Subgroups — C₅×#21703 #11944423

Order 1280.

1062 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
6	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2326	C₂	1	1	yes	maximal, characteristic
8	C₅×#1973	C₂	1	1	yes	maximal, characteristic
9	C₅×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1968	C₂	1	1	yes	maximal, characteristic
12	C₅×#1958	C₂	1	1	yes	maximal, characteristic
13	C₅×#1956	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₅×#497	C₄	1	8	yes	complemented
27	C₅×#441	—	2	4	no	—
28	C₅×#440	—	2	4	no	—
29	C₄×C₅×Q₁₆	—	2	4	no	—
30	C₄×C₅×SD₁₆	—	2	4	no	—
31	C₂×C₅×#107	C₂²	1	1	yes	characteristic
32	C₂×C₅×#107	C₂²	1	1	yes	characteristic
33	C₂×C₅×#106	C₂²	1	1	yes	characteristic
34	C₂×C₅×#106	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×#103	C₂²	1	1	yes	characteristic
37	C₂×C₅×#103	C₂²	1	1	yes	characteristic
38	C₂×C₅×#103	C₂²	1	1	yes	characteristic
39	C₂×C₅×#103	C₂²	1	1	yes	characteristic
40	C₂×C₅×#103	C₂²	1	1	yes	characteristic
41	C₂×C₅×#102	C₂²	1	1	yes	characteristic
42	C₂×C₅×#102	C₂²	1	1	yes	characteristic
43	C₂×C₅×#97	C₂²	1	1	yes	characteristic
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic
45	C₂×C₅×#97	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
49	C₅×#391	C₂²	1	1	yes	characteristic
50	C₅×#391	C₂²	1	1	yes	characteristic
51	C₅×#391	C₂²	1	1	yes	characteristic
52	C₅×#390	C₂²	1	1	yes	characteristic
53	C₅×#388	—	2	2	no	—
54	C₅×#387	—	2	2	no	—
55	C₅×#387	—	2	2	no	—
56	C₅×#385	—	2	2	no	—
57	C₅×#384	C₂²	1	1	yes	characteristic
58	C₅×#382	C₂²	1	1	yes	characteristic
59	C₅×#376	C₂²	1	1	yes	characteristic
60	#21703	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	—	2	1	no	—
66	C₂×C₅×Q₁₆	—	2	2	no	—
67	C₂×C₅×Q₁₆	—	2	2	no	—
68	C₂×C₅×Q₁₆	—	2	2	no	—
69	C₂×C₅×Q₁₆	—	2	2	no	—
70	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
71	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×SD₁₆	—	2	2	no	—
74	C₂×C₅×SD₁₆	—	2	2	no	—
75	C₂×C₅×SD₁₆	—	2	2	no	—
76	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
77	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Q₈	—	2	2	no	—
83	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
84	C₅×#124	—	2	2	no	—
85	C₅×#124	C₂×C₄	1	4	yes	—
86	C₄×C₅×Q₈	—	2	2	no	—
87	C₄×C₅×Q₈	—	2	2	no	—
88	C₄×C₅×Q₈	—	2	2	no	—
89	C₄×C₅×Q₈	—	2	2	no	—
90	C₄×C₅×Q₈	—	2	2	no	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×D₄	—	2	2	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₂×C₅×C₄⋊C₄	—	2	2	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	2	no	—
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	2	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₄²×C₅	—	2	1	no	—
107	C₂×C₄²×C₅	—	2	1	no	—
108	C₂×C₄²×C₅	—	2	1	no	—
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₅×#107	—	2	2	no	—
113	C₅×#107	—	2	2	no	—
114	C₅×#106	—	2	2	no	—
115	C₅×#106	—	2	2	no	—
116	C₅×#103	—	2	2	no	—
117	C₅×#103	—	2	2	no	—
118	C₅×#103	—	2	2	no	—
119	C₅×#103	—	2	2	no	—
120	C₅×#103	—	2	2	no	—
121	C₅×#103	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	2	2	no	—
124	C₅×#97	—	2	2	no	—
125	C₅×#97	C₂×C₄	1	4	yes	complemented
126	C₅×#97	D₄	1	4	yes	—
127	C₄×C₅×C₈	—	2	2	no	—
128	C₄×C₅×C₈	—	2	2	no	—
129	C₄×C₅×C₈	D₄	1	4	yes	—
130	C₅×#95	—	2	2	no	—
131	C₅×#95	—	2	2	no	—
132	C₅×#95	—	2	2	no	—
133	C₅×#95	—	2	2	no	—
134	C₅×#95	D₄	1	2	yes	—
135	C₅×#95	D₄	1	2	yes	—
136	C₂×#497	C₂×C₅	1	1	yes	characteristic
137	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#440	C₂×C₅	1	1	yes	characteristic
139	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic
141	#2327	C₂×C₅	1	1	yes	characteristic, complemented
142	#2326	C₂×C₅	1	1	yes	characteristic
143	#1973	C₂×C₅	1	1	yes	characteristic
144	#1971	C₂×C₅	1	1	yes	characteristic, complemented
145	#1969	C₂×C₅	1	1	yes	characteristic, complemented
146	#1968	C₂×C₅	1	1	yes	characteristic
147	#1958	C₂×C₅	1	1	yes	characteristic
148	#1956	C₂×C₅	1	1	yes	characteristic, complemented
149	#1847	C₂×C₅	1	1	yes	characteristic, complemented
150	#1726	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂⁴×C₅	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
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	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
168	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
169	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	4	2	no	—
184	C₂²×C₄×C₅	—	8	2	no	—
185	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
190	C₅×Q₁₆	—	2	8	no	—
191	C₅×Q₁₆	—	2	8	no	—
192	C₅×SD₁₆	—	2	8	no	—
193	C₅×SD₁₆	—	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	C₂²×C₄	1	2	yes	—
199	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
200	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
201	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
202	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
203	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
204	C₂×C₅×C₈	#41	1	2	yes	—
205	C₂×C₅×C₈	#41	1	2	yes	—
206	C₅×C₄⋊C₄	—	2	8	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	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	4	2	no	—
216	C₅×C₄⋊C₄	—	4	2	no	—
217	C₅×C₄⋊C₄	—	4	2	no	—
218	C₅×C₄⋊C₄	—	8	2	no	—
219	C₅×C₂²⋊C₄	—	2	8	no	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₅×C₂²⋊C₄	—	8	2	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	4	2	no	—
225	C₄²×C₅	—	4	2	no	—
226	C₄²×C₅	—	4	2	no	—
227	C₄²×C₅	C₂²×C₄	1	2	yes	—
228	C₄²×C₅	C₂×D₄	1	2	yes	—
229	C₄²×C₅	C₂×D₄	1	2	yes	—
230	C₄²×C₅	#41	1	2	yes	—
231	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
233	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×#124	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
241	#497	C₄×C₅	1	8	yes	complemented
242	#441	—	2	4	no	—
243	#440	—	2	4	no	—
244	C₄×Q₁₆	—	2	4	no	—
245	C₄×SD₁₆	—	2	4	no	—
246	C₂×#107	C₂²×C₅	1	1	yes	characteristic
247	C₂×#107	C₂²×C₅	1	1	yes	characteristic
248	C₂×#106	C₂²×C₅	1	1	yes	characteristic
249	C₂×#106	C₂²×C₅	1	1	yes	characteristic
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic
251	C₂×#103	C₂²×C₅	1	1	yes	characteristic
252	C₂×#103	C₂²×C₅	1	1	yes	characteristic
253	C₂×#103	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×#102	C₂²×C₅	1	1	yes	characteristic
257	C₂×#102	C₂²×C₅	1	1	yes	characteristic
258	C₂×#97	C₂²×C₅	1	1	yes	characteristic
259	C₂×#97	C₂²×C₅	1	1	yes	characteristic
260	C₂×#97	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	#391	C₂²×C₅	1	1	yes	characteristic
265	#391	C₂²×C₅	1	1	yes	characteristic
266	#391	C₂²×C₅	1	1	yes	characteristic
267	#390	C₂²×C₅	1	1	yes	characteristic
268	#388	—	2	2	no	—
269	#387	—	2	2	no	—
270	#387	—	2	2	no	—
271	#385	—	2	2	no	—
272	#384	C₂²×C₅	1	1	yes	characteristic
273	#382	C₂²×C₅	1	1	yes	characteristic
274	#376	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	4	1	no	—
277	C₂³×C₅	—	4	1	no	—
278	C₂³×C₅	—	4	2	no	—
279	C₂³×C₅	—	4	2	no	—
280	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₅×Q₈	—	2	2	no	—
282	C₅×Q₈	—	2	2	no	—
283	C₅×Q₈	—	2	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	4	1	no	—
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	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	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	2	no	—
318	C₂×C₄×C₅	—	4	2	no	—
319	C₂×C₄×C₅	—	4	2	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	8	4	no	—
322	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
323	C₂×C₄×C₅	#127	1	2	yes	—
324	C₂×C₄×C₅	#127	1	2	yes	—
325	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
331	C₅×C₈	—	2	2	no	—
332	C₅×C₈	—	2	2	no	—
333	C₅×C₈	C₄×D₄	1	4	yes	—
334	C₅×C₈	C₄×D₄	1	4	yes	—
335	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
338	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂×Q₁₆	—	2	2	no	—
341	C₂×Q₁₆	—	2	2	no	—
342	C₂×Q₁₆	—	2	2	no	—
343	C₂×Q₁₆	—	2	2	no	—
344	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
345	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×SD₁₆	—	2	2	no	—
350	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
351	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
352	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
358	#124	—	2	2	no	—
359	#124	C₂×C₄×C₅	1	4	yes	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
386	#107	—	2	2	no	—
387	#107	—	2	2	no	—
388	#106	—	2	2	no	—
389	#106	—	2	2	no	—
390	#103	—	2	2	no	—
391	#103	—	2	2	no	—
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#103	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	2	no	—
398	#97	—	2	2	no	—
399	#97	C₂×C₄×C₅	1	4	yes	complemented
400	#97	C₅×D₄	1	4	yes	—
401	C₄×C₈	—	2	2	no	—
402	C₄×C₈	—	2	2	no	—
403	C₄×C₈	C₅×D₄	1	4	yes	—
404	#95	—	2	2	no	—
405	#95	—	2	2	no	—
406	#95	—	2	2	no	—
407	#95	—	2	2	no	—
408	#95	C₅×D₄	1	2	yes	—
409	#95	C₅×D₄	1	2	yes	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	4	no	—
412	C₂²×C₅	—	8	1	no	—
413	C₂²×C₅	—	8	1	no	—
414	C₂²×C₅	—	8	2	no	—
415	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
416	C₂²×C₅	C₂×#127	1	1	yes	characteristic
417	C₂²×C₅	#532	1	1	yes	characteristic
418	C₂²×C₅	#577	1	2	yes	—
419	C₂²×C₅	#578	1	2	yes	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	4	no	—
423	C₄×C₅	—	4	2	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	2	no	—
426	C₄×C₅	—	4	2	no	—
427	C₄×C₅	—	8	1	no	—
428	C₄×C₅	—	8	1	no	—
429	C₄×C₅	—	8	1	no	—
430	C₄×C₅	—	8	1	no	—
431	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
432	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
433	C₄×C₅	#532	1	1	yes	characteristic
434	C₄×C₅	#532	1	1	yes	characteristic
435	C₂⁴	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
452	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
453	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	8	2	no	—
469	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
470	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
471	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
474	Q₁₆	—	2	8	no	—
475	Q₁₆	—	2	8	no	—
476	SD₁₆	—	2	8	no	—
477	SD₁₆	—	2	8	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
483	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
484	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
485	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
486	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
487	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
488	C₂×C₈	C₅×#41	1	2	yes	—
489	C₂×C₈	C₅×#41	1	2	yes	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	8	2	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₂²⋊C₄	—	8	2	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₄²	—	4	2	no	—
511	C₄²	C₂²×C₄×C₅	1	2	yes	—
512	C₄²	C₂×C₅×D₄	1	2	yes	—
513	C₄²	C₂×C₅×D₄	1	2	yes	—
514	C₄²	C₅×#41	1	2	yes	—
515	C₂×C₅	—	8	2	no	—
516	C₂×C₅	C₄×#127	1	1	yes	characteristic
517	C₂×C₅	#2947	1	2	yes	—
518	C₂×C₅	#3154	1	1	yes	characteristic
519	C₂×C₅	#3156	1	1	yes	characteristic
520	C₂×C₅	#3178	1	2	yes	—
521	C₂³	—	2	2	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
527	Q₈	—	2	2	no	—
528	Q₈	—	2	2	no	—
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	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	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	8	4	no	—
568	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
569	C₂×C₄	C₅×#127	1	2	yes	—
570	C₂×C₄	C₅×#127	1	2	yes	—
571	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
572	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂×C₅×#41	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	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	C₄×C₅×D₄	1	4	yes	—
580	C₈	C₄×C₅×D₄	1	4	yes	—
581	C₅	#21703	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²	—	4	2	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	8	1	no	—
586	C₂²	—	8	2	no	—
587	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
588	C₂²	C₂×C₅×#127	1	1	yes	characteristic
589	C₂²	C₅×#532	1	1	yes	characteristic
590	C₂²	C₅×#577	1	2	yes	—
591	C₂²	C₅×#578	1	2	yes	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	4	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
604	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
605	C₄	C₅×#532	1	1	yes	characteristic
606	C₄	C₅×#532	1	1	yes	characteristic
607	C₂	—	8	2	no	—
608	C₂	C₄×C₅×#127	1	1	yes	characteristic
609	C₂	C₅×#2947	1	2	yes	—
610	C₂	C₅×#3154	1	1	yes	characteristic
611	C₂	C₅×#3156	1	1	yes	characteristic
612	C₂	C₅×#3178	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#441	C₂	semidirect
4. C₂×C₄×C₅×Q₁₆	C₂	semidirect
6. C₅×#2327	C₂	semidirect
9. C₅×#1971	C₂	semidirect
10. C₅×#1969	C₂	semidirect
13. C₅×#1956	C₂	semidirect
14. C₅×#1847	C₂	semidirect
15. C₅×#1726	C₂	semidirect
26. C₅×#497	C₄	semidirect
60. #21703	C₅	direct (N × H)
70. C₂×C₅×Q₁₆	C₂×C₄	semidirect
71. C₂×C₅×Q₁₆	C₂×C₄	semidirect
83. C₅×C₄⋊Q₈	C₂×C₄	semidirect
125. C₅×#97	C₂×C₄	semidirect
137. C₂×#441	C₂×C₅	semidirect
139. C₂×C₄×Q₁₆	C₂×C₅	semidirect
141. #2327	C₂×C₅	semidirect
144. #1971	C₂×C₅	semidirect
145. #1969	C₂×C₅	semidirect
148. #1956	C₂×C₅	semidirect
149. #1847	C₂×C₅	semidirect
150. #1726	C₂×C₅	semidirect
241. #497	C₄×C₅	semidirect
344. C₂×Q₁₆	C₂×C₄×C₅	semidirect
345. C₂×Q₁₆	C₂×C₄×C₅	semidirect
357. C₄⋊Q₈	C₂×C₄×C₅	semidirect
399. #97	C₂×C₄×C₅	semidirect
581. C₅	#21703	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×#497	2
C₂×C₅×#441	2
C₂×C₅×#440	2
C₂×C₄×C₅×Q₁₆	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2327	2
C₅×#2326	2
C₅×#1973	2
C₅×#1971	2
C₅×#1969	2
C₅×#1968	2
C₅×#1958	2
C₅×#1956	2
C₅×#1847	2
C₅×#1726	2
#21703	5

Subgroups — C5×#21703 #11944423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21703 #11944423