Subgroups — C₅×#34965 #11957685

Order 1280.

3114 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2603	C₂	1	4	yes	maximal, complemented
4	C₅×#2566	C₂	1	2	yes	maximal, complemented
5	C₅×#2544	C₂	1	2	yes	maximal, complemented
6	C₅×#2504	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2435	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2433	C₂	1	1	yes	maximal, characteristic
10	C₅×#2411	C₂	1	4	yes	maximal, complemented
11	C₅×#2392	C₂	1	4	yes	maximal, complemented
12	C₄×C₅×#127	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
14	C₄×C₅×#120	C₂	1	4	yes	maximal, complemented
15	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
18	C₂×C₅×#127	C₂²	1	2	yes	—
19	C₅×#529	—	2	8	no	—
20	C₂×C₅×#126	C₂²	1	2	yes	complemented
21	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×#124	C₂²	1	2	yes	—
23	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#123	C₂²	1	2	yes	—
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#121	C₂²	1	1	yes	characteristic
27	C₂×C₅×#120	C₂²	1	4	yes	—
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×D₄	—	2	8	no	—
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×D₄	C₂²	1	8	yes	complemented
37	C₂×C₅×#117	C₂²	1	2	yes	—
38	C₂×C₅×#117	C₂²	1	2	yes	complemented
39	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
42	C₅×#398	C₂²	1	4	yes	complemented
43	C₅×#397	C₂²	1	4	yes	complemented
44	C₅×#396	C₂²	1	8	yes	complemented
45	C₅×#394	C₂²	1	4	yes	—
46	C₅×#394	C₂²	1	8	yes	complemented
47	C₅×#392	C₂²	1	4	yes	—
48	C₅×#391	C₂²	1	2	yes	complemented
49	C₅×#390	C₂²	1	2	yes	—
50	C₅×#390	C₂²	1	2	yes	—
51	C₅×#390	C₂²	1	2	yes	complemented
52	C₅×#390	C₂²	1	8	yes	complemented
53	C₅×#388	C₂²	1	8	yes	complemented
54	C₅×#386	C₂²	1	4	yes	—
55	C₅×#386	C₂²	1	8	yes	complemented
56	C₅×#385	C₂²	1	4	yes	—
57	C₅×#385	C₂²	1	8	yes	complemented
58	C₅×#384	C₂²	1	2	yes	complemented
59	C₅×#382	C₂²	1	2	yes	complemented
60	C₅×#379	C₂²	1	4	yes	—
61	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
62	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
67	C₅×#376	C₂²	1	2	yes	complemented
68	C₄³×C₅	C₂²	1	2	yes	complemented
69	#34965	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁵×C₅	C₂³	1	2	yes	—
71	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×D₄	—	2	8	no	—
73	C₂²×C₅×D₄	—	2	4	no	—
74	C₂²×C₅×D₄	C₂³	1	2	yes	—
75	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₂²×C₅×D₄	C₂³	1	2	yes	—
77	C₂²×C₅×D₄	C₂³	1	8	yes	—
78	C₂²×C₅×D₄	C₂³	1	2	yes	—
79	C₂³×C₄×C₅	—	2	8	no	—
80	C₂³×C₄×C₅	—	4	8	no	—
81	C₂³×C₄×C₅	C₂³	1	4	yes	—
82	C₂³×C₄×C₅	C₂³	1	2	yes	—
83	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂³	1	2	yes	—
87	C₂³×C₄×C₅	C₂³	1	4	yes	—
88	C₅×#127	—	2	8	no	—
89	C₅×#126	—	2	8	no	—
90	C₅×#125	—	2	4	no	—
91	C₅×#124	—	2	8	no	—
92	C₅×#124	—	2	4	no	—
93	C₅×#123	—	2	8	no	—
94	C₅×C₂²⋊Q₈	—	2	4	no	—
95	C₅×#121	—	2	4	no	—
96	C₅×#120	—	2	16	no	—
97	C₄×C₅×Q₈	—	2	4	no	—
98	C₄×C₅×D₄	—	2	8	no	—
99	C₄×C₅×D₄	—	2	8	no	—
100	C₄×C₅×D₄	—	2	8	no	—
101	C₄×C₅×D₄	—	2	8	no	—
102	C₄×C₅×D₄	—	2	8	no	—
103	C₄×C₅×D₄	—	2	4	no	—
104	C₄×C₅×D₄	—	4	16	no	—
105	C₅×#117	—	2	8	no	—
106	C₅×#117	—	2	8	no	—
107	C₂×C₅×C₄⋊C₄	—	2	4	no	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₄²×C₅	D₄	1	8	yes	complemented
133	C₂×C₄²×C₅	C₂³	1	4	yes	—
134	C₂×C₄²×C₅	C₂³	1	2	yes	—
135	C₂×C₄²×C₅	C₂³	1	2	yes	—
136	C₂×C₄²×C₅	C₂³	1	4	yes	—
137	C₂×C₄²×C₅	C₂³	1	2	yes	—
138	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₅×#95	C₂³	1	4	yes	—
143	C₅×#95	C₂³	1	2	yes	—
144	C₅×#95	C₂³	1	2	yes	—
145	C₅×#95	C₂³	1	8	yes	—
146	C₅×#95	C₂³	1	8	yes	—
147	C₂×#529	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂²×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
149	#2603	C₂×C₅	1	4	yes	complemented
150	#2566	C₂×C₅	1	2	yes	complemented
151	#2544	C₂×C₅	1	2	yes	complemented
152	#2504	C₂×C₅	1	1	yes	characteristic, complemented
153	#2502	C₂×C₅	1	1	yes	characteristic, complemented
154	#2435	C₂×C₅	1	1	yes	characteristic, complemented
155	#2433	C₂×C₅	1	1	yes	characteristic
156	#2411	C₂×C₅	1	4	yes	complemented
157	#2392	C₂×C₅	1	4	yes	complemented
158	C₄×#127	C₂×C₅	1	2	yes	complemented
159	C₄×#124	C₂×C₅	1	2	yes	complemented
160	C₄×#120	C₂×C₅	1	4	yes	complemented
161	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂⁴×C₅	—	2	4	no	—
163	C₂⁴×C₅	—	2	8	no	—
164	C₂⁴×C₅	—	2	8	no	—
165	C₂⁴×C₅	—	4	4	no	—
166	C₂⁴×C₅	C₂⁴	1	2	yes	—
167	C₂⁴×C₅	C₂⁴	1	4	yes	—
168	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₅×Q₈	—	2	2	no	—
170	C₂×C₅×Q₈	—	2	4	no	—
171	C₂×C₅×D₄	—	2	32	no	—
172	C₂×C₅×D₄	—	2	8	no	—
173	C₂×C₅×D₄	—	2	4	no	—
174	C₂×C₅×D₄	—	2	8	no	—
175	C₂×C₅×D₄	—	2	16	no	—
176	C₂×C₅×D₄	—	2	4	no	—
177	C₂×C₅×D₄	—	2	4	no	—
178	C₂×C₅×D₄	—	2	2	no	—
179	C₂×C₅×D₄	—	2	4	no	—
180	C₂×C₅×D₄	—	2	16	no	—
181	C₂×C₅×D₄	—	2	4	no	—
182	C₂×C₅×D₄	—	4	8	no	—
183	C₂×C₅×D₄	#41	1	8	yes	—
184	C₂²×C₄×C₅	—	2	4	no	—
185	C₂²×C₄×C₅	—	2	4	no	—
186	C₂²×C₄×C₅	—	2	4	no	—
187	C₂²×C₄×C₅	—	2	4	no	—
188	C₂²×C₄×C₅	—	2	4	no	—
189	C₂²×C₄×C₅	—	2	8	no	—
190	C₂²×C₄×C₅	—	2	8	no	—
191	C₂²×C₄×C₅	—	2	8	no	—
192	C₂²×C₄×C₅	—	2	16	no	—
193	C₂²×C₄×C₅	—	4	8	no	—
194	C₂²×C₄×C₅	—	4	4	no	—
195	C₂²×C₄×C₅	—	4	32	no	—
196	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₅×C₄⋊C₄	—	2	4	no	—
212	C₅×C₄⋊C₄	—	2	4	no	—
213	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	2	4	no	—
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	4	no	—
217	C₅×C₄⋊C₄	—	2	2	no	—
218	C₅×C₄⋊C₄	—	2	4	no	—
219	C₅×C₄⋊C₄	—	2	8	no	—
220	C₅×C₄⋊C₄	—	4	8	no	—
221	C₅×C₂²⋊C₄	—	2	4	no	—
222	C₅×C₂²⋊C₄	—	2	4	no	—
223	C₅×C₂²⋊C₄	—	2	16	no	—
224	C₅×C₂²⋊C₄	—	2	8	no	—
225	C₅×C₂²⋊C₄	—	2	8	no	—
226	C₅×C₂²⋊C₄	—	2	4	no	—
227	C₅×C₂²⋊C₄	—	2	4	no	—
228	C₅×C₂²⋊C₄	—	2	4	no	—
229	C₅×C₂²⋊C₄	—	2	4	no	—
230	C₅×C₂²⋊C₄	—	2	16	no	—
231	C₅×C₂²⋊C₄	—	4	8	no	—
232	C₅×C₂²⋊C₄	—	4	8	no	—
233	C₅×C₂²⋊C₄	#41	1	8	yes	—
234	C₄²×C₅	—	2	4	no	—
235	C₄²×C₅	—	2	8	no	—
236	C₄²×C₅	—	2	4	no	—
237	C₄²×C₅	—	2	4	no	—
238	C₄²×C₅	—	2	8	no	—
239	C₄²×C₅	C₂×D₄	1	4	yes	—
240	C₄²×C₅	C₂×D₄	1	4	yes	—
241	C₄²×C₅	C₂×D₄	1	4	yes	—
242	C₄²×C₅	C₂×D₄	1	4	yes	—
243	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
244	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
245	C₂×#127	C₂²×C₅	1	2	yes	—
246	#529	—	2	8	no	—
247	C₂×#126	C₂²×C₅	1	2	yes	complemented
248	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₂×#124	C₂²×C₅	1	2	yes	—
250	C₂×#124	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂×#123	C₂²×C₅	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
253	C₂×#121	C₂²×C₅	1	1	yes	characteristic
254	C₂×#120	C₂²×C₅	1	4	yes	—
255	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₂×C₄×D₄	—	2	8	no	—
257	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
259	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
261	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
262	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×C₄×D₄	C₂²×C₅	1	8	yes	complemented
264	C₂×#117	C₂²×C₅	1	2	yes	—
265	C₂×#117	C₂²×C₅	1	2	yes	complemented
266	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
268	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
269	#398	C₂²×C₅	1	4	yes	complemented
270	#397	C₂²×C₅	1	4	yes	complemented
271	#396	C₂²×C₅	1	8	yes	complemented
272	#394	C₂²×C₅	1	4	yes	—
273	#394	C₂²×C₅	1	8	yes	complemented
274	#392	C₂²×C₅	1	4	yes	—
275	#391	C₂²×C₅	1	2	yes	complemented
276	#390	C₂²×C₅	1	2	yes	—
277	#390	C₂²×C₅	1	2	yes	—
278	#390	C₂²×C₅	1	8	yes	complemented
279	#390	C₂²×C₅	1	2	yes	complemented
280	#388	C₂²×C₅	1	8	yes	complemented
281	#386	C₂²×C₅	1	4	yes	—
282	#386	C₂²×C₅	1	8	yes	complemented
283	#385	C₂²×C₅	1	4	yes	—
284	#385	C₂²×C₅	1	8	yes	complemented
285	#384	C₂²×C₅	1	2	yes	complemented
286	#382	C₂²×C₅	1	2	yes	complemented
287	#379	C₂²×C₅	1	4	yes	—
288	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
289	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
290	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
294	#376	C₂²×C₅	1	2	yes	complemented
295	C₄³	C₂²×C₅	1	2	yes	complemented
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	2	16	no	—
299	C₂³×C₅	—	2	4	no	—
300	C₂³×C₅	—	2	8	no	—
301	C₂³×C₅	—	2	4	no	—
302	C₂³×C₅	—	2	8	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	2	4	no	—
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	2	4	no	—
307	C₂³×C₅	—	4	32	no	—
308	C₂³×C₅	—	4	8	no	—
309	C₂³×C₅	—	4	8	no	—
310	C₂³×C₅	C₂²×D₄	1	2	yes	—
311	C₂³×C₅	C₂×#41	1	8	yes	—
312	C₂³×C₅	C₂×#41	1	4	yes	—
313	C₂³×C₅	C₂⁵	1	1	yes	characteristic
314	C₅×Q₈	—	4	4	no	—
315	C₅×D₄	—	2	16	no	—
316	C₅×D₄	—	2	16	no	—
317	C₅×D₄	—	4	32	no	—
318	C₅×D₄	—	4	8	no	—
319	C₅×D₄	—	4	4	no	—
320	C₂×C₄×C₅	—	2	8	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	4	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	4	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	8	no	—
328	C₂×C₄×C₅	—	2	8	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	4	no	—
333	C₂×C₄×C₅	—	2	4	no	—
334	C₂×C₄×C₅	—	2	4	no	—
335	C₂×C₄×C₅	—	2	4	no	—
336	C₂×C₄×C₅	—	2	4	no	—
337	C₂×C₄×C₅	—	2	4	no	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	2	8	no	—
340	C₂×C₄×C₅	—	4	16	no	—
341	C₂×C₄×C₅	—	4	8	no	—
342	C₂×C₄×C₅	—	4	8	no	—
343	C₂×C₄×C₅	—	4	16	no	—
344	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₅	C₂×#41	1	8	yes	—
351	C₂×C₄×C₅	C₂×#41	1	4	yes	—
352	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
353	C₂⁵	C₂³×C₅	1	2	yes	—
354	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
355	C₂²×D₄	—	2	8	no	—
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	C₂³×C₅	1	2	yes	—
358	C₂²×D₄	C₂³×C₅	1	2	yes	—
359	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₅	1	8	yes	—
361	C₂²×D₄	C₂³×C₅	1	2	yes	—
362	C₂³×C₄	—	2	8	no	—
363	C₂³×C₄	—	4	8	no	—
364	C₂³×C₄	C₂³×C₅	1	2	yes	—
365	C₂³×C₄	C₂³×C₅	1	4	yes	—
366	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₅	1	2	yes	—
370	C₂³×C₄	C₂³×C₅	1	4	yes	—
371	#127	—	2	8	no	—
372	#126	—	2	8	no	—
373	#125	—	2	4	no	—
374	#124	—	2	8	no	—
375	#124	—	2	4	no	—
376	#123	—	2	8	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	#121	—	2	4	no	—
379	#120	—	2	16	no	—
380	C₄×Q₈	—	2	4	no	—
381	C₄×D₄	—	2	8	no	—
382	C₄×D₄	—	2	8	no	—
383	C₄×D₄	—	2	8	no	—
384	C₄×D₄	—	2	8	no	—
385	C₄×D₄	—	2	8	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	4	16	no	—
388	#117	—	2	8	no	—
389	#117	—	2	8	no	—
390	C₂×C₄⋊C₄	—	2	4	no	—
391	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
401	C₂×C₂²⋊C₄	—	2	8	no	—
402	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
415	C₂×C₄²	C₅×D₄	1	8	yes	complemented
416	C₂×C₄²	C₂³×C₅	1	4	yes	—
417	C₂×C₄²	C₂³×C₅	1	2	yes	—
418	C₂×C₄²	C₂³×C₅	1	4	yes	—
419	C₂×C₄²	C₂³×C₅	1	2	yes	—
420	C₂×C₄²	C₂³×C₅	1	2	yes	—
421	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
425	#95	C₂³×C₅	1	4	yes	—
426	#95	C₂³×C₅	1	2	yes	—
427	#95	C₂³×C₅	1	2	yes	—
428	#95	C₂³×C₅	1	8	yes	—
429	#95	C₂³×C₅	1	8	yes	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	8	no	—
433	C₂²×C₅	—	2	8	no	—
434	C₂²×C₅	—	2	16	no	—
435	C₂²×C₅	—	4	32	no	—
436	C₂²×C₅	—	4	4	no	—
437	C₂²×C₅	—	4	4	no	—
438	C₂²×C₅	—	4	8	no	—
439	C₂²×C₅	—	4	2	no	—
440	C₂²×C₅	—	4	2	no	—
441	C₂²×C₅	—	4	2	no	—
442	C₂²×C₅	—	4	8	no	—
443	C₂²×C₅	#532	1	4	yes	—
444	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
445	C₂²×C₅	C₂²×#41	1	2	yes	—
446	C₂²×C₅	C₂²×#41	1	2	yes	—
447	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	2	8	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	—	4	4	no	—
457	C₄×C₅	—	4	4	no	—
458	C₄×C₅	#525	1	4	yes	—
459	C₄×C₅	#535	1	4	yes	—
460	C₂⁴	—	2	4	no	—
461	C₂⁴	—	2	8	no	—
462	C₂⁴	—	2	8	no	—
463	C₂⁴	—	4	4	no	—
464	C₂⁴	C₂⁴×C₅	1	2	yes	—
465	C₂⁴	C₂⁴×C₅	1	4	yes	—
466	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×D₄	—	2	32	no	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	2	16	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	16	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	4	8	no	—
481	C₂×D₄	C₅×#41	1	8	yes	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	2	8	no	—
490	C₂²×C₄	—	2	16	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	—	4	32	no	—
494	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
495	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
496	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	4	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	8	no	—
518	C₄⋊C₄	—	4	8	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	4	no	—
528	C₂²⋊C₄	—	2	16	no	—
529	C₂²⋊C₄	—	4	8	no	—
530	C₂²⋊C₄	—	4	8	no	—
531	C₂²⋊C₄	C₅×#41	1	8	yes	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	8	no	—
534	C₄²	—	2	4	no	—
535	C₄²	—	2	4	no	—
536	C₄²	—	2	8	no	—
537	C₄²	C₂×C₅×D₄	1	4	yes	—
538	C₄²	C₂×C₅×D₄	1	4	yes	—
539	C₄²	C₂×C₅×D₄	1	4	yes	—
540	C₄²	C₂×C₅×D₄	1	4	yes	—
541	C₂×C₅	—	2	4	no	—
542	C₂×C₅	—	4	8	no	—
543	C₂×C₅	—	8	2	no	—
544	C₂×C₅	C₂×#525	1	1	yes	characteristic
545	C₂×C₅	C₂×#532	1	1	yes	characteristic
546	C₂×C₅	C₂×#535	1	1	yes	characteristic
547	C₂×C₅	#3481	1	4	yes	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	16	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	8	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	8	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	4	32	no	—
560	C₂³	—	4	8	no	—
561	C₂³	—	4	8	no	—
562	C₂³	C₂²×C₅×D₄	1	2	yes	—
563	C₂³	C₂×C₅×#41	1	8	yes	—
564	C₂³	C₂×C₅×#41	1	4	yes	—
565	C₂³	C₂⁵×C₅	1	1	yes	characteristic
566	Q₈	—	4	4	no	—
567	D₄	—	2	16	no	—
568	D₄	—	2	16	no	—
569	D₄	—	4	32	no	—
570	D₄	—	4	8	no	—
571	D₄	—	4	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	8	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	4	16	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	4	16	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
597	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
598	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
599	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
600	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
601	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
602	C₂×C₄	C₂×C₅×#41	1	8	yes	—
603	C₂×C₄	C₂×C₅×#41	1	4	yes	—
604	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
605	C₅	#34965	1	1	yes	characteristic, direct product factor, Sylow
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	16	no	—
611	C₂²	—	4	32	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	8	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	8	no	—
619	C₂²	C₅×#532	1	4	yes	—
620	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
621	C₂²	C₂²×C₅×#41	1	2	yes	—
622	C₂²	C₂²×C₅×#41	1	2	yes	—
623	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	8	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	4	no	—
634	C₄	C₅×#525	1	4	yes	—
635	C₄	C₅×#535	1	4	yes	—
636	C₂	—	2	4	no	—
637	C₂	—	4	8	no	—
638	C₂	—	8	2	no	—
639	C₂	C₂×C₅×#525	1	1	yes	characteristic
640	C₂	C₂×C₅×#532	1	1	yes	characteristic
641	C₂	C₂×C₅×#535	1	1	yes	characteristic
642	C₂	C₅×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₅×#2433	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#529	C₂	semidirect
2. C₂²×C₄×C₅×D₄	C₂	semidirect
3. C₅×#2603	C₂	semidirect
4. C₅×#2566	C₂	semidirect
5. C₅×#2544	C₂	semidirect
6. C₅×#2504	C₂	semidirect
7. C₅×#2502	C₂	semidirect
8. C₅×#2435	C₂	semidirect
10. C₅×#2411	C₂	semidirect
11. C₅×#2392	C₂	semidirect
12. C₄×C₅×#127	C₂	semidirect
13. C₄×C₅×#124	C₂	semidirect
14. C₄×C₅×#120	C₂	semidirect
15. C₄×C₅×#117	C₂	semidirect
20. C₂×C₅×#126	C₂²	semidirect
21. C₂×C₅×#125	C₂²	semidirect
23. C₂×C₅×#124	C₂²	semidirect
28. C₂×C₄×C₅×Q₈	C₂²	semidirect
35. C₂×C₄×C₅×D₄	C₂²	semidirect
36. C₂×C₄×C₅×D₄	C₂²	semidirect
38. C₂×C₅×#117	C₂²	semidirect
42. C₅×#398	C₂²	semidirect
43. C₅×#397	C₂²	semidirect
44. C₅×#396	C₂²	semidirect
46. C₅×#394	C₂²	semidirect
48. C₅×#391	C₂²	semidirect
51. C₅×#390	C₂²	semidirect
52. C₅×#390	C₂²	semidirect
53. C₅×#388	C₂²	semidirect
55. C₅×#386	C₂²	semidirect
57. C₅×#385	C₂²	semidirect
58. C₅×#384	C₂²	semidirect
59. C₅×#382	C₂²	semidirect
61. C₄×C₅×C₄⋊C₄	C₂²	semidirect
62. C₄×C₅×C₄⋊C₄	C₂²	semidirect
66. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
67. C₅×#376	C₂²	semidirect
68. C₄³×C₅	C₂²	semidirect
69. #34965	C₅	direct (N × H)
132. C₂×C₄²×C₅	D₄	semidirect
147. C₂×#529	C₂×C₅	semidirect
148. C₂²×C₄×D₄	C₂×C₅	semidirect
149. #2603	C₂×C₅	semidirect
150. #2566	C₂×C₅	semidirect
151. #2544	C₂×C₅	semidirect
152. #2504	C₂×C₅	semidirect
153. #2502	C₂×C₅	semidirect
154. #2435	C₂×C₅	semidirect
156. #2411	C₂×C₅	semidirect
157. #2392	C₂×C₅	semidirect
158. C₄×#127	C₂×C₅	semidirect
159. C₄×#124	C₂×C₅	semidirect
160. C₄×#120	C₂×C₅	semidirect
161. C₄×#117	C₂×C₅	semidirect
247. C₂×#126	C₂²×C₅	semidirect
248. C₂×#125	C₂²×C₅	semidirect
250. C₂×#124	C₂²×C₅	semidirect
255. C₂×C₄×Q₈	C₂²×C₅	semidirect
262. C₂×C₄×D₄	C₂²×C₅	semidirect
263. C₂×C₄×D₄	C₂²×C₅	semidirect
265. C₂×#117	C₂²×C₅	semidirect
269. #398	C₂²×C₅	semidirect
270. #397	C₂²×C₅	semidirect
271. #396	C₂²×C₅	semidirect
273. #394	C₂²×C₅	semidirect
275. #391	C₂²×C₅	semidirect
278. #390	C₂²×C₅	semidirect
279. #390	C₂²×C₅	semidirect
280. #388	C₂²×C₅	semidirect
282. #386	C₂²×C₅	semidirect
284. #385	C₂²×C₅	semidirect
285. #384	C₂²×C₅	semidirect
286. #382	C₂²×C₅	semidirect
288. C₄×C₄⋊C₄	C₂²×C₅	semidirect
289. C₄×C₄⋊C₄	C₂²×C₅	semidirect
293. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
294. #376	C₂²×C₅	semidirect
295. C₄³	C₂²×C₅	semidirect
415. C₂×C₄²	C₅×D₄	semidirect
605. C₅	#34965	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×#529	2
C₂²×C₄×C₅×D₄	2
C₅×#2603	2
C₅×#2566	2
C₅×#2544	2
C₅×#2504	2
C₅×#2502	2
C₅×#2435	2
C₅×#2433	2
C₅×#2411	2
C₅×#2392	2
C₄×C₅×#127	2
C₄×C₅×#124	2
C₄×C₅×#120	2
C₄×C₅×#117	2
#34965	5

Subgroups — C5×#34965 #11957685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34965 #11957685