Subgroups — C₂×#10610311 #12963622

Order 1280.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66079	C₂	1	2	yes	maximal, complemented
2	C₂²×#4050	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#3951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#65294	C₂	1	2	yes	maximal, complemented
6	#10610311	C₂	1	16	yes	maximal, direct product factor
7	C₂×#65006	C₂	1	4	yes	maximal, complemented
8	C₂×#64989	C₂	1	4	yes	maximal, complemented
9	C₂²×#709	C₂²	1	2	yes	—
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂²×#681	C₂²	1	2	yes	—
14	#66079	—	2	8	no	—
15	#66079	C₂²	1	16	yes	complemented
16	C₂×#4053	—	2	4	no	—
17	C₂×D₅×M₁₆	—	2	4	no	—
18	C₂²×Dic₂₀	C₄	1	1	yes	characteristic, complemented
19	C₂×#4050	C₄	1	2	yes	complemented
20	C₂×#4050	C₄	1	2	yes	complemented
21	C₂×#4050	C₄	1	8	yes	complemented
22	C₂×#4050	C₂²	1	2	yes	—
23	C₂×#4050	C₂²	1	2	yes	—
24	C₂×#4050	C₂²	1	8	yes	—
25	C₂²×D₄₀	C₄	1	1	yes	characteristic, complemented
26	C₂²×#677	C₄	1	2	yes	complemented
27	C₂×#4047	C₂²	1	8	yes	complemented
28	C₅×#405	C₂²	1	8	yes	complemented
29	C₂×C₅×#97	C₂²	1	2	yes	complemented
30	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
31	C₂×#3951	C₂²	1	2	yes	complemented
32	C₂×#3951	C₂²	1	2	yes	complemented
33	C₂×#3951	C₂²	1	8	yes	complemented
34	#65294	C₂²	1	16	yes	complemented
35	C₂×#3937	C₂²	1	8	yes	complemented
36	#65006	C₂²	1	32	yes	complemented
37	#64989	C₂²	1	32	yes	complemented
38	C₂×#2957	—	5	1	no	maximal, Sylow
39	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₂²⋊D₅	—	2	2	no	—
41	C₂×#709	—	2	2	no	—
42	C₂×#709	—	2	4	no	—
43	C₂×#709	—	2	2	no	—
44	C₂×#709	—	2	4	no	—
45	C₂×#709	C₂×C₄	1	4	yes	—
46	C₂×#709	C₂×C₄	1	8	yes	—
47	C₂×#709	C₂³	1	8	yes	—
48	C₂×#709	C₂³	1	4	yes	—
49	C₂²×D₂₀	C₂×C₄	1	2	yes	—
50	C₂²×C₄×D₅	—	2	2	no	—
51	C₂²×Dic₁₀	C₂×C₄	1	2	yes	—
52	C₂×C₅×M₁₆	D₄	1	2	yes	—
53	C₂×C₅×M₁₆	D₄	1	2	yes	—
54	C₂×C₅×M₁₆	D₄	1	4	yes	—
55	C₂×C₅×M₁₆	C₂³	1	4	yes	—
56	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	4	yes	—
64	C₂²×C₅×C₈	C₂³	1	2	yes	—
65	C₅×#117	—	2	2	no	—
66	C₅×#117	C₂³	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₂×#681	—	2	2	no	—
71	C₂×#681	—	2	4	no	—
72	C₂×#681	C₂³	1	8	yes	—
73	C₂×#681	C₂³	1	4	yes	—
74	C₂²×#168	—	2	2	no	—
75	#4053	—	2	32	no	—
76	D₅×M₁₆	—	2	32	no	—
77	C₂×Dic₂₀	C₂×C₄	1	2	yes	—
78	C₂×Dic₂₀	C₂×C₄	1	2	yes	—
79	C₂×Dic₂₀	C₂×C₄	1	8	yes	complemented
80	#4050	C₂×C₄	1	8	yes	—
81	#4050	C₂×C₄	1	8	yes	—
82	#4050	C₂×C₄	1	16	yes	complemented
83	#4050	C₂×C₄	1	16	yes	complemented
84	#4050	C₂³	1	8	yes	—
85	#4050	C₂³	1	8	yes	—
86	C₂×D₄₀	C₂×C₄	1	2	yes	—
87	C₂×D₄₀	C₂×C₄	1	2	yes	—
88	C₂×D₄₀	C₂×C₄	1	8	yes	complemented
89	C₂×#677	C₂×C₄	1	4	yes	—
90	C₂×#677	C₂×C₄	1	4	yes	—
91	C₂×#677	C₂×C₄	1	16	yes	complemented
92	#4047	—	2	16	no	—
93	#4047	C₂³	1	32	yes	complemented
94	C₂×#676	—	2	8	no	—
95	C₂×C₈×D₅	—	2	8	no	—
96	C₅×#97	C₂³	1	8	yes	complemented
97	C₄×C₅×C₈	C₂³	1	8	yes	complemented
98	#3951	C₂³	1	8	yes	complemented
99	#3951	C₂³	1	8	yes	complemented
100	#3937	C₂³	1	32	yes	complemented
101	C₂²×#135	—	5	1	no	—
102	C₂×#568	—	5	2	no	—
103	#2957	—	5	16	no	—
104	C₂×#444	—	5	4	no	—
105	C₂×#443	—	5	4	no	—
106	C₂²×#108	—	5	1	no	—
107	C₂×#421	—	5	2	no	—
108	C₂×#405	D₅	1	1	yes	characteristic, complemented
109	C₂⁴×C₅	#41	1	1	yes	characteristic
110	C₂³×D₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₅	#41	1	1	yes	characteristic
119	C₂²×C₄×C₅	#41	1	2	yes	—
120	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
122	C₂×C₂²⋊D₅	—	2	4	no	—
123	C₂×C₂²⋊D₅	—	2	8	no	—
124	C₂×C₂²⋊D₅	—	2	4	no	—
125	C₂×C₂²⋊D₅	—	2	8	no	—
126	C₂²×Dic₅	—	2	2	no	—
127	#709	—	2	8	no	—
128	#709	—	2	8	no	—
129	#709	—	2	8	no	—
130	#709	—	2	4	no	—
131	#709	—	2	8	no	—
132	#709	—	2	4	no	—
133	#709	—	2	8	no	—
134	#709	C₂²×C₄	1	8	yes	—
135	#709	C₂²×C₄	1	16	yes	—
136	#709	C₂⁴	1	8	yes	—
137	C₂×D₂₀	—	2	2	no	—
138	C₂×D₂₀	—	2	4	no	—
139	C₂×D₂₀	C₂²×C₄	1	4	yes	—
140	C₂×D₂₀	C₂²×C₄	1	8	yes	—
141	C₂×C₄×D₅	—	2	4	no	—
142	C₂×C₄×D₅	—	2	8	no	—
143	C₂×C₄×D₅	—	2	4	no	—
144	C₂×C₄×D₅	—	2	8	no	—
145	C₂×Dic₁₀	—	2	2	no	—
146	C₂×Dic₁₀	—	2	4	no	—
147	C₂×Dic₁₀	C₂²×C₄	1	4	yes	—
148	C₂×Dic₁₀	C₂²×C₄	1	8	yes	—
149	C₅×M₁₆	C₂×D₄	1	8	yes	—
150	C₅×M₁₆	C₂×D₄	1	8	yes	—
151	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
154	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
157	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
158	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
160	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
161	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
162	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
163	C₂×C₅×C₈	C₂⁴	1	2	yes	—
164	C₂×C₅×C₈	C₂⁴	1	2	yes	—
165	C₂×C₅×C₈	C₂⁴	1	4	yes	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₂²⋊C₄	—	2	4	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	C₂⁴	1	4	yes	—
170	#681	—	2	4	no	—
171	#681	—	2	8	no	—
172	#681	C₂⁴	1	8	yes	—
173	C₂×#168	—	2	4	no	—
174	C₂×#168	—	2	8	no	—
175	Dic₂₀	C₂²×C₄	1	8	yes	—
176	Dic₂₀	C₂²×C₄	1	8	yes	—
177	D₄₀	C₂²×C₄	1	8	yes	—
178	D₄₀	C₂²×C₄	1	8	yes	—
179	#677	C₂²×C₄	1	16	yes	—
180	#677	C₂²×C₄	1	16	yes	—
181	#676	—	2	32	no	—
182	C₈×D₅	—	2	32	no	—
183	C₂²×#41	—	5	2	no	—
184	C₂×#135	—	5	2	no	—
185	C₂×#135	—	5	2	no	—
186	C₂×#135	—	5	8	no	—
187	C₂×#135	—	5	2	no	—
188	C₂×#135	—	5	2	no	—
189	C₂×#135	—	5	8	no	—
190	C₂²×Q₁₆	—	5	1	no	—
191	C₂²×SD₁₆	—	5	2	no	—
192	C₂²×D₈	—	5	1	no	—
193	#568	—	5	16	no	—
194	#568	—	10	8	no	—
195	C₂×#131	—	5	8	no	—
196	C₂×#131	—	10	4	no	—
197	C₂²×M₁₆	—	5	2	no	—
198	C₂²×M₁₆	—	10	4	no	—
199	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
200	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
201	C₂×#117	C₂×D₅	1	1	yes	characteristic
202	#444	—	5	32	no	—
203	#443	—	5	32	no	—
204	C₂×#108	—	5	2	no	—
205	C₂×#108	—	5	2	no	—
206	C₂×#108	—	5	8	no	—
207	#421	—	5	16	no	—
208	C₂×#104	—	5	8	no	—
209	#405	C₂×D₅	1	8	yes	complemented
210	C₂×#97	C₂×D₅	1	2	yes	complemented
211	C₂×C₄×C₈	C₂×D₅	1	2	yes	complemented
212	C₂³×C₅	—	4	2	no	—
213	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₅	C₄×D₄	1	2	yes	—
216	C₂³×C₅	C₂×#41	1	1	yes	characteristic
217	C₂³×C₅	C₂×#41	1	2	yes	—
218	C₂²×D₅	—	2	4	no	—
219	C₂²×D₅	—	2	8	no	—
220	C₂²×D₅	—	8	4	no	—
221	C₂×C₄×C₅	—	2	4	no	—
222	C₂×C₄×C₅	—	4	4	no	—
223	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
230	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#41	1	2	yes	—
240	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
241	C₂²⋊D₅	—	2	8	no	—
242	C₂²⋊D₅	—	2	16	no	—
243	C₂²⋊D₅	—	2	8	no	—
244	C₂×Dic₅	—	2	8	no	—
245	C₂×Dic₅	—	2	4	no	—
246	D₂₀	—	2	4	no	—
247	D₂₀	—	2	8	no	—
248	D₂₀	C₂³×C₄	1	8	yes	—
249	C₄×D₅	—	2	8	no	—
250	C₄×D₅	—	2	16	no	—
251	C₄×D₅	—	2	8	no	—
252	Dic₁₀	—	2	4	no	—
253	Dic₁₀	—	2	8	no	—
254	Dic₁₀	C₂³×C₄	1	8	yes	—
255	C₅×C₈	C₂³×C₄	1	2	yes	—
256	C₅×C₈	C₂³×C₄	1	2	yes	—
257	C₅×C₈	C₂³×C₄	1	2	yes	—
258	C₅×C₈	C₂³×C₄	1	2	yes	—
259	C₅×C₈	C₂²×D₄	1	8	yes	—
260	#168	—	2	8	no	—
261	C₂×#41	—	5	4	no	—
262	C₂×#41	—	5	8	no	—
263	C₂×#41	—	5	4	no	—
264	C₂×#41	—	5	8	no	—
265	C₂×#41	—	10	2	no	—
266	C₂×#41	—	10	4	no	—
267	C₂×#41	—	10	2	no	—
268	C₂×#41	—	10	4	no	—
269	C₂²×Q₈	—	5	2	no	—
270	C₂²×D₄	—	5	2	no	—
271	C₂²×D₄	—	10	2	no	—
272	C₂³×C₄	—	10	2	no	—
273	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
274	#135	—	5	8	no	—
275	#135	—	5	8	no	—
276	#135	—	5	16	no	—
277	#135	—	5	16	no	—
278	#135	—	5	8	no	—
279	#135	—	5	8	no	—
280	C₂×Q₁₆	—	5	2	no	—
281	C₂×Q₁₆	—	5	2	no	—
282	C₂×Q₁₆	—	5	8	no	—
283	C₂×SD₁₆	—	5	4	no	—
284	C₂×SD₁₆	—	5	4	no	—
285	C₂×SD₁₆	—	5	16	no	—
286	C₂×D₈	—	5	2	no	—
287	C₂×D₈	—	5	2	no	—
288	C₂×D₈	—	5	8	no	—
289	#131	—	5	32	no	—
290	#131	—	10	32	no	—
291	#131	—	10	16	no	—
292	C₂×M₁₆	—	5	4	no	—
293	C₂×M₁₆	—	5	8	no	—
294	C₂×M₁₆	—	10	2	no	—
295	C₂×M₁₆	—	10	4	no	—
296	C₂×M₁₆	—	10	32	no	—
297	C₂×M₁₆	—	10	8	no	—
298	C₂×M₁₆	D₂₀	1	2	yes	—
299	C₂×M₁₆	D₂₀	1	2	yes	—
300	C₂×M₁₆	D₂₀	1	4	yes	—
301	C₂×M₁₆	C₂²×D₅	1	4	yes	—
302	C₂²×C₈	—	10	2	no	—
303	C₂²×C₈	—	10	8	no	—
304	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
305	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
306	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
307	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
308	C₂²×C₈	C₄×D₅	1	4	yes	—
309	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
310	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
311	C₂²×C₈	C₂²×D₅	1	4	yes	—
312	C₂²×C₈	C₂²×D₅	1	2	yes	—
313	#117	—	2	2	no	—
314	#117	C₂²×D₅	1	4	yes	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	C₂²×D₅	1	2	yes	—
318	#108	—	5	8	no	—
319	#108	—	5	8	no	—
320	#104	—	5	32	no	—
321	#97	C₂²×D₅	1	8	yes	complemented
322	C₄×C₈	C₂²×D₅	1	8	yes	complemented
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	4	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	C₂×C₄×D₄	1	2	yes	—
329	C₂²×C₅	C₂×C₄×D₄	1	2	yes	—
330	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
331	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
333	C₂×D₅	—	2	8	no	—
334	C₂×D₅	—	4	8	no	—
335	C₂×D₅	—	8	8	no	—
336	C₄×C₅	—	4	4	no	—
337	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
338	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
340	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₅	C₂⁴×C₄	1	1	yes	characteristic
342	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
343	Dic₅	—	2	8	no	—
344	C₂⁴	—	10	2	no	—
345	C₂⁴	#709	1	1	yes	characteristic
346	#41	—	5	8	no	—
347	#41	—	5	16	no	—
348	#41	—	5	8	no	—
349	#41	—	10	8	no	—
350	#41	—	10	4	no	—
351	#41	—	10	4	no	—
352	#41	—	10	8	no	—
353	#41	—	10	8	no	—
354	#41	—	10	8	no	—
355	#41	—	10	8	no	—
356	C₂×Q₈	—	5	4	no	—
357	C₂×Q₈	—	5	8	no	—
358	C₂×Q₈	—	10	2	no	—
359	C₂×Q₈	—	10	4	no	—
360	C₂×D₄	—	5	4	no	—
361	C₂×D₄	—	5	8	no	—
362	C₂×D₄	—	10	4	no	—
363	C₂×D₄	—	10	8	no	—
364	C₂×D₄	—	10	4	no	—
365	C₂×D₄	—	10	8	no	—
366	C₂×D₄	—	10	2	no	—
367	C₂×D₄	—	10	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	10	2	no	—
370	C₂²×C₄	—	10	8	no	—
371	C₂²×C₄	—	10	4	no	—
372	C₂²×C₄	—	10	4	no	—
373	C₂²×C₄	—	10	8	no	—
374	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
377	C₂²×C₄	C₂×D₂₀	1	2	yes	—
378	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
380	C₂²×C₄	#709	1	1	yes	characteristic
381	C₂²×C₄	#709	1	2	yes	—
382	C₂²×C₄	C₂³×D₅	1	2	yes	—
383	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
384	Q₁₆	—	5	8	no	—
385	Q₁₆	—	5	8	no	—
386	SD₁₆	—	5	16	no	—
387	SD₁₆	—	5	16	no	—
388	D₈	—	5	8	no	—
389	D₈	—	5	8	no	—
390	M₁₆	—	5	8	no	—
391	M₁₆	—	10	8	no	—
392	M₁₆	—	10	4	no	—
393	M₁₆	—	10	32	no	—
394	M₁₆	C₂×D₂₀	1	8	yes	—
395	M₁₆	C₂×D₂₀	1	8	yes	—
396	C₂×C₈	—	10	8	no	—
397	C₂×C₈	—	10	4	no	—
398	C₂×C₈	—	10	32	no	—
399	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
400	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
402	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
403	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
405	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
408	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
409	C₂×C₈	C₂×D₂₀	1	4	yes	—
410	C₂×C₈	C₂×D₂₀	1	4	yes	—
411	C₂×C₈	C₂³×D₅	1	2	yes	—
412	C₂×C₈	C₂³×D₅	1	2	yes	—
413	C₂×C₈	C₂³×D₅	1	4	yes	—
414	C₄⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	C₂³×D₅	1	4	yes	—
418	C₂×C₅	—	2	1	no	—
419	C₂×C₅	—	2	2	no	—
420	C₂×C₅	—	2	1	no	—
421	C₂×C₅	—	2	2	no	—
422	C₂×C₅	#2957	1	2	yes	complemented
423	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
424	D₅	—	4	8	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	10	4	no	—
427	C₂³	—	10	8	no	—
428	C₂³	—	40	4	no	—
429	C₂³	C₄×D₂₀	1	1	yes	characteristic
430	C₂³	C₄×D₂₀	1	1	yes	characteristic
431	C₂³	C₄×D₂₀	1	2	yes	—
432	C₂³	C₂×#709	1	1	yes	characteristic
433	C₂³	C₂×#709	1	2	yes	—
434	Q₈	—	5	8	no	—
435	Q₈	—	10	8	no	—
436	Q₈	—	10	4	no	—
437	D₄	—	5	8	no	—
438	D₄	—	10	16	no	—
439	D₄	—	10	8	no	—
440	D₄	—	10	8	no	—
441	D₄	—	10	8	no	—
442	D₄	—	10	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	10	8	no	—
446	C₂×C₄	—	10	4	no	—
447	C₂×C₄	—	10	16	no	—
448	C₂×C₄	—	10	8	no	—
449	C₂×C₄	—	10	8	no	—
450	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
451	C₂×C₄	C₄×D₂₀	1	2	yes	—
452	C₂×C₄	C₄×D₂₀	1	2	yes	—
453	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
454	C₂×C₄	C₄×D₂₀	1	2	yes	—
455	C₂×C₄	C₄×D₂₀	1	2	yes	—
456	C₂×C₄	C₄×D₂₀	1	2	yes	—
457	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
460	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₂₀	1	2	yes	—
462	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₂₀	1	2	yes	—
464	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
465	C₂×C₄	C₂×#709	1	1	yes	characteristic
466	C₂×C₄	C₂×#709	1	2	yes	—
467	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
468	C₈	—	10	8	no	—
469	C₈	C₂²×C₄×D₅	1	2	yes	—
470	C₈	C₂²×C₄×D₅	1	2	yes	—
471	C₈	C₂²×C₄×D₅	1	2	yes	—
472	C₈	C₂²×C₄×D₅	1	2	yes	—
473	C₈	C₂²×D₂₀	1	8	yes	—
474	C₅	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	10	8	no	—
481	C₂²	—	20	8	no	—
482	C₂²	—	40	8	no	—
483	C₂²	C₂×C₄×D₂₀	1	2	yes	—
484	C₂²	C₂×C₄×D₂₀	1	2	yes	—
485	C₂²	C₂×C₄×D₂₀	1	1	yes	characteristic
486	C₂²	C₂×C₄×D₂₀	1	1	yes	characteristic
487	C₂²	C₂²×#709	1	1	yes	characteristic
488	C₄	—	4	4	no	—
489	C₄	—	10	8	no	—
490	C₄	C₂×C₄×D₂₀	1	2	yes	—
491	C₄	C₂×C₄×D₂₀	1	1	yes	characteristic
492	C₄	C₂×C₄×D₂₀	1	2	yes	—
493	C₄	C₂×C₄×D₂₀	1	1	yes	characteristic
494	C₄	C₂³×C₄×D₅	1	1	yes	characteristic
495	C₄	C₂³×D₂₀	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	20	8	no	—
501	C₂	#10610311	1	2	yes	direct product factor
502	C₂	C₂²×C₄×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₀
commutator	C₄×C₅	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₂×C₅×#405	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂²×#4050	C₂
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	C₂×#405	D₅
hypocenter	C₅	C₂×#2957
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. C₂×#66079	C₂	semidirect
3. C₂×C₅×#405	C₂	semidirect
4. C₂²×#3951	C₂	semidirect
5. C₂×#65294	C₂	semidirect
6. #10610311	C₂	direct (N × H)
7. C₂×#65006	C₂	semidirect
8. C₂×#64989	C₂	semidirect
15. #66079	C₂²	semidirect
18. C₂²×Dic₂₀	C₄	semidirect
19. C₂×#4050	C₄	semidirect
20. C₂×#4050	C₄	semidirect
21. C₂×#4050	C₄	semidirect
25. C₂²×D₄₀	C₄	semidirect
26. C₂²×#677	C₄	semidirect
27. C₂×#4047	C₂²	semidirect
28. C₅×#405	C₂²	semidirect
29. C₂×C₅×#97	C₂²	semidirect
30. C₂×C₄×C₅×C₈	C₂²	semidirect
31. C₂×#3951	C₂²	semidirect
32. C₂×#3951	C₂²	semidirect
33. C₂×#3951	C₂²	semidirect
34. #65294	C₂²	semidirect
35. C₂×#3937	C₂²	semidirect
36. #65006	C₂²	semidirect
37. #64989	C₂²	semidirect
79. C₂×Dic₂₀	C₂×C₄	semidirect
82. #4050	C₂×C₄	semidirect
83. #4050	C₂×C₄	semidirect
88. C₂×D₄₀	C₂×C₄	semidirect
91. C₂×#677	C₂×C₄	semidirect
93. #4047	C₂³	semidirect
96. C₅×#97	C₂³	semidirect
97. C₄×C₅×C₈	C₂³	semidirect
98. #3951	C₂³	semidirect
99. #3951	C₂³	semidirect
100. #3937	C₂³	semidirect
108. C₂×#405	D₅	semidirect
209. #405	C₂×D₅	semidirect
210. C₂×#97	C₂×D₅	semidirect
211. C₂×C₄×C₈	C₂×D₅	semidirect
321. #97	C₂²×D₅	semidirect
322. C₄×C₈	C₂²×D₅	semidirect
422. C₂×C₅	#2957	semidirect
474. C₅	C₂×#2957	semidirect
501. C₂	#10610311	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×#66079	2
C₂²×#4050	2
C₂×C₅×#405	2
C₂²×#3951	2
C₂×#65294	2
#10610311	2
C₂×#65006	2
C₂×#64989	2
C₂×#2957	5

Subgroups — C2×#10610311 #12963622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10610311 #12963622