Subgroups — C₂×#10601087 #12128222

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
2	C₂×#65525	C₂	1	1	yes	maximal, characteristic
3	C₂×#65526	C₂	1	1	yes	maximal, characteristic
4	C₂×#65391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#64772	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64753	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64751	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601087	C₂	1	8	yes	maximal, direct product factor
9	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×#4072	C₂²	1	1	yes	characteristic
13	C₂²×#681	C₂²	1	1	yes	characteristic
14	C₂²×#681	C₂²	1	1	yes	characteristic
15	C₂²×#681	C₂²	1	1	yes	characteristic
16	C₅×#416	—	2	2	no	—
17	C₅×#416	C₂²	1	4	yes	—
18	C₂×C₅×#103	—	2	1	no	—
19	C₂×C₅×#102	—	2	1	no	—
20	#65526	—	2	2	no	—
21	#65526	C₂²	1	4	yes	—
22	#65525	—	2	2	no	—
23	#65525	C₂²	1	4	yes	—
24	C₂×#3969	—	2	2	no	—
25	C₂×#3968	—	2	1	no	—
26	C₂×#3965	—	2	1	no	—
27	#65391	—	2	2	no	—
28	#65391	C₂²	1	4	yes	complemented
29	C₂×#3946	—	2	2	no	—
30	#64772	C₂²	1	4	yes	complemented
31	#64753	C₂²	1	4	yes	complemented
32	#64751	C₂²	1	4	yes	complemented
33	C₂×#2080	—	5	1	no	maximal, Sylow
34	C₂×C₅×#41	—	2	1	no	—
35	C₂×C₅×#41	—	2	1	no	—
36	C₂×C₅×#41	—	2	1	no	—
37	C₂×C₅×#41	—	2	1	no	—
38	C₂×C₅×#41	—	2	1	no	—
39	C₂×C₅×#41	—	2	1	no	—
40	C₂×C₅×#41	—	2	1	no	—
41	C₂×C₅×#41	—	2	1	no	—
42	C₂×C₅×#41	—	2	1	no	—
43	C₂×C₅×#41	—	2	1	no	—
44	C₂×C₅×#41	D₄	1	2	yes	—
45	C₂×C₅×#41	C₂³	1	2	yes	—
46	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×D₄	—	2	1	no	—
48	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	—	2	1	no	—
52	C₂²×C₅×C₈	—	2	1	no	—
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	—	2	1	no	—
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₅×#117	—	2	1	no	—
59	C₅×#117	—	2	1	no	—
60	C₅×#117	—	2	1	no	—
61	C₅×#117	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₂²⋊Dic₅	—	2	1	no	—
66	#4072	—	2	1	no	—
67	#4072	—	2	1	no	—
68	#4072	D₄	1	2	yes	—
69	#4072	C₂³	1	2	yes	—
70	C₂×C₄⋊Dic₅	—	2	1	no	—
71	C₂×C₄×Dic₅	D₄	1	2	yes	—
72	C₂×#681	—	2	1	no	—
73	C₂×#681	—	2	1	no	—
74	C₂×#681	—	2	1	no	—
75	C₂×#681	—	2	1	no	—
76	C₂×#681	—	2	1	no	—
77	C₂×#681	—	2	1	no	—
78	C₂×#681	—	2	1	no	—
79	C₂×#681	—	2	1	no	—
80	C₂×#681	—	2	1	no	—
81	C₂×#681	—	2	1	no	—
82	C₂×#681	—	2	1	no	—
83	C₂×#681	—	2	1	no	—
84	C₂×#681	—	2	1	no	—
85	C₂×#681	—	2	1	no	—
86	C₂×#681	—	2	1	no	—
87	C₂×#681	C₂³	1	2	yes	—
88	C₂×#681	C₂³	1	2	yes	—
89	C₂×#681	C₂³	1	2	yes	—
90	C₂²×#168	—	2	1	no	—
91	C₂²×#168	—	2	1	no	—
92	C₂²×#168	—	2	1	no	—
93	C₅×#103	—	2	4	no	—
94	C₅×#102	—	2	4	no	—
95	#3969	—	2	8	no	—
96	#3968	—	2	4	no	—
97	#3965	—	2	4	no	—
98	#3946	—	2	8	no	—
99	C₂×#424	—	5	1	no	—
100	C₂×#421	—	5	1	no	—
101	C₂×#416	D₅	1	1	yes	characteristic
102	C₂×#413	—	5	1	no	—
103	#2080	—	5	8	no	—
104	C₂×#344	—	5	1	no	—
105	C₂×#341	—	5	1	no	—
106	C₂×H(3,ℤ/4)	—	5	1	no	—
107	C₂⁴×C₅	—	2	1	no	—
108	C₂⁴×C₅	#41	1	1	yes	characteristic
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	2	2	no	—
115	C₅×#41	—	2	2	no	—
116	C₅×#41	—	2	2	no	—
117	C₅×#41	—	4	1	no	—
118	C₅×#41	—	4	1	no	—
119	C₅×#41	—	4	1	no	—
120	C₅×#41	—	4	1	no	—
121	C₅×#41	—	4	1	no	—
122	C₅×#41	—	4	1	no	—
123	C₅×#41	—	4	1	no	—
124	C₅×#41	—	4	1	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
131	C₂×C₅×D₄	—	2	2	no	—
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	4	1	no	—
139	C₂×C₅×D₄	—	4	1	no	—
140	C₂×C₅×D₄	—	4	1	no	—
141	C₂×C₅×D₄	—	4	1	no	—
142	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	4	1	no	—
147	C₂²×C₄×C₅	—	4	1	no	—
148	C₂²×C₄×C₅	—	4	1	no	—
149	C₂²×C₄×C₅	—	4	1	no	—
150	C₂²×C₄×C₅	—	4	1	no	—
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	#41	1	1	yes	characteristic
156	C₂²×C₄×C₅	#41	1	1	yes	characteristic
157	C₂²×C₄×C₅	#41	1	1	yes	characteristic
158	C₂²×C₄×C₅	#41	1	1	yes	characteristic
159	C₂²×C₄×C₅	#41	1	1	yes	characteristic
160	C₂²×C₄×C₅	#41	1	1	yes	characteristic
161	C₂²×C₄×C₅	#41	1	1	yes	characteristic
162	C₂²×C₄×C₅	#41	1	1	yes	characteristic
163	C₂²×C₄×C₅	#41	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₂²×Dic₅	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	2	2	no	—
168	C₂×C₅×C₈	—	2	2	no	—
169	C₂×C₅×C₈	—	4	1	no	—
170	C₂×C₅×C₈	—	4	1	no	—
171	C₂×C₅×C₈	—	4	1	no	—
172	C₂×C₅×C₈	—	4	1	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	4	1	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	—	4	1	no	—
177	C₄²×C₅	—	2	2	no	—
178	C₄²×C₅	—	4	1	no	—
179	C₂²⋊Dic₅	—	2	2	no	—
180	C₂²⋊Dic₅	—	2	2	no	—
181	C₄⋊Dic₅	—	2	2	no	—
182	C₄⋊Dic₅	—	2	2	no	—
183	C₄×Dic₅	—	2	2	no	—
184	C₄×Dic₅	C₂×D₄	1	4	yes	—
185	#681	—	2	2	no	—
186	#681	—	2	2	no	—
187	#681	—	2	2	no	—
188	#681	—	2	2	no	—
189	#681	—	2	2	no	—
190	#681	—	2	2	no	—
191	#681	—	4	1	no	—
192	#681	—	4	1	no	—
193	#681	—	4	1	no	—
194	#681	—	4	1	no	—
195	#681	—	4	1	no	—
196	#681	—	4	1	no	—
197	C₂×#168	—	2	2	no	—
198	C₂×#168	—	2	2	no	—
199	C₂×#168	—	2	2	no	—
200	C₂×#168	—	4	1	no	—
201	C₂×#168	—	4	1	no	—
202	C₂×#168	—	4	1	no	—
203	C₂×#168	—	4	1	no	—
204	C₂×#168	—	4	1	no	—
205	C₂×#168	—	4	1	no	—
206	C₂²×#41	C₂×D₅	1	1	yes	characteristic
207	C₂²×M₁₆	—	5	1	no	—
208	C₂²×M₁₆	—	5	1	no	—
209	C₂²×M₁₆	—	5	1	no	—
210	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
211	C₂×#117	—	5	1	no	—
212	C₂×#117	C₂×D₅	1	1	yes	characteristic
213	#424	—	5	4	no	—
214	#424	—	10	2	no	—
215	C₂×C₄⋊C₈	—	10	2	no	—
216	#421	—	5	4	no	—
217	#421	—	10	2	no	—
218	C₂×#104	—	10	2	no	—
219	#416	—	2	2	no	—
220	#416	C₂×D₅	1	4	yes	—
221	C₂×#103	—	2	1	no	—
222	C₂×#102	—	2	1	no	—
223	#413	—	5	4	no	—
224	#413	—	10	2	no	—
225	C₂×#101	—	10	1	no	—
226	C₂×#100	—	10	1	no	—
227	#344	—	5	4	no	—
228	#341	—	5	4	no	—
229	H(3,ℤ/4)	—	5	4	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	—	4	2	no	—
232	C₂³×C₅	—	4	1	no	—
233	C₂³×C₅	—	4	1	no	—
234	C₂³×C₅	—	8	2	no	—
235	C₂³×C₅	#123	1	1	yes	characteristic
236	C₂³×C₅	#123	1	1	yes	characteristic
237	C₂³×C₅	#123	1	1	yes	characteristic
238	C₂³×C₅	#123	1	1	yes	characteristic
239	C₂³×C₅	#126	1	1	yes	characteristic
240	C₂³×C₅	#126	1	1	yes	characteristic
241	C₂³×C₅	C₂×#41	1	1	yes	characteristic
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	—	2	2	no	—
244	C₅×Q₈	—	4	1	no	—
245	C₅×Q₈	—	4	1	no	—
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	4	2	no	—
249	C₅×D₄	—	4	2	no	—
250	C₅×D₄	—	4	2	no	—
251	C₅×D₄	—	4	2	no	—
252	C₅×D₄	—	4	1	no	—
253	C₅×D₄	—	4	1	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	—	4	2	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	—	8	2	no	—
263	C₂×C₄×C₅	#121	1	1	yes	characteristic
264	C₂×C₄×C₅	#121	1	1	yes	characteristic
265	C₂×C₄×C₅	#121	1	1	yes	characteristic
266	C₂×C₄×C₅	#121	1	1	yes	characteristic
267	C₂×C₄×C₅	#123	1	1	yes	characteristic
268	C₂×C₄×C₅	#123	1	1	yes	characteristic
269	C₂×C₄×C₅	#123	1	1	yes	characteristic
270	C₂×C₄×C₅	#123	1	1	yes	characteristic
271	C₂×C₄×C₅	#123	1	1	yes	characteristic
272	C₂×C₄×C₅	#123	1	1	yes	characteristic
273	C₂×C₄×C₅	#123	1	1	yes	characteristic
274	C₂×C₄×C₅	#123	1	1	yes	characteristic
275	C₂×C₄×C₅	#124	1	1	yes	characteristic
276	C₂×C₄×C₅	#124	1	1	yes	characteristic
277	C₂×C₄×C₅	#124	1	1	yes	characteristic
278	C₂×C₄×C₅	#124	1	1	yes	characteristic
279	C₂×C₄×C₅	#126	1	1	yes	characteristic
280	C₂×C₄×C₅	#126	1	1	yes	characteristic
281	C₂×C₄×C₅	#126	1	1	yes	characteristic
282	C₂×C₄×C₅	#126	1	1	yes	characteristic
283	C₂×C₄×C₅	#126	1	1	yes	characteristic
284	C₂×C₄×C₅	#126	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
291	C₂×Dic₅	—	2	4	no	—
292	C₂×Dic₅	—	4	4	no	—
293	C₅×C₈	—	4	2	no	—
294	#168	—	4	2	no	—
295	#168	—	4	2	no	—
296	#168	—	4	2	no	—
297	C₂×#41	—	2	1	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	—	2	1	no	—
301	C₂×#41	—	2	1	no	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	2	1	no	—
307	C₂×#41	C₂²⋊D₅	1	2	yes	—
308	C₂×#41	C₂²×D₅	1	2	yes	—
309	C₂²×Q₈	C₂²⋊D₅	1	1	yes	characteristic
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	C₂²⋊D₅	1	1	yes	characteristic
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
314	C₂×M₁₆	—	5	2	no	—
315	C₂×M₁₆	—	5	2	no	—
316	C₂×M₁₆	—	5	2	no	—
317	C₂×M₁₆	—	10	1	no	—
318	C₂×M₁₆	—	10	1	no	—
319	C₂×M₁₆	—	10	1	no	—
320	C₂×M₁₆	—	10	1	no	—
321	C₂×M₁₆	—	10	1	no	—
322	C₂×M₁₆	—	10	1	no	—
323	C₂×M₁₆	—	10	1	no	—
324	C₂×M₁₆	—	10	1	no	—
325	C₂×M₁₆	—	10	1	no	—
326	C₂×M₁₆	—	10	1	no	—
327	C₂×M₁₆	—	10	1	no	—
328	C₂×M₁₆	—	10	1	no	—
329	C₂×M₁₆	—	10	1	no	—
330	C₂×M₁₆	—	10	1	no	—
331	C₂×M₁₆	—	10	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	10	1	no	—
339	C₂²×C₈	—	10	1	no	—
340	C₂²×C₈	—	10	1	no	—
341	C₂²×C₈	C₂²×D₅	1	2	yes	—
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	—	5	2	no	—
346	#117	—	5	2	no	—
347	#117	—	10	1	no	—
348	#117	—	10	1	no	—
349	#117	C₂²×D₅	1	2	yes	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	10	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	10	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	5	2	no	—
356	C₄⋊C₈	—	10	8	no	—
357	#104	—	10	8	no	—
358	#103	—	2	4	no	—
359	#102	—	2	4	no	—
360	#101	—	10	4	no	—
361	#100	—	10	4	no	—
362	C₂²×C₅	—	2	2	no	—
363	C₂²×C₅	—	2	2	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	—	4	1	no	—
366	C₂²×C₅	—	4	1	no	—
367	C₂²×C₅	—	4	1	no	—
368	C₂²×C₅	—	4	1	no	—
369	C₂²×C₅	—	4	2	no	—
370	C₂²×C₅	—	8	2	no	—
371	C₂²×C₅	—	8	2	no	—
372	C₂²×C₅	—	8	2	no	—
373	C₂²×C₅	#397	1	1	yes	characteristic
374	C₂²×C₅	#397	1	1	yes	characteristic
375	C₂²×C₅	#397	1	1	yes	characteristic
376	C₂²×C₅	#397	1	1	yes	characteristic
377	C₂²×C₅	C₂×#123	1	1	yes	characteristic
378	C₂²×C₅	C₂×#123	1	1	yes	characteristic
379	C₂²×C₅	C₂×#126	1	1	yes	characteristic
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	—	8	2	no	—
382	C₄×C₅	#397	1	1	yes	characteristic
383	C₄×C₅	#397	1	1	yes	characteristic
384	C₄×C₅	#397	1	1	yes	characteristic
385	C₄×C₅	#397	1	1	yes	characteristic
386	C₄×C₅	C₂×#121	1	1	yes	characteristic
387	C₄×C₅	C₂×#123	1	1	yes	characteristic
388	C₄×C₅	C₂×#124	1	1	yes	characteristic
389	C₄×C₅	C₂×#126	1	1	yes	characteristic
390	Dic₅	—	4	4	no	—
391	C₂⁴	—	2	1	no	—
392	C₂⁴	#711	1	1	yes	characteristic
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	4	1	no	—
402	#41	—	4	1	no	—
403	#41	—	4	1	no	—
404	#41	—	4	1	no	—
405	#41	—	4	1	no	—
406	#41	—	4	1	no	—
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	C₂×C₂²⋊D₅	1	2	yes	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	C₂×C₂²⋊D₅	1	2	yes	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	10	2	no	—
436	C₂²×C₄	#709	1	1	yes	characteristic
437	C₂²×C₄	#709	1	1	yes	characteristic
438	C₂²×C₄	#709	1	1	yes	characteristic
439	C₂²×C₄	#709	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
442	C₂²×C₄	#711	1	1	yes	characteristic
443	C₂²×C₄	#711	1	1	yes	characteristic
444	C₂²×C₄	#711	1	1	yes	characteristic
445	C₂²×C₄	#711	1	1	yes	characteristic
446	C₂²×C₄	#711	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
449	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
450	M₁₆	—	10	2	no	—
451	M₁₆	—	10	2	no	—
452	M₁₆	—	10	2	no	—
453	M₁₆	—	10	2	no	—
454	M₁₆	—	10	2	no	—
455	M₁₆	—	10	2	no	—
456	M₁₆	—	20	1	no	—
457	M₁₆	—	20	1	no	—
458	M₁₆	—	20	1	no	—
459	M₁₆	—	20	1	no	—
460	M₁₆	—	20	1	no	—
461	M₁₆	—	20	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	—	4	1	no	—
468	C₂×C₈	—	4	1	no	—
469	C₂×C₈	—	10	2	no	—
470	C₂×C₈	—	10	2	no	—
471	C₂×C₈	—	10	2	no	—
472	C₂×C₈	—	20	1	no	—
473	C₂×C₈	—	20	1	no	—
474	C₂×C₈	—	20	1	no	—
475	C₂×C₈	—	20	1	no	—
476	C₂×C₈	—	20	1	no	—
477	C₂×C₈	—	20	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	10	2	no	—
481	C₄⋊C₄	—	10	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	10	2	no	—
485	C₂²⋊C₄	—	10	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	4	1	no	—
488	C₄²	—	5	4	no	—
489	C₄²	—	10	2	no	—
490	C₂×C₅	—	2	1	no	—
491	C₂×C₅	—	2	1	no	—
492	C₂×C₅	—	2	1	no	—
493	C₂×C₅	—	2	1	no	—
494	C₂×C₅	—	2	1	no	—
495	C₂×C₅	—	2	1	no	—
496	C₂×C₅	—	8	2	no	—
497	C₂×C₅	#2080	1	2	yes	complemented
498	C₂×C₅	C₂×#397	1	1	yes	characteristic
499	C₂³	—	2	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	8	2	no	—
504	C₂³	#4025	1	1	yes	characteristic
505	C₂³	#4025	1	1	yes	characteristic
506	C₂³	#4029	1	1	yes	characteristic
507	C₂³	#4029	1	1	yes	characteristic
508	C₂³	#4081	1	1	yes	characteristic
509	C₂³	#4081	1	1	yes	characteristic
510	C₂³	C₂×#711	1	1	yes	characteristic
511	Q₈	—	2	2	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	10	4	no	—
533	C₂×C₄	—	20	4	no	—
534	C₂×C₄	#4025	1	1	yes	characteristic
535	C₂×C₄	#4025	1	1	yes	characteristic
536	C₂×C₄	#4025	1	1	yes	characteristic
537	C₂×C₄	#4025	1	1	yes	characteristic
538	C₂×C₄	#4025	1	1	yes	characteristic
539	C₂×C₄	#4025	1	1	yes	characteristic
540	C₂×C₄	#4029	1	1	yes	characteristic
541	C₂×C₄	#4029	1	1	yes	characteristic
542	C₂×C₄	#4031	1	1	yes	characteristic
543	C₂×C₄	#4031	1	1	yes	characteristic
544	C₂×C₄	#4031	1	1	yes	characteristic
545	C₂×C₄	#4031	1	1	yes	characteristic
546	C₂×C₄	#4075	1	1	yes	characteristic
547	C₂×C₄	#4075	1	1	yes	characteristic
548	C₂×C₄	#4075	1	1	yes	characteristic
549	C₂×C₄	#4075	1	1	yes	characteristic
550	C₂×C₄	#4081	1	1	yes	characteristic
551	C₂×C₄	#4081	1	1	yes	characteristic
552	C₂×C₄	#4085	1	1	yes	characteristic
553	C₂×C₄	#4085	1	1	yes	characteristic
554	C₂×C₄	#4085	1	1	yes	characteristic
555	C₂×C₄	#4085	1	1	yes	characteristic
556	C₂×C₄	C₂×#709	1	1	yes	characteristic
557	C₂×C₄	C₂×#709	1	1	yes	characteristic
558	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
559	C₂×C₄	C₂×#711	1	1	yes	characteristic
560	C₂×C₄	C₂×#711	1	1	yes	characteristic
561	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
562	C₈	—	4	2	no	—
563	C₈	—	20	2	no	—
564	C₈	—	20	2	no	—
565	C₈	—	20	2	no	—
566	C₅	C₂×#2080	1	1	yes	characteristic, complemented, Sylow
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	—	8	2	no	—
578	C₂²	#65241	1	1	yes	characteristic
579	C₂²	#65241	1	1	yes	characteristic
580	C₂²	#65241	1	1	yes	characteristic
581	C₂²	#65241	1	1	yes	characteristic
582	C₂²	C₂×#4025	1	1	yes	characteristic
583	C₂²	C₂×#4029	1	1	yes	characteristic
584	C₂²	C₂×#4081	1	1	yes	characteristic
585	C₄	—	4	2	no	—
586	C₄	—	8	2	no	—
587	C₄	—	20	4	no	—
588	C₄	#65241	1	1	yes	characteristic
589	C₄	#65241	1	1	yes	characteristic
590	C₄	#65241	1	1	yes	characteristic
591	C₄	#65241	1	1	yes	characteristic
592	C₄	C₂×#4025	1	1	yes	characteristic
593	C₄	C₂×#4031	1	1	yes	characteristic
594	C₄	C₂×#4075	1	1	yes	characteristic
595	C₄	C₂×#4085	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	8	2	no	—
603	C₂	#10601087	1	2	yes	direct product factor
604	C₂	C₂×#65241	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#4031
commutator, cosocle	C₂²×C₄×C₅	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂×C₅×#416	C₂
socle	C₂²×C₅	#397
prime radical	C₂²×C₅×#41	C₂²
hypercenter	C₂×#416	D₅
hypocenter	C₅	C₂×#2080
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#416

Complements

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

N	H ≅ G/N	type
4. C₂×#65391	C₂	semidirect
5. C₂×#64772	C₂	semidirect
6. C₂×#64753	C₂	semidirect
7. C₂×#64751	C₂	semidirect
8. #10601087	C₂	direct (N × H)
28. #65391	C₂²	semidirect
30. #64772	C₂²	semidirect
31. #64753	C₂²	semidirect
32. #64751	C₂²	semidirect
497. C₂×C₅	#2080	semidirect
566. C₅	C₂×#2080	semidirect
603. C₂	#10601087	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#416	2
C₂×#65525	2
C₂×#65526	2
C₂×#65391	2
C₂×#64772	2
C₂×#64753	2
C₂×#64751	2
#10601087	2
C₂×#2080	5

Subgroups — C2×#10601087 #12128222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10601087 #12128222