Subgroups — C₅×#22393 #11945113

Order 1280.

762 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₅×#1985	C₂	1	2	yes	maximal, complemented
3	C₅×#1924	C₂	1	2	yes	maximal, complemented
4	C₅×#1923	C₂	1	2	yes	maximal, complemented
5	C₅×#1870	C₂	1	2	yes	maximal
6	C₅×#1851	C₂	1	2	yes	maximal, complemented
7	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1753	C₂	1	2	yes	maximal, complemented
10	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
11	C₂×C₅×#124	C₄	1	1	yes	characteristic
12	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊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	1	yes	characteristic
22	C₅×#391	C₄	1	1	yes	characteristic
23	C₅×#390	C₄	1	1	yes	characteristic
24	C₅×#388	C₄	1	2	yes	—
25	C₅×#388	C₄	1	2	yes	—
26	C₅×#382	C₄	1	1	yes	characteristic
27	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₅	C₂²	1	1	yes	characteristic
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	1	yes	characteristic
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	1	yes	characteristic
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	#22393	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂³	1	2	yes	—
41	C₂×C₅×M₁₆	—	2	4	no	—
42	C₂×C₅×M₁₆	—	4	2	no	—
43	C₂×C₅×M₁₆	—	4	2	no	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×#124	—	2	4	no	—
49	C₄×C₅×Q₈	—	4	2	no	—
50	C₄×C₅×D₄	—	4	2	no	—
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	2	yes	—
67	C₅×C₄⋊C₈	—	2	4	no	—
68	C₅×C₄⋊C₈	—	4	2	no	—
69	C₅×C₂²⋊C₈	—	2	4	no	—
70	C₅×C₂²⋊C₈	—	4	2	no	—
71	C₅×C₂²⋊C₈	—	4	2	no	—
72	C₅×#97	—	4	2	no	—
73	C₄×C₅×C₈	—	4	1	no	—
74	C₄×C₅×C₈	—	4	1	no	—
75	C₅×#95	C₂×C₄	1	2	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	C₄×#124	C₂×C₅	1	1	yes	characteristic
80	#1985	C₂×C₅	1	2	yes	complemented
81	#1924	C₂×C₅	1	2	yes	complemented
82	#1923	C₂×C₅	1	2	yes	complemented
83	#1870	C₂×C₅	1	2	yes	—
84	#1851	C₂×C₅	1	2	yes	complemented
85	#1839	C₂×C₅	1	1	yes	characteristic, complemented
86	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
87	#1753	C₂×C₅	1	2	yes	complemented
88	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₅×Q₈	—	2	2	no	—
90	C₂×C₅×Q₈	—	4	1	no	—
91	C₂×C₅×Q₈	—	4	1	no	—
92	C₂×C₅×D₄	—	2	2	no	—
93	C₂×C₅×D₄	—	4	1	no	—
94	C₂×C₅×D₄	—	4	1	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₅×M₁₆	—	4	8	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	#41	1	4	yes	—
124	C₅×C₄⋊C₄	—	4	1	no	—
125	C₅×C₄⋊C₄	—	4	1	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	2	4	no	—
128	C₅×C₂²⋊C₄	—	2	4	no	—
129	C₅×C₂²⋊C₄	—	2	4	no	—
130	C₅×C₂²⋊C₄	—	4	2	no	—
131	C₅×C₂²⋊C₄	—	4	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	2	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	4	1	no	—
140	C₄²×C₅	—	4	1	no	—
141	C₄²×C₅	M₁₆	1	4	yes	complemented
142	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
143	C₂×#124	C₄×C₅	1	1	yes	characteristic
144	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
147	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
149	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×C₂²⋊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	1	yes	characteristic
154	#391	C₄×C₅	1	1	yes	characteristic
155	#390	C₄×C₅	1	1	yes	characteristic
156	#388	C₄×C₅	1	2	yes	—
157	#388	C₄×C₅	1	2	yes	—
158	#382	C₄×C₅	1	1	yes	characteristic
159	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
160	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
161	C₄³	C₂²×C₅	1	1	yes	characteristic
162	#336	C₂²×C₅	1	1	yes	characteristic
163	#336	C₂²×C₅	1	2	yes	—
164	#336	C₂²×C₅	1	2	yes	—
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	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	2	2	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₅×Q₈	—	4	4	no	—
178	C₅×D₄	—	4	4	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	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	1	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
207	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
208	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
209	C₂×C₄×C₅	#131	1	2	yes	—
210	C₂×C₄×C₅	C₂×#41	1	2	yes	—
211	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
214	C₅×C₈	—	2	4	no	—
215	C₅×C₈	—	4	2	no	—
216	C₅×C₈	—	4	2	no	—
217	C₅×C₈	—	4	2	no	—
218	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₅	1	2	yes	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	4	2	no	—
223	C₂×M₁₆	—	4	2	no	—
224	C₂²×C₈	C₂³×C₅	1	2	yes	—
225	C₂²×C₈	C₂³×C₅	1	2	yes	—
226	C₂²×C₈	C₂³×C₅	1	2	yes	—
227	C₂²×C₈	C₂³×C₅	1	2	yes	—
228	#124	—	2	4	no	—
229	C₄×Q₈	—	4	2	no	—
230	C₄×D₄	—	4	2	no	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
239	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₅	1	2	yes	—
245	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
247	C₄⋊C₈	—	2	4	no	—
248	C₄⋊C₈	—	4	2	no	—
249	C₂²⋊C₈	—	2	4	no	—
250	C₂²⋊C₈	—	4	2	no	—
251	C₂²⋊C₈	—	4	2	no	—
252	#97	—	4	2	no	—
253	C₄×C₈	—	4	1	no	—
254	C₄×C₈	—	4	1	no	—
255	#95	C₂×C₄×C₅	1	2	yes	—
256	#95	C₂×C₄×C₅	1	2	yes	—
257	#95	C₂×C₄×C₅	1	2	yes	—
258	#95	C₂×C₄×C₅	1	2	yes	—
259	C₂²×C₅	—	4	2	no	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	—	4	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	C₄×#41	1	1	yes	characteristic
267	C₂²×C₅	#518	1	1	yes	characteristic
268	C₂²×C₅	#520	1	1	yes	characteristic
269	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
270	C₂²×C₅	C₂×#131	1	1	yes	characteristic
271	C₂²×C₅	#568	1	1	yes	characteristic
272	C₂²×C₅	#568	1	1	yes	characteristic
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	1	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	1	no	—
281	C₄×C₅	—	4	2	no	—
282	C₄×C₅	#538	1	2	yes	—
283	C₄×C₅	#542	1	2	yes	—
284	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
307	M₁₆	—	4	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	C₅×#41	1	4	yes	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₅×M₁₆	1	4	yes	complemented
338	C₂×C₅	—	8	2	no	—
339	C₂×C₅	#2337	1	1	yes	characteristic
340	C₂×C₅	#2965	1	1	yes	characteristic
341	C₂×C₅	#2967	1	1	yes	characteristic
342	C₂×C₅	#2975	1	1	yes	characteristic
343	C₂×C₅	#2981	1	1	yes	characteristic
344	C₂×C₅	#2989	1	1	yes	characteristic
345	C₂×C₅	#2992	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
354	Q₈	—	4	4	no	—
355	D₄	—	4	4	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
384	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
385	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
386	C₂×C₄	C₅×#131	1	2	yes	—
387	C₂×C₄	C₂×C₅×#41	1	2	yes	—
388	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₅	#22393	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	C₄×C₅×#41	1	1	yes	characteristic
404	C₂²	C₅×#518	1	1	yes	characteristic
405	C₂²	C₅×#520	1	1	yes	characteristic
406	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
407	C₂²	C₂×C₅×#131	1	1	yes	characteristic
408	C₂²	C₅×#568	1	1	yes	characteristic
409	C₂²	C₅×#568	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	C₅×#538	1	2	yes	—
420	C₄	C₅×#542	1	2	yes	—
421	C₂	—	8	2	no	—
422	C₂	C₅×#2337	1	1	yes	characteristic
423	C₂	C₅×#2965	1	1	yes	characteristic
424	C₂	C₅×#2967	1	1	yes	characteristic
425	C₂	C₅×#2975	1	1	yes	characteristic
426	C₂	C₅×#2981	1	1	yes	characteristic
427	C₂	C₅×#2989	1	1	yes	characteristic
428	C₂	C₅×#2992	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
2. C₅×#1985	C₂	semidirect
3. C₅×#1924	C₂	semidirect
4. C₅×#1923	C₂	semidirect
6. C₅×#1851	C₂	semidirect
7. C₅×#1839	C₂	semidirect
8. C₄×C₅×C₄⋊C₈	C₂	semidirect
9. C₅×#1753	C₂	semidirect
37. #22393	C₅	direct (N × H)
80. #1985	C₂×C₅	semidirect
81. #1924	C₂×C₅	semidirect
82. #1923	C₂×C₅	semidirect
84. #1851	C₂×C₅	semidirect
85. #1839	C₂×C₅	semidirect
86. C₄×C₄⋊C₈	C₂×C₅	semidirect
87. #1753	C₂×C₅	semidirect
141. C₄²×C₅	M₁₆	semidirect
337. C₄²	C₅×M₁₆	semidirect
395. C₅	#22393	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×#124	2
C₅×#1985	2
C₅×#1924	2
C₅×#1923	2
C₅×#1870	2
C₅×#1851	2
C₅×#1839	2
C₄×C₅×C₄⋊C₈	2
C₅×#1753	2
#22393	5

Subgroups — C5×#22393 #11945113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22393 #11945113