Subgroups — C₅×#22301 #11945021

Order 1280.

654 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₅×#1940	C₂	1	2	yes	maximal
3	C₅×#1939	C₂	1	1	yes	maximal, characteristic
4	C₅×#1939	C₂	1	1	yes	maximal, characteristic
5	C₅×#1939	C₂	1	2	yes	maximal
6	C₅×#1917	C₂	1	2	yes	maximal
7	C₅×#1916	C₂	1	2	yes	maximal
8	C₅×#1842	C₂	1	1	yes	maximal, characteristic
9	C₅×#1770	C₂	1	1	yes	maximal, characteristic
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₅×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#125	C₄	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×#389	C₄	1	1	yes	characteristic
24	C₅×#389	C₄	1	1	yes	characteristic
25	C₅×#387	C₄	1	2	yes	—
26	C₅×#387	C₄	1	2	yes	—
27	C₅×#382	C₄	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	1	yes	characteristic
36	C₅×#336	C₂²	1	2	yes	—
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	#22301	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₅×#125	—	2	4	no	—
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂³	1	2	yes	—
64	C₂×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×C₄⋊C₈	—	2	2	no	—
67	C₅×C₄⋊C₈	—	2	2	no	—
68	C₅×C₄⋊C₈	—	4	2	no	—
69	C₅×C₄⋊C₈	—	4	2	no	—
70	C₅×C₄⋊C₈	—	4	2	no	—
71	C₅×C₄⋊C₈	—	4	2	no	—
72	C₅×#97	—	4	2	no	—
73	C₄×C₅×C₈	—	2	2	no	—
74	C₄×C₅×C₈	—	4	2	no	—
75	C₄×C₅×C₈	Q₈	1	4	yes	—
76	C₅×#95	C₂×C₄	1	2	yes	—
77	C₅×#95	C₂×C₄	1	2	yes	—
78	C₅×#95	C₂×C₄	1	2	yes	—
79	C₅×#95	C₂×C₄	1	2	yes	—
80	C₅×#95	C₂×C₄	1	2	yes	—
81	C₅×#95	C₂×C₄	1	2	yes	—
82	C₄×#125	C₂×C₅	1	1	yes	characteristic
83	#1940	C₂×C₅	1	2	yes	—
84	#1939	C₂×C₅	1	1	yes	characteristic
85	#1939	C₂×C₅	1	1	yes	characteristic
86	#1939	C₂×C₅	1	2	yes	—
87	#1917	C₂×C₅	1	2	yes	—
88	#1916	C₂×C₅	1	2	yes	—
89	#1842	C₂×C₅	1	1	yes	characteristic
90	#1770	C₂×C₅	1	1	yes	characteristic
91	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
92	#1744	C₂×C₅	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₂×C₅×C₈	—	2	1	no	—
105	C₂×C₅×C₈	—	2	1	no	—
106	C₂×C₅×C₈	—	2	1	no	—
107	C₂×C₅×C₈	—	2	1	no	—
108	C₂×C₅×C₈	—	2	1	no	—
109	C₂×C₅×C₈	—	2	1	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	1	no	—
120	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
121	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
122	C₅×C₄⋊C₄	—	2	4	no	—
123	C₅×C₄⋊C₄	—	2	4	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	C₂×Q₈	1	2	yes	—
143	C₄²×C₅	#41	1	2	yes	—
144	C₂×#125	C₄×C₅	1	1	yes	characteristic
145	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
148	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
149	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₂×#97	C₂²×C₅	1	2	yes	—
152	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
154	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
155	#389	C₄×C₅	1	1	yes	characteristic
156	#389	C₄×C₅	1	1	yes	characteristic
157	#387	C₄×C₅	1	2	yes	—
158	#387	C₄×C₅	1	2	yes	—
159	#382	C₄×C₅	1	1	yes	characteristic
160	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
161	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
162	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₄³	C₂²×C₅	1	1	yes	characteristic
165	#336	C₂²×C₅	1	1	yes	characteristic
166	#336	C₂²×C₅	1	2	yes	—
167	#336	C₂²×C₅	1	2	yes	—
168	#336	C₂²×C₅	1	2	yes	—
169	#336	C₂²×C₅	1	1	yes	characteristic
170	#336	C₂²×C₅	1	2	yes	—
171	#336	C₂²×C₅	1	1	yes	characteristic
172	#336	C₂²×C₅	1	1	yes	characteristic
173	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
198	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
199	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
200	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₅	#131	1	2	yes	—
202	C₂×C₄×C₅	#131	1	2	yes	—
203	C₂×C₄×C₅	#131	1	2	yes	—
204	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
209	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
210	C₅×C₈	—	2	2	no	—
211	C₅×C₈	—	2	2	no	—
212	C₅×C₈	—	4	1	no	—
213	C₅×C₈	—	4	2	no	—
214	C₅×C₈	—	4	2	no	—
215	C₅×C₈	—	4	1	no	—
216	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₅	1	2	yes	—
219	C₂²×C₈	C₂³×C₅	1	2	yes	—
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
222	#125	—	2	4	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₅	1	2	yes	—
238	C₂×C₄²	C₂³×C₅	1	2	yes	—
239	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	4	2	no	—
243	C₄⋊C₈	—	4	2	no	—
244	C₄⋊C₈	—	4	2	no	—
245	C₄⋊C₈	—	4	2	no	—
246	#97	—	4	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	4	2	no	—
249	C₄×C₈	C₅×Q₈	1	4	yes	—
250	#95	C₂×C₄×C₅	1	2	yes	—
251	#95	C₂×C₄×C₅	1	2	yes	—
252	#95	C₂×C₄×C₅	1	2	yes	—
253	#95	C₂×C₄×C₅	1	2	yes	—
254	#95	C₂×C₄×C₅	1	2	yes	—
255	#95	C₂×C₄×C₅	1	2	yes	—
256	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
257	C₂²×C₅	#520	1	1	yes	characteristic
258	C₂²×C₅	#520	1	1	yes	characteristic
259	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
260	C₂²×C₅	C₂×#131	1	1	yes	characteristic
261	C₂²×C₅	C₂×#131	1	1	yes	characteristic
262	C₂²×C₅	C₂×#131	1	1	yes	characteristic
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	4	no	—
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	4	1	no	—
268	C₄×C₅	—	4	1	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	#446	1	4	yes	—
273	C₄×C₅	#540	1	1	yes	characteristic
274	C₄×C₅	#541	1	1	yes	characteristic
275	C₄×C₅	#544	1	1	yes	characteristic
276	C₄×C₅	#544	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
305	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂×C₅×Q₈	1	2	yes	—
327	C₄²	C₅×#41	1	2	yes	—
328	C₂×C₅	#2330	1	1	yes	characteristic
329	C₂×C₅	C₂×#446	1	1	yes	characteristic
330	C₂×C₅	#2960	1	1	yes	characteristic
331	C₂×C₅	#2990	1	1	yes	characteristic
332	C₂×C₅	#2991	1	1	yes	characteristic
333	C₂×C₅	#2994	1	1	yes	characteristic
334	C₂×C₅	#2994	1	1	yes	characteristic
335	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
360	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
361	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
362	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
363	C₂×C₄	C₅×#131	1	2	yes	—
364	C₂×C₄	C₅×#131	1	2	yes	—
365	C₂×C₄	C₅×#131	1	2	yes	—
366	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
368	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
371	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	2	2	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₅	#22301	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
380	C₂²	C₅×#520	1	1	yes	characteristic
381	C₂²	C₅×#520	1	1	yes	characteristic
382	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
383	C₂²	C₂×C₅×#131	1	1	yes	characteristic
384	C₂²	C₂×C₅×#131	1	1	yes	characteristic
385	C₂²	C₂×C₅×#131	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	C₅×#446	1	4	yes	—
396	C₄	C₅×#540	1	1	yes	characteristic
397	C₄	C₅×#541	1	1	yes	characteristic
398	C₄	C₅×#544	1	1	yes	characteristic
399	C₄	C₅×#544	1	1	yes	characteristic
400	C₂	C₅×#2330	1	1	yes	characteristic
401	C₂	C₂×C₅×#446	1	1	yes	characteristic
402	C₂	C₅×#2960	1	1	yes	characteristic
403	C₂	C₅×#2990	1	1	yes	characteristic
404	C₂	C₅×#2991	1	1	yes	characteristic
405	C₂	C₅×#2994	1	1	yes	characteristic
406	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, prime radical	C₂³×C₅	C₂³×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
41. #22301	C₅	direct (N × H)
378. C₅	#22301	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#125	2
C₅×#1940	2
C₅×#1939	2
C₅×#1917	2
C₅×#1916	2
C₅×#1842	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₅×#1744	2
#22301	5

Subgroups — C5×#22301 #11945021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22301 #11945021