Subgroups — C₂²×#65943 #13006209

Order 1280.

20038 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	C₂³×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₅	C₂	1	2	yes	maximal, complemented
3	C₂⁴×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#4083	C₂	1	2	yes	maximal, complemented
6	C₂²×#4086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#65943	C₂	1	48	yes	maximal, direct product factor
9	C₂²×#4041	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#4039	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#4030	C₂	1	2	yes	maximal, complemented
12	C₂²×#4028	C₂	1	2	yes	maximal, complemented
13	C₂⁵×D₅	C₂²	1	2	yes	complemented
14	C₂⁵×D₅	C₂²	1	2	yes	complemented
15	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₂³×C₂²⋊D₅	C₂²	1	2	yes	complemented
20	C₂³×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₂³×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₅	—	2	32	no	—
23	C₂²×D₄×D₅	—	2	16	no	—
24	C₂²×D₄×D₅	C₂²	1	24	yes	complemented
25	C₂²×D₄×D₅	C₂²	1	48	yes	complemented
26	C₂³×D₂₀	—	2	16	no	—
27	C₂³×D₂₀	C₂²	1	1	yes	characteristic
28	C₂³×D₂₀	C₂²	1	24	yes	complemented
29	C₂³×D₂₀	C₂²	1	1	yes	characteristic, complemented
30	C₂³×D₂₀	C₂²	1	2	yes	complemented
31	C₂³×D₂₀	C₂²	1	2	yes	complemented
32	C₂³×C₄×D₅	C₂²	1	2	yes	complemented
33	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#121	C₂²	1	24	yes	complemented
35	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
38	C₂×#4086	C₂²	1	24	yes	complemented
39	C₂×#4083	C₂²	1	48	yes	complemented
40	C₂×C₄×C₂²⋊D₅	C₂²	1	24	yes	complemented
41	C₂²×#685	C₂²	1	2	yes	complemented
42	C₂²×#685	C₂²	1	2	yes	complemented
43	C₂²×#685	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#683	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
46	#65943	C₂²	1	256	yes	direct product factor
47	C₂×#4041	C₂²	1	24	yes	complemented
48	C₂×#4039	C₂²	1	24	yes	complemented
49	C₂×#4030	C₂²	1	48	yes	complemented
50	C₂×#4028	C₂²	1	48	yes	complemented
51	C₂²×D₄²	—	5	1	no	maximal, Sylow
52	C₂⁵×C₅	C₂³	1	2	yes	—
53	C₂⁵×C₅	C₂³	1	1	yes	characteristic
54	C₂⁴×D₅	—	2	16	no	—
55	C₂⁴×D₅	—	2	16	no	—
56	C₂⁴×D₅	—	2	16	no	—
57	C₂⁴×D₅	—	2	16	no	—
58	C₂⁴×D₅	—	4	8	no	—
59	C₂⁴×D₅	—	4	8	no	—
60	C₂⁴×D₅	C₂³	1	2	yes	—
61	C₂⁴×D₅	C₂³	1	2	yes	—
62	C₂⁴×D₅	C₂³	1	1	yes	characteristic
63	C₂⁴×D₅	C₂³	1	24	yes	complemented
64	C₂⁴×D₅	C₂³	1	24	yes	complemented
65	C₂²×C₅×D₄	—	2	16	no	—
66	C₂²×C₅×D₄	—	2	8	no	—
67	C₂²×C₅×D₄	C₂³	1	24	yes	complemented
68	C₂²×C₅×D₄	C₂³	1	12	yes	complemented
69	C₂³×C₄×C₅	—	2	8	no	—
70	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂³	1	2	yes	—
72	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅	C₂³	1	12	yes	complemented
74	C₂²×C₂²⋊D₅	—	2	16	no	—
75	C₂²×C₂²⋊D₅	—	2	16	no	—
76	C₂²×C₂²⋊D₅	—	4	8	no	—
77	C₂²×C₂²⋊D₅	D₄	1	16	yes	complemented
78	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
79	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
80	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
81	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
82	C₂³×Dic₅	C₂³	1	1	yes	characteristic
83	C₂³×Dic₅	C₂³	1	1	yes	characteristic
84	C₂³×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×D₄×D₅	—	2	384	no	—
86	C₂×D₄×D₅	—	2	192	no	—
87	C₂×D₄×D₅	C₂³	1	64	yes	complemented
88	C₂×D₄×D₅	C₂³	1	128	yes	complemented
89	C₂²×D₂₀	—	2	16	no	—
90	C₂²×D₂₀	—	2	16	no	—
91	C₂²×D₂₀	—	2	8	no	—
92	C₂²×D₂₀	—	2	192	no	—
93	C₂²×D₂₀	D₄	1	16	yes	complemented
94	C₂²×D₂₀	C₂³	1	12	yes	—
95	C₂²×D₂₀	C₂³	1	64	yes	complemented
96	C₂²×D₂₀	C₂³	1	24	yes	complemented
97	C₂²×D₂₀	C₂³	1	24	yes	complemented
98	C₂²×D₂₀	C₂³	1	12	yes	complemented
99	C₂²×C₄×D₅	—	2	8	no	—
100	C₂²×C₄×D₅	—	2	16	no	—
101	C₂²×C₄×D₅	C₂³	1	24	yes	complemented
102	C₂²×C₄×D₅	C₂³	1	12	yes	complemented
103	C₅×#121	C₂³	1	64	yes	complemented
104	C₂×C₅×C₄⋊C₄	C₂³	1	12	yes	complemented
105	C₂×C₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
106	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	complemented
107	#4086	C₂³	1	64	yes	complemented
108	#4083	C₂³	1	128	yes	complemented
109	C₄×C₂²⋊D₅	C₂³	1	64	yes	complemented
110	C₂×#685	C₂³	1	12	yes	complemented
111	C₂×#685	C₂³	1	24	yes	complemented
112	C₂×#685	C₂³	1	24	yes	complemented
113	C₂×#683	C₂³	1	12	yes	complemented
114	C₂×C₄×Dic₅	C₂³	1	12	yes	complemented
115	#4041	C₂³	1	64	yes	complemented
116	#4039	C₂³	1	64	yes	complemented
117	#4030	C₂³	1	128	yes	complemented
118	#4028	C₂³	1	128	yes	complemented
119	C₂⁴×D₄	—	5	2	no	—
120	C₂⁴×D₄	—	5	1	no	—
121	C₂⁴×D₄	—	5	1	no	—
122	C₂×D₄²	—	5	48	no	—
123	C₂²×#127	—	5	1	no	—
124	C₂²×#121	—	5	1	no	—
125	C₂²×#121	—	5	2	no	—
126	C₂²×#121	D₅	1	1	yes	characteristic, complemented
127	C₂²×#120	—	5	2	no	—
128	C₂²×#120	—	5	2	no	—
129	C₂²×C₄×D₄	—	5	1	no	—
130	C₂²×C₄×D₄	—	5	1	no	—
131	C₂⁴×C₅	—	2	4	no	—
132	C₂⁴×C₅	—	2	4	no	—
133	C₂⁴×C₅	—	2	8	no	—
134	C₂⁴×C₅	—	2	8	no	—
135	C₂⁴×C₅	—	2	8	no	—
136	C₂⁴×C₅	C₂×D₄	1	8	yes	complemented
137	C₂⁴×C₅	C₂⁴	1	12	yes	—
138	C₂⁴×C₅	C₂⁴	1	6	yes	—
139	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
140	C₂³×D₅	—	2	4	no	—
141	C₂³×D₅	—	2	8	no	—
142	C₂³×D₅	—	2	8	no	—
143	C₂³×D₅	—	2	4	no	—
144	C₂³×D₅	—	2	8	no	—
145	C₂³×D₅	—	2	8	no	—
146	C₂³×D₅	—	2	96	no	—
147	C₂³×D₅	—	2	8	no	—
148	C₂³×D₅	—	2	96	no	—
149	C₂³×D₅	—	2	96	no	—
150	C₂³×D₅	—	2	96	no	—
151	C₂³×D₅	—	4	48	no	—
152	C₂³×D₅	—	4	48	no	—
153	C₂³×D₅	—	4	128	no	—
154	C₂³×D₅	—	4	128	no	—
155	C₂³×D₅	C₂×D₄	1	8	yes	complemented
156	C₂³×D₅	C₂×D₄	1	16	yes	complemented
157	C₂³×D₅	C₂⁴	1	12	yes	—
158	C₂³×D₅	C₂⁴	1	12	yes	—
159	C₂³×D₅	C₂⁴	1	6	yes	—
160	C₂³×D₅	C₂⁴	1	32	yes	complemented
161	C₂³×D₅	C₂⁴	1	32	yes	complemented
162	C₂×C₅×D₄	—	2	96	no	—
163	C₂×C₅×D₄	—	2	48	no	—
164	C₂×C₅×D₄	C₂⁴	1	32	yes	complemented
165	C₂×C₅×D₄	C₂⁴	1	16	yes	complemented
166	C₂²×C₄×C₅	—	2	8	no	—
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	48	no	—
169	C₂²×C₄×C₅	C₂×D₄	1	8	yes	complemented
170	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
171	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
172	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	16	yes	complemented
174	C₂×C₂²⋊D₅	—	2	96	no	—
175	C₂×C₂²⋊D₅	—	2	96	no	—
176	C₂×C₂²⋊D₅	—	4	48	no	—
177	C₂×C₂²⋊D₅	C₂×D₄	1	96	yes	complemented
178	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
179	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
180	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
181	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	complemented
182	C₂²×Dic₅	—	2	4	no	—
183	C₂²×Dic₅	—	2	4	no	—
184	C₂²×Dic₅	C₂×D₄	1	8	yes	complemented
185	C₂²×Dic₅	C₂⁴	1	6	yes	—
186	C₂²×Dic₅	C₂⁴	1	6	yes	—
187	C₂²×Dic₅	C₂⁴	1	6	yes	—
188	D₄×D₅	—	2	512	no	—
189	D₄×D₅	—	2	256	no	—
190	C₂×D₂₀	—	2	96	no	—
191	C₂×D₂₀	—	2	96	no	—
192	C₂×D₂₀	—	2	48	no	—
193	C₂×D₂₀	—	2	256	no	—
194	C₂×D₂₀	C₂×D₄	1	96	yes	complemented
195	C₂×D₂₀	C₂⁴	1	16	yes	—
196	C₂×D₂₀	C₂⁴	1	32	yes	complemented
197	C₂×D₂₀	C₂⁴	1	16	yes	complemented
198	C₂×D₂₀	C₂⁴	1	32	yes	complemented
199	C₂×C₄×D₅	—	2	48	no	—
200	C₂×C₄×D₅	—	2	96	no	—
201	C₂×C₄×D₅	C₂⁴	1	32	yes	complemented
202	C₂×C₄×D₅	C₂⁴	1	16	yes	complemented
203	C₅×C₄⋊C₄	C₂⁴	1	16	yes	complemented
204	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
205	C₂²⋊Dic₅	C₂⁴	1	16	yes	complemented
206	#685	C₂⁴	1	16	yes	complemented
207	#685	C₂⁴	1	32	yes	complemented
208	#685	C₂⁴	1	32	yes	complemented
209	#683	C₂⁴	1	16	yes	complemented
210	C₄×Dic₅	C₂⁴	1	16	yes	complemented
211	C₂⁶	—	5	2	no	—
212	C₂⁶	—	5	2	no	—
213	C₂³×D₄	—	5	1	no	—
214	C₂³×D₄	—	5	2	no	—
215	C₂³×D₄	—	5	2	no	—
216	C₂³×D₄	—	5	2	no	—
217	C₂³×D₄	—	5	48	no	—
218	C₂³×D₄	—	5	24	no	—
219	C₂³×D₄	—	5	1	no	—
220	C₂³×D₄	—	5	2	no	—
221	C₂³×D₄	—	5	2	no	—
222	C₂³×D₄	—	5	1	no	—
223	C₂³×D₄	—	5	24	no	—
224	C₂³×D₄	—	10	16	no	—
225	C₂³×D₄	—	10	32	no	—
226	C₂³×D₄	—	10	16	no	—
227	C₂³×D₄	C₂×D₅	1	2	yes	complemented
228	C₂³×D₄	C₂×D₅	1	1	yes	characteristic, complemented
229	C₂⁴×C₄	—	5	2	no	—
230	C₂⁴×C₄	—	5	1	no	—
231	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic, complemented
232	D₄²	—	5	256	no	—
233	C₂×#127	—	5	24	no	—
234	C₂×#121	—	5	24	no	—
235	C₂×#121	—	5	48	no	—
236	C₂×#121	C₂×D₅	1	24	yes	complemented
237	C₂×#120	—	5	48	no	—
238	C₂×#120	—	5	48	no	—
239	C₂×C₄×D₄	—	5	24	no	—
240	C₂×C₄×D₄	—	5	24	no	—
241	C₂²×C₄⋊C₄	—	5	1	no	—
242	C₂²×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
243	C₂²×C₂²⋊C₄	—	5	1	no	—
244	C₂²×C₂²⋊C₄	—	5	2	no	—
245	C₂²×C₂²⋊C₄	—	5	1	no	—
246	C₂²×C₂²⋊C₄	—	5	2	no	—
247	C₂²×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
248	C₂²×C₄²	—	5	1	no	—
249	C₂³×C₅	—	2	32	no	—
250	C₂³×C₅	—	2	12	no	—
251	C₂³×C₅	—	2	12	no	—
252	C₂³×C₅	—	2	24	no	—
253	C₂³×C₅	—	2	24	no	—
254	C₂³×C₅	—	2	24	no	—
255	C₂³×C₅	—	4	32	no	—
256	C₂³×C₅	C₂²×D₄	1	4	yes	—
257	C₂³×C₅	C₂²×D₄	1	4	yes	—
258	C₂³×C₅	C₂²×D₄	1	24	yes	complemented
259	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
260	C₂³×C₅	C₂⁵	1	8	yes	—
261	C₂³×C₅	C₂⁵	1	4	yes	—
262	C₂³×C₅	C₂⁵	1	3	yes	—
263	C₂²×D₅	—	2	32	no	—
264	C₂²×D₅	—	2	64	no	—
265	C₂²×D₅	—	2	12	no	—
266	C₂²×D₅	—	2	24	no	—
267	C₂²×D₅	—	2	24	no	—
268	C₂²×D₅	—	2	12	no	—
269	C₂²×D₅	—	2	24	no	—
270	C₂²×D₅	—	2	24	no	—
271	C₂²×D₅	—	2	64	no	—
272	C₂²×D₅	—	2	24	no	—
273	C₂²×D₅	—	2	64	no	—
274	C₂²×D₅	—	2	64	no	—
275	C₂²×D₅	—	2	64	no	—
276	C₂²×D₅	—	4	32	no	—
277	C₂²×D₅	—	4	32	no	—
278	C₂²×D₅	—	4	384	no	—
279	C₂²×D₅	—	4	384	no	—
280	C₂²×D₅	—	4	32	no	—
281	C₂²×D₅	C₂²×D₄	1	24	yes	complemented
282	C₂²×D₅	C₂²×D₄	1	48	yes	complemented
283	C₂²×D₅	C₂⁵	1	8	yes	—
284	C₂²×D₅	C₂⁵	1	8	yes	—
285	C₂²×D₅	C₂⁵	1	4	yes	—
286	C₅×D₄	—	2	64	no	—
287	C₅×D₄	—	2	32	no	—
288	C₂×C₄×C₅	—	2	24	no	—
289	C₂×C₄×C₅	—	2	12	no	—
290	C₂×C₄×C₅	—	2	32	no	—
291	C₂×C₄×C₅	C₂²×D₄	1	24	yes	complemented
292	C₂×C₄×C₅	C₂⁵	1	4	yes	—
293	C₂×C₄×C₅	C₂⁵	1	8	yes	—
294	C₂×C₄×C₅	C₂⁵	1	4	yes	—
295	C₂²⋊D₅	—	2	64	no	—
296	C₂²⋊D₅	—	2	64	no	—
297	C₂²⋊D₅	—	4	32	no	—
298	C₂²⋊D₅	C₂²×D₄	1	64	yes	complemented
299	C₂×Dic₅	—	2	12	no	—
300	C₂×Dic₅	—	2	12	no	—
301	C₂×Dic₅	C₂²×D₄	1	24	yes	complemented
302	C₂×Dic₅	C₂⁵	1	4	yes	—
303	C₂×Dic₅	C₂⁵	1	4	yes	—
304	C₂×Dic₅	C₂⁵	1	4	yes	—
305	D₂₀	—	2	64	no	—
306	D₂₀	—	2	64	no	—
307	D₂₀	—	2	32	no	—
308	D₂₀	C₂²×D₄	1	64	yes	complemented
309	C₄×D₅	—	2	32	no	—
310	C₄×D₅	—	2	64	no	—
311	C₂⁵	—	5	2	no	—
312	C₂⁵	—	5	1	no	—
313	C₂⁵	—	5	2	no	—
314	C₂⁵	—	5	24	no	—
315	C₂⁵	—	5	24	no	—
316	C₂⁵	—	10	16	no	—
317	C₂⁵	—	10	16	no	—
318	C₂⁵	—	10	16	no	—
319	C₂⁵	—	10	16	no	—
320	C₂⁵	—	20	8	no	—
321	C₂⁵	—	20	8	no	—
322	C₂⁵	C₂²×D₅	1	2	yes	—
323	C₂⁵	C₂²×D₅	1	1	yes	characteristic
324	C₂²×D₄	—	2	16	no	—
325	C₂²×D₄	—	2	8	no	—
326	C₂²×D₄	—	5	16	no	—
327	C₂²×D₄	—	5	12	no	—
328	C₂²×D₄	—	5	24	no	—
329	C₂²×D₄	—	5	24	no	—
330	C₂²×D₄	—	5	24	no	—
331	C₂²×D₄	—	5	128	no	—
332	C₂²×D₄	—	5	64	no	—
333	C₂²×D₄	—	5	16	no	—
334	C₂²×D₄	—	5	12	no	—
335	C₂²×D₄	—	5	24	no	—
336	C₂²×D₄	—	5	24	no	—
337	C₂²×D₄	—	5	12	no	—
338	C₂²×D₄	—	5	64	no	—
339	C₂²×D₄	—	10	192	no	—
340	C₂²×D₄	—	10	16	no	—
341	C₂²×D₄	—	10	16	no	—
342	C₂²×D₄	—	10	16	no	—
343	C₂²×D₄	—	10	384	no	—
344	C₂²×D₄	—	10	192	no	—
345	C₂²×D₄	—	10	16	no	—
346	C₂²×D₄	—	10	8	no	—
347	C₂²×D₄	—	20	8	no	—
348	C₂²×D₄	C₂²×D₅	1	24	yes	complemented
349	C₂²×D₄	C₂²×D₅	1	12	yes	complemented
350	C₂³×C₄	—	2	8	no	—
351	C₂³×C₄	—	5	1	no	—
352	C₂³×C₄	—	5	1	no	—
353	C₂³×C₄	—	5	1	no	—
354	C₂³×C₄	—	5	24	no	—
355	C₂³×C₄	—	5	12	no	—
356	C₂³×C₄	—	10	16	no	—
357	C₂³×C₄	—	10	8	no	—
358	C₂³×C₄	C₂²×D₅	1	2	yes	—
359	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
360	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
361	C₂³×C₄	C₂²×D₅	1	12	yes	complemented
362	#127	—	5	64	no	—
363	#121	—	5	64	no	—
364	#121	—	5	128	no	—
365	#121	C₂²×D₅	1	64	yes	complemented
366	#120	—	5	128	no	—
367	#120	—	5	128	no	—
368	C₄×D₄	—	5	64	no	—
369	C₄×D₄	—	5	64	no	—
370	C₂×C₄⋊C₄	—	5	12	no	—
371	C₂×C₄⋊C₄	C₂²×D₅	1	12	yes	complemented
372	C₂×C₂²⋊C₄	—	5	12	no	—
373	C₂×C₂²⋊C₄	—	5	24	no	—
374	C₂×C₂²⋊C₄	—	5	12	no	—
375	C₂×C₂²⋊C₄	—	5	24	no	—
376	C₂×C₂²⋊C₄	C₂²×D₅	1	24	yes	complemented
377	C₂×C₄²	—	5	12	no	—
378	C₂²×C₅	—	2	4	no	—
379	C₂²×C₅	—	2	4	no	—
380	C₂²×C₅	—	2	48	no	—
381	C₂²×C₅	—	2	8	no	—
382	C₂²×C₅	—	2	8	no	—
383	C₂²×C₅	—	2	8	no	—
384	C₂²×C₅	—	4	48	no	—
385	C₂²×C₅	D₄²	1	16	yes	complemented
386	C₂²×C₅	C₂³×D₄	1	6	yes	—
387	C₂²×C₅	C₂³×D₄	1	6	yes	—
388	C₂²×C₅	C₂³×D₄	1	8	yes	complemented
389	C₂²×C₅	C₂×H(5,𝔽₂)	1	6	yes	—
390	C₂²×C₅	C₂⁶	1	1	yes	characteristic
391	C₂×D₅	—	2	4	no	—
392	C₂×D₅	—	2	8	no	—
393	C₂×D₅	—	2	8	no	—
394	C₂×D₅	—	2	4	no	—
395	C₂×D₅	—	2	48	no	—
396	C₂×D₅	—	2	96	no	—
397	C₂×D₅	—	2	8	no	—
398	C₂×D₅	—	2	8	no	—
399	C₂×D₅	—	2	8	no	—
400	C₂×D₅	—	4	128	no	—
401	C₂×D₅	—	4	128	no	—
402	C₂×D₅	—	4	48	no	—
403	C₂×D₅	C₂³×D₄	1	8	yes	complemented
404	C₂×D₅	C₂³×D₄	1	16	yes	complemented
405	C₄×C₅	—	2	8	no	—
406	C₄×C₅	—	2	4	no	—
407	C₄×C₅	C₂³×D₄	1	8	yes	complemented
408	Dic₅	—	2	4	no	—
409	Dic₅	—	2	4	no	—
410	Dic₅	C₂³×D₄	1	8	yes	complemented
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	8	no	—
414	C₂⁴	—	2	8	no	—
415	C₂⁴	—	2	8	no	—
416	C₂⁴	—	5	8	no	—
417	C₂⁴	—	5	16	no	—
418	C₂⁴	—	5	6	no	—
419	C₂⁴	—	5	12	no	—
420	C₂⁴	—	5	12	no	—
421	C₂⁴	—	5	32	no	—
422	C₂⁴	—	5	32	no	—
423	C₂⁴	—	10	96	no	—
424	C₂⁴	—	10	96	no	—
425	C₂⁴	—	10	96	no	—
426	C₂⁴	—	10	8	no	—
427	C₂⁴	—	10	4	no	—
428	C₂⁴	—	10	8	no	—
429	C₂⁴	—	10	4	no	—
430	C₂⁴	—	10	8	no	—
431	C₂⁴	—	10	8	no	—
432	C₂⁴	—	10	96	no	—
433	C₂⁴	—	10	8	no	—
434	C₂⁴	—	20	48	no	—
435	C₂⁴	—	20	48	no	—
436	C₂⁴	—	20	128	no	—
437	C₂⁴	—	20	128	no	—
438	C₂⁴	D₄×D₅	1	8	yes	complemented
439	C₂⁴	C₂³×D₅	1	12	yes	—
440	C₂⁴	C₂³×D₅	1	6	yes	—
441	C₂⁴	C₂³×D₅	1	1	yes	characteristic
442	C₂×D₄	—	2	96	no	—
443	C₂×D₄	—	2	48	no	—
444	C₂×D₄	—	5	96	no	—
445	C₂×D₄	—	5	16	no	—
446	C₂×D₄	—	5	32	no	—
447	C₂×D₄	—	5	32	no	—
448	C₂×D₄	—	5	32	no	—
449	C₂×D₄	—	5	96	no	—
450	C₂×D₄	—	5	16	no	—
451	C₂×D₄	—	5	32	no	—
452	C₂×D₄	—	5	32	no	—
453	C₂×D₄	—	5	16	no	—
454	C₂×D₄	—	10	256	no	—
455	C₂×D₄	—	10	96	no	—
456	C₂×D₄	—	10	96	no	—
457	C₂×D₄	—	10	96	no	—
458	C₂×D₄	—	10	512	no	—
459	C₂×D₄	—	10	256	no	—
460	C₂×D₄	—	10	96	no	—
461	C₂×D₄	—	10	48	no	—
462	C₂×D₄	—	20	48	no	—
463	C₂×D₄	C₂³×D₅	1	32	yes	complemented
464	C₂×D₄	C₂³×D₅	1	16	yes	complemented
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	2	48	no	—
468	C₂²×C₄	—	5	8	no	—
469	C₂²×C₄	—	5	6	no	—
470	C₂²×C₄	—	5	6	no	—
471	C₂²×C₄	—	5	6	no	—
472	C₂²×C₄	—	5	32	no	—
473	C₂²×C₄	—	5	16	no	—
474	C₂²×C₄	—	10	96	no	—
475	C₂²×C₄	—	10	4	no	—
476	C₂²×C₄	—	10	4	no	—
477	C₂²×C₄	—	10	48	no	—
478	C₂²×C₄	D₄×D₅	1	8	yes	complemented
479	C₂²×C₄	C₂³×D₅	1	12	yes	—
480	C₂²×C₄	C₂³×D₅	1	6	yes	—
481	C₂²×C₄	C₂³×D₅	1	6	yes	—
482	C₂²×C₄	C₂³×D₅	1	16	yes	complemented
483	C₄⋊C₄	—	5	16	no	—
484	C₄⋊C₄	C₂³×D₅	1	16	yes	complemented
485	C₂²⋊C₄	—	5	16	no	—
486	C₂²⋊C₄	—	5	32	no	—
487	C₂²⋊C₄	—	5	16	no	—
488	C₂²⋊C₄	—	5	32	no	—
489	C₂²⋊C₄	C₂³×D₅	1	32	yes	complemented
490	C₄²	—	5	16	no	—
491	C₂×C₅	—	2	8	no	—
492	C₂×C₅	—	4	8	no	—
493	C₂×C₅	C₂×D₄²	1	12	yes	complemented
494	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
495	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
496	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
497	D₅	—	2	8	no	—
498	D₅	—	2	16	no	—
499	D₅	—	4	8	no	—
500	C₂³	—	2	32	no	—
501	C₂³	—	2	12	no	—
502	C₂³	—	2	12	no	—
503	C₂³	—	2	24	no	—
504	C₂³	—	2	24	no	—
505	C₂³	—	2	24	no	—
506	C₂³	—	4	32	no	—
507	C₂³	—	5	24	no	—
508	C₂³	—	5	48	no	—
509	C₂³	—	5	4	no	—
510	C₂³	—	5	8	no	—
511	C₂³	—	5	8	no	—
512	C₂³	—	10	64	no	—
513	C₂³	—	10	64	no	—
514	C₂³	—	10	64	no	—
515	C₂³	—	10	64	no	—
516	C₂³	—	10	32	no	—
517	C₂³	—	10	24	no	—
518	C₂³	—	10	12	no	—
519	C₂³	—	10	24	no	—
520	C₂³	—	10	12	no	—
521	C₂³	—	10	24	no	—
522	C₂³	—	10	24	no	—
523	C₂³	—	10	64	no	—
524	C₂³	—	10	24	no	—
525	C₂³	—	20	32	no	—
526	C₂³	—	20	32	no	—
527	C₂³	—	20	384	no	—
528	C₂³	—	20	384	no	—
529	C₂³	—	20	32	no	—
530	C₂³	C₂×D₄×D₅	1	4	yes	—
531	C₂³	C₂×D₄×D₅	1	4	yes	—
532	C₂³	C₂×D₄×D₅	1	24	yes	complemented
533	C₂³	#4149	1	4	yes	—
534	C₂³	C₂⁴×D₅	1	8	yes	—
535	C₂³	C₂⁴×D₅	1	4	yes	—
536	C₂³	C₂⁴×D₅	1	3	yes	—
537	D₄	—	2	64	no	—
538	D₄	—	2	32	no	—
539	D₄	—	5	64	no	—
540	D₄	—	5	64	no	—
541	D₄	—	10	64	no	—
542	D₄	—	10	64	no	—
543	D₄	—	10	64	no	—
544	D₄	—	10	64	no	—
545	D₄	—	10	32	no	—
546	D₄	—	20	32	no	—
547	C₂×C₄	—	2	12	no	—
548	C₂×C₄	—	2	24	no	—
549	C₂×C₄	—	2	32	no	—
550	C₂×C₄	—	5	24	no	—
551	C₂×C₄	—	5	4	no	—
552	C₂×C₄	—	5	4	no	—
553	C₂×C₄	—	5	4	no	—
554	C₂×C₄	—	10	64	no	—
555	C₂×C₄	—	10	12	no	—
556	C₂×C₄	—	10	12	no	—
557	C₂×C₄	—	10	32	no	—
558	C₂×C₄	C₂×D₄×D₅	1	24	yes	complemented
559	C₂×C₄	C₂⁴×D₅	1	8	yes	—
560	C₂×C₄	C₂⁴×D₅	1	4	yes	—
561	C₂×C₄	C₂⁴×D₅	1	4	yes	—
562	C₅	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
563	C₂²	—	2	4	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	2	48	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	4	48	no	—
570	C₂²	—	5	8	no	—
571	C₂²	—	5	16	no	—
572	C₂²	—	10	8	no	—
573	C₂²	—	10	4	no	—
574	C₂²	—	10	8	no	—
575	C₂²	—	10	4	no	—
576	C₂²	—	10	96	no	—
577	C₂²	—	10	48	no	—
578	C₂²	—	10	8	no	—
579	C₂²	—	10	8	no	—
580	C₂²	—	10	8	no	—
581	C₂²	—	20	128	no	—
582	C₂²	—	20	128	no	—
583	C₂²	—	20	48	no	—
584	C₂²	#65943	1	16	yes	direct product factor
585	C₂²	C₂²×D₄×D₅	1	6	yes	—
586	C₂²	C₂²×D₄×D₅	1	6	yes	—
587	C₂²	C₂²×D₄×D₅	1	8	yes	complemented
588	C₂²	C₂×#4149	1	6	yes	—
589	C₂²	C₂⁵×D₅	1	1	yes	characteristic
590	C₄	—	2	4	no	—
591	C₄	—	2	8	no	—
592	C₄	—	5	8	no	—
593	C₄	—	10	4	no	—
594	C₄	—	10	4	no	—
595	C₄	C₂²×D₄×D₅	1	8	yes	complemented
596	C₂	—	2	8	no	—
597	C₂	—	4	8	no	—
598	C₂	—	10	16	no	—
599	C₂	—	10	8	no	—
600	C₂	—	20	8	no	—
601	C₂	C₂×#65943	1	12	yes	direct product factor
602	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
603	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
604	C₂	C₂²×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂²×C₅×#121	C₂
socle	C₂⁴×C₅	C₂⁴
hypercenter	C₂²×#121	D₅
hypocenter	C₅	C₂²×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₅	C₂	semidirect
2. C₂³×D₄×D₅	C₂	semidirect
3. C₂⁴×D₂₀	C₂	semidirect
4. C₂²×C₅×#121	C₂	semidirect
5. C₂²×#4083	C₂	semidirect
6. C₂²×#4086	C₂	semidirect
7. C₂²×C₄×C₂²⋊D₅	C₂	semidirect
8. C₂×#65943	C₂	direct (N × H)
9. C₂²×#4041	C₂	semidirect
10. C₂²×#4039	C₂	semidirect
11. C₂²×#4030	C₂	semidirect
12. C₂²×#4028	C₂	semidirect
13. C₂⁵×D₅	C₂²	semidirect
14. C₂⁵×D₅	C₂²	semidirect
15. C₂³×C₅×D₄	C₂²	semidirect
16. C₂³×C₅×D₄	C₂²	semidirect
17. C₂⁴×C₄×C₅	C₂²	semidirect
19. C₂³×C₂²⋊D₅	C₂²	semidirect
20. C₂³×C₂²⋊D₅	C₂²	semidirect
21. C₂³×C₂²⋊D₅	C₂²	semidirect
24. C₂²×D₄×D₅	C₂²	semidirect
25. C₂²×D₄×D₅	C₂²	semidirect
28. C₂³×D₂₀	C₂²	semidirect
29. C₂³×D₂₀	C₂²	semidirect
30. C₂³×D₂₀	C₂²	semidirect
31. C₂³×D₂₀	C₂²	semidirect
32. C₂³×C₄×D₅	C₂²	semidirect
33. C₂³×C₄×D₅	C₂²	semidirect
34. C₂×C₅×#121	C₂²	semidirect
35. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
36. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
37. C₂²×C₂²⋊Dic₅	C₂²	semidirect
38. C₂×#4086	C₂²	semidirect
39. C₂×#4083	C₂²	semidirect
40. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
41. C₂²×#685	C₂²	semidirect
42. C₂²×#685	C₂²	semidirect
43. C₂²×#685	C₂²	semidirect
44. C₂²×#683	C₂²	semidirect
45. C₂²×C₄×Dic₅	C₂²	semidirect
46. #65943	C₂²	direct (N × H)
47. C₂×#4041	C₂²	semidirect
48. C₂×#4039	C₂²	semidirect
49. C₂×#4030	C₂²	semidirect
50. C₂×#4028	C₂²	semidirect
63. C₂⁴×D₅	C₂³	semidirect
64. C₂⁴×D₅	C₂³	semidirect
67. C₂²×C₅×D₄	C₂³	semidirect
68. C₂²×C₅×D₄	C₂³	semidirect
73. C₂³×C₄×C₅	C₂³	semidirect
77. C₂²×C₂²⋊D₅	D₄	semidirect
79. C₂²×C₂²⋊D₅	C₂³	semidirect
80. C₂²×C₂²⋊D₅	C₂³	semidirect
81. C₂²×C₂²⋊D₅	C₂³	semidirect
87. C₂×D₄×D₅	C₂³	semidirect
88. C₂×D₄×D₅	C₂³	semidirect
93. C₂²×D₂₀	D₄	semidirect
95. C₂²×D₂₀	C₂³	semidirect
96. C₂²×D₂₀	C₂³	semidirect
97. C₂²×D₂₀	C₂³	semidirect
98. C₂²×D₂₀	C₂³	semidirect
101. C₂²×C₄×D₅	C₂³	semidirect
102. C₂²×C₄×D₅	C₂³	semidirect
103. C₅×#121	C₂³	semidirect
104. C₂×C₅×C₄⋊C₄	C₂³	semidirect
105. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
106. C₂×C₂²⋊Dic₅	C₂³	semidirect
107. #4086	C₂³	semidirect
108. #4083	C₂³	semidirect
109. C₄×C₂²⋊D₅	C₂³	semidirect
110. C₂×#685	C₂³	semidirect
111. C₂×#685	C₂³	semidirect
112. C₂×#685	C₂³	semidirect
113. C₂×#683	C₂³	semidirect
114. C₂×C₄×Dic₅	C₂³	semidirect
115. #4041	C₂³	semidirect
116. #4039	C₂³	semidirect
117. #4030	C₂³	semidirect
118. #4028	C₂³	semidirect
126. C₂²×#121	D₅	semidirect
136. C₂⁴×C₅	C₂×D₄	semidirect
155. C₂³×D₅	C₂×D₄	semidirect
156. C₂³×D₅	C₂×D₄	semidirect
160. C₂³×D₅	C₂⁴	semidirect
161. C₂³×D₅	C₂⁴	semidirect
164. C₂×C₅×D₄	C₂⁴	semidirect
165. C₂×C₅×D₄	C₂⁴	semidirect
169. C₂²×C₄×C₅	C₂×D₄	semidirect
173. C₂²×C₄×C₅	C₂⁴	semidirect
177. C₂×C₂²⋊D₅	C₂×D₄	semidirect
179. C₂×C₂²⋊D₅	C₂⁴	semidirect
180. C₂×C₂²⋊D₅	C₂⁴	semidirect
181. C₂×C₂²⋊D₅	C₂⁴	semidirect
184. C₂²×Dic₅	C₂×D₄	semidirect
194. C₂×D₂₀	C₂×D₄	semidirect
196. C₂×D₂₀	C₂⁴	semidirect
197. C₂×D₂₀	C₂⁴	semidirect
198. C₂×D₂₀	C₂⁴	semidirect
201. C₂×C₄×D₅	C₂⁴	semidirect
202. C₂×C₄×D₅	C₂⁴	semidirect
203. C₅×C₄⋊C₄	C₂⁴	semidirect
204. C₅×C₂²⋊C₄	C₂⁴	semidirect
205. C₂²⋊Dic₅	C₂⁴	semidirect
206. #685	C₂⁴	semidirect
207. #685	C₂⁴	semidirect
208. #685	C₂⁴	semidirect
209. #683	C₂⁴	semidirect
210. C₄×Dic₅	C₂⁴	semidirect
227. C₂³×D₄	C₂×D₅	semidirect
228. C₂³×D₄	C₂×D₅	semidirect
231. C₂⁴×C₄	C₂×D₅	semidirect
236. C₂×#121	C₂×D₅	semidirect
242. C₂²×C₄⋊C₄	C₂×D₅	semidirect
247. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
258. C₂³×C₅	C₂²×D₄	semidirect
281. C₂²×D₅	C₂²×D₄	semidirect
282. C₂²×D₅	C₂²×D₄	semidirect
291. C₂×C₄×C₅	C₂²×D₄	semidirect
298. C₂²⋊D₅	C₂²×D₄	semidirect
301. C₂×Dic₅	C₂²×D₄	semidirect
308. D₂₀	C₂²×D₄	semidirect
348. C₂²×D₄	C₂²×D₅	semidirect
349. C₂²×D₄	C₂²×D₅	semidirect
361. C₂³×C₄	C₂²×D₅	semidirect
365. #121	C₂²×D₅	semidirect
371. C₂×C₄⋊C₄	C₂²×D₅	semidirect
376. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
385. C₂²×C₅	D₄²	semidirect
388. C₂²×C₅	C₂³×D₄	semidirect
403. C₂×D₅	C₂³×D₄	semidirect
404. C₂×D₅	C₂³×D₄	semidirect
407. C₄×C₅	C₂³×D₄	semidirect
410. Dic₅	C₂³×D₄	semidirect
438. C₂⁴	D₄×D₅	semidirect
463. C₂×D₄	C₂³×D₅	semidirect
464. C₂×D₄	C₂³×D₅	semidirect
478. C₂²×C₄	D₄×D₅	semidirect
482. C₂²×C₄	C₂³×D₅	semidirect
484. C₄⋊C₄	C₂³×D₅	semidirect
489. C₂²⋊C₄	C₂³×D₅	semidirect
493. C₂×C₅	C₂×D₄²	semidirect
532. C₂³	C₂×D₄×D₅	semidirect
558. C₂×C₄	C₂×D₄×D₅	semidirect
562. C₅	C₂²×D₄²	semidirect
584. C₂²	#65943	direct (N × H)
587. C₂²	C₂²×D₄×D₅	semidirect
595. C₄	C₂²×D₄×D₅	semidirect
601. C₂	C₂×#65943	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₅	2
C₂⁴×D₂₀	2
C₂²×C₅×#121	2
C₂²×#4083	2
C₂²×#4086	2
C₂²×C₄×C₂²⋊D₅	2
C₂×#65943	2
C₂²×#4041	2
C₂²×#4039	2
C₂²×#4030	2
C₂²×#4028	2
C₂²×D₄²	5

Subgroups — C22×#65943 #13006209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#65943 #13006209