Subgroups — C₅×#22704 #11945424

Order 1280.

938 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#2352	C₂	1	2	yes	maximal
3	C₅×#1949	C₂	1	2	yes	maximal, complemented
4	C₅×#1854	C₂	1	2	yes	maximal, complemented
5	C₅×#1852	C₂	1	2	yes	maximal, complemented
6	C₅×#1835	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1735	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	2	yes	—
16	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₅×C₈×D₄	C₄	1	8	yes	complemented
18	C₂×C₅×#107	C₂²	1	2	yes	—
19	C₂×C₅×#107	C₂²	1	2	yes	—
20	C₂×C₅×#106	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#388	—	2	2	no	—
26	C₅×#387	—	2	2	no	—
27	C₅×#386	—	2	2	no	—
28	C₅×#382	C₂²	1	2	yes	—
29	C₅×#380	C₂²	1	2	yes	—
30	C₅×#380	C₂²	1	2	yes	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
33	C₅×#340	C₂²	1	1	yes	characteristic
34	C₅×#340	C₂²	1	1	yes	characteristic
35	C₅×#340	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	#22704	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	—	2	2	no	—
43	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	—	4	2	no	—
46	C₂²×C₅×C₈	—	4	2	no	—
47	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
48	C₂²×C₅×C₈	C₂×C₄	1	4	yes	complemented
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
54	C₄×C₅×D₄	Q₈	1	4	yes	—
55	C₅×#117	—	2	4	no	—
56	C₅×#117	—	4	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	4	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	—	4	2	no	—
60	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#107	—	2	4	no	—
74	C₅×#107	—	4	2	no	—
75	C₅×#106	—	4	2	no	—
76	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
77	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
78	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
79	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
86	#2352	C₂×C₅	1	2	yes	—
87	#1949	C₂×C₅	1	2	yes	complemented
88	#1854	C₂×C₅	1	2	yes	complemented
89	#1852	C₂×C₅	1	2	yes	complemented
90	#1835	C₂×C₅	1	1	yes	characteristic, complemented
91	#1808	C₂×C₅	1	1	yes	characteristic, complemented
92	#1807	C₂×C₅	1	1	yes	characteristic, complemented
93	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
94	#1735	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#340	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₅×D₄	—	2	4	no	—
99	C₂×C₅×D₄	C₄⋊C₄	1	4	yes	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	4	4	no	—
109	C₂²×C₄×C₅	—	4	4	no	—
110	C₂²×C₄×C₅	—	8	2	no	—
111	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
124	C₂×C₅×C₈	—	4	4	no	—
125	C₂×C₅×C₈	—	4	4	no	—
126	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
128	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	4	4	no	—
138	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
139	C₅×C₄⋊C₄	#41	1	4	yes	—
140	C₅×C₂²⋊C₄	—	4	4	no	—
141	C₅×C₂²⋊C₄	—	4	4	no	—
142	C₅×C₂²⋊C₄	—	8	2	no	—
143	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
144	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
145	C₄²×C₅	—	4	4	no	—
146	C₄²×C₅	—	8	2	no	—
147	C₄²×C₅	C₂²×C₄	1	2	yes	—
148	C₄²×C₅	C₂×Q₈	1	2	yes	—
149	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
150	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×#117	C₂²×C₅	1	2	yes	—
153	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
154	C₈×D₄	C₄×C₅	1	8	yes	complemented
155	C₂×#107	C₂²×C₅	1	2	yes	—
156	C₂×#107	C₂²×C₅	1	2	yes	—
157	C₂×#106	C₂²×C₅	1	2	yes	—
158	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
162	#388	—	2	2	no	—
163	#387	—	2	2	no	—
164	#386	—	2	2	no	—
165	#382	C₂²×C₅	1	2	yes	—
166	#380	C₂²×C₅	1	2	yes	—
167	#380	C₂²×C₅	1	2	yes	—
168	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
169	C₄×C₂²⋊C₄	—	2	2	no	—
170	#340	C₂²×C₅	1	1	yes	characteristic
171	#340	C₂²×C₅	1	1	yes	characteristic
172	#340	C₂²×C₅	1	1	yes	characteristic
173	#340	C₂²×C₅	1	2	yes	—
174	#340	C₂²×C₅	1	2	yes	—
175	#340	C₂²×C₅	1	2	yes	—
176	#340	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₅	—	2	2	no	—
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	—	2	1	no	—
183	C₂³×C₅	—	2	1	no	—
184	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
185	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
186	C₂³×C₅	#135	1	4	yes	—
187	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₅×D₄	—	2	8	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	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	2	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	4	no	—
201	C₂×C₄×C₅	—	4	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	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	8	8	no	—
213	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
214	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#41	1	2	yes	—
220	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	2	2	no	—
225	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₈	—	4	2	no	—
230	C₂²×C₈	—	4	2	no	—
231	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
232	C₂²×C₈	C₂×C₄×C₅	1	4	yes	complemented
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
237	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
238	C₄×D₄	C₅×Q₈	1	4	yes	—
239	#117	—	2	4	no	—
240	#117	—	4	2	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	4	2	no	—
244	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#107	—	2	4	no	—
258	#107	—	4	2	no	—
259	#106	—	4	2	no	—
260	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
261	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
262	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
263	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	4	no	—
272	C₂²×C₅	—	2	4	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	#427	1	4	yes	—
279	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
280	C₂²×C₅	#546	1	2	yes	—
281	C₂²×C₅	C₂×#135	1	2	yes	—
282	C₂²×C₅	#576	1	1	yes	characteristic
283	C₂²×C₅	#578	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	4	4	no	—
289	C₄×C₅	—	8	2	no	—
290	C₄×C₅	—	8	2	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	C₄×#41	1	1	yes	characteristic
293	C₄×C₅	#518	1	1	yes	characteristic
294	C₄×C₅	#554	1	2	yes	—
295	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	C₅×C₄⋊C₄	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
317	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	—	4	4	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	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
338	C₄⋊C₄	C₅×#41	1	4	yes	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
343	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
344	C₄²	—	4	4	no	—
345	C₄²	—	8	2	no	—
346	C₄²	C₂²×C₄×C₅	1	2	yes	—
347	C₄²	C₂×C₅×Q₈	1	2	yes	—
348	C₂×C₅	—	2	4	no	—
349	C₂×C₅	—	4	2	no	—
350	C₂×C₅	#2349	1	1	yes	characteristic
351	C₂×C₅	C₂×#427	1	1	yes	characteristic
352	C₂×C₅	#2913	1	1	yes	characteristic
353	C₂×C₅	#3297	1	2	yes	—
354	C₂×C₅	#3300	1	2	yes	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
363	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
364	C₂³	C₅×#135	1	4	yes	—
365	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
366	D₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	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	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	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	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	8	no	—
391	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
392	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
393	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
394	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
397	C₂×C₄	C₂×C₅×#41	1	2	yes	—
398	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
399	C₈	—	2	2	no	—
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₅	#22704	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₅×#427	1	4	yes	—
414	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
415	C₂²	C₅×#546	1	2	yes	—
416	C₂²	C₂×C₅×#135	1	2	yes	—
417	C₂²	C₅×#576	1	1	yes	characteristic
418	C₂²	C₅×#578	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	2	no	—
427	C₄	C₄×C₅×#41	1	1	yes	characteristic
428	C₄	C₅×#518	1	1	yes	characteristic
429	C₄	C₅×#554	1	2	yes	—
430	C₂	—	2	4	no	—
431	C₂	—	4	2	no	—
432	C₂	C₅×#2349	1	1	yes	characteristic
433	C₂	C₂×C₅×#427	1	1	yes	characteristic
434	C₂	C₅×#2913	1	1	yes	characteristic
435	C₂	C₅×#3297	1	2	yes	—
436	C₂	C₅×#3300	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₅×#1949	C₂	semidirect
4. C₅×#1854	C₂	semidirect
5. C₅×#1852	C₂	semidirect
6. C₅×#1835	C₂	semidirect
7. C₅×#1808	C₂	semidirect
8. C₅×#1807	C₂	semidirect
9. C₄×C₅×#107	C₂	semidirect
10. C₅×#1735	C₂	semidirect
11. C₂×C₅×#340	C₂	semidirect
17. C₅×C₈×D₄	C₄	semidirect
40. #22704	C₅	direct (N × H)
48. C₂²×C₅×C₈	C₂×C₄	semidirect
76. C₅×C₄⋊C₈	C₂×C₄	semidirect
78. C₅×C₂²⋊C₈	C₂×C₄	semidirect
79. C₄×C₅×C₈	C₂×C₄	semidirect
87. #1949	C₂×C₅	semidirect
88. #1854	C₂×C₅	semidirect
89. #1852	C₂×C₅	semidirect
90. #1835	C₂×C₅	semidirect
91. #1808	C₂×C₅	semidirect
92. #1807	C₂×C₅	semidirect
93. C₄×#107	C₂×C₅	semidirect
94. #1735	C₂×C₅	semidirect
95. C₂×#340	C₂×C₅	semidirect
154. C₈×D₄	C₄×C₅	semidirect
232. C₂²×C₈	C₂×C₄×C₅	semidirect
260. C₄⋊C₈	C₂×C₄×C₅	semidirect
262. C₂²⋊C₈	C₂×C₄×C₅	semidirect
263. C₄×C₈	C₂×C₄×C₅	semidirect
403. C₅	#22704	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×C₈×D₄	2
C₅×#2352	2
C₅×#1949	2
C₅×#1854	2
C₅×#1852	2
C₅×#1835	2
C₅×#1808	2
C₅×#1807	2
C₄×C₅×#107	2
C₅×#1735	2
C₂×C₅×#340	2
#22704	5

Subgroups — C5×#22704 #11945424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22704 #11945424