Subgroups — C₂×#10617687 #13007194

Order 1280.

12378 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#4144	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#4076	C₂	1	4	yes	maximal, complemented
4	#10617687	C₂	1	32	yes	maximal, direct product factor
5	C₂×#65888	C₂	1	8	yes	maximal, complemented
6	C₂×D₄×D₂₀	C₂	1	4	yes	maximal, complemented
7	C₂×#65889	C₂	1	4	yes	maximal, complemented
8	C₂×#65844	C₂	1	2	yes	maximal, complemented
9	C₂×#65827	C₂	1	4	yes	maximal, complemented
10	C₂×#65811	C₂	1	2	yes	maximal, complemented
11	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₅	C₂²	1	2	yes	complemented
13	C₂³×C₂²⋊D₅	C₂²	1	8	yes	complemented
14	C₂×#4144	—	2	32	no	—
15	C₂×#4144	C₂²	1	32	yes	complemented
16	C₂²×#711	C₂²	1	8	yes	complemented
17	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
18	C₂²×#709	C₂²	1	4	yes	complemented
19	C₂³×D₂₀	C₂²	1	4	yes	complemented
20	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
21	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
22	C₂×C₄×C₅×D₄	C₂²	1	16	yes	complemented
23	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₂×#4076	C₂²	1	8	yes	complemented
27	C₂×#4076	C₂²	1	8	yes	complemented
28	C₂×#4076	C₂²	1	8	yes	complemented
29	C₂×#4076	C₂²	1	4	yes	complemented
30	C₂×#4076	C₂²	1	4	yes	complemented
31	C₂×#4076	C₂²	1	64	yes	complemented
32	C₂²×#685	C₂²	1	8	yes	complemented
33	C₂²×C₄⋊Dic₅	C₂²	1	4	yes	complemented
34	#65889	C₂²	1	64	yes	complemented
35	#65888	C₂²	1	128	yes	complemented
36	D₄×D₂₀	C₂²	1	64	yes	complemented
37	#65844	C₂²	1	32	yes	complemented
38	C₂×#4043	C₂²	1	8	yes	complemented
39	C₂×#4041	C₂²	1	8	yes	complemented
40	#65827	C₂²	1	64	yes	complemented
41	C₂×#4032	C₂²	1	16	yes	complemented
42	C₂×#4028	C₂²	1	16	yes	complemented
43	#65811	C₂²	1	32	yes	complemented
44	C₂×#4021	C₂²	1	4	yes	complemented
45	C₂×#4020	C₂²	1	2	yes	complemented
46	C₂×C₄×D₂₀	C₂²	1	4	yes	complemented
47	C₂×C₄×D₂₀	C₂²	1	4	yes	complemented
48	C₂×#4015	C₂²	1	2	yes	complemented
49	C₂×#3496	—	5	1	no	maximal, Sylow
50	C₂⁵×C₅	C₂³	1	2	yes	—
51	C₂⁴×D₅	C₂³	1	8	yes	—
52	C₂²×C₅×D₄	D₄	1	16	yes	complemented
53	C₂²×C₅×D₄	C₂³	1	4	yes	—
54	C₂²×C₅×D₄	C₂³	1	8	yes	—
55	C₂³×C₄×C₅	—	4	8	no	—
56	C₂³×C₄×C₅	C₂³	1	4	yes	—
57	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₅	C₂³	1	4	yes	—
59	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂³	1	2	yes	—
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂³	1	16	yes	complemented
63	C₂²×C₂²⋊D₅	—	2	64	no	—
64	C₂²×C₂²⋊D₅	C₂³	1	16	yes	—
65	C₂²×C₂²⋊D₅	C₂³	1	8	yes	—
66	C₂²×C₂²⋊D₅	C₂³	1	64	yes	complemented
67	C₂³×Dic₅	C₂³	1	8	yes	—
68	#4144	—	2	256	no	—
69	C₂×#711	—	2	64	no	—
70	C₂×#711	C₂³	1	64	yes	complemented
71	C₂×D₄×D₅	—	2	64	no	—
72	C₂×D₄×D₅	C₂³	1	64	yes	complemented
73	C₂×#709	—	2	32	no	—
74	C₂×#709	C₂³	1	32	yes	complemented
75	C₂²×D₂₀	—	4	16	no	—
76	C₂²×D₂₀	C₂³	1	4	yes	—
77	C₂²×D₂₀	C₂³	1	4	yes	—
78	C₂²×D₂₀	C₂³	1	4	yes	—
79	C₂²×D₂₀	C₂³	1	8	yes	—
80	C₂²×D₂₀	C₂³	1	32	yes	complemented
81	C₂²×C₄×D₅	C₂³	1	8	yes	—
82	C₂²×Dic₁₀	C₂³	1	4	yes	—
83	C₄×C₅×D₄	C₂³	1	32	yes	complemented
84	C₄×C₅×D₄	C₂³	1	32	yes	complemented
85	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
87	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
89	C₂×C₄²×C₅	C₂³	1	2	yes	—
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
92	#4076	C₂³	1	32	yes	complemented
93	#4076	C₂³	1	32	yes	complemented
94	#4076	C₂³	1	64	yes	complemented
95	#4076	C₂³	1	64	yes	complemented
96	#4076	C₂³	1	64	yes	complemented
97	C₂×#685	C₂³	1	8	yes	—
98	C₂×#685	C₂³	1	8	yes	—
99	C₂×#685	C₂³	1	16	yes	—
100	C₂×#685	C₂³	1	64	yes	complemented
101	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
102	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
103	C₂×C₄⋊Dic₅	C₂³	1	8	yes	—
104	C₂×C₄⋊Dic₅	C₂³	1	32	yes	complemented
105	#4043	C₂³	1	64	yes	complemented
106	#4041	C₂³	1	64	yes	complemented
107	#4032	C₂³	1	128	yes	complemented
108	#4028	C₂³	1	128	yes	complemented
109	#4021	C₂³	1	32	yes	complemented
110	#4020	C₂³	1	16	yes	complemented
111	C₄×D₂₀	C₂³	1	32	yes	complemented
112	C₄×D₂₀	C₂³	1	32	yes	complemented
113	#4015	C₂³	1	16	yes	complemented
114	C₂²×H(5,𝔽₂)	—	5	2	no	—
115	#3496	—	5	32	no	—
116	C₂×#547	—	5	4	no	—
117	C₂×#546	—	5	8	no	—
118	C₂×D₄²	—	5	4	no	—
119	C₂×#537	—	5	2	no	—
120	C₂×#534	—	5	4	no	—
121	C₂×#532	—	5	2	no	—
122	C₂²×#121	—	5	4	no	—
123	C₂²×C₄×D₄	D₅	1	1	yes	characteristic, complemented
124	C₂⁴×C₅	—	4	4	no	—
125	C₂⁴×C₅	—	4	4	no	—
126	C₂⁴×C₅	C₂×D₄	1	16	yes	complemented
127	C₂⁴×C₅	C₂⁴	1	4	yes	—
128	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
129	C₂⁴×C₅	C₂⁴	1	8	yes	—
130	C₂³×D₅	—	2	32	no	—
131	C₂³×D₅	—	4	16	no	—
132	C₂³×D₅	—	4	16	no	—
133	C₂³×D₅	C₂⁴	1	8	yes	—
134	C₂³×D₅	C₂⁴	1	32	yes	—
135	C₂×C₅×D₄	C₂×D₄	1	32	yes	complemented
136	C₂×C₅×D₄	C₂×D₄	1	64	yes	complemented
137	C₂×C₅×D₄	C₂⁴	1	16	yes	—
138	C₂²×C₄×C₅	—	2	16	no	—
139	C₂²×C₄×C₅	—	2	4	no	—
140	C₂²×C₄×C₅	—	4	32	no	—
141	C₂²×C₄×C₅	—	4	4	no	—
142	C₂²×C₄×C₅	—	4	8	no	—
143	C₂²×C₄×C₅	—	4	2	no	—
144	C₂²×C₄×C₅	C₂×D₄	1	8	yes	complemented
145	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
152	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
153	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂×C₂²⋊D₅	—	2	32	no	—
157	C₂×C₂²⋊D₅	—	2	64	no	—
158	C₂×C₂²⋊D₅	—	2	256	no	—
159	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	—
160	C₂×C₂²⋊D₅	C₂⁴	1	64	yes	—
161	C₂²×Dic₅	—	2	32	no	—
162	C₂²×Dic₅	C₂⁴	1	8	yes	—
163	C₂²×Dic₅	C₂⁴	1	32	yes	—
164	#711	—	2	256	no	—
165	D₄×D₅	—	2	256	no	—
166	#709	—	2	128	no	—
167	C₂×D₂₀	—	2	16	no	—
168	C₂×D₂₀	—	2	16	no	—
169	C₂×D₂₀	—	4	64	no	—
170	C₂×D₂₀	—	4	16	no	—
171	C₂×D₂₀	—	4	8	no	—
172	C₂×D₂₀	C₂⁴	1	16	yes	—
173	C₂×D₂₀	C₂⁴	1	16	yes	—
174	C₂×D₂₀	C₂⁴	1	32	yes	—
175	C₂×D₂₀	C₂⁴	1	16	yes	—
176	C₂×C₄×D₅	—	2	32	no	—
177	C₂×C₄×D₅	C₂⁴	1	32	yes	—
178	C₂×Dic₁₀	—	2	16	no	—
179	C₂×Dic₁₀	C₂⁴	1	16	yes	—
180	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
181	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
182	C₄²×C₅	C₂⁴	1	8	yes	—
183	C₄²×C₅	C₂⁴	1	8	yes	—
184	#685	C₂⁴	1	32	yes	—
185	#685	C₂⁴	1	32	yes	—
186	#685	C₂⁴	1	64	yes	—
187	C₄⋊Dic₅	C₂⁴	1	16	yes	—
188	C₄⋊Dic₅	C₂⁴	1	16	yes	—
189	C₄⋊Dic₅	C₂⁴	1	32	yes	—
190	C₂×H(5,𝔽₂)	—	5	32	no	—
191	C₂×H(5,𝔽₂)	—	10	32	no	—
192	C₂²×#41	—	5	8	no	—
193	C₂²×#41	—	5	4	no	—
194	C₂³×D₄	—	5	8	no	—
195	C₂³×D₄	—	5	8	no	—
196	C₂³×D₄	—	5	4	no	—
197	C₂³×D₄	C₂×D₅	1	1	yes	characteristic
198	C₂⁴×C₄	C₂×D₅	1	2	yes	complemented
199	#547	—	5	64	no	—
200	#546	—	5	128	no	—
201	D₄²	—	5	64	no	—
202	#537	—	5	32	no	—
203	#534	—	5	64	no	—
204	#532	—	5	32	no	—
205	C₂×C₄⋊Q₈	—	5	2	no	—
206	C₂×#127	—	5	2	no	—
207	C₂×#124	—	5	4	no	—
208	C₂×#123	—	5	16	no	—
209	C₂×C₂²⋊Q₈	—	5	8	no	—
210	C₂×#121	—	5	4	no	—
211	C₂×#121	—	5	8	no	—
212	C₂×#121	—	5	8	no	—
213	C₂×#121	—	5	8	no	—
214	C₂×#121	—	5	4	no	—
215	C₂×#121	—	5	64	no	—
216	C₂×#121	—	5	8	no	—
217	C₂×#120	—	5	16	no	—
218	C₂×C₄×D₄	—	5	4	no	—
219	C₂×C₄×D₄	—	5	4	no	—
220	C₂×C₄×D₄	C₂×D₅	1	4	yes	complemented
221	C₂×C₄×D₄	C₂×D₅	1	4	yes	complemented
222	C₂×C₄×D₄	C₂×D₅	1	16	yes	complemented
223	C₂²×C₄⋊C₄	—	5	4	no	—
224	C₂²×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
225	C₂²×C₂²⋊C₄	—	5	8	no	—
226	C₂²×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
227	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	8	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	—	2	8	no	—
232	C₂³×C₅	—	4	8	no	—
233	C₂³×C₅	—	4	32	no	—
234	C₂³×C₅	—	4	8	no	—
235	C₂³×C₅	C₂²×D₄	1	16	yes	—
236	C₂³×C₅	C₂²×D₄	1	4	yes	—
237	C₂³×C₅	C₂²×D₄	1	32	yes	complemented
238	C₂³×C₅	C₂⁵	1	8	yes	—
239	C₂³×C₅	C₂⁵	1	2	yes	—
240	C₂³×C₅	C₂⁵	1	1	yes	characteristic
241	C₂²×D₅	—	2	16	no	—
242	C₂²×D₅	—	2	16	no	—
243	C₂²×D₅	—	2	16	no	—
244	C₂²×D₅	—	2	64	no	—
245	C₂²×D₅	—	4	32	no	—
246	C₂²×D₅	—	4	32	no	—
247	C₂²×D₅	—	8	64	no	—
248	C₂²×D₅	C₂⁵	1	16	yes	—
249	C₅×D₄	C₂²×D₄	1	64	yes	complemented
250	C₂×C₄×C₅	—	2	8	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	2	32	no	—
254	C₂×C₄×C₅	—	2	8	no	—
255	C₂×C₄×C₅	—	4	8	no	—
256	C₂×C₄×C₅	—	4	16	no	—
257	C₂×C₄×C₅	—	4	4	no	—
258	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
259	C₂×C₄×C₅	C₂²×D₄	1	16	yes	complemented
260	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	complemented
261	C₂×C₄×C₅	C₂⁵	1	4	yes	—
262	C₂×C₄×C₅	C₂⁵	1	8	yes	—
263	C₂×C₄×C₅	C₂⁵	1	2	yes	—
264	C₂×C₄×C₅	C₂⁵	1	4	yes	—
265	C₂×C₄×C₅	C₂⁵	1	2	yes	—
266	C₂²⋊D₅	—	2	64	no	—
267	C₂²⋊D₅	—	2	128	no	—
268	C₂×Dic₅	—	2	16	no	—
269	C₂×Dic₅	—	2	64	no	—
270	C₂×Dic₅	C₂⁵	1	16	yes	—
271	D₂₀	—	2	32	no	—
272	D₂₀	—	2	32	no	—
273	D₂₀	—	4	32	no	—
274	D₂₀	—	4	16	no	—
275	C₄×D₅	—	2	64	no	—
276	Dic₁₀	—	2	32	no	—
277	C₂⁵	—	5	8	no	—
278	C₂⁵	C₂²×D₅	1	2	yes	—
279	H(5,𝔽₂)	—	10	256	no	—
280	C₂×#41	—	5	64	no	—
281	C₂×#41	—	5	32	no	—
282	C₂×#41	—	10	64	no	—
283	C₂×#41	—	10	32	no	—
284	C₂²×Q₈	—	5	4	no	—
285	C₂²×D₄	—	5	16	no	—
286	C₂²×D₄	—	5	8	no	—
287	C₂²×D₄	—	5	64	no	—
288	C₂²×D₄	—	5	64	no	—
289	C₂²×D₄	—	5	4	no	—
290	C₂²×D₄	—	5	4	no	—
291	C₂²×D₄	—	5	4	no	—
292	C₂²×D₄	—	5	8	no	—
293	C₂²×D₄	—	5	32	no	—
294	C₂²×D₄	—	10	64	no	—
295	C₂²×D₄	—	10	64	no	—
296	C₂²×D₄	—	20	16	no	—
297	C₂²×D₄	D₂₀	1	16	yes	complemented
298	C₂²×D₄	C₂²×D₅	1	4	yes	—
299	C₂²×D₄	C₂²×D₅	1	8	yes	—
300	C₂³×C₄	—	4	8	no	—
301	C₂³×C₄	—	5	8	no	—
302	C₂³×C₄	—	5	8	no	—
303	C₂³×C₄	C₂²×D₅	1	4	yes	—
304	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
305	C₂³×C₄	C₂²×D₅	1	4	yes	—
306	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
307	C₂³×C₄	C₂²×D₅	1	2	yes	—
308	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
309	C₂³×C₄	C₂²×D₅	1	16	yes	complemented
310	C₄⋊Q₈	—	5	16	no	—
311	#127	—	5	16	no	—
312	#124	—	5	32	no	—
313	#123	—	5	128	no	—
314	C₂²⋊Q₈	—	5	64	no	—
315	#121	—	5	32	no	—
316	#121	—	5	64	no	—
317	#121	—	5	64	no	—
318	#121	—	5	64	no	—
319	#121	—	5	32	no	—
320	#121	—	5	64	no	—
321	#120	—	5	128	no	—
322	C₄×D₄	—	5	32	no	—
323	C₄×D₄	—	5	32	no	—
324	C₄×D₄	C₂²×D₅	1	32	yes	complemented
325	C₄×D₄	C₂²×D₅	1	32	yes	complemented
326	C₂×C₄⋊C₄	—	5	4	no	—
327	C₂×C₄⋊C₄	—	5	8	no	—
328	C₂×C₄⋊C₄	—	5	32	no	—
329	C₂×C₄⋊C₄	—	5	4	no	—
330	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
331	C₂×C₄⋊C₄	C₂²×D₅	1	8	yes	complemented
332	C₂×C₂²⋊C₄	—	5	8	no	—
333	C₂×C₂²⋊C₄	—	5	16	no	—
334	C₂×C₂²⋊C₄	—	5	64	no	—
335	C₂×C₂²⋊C₄	—	5	8	no	—
336	C₂×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
337	C₂×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
338	C₂×C₄²	C₂²×D₅	1	2	yes	—
339	C₂×C₄²	C₂²×D₅	1	2	yes	—
340	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	8	no	—
343	C₂²×C₅	—	2	2	no	—
344	C₂²×C₅	—	2	8	no	—
345	C₂²×C₅	—	2	32	no	—
346	C₂²×C₅	—	2	8	no	—
347	C₂²×C₅	—	4	32	no	—
348	C₂²×C₅	C₂³×D₄	1	16	yes	—
349	C₂²×C₅	C₂³×D₄	1	4	yes	—
350	C₂²×C₅	C₂³×D₄	1	2	yes	—
351	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
352	C₂²×C₅	#585	1	2	yes	—
353	C₂²×C₅	C₂⁶	1	1	yes	characteristic
354	C₂×D₅	—	2	16	no	—
355	C₂×D₅	—	2	16	no	—
356	C₂×D₅	—	2	16	no	—
357	C₂×D₅	—	4	32	no	—
358	C₂×D₅	—	8	64	no	—
359	C₄×C₅	—	2	8	no	—
360	C₄×C₅	—	2	2	no	—
361	C₄×C₅	—	2	4	no	—
362	C₄×C₅	C₂³×D₄	1	8	yes	—
363	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	complemented
364	Dic₅	—	2	16	no	—
365	C₂⁴	—	4	4	no	—
366	C₂⁴	—	4	4	no	—
367	C₂⁴	—	5	8	no	—
368	C₂⁴	—	5	32	no	—
369	C₂⁴	—	10	32	no	—
370	C₂⁴	—	20	16	no	—
371	C₂⁴	—	20	16	no	—
372	C₂⁴	C₂×D₂₀	1	16	yes	complemented
373	C₂⁴	C₂³×D₅	1	4	yes	—
374	C₂⁴	C₂³×D₅	1	1	yes	characteristic
375	C₂⁴	C₂³×D₅	1	8	yes	—
376	#41	—	10	256	no	—
377	#41	—	10	128	no	—
378	C₂×Q₈	—	5	16	no	—
379	C₂×Q₈	—	10	16	no	—
380	C₂×D₄	—	5	64	no	—
381	C₂×D₄	—	5	32	no	—
382	C₂×D₄	—	5	16	no	—
383	C₂×D₄	—	5	16	no	—
384	C₂×D₄	—	5	16	no	—
385	C₂×D₄	—	5	32	no	—
386	C₂×D₄	—	10	64	no	—
387	C₂×D₄	—	10	32	no	—
388	C₂×D₄	—	10	256	no	—
389	C₂×D₄	—	10	256	no	—
390	C₂×D₄	—	10	16	no	—
391	C₂×D₄	—	10	16	no	—
392	C₂×D₄	—	20	64	no	—
393	C₂×D₄	—	20	16	no	—
394	C₂×D₄	—	20	8	no	—
395	C₂×D₄	C₂×D₂₀	1	32	yes	complemented
396	C₂×D₄	C₂×D₂₀	1	64	yes	complemented
397	C₂×D₄	C₂³×D₅	1	16	yes	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	16	no	—
400	C₂²×C₄	—	4	32	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	5	32	no	—
405	C₂²×C₄	—	5	8	no	—
406	C₂²×C₄	—	5	32	no	—
407	C₂²×C₄	—	10	32	no	—
408	C₂²×C₄	—	10	32	no	—
409	C₂²×C₄	C₂×D₂₀	1	8	yes	complemented
410	C₂²×C₄	C₂³×D₅	1	4	yes	—
411	C₂²×C₄	C₂³×D₅	1	16	yes	—
412	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
413	C₂²×C₄	C₂³×D₅	1	2	yes	—
414	C₂²×C₄	C₂³×D₅	1	4	yes	—
415	C₂²×C₄	C₂³×D₅	1	4	yes	—
416	C₂²×C₄	C₂³×D₅	1	16	yes	—
417	C₂²×C₄	C₂³×D₅	1	8	yes	—
418	C₂²×C₄	C₂³×D₅	1	2	yes	—
419	C₂²×C₄	C₂³×D₅	1	4	yes	—
420	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
421	C₄⋊C₄	—	5	16	no	—
422	C₄⋊C₄	—	5	32	no	—
423	C₄⋊C₄	—	5	16	no	—
424	C₄⋊C₄	C₂³×D₅	1	16	yes	—
425	C₂²⋊C₄	—	5	32	no	—
426	C₂²⋊C₄	—	5	64	no	—
427	C₂²⋊C₄	—	5	32	no	—
428	C₂²⋊C₄	C₂³×D₅	1	32	yes	—
429	C₄²	C₂³×D₅	1	8	yes	—
430	C₄²	C₂³×D₅	1	8	yes	—
431	C₂×C₅	—	2	16	no	—
432	C₂×C₅	—	2	4	no	—
433	C₂×C₅	#3496	1	4	yes	complemented
434	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
435	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×C₅	C₂×#585	1	1	yes	characteristic
437	D₅	—	4	16	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	8	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	32	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	5	16	no	—
446	C₂³	—	10	16	no	—
447	C₂³	—	10	16	no	—
448	C₂³	—	10	16	no	—
449	C₂³	—	10	64	no	—
450	C₂³	—	20	32	no	—
451	C₂³	—	20	32	no	—
452	C₂³	—	40	64	no	—
453	C₂³	C₂²×D₂₀	1	16	yes	—
454	C₂³	C₂²×D₂₀	1	4	yes	—
455	C₂³	C₂²×D₂₀	1	32	yes	complemented
456	C₂³	C₂⁴×D₅	1	8	yes	—
457	C₂³	C₂⁴×D₅	1	2	yes	—
458	C₂³	C₂⁴×D₅	1	1	yes	characteristic
459	Q₈	—	10	32	no	—
460	D₄	—	10	128	no	—
461	D₄	—	10	64	no	—
462	D₄	—	10	32	no	—
463	D₄	—	10	32	no	—
464	D₄	—	20	32	no	—
465	D₄	—	20	16	no	—
466	D₄	C₂²×D₂₀	1	64	yes	complemented
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	32	no	—
472	C₂×C₄	—	4	16	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	5	16	no	—
476	C₂×C₄	—	10	16	no	—
477	C₂×C₄	—	10	64	no	—
478	C₂×C₄	—	10	64	no	—
479	C₂×C₄	C₂²×D₂₀	1	8	yes	—
480	C₂×C₄	C₂²×D₂₀	1	16	yes	complemented
481	C₂×C₄	#4144	1	4	yes	complemented
482	C₂×C₄	C₂⁴×D₅	1	2	yes	—
483	C₂×C₄	C₂⁴×D₅	1	4	yes	—
484	C₂×C₄	C₂⁴×D₅	1	8	yes	—
485	C₂×C₄	C₂⁴×D₅	1	4	yes	—
486	C₂×C₄	C₂⁴×D₅	1	2	yes	—
487	C₅	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	8	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	32	no	—
494	C₂²	—	4	32	no	—
495	C₂²	—	10	16	no	—
496	C₂²	—	10	16	no	—
497	C₂²	—	10	16	no	—
498	C₂²	—	20	32	no	—
499	C₂²	—	40	64	no	—
500	C₂²	C₂³×D₂₀	1	16	yes	—
501	C₂²	C₂³×D₂₀	1	4	yes	—
502	C₂²	C₂³×D₂₀	1	2	yes	—
503	C₂²	C₂×#4144	1	2	yes	—
504	C₂²	#66283	1	2	yes	—
505	C₂²	C₂⁵×D₅	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	8	no	—
508	C₄	—	2	4	no	—
509	C₄	—	10	16	no	—
510	C₄	C₂³×D₂₀	1	8	yes	—
511	C₄	C₂×#4144	1	4	yes	complemented
512	C₂	—	2	4	no	—
513	C₂	—	2	16	no	—
514	C₂	—	20	16	no	—
515	C₂	#10617687	1	4	yes	direct product factor
516	C₂	C₂⁴×D₂₀	1	1	yes	characteristic
517	C₂	C₂²×#4144	1	1	yes	characteristic
518	C₂	C₂×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂²×C₄×C₅×D₄	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂²×C₄×D₄	D₅
hypocenter	C₅	C₂×#3496
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#4144	C₂	semidirect
2. C₂²×C₄×C₅×D₄	C₂	semidirect
3. C₂²×#4076	C₂	semidirect
4. #10617687	C₂	direct (N × H)
5. C₂×#65888	C₂	semidirect
6. C₂×D₄×D₂₀	C₂	semidirect
7. C₂×#65889	C₂	semidirect
8. C₂×#65844	C₂	semidirect
9. C₂×#65827	C₂	semidirect
10. C₂×#65811	C₂	semidirect
12. C₂⁴×C₄×C₅	C₂²	semidirect
13. C₂³×C₂²⋊D₅	C₂²	semidirect
15. C₂×#4144	C₂²	semidirect
16. C₂²×#711	C₂²	semidirect
17. C₂²×D₄×D₅	C₂²	semidirect
18. C₂²×#709	C₂²	semidirect
19. C₂³×D₂₀	C₂²	semidirect
20. C₂×C₄×C₅×D₄	C₂²	semidirect
21. C₂×C₄×C₅×D₄	C₂²	semidirect
22. C₂×C₄×C₅×D₄	C₂²	semidirect
23. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₄²×C₅	C₂²	semidirect
26. C₂×#4076	C₂²	semidirect
27. C₂×#4076	C₂²	semidirect
28. C₂×#4076	C₂²	semidirect
29. C₂×#4076	C₂²	semidirect
30. C₂×#4076	C₂²	semidirect
31. C₂×#4076	C₂²	semidirect
32. C₂²×#685	C₂²	semidirect
33. C₂²×C₄⋊Dic₅	C₂²	semidirect
34. #65889	C₂²	semidirect
35. #65888	C₂²	semidirect
36. D₄×D₂₀	C₂²	semidirect
37. #65844	C₂²	semidirect
38. C₂×#4043	C₂²	semidirect
39. C₂×#4041	C₂²	semidirect
40. #65827	C₂²	semidirect
41. C₂×#4032	C₂²	semidirect
42. C₂×#4028	C₂²	semidirect
43. #65811	C₂²	semidirect
44. C₂×#4021	C₂²	semidirect
45. C₂×#4020	C₂²	semidirect
46. C₂×C₄×D₂₀	C₂²	semidirect
47. C₂×C₄×D₂₀	C₂²	semidirect
48. C₂×#4015	C₂²	semidirect
52. C₂²×C₅×D₄	D₄	semidirect
62. C₂³×C₄×C₅	C₂³	semidirect
66. C₂²×C₂²⋊D₅	C₂³	semidirect
70. C₂×#711	C₂³	semidirect
72. C₂×D₄×D₅	C₂³	semidirect
74. C₂×#709	C₂³	semidirect
80. C₂²×D₂₀	C₂³	semidirect
83. C₄×C₅×D₄	C₂³	semidirect
84. C₄×C₅×D₄	C₂³	semidirect
86. C₂×C₅×C₄⋊C₄	C₂³	semidirect
88. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
91. C₂×C₄²×C₅	C₂³	semidirect
92. #4076	C₂³	semidirect
93. #4076	C₂³	semidirect
94. #4076	C₂³	semidirect
95. #4076	C₂³	semidirect
96. #4076	C₂³	semidirect
100. C₂×#685	C₂³	semidirect
104. C₂×C₄⋊Dic₅	C₂³	semidirect
105. #4043	C₂³	semidirect
106. #4041	C₂³	semidirect
107. #4032	C₂³	semidirect
108. #4028	C₂³	semidirect
109. #4021	C₂³	semidirect
110. #4020	C₂³	semidirect
111. C₄×D₂₀	C₂³	semidirect
112. C₄×D₂₀	C₂³	semidirect
113. #4015	C₂³	semidirect
123. C₂²×C₄×D₄	D₅	semidirect
126. C₂⁴×C₅	C₂×D₄	semidirect
135. C₂×C₅×D₄	C₂×D₄	semidirect
136. C₂×C₅×D₄	C₂×D₄	semidirect
144. C₂²×C₄×C₅	C₂×D₄	semidirect
198. C₂⁴×C₄	C₂×D₅	semidirect
220. C₂×C₄×D₄	C₂×D₅	semidirect
221. C₂×C₄×D₄	C₂×D₅	semidirect
222. C₂×C₄×D₄	C₂×D₅	semidirect
224. C₂²×C₄⋊C₄	C₂×D₅	semidirect
226. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
227. C₂²×C₄²	C₂×D₅	semidirect
237. C₂³×C₅	C₂²×D₄	semidirect
249. C₅×D₄	C₂²×D₄	semidirect
259. C₂×C₄×C₅	C₂²×D₄	semidirect
260. C₂×C₄×C₅	H(5,𝔽₂)	semidirect
297. C₂²×D₄	D₂₀	semidirect
309. C₂³×C₄	C₂²×D₅	semidirect
324. C₄×D₄	C₂²×D₅	semidirect
325. C₄×D₄	C₂²×D₅	semidirect
331. C₂×C₄⋊C₄	C₂²×D₅	semidirect
337. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
340. C₂×C₄²	C₂²×D₅	semidirect
363. C₄×C₅	C₂×H(5,𝔽₂)	semidirect
372. C₂⁴	C₂×D₂₀	semidirect
395. C₂×D₄	C₂×D₂₀	semidirect
396. C₂×D₄	C₂×D₂₀	semidirect
409. C₂²×C₄	C₂×D₂₀	semidirect
433. C₂×C₅	#3496	semidirect
455. C₂³	C₂²×D₂₀	semidirect
466. D₄	C₂²×D₂₀	semidirect
480. C₂×C₄	C₂²×D₂₀	semidirect
481. C₂×C₄	#4144	semidirect
487. C₅	C₂×#3496	semidirect
511. C₄	C₂×#4144	semidirect
515. C₂	#10617687	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#4144	2
C₂²×C₄×C₅×D₄	2
C₂²×#4076	2
#10617687	2
C₂×#65888	2
C₂×D₄×D₂₀	2
C₂×#65889	2
C₂×#65844	2
C₂×#65827	2
C₂×#65811	2
C₂×#3496	5

Subgroups — C2×#10617687 #13007194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10617687 #13007194