Subgroups — C₅×#26351 #11949071

Order 1280.

802 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
3	C₅×#2441	C₂	1	1	yes	maximal, characteristic
4	C₅×#2362	C₂	1	1	yes	maximal, characteristic
5	C₅×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2088	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1892	C₂	1	1	yes	maximal, characteristic
12	C₅×#1873	C₂	1	1	yes	maximal, characteristic
13	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1854	C₂	1	1	yes	maximal, characteristic
15	C₅×#1850	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#125	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₅×#479	—	2	4	no	—
23	C₅×#427	—	2	4	no	—
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic
26	C₂×C₅×#107	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×#106	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊C₈	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×#399	—	2	1	no	—
38	C₅×#396	—	2	1	no	—
39	C₅×#391	C₂²	1	1	yes	characteristic
40	C₅×#389	—	2	1	no	—
41	C₅×#389	C₂²	1	1	yes	characteristic
42	C₅×#389	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#388	—	2	1	no	—
45	C₅×#388	—	2	1	no	—
46	C₅×#387	—	2	1	no	—
47	C₅×#387	—	2	1	no	—
48	C₅×#384	C₂²	1	1	yes	characteristic
49	C₅×#380	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₄⋊C₄	—	2	1	no	—
51	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₂²⋊C₄	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×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#26351	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₂²×C₅×C₈	—	2	2	no	—
66	C₂²×C₅×C₈	—	2	2	no	—
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₅×#125	—	2	2	no	—
72	C₅×#125	—	4	1	no	—
73	C₅×C₂²⋊Q₈	—	2	2	no	—
74	C₅×C₂²⋊Q₈	Q₈	1	4	yes	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	4	1	no	—
77	C₅×#117	—	2	2	no	—
78	C₅×#117	—	2	2	no	—
79	C₅×#117	—	4	1	no	—
80	C₅×#117	—	4	1	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	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₅	—	2	1	no	—
104	C₂×C₄²×C₅	—	2	1	no	—
105	C₂×C₄²×C₅	—	2	1	no	—
106	C₂×C₄²×C₅	—	2	1	no	—
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₅×#107	—	2	2	no	—
110	C₅×#107	—	2	2	no	—
111	C₅×#107	—	2	2	no	—
112	C₅×#106	—	2	2	no	—
113	C₅×#106	—	4	1	no	—
114	C₅×#106	D₄	1	4	yes	—
115	C₅×C₄⋊C₈	—	2	2	no	—
116	C₅×C₄⋊C₈	—	2	2	no	—
117	C₅×#103	—	2	2	no	—
118	C₅×#103	—	2	2	no	—
119	C₅×#103	—	2	2	no	—
120	C₅×#103	—	4	1	no	—
121	C₅×C₂²⋊C₈	—	2	2	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	C₅×#95	—	2	1	no	—
129	C₅×#95	D₄	1	1	yes	characteristic
130	C₅×#95	D₄	1	1	yes	characteristic
131	C₂×#479	C₂×C₅	1	1	yes	characteristic, complemented
132	C₂×#427	C₂×C₅	1	1	yes	characteristic
133	#2441	C₂×C₅	1	1	yes	characteristic
134	#2362	C₂×C₅	1	1	yes	characteristic
135	#2096	C₂×C₅	1	1	yes	characteristic, complemented
136	#2088	C₂×C₅	1	1	yes	characteristic, complemented
137	#2068	C₂×C₅	1	1	yes	characteristic, complemented
138	#2059	C₂×C₅	1	1	yes	characteristic, complemented
139	#1947	C₂×C₅	1	1	yes	characteristic, complemented
140	#1920	C₂×C₅	1	1	yes	characteristic, complemented
141	#1892	C₂×C₅	1	1	yes	characteristic
142	#1873	C₂×C₅	1	1	yes	characteristic
143	#1863	C₂×C₅	1	1	yes	characteristic, complemented
144	#1854	C₂×C₅	1	1	yes	characteristic
145	#1850	C₂×C₅	1	1	yes	characteristic
146	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	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	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
171	C₂²×C₄×C₅	#41	1	2	yes	—
172	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂×C₅×C₈	—	2	8	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
185	C₂×C₅×C₈	#41	1	2	yes	—
186	C₅×C₄⋊C₄	—	2	4	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	4	2	no	—
199	C₅×C₄⋊C₄	—	4	2	no	—
200	C₅×C₄⋊C₄	—	4	2	no	—
201	C₅×C₄⋊C₄	—	4	2	no	—
202	C₅×C₄⋊C₄	—	4	2	no	—
203	C₅×C₄⋊C₄	—	4	2	no	—
204	C₅×C₄⋊C₄	—	8	1	no	—
205	C₅×C₄⋊C₄	—	8	1	no	—
206	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
208	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	4	2	no	—
213	C₅×C₂²⋊C₄	—	4	2	no	—
214	C₅×C₂²⋊C₄	—	8	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	4	2	no	—
220	C₄²×C₅	—	4	2	no	—
221	C₄²×C₅	—	4	2	no	—
222	C₄²×C₅	—	4	2	no	—
223	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
224	C₂×#125	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×#117	C₂²×C₅	1	1	yes	characteristic
228	C₂×#117	C₂²×C₅	1	1	yes	characteristic
229	#479	—	2	4	no	—
230	#427	—	2	4	no	—
231	C₂×#107	C₂²×C₅	1	1	yes	characteristic
232	C₂×#107	C₂²×C₅	1	1	yes	characteristic
233	C₂×#107	C₂²×C₅	1	1	yes	characteristic
234	C₂×#106	C₂²×C₅	1	1	yes	characteristic
235	C₂×#106	C₂²×C₅	1	1	yes	characteristic
236	C₂×#106	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×#103	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×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
244	#399	—	2	1	no	—
245	#396	—	2	1	no	—
246	#391	C₂²×C₅	1	1	yes	characteristic
247	#389	—	2	1	no	—
248	#389	C₂²×C₅	1	1	yes	characteristic
249	#389	C₂²×C₅	1	1	yes	characteristic
250	#389	C₂²×C₅	1	1	yes	characteristic
251	#388	—	2	1	no	—
252	#388	—	2	1	no	—
253	#387	—	2	1	no	—
254	#387	—	2	1	no	—
255	#384	C₂²×C₅	1	1	yes	characteristic
256	#380	C₂²×C₅	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	#340	C₂²×C₅	1	1	yes	characteristic
261	#340	C₂²×C₅	1	1	yes	characteristic
262	#340	C₂²×C₅	1	1	yes	characteristic
263	#340	C₂²×C₅	1	1	yes	characteristic
264	#340	C₂²×C₅	1	1	yes	characteristic
265	#340	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	#336	C₂²×C₅	1	1	yes	characteristic
268	C₂³×C₅	—	2	1	no	—
269	C₂³×C₅	—	2	1	no	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
275	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	2	2	no	—
278	C₅×Q₈	—	4	1	no	—
279	C₅×Q₈	—	4	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	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	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	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	C₂²⋊Q₈	1	2	yes	—
322	C₂×C₄×C₅	#135	1	2	yes	—
323	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
329	C₅×C₈	—	2	2	no	—
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	4	1	no	—
332	C₅×C₈	—	4	1	no	—
333	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
342	#125	—	2	2	no	—
343	#125	—	4	1	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	C₅×Q₈	1	4	yes	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	4	1	no	—
348	#117	—	2	2	no	—
349	#117	—	2	2	no	—
350	#117	—	4	1	no	—
351	#117	—	4	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	#107	—	2	2	no	—
381	#107	—	2	2	no	—
382	#107	—	2	2	no	—
383	#106	—	2	2	no	—
384	#106	—	4	1	no	—
385	#106	C₅×D₄	1	4	yes	—
386	C₄⋊C₈	—	2	2	no	—
387	C₄⋊C₈	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	—	2	2	no	—
391	#103	—	4	1	no	—
392	C₂²⋊C₈	—	2	2	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	C₅×D₄	1	1	yes	characteristic
401	#95	C₅×D₄	1	1	yes	characteristic
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
410	C₂²×C₅	D₄²	1	1	yes	characteristic
411	C₂²×C₅	#547	1	1	yes	characteristic
412	C₂²×C₅	C₂×#135	1	1	yes	characteristic
413	C₂²×C₅	#575	1	1	yes	characteristic
414	C₂²×C₅	#577	1	1	yes	characteristic
415	C₂²×C₅	#578	1	1	yes	characteristic
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	4	2	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	8	1	no	—
426	C₄×C₅	—	8	1	no	—
427	C₄×C₅	—	8	1	no	—
428	C₄×C₅	—	8	1	no	—
429	C₄×C₅	#525	1	1	yes	characteristic
430	C₄×C₅	#539	1	1	yes	characteristic
431	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
432	C₄×C₅	#554	1	1	yes	characteristic
433	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
458	C₂²×C₄	C₅×#41	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
460	C₂×C₈	—	2	8	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
472	C₂×C₈	C₅×#41	1	2	yes	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	8	1	no	—
492	C₄⋊C₄	—	8	1	no	—
493	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
494	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
495	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	8	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₂×C₅	—	4	2	no	—
511	C₂×C₅	#2449	1	1	yes	characteristic
512	C₂×C₅	#3076	1	1	yes	characteristic
513	C₂×C₅	#3082	1	1	yes	characteristic
514	C₂×C₅	#3269	1	1	yes	characteristic
515	C₂×C₅	#3284	1	1	yes	characteristic
516	C₂×C₅	#3336	1	1	yes	characteristic
517	C₂×C₅	#3350	1	1	yes	characteristic
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
525	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
526	Q₈	—	2	2	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
572	C₂×C₄	C₅×#135	1	2	yes	—
573	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
575	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
576	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
577	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
579	C₈	—	2	2	no	—
580	C₈	—	2	2	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₅	#26351	1	1	yes	characteristic, direct product factor, Sylow
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
592	C₂²	C₅×D₄²	1	1	yes	characteristic
593	C₂²	C₅×#547	1	1	yes	characteristic
594	C₂²	C₂×C₅×#135	1	1	yes	characteristic
595	C₂²	C₅×#575	1	1	yes	characteristic
596	C₂²	C₅×#577	1	1	yes	characteristic
597	C₂²	C₅×#578	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	2	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	1	no	—
611	C₄	C₅×#525	1	1	yes	characteristic
612	C₄	C₅×#539	1	1	yes	characteristic
613	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
614	C₄	C₅×#554	1	1	yes	characteristic
615	C₂	—	4	2	no	—
616	C₂	C₅×#2449	1	1	yes	characteristic
617	C₂	C₅×#3076	1	1	yes	characteristic
618	C₂	C₅×#3082	1	1	yes	characteristic
619	C₂	C₅×#3269	1	1	yes	characteristic
620	C₂	C₅×#3284	1	1	yes	characteristic
621	C₂	C₅×#3336	1	1	yes	characteristic
622	C₂	C₅×#3350	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂²×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
1. C₂×C₅×#479	C₂	semidirect
5. C₅×#2096	C₂	semidirect
6. C₅×#2088	C₂	semidirect
7. C₅×#2068	C₂	semidirect
8. C₅×#2059	C₂	semidirect
9. C₅×#1947	C₂	semidirect
10. C₅×#1920	C₂	semidirect
13. C₅×#1863	C₂	semidirect
61. #26351	C₅	direct (N × H)
131. C₂×#479	C₂×C₅	semidirect
135. #2096	C₂×C₅	semidirect
136. #2088	C₂×C₅	semidirect
137. #2068	C₂×C₅	semidirect
138. #2059	C₂×C₅	semidirect
139. #1947	C₂×C₅	semidirect
140. #1920	C₂×C₅	semidirect
143. #1863	C₂×C₅	semidirect
583. C₅	#26351	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×#479	2
C₂×C₅×#427	2
C₅×#2441	2
C₅×#2362	2
C₅×#2096	2
C₅×#2088	2
C₅×#2068	2
C₅×#2059	2
C₅×#1947	2
C₅×#1920	2
C₅×#1892	2
C₅×#1873	2
C₅×#1863	2
C₅×#1854	2
C₅×#1850	2
#26351	5

Subgroups — C5×#26351 #11949071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26351 #11949071