Subgroups — C₅×#23095 #11945815

Order 1280.

966 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#460	C₂	1	1	yes	maximal, characteristic
2	C₅×#2366	C₂	1	1	yes	maximal, characteristic
3	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1968	C₂	1	2	yes	maximal, complemented
5	C₅×#1957	C₂	1	1	yes	maximal, characteristic
6	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1926	C₂	1	2	yes	maximal, complemented
8	C₅×#1877	C₂	1	2	yes	maximal, complemented
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	—	2	1	no	—
16	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₅×#460	C₄	1	8	yes	complemented
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	1	yes	characteristic
21	C₂×C₅×#103	C₂²	1	1	yes	characteristic
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₅×#102	C₂²	1	2	yes	—
24	C₂×C₅×#102	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₅×#391	C₂²	1	2	yes	—
28	C₅×#390	—	2	1	no	—
29	C₅×#390	C₂²	1	2	yes	—
30	C₅×#387	—	2	2	no	—
31	C₅×#386	—	2	2	no	—
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#382	—	2	1	no	—
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	2	yes	—
42	#23095	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	C₂³	1	2	yes	—
47	C₂³×C₄×C₅	—	2	2	no	—
48	C₂×C₅×SD₁₆	—	4	2	no	—
49	C₂×C₅×SD₁₆	—	4	2	no	—
50	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₅×#127	—	2	2	no	—
55	C₅×#127	C₂×C₄	1	4	yes	—
56	C₄×C₅×Q₈	—	2	2	no	—
57	C₄×C₅×Q₈	C₂×C₄	1	4	yes	complemented
58	C₄×C₅×D₄	—	2	4	no	—
59	C₄×C₅×D₄	—	4	2	no	—
60	C₄×C₅×D₄	—	4	4	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	C₂³	1	2	yes	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₅×#106	—	4	2	no	—
79	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
80	C₅×#103	—	2	2	no	—
81	C₅×#103	—	2	2	no	—
82	C₅×#102	—	2	4	no	—
83	C₅×#102	—	4	2	no	—
84	C₅×#102	C₂×C₄	1	8	yes	complemented
85	C₄×C₅×C₈	—	2	2	no	—
86	C₄×C₅×C₈	—	4	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	D₄	1	2	yes	—
92	C₂×#460	C₂×C₅	1	1	yes	characteristic
93	#2366	C₂×C₅	1	1	yes	characteristic
94	#2355	C₂×C₅	1	1	yes	characteristic, complemented
95	#1968	C₂×C₅	1	2	yes	complemented
96	#1957	C₂×C₅	1	1	yes	characteristic
97	#1948	C₂×C₅	1	1	yes	characteristic, complemented
98	#1926	C₂×C₅	1	2	yes	complemented
99	#1877	C₂×C₅	1	2	yes	complemented
100	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
101	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
102	C₄×#102	C₂×C₅	1	2	yes	complemented
103	C₂⁴×C₅	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	2	4	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	4	2	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	—	8	1	no	—
120	C₂×C₅×D₄	—	8	1	no	—
121	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	4	4	no	—
128	C₂²×C₄×C₅	—	4	4	no	—
129	C₂²×C₄×C₅	—	8	2	no	—
130	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₅×SD₁₆	—	4	8	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
144	C₂×C₅×C₈	#41	1	2	yes	—
145	C₅×C₄⋊C₄	—	2	4	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	4	2	no	—
154	C₅×C₄⋊C₄	—	8	1	no	—
155	C₅×C₄⋊C₄	SD₁₆	1	4	yes	complemented
156	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
157	C₅×C₄⋊C₄	#41	1	2	yes	—
158	C₅×C₂²⋊C₄	—	4	4	no	—
159	C₅×C₂²⋊C₄	—	4	4	no	—
160	C₅×C₂²⋊C₄	—	8	2	no	—
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	4	2	no	—
165	C₄²×C₅	—	8	2	no	—
166	C₄²×C₅	C₂²×C₄	1	2	yes	—
167	C₄²×C₅	#41	1	2	yes	—
168	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
169	C₂×#127	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄×D₄	—	2	1	no	—
172	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
173	#460	C₄×C₅	1	8	yes	complemented
174	C₂×#106	C₂²×C₅	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂×#103	C₂²×C₅	1	1	yes	characteristic
177	C₂×#103	C₂²×C₅	1	1	yes	characteristic
178	C₂×#102	C₂²×C₅	1	2	yes	—
179	C₂×#102	C₂²×C₅	1	2	yes	—
180	C₂×#102	C₂²×C₅	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
183	#391	C₂²×C₅	1	2	yes	—
184	#390	—	2	1	no	—
185	#390	C₂²×C₅	1	2	yes	—
186	#387	—	2	2	no	—
187	#386	—	2	2	no	—
188	#384	C₂²×C₅	1	1	yes	characteristic
189	#382	—	2	1	no	—
190	C₄×C₄⋊C₄	—	2	1	no	—
191	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	#340	C₂²×C₅	1	2	yes	—
195	#340	C₂²×C₅	1	1	yes	characteristic
196	#340	C₂²×C₅	1	1	yes	characteristic
197	#336	C₂²×C₅	1	2	yes	—
198	C₂³×C₅	—	2	4	no	—
199	C₂³×C₅	—	4	2	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	—	4	2	no	—
205	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₅×Q₈	—	2	2	no	—
207	C₅×Q₈	—	2	2	no	—
208	C₅×Q₈	—	4	1	no	—
209	C₅×Q₈	—	4	1	no	—
210	C₅×D₄	—	2	4	no	—
211	C₅×D₄	—	2	4	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	4	8	no	—
215	C₅×D₄	—	8	4	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	8	8	no	—
239	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
240	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
241	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
242	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
243	C₂×C₄×C₅	#135	1	2	yes	—
244	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₅×C₈	—	2	4	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	4	1	no	—
253	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	C₂³×C₅	1	2	yes	—
257	C₂³×C₄	—	2	2	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×SD₁₆	—	4	2	no	—
260	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
261	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₅	1	2	yes	—
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	#127	—	2	2	no	—
265	#127	C₂×C₄×C₅	1	4	yes	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	C₂×C₄×C₅	1	4	yes	complemented
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	—	4	2	no	—
270	C₄×D₄	—	4	4	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₅	1	2	yes	—
287	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
288	#106	—	4	2	no	—
289	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
290	#103	—	2	2	no	—
291	#103	—	2	2	no	—
292	#102	—	2	4	no	—
293	#102	—	4	2	no	—
294	#102	C₂×C₄×C₅	1	8	yes	complemented
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	4	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	C₅×D₄	1	2	yes	—
302	C₂²×C₅	—	4	4	no	—
303	C₂²×C₅	—	4	4	no	—
304	C₂²×C₅	—	4	4	no	—
305	C₂²×C₅	—	8	2	no	—
306	C₂²×C₅	—	8	2	no	—
307	C₂²×C₅	—	8	2	no	—
308	C₂²×C₅	—	8	2	no	—
309	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₅	#546	1	1	yes	characteristic
311	C₂²×C₅	#550	1	1	yes	characteristic
312	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
313	C₂²×C₅	C₂×#135	1	1	yes	characteristic
314	C₂²×C₅	#576	1	1	yes	characteristic
315	C₂²×C₅	#577	1	1	yes	characteristic
316	C₄×C₅	—	2	2	no	—
317	C₄×C₅	—	2	4	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	8	1	no	—
323	C₄×C₅	—	8	2	no	—
324	C₄×C₅	C₄×SD₁₆	1	4	yes	—
325	C₄×C₅	C₄×#41	1	1	yes	characteristic
326	C₄×C₅	#518	1	1	yes	characteristic
327	C₄×C₅	#553	1	1	yes	characteristic
328	C₄×C₅	#555	1	1	yes	characteristic
329	C₂⁴	—	2	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	8	1	no	—
346	C₂×D₄	—	8	1	no	—
347	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	8	2	no	—
356	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
357	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
361	SD₁₆	—	4	8	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
370	C₂×C₈	C₅×#41	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	8	1	no	—
381	C₄⋊C₄	C₅×SD₁₆	1	4	yes	complemented
382	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
383	C₄⋊C₄	C₅×#41	1	2	yes	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	—	8	2	no	—
392	C₄²	C₂²×C₄×C₅	1	2	yes	—
393	C₄²	C₅×#41	1	2	yes	—
394	C₂×C₅	—	8	4	no	—
395	C₂×C₅	#2363	1	1	yes	characteristic
396	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
397	C₂×C₅	#2946	1	1	yes	characteristic
398	C₂×C₅	#3295	1	1	yes	characteristic
399	C₂×C₅	#3304	1	1	yes	characteristic
400	C₂×C₅	#3392	1	1	yes	characteristic
401	C₂×C₅	#3396	1	1	yes	characteristic
402	C₂³	—	2	4	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	8	no	—
443	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
444	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
445	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
446	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
447	C₂×C₄	C₅×#135	1	2	yes	—
448	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
450	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
452	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
454	C₈	—	2	4	no	—
455	C₈	—	2	2	no	—
456	C₈	—	4	1	no	—
457	C₅	#23095	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
466	C₂²	C₅×#546	1	1	yes	characteristic
467	C₂²	C₅×#550	1	1	yes	characteristic
468	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
469	C₂²	C₂×C₅×#135	1	1	yes	characteristic
470	C₂²	C₅×#576	1	1	yes	characteristic
471	C₂²	C₅×#577	1	1	yes	characteristic
472	C₄	—	2	4	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	C₄×C₅×SD₁₆	1	4	yes	—
481	C₄	C₄×C₅×#41	1	1	yes	characteristic
482	C₄	C₅×#518	1	1	yes	characteristic
483	C₄	C₅×#553	1	1	yes	characteristic
484	C₄	C₅×#555	1	1	yes	characteristic
485	C₂	—	8	4	no	—
486	C₂	C₅×#2363	1	1	yes	characteristic
487	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
488	C₂	C₅×#2946	1	1	yes	characteristic
489	C₂	C₅×#3295	1	1	yes	characteristic
490	C₂	C₅×#3304	1	1	yes	characteristic
491	C₂	C₅×#3392	1	1	yes	characteristic
492	C₂	C₅×#3396	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	C₂×C₅×#127	C₂²
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
3. C₅×#2355	C₂	semidirect
4. C₅×#1968	C₂	semidirect
6. C₅×#1948	C₂	semidirect
7. C₅×#1926	C₂	semidirect
8. C₅×#1877	C₂	semidirect
9. C₅×C₈×C₄⋊C₄	C₂	semidirect
10. C₄×C₅×#103	C₂	semidirect
11. C₄×C₅×#102	C₂	semidirect
17. C₅×#460	C₄	semidirect
42. #23095	C₅	direct (N × H)
50. C₂×C₅×SD₁₆	C₂×C₄	semidirect
57. C₄×C₅×Q₈	C₂×C₄	semidirect
79. C₅×C₄⋊C₈	C₂×C₄	semidirect
84. C₅×#102	C₂×C₄	semidirect
94. #2355	C₂×C₅	semidirect
95. #1968	C₂×C₅	semidirect
97. #1948	C₂×C₅	semidirect
98. #1926	C₂×C₅	semidirect
99. #1877	C₂×C₅	semidirect
100. C₈×C₄⋊C₄	C₂×C₅	semidirect
101. C₄×#103	C₂×C₅	semidirect
102. C₄×#102	C₂×C₅	semidirect
155. C₅×C₄⋊C₄	SD₁₆	semidirect
173. #460	C₄×C₅	semidirect
260. C₂×SD₁₆	C₂×C₄×C₅	semidirect
267. C₄×Q₈	C₂×C₄×C₅	semidirect
289. C₄⋊C₈	C₂×C₄×C₅	semidirect
294. #102	C₂×C₄×C₅	semidirect
381. C₄⋊C₄	C₅×SD₁₆	semidirect
457. C₅	#23095	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×#460	2
C₅×#2366	2
C₅×#2355	2
C₅×#1968	2
C₅×#1957	2
C₅×#1948	2
C₅×#1926	2
C₅×#1877	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#103	2
C₄×C₅×#102	2
#23095	5

Subgroups — C5×#23095 #11945815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23095 #11945815