Subgroups — C₂×#10619140 #13007183

Order 1280.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#4144	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#4099	C₂	1	4	yes	maximal, complemented
4	#10619140	C₂	1	32	yes	maximal, direct product factor
5	C₂×D₄×C₂²⋊D₅	C₂	1	8	yes	maximal, complemented
6	C₂×#66139	C₂	1	2	yes	maximal, complemented
7	C₂×#66138	C₂	1	4	yes	maximal, complemented
8	C₂×#66140	C₂	1	8	yes	maximal, complemented
9	C₂×#66132	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66125	C₂	1	2	yes	maximal, complemented
11	C₂⁶×C₅	C₂²	1	2	yes	complemented
12	C₂³×C₅×D₄	—	2	16	no	—
13	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₅×D₄	C₂²	1	2	yes	complemented
15	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₅×D₄	C₂²	1	8	yes	complemented
17	C₂³×C₅×D₄	C₂²	1	16	yes	complemented
18	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₅	C₂²	1	4	yes	complemented
20	C₂³×C₂²⋊D₅	C₂²	1	8	yes	complemented
21	C₂×#4144	—	2	16	no	—
22	C₂×#4144	C₂²	1	16	yes	complemented
23	C₂²×#711	C₂²	1	4	yes	complemented
24	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
25	C₂²×#709	C₂²	1	2	yes	complemented
26	C₂×#4099	C₂²	1	4	yes	complemented
27	C₂×#4099	C₂²	1	8	yes	complemented
28	C₂×#4099	C₂²	1	16	yes	complemented
29	C₂×#4099	C₂²	1	64	yes	complemented
30	C₂²×C₂²⋊Dic₅	C₂²	1	4	yes	complemented
31	C₂²×C₂²⋊Dic₅	C₂²	1	8	yes	complemented
32	#66140	C₂²	1	128	yes	complemented
33	#66139	C₂²	1	32	yes	complemented
34	#66138	C₂²	1	64	yes	complemented
35	C₂×#4086	C₂²	1	4	yes	complemented
36	C₂×#4085	C₂²	1	16	yes	complemented
37	D₄×C₂²⋊D₅	C₂²	1	128	yes	complemented
38	C₂×#4084	C₂²	1	8	yes	complemented
39	C₂×#4083	C₂²	1	8	yes	complemented
40	#66132	C₂²	1	16	yes	complemented
41	C₂×#4082	C₂²	1	4	yes	complemented
42	C₂×#4081	C₂²	1	8	yes	complemented
43	C₂×D₄×Dic₅	C₂²	1	8	yes	complemented
44	#66125	C₂²	1	32	yes	complemented
45	C₂×#4076	C₂²	1	4	yes	complemented
46	C₂×#4075	C₂²	1	4	yes	complemented
47	C₂×C₄×C₂²⋊D₅	C₂²	1	8	yes	complemented
48	C₂×#4072	C₂²	1	2	yes	complemented
49	C₂×#4070	C₂²	1	4	yes	complemented
50	C₂×#3484	—	5	1	no	maximal, Sylow
51	C₂⁵×C₅	—	2	16	no	—
52	C₂⁵×C₅	—	4	16	no	—
53	C₂⁵×C₅	C₂³	1	1	yes	characteristic
54	C₂⁵×C₅	C₂³	1	8	yes	—
55	C₂⁵×C₅	C₂³	1	2	yes	—
56	C₂⁵×C₅	C₂³	1	2	yes	—
57	C₂⁵×C₅	C₂³	1	16	yes	complemented
58	C₂⁴×D₅	C₂³	1	4	yes	complemented
59	C₂²×C₅×D₄	—	2	16	no	—
60	C₂²×C₅×D₄	—	2	64	no	—
61	C₂²×C₅×D₄	—	2	128	no	—
62	C₂²×C₅×D₄	—	2	8	no	—
63	C₂²×C₅×D₄	D₄	1	16	yes	complemented
64	C₂²×C₅×D₄	C₂³	1	8	yes	—
65	C₂²×C₅×D₄	C₂³	1	4	yes	—
66	C₂²×C₅×D₄	C₂³	1	4	yes	—
67	C₂²×C₅×D₄	C₂³	1	8	yes	—
68	C₂²×C₅×D₄	C₂³	1	64	yes	complemented
69	C₂²×C₅×D₄	C₂³	1	16	yes	complemented
70	C₂²×C₅×D₄	C₂³	1	8	yes	complemented
71	C₂³×C₄×C₅	—	2	8	no	—
72	C₂³×C₄×C₅	C₂³	1	4	yes	—
73	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂³	1	8	yes	complemented
76	C₂²×C₂²⋊D₅	—	2	32	no	—
77	C₂²×C₂²⋊D₅	—	4	32	no	—
78	C₂²×C₂²⋊D₅	C₂³	1	8	yes	—
79	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
80	C₂²×C₂²⋊D₅	C₂³	1	8	yes	complemented
81	C₂²×C₂²⋊D₅	C₂³	1	16	yes	complemented
82	C₂²×C₂²⋊D₅	C₂³	1	32	yes	complemented
83	C₂²×C₂²⋊D₅	C₂³	1	64	yes	complemented
84	C₂³×Dic₅	C₂³	1	4	yes	complemented
85	C₂³×Dic₅	C₂³	1	8	yes	complemented
86	#4144	—	2	128	no	—
87	C₂×#711	—	2	32	no	—
88	C₂×#711	C₂³	1	32	yes	complemented
89	C₂×D₄×D₅	—	2	32	no	—
90	C₂×D₄×D₅	C₂³	1	32	yes	complemented
91	C₂×#709	—	2	16	no	—
92	C₂×#709	C₂³	1	16	yes	complemented
93	C₂²×D₂₀	C₂³	1	2	yes	complemented
94	C₂²×C₄×D₅	C₂³	1	4	yes	complemented
95	C₂²×Dic₁₀	C₂³	1	2	yes	complemented
96	#4099	C₂³	1	32	yes	complemented
97	#4099	C₂³	1	128	yes	complemented
98	#4099	C₂³	1	64	yes	complemented
99	C₂×C₂²⋊Dic₅	C₂³	1	8	yes	—
100	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
101	C₂×C₂²⋊Dic₅	C₂³	1	32	yes	complemented
102	C₂×C₂²⋊Dic₅	C₂³	1	64	yes	complemented
103	C₂×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
104	C₂×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
105	#4086	C₂³	1	32	yes	complemented
106	#4085	C₂³	1	128	yes	complemented
107	#4084	C₂³	1	64	yes	complemented
108	#4083	C₂³	1	64	yes	complemented
109	#4082	C₂³	1	32	yes	complemented
110	#4081	C₂³	1	64	yes	complemented
111	D₄×Dic₅	C₂³	1	64	yes	complemented
112	#4076	C₂³	1	32	yes	complemented
113	#4075	C₂³	1	32	yes	complemented
114	C₄×C₂²⋊D₅	C₂³	1	64	yes	complemented
115	C₂×#685	C₂³	1	8	yes	complemented
116	#4072	C₂³	1	16	yes	complemented
117	C₂×C₄⋊Dic₅	C₂³	1	4	yes	complemented
118	#4070	C₂³	1	32	yes	complemented
119	C₂×#683	C₂³	1	8	yes	complemented
120	C₂×C₄×Dic₅	C₂³	1	4	yes	complemented
121	C₂²×H(5,𝔽₂)	—	5	1	no	—
122	C₂⁴×D₄	D₅	1	1	yes	characteristic, complemented
123	#3484	—	5	32	no	—
124	C₂×#546	—	5	8	no	—
125	C₂×D₄²	—	5	8	no	—
126	C₂×#535	—	5	2	no	—
127	C₂×#534	—	5	4	no	—
128	C₂×#525	—	5	2	no	—
129	C₂²×#120	—	5	4	no	—
130	C₂×#518	—	5	1	no	—
131	C₂⁴×C₅	—	2	4	no	—
132	C₂⁴×C₅	—	2	8	no	—
133	C₂⁴×C₅	—	2	32	no	—
134	C₂⁴×C₅	—	2	8	no	—
135	C₂⁴×C₅	—	2	64	no	—
136	C₂⁴×C₅	—	2	32	no	—
137	C₂⁴×C₅	—	4	8	no	—
138	C₂⁴×C₅	—	4	16	no	—
139	C₂⁴×C₅	—	4	8	no	—
140	C₂⁴×C₅	—	4	64	no	—
141	C₂⁴×C₅	—	4	128	no	—
142	C₂⁴×C₅	C₂×D₄	1	16	yes	complemented
143	C₂⁴×C₅	C₂⁴	1	4	yes	—
144	C₂⁴×C₅	C₂⁴	1	4	yes	—
145	C₂⁴×C₅	C₂⁴	1	32	yes	—
146	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₅	C₂⁴	1	4	yes	—
148	C₂⁴×C₅	C₂⁴	1	2	yes	—
149	C₂⁴×C₅	C₂⁴	1	8	yes	—
150	C₂⁴×C₅	C₂⁴	1	8	yes	—
151	C₂³×D₅	—	2	16	no	—
152	C₂³×D₅	—	4	16	no	—
153	C₂³×D₅	C₂⁴	1	4	yes	—
154	C₂³×D₅	C₂⁴	1	16	yes	complemented
155	C₂×C₅×D₄	—	2	32	no	—
156	C₂×C₅×D₄	—	2	64	no	—
157	C₂×C₅×D₄	—	2	256	no	—
158	C₂×C₅×D₄	—	2	16	no	—
159	C₂×C₅×D₄	—	2	32	no	—
160	C₂×C₅×D₄	C₂×D₄	1	32	yes	complemented
161	C₂×C₅×D₄	C₂×D₄	1	64	yes	complemented
162	C₂×C₅×D₄	C₂⁴	1	32	yes	—
163	C₂×C₅×D₄	C₂⁴	1	16	yes	—
164	C₂×C₅×D₄	C₂⁴	1	16	yes	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	2	16	no	—
167	C₂²×C₄×C₅	—	2	32	no	—
168	C₂²×C₄×C₅	C₂×D₄	1	8	yes	complemented
169	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
171	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
174	C₂×C₂²⋊D₅	—	2	16	no	—
175	C₂×C₂²⋊D₅	—	2	32	no	—
176	C₂×C₂²⋊D₅	—	2	128	no	—
177	C₂×C₂²⋊D₅	—	2	32	no	—
178	C₂×C₂²⋊D₅	—	4	32	no	—
179	C₂×C₂²⋊D₅	—	4	128	no	—
180	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
181	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	—
182	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
183	C₂×C₂²⋊D₅	C₂⁴	1	64	yes	complemented
184	C₂²×Dic₅	—	2	16	no	—
185	C₂²×Dic₅	—	4	16	no	—
186	C₂²×Dic₅	C₂⁴	1	4	yes	—
187	C₂²×Dic₅	C₂⁴	1	8	yes	—
188	C₂²×Dic₅	C₂⁴	1	16	yes	complemented
189	C₂²×Dic₅	C₂⁴	1	32	yes	complemented
190	#711	—	2	128	no	—
191	D₄×D₅	—	2	128	no	—
192	#709	—	2	64	no	—
193	C₂×D₂₀	—	2	8	no	—
194	C₂×D₂₀	C₂⁴	1	8	yes	complemented
195	C₂×C₄×D₅	—	2	16	no	—
196	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
197	C₂×Dic₁₀	—	2	8	no	—
198	C₂×Dic₁₀	C₂⁴	1	8	yes	complemented
199	C₂²⋊Dic₅	C₂⁴	1	32	yes	—
200	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
201	C₂²⋊Dic₅	C₂⁴	1	32	yes	complemented
202	C₂²⋊Dic₅	C₂⁴	1	64	yes	complemented
203	#685	C₂⁴	1	32	yes	complemented
204	C₄⋊Dic₅	C₂⁴	1	16	yes	complemented
205	#683	C₂⁴	1	32	yes	complemented
206	C₄×Dic₅	C₂⁴	1	16	yes	complemented
207	C₂⁶	C₂×D₅	1	2	yes	complemented
208	C₂×H(5,𝔽₂)	—	5	16	no	—
209	C₂×H(5,𝔽₂)	—	10	16	no	—
210	C₂²×#41	—	5	4	no	—
211	C₂²×#41	—	5	2	no	—
212	C₂³×D₄	—	2	16	no	—
213	C₂³×D₄	—	5	4	no	—
214	C₂³×D₄	—	5	8	no	—
215	C₂³×D₄	—	5	4	no	—
216	C₂³×D₄	C₂×D₅	1	1	yes	characteristic
217	C₂³×D₄	C₂×D₅	1	2	yes	complemented
218	C₂³×D₄	C₂×D₅	1	1	yes	characteristic, complemented
219	C₂³×D₄	C₂×D₅	1	8	yes	complemented
220	C₂³×D₄	C₂×D₅	1	16	yes	complemented
221	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic, complemented
222	#546	—	5	128	no	—
223	D₄²	—	5	128	no	—
224	#535	—	5	32	no	—
225	#534	—	5	64	no	—
226	C₂×#127	—	5	4	no	—
227	C₂×#124	—	5	4	no	—
228	#525	—	5	32	no	—
229	C₂×#123	—	5	8	no	—
230	C₂×#123	—	5	4	no	—
231	C₂×C₂²⋊Q₈	—	5	4	no	—
232	C₂×#121	—	5	8	no	—
233	C₂×#121	—	5	16	no	—
234	C₂×#121	—	5	4	no	—
235	C₂×#120	—	5	4	no	—
236	C₂×#120	—	5	8	no	—
237	C₂×#120	—	5	16	no	—
238	C₂×#120	—	5	64	no	—
239	C₂×#120	—	5	8	no	—
240	#518	—	5	16	no	—
241	C₂×C₄×D₄	—	5	8	no	—
242	C₂×C₄×D₄	—	5	8	no	—
243	C₂×#117	—	5	2	no	—
244	C₂²×C₂²⋊C₄	—	5	4	no	—
245	C₂²×C₂²⋊C₄	—	5	8	no	—
246	C₂³×C₅	—	2	32	no	—
247	C₂³×C₅	—	2	8	no	—
248	C₂³×C₅	—	2	4	no	—
249	C₂³×C₅	—	2	16	no	—
250	C₂³×C₅	—	2	4	no	—
251	C₂³×C₅	—	2	4	no	—
252	C₂³×C₅	—	2	16	no	—
253	C₂³×C₅	—	2	64	no	—
254	C₂³×C₅	—	2	16	no	—
255	C₂³×C₅	—	2	8	no	—
256	C₂³×C₅	—	2	16	no	—
257	C₂³×C₅	—	2	64	no	—
258	C₂³×C₅	—	4	32	no	—
259	C₂³×C₅	—	4	16	no	—
260	C₂³×C₅	—	4	32	no	—
261	C₂³×C₅	—	4	16	no	—
262	C₂³×C₅	—	4	128	no	—
263	C₂³×C₅	—	4	256	no	—
264	C₂³×C₅	—	4	32	no	—
265	C₂³×C₅	C₂²×D₄	1	16	yes	—
266	C₂³×C₅	C₂²×D₄	1	4	yes	—
267	C₂³×C₅	C₂²×D₄	1	32	yes	complemented
268	C₂³×C₅	H(5,𝔽₂)	1	8	yes	complemented
269	C₂³×C₅	C₂⁵	1	8	yes	—
270	C₂³×C₅	C₂⁵	1	2	yes	—
271	C₂³×C₅	C₂⁵	1	8	yes	—
272	C₂³×C₅	C₂⁵	1	4	yes	—
273	C₂³×C₅	C₂⁵	1	1	yes	characteristic
274	C₂²×D₅	—	2	8	no	—
275	C₂²×D₅	—	2	16	no	—
276	C₂²×D₅	—	2	32	no	—
277	C₂²×D₅	—	4	32	no	—
278	C₂²×D₅	—	8	32	no	—
279	C₂²×D₅	C₂⁵	1	8	yes	—
280	C₅×D₄	—	2	64	no	—
281	C₅×D₄	—	2	32	no	—
282	C₅×D₄	C₂²×D₄	1	64	yes	complemented
283	C₂×C₄×C₅	—	2	8	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	2	32	no	—
286	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
287	C₂×C₄×C₅	C₂²×D₄	1	16	yes	complemented
288	C₂×C₄×C₅	C₂⁵	1	4	yes	—
289	C₂×C₄×C₅	C₂⁵	1	4	yes	—
290	C₂²⋊D₅	—	2	32	no	—
291	C₂²⋊D₅	—	2	64	no	—
292	C₂²⋊D₅	—	2	64	no	—
293	C₂²⋊D₅	—	4	64	no	—
294	C₂×Dic₅	—	2	8	no	—
295	C₂×Dic₅	—	2	32	no	—
296	C₂×Dic₅	—	2	16	no	—
297	C₂×Dic₅	—	4	32	no	—
298	C₂×Dic₅	C₂⁵	1	16	yes	—
299	C₂×Dic₅	C₂⁵	1	8	yes	—
300	D₂₀	—	2	16	no	—
301	C₄×D₅	—	2	32	no	—
302	Dic₁₀	—	2	16	no	—
303	C₂⁵	—	2	16	no	—
304	C₂⁵	—	4	16	no	—
305	C₂⁵	—	5	4	no	—
306	C₂⁵	C₂²×D₅	1	1	yes	characteristic
307	C₂⁵	C₂²×D₅	1	8	yes	—
308	C₂⁵	C₂²×D₅	1	2	yes	—
309	C₂⁵	C₂²×D₅	1	2	yes	—
310	C₂⁵	C₂²×D₅	1	16	yes	complemented
311	H(5,𝔽₂)	—	10	128	no	—
312	C₂×#41	—	5	32	no	—
313	C₂×#41	—	5	16	no	—
314	C₂×#41	—	10	32	no	—
315	C₂×#41	—	10	16	no	—
316	C₂²×Q₈	—	5	2	no	—
317	C₂²×D₄	—	2	16	no	—
318	C₂²×D₄	—	2	64	no	—
319	C₂²×D₄	—	2	128	no	—
320	C₂²×D₄	—	2	8	no	—
321	C₂²×D₄	—	5	8	no	—
322	C₂²×D₄	—	5	4	no	—
323	C₂²×D₄	—	5	8	no	—
324	C₂²×D₄	—	5	32	no	—
325	C₂²×D₄	—	5	16	no	—
326	C₂²×D₄	—	5	64	no	—
327	C₂²×D₄	—	5	32	no	—
328	C₂²×D₄	—	5	2	no	—
329	C₂²×D₄	—	10	32	no	—
330	C₂²×D₄	—	10	32	no	—
331	C₂²×D₄	—	20	32	no	—
332	C₂²×D₄	C₂²⋊D₅	1	16	yes	complemented
333	C₂²×D₄	C₂²×D₅	1	8	yes	—
334	C₂²×D₄	C₂²×D₅	1	4	yes	—
335	C₂²×D₄	C₂²×D₅	1	4	yes	—
336	C₂²×D₄	C₂²×D₅	1	8	yes	—
337	C₂²×D₄	C₂²×D₅	1	16	yes	complemented
338	C₂²×D₄	C₂²×D₅	1	8	yes	complemented
339	C₂²×D₄	C₂²×D₅	1	64	yes	complemented
340	C₂³×C₄	—	2	8	no	—
341	C₂³×C₄	—	5	4	no	—
342	C₂³×C₄	—	5	8	no	—
343	C₂³×C₄	—	5	4	no	—
344	C₂³×C₄	C₂²×D₅	1	4	yes	—
345	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
346	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
347	C₂³×C₄	C₂²×D₅	1	8	yes	complemented
348	#127	—	5	32	no	—
349	#124	—	5	32	no	—
350	#123	—	5	64	no	—
351	#123	—	5	32	no	—
352	C₂²⋊Q₈	—	5	32	no	—
353	#121	—	5	128	no	—
354	#121	—	5	64	no	—
355	#121	—	5	32	no	—
356	#120	—	5	32	no	—
357	#120	—	5	64	no	—
358	#120	—	5	128	no	—
359	#120	—	5	64	no	—
360	C₄×D₄	—	5	64	no	—
361	C₄×D₄	—	5	64	no	—
362	#117	—	5	16	no	—
363	C₂×C₄⋊C₄	—	5	4	no	—
364	C₂×C₄⋊C₄	—	5	8	no	—
365	C₂×C₂²⋊C₄	—	5	4	no	—
366	C₂×C₂²⋊C₄	—	5	8	no	—
367	C₂×C₂²⋊C₄	—	5	8	no	—
368	C₂×C₂²⋊C₄	—	5	32	no	—
369	C₂×C₂²⋊C₄	—	5	16	no	—
370	C₂×C₂²⋊C₄	—	5	64	no	—
371	C₂×C₂²⋊C₄	—	5	8	no	—
372	C₂×C₄²	—	5	4	no	—
373	C₂²×C₅	—	2	32	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	2	16	no	—
376	C₂²×C₅	—	2	4	no	—
377	C₂²×C₅	—	2	4	no	—
378	C₂²×C₅	—	2	32	no	—
379	C₂²×C₅	—	2	8	no	—
380	C₂²×C₅	—	2	16	no	—
381	C₂²×C₅	—	2	8	no	—
382	C₂²×C₅	—	2	16	no	—
383	C₂²×C₅	—	4	32	no	—
384	C₂²×C₅	—	4	128	no	—
385	C₂²×C₅	—	4	32	no	—
386	C₂²×C₅	—	4	16	no	—
387	C₂²×C₅	C₂³×D₄	1	16	yes	—
388	C₂²×C₅	C₂³×D₄	1	4	yes	—
389	C₂²×C₅	C₂³×D₄	1	2	yes	—
390	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
391	C₂²×C₅	C₂×H(5,𝔽₂)	1	8	yes	complemented
392	C₂²×C₅	C₂⁶	1	1	yes	characteristic
393	C₂×D₅	—	2	8	no	—
394	C₂×D₅	—	2	16	no	—
395	C₂×D₅	—	4	16	no	—
396	C₂×D₅	—	8	32	no	—
397	C₄×C₅	—	2	4	no	—
398	C₄×C₅	C₂³×D₄	1	8	yes	—
399	Dic₅	—	2	8	no	—
400	Dic₅	—	2	16	no	—
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	32	no	—
404	C₂⁴	—	2	32	no	—
405	C₂⁴	—	2	8	no	—
406	C₂⁴	—	2	64	no	—
407	C₂⁴	—	4	8	no	—
408	C₂⁴	—	4	16	no	—
409	C₂⁴	—	4	8	no	—
410	C₂⁴	—	4	64	no	—
411	C₂⁴	—	4	128	no	—
412	C₂⁴	—	5	4	no	—
413	C₂⁴	—	5	16	no	—
414	C₂⁴	—	10	16	no	—
415	C₂⁴	—	20	16	no	—
416	C₂⁴	C₂×C₂²⋊D₅	1	16	yes	complemented
417	C₂⁴	C₂³×D₅	1	4	yes	—
418	C₂⁴	C₂³×D₅	1	4	yes	—
419	C₂⁴	C₂³×D₅	1	32	yes	—
420	C₂⁴	C₂³×D₅	1	2	yes	—
421	C₂⁴	C₂³×D₅	1	1	yes	characteristic
422	C₂⁴	C₂³×D₅	1	4	yes	—
423	C₂⁴	C₂³×D₅	1	8	yes	—
424	C₂⁴	C₂³×D₅	1	8	yes	—
425	#41	—	10	128	no	—
426	#41	—	10	64	no	—
427	C₂×Q₈	—	5	8	no	—
428	C₂×Q₈	—	10	8	no	—
429	C₂×D₄	—	2	32	no	—
430	C₂×D₄	—	2	64	no	—
431	C₂×D₄	—	2	256	no	—
432	C₂×D₄	—	2	16	no	—
433	C₂×D₄	—	2	32	no	—
434	C₂×D₄	—	5	32	no	—
435	C₂×D₄	—	5	16	no	—
436	C₂×D₄	—	5	32	no	—
437	C₂×D₄	—	5	64	no	—
438	C₂×D₄	—	5	8	no	—
439	C₂×D₄	—	10	32	no	—
440	C₂×D₄	—	10	16	no	—
441	C₂×D₄	—	10	32	no	—
442	C₂×D₄	—	10	128	no	—
443	C₂×D₄	—	10	128	no	—
444	C₂×D₄	—	10	8	no	—
445	C₂×D₄	—	20	32	no	—
446	C₂×D₄	—	20	128	no	—
447	C₂×D₄	C₂×C₂²⋊D₅	1	32	yes	complemented
448	C₂×D₄	C₂×C₂²⋊D₅	1	64	yes	complemented
449	C₂×D₄	C₂³×D₅	1	32	yes	—
450	C₂×D₄	C₂³×D₅	1	16	yes	—
451	C₂×D₄	C₂³×D₅	1	16	yes	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	16	no	—
454	C₂²×C₄	—	2	32	no	—
455	C₂²×C₄	—	5	16	no	—
456	C₂²×C₄	—	5	8	no	—
457	C₂²×C₄	—	5	4	no	—
458	C₂²×C₄	—	5	32	no	—
459	C₂²×C₄	—	5	16	no	—
460	C₂²×C₄	—	10	16	no	—
461	C₂²×C₄	—	10	16	no	—
462	C₂²×C₄	—	20	16	no	—
463	C₂²×C₄	C₂×C₂²⋊D₅	1	8	yes	complemented
464	C₂²×C₄	C₂³×D₅	1	16	yes	—
465	C₂²×C₄	C₂³×D₅	1	4	yes	—
466	C₂²×C₄	C₂³×D₅	1	2	yes	—
467	C₂²×C₄	C₂³×D₅	1	2	yes	—
468	C₂²×C₄	C₂³×D₅	1	4	yes	—
469	C₄⋊C₄	—	5	16	no	—
470	C₄⋊C₄	—	5	32	no	—
471	C₂²⋊C₄	—	5	16	no	—
472	C₂²⋊C₄	—	5	32	no	—
473	C₂²⋊C₄	—	5	32	no	—
474	C₂²⋊C₄	—	5	64	no	—
475	C₂²⋊C₄	—	5	32	no	—
476	C₄²	—	5	16	no	—
477	C₂×C₅	—	2	16	no	—
478	C₂×C₅	—	2	4	no	—
479	C₂×C₅	—	2	8	no	—
480	C₂×C₅	—	4	8	no	—
481	C₂×C₅	#3484	1	4	yes	complemented
482	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
483	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
484	D₅	—	4	8	no	—
485	C₂³	—	2	32	no	—
486	C₂³	—	2	16	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	16	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	64	no	—
494	C₂³	—	2	64	no	—
495	C₂³	—	2	16	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	4	32	no	—
498	C₂³	—	4	16	no	—
499	C₂³	—	4	32	no	—
500	C₂³	—	4	16	no	—
501	C₂³	—	4	128	no	—
502	C₂³	—	4	256	no	—
503	C₂³	—	4	32	no	—
504	C₂³	—	5	8	no	—
505	C₂³	—	10	16	no	—
506	C₂³	—	10	8	no	—
507	C₂³	—	10	32	no	—
508	C₂³	—	20	32	no	—
509	C₂³	—	40	32	no	—
510	C₂³	#4144	1	8	yes	complemented
511	C₂³	C₂²×C₂²⋊D₅	1	4	yes	—
512	C₂³	C₂²×C₂²⋊D₅	1	16	yes	—
513	C₂³	C₂²×C₂²⋊D₅	1	32	yes	complemented
514	C₂³	C₂⁴×D₅	1	8	yes	—
515	C₂³	C₂⁴×D₅	1	4	yes	—
516	C₂³	C₂⁴×D₅	1	2	yes	—
517	C₂³	C₂⁴×D₅	1	8	yes	—
518	C₂³	C₂⁴×D₅	1	1	yes	characteristic
519	Q₈	—	10	16	no	—
520	D₄	—	2	64	no	—
521	D₄	—	2	32	no	—
522	D₄	—	10	64	no	—
523	D₄	—	10	32	no	—
524	D₄	—	10	64	no	—
525	D₄	—	10	16	no	—
526	D₄	—	20	64	no	—
527	D₄	C₂²×C₂²⋊D₅	1	64	yes	complemented
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	32	no	—
531	C₂×C₄	—	5	16	no	—
532	C₂×C₄	—	5	8	no	—
533	C₂×C₄	—	10	16	no	—
534	C₂×C₄	—	10	8	no	—
535	C₂×C₄	—	10	32	no	—
536	C₂×C₄	—	10	32	no	—
537	C₂×C₄	—	20	32	no	—
538	C₂×C₄	C₂²×C₂²⋊D₅	1	8	yes	—
539	C₂×C₄	C₂²×C₂²⋊D₅	1	16	yes	complemented
540	C₂×C₄	C₂⁴×D₅	1	4	yes	—
541	C₂×C₄	C₂⁴×D₅	1	4	yes	—
542	C₅	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
543	C₂²	—	2	32	no	—
544	C₂²	—	2	16	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	2	32	no	—
547	C₂²	—	2	16	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	16	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	4	32	no	—
554	C₂²	—	4	128	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	10	16	no	—
558	C₂²	—	10	8	no	—
559	C₂²	—	20	16	no	—
560	C₂²	—	40	32	no	—
561	C₂²	C₂×#4144	1	4	yes	—
562	C₂²	C₂×#4144	1	8	yes	complemented
563	C₂²	C₂³×C₂²⋊D₅	1	4	yes	—
564	C₂²	C₂³×C₂²⋊D₅	1	16	yes	—
565	C₂²	C₂³×C₂²⋊D₅	1	2	yes	—
566	C₂²	C₂⁵×D₅	1	1	yes	characteristic
567	C₄	—	2	4	no	—
568	C₄	—	10	16	no	—
569	C₄	—	10	8	no	—
570	C₄	C₂³×C₂²⋊D₅	1	8	yes	—
571	C₂	—	2	8	no	—
572	C₂	—	2	4	no	—
573	C₂	—	2	16	no	—
574	C₂	—	4	8	no	—
575	C₂	—	20	8	no	—
576	C₂	#10619140	1	4	yes	direct product factor
577	C₂	C₂²×#4144	1	2	yes	—
578	C₂	C₂⁴×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂⁴×C₅×D₄	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂⁴×D₄	D₅
hypocenter	C₅	C₂×#3484
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×D₄	C₂	semidirect
2. C₂²×#4144	C₂	semidirect
3. C₂²×#4099	C₂	semidirect
4. #10619140	C₂	direct (N × H)
5. C₂×D₄×C₂²⋊D₅	C₂	semidirect
6. C₂×#66139	C₂	semidirect
7. C₂×#66138	C₂	semidirect
8. C₂×#66140	C₂	semidirect
9. C₂×#66132	C₂	semidirect
10. C₂×#66125	C₂	semidirect
11. C₂⁶×C₅	C₂²	semidirect
14. C₂³×C₅×D₄	C₂²	semidirect
15. C₂³×C₅×D₄	C₂²	semidirect
16. C₂³×C₅×D₄	C₂²	semidirect
17. C₂³×C₅×D₄	C₂²	semidirect
18. C₂⁴×C₄×C₅	C₂²	semidirect
19. C₂³×C₂²⋊D₅	C₂²	semidirect
20. C₂³×C₂²⋊D₅	C₂²	semidirect
22. C₂×#4144	C₂²	semidirect
23. C₂²×#711	C₂²	semidirect
24. C₂²×D₄×D₅	C₂²	semidirect
25. C₂²×#709	C₂²	semidirect
26. C₂×#4099	C₂²	semidirect
27. C₂×#4099	C₂²	semidirect
28. C₂×#4099	C₂²	semidirect
29. C₂×#4099	C₂²	semidirect
30. C₂²×C₂²⋊Dic₅	C₂²	semidirect
31. C₂²×C₂²⋊Dic₅	C₂²	semidirect
32. #66140	C₂²	semidirect
33. #66139	C₂²	semidirect
34. #66138	C₂²	semidirect
35. C₂×#4086	C₂²	semidirect
36. C₂×#4085	C₂²	semidirect
37. D₄×C₂²⋊D₅	C₂²	semidirect
38. C₂×#4084	C₂²	semidirect
39. C₂×#4083	C₂²	semidirect
40. #66132	C₂²	semidirect
41. C₂×#4082	C₂²	semidirect
42. C₂×#4081	C₂²	semidirect
43. C₂×D₄×Dic₅	C₂²	semidirect
44. #66125	C₂²	semidirect
45. C₂×#4076	C₂²	semidirect
46. C₂×#4075	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
48. C₂×#4072	C₂²	semidirect
49. C₂×#4070	C₂²	semidirect
57. C₂⁵×C₅	C₂³	semidirect
58. C₂⁴×D₅	C₂³	semidirect
63. C₂²×C₅×D₄	D₄	semidirect
68. C₂²×C₅×D₄	C₂³	semidirect
69. C₂²×C₅×D₄	C₂³	semidirect
70. C₂²×C₅×D₄	C₂³	semidirect
75. C₂³×C₄×C₅	C₂³	semidirect
80. C₂²×C₂²⋊D₅	C₂³	semidirect
81. C₂²×C₂²⋊D₅	C₂³	semidirect
82. C₂²×C₂²⋊D₅	C₂³	semidirect
83. C₂²×C₂²⋊D₅	C₂³	semidirect
84. C₂³×Dic₅	C₂³	semidirect
85. C₂³×Dic₅	C₂³	semidirect
88. C₂×#711	C₂³	semidirect
90. C₂×D₄×D₅	C₂³	semidirect
92. C₂×#709	C₂³	semidirect
93. C₂²×D₂₀	C₂³	semidirect
94. C₂²×C₄×D₅	C₂³	semidirect
95. C₂²×Dic₁₀	C₂³	semidirect
96. #4099	C₂³	semidirect
97. #4099	C₂³	semidirect
98. #4099	C₂³	semidirect
101. C₂×C₂²⋊Dic₅	C₂³	semidirect
102. C₂×C₂²⋊Dic₅	C₂³	semidirect
103. C₂×C₂²⋊Dic₅	C₂³	semidirect
104. C₂×C₂²⋊Dic₅	C₂³	semidirect
105. #4086	C₂³	semidirect
106. #4085	C₂³	semidirect
107. #4084	C₂³	semidirect
108. #4083	C₂³	semidirect
109. #4082	C₂³	semidirect
110. #4081	C₂³	semidirect
111. D₄×Dic₅	C₂³	semidirect
112. #4076	C₂³	semidirect
113. #4075	C₂³	semidirect
114. C₄×C₂²⋊D₅	C₂³	semidirect
115. C₂×#685	C₂³	semidirect
116. #4072	C₂³	semidirect
117. C₂×C₄⋊Dic₅	C₂³	semidirect
118. #4070	C₂³	semidirect
119. C₂×#683	C₂³	semidirect
120. C₂×C₄×Dic₅	C₂³	semidirect
122. C₂⁴×D₄	D₅	semidirect
142. C₂⁴×C₅	C₂×D₄	semidirect
154. C₂³×D₅	C₂⁴	semidirect
160. C₂×C₅×D₄	C₂×D₄	semidirect
161. C₂×C₅×D₄	C₂×D₄	semidirect
168. C₂²×C₄×C₅	C₂×D₄	semidirect
182. C₂×C₂²⋊D₅	C₂⁴	semidirect
183. C₂×C₂²⋊D₅	C₂⁴	semidirect
188. C₂²×Dic₅	C₂⁴	semidirect
189. C₂²×Dic₅	C₂⁴	semidirect
194. C₂×D₂₀	C₂⁴	semidirect
196. C₂×C₄×D₅	C₂⁴	semidirect
198. C₂×Dic₁₀	C₂⁴	semidirect
201. C₂²⋊Dic₅	C₂⁴	semidirect
202. C₂²⋊Dic₅	C₂⁴	semidirect
203. #685	C₂⁴	semidirect
204. C₄⋊Dic₅	C₂⁴	semidirect
205. #683	C₂⁴	semidirect
206. C₄×Dic₅	C₂⁴	semidirect
207. C₂⁶	C₂×D₅	semidirect
217. C₂³×D₄	C₂×D₅	semidirect
218. C₂³×D₄	C₂×D₅	semidirect
219. C₂³×D₄	C₂×D₅	semidirect
220. C₂³×D₄	C₂×D₅	semidirect
221. C₂⁴×C₄	C₂×D₅	semidirect
267. C₂³×C₅	C₂²×D₄	semidirect
268. C₂³×C₅	H(5,𝔽₂)	semidirect
282. C₅×D₄	C₂²×D₄	semidirect
287. C₂×C₄×C₅	C₂²×D₄	semidirect
310. C₂⁵	C₂²×D₅	semidirect
332. C₂²×D₄	C₂²⋊D₅	semidirect
337. C₂²×D₄	C₂²×D₅	semidirect
338. C₂²×D₄	C₂²×D₅	semidirect
339. C₂²×D₄	C₂²×D₅	semidirect
347. C₂³×C₄	C₂²×D₅	semidirect
391. C₂²×C₅	C₂×H(5,𝔽₂)	semidirect
416. C₂⁴	C₂×C₂²⋊D₅	semidirect
447. C₂×D₄	C₂×C₂²⋊D₅	semidirect
448. C₂×D₄	C₂×C₂²⋊D₅	semidirect
463. C₂²×C₄	C₂×C₂²⋊D₅	semidirect
481. C₂×C₅	#3484	semidirect
510. C₂³	#4144	semidirect
513. C₂³	C₂²×C₂²⋊D₅	semidirect
527. D₄	C₂²×C₂²⋊D₅	semidirect
539. C₂×C₄	C₂²×C₂²⋊D₅	semidirect
542. C₅	C₂×#3484	semidirect
562. C₂²	C₂×#4144	semidirect
576. C₂	#10619140	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×D₄	2
C₂²×#4144	2
C₂²×#4099	2
#10619140	2
C₂×D₄×C₂²⋊D₅	2
C₂×#66139	2
C₂×#66138	2
C₂×#66140	2
C₂×#66132	2
C₂×#66125	2
C₂×#3484	5

Subgroups — C2×#10619140 #13007183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10619140 #13007183