	2	1	no	—
182	C₂×C₄⋊C₈	C₂×C₄	1	4	yes	—
183	C₂×C₄⋊C₈	C₂×C₄	1	4	yes	—
184	C₂×C₄⋊C₈	C₂³	1	4	yes	—
185	C₂×C₄⋊C₈	C₂³	1	2	yes	—
186	C₂×C₄⋊C₈	C₂³	1	4	yes	—
187	C₂×C₄⋊C₈	C₂³	1	2	yes	—
188	C₂×C₄⋊C₈	C₂³	1	4	yes	—
189	#407	—	2	2	no	—
190	#407	—	2	2	no	—
191	#407	—	2	2	no	—
192	#407	—	2	2	no	—
193	#407	C₂×C₄	1	4	yes	—
194	#407	C₂×C₄	1	4	yes	—
195	#407	C₂×C₄	1	4	yes	—
196	#407	C₂×C₄	1	4	yes	—
197	C₂×C₂²⋊C₈	—	2	2	no	—
198	C₂×C₂²⋊C₈	—	2	2	no	—
199	C₂×C₂²⋊C₈	C₂×C₄	1	4	yes	—
200	C₂×C₂²⋊C₈	C₂×C₄	1	4	yes	—
201	C₄×M₁₆	—	2	2	no	—
202	C₄×M₁₆	—	2	2	no	—
203	C₄×M₁₆	—	2	2	no	—
204	C₄×M₁₆	—	2	2	no	—
205	C₄×M₁₆	C₂×C₄	1	4	yes	—
206	C₄×M₁₆	C₂×C₄	1	4	yes	—
207	C₄×M₁₆	C₂³	1	4	yes	—
208	C₄×M₁₆	C₂³	1	4	yes	—
209	C₂×#97	—	2	2	no	—
210	C₂×#97	C₂×C₄	1	4	yes	—
211	C₂×C₄×C₈	—	2	2	no	—
212	C₂×C₄×C₈	C₂³	1	4	yes	—
213	#335	C₂³	1	32	yes	complemented
214	#334	C₂³	1	32	yes	complemented
215	C₂⁵	C₄⋊C₄	1	1	yes	characteristic
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	4	no	—
218	C₂³×C₄	—	4	4	no	—
219	C₂³×C₄	—	4	4	no	—
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	C₄⋊C₄	1	1	yes	characteristic
229	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
230	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
231	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
232	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
233	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
234	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
235	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
236	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
237	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
238	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
239	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
240	C₂³×C₄	C₄⋊C₄	1	1	yes	characteristic
241	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
242	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
243	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
244	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
245	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
246	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
247	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
248	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
249	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
250	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
251	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
252	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
253	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
254	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
255	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
256	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
257	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
258	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
259	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
260	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
261	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	—	2	4	no	—
264	C₂×M₁₆	—	2	4	no	—
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	4	8	no	—
271	C₂×M₁₆	—	4	8	no	—
272	C₂×M₁₆	—	4	8	no	—
273	C₂×M₁₆	—	4	8	no	—
274	C₂×M₁₆	—	4	8	no	—
275	C₂×M₁₆	—	4	8	no	—
276	C₂×M₁₆	—	4	4	no	—
277	C₂×M₁₆	—	4	8	no	—
278	C₂×M₁₆	—	4	4	no	—
279	C₂×M₁₆	C₂²×C₄	1	8	yes	—
280	C₂×M₁₆	C₂²×C₄	1	8	yes	—
281	C₂²×C₈	—	2	4	no	—
282	C₂²×C₈	—	2	4	no	—
283	C₂²×C₈	—	2	4	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	4	8	no	—
287	C₂²×C₈	C₂²×C₄	1	8	yes	—
288	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
289	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
290	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
291	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
292	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
293	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
294	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
295	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
296	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
297	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
298	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
301	C₂×C₄²	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
331	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
332	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
333	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
334	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
335	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
336	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
337	C₂×C₄²	C₂²×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	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₄²	C₂²×C₄	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×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×D₄	1	1	yes	characteristic
371	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
372	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
373	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
374	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
375	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
376	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
377	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
378	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
379	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
380	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
381	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
382	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
383	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
384	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
385	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
386	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
387	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
388	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
389	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
390	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
391	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
392	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
393	C₂×C₄²	C₂⁴	1	1	yes	characteristic
394	C₂×C₄²	C₂⁴	1	1	yes	characteristic
395	C₂×C₄²	C₂⁴	1	1	yes	characteristic
396	C₂×C₄²	C₂⁴	1	1	yes	characteristic
397	C₂×C₄²	C₂⁴	1	1	yes	characteristic
398	C₂×C₄²	C₂⁴	1	1	yes	characteristic
399	C₂×C₄²	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₈	—	2	4	no	—
405	C₄⋊C₈	—	2	4	no	—
406	C₄⋊C₈	—	2	4	no	—
407	C₄⋊C₈	—	2	2	no	—
408	C₄⋊C₈	—	2	2	no	—
409	C₄⋊C₈	—	2	2	no	—
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	2	2	no	—
412	C₄⋊C₈	—	2	2	no	—
413	C₄⋊C₈	C₂²×C₄	1	8	yes	—
414	C₄⋊C₈	C₂²×C₄	1	8	yes	—
415	C₄⋊C₈	C₂²×C₄	1	8	yes	—
416	C₄⋊C₈	C₂²×C₄	1	8	yes	—
417	C₄⋊C₈	C₂⁴	1	4	yes	—
418	C₄⋊C₈	C₂⁴	1	8	yes	—
419	C₄⋊C₈	C₂⁴	1	4	yes	—
420	C₂²⋊C₈	—	2	4	no	—
421	C₂²⋊C₈	—	2	4	no	—
422	C₂²⋊C₈	—	2	4	no	—
423	C₂²⋊C₈	—	2	4	no	—
424	C₂²⋊C₈	C₂²×C₄	1	8	yes	—
425	C₂²⋊C₈	C₂²×C₄	1	8	yes	—
426	C₂²⋊C₈	C₂²×C₄	1	8	yes	—
427	C₂²⋊C₈	C₂²×C₄	1	8	yes	—
428	#97	—	2	4	no	—
429	#97	—	2	4	no	—
430	#97	C₂²×C₄	1	8	yes	—
431	#97	C₂²×C₄	1	8	yes	—
432	C₄×C₈	—	2	4	no	—
433	C₄×C₈	—	2	4	no	—
434	C₄×C₈	C₂²×C₄	1	8	yes	—
435	C₄×C₈	C₂⁴	1	8	yes	—
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	4	2	no	—
438	C₂⁴	—	4	2	no	—
439	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
440	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
441	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
442	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
443	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
444	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
445	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₄⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
540	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
541	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
542	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
544	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
550	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
551	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
552	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
554	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
556	C₂²×C₄	AGL(1,ℤ/8)	1	4	yes	—
557	C₂²×C₄	#137	1	4	yes	—
558	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
559	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
560	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
561	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
562	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
563	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
564	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
565	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
566	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
573	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
574	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
575	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
576	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
577	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
578	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
579	M₁₆	—	2	16	no	—
580	M₁₆	—	4	8	no	—
581	M₁₆	—	4	8	no	—
582	M₁₆	—	4	8	no	—
583	M₁₆	—	4	4	no	—
584	M₁₆	—	4	4	no	—
585	M₁₆	—	4	8	no	—
586	M₁₆	—	4	8	no	—
587	M₁₆	—	4	4	no	—
588	M₁₆	—	4	4	no	—
589	C₂×C₈	—	2	4	no	—
590	C₂×C₈	—	2	4	no	—
591	C₂×C₈	—	2	8	no	—
592	C₂×C₈	—	4	8	no	—
593	C₂×C₈	—	4	8	no	—
594	C₂×C₈	—	4	8	no	—
595	C₂×C₈	—	4	8	no	—
596	C₂×C₈	—	4	4	no	—
597	C₂×C₈	—	4	4	no	—
598	C₂×C₈	C₂³×C₄	1	16	yes	—
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	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	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
625	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
626	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
627	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
628	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
629	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
630	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
631	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
632	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
633	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
634	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
635	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
636	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
637	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
638	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
639	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
640	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
641	C₄²	C₂³×C₄	1	1	yes	characteristic
642	C₄²	C₂³×C₄	1	1	yes	characteristic
643	C₄²	C₂³×C₄	1	1	yes	characteristic
644	C₄²	C₂³×C₄	1	1	yes	characteristic
645	C₄²	C₂³×C₄	1	1	yes	characteristic
646	C₄²	C₂³×C₄	1	1	yes	characteristic
647	C₄²	C₂³×C₄	1	1	yes	characteristic
648	C₄²	C₂²×D₄	1	1	yes	characteristic
649	C₄²	C₂²×D₄	1	1	yes	characteristic
650	C₄²	C₂²×D₄	1	1	yes	characteristic
651	C₄²	C₂²×D₄	1	1	yes	characteristic
652	C₄²	C₂²×D₄	1	1	yes	characteristic
653	C₄²	C₂²×D₄	1	1	yes	characteristic
654	C₄²	C₂²×D₄	1	1	yes	characteristic
655	C₄²	C₂²×Q₈	1	1	yes	characteristic
656	C₄²	C₂²×Q₈	1	1	yes	characteristic
657	C₄²	C₂²×Q₈	1	1	yes	characteristic
658	C₄²	C₂²×Q₈	1	1	yes	characteristic
659	C₄²	C₂²×Q₈	1	1	yes	characteristic
660	C₄²	C₂²×Q₈	1	1	yes	characteristic
661	C₄²	C₂²×Q₈	1	1	yes	characteristic
662	C₄²	C₂⁵	1	1	yes	characteristic
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	16	no	—
684	C₂³	#428	1	4	yes	—
685	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
686	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
687	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
688	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
689	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
690	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
691	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	#428	1	4	yes	—
773	C₂×C₄	#428	1	4	yes	—
774	C₂×C₄	#428	1	4	yes	—
775	C₂×C₄	#430	1	4	yes	—
776	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
777	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
778	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
779	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
780	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
781	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
782	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
783	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
784	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
785	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
786	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
787	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
788	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
789	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
790	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
791	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
792	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
793	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
794	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
795	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
797	C₂×C₄	#568	1	4	yes	—
798	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
799	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
800	C₂×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
801	C₂×C₄	C₂×#137	1	2	yes	—
802	C₂×C₄	C₂×#137	1	2	yes	—
803	C₂×C₄	C₂×#137	1	2	yes	—
804	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
805	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
806	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
807	C₈	—	2	16	no	—
808	C₈	—	4	8	no	—
809	C₈	—	4	4	no	—
810	C₈	—	4	4	no	—
811	C₂²	—	2	8	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	4	no	—
834	C₂²	#2905	1	2	yes	—
835	C₂²	C₂×#428	1	2	yes	—
836	C₂²	C₂×#428	1	2	yes	—
837	C₂²	C₂×#428	1	2	yes	—
838	C₂²	C₂×#430	1	2	yes	—
839	C₂²	C₂³×C₄⋊C₄	1	1	yes	characteristic
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	#2905	1	2	yes	—
857	C₄	C₂×#428	1	2	yes	—
858	C₄	C₂×#428	1	2	yes	—
859	C₄	C₂×#428	1	2	yes	—
860	C₄	C₂×#430	1	2	yes	—
861	C₄	C₂×#430	1	2	yes	—
862	C₄	C₂×#568	1	2	yes	—
863	C₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
864	C₄	C₂²×#137	1	1	yes	characteristic
865	C₂	—	2	2	no	—
866	C₂	—	2	2	no	—
867	C₂	—	2	2	no	—
868	C₂	—	2	2	no	—
869	C₂	—	2	2	no	—
870	C₂	—	4	1	no	—
871	C₂	—	4	1	no	—
872	C₂	C₂×#2905	1	1	yes	characteristic
873	C₂	C₂²×#428	1	1	yes	characteristic
874	C₂	C₂²×#430	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. #17822	C₂	semidirect
5. #17820	C₂	semidirect
6. #17817	C₂	semidirect
7. #17814	C₂	semidirect
8. #17813	C₂	semidirect
9. #17809	C₂	semidirect
10. #17807	C₂	semidirect
11. #17796	C₂	semidirect
59. #1574	C₂²	semidirect
60. #1573	C₂²	semidirect
61. #1571	C₂²	semidirect
62. #1571	C₂²	semidirect
63. #1570	C₂²	semidirect
64. #1570	C₂²	semidirect
65. #1569	C₂²	semidirect
66. #1567	C₂²	semidirect
67. #1566	C₂²	semidirect
68. #1565	C₂²	semidirect
213. #335	C₂³	semidirect
214. #334	C₂³	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×#423	2
#17822	2
#17820	2
#17817	2
#17814	2
#17813	2
#17809	2
#17807	2
#17796	2