Subgroups — C₅×#20556 #11943276

Order 1280.

1098 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	2	yes	maximal
2	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#1771	C₂	1	2	yes	maximal, complemented
4	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1753	C₂	1	2	yes	maximal, complemented
6	C₅×#1752	C₂	1	2	yes	maximal, complemented
7	C₅×#1749	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1728	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₅×C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×D₄	C₄	1	2	yes	—
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#435	C₄	1	16	yes	complemented
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×#97	C₂²	1	2	yes	—
23	C₂×C₅×#97	C₂²	1	2	yes	—
24	C₂×C₅×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
29	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
30	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#336	C₂²	1	1	yes	characteristic
34	C₅×#336	C₂²	1	1	yes	characteristic
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	1	yes	characteristic
39	C₅×#336	C₂²	1	2	yes	—
40	#20556	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×M₁₆	—	4	2	no	—
47	C₂×C₅×M₁₆	—	4	2	no	—
48	C₂×C₅×M₁₆	C₂×C₄	1	8	yes	complemented
49	C₂²×C₅×C₈	—	4	2	no	—
50	C₂²×C₅×C₈	—	4	2	no	—
51	C₂²×C₅×C₈	C₂×C₄	1	8	yes	complemented
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₄×C₅×D₄	—	2	8	no	—
57	C₄×C₅×D₄	C₂×C₄	1	8	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	1	yes	characteristic
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	—	4	2	no	—
65	C₂×C₄²×C₅	—	4	2	no	—
66	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
76	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
77	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
78	C₅×#97	—	4	2	no	—
79	C₅×#97	—	4	2	no	—
80	C₅×#97	C₂×C₄	1	8	yes	complemented
81	C₄×C₅×C₈	—	4	2	no	—
82	C₅×#95	C₂×C₄	1	2	yes	—
83	C₅×#95	C₂×C₄	1	2	yes	—
84	C₅×#95	C₂×C₄	1	2	yes	—
85	C₂×#435	C₂×C₅	1	2	yes	—
86	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
87	#1771	C₂×C₅	1	2	yes	complemented
88	#1767	C₂×C₅	1	1	yes	characteristic, complemented
89	#1753	C₂×C₅	1	2	yes	complemented
90	#1752	C₂×C₅	1	2	yes	complemented
91	#1749	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
93	#1745	C₂×C₅	1	1	yes	characteristic, complemented
94	#1728	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#336	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₅×D₄	—	2	4	no	—
99	C₂×C₅×D₄	C₄²	1	4	yes	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	2	1	no	—
106	C₂²×C₄×C₅	—	2	4	no	—
107	C₂²×C₄×C₅	—	4	2	no	—
108	C₂²×C₄×C₅	—	4	2	no	—
109	C₂²×C₄×C₅	—	4	2	no	—
110	C₂²×C₄×C₅	—	4	2	no	—
111	C₂²×C₄×C₅	M₁₆	1	8	yes	complemented
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	1	yes	characteristic
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	4	yes	—
119	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₅×M₁₆	—	4	8	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	4	8	no	—
133	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
134	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
136	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	C₄²	1	4	yes	—
139	C₅×C₂²⋊C₄	—	2	4	no	—
140	C₅×C₂²⋊C₄	—	2	4	no	—
141	C₅×C₂²⋊C₄	C₄²	1	4	yes	—
142	C₅×C₂²⋊C₄	C₄²	1	4	yes	—
143	C₄²×C₅	—	2	4	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	—	4	2	no	—
150	C₄²×C₅	—	4	2	no	—
151	C₄²×C₅	—	4	2	no	—
152	C₄²×C₅	C₂²×C₄	1	4	yes	—
153	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
154	C₂³×C₈	C₂²×C₅	1	2	yes	—
155	C₂×C₄×D₄	C₄×C₅	1	2	yes	—
156	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
159	#435	C₄×C₅	1	16	yes	complemented
160	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
161	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
162	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
163	C₂×#97	C₂²×C₅	1	2	yes	—
164	C₂×#97	C₂²×C₅	1	2	yes	—
165	C₂×#97	C₂²×C₅	1	2	yes	—
166	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
167	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
168	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
170	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
171	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₄³	C₂²×C₅	1	1	yes	characteristic
174	#336	C₂²×C₅	1	1	yes	characteristic
175	#336	C₂²×C₅	1	1	yes	characteristic
176	#336	C₂²×C₅	1	2	yes	—
177	#336	C₂²×C₅	1	1	yes	characteristic
178	#336	C₂²×C₅	1	2	yes	—
179	#336	C₂²×C₅	1	1	yes	characteristic
180	#336	C₂²×C₅	1	2	yes	—
181	C₂³×C₅	—	2	1	no	—
182	C₂³×C₅	—	2	1	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	—	2	1	no	—
185	C₂³×C₅	—	2	1	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	C₂×C₄²	1	2	yes	—
189	C₂³×C₅	C₂×C₄²	1	2	yes	—
190	C₂³×C₅	C₂×M₁₆	1	4	yes	—
191	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
192	C₅×D₄	—	2	8	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	2	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	2	no	—
213	C₂×C₄×C₅	—	4	8	no	—
214	C₂×C₄×C₅	—	4	8	no	—
215	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
218	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
219	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
220	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
221	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
224	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
225	C₅×C₈	—	2	4	no	—
226	C₅×C₈	—	2	4	no	—
227	C₅×C₈	—	2	4	no	—
228	C₅×C₈	—	2	4	no	—
229	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
230	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
231	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
232	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂×M₁₆	—	4	2	no	—
235	C₂×M₁₆	—	4	2	no	—
236	C₂×M₁₆	C₂×C₄×C₅	1	8	yes	complemented
237	C₂²×C₈	—	4	2	no	—
238	C₂²×C₈	—	4	2	no	—
239	C₂²×C₈	C₂×C₄×C₅	1	8	yes	complemented
240	C₂²×C₈	C₂³×C₅	1	2	yes	—
241	C₂²×C₈	C₂³×C₅	1	2	yes	—
242	C₂²×C₈	C₂³×C₅	1	2	yes	—
243	C₂²×C₈	C₂³×C₅	1	2	yes	—
244	C₄×D₄	—	2	8	no	—
245	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
249	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂×C₄²	—	4	2	no	—
253	C₂×C₄²	—	4	2	no	—
254	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
255	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
257	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
258	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
263	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
264	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
265	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
266	#97	—	4	2	no	—
267	#97	—	4	2	no	—
268	#97	C₂×C₄×C₅	1	8	yes	complemented
269	C₄×C₈	—	4	2	no	—
270	#95	C₂×C₄×C₅	1	2	yes	—
271	#95	C₂×C₄×C₅	1	2	yes	—
272	#95	C₂×C₄×C₅	1	2	yes	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	4	no	—
275	C₂²×C₅	—	2	4	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	2	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	C₄×M₁₆	1	4	yes	—
283	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
284	C₂²×C₅	#518	1	1	yes	characteristic
285	C₂²×C₅	#520	1	1	yes	characteristic
286	C₂²×C₅	C₂²×M₁₆	1	2	yes	—
287	C₂²×C₅	#568	1	2	yes	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	4	no	—
291	C₄×C₅	—	2	4	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	#518	1	2	yes	—
297	C₄×C₅	#520	1	2	yes	—
298	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	C₄²×C₅	1	4	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	C₅×M₁₆	1	8	yes	complemented
314	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
321	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
322	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
325	M₁₆	—	4	8	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	8	no	—
335	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
336	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
337	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
338	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	C₄²×C₅	1	4	yes	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	C₄²×C₅	1	4	yes	—
344	C₂²⋊C₄	C₄²×C₅	1	4	yes	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	2	no	—
352	C₄²	—	4	2	no	—
353	C₄²	—	4	2	no	—
354	C₄²	C₂²×C₄×C₅	1	4	yes	—
355	C₂×C₅	—	2	4	no	—
356	C₂×C₅	—	4	2	no	—
357	C₂×C₅	#2275	1	1	yes	characteristic
358	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
359	C₂×C₅	#2875	1	1	yes	characteristic
360	C₂×C₅	#2973	1	2	yes	—
361	C₂×C₅	#2989	1	2	yes	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	C₂×C₄²×C₅	1	2	yes	—
370	C₂³	C₂×C₄²×C₅	1	2	yes	—
371	C₂³	C₂×C₅×M₁₆	1	4	yes	—
372	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
373	D₄	—	2	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
397	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
398	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
399	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
400	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
401	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
402	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
403	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	4	no	—
407	C₈	—	2	4	no	—
408	C₈	—	2	4	no	—
409	C₈	—	2	4	no	—
410	C₅	#20556	1	1	yes	characteristic, direct product factor, Sylow
411	C₂²	—	2	4	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	C₄×C₅×M₁₆	1	4	yes	—
421	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
422	C₂²	C₅×#518	1	1	yes	characteristic
423	C₂²	C₅×#520	1	1	yes	characteristic
424	C₂²	C₂²×C₅×M₁₆	1	2	yes	—
425	C₂²	C₅×#568	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	C₅×#518	1	2	yes	—
435	C₄	C₅×#520	1	2	yes	—
436	C₂	—	2	4	no	—
437	C₂	—	4	2	no	—
438	C₂	C₅×#2275	1	1	yes	characteristic
439	C₂	C₂×C₄×C₅×M₁₆	1	1	yes	characteristic
440	C₂	C₅×#2875	1	1	yes	characteristic
441	C₂	C₅×#2973	1	2	yes	—
442	C₂	C₅×#2989	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1771	C₂	semidirect
4. C₅×#1767	C₂	semidirect
5. C₅×#1753	C₂	semidirect
6. C₅×#1752	C₂	semidirect
7. C₅×#1749	C₂	semidirect
8. C₄×C₅×C₂²⋊C₈	C₂	semidirect
9. C₅×#1745	C₂	semidirect
10. C₅×#1728	C₂	semidirect
11. C₂×C₅×#336	C₂	semidirect
18. C₅×#435	C₄	semidirect
40. #20556	C₅	direct (N × H)
48. C₂×C₅×M₁₆	C₂×C₄	semidirect
51. C₂²×C₅×C₈	C₂×C₄	semidirect
75. C₅×C₄⋊C₈	C₂×C₄	semidirect
76. C₅×C₂²⋊C₈	C₂×C₄	semidirect
77. C₅×C₂²⋊C₈	C₂×C₄	semidirect
80. C₅×#97	C₂×C₄	semidirect
87. #1771	C₂×C₅	semidirect
88. #1767	C₂×C₅	semidirect
89. #1753	C₂×C₅	semidirect
90. #1752	C₂×C₅	semidirect
91. #1749	C₂×C₅	semidirect
92. C₄×C₂²⋊C₈	C₂×C₅	semidirect
93. #1745	C₂×C₅	semidirect
94. #1728	C₂×C₅	semidirect
95. C₂×#336	C₂×C₅	semidirect
111. C₂²×C₄×C₅	M₁₆	semidirect
159. #435	C₄×C₅	semidirect
236. C₂×M₁₆	C₂×C₄×C₅	semidirect
239. C₂²×C₈	C₂×C₄×C₅	semidirect
263. C₄⋊C₈	C₂×C₄×C₅	semidirect
264. C₂²⋊C₈	C₂×C₄×C₅	semidirect
265. C₂²⋊C₈	C₂×C₄×C₅	semidirect
268. #97	C₂×C₄×C₅	semidirect
313. C₂²×C₄	C₅×M₁₆	semidirect
410. C₅	#20556	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×#435	2
C₄²×C₅×D₄	2
C₅×#1771	2
C₅×#1767	2
C₅×#1753	2
C₅×#1752	2
C₅×#1749	2
C₄×C₅×C₂²⋊C₈	2
C₅×#1745	2
C₅×#1728	2
C₂×C₅×#336	2
#20556	5

Subgroups — C5×#20556 #11943276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20556 #11943276