Subgroups — C₅×#29464 #11952184

Order 1280.

850 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
3	C₅×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2034	C₂	1	1	yes	maximal, characteristic
6	C₅×#2000	C₂	1	1	yes	maximal, characteristic
7	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1941	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	—	2	1	no	—
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×#106	C₂²	1	1	yes	characteristic
25	C₂×C₅×#103	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#391	C₂²	1	1	yes	characteristic
36	C₅×#391	C₂²	1	1	yes	characteristic
37	C₅×#390	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#388	—	2	1	no	—
42	C₅×#387	—	2	1	no	—
43	C₅×#387	—	2	1	no	—
44	C₅×#386	—	2	1	no	—
45	C₅×#385	—	2	1	no	—
46	C₅×#381	—	2	1	no	—
47	C₅×#380	C₂²	1	1	yes	characteristic
48	C₅×#380	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#29464	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×SD₁₆	—	2	2	no	—
68	C₂×C₅×SD₁₆	—	2	2	no	—
69	C₂×C₅×SD₁₆	—	4	1	no	—
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₅×C₂²⋊Q₈	—	4	1	no	—
75	C₅×C₂²⋊Q₈	—	4	1	no	—
76	C₅×#121	—	2	2	no	—
77	C₅×#121	—	2	2	no	—
78	C₄×C₅×D₄	—	4	1	no	—
79	C₄×C₅×D₄	—	4	1	no	—
80	C₄×C₅×D₄	—	4	4	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	—	4	1	no	—
100	C₂×C₄²×C₅	—	4	1	no	—
101	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×#106	—	2	2	no	—
106	C₅×#106	—	2	2	no	—
107	C₅×#106	—	4	1	no	—
108	C₅×#103	—	2	2	no	—
109	C₅×#103	—	2	2	no	—
110	C₅×#103	—	4	1	no	—
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	—	4	1	no	—
114	C₅×C₂²⋊C₈	—	2	2	no	—
115	C₅×C₂²⋊C₈	—	2	2	no	—
116	C₄×C₅×C₈	—	4	1	no	—
117	C₄×C₅×C₈	—	4	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	no	—
127	C₅×#95	—	2	1	no	—
128	#2855	C₂×C₅	1	1	yes	characteristic, complemented
129	C₄×#121	C₂×C₅	1	1	yes	characteristic
130	#2077	C₂×C₅	1	1	yes	characteristic, complemented
131	#2035	C₂×C₅	1	1	yes	characteristic, complemented
132	#2034	C₂×C₅	1	1	yes	characteristic
133	#2000	C₂×C₅	1	1	yes	characteristic
134	#1968	C₂×C₅	1	1	yes	characteristic, complemented
135	#1941	C₂×C₅	1	1	yes	characteristic, complemented
136	#1934	C₂×C₅	1	1	yes	characteristic, complemented
137	#1933	C₂×C₅	1	1	yes	characteristic, complemented
138	#1927	C₂×C₅	1	1	yes	characteristic, complemented
139	#1920	C₂×C₅	1	1	yes	characteristic, complemented
140	#1877	C₂×C₅	1	1	yes	characteristic, complemented
141	#1864	C₂×C₅	1	1	yes	characteristic, complemented
142	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂⁴×C₅	—	2	1	no	—
144	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	—	2	1	no	—
148	C₂×C₅×Q₈	—	2	1	no	—
149	C₂×C₅×Q₈	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	1	no	—
151	C₂×C₅×D₄	—	2	4	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	4	2	no	—
158	C₂×C₅×D₄	—	4	2	no	—
159	C₂×C₅×D₄	#41	1	2	yes	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	2	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	1	no	—
175	C₂²×C₄×C₅	—	4	1	no	—
176	C₂²×C₄×C₅	—	4	1	no	—
177	C₂²×C₄×C₅	—	4	1	no	—
178	C₂²×C₄×C₅	—	4	2	no	—
179	C₂²×C₄×C₅	—	4	2	no	—
180	C₂²×C₄×C₅	—	4	2	no	—
181	C₂²×C₄×C₅	SD₁₆	1	4	yes	complemented
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	C₂⁴	1	1	yes	characteristic
188	C₅×SD₁₆	—	4	4	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	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	#41	1	2	yes	—
200	C₂×C₅×C₈	#41	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
213	C₅×C₄⋊C₄	—	4	2	no	—
214	C₅×C₄⋊C₄	—	4	2	no	—
215	C₅×C₄⋊C₄	—	4	2	no	—
216	C₅×C₄⋊C₄	#41	1	2	yes	—
217	C₅×C₂²⋊C₄	—	2	4	no	—
218	C₅×C₂²⋊C₄	—	4	2	no	—
219	C₅×C₂²⋊C₄	—	4	2	no	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₅×C₂²⋊C₄	—	4	2	no	—
222	C₅×C₂²⋊C₄	—	4	2	no	—
223	C₅×C₂²⋊C₄	—	4	2	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	4	1	no	—
229	C₄²×C₅	—	4	1	no	—
230	C₄²×C₅	—	4	2	no	—
231	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₂×#121	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
237	C₂×#106	C₂²×C₅	1	1	yes	characteristic
238	C₂×#106	C₂²×C₅	1	1	yes	characteristic
239	C₂×#106	C₂²×C₅	1	1	yes	characteristic
240	C₂×#103	C₂²×C₅	1	1	yes	characteristic
241	C₂×#103	C₂²×C₅	1	1	yes	characteristic
242	C₂×#103	C₂²×C₅	1	1	yes	characteristic
243	C₂×#102	C₂²×C₅	1	1	yes	characteristic
244	C₂×#102	C₂²×C₅	1	1	yes	characteristic
245	C₂×#102	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
250	#391	C₂²×C₅	1	1	yes	characteristic
251	#391	C₂²×C₅	1	1	yes	characteristic
252	#390	C₂²×C₅	1	1	yes	characteristic
253	#389	C₂²×C₅	1	1	yes	characteristic
254	#389	C₂²×C₅	1	1	yes	characteristic
255	#389	C₂²×C₅	1	1	yes	characteristic
256	#388	—	2	1	no	—
257	#387	—	2	1	no	—
258	#387	—	2	1	no	—
259	#386	—	2	1	no	—
260	#385	—	2	1	no	—
261	#381	—	2	1	no	—
262	#380	C₂²×C₅	1	1	yes	characteristic
263	#380	C₂²×C₅	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	—	2	1	no	—
266	#340	C₂²×C₅	1	1	yes	characteristic
267	#340	C₂²×C₅	1	1	yes	characteristic
268	#340	C₂²×C₅	1	1	yes	characteristic
269	#340	C₂²×C₅	1	1	yes	characteristic
270	#340	C₂²×C₅	1	1	yes	characteristic
271	#340	C₂²×C₅	1	1	yes	characteristic
272	#336	C₂²×C₅	1	1	yes	characteristic
273	#336	C₂²×C₅	1	1	yes	characteristic
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	2	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	—	4	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	C₂×SD₁₆	1	2	yes	—
288	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	—	4	1	no	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	4	8	no	—
296	C₅×D₄	—	4	1	no	—
297	C₅×D₄	—	4	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
312	C₂×C₄×C₅	—	4	4	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	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	—	8	4	no	—
338	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
339	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
340	C₂×C₄×C₅	#135	1	2	yes	—
341	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
347	C₅×C₈	—	2	2	no	—
348	C₅×C₈	—	2	2	no	—
349	C₅×C₈	—	4	1	no	—
350	C₅×C₈	—	4	1	no	—
351	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
356	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	—	4	1	no	—
361	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₂²⋊Q₈	—	4	1	no	—
366	C₂²⋊Q₈	—	4	1	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	C₄×D₄	—	4	1	no	—
370	C₄×D₄	—	4	1	no	—
371	C₄×D₄	—	4	4	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	4	1	no	—
391	C₂×C₄²	—	4	1	no	—
392	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
393	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
396	#106	—	2	2	no	—
397	#106	—	2	2	no	—
398	#106	—	4	1	no	—
399	#103	—	2	2	no	—
400	#103	—	2	2	no	—
401	#103	—	4	1	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	4	1	no	—
405	C₂²⋊C₈	—	2	2	no	—
406	C₂²⋊C₈	—	2	2	no	—
407	C₄×C₈	—	4	1	no	—
408	C₄×C₈	—	4	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	C₂²×C₅	—	2	2	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	2	no	—
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	—	4	2	no	—
429	C₂²×C₅	—	8	1	no	—
430	C₂²×C₅	—	8	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	#525	1	1	yes	characteristic
434	C₂²×C₅	#532	1	1	yes	characteristic
435	C₂²×C₅	#534	1	1	yes	characteristic
436	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
437	C₂²×C₅	C₂×#135	1	1	yes	characteristic
438	C₂²×C₅	#575	1	1	yes	characteristic
439	C₂²×C₅	#575	1	1	yes	characteristic
440	C₄×C₅	—	2	2	no	—
441	C₄×C₅	—	2	2	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	4	2	no	—
444	C₄×C₅	—	4	1	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	—	8	1	no	—
447	C₄×C₅	—	8	1	no	—
448	C₄×C₅	—	8	1	no	—
449	C₄×C₅	—	8	1	no	—
450	C₄×C₅	—	8	1	no	—
451	C₄×C₅	—	8	1	no	—
452	C₄×C₅	#551	1	1	yes	characteristic
453	C₄×C₅	#553	1	1	yes	characteristic
454	C₄×C₅	#553	1	1	yes	characteristic
455	C₄×C₅	#559	1	1	yes	characteristic
456	C₂⁴	—	2	1	no	—
457	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	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×D₄	—	2	4	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	C₅×#41	1	2	yes	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
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	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	C₅×SD₁₆	1	4	yes	complemented
495	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
501	SD₁₆	—	4	4	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	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	C₅×#41	1	2	yes	—
513	C₂×C₈	C₅×#41	1	2	yes	—
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	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	C₅×#41	1	2	yes	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	4	1	no	—
542	C₄²	—	4	1	no	—
543	C₄²	—	4	2	no	—
544	C₂×C₅	—	4	2	no	—
545	C₂×C₅	—	8	2	no	—
546	C₂×C₅	#2602	1	1	yes	characteristic
547	C₂×C₅	#3101	1	1	yes	characteristic
548	C₂×C₅	#3102	1	1	yes	characteristic
549	C₂×C₅	#3167	1	1	yes	characteristic
550	C₂×C₅	#3183	1	1	yes	characteristic
551	C₂×C₅	#3187	1	1	yes	characteristic
552	C₂×C₅	#3191	1	1	yes	characteristic
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	C₂×C₅×SD₁₆	1	2	yes	—
567	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	4	8	no	—
575	D₄	—	4	1	no	—
576	D₄	—	4	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	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	4	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	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	8	4	no	—
617	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
618	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
619	C₂×C₄	C₅×#135	1	2	yes	—
620	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
621	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
622	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
623	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
624	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
626	C₈	—	2	2	no	—
627	C₈	—	2	2	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₅	#29464	1	1	yes	characteristic, direct product factor, Sylow
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	C₅×#525	1	1	yes	characteristic
646	C₂²	C₅×#532	1	1	yes	characteristic
647	C₂²	C₅×#534	1	1	yes	characteristic
648	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
649	C₂²	C₂×C₅×#135	1	1	yes	characteristic
650	C₂²	C₅×#575	1	1	yes	characteristic
651	C₂²	C₅×#575	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	C₅×#551	1	1	yes	characteristic
665	C₄	C₅×#553	1	1	yes	characteristic
666	C₄	C₅×#553	1	1	yes	characteristic
667	C₄	C₅×#559	1	1	yes	characteristic
668	C₂	—	4	2	no	—
669	C₂	—	8	2	no	—
670	C₂	C₅×#2602	1	1	yes	characteristic
671	C₂	C₅×#3101	1	1	yes	characteristic
672	C₂	C₅×#3102	1	1	yes	characteristic
673	C₂	C₅×#3167	1	1	yes	characteristic
674	C₂	C₅×#3183	1	1	yes	characteristic
675	C₂	C₅×#3187	1	1	yes	characteristic
676	C₂	C₅×#3191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2855	C₂	semidirect
3. C₅×#2077	C₂	semidirect
4. C₅×#2035	C₂	semidirect
7. C₅×#1968	C₂	semidirect
8. C₅×#1941	C₂	semidirect
9. C₅×#1934	C₂	semidirect
10. C₅×#1933	C₂	semidirect
11. C₅×#1927	C₂	semidirect
12. C₅×#1920	C₂	semidirect
13. C₅×#1877	C₂	semidirect
14. C₅×#1864	C₂	semidirect
15. C₄×C₅×C₂²⋊C₈	C₂	semidirect
59. #29464	C₅	direct (N × H)
128. #2855	C₂×C₅	semidirect
130. #2077	C₂×C₅	semidirect
131. #2035	C₂×C₅	semidirect
134. #1968	C₂×C₅	semidirect
135. #1941	C₂×C₅	semidirect
136. #1934	C₂×C₅	semidirect
137. #1933	C₂×C₅	semidirect
138. #1927	C₂×C₅	semidirect
139. #1920	C₂×C₅	semidirect
140. #1877	C₂×C₅	semidirect
141. #1864	C₂×C₅	semidirect
142. C₄×C₂²⋊C₈	C₂×C₅	semidirect
181. C₂²×C₄×C₅	SD₁₆	semidirect
494. C₂²×C₄	C₅×SD₁₆	semidirect
630. C₅	#29464	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#2855	2
C₄×C₅×#121	2
C₅×#2077	2
C₅×#2035	2
C₅×#2034	2
C₅×#2000	2
C₅×#1968	2
C₅×#1941	2
C₅×#1934	2
C₅×#1933	2
C₅×#1927	2
C₅×#1920	2
C₅×#1877	2
C₅×#1864	2
C₄×C₅×C₂²⋊C₈	2
#29464	5

Subgroups — C5×#29464 #11952184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29464 #11952184