Subgroups — C₂×#10618143 #13007617

Order 1280.

12982 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#4149	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#66164	C₂	1	2	yes	maximal, complemented
4	#10618143	C₂	1	32	yes	maximal, direct product factor
5	C₂×#66059	C₂	1	2	yes	maximal, complemented
6	C₂×D₅×#127	C₂	1	2	yes	maximal, complemented
7	C₂×#66008	C₂	1	4	yes	maximal, complemented
8	C₂×#65943	C₂	1	8	yes	maximal, complemented
9	C₂×D₄×D₂₀	C₂	1	4	yes	maximal, complemented
10	C₂×#65887	C₂	1	4	yes	maximal, complemented
11	C₂²×#4020	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₅×#41	C₂²	1	2	yes	complemented
14	C₂×#4149	—	2	32	no	—
15	C₂×#4149	C₂²	1	32	yes	complemented
16	C₂²×#713	C₂²	1	4	yes	complemented
17	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
18	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
19	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
20	C₂²×#709	C₂²	1	1	yes	characteristic
21	C₂²×#709	C₂²	1	4	yes	complemented
22	C₂³×D₂₀	C₂²	1	2	yes	complemented
23	C₂³×D₂₀	C₂²	1	4	yes	complemented
24	C₂³×D₂₀	C₂²	1	4	yes	complemented
25	C₅×#532	C₂²	1	16	yes	complemented
26	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#124	C₂²	1	2	yes	complemented
29	C₂×C₅×#121	C₂²	1	4	yes	complemented
30	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
31	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
32	#66164	C₂²	1	32	yes	complemented
33	C₂×#4093	C₂²	1	4	yes	complemented
34	C₂×#4086	C₂²	1	4	yes	complemented
35	C₂×#4086	C₂²	1	8	yes	complemented
36	C₂×#4083	C₂²	1	8	yes	complemented
37	C₂×#4076	C₂²	1	8	yes	complemented
38	C₂×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
39	C₂×#4072	C₂²	1	1	yes	characteristic, complemented
40	#66059	C₂²	1	32	yes	complemented
41	D₅×#127	C₂²	1	32	yes	complemented
42	#66008	C₂²	1	64	yes	complemented
43	#65943	C₂²	1	128	yes	complemented
44	#65887	C₂²	1	64	yes	complemented
45	D₄×D₂₀	C₂²	1	64	yes	complemented
46	C₂×#4041	C₂²	1	8	yes	complemented
47	C₂×#4039	C₂²	1	8	yes	complemented
48	C₂×#4030	C₂²	1	16	yes	complemented
49	C₂×#4028	C₂²	1	16	yes	complemented
50	C₂×#4020	C₂²	1	4	yes	complemented
51	C₂×#4020	C₂²	1	2	yes	complemented
52	C₂×#4020	C₂²	1	2	yes	complemented
53	C₂×#4020	C₂²	1	16	yes	complemented
54	C₄×#709	C₂²	1	16	yes	complemented
55	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
56	C₂×#4018	C₂²	1	2	yes	complemented
57	C₂×C₄²×D₅	C₂²	1	2	yes	complemented
58	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
59	C₂×#3498	—	5	1	no	maximal, Sylow
60	C₂⁴×D₅	C₂³	1	8	yes	—
61	C₂⁴×D₅	C₂³	1	4	yes	—
62	C₂×C₅×#41	—	2	16	no	—
63	C₂×C₅×#41	C₂³	1	16	yes	complemented
64	C₂²×C₅×Q₈	C₂³	1	2	yes	—
65	C₂²×C₅×D₄	C₂³	1	4	yes	—
66	C₂²×C₅×D₄	C₂³	1	4	yes	—
67	C₂²×C₅×D₄	C₂³	1	2	yes	—
68	C₂³×C₄×C₅	C₂³	1	2	yes	—
69	C₂³×C₄×C₅	C₂³	1	4	yes	—
70	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₂²⋊D₅	C₂³	1	8	yes	—
72	C₂²×C₂²⋊D₅	C₂³	1	16	yes	—
73	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
74	#4149	—	2	256	no	—
75	C₂×#713	—	2	32	no	—
76	C₂×#713	C₂³	1	32	yes	complemented
77	C₂×D₄×D₅	—	2	64	no	—
78	C₂×D₄×D₅	—	2	32	no	—
79	C₂×D₄×D₅	—	4	32	no	—
80	C₂×D₄×D₅	C₂³	1	32	yes	complemented
81	C₂×D₄×D₅	C₂³	1	64	yes	complemented
82	C₂×D₄×D₅	C₂³	1	64	yes	complemented
83	C₂×#709	—	2	32	no	—
84	C₂×#709	D₄	1	16	yes	complemented
85	C₂×#709	C₂³	1	8	yes	—
86	C₂×#709	C₂³	1	32	yes	complemented
87	C₂²×D₂₀	—	2	16	no	—
88	C₂²×D₂₀	—	2	32	no	—
89	C₂²×D₂₀	—	4	16	no	—
90	C₂²×D₂₀	C₂³	1	8	yes	—
91	C₂²×D₂₀	C₂³	1	4	yes	—
92	C₂²×D₂₀	C₂³	1	4	yes	—
93	C₂²×D₂₀	C₂³	1	8	yes	—
94	C₂²×D₂₀	C₂³	1	8	yes	—
95	C₂²×D₂₀	C₂³	1	1	yes	characteristic
96	C₂²×D₂₀	C₂³	1	16	yes	complemented
97	C₂²×D₂₀	C₂³	1	32	yes	complemented
98	C₂²×D₂₀	C₂³	1	32	yes	complemented
99	C₂²×C₄×D₅	C₂³	1	4	yes	—
100	C₂²×C₄×D₅	C₂³	1	8	yes	—
101	C₂²×C₄×D₅	C₂³	1	2	yes	—
102	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
104	C₅×#127	C₂³	1	8	yes	complemented
105	C₅×#124	C₂³	1	16	yes	complemented
106	C₅×#121	C₂³	1	32	yes	complemented
107	C₄×C₅×D₄	C₂³	1	32	yes	complemented
108	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₄²×C₅	C₂³	1	2	yes	—
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
114	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
115	#4093	C₂³	1	32	yes	complemented
116	#4086	C₂³	1	64	yes	complemented
117	#4086	C₂³	1	32	yes	complemented
118	#4083	C₂³	1	64	yes	complemented
119	#4076	C₂³	1	64	yes	complemented
120	C₄×C₂²⋊D₅	C₂³	1	32	yes	complemented
121	C₂×#685	C₂³	1	4	yes	—
122	C₂×#685	C₂³	1	16	yes	—
123	#4072	C₂³	1	8	yes	complemented
124	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
125	C₂×#683	C₂³	1	4	yes	—
126	C₂×C₄×Dic₅	C₂³	1	4	yes	—
127	C₂×C₄×Dic₅	C₂³	1	2	yes	—
128	#4041	C₂³	1	64	yes	complemented
129	#4039	C₂³	1	64	yes	complemented
130	#4030	C₂³	1	128	yes	complemented
131	#4028	C₂³	1	128	yes	complemented
132	#4020	C₂³	1	16	yes	complemented
133	#4020	C₂³	1	32	yes	complemented
134	#4020	C₂³	1	16	yes	complemented
135	C₄×D₂₀	C₂³	1	16	yes	complemented
136	#4018	C₂³	1	16	yes	complemented
137	C₄²×D₅	C₂³	1	16	yes	complemented
138	C₄×Dic₁₀	C₂³	1	16	yes	complemented
139	C₂²×H(5,𝔽₂)	—	5	2	no	—
140	#3498	—	5	32	no	—
141	C₂×#550	—	5	4	no	—
142	C₂×D₄²	—	5	8	no	—
143	C₂×D₄²	—	5	4	no	—
144	C₂×#535	—	5	2	no	—
145	C₂×#535	—	5	4	no	—
146	C₂×#532	—	5	2	no	—
147	C₂×#532	D₅	1	1	yes	characteristic, complemented
148	C₂²×#127	—	5	1	no	—
149	C₂²×#127	—	5	2	no	—
150	C₂×C₄×#41	—	5	1	no	—
151	C₂⁴×C₅	C₂⁴	1	4	yes	—
152	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
153	C₂³×D₅	—	2	16	no	—
154	C₂³×D₅	—	2	32	no	—
155	C₂³×D₅	—	4	16	no	—
156	C₂³×D₅	—	4	32	no	—
157	C₂³×D₅	C₂⁴	1	8	yes	—
158	C₂³×D₅	C₂⁴	1	2	yes	—
159	C₂³×D₅	C₂⁴	1	16	yes	—
160	C₂³×D₅	C₂⁴	1	32	yes	—
161	C₅×#41	—	2	64	no	—
162	C₂×C₅×Q₈	—	2	8	no	—
163	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
164	C₂×C₅×D₄	—	2	16	no	—
165	C₂×C₅×D₄	—	2	8	no	—
166	C₂×C₅×D₄	—	2	16	no	—
167	C₂×C₅×D₄	C₂⁴	1	16	yes	—
168	C₂×C₅×D₄	C₂⁴	1	16	yes	—
169	C₂×C₅×D₄	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₅	—	2	16	no	—
171	C₂²×C₄×C₅	—	2	8	no	—
172	C₂²×C₄×C₅	C₂×D₄	1	8	yes	complemented
173	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
177	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
181	C₂×C₂²⋊D₅	—	2	32	no	—
182	C₂×C₂²⋊D₅	—	4	32	no	—
183	C₂×C₂²⋊D₅	C₂×D₄	1	16	yes	complemented
184	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	—
185	C₂×C₂²⋊D₅	C₂⁴	1	64	yes	—
186	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
187	C₂²×Dic₅	C₂⁴	1	4	yes	—
188	C₂²×Dic₅	C₂⁴	1	2	yes	—
189	#713	—	2	128	no	—
190	D₄×D₅	—	2	256	no	—
191	D₄×D₅	—	2	128	no	—
192	D₄×D₅	—	4	128	no	—
193	#709	—	2	128	no	—
194	#709	C₂×D₄	1	64	yes	complemented
195	C₂×D₂₀	—	2	32	no	—
196	C₂×D₂₀	—	2	16	no	—
197	C₂×D₂₀	—	2	16	no	—
198	C₂×D₂₀	—	2	64	no	—
199	C₂×D₂₀	—	2	32	no	—
200	C₂×D₂₀	—	2	128	no	—
201	C₂×D₂₀	—	4	64	no	—
202	C₂×D₂₀	—	4	16	no	—
203	C₂×D₂₀	C₂×D₄	1	8	yes	complemented
204	C₂×D₂₀	C₂⁴	1	16	yes	—
205	C₂×D₂₀	C₂⁴	1	16	yes	—
206	C₂×D₂₀	C₂⁴	1	32	yes	—
207	C₂×D₂₀	C₂⁴	1	32	yes	—
208	C₂×D₂₀	C₂⁴	1	32	yes	—
209	C₂×D₂₀	C₂⁴	1	4	yes	—
210	C₂×C₄×D₅	—	2	16	no	—
211	C₂×C₄×D₅	—	2	32	no	—
212	C₂×C₄×D₅	C₂×D₄	1	16	yes	complemented
213	C₂×C₄×D₅	C₂⁴	1	32	yes	—
214	C₂×C₄×D₅	C₂⁴	1	16	yes	—
215	C₂×C₄×D₅	C₂⁴	1	8	yes	—
216	C₂×Dic₁₀	C₂×D₄	1	8	yes	complemented
217	C₂×Dic₁₀	C₂⁴	1	4	yes	—
218	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
219	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
220	C₄²×C₅	C₂⁴	1	8	yes	—
221	C₄²×C₅	C₂⁴	1	4	yes	—
222	C₄²×C₅	C₂⁴	1	4	yes	—
223	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
224	#685	C₂⁴	1	16	yes	—
225	#685	C₂⁴	1	64	yes	—
226	C₄⋊Dic₅	C₂⁴	1	8	yes	—
227	#683	C₂⁴	1	16	yes	—
228	C₄×Dic₅	C₂⁴	1	16	yes	—
229	C₄×Dic₅	C₂⁴	1	8	yes	—
230	C₂×H(5,𝔽₂)	—	5	32	no	—
231	C₂×H(5,𝔽₂)	—	10	32	no	—
232	C₂²×#41	—	5	4	no	—
233	C₂²×#41	—	5	1	no	—
234	C₂²×#41	—	5	4	no	—
235	C₂²×#41	C₂×D₅	1	2	yes	complemented
236	C₂³×D₄	—	5	4	no	—
237	C₂³×D₄	—	5	8	no	—
238	C₂³×D₄	—	5	8	no	—
239	C₂³×D₄	—	5	2	no	—
240	C₂³×D₄	—	5	4	no	—
241	C₂³×D₄	—	5	4	no	—
242	#550	—	5	64	no	—
243	D₄²	—	5	128	no	—
244	D₄²	—	5	64	no	—
245	#535	—	5	32	no	—
246	#535	—	5	64	no	—
247	#532	—	5	32	no	—
248	#532	C₂×D₅	1	16	yes	complemented
249	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂×#127	—	5	4	no	—
251	C₂×#127	—	5	8	no	—
252	C₂×#127	—	5	32	no	—
253	C₂×#127	—	5	2	no	—
254	C₂×#127	—	5	2	no	—
255	C₂×#127	—	5	4	no	—
256	C₂×#127	—	5	16	no	—
257	C₂×#127	C₂×D₅	1	1	yes	characteristic, complemented
258	C₂×#124	—	5	4	no	—
259	C₂×#124	C₂×D₅	1	2	yes	complemented
260	C₂×#121	—	5	8	no	—
261	C₂×#121	—	5	8	no	—
262	C₂×#121	—	5	16	no	—
263	C₂×#121	C₂×D₅	1	4	yes	complemented
264	C₂×#120	—	5	8	no	—
265	C₂×#120	—	5	16	no	—
266	C₄×#41	—	5	16	no	—
267	C₂×C₄×Q₈	—	5	2	no	—
268	C₂×C₄×D₄	—	5	4	no	—
269	C₂×C₄×D₄	—	5	8	no	—
270	C₂×C₄×D₄	—	5	2	no	—
271	C₂×C₄×D₄	C₂×D₅	1	4	yes	complemented
272	C₂×#117	—	5	1	no	—
273	C₂×#117	—	5	2	no	—
274	C₂²×C₄²	—	5	2	no	—
275	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
276	C₂³×C₅	—	2	4	no	—
277	C₂³×C₅	—	2	8	no	—
278	C₂³×C₅	—	2	16	no	—
279	C₂³×C₅	C₂²×D₄	1	4	yes	—
280	C₂³×C₅	C₂⁵	1	8	yes	—
281	C₂³×C₅	C₂⁵	1	2	yes	—
282	C₂³×C₅	C₂⁵	1	1	yes	characteristic
283	C₂²×D₅	—	2	8	no	—
284	C₂²×D₅	—	2	16	no	—
285	C₂²×D₅	—	2	32	no	—
286	C₂²×D₅	—	2	32	no	—
287	C₂²×D₅	—	2	64	no	—
288	C₂²×D₅	—	4	32	no	—
289	C₂²×D₅	—	4	64	no	—
290	C₂²×D₅	—	8	64	no	—
291	C₂²×D₅	—	8	32	no	—
292	C₂²×D₅	C₂²×D₄	1	8	yes	—
293	C₂²×D₅	C₂⁵	1	16	yes	—
294	C₂²×D₅	C₂⁵	1	4	yes	—
295	C₅×Q₈	—	2	16	no	—
296	C₅×D₄	—	2	32	no	—
297	C₅×D₄	—	2	16	no	—
298	C₅×D₄	—	2	32	no	—
299	C₂×C₄×C₅	—	2	8	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	32	no	—
302	C₂×C₄×C₅	—	2	16	no	—
303	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
304	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₅	C₂²×D₄	1	16	yes	complemented
306	C₂×C₄×C₅	H(5,𝔽₂)	1	8	yes	complemented
307	C₂×C₄×C₅	C₂⁵	1	4	yes	—
308	C₂×C₄×C₅	C₂⁵	1	8	yes	—
309	C₂×C₄×C₅	C₂⁵	1	2	yes	—
310	C₂×C₄×C₅	C₂⁵	1	2	yes	—
311	C₂×C₄×C₅	C₂⁵	1	4	yes	—
312	C₂²⋊D₅	—	2	64	no	—
313	C₂²⋊D₅	—	4	64	no	—
314	C₂²⋊D₅	C₂²×D₄	1	32	yes	complemented
315	C₂×Dic₅	—	2	8	no	—
316	C₂×Dic₅	C₂²×D₄	1	8	yes	—
317	C₂×Dic₅	C₂⁵	1	8	yes	—
318	C₂×Dic₅	C₂⁵	1	4	yes	—
319	D₂₀	—	2	64	no	—
320	D₂₀	—	2	32	no	—
321	D₂₀	—	2	32	no	—
322	D₂₀	—	2	64	no	—
323	D₂₀	—	4	32	no	—
324	D₂₀	C₂²×D₄	1	16	yes	complemented
325	C₄×D₅	—	2	32	no	—
326	C₄×D₅	—	2	64	no	—
327	C₄×D₅	C₂²×D₄	1	32	yes	complemented
328	Dic₁₀	C₂²×D₄	1	16	yes	complemented
329	C₂⁵	—	5	8	no	—
330	C₂⁵	—	5	4	no	—
331	H(5,𝔽₂)	—	10	256	no	—
332	C₂×#41	—	2	16	no	—
333	C₂×#41	—	5	32	no	—
334	C₂×#41	—	5	16	no	—
335	C₂×#41	—	5	8	no	—
336	C₂×#41	—	5	32	no	—
337	C₂×#41	—	10	32	no	—
338	C₂×#41	—	10	32	no	—
339	C₂×#41	C₂²×D₅	1	16	yes	complemented
340	C₂²×Q₈	—	5	1	no	—
341	C₂²×Q₈	C₂²×D₅	1	2	yes	—
342	C₂²×D₄	—	5	2	no	—
343	C₂²×D₄	—	5	8	no	—
344	C₂²×D₄	—	5	16	no	—
345	C₂²×D₄	—	5	32	no	—
346	C₂²×D₄	—	5	64	no	—
347	C₂²×D₄	—	5	64	no	—
348	C₂²×D₄	—	5	1	no	—
349	C₂²×D₄	—	5	8	no	—
350	C₂²×D₄	—	5	8	no	—
351	C₂²×D₄	—	5	4	no	—
352	C₂²×D₄	—	5	4	no	—
353	C₂²×D₄	—	5	16	no	—
354	C₂²×D₄	—	5	32	no	—
355	C₂²×D₄	—	5	8	no	—
356	C₂²×D₄	—	5	32	no	—
357	C₂²×D₄	—	10	32	no	—
358	C₂²×D₄	—	10	32	no	—
359	C₂²×D₄	—	10	64	no	—
360	C₂²×D₄	—	10	16	no	—
361	C₂²×D₄	—	20	16	no	—
362	C₂²×D₄	—	20	32	no	—
363	C₂²×D₄	C₂²×D₅	1	4	yes	—
364	C₂²×D₄	C₂²×D₅	1	4	yes	—
365	C₂²×D₄	C₂²×D₅	1	2	yes	—
366	C₂³×C₄	—	5	2	no	—
367	C₂³×C₄	—	5	4	no	—
368	C₂³×C₄	—	5	8	no	—
369	C₂³×C₄	C₂²×D₅	1	2	yes	—
370	C₂³×C₄	C₂²×D₅	1	4	yes	—
371	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
372	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
373	#127	—	5	32	no	—
374	#127	—	5	64	no	—
375	#127	—	5	16	no	—
376	#127	—	5	16	no	—
377	#127	—	5	32	no	—
378	#127	C₂²×D₅	1	8	yes	complemented
379	#124	—	5	32	no	—
380	#124	C₂²×D₅	1	16	yes	complemented
381	#121	—	5	64	no	—
382	#121	—	5	64	no	—
383	#121	—	5	128	no	—
384	#121	C₂²×D₅	1	32	yes	complemented
385	#120	—	5	64	no	—
386	#120	—	5	128	no	—
387	C₄×Q₈	—	5	16	no	—
388	C₄×D₄	—	5	32	no	—
389	C₄×D₄	—	5	64	no	—
390	C₄×D₄	—	5	16	no	—
391	C₄×D₄	C₂²×D₅	1	32	yes	complemented
392	#117	—	5	8	no	—
393	#117	—	5	16	no	—
394	C₂×C₄⋊C₄	—	5	4	no	—
395	C₂×C₄⋊C₄	—	5	2	no	—
396	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
397	C₂×C₂²⋊C₄	—	5	2	no	—
398	C₂×C₂²⋊C₄	—	5	4	no	—
399	C₂×C₂²⋊C₄	—	5	16	no	—
400	C₂×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
401	C₂×C₄²	—	5	2	no	—
402	C₂×C₄²	—	5	4	no	—
403	C₂×C₄²	—	5	16	no	—
404	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₅	1	2	yes	—
406	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
407	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
408	C₂²×C₅	—	2	4	no	—
409	C₂²×C₅	—	2	8	no	—
410	C₂²×C₅	—	2	8	no	—
411	C₂²×C₅	—	2	16	no	—
412	C₂²×C₅	—	4	16	no	—
413	C₂²×C₅	C₂³×D₄	1	4	yes	—
414	C₂²×C₅	C₂³×D₄	1	2	yes	—
415	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
416	C₂²×C₅	C₂⁶	1	1	yes	characteristic
417	C₂×D₅	—	2	8	no	—
418	C₂×D₅	—	2	16	no	—
419	C₂×D₅	—	2	16	no	—
420	C₂×D₅	—	2	32	no	—
421	C₂×D₅	—	4	32	no	—
422	C₂×D₅	—	8	64	no	—
423	C₂×D₅	—	8	32	no	—
424	C₂×D₅	C₂³×D₄	1	8	yes	—
425	C₄×C₅	—	2	8	no	—
426	C₄×C₅	—	2	4	no	—
427	C₄×C₅	C₂³×D₄	1	4	yes	—
428	C₄×C₅	C₂³×D₄	1	4	yes	—
429	C₄×C₅	C₂×H(5,𝔽₂)	1	8	yes	complemented
430	Dic₅	—	2	8	no	—
431	Dic₅	C₂³×D₄	1	8	yes	—
432	C₂⁴	—	5	2	no	—
433	C₂⁴	—	5	8	no	—
434	C₂⁴	—	5	32	no	—
435	C₂⁴	—	5	16	no	—
436	C₂⁴	—	10	32	no	—
437	C₂⁴	—	10	16	no	—
438	C₂⁴	—	20	16	no	—
439	C₂⁴	—	20	32	no	—
440	C₂⁴	C₂³×D₅	1	4	yes	—
441	C₂⁴	C₂³×D₅	1	1	yes	characteristic
442	#41	—	2	64	no	—
443	#41	—	5	64	no	—
444	#41	—	10	128	no	—
445	#41	—	10	128	no	—
446	C₂×Q₈	—	2	8	no	—
447	C₂×Q₈	—	5	8	no	—
448	C₂×Q₈	—	5	4	no	—
449	C₂×Q₈	C₂³×D₅	1	8	yes	—
450	C₂×D₄	—	2	16	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	16	no	—
453	C₂×D₄	—	5	16	no	—
454	C₂×D₄	—	5	8	no	—
455	C₂×D₄	—	5	32	no	—
456	C₂×D₄	—	5	64	no	—
457	C₂×D₄	—	5	8	no	—
458	C₂×D₄	—	5	4	no	—
459	C₂×D₄	—	5	32	no	—
460	C₂×D₄	—	5	32	no	—
461	C₂×D₄	—	5	16	no	—
462	C₂×D₄	—	5	16	no	—
463	C₂×D₄	—	5	32	no	—
464	C₂×D₄	—	10	128	no	—
465	C₂×D₄	—	10	32	no	—
466	C₂×D₄	—	10	128	no	—
467	C₂×D₄	—	10	32	no	—
468	C₂×D₄	—	10	256	no	—
469	C₂×D₄	—	10	16	no	—
470	C₂×D₄	—	10	16	no	—
471	C₂×D₄	—	10	64	no	—
472	C₂×D₄	—	10	32	no	—
473	C₂×D₄	—	20	64	no	—
474	C₂×D₄	—	20	16	no	—
475	C₂×D₄	—	20	128	no	—
476	C₂×D₄	—	20	32	no	—
477	C₂×D₄	C₂³×D₅	1	16	yes	—
478	C₂×D₄	C₂³×D₅	1	16	yes	—
479	C₂×D₄	C₂³×D₅	1	8	yes	—
480	C₂²×C₄	—	2	16	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	5	2	no	—
483	C₂²×C₄	—	5	16	no	—
484	C₂²×C₄	—	5	8	no	—
485	C₂²×C₄	—	5	4	no	—
486	C₂²×C₄	—	5	16	no	—
487	C₂²×C₄	—	5	32	no	—
488	C₂²×C₄	—	10	32	no	—
489	C₂²×C₄	—	10	16	no	—
490	C₂²×C₄	D₄×D₅	1	8	yes	complemented
491	C₂²×C₄	C₂³×D₅	1	8	yes	—
492	C₂²×C₄	C₂³×D₅	1	16	yes	—
493	C₂²×C₄	C₂³×D₅	1	2	yes	—
494	C₂²×C₄	C₂³×D₅	1	4	yes	—
495	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
496	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
497	C₂²×C₄	C₂³×D₅	1	4	yes	—
498	C₂²×C₄	C₂³×D₅	1	2	yes	—
499	C₄⋊C₄	—	5	16	no	—
500	C₄⋊C₄	—	5	8	no	—
501	C₄⋊C₄	C₂³×D₅	1	16	yes	—
502	C₂²⋊C₄	—	5	8	no	—
503	C₂²⋊C₄	—	5	16	no	—
504	C₂²⋊C₄	—	5	64	no	—
505	C₂²⋊C₄	C₂³×D₅	1	32	yes	—
506	C₄²	—	5	8	no	—
507	C₄²	—	5	16	no	—
508	C₄²	C₂³×D₅	1	4	yes	—
509	C₄²	C₂³×D₅	1	4	yes	—
510	C₄²	C₂³×D₅	1	8	yes	—
511	C₂×C₅	—	2	4	no	—
512	C₂×C₅	—	4	8	no	—
513	C₂×C₅	#3498	1	4	yes	complemented
514	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
515	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
516	D₅	—	2	8	no	—
517	D₅	—	4	16	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	16	no	—
521	C₂³	—	5	8	no	—
522	C₂³	—	5	4	no	—
523	C₂³	—	5	16	no	—
524	C₂³	—	10	64	no	—
525	C₂³	—	10	8	no	—
526	C₂³	—	10	16	no	—
527	C₂³	—	10	32	no	—
528	C₂³	—	10	32	no	—
529	C₂³	—	20	32	no	—
530	C₂³	—	20	64	no	—
531	C₂³	—	40	32	no	—
532	C₂³	—	40	64	no	—
533	C₂³	C₂×D₄×D₅	1	4	yes	—
534	C₂³	C₂⁴×D₅	1	8	yes	—
535	C₂³	C₂⁴×D₅	1	2	yes	—
536	C₂³	C₂⁴×D₅	1	1	yes	characteristic
537	Q₈	—	2	16	no	—
538	Q₈	—	5	16	no	—
539	D₄	—	2	32	no	—
540	D₄	—	2	16	no	—
541	D₄	—	2	32	no	—
542	D₄	—	5	32	no	—
543	D₄	—	5	16	no	—
544	D₄	—	10	64	no	—
545	D₄	—	10	64	no	—
546	D₄	—	10	32	no	—
547	D₄	—	10	32	no	—
548	D₄	—	10	64	no	—
549	D₄	—	20	32	no	—
550	D₄	—	20	64	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	32	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	5	8	no	—
556	C₂×C₄	—	5	4	no	—
557	C₂×C₄	—	5	32	no	—
558	C₂×C₄	—	5	8	no	—
559	C₂×C₄	—	10	64	no	—
560	C₂×C₄	—	10	8	no	—
561	C₂×C₄	—	10	32	no	—
562	C₂×C₄	C₂×D₄×D₅	1	4	yes	—
563	C₂×C₄	C₂×D₄×D₅	1	4	yes	—
564	C₂×C₄	C₂×D₄×D₅	1	16	yes	complemented
565	C₂×C₄	#4149	1	8	yes	complemented
566	C₂×C₄	C₂⁴×D₅	1	4	yes	—
567	C₂×C₄	C₂⁴×D₅	1	8	yes	—
568	C₂×C₄	C₂⁴×D₅	1	2	yes	—
569	C₂×C₄	C₂⁴×D₅	1	2	yes	—
570	C₂×C₄	C₂⁴×D₅	1	4	yes	—
571	C₅	C₂×#3498	1	1	yes	characteristic, complemented, Sylow
572	C₂²	—	2	8	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	4	16	no	—
577	C₂²	—	5	8	no	—
578	C₂²	—	10	16	no	—
579	C₂²	—	10	8	no	—
580	C₂²	—	10	16	no	—
581	C₂²	—	10	32	no	—
582	C₂²	—	20	32	no	—
583	C₂²	—	40	32	no	—
584	C₂²	—	40	64	no	—
585	C₂²	C₂²×D₄×D₅	1	4	yes	—
586	C₂²	C₂²×D₄×D₅	1	2	yes	—
587	C₂²	C₂×#4149	1	4	yes	—
588	C₂²	C₂⁵×D₅	1	1	yes	characteristic
589	C₄	—	2	8	no	—
590	C₄	—	2	4	no	—
591	C₄	—	5	8	no	—
592	C₄	—	10	8	no	—
593	C₄	C₂²×D₄×D₅	1	4	yes	—
594	C₄	C₂²×D₄×D₅	1	4	yes	—
595	C₄	C₂×#4149	1	8	yes	complemented
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	10	8	no	—
599	C₂	—	20	16	no	—
600	C₂	#10618143	1	4	yes	direct product factor
601	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
602	C₂	C₂²×#4149	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#532	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#532	D₅
hypocenter	C₅	C₂×#3498
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#4149	C₂	semidirect
2. C₂×C₅×#532	C₂	semidirect
3. C₂×#66164	C₂	semidirect
4. #10618143	C₂	direct (N × H)
5. C₂×#66059	C₂	semidirect
6. C₂×D₅×#127	C₂	semidirect
7. C₂×#66008	C₂	semidirect
8. C₂×#65943	C₂	semidirect
9. C₂×D₄×D₂₀	C₂	semidirect
10. C₂×#65887	C₂	semidirect
11. C₂²×#4020	C₂	semidirect
12. C₂×C₄×#709	C₂	semidirect
13. C₂²×C₅×#41	C₂²	semidirect
15. C₂×#4149	C₂²	semidirect
16. C₂²×#713	C₂²	semidirect
17. C₂²×D₄×D₅	C₂²	semidirect
18. C₂²×D₄×D₅	C₂²	semidirect
19. C₂²×D₄×D₅	C₂²	semidirect
21. C₂²×#709	C₂²	semidirect
22. C₂³×D₂₀	C₂²	semidirect
23. C₂³×D₂₀	C₂²	semidirect
24. C₂³×D₂₀	C₂²	semidirect
25. C₅×#532	C₂²	semidirect
26. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₅×#127	C₂²	semidirect
28. C₂×C₅×#124	C₂²	semidirect
29. C₂×C₅×#121	C₂²	semidirect
30. C₂×C₄×C₅×D₄	C₂²	semidirect
31. C₂²×C₄²×C₅	C₂²	semidirect
32. #66164	C₂²	semidirect
33. C₂×#4093	C₂²	semidirect
34. C₂×#4086	C₂²	semidirect
35. C₂×#4086	C₂²	semidirect
36. C₂×#4083	C₂²	semidirect
37. C₂×#4076	C₂²	semidirect
38. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
39. C₂×#4072	C₂²	semidirect
40. #66059	C₂²	semidirect
41. D₅×#127	C₂²	semidirect
42. #66008	C₂²	semidirect
43. #65943	C₂²	semidirect
44. #65887	C₂²	semidirect
45. D₄×D₂₀	C₂²	semidirect
46. C₂×#4041	C₂²	semidirect
47. C₂×#4039	C₂²	semidirect
48. C₂×#4030	C₂²	semidirect
49. C₂×#4028	C₂²	semidirect
50. C₂×#4020	C₂²	semidirect
51. C₂×#4020	C₂²	semidirect
52. C₂×#4020	C₂²	semidirect
53. C₂×#4020	C₂²	semidirect
54. C₄×#709	C₂²	semidirect
55. C₂×C₄×D₂₀	C₂²	semidirect
56. C₂×#4018	C₂²	semidirect
57. C₂×C₄²×D₅	C₂²	semidirect
58. C₂×C₄×Dic₁₀	C₂²	semidirect
63. C₂×C₅×#41	C₂³	semidirect
76. C₂×#713	C₂³	semidirect
80. C₂×D₄×D₅	C₂³	semidirect
81. C₂×D₄×D₅	C₂³	semidirect
82. C₂×D₄×D₅	C₂³	semidirect
84. C₂×#709	D₄	semidirect
86. C₂×#709	C₂³	semidirect
96. C₂²×D₂₀	C₂³	semidirect
97. C₂²×D₂₀	C₂³	semidirect
98. C₂²×D₂₀	C₂³	semidirect
103. C₅×C₄⋊Q₈	C₂³	semidirect
104. C₅×#127	C₂³	semidirect
105. C₅×#124	C₂³	semidirect
106. C₅×#121	C₂³	semidirect
107. C₄×C₅×D₄	C₂³	semidirect
113. C₂×C₄²×C₅	C₂³	semidirect
115. #4093	C₂³	semidirect
116. #4086	C₂³	semidirect
117. #4086	C₂³	semidirect
118. #4083	C₂³	semidirect
119. #4076	C₂³	semidirect
120. C₄×C₂²⋊D₅	C₂³	semidirect
123. #4072	C₂³	semidirect
128. #4041	C₂³	semidirect
129. #4039	C₂³	semidirect
130. #4030	C₂³	semidirect
131. #4028	C₂³	semidirect
132. #4020	C₂³	semidirect
133. #4020	C₂³	semidirect
134. #4020	C₂³	semidirect
135. C₄×D₂₀	C₂³	semidirect
136. #4018	C₂³	semidirect
137. C₄²×D₅	C₂³	semidirect
138. C₄×Dic₁₀	C₂³	semidirect
147. C₂×#532	D₅	semidirect
172. C₂²×C₄×C₅	C₂×D₄	semidirect
183. C₂×C₂²⋊D₅	C₂×D₄	semidirect
194. #709	C₂×D₄	semidirect
203. C₂×D₂₀	C₂×D₄	semidirect
212. C₂×C₄×D₅	C₂×D₄	semidirect
216. C₂×Dic₁₀	C₂×D₄	semidirect
235. C₂²×#41	C₂×D₅	semidirect
248. #532	C₂×D₅	semidirect
249. C₂×C₄⋊Q₈	C₂×D₅	semidirect
257. C₂×#127	C₂×D₅	semidirect
259. C₂×#124	C₂×D₅	semidirect
263. C₂×#121	C₂×D₅	semidirect
271. C₂×C₄×D₄	C₂×D₅	semidirect
275. C₂²×C₄²	C₂×D₅	semidirect
305. C₂×C₄×C₅	C₂²×D₄	semidirect
306. C₂×C₄×C₅	H(5,𝔽₂)	semidirect
314. C₂²⋊D₅	C₂²×D₄	semidirect
324. D₂₀	C₂²×D₄	semidirect
327. C₄×D₅	C₂²×D₄	semidirect
328. Dic₁₀	C₂²×D₄	semidirect
339. C₂×#41	C₂²×D₅	semidirect
372. C₄⋊Q₈	C₂²×D₅	semidirect
378. #127	C₂²×D₅	semidirect
380. #124	C₂²×D₅	semidirect
384. #121	C₂²×D₅	semidirect
391. C₄×D₄	C₂²×D₅	semidirect
407. C₂×C₄²	C₂²×D₅	semidirect
429. C₄×C₅	C₂×H(5,𝔽₂)	semidirect
490. C₂²×C₄	D₄×D₅	semidirect
513. C₂×C₅	#3498	semidirect
564. C₂×C₄	C₂×D₄×D₅	semidirect
565. C₂×C₄	#4149	semidirect
571. C₅	C₂×#3498	semidirect
595. C₄	C₂×#4149	semidirect
600. C₂	#10618143	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×#4149	2
C₂×C₅×#532	2
C₂×#66164	2
#10618143	2
C₂×#66059	2
C₂×D₅×#127	2
C₂×#66008	2
C₂×#65943	2
C₂×D₄×D₂₀	2
C₂×#65887	2
C₂²×#4020	2
C₂×C₄×#709	2
C₂×#3498	5

Subgroups — C2×#10618143 #13007617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618143 #13007617