Subgroups — C₂×#10618153 #13007103

Order 1280.

8802 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66164	C₂	1	4	yes	maximal, complemented
3	#10618153	C₂	1	32	yes	maximal, direct product factor
4	C₂×#66068	C₂	1	2	yes	maximal, complemented
5	C₂×#66051	C₂	1	2	yes	maximal, complemented
6	C₂×#66017	C₂	1	4	yes	maximal, complemented
7	C₂×#65941	C₂	1	8	yes	maximal, complemented
8	C₂×D₄×D₂₀	C₂	1	4	yes	maximal, complemented
9	C₂×#65897	C₂	1	4	yes	maximal, complemented
10	C₂×#65811	C₂	1	2	yes	maximal, complemented
11	C₂²×C₅×#41	C₂²	1	2	yes	complemented
12	C₂²×D₄×D₅	C₂²	1	8	yes	complemented
13	C₂²×#709	C₂²	1	4	yes	complemented
14	C₂³×D₂₀	C₂²	1	4	yes	complemented
15	C₅×#532	C₂²	1	16	yes	complemented
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×#127	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	2	yes	complemented
19	C₂×C₅×#121	C₂²	1	4	yes	complemented
20	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
22	#66164	C₂²	1	64	yes	complemented
23	C₂×#4093	C₂²	1	8	yes	complemented
24	C₂×#4086	C₂²	1	8	yes	complemented
25	C₂×#4084	C₂²	1	8	yes	complemented
26	C₂×#4083	C₂²	1	8	yes	complemented
27	C₂×#4083	C₂²	1	8	yes	complemented
28	C₂×#4076	C₂²	1	4	yes	complemented
29	C₂×#4076	C₂²	1	8	yes	complemented
30	C₂×#4076	C₂²	1	4	yes	complemented
31	C₂×#4072	C₂²	1	4	yes	complemented
32	#66068	C₂²	1	32	yes	complemented
33	#66051	C₂²	1	32	yes	complemented
34	#66017	C₂²	1	64	yes	complemented
35	#65941	C₂²	1	128	yes	complemented
36	#65897	C₂²	1	64	yes	complemented
37	D₄×D₂₀	C₂²	1	64	yes	complemented
38	C₂×#4041	C₂²	1	8	yes	complemented
39	C₂×#4038	C₂²	1	8	yes	complemented
40	C₂×#4031	C₂²	1	16	yes	complemented
41	C₂×#4028	C₂²	1	16	yes	complemented
42	#65811	C₂²	1	32	yes	complemented
43	C₂×#4021	C₂²	1	4	yes	complemented
44	C₂×#4020	C₂²	1	2	yes	—
45	C₂×C₄×D₂₀	C₂²	1	4	yes	complemented
46	C₂×C₄×D₂₀	C₂²	1	4	yes	complemented
47	C₂×#4015	C₂²	1	2	yes	complemented
48	C₂×#3549	—	5	1	no	maximal, Sylow
49	C₂⁴×D₅	C₂³	1	8	yes	—
50	C₂×C₅×#41	—	4	8	no	—
51	C₂×C₅×#41	C₂³	1	16	yes	complemented
52	C₂²×C₅×Q₈	C₂³	1	2	yes	—
53	C₂²×C₅×D₄	C₂³	1	4	yes	—
54	C₂²×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₅×D₄	C₂³	1	4	yes	—
56	C₂³×C₄×C₅	C₂³	1	4	yes	—
57	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₂²⋊D₅	C₂³	1	16	yes	—
60	C₂²×C₂²⋊D₅	C₂³	1	8	yes	—
61	C₂×D₄×D₅	—	4	32	no	—
62	C₂×D₄×D₅	C₂³	1	64	yes	complemented
63	C₂×#709	—	4	16	no	—
64	C₂×#709	C₂³	1	32	yes	complemented
65	C₂²×D₂₀	—	4	16	no	—
66	C₂²×D₂₀	C₂³	1	4	yes	—
67	C₂²×D₂₀	C₂³	1	4	yes	—
68	C₂²×D₂₀	C₂³	1	4	yes	—
69	C₂²×D₂₀	C₂³	1	8	yes	—
70	C₂²×D₂₀	C₂³	1	32	yes	complemented
71	C₂²×C₄×D₅	C₂³	1	8	yes	—
72	C₂²×Dic₁₀	C₂³	1	4	yes	—
73	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
74	C₅×#127	C₂³	1	8	yes	—
75	C₅×#124	C₂³	1	16	yes	complemented
76	C₅×#121	C₂³	1	32	yes	complemented
77	C₄×C₅×D₄	C₂³	1	32	yes	complemented
78	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₂×C₄²×C₅	C₂³	1	2	yes	—
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
84	C₂×C₂²⋊Dic₅	C₂³	1	8	yes	—
85	#4093	C₂³	1	64	yes	complemented
86	#4086	C₂³	1	64	yes	complemented
87	#4084	C₂³	1	64	yes	complemented
88	#4083	C₂³	1	64	yes	complemented
89	#4083	C₂³	1	64	yes	complemented
90	#4076	C₂³	1	32	yes	complemented
91	#4076	C₂³	1	32	yes	complemented
92	#4076	C₂³	1	64	yes	complemented
93	C₂×#685	C₂³	1	8	yes	—
94	C₂×#685	C₂³	1	8	yes	—
95	C₂×#685	C₂³	1	16	yes	—
96	#4072	C₂³	1	32	yes	complemented
97	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
98	C₂×C₄⋊Dic₅	C₂³	1	4	yes	—
99	C₂×C₄×Dic₅	C₂³	1	8	yes	—
100	#4041	C₂³	1	64	yes	complemented
101	#4038	C₂³	1	64	yes	complemented
102	#4031	C₂³	1	128	yes	complemented
103	#4028	C₂³	1	128	yes	complemented
104	#4021	C₂³	1	32	yes	complemented
105	#4020	C₂³	1	16	yes	—
106	C₄×D₂₀	C₂³	1	32	yes	complemented
107	C₄×D₂₀	C₂³	1	32	yes	complemented
108	#4015	C₂³	1	16	yes	complemented
109	#3549	—	5	32	no	—
110	C₂×H(3,𝔽₄)	—	5	4	no	—
111	C₂×#555	—	5	2	no	—
112	C₂×#555	—	5	4	no	—
113	C₂×D₄²	—	5	2	no	—
114	C₂×D₄²	—	5	4	no	—
115	C₂×#535	—	5	4	no	—
116	C₂×#535	—	5	8	no	—
117	C₂×#532	—	5	2	no	—
118	C₂×#532	D₅	1	1	yes	characteristic, complemented
119	C₂⁴×C₅	C₂⁴	1	4	yes	—
120	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
121	C₂³×D₅	—	4	16	no	—
122	C₂³×D₅	—	4	32	no	—
123	C₂³×D₅	C₂⁴	1	8	yes	—
124	C₂³×D₅	C₂⁴	1	32	yes	—
125	C₅×#41	—	4	32	no	—
126	C₂×C₅×Q₈	—	4	4	no	—
127	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
128	C₂×C₅×D₄	—	2	16	no	—
129	C₂×C₅×D₄	—	4	8	no	—
130	C₂×C₅×D₄	—	4	4	no	—
131	C₂×C₅×D₄	C₂⁴	1	16	yes	—
132	C₂×C₅×D₄	C₂⁴	1	16	yes	—
133	C₂×C₅×D₄	C₂⁴	1	8	yes	—
134	C₂²×C₄×C₅	—	2	16	no	—
135	C₂²×C₄×C₅	—	2	8	no	—
136	C₂²×C₄×C₅	—	2	4	no	—
137	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
143	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂×C₂²⋊D₅	—	4	16	no	—
146	C₂×C₂²⋊D₅	—	4	32	no	—
147	C₂×C₂²⋊D₅	C₂⁴	1	32	yes	—
148	C₂×C₂²⋊D₅	C₂⁴	1	64	yes	—
149	C₂²×Dic₅	C₂⁴	1	8	yes	—
150	D₄×D₅	—	4	128	no	—
151	#709	—	4	64	no	—
152	C₂×D₂₀	—	2	16	no	—
153	C₂×D₂₀	—	2	16	no	—
154	C₂×D₂₀	—	4	64	no	—
155	C₂×D₂₀	—	4	16	no	—
156	C₂×D₂₀	—	4	8	no	—
157	C₂×D₂₀	C₂⁴	1	16	yes	—
158	C₂×D₂₀	C₂⁴	1	16	yes	—
159	C₂×D₂₀	C₂⁴	1	32	yes	—
160	C₂×D₂₀	C₂⁴	1	16	yes	—
161	C₂×C₄×D₅	—	2	32	no	—
162	C₂×C₄×D₅	C₂⁴	1	32	yes	—
163	C₂×Dic₁₀	—	4	8	no	—
164	C₂×Dic₁₀	C₂⁴	1	16	yes	—
165	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
166	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
167	C₄²×C₅	C₂⁴	1	8	yes	—
168	C₄²×C₅	C₂⁴	1	4	yes	—
169	C₄²×C₅	C₂⁴	1	4	yes	—
170	C₂²⋊Dic₅	C₂⁴	1	32	yes	—
171	#685	C₂⁴	1	32	yes	—
172	#685	C₂⁴	1	32	yes	—
173	#685	C₂⁴	1	64	yes	—
174	C₄⋊Dic₅	C₂⁴	1	16	yes	—
175	C₄⋊Dic₅	C₂⁴	1	16	yes	—
176	C₄×Dic₅	C₂⁴	1	32	yes	—
177	C₂²×#41	—	5	4	no	—
178	C₂²×#41	C₂×D₅	1	2	yes	complemented
179	C₂³×D₄	—	5	8	no	—
180	C₂³×D₄	—	5	4	no	—
181	H(3,𝔽₄)	—	5	64	no	—
182	#555	—	5	32	no	—
183	#555	—	5	64	no	—
184	D₄²	—	5	32	no	—
185	D₄²	—	5	64	no	—
186	#535	—	5	64	no	—
187	#535	—	5	128	no	—
188	#532	—	5	32	no	—
189	#532	C₂×D₅	1	16	yes	complemented
190	C₂×C₄⋊Q₈	—	5	2	no	—
191	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
192	C₂×#127	—	5	8	no	—
193	C₂×#127	—	5	2	no	—
194	C₂×#127	C₂×D₅	1	1	yes	characteristic
195	C₂×#124	—	5	8	no	—
196	C₂×#124	—	5	16	no	—
197	C₂×#124	—	5	4	no	—
198	C₂×#124	C₂×D₅	1	2	yes	complemented
199	C₂×#121	—	5	8	no	—
200	C₂×#121	—	5	4	no	—
201	C₂×#121	—	5	4	no	—
202	C₂×#121	—	5	8	no	—
203	C₂×#121	—	5	8	no	—
204	C₂×#121	C₂×D₅	1	4	yes	complemented
205	C₂×#120	—	5	8	no	—
206	C₂×#120	—	5	8	no	—
207	C₂×#120	—	5	16	no	—
208	C₂×C₄×D₄	—	5	4	no	—
209	C₂×C₄×D₄	—	5	4	no	—
210	C₂×C₄×D₄	C₂×D₅	1	4	yes	complemented
211	C₂×#117	—	5	4	no	—
212	C₂×#117	—	5	8	no	—
213	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
214	C₂³×C₅	—	2	4	no	—
215	C₂³×C₅	—	2	16	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	8	no	—
218	C₂³×C₅	C₂⁵	1	8	yes	—
219	C₂³×C₅	C₂⁵	1	2	yes	—
220	C₂³×C₅	C₂⁵	1	1	yes	characteristic
221	C₂²×D₅	—	2	16	no	—
222	C₂²×D₅	—	2	16	no	—
223	C₂²×D₅	—	2	16	no	—
224	C₂²×D₅	—	4	32	no	—
225	C₂²×D₅	—	4	64	no	—
226	C₂²×D₅	—	8	64	no	—
227	C₂²×D₅	C₂⁵	1	16	yes	—
228	C₅×Q₈	—	4	8	no	—
229	C₅×D₄	—	2	32	no	—
230	C₅×D₄	—	4	16	no	—
231	C₅×D₄	—	4	8	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	8	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	32	no	—
236	C₂×C₄×C₅	—	2	16	no	—
237	C₂×C₄×C₅	—	2	8	no	—
238	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
239	C₂×C₄×C₅	H(5,𝔽₂)	1	8	yes	—
240	C₂×C₄×C₅	C₂⁵	1	8	yes	—
241	C₂×C₄×C₅	C₂⁵	1	2	yes	—
242	C₂×C₄×C₅	C₂⁵	1	4	yes	—
243	C₂×C₄×C₅	C₂⁵	1	2	yes	—
244	C₂×C₄×C₅	C₂⁵	1	4	yes	—
245	C₂²⋊D₅	—	4	32	no	—
246	C₂²⋊D₅	—	4	64	no	—
247	C₂×Dic₅	—	2	16	no	—
248	C₂×Dic₅	C₂⁵	1	16	yes	—
249	D₂₀	—	2	32	no	—
250	D₂₀	—	2	32	no	—
251	D₂₀	—	4	32	no	—
252	D₂₀	—	4	16	no	—
253	C₄×D₅	—	2	64	no	—
254	Dic₁₀	—	4	16	no	—
255	C₂⁵	—	5	8	no	—
256	C₂×#41	—	4	8	no	—
257	C₂×#41	—	5	32	no	—
258	C₂×#41	—	20	16	no	—
259	C₂×#41	C₂²×D₅	1	16	yes	complemented
260	C₂²×Q₈	—	5	4	no	—
261	C₂²×Q₈	C₂²×D₅	1	2	yes	—
262	C₂²×D₄	—	5	16	no	—
263	C₂²×D₄	—	5	8	no	—
264	C₂²×D₄	—	5	64	no	—
265	C₂²×D₄	—	5	4	no	—
266	C₂²×D₄	—	5	4	no	—
267	C₂²×D₄	—	5	4	no	—
268	C₂²×D₄	—	5	8	no	—
269	C₂²×D₄	—	5	32	no	—
270	C₂²×D₄	—	20	16	no	—
271	C₂²×D₄	—	20	32	no	—
272	C₂²×D₄	C₂²×D₅	1	4	yes	—
273	C₂²×D₄	C₂²×D₅	1	2	yes	—
274	C₂²×D₄	C₂²×D₅	1	4	yes	—
275	C₂³×C₄	—	5	8	no	—
276	C₂³×C₄	C₂²×D₅	1	4	yes	—
277	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₅	1	2	yes	—
279	C₄⋊Q₈	—	5	16	no	—
280	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
281	#127	—	5	64	no	—
282	#127	—	5	16	no	—
283	#127	C₂²×D₅	1	8	yes	—
284	#124	—	5	64	no	—
285	#124	—	5	128	no	—
286	#124	—	5	32	no	—
287	#124	C₂²×D₅	1	16	yes	complemented
288	#121	—	5	64	no	—
289	#121	—	5	32	no	—
290	#121	—	5	32	no	—
291	#121	—	5	64	no	—
292	#121	—	5	64	no	—
293	#121	C₂²×D₅	1	32	yes	complemented
294	#120	—	5	64	no	—
295	#120	—	5	64	no	—
296	#120	—	5	128	no	—
297	C₄×D₄	—	5	32	no	—
298	C₄×D₄	—	5	32	no	—
299	C₄×D₄	C₂²×D₅	1	32	yes	complemented
300	#117	—	5	32	no	—
301	#117	—	5	64	no	—
302	C₂×C₄⋊C₄	—	5	4	no	—
303	C₂×C₄⋊C₄	—	5	4	no	—
304	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
305	C₂×C₂²⋊C₄	—	5	8	no	—
306	C₂×C₂²⋊C₄	—	5	16	no	—
307	C₂×C₂²⋊C₄	—	5	8	no	—
308	C₂×C₂²⋊C₄	—	5	8	no	—
309	C₂×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
310	C₂×C₄²	—	5	8	no	—
311	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
312	C₂×C₄²	C₂²×D₅	1	2	yes	—
313	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
315	C₂²×C₅	—	2	4	no	—
316	C₂²×C₅	—	2	16	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	8	no	—
319	C₂²×C₅	—	4	16	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
322	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
323	C₂²×C₅	C₂⁶	1	1	yes	characteristic
324	C₂×D₅	—	2	16	no	—
325	C₂×D₅	—	2	16	no	—
326	C₂×D₅	—	2	16	no	—
327	C₂×D₅	—	4	32	no	—
328	C₂×D₅	—	8	64	no	—
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	2	8	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
333	C₄×C₅	C₂×H(5,𝔽₂)	1	8	yes	—
334	Dic₅	—	2	16	no	—
335	C₂⁴	—	5	8	no	—
336	C₂⁴	—	5	32	no	—
337	C₂⁴	—	20	16	no	—
338	C₂⁴	—	20	32	no	—
339	C₂⁴	C₂³×D₅	1	4	yes	—
340	C₂⁴	C₂³×D₅	1	1	yes	characteristic
341	#41	—	4	32	no	—
342	#41	—	20	64	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	5	16	no	—
345	C₂×Q₈	—	20	8	no	—
346	C₂×Q₈	C₂³×D₅	1	8	yes	—
347	C₂×D₄	—	2	16	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	—	5	64	no	—
351	C₂×D₄	—	5	32	no	—
352	C₂×D₄	—	5	16	no	—
353	C₂×D₄	—	5	16	no	—
354	C₂×D₄	—	5	16	no	—
355	C₂×D₄	—	5	32	no	—
356	C₂×D₄	—	10	16	no	—
357	C₂×D₄	—	10	16	no	—
358	C₂×D₄	—	20	64	no	—
359	C₂×D₄	—	20	16	no	—
360	C₂×D₄	—	20	8	no	—
361	C₂×D₄	—	20	128	no	—
362	C₂×D₄	—	20	32	no	—
363	C₂×D₄	—	20	16	no	—
364	C₂×D₄	C₂³×D₅	1	16	yes	—
365	C₂×D₄	C₂³×D₅	1	8	yes	—
366	C₂×D₄	C₂³×D₅	1	16	yes	—
367	C₂²×C₄	—	2	16	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	5	8	no	—
371	C₂²×C₄	—	5	32	no	—
372	C₂²×C₄	—	10	32	no	—
373	C₂²×C₄	C₂³×D₅	1	4	yes	—
374	C₂²×C₄	C₂³×D₅	1	8	yes	—
375	C₂²×C₄	C₂³×D₅	1	16	yes	—
376	C₂²×C₄	C₂³×D₅	1	4	yes	—
377	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
378	C₂²×C₄	C₂³×D₅	1	2	yes	—
379	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
380	C₂²×C₄	C₂³×D₅	1	2	yes	—
381	C₄⋊C₄	—	5	16	no	—
382	C₄⋊C₄	—	5	16	no	—
383	C₄⋊C₄	C₂³×D₅	1	16	yes	—
384	C₂²⋊C₄	—	5	32	no	—
385	C₂²⋊C₄	—	5	64	no	—
386	C₂²⋊C₄	—	5	32	no	—
387	C₂²⋊C₄	—	5	32	no	—
388	C₂²⋊C₄	C₂³×D₅	1	32	yes	—
389	C₄²	—	5	32	no	—
390	C₄²	C₂³×D₅	1	4	yes	—
391	C₄²	C₂³×D₅	1	8	yes	—
392	C₄²	C₂³×D₅	1	4	yes	—
393	C₂×C₅	—	4	8	no	—
394	C₂×C₅	—	4	2	no	—
395	C₂×C₅	#3549	1	4	yes	complemented
396	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
398	D₅	—	4	16	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	16	no	—
403	C₂³	—	5	16	no	—
404	C₂³	—	10	16	no	—
405	C₂³	—	10	16	no	—
406	C₂³	—	10	16	no	—
407	C₂³	—	20	32	no	—
408	C₂³	—	20	64	no	—
409	C₂³	—	40	64	no	—
410	C₂³	C₂⁴×D₅	1	8	yes	—
411	C₂³	C₂⁴×D₅	1	2	yes	—
412	C₂³	C₂⁴×D₅	1	1	yes	characteristic
413	Q₈	—	4	8	no	—
414	Q₈	—	20	16	no	—
415	D₄	—	2	32	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	16	no	—
418	D₄	—	10	32	no	—
419	D₄	—	10	32	no	—
420	D₄	—	20	32	no	—
421	D₄	—	20	16	no	—
422	D₄	—	20	64	no	—
423	D₄	—	20	32	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	32	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	16	no	—
430	C₂×C₄	—	5	16	no	—
431	C₂×C₄	—	10	16	no	—
432	C₂×C₄	—	10	64	no	—
433	C₂×C₄	#4144	1	4	yes	—
434	C₂×C₄	#4149	1	8	yes	—
435	C₂×C₄	C₂⁴×D₅	1	8	yes	—
436	C₂×C₄	C₂⁴×D₅	1	2	yes	—
437	C₂×C₄	C₂⁴×D₅	1	4	yes	—
438	C₂×C₄	C₂⁴×D₅	1	2	yes	—
439	C₂×C₄	C₂⁴×D₅	1	4	yes	—
440	C₅	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	2	2	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	16	no	—
445	C₂²	—	4	16	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	10	16	no	—
448	C₂²	—	10	16	no	—
449	C₂²	—	10	16	no	—
450	C₂²	—	20	32	no	—
451	C₂²	—	40	64	no	—
452	C₂²	C₂×#4144	1	2	yes	—
453	C₂²	C₂×#4149	1	4	yes	—
454	C₂²	C₂⁵×D₅	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	8	no	—
457	C₄	—	2	4	no	—
458	C₄	—	10	16	no	—
459	C₄	C₂×#4144	1	4	yes	—
460	C₄	C₂×#4149	1	8	yes	—
461	C₂	—	4	8	no	—
462	C₂	—	4	2	no	—
463	C₂	—	20	16	no	—
464	C₂	#10618153	1	4	yes	direct product factor
465	C₂	C₂²×#4144	1	1	yes	characteristic
466	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×#3549
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. C₂×C₅×#532	C₂	semidirect
2. C₂×#66164	C₂	semidirect
3. #10618153	C₂	direct (N × H)
4. C₂×#66068	C₂	semidirect
5. C₂×#66051	C₂	semidirect
6. C₂×#66017	C₂	semidirect
7. C₂×#65941	C₂	semidirect
8. C₂×D₄×D₂₀	C₂	semidirect
9. C₂×#65897	C₂	semidirect
10. C₂×#65811	C₂	semidirect
11. C₂²×C₅×#41	C₂²	semidirect
12. C₂²×D₄×D₅	C₂²	semidirect
13. C₂²×#709	C₂²	semidirect
14. C₂³×D₂₀	C₂²	semidirect
15. C₅×#532	C₂²	semidirect
16. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₅×#124	C₂²	semidirect
19. C₂×C₅×#121	C₂²	semidirect
20. C₂×C₄×C₅×D₄	C₂²	semidirect
21. C₂²×C₄²×C₅	C₂²	semidirect
22. #66164	C₂²	semidirect
23. C₂×#4093	C₂²	semidirect
24. C₂×#4086	C₂²	semidirect
25. C₂×#4084	C₂²	semidirect
26. C₂×#4083	C₂²	semidirect
27. C₂×#4083	C₂²	semidirect
28. C₂×#4076	C₂²	semidirect
29. C₂×#4076	C₂²	semidirect
30. C₂×#4076	C₂²	semidirect
31. C₂×#4072	C₂²	semidirect
32. #66068	C₂²	semidirect
33. #66051	C₂²	semidirect
34. #66017	C₂²	semidirect
35. #65941	C₂²	semidirect
36. #65897	C₂²	semidirect
37. D₄×D₂₀	C₂²	semidirect
38. C₂×#4041	C₂²	semidirect
39. C₂×#4038	C₂²	semidirect
40. C₂×#4031	C₂²	semidirect
41. C₂×#4028	C₂²	semidirect
42. #65811	C₂²	semidirect
43. C₂×#4021	C₂²	semidirect
45. C₂×C₄×D₂₀	C₂²	semidirect
46. C₂×C₄×D₂₀	C₂²	semidirect
47. C₂×#4015	C₂²	semidirect
51. C₂×C₅×#41	C₂³	semidirect
62. C₂×D₄×D₅	C₂³	semidirect
64. C₂×#709	C₂³	semidirect
70. C₂²×D₂₀	C₂³	semidirect
73. C₅×C₄⋊Q₈	C₂³	semidirect
75. C₅×#124	C₂³	semidirect
76. C₅×#121	C₂³	semidirect
77. C₄×C₅×D₄	C₂³	semidirect
83. C₂×C₄²×C₅	C₂³	semidirect
85. #4093	C₂³	semidirect
86. #4086	C₂³	semidirect
87. #4084	C₂³	semidirect
88. #4083	C₂³	semidirect
89. #4083	C₂³	semidirect
90. #4076	C₂³	semidirect
91. #4076	C₂³	semidirect
92. #4076	C₂³	semidirect
96. #4072	C₂³	semidirect
100. #4041	C₂³	semidirect
101. #4038	C₂³	semidirect
102. #4031	C₂³	semidirect
103. #4028	C₂³	semidirect
104. #4021	C₂³	semidirect
106. C₄×D₂₀	C₂³	semidirect
107. C₄×D₂₀	C₂³	semidirect
108. #4015	C₂³	semidirect
118. C₂×#532	D₅	semidirect
178. C₂²×#41	C₂×D₅	semidirect
189. #532	C₂×D₅	semidirect
191. C₂×C₄⋊Q₈	C₂×D₅	semidirect
198. C₂×#124	C₂×D₅	semidirect
204. C₂×#121	C₂×D₅	semidirect
210. C₂×C₄×D₄	C₂×D₅	semidirect
213. C₂²×C₄²	C₂×D₅	semidirect
259. C₂×#41	C₂²×D₅	semidirect
280. C₄⋊Q₈	C₂²×D₅	semidirect
287. #124	C₂²×D₅	semidirect
293. #121	C₂²×D₅	semidirect
299. C₄×D₄	C₂²×D₅	semidirect
314. C₂×C₄²	C₂²×D₅	semidirect
395. C₂×C₅	#3549	semidirect
440. C₅	C₂×#3549	semidirect
464. C₂	#10618153	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×C₅×#532	2
C₂×#66164	2
#10618153	2
C₂×#66068	2
C₂×#66051	2
C₂×#66017	2
C₂×#65941	2
C₂×D₄×D₂₀	2
C₂×#65897	2
C₂×#65811	2
C₂×#3549	5

Subgroups — C2×#10618153 #13007103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618153 #13007103