Subgroups — C₅×#22963 #11945683

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#476	C₂	1	1	yes	maximal, characteristic
2	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1941	C₂	1	2	yes	maximal, complemented
7	C₅×#1919	C₂	1	2	yes	maximal, complemented
8	C₅×#1864	C₂	1	2	yes	maximal
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#102	C₂	1	2	yes	maximal
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
16	C₅×#476	C₄	1	8	yes	complemented
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#102	C₂²	1	1	yes	characteristic
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#102	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₅×#391	—	2	2	no	—
26	C₅×#389	—	2	1	no	—
27	C₅×#389	C₂²	1	2	yes	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#385	—	2	2	no	—
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₅×#380	—	2	1	no	—
32	C₄×C₅×C₄⋊C₄	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	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	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#22963	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂³×C₄×C₅	—	2	2	no	—
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	—	2	2	no	—
51	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
52	C₄×C₅×D₄	—	2	4	no	—
53	C₄×C₅×D₄	—	2	2	no	—
54	C₄×C₅×D₄	—	4	2	no	—
55	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	—	4	4	no	—
62	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	C₂³	1	2	yes	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#106	—	4	2	no	—
76	C₅×#106	C₂×C₄	1	8	yes	complemented
77	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
78	C₅×#102	—	2	2	no	—
79	C₅×#102	C₂×C₄	1	8	yes	—
80	C₅×#102	Q₈	1	4	yes	complemented
81	C₄×C₅×C₈	—	2	2	no	—
82	C₄×C₅×C₈	—	4	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	1	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	D₄	1	2	yes	—
88	C₂×#476	C₂×C₅	1	1	yes	characteristic
89	#2369	C₂×C₅	1	1	yes	characteristic, complemented
90	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
91	#1990	C₂×C₅	1	1	yes	characteristic, complemented
92	#1948	C₂×C₅	1	1	yes	characteristic, complemented
93	#1941	C₂×C₅	1	2	yes	complemented
94	#1919	C₂×C₅	1	2	yes	complemented
95	#1864	C₂×C₅	1	2	yes	—
96	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
97	C₄×#102	C₂×C₅	1	2	yes	—
98	C₄×#102	C₂×C₅	1	1	yes	characteristic
99	C₂⁴×C₅	—	2	1	no	—
100	C₂×C₅×Q₈	—	2	4	no	—
101	C₂×C₅×Q₈	—	8	1	no	—
102	C₂×C₅×Q₈	—	8	1	no	—
103	C₂×C₅×D₄	—	2	1	no	—
104	C₂×C₅×D₄	—	2	1	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
107	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
108	C₂×C₅×D₄	#41	1	2	yes	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	4	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	4	4	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	—	4	2	no	—
118	C₂²×C₄×C₅	—	4	4	no	—
119	C₂²×C₄×C₅	—	8	2	no	—
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	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	C₂²×C₄	1	4	yes	—
133	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
134	C₅×C₄⋊C₄	—	2	4	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	4	4	no	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	—	8	1	no	—
146	C₅×C₄⋊C₄	—	8	2	no	—
147	C₅×C₄⋊C₄	SD₁₆	1	4	yes	—
148	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
149	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
150	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
151	C₅×C₂²⋊C₄	—	2	4	no	—
152	C₅×C₂²⋊C₄	—	4	4	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	4	2	no	—
156	C₄²×C₅	—	8	2	no	—
157	C₄²×C₅	C₂²×C₄	1	2	yes	—
158	C₄²×C₅	#41	1	2	yes	—
159	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
161	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
162	C₂²×C₄⋊C₄	—	2	1	no	—
163	#476	C₄×C₅	1	8	yes	complemented
164	C₂×#106	C₂²×C₅	1	2	yes	—
165	C₂×#106	C₂²×C₅	1	2	yes	—
166	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×#102	C₂²×C₅	1	1	yes	characteristic
168	C₂×#102	C₂²×C₅	1	2	yes	—
169	C₂×#102	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
172	#391	—	2	2	no	—
173	#389	—	2	1	no	—
174	#389	C₂²×C₅	1	2	yes	—
175	#389	C₂²×C₅	1	2	yes	—
176	#385	—	2	2	no	—
177	#384	C₂²×C₅	1	1	yes	characteristic
178	#380	—	2	1	no	—
179	C₄×C₄⋊C₄	—	2	1	no	—
180	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
181	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	#340	C₂²×C₅	1	2	yes	—
184	#340	C₂²×C₅	1	1	yes	characteristic
185	#340	C₂²×C₅	1	2	yes	—
186	#340	C₂²×C₅	1	1	yes	characteristic
187	#340	C₂²×C₅	1	2	yes	—
188	#336	C₂²×C₅	1	2	yes	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	—	2	2	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	4	1	no	—
193	C₂³×C₅	—	4	1	no	—
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₅×Q₈	—	8	4	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	2	2	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	C₄×Q₈	1	4	yes	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	8	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	8	8	no	—
226	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
229	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
230	C₂×C₄×C₅	#135	1	2	yes	—
231	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
237	C₅×C₈	—	2	4	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	4	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	—	2	2	no	—
244	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₅	1	2	yes	—
246	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
249	C₄×D₄	—	2	4	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	4	2	no	—
252	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	4	4	no	—
259	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂³×C₅	1	2	yes	—
271	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
272	#106	—	4	2	no	—
273	#106	C₂×C₄×C₅	1	8	yes	complemented
274	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
275	#102	—	2	2	no	—
276	#102	C₂×C₄×C₅	1	8	yes	—
277	#102	C₅×Q₈	1	4	yes	complemented
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	4	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	1	no	—
283	#95	—	2	2	no	—
284	#95	C₅×D₄	1	2	yes	—
285	C₂²×C₅	—	2	4	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	—	4	2	no	—
289	C₂²×C₅	—	4	2	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₅	#546	1	1	yes	characteristic
294	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
295	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
296	C₂²×C₅	C₂×#135	1	1	yes	characteristic
297	C₂²×C₅	#576	1	1	yes	characteristic
298	C₂²×C₅	#577	1	1	yes	characteristic
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	2	4	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	4	2	no	—
303	C₄×C₅	—	4	4	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	8	2	no	—
306	C₄×C₅	—	8	1	no	—
307	C₄×C₅	C₄×SD₁₆	1	4	yes	—
308	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
309	C₄×C₅	#520	1	1	yes	characteristic
310	C₄×C₅	#552	1	1	yes	characteristic
311	C₄×C₅	#554	1	1	yes	characteristic
312	C₂⁴	—	2	1	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	8	1	no	—
315	C₂×Q₈	—	8	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
320	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
321	C₂×D₄	C₅×#41	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
334	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
336	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
346	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	8	1	no	—
359	C₄⋊C₄	—	8	2	no	—
360	C₄⋊C₄	C₅×SD₁₆	1	4	yes	—
361	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
362	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	8	2	no	—
370	C₄²	C₂²×C₄×C₅	1	2	yes	—
371	C₄²	C₅×#41	1	2	yes	—
372	C₂×C₅	—	4	4	no	—
373	C₂×C₅	#2360	1	1	yes	characteristic
374	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
375	C₂×C₅	#2946	1	1	yes	characteristic
376	C₂×C₅	#3295	1	1	yes	characteristic
377	C₂×C₅	#3303	1	1	yes	characteristic
378	C₂×C₅	Q₈×SD₁₆	1	1	yes	characteristic
379	C₂×C₅	#3380	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
388	Q₈	—	8	4	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	C₄×C₅×Q₈	1	4	yes	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	8	8	no	—
417	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
418	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
419	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
420	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
421	C₂×C₄	C₅×#135	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
424	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
425	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
426	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
428	C₈	—	2	4	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₅	#22963	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
440	C₂²	C₅×#546	1	1	yes	characteristic
441	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
442	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
443	C₂²	C₂×C₅×#135	1	1	yes	characteristic
444	C₂²	C₅×#576	1	1	yes	characteristic
445	C₂²	C₅×#577	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	4	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	C₄×C₅×SD₁₆	1	4	yes	—
455	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
456	C₄	C₅×#520	1	1	yes	characteristic
457	C₄	C₅×#552	1	1	yes	characteristic
458	C₄	C₅×#554	1	1	yes	characteristic
459	C₂	—	4	4	no	—
460	C₂	C₅×#2360	1	1	yes	characteristic
461	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
462	C₂	C₅×#2946	1	1	yes	characteristic
463	C₂	C₅×#3295	1	1	yes	characteristic
464	C₂	C₅×#3303	1	1	yes	characteristic
465	C₂	C₅×Q₈×SD₁₆	1	1	yes	characteristic
466	C₂	C₅×#3380	1	1	yes	characteristic

	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	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2369	C₂	semidirect
4. C₅×#1990	C₂	semidirect
5. C₅×#1948	C₂	semidirect
6. C₅×#1941	C₂	semidirect
7. C₅×#1919	C₂	semidirect
9. C₅×C₈×C₄⋊C₄	C₂	semidirect
16. C₅×#476	C₄	semidirect
42. #22963	C₅	direct (N × H)
51. C₅×C₄⋊Q₈	C₂×C₄	semidirect
76. C₅×#106	C₂×C₄	semidirect
77. C₅×C₄⋊C₈	C₂×C₄	semidirect
80. C₅×#102	Q₈	semidirect
89. #2369	C₂×C₅	semidirect
91. #1990	C₂×C₅	semidirect
92. #1948	C₂×C₅	semidirect
93. #1941	C₂×C₅	semidirect
94. #1919	C₂×C₅	semidirect
96. C₈×C₄⋊C₄	C₂×C₅	semidirect
163. #476	C₄×C₅	semidirect
248. C₄⋊Q₈	C₂×C₄×C₅	semidirect
273. #106	C₂×C₄×C₅	semidirect
274. C₄⋊C₈	C₂×C₄×C₅	semidirect
277. #102	C₅×Q₈	semidirect
431. C₅	#22963	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×#476	2
C₅×#2369	2
C₅×D₄×C₄⋊C₄	2
C₅×#1990	2
C₅×#1948	2
C₅×#1941	2
C₅×#1919	2
C₅×#1864	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#102	2
#22963	5

Subgroups — C5×#22963 #11945683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22963 #11945683