Subgroups — C₅×#22950 #11945670

Order 1280.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3091	C₂	1	1	yes	maximal, characteristic
2	C₅×#2933	C₂	1	1	yes	maximal, characteristic
3	C₅×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1896	C₂	1	1	yes	maximal, characteristic
10	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1773	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1749	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₅×#525	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₅×#485	C₄	1	1	yes	characteristic, complemented
22	C₅×#485	C₄	1	1	yes	characteristic, complemented
23	C₅×#484	C₄	1	1	yes	characteristic, complemented
24	C₅×#483	C₄	1	1	yes	characteristic, complemented
25	C₅×#482	C₄	1	1	yes	characteristic, complemented
26	C₅×#482	C₄	1	1	yes	characteristic, complemented
27	C₅×#481	C₄	1	1	yes	characteristic, complemented
28	C₅×#480	C₄	1	1	yes	characteristic, complemented
29	C₅×#436	—	2	1	no	—
30	C₅×#435	—	2	1	no	—
31	C₅×#435	—	2	1	no	—
32	C₅×C₈×D₄	—	2	1	no	—
33	C₅×#433	—	2	1	no	—
34	C₅×#433	—	2	1	no	—
35	C₅×#432	—	2	1	no	—
36	C₅×#431	—	2	1	no	—
37	C₂×C₅×#108	C₂²	1	1	yes	characteristic
38	C₂×C₅×#108	C₂²	1	1	yes	characteristic
39	C₅×#427	C₂²	1	1	yes	characteristic
40	C₅×#427	C₂²	1	1	yes	characteristic
41	C₅×#424	C₂²	1	1	yes	characteristic
42	C₅×#424	C₂²	1	1	yes	characteristic
43	C₅×#424	C₂²	1	1	yes	characteristic
44	C₂×C₅×#104	C₂²	1	1	yes	characteristic
45	C₂×C₅×#104	C₂²	1	1	yes	characteristic
46	C₅×#416	C₂²	1	1	yes	characteristic
47	C₅×#416	C₂²	1	1	yes	characteristic
48	C₅×#408	C₂²	1	1	yes	characteristic
49	C₅×#407	C₂²	1	1	yes	characteristic
50	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×#405	C₂²	1	1	yes	characteristic
53	C₅×#405	C₂²	1	1	yes	characteristic
54	C₅×#405	C₂²	1	1	yes	characteristic
55	C₂×C₅×#97	C₂²	1	1	yes	characteristic
56	C₂×C₅×#97	C₂²	1	1	yes	characteristic
57	C₅×#341	C₂²	1	1	yes	characteristic
58	C₅×#341	C₂²	1	1	yes	characteristic
59	C₅×#339	C₂²	1	1	yes	characteristic
60	C₅×#339	C₂²	1	1	yes	characteristic
61	C₅×#339	C₂²	1	1	yes	characteristic
62	C₅×#339	C₂²	1	1	yes	characteristic
63	C₅×#339	C₂²	1	1	yes	characteristic
64	C₅×#339	C₂²	1	1	yes	characteristic
65	C₅×#336	C₂²	1	1	yes	characteristic
66	C₅×#336	C₂²	1	1	yes	characteristic
67	#22950	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅	—	2	1	no	—
70	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₅×#131	—	2	2	no	—
72	C₅×#131	—	4	1	no	—
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	2	no	—
76	C₂×C₅×M₁₆	—	4	1	no	—
77	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₅×#123	—	2	1	no	—
88	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
90	C₅×#121	C₂×C₄	1	1	yes	characteristic
91	C₅×#121	C₂×C₄	1	1	yes	characteristic
92	C₅×#120	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	—	2	1	no	—
95	C₅×#117	—	2	1	no	—
96	C₅×#117	—	2	1	no	—
97	C₅×#117	C₂×C₄	1	1	yes	characteristic
98	C₅×#117	C₂×C₄	1	1	yes	characteristic
99	C₅×#117	C₂³	1	1	yes	characteristic
100	C₅×#117	C₂³	1	1	yes	characteristic
101	C₅×#117	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₄²×C₅	—	2	1	no	—
106	C₂×C₄²×C₅	—	2	2	no	—
107	C₂×C₄²×C₅	—	2	1	no	—
108	C₂×C₄²×C₅	—	4	1	no	—
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₅×#108	—	2	2	no	—
112	C₅×#108	—	4	1	no	—
113	C₅×#107	C₂×C₄	1	1	yes	characteristic, complemented
114	C₅×#107	C₂×C₄	1	1	yes	characteristic, complemented
115	C₅×#107	C₂×C₄	1	1	yes	characteristic, complemented
116	C₅×#107	C₂×C₄	1	1	yes	characteristic, complemented
117	C₅×#106	C₂×C₄	1	1	yes	characteristic, complemented
118	C₅×#106	C₂×C₄	1	1	yes	characteristic, complemented
119	C₅×#106	C₂×C₄	1	1	yes	characteristic, complemented
120	C₅×#106	C₂×C₄	1	1	yes	characteristic, complemented
121	C₅×C₄⋊C₈	—	2	1	no	—
122	C₅×C₄⋊C₈	—	2	1	no	—
123	C₅×C₄⋊C₈	—	2	1	no	—
124	C₅×C₄⋊C₈	—	2	1	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	1	no	—
127	C₅×#104	—	2	2	no	—
128	C₅×#104	—	4	1	no	—
129	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
130	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
131	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
132	C₅×#103	C₂×C₄	1	1	yes	characteristic, complemented
133	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
134	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
135	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
136	C₅×#102	C₂×C₄	1	1	yes	characteristic, complemented
137	C₅×C₂²⋊C₈	—	2	1	no	—
138	C₅×C₂²⋊C₈	—	2	1	no	—
139	C₅×C₂²⋊C₈	—	2	1	no	—
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
142	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
143	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
144	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
145	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
146	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
147	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
148	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
149	C₅×#97	—	2	1	no	—
150	C₅×#97	—	2	1	no	—
151	C₅×#97	—	2	1	no	—
152	C₅×#97	—	2	2	no	—
153	C₅×#97	—	4	1	no	—
154	C₄×C₅×C₈	—	2	1	no	—
155	C₄×C₅×C₈	—	2	1	no	—
156	C₄×C₅×C₈	—	2	1	no	—
157	#3091	C₂×C₅	1	1	yes	characteristic
158	#2933	C₂×C₅	1	1	yes	characteristic
159	#2924	C₂×C₅	1	1	yes	characteristic, complemented
160	#1946	C₂×C₅	1	1	yes	characteristic, complemented
161	#1938	C₂×C₅	1	1	yes	characteristic, complemented
162	#1929	C₂×C₅	1	1	yes	characteristic, complemented
163	#1922	C₂×C₅	1	1	yes	characteristic, complemented
164	#1922	C₂×C₅	1	1	yes	characteristic, complemented
165	#1896	C₂×C₅	1	1	yes	characteristic
166	#1866	C₂×C₅	1	1	yes	characteristic, complemented
167	#1855	C₂×C₅	1	1	yes	characteristic, complemented
168	#1773	C₂×C₅	1	1	yes	characteristic, complemented
169	#1765	C₂×C₅	1	1	yes	characteristic, complemented
170	#1749	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂⁴×C₅	#41	1	1	yes	characteristic
173	C₅×#41	—	2	1	no	—
174	C₅×#41	—	2	1	no	—
175	C₅×#41	—	2	1	no	—
176	C₅×#41	—	2	1	no	—
177	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	4	2	no	—
192	C₂²×C₄×C₅	—	4	2	no	—
193	C₂²×C₄×C₅	—	4	2	no	—
194	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	#41	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₅×M₁₆	—	2	1	no	—
201	C₅×M₁₆	—	2	1	no	—
202	C₅×M₁₆	—	2	1	no	—
203	C₅×M₁₆	—	2	1	no	—
204	C₅×M₁₆	—	2	1	no	—
205	C₅×M₁₆	—	2	1	no	—
206	C₅×M₁₆	—	2	1	no	—
207	C₅×M₁₆	—	4	2	no	—
208	C₅×M₁₆	—	4	2	no	—
209	C₅×M₁₆	#41	1	2	yes	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	4	2	no	—
223	C₂×C₅×C₈	—	4	2	no	—
224	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
229	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
230	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
231	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
237	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
238	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
239	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
240	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
241	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
242	C₅×C₂²⋊C₄	—	2	1	no	—
243	C₅×C₂²⋊C₄	—	2	1	no	—
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	2	1	no	—
247	C₅×C₂²⋊C₄	—	2	1	no	—
248	C₅×C₂²⋊C₄	—	2	1	no	—
249	C₅×C₂²⋊C₄	—	2	1	no	—
250	C₅×C₂²⋊C₄	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	C₄²×C₅	—	2	1	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	—	2	1	no	—
259	C₄²×C₅	—	4	2	no	—
260	C₄²×C₅	#41	1	2	yes	—
261	C₂×#131	C₂²×C₅	1	1	yes	characteristic
262	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
263	#525	C₂²×C₅	1	1	yes	characteristic
264	C₂×#117	C₂²×C₅	1	1	yes	characteristic
265	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
266	#485	C₄×C₅	1	1	yes	characteristic, complemented
267	#485	C₄×C₅	1	1	yes	characteristic, complemented
268	#484	C₄×C₅	1	1	yes	characteristic, complemented
269	#483	C₄×C₅	1	1	yes	characteristic, complemented
270	#482	C₄×C₅	1	1	yes	characteristic, complemented
271	#482	C₄×C₅	1	1	yes	characteristic, complemented
272	#481	C₄×C₅	1	1	yes	characteristic, complemented
273	#480	C₄×C₅	1	1	yes	characteristic, complemented
274	#436	—	2	1	no	—
275	#435	—	2	1	no	—
276	#435	—	2	1	no	—
277	C₈×D₄	—	2	1	no	—
278	#433	—	2	1	no	—
279	#433	—	2	1	no	—
280	#432	—	2	1	no	—
281	#431	—	2	1	no	—
282	C₂×#108	C₂²×C₅	1	1	yes	characteristic
283	C₂×#108	C₂²×C₅	1	1	yes	characteristic
284	#427	C₂²×C₅	1	1	yes	characteristic
285	#427	C₂²×C₅	1	1	yes	characteristic
286	#424	C₂²×C₅	1	1	yes	characteristic
287	#424	C₂²×C₅	1	1	yes	characteristic
288	#424	C₂²×C₅	1	1	yes	characteristic
289	C₂×#104	C₂²×C₅	1	1	yes	characteristic
290	C₂×#104	C₂²×C₅	1	1	yes	characteristic
291	#416	C₂²×C₅	1	1	yes	characteristic
292	#416	C₂²×C₅	1	1	yes	characteristic
293	#408	C₂²×C₅	1	1	yes	characteristic
294	#407	C₂²×C₅	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
297	#405	C₂²×C₅	1	1	yes	characteristic
298	#405	C₂²×C₅	1	1	yes	characteristic
299	#405	C₂²×C₅	1	1	yes	characteristic
300	C₂×#97	C₂²×C₅	1	1	yes	characteristic
301	C₂×#97	C₂²×C₅	1	1	yes	characteristic
302	#341	C₂²×C₅	1	1	yes	characteristic
303	#341	C₂²×C₅	1	1	yes	characteristic
304	#339	C₂²×C₅	1	1	yes	characteristic
305	#339	C₂²×C₅	1	1	yes	characteristic
306	#339	C₂²×C₅	1	1	yes	characteristic
307	#339	C₂²×C₅	1	1	yes	characteristic
308	#339	C₂²×C₅	1	1	yes	characteristic
309	#339	C₂²×C₅	1	1	yes	characteristic
310	#336	C₂²×C₅	1	1	yes	characteristic
311	#336	C₂²×C₅	1	1	yes	characteristic
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	2	no	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
318	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
319	C₂³×C₅	C₂×#41	1	1	yes	characteristic
320	C₅×Q₈	—	2	1	no	—
321	C₅×Q₈	—	2	1	no	—
322	C₅×D₄	—	2	1	no	—
323	C₅×D₄	—	2	1	no	—
324	C₅×D₄	—	4	1	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	—	4	2	no	—
327	C₅×D₄	—	8	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	8	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	2	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	8	1	no	—
356	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
364	C₅×C₈	—	2	1	no	—
365	C₅×C₈	—	2	1	no	—
366	C₅×C₈	—	2	1	no	—
367	C₅×C₈	—	2	1	no	—
368	C₅×C₈	—	2	1	no	—
369	C₅×C₈	—	2	1	no	—
370	C₅×C₈	—	2	2	no	—
371	C₅×C₈	—	2	1	no	—
372	C₅×C₈	—	2	1	no	—
373	C₅×C₈	—	4	1	no	—
374	C₅×C₈	—	4	1	no	—
375	C₅×C₈	—	4	1	no	—
376	C₂×#41	C₂³×C₅	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
379	#131	—	2	2	no	—
380	#131	—	4	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂×M₁₆	—	4	1	no	—
385	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
386	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
387	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
388	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
395	#123	—	2	1	no	—
396	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
397	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
398	#121	C₂×C₄×C₅	1	1	yes	characteristic
399	#121	C₂×C₄×C₅	1	1	yes	characteristic
400	#120	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	C₂×C₄×C₅	1	1	yes	characteristic
406	#117	C₂×C₄×C₅	1	1	yes	characteristic
407	#117	C₂³×C₅	1	1	yes	characteristic
408	#117	C₂³×C₅	1	1	yes	characteristic
409	#117	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	2	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	4	1	no	—
417	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
419	#108	—	2	2	no	—
420	#108	—	4	1	no	—
421	#107	C₂×C₄×C₅	1	1	yes	characteristic, complemented
422	#107	C₂×C₄×C₅	1	1	yes	characteristic, complemented
423	#107	C₂×C₄×C₅	1	1	yes	characteristic, complemented
424	#107	C₂×C₄×C₅	1	1	yes	characteristic, complemented
425	#106	C₂×C₄×C₅	1	1	yes	characteristic, complemented
426	#106	C₂×C₄×C₅	1	1	yes	characteristic, complemented
427	#106	C₂×C₄×C₅	1	1	yes	characteristic, complemented
428	#106	C₂×C₄×C₅	1	1	yes	characteristic, complemented
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	C₄⋊C₈	—	2	1	no	—
432	C₄⋊C₈	—	2	1	no	—
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	—	2	1	no	—
435	#104	—	2	2	no	—
436	#104	—	4	1	no	—
437	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
438	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
439	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
440	#103	C₂×C₄×C₅	1	1	yes	characteristic, complemented
441	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
442	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
443	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
444	#102	C₂×C₄×C₅	1	1	yes	characteristic, complemented
445	C₂²⋊C₈	—	2	1	no	—
446	C₂²⋊C₈	—	2	1	no	—
447	C₂²⋊C₈	—	2	1	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
450	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
451	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
452	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
453	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
454	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
455	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
456	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
457	#97	—	2	1	no	—
458	#97	—	2	1	no	—
459	#97	—	2	1	no	—
460	#97	—	2	2	no	—
461	#97	—	4	1	no	—
462	C₄×C₈	—	2	1	no	—
463	C₄×C₈	—	2	1	no	—
464	C₄×C₈	—	2	1	no	—
465	C₂²×C₅	—	2	1	no	—
466	C₂²×C₅	—	2	1	no	—
467	C₂²×C₅	—	2	1	no	—
468	C₂²×C₅	—	2	1	no	—
469	C₂²×C₅	—	2	1	no	—
470	C₂²×C₅	—	2	1	no	—
471	C₂²×C₅	—	2	1	no	—
472	C₂²×C₅	—	4	2	no	—
473	C₂²×C₅	—	4	2	no	—
474	C₂²×C₅	—	4	1	no	—
475	C₂²×C₅	—	4	1	no	—
476	C₂²×C₅	—	4	1	no	—
477	C₂²×C₅	#444	1	2	yes	—
478	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
479	C₂²×C₅	#551	1	1	yes	characteristic
480	C₂²×C₅	#552	1	1	yes	characteristic
481	C₄×C₅	—	2	1	no	—
482	C₄×C₅	—	2	1	no	—
483	C₄×C₅	—	4	2	no	—
484	C₄×C₅	—	4	2	no	—
485	C₄×C₅	—	4	1	no	—
486	C₄×C₅	—	4	1	no	—
487	C₄×C₅	—	4	1	no	—
488	C₄×C₅	—	4	1	no	—
489	C₄×C₅	—	4	1	no	—
490	C₄×C₅	—	4	1	no	—
491	C₄×C₅	—	4	1	no	—
492	C₄×C₅	C₄×#41	1	1	yes	characteristic
493	C₄×C₅	#520	1	1	yes	characteristic
494	C₄×C₅	#546	1	1	yes	characteristic
495	C₄×C₅	#547	1	1	yes	characteristic
496	C₂⁴	C₅×#41	1	1	yes	characteristic
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
522	C₂²×C₄	C₅×#41	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
524	M₁₆	—	2	1	no	—
525	M₁₆	—	2	1	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	—	2	1	no	—
528	M₁₆	—	2	1	no	—
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	4	2	no	—
532	M₁₆	—	4	2	no	—
533	M₁₆	C₅×#41	1	2	yes	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	4	2	no	—
547	C₂×C₈	—	4	2	no	—
548	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
549	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
550	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
551	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
552	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
553	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
554	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
561	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
562	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
563	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
564	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	4	2	no	—
584	C₄²	C₅×#41	1	2	yes	—
585	C₂×C₅	—	2	1	no	—
586	C₂×C₅	—	2	1	no	—
587	C₂×C₅	—	2	2	no	—
588	C₂×C₅	—	4	1	no	—
589	C₂×C₅	—	8	1	no	—
590	C₂×C₅	#2359	1	1	yes	characteristic
591	C₂×C₅	C₂×#444	1	1	yes	characteristic
592	C₂×C₅	#2956	1	1	yes	characteristic
593	C₂³	—	2	2	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
599	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
600	C₂³	C₂×C₅×#41	1	1	yes	characteristic
601	Q₈	—	2	1	no	—
602	Q₈	—	2	1	no	—
603	D₄	—	2	1	no	—
604	D₄	—	2	1	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	8	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	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	8	1	no	—
637	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
638	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
639	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
640	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
641	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
642	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
643	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
645	C₈	—	2	1	no	—
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	1	no	—
649	C₈	—	2	1	no	—
650	C₈	—	2	1	no	—
651	C₈	—	2	2	no	—
652	C₈	—	2	1	no	—
653	C₈	—	2	1	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	1	no	—
657	C₅	#22950	1	1	yes	characteristic, direct product factor, Sylow
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	C₅×#444	1	2	yes	—
671	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
672	C₂²	C₅×#551	1	1	yes	characteristic
673	C₂²	C₅×#552	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	1	no	—
685	C₄	C₄×C₅×#41	1	1	yes	characteristic
686	C₄	C₅×#520	1	1	yes	characteristic
687	C₄	C₅×#546	1	1	yes	characteristic
688	C₄	C₅×#547	1	1	yes	characteristic
689	C₂	—	2	1	no	—
690	C₂	—	2	2	no	—
691	C₂	—	2	1	no	—
692	C₂	—	4	1	no	—
693	C₂	—	8	1	no	—
694	C₂	C₅×#2359	1	1	yes	characteristic
695	C₂	C₂×C₅×#444	1	1	yes	characteristic
696	C₂	C₅×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2924	C₂	semidirect
4. C₅×#1946	C₂	semidirect
5. C₅×#1938	C₂	semidirect
6. C₅×#1929	C₂	semidirect
7. C₅×#1922	C₂	semidirect
8. C₅×#1922	C₂	semidirect
10. C₅×#1866	C₂	semidirect
11. C₅×#1855	C₂	semidirect
12. C₅×#1773	C₂	semidirect
13. C₅×#1765	C₂	semidirect
14. C₅×#1749	C₂	semidirect
15. C₂×C₅×#339	C₂	semidirect
21. C₅×#485	C₄	semidirect
22. C₅×#485	C₄	semidirect
23. C₅×#484	C₄	semidirect
24. C₅×#483	C₄	semidirect
25. C₅×#482	C₄	semidirect
26. C₅×#482	C₄	semidirect
27. C₅×#481	C₄	semidirect
28. C₅×#480	C₄	semidirect
67. #22950	C₅	direct (N × H)
113. C₅×#107	C₂×C₄	semidirect
114. C₅×#107	C₂×C₄	semidirect
115. C₅×#107	C₂×C₄	semidirect
116. C₅×#107	C₂×C₄	semidirect
117. C₅×#106	C₂×C₄	semidirect
118. C₅×#106	C₂×C₄	semidirect
119. C₅×#106	C₂×C₄	semidirect
120. C₅×#106	C₂×C₄	semidirect
129. C₅×#103	C₂×C₄	semidirect
130. C₅×#103	C₂×C₄	semidirect
131. C₅×#103	C₂×C₄	semidirect
132. C₅×#103	C₂×C₄	semidirect
133. C₅×#102	C₂×C₄	semidirect
134. C₅×#102	C₂×C₄	semidirect
135. C₅×#102	C₂×C₄	semidirect
136. C₅×#102	C₂×C₄	semidirect
159. #2924	C₂×C₅	semidirect
160. #1946	C₂×C₅	semidirect
161. #1938	C₂×C₅	semidirect
162. #1929	C₂×C₅	semidirect
163. #1922	C₂×C₅	semidirect
164. #1922	C₂×C₅	semidirect
166. #1866	C₂×C₅	semidirect
167. #1855	C₂×C₅	semidirect
168. #1773	C₂×C₅	semidirect
169. #1765	C₂×C₅	semidirect
170. #1749	C₂×C₅	semidirect
171. C₂×#339	C₂×C₅	semidirect
266. #485	C₄×C₅	semidirect
267. #485	C₄×C₅	semidirect
268. #484	C₄×C₅	semidirect
269. #483	C₄×C₅	semidirect
270. #482	C₄×C₅	semidirect
271. #482	C₄×C₅	semidirect
272. #481	C₄×C₅	semidirect
273. #480	C₄×C₅	semidirect
421. #107	C₂×C₄×C₅	semidirect
422. #107	C₂×C₄×C₅	semidirect
423. #107	C₂×C₄×C₅	semidirect
424. #107	C₂×C₄×C₅	semidirect
425. #106	C₂×C₄×C₅	semidirect
426. #106	C₂×C₄×C₅	semidirect
427. #106	C₂×C₄×C₅	semidirect
428. #106	C₂×C₄×C₅	semidirect
437. #103	C₂×C₄×C₅	semidirect
438. #103	C₂×C₄×C₅	semidirect
439. #103	C₂×C₄×C₅	semidirect
440. #103	C₂×C₄×C₅	semidirect
441. #102	C₂×C₄×C₅	semidirect
442. #102	C₂×C₄×C₅	semidirect
443. #102	C₂×C₄×C₅	semidirect
444. #102	C₂×C₄×C₅	semidirect
657. C₅	#22950	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×#3091	2
C₅×#2933	2
C₅×#2924	2
C₅×#1946	2
C₅×#1938	2
C₅×#1929	2
C₅×#1922	2
C₅×#1896	2
C₅×#1866	2
C₅×#1855	2
C₅×#1773	2
C₅×#1765	2
C₅×#1749	2
C₂×C₅×#339	2
#22950	5

Subgroups — C5×#22950 #11945670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22950 #11945670