Subgroups — C₅×#22317 #11945037

Order 1280.

758 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#1984	C₂	1	2	yes	maximal, complemented
3	C₅×#1923	C₂	1	2	yes	maximal
4	C₅×#1923	C₂	1	2	yes	maximal
5	C₅×#1916	C₂	1	2	yes	maximal, complemented
6	C₅×#1916	C₂	1	2	yes	maximal, complemented
7	C₅×#1817	C₂	1	1	yes	maximal, characteristic
8	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×#391	C₄	1	1	yes	characteristic
23	C₅×#389	C₄	1	1	yes	characteristic
24	C₅×#387	C₄	1	2	yes	—
25	C₅×#385	C₄	1	2	yes	—
26	C₅×#380	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	#22317	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₅×C₂²⋊Q₈	C₈	1	8	yes	complemented
47	C₄×C₅×Q₈	—	4	1	no	—
48	C₄×C₅×Q₈	—	4	1	no	—
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
55	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₅	—	4	1	no	—
58	C₂×C₄²×C₅	—	4	1	no	—
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	2	yes	—
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊C₈	—	2	4	no	—
66	C₅×C₄⋊C₈	—	4	2	no	—
67	C₅×C₂²⋊C₈	—	2	4	no	—
68	C₅×C₂²⋊C₈	—	4	1	no	—
69	C₅×C₂²⋊C₈	—	4	1	no	—
70	C₄×C₅×C₈	—	2	4	no	—
71	C₄×C₅×C₈	—	4	1	no	—
72	C₄×C₅×C₈	—	4	1	no	—
73	C₄×C₅×C₈	—	4	2	no	—
74	C₅×#95	C₂×C₄	1	2	yes	—
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×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
80	#1984	C₂×C₅	1	2	yes	complemented
81	#1923	C₂×C₅	1	2	yes	—
82	#1923	C₂×C₅	1	2	yes	—
83	#1916	C₂×C₅	1	2	yes	complemented
84	#1916	C₂×C₅	1	2	yes	complemented
85	#1817	C₂×C₅	1	1	yes	characteristic
86	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
87	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
88	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₅×Q₈	—	4	1	no	—
90	C₂×C₅×Q₈	—	4	1	no	—
91	C₂×C₅×Q₈	C₂×C₈	1	4	yes	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	1	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	4	1	no	—
98	C₂²×C₄×C₅	—	4	1	no	—
99	C₂²×C₄×C₅	—	4	1	no	—
100	C₂²×C₄×C₅	—	4	1	no	—
101	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
109	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
125	C₅×C₄⋊C₄	—	4	1	no	—
126	C₅×C₄⋊C₄	—	4	1	no	—
127	C₅×C₄⋊C₄	—	4	2	no	—
128	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
129	C₅×C₄⋊C₄	C₂×C₈	1	8	yes	—
130	C₅×C₂²⋊C₄	—	4	2	no	—
131	C₅×C₂²⋊C₄	C₂×C₈	1	8	yes	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	1	no	—
135	C₄²×C₅	—	2	1	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	4	1	no	—
141	C₄²×C₅	—	4	1	no	—
142	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
143	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
146	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
147	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
151	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
153	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
154	#391	C₄×C₅	1	1	yes	characteristic
155	#389	C₄×C₅	1	1	yes	characteristic
156	#387	C₄×C₅	1	2	yes	—
157	#385	C₄×C₅	1	2	yes	—
158	#380	C₄×C₅	1	1	yes	characteristic
159	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
161	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
162	#336	C₂²×C₅	1	2	yes	—
163	#336	C₂²×C₅	1	2	yes	—
164	#336	C₂²×C₅	1	2	yes	—
165	#336	C₂²×C₅	1	2	yes	—
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	1	no	—
170	C₂³×C₅	—	2	1	no	—
171	C₂³×C₅	—	2	1	no	—
172	C₂³×C₅	—	2	1	no	—
173	C₂³×C₅	—	2	1	no	—
174	C₂³×C₅	—	2	1	no	—
175	C₂³×C₅	C₂²×C₈	1	2	yes	—
176	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₅×Q₈	—	4	4	no	—
178	C₂×C₄×C₅	—	2	2	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	2	no	—
183	C₂×C₄×C₅	—	2	2	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	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	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	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	4	4	no	—
201	C₂×C₄×C₅	—	4	4	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
205	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
206	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
207	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
208	C₂×C₄×C₅	#131	1	2	yes	—
209	C₂×C₄×C₅	C₂×#41	1	2	yes	—
210	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
213	C₅×C₈	—	2	4	no	—
214	C₅×C₈	—	4	2	no	—
215	C₅×C₈	—	4	2	no	—
216	C₅×C₈	—	4	2	no	—
217	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	2	yes	—
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₈	C₂³×C₅	1	2	yes	—
224	C₂²×C₈	C₂³×C₅	1	2	yes	—
225	C₂²⋊Q₈	C₅×C₈	1	8	yes	complemented
226	C₄×Q₈	—	4	1	no	—
227	C₄×Q₈	—	4	1	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₄²	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₅	1	2	yes	—
242	C₂×C₄²	C₂³×C₅	1	2	yes	—
243	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
244	C₄⋊C₈	—	2	4	no	—
245	C₄⋊C₈	—	4	2	no	—
246	C₂²⋊C₈	—	2	4	no	—
247	C₂²⋊C₈	—	4	1	no	—
248	C₂²⋊C₈	—	4	1	no	—
249	C₄×C₈	—	2	4	no	—
250	C₄×C₈	—	4	1	no	—
251	C₄×C₈	—	4	1	no	—
252	C₄×C₈	—	4	2	no	—
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	#95	C₂×C₄×C₅	1	2	yes	—
257	#95	C₂×C₄×C₅	1	2	yes	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	2	2	no	—
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	4	1	no	—
263	C₂²×C₅	—	4	1	no	—
264	C₂²×C₅	—	4	1	no	—
265	C₂²×C₅	C₄×#41	1	1	yes	characteristic
266	C₂²×C₅	#518	1	1	yes	characteristic
267	C₂²×C₅	#519	1	1	yes	characteristic
268	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
269	C₂²×C₅	C₂×#131	1	1	yes	characteristic
270	C₂²×C₅	#568	1	1	yes	characteristic
271	C₂²×C₅	#568	1	1	yes	characteristic
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	2	4	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	4	1	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	1	no	—
281	C₄×C₅	#539	1	2	yes	—
282	C₄×C₅	#542	1	2	yes	—
283	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	C₂×C₅×C₈	1	4	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
297	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
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	C₂×C₈	—	2	2	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	C₅×#41	1	4	yes	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
324	C₄⋊C₄	C₂×C₅×C₈	1	8	yes	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	C₂×C₅×C₈	1	8	yes	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₂×C₅	—	4	2	no	—
338	C₂×C₅	#2332	1	1	yes	characteristic
339	C₂×C₅	C₈×#41	1	1	yes	characteristic
340	C₂×C₅	#2967	1	1	yes	characteristic
341	C₂×C₅	#2972	1	1	yes	characteristic
342	C₂×C₅	#2976	1	1	yes	characteristic
343	C₂×C₅	#2982	1	1	yes	characteristic
344	C₂×C₅	#2985	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	C₂²×C₅×C₈	1	2	yes	—
352	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
353	Q₈	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
381	C₂×C₄	C₂²×C₅×C₈	1	4	yes	—
382	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
383	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
384	C₂×C₄	C₅×#131	1	2	yes	—
385	C₂×C₄	C₂×C₅×#41	1	2	yes	—
386	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
389	C₈	—	2	4	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	2	no	—
393	C₅	#22317	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₄×C₅×#41	1	1	yes	characteristic
402	C₂²	C₅×#518	1	1	yes	characteristic
403	C₂²	C₅×#519	1	1	yes	characteristic
404	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
405	C₂²	C₂×C₅×#131	1	1	yes	characteristic
406	C₂²	C₅×#568	1	1	yes	characteristic
407	C₂²	C₅×#568	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	2	no	—
417	C₄	C₅×#539	1	2	yes	—
418	C₄	C₅×#542	1	2	yes	—
419	C₂	—	4	2	no	—
420	C₂	C₅×#2332	1	1	yes	characteristic
421	C₂	C₅×C₈×#41	1	1	yes	characteristic
422	C₂	C₅×#2967	1	1	yes	characteristic
423	C₂	C₅×#2972	1	1	yes	characteristic
424	C₂	C₅×#2976	1	1	yes	characteristic
425	C₂	C₅×#2982	1	1	yes	characteristic
426	C₂	C₅×#2985	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
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
2. C₅×#1984	C₂	semidirect
5. C₅×#1916	C₂	semidirect
6. C₅×#1916	C₂	semidirect
8. C₅×C₈×C₄⋊C₄	C₂	semidirect
37. #22317	C₅	direct (N × H)
46. C₅×C₂²⋊Q₈	C₈	semidirect
80. #1984	C₂×C₅	semidirect
83. #1916	C₂×C₅	semidirect
84. #1916	C₂×C₅	semidirect
86. C₈×C₄⋊C₄	C₂×C₅	semidirect
225. C₂²⋊Q₈	C₅×C₈	semidirect
393. C₅	#22317	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×C₂²⋊Q₈	2
C₅×#1984	2
C₅×#1923	2
C₅×#1916	2
C₅×#1817	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×C₂²⋊C₈	2
#22317	5

Subgroups — C5×#22317 #11945037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22317 #11945037