Subgroups — #498115

Order 512.

747 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2170	C₂	1	1	yes	maximal, characteristic, complemented
2	#33436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#2117	C₂	1	1	yes	maximal, characteristic, complemented
4	#33334	C₂	1	1	yes	maximal, characteristic, complemented
5	#21466	C₂	1	1	yes	maximal, characteristic
6	#13196	C₂	1	1	yes	maximal, characteristic, complemented
7	#13124	C₂	1	1	yes	maximal, characteristic, complemented
8	#13122	C₂	1	1	yes	maximal, characteristic, complemented
9	#12984	C₂	1	1	yes	maximal, characteristic, complemented
10	#12980	C₂	1	1	yes	maximal, characteristic, complemented
11	#12980	C₂	1	1	yes	maximal, characteristic, complemented
12	#12917	C₂	1	1	yes	maximal, characteristic, complemented
13	#12914	C₂	1	1	yes	maximal, characteristic, complemented
14	#12615	C₂	1	1	yes	maximal, characteristic, complemented
15	#12612	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#131	C₂²	1	1	yes	characteristic
17	C₂×#504	C₂²	1	1	yes	characteristic
18	C₂×#504	C₂²	1	1	yes	characteristic
19	C₂×#504	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₃₂	C₂²	1	1	yes	characteristic
21	C₂²×M₃₂	C₂²	1	1	yes	characteristic
22	#3002	C₄	1	1	yes	characteristic
23	C₂×#443	C₂²	1	1	yes	characteristic
24	C₂×#443	C₂²	1	1	yes	characteristic
25	#2929	C₂²	1	1	yes	characteristic
26	#2170	—	2	4	no	—
27	#2169	—	2	1	no	—
28	#2168	—	2	1	no	—
29	#2168	—	2	1	no	—
30	D₄×C₁₆	—	2	1	no	—
31	C₂×#364	C₂²	1	1	yes	characteristic, complemented
32	C₂×#364	C₂²	1	1	yes	characteristic, complemented
33	#2151	C₂²	1	1	yes	characteristic, complemented
34	#2117	—	2	4	no	—
35	C₂×#350	C₂²	1	1	yes	characteristic
36	C₂×#350	C₂²	1	1	yes	characteristic
37	C₂×#350	C₂²	1	1	yes	characteristic
38	C₂×#350	C₂²	1	1	yes	characteristic
39	C₂×#350	C₂²	1	1	yes	characteristic, complemented
40	C₂×#350	C₂²	1	1	yes	characteristic, complemented
41	#2113	—	2	1	no	—
42	#2113	—	2	1	no	—
43	#2113	C₂²	1	1	yes	characteristic
44	#2113	C₂²	1	1	yes	characteristic
45	#2113	C₂²	1	1	yes	characteristic, complemented
46	#2112	—	2	1	no	—
47	#2112	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₁₆	—	2	1	no	—
49	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
50	#2108	C₂²	1	1	yes	characteristic, complemented
51	C₂×#346	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic, complemented
53	#1876	C₄	1	1	yes	characteristic
54	#1876	C₄	1	1	yes	characteristic
55	#1871	C₄	1	1	yes	characteristic
56	#1866	C₄	1	1	yes	characteristic
57	#1866	C₄	1	1	yes	characteristic
58	#1855	C₄	1	1	yes	characteristic
59	#1789	C₄	1	1	yes	characteristic
60	#1764	C₂²	1	1	yes	characteristic
61	#1764	C₂²	1	1	yes	characteristic
62	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
63	#1379	C₂²	1	1	yes	characteristic, complemented
64	#1379	C₂²	1	1	yes	characteristic, complemented
65	#1376	C₂²	1	1	yes	characteristic, complemented
66	#1376	C₂²	1	1	yes	characteristic, complemented
67	#1374	C₂²	1	1	yes	characteristic, complemented
68	#1374	C₂²	1	1	yes	characteristic, complemented
69	C₂²×#41	C₂×C₄	1	1	yes	characteristic
70	C₂×#135	C₂×C₄	1	1	yes	characteristic
71	C₂×#135	C₂×C₄	1	1	yes	characteristic
72	C₂×#131	—	2	1	no	—
73	C₂×#131	—	2	1	no	—
74	C₂×#131	—	2	2	no	—
75	C₂×#131	—	2	2	no	—
76	C₂×#131	—	4	1	no	—
77	C₂×#131	—	4	1	no	—
78	C₂×#131	C₂×C₄	1	1	yes	characteristic
79	C₂×#131	C₂×C₄	1	1	yes	characteristic
80	C₂×#131	C₂³	1	1	yes	characteristic
81	C₂×#131	C₂³	1	1	yes	characteristic
82	C₂×#131	C₂³	1	1	yes	characteristic
83	C₂²×M₁₆	—	2	1	no	—
84	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₈	—	2	1	no	—
86	C₂³×C₈	C₂³	1	1	yes	characteristic
87	#525	C₂×C₄	1	1	yes	characteristic
88	#504	—	2	2	no	—
89	#504	—	2	2	no	—
90	#504	—	2	2	no	—
91	#504	—	4	1	no	—
92	#504	—	4	1	no	—
93	#504	—	4	1	no	—
94	C₂×M₃₂	—	2	1	no	—
95	C₂×M₃₂	—	2	1	no	—
96	C₂×M₃₂	—	2	1	no	—
97	C₂×M₃₂	—	2	1	no	—
98	C₂×M₃₂	—	2	1	no	—
99	C₂×M₃₂	—	2	2	no	—
100	C₂×M₃₂	—	2	1	no	—
101	C₂×M₃₂	—	2	2	no	—
102	C₂×M₃₂	—	4	1	no	—
103	C₂×M₃₂	—	4	1	no	—
104	C₂×M₃₂	C₂³	1	1	yes	characteristic
105	C₂×M₃₂	C₂³	1	1	yes	characteristic
106	C₂×M₃₂	C₂³	1	1	yes	characteristic
107	C₂×M₃₂	C₂³	1	1	yes	characteristic
108	C₂²×C₁₆	—	2	1	no	—
109	C₂²×C₁₆	—	2	1	no	—
110	C₂²×C₁₆	—	2	1	no	—
111	C₂²×C₁₆	—	2	1	no	—
112	C₂²×C₁₆	C₂³	1	1	yes	characteristic
113	C₂²×C₁₆	C₂³	1	1	yes	characteristic
114	C₂²×C₁₆	C₂³	1	1	yes	characteristic
115	C₂²×C₁₆	C₂³	1	1	yes	characteristic
116	#452	C₈	1	1	yes	characteristic
117	#452	C₈	1	1	yes	characteristic
118	#451	C₈	1	1	yes	characteristic
119	#450	C₈	1	1	yes	characteristic
120	#449	C₈	1	1	yes	characteristic
121	#449	C₈	1	1	yes	characteristic
122	#448	C₈	1	1	yes	characteristic
123	#447	C₈	1	1	yes	characteristic
124	#443	—	2	2	no	—
125	#443	—	2	2	no	—
126	#443	—	4	1	no	—
127	#443	—	4	1	no	—
128	#435	—	2	1	no	—
129	#435	—	2	1	no	—
130	C₈×D₄	—	2	1	no	—
131	C₈×D₄	—	2	1	no	—
132	C₂×#108	C₂×C₄	1	1	yes	characteristic
133	C₂×#108	C₂×C₄	1	1	yes	characteristic
134	#424	C₂×C₄	1	1	yes	characteristic
135	C₂×#104	C₂×C₄	1	1	yes	characteristic
136	C₂×#104	C₂×C₄	1	1	yes	characteristic
137	C₂×#104	C₂×C₄	1	1	yes	characteristic
138	C₂×#104	C₂×C₄	1	1	yes	characteristic
139	C₂×#104	C₂×C₄	1	1	yes	characteristic
140	C₂×#104	C₂×C₄	1	1	yes	characteristic
141	#416	C₂×C₄	1	1	yes	characteristic
142	#416	C₂×C₄	1	1	yes	characteristic
143	#408	C₂×C₄	1	1	yes	characteristic
144	#407	C₂×C₄	1	1	yes	characteristic
145	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
146	#405	C₂³	1	1	yes	characteristic
147	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
148	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
149	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
150	#364	—	2	2	no	—
151	#364	—	4	1	no	—
152	C₄⋊C₁₆	—	2	1	no	—
153	C₄⋊C₁₆	—	2	1	no	—
154	#350	—	2	2	no	—
155	#350	—	2	2	no	—
156	#350	—	2	2	no	—
157	#350	—	2	2	no	—
158	#350	—	4	1	no	—
159	#350	D₄	1	4	yes	complemented
160	C₂²⋊C₁₆	—	2	1	no	—
161	C₂²⋊C₁₆	—	2	1	no	—
162	C₂²⋊C₁₆	—	2	1	no	—
163	C₂²⋊C₁₆	—	2	1	no	—
164	C₂²⋊C₁₆	—	2	1	no	—
165	C₂²⋊C₁₆	—	2	1	no	—
166	C₂²⋊C₁₆	—	2	1	no	—
167	C₂²⋊C₁₆	—	2	1	no	—
168	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
169	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
170	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
171	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
172	#346	—	2	1	no	—
173	#346	—	4	1	no	—
174	C₄×C₁₆	—	2	2	no	—
175	C₄×C₁₆	—	2	1	no	—
176	#341	C₂×C₄	1	1	yes	characteristic
177	#341	C₂×C₄	1	1	yes	characteristic
178	#339	C₂×C₄	1	1	yes	characteristic
179	#339	C₂×C₄	1	1	yes	characteristic
180	#336	C₂×C₄	1	1	yes	characteristic
181	#336	C₂×C₄	1	1	yes	characteristic
182	C₂×#41	—	2	1	no	—
183	C₂×#41	—	2	1	no	—
184	C₂×#41	—	2	2	no	—
185	C₂×#41	—	2	2	no	—
186	C₂×#41	—	4	1	no	—
187	C₂×#41	—	4	1	no	—
188	C₂×#41	C₂×C₈	1	1	yes	characteristic
189	C₂×#41	C₂×C₈	1	1	yes	characteristic
190	C₂×#41	C₂²×C₄	1	1	yes	characteristic
191	C₂×#41	C₂²×C₄	1	1	yes	characteristic
192	C₂×#41	C₂²×C₄	1	1	yes	characteristic
193	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
194	C₂²×D₄	—	2	1	no	—
195	C₂²×D₄	C₂×C₈	1	1	yes	characteristic
196	C₂³×C₄	—	2	1	no	—
197	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
198	#135	—	2	2	no	—
199	#135	—	2	2	no	—
200	#135	—	4	1	no	—
201	#135	—	4	1	no	—
202	C₂×Q₁₆	C₂×C₈	1	1	yes	characteristic
203	C₂×Q₁₆	C₂×C₈	1	1	yes	characteristic
204	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
205	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
206	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
207	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
208	C₂×D₈	C₂×C₈	1	1	yes	characteristic
209	C₂×D₈	C₂×C₈	1	1	yes	characteristic
210	#131	—	2	1	no	—
211	#131	—	2	1	no	—
212	#131	—	2	2	no	—
213	#131	—	2	2	no	—
214	#131	—	2	1	no	—
215	#131	—	2	1	no	—
216	#131	—	2	1	no	—
217	#131	—	2	1	no	—
218	#131	—	2	1	no	—
219	#131	—	2	1	no	—
220	#131	—	2	1	no	—
221	#131	—	2	1	no	—
222	#131	—	4	2	no	—
223	#131	—	4	2	no	—
224	#131	—	4	1	no	—
225	#131	—	4	1	no	—
226	#131	—	4	2	no	—
227	#131	—	4	2	no	—
228	#131	C₂×D₄	1	2	yes	—
229	#131	#41	1	2	yes	—
230	C₂×M₁₆	—	2	1	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂×M₁₆	—	4	2	no	—
239	C₂×M₁₆	—	4	1	no	—
240	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
241	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
242	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
243	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	4	2	no	—
255	C₂²×C₈	—	4	2	no	—
256	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
257	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
258	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₈	#41	1	1	yes	characteristic
262	C₂²×C₈	#41	1	1	yes	characteristic
263	C₂²×C₈	C₂⁴	1	1	yes	characteristic
264	#123	—	2	1	no	—
265	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
266	C₂²⋊Q₈	C₂×C₈	1	1	yes	characteristic
267	#121	C₂×C₈	1	1	yes	characteristic
268	#121	C₂×C₈	1	1	yes	characteristic
269	#120	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	#117	C₂²×C₄	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
275	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
276	M₃₂	—	2	1	no	—
277	M₃₂	—	2	1	no	—
278	M₃₂	—	2	1	no	—
279	M₃₂	—	2	1	no	—
280	M₃₂	—	2	1	no	—
281	M₃₂	—	2	1	no	—
282	M₃₂	—	2	1	no	—
283	M₃₂	—	4	2	no	—
284	M₃₂	—	4	2	no	—
285	M₃₂	—	4	2	no	—
286	M₃₂	—	4	2	no	—
287	M₃₂	—	4	2	no	—
288	M₃₂	—	4	2	no	—
289	M₃₂	C₂×D₄	1	2	yes	—
290	C₂×C₁₆	—	2	1	no	—
291	C₂×C₁₆	—	2	1	no	—
292	C₂×C₁₆	—	2	1	no	—
293	C₂×C₁₆	—	2	1	no	—
294	C₂×C₁₆	—	2	1	no	—
295	C₂×C₁₆	—	2	1	no	—
296	C₂×C₁₆	—	2	1	no	—
297	C₂×C₁₆	—	2	1	no	—
298	C₂×C₁₆	—	2	1	no	—
299	C₂×C₁₆	—	2	1	no	—
300	C₂×C₁₆	—	2	1	no	—
301	C₂×C₁₆	—	2	1	no	—
302	C₂×C₁₆	—	2	1	no	—
303	C₂×C₁₆	—	4	2	no	—
304	C₂×C₁₆	—	4	2	no	—
305	C₂×C₁₆	—	4	2	no	—
306	C₂×C₁₆	—	4	2	no	—
307	C₂×C₁₆	C₂×D₄	1	2	yes	—
308	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
309	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
310	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
311	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
312	#108	—	2	2	no	—
313	#108	—	4	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	#104	—	2	2	no	—
317	#104	—	2	2	no	—
318	#104	—	2	2	no	—
319	#104	—	4	1	no	—
320	#104	—	4	1	no	—
321	#104	—	4	1	no	—
322	#103	C₂×C₈	1	1	yes	characteristic
323	#103	C₂×C₈	1	1	yes	characteristic
324	#103	C₂×C₈	1	1	yes	characteristic
325	#103	C₂×C₈	1	1	yes	characteristic
326	#102	C₂×C₈	1	1	yes	characteristic
327	#102	C₂×C₈	1	1	yes	characteristic
328	#102	C₂×C₈	1	1	yes	characteristic
329	#102	C₂×C₈	1	1	yes	characteristic
330	C₂²⋊C₈	—	2	1	no	—
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	C₂×C₈	1	1	yes	characteristic
335	C₂²⋊C₈	C₂×C₈	1	1	yes	characteristic
336	C₂²⋊C₈	C₂×C₈	1	1	yes	characteristic
337	C₂²⋊C₈	C₂×C₈	1	1	yes	characteristic
338	#97	—	2	1	no	—
339	C₄×C₈	—	2	1	no	—
340	C₄×C₈	—	2	1	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	2	1	no	—
344	#95	—	2	1	no	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	#131	1	1	yes	characteristic
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	—	2	2	no	—
350	#41	—	2	2	no	—
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	#41	—	2	1	no	—
354	#41	—	2	1	no	—
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	4	2	no	—
360	#41	—	4	2	no	—
361	#41	—	4	1	no	—
362	#41	—	4	1	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	C₄×D₄	1	2	yes	—
366	#41	#131	1	2	yes	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	1	no	—
370	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
371	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
372	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
386	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
387	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
406	C₂²×C₄	#131	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
408	Q₁₆	—	2	2	no	—
409	Q₁₆	—	4	1	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	4	1	no	—
413	SD₁₆	—	4	1	no	—
414	D₈	—	2	2	no	—
415	D₈	—	4	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	2	1	no	—
422	M₁₆	—	2	1	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	4	2	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	—	4	2	no	—
428	M₁₆	—	4	1	no	—
429	M₁₆	—	4	1	no	—
430	M₁₆	—	4	1	no	—
431	M₁₆	—	4	1	no	—
432	M₁₆	C₄×D₄	1	2	yes	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	4	2	no	—
454	C₂×C₈	—	4	2	no	—
455	C₂×C₈	—	4	2	no	—
456	C₂×C₈	—	4	1	no	—
457	C₂×C₈	—	4	1	no	—
458	C₂×C₈	—	4	1	no	—
459	C₂×C₈	—	4	1	no	—
460	C₂×C₈	C₄×D₄	1	1	yes	characteristic
461	C₂×C₈	C₄×D₄	1	1	yes	characteristic
462	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
463	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
464	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
465	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
466	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₈	C₂×#41	1	1	yes	characteristic
469	C₂×C₈	C₂×#41	1	1	yes	characteristic
470	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₁₆	—	2	1	no	—
488	C₁₆	—	2	1	no	—
489	C₁₆	—	2	2	no	—
490	C₁₆	—	2	1	no	—
491	C₁₆	—	2	1	no	—
492	C₁₆	—	2	2	no	—
493	C₁₆	—	4	1	no	—
494	C₁₆	—	4	1	no	—
495	C₁₆	—	4	1	no	—
496	C₁₆	—	4	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	8	1	no	—
507	C₂³	C₈×D₄	1	1	yes	characteristic
508	C₂³	C₈×D₄	1	1	yes	characteristic
509	C₂³	C₂×#131	1	1	yes	characteristic
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	4	2	no	—
516	Q₈	C₈×D₄	1	2	yes	—
517	D₄	—	2	2	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	8	1	no	—
533	D₄	C₈×D₄	1	2	yes	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	C₈×D₄	1	1	yes	characteristic
565	C₂×C₄	C₈×D₄	1	1	yes	characteristic
566	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
568	C₂×C₄	#518	1	1	yes	characteristic
569	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
570	C₂×C₄	C₂×#131	1	1	yes	characteristic
571	C₂×C₄	#568	1	1	yes	characteristic
572	C₈	—	2	1	no	—
573	C₈	—	2	1	no	—
574	C₈	—	2	2	no	—
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	D₄²	1	1	yes	characteristic
583	C₈	#546	1	1	yes	characteristic
584	C₈	#546	1	1	yes	characteristic
585	C₈	#551	1	1	yes	characteristic
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	4	no	—
606	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
607	C₂²	#2933	1	1	yes	characteristic
608	C₂²	#2977	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	8	1	no	—
618	C₄	#2358	1	1	yes	characteristic
619	C₄	C₂×C₈×D₄	1	1	yes	characteristic
620	C₄	#2933	1	1	yes	characteristic
621	C₄	#2972	1	1	yes	characteristic
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	4	1	no	—
625	C₂	—	4	1	no	—
626	C₂	—	4	2	no	—
627	C₂	—	8	1	no	—
628	C₂	—	8	1	no	—
629	C₂	#22842	1	1	yes	characteristic
630	C₂	#33441	1	1	yes	characteristic
631	C₂	#33443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₄
commutator	C₂×C₄	C₂³×C₈
Frattini, cosocle	C₂²×C₈	C₂⁴
socle	C₂²	C₂×C₈×D₄
prime radical	#3002	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#2170	C₂	semidirect
2. #33436	C₂	semidirect
3. C₂×#2117	C₂	semidirect
4. #33334	C₂	semidirect
6. #13196	C₂	semidirect
7. #13124	C₂	semidirect
8. #13122	C₂	semidirect
9. #12984	C₂	semidirect
10. #12980	C₂	semidirect
11. #12980	C₂	semidirect
12. #12917	C₂	semidirect
13. #12914	C₂	semidirect
14. #12615	C₂	semidirect
15. #12612	C₂	semidirect
19. C₂×#504	C₂²	semidirect
31. C₂×#364	C₂²	semidirect
32. C₂×#364	C₂²	semidirect
33. #2151	C₂²	semidirect
39. C₂×#350	C₂²	semidirect
40. C₂×#350	C₂²	semidirect
45. #2113	C₂²	semidirect
50. #2108	C₂²	semidirect
51. C₂×#346	C₂²	semidirect
52. C₂×C₄×C₁₆	C₂²	semidirect
63. #1379	C₂²	semidirect
64. #1379	C₂²	semidirect
65. #1376	C₂²	semidirect
66. #1376	C₂²	semidirect
67. #1374	C₂²	semidirect
68. #1374	C₂²	semidirect
159. #350	D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2170	2
#33436	2
C₂×#2117	2
#33334	2
#21466	2
#13196	2
#13124	2
#13122	2
#12984	2
#12980	2
#12917	2
#12914	2
#12615	2
#12612	2