Subgroups — C₂×C₅×#3500 #11985526

Order 1280.

11534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3500	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₅×#548	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#546	C₂	1	12	yes	maximal, complemented
6	C₂×C₅×#536	C₂	1	3	yes	maximal, complemented
7	C₂×C₅×#535	C₂	1	3	yes	maximal, complemented
8	C₂×C₅×#532	C₂	1	3	yes	maximal, complemented
9	C₂²×C₅×#124	C₂	1	3	yes	maximal, complemented
10	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×2₋¹⁺⁴	—	2	16	no	—
12	C₂×C₅×2₋¹⁺⁴	C₂²	1	16	yes	complemented
13	C₂×C₅×H(5,𝔽₂)	—	2	16	no	—
14	C₂×C₅×H(5,𝔽₂)	C₂²	1	16	yes	complemented
15	C₂²×C₅×#41	C₂²	1	3	yes	—
16	C₂²×C₅×#41	C₂²	1	2	yes	—
17	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#41	C₂²	1	3	yes	complemented
19	C₂²×C₅×#41	C₂²	1	6	yes	complemented
20	C₂³×C₅×Q₈	C₂²	1	3	yes	complemented
21	C₂³×C₅×Q₈	C₂²	1	2	yes	complemented
22	C₂³×C₅×D₄	C₂²	1	3	yes	—
23	C₂³×C₅×D₄	C₂²	1	6	yes	—
24	C₅×#548	C₂²	1	64	yes	complemented
25	C₅×#546	C₂²	1	192	yes	complemented
26	C₅×#536	C₂²	1	48	yes	complemented
27	C₅×#535	C₂²	1	48	yes	complemented
28	C₅×#532	C₂²	1	48	yes	complemented
29	C₂×C₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
30	C₂×C₅×#127	C₂²	1	3	yes	complemented
31	C₂×C₅×#124	C₂²	1	3	yes	complemented
32	C₂×C₅×#124	C₂²	1	6	yes	complemented
33	C₂×C₅×#124	C₂²	1	12	yes	complemented
34	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#124	C₂²	1	48	yes	complemented
36	C₂×C₅×#123	C₂²	1	12	yes	complemented
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	12	yes	complemented
38	C₂×C₅×#121	C₂²	1	12	yes	complemented
39	C₂×C₅×#121	C₂²	1	12	yes	complemented
40	C₂×C₅×#120	C₂²	1	12	yes	complemented
41	C₄×C₅×#41	C₂²	1	16	yes	complemented
42	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
43	C₂×C₄×C₅×D₄	C₂²	1	6	yes	complemented
44	C₂×C₄×C₅×D₄	C₂²	1	12	yes	complemented
45	C₂×C₅×#117	C₂²	1	3	yes	complemented
46	C₂²×C₅×C₂²⋊C₄	C₂²	1	12	yes	complemented
47	C₂²×C₄²×C₅	C₂²	1	3	yes	complemented
48	C₂×#3500	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂⁵×C₅	C₂³	1	6	yes	—
50	C₅×2₋¹⁺⁴	—	2	128	no	—
51	C₅×H(5,𝔽₂)	—	2	128	no	—
52	C₂×C₅×#41	—	2	16	no	—
53	C₂×C₅×#41	—	2	48	no	—
54	C₂×C₅×#41	—	2	24	no	—
55	C₂×C₅×#41	—	2	24	no	—
56	C₂×C₅×#41	D₄	1	16	yes	complemented
57	C₂×C₅×#41	C₂³	1	24	yes	—
58	C₂×C₅×#41	C₂³	1	16	yes	—
59	C₂×C₅×#41	C₂³	1	8	yes	—
60	C₂×C₅×#41	C₂³	1	24	yes	complemented
61	C₂×C₅×#41	C₂³	1	48	yes	complemented
62	C₂²×C₅×Q₈	—	2	16	no	—
63	C₂²×C₅×Q₈	—	2	24	no	—
64	C₂²×C₅×Q₈	C₂³	1	6	yes	—
65	C₂²×C₅×Q₈	C₂³	1	3	yes	—
66	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×Q₈	C₂³	1	24	yes	complemented
69	C₂²×C₅×Q₈	C₂³	1	16	yes	complemented
70	C₂²×C₅×D₄	—	2	48	no	—
71	C₂²×C₅×D₄	—	2	24	no	—
72	C₂²×C₅×D₄	C₂³	1	6	yes	—
73	C₂²×C₅×D₄	C₂³	1	6	yes	—
74	C₂²×C₅×D₄	C₂³	1	6	yes	—
75	C₂²×C₅×D₄	C₂³	1	3	yes	—
76	C₂²×C₅×D₄	C₂³	1	24	yes	—
77	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂²×C₅×D₄	C₂³	1	48	yes	—
79	C₂²×C₅×D₄	C₂³	1	12	yes	—
80	C₂²×C₅×D₄	C₂³	1	3	yes	—
81	C₂³×C₄×C₅	C₂³	1	6	yes	—
82	C₂³×C₄×C₅	C₂³	1	6	yes	—
83	C₂³×C₄×C₅	C₂³	1	6	yes	—
84	C₂³×C₄×C₅	C₂³	1	6	yes	—
85	C₂³×C₄×C₅	C₂³	1	3	yes	—
86	C₅×C₄⋊Q₈	C₂³	1	24	yes	complemented
87	C₅×#127	C₂³	1	24	yes	complemented
88	C₅×#124	C₂³	1	24	yes	complemented
89	C₅×#124	C₂³	1	48	yes	complemented
90	C₅×#124	C₂³	1	96	yes	complemented
91	C₅×#124	C₂³	1	8	yes	complemented
92	C₅×#123	C₂³	1	96	yes	complemented
93	C₅×C₂²⋊Q₈	C₂³	1	96	yes	complemented
94	C₅×#121	C₂³	1	96	yes	complemented
95	C₅×#121	C₂³	1	96	yes	complemented
96	C₅×#120	C₂³	1	96	yes	complemented
97	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
98	C₄×C₅×D₄	C₂³	1	48	yes	complemented
99	C₄×C₅×D₄	C₂³	1	96	yes	complemented
100	C₅×#117	C₂³	1	24	yes	complemented
101	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	12	yes	—
103	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
104	C₂×C₅×C₂²⋊C₄	C₂³	1	24	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
106	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₅×C₂²⋊C₄	C₂³	1	96	yes	complemented
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅	C₂³	1	3	yes	—
110	C₂×C₄²×C₅	C₂³	1	6	yes	—
111	C₂×C₄²×C₅	C₂³	1	24	yes	complemented
112	C₂²×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂²×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
114	#3500	C₂×C₅	1	32	yes	direct product factor
115	C₂×#548	C₂×C₅	1	4	yes	complemented
116	C₂×#546	C₂×C₅	1	12	yes	complemented
117	C₂×#536	C₂×C₅	1	3	yes	complemented
118	C₂×#535	C₂×C₅	1	3	yes	complemented
119	C₂×#532	C₂×C₅	1	3	yes	complemented
120	C₂²×#124	C₂×C₅	1	3	yes	complemented
121	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	2	24	no	—
123	C₂⁴×C₅	—	4	24	no	—
124	C₂⁴×C₅	C₂⁴	1	6	yes	—
125	C₂⁴×C₅	C₂⁴	1	2	yes	—
126	C₂⁴×C₅	C₂⁴	1	3	yes	—
127	C₂⁴×C₅	C₂⁴	1	24	yes	—
128	C₅×#41	—	2	64	no	—
129	C₅×#41	—	2	192	no	—
130	C₅×#41	—	2	96	no	—
131	C₅×#41	—	2	96	no	—
132	C₅×#41	C₂×D₄	1	64	yes	complemented
133	C₂×C₅×Q₈	—	2	64	no	—
134	C₂×C₅×Q₈	—	2	24	no	—
135	C₂×C₅×Q₈	—	2	12	no	—
136	C₂×C₅×Q₈	—	2	96	no	—
137	C₂×C₅×Q₈	—	2	4	no	—
138	C₂×C₅×Q₈	C₂×D₄	1	8	yes	—
139	C₂×C₅×Q₈	C₂⁴	1	24	yes	—
140	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
141	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
142	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
143	C₂×C₅×D₄	—	2	24	no	—
144	C₂×C₅×D₄	—	2	24	no	—
145	C₂×C₅×D₄	—	2	192	no	—
146	C₂×C₅×D₄	—	2	24	no	—
147	C₂×C₅×D₄	—	2	12	no	—
148	C₂×C₅×D₄	—	2	96	no	—
149	C₂×C₅×D₄	—	2	4	no	—
150	C₂×C₅×D₄	—	4	24	no	—
151	C₂×C₅×D₄	C₂×D₄	1	24	yes	—
152	C₂×C₅×D₄	C₂⁴	1	24	yes	—
153	C₂×C₅×D₄	C₂⁴	1	24	yes	—
154	C₂×C₅×D₄	C₂⁴	1	24	yes	—
155	C₂×C₅×D₄	C₂⁴	1	12	yes	—
156	C₂×C₅×D₄	C₂⁴	1	4	yes	—
157	C₂×C₅×D₄	C₂⁴	1	48	yes	—
158	C₂×C₅×D₄	C₂⁴	1	12	yes	—
159	C₂²×C₄×C₅	—	2	24	no	—
160	C₂²×C₄×C₅	—	2	24	no	—
161	C₂²×C₄×C₅	—	2	24	no	—
162	C₂²×C₄×C₅	—	4	12	no	—
163	C₂²×C₄×C₅	C₂×D₄	1	24	yes	—
164	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
165	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
166	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
167	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
169	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
172	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
175	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
176	C₅×C₄⋊C₄	C₂⁴	1	48	yes	—
177	C₅×C₂²⋊C₄	C₂⁴	1	48	yes	—
178	C₅×C₂²⋊C₄	C₂⁴	1	96	yes	—
179	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
180	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
181	C₄²×C₅	C₂⁴	1	4	yes	—
182	C₄²×C₅	C₂⁴	1	12	yes	—
183	C₄²×C₅	C₂⁴	1	24	yes	—
184	C₂×2₋¹⁺⁴	—	2	16	no	—
185	C₂×2₋¹⁺⁴	C₂²×C₅	1	16	yes	complemented
186	C₂×H(5,𝔽₂)	—	2	16	no	—
187	C₂×H(5,𝔽₂)	C₂²×C₅	1	16	yes	complemented
188	C₂²×#41	C₂²×C₅	1	3	yes	—
189	C₂²×#41	C₂²×C₅	1	2	yes	—
190	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
191	C₂²×#41	C₂²×C₅	1	3	yes	complemented
192	C₂²×#41	C₂²×C₅	1	6	yes	complemented
193	C₂³×Q₈	C₂²×C₅	1	3	yes	complemented
194	C₂³×Q₈	C₂²×C₅	1	2	yes	complemented
195	C₂³×D₄	C₂²×C₅	1	3	yes	—
196	C₂³×D₄	C₂²×C₅	1	6	yes	—
197	#548	C₂²×C₅	1	64	yes	complemented
198	#546	C₂²×C₅	1	192	yes	complemented
199	#536	C₂²×C₅	1	48	yes	complemented
200	#535	C₂²×C₅	1	48	yes	complemented
201	#532	C₂²×C₅	1	48	yes	complemented
202	C₂×C₄⋊Q₈	C₂²×C₅	1	3	yes	complemented
203	C₂×#127	C₂²×C₅	1	3	yes	complemented
204	C₂×#124	C₂²×C₅	1	3	yes	complemented
205	C₂×#124	C₂²×C₅	1	6	yes	complemented
206	C₂×#124	C₂²×C₅	1	12	yes	complemented
207	C₂×#124	C₂²×C₅	1	1	yes	characteristic, complemented
208	C₂×#124	C₂²×C₅	1	48	yes	complemented
209	C₂×#123	C₂²×C₅	1	12	yes	complemented
210	C₂×C₂²⋊Q₈	C₂²×C₅	1	12	yes	complemented
211	C₂×#121	C₂²×C₅	1	12	yes	complemented
212	C₂×#121	C₂²×C₅	1	12	yes	complemented
213	C₂×#120	C₂²×C₅	1	12	yes	complemented
214	C₄×#41	C₂²×C₅	1	16	yes	complemented
215	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
216	C₂×C₄×D₄	C₂²×C₅	1	6	yes	complemented
217	C₂×C₄×D₄	C₂²×C₅	1	12	yes	complemented
218	C₂×#117	C₂²×C₅	1	3	yes	complemented
219	C₂²×C₂²⋊C₄	C₂²×C₅	1	12	yes	complemented
220	C₂²×C₄²	C₂²×C₅	1	3	yes	complemented
221	C₂³×C₅	—	2	12	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	2	12	no	—
224	C₂³×C₅	—	2	8	no	—
225	C₂³×C₅	—	2	24	no	—
226	C₂³×C₅	—	2	48	no	—
227	C₂³×C₅	—	4	48	no	—
228	C₂³×C₅	—	8	48	no	—
229	C₂³×C₅	C₂²×D₄	1	12	yes	—
230	C₂³×C₅	C₂⁵	1	12	yes	—
231	C₂³×C₅	C₂⁵	1	4	yes	—
232	C₂³×C₅	C₂⁵	1	6	yes	—
233	C₂³×C₅	C₂⁵	1	1	yes	characteristic
234	C₅×Q₈	—	2	48	no	—
235	C₅×Q₈	—	2	24	no	—
236	C₅×Q₈	—	2	8	no	—
237	C₅×Q₈	C₂²×D₄	1	16	yes	—
238	C₅×D₄	—	2	48	no	—
239	C₅×D₄	—	2	48	no	—
240	C₅×D₄	—	2	48	no	—
241	C₅×D₄	—	2	24	no	—
242	C₅×D₄	—	2	8	no	—
243	C₅×D₄	—	4	48	no	—
244	C₅×D₄	C₂²×D₄	1	48	yes	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	12	no	—
247	C₂×C₄×C₅	—	2	48	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	12	no	—
250	C₂×C₄×C₅	—	2	48	no	—
251	C₂×C₄×C₅	—	2	48	no	—
252	C₂×C₄×C₅	—	4	24	no	—
253	C₂×C₄×C₅	C₂²×D₄	1	12	yes	—
254	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₅	C₂²×D₄	1	48	yes	—
256	C₂×C₄×C₅	C₂⁵	1	4	yes	—
257	C₂×C₄×C₅	C₂⁵	1	12	yes	—
258	C₂×C₄×C₅	C₂⁵	1	12	yes	—
259	C₂×C₄×C₅	C₂⁵	1	4	yes	—
260	C₂×C₄×C₅	C₂⁵	1	2	yes	—
261	C₂×C₄×C₅	C₂⁵	1	6	yes	—
262	C₂⁵	C₂³×C₅	1	6	yes	—
263	2₋¹⁺⁴	—	2	128	no	—
264	H(5,𝔽₂)	—	2	128	no	—
265	C₂×#41	—	2	16	no	—
266	C₂×#41	—	2	48	no	—
267	C₂×#41	—	2	24	no	—
268	C₂×#41	—	2	24	no	—
269	C₂×#41	C₅×D₄	1	16	yes	complemented
270	C₂×#41	C₂³×C₅	1	24	yes	—
271	C₂×#41	C₂³×C₅	1	16	yes	—
272	C₂×#41	C₂³×C₅	1	8	yes	—
273	C₂×#41	C₂³×C₅	1	24	yes	complemented
274	C₂×#41	C₂³×C₅	1	48	yes	complemented
275	C₂²×Q₈	—	2	16	no	—
276	C₂²×Q₈	—	2	24	no	—
277	C₂²×Q₈	C₂³×C₅	1	6	yes	—
278	C₂²×Q₈	C₂³×C₅	1	3	yes	—
279	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
280	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₅	1	24	yes	complemented
282	C₂²×Q₈	C₂³×C₅	1	16	yes	complemented
283	C₂²×D₄	—	2	48	no	—
284	C₂²×D₄	—	2	24	no	—
285	C₂²×D₄	C₂³×C₅	1	6	yes	—
286	C₂²×D₄	C₂³×C₅	1	6	yes	—
287	C₂²×D₄	C₂³×C₅	1	6	yes	—
288	C₂²×D₄	C₂³×C₅	1	3	yes	—
289	C₂²×D₄	C₂³×C₅	1	24	yes	—
290	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₅	1	48	yes	—
292	C₂²×D₄	C₂³×C₅	1	12	yes	—
293	C₂²×D₄	C₂³×C₅	1	3	yes	—
294	C₂³×C₄	C₂³×C₅	1	6	yes	—
295	C₂³×C₄	C₂³×C₅	1	6	yes	—
296	C₂³×C₄	C₂³×C₅	1	6	yes	—
297	C₂³×C₄	C₂³×C₅	1	6	yes	—
298	C₂³×C₄	C₂³×C₅	1	3	yes	—
299	C₄⋊Q₈	C₂³×C₅	1	24	yes	complemented
300	#127	C₂³×C₅	1	24	yes	complemented
301	#124	C₂³×C₅	1	24	yes	complemented
302	#124	C₂³×C₅	1	48	yes	complemented
303	#124	C₂³×C₅	1	96	yes	complemented
304	#124	C₂³×C₅	1	8	yes	complemented
305	#123	C₂³×C₅	1	96	yes	complemented
306	C₂²⋊Q₈	C₂³×C₅	1	96	yes	complemented
307	#121	C₂³×C₅	1	96	yes	complemented
308	#121	C₂³×C₅	1	96	yes	complemented
309	#120	C₂³×C₅	1	96	yes	complemented
310	C₄×Q₈	C₂³×C₅	1	16	yes	complemented
311	C₄×D₄	C₂³×C₅	1	48	yes	complemented
312	C₄×D₄	C₂³×C₅	1	96	yes	complemented
313	#117	C₂³×C₅	1	24	yes	complemented
314	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
315	C₂×C₄⋊C₄	C₂³×C₅	1	12	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₅	1	12	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₅	1	24	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₅	1	96	yes	complemented
321	C₂×C₄²	C₂³×C₅	1	3	yes	—
322	C₂×C₄²	C₂³×C₅	1	6	yes	—
323	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅	1	24	yes	complemented
325	C₂²×C₅	—	2	12	no	—
326	C₂²×C₅	—	2	24	no	—
327	C₂²×C₅	—	2	4	no	—
328	C₂²×C₅	—	2	12	no	—
329	C₂²×C₅	—	2	8	no	—
330	C₂²×C₅	—	2	24	no	—
331	C₂²×C₅	—	4	8	no	—
332	C₂²×C₅	—	4	24	no	—
333	C₂²×C₅	—	8	48	no	—
334	C₂²×C₅	C₂³×D₄	1	12	yes	—
335	C₂²×C₅	C₂³×D₄	1	2	yes	—
336	C₂²×C₅	#585	1	4	yes	—
337	C₂²×C₅	C₂⁶	1	1	yes	characteristic
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	2	12	no	—
340	C₄×C₅	—	2	4	no	—
341	C₄×C₅	—	2	12	no	—
342	C₄×C₅	C₂³×D₄	1	12	yes	—
343	C₄×C₅	C₂³×D₄	1	4	yes	—
344	C₂⁴	—	2	24	no	—
345	C₂⁴	—	4	24	no	—
346	C₂⁴	C₂⁴×C₅	1	6	yes	—
347	C₂⁴	C₂⁴×C₅	1	2	yes	—
348	C₂⁴	C₂⁴×C₅	1	3	yes	—
349	C₂⁴	C₂⁴×C₅	1	24	yes	—
350	#41	—	2	64	no	—
351	#41	—	2	192	no	—
352	#41	—	2	96	no	—
353	#41	—	2	96	no	—
354	#41	C₂×C₅×D₄	1	64	yes	complemented
355	C₂×Q₈	—	2	64	no	—
356	C₂×Q₈	—	2	24	no	—
357	C₂×Q₈	—	2	12	no	—
358	C₂×Q₈	—	2	96	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	C₂×C₅×D₄	1	8	yes	—
361	C₂×Q₈	C₂⁴×C₅	1	24	yes	—
362	C₂×Q₈	C₂⁴×C₅	1	12	yes	—
363	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
364	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
365	C₂×D₄	—	2	24	no	—
366	C₂×D₄	—	2	24	no	—
367	C₂×D₄	—	2	192	no	—
368	C₂×D₄	—	2	24	no	—
369	C₂×D₄	—	2	12	no	—
370	C₂×D₄	—	2	96	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	4	24	no	—
373	C₂×D₄	C₂×C₅×D₄	1	24	yes	—
374	C₂×D₄	C₂⁴×C₅	1	24	yes	—
375	C₂×D₄	C₂⁴×C₅	1	24	yes	—
376	C₂×D₄	C₂⁴×C₅	1	24	yes	—
377	C₂×D₄	C₂⁴×C₅	1	12	yes	—
378	C₂×D₄	C₂⁴×C₅	1	4	yes	—
379	C₂×D₄	C₂⁴×C₅	1	48	yes	—
380	C₂×D₄	C₂⁴×C₅	1	12	yes	—
381	C₂²×C₄	—	2	24	no	—
382	C₂²×C₄	—	2	24	no	—
383	C₂²×C₄	—	2	24	no	—
384	C₂²×C₄	—	4	12	no	—
385	C₂²×C₄	C₂×C₅×D₄	1	24	yes	—
386	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
388	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
389	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
391	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
392	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
393	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
394	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
396	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
397	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
398	C₄⋊C₄	C₂⁴×C₅	1	48	yes	—
399	C₂²⋊C₄	C₂⁴×C₅	1	48	yes	—
400	C₂²⋊C₄	C₂⁴×C₅	1	96	yes	—
401	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
402	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
403	C₄²	C₂⁴×C₅	1	4	yes	—
404	C₄²	C₂⁴×C₅	1	12	yes	—
405	C₄²	C₂⁴×C₅	1	24	yes	—
406	C₂×C₅	—	2	12	no	—
407	C₂×C₅	—	4	4	no	—
408	C₂×C₅	—	4	12	no	—
409	C₂×C₅	#3500	1	4	yes	direct product factor
410	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
411	C₂×C₅	C₂×#585	1	2	yes	—
412	C₂³	—	2	12	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	12	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	24	no	—
417	C₂³	—	2	48	no	—
418	C₂³	—	4	48	no	—
419	C₂³	—	8	48	no	—
420	C₂³	C₂²×C₅×D₄	1	12	yes	—
421	C₂³	C₂⁵×C₅	1	12	yes	—
422	C₂³	C₂⁵×C₅	1	4	yes	—
423	C₂³	C₂⁵×C₅	1	6	yes	—
424	C₂³	C₂⁵×C₅	1	1	yes	characteristic
425	Q₈	—	2	48	no	—
426	Q₈	—	2	24	no	—
427	Q₈	—	2	8	no	—
428	Q₈	C₂²×C₅×D₄	1	16	yes	—
429	D₄	—	2	48	no	—
430	D₄	—	2	48	no	—
431	D₄	—	2	48	no	—
432	D₄	—	2	24	no	—
433	D₄	—	2	8	no	—
434	D₄	—	4	48	no	—
435	D₄	C₂²×C₅×D₄	1	48	yes	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	12	no	—
438	C₂×C₄	—	2	48	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	12	no	—
441	C₂×C₄	—	2	48	no	—
442	C₂×C₄	—	2	48	no	—
443	C₂×C₄	—	4	24	no	—
444	C₂×C₄	C₂²×C₅×D₄	1	12	yes	—
445	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
446	C₂×C₄	C₂²×C₅×D₄	1	48	yes	—
447	C₂×C₄	C₂⁵×C₅	1	4	yes	—
448	C₂×C₄	C₂⁵×C₅	1	12	yes	—
449	C₂×C₄	C₂⁵×C₅	1	12	yes	—
450	C₂×C₄	C₂⁵×C₅	1	4	yes	—
451	C₂×C₄	C₂⁵×C₅	1	2	yes	—
452	C₂×C₄	C₂⁵×C₅	1	6	yes	—
453	C₅	C₂×#3500	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	12	no	—
455	C₂²	—	2	24	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	12	no	—
458	C₂²	—	2	8	no	—
459	C₂²	—	2	24	no	—
460	C₂²	—	4	24	no	—
461	C₂²	—	4	8	no	—
462	C₂²	—	8	48	no	—
463	C₂²	C₂³×C₅×D₄	1	12	yes	—
464	C₂²	C₂³×C₅×D₄	1	2	yes	—
465	C₂²	C₅×#585	1	4	yes	—
466	C₂²	C₂⁶×C₅	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	12	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	12	no	—
471	C₄	C₂³×C₅×D₄	1	12	yes	—
472	C₄	C₂³×C₅×D₄	1	4	yes	—
473	C₂	—	2	12	no	—
474	C₂	—	4	12	no	—
475	C₂	—	4	4	no	—
476	C₂	C₅×#3500	1	4	yes	direct product factor
477	C₂	C₂⁴×C₅×D₄	1	1	yes	characteristic
478	C₂	C₂×C₅×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×2₋¹⁺⁴	C₂	semidirect
2. C₂²×C₅×H(5,𝔽₂)	C₂	semidirect
3. C₅×#3500	C₂	direct (N × H)
4. C₂×C₅×#548	C₂	semidirect
5. C₂×C₅×#546	C₂	semidirect
6. C₂×C₅×#536	C₂	semidirect
7. C₂×C₅×#535	C₂	semidirect
8. C₂×C₅×#532	C₂	semidirect
9. C₂²×C₅×#124	C₂	semidirect
10. C₂×C₄×C₅×#41	C₂	semidirect
12. C₂×C₅×2₋¹⁺⁴	C₂²	semidirect
14. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₅×#41	C₂²	semidirect
19. C₂²×C₅×#41	C₂²	semidirect
20. C₂³×C₅×Q₈	C₂²	semidirect
21. C₂³×C₅×Q₈	C₂²	semidirect
24. C₅×#548	C₂²	semidirect
25. C₅×#546	C₂²	semidirect
26. C₅×#536	C₂²	semidirect
27. C₅×#535	C₂²	semidirect
28. C₅×#532	C₂²	semidirect
29. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₅×#127	C₂²	semidirect
31. C₂×C₅×#124	C₂²	semidirect
32. C₂×C₅×#124	C₂²	semidirect
33. C₂×C₅×#124	C₂²	semidirect
34. C₂×C₅×#124	C₂²	semidirect
35. C₂×C₅×#124	C₂²	semidirect
36. C₂×C₅×#123	C₂²	semidirect
37. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₅×#121	C₂²	semidirect
39. C₂×C₅×#121	C₂²	semidirect
40. C₂×C₅×#120	C₂²	semidirect
41. C₄×C₅×#41	C₂²	semidirect
42. C₂×C₄×C₅×Q₈	C₂²	semidirect
43. C₂×C₄×C₅×D₄	C₂²	semidirect
44. C₂×C₄×C₅×D₄	C₂²	semidirect
45. C₂×C₅×#117	C₂²	semidirect
46. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
47. C₂²×C₄²×C₅	C₂²	semidirect
48. C₂×#3500	C₅	direct (N × H)
56. C₂×C₅×#41	D₄	semidirect
60. C₂×C₅×#41	C₂³	semidirect
61. C₂×C₅×#41	C₂³	semidirect
68. C₂²×C₅×Q₈	C₂³	semidirect
69. C₂²×C₅×Q₈	C₂³	semidirect
86. C₅×C₄⋊Q₈	C₂³	semidirect
87. C₅×#127	C₂³	semidirect
88. C₅×#124	C₂³	semidirect
89. C₅×#124	C₂³	semidirect
90. C₅×#124	C₂³	semidirect
91. C₅×#124	C₂³	semidirect
92. C₅×#123	C₂³	semidirect
93. C₅×C₂²⋊Q₈	C₂³	semidirect
94. C₅×#121	C₂³	semidirect
95. C₅×#121	C₂³	semidirect
96. C₅×#120	C₂³	semidirect
97. C₄×C₅×Q₈	C₂³	semidirect
98. C₄×C₅×D₄	C₂³	semidirect
99. C₄×C₅×D₄	C₂³	semidirect
100. C₅×#117	C₂³	semidirect
107. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
111. C₂×C₄²×C₅	C₂³	semidirect
112. C₂²×2₋¹⁺⁴	C₂×C₅	semidirect
113. C₂²×H(5,𝔽₂)	C₂×C₅	semidirect
114. #3500	C₂×C₅	direct (N × H)
115. C₂×#548	C₂×C₅	semidirect
116. C₂×#546	C₂×C₅	semidirect
117. C₂×#536	C₂×C₅	semidirect
118. C₂×#535	C₂×C₅	semidirect
119. C₂×#532	C₂×C₅	semidirect
120. C₂²×#124	C₂×C₅	semidirect
121. C₂×C₄×#41	C₂×C₅	semidirect
132. C₅×#41	C₂×D₄	semidirect
185. C₂×2₋¹⁺⁴	C₂²×C₅	semidirect
187. C₂×H(5,𝔽₂)	C₂²×C₅	semidirect
191. C₂²×#41	C₂²×C₅	semidirect
192. C₂²×#41	C₂²×C₅	semidirect
193. C₂³×Q₈	C₂²×C₅	semidirect
194. C₂³×Q₈	C₂²×C₅	semidirect
197. #548	C₂²×C₅	semidirect
198. #546	C₂²×C₅	semidirect
199. #536	C₂²×C₅	semidirect
200. #535	C₂²×C₅	semidirect
201. #532	C₂²×C₅	semidirect
202. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
203. C₂×#127	C₂²×C₅	semidirect
204. C₂×#124	C₂²×C₅	semidirect
205. C₂×#124	C₂²×C₅	semidirect
206. C₂×#124	C₂²×C₅	semidirect
207. C₂×#124	C₂²×C₅	semidirect
208. C₂×#124	C₂²×C₅	semidirect
209. C₂×#123	C₂²×C₅	semidirect
210. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
211. C₂×#121	C₂²×C₅	semidirect
212. C₂×#121	C₂²×C₅	semidirect
213. C₂×#120	C₂²×C₅	semidirect
214. C₄×#41	C₂²×C₅	semidirect
215. C₂×C₄×Q₈	C₂²×C₅	semidirect
216. C₂×C₄×D₄	C₂²×C₅	semidirect
217. C₂×C₄×D₄	C₂²×C₅	semidirect
218. C₂×#117	C₂²×C₅	semidirect
219. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
220. C₂²×C₄²	C₂²×C₅	semidirect
269. C₂×#41	C₅×D₄	semidirect
273. C₂×#41	C₂³×C₅	semidirect
274. C₂×#41	C₂³×C₅	semidirect
281. C₂²×Q₈	C₂³×C₅	semidirect
282. C₂²×Q₈	C₂³×C₅	semidirect
299. C₄⋊Q₈	C₂³×C₅	semidirect
300. #127	C₂³×C₅	semidirect
301. #124	C₂³×C₅	semidirect
302. #124	C₂³×C₅	semidirect
303. #124	C₂³×C₅	semidirect
304. #124	C₂³×C₅	semidirect
305. #123	C₂³×C₅	semidirect
306. C₂²⋊Q₈	C₂³×C₅	semidirect
307. #121	C₂³×C₅	semidirect
308. #121	C₂³×C₅	semidirect
309. #120	C₂³×C₅	semidirect
310. C₄×Q₈	C₂³×C₅	semidirect
311. C₄×D₄	C₂³×C₅	semidirect
312. C₄×D₄	C₂³×C₅	semidirect
313. #117	C₂³×C₅	semidirect
320. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
324. C₂×C₄²	C₂³×C₅	semidirect
354. #41	C₂×C₅×D₄	semidirect
409. C₂×C₅	#3500	direct (N × H)
453. C₅	C₂×#3500	direct (N × H)
476. C₂	C₅×#3500	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×C₅×2₋¹⁺⁴	2
C₂²×C₅×H(5,𝔽₂)	2
C₅×#3500	2
C₂×C₅×#548	2
C₂×C₅×#546	2
C₂×C₅×#536	2
C₂×C₅×#535	2
C₂×C₅×#532	2
C₂²×C₅×#124	2
C₂×C₄×C₅×#41	2
C₂×#3500	5

Subgroups — C2×C5×#3500 #11985526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3500 #11985526