Subgroups — #207301

Order 512.

656 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21922	C₂	1	1	yes	maximal, characteristic
2	#20543	C₂	1	1	yes	maximal, characteristic
3	C₄×#433	C₂	1	1	yes	maximal, characteristic
4	#9603	C₂	1	1	yes	maximal, characteristic, complemented
5	#9603	C₂	1	1	yes	maximal, characteristic, complemented
6	#9602	C₂	1	1	yes	maximal, characteristic, complemented
7	#9601	C₂	1	1	yes	maximal, characteristic, complemented
8	#8831	C₂	1	1	yes	maximal, characteristic
9	#8831	C₂	1	1	yes	maximal, characteristic
10	#8830	C₂	1	1	yes	maximal, characteristic
11	#8829	C₂	1	1	yes	maximal, characteristic
12	#8275	C₂	1	1	yes	maximal, characteristic, complemented
13	#8275	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#335	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#334	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#433	C₄	1	1	yes	characteristic
17	C₂×#433	C₄	1	1	yes	characteristic
18	C₂×#431	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×#117	C₂²	1	1	yes	characteristic
21	#1923	—	2	1	no	—
22	#1923	—	2	1	no	—
23	#1916	—	2	1	no	—
24	#1916	—	2	1	no	—
25	#1842	C₂²	1	1	yes	characteristic
26	#1831	C₂²	1	1	yes	characteristic
27	#1797	C₂²	1	1	yes	characteristic
28	#1797	C₂²	1	1	yes	characteristic
29	C₈×C₄⋊C₄	—	2	1	no	—
30	C₈×C₄⋊C₄	—	2	1	no	—
31	#1768	C₄	1	1	yes	characteristic
32	#1768	C₄	1	1	yes	characteristic
33	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₈×C₂²⋊C₄	—	2	1	no	—
42	C₈×C₂²⋊C₄	—	2	1	no	—
43	#1750	C₄	1	1	yes	characteristic
44	#1750	C₄	1	1	yes	characteristic
45	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	#1746	C₄	1	1	yes	characteristic
48	#1746	C₄	1	1	yes	characteristic
49	C₄×#97	C₂²	1	1	yes	characteristic
50	C₄²×C₈	C₂²	1	1	yes	characteristic
51	C₂×#335	C₂²	1	1	yes	characteristic
52	C₂×#335	C₂²	1	1	yes	characteristic
53	C₂×#335	C₂²	1	1	yes	characteristic
54	C₂×#335	C₂²	1	1	yes	characteristic
55	C₂×#334	C₂²	1	1	yes	characteristic
56	C₂×#334	C₂²	1	1	yes	characteristic
57	C₂×#334	C₂²	1	1	yes	characteristic
58	C₂×#334	C₂²	1	1	yes	characteristic
59	#1277	C₂²	1	1	yes	characteristic
60	#1277	C₂²	1	1	yes	characteristic
61	#1277	C₂²	1	1	yes	characteristic
62	#1277	C₂²	1	1	yes	characteristic
63	#1277	C₂²	1	1	yes	characteristic
64	#1277	C₂²	1	1	yes	characteristic
65	#1277	C₂²	1	1	yes	characteristic
66	#1277	C₂²	1	1	yes	characteristic
67	C₂³×C₈	—	2	1	no	—
68	C₂×#117	C₂×C₄	1	1	yes	characteristic
69	C₂×#117	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄²	C₂³	1	1	yes	characteristic
71	#433	—	2	4	no	—
72	#433	C₈	1	8	yes	complemented
73	#431	—	2	2	no	—
74	#431	—	2	2	no	—
75	C₂×C₄⋊C₈	—	2	1	no	—
76	C₂×C₄⋊C₈	—	2	2	no	—
77	C₂×C₄⋊C₈	—	2	2	no	—
78	C₂×C₄⋊C₈	—	2	1	no	—
79	C₂×C₄⋊C₈	—	2	1	no	—
80	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₈	—	2	1	no	—
93	C₂×C₂²⋊C₈	—	2	1	no	—
94	C₂×C₂²⋊C₈	—	2	1	no	—
95	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₂×#97	C₂×C₄	1	1	yes	characteristic
100	C₂×#97	C₂×C₄	1	1	yes	characteristic
101	C₂×#97	C₂×C₄	1	1	yes	characteristic
102	C₂×#97	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄×C₈	—	2	1	no	—
104	C₂×C₄×C₈	—	2	1	no	—
105	C₂×C₄×C₈	—	2	1	no	—
106	C₂×C₄×C₈	—	2	1	no	—
107	C₂×C₄×C₈	—	2	1	no	—
108	C₂×C₄×C₈	—	2	1	no	—
109	C₂×C₄×C₈	—	2	1	no	—
110	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
115	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
116	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
118	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
120	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
121	C₄×C₄⋊C₄	Q₈	1	1	yes	characteristic
122	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
125	C₄×C₂²⋊C₄	Q₈	1	1	yes	characteristic
126	#376	C₂×C₄	1	1	yes	characteristic
127	#376	C₂×C₄	1	1	yes	characteristic
128	C₄³	C₂³	1	1	yes	characteristic
129	C₄³	C₂³	1	1	yes	characteristic
130	#336	—	2	1	no	—
131	#336	—	2	1	no	—
132	#336	—	2	1	no	—
133	#336	—	2	1	no	—
134	#336	—	2	1	no	—
135	#336	—	2	1	no	—
136	#336	—	2	1	no	—
137	#336	—	2	1	no	—
138	#336	—	2	1	no	—
139	#336	—	2	1	no	—
140	#336	C₂×C₄	1	1	yes	characteristic
141	#336	C₂×C₄	1	1	yes	characteristic
142	#336	C₂×C₄	1	1	yes	characteristic
143	#336	C₂×C₄	1	1	yes	characteristic
144	#336	C₂×C₄	1	1	yes	characteristic
145	#336	C₂×C₄	1	1	yes	characteristic
146	#336	C₂×C₄	1	1	yes	characteristic
147	#336	C₂×C₄	1	1	yes	characteristic
148	#335	—	2	2	no	—
149	#335	—	2	2	no	—
150	#335	—	2	2	no	—
151	#335	—	2	2	no	—
152	#334	—	2	2	no	—
153	#334	—	2	2	no	—
154	#334	—	2	2	no	—
155	#334	—	2	2	no	—
156	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
157	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	4	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	8	1	no	—
169	C₂²×C₈	—	8	1	no	—
170	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
178	#117	—	2	2	no	—
179	#117	—	2	2	no	—
180	#117	C₂×C₈	1	4	yes	—
181	#117	M₁₆	1	4	yes	—
182	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄²	—	2	1	no	—
191	C₂×C₄²	—	2	1	no	—
192	C₂×C₄²	—	2	1	no	—
193	C₂×C₄²	—	2	1	no	—
194	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
200	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
201	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
202	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
203	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
205	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
206	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
207	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
208	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
209	C₂×C₄²	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₈	—	2	4	no	—
211	C₄⋊C₈	—	2	2	no	—
212	C₄⋊C₈	—	2	2	no	—
213	C₄⋊C₈	—	2	1	no	—
214	C₄⋊C₈	—	2	1	no	—
215	C₄⋊C₈	—	2	1	no	—
216	C₄⋊C₈	—	2	1	no	—
217	C₄⋊C₈	—	2	1	no	—
218	C₄⋊C₈	—	2	1	no	—
219	C₄⋊C₈	—	2	1	no	—
220	C₄⋊C₈	—	2	1	no	—
221	C₄⋊C₈	—	2	1	no	—
222	C₄⋊C₈	—	2	1	no	—
223	C₄⋊C₈	—	2	1	no	—
224	C₄⋊C₈	—	2	1	no	—
225	C₄⋊C₈	—	8	1	no	—
226	C₄⋊C₈	—	8	1	no	—
227	C₄⋊C₈	C₂×C₈	1	4	yes	complemented
228	C₄⋊C₈	C₂×C₈	1	4	yes	complemented
229	C₄⋊C₈	#41	1	2	yes	—
230	C₄⋊C₈	#41	1	2	yes	—
231	C₄⋊C₈	#41	1	2	yes	—
232	C₄⋊C₈	#41	1	2	yes	—
233	C₂²⋊C₈	—	2	4	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂²⋊C₈	—	8	1	no	—
237	C₂²⋊C₈	—	8	1	no	—
238	C₂²⋊C₈	C₂×C₈	1	4	yes	—
239	C₂²⋊C₈	C₂×C₈	1	4	yes	—
240	#97	—	2	2	no	—
241	#97	—	2	2	no	—
242	#97	—	2	2	no	—
243	#97	C₂×C₈	1	4	yes	complemented
244	C₄×C₈	—	2	4	no	—
245	C₄×C₈	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	2	1	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	8	1	no	—
257	C₄×C₈	—	8	1	no	—
258	C₄×C₈	—	8	1	no	—
259	C₄×C₈	—	8	1	no	—
260	C₄×C₈	—	8	1	no	—
261	C₄×C₈	—	8	1	no	—
262	C₄×C₈	C₂×C₈	1	4	yes	complemented
263	#95	C₄⋊C₄	1	1	yes	characteristic
264	#95	C₄⋊C₄	1	1	yes	characteristic
265	#95	C₄⋊C₄	1	1	yes	characteristic
266	#95	C₄⋊C₄	1	1	yes	characteristic
267	#95	C₄⋊C₄	1	1	yes	characteristic
268	#95	C₄⋊C₄	1	1	yes	characteristic
269	#95	C₄⋊C₄	1	1	yes	characteristic
270	#95	C₄⋊C₄	1	1	yes	characteristic
271	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₈	1	2	yes	—
298	C₂²×C₄	C₂×M₁₆	1	2	yes	—
299	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
300	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
301	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	8	4	no	—
347	C₂×C₈	C₂²×C₈	1	2	yes	—
348	C₂×C₈	C₂²×C₈	1	2	yes	—
349	C₂×C₈	C₂²×C₈	1	2	yes	—
350	C₂×C₈	C₂²×C₈	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	C₄⋊C₈	1	4	yes	—
354	C₄⋊C₄	C₄⋊C₈	1	4	yes	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
358	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	4	1	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	C₂²×C₈	1	2	yes	—
380	C₄²	C₂²×C₈	1	2	yes	—
381	C₄²	C₂×M₁₆	1	2	yes	—
382	C₄²	C₂×M₁₆	1	2	yes	—
383	C₄²	#131	1	2	yes	—
384	C₄²	#131	1	2	yes	—
385	C₄²	C₂×#41	1	1	yes	characteristic
386	C₄²	C₂×#41	1	1	yes	characteristic
387	C₄²	C₂×#41	1	1	yes	characteristic
388	C₄²	C₂×#41	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	C₂×C₄⋊C₈	1	2	yes	—
396	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
436	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
437	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
438	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
439	C₂×C₄	C₂×C₄⋊C₈	1	2	yes	—
440	C₂×C₄	#424	1	2	yes	—
441	C₂×C₄	#424	1	2	yes	—
442	C₂×C₄	C₄×#41	1	1	yes	characteristic
443	C₂×C₄	C₄×#41	1	1	yes	characteristic
444	C₂×C₄	#525	1	1	yes	characteristic
445	C₂×C₄	#525	1	1	yes	characteristic
446	C₂×C₄	#533	1	1	yes	characteristic
447	C₂×C₄	#533	1	1	yes	characteristic
448	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
449	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
450	C₂×C₄	C₂×#131	1	1	yes	characteristic
451	C₂×C₄	C₂×#131	1	1	yes	characteristic
452	C₂×C₄	#576	1	1	yes	characteristic
453	C₂×C₄	#577	1	1	yes	characteristic
454	C₂×C₄	#577	1	1	yes	characteristic
455	C₂×C₄	#578	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	2	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	4	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	8	1	no	—
469	C₈	—	8	1	no	—
470	C₈	—	8	1	no	—
471	C₈	—	8	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	#2296	1	1	yes	characteristic
480	C₂²	C₂²×C₄⋊C₈	1	1	yes	characteristic
481	C₂²	C₂×#424	1	1	yes	characteristic
482	C₂²	#2912	1	1	yes	characteristic
483	C₂²	#2913	1	1	yes	characteristic
484	C₂²	#2916	1	1	yes	characteristic
485	C₂²	#2916	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	C₈×#41	1	1	yes	characteristic
500	C₄	C₈×#41	1	1	yes	characteristic
501	C₄	#2965	1	1	yes	characteristic
502	C₄	#2965	1	1	yes	characteristic
503	C₄	#3118	1	1	yes	characteristic
504	C₄	#3119	1	1	yes	characteristic
505	C₄	#3120	1	1	yes	characteristic
506	C₄	#3121	1	1	yes	characteristic
507	C₂	—	4	2	no	—
508	C₂	#17788	1	1	yes	characteristic
509	C₂	#17789	1	1	yes	characteristic
510	C₂	#17811	1	1	yes	characteristic
511	C₂	#17812	1	1	yes	characteristic
512	C₂	#21349	1	1	yes	characteristic
513	C₂	#21367	1	1	yes	characteristic
514	C₂	#21372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄
commutator	C₂×C₄	C₂³×C₈
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂³	C₂²×C₄⋊C₄
prime radical	C₂⁴	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #9603	C₂	semidirect
5. #9603	C₂	semidirect
6. #9602	C₂	semidirect
7. #9601	C₂	semidirect
12. #8275	C₂	semidirect
13. #8275	C₂	semidirect
14. C₄×#335	C₂	semidirect
15. C₄×#334	C₂	semidirect
72. #433	C₈	semidirect
227. C₄⋊C₈	C₂×C₈	semidirect
228. C₄⋊C₈	C₂×C₈	semidirect
243. #97	C₂×C₈	semidirect
262. C₄×C₈	C₂×C₈	semidirect

Maximal subgroups

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

subgroup	index
#21922	2
#20543	2
C₄×#433	2
#9603	2
#9602	2
#9601	2
#8831	2
#8830	2
#8829	2
#8275	2
C₄×#335	2
C₄×#334	2