Subgroups — C₅×#20439 #11943159

Order 1280.

1130 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅×#2296	C₂	1	1	yes	maximal, characteristic
6	C₅×#1771	C₂	1	2	yes	maximal, complemented
7	C₅×#1771	C₂	1	2	yes	maximal, complemented
8	C₅×#1770	C₂	1	2	yes	maximal, complemented
9	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#1729	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₅×#424	C₄	1	8	yes	complemented
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
22	C₅×#405	—	2	4	no	—
23	C₅×#405	C₄	1	8	yes	complemented
24	C₄×C₅×M₁₆	—	2	4	no	—
25	C₂×C₅×#97	C₂²	1	2	yes	—
26	C₂×C₅×#97	C₂²	1	2	yes	—
27	C₂×C₅×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
31	C₅×#389	C₄	1	2	yes	—
32	C₅×#389	C₄	1	2	yes	—
33	C₅×#385	C₄	1	4	yes	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	1	yes	characteristic
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	1	yes	characteristic
39	C₅×#336	C₂²	1	1	yes	characteristic
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	2	yes	—
42	#20439	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×M₁₆	—	2	2	no	—
46	C₂×C₅×M₁₆	—	2	2	no	—
47	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
49	C₂×C₅×M₁₆	D₄	1	4	yes	—
50	C₂×C₅×M₁₆	Q₈	1	4	yes	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	—	2	2	no	—
55	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
56	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	2	yes	—
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	2	yes	—
63	C₅×#117	—	2	2	no	—
64	C₅×#117	—	2	2	no	—
65	C₅×#117	C₂×C₄	1	4	yes	—
66	C₅×#117	C₂×C₄	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	2	yes	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
82	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
83	C₅×#97	—	2	4	no	—
84	C₅×#97	—	2	4	no	—
85	C₅×#97	C₂×C₄	1	8	yes	complemented
86	C₄×C₅×C₈	—	2	4	no	—
87	C₄×C₅×C₈	—	2	4	no	—
88	C₄×C₅×C₈	C₂×C₄	1	8	yes	complemented
89	C₅×#95	C₂×C₄	1	4	yes	—
90	C₅×#95	C₂×C₄	1	4	yes	—
91	C₂×#424	C₂×C₅	1	1	yes	characteristic
92	C₂×#405	C₂×C₅	1	1	yes	characteristic
93	C₂×#405	C₂×C₅	1	1	yes	characteristic
94	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
95	#2296	C₂×C₅	1	1	yes	characteristic
96	#1771	C₂×C₅	1	2	yes	complemented
97	#1771	C₂×C₅	1	2	yes	complemented
98	#1770	C₂×C₅	1	2	yes	complemented
99	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
100	#1729	C₂×C₅	1	1	yes	characteristic
101	C₂×#336	C₂×C₅	1	1	yes	characteristic
102	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	—	2	4	no	—
104	C₂²×C₄×C₅	—	2	4	no	—
105	C₂²×C₄×C₅	—	4	2	no	—
106	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₅	#41	1	2	yes	—
117	C₂²×C₄×C₅	#41	1	2	yes	—
118	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₅×M₁₆	—	2	8	no	—
120	C₅×M₁₆	C₄⋊C₄	1	16	yes	complemented
121	C₂×C₅×C₈	—	2	8	no	—
122	C₂×C₅×C₈	—	2	8	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	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
139	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
140	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	8	no	—
143	C₅×C₄⋊C₄	—	4	4	no	—
144	C₅×C₄⋊C₄	C₄²	1	4	yes	—
145	C₅×C₄⋊C₄	C₄²	1	4	yes	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	C₄²	1	8	yes	—
148	C₄²×C₅	—	2	4	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	C₂²×C₄	1	4	yes	—
156	C₄²×C₅	C₂²×C₄	1	4	yes	—
157	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
158	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
159	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×#117	C₂²×C₅	1	1	yes	characteristic
162	C₂×#117	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
164	#424	C₄×C₅	1	8	yes	complemented
165	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
166	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
167	#405	—	2	4	no	—
168	#405	C₄×C₅	1	8	yes	complemented
169	C₄×M₁₆	—	2	4	no	—
170	C₂×#97	C₂²×C₅	1	2	yes	—
171	C₂×#97	C₂²×C₅	1	2	yes	—
172	C₂×#97	C₂²×C₅	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
174	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
175	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
176	#389	C₄×C₅	1	2	yes	—
177	#389	C₄×C₅	1	2	yes	—
178	#385	C₄×C₅	1	4	yes	—
179	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
180	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
181	#336	C₂²×C₅	1	1	yes	characteristic
182	#336	C₂²×C₅	1	1	yes	characteristic
183	#336	C₂²×C₅	1	1	yes	characteristic
184	#336	C₂²×C₅	1	1	yes	characteristic
185	#336	C₂²×C₅	1	2	yes	—
186	#336	C₂²×C₅	1	2	yes	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	C₂×C₄²	1	2	yes	—
190	C₂³×C₅	C₄×D₄	1	2	yes	—
191	C₂³×C₅	C₄×Q₈	1	2	yes	—
192	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	4	8	no	—
204	C₂×C₄×C₅	C₂×C₄²	1	4	yes	—
205	C₂×C₄×C₅	C₂×C₄²	1	4	yes	—
206	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
207	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
208	C₂×C₄×C₅	#117	1	4	yes	—
209	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
210	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
212	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
213	C₂×C₄×C₅	#131	1	4	yes	—
214	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	2	4	no	—
225	C₅×C₈	C₂×C₄⋊C₄	1	8	yes	—
226	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
227	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
231	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
232	C₂×M₁₆	C₅×D₄	1	4	yes	—
233	C₂×M₁₆	C₅×Q₈	1	4	yes	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
239	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
240	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₅	1	2	yes	—
245	C₂²×C₈	C₂³×C₅	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	C₂×C₄×C₅	1	4	yes	—
249	#117	C₂×C₄×C₅	1	4	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
260	C₂×C₄²	C₂³×C₅	1	2	yes	—
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₅	1	2	yes	—
264	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
265	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
266	#97	—	2	4	no	—
267	#97	—	2	4	no	—
268	#97	C₂×C₄×C₅	1	8	yes	complemented
269	C₄×C₈	—	2	4	no	—
270	C₄×C₈	—	2	4	no	—
271	C₄×C₈	C₂×C₄×C₅	1	8	yes	complemented
272	#95	C₂×C₄×C₅	1	4	yes	—
273	#95	C₂×C₄×C₅	1	4	yes	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	2	4	no	—
277	C₂²×C₅	—	2	4	no	—
278	C₂²×C₅	C₄×C₄⋊C₄	1	4	yes	—
279	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
280	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
282	C₂²×C₅	C₂×#131	1	2	yes	—
283	C₂²×C₅	#568	1	2	yes	—
284	C₄×C₅	—	2	4	no	—
285	C₄×C₅	—	2	4	no	—
286	C₄×C₅	—	2	4	no	—
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	C₄×C₄⋊C₄	1	4	yes	—
290	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
291	C₄×C₅	C₂×#117	1	1	yes	characteristic
292	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
294	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
300	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
306	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
308	C₂²×C₄	C₅×#41	1	2	yes	—
309	C₂²×C₄	C₅×#41	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
311	M₁₆	—	2	8	no	—
312	M₁₆	C₅×C₄⋊C₄	1	16	yes	complemented
313	C₂×C₈	—	2	8	no	—
314	C₂×C₈	—	2	8	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
326	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
327	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
330	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
331	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
332	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	C₄²×C₅	1	4	yes	—
337	C₄⋊C₄	C₄²×C₅	1	4	yes	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	C₄²×C₅	1	8	yes	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	2	no	—
347	C₄²	C₂²×C₄×C₅	1	4	yes	—
348	C₄²	C₂²×C₄×C₅	1	4	yes	—
349	C₂×C₅	—	2	4	no	—
350	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₅	C₄×#131	1	1	yes	characteristic
352	C₂×C₅	#2875	1	1	yes	characteristic
353	C₂×C₅	#2933	1	2	yes	—
354	C₂×C₅	#2962	1	2	yes	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	C₂×C₄²×C₅	1	2	yes	—
358	C₂³	C₄×C₅×D₄	1	2	yes	—
359	C₂³	C₄×C₅×Q₈	1	2	yes	—
360	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	C₂×C₄²×C₅	1	4	yes	—
373	C₂×C₄	C₂×C₄²×C₅	1	4	yes	—
374	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
375	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
376	C₂×C₄	C₅×#117	1	4	yes	—
377	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
378	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
379	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
380	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
381	C₂×C₄	C₅×#131	1	4	yes	—
382	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
383	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
386	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	2	4	no	—
393	C₈	C₂×C₅×C₄⋊C₄	1	8	yes	—
394	C₅	#20439	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	C₄×C₅×C₄⋊C₄	1	4	yes	—
400	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
401	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
402	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
403	C₂²	C₂×C₅×#131	1	2	yes	—
404	C₂²	C₅×#568	1	2	yes	—
405	C₄	—	2	4	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	C₄×C₅×C₄⋊C₄	1	4	yes	—
411	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
412	C₄	C₂×C₅×#117	1	1	yes	characteristic
413	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
414	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
415	C₂	—	2	4	no	—
416	C₂	C₂×C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
417	C₂	C₄×C₅×#131	1	1	yes	characteristic
418	C₂	C₅×#2875	1	1	yes	characteristic
419	C₂	C₅×#2933	1	2	yes	—
420	C₂	C₅×#2962	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	C₂⁴×C₅	C₂²×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
6. C₅×#1771	C₂	semidirect
7. C₅×#1771	C₂	semidirect
8. C₅×#1770	C₂	semidirect
9. C₅×C₈×C₄⋊C₄	C₂	semidirect
19. C₅×#424	C₄	semidirect
23. C₅×#405	C₄	semidirect
42. #20439	C₅	direct (N × H)
81. C₅×C₄⋊C₈	C₂×C₄	semidirect
82. C₅×C₄⋊C₈	C₂×C₄	semidirect
85. C₅×#97	C₂×C₄	semidirect
88. C₄×C₅×C₈	C₂×C₄	semidirect
96. #1771	C₂×C₅	semidirect
97. #1771	C₂×C₅	semidirect
98. #1770	C₂×C₅	semidirect
99. C₈×C₄⋊C₄	C₂×C₅	semidirect
120. C₅×M₁₆	C₄⋊C₄	semidirect
164. #424	C₄×C₅	semidirect
168. #405	C₄×C₅	semidirect
264. C₄⋊C₈	C₂×C₄×C₅	semidirect
265. C₄⋊C₈	C₂×C₄×C₅	semidirect
268. #97	C₂×C₄×C₅	semidirect
271. C₄×C₈	C₂×C₄×C₅	semidirect
312. M₁₆	C₅×C₄⋊C₄	semidirect
394. C₅	#20439	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×#424	2
C₂×C₅×#405	2
C₂×C₄×C₅×M₁₆	2
C₅×#2296	2
C₅×#1771	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₅×#1729	2
C₂×C₅×#336	2
#20439	5

Subgroups — C5×#20439 #11943159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20439 #11943159