Subgroups — C₅×#35332 #11958052

Order 1280.

2186 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#540	C₂	1	1	yes	maximal, characteristic
3	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2850	C₂	1	2	yes	maximal, complemented
6	C₅×#2642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2620	C₂	1	2	yes	maximal, complemented
9	C₅×#2559	C₂	1	8	yes	maximal, complemented
10	C₅×#2558	C₂	1	8	yes	maximal, complemented
11	C₅×#2326	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#541	—	2	8	no	—
15	C₅×#540	—	2	8	no	—
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×#125	C₂²	1	4	yes	—
20	C₂×C₅×#125	C₂²	1	1	yes	characteristic
21	C₂×C₅×#125	C₂²	1	1	yes	characteristic
22	C₂×C₅×#124	C₂²	1	2	yes	—
23	C₂×C₅×#124	C₂²	1	2	yes	—
24	C₂×C₅×#123	C₂²	1	4	yes	—
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₅×#121	C₂²	1	4	yes	—
27	C₂×C₅×#121	C₂²	1	2	yes	—
28	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₂×C₅×#117	C₂²	1	1	yes	characteristic
31	C₂×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₅×#400	C₂²	1	8	yes	—
34	C₅×#396	C₂²	1	8	yes	—
35	C₅×#394	C₂²	1	8	yes	—
36	C₅×#394	C₂²	1	8	yes	—
37	C₅×#391	C₂²	1	2	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#390	C₂²	1	8	yes	—
40	C₅×#390	C₂²	1	2	yes	—
41	C₅×#390	C₂²	1	2	yes	—
42	C₅×#389	C₂²	1	8	yes	—
43	C₅×#388	C₂²	1	8	yes	—
44	C₅×#388	C₂²	1	8	yes	—
45	C₅×#388	C₂²	1	8	yes	—
46	C₅×#386	C₂²	1	8	yes	—
47	C₅×#385	C₂²	1	8	yes	—
48	C₅×#384	C₂²	1	2	yes	—
49	C₅×#382	C₂²	1	2	yes	—
50	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
51	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
52	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
53	C₅×#376	C₂²	1	1	yes	characteristic
54	C₅×#376	C₂²	1	1	yes	characteristic
55	C₄³×C₅	C₂²	1	1	yes	characteristic
56	C₄³×C₅	C₂²	1	1	yes	characteristic
57	#35332	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₅×Q₈	C₂³	1	2	yes	—
59	C₂²×C₅×D₄	C₂³	1	2	yes	—
60	C₂²×C₅×D₄	C₂³	1	4	yes	—
61	C₂²×C₅×D₄	C₂³	1	4	yes	—
62	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂³	1	4	yes	—
64	C₂³×C₄×C₅	C₂³	1	2	yes	—
65	C₅×C₄⋊Q₈	—	2	4	no	—
66	C₅×#127	—	2	4	no	—
67	C₅×#126	—	2	16	no	—
68	C₅×#125	—	2	16	no	—
69	C₅×#125	—	2	4	no	—
70	C₅×#125	—	2	4	no	—
71	C₅×#124	—	2	8	no	—
72	C₅×#124	—	2	8	no	—
73	C₅×#123	—	2	16	no	—
74	C₅×C₂²⋊Q₈	—	2	8	no	—
75	C₅×#121	—	2	8	no	—
76	C₅×#121	—	2	16	no	—
77	C₄×C₅×Q₈	—	2	8	no	—
78	C₄×C₅×D₄	—	2	8	no	—
79	C₅×#117	—	2	4	no	—
80	C₅×#117	D₄	1	8	yes	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	4	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	8	yes	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂³	1	8	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	8	yes	—
116	C₂×#541	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×#540	C₂×C₅	1	1	yes	characteristic
118	#2859	C₂×C₅	1	1	yes	characteristic, complemented
119	#2858	C₂×C₅	1	1	yes	characteristic, complemented
120	#2850	C₂×C₅	1	2	yes	complemented
121	#2642	C₂×C₅	1	1	yes	characteristic, complemented
122	#2641	C₂×C₅	1	1	yes	characteristic, complemented
123	#2620	C₂×C₅	1	2	yes	complemented
124	#2559	C₂×C₅	1	8	yes	complemented
125	#2558	C₂×C₅	1	8	yes	complemented
126	#2326	C₂×C₅	1	2	yes	complemented
127	C₄×#124	C₂×C₅	1	2	yes	complemented
128	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂⁴×C₅	C₂⁴	1	4	yes	—
130	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×C₅×Q₈	—	2	4	no	—
132	C₂×C₅×Q₈	—	2	4	no	—
133	C₂×C₅×Q₈	—	2	4	no	—
134	C₂×C₅×D₄	—	2	8	no	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	—	2	8	no	—
137	C₂×C₅×D₄	—	2	4	no	—
138	C₂×C₅×D₄	—	2	4	no	—
139	C₂×C₅×D₄	—	4	8	no	—
140	C₂×C₅×D₄	—	4	8	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	8	no	—
145	C₂²×C₄×C₅	—	4	4	no	—
146	C₂²×C₄×C₅	—	4	8	no	—
147	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	4	no	—
161	C₅×C₄⋊C₄	—	2	8	no	—
162	C₅×C₄⋊C₄	—	2	8	no	—
163	C₅×C₄⋊C₄	—	2	8	no	—
164	C₅×C₄⋊C₄	—	2	8	no	—
165	C₅×C₄⋊C₄	—	2	8	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	4	8	no	—
168	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
169	C₅×C₂²⋊C₄	—	2	8	no	—
170	C₅×C₂²⋊C₄	—	2	8	no	—
171	C₅×C₂²⋊C₄	—	2	8	no	—
172	C₅×C₂²⋊C₄	—	2	4	no	—
173	C₅×C₂²⋊C₄	—	2	16	no	—
174	C₅×C₂²⋊C₄	—	2	16	no	—
175	C₅×C₂²⋊C₄	—	4	8	no	—
176	C₅×C₂²⋊C₄	—	4	8	no	—
177	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
178	C₄²×C₅	—	2	8	no	—
179	C₄²×C₅	—	2	4	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	4	4	no	—
183	C₄²×C₅	—	4	4	no	—
184	C₄²×C₅	C₂×D₄	1	4	yes	—
185	C₄²×C₅	C₂×D₄	1	4	yes	—
186	C₄²×C₅	#41	1	4	yes	—
187	C₄²×C₅	#41	1	4	yes	—
188	#541	—	2	8	no	—
189	#540	—	2	8	no	—
190	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×#127	C₂²×C₅	1	1	yes	characteristic
192	C₂×#126	C₂²×C₅	1	4	yes	—
193	C₂×#125	C₂²×C₅	1	1	yes	characteristic
194	C₂×#125	C₂²×C₅	1	1	yes	characteristic
195	C₂×#125	C₂²×C₅	1	4	yes	—
196	C₂×#124	C₂²×C₅	1	2	yes	—
197	C₂×#124	C₂²×C₅	1	2	yes	—
198	C₂×#123	C₂²×C₅	1	4	yes	—
199	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
200	C₂×#121	C₂²×C₅	1	2	yes	—
201	C₂×#121	C₂²×C₅	1	4	yes	—
202	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
203	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
204	C₂×#117	C₂²×C₅	1	1	yes	characteristic
205	C₂×#117	C₂²×C₅	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
207	#400	C₂²×C₅	1	8	yes	—
208	#396	C₂²×C₅	1	8	yes	—
209	#394	C₂²×C₅	1	8	yes	—
210	#394	C₂²×C₅	1	8	yes	—
211	#391	C₂²×C₅	1	2	yes	—
212	#391	C₂²×C₅	1	2	yes	—
213	#390	C₂²×C₅	1	2	yes	—
214	#390	C₂²×C₅	1	8	yes	—
215	#390	C₂²×C₅	1	2	yes	—
216	#389	C₂²×C₅	1	8	yes	—
217	#388	C₂²×C₅	1	8	yes	—
218	#388	C₂²×C₅	1	8	yes	—
219	#388	C₂²×C₅	1	8	yes	—
220	#386	C₂²×C₅	1	8	yes	—
221	#385	C₂²×C₅	1	8	yes	—
222	#384	C₂²×C₅	1	2	yes	—
223	#382	C₂²×C₅	1	2	yes	—
224	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
225	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
226	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
227	#376	C₂²×C₅	1	1	yes	characteristic
228	#376	C₂²×C₅	1	1	yes	characteristic
229	C₄³	C₂²×C₅	1	1	yes	characteristic
230	C₄³	C₂²×C₅	1	1	yes	characteristic
231	C₂³×C₅	—	2	1	no	—
232	C₂³×C₅	—	2	1	no	—
233	C₂³×C₅	—	2	4	no	—
234	C₂³×C₅	—	2	4	no	—
235	C₂³×C₅	—	2	4	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	2	8	no	—
238	C₂³×C₅	—	2	8	no	—
239	C₂³×C₅	C₂²×D₄	1	2	yes	—
240	C₂³×C₅	C₂⁵	1	1	yes	characteristic
241	C₅×Q₈	—	4	8	no	—
242	C₅×D₄	—	4	8	no	—
243	C₅×D₄	—	8	8	no	—
244	C₅×D₄	—	8	8	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	8	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	2	no	—
256	C₂×C₄×C₅	—	2	2	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	8	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	2	8	no	—
263	C₂×C₄×C₅	—	4	8	no	—
264	C₂×C₄×C₅	—	8	8	no	—
265	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
266	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₅	C₂×#41	1	4	yes	—
270	C₂×C₄×C₅	C₂×#41	1	4	yes	—
271	C₂×C₄×C₅	C₂×#41	1	2	yes	—
272	C₂×C₄×C₅	C₂×#41	1	2	yes	—
273	C₂²×Q₈	C₂³×C₅	1	2	yes	—
274	C₂²×D₄	C₂³×C₅	1	2	yes	—
275	C₂²×D₄	C₂³×C₅	1	4	yes	—
276	C₂²×D₄	C₂³×C₅	1	4	yes	—
277	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₅	1	4	yes	—
279	C₂³×C₄	C₂³×C₅	1	2	yes	—
280	C₄⋊Q₈	—	2	4	no	—
281	#127	—	2	4	no	—
282	#126	—	2	16	no	—
283	#125	—	2	16	no	—
284	#125	—	2	4	no	—
285	#125	—	2	4	no	—
286	#124	—	2	8	no	—
287	#124	—	2	8	no	—
288	#123	—	2	16	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	#121	—	2	8	no	—
291	#121	—	2	16	no	—
292	C₄×Q₈	—	2	8	no	—
293	C₄×D₄	—	2	8	no	—
294	#117	—	2	4	no	—
295	#117	C₅×D₄	1	8	yes	—
296	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
301	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
302	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
304	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
305	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
315	C₂×C₄²	—	2	4	no	—
316	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₅	1	4	yes	—
318	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₅	1	2	yes	—
320	C₂×C₄²	C₂³×C₅	1	4	yes	—
321	C₂×C₄²	C₂³×C₅	1	4	yes	—
322	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
326	#95	C₂³×C₅	1	4	yes	—
327	#95	C₂³×C₅	1	4	yes	—
328	#95	C₂³×C₅	1	8	yes	—
329	#95	C₂³×C₅	1	8	yes	—
330	#95	C₂³×C₅	1	8	yes	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	2	4	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	4	no	—
336	C₂²×C₅	—	4	8	no	—
337	C₂²×C₅	—	4	4	no	—
338	C₂²×C₅	—	4	4	no	—
339	C₂²×C₅	—	4	8	no	—
340	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
341	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₅	#585	1	4	yes	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	2	4	no	—
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	—	2	4	no	—
348	C₄×C₅	—	2	4	no	—
349	C₄×C₅	—	4	4	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	—	4	4	no	—
352	C₄×C₅	—	4	4	no	—
353	C₄×C₅	—	4	2	no	—
354	C₄×C₅	#532	1	4	yes	—
355	C₂⁴	C₂⁴×C₅	1	4	yes	—
356	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	4	8	no	—
366	C₂×D₄	—	4	8	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	4	8	no	—
394	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	16	no	—
400	C₂²⋊C₄	—	2	16	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
404	C₄²	—	2	8	no	—
405	C₄²	—	2	4	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	4	4	no	—
409	C₄²	—	4	4	no	—
410	C₄²	C₂×C₅×D₄	1	4	yes	—
411	C₄²	C₂×C₅×D₄	1	4	yes	—
412	C₄²	C₅×#41	1	4	yes	—
413	C₄²	C₅×#41	1	4	yes	—
414	C₂×C₅	—	4	2	no	—
415	C₂×C₅	—	8	4	no	—
416	C₂×C₅	C₂×#532	1	1	yes	characteristic
417	C₂×C₅	#3455	1	2	yes	—
418	C₂×C₅	#3500	1	2	yes	—
419	C₂×C₅	#3512	1	2	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	8	no	—
428	C₂³	C₂²×C₅×D₄	1	2	yes	—
429	C₂³	C₂⁵×C₅	1	1	yes	characteristic
430	Q₈	—	4	8	no	—
431	D₄	—	4	8	no	—
432	D₄	—	8	8	no	—
433	D₄	—	8	8	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	8	8	no	—
454	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
455	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
456	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
457	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
458	C₂×C₄	C₂×C₅×#41	1	4	yes	—
459	C₂×C₄	C₂×C₅×#41	1	4	yes	—
460	C₂×C₄	C₂×C₅×#41	1	2	yes	—
461	C₂×C₄	C₂×C₅×#41	1	2	yes	—
462	C₅	#35332	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	2	2	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	8	no	—
472	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
473	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
474	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
475	C₂²	C₅×#585	1	4	yes	—
476	C₄	—	2	2	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	4	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	2	no	—
486	C₄	C₅×#532	1	4	yes	—
487	C₂	—	4	2	no	—
488	C₂	—	8	4	no	—
489	C₂	C₂×C₅×#532	1	1	yes	characteristic
490	C₂	C₅×#3455	1	2	yes	—
491	C₂	C₅×#3500	1	2	yes	—
492	C₂	C₅×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#540	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×#541	C₂	semidirect
3. C₅×#2859	C₂	semidirect
4. C₅×#2858	C₂	semidirect
5. C₅×#2850	C₂	semidirect
6. C₅×#2642	C₂	semidirect
7. C₅×#2641	C₂	semidirect
8. C₅×#2620	C₂	semidirect
9. C₅×#2559	C₂	semidirect
10. C₅×#2558	C₂	semidirect
11. C₅×#2326	C₂	semidirect
12. C₄×C₅×#124	C₂	semidirect
13. C₄×C₅×#117	C₂	semidirect
57. #35332	C₅	direct (N × H)
116. C₂×#541	C₂×C₅	semidirect
118. #2859	C₂×C₅	semidirect
119. #2858	C₂×C₅	semidirect
120. #2850	C₂×C₅	semidirect
121. #2642	C₂×C₅	semidirect
122. #2641	C₂×C₅	semidirect
123. #2620	C₂×C₅	semidirect
124. #2559	C₂×C₅	semidirect
125. #2558	C₂×C₅	semidirect
126. #2326	C₂×C₅	semidirect
127. C₄×#124	C₂×C₅	semidirect
128. C₄×#117	C₂×C₅	semidirect
462. C₅	#35332	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×#541	2
C₂×C₅×#540	2
C₅×#2859	2
C₅×#2858	2
C₅×#2850	2
C₅×#2642	2
C₅×#2641	2
C₅×#2620	2
C₅×#2559	2
C₅×#2558	2
C₅×#2326	2
C₄×C₅×#124	2
C₄×C₅×#117	2
#35332	5

Subgroups — C5×#35332 #11958052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35332 #11958052