Subgroups — C₅×#21523 #11944243

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#465	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2324	C₂	1	1	yes	maximal, characteristic
5	C₅×#2323	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1895	C₂	1	1	yes	maximal, characteristic
11	C₅×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1807	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₅×#465	C₄	1	8	yes	complemented
25	C₄×C₅×SD₁₆	—	2	4	no	—
26	C₂×C₅×#106	C₂²	1	1	yes	characteristic
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₅×#405	—	2	4	no	—
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₅×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₅×#391	C₂²	1	1	yes	characteristic
41	C₅×#390	—	2	1	no	—
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#389	—	2	1	no	—
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#388	—	2	1	no	—
47	C₅×#388	—	2	1	no	—
48	C₅×#388	—	2	1	no	—
49	C₅×#387	—	2	1	no	—
50	C₅×#386	—	2	1	no	—
51	C₅×#385	—	2	1	no	—
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₅×#380	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₄⋊C₄	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×#340	C₂²	1	1	yes	characteristic
61	C₅×#340	C₂²	1	1	yes	characteristic
62	#21523	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×SD₁₆	—	2	2	no	—
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
71	C₂×C₅×M₁₆	—	2	2	no	—
72	C₂×C₅×M₁₆	—	2	2	no	—
73	C₂×C₅×M₁₆	—	2	2	no	—
74	C₂²×C₅×C₈	—	2	2	no	—
75	C₂²×C₅×C₈	—	2	2	no	—
76	C₂²×C₅×C₈	C₂×C₄	1	4	yes	complemented
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₅×C₂²⋊Q₈	—	2	2	no	—
82	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
83	C₅×#121	—	2	2	no	—
84	C₅×#121	C₂×C₄	1	4	yes	—
85	C₄×C₅×Q₈	—	2	2	no	—
86	C₄×C₅×Q₈	—	2	2	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₅×#117	—	2	2	no	—
90	C₅×#117	—	2	2	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	D₄	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	—	2	1	no	—
113	C₂×C₄²×C₅	—	2	1	no	—
114	C₂×C₄²×C₅	—	2	1	no	—
115	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₅×#106	—	2	2	no	—
118	C₅×#106	—	2	2	no	—
119	C₅×#106	C₂×C₄	1	4	yes	complemented
120	C₅×#103	—	2	2	no	—
121	C₅×#103	—	2	2	no	—
122	C₅×#103	C₂×C₄	1	4	yes	complemented
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×#102	C₂×C₄	1	4	yes	—
126	C₅×#97	—	2	2	no	—
127	C₅×#97	—	2	2	no	—
128	C₄×C₅×C₈	—	2	2	no	—
129	C₄×C₅×C₈	D₄	1	4	yes	complemented
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	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	—	2	1	no	—
138	C₂×#465	C₂×C₅	1	1	yes	characteristic
139	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
141	#2324	C₂×C₅	1	1	yes	characteristic
142	#2323	C₂×C₅	1	1	yes	characteristic, complemented
143	#1968	C₂×C₅	1	1	yes	characteristic, complemented
144	#1941	C₂×C₅	1	1	yes	characteristic, complemented
145	#1936	C₂×C₅	1	1	yes	characteristic, complemented
146	#1935	C₂×C₅	1	1	yes	characteristic, complemented
147	#1895	C₂×C₅	1	1	yes	characteristic
148	#1894	C₂×C₅	1	1	yes	characteristic, complemented
149	#1807	C₂×C₅	1	1	yes	characteristic, complemented
150	C₄×#106	C₂×C₅	1	1	yes	characteristic, complemented
151	#1763	C₂×C₅	1	1	yes	characteristic, complemented
152	#1762	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
161	C₂×C₅×D₄	—	2	4	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	8	1	no	—
168	C₂×C₅×D₄	—	8	1	no	—
169	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
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	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	8	1	no	—
183	C₂²×C₄×C₅	—	8	1	no	—
184	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	#41	1	2	yes	—
191	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₅×SD₁₆	—	2	8	no	—
193	C₅×M₁₆	—	2	8	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	8	no	—
201	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
202	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
203	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
204	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
205	C₂×C₅×C₈	#41	1	2	yes	—
206	C₂×C₅×C₈	#41	1	2	yes	—
207	C₅×C₄⋊C₄	—	2	4	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	2	2	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	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	4	2	no	—
221	C₅×C₄⋊C₄	—	8	1	no	—
222	C₅×C₄⋊C₄	—	8	1	no	—
223	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
224	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
225	C₅×C₂²⋊C₄	—	2	4	no	—
226	C₅×C₂²⋊C₄	—	2	4	no	—
227	C₅×C₂²⋊C₄	—	2	2	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	4	2	no	—
230	C₅×C₂²⋊C₄	—	8	1	no	—
231	C₅×C₂²⋊C₄	—	8	1	no	—
232	C₅×C₂²⋊C₄	—	8	1	no	—
233	C₅×C₂²⋊C₄	—	8	1	no	—
234	C₄²×C₅	—	2	1	no	—
235	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	—	4	2	no	—
237	C₄²×C₅	—	8	1	no	—
238	C₄²×C₅	—	8	1	no	—
239	C₄²×C₅	C₂×D₄	1	2	yes	—
240	C₄²×C₅	#41	1	2	yes	—
241	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×#121	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×#117	C₂²×C₅	1	1	yes	characteristic
249	#465	C₄×C₅	1	8	yes	complemented
250	C₄×SD₁₆	—	2	4	no	—
251	C₂×#106	C₂²×C₅	1	1	yes	characteristic
252	C₂×#106	C₂²×C₅	1	1	yes	characteristic
253	C₂×#106	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	#405	—	2	4	no	—
261	C₂×#97	C₂²×C₅	1	1	yes	characteristic
262	C₂×#97	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
265	#391	C₂²×C₅	1	1	yes	characteristic
266	#390	—	2	1	no	—
267	#390	C₂²×C₅	1	1	yes	characteristic
268	#389	—	2	1	no	—
269	#389	C₂²×C₅	1	1	yes	characteristic
270	#389	C₂²×C₅	1	1	yes	characteristic
271	#388	—	2	1	no	—
272	#388	—	2	1	no	—
273	#388	—	2	1	no	—
274	#387	—	2	1	no	—
275	#386	—	2	1	no	—
276	#385	—	2	1	no	—
277	#380	C₂²×C₅	1	1	yes	characteristic
278	#380	C₂²×C₅	1	1	yes	characteristic
279	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	#340	C₂²×C₅	1	1	yes	characteristic
282	#340	C₂²×C₅	1	1	yes	characteristic
283	#340	C₂²×C₅	1	1	yes	characteristic
284	#340	C₂²×C₅	1	1	yes	characteristic
285	#340	C₂²×C₅	1	1	yes	characteristic
286	#340	C₂²×C₅	1	1	yes	characteristic
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	4	1	no	—
295	C₂³×C₅	—	4	1	no	—
296	C₂³×C₅	—	4	1	no	—
297	C₂³×C₅	—	4	1	no	—
298	C₂³×C₅	—	4	1	no	—
299	C₂³×C₅	—	4	1	no	—
300	C₂³×C₅	C₄×D₄	1	2	yes	—
301	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
302	C₅×Q₈	—	2	2	no	—
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	4	1	no	—
305	C₅×Q₈	—	4	1	no	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	8	4	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	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	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	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	8	4	no	—
349	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
350	C₂×C₄×C₅	#121	1	2	yes	—
351	C₂×C₄×C₅	#121	1	2	yes	—
352	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
358	C₅×C₈	—	2	2	no	—
359	C₅×C₈	—	2	2	no	—
360	C₅×C₈	—	2	2	no	—
361	C₅×C₈	C₄×D₄	1	4	yes	—
362	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	2	2	no	—
375	C₂²×C₈	C₂×C₄×C₅	1	4	yes	complemented
376	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
382	#121	—	2	2	no	—
383	#121	C₂×C₄×C₅	1	4	yes	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	#117	—	2	2	no	—
389	#117	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
416	#106	—	2	2	no	—
417	#106	—	2	2	no	—
418	#106	C₂×C₄×C₅	1	4	yes	complemented
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#103	C₂×C₄×C₅	1	4	yes	complemented
422	#102	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	C₂×C₄×C₅	1	4	yes	—
425	#97	—	2	2	no	—
426	#97	—	2	2	no	—
427	C₄×C₈	—	2	2	no	—
428	C₄×C₈	C₅×D₄	1	4	yes	complemented
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	8	1	no	—
448	C₂²×C₅	—	8	1	no	—
449	C₂²×C₅	—	8	1	no	—
450	C₂²×C₅	—	8	1	no	—
451	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
452	C₂²×C₅	C₂×#121	1	1	yes	characteristic
453	C₂²×C₅	#532	1	1	yes	characteristic
454	C₂²×C₅	#577	1	1	yes	characteristic
455	C₂²×C₅	#577	1	1	yes	characteristic
456	C₂²×C₅	#577	1	1	yes	characteristic
457	C₂²×C₅	#577	1	1	yes	characteristic
458	C₄×C₅	—	2	2	no	—
459	C₄×C₅	—	2	2	no	—
460	C₄×C₅	—	2	2	no	—
461	C₄×C₅	—	4	2	no	—
462	C₄×C₅	—	4	2	no	—
463	C₄×C₅	—	4	1	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	4	2	no	—
466	C₄×C₅	—	8	1	no	—
467	C₄×C₅	—	8	1	no	—
468	C₄×C₅	—	8	1	no	—
469	C₄×C₅	—	8	1	no	—
470	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
471	C₄×C₅	C₄×#41	1	1	yes	characteristic
472	C₄×C₅	#525	1	1	yes	characteristic
473	C₄×C₅	#529	1	1	yes	characteristic
474	C₂⁴	—	2	1	no	—
475	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	8	1	no	—
489	C₂×D₄	—	8	1	no	—
490	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	—	8	1	no	—
505	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
506	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
511	C₂²×C₄	C₅×#41	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	SD₁₆	—	2	8	no	—
514	M₁₆	—	2	8	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	8	no	—
522	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
523	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
524	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
525	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
526	C₂×C₈	C₅×#41	1	2	yes	—
527	C₂×C₈	C₅×#41	1	2	yes	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
545	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	8	1	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₂²⋊C₄	—	8	1	no	—
554	C₂²⋊C₄	—	8	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	4	2	no	—
558	C₄²	—	8	1	no	—
559	C₄²	—	8	1	no	—
560	C₄²	C₂×C₅×D₄	1	2	yes	—
561	C₄²	C₅×#41	1	2	yes	—
562	C₂×C₅	—	4	2	no	—
563	C₂×C₅	—	8	2	no	—
564	C₂×C₅	C₄×#121	1	1	yes	characteristic
565	C₂×C₅	#2949	1	1	yes	characteristic
566	C₂×C₅	#2952	1	1	yes	characteristic
567	C₂×C₅	#3057	1	1	yes	characteristic
568	C₂×C₅	#3060	1	1	yes	characteristic
569	C₂×C₅	#3173	1	1	yes	characteristic
570	C₂×C₅	#3174	1	1	yes	characteristic
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	C₄×C₅×D₄	1	2	yes	—
585	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	8	4	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
634	C₂×C₄	C₅×#121	1	2	yes	—
635	C₂×C₄	C₅×#121	1	2	yes	—
636	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
637	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
638	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
639	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
640	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
641	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
642	C₈	—	2	2	no	—
643	C₈	—	2	2	no	—
644	C₈	—	2	2	no	—
645	C₈	C₄×C₅×D₄	1	4	yes	—
646	C₅	#21523	1	1	yes	characteristic, direct product factor, Sylow
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
662	C₂²	C₂×C₅×#121	1	1	yes	characteristic
663	C₂²	C₅×#532	1	1	yes	characteristic
664	C₂²	C₅×#577	1	1	yes	characteristic
665	C₂²	C₅×#577	1	1	yes	characteristic
666	C₂²	C₅×#577	1	1	yes	characteristic
667	C₂²	C₅×#577	1	1	yes	characteristic
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	—	8	1	no	—
679	C₄	—	8	1	no	—
680	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
681	C₄	C₄×C₅×#41	1	1	yes	characteristic
682	C₄	C₅×#525	1	1	yes	characteristic
683	C₄	C₅×#529	1	1	yes	characteristic
684	C₂	—	4	2	no	—
685	C₂	—	8	2	no	—
686	C₂	C₄×C₅×#121	1	1	yes	characteristic
687	C₂	C₅×#2949	1	1	yes	characteristic
688	C₂	C₅×#2952	1	1	yes	characteristic
689	C₂	C₅×#3057	1	1	yes	characteristic
690	C₂	C₅×#3060	1	1	yes	characteristic
691	C₂	C₅×#3173	1	1	yes	characteristic
692	C₂	C₅×#3174	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×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×SD₁₆	C₂	semidirect
3. C₂×C₅×#405	C₂	semidirect
5. C₅×#2323	C₂	semidirect
6. C₅×#1968	C₂	semidirect
7. C₅×#1941	C₂	semidirect
8. C₅×#1936	C₂	semidirect
9. C₅×#1935	C₂	semidirect
11. C₅×#1894	C₂	semidirect
12. C₅×#1807	C₂	semidirect
13. C₄×C₅×#106	C₂	semidirect
14. C₅×#1763	C₂	semidirect
15. C₅×#1762	C₂	semidirect
24. C₅×#465	C₄	semidirect
62. #21523	C₅	direct (N × H)
76. C₂²×C₅×C₈	C₂×C₄	semidirect
82. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
119. C₅×#106	C₂×C₄	semidirect
122. C₅×#103	C₂×C₄	semidirect
129. C₄×C₅×C₈	D₄	semidirect
139. C₂×C₄×SD₁₆	C₂×C₅	semidirect
140. C₂×#405	C₂×C₅	semidirect
142. #2323	C₂×C₅	semidirect
143. #1968	C₂×C₅	semidirect
144. #1941	C₂×C₅	semidirect
145. #1936	C₂×C₅	semidirect
146. #1935	C₂×C₅	semidirect
148. #1894	C₂×C₅	semidirect
149. #1807	C₂×C₅	semidirect
150. C₄×#106	C₂×C₅	semidirect
151. #1763	C₂×C₅	semidirect
152. #1762	C₂×C₅	semidirect
249. #465	C₄×C₅	semidirect
375. C₂²×C₈	C₂×C₄×C₅	semidirect
381. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
418. #106	C₂×C₄×C₅	semidirect
421. #103	C₂×C₄×C₅	semidirect
428. C₄×C₈	C₅×D₄	semidirect
646. C₅	#21523	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×#465	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×#405	2
C₅×#2324	2
C₅×#2323	2
C₅×#1968	2
C₅×#1941	2
C₅×#1936	2
C₅×#1935	2
C₅×#1895	2
C₅×#1894	2
C₅×#1807	2
C₄×C₅×#106	2
C₅×#1763	2
C₅×#1762	2
#21523	5

Subgroups — C5×#21523 #11944243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21523 #11944243