Subgroups — C₅×#22872 #11945592

Order 1280.

1186 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₅×#117	C₂²	1	1	yes	characteristic
25	C₅×#449	C₄	1	8	yes	complemented
26	C₄×C₅×D₈	—	2	4	no	—
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₅×#416	—	2	4	no	—
30	C₂×C₅×#103	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×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×C₈	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×#391	C₂²	1	1	yes	characteristic
43	C₅×#390	—	2	1	no	—
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#388	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#386	—	2	1	no	—
50	C₅×#381	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₅×#95	—	2	1	no	—
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	#22872	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂×C₅×#41	—	2	2	no	—
64	C₂×C₅×#41	—	2	2	no	—
65	C₂×C₅×#41	—	2	2	no	—
66	C₂×C₅×#41	—	4	1	no	—
67	C₂×C₅×#41	—	4	1	no	—
68	C₂×C₅×#41	C₂×C₄	1	4	yes	complemented
69	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₂²×C₅×D₄	—	2	1	no	—
72	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
73	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	—	2	1	no	—
76	C₂³×C₄×C₅	—	2	1	no	—
77	C₂³×C₄×C₅	—	2	1	no	—
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×SD₁₆	—	4	1	no	—
80	C₂×C₅×SD₁₆	—	4	1	no	—
81	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
82	C₂×C₅×D₈	—	2	2	no	—
83	C₂×C₅×D₈	—	2	2	no	—
84	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
85	C₂²×C₅×C₈	—	2	2	no	—
86	C₂²×C₅×C₈	—	2	2	no	—
87	C₂²×C₅×C₈	—	4	1	no	—
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₅×#121	—	2	2	no	—
93	C₅×#121	C₂×C₄	1	4	yes	complemented
94	C₄×C₅×D₄	—	2	2	no	—
95	C₄×C₅×D₄	—	2	2	no	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₄×C₅×D₄	—	4	1	no	—
98	C₄×C₅×D₄	—	4	1	no	—
99	C₄×C₅×D₄	—	4	1	no	—
100	C₅×#117	—	2	2	no	—
101	C₅×#117	—	4	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
117	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅	—	2	1	no	—
119	C₂×C₄²×C₅	—	2	1	no	—
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₅×#107	—	2	2	no	—
123	C₅×#106	—	4	1	no	—
124	C₅×#103	—	2	2	no	—
125	C₅×#103	—	2	2	no	—
126	C₅×#103	C₂×C₄	1	4	yes	complemented
127	C₅×#102	—	2	2	no	—
128	C₅×#102	—	2	2	no	—
129	C₅×#102	—	4	1	no	—
130	C₅×#102	C₂×C₄	1	4	yes	complemented
131	C₅×#102	D₄	1	4	yes	complemented
132	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
133	C₄×C₅×C₈	—	2	2	no	—
134	C₄×C₅×C₈	—	4	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	—	2	1	no	—
138	C₅×#95	—	2	1	no	—
139	C₅×#95	—	2	1	no	—
140	C₅×#95	—	2	1	no	—
141	C₅×#95	—	2	1	no	—
142	C₅×#95	D₄	1	1	yes	characteristic
143	C₅×#95	D₄	1	1	yes	characteristic
144	C₂×#449	C₂×C₅	1	1	yes	characteristic
145	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#416	C₂×C₅	1	1	yes	characteristic, complemented
147	#2363	C₂×C₅	1	1	yes	characteristic, complemented
148	#2339	C₂×C₅	1	1	yes	characteristic, complemented
149	#1968	C₂×C₅	1	1	yes	characteristic, complemented
150	#1933	C₂×C₅	1	1	yes	characteristic, complemented
151	#1928	C₂×C₅	1	1	yes	characteristic, complemented
152	#1893	C₂×C₅	1	1	yes	characteristic, complemented
153	#1879	C₂×C₅	1	1	yes	characteristic, complemented
154	#1877	C₂×C₅	1	1	yes	characteristic, complemented
155	#1864	C₂×C₅	1	1	yes	characteristic, complemented
156	#1854	C₂×C₅	1	1	yes	characteristic, complemented
157	C₄×#102	C₂×C₅	1	1	yes	characteristic, complemented
158	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂⁴×C₅	—	2	1	no	—
160	C₂⁴×C₅	—	2	1	no	—
161	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
162	C₅×#41	—	2	8	no	—
163	C₅×#41	—	4	4	no	—
164	C₅×#41	—	4	4	no	—
165	C₅×#41	—	4	4	no	—
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	1	no	—
171	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
172	C₂×C₅×D₄	—	2	4	no	—
173	C₂×C₅×D₄	—	2	4	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	2	1	no	—
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	4	2	no	—
183	C₂×C₅×D₄	—	4	2	no	—
184	C₂×C₅×D₄	—	8	1	no	—
185	C₂×C₅×D₄	—	8	1	no	—
186	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
187	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
188	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
189	C₂×C₅×D₄	#41	1	2	yes	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	4	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	—	4	2	no	—
202	C₂²×C₄×C₅	—	4	2	no	—
203	C₂²×C₄×C₅	—	4	2	no	—
204	C₂²×C₄×C₅	—	4	2	no	—
205	C₂²×C₄×C₅	—	4	2	no	—
206	C₂²×C₄×C₅	—	4	2	no	—
207	C₂²×C₄×C₅	—	4	2	no	—
208	C₂²×C₄×C₅	—	4	2	no	—
209	C₂²×C₄×C₅	—	8	1	no	—
210	C₂²×C₄×C₅	—	8	1	no	—
211	C₂²×C₄×C₅	—	8	1	no	—
212	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
213	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	#41	1	2	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₅×SD₁₆	—	4	4	no	—
221	C₅×D₈	—	2	8	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	2	1	no	—
225	C₂×C₅×C₈	—	2	1	no	—
226	C₂×C₅×C₈	—	2	1	no	—
227	C₂×C₅×C₈	—	2	1	no	—
228	C₂×C₅×C₈	—	2	1	no	—
229	C₂×C₅×C₈	—	2	1	no	—
230	C₂×C₅×C₈	—	2	1	no	—
231	C₂×C₅×C₈	—	4	4	no	—
232	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
233	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
234	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	2	1	no	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	—	2	1	no	—
243	C₅×C₄⋊C₄	—	8	1	no	—
244	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
245	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	4	2	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₅×C₂²⋊C₄	—	4	2	no	—
252	C₅×C₂²⋊C₄	—	4	2	no	—
253	C₅×C₂²⋊C₄	—	4	2	no	—
254	C₅×C₂²⋊C₄	—	8	1	no	—
255	C₅×C₂²⋊C₄	—	8	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	—	2	1	no	—
259	C₄²×C₅	—	2	1	no	—
260	C₄²×C₅	—	4	2	no	—
261	C₄²×C₅	—	8	1	no	—
262	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
264	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×#121	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×#117	C₂²×C₅	1	1	yes	characteristic
271	#449	C₄×C₅	1	8	yes	complemented
272	C₄×D₈	—	2	4	no	—
273	C₂×#107	C₂²×C₅	1	1	yes	characteristic
274	C₂×#106	C₂²×C₅	1	1	yes	characteristic
275	#416	—	2	4	no	—
276	C₂×#103	C₂²×C₅	1	1	yes	characteristic
277	C₂×#103	C₂²×C₅	1	1	yes	characteristic
278	C₂×#103	C₂²×C₅	1	1	yes	characteristic
279	C₂×#102	C₂²×C₅	1	1	yes	characteristic
280	C₂×#102	C₂²×C₅	1	1	yes	characteristic
281	C₂×#102	C₂²×C₅	1	1	yes	characteristic
282	C₂×#102	C₂²×C₅	1	1	yes	characteristic
283	C₂×#102	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
287	#391	C₂²×C₅	1	1	yes	characteristic
288	#391	C₂²×C₅	1	1	yes	characteristic
289	#390	—	2	1	no	—
290	#390	C₂²×C₅	1	1	yes	characteristic
291	#389	C₂²×C₅	1	1	yes	characteristic
292	#388	—	2	1	no	—
293	#386	—	2	1	no	—
294	#386	—	2	1	no	—
295	#386	—	2	1	no	—
296	#381	—	2	1	no	—
297	#380	C₂²×C₅	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
299	C₄×C₂²⋊C₄	—	2	1	no	—
300	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×#95	—	2	1	no	—
302	#340	C₂²×C₅	1	1	yes	characteristic
303	#340	C₂²×C₅	1	1	yes	characteristic
304	#340	C₂²×C₅	1	1	yes	characteristic
305	#340	C₂²×C₅	1	1	yes	characteristic
306	#336	C₂²×C₅	1	1	yes	characteristic
307	#336	C₂²×C₅	1	1	yes	characteristic
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	2	no	—
311	C₂³×C₅	—	2	2	no	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	—	2	1	no	—
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	—	4	1	no	—
320	C₂³×C₅	—	4	1	no	—
321	C₂³×C₅	—	4	1	no	—
322	C₂³×C₅	—	4	1	no	—
323	C₂³×C₅	—	4	1	no	—
324	C₂³×C₅	—	4	1	no	—
325	C₂³×C₅	—	4	1	no	—
326	C₂³×C₅	—	4	1	no	—
327	C₂³×C₅	—	4	1	no	—
328	C₂³×C₅	C₄×D₄	1	2	yes	—
329	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₅×Q₈	—	2	2	no	—
331	C₅×Q₈	—	2	2	no	—
332	C₅×Q₈	—	4	1	no	—
333	C₅×Q₈	—	4	1	no	—
334	C₅×D₄	—	2	2	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	2	2	no	—
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	2	2	no	—
339	C₅×D₄	—	4	8	no	—
340	C₅×D₄	—	4	1	no	—
341	C₅×D₄	—	4	1	no	—
342	C₅×D₄	—	8	4	no	—
343	C₅×D₄	C₄×D₄	1	4	yes	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	4	8	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	1	no	—
373	C₂×C₄×C₅	—	4	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	4	1	no	—
376	C₂×C₄×C₅	—	4	1	no	—
377	C₂×C₄×C₅	—	4	1	no	—
378	C₂×C₄×C₅	—	4	1	no	—
379	C₂×C₄×C₅	—	8	4	no	—
380	C₂×C₄×C₅	—	8	4	no	—
381	C₂×C₄×C₅	—	8	4	no	—
382	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
383	C₂×C₄×C₅	#135	1	2	yes	—
384	C₂×C₄×C₅	#135	1	2	yes	—
385	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
386	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
389	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
391	C₅×C₈	—	2	2	no	—
392	C₅×C₈	—	2	2	no	—
393	C₅×C₈	—	2	2	no	—
394	C₅×C₈	—	4	1	no	—
395	C₂×#41	—	2	2	no	—
396	C₂×#41	—	2	2	no	—
397	C₂×#41	—	2	2	no	—
398	C₂×#41	—	4	1	no	—
399	C₂×#41	—	4	1	no	—
400	C₂×#41	C₂×C₄×C₅	1	4	yes	complemented
401	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
405	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂×SD₁₆	—	4	1	no	—
412	C₂×SD₁₆	—	4	1	no	—
413	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
414	C₂×D₈	—	2	2	no	—
415	C₂×D₈	—	2	2	no	—
416	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
417	C₂²×C₈	—	2	2	no	—
418	C₂²×C₈	—	2	2	no	—
419	C₂²×C₈	—	4	1	no	—
420	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
424	#121	—	2	2	no	—
425	#121	C₂×C₄×C₅	1	4	yes	complemented
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	4	1	no	—
430	C₄×D₄	—	4	1	no	—
431	C₄×D₄	—	4	1	no	—
432	#117	—	2	2	no	—
433	#117	—	4	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
454	#107	—	2	2	no	—
455	#106	—	4	1	no	—
456	#103	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	C₂×C₄×C₅	1	4	yes	complemented
459	#102	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	4	1	no	—
462	#102	C₂×C₄×C₅	1	4	yes	complemented
463	#102	C₅×D₄	1	4	yes	complemented
464	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
465	C₄×C₈	—	2	2	no	—
466	C₄×C₈	—	4	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	C₅×D₄	1	1	yes	characteristic
475	#95	C₅×D₄	1	1	yes	characteristic
476	C₂²×C₅	—	2	2	no	—
477	C₂²×C₅	—	2	4	no	—
478	C₂²×C₅	—	2	2	no	—
479	C₂²×C₅	—	2	2	no	—
480	C₂²×C₅	—	4	2	no	—
481	C₂²×C₅	—	4	2	no	—
482	C₂²×C₅	—	4	2	no	—
483	C₂²×C₅	—	4	1	no	—
484	C₂²×C₅	—	4	1	no	—
485	C₂²×C₅	—	4	2	no	—
486	C₂²×C₅	—	4	2	no	—
487	C₂²×C₅	—	4	1	no	—
488	C₂²×C₅	—	4	1	no	—
489	C₂²×C₅	—	4	2	no	—
490	C₂²×C₅	—	4	2	no	—
491	C₂²×C₅	—	4	2	no	—
492	C₂²×C₅	—	4	2	no	—
493	C₂²×C₅	—	8	1	no	—
494	C₂²×C₅	—	8	1	no	—
495	C₂²×C₅	—	8	1	no	—
496	C₂²×C₅	—	8	1	no	—
497	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
498	C₂²×C₅	D₄²	1	1	yes	characteristic
499	C₂²×C₅	#546	1	1	yes	characteristic
500	C₂²×C₅	C₂×#135	1	1	yes	characteristic
501	C₂²×C₅	C₂×#135	1	1	yes	characteristic
502	C₂²×C₅	#576	1	1	yes	characteristic
503	C₂²×C₅	#577	1	1	yes	characteristic
504	C₄×C₅	—	2	2	no	—
505	C₄×C₅	—	2	2	no	—
506	C₄×C₅	—	2	2	no	—
507	C₄×C₅	—	4	2	no	—
508	C₄×C₅	—	4	2	no	—
509	C₄×C₅	—	4	2	no	—
510	C₄×C₅	—	4	1	no	—
511	C₄×C₅	—	4	1	no	—
512	C₄×C₅	—	8	1	no	—
513	C₄×C₅	—	8	1	no	—
514	C₄×C₅	—	8	1	no	—
515	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
516	C₄×C₅	#518	1	1	yes	characteristic
517	C₄×C₅	#546	1	1	yes	characteristic
518	C₄×C₅	#551	1	1	yes	characteristic
519	C₂⁴	—	2	1	no	—
520	C₂⁴	—	2	1	no	—
521	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
522	#41	—	2	8	no	—
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	4	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	8	1	no	—
545	C₂×D₄	—	8	1	no	—
546	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
547	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
548	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
549	C₂×D₄	C₅×#41	1	2	yes	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	8	1	no	—
570	C₂²×C₄	—	8	1	no	—
571	C₂²×C₄	—	8	1	no	—
572	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
573	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
574	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
575	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
576	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
577	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
578	C₂²×C₄	C₅×#41	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
580	SD₁₆	—	4	4	no	—
581	D₈	—	2	8	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	4	4	no	—
592	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
593	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
594	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	8	1	no	—
604	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
605	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	4	2	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	—	8	1	no	—
615	C₂²⋊C₄	—	8	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	4	2	no	—
621	C₄²	—	8	1	no	—
622	C₂×C₅	—	4	2	no	—
623	C₂×C₅	—	4	4	no	—
624	C₂×C₅	—	8	2	no	—
625	C₂×C₅	#2358	1	1	yes	characteristic
626	C₂×C₅	C₄×#135	1	1	yes	characteristic
627	C₂×C₅	#2946	1	1	yes	characteristic
628	C₂×C₅	#3280	1	1	yes	characteristic
629	C₂×C₅	#3284	1	1	yes	characteristic
630	C₂×C₅	#3297	1	1	yes	characteristic
631	C₂×C₅	#3303	1	1	yes	characteristic
632	C₂³	—	2	2	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	C₄×C₅×D₄	1	2	yes	—
653	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	8	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	8	4	no	—
667	D₄	C₄×C₅×D₄	1	4	yes	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	—	8	4	no	—
706	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
707	C₂×C₄	C₅×#135	1	2	yes	—
708	C₂×C₄	C₅×#135	1	2	yes	—
709	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
711	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
712	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
713	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
715	C₈	—	2	2	no	—
716	C₈	—	2	2	no	—
717	C₈	—	2	2	no	—
718	C₈	—	4	1	no	—
719	C₅	#22872	1	1	yes	characteristic, direct product factor, Sylow
720	C₂²	—	2	2	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
742	C₂²	C₅×D₄²	1	1	yes	characteristic
743	C₂²	C₅×#546	1	1	yes	characteristic
744	C₂²	C₂×C₅×#135	1	1	yes	characteristic
745	C₂²	C₂×C₅×#135	1	1	yes	characteristic
746	C₂²	C₅×#576	1	1	yes	characteristic
747	C₂²	C₅×#577	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	8	1	no	—
757	C₄	—	8	1	no	—
758	C₄	—	8	1	no	—
759	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
760	C₄	C₅×#518	1	1	yes	characteristic
761	C₄	C₅×#546	1	1	yes	characteristic
762	C₄	C₅×#551	1	1	yes	characteristic
763	C₂	—	4	2	no	—
764	C₂	—	4	4	no	—
765	C₂	—	8	2	no	—
766	C₂	C₅×#2358	1	1	yes	characteristic
767	C₂	C₄×C₅×#135	1	1	yes	characteristic
768	C₂	C₅×#2946	1	1	yes	characteristic
769	C₂	C₅×#3280	1	1	yes	characteristic
770	C₂	C₅×#3284	1	1	yes	characteristic
771	C₂	C₅×#3297	1	1	yes	characteristic
772	C₂	C₅×#3303	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×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×D₈	C₂	semidirect
3. C₂×C₅×#416	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2339	C₂	semidirect
6. C₅×#1968	C₂	semidirect
7. C₅×#1933	C₂	semidirect
8. C₅×#1928	C₂	semidirect
9. C₅×#1893	C₂	semidirect
10. C₅×#1879	C₂	semidirect
11. C₅×#1877	C₂	semidirect
12. C₅×#1864	C₂	semidirect
13. C₅×#1854	C₂	semidirect
14. C₄×C₅×#102	C₂	semidirect
15. C₅×C₈×C₂²⋊C₄	C₂	semidirect
25. C₅×#449	C₄	semidirect
62. #22872	C₅	direct (N × H)
68. C₂×C₅×#41	C₂×C₄	semidirect
81. C₂×C₅×SD₁₆	C₂×C₄	semidirect
93. C₅×#121	C₂×C₄	semidirect
126. C₅×#103	C₂×C₄	semidirect
130. C₅×#102	C₂×C₄	semidirect
131. C₅×#102	D₄	semidirect
132. C₅×C₂²⋊C₈	C₂×C₄	semidirect
145. C₂×C₄×D₈	C₂×C₅	semidirect
146. C₂×#416	C₂×C₅	semidirect
147. #2363	C₂×C₅	semidirect
148. #2339	C₂×C₅	semidirect
149. #1968	C₂×C₅	semidirect
150. #1933	C₂×C₅	semidirect
151. #1928	C₂×C₅	semidirect
152. #1893	C₂×C₅	semidirect
153. #1879	C₂×C₅	semidirect
154. #1877	C₂×C₅	semidirect
155. #1864	C₂×C₅	semidirect
156. #1854	C₂×C₅	semidirect
157. C₄×#102	C₂×C₅	semidirect
158. C₈×C₂²⋊C₄	C₂×C₅	semidirect
271. #449	C₄×C₅	semidirect
400. C₂×#41	C₂×C₄×C₅	semidirect
413. C₂×SD₁₆	C₂×C₄×C₅	semidirect
425. #121	C₂×C₄×C₅	semidirect
458. #103	C₂×C₄×C₅	semidirect
462. #102	C₂×C₄×C₅	semidirect
463. #102	C₅×D₄	semidirect
464. C₂²⋊C₈	C₂×C₄×C₅	semidirect
719. C₅	#22872	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×#449	2
C₂×C₄×C₅×D₈	2
C₂×C₅×#416	2
C₅×#2363	2
C₅×#2339	2
C₅×#1968	2
C₅×#1933	2
C₅×#1928	2
C₅×#1893	2
C₅×#1879	2
C₅×#1877	2
C₅×#1864	2
C₅×#1854	2
C₄×C₅×#102	2
C₅×C₈×C₂²⋊C₄	2
#22872	5

Subgroups — C5×#22872 #11945592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22872 #11945592