Subgroups — C₅×#35331 #11958051

Order 1280.

2202 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#542	C₂	1	2	yes	maximal, complemented
2	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2850	C₂	1	2	yes	maximal, complemented
5	C₅×#2640	C₂	1	2	yes	maximal, complemented
6	C₅×#2621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2619	C₂	1	1	yes	maximal, characteristic
8	C₅×#2560	C₂	1	8	yes	maximal, complemented
9	C₅×#2557	C₂	1	8	yes	maximal, complemented
10	C₅×#2328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#542	—	2	16	no	—
15	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#127	C₂²	1	1	yes	characteristic
18	C₂×C₅×#126	C₂²	1	4	yes	—
19	C₂×C₅×#124	C₂²	1	4	yes	—
20	C₂×C₅×#124	C₂²	1	2	yes	—
21	C₂×C₅×#124	C₂²	1	2	yes	—
22	C₂×C₅×#123	C₂²	1	4	yes	—
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₅×#121	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
27	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₂×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₅×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₅×#398	C₂²	1	4	yes	—
32	C₅×#397	C₂²	1	4	yes	—
33	C₅×#397	C₂²	1	8	yes	—
34	C₅×#394	C₂²	1	4	yes	—
35	C₅×#393	C₂²	1	8	yes	—
36	C₅×#392	C₂²	1	4	yes	—
37	C₅×#391	C₂²	1	8	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#391	C₂²	1	2	yes	—
40	C₅×#390	C₂²	1	8	yes	—
41	C₅×#390	C₂²	1	2	yes	—
42	C₅×#390	C₂²	1	2	yes	—
43	C₅×#388	C₂²	1	8	yes	—
44	C₅×#388	C₂²	1	8	yes	—
45	C₅×#387	C₂²	1	8	yes	—
46	C₅×#386	C₂²	1	8	yes	—
47	C₅×#386	C₂²	1	8	yes	—
48	C₅×#382	C₂²	1	2	yes	—
49	C₅×#382	C₂²	1	1	yes	characteristic
50	C₅×#382	C₂²	1	1	yes	characteristic
51	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
52	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
54	C₅×#376	C₂²	1	1	yes	characteristic
55	C₅×#376	C₂²	1	1	yes	characteristic
56	C₄³×C₅	C₂²	1	1	yes	characteristic
57	C₄³×C₅	C₂²	1	1	yes	characteristic
58	#35331	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂²×C₅×Q₈	C₂³	1	2	yes	—
60	C₂²×C₅×Q₈	C₂³	1	4	yes	—
61	C₂²×C₅×D₄	C₂³	1	2	yes	—
62	C₂²×C₅×D₄	C₂³	1	4	yes	—
63	C₂²×C₅×D₄	C₂³	1	4	yes	—
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂³	1	2	yes	—
66	C₂³×C₄×C₅	C₂³	1	4	yes	—
67	C₅×C₄⋊Q₈	—	2	8	no	—
68	C₅×C₄⋊Q₈	—	2	4	no	—
69	C₅×#127	—	2	4	no	—
70	C₅×#126	—	2	16	no	—
71	C₅×#124	—	2	16	no	—
72	C₅×#124	—	2	8	no	—
73	C₅×#124	—	2	8	no	—
74	C₅×#123	—	2	16	no	—
75	C₅×C₂²⋊Q₈	—	2	8	no	—
76	C₅×C₂²⋊Q₈	—	2	16	no	—
77	C₅×#121	—	2	8	no	—
78	C₄×C₅×Q₈	—	2	8	no	—
79	C₄×C₅×D₄	—	2	8	no	—
80	C₅×#117	—	2	4	no	—
81	C₅×#117	D₄	1	8	yes	complemented
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
100	C₂×C₄²×C₅	—	2	4	no	—
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	4	yes	—
104	C₂×C₄²×C₅	C₂³	1	2	yes	—
105	C₂×C₄²×C₅	C₂³	1	4	yes	—
106	C₂×C₄²×C₅	C₂³	1	4	yes	—
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₅×#95	C₂³	1	4	yes	—
112	C₅×#95	C₂³	1	4	yes	—
113	C₅×#95	C₂³	1	8	yes	—
114	C₅×#95	C₂³	1	8	yes	—
115	C₅×#95	C₂³	1	4	yes	—
116	C₅×#95	C₂³	1	4	yes	—
117	C₅×#95	C₂³	1	8	yes	—
118	C₂×#542	C₂×C₅	1	2	yes	complemented
119	#2862	C₂×C₅	1	1	yes	characteristic, complemented
120	#2858	C₂×C₅	1	1	yes	characteristic, complemented
121	#2850	C₂×C₅	1	2	yes	complemented
122	#2640	C₂×C₅	1	2	yes	complemented
123	#2621	C₂×C₅	1	1	yes	characteristic, complemented
124	#2619	C₂×C₅	1	1	yes	characteristic
125	#2560	C₂×C₅	1	8	yes	complemented
126	#2557	C₂×C₅	1	8	yes	complemented
127	#2328	C₂×C₅	1	1	yes	characteristic, complemented
128	#2327	C₂×C₅	1	1	yes	characteristic, complemented
129	C₄×#124	C₂×C₅	1	2	yes	complemented
130	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂⁴×C₅	C₂⁴	1	4	yes	—
132	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₅×Q₈	—	2	4	no	—
134	C₂×C₅×Q₈	—	2	8	no	—
135	C₂×C₅×Q₈	—	2	4	no	—
136	C₂×C₅×Q₈	—	2	4	no	—
137	C₂×C₅×Q₈	—	4	8	no	—
138	C₂×C₅×D₄	—	2	8	no	—
139	C₂×C₅×D₄	—	2	4	no	—
140	C₂×C₅×D₄	—	2	4	no	—
141	C₂×C₅×D₄	—	2	4	no	—
142	C₂×C₅×D₄	—	2	8	no	—
143	C₂×C₅×D₄	—	4	8	no	—
144	C₂×C₅×D₄	—	4	8	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	8	no	—
149	C₂²×C₄×C₅	—	4	4	no	—
150	C₂²×C₄×C₅	—	4	8	no	—
151	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	8	no	—
166	C₅×C₄⋊C₄	—	2	8	no	—
167	C₅×C₄⋊C₄	—	2	8	no	—
168	C₅×C₄⋊C₄	—	2	4	no	—
169	C₅×C₄⋊C₄	—	2	8	no	—
170	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
171	C₅×C₂²⋊C₄	—	2	8	no	—
172	C₅×C₂²⋊C₄	—	2	8	no	—
173	C₅×C₂²⋊C₄	—	2	8	no	—
174	C₅×C₂²⋊C₄	—	2	8	no	—
175	C₅×C₂²⋊C₄	—	2	8	no	—
176	C₅×C₂²⋊C₄	—	2	4	no	—
177	C₅×C₂²⋊C₄	—	2	16	no	—
178	C₅×C₂²⋊C₄	—	4	8	no	—
179	C₅×C₂²⋊C₄	—	4	8	no	—
180	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
181	C₄²×C₅	—	2	8	no	—
182	C₄²×C₅	—	2	4	no	—
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	—	2	2	no	—
185	C₄²×C₅	—	4	4	no	—
186	C₄²×C₅	—	4	4	no	—
187	C₄²×C₅	C₂×D₄	1	4	yes	—
188	C₄²×C₅	C₂×D₄	1	4	yes	—
189	C₄²×C₅	#41	1	4	yes	—
190	C₄²×C₅	#41	1	4	yes	—
191	#542	—	2	16	no	—
192	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
194	C₂×#127	C₂²×C₅	1	1	yes	characteristic
195	C₂×#126	C₂²×C₅	1	4	yes	—
196	C₂×#124	C₂²×C₅	1	2	yes	—
197	C₂×#124	C₂²×C₅	1	2	yes	—
198	C₂×#124	C₂²×C₅	1	4	yes	—
199	C₂×#123	C₂²×C₅	1	4	yes	—
200	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
201	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
202	C₂×#121	C₂²×C₅	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
204	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
205	C₂×#117	C₂²×C₅	1	1	yes	characteristic
206	C₂×#117	C₂²×C₅	1	1	yes	characteristic
207	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
208	#398	C₂²×C₅	1	4	yes	—
209	#397	C₂²×C₅	1	8	yes	—
210	#397	C₂²×C₅	1	4	yes	—
211	#394	C₂²×C₅	1	4	yes	—
212	#393	C₂²×C₅	1	8	yes	—
213	#392	C₂²×C₅	1	4	yes	—
214	#391	C₂²×C₅	1	8	yes	—
215	#391	C₂²×C₅	1	2	yes	—
216	#391	C₂²×C₅	1	2	yes	—
217	#390	C₂²×C₅	1	8	yes	—
218	#390	C₂²×C₅	1	2	yes	—
219	#390	C₂²×C₅	1	2	yes	—
220	#388	C₂²×C₅	1	8	yes	—
221	#388	C₂²×C₅	1	8	yes	—
222	#387	C₂²×C₅	1	8	yes	—
223	#386	C₂²×C₅	1	8	yes	—
224	#386	C₂²×C₅	1	8	yes	—
225	#382	C₂²×C₅	1	1	yes	characteristic
226	#382	C₂²×C₅	1	1	yes	characteristic
227	#382	C₂²×C₅	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
230	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
231	#376	C₂²×C₅	1	1	yes	characteristic
232	#376	C₂²×C₅	1	1	yes	characteristic
233	C₄³	C₂²×C₅	1	1	yes	characteristic
234	C₄³	C₂²×C₅	1	1	yes	characteristic
235	C₂³×C₅	—	2	1	no	—
236	C₂³×C₅	—	2	1	no	—
237	C₂³×C₅	—	2	4	no	—
238	C₂³×C₅	—	2	4	no	—
239	C₂³×C₅	—	2	4	no	—
240	C₂³×C₅	—	2	4	no	—
241	C₂³×C₅	—	2	8	no	—
242	C₂³×C₅	—	2	8	no	—
243	C₂³×C₅	C₂²×D₄	1	2	yes	—
244	C₂³×C₅	C₂⁵	1	1	yes	characteristic
245	C₅×Q₈	—	4	8	no	—
246	C₅×Q₈	—	8	8	no	—
247	C₅×D₄	—	4	8	no	—
248	C₅×D₄	—	8	8	no	—
249	C₅×D₄	—	8	8	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	4	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	2	8	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	—	2	4	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	4	no	—
263	C₂×C₄×C₅	—	2	4	no	—
264	C₂×C₄×C₅	—	2	4	no	—
265	C₂×C₄×C₅	—	2	4	no	—
266	C₂×C₄×C₅	—	2	8	no	—
267	C₂×C₄×C₅	—	2	8	no	—
268	C₂×C₄×C₅	—	4	8	no	—
269	C₂×C₄×C₅	—	8	8	no	—
270	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
272	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₅	C₂×#41	1	4	yes	—
275	C₂×C₄×C₅	C₂×#41	1	4	yes	—
276	C₂×C₄×C₅	C₂×#41	1	2	yes	—
277	C₂×C₄×C₅	C₂×#41	1	2	yes	—
278	C₂²×Q₈	C₂³×C₅	1	2	yes	—
279	C₂²×Q₈	C₂³×C₅	1	4	yes	—
280	C₂²×D₄	C₂³×C₅	1	2	yes	—
281	C₂²×D₄	C₂³×C₅	1	4	yes	—
282	C₂²×D₄	C₂³×C₅	1	4	yes	—
283	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₅	1	4	yes	—
285	C₂³×C₄	C₂³×C₅	1	2	yes	—
286	C₄⋊Q₈	—	2	8	no	—
287	C₄⋊Q₈	—	2	4	no	—
288	#127	—	2	4	no	—
289	#126	—	2	16	no	—
290	#124	—	2	16	no	—
291	#124	—	2	8	no	—
292	#124	—	2	8	no	—
293	#123	—	2	16	no	—
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	—	2	16	no	—
296	#121	—	2	8	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×D₄	—	2	8	no	—
299	#117	—	2	4	no	—
300	#117	C₅×D₄	1	8	yes	complemented
301	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
319	C₂×C₄²	—	2	4	no	—
320	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₅	1	4	yes	—
322	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₅	1	2	yes	—
324	C₂×C₄²	C₂³×C₅	1	4	yes	—
325	C₂×C₄²	C₂³×C₅	1	4	yes	—
326	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
330	#95	C₂³×C₅	1	4	yes	—
331	#95	C₂³×C₅	1	4	yes	—
332	#95	C₂³×C₅	1	8	yes	—
333	#95	C₂³×C₅	1	8	yes	—
334	#95	C₂³×C₅	1	4	yes	—
335	#95	C₂³×C₅	1	4	yes	—
336	#95	C₂³×C₅	1	8	yes	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	2	4	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	4	2	no	—
341	C₂²×C₅	—	4	4	no	—
342	C₂²×C₅	—	4	8	no	—
343	C₂²×C₅	—	4	4	no	—
344	C₂²×C₅	—	4	4	no	—
345	C₂²×C₅	—	4	8	no	—
346	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
347	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
349	C₂²×C₅	#585	1	4	yes	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	4	no	—
352	C₄×C₅	—	2	4	no	—
353	C₄×C₅	—	2	4	no	—
354	C₄×C₅	—	2	4	no	—
355	C₄×C₅	—	4	4	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	—	4	4	no	—
358	C₄×C₅	—	4	4	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	#532	1	4	yes	—
361	C₂⁴	C₂⁴×C₅	1	4	yes	—
362	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	4	8	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	16	no	—
408	C₂²⋊C₄	—	4	8	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
411	C₄²	—	2	8	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	4	4	no	—
416	C₄²	—	4	4	no	—
417	C₄²	C₂×C₅×D₄	1	4	yes	—
418	C₄²	C₂×C₅×D₄	1	4	yes	—
419	C₄²	C₅×#41	1	4	yes	—
420	C₄²	C₅×#41	1	4	yes	—
421	C₂×C₅	—	4	2	no	—
422	C₂×C₅	—	8	4	no	—
423	C₂×C₅	C₂×#532	1	1	yes	characteristic
424	C₂×C₅	#3455	1	2	yes	—
425	C₂×C₅	#3500	1	2	yes	—
426	C₂×C₅	#3510	1	2	yes	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	8	no	—
435	C₂³	C₂²×C₅×D₄	1	2	yes	—
436	C₂³	C₂⁵×C₅	1	1	yes	characteristic
437	Q₈	—	4	8	no	—
438	Q₈	—	8	8	no	—
439	D₄	—	4	8	no	—
440	D₄	—	8	8	no	—
441	D₄	—	8	8	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	8	8	no	—
462	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
463	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
464	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
465	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
466	C₂×C₄	C₂×C₅×#41	1	4	yes	—
467	C₂×C₄	C₂×C₅×#41	1	4	yes	—
468	C₂×C₄	C₂×C₅×#41	1	2	yes	—
469	C₂×C₄	C₂×C₅×#41	1	2	yes	—
470	C₅	#35331	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	8	no	—
480	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
481	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
482	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
483	C₂²	C₅×#585	1	4	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	4	no	—
486	C₄	—	2	4	no	—
487	C₄	—	2	4	no	—
488	C₄	—	2	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	2	no	—
494	C₄	C₅×#532	1	4	yes	—
495	C₂	—	4	2	no	—
496	C₂	—	8	4	no	—
497	C₂	C₂×C₅×#532	1	1	yes	characteristic
498	C₂	C₅×#3455	1	2	yes	—
499	C₂	C₅×#3500	1	2	yes	—
500	C₂	C₅×#3510	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₅×#2619	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#542	C₂	semidirect
2. C₅×#2862	C₂	semidirect
3. C₅×#2858	C₂	semidirect
4. C₅×#2850	C₂	semidirect
5. C₅×#2640	C₂	semidirect
6. C₅×#2621	C₂	semidirect
8. C₅×#2560	C₂	semidirect
9. C₅×#2557	C₂	semidirect
10. C₅×#2328	C₂	semidirect
11. C₅×#2327	C₂	semidirect
12. C₄×C₅×#124	C₂	semidirect
13. C₄×C₅×#117	C₂	semidirect
58. #35331	C₅	direct (N × H)
81. C₅×#117	D₄	semidirect
118. C₂×#542	C₂×C₅	semidirect
119. #2862	C₂×C₅	semidirect
120. #2858	C₂×C₅	semidirect
121. #2850	C₂×C₅	semidirect
122. #2640	C₂×C₅	semidirect
123. #2621	C₂×C₅	semidirect
125. #2560	C₂×C₅	semidirect
126. #2557	C₂×C₅	semidirect
127. #2328	C₂×C₅	semidirect
128. #2327	C₂×C₅	semidirect
129. C₄×#124	C₂×C₅	semidirect
130. C₄×#117	C₂×C₅	semidirect
300. #117	C₅×D₄	semidirect
470. C₅	#35331	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×#542	2
C₅×#2862	2
C₅×#2858	2
C₅×#2850	2
C₅×#2640	2
C₅×#2621	2
C₅×#2619	2
C₅×#2560	2
C₅×#2557	2
C₅×#2328	2
C₅×#2327	2
C₄×C₅×#124	2
C₄×C₅×#117	2
#35331	5

Subgroups — C5×#35331 #11958051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35331 #11958051