Subgroups — C₂×#10617749 #13007660

Order 1280.

8622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66164	C₂	1	2	yes	maximal, complemented
3	#10617749	C₂	1	32	yes	maximal, direct product factor
4	C₂×#65919	C₂	1	4	yes	maximal, complemented
5	C₂×#65884	C₂	1	8	yes	maximal, complemented
6	C₂×#65887	C₂	1	4	yes	maximal, complemented
7	C₂×#65869	C₂	1	4	yes	maximal, complemented
8	C₂×#65855	C₂	1	2	yes	maximal, complemented
9	C₂×#65811	C₂	1	4	yes	maximal, complemented
10	C₂²×#4020	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂²×#709	C₂²	1	8	yes	complemented
14	C₂³×D₂₀	C₂²	1	2	yes	—
15	C₂³×D₂₀	C₂²	1	4	yes	—
16	C₄×C₅×#41	C₂²	1	16	yes	complemented
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
18	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
19	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	2	yes	complemented
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
24	#66164	C₂²	1	32	yes	complemented
25	C₂×#4093	C₂²	1	4	yes	complemented
26	C₂×#4086	C₂²	1	4	yes	complemented
27	C₂×#4083	C₂²	1	8	yes	—
28	C₂×#4076	C₂²	1	8	yes	complemented
29	C₂×#4076	C₂²	1	8	yes	complemented
30	C₂×#4072	C₂²	1	2	yes	—
31	C₂×#4070	C₂²	1	4	yes	—
32	#65919	C₂²	1	64	yes	complemented
33	#65887	C₂²	1	64	yes	complemented
34	#65884	C₂²	1	128	yes	complemented
35	#65869	C₂²	1	64	yes	complemented
36	#65855	C₂²	1	32	yes	complemented
37	C₂×#4040	C₂²	1	16	yes	complemented
38	C₂×#4039	C₂²	1	8	yes	complemented
39	C₂×#4030	C₂²	1	16	yes	complemented
40	C₂×D₅×C₂²⋊C₄	C₂²	1	8	yes	—
41	#65811	C₂²	1	64	yes	complemented
42	C₂×#4021	C₂²	1	8	yes	complemented
43	C₂×#4020	C₂²	1	2	yes	—
44	C₂×#4020	C₂²	1	4	yes	—
45	C₂×#4020	C₂²	1	2	yes	—
46	C₂×#4020	C₂²	1	16	yes	complemented
47	C₂×C₄×D₂₀	C₂²	1	8	yes	complemented
48	C₂×C₄×D₂₀	C₂²	1	8	yes	complemented
49	#65804	C₂²	1	16	yes	complemented
50	C₂×#4016	C₂²	1	2	yes	complemented
51	C₂×#4015	C₂²	1	2	yes	complemented
52	C₂×C₄×Dic₁₀	C₂²	1	4	yes	complemented
53	C₂×#3508	—	5	1	no	maximal, Sylow
54	C₂⁴×D₅	C₂³	1	4	yes	—
55	C₂×C₅×#41	—	2	8	no	—
56	C₂×C₅×#41	C₂³	1	8	yes	—
57	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂³	1	2	yes	—
61	C₂³×C₄×C₅	C₂³	1	2	yes	—
62	C₂³×C₄×C₅	C₂³	1	4	yes	—
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₂²⋊D₅	C₂³	1	16	yes	—
65	C₂×#709	—	4	32	no	—
66	C₂×#709	C₂³	1	64	yes	complemented
67	C₂²×D₂₀	—	2	16	no	—
68	C₂²×D₂₀	—	4	16	no	—
69	C₂²×D₂₀	C₂³	1	4	yes	—
70	C₂²×D₂₀	C₂³	1	8	yes	—
71	C₂²×D₂₀	C₂³	1	4	yes	—
72	C₂²×D₂₀	C₂³	1	16	yes	—
73	C₂²×D₂₀	C₂³	1	8	yes	—
74	C₂²×D₂₀	C₂³	1	32	yes	—
75	C₂²×C₄×D₅	C₂³	1	16	yes	—
76	C₂²×Dic₁₀	C₂³	1	4	yes	—
77	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
78	C₄×C₅×D₄	C₂³	1	32	yes	—
79	C₄×C₅×D₄	C₂³	1	16	yes	complemented
80	C₅×#117	C₂³	1	8	yes	—
81	C₅×#117	C₂³	1	16	yes	complemented
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₄²×C₅	C₂³	1	2	yes	—
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	8	yes	—
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₂×C₄²×C₅	C₂³	1	4	yes	—
92	C₂×C₄²×C₅	C₂³	1	16	yes	complemented
93	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
94	#4093	C₂³	1	32	yes	complemented
95	#4086	C₂³	1	32	yes	complemented
96	#4083	C₂³	1	64	yes	—
97	#4076	C₂³	1	64	yes	complemented
98	#4076	C₂³	1	64	yes	complemented
99	C₂×#685	C₂³	1	16	yes	—
100	C₂×#685	C₂³	1	16	yes	—
101	#4072	C₂³	1	16	yes	—
102	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
103	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
104	#4070	C₂³	1	32	yes	—
105	C₂×#683	C₂³	1	8	yes	—
106	C₂×C₄×Dic₅	C₂³	1	4	yes	—
107	#4040	C₂³	1	128	yes	complemented
108	#4039	C₂³	1	64	yes	complemented
109	#4030	C₂³	1	128	yes	complemented
110	D₅×C₂²⋊C₄	C₂³	1	64	yes	—
111	#4021	C₂³	1	64	yes	complemented
112	#4020	C₂³	1	16	yes	—
113	#4020	C₂³	1	16	yes	—
114	#4020	C₂³	1	32	yes	—
115	C₄×D₂₀	C₂³	1	64	yes	complemented
116	C₄×D₂₀	C₂³	1	64	yes	complemented
117	#4016	C₂³	1	16	yes	complemented
118	#4015	C₂³	1	16	yes	complemented
119	C₄×Dic₁₀	C₂³	1	32	yes	complemented
120	#3508	—	5	32	no	—
121	C₂×#559	—	5	4	no	—
122	C₂×#550	—	5	4	no	—
123	C₂×#546	—	5	8	no	—
124	C₂×#540	—	5	4	no	—
125	C₂×#535	—	5	2	no	—
126	C₂×#533	—	5	1	no	—
127	C₂×#532	—	5	4	no	—
128	C₂²×#127	—	5	1	no	—
129	C₂×#518	—	5	2	no	—
130	C₂×C₄×#41	D₅	1	1	yes	characteristic, complemented
131	C₂⁴×C₅	C₂⁴	1	2	yes	—
132	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
133	C₂³×D₅	—	2	16	no	—
134	C₂³×D₅	—	4	16	no	—
135	C₂³×D₅	C₂⁴	1	8	yes	—
136	C₂³×D₅	C₂⁴	1	16	yes	—
137	C₅×#41	—	2	32	no	—
138	C₂×C₅×Q₈	—	2	4	no	—
139	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
140	C₂×C₅×D₄	—	2	8	no	—
141	C₂×C₅×D₄	—	2	4	no	—
142	C₂×C₅×D₄	C₂⁴	1	8	yes	—
143	C₂×C₅×D₄	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₅	—	2	8	no	—
145	C₂²×C₄×C₅	—	2	8	no	—
146	C₂²×C₄×C₅	—	2	16	no	—
147	C₂²×C₄×C₅	#41	1	8	yes	complemented
148	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
152	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
153	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
158	C₂×C₂²⋊D₅	—	4	32	no	—
159	C₂×C₂²⋊D₅	C₂⁴	1	64	yes	—
160	C₂²×Dic₅	C₂⁴	1	8	yes	—
161	#709	—	4	128	no	—
162	C₂×D₂₀	—	2	16	no	—
163	C₂×D₂₀	—	2	16	no	—
164	C₂×D₂₀	—	2	64	no	—
165	C₂×D₂₀	—	2	32	no	—
166	C₂×D₂₀	—	4	64	no	—
167	C₂×D₂₀	—	4	16	no	—
168	C₂×D₂₀	C₂⁴	1	32	yes	—
169	C₂×D₂₀	C₂⁴	1	16	yes	—
170	C₂×D₂₀	C₂⁴	1	16	yes	—
171	C₂×D₂₀	C₂⁴	1	32	yes	—
172	C₂×C₄×D₅	—	4	32	no	—
173	C₂×C₄×D₅	C₂⁴	1	64	yes	—
174	C₂×Dic₁₀	—	2	16	no	—
175	C₂×Dic₁₀	C₂⁴	1	16	yes	—
176	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
177	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
178	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
179	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
180	C₄²×C₅	C₂⁴	1	4	yes	—
181	C₄²×C₅	C₂⁴	1	4	yes	—
182	C₄²×C₅	C₂⁴	1	8	yes	—
183	C₄²×C₅	C₂⁴	1	8	yes	—
184	C₄²×C₅	C₂⁴	1	16	yes	—
185	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
186	#685	C₂⁴	1	64	yes	—
187	#685	C₂⁴	1	64	yes	—
188	C₄⋊Dic₅	C₂⁴	1	16	yes	—
189	C₄⋊Dic₅	C₂⁴	1	16	yes	—
190	#683	C₂⁴	1	32	yes	—
191	C₄×Dic₅	C₂⁴	1	16	yes	—
192	C₂²×#41	—	5	8	no	—
193	C₂²×#41	C₂×D₅	1	1	yes	characteristic
194	C₂³×D₄	—	5	2	no	—
195	C₂³×D₄	—	5	4	no	—
196	#559	—	5	64	no	—
197	#550	—	5	64	no	—
198	#546	—	5	128	no	—
199	#540	—	5	64	no	—
200	#535	—	5	32	no	—
201	#533	—	5	16	no	—
202	#532	—	5	64	no	—
203	C₂×C₄⋊Q₈	—	5	2	no	—
204	C₂×#127	—	5	4	no	—
205	C₂×#127	—	5	2	no	—
206	C₂×#127	—	5	2	no	—
207	C₂×#127	—	5	4	no	—
208	C₂×#127	—	5	16	no	—
209	C₂×#125	—	5	2	no	—
210	C₂×#124	—	5	4	no	—
211	C₂×#124	—	5	8	no	—
212	C₂×#123	—	5	16	no	—
213	C₂×C₂²⋊Q₈	—	5	4	no	—
214	C₂×#121	—	5	8	no	—
215	C₂×#121	—	5	8	no	—
216	C₂×#121	—	5	16	no	—
217	C₂×#120	—	5	8	no	—
218	#518	—	5	32	no	—
219	C₄×#41	C₂×D₅	1	16	yes	complemented
220	C₂×C₄×Q₈	—	5	4	no	—
221	C₂×C₄×Q₈	C₂×D₅	1	2	yes	complemented
222	C₂×C₄×D₄	—	5	8	no	—
223	C₂×C₄×D₄	—	5	8	no	—
224	C₂×C₄×D₄	—	5	8	no	—
225	C₂×C₄×D₄	C₂×D₅	1	4	yes	—
226	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
227	C₂×#117	—	5	2	no	—
228	C₂×#117	C₂×D₅	1	1	yes	characteristic
229	C₂×#117	C₂×D₅	1	2	yes	complemented
230	C₂²×C₂²⋊C₄	—	5	8	no	—
231	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
232	C₂²×C₄²	C₂×D₅	1	2	yes	complemented
233	C₂³×C₅	—	2	4	no	—
234	C₂³×C₅	—	2	4	no	—
235	C₂³×C₅	—	2	8	no	—
236	C₂³×C₅	C₂×#41	1	4	yes	—
237	C₂³×C₅	C₂⁵	1	4	yes	—
238	C₂³×C₅	C₂⁵	1	2	yes	—
239	C₂³×C₅	C₂⁵	1	1	yes	characteristic
240	C₂²×D₅	—	2	16	no	—
241	C₂²×D₅	—	2	32	no	—
242	C₂²×D₅	—	2	32	no	—
243	C₂²×D₅	—	4	32	no	—
244	C₂²×D₅	—	8	32	no	—
245	C₂²×D₅	C₂⁵	1	16	yes	—
246	C₅×Q₈	—	2	8	no	—
247	C₅×D₄	—	2	16	no	—
248	C₅×D₄	—	2	8	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	8	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	2	16	no	—
253	C₂×C₄×C₅	—	2	16	no	—
254	C₂×C₄×C₅	—	2	32	no	—
255	C₂×C₄×C₅	C₂×#41	1	4	yes	—
256	C₂×C₄×C₅	C₂×#41	1	4	yes	—
257	C₂×C₄×C₅	C₂×#41	1	16	yes	complemented
258	C₂×C₄×C₅	H(5,𝔽₂)	1	8	yes	—
259	C₂×C₄×C₅	C₂⁵	1	4	yes	—
260	C₂×C₄×C₅	C₂⁵	1	4	yes	—
261	C₂×C₄×C₅	C₂⁵	1	8	yes	—
262	C₂×C₄×C₅	C₂⁵	1	2	yes	—
263	C₂×C₄×C₅	C₂⁵	1	2	yes	—
264	C₂×C₄×C₅	C₂⁵	1	4	yes	—
265	C₂²⋊D₅	—	4	64	no	—
266	C₂×Dic₅	—	2	16	no	—
267	C₂×Dic₅	C₂⁵	1	16	yes	—
268	D₂₀	—	2	32	no	—
269	D₂₀	—	2	32	no	—
270	D₂₀	—	2	64	no	—
271	D₂₀	—	4	32	no	—
272	C₄×D₅	—	4	64	no	—
273	Dic₁₀	—	2	32	no	—
274	C₂⁵	—	5	4	no	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	—	5	64	no	—
277	C₂×#41	—	20	32	no	—
278	C₂×#41	C₂²×D₅	1	8	yes	—
279	C₂²×Q₈	—	5	4	no	—
280	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
281	C₂²×D₄	—	5	16	no	—
282	C₂²×D₄	—	5	4	no	—
283	C₂²×D₄	—	5	4	no	—
284	C₂²×D₄	—	5	8	no	—
285	C₂²×D₄	—	5	16	no	—
286	C₂²×D₄	—	5	8	no	—
287	C₂²×D₄	—	5	32	no	—
288	C₂²×D₄	—	10	16	no	—
289	C₂²×D₄	—	20	16	no	—
290	C₂²×D₄	C₂²×D₅	1	2	yes	—
291	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
292	C₂³×C₄	—	5	16	no	—
293	C₂³×C₄	C₂²×D₅	1	2	yes	—
294	C₂³×C₄	C₂²×D₅	1	2	yes	—
295	C₂³×C₄	C₂²×D₅	1	4	yes	—
296	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
297	C₄⋊Q₈	—	5	16	no	—
298	#127	—	5	32	no	—
299	#127	—	5	16	no	—
300	#127	—	5	16	no	—
301	#127	—	5	32	no	—
302	#125	—	5	16	no	—
303	#124	—	5	32	no	—
304	#124	—	5	64	no	—
305	#123	—	5	128	no	—
306	C₂²⋊Q₈	—	5	32	no	—
307	#121	—	5	64	no	—
308	#121	—	5	64	no	—
309	#121	—	5	128	no	—
310	#120	—	5	64	no	—
311	C₄×Q₈	—	5	32	no	—
312	C₄×Q₈	C₂²×D₅	1	16	yes	complemented
313	C₄×D₄	—	5	64	no	—
314	C₄×D₄	—	5	64	no	—
315	C₄×D₄	—	5	64	no	—
316	C₄×D₄	C₂²×D₅	1	32	yes	—
317	C₄×D₄	C₂²×D₅	1	16	yes	complemented
318	#117	—	5	16	no	—
319	#117	C₂²×D₅	1	8	yes	—
320	#117	C₂²×D₅	1	16	yes	complemented
321	C₂×C₄⋊C₄	—	5	4	no	—
322	C₂×C₄⋊C₄	—	5	4	no	—
323	C₂×C₄⋊C₄	—	5	8	no	—
324	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
325	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
326	C₂×C₂²⋊C₄	—	5	4	no	—
327	C₂×C₂²⋊C₄	—	5	16	no	—
328	C₂×C₂²⋊C₄	—	5	16	no	—
329	C₂×C₂²⋊C₄	—	5	64	no	—
330	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
332	C₂×C₄²	—	5	4	no	—
333	C₂×C₄²	C₂²×D₅	1	2	yes	—
334	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₅	1	4	yes	—
336	C₂×C₄²	C₂²×D₅	1	2	yes	—
337	C₂×C₄²	C₂²×D₅	1	8	yes	—
338	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
339	C₂×C₄²	C₂²×D₅	1	16	yes	complemented
340	C₂²×C₅	—	2	4	no	—
341	C₂²×C₅	—	2	8	no	—
342	C₂²×C₅	—	2	4	no	—
343	C₂²×C₅	—	2	8	no	—
344	C₂²×C₅	—	4	8	no	—
345	C₂²×C₅	C₂²×#41	1	4	yes	—
346	C₂²×C₅	C₂²×#41	1	2	yes	—
347	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
348	C₂²×C₅	C₂⁶	1	1	yes	characteristic
349	C₂×D₅	—	2	16	no	—
350	C₂×D₅	—	2	32	no	—
351	C₂×D₅	—	4	32	no	—
352	C₂×D₅	—	8	32	no	—
353	C₄×C₅	—	2	4	no	—
354	C₄×C₅	—	2	8	no	—
355	C₄×C₅	—	2	4	no	—
356	C₄×C₅	C₂²×#41	1	4	yes	—
357	C₄×C₅	C₂²×#41	1	4	yes	—
358	C₄×C₅	C₂×H(5,𝔽₂)	1	8	yes	—
359	Dic₅	—	2	16	no	—
360	C₂⁴	—	5	8	no	—
361	C₂⁴	—	5	16	no	—
362	C₂⁴	—	10	16	no	—
363	C₂⁴	—	20	16	no	—
364	C₂⁴	C₂³×D₅	1	2	yes	—
365	C₂⁴	C₂³×D₅	1	1	yes	characteristic
366	#41	—	2	32	no	—
367	#41	—	20	128	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	5	16	no	—
370	C₂×Q₈	—	10	16	no	—
371	C₂×Q₈	C₂³×D₅	1	4	yes	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	5	64	no	—
375	C₂×D₄	—	5	16	no	—
376	C₂×D₄	—	5	16	no	—
377	C₂×D₄	—	5	32	no	—
378	C₂×D₄	—	5	32	no	—
379	C₂×D₄	—	10	16	no	—
380	C₂×D₄	—	10	16	no	—
381	C₂×D₄	—	10	64	no	—
382	C₂×D₄	—	10	32	no	—
383	C₂×D₄	—	20	64	no	—
384	C₂×D₄	—	20	16	no	—
385	C₂×D₄	—	20	32	no	—
386	C₂×D₄	C₂³×D₅	1	8	yes	—
387	C₂×D₄	C₂³×D₅	1	4	yes	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	16	no	—
391	C₂²×C₄	—	5	8	no	—
392	C₂²×C₄	—	5	64	no	—
393	C₂²×C₄	—	20	32	no	—
394	C₂²×C₄	#709	1	8	yes	complemented
395	C₂²×C₄	C₂³×D₅	1	8	yes	—
396	C₂²×C₄	C₂³×D₅	1	8	yes	—
397	C₂²×C₄	C₂³×D₅	1	16	yes	—
398	C₂²×C₄	C₂³×D₅	1	2	yes	—
399	C₂²×C₄	C₂³×D₅	1	4	yes	—
400	C₂²×C₄	C₂³×D₅	1	2	yes	—
401	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
402	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₅	1	4	yes	—
404	C₂²×C₄	C₂³×D₅	1	2	yes	—
405	C₄⋊C₄	—	5	16	no	—
406	C₄⋊C₄	—	5	16	no	—
407	C₄⋊C₄	—	5	32	no	—
408	C₄⋊C₄	C₂³×D₅	1	8	yes	—
409	C₄⋊C₄	C₂³×D₅	1	16	yes	—
410	C₂²⋊C₄	—	5	16	no	—
411	C₂²⋊C₄	—	5	64	no	—
412	C₂²⋊C₄	—	5	64	no	—
413	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
414	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
415	C₄²	—	5	16	no	—
416	C₄²	C₂³×D₅	1	4	yes	—
417	C₄²	C₂³×D₅	1	4	yes	—
418	C₄²	C₂³×D₅	1	8	yes	—
419	C₄²	C₂³×D₅	1	8	yes	—
420	C₄²	C₂³×D₅	1	16	yes	—
421	C₂×C₅	—	2	4	no	—
422	C₂×C₅	—	4	4	no	—
423	C₂×C₅	#3508	1	4	yes	complemented
424	C₂×C₅	C₂³×#41	1	1	yes	characteristic
425	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
426	D₅	—	4	16	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	5	16	no	—
431	C₂³	—	10	16	no	—
432	C₂³	—	10	32	no	—
433	C₂³	—	10	32	no	—
434	C₂³	—	20	32	no	—
435	C₂³	—	40	32	no	—
436	C₂³	C₂×#709	1	4	yes	—
437	C₂³	C₂⁴×D₅	1	4	yes	—
438	C₂³	C₂⁴×D₅	1	2	yes	—
439	C₂³	C₂⁴×D₅	1	1	yes	characteristic
440	Q₈	—	2	8	no	—
441	Q₈	—	10	32	no	—
442	D₄	—	2	16	no	—
443	D₄	—	2	8	no	—
444	D₄	—	10	32	no	—
445	D₄	—	10	32	no	—
446	D₄	—	10	64	no	—
447	D₄	—	20	32	no	—
448	D₄	—	20	64	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	16	no	—
453	C₂×C₄	—	2	16	no	—
454	C₂×C₄	—	2	32	no	—
455	C₂×C₄	—	5	16	no	—
456	C₂×C₄	—	10	16	no	—
457	C₂×C₄	—	20	64	no	—
458	C₂×C₄	C₂×#709	1	4	yes	—
459	C₂×C₄	C₂×#709	1	4	yes	—
460	C₂×C₄	C₂×#709	1	16	yes	complemented
461	C₂×C₄	#4149	1	8	yes	—
462	C₂×C₄	C₂⁴×D₅	1	4	yes	—
463	C₂×C₄	C₂⁴×D₅	1	8	yes	—
464	C₂×C₄	C₂⁴×D₅	1	4	yes	—
465	C₂×C₄	C₂⁴×D₅	1	2	yes	—
466	C₂×C₄	C₂⁴×D₅	1	2	yes	—
467	C₂×C₄	C₂⁴×D₅	1	4	yes	—
468	C₅	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
469	C₂²	—	2	4	no	—
470	C₂²	—	2	8	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	10	16	no	—
475	C₂²	—	10	32	no	—
476	C₂²	—	20	32	no	—
477	C₂²	—	40	32	no	—
478	C₂²	C₂²×#709	1	4	yes	—
479	C₂²	C₂²×#709	1	2	yes	—
480	C₂²	C₂×#4149	1	4	yes	—
481	C₂²	C₂⁵×D₅	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	2	8	no	—
484	C₄	—	2	4	no	—
485	C₄	—	10	16	no	—
486	C₄	C₂²×#709	1	4	yes	—
487	C₄	C₂²×#709	1	4	yes	—
488	C₄	C₂×#4149	1	8	yes	—
489	C₂	—	2	4	no	—
490	C₂	—	4	4	no	—
491	C₂	—	20	16	no	—
492	C₂	#10617749	1	4	yes	direct product factor
493	C₂	C₂³×#709	1	1	yes	characteristic
494	C₂	C₂²×#4149	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₄×C₅×#41	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×C₄×#41	D₅
hypocenter	C₅	C₂×#3508
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×#41	C₂	semidirect
2. C₂×#66164	C₂	semidirect
3. #10617749	C₂	direct (N × H)
4. C₂×#65919	C₂	semidirect
5. C₂×#65884	C₂	semidirect
6. C₂×#65887	C₂	semidirect
7. C₂×#65869	C₂	semidirect
8. C₂×#65855	C₂	semidirect
9. C₂×#65811	C₂	semidirect
10. C₂²×#4020	C₂	semidirect
11. C₂×#65804	C₂	semidirect
13. C₂²×#709	C₂²	semidirect
16. C₄×C₅×#41	C₂²	semidirect
17. C₂×C₄×C₅×Q₈	C₂²	semidirect
19. C₂×C₄×C₅×D₄	C₂²	semidirect
21. C₂×C₅×#117	C₂²	semidirect
23. C₂²×C₄²×C₅	C₂²	semidirect
24. #66164	C₂²	semidirect
25. C₂×#4093	C₂²	semidirect
26. C₂×#4086	C₂²	semidirect
28. C₂×#4076	C₂²	semidirect
29. C₂×#4076	C₂²	semidirect
32. #65919	C₂²	semidirect
33. #65887	C₂²	semidirect
34. #65884	C₂²	semidirect
35. #65869	C₂²	semidirect
36. #65855	C₂²	semidirect
37. C₂×#4040	C₂²	semidirect
38. C₂×#4039	C₂²	semidirect
39. C₂×#4030	C₂²	semidirect
41. #65811	C₂²	semidirect
42. C₂×#4021	C₂²	semidirect
46. C₂×#4020	C₂²	semidirect
47. C₂×C₄×D₂₀	C₂²	semidirect
48. C₂×C₄×D₂₀	C₂²	semidirect
49. #65804	C₂²	semidirect
50. C₂×#4016	C₂²	semidirect
51. C₂×#4015	C₂²	semidirect
52. C₂×C₄×Dic₁₀	C₂²	semidirect
66. C₂×#709	C₂³	semidirect
77. C₄×C₅×Q₈	C₂³	semidirect
79. C₄×C₅×D₄	C₂³	semidirect
81. C₅×#117	C₂³	semidirect
92. C₂×C₄²×C₅	C₂³	semidirect
94. #4093	C₂³	semidirect
95. #4086	C₂³	semidirect
97. #4076	C₂³	semidirect
98. #4076	C₂³	semidirect
107. #4040	C₂³	semidirect
108. #4039	C₂³	semidirect
109. #4030	C₂³	semidirect
111. #4021	C₂³	semidirect
115. C₄×D₂₀	C₂³	semidirect
116. C₄×D₂₀	C₂³	semidirect
117. #4016	C₂³	semidirect
118. #4015	C₂³	semidirect
119. C₄×Dic₁₀	C₂³	semidirect
130. C₂×C₄×#41	D₅	semidirect
147. C₂²×C₄×C₅	#41	semidirect
219. C₄×#41	C₂×D₅	semidirect
221. C₂×C₄×Q₈	C₂×D₅	semidirect
226. C₂×C₄×D₄	C₂×D₅	semidirect
229. C₂×#117	C₂×D₅	semidirect
232. C₂²×C₄²	C₂×D₅	semidirect
257. C₂×C₄×C₅	C₂×#41	semidirect
312. C₄×Q₈	C₂²×D₅	semidirect
317. C₄×D₄	C₂²×D₅	semidirect
320. #117	C₂²×D₅	semidirect
339. C₂×C₄²	C₂²×D₅	semidirect
394. C₂²×C₄	#709	semidirect
423. C₂×C₅	#3508	semidirect
460. C₂×C₄	C₂×#709	semidirect
468. C₅	C₂×#3508	semidirect
492. C₂	#10617749	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×C₄×C₅×#41	2
C₂×#66164	2
#10617749	2
C₂×#65919	2
C₂×#65884	2
C₂×#65887	2
C₂×#65869	2
C₂×#65855	2
C₂×#65811	2
C₂²×#4020	2
C₂×#65804	2
C₂×#3508	5

Subgroups — C2×#10617749 #13007660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10617749 #13007660