Subgroups — C₅×#21511 #11944231

Order 1280.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#2326	C₂	1	1	yes	maximal, characteristic
5	C₅×#2276	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1983	C₂	1	1	yes	maximal, characteristic
7	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1926	C₂	1	1	yes	maximal, characteristic
10	C₅×#1880	C₂	1	1	yes	maximal, characteristic
11	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₅×#464	C₄	1	8	yes	complemented
25	C₅×#441	—	2	4	no	—
26	C₄×C₅×SD₁₆	—	2	4	no	—
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₅×#103	C₂²	1	1	yes	characteristic
34	C₂×C₅×#103	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×#102	C₂²	1	1	yes	characteristic
37	C₂×C₅×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#391	C₂²	1	1	yes	characteristic
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#388	—	2	1	no	—
44	C₅×#388	—	2	1	no	—
45	C₅×#385	—	2	1	no	—
46	C₅×#385	—	2	1	no	—
47	C₅×#384	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	—	2	1	no	—
49	C₄×C₅×C₄⋊C₄	—	2	1	no	—
50	C₄×C₅×C₄⋊C₄	—	2	1	no	—
51	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₅×#376	—	2	1	no	—
55	C₅×#376	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#340	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	#21511	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂×C₅×Q₁₆	—	2	2	no	—
68	C₂×C₅×Q₁₆	—	2	2	no	—
69	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×#124	—	2	2	no	—
78	C₅×#124	C₂×C₄	1	4	yes	—
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	—	2	2	no	—
84	C₄×C₅×Q₈	—	2	2	no	—
85	C₄×C₅×Q₈	C₂×C₄	1	4	yes	complemented
86	C₄×C₅×Q₈	D₄	1	4	yes	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₄²×C₅	—	2	1	no	—
106	C₂×C₄²×C₅	—	2	1	no	—
107	C₂×C₄²×C₅	—	2	1	no	—
108	C₂×C₄²×C₅	—	2	1	no	—
109	C₂×C₄²×C₅	—	2	1	no	—
110	C₂×C₄²×C₅	—	2	1	no	—
111	C₂×C₄²×C₅	—	2	1	no	—
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₅×#106	—	2	2	no	—
116	C₅×#106	—	2	2	no	—
117	C₅×C₄⋊C₈	—	2	2	no	—
118	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
119	C₅×#103	—	2	2	no	—
120	C₅×#103	—	2	2	no	—
121	C₅×#103	—	2	2	no	—
122	C₅×#103	—	2	2	no	—
123	C₅×#103	C₂×C₄	1	4	yes	complemented
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	2	2	no	—
126	C₅×#102	C₂×C₄	1	4	yes	—
127	C₅×#97	—	2	2	no	—
128	C₄×C₅×C₈	—	2	2	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	—	2	1	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	D₄	1	1	yes	characteristic
135	C₅×#95	D₄	1	1	yes	characteristic
136	C₅×#95	D₄	1	1	yes	characteristic
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₂×#464	C₂×C₅	1	1	yes	characteristic
139	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic
141	#2326	C₂×C₅	1	1	yes	characteristic
142	#2276	C₂×C₅	1	1	yes	characteristic, complemented
143	#1983	C₂×C₅	1	1	yes	characteristic
144	#1948	C₂×C₅	1	1	yes	characteristic, complemented
145	#1927	C₂×C₅	1	1	yes	characteristic, complemented
146	#1926	C₂×C₅	1	1	yes	characteristic
147	#1880	C₂×C₅	1	1	yes	characteristic
148	#1878	C₂×C₅	1	1	yes	characteristic, complemented
149	#1803	C₂×C₅	1	1	yes	characteristic, complemented
150	#1768	C₂×C₅	1	1	yes	characteristic, complemented
151	#1762	C₂×C₅	1	1	yes	characteristic
152	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
163	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
164	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
165	C₂×C₅×Q₈	#41	1	2	yes	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	4	2	no	—
180	C₂²×C₄×C₅	—	8	1	no	—
181	C₂²×C₄×C₅	—	8	1	no	—
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
189	C₅×Q₁₆	—	2	8	no	—
190	C₅×SD₁₆	—	2	8	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
202	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
203	C₅×C₄⋊C₄	—	2	4	no	—
204	C₅×C₄⋊C₄	—	2	4	no	—
205	C₅×C₄⋊C₄	—	2	4	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	4	2	no	—
214	C₅×C₄⋊C₄	—	8	1	no	—
215	C₅×C₄⋊C₄	—	8	1	no	—
216	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
217	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₅×C₄⋊C₄	#41	1	2	yes	—
219	C₅×C₂²⋊C₄	—	2	4	no	—
220	C₅×C₂²⋊C₄	—	2	4	no	—
221	C₅×C₂²⋊C₄	—	4	2	no	—
222	C₅×C₂²⋊C₄	—	8	1	no	—
223	C₅×C₂²⋊C₄	—	8	1	no	—
224	C₄²×C₅	—	2	4	no	—
225	C₄²×C₅	—	2	4	no	—
226	C₄²×C₅	—	2	4	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	4	2	no	—
230	C₄²×C₅	—	8	1	no	—
231	C₄²×C₅	—	8	1	no	—
232	C₄²×C₅	—	8	1	no	—
233	C₄²×C₅	C₂²×C₄	1	2	yes	—
234	C₄²×C₅	C₂×D₄	1	2	yes	—
235	C₄²×C₅	#41	1	2	yes	—
236	C₄²×C₅	#41	1	2	yes	—
237	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
239	C₂×#124	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
245	#464	C₄×C₅	1	8	yes	complemented
246	#441	—	2	4	no	—
247	C₄×SD₁₆	—	2	4	no	—
248	C₂×#106	C₂²×C₅	1	1	yes	characteristic
249	C₂×#106	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×#103	C₂²×C₅	1	1	yes	characteristic
253	C₂×#103	C₂²×C₅	1	1	yes	characteristic
254	C₂×#103	C₂²×C₅	1	1	yes	characteristic
255	C₂×#103	C₂²×C₅	1	1	yes	characteristic
256	C₂×#103	C₂²×C₅	1	1	yes	characteristic
257	C₂×#102	C₂²×C₅	1	1	yes	characteristic
258	C₂×#102	C₂²×C₅	1	1	yes	characteristic
259	C₂×#102	C₂²×C₅	1	1	yes	characteristic
260	C₂×#97	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
262	#391	C₂²×C₅	1	1	yes	characteristic
263	#390	C₂²×C₅	1	1	yes	characteristic
264	#388	—	2	1	no	—
265	#388	—	2	1	no	—
266	#385	—	2	1	no	—
267	#385	—	2	1	no	—
268	#384	C₂²×C₅	1	1	yes	characteristic
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	—	2	1	no	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	#376	—	2	1	no	—
276	#376	C₂²×C₅	1	1	yes	characteristic
277	#340	C₂²×C₅	1	1	yes	characteristic
278	#340	C₂²×C₅	1	1	yes	characteristic
279	#340	C₂²×C₅	1	1	yes	characteristic
280	#340	C₂²×C₅	1	1	yes	characteristic
281	#336	C₂²×C₅	1	1	yes	characteristic
282	#336	C₂²×C₅	1	1	yes	characteristic
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	—	4	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	4	1	no	—
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₅×Q₈	—	2	2	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	—	2	2	no	—
295	C₅×Q₈	—	2	2	no	—
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×Q₈	C₄×D₄	1	4	yes	—
299	C₅×D₄	—	2	2	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	4	1	no	—
302	C₅×D₄	—	4	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	8	4	no	—
339	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
340	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
341	C₂×C₄×C₅	#121	1	2	yes	—
342	C₂×C₄×C₅	#121	1	2	yes	—
343	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₅×C₈	—	2	2	no	—
350	C₅×C₈	—	2	2	no	—
351	C₅×C₈	—	4	1	no	—
352	C₅×C₈	—	4	1	no	—
353	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂×Q₁₆	—	2	2	no	—
358	C₂×Q₁₆	—	2	2	no	—
359	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×SD₁₆	—	2	2	no	—
362	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
363	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
367	#124	—	2	2	no	—
368	#124	C₂×C₄×C₅	1	4	yes	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×Q₈	C₂×C₄×C₅	1	4	yes	complemented
376	C₄×Q₈	C₅×D₄	1	4	yes	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
405	#106	—	2	2	no	—
406	#106	—	2	2	no	—
407	C₄⋊C₈	—	2	2	no	—
408	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	#103	—	2	2	no	—
413	#103	C₂×C₄×C₅	1	4	yes	complemented
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	C₂×C₄×C₅	1	4	yes	—
417	#97	—	2	2	no	—
418	C₄×C₈	—	2	2	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	C₅×D₄	1	1	yes	characteristic
425	#95	C₅×D₄	1	1	yes	characteristic
426	#95	C₅×D₄	1	1	yes	characteristic
427	#95	C₅×D₄	1	1	yes	characteristic
428	C₂²×C₅	—	4	2	no	—
429	C₂²×C₅	—	4	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	—	8	1	no	—
434	C₂²×C₅	—	8	1	no	—
435	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
436	C₂²×C₅	C₂×#121	1	1	yes	characteristic
437	C₂²×C₅	#525	1	1	yes	characteristic
438	C₂²×C₅	#577	1	1	yes	characteristic
439	C₂²×C₅	#577	1	1	yes	characteristic
440	C₂²×C₅	#577	1	1	yes	characteristic
441	C₂²×C₅	#578	1	1	yes	characteristic
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	4	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	—	4	2	no	—
450	C₄×C₅	—	4	2	no	—
451	C₄×C₅	—	4	2	no	—
452	C₄×C₅	—	4	2	no	—
453	C₄×C₅	—	8	1	no	—
454	C₄×C₅	—	8	1	no	—
455	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
456	C₄×C₅	C₄×#41	1	1	yes	characteristic
457	C₄×C₅	#529	1	1	yes	characteristic
458	C₄×C₅	#532	1	1	yes	characteristic
459	C₂⁴	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
469	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
470	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
471	C₂×Q₈	C₅×#41	1	2	yes	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	8	1	no	—
487	C₂²×C₄	—	8	1	no	—
488	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
495	Q₁₆	—	2	8	no	—
496	SD₁₆	—	2	8	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
508	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	8	1	no	—
521	C₄⋊C₄	—	8	1	no	—
522	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
523	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
524	C₄⋊C₄	C₅×#41	1	2	yes	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	8	1	no	—
529	C₂²⋊C₄	—	8	1	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	4	2	no	—
536	C₄²	—	8	1	no	—
537	C₄²	—	8	1	no	—
538	C₄²	—	8	1	no	—
539	C₄²	C₂²×C₄×C₅	1	2	yes	—
540	C₄²	C₂×C₅×D₄	1	2	yes	—
541	C₄²	C₅×#41	1	2	yes	—
542	C₄²	C₅×#41	1	2	yes	—
543	C₂×C₅	—	8	2	no	—
544	C₂×C₅	C₄×#121	1	1	yes	characteristic
545	C₂×C₅	#2947	1	1	yes	characteristic
546	C₂×C₅	#2952	1	1	yes	characteristic
547	C₂×C₅	#3043	1	1	yes	characteristic
548	C₂×C₅	#3046	1	1	yes	characteristic
549	C₂×C₅	#3121	1	1	yes	characteristic
550	C₂×C₅	#3125	1	1	yes	characteristic
551	C₂³	—	2	2	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
559	Q₈	—	2	2	no	—
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	Q₈	C₄×C₅×D₄	1	4	yes	—
567	D₄	—	2	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	8	4	no	—
607	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
608	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
609	C₂×C₄	C₅×#121	1	2	yes	—
610	C₂×C₄	C₅×#121	1	2	yes	—
611	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
612	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
613	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
614	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
615	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
616	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
617	C₈	—	2	2	no	—
618	C₈	—	2	2	no	—
619	C₈	—	4	1	no	—
620	C₈	—	4	1	no	—
621	C₅	#21511	1	1	yes	characteristic, direct product factor, Sylow
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
630	C₂²	C₂×C₅×#121	1	1	yes	characteristic
631	C₂²	C₅×#525	1	1	yes	characteristic
632	C₂²	C₅×#577	1	1	yes	characteristic
633	C₂²	C₅×#577	1	1	yes	characteristic
634	C₂²	C₅×#577	1	1	yes	characteristic
635	C₂²	C₅×#578	1	1	yes	characteristic
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	4	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
650	C₄	C₄×C₅×#41	1	1	yes	characteristic
651	C₄	C₅×#529	1	1	yes	characteristic
652	C₄	C₅×#532	1	1	yes	characteristic
653	C₂	—	8	2	no	—
654	C₂	C₄×C₅×#121	1	1	yes	characteristic
655	C₂	C₅×#2947	1	1	yes	characteristic
656	C₂	C₅×#2952	1	1	yes	characteristic
657	C₂	C₅×#3043	1	1	yes	characteristic
658	C₂	C₅×#3046	1	1	yes	characteristic
659	C₂	C₅×#3121	1	1	yes	characteristic
660	C₂	C₅×#3125	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 ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#441	C₂	semidirect
5. C₅×#2276	C₂	semidirect
7. C₅×#1948	C₂	semidirect
8. C₅×#1927	C₂	semidirect
11. C₅×#1878	C₂	semidirect
12. C₅×#1803	C₂	semidirect
13. C₅×#1768	C₂	semidirect
15. C₄×C₅×#103	C₂	semidirect
24. C₅×#464	C₄	semidirect
62. #21511	C₅	direct (N × H)
69. C₂×C₅×Q₁₆	C₂×C₄	semidirect
85. C₄×C₅×Q₈	C₂×C₄	semidirect
118. C₅×C₄⋊C₈	C₂×C₄	semidirect
123. C₅×#103	C₂×C₄	semidirect
139. C₂×#441	C₂×C₅	semidirect
142. #2276	C₂×C₅	semidirect
144. #1948	C₂×C₅	semidirect
145. #1927	C₂×C₅	semidirect
148. #1878	C₂×C₅	semidirect
149. #1803	C₂×C₅	semidirect
150. #1768	C₂×C₅	semidirect
152. C₄×#103	C₂×C₅	semidirect
245. #464	C₄×C₅	semidirect
359. C₂×Q₁₆	C₂×C₄×C₅	semidirect
375. C₄×Q₈	C₂×C₄×C₅	semidirect
408. C₄⋊C₈	C₂×C₄×C₅	semidirect
413. #103	C₂×C₄×C₅	semidirect
621. C₅	#21511	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×#464	2
C₂×C₅×#441	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2326	2
C₅×#2276	2
C₅×#1983	2
C₅×#1948	2
C₅×#1927	2
C₅×#1926	2
C₅×#1880	2
C₅×#1878	2
C₅×#1803	2
C₅×#1768	2
C₅×#1762	2
C₄×C₅×#103	2
#21511	5

Subgroups — C5×#21511 #11944231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21511 #11944231