Subgroups — C₅×#22796 #11945516

Order 1280.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#433	C₂	1	2	yes	maximal, complemented
2	C₅×#2293	C₂	1	1	yes	maximal, characteristic
3	C₅×#1954	C₂	1	1	yes	maximal, characteristic
4	C₅×#1954	C₂	1	1	yes	maximal, characteristic
5	C₅×#1924	C₂	1	2	yes	maximal, complemented
6	C₅×#1923	C₂	1	2	yes	maximal, complemented
7	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1798	C₂	1	2	yes	maximal, complemented
9	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	2	yes	—
14	C₅×#433	—	2	8	no	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₅×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
29	C₅×#390	C₄	1	1	yes	characteristic
30	C₅×#390	C₄	1	1	yes	characteristic
31	C₅×#389	C₄	1	1	yes	characteristic
32	C₅×#389	C₄	1	1	yes	characteristic
33	C₅×#388	C₄	1	2	yes	—
34	C₅×#388	C₄	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₄³×C₅	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	1	yes	characteristic
39	C₅×#336	C₂²	1	1	yes	characteristic
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#22796	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₄×C₅×D₄	—	2	2	no	—
52	C₄×C₅×D₄	—	2	2	no	—
53	C₅×#117	—	2	4	no	—
54	C₅×#117	—	2	4	no	—
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	2	yes	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	2	4	no	—
74	C₅×C₄⋊C₈	—	2	2	no	—
75	C₅×C₄⋊C₈	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	4	2	no	—
78	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
79	C₅×C₂²⋊C₈	—	2	4	no	—
80	C₅×C₂²⋊C₈	—	2	4	no	—
81	C₅×C₂²⋊C₈	—	4	2	no	—
82	C₅×C₂²⋊C₈	—	4	2	no	—
83	C₅×#97	—	2	4	no	—
84	C₄×C₅×C₈	—	2	4	no	—
85	C₄×C₅×C₈	—	2	2	no	—
86	C₄×C₅×C₈	—	2	2	no	—
87	C₅×#95	C₂×C₄	1	2	yes	—
88	C₅×#95	C₂×C₄	1	2	yes	—
89	C₅×#95	C₂×C₄	1	2	yes	—
90	C₂×#433	C₂×C₅	1	2	yes	complemented
91	#2293	C₂×C₅	1	1	yes	characteristic
92	#1954	C₂×C₅	1	1	yes	characteristic
93	#1954	C₂×C₅	1	1	yes	characteristic
94	#1924	C₂×C₅	1	2	yes	complemented
95	#1923	C₂×C₅	1	2	yes	complemented
96	#1842	C₂×C₅	1	1	yes	characteristic, complemented
97	#1798	C₂×C₅	1	2	yes	complemented
98	#1770	C₂×C₅	1	1	yes	characteristic, complemented
99	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₂²⋊C₄	—	2	4	no	—
145	C₅×C₂²⋊C₄	—	2	4	no	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	2	2	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	4	1	no	—
157	C₄²×C₅	C₂×D₄	1	2	yes	—
158	C₄²×C₅	#41	1	2	yes	—
159	C₄²×C₅	#41	1	2	yes	—
160	C₄²×C₅	#41	1	2	yes	—
161	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×#117	C₂²×C₅	1	2	yes	—
163	#433	—	2	8	no	—
164	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
166	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
169	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
171	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
172	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
173	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
174	C₂×#97	C₂²×C₅	1	2	yes	—
175	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
178	#390	C₄×C₅	1	1	yes	characteristic
179	#390	C₄×C₅	1	1	yes	characteristic
180	#389	C₄×C₅	1	1	yes	characteristic
181	#389	C₄×C₅	1	1	yes	characteristic
182	#388	C₄×C₅	1	2	yes	—
183	#388	C₄×C₅	1	2	yes	—
184	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
186	C₄³	C₂²×C₅	1	1	yes	characteristic
187	#336	C₂²×C₅	1	2	yes	—
188	#336	C₂²×C₅	1	2	yes	—
189	#336	C₂²×C₅	1	1	yes	characteristic
190	#336	C₂²×C₅	1	1	yes	characteristic
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₅×D₄	—	4	4	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	#117	1	2	yes	—
225	C₂×C₄×C₅	#117	1	2	yes	—
226	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₅	#131	1	2	yes	—
229	C₂×C₄×C₅	#131	1	2	yes	—
230	C₂×C₄×C₅	#131	1	2	yes	—
231	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	4	2	no	—
240	C₅×C₈	—	4	2	no	—
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	1	no	—
243	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₅	1	2	yes	—
248	C₂²×C₈	C₂³×C₅	1	2	yes	—
249	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	#117	—	2	4	no	—
254	#117	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
265	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₅	1	2	yes	—
270	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	4	2	no	—
278	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
279	C₂²⋊C₈	—	2	4	no	—
280	C₂²⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	—	4	2	no	—
282	C₂²⋊C₈	—	4	2	no	—
283	#97	—	2	4	no	—
284	C₄×C₈	—	2	4	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	—	2	2	no	—
287	#95	C₂×C₄×C₅	1	2	yes	—
288	#95	C₂×C₄×C₅	1	2	yes	—
289	#95	C₂×C₄×C₅	1	2	yes	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	4	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	C₂×#117	1	1	yes	characteristic
298	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₅	#520	1	1	yes	characteristic
300	C₂²×C₅	C₂×#131	1	1	yes	characteristic
301	C₂²×C₅	C₂×#131	1	1	yes	characteristic
302	C₂²×C₅	C₂×#131	1	1	yes	characteristic
303	C₂²×C₅	#568	1	1	yes	characteristic
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	#433	1	4	yes	complemented
313	C₄×C₅	#547	1	1	yes	characteristic
314	C₄×C₅	#550	1	1	yes	characteristic
315	C₄×C₅	#555	1	1	yes	characteristic
316	C₄×C₅	#556	1	1	yes	characteristic
317	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
331	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
354	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	4	1	no	—
373	C₄²	C₂×C₅×D₄	1	2	yes	—
374	C₄²	C₅×#41	1	2	yes	—
375	C₄²	C₅×#41	1	2	yes	—
376	C₄²	C₅×#41	1	2	yes	—
377	C₂×C₅	—	8	2	no	—
378	C₂×C₅	#2354	1	1	yes	characteristic
379	C₂×C₅	C₂×#433	1	1	yes	characteristic
380	C₂×C₅	#2925	1	1	yes	characteristic
381	C₂×C₅	#2931	1	1	yes	characteristic
382	C₂×C₅	#2935	1	1	yes	characteristic
383	C₂×C₅	#2993	1	1	yes	characteristic
384	C₂×C₅	#2994	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
393	D₄	—	4	4	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	C₅×#117	1	2	yes	—
419	C₂×C₄	C₅×#117	1	2	yes	—
420	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
421	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
422	C₂×C₄	C₅×#131	1	2	yes	—
423	C₂×C₄	C₅×#131	1	2	yes	—
424	C₂×C₄	C₅×#131	1	2	yes	—
425	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
426	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
428	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
429	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₅	#22796	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×C₅×#117	1	1	yes	characteristic
446	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
447	C₂²	C₅×#520	1	1	yes	characteristic
448	C₂²	C₂×C₅×#131	1	1	yes	characteristic
449	C₂²	C₂×C₅×#131	1	1	yes	characteristic
450	C₂²	C₂×C₅×#131	1	1	yes	characteristic
451	C₂²	C₅×#568	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	C₅×#433	1	4	yes	complemented
461	C₄	C₅×#547	1	1	yes	characteristic
462	C₄	C₅×#550	1	1	yes	characteristic
463	C₄	C₅×#555	1	1	yes	characteristic
464	C₄	C₅×#556	1	1	yes	characteristic
465	C₂	—	8	2	no	—
466	C₂	C₅×#2354	1	1	yes	characteristic
467	C₂	C₂×C₅×#433	1	1	yes	characteristic
468	C₂	C₅×#2925	1	1	yes	characteristic
469	C₂	C₅×#2931	1	1	yes	characteristic
470	C₂	C₅×#2935	1	1	yes	characteristic
471	C₂	C₅×#2993	1	1	yes	characteristic
472	C₂	C₅×#2994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×C₄
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×#433	C₂	semidirect
5. C₅×#1924	C₂	semidirect
6. C₅×#1923	C₂	semidirect
7. C₅×#1842	C₂	semidirect
8. C₅×#1798	C₂	semidirect
9. C₅×#1770	C₂	semidirect
10. C₅×C₈×C₄⋊C₄	C₂	semidirect
11. C₄×C₅×C₄⋊C₈	C₂	semidirect
42. #22796	C₅	direct (N × H)
78. C₅×C₄⋊C₈	D₄	semidirect
90. C₂×#433	C₂×C₅	semidirect
94. #1924	C₂×C₅	semidirect
95. #1923	C₂×C₅	semidirect
96. #1842	C₂×C₅	semidirect
97. #1798	C₂×C₅	semidirect
98. #1770	C₂×C₅	semidirect
99. C₈×C₄⋊C₄	C₂×C₅	semidirect
100. C₄×C₄⋊C₈	C₂×C₅	semidirect
278. C₄⋊C₈	C₅×D₄	semidirect
312. C₄×C₅	#433	semidirect
437. C₅	#22796	direct (N × H)
460. C₄	C₅×#433	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#433	2
C₅×#2293	2
C₅×#1954	2
C₅×#1924	2
C₅×#1923	2
C₅×#1842	2
C₅×#1798	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×C₄⋊C₈	2
#22796	5

Subgroups — C5×#22796 #11945516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22796 #11945516